/* Generated by Cython 0.27 */

/* BEGIN: Cython Metadata
{
    "distutils": {
        "depends": [
            "/home/nico/.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/numpy/core/include/numpy/arrayobject.h",
            "/home/nico/.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/numpy/core/include/numpy/ufuncobject.h"
        ],
        "include_dirs": [
            "/home/nico/.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/numpy/core/include"
        ],
        "name": "surprise.prediction_algorithms.matrix_factorization",
        "sources": [
            "surprise/prediction_algorithms/matrix_factorization.pyx"
        ]
    },
    "module_name": "surprise.prediction_algorithms.matrix_factorization"
}
END: Cython Metadata */

#define PY_SSIZE_T_CLEAN
#include "Python.h"
#ifndef Py_PYTHON_H
    #error Python headers needed to compile C extensions, please install development version of Python.
#elif PY_VERSION_HEX < 0x02060000 || (0x03000000 <= PY_VERSION_HEX && PY_VERSION_HEX < 0x03030000)
    #error Cython requires Python 2.6+ or Python 3.3+.
#else
#define CYTHON_ABI "0_27"
#define CYTHON_FUTURE_DIVISION 1
#include <stddef.h>
#ifndef offsetof
  #define offsetof(type, member) ( (size_t) & ((type*)0) -> member )
#endif
#if !defined(WIN32) && !defined(MS_WINDOWS)
  #ifndef __stdcall
    #define __stdcall
  #endif
  #ifndef __cdecl
    #define __cdecl
  #endif
  #ifndef __fastcall
    #define __fastcall
  #endif
#endif
#ifndef DL_IMPORT
  #define DL_IMPORT(t) t
#endif
#ifndef DL_EXPORT
  #define DL_EXPORT(t) t
#endif
#define __PYX_COMMA ,
#ifndef HAVE_LONG_LONG
  #if PY_VERSION_HEX >= 0x02070000
    #define HAVE_LONG_LONG
  #endif
#endif
#ifndef PY_LONG_LONG
  #define PY_LONG_LONG LONG_LONG
#endif
#ifndef Py_HUGE_VAL
  #define Py_HUGE_VAL HUGE_VAL
#endif
#ifdef PYPY_VERSION
  #define CYTHON_COMPILING_IN_PYPY 1
  #define CYTHON_COMPILING_IN_PYSTON 0
  #define CYTHON_COMPILING_IN_CPYTHON 0
  #undef CYTHON_USE_TYPE_SLOTS
  #define CYTHON_USE_TYPE_SLOTS 0
  #undef CYTHON_USE_PYTYPE_LOOKUP
  #define CYTHON_USE_PYTYPE_LOOKUP 0
  #if PY_VERSION_HEX < 0x03050000
    #undef CYTHON_USE_ASYNC_SLOTS
    #define CYTHON_USE_ASYNC_SLOTS 0
  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
    #define CYTHON_USE_ASYNC_SLOTS 1
  #endif
  #undef CYTHON_USE_PYLIST_INTERNALS
  #define CYTHON_USE_PYLIST_INTERNALS 0
  #undef CYTHON_USE_UNICODE_INTERNALS
  #define CYTHON_USE_UNICODE_INTERNALS 0
  #undef CYTHON_USE_UNICODE_WRITER
  #define CYTHON_USE_UNICODE_WRITER 0
  #undef CYTHON_USE_PYLONG_INTERNALS
  #define CYTHON_USE_PYLONG_INTERNALS 0
  #undef CYTHON_AVOID_BORROWED_REFS
  #define CYTHON_AVOID_BORROWED_REFS 1
  #undef CYTHON_ASSUME_SAFE_MACROS
  #define CYTHON_ASSUME_SAFE_MACROS 0
  #undef CYTHON_UNPACK_METHODS
  #define CYTHON_UNPACK_METHODS 0
  #undef CYTHON_FAST_THREAD_STATE
  #define CYTHON_FAST_THREAD_STATE 0
  #undef CYTHON_FAST_PYCALL
  #define CYTHON_FAST_PYCALL 0
  #undef CYTHON_PEP489_MULTI_PHASE_INIT
  #define CYTHON_PEP489_MULTI_PHASE_INIT 0
  #undef CYTHON_USE_TP_FINALIZE
  #define CYTHON_USE_TP_FINALIZE 0
#elif defined(PYSTON_VERSION)
  #define CYTHON_COMPILING_IN_PYPY 0
  #define CYTHON_COMPILING_IN_PYSTON 1
  #define CYTHON_COMPILING_IN_CPYTHON 0
  #ifndef CYTHON_USE_TYPE_SLOTS
    #define CYTHON_USE_TYPE_SLOTS 1
  #endif
  #undef CYTHON_USE_PYTYPE_LOOKUP
  #define CYTHON_USE_PYTYPE_LOOKUP 0
  #undef CYTHON_USE_ASYNC_SLOTS
  #define CYTHON_USE_ASYNC_SLOTS 0
  #undef CYTHON_USE_PYLIST_INTERNALS
  #define CYTHON_USE_PYLIST_INTERNALS 0
  #ifndef CYTHON_USE_UNICODE_INTERNALS
    #define CYTHON_USE_UNICODE_INTERNALS 1
  #endif
  #undef CYTHON_USE_UNICODE_WRITER
  #define CYTHON_USE_UNICODE_WRITER 0
  #undef CYTHON_USE_PYLONG_INTERNALS
  #define CYTHON_USE_PYLONG_INTERNALS 0
  #ifndef CYTHON_AVOID_BORROWED_REFS
    #define CYTHON_AVOID_BORROWED_REFS 0
  #endif
  #ifndef CYTHON_ASSUME_SAFE_MACROS
    #define CYTHON_ASSUME_SAFE_MACROS 1
  #endif
  #ifndef CYTHON_UNPACK_METHODS
    #define CYTHON_UNPACK_METHODS 1
  #endif
  #undef CYTHON_FAST_THREAD_STATE
  #define CYTHON_FAST_THREAD_STATE 0
  #undef CYTHON_FAST_PYCALL
  #define CYTHON_FAST_PYCALL 0
  #undef CYTHON_PEP489_MULTI_PHASE_INIT
  #define CYTHON_PEP489_MULTI_PHASE_INIT 0
  #undef CYTHON_USE_TP_FINALIZE
  #define CYTHON_USE_TP_FINALIZE 0
#else
  #define CYTHON_COMPILING_IN_PYPY 0
  #define CYTHON_COMPILING_IN_PYSTON 0
  #define CYTHON_COMPILING_IN_CPYTHON 1
  #ifndef CYTHON_USE_TYPE_SLOTS
    #define CYTHON_USE_TYPE_SLOTS 1
  #endif
  #if PY_VERSION_HEX < 0x02070000
    #undef CYTHON_USE_PYTYPE_LOOKUP
    #define CYTHON_USE_PYTYPE_LOOKUP 0
  #elif !defined(CYTHON_USE_PYTYPE_LOOKUP)
    #define CYTHON_USE_PYTYPE_LOOKUP 1
  #endif
  #if PY_MAJOR_VERSION < 3
    #undef CYTHON_USE_ASYNC_SLOTS
    #define CYTHON_USE_ASYNC_SLOTS 0
  #elif !defined(CYTHON_USE_ASYNC_SLOTS)
    #define CYTHON_USE_ASYNC_SLOTS 1
  #endif
  #if PY_VERSION_HEX < 0x02070000
    #undef CYTHON_USE_PYLONG_INTERNALS
    #define CYTHON_USE_PYLONG_INTERNALS 0
  #elif !defined(CYTHON_USE_PYLONG_INTERNALS)
    #define CYTHON_USE_PYLONG_INTERNALS 1
  #endif
  #ifndef CYTHON_USE_PYLIST_INTERNALS
    #define CYTHON_USE_PYLIST_INTERNALS 1
  #endif
  #ifndef CYTHON_USE_UNICODE_INTERNALS
    #define CYTHON_USE_UNICODE_INTERNALS 1
  #endif
  #if PY_VERSION_HEX < 0x030300F0
    #undef CYTHON_USE_UNICODE_WRITER
    #define CYTHON_USE_UNICODE_WRITER 0
  #elif !defined(CYTHON_USE_UNICODE_WRITER)
    #define CYTHON_USE_UNICODE_WRITER 1
  #endif
  #ifndef CYTHON_AVOID_BORROWED_REFS
    #define CYTHON_AVOID_BORROWED_REFS 0
  #endif
  #ifndef CYTHON_ASSUME_SAFE_MACROS
    #define CYTHON_ASSUME_SAFE_MACROS 1
  #endif
  #ifndef CYTHON_UNPACK_METHODS
    #define CYTHON_UNPACK_METHODS 1
  #endif
  #ifndef CYTHON_FAST_THREAD_STATE
    #define CYTHON_FAST_THREAD_STATE 1
  #endif
  #ifndef CYTHON_FAST_PYCALL
    #define CYTHON_FAST_PYCALL 1
  #endif
  #ifndef CYTHON_PEP489_MULTI_PHASE_INIT
    #define CYTHON_PEP489_MULTI_PHASE_INIT (PY_VERSION_HEX >= 0x03050000)
  #endif
  #ifndef CYTHON_USE_TP_FINALIZE
    #define CYTHON_USE_TP_FINALIZE (PY_VERSION_HEX >= 0x030400a1)
  #endif
#endif
#if !defined(CYTHON_FAST_PYCCALL)
#define CYTHON_FAST_PYCCALL  (CYTHON_FAST_PYCALL && PY_VERSION_HEX >= 0x030600B1)
#endif
#if CYTHON_USE_PYLONG_INTERNALS
  #include "longintrepr.h"
  #undef SHIFT
  #undef BASE
  #undef MASK
#endif
#if CYTHON_COMPILING_IN_PYPY && PY_VERSION_HEX < 0x02070600 && !defined(Py_OptimizeFlag)
  #define Py_OptimizeFlag 0
#endif
#define __PYX_BUILD_PY_SSIZE_T "n"
#define CYTHON_FORMAT_SSIZE_T "z"
#if PY_MAJOR_VERSION < 3
  #define __Pyx_BUILTIN_MODULE_NAME "__builtin__"
  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
          PyCode_New(a+k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
  #define __Pyx_DefaultClassType PyClass_Type
#else
  #define __Pyx_BUILTIN_MODULE_NAME "builtins"
  #define __Pyx_PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)\
          PyCode_New(a, k, l, s, f, code, c, n, v, fv, cell, fn, name, fline, lnos)
  #define __Pyx_DefaultClassType PyType_Type
#endif
#ifndef Py_TPFLAGS_CHECKTYPES
  #define Py_TPFLAGS_CHECKTYPES 0
#endif
#ifndef Py_TPFLAGS_HAVE_INDEX
  #define Py_TPFLAGS_HAVE_INDEX 0
#endif
#ifndef Py_TPFLAGS_HAVE_NEWBUFFER
  #define Py_TPFLAGS_HAVE_NEWBUFFER 0
#endif
#ifndef Py_TPFLAGS_HAVE_FINALIZE
  #define Py_TPFLAGS_HAVE_FINALIZE 0
#endif
#if PY_VERSION_HEX < 0x030700A0 || !defined(METH_FASTCALL)
  #ifndef METH_FASTCALL
     #define METH_FASTCALL 0x80
  #endif
  typedef PyObject *(*__Pyx_PyCFunctionFast) (PyObject *self, PyObject **args, Py_ssize_t nargs);
  typedef PyObject *(*__Pyx_PyCFunctionFastWithKeywords) (PyObject *self, PyObject **args,
                                                          Py_ssize_t nargs, PyObject *kwnames);
#else
  #define __Pyx_PyCFunctionFast _PyCFunctionFast
  #define __Pyx_PyCFunctionFastWithKeywords _PyCFunctionFastWithKeywords
#endif
#if CYTHON_FAST_PYCCALL
#define __Pyx_PyFastCFunction_Check(func)\
    ((PyCFunction_Check(func) && (METH_FASTCALL == (PyCFunction_GET_FLAGS(func) & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS)))))
#else
#define __Pyx_PyFastCFunction_Check(func) 0
#endif
#if !CYTHON_FAST_THREAD_STATE || PY_VERSION_HEX < 0x02070000
  #define __Pyx_PyThreadState_Current PyThreadState_GET()
#elif PY_VERSION_HEX >= 0x03050200
  #define __Pyx_PyThreadState_Current _PyThreadState_UncheckedGet()
#elif PY_VERSION_HEX >= 0x03000000
  #define __Pyx_PyThreadState_Current PyThreadState_Get()
#else
  #define __Pyx_PyThreadState_Current _PyThreadState_Current
#endif
#if CYTHON_COMPILING_IN_CPYTHON || defined(_PyDict_NewPresized)
#define __Pyx_PyDict_NewPresized(n)  ((n <= 8) ? PyDict_New() : _PyDict_NewPresized(n))
#else
#define __Pyx_PyDict_NewPresized(n)  PyDict_New()
#endif
#if PY_MAJOR_VERSION >= 3 || CYTHON_FUTURE_DIVISION
  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_TrueDivide(x,y)
  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceTrueDivide(x,y)
#else
  #define __Pyx_PyNumber_Divide(x,y)         PyNumber_Divide(x,y)
  #define __Pyx_PyNumber_InPlaceDivide(x,y)  PyNumber_InPlaceDivide(x,y)
#endif
#if PY_VERSION_HEX > 0x03030000 && defined(PyUnicode_KIND)
  #define CYTHON_PEP393_ENABLED 1
  #define __Pyx_PyUnicode_READY(op)       (likely(PyUnicode_IS_READY(op)) ?\
                                              0 : _PyUnicode_Ready((PyObject *)(op)))
  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_LENGTH(u)
  #define __Pyx_PyUnicode_READ_CHAR(u, i) PyUnicode_READ_CHAR(u, i)
  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   PyUnicode_MAX_CHAR_VALUE(u)
  #define __Pyx_PyUnicode_KIND(u)         PyUnicode_KIND(u)
  #define __Pyx_PyUnicode_DATA(u)         PyUnicode_DATA(u)
  #define __Pyx_PyUnicode_READ(k, d, i)   PyUnicode_READ(k, d, i)
  #define __Pyx_PyUnicode_WRITE(k, d, i, ch)  PyUnicode_WRITE(k, d, i, ch)
  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != (likely(PyUnicode_IS_READY(u)) ? PyUnicode_GET_LENGTH(u) : PyUnicode_GET_SIZE(u)))
#else
  #define CYTHON_PEP393_ENABLED 0
  #define PyUnicode_1BYTE_KIND  1
  #define PyUnicode_2BYTE_KIND  2
  #define PyUnicode_4BYTE_KIND  4
  #define __Pyx_PyUnicode_READY(op)       (0)
  #define __Pyx_PyUnicode_GET_LENGTH(u)   PyUnicode_GET_SIZE(u)
  #define __Pyx_PyUnicode_READ_CHAR(u, i) ((Py_UCS4)(PyUnicode_AS_UNICODE(u)[i]))
  #define __Pyx_PyUnicode_MAX_CHAR_VALUE(u)   ((sizeof(Py_UNICODE) == 2) ? 65535 : 1114111)
  #define __Pyx_PyUnicode_KIND(u)         (sizeof(Py_UNICODE))
  #define __Pyx_PyUnicode_DATA(u)         ((void*)PyUnicode_AS_UNICODE(u))
  #define __Pyx_PyUnicode_READ(k, d, i)   ((void)(k), (Py_UCS4)(((Py_UNICODE*)d)[i]))
  #define __Pyx_PyUnicode_WRITE(k, d, i, ch)  (((void)(k)), ((Py_UNICODE*)d)[i] = ch)
  #define __Pyx_PyUnicode_IS_TRUE(u)      (0 != PyUnicode_GET_SIZE(u))
#endif
#if CYTHON_COMPILING_IN_PYPY
  #define __Pyx_PyUnicode_Concat(a, b)      PyNumber_Add(a, b)
  #define __Pyx_PyUnicode_ConcatSafe(a, b)  PyNumber_Add(a, b)
#else
  #define __Pyx_PyUnicode_Concat(a, b)      PyUnicode_Concat(a, b)
  #define __Pyx_PyUnicode_ConcatSafe(a, b)  ((unlikely((a) == Py_None) || unlikely((b) == Py_None)) ?\
      PyNumber_Add(a, b) : __Pyx_PyUnicode_Concat(a, b))
#endif
#if CYTHON_COMPILING_IN_PYPY && !defined(PyUnicode_Contains)
  #define PyUnicode_Contains(u, s)  PySequence_Contains(u, s)
#endif
#if CYTHON_COMPILING_IN_PYPY && !defined(PyByteArray_Check)
  #define PyByteArray_Check(obj)  PyObject_TypeCheck(obj, &PyByteArray_Type)
#endif
#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Format)
  #define PyObject_Format(obj, fmt)  PyObject_CallMethod(obj, "__format__", "O", fmt)
#endif
#if CYTHON_COMPILING_IN_PYPY && !defined(PyObject_Malloc)
  #define PyObject_Malloc(s)   PyMem_Malloc(s)
  #define PyObject_Free(p)     PyMem_Free(p)
  #define PyObject_Realloc(p)  PyMem_Realloc(p)
#endif
#if CYTHON_COMPILING_IN_PYSTON
  #define __Pyx_PyCode_HasFreeVars(co)  PyCode_HasFreeVars(co)
  #define __Pyx_PyFrame_SetLineNumber(frame, lineno) PyFrame_SetLineNumber(frame, lineno)
#else
  #define __Pyx_PyCode_HasFreeVars(co)  (PyCode_GetNumFree(co) > 0)
  #define __Pyx_PyFrame_SetLineNumber(frame, lineno)  (frame)->f_lineno = (lineno)
#endif
#define __Pyx_PyString_FormatSafe(a, b)   ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : __Pyx_PyString_Format(a, b))
#define __Pyx_PyUnicode_FormatSafe(a, b)  ((unlikely((a) == Py_None)) ? PyNumber_Remainder(a, b) : PyUnicode_Format(a, b))
#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyString_Format(a, b)  PyUnicode_Format(a, b)
#else
  #define __Pyx_PyString_Format(a, b)  PyString_Format(a, b)
#endif
#if PY_MAJOR_VERSION < 3 && !defined(PyObject_ASCII)
  #define PyObject_ASCII(o)            PyObject_Repr(o)
#endif
#if PY_MAJOR_VERSION >= 3
  #define PyBaseString_Type            PyUnicode_Type
  #define PyStringObject               PyUnicodeObject
  #define PyString_Type                PyUnicode_Type
  #define PyString_Check               PyUnicode_Check
  #define PyString_CheckExact          PyUnicode_CheckExact
#endif
#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyBaseString_Check(obj) PyUnicode_Check(obj)
  #define __Pyx_PyBaseString_CheckExact(obj) PyUnicode_CheckExact(obj)
#else
  #define __Pyx_PyBaseString_Check(obj) (PyString_Check(obj) || PyUnicode_Check(obj))
  #define __Pyx_PyBaseString_CheckExact(obj) (PyString_CheckExact(obj) || PyUnicode_CheckExact(obj))
#endif
#ifndef PySet_CheckExact
  #define PySet_CheckExact(obj)        (Py_TYPE(obj) == &PySet_Type)
#endif
#define __Pyx_PyException_Check(obj) __Pyx_TypeCheck(obj, PyExc_Exception)
#if PY_MAJOR_VERSION >= 3
  #define PyIntObject                  PyLongObject
  #define PyInt_Type                   PyLong_Type
  #define PyInt_Check(op)              PyLong_Check(op)
  #define PyInt_CheckExact(op)         PyLong_CheckExact(op)
  #define PyInt_FromString             PyLong_FromString
  #define PyInt_FromUnicode            PyLong_FromUnicode
  #define PyInt_FromLong               PyLong_FromLong
  #define PyInt_FromSize_t             PyLong_FromSize_t
  #define PyInt_FromSsize_t            PyLong_FromSsize_t
  #define PyInt_AsLong                 PyLong_AsLong
  #define PyInt_AS_LONG                PyLong_AS_LONG
  #define PyInt_AsSsize_t              PyLong_AsSsize_t
  #define PyInt_AsUnsignedLongMask     PyLong_AsUnsignedLongMask
  #define PyInt_AsUnsignedLongLongMask PyLong_AsUnsignedLongLongMask
  #define PyNumber_Int                 PyNumber_Long
#endif
#if PY_MAJOR_VERSION >= 3
  #define PyBoolObject                 PyLongObject
#endif
#if PY_MAJOR_VERSION >= 3 && CYTHON_COMPILING_IN_PYPY
  #ifndef PyUnicode_InternFromString
    #define PyUnicode_InternFromString(s) PyUnicode_FromString(s)
  #endif
#endif
#if PY_VERSION_HEX < 0x030200A4
  typedef long Py_hash_t;
  #define __Pyx_PyInt_FromHash_t PyInt_FromLong
  #define __Pyx_PyInt_AsHash_t   PyInt_AsLong
#else
  #define __Pyx_PyInt_FromHash_t PyInt_FromSsize_t
  #define __Pyx_PyInt_AsHash_t   PyInt_AsSsize_t
#endif
#if PY_MAJOR_VERSION >= 3
  #define __Pyx_PyMethod_New(func, self, klass) ((self) ? PyMethod_New(func, self) : PyInstanceMethod_New(func))
#else
  #define __Pyx_PyMethod_New(func, self, klass) PyMethod_New(func, self, klass)
#endif
#ifndef __has_attribute
  #define __has_attribute(x) 0
#endif
#ifndef __has_cpp_attribute
  #define __has_cpp_attribute(x) 0
#endif
#if CYTHON_USE_ASYNC_SLOTS
  #if PY_VERSION_HEX >= 0x030500B1
    #define __Pyx_PyAsyncMethodsStruct PyAsyncMethods
    #define __Pyx_PyType_AsAsync(obj) (Py_TYPE(obj)->tp_as_async)
  #else
    #define __Pyx_PyType_AsAsync(obj) ((__Pyx_PyAsyncMethodsStruct*) (Py_TYPE(obj)->tp_reserved))
  #endif
#else
  #define __Pyx_PyType_AsAsync(obj) NULL
#endif
#ifndef __Pyx_PyAsyncMethodsStruct
    typedef struct {
        unaryfunc am_await;
        unaryfunc am_aiter;
        unaryfunc am_anext;
    } __Pyx_PyAsyncMethodsStruct;
#endif
#ifndef CYTHON_RESTRICT
  #if defined(__GNUC__)
    #define CYTHON_RESTRICT __restrict__
  #elif defined(_MSC_VER) && _MSC_VER >= 1400
    #define CYTHON_RESTRICT __restrict
  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define CYTHON_RESTRICT restrict
  #else
    #define CYTHON_RESTRICT
  #endif
#endif
#ifndef CYTHON_UNUSED
# if defined(__GNUC__)
#   if !(defined(__cplusplus)) || (__GNUC__ > 3 || (__GNUC__ == 3 && __GNUC_MINOR__ >= 4))
#     define CYTHON_UNUSED __attribute__ ((__unused__))
#   else
#     define CYTHON_UNUSED
#   endif
# elif defined(__ICC) || (defined(__INTEL_COMPILER) && !defined(_MSC_VER))
#   define CYTHON_UNUSED __attribute__ ((__unused__))
# else
#   define CYTHON_UNUSED
# endif
#endif
#ifndef CYTHON_MAYBE_UNUSED_VAR
#  if defined(__cplusplus)
     template<class T> void CYTHON_MAYBE_UNUSED_VAR( const T& ) { }
#  else
#    define CYTHON_MAYBE_UNUSED_VAR(x) (void)(x)
#  endif
#endif
#ifndef CYTHON_NCP_UNUSED
# if CYTHON_COMPILING_IN_CPYTHON
#  define CYTHON_NCP_UNUSED
# else
#  define CYTHON_NCP_UNUSED CYTHON_UNUSED
# endif
#endif
#define __Pyx_void_to_None(void_result) ((void)(void_result), Py_INCREF(Py_None), Py_None)
#ifdef _MSC_VER
    #ifndef _MSC_STDINT_H_
        #if _MSC_VER < 1300
           typedef unsigned char     uint8_t;
           typedef unsigned int      uint32_t;
        #else
           typedef unsigned __int8   uint8_t;
           typedef unsigned __int32  uint32_t;
        #endif
    #endif
#else
   #include <stdint.h>
#endif
#ifndef CYTHON_FALLTHROUGH
  #ifdef __cplusplus
    #if __has_cpp_attribute(fallthrough)
      #define CYTHON_FALLTHROUGH [[fallthrough]]
    #elif __has_cpp_attribute(clang::fallthrough)
      #define CYTHON_FALLTHROUGH [[clang::fallthrough]]
    #endif
  #endif
  #ifndef CYTHON_FALLTHROUGH
    #if __has_attribute(fallthrough) || (defined(__GNUC__) && defined(__attribute__))
      #define CYTHON_FALLTHROUGH __attribute__((fallthrough))
    #else
      #define CYTHON_FALLTHROUGH
    #endif
  #endif
#endif

#ifndef CYTHON_INLINE
  #if defined(__clang__)
    #define CYTHON_INLINE __inline__ __attribute__ ((__unused__))
  #elif defined(__GNUC__)
    #define CYTHON_INLINE __inline__
  #elif defined(_MSC_VER)
    #define CYTHON_INLINE __inline
  #elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define CYTHON_INLINE inline
  #else
    #define CYTHON_INLINE
  #endif
#endif

#if defined(WIN32) || defined(MS_WINDOWS)
  #define _USE_MATH_DEFINES
#endif
#include <math.h>
#ifdef NAN
#define __PYX_NAN() ((float) NAN)
#else
static CYTHON_INLINE float __PYX_NAN() {
  float value;
  memset(&value, 0xFF, sizeof(value));
  return value;
}
#endif
#if defined(__CYGWIN__) && defined(_LDBL_EQ_DBL)
#define __Pyx_truncl trunc
#else
#define __Pyx_truncl truncl
#endif


#define __PYX_ERR(f_index, lineno, Ln_error) \
{ \
  __pyx_filename = __pyx_f[f_index]; __pyx_lineno = lineno; __pyx_clineno = __LINE__; goto Ln_error; \
}

#ifndef __PYX_EXTERN_C
  #ifdef __cplusplus
    #define __PYX_EXTERN_C extern "C"
  #else
    #define __PYX_EXTERN_C extern
  #endif
#endif

#define __PYX_HAVE__surprise__prediction_algorithms__matrix_factorization
#define __PYX_HAVE_API__surprise__prediction_algorithms__matrix_factorization
#include <string.h>
#include <stdio.h>
#include "numpy/arrayobject.h"
#include "numpy/ufuncobject.h"
#ifdef _OPENMP
#include <omp.h>
#endif /* _OPENMP */

#if defined(PYREX_WITHOUT_ASSERTIONS) && !defined(CYTHON_WITHOUT_ASSERTIONS)
#define CYTHON_WITHOUT_ASSERTIONS
#endif

typedef struct {PyObject **p; const char *s; const Py_ssize_t n; const char* encoding;
                const char is_unicode; const char is_str; const char intern; } __Pyx_StringTabEntry;

#define __PYX_DEFAULT_STRING_ENCODING_IS_ASCII 0
#define __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT 0
#define __PYX_DEFAULT_STRING_ENCODING ""
#define __Pyx_PyObject_FromString __Pyx_PyBytes_FromString
#define __Pyx_PyObject_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
#define __Pyx_uchar_cast(c) ((unsigned char)c)
#define __Pyx_long_cast(x) ((long)x)
#define __Pyx_fits_Py_ssize_t(v, type, is_signed)  (\
    (sizeof(type) < sizeof(Py_ssize_t))  ||\
    (sizeof(type) > sizeof(Py_ssize_t) &&\
          likely(v < (type)PY_SSIZE_T_MAX ||\
                 v == (type)PY_SSIZE_T_MAX)  &&\
          (!is_signed || likely(v > (type)PY_SSIZE_T_MIN ||\
                                v == (type)PY_SSIZE_T_MIN)))  ||\
    (sizeof(type) == sizeof(Py_ssize_t) &&\
          (is_signed || likely(v < (type)PY_SSIZE_T_MAX ||\
                               v == (type)PY_SSIZE_T_MAX)))  )
#if defined (__cplusplus) && __cplusplus >= 201103L
    #include <cstdlib>
    #define __Pyx_sst_abs(value) std::abs(value)
#elif SIZEOF_INT >= SIZEOF_SIZE_T
    #define __Pyx_sst_abs(value) abs(value)
#elif SIZEOF_LONG >= SIZEOF_SIZE_T
    #define __Pyx_sst_abs(value) labs(value)
#elif defined (_MSC_VER)
    #define __Pyx_sst_abs(value) ((Py_ssize_t)_abs64(value))
#elif defined (__STDC_VERSION__) && __STDC_VERSION__ >= 199901L
    #define __Pyx_sst_abs(value) llabs(value)
#elif defined (__GNUC__)
    #define __Pyx_sst_abs(value) __builtin_llabs(value)
#else
    #define __Pyx_sst_abs(value) ((value<0) ? -value : value)
#endif
static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject*);
static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject*, Py_ssize_t* length);
#define __Pyx_PyByteArray_FromString(s) PyByteArray_FromStringAndSize((const char*)s, strlen((const char*)s))
#define __Pyx_PyByteArray_FromStringAndSize(s, l) PyByteArray_FromStringAndSize((const char*)s, l)
#define __Pyx_PyBytes_FromString        PyBytes_FromString
#define __Pyx_PyBytes_FromStringAndSize PyBytes_FromStringAndSize
static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char*);
#if PY_MAJOR_VERSION < 3
    #define __Pyx_PyStr_FromString        __Pyx_PyBytes_FromString
    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyBytes_FromStringAndSize
#else
    #define __Pyx_PyStr_FromString        __Pyx_PyUnicode_FromString
    #define __Pyx_PyStr_FromStringAndSize __Pyx_PyUnicode_FromStringAndSize
#endif
#define __Pyx_PyBytes_AsWritableString(s)     ((char*) PyBytes_AS_STRING(s))
#define __Pyx_PyBytes_AsWritableSString(s)    ((signed char*) PyBytes_AS_STRING(s))
#define __Pyx_PyBytes_AsWritableUString(s)    ((unsigned char*) PyBytes_AS_STRING(s))
#define __Pyx_PyBytes_AsString(s)     ((const char*) PyBytes_AS_STRING(s))
#define __Pyx_PyBytes_AsSString(s)    ((const signed char*) PyBytes_AS_STRING(s))
#define __Pyx_PyBytes_AsUString(s)    ((const unsigned char*) PyBytes_AS_STRING(s))
#define __Pyx_PyObject_AsWritableString(s)    ((char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsWritableSString(s)    ((signed char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsWritableUString(s)    ((unsigned char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsSString(s)    ((const signed char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_AsUString(s)    ((const unsigned char*) __Pyx_PyObject_AsString(s))
#define __Pyx_PyObject_FromCString(s)  __Pyx_PyObject_FromString((const char*)s)
#define __Pyx_PyBytes_FromCString(s)   __Pyx_PyBytes_FromString((const char*)s)
#define __Pyx_PyByteArray_FromCString(s)   __Pyx_PyByteArray_FromString((const char*)s)
#define __Pyx_PyStr_FromCString(s)     __Pyx_PyStr_FromString((const char*)s)
#define __Pyx_PyUnicode_FromCString(s) __Pyx_PyUnicode_FromString((const char*)s)
static CYTHON_INLINE size_t __Pyx_Py_UNICODE_strlen(const Py_UNICODE *u) {
    const Py_UNICODE *u_end = u;
    while (*u_end++) ;
    return (size_t)(u_end - u - 1);
}
#define __Pyx_PyUnicode_FromUnicode(u)       PyUnicode_FromUnicode(u, __Pyx_Py_UNICODE_strlen(u))
#define __Pyx_PyUnicode_FromUnicodeAndLength PyUnicode_FromUnicode
#define __Pyx_PyUnicode_AsUnicode            PyUnicode_AsUnicode
#define __Pyx_NewRef(obj) (Py_INCREF(obj), obj)
#define __Pyx_Owned_Py_None(b) __Pyx_NewRef(Py_None)
#define __Pyx_PyBool_FromLong(b) ((b) ? __Pyx_NewRef(Py_True) : __Pyx_NewRef(Py_False))
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject*);
static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x);
#define __Pyx_PySequence_Tuple(obj)\
    (likely(PyTuple_CheckExact(obj)) ? __Pyx_NewRef(obj) : PySequence_Tuple(obj))
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject*);
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t);
#if CYTHON_ASSUME_SAFE_MACROS
#define __pyx_PyFloat_AsDouble(x) (PyFloat_CheckExact(x) ? PyFloat_AS_DOUBLE(x) : PyFloat_AsDouble(x))
#else
#define __pyx_PyFloat_AsDouble(x) PyFloat_AsDouble(x)
#endif
#define __pyx_PyFloat_AsFloat(x) ((float) __pyx_PyFloat_AsDouble(x))
#if PY_MAJOR_VERSION >= 3
#define __Pyx_PyNumber_Int(x) (PyLong_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Long(x))
#else
#define __Pyx_PyNumber_Int(x) (PyInt_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Int(x))
#endif
#define __Pyx_PyNumber_Float(x) (PyFloat_CheckExact(x) ? __Pyx_NewRef(x) : PyNumber_Float(x))
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
static int __Pyx_sys_getdefaultencoding_not_ascii;
static int __Pyx_init_sys_getdefaultencoding_params(void) {
    PyObject* sys;
    PyObject* default_encoding = NULL;
    PyObject* ascii_chars_u = NULL;
    PyObject* ascii_chars_b = NULL;
    const char* default_encoding_c;
    sys = PyImport_ImportModule("sys");
    if (!sys) goto bad;
    default_encoding = PyObject_CallMethod(sys, (char*) "getdefaultencoding", NULL);
    Py_DECREF(sys);
    if (!default_encoding) goto bad;
    default_encoding_c = PyBytes_AsString(default_encoding);
    if (!default_encoding_c) goto bad;
    if (strcmp(default_encoding_c, "ascii") == 0) {
        __Pyx_sys_getdefaultencoding_not_ascii = 0;
    } else {
        char ascii_chars[128];
        int c;
        for (c = 0; c < 128; c++) {
            ascii_chars[c] = c;
        }
        __Pyx_sys_getdefaultencoding_not_ascii = 1;
        ascii_chars_u = PyUnicode_DecodeASCII(ascii_chars, 128, NULL);
        if (!ascii_chars_u) goto bad;
        ascii_chars_b = PyUnicode_AsEncodedString(ascii_chars_u, default_encoding_c, NULL);
        if (!ascii_chars_b || !PyBytes_Check(ascii_chars_b) || memcmp(ascii_chars, PyBytes_AS_STRING(ascii_chars_b), 128) != 0) {
            PyErr_Format(
                PyExc_ValueError,
                "This module compiled with c_string_encoding=ascii, but default encoding '%.200s' is not a superset of ascii.",
                default_encoding_c);
            goto bad;
        }
        Py_DECREF(ascii_chars_u);
        Py_DECREF(ascii_chars_b);
    }
    Py_DECREF(default_encoding);
    return 0;
bad:
    Py_XDECREF(default_encoding);
    Py_XDECREF(ascii_chars_u);
    Py_XDECREF(ascii_chars_b);
    return -1;
}
#endif
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT && PY_MAJOR_VERSION >= 3
#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_DecodeUTF8(c_str, size, NULL)
#else
#define __Pyx_PyUnicode_FromStringAndSize(c_str, size) PyUnicode_Decode(c_str, size, __PYX_DEFAULT_STRING_ENCODING, NULL)
#if __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
static char* __PYX_DEFAULT_STRING_ENCODING;
static int __Pyx_init_sys_getdefaultencoding_params(void) {
    PyObject* sys;
    PyObject* default_encoding = NULL;
    char* default_encoding_c;
    sys = PyImport_ImportModule("sys");
    if (!sys) goto bad;
    default_encoding = PyObject_CallMethod(sys, (char*) (const char*) "getdefaultencoding", NULL);
    Py_DECREF(sys);
    if (!default_encoding) goto bad;
    default_encoding_c = PyBytes_AsString(default_encoding);
    if (!default_encoding_c) goto bad;
    __PYX_DEFAULT_STRING_ENCODING = (char*) malloc(strlen(default_encoding_c));
    if (!__PYX_DEFAULT_STRING_ENCODING) goto bad;
    strcpy(__PYX_DEFAULT_STRING_ENCODING, default_encoding_c);
    Py_DECREF(default_encoding);
    return 0;
bad:
    Py_XDECREF(default_encoding);
    return -1;
}
#endif
#endif


/* Test for GCC > 2.95 */
#if defined(__GNUC__)     && (__GNUC__ > 2 || (__GNUC__ == 2 && (__GNUC_MINOR__ > 95)))
  #define likely(x)   __builtin_expect(!!(x), 1)
  #define unlikely(x) __builtin_expect(!!(x), 0)
#else /* !__GNUC__ or GCC < 2.95 */
  #define likely(x)   (x)
  #define unlikely(x) (x)
#endif /* __GNUC__ */
static CYTHON_INLINE void __Pyx_pretend_to_initialize(void* ptr) { (void)ptr; }

static PyObject *__pyx_m;
static PyObject *__pyx_d;
static PyObject *__pyx_b;
static PyObject *__pyx_cython_runtime;
static PyObject *__pyx_empty_tuple;
static PyObject *__pyx_empty_bytes;
static PyObject *__pyx_empty_unicode;
static int __pyx_lineno;
static int __pyx_clineno = 0;
static const char * __pyx_cfilenm= __FILE__;
static const char *__pyx_filename;

/* Header.proto */
#if !defined(CYTHON_CCOMPLEX)
  #if defined(__cplusplus)
    #define CYTHON_CCOMPLEX 1
  #elif defined(_Complex_I)
    #define CYTHON_CCOMPLEX 1
  #else
    #define CYTHON_CCOMPLEX 0
  #endif
#endif
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    #include <complex>
  #else
    #include <complex.h>
  #endif
#endif
#if CYTHON_CCOMPLEX && !defined(__cplusplus) && defined(__sun__) && defined(__GNUC__)
  #undef _Complex_I
  #define _Complex_I 1.0fj
#endif


static const char *__pyx_f[] = {
  "surprise/prediction_algorithms/matrix_factorization.pyx",
  "__init__.pxd",
  "type.pxd",
};
/* BufferFormatStructs.proto */
#define IS_UNSIGNED(type) (((type) -1) > 0)
struct __Pyx_StructField_;
#define __PYX_BUF_FLAGS_PACKED_STRUCT (1 << 0)
typedef struct {
  const char* name;
  struct __Pyx_StructField_* fields;
  size_t size;
  size_t arraysize[8];
  int ndim;
  char typegroup;
  char is_unsigned;
  int flags;
} __Pyx_TypeInfo;
typedef struct __Pyx_StructField_ {
  __Pyx_TypeInfo* type;
  const char* name;
  size_t offset;
} __Pyx_StructField;
typedef struct {
  __Pyx_StructField* field;
  size_t parent_offset;
} __Pyx_BufFmt_StackElem;
typedef struct {
  __Pyx_StructField root;
  __Pyx_BufFmt_StackElem* head;
  size_t fmt_offset;
  size_t new_count, enc_count;
  size_t struct_alignment;
  int is_complex;
  char enc_type;
  char new_packmode;
  char enc_packmode;
  char is_valid_array;
} __Pyx_BufFmt_Context;


/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":743
 * # in Cython to enable them only on the right systems.
 * 
 * ctypedef npy_int8       int8_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t
 */
typedef npy_int8 __pyx_t_5numpy_int8_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":744
 * 
 * ctypedef npy_int8       int8_t
 * ctypedef npy_int16      int16_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t
 */
typedef npy_int16 __pyx_t_5numpy_int16_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":745
 * ctypedef npy_int8       int8_t
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_int64      int64_t
 * #ctypedef npy_int96      int96_t
 */
typedef npy_int32 __pyx_t_5numpy_int32_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":746
 * ctypedef npy_int16      int16_t
 * ctypedef npy_int32      int32_t
 * ctypedef npy_int64      int64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_int96      int96_t
 * #ctypedef npy_int128     int128_t
 */
typedef npy_int64 __pyx_t_5numpy_int64_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":750
 * #ctypedef npy_int128     int128_t
 * 
 * ctypedef npy_uint8      uint8_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
 */
typedef npy_uint8 __pyx_t_5numpy_uint8_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":751
 * 
 * ctypedef npy_uint8      uint8_t
 * ctypedef npy_uint16     uint16_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t
 */
typedef npy_uint16 __pyx_t_5numpy_uint16_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":752
 * ctypedef npy_uint8      uint8_t
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uint64     uint64_t
 * #ctypedef npy_uint96     uint96_t
 */
typedef npy_uint32 __pyx_t_5numpy_uint32_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":753
 * ctypedef npy_uint16     uint16_t
 * ctypedef npy_uint32     uint32_t
 * ctypedef npy_uint64     uint64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_uint96     uint96_t
 * #ctypedef npy_uint128    uint128_t
 */
typedef npy_uint64 __pyx_t_5numpy_uint64_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":757
 * #ctypedef npy_uint128    uint128_t
 * 
 * ctypedef npy_float32    float32_t             # <<<<<<<<<<<<<<
 * ctypedef npy_float64    float64_t
 * #ctypedef npy_float80    float80_t
 */
typedef npy_float32 __pyx_t_5numpy_float32_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":758
 * 
 * ctypedef npy_float32    float32_t
 * ctypedef npy_float64    float64_t             # <<<<<<<<<<<<<<
 * #ctypedef npy_float80    float80_t
 * #ctypedef npy_float128   float128_t
 */
typedef npy_float64 __pyx_t_5numpy_float64_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":767
 * # The int types are mapped a bit surprising --
 * # numpy.int corresponds to 'l' and numpy.long to 'q'
 * ctypedef npy_long       int_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longlong   long_t
 * ctypedef npy_longlong   longlong_t
 */
typedef npy_long __pyx_t_5numpy_int_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":768
 * # numpy.int corresponds to 'l' and numpy.long to 'q'
 * ctypedef npy_long       int_t
 * ctypedef npy_longlong   long_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longlong   longlong_t
 * 
 */
typedef npy_longlong __pyx_t_5numpy_long_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":769
 * ctypedef npy_long       int_t
 * ctypedef npy_longlong   long_t
 * ctypedef npy_longlong   longlong_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_ulong      uint_t
 */
typedef npy_longlong __pyx_t_5numpy_longlong_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":771
 * ctypedef npy_longlong   longlong_t
 * 
 * ctypedef npy_ulong      uint_t             # <<<<<<<<<<<<<<
 * ctypedef npy_ulonglong  ulong_t
 * ctypedef npy_ulonglong  ulonglong_t
 */
typedef npy_ulong __pyx_t_5numpy_uint_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":772
 * 
 * ctypedef npy_ulong      uint_t
 * ctypedef npy_ulonglong  ulong_t             # <<<<<<<<<<<<<<
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 */
typedef npy_ulonglong __pyx_t_5numpy_ulong_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":773
 * ctypedef npy_ulong      uint_t
 * ctypedef npy_ulonglong  ulong_t
 * ctypedef npy_ulonglong  ulonglong_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_intp       intp_t
 */
typedef npy_ulonglong __pyx_t_5numpy_ulonglong_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":775
 * ctypedef npy_ulonglong  ulonglong_t
 * 
 * ctypedef npy_intp       intp_t             # <<<<<<<<<<<<<<
 * ctypedef npy_uintp      uintp_t
 * 
 */
typedef npy_intp __pyx_t_5numpy_intp_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":776
 * 
 * ctypedef npy_intp       intp_t
 * ctypedef npy_uintp      uintp_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_double     float_t
 */
typedef npy_uintp __pyx_t_5numpy_uintp_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":778
 * ctypedef npy_uintp      uintp_t
 * 
 * ctypedef npy_double     float_t             # <<<<<<<<<<<<<<
 * ctypedef npy_double     double_t
 * ctypedef npy_longdouble longdouble_t
 */
typedef npy_double __pyx_t_5numpy_float_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":779
 * 
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t             # <<<<<<<<<<<<<<
 * ctypedef npy_longdouble longdouble_t
 * 
 */
typedef npy_double __pyx_t_5numpy_double_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":780
 * ctypedef npy_double     float_t
 * ctypedef npy_double     double_t
 * ctypedef npy_longdouble longdouble_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_cfloat      cfloat_t
 */
typedef npy_longdouble __pyx_t_5numpy_longdouble_t;
/* Declarations.proto */
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    typedef ::std::complex< float > __pyx_t_float_complex;
  #else
    typedef float _Complex __pyx_t_float_complex;
  #endif
#else
    typedef struct { float real, imag; } __pyx_t_float_complex;
#endif
static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float, float);

/* Declarations.proto */
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    typedef ::std::complex< double > __pyx_t_double_complex;
  #else
    typedef double _Complex __pyx_t_double_complex;
  #endif
#else
    typedef struct { double real, imag; } __pyx_t_double_complex;
#endif
static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double, double);


/*--- Type declarations ---*/
struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate;
struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":782
 * ctypedef npy_longdouble longdouble_t
 * 
 * ctypedef npy_cfloat      cfloat_t             # <<<<<<<<<<<<<<
 * ctypedef npy_cdouble     cdouble_t
 * ctypedef npy_clongdouble clongdouble_t
 */
typedef npy_cfloat __pyx_t_5numpy_cfloat_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":783
 * 
 * ctypedef npy_cfloat      cfloat_t
 * ctypedef npy_cdouble     cdouble_t             # <<<<<<<<<<<<<<
 * ctypedef npy_clongdouble clongdouble_t
 * 
 */
typedef npy_cdouble __pyx_t_5numpy_cdouble_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":784
 * ctypedef npy_cfloat      cfloat_t
 * ctypedef npy_cdouble     cdouble_t
 * ctypedef npy_clongdouble clongdouble_t             # <<<<<<<<<<<<<<
 * 
 * ctypedef npy_cdouble     complex_t
 */
typedef npy_clongdouble __pyx_t_5numpy_clongdouble_t;

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":786
 * ctypedef npy_clongdouble clongdouble_t
 * 
 * ctypedef npy_cdouble     complex_t             # <<<<<<<<<<<<<<
 * 
 * cdef inline object PyArray_MultiIterNew1(a):
 */
typedef npy_cdouble __pyx_t_5numpy_complex_t;

/* "surprise/prediction_algorithms/matrix_factorization.pyx":440
 *         self.yj = yj
 * 
 *     def estimate(self, u, i):             # <<<<<<<<<<<<<<
 * 
 *         est = self.trainset.global_mean
 */
struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate {
  PyObject_HEAD
  PyObject *__pyx_v_self;
  PyObject *__pyx_v_u;
};


/* "surprise/prediction_algorithms/matrix_factorization.pyx":452
 *         if self.trainset.knows_user(u) and self.trainset.knows_item(i):
 *             Iu = len(self.trainset.ur[u])  # nb of items rated by u
 *             u_impl_feedback = (sum(self.yj[j] for (j, _)             # <<<<<<<<<<<<<<
 *                                in self.trainset.ur[u]) / np.sqrt(Iu))
 *             est += np.dot(self.qi[i], self.pu[u] + u_impl_feedback)
 */
struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr {
  PyObject_HEAD
  struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate *__pyx_outer_scope;
  PyObject *__pyx_v__;
  PyObject *__pyx_v_j;
  PyObject *__pyx_t_0;
  Py_ssize_t __pyx_t_1;
  PyObject *(*__pyx_t_2)(PyObject *);
};


/* --- Runtime support code (head) --- */
/* Refnanny.proto */
#ifndef CYTHON_REFNANNY
  #define CYTHON_REFNANNY 0
#endif
#if CYTHON_REFNANNY
  typedef struct {
    void (*INCREF)(void*, PyObject*, int);
    void (*DECREF)(void*, PyObject*, int);
    void (*GOTREF)(void*, PyObject*, int);
    void (*GIVEREF)(void*, PyObject*, int);
    void* (*SetupContext)(const char*, int, const char*);
    void (*FinishContext)(void**);
  } __Pyx_RefNannyAPIStruct;
  static __Pyx_RefNannyAPIStruct *__Pyx_RefNanny = NULL;
  static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname);
  #define __Pyx_RefNannyDeclarations void *__pyx_refnanny = NULL;
#ifdef WITH_THREAD
  #define __Pyx_RefNannySetupContext(name, acquire_gil)\
          if (acquire_gil) {\
              PyGILState_STATE __pyx_gilstate_save = PyGILState_Ensure();\
              __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__);\
              PyGILState_Release(__pyx_gilstate_save);\
          } else {\
              __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__);\
          }
#else
  #define __Pyx_RefNannySetupContext(name, acquire_gil)\
          __pyx_refnanny = __Pyx_RefNanny->SetupContext((name), __LINE__, __FILE__)
#endif
  #define __Pyx_RefNannyFinishContext()\
          __Pyx_RefNanny->FinishContext(&__pyx_refnanny)
  #define __Pyx_INCREF(r)  __Pyx_RefNanny->INCREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
  #define __Pyx_DECREF(r)  __Pyx_RefNanny->DECREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
  #define __Pyx_GOTREF(r)  __Pyx_RefNanny->GOTREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
  #define __Pyx_GIVEREF(r) __Pyx_RefNanny->GIVEREF(__pyx_refnanny, (PyObject *)(r), __LINE__)
  #define __Pyx_XINCREF(r)  do { if((r) != NULL) {__Pyx_INCREF(r); }} while(0)
  #define __Pyx_XDECREF(r)  do { if((r) != NULL) {__Pyx_DECREF(r); }} while(0)
  #define __Pyx_XGOTREF(r)  do { if((r) != NULL) {__Pyx_GOTREF(r); }} while(0)
  #define __Pyx_XGIVEREF(r) do { if((r) != NULL) {__Pyx_GIVEREF(r);}} while(0)
#else
  #define __Pyx_RefNannyDeclarations
  #define __Pyx_RefNannySetupContext(name, acquire_gil)
  #define __Pyx_RefNannyFinishContext()
  #define __Pyx_INCREF(r) Py_INCREF(r)
  #define __Pyx_DECREF(r) Py_DECREF(r)
  #define __Pyx_GOTREF(r)
  #define __Pyx_GIVEREF(r)
  #define __Pyx_XINCREF(r) Py_XINCREF(r)
  #define __Pyx_XDECREF(r) Py_XDECREF(r)
  #define __Pyx_XGOTREF(r)
  #define __Pyx_XGIVEREF(r)
#endif
#define __Pyx_XDECREF_SET(r, v) do {\
        PyObject *tmp = (PyObject *) r;\
        r = v; __Pyx_XDECREF(tmp);\
    } while (0)
#define __Pyx_DECREF_SET(r, v) do {\
        PyObject *tmp = (PyObject *) r;\
        r = v; __Pyx_DECREF(tmp);\
    } while (0)
#define __Pyx_CLEAR(r)    do { PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);} while(0)
#define __Pyx_XCLEAR(r)   do { if((r) != NULL) {PyObject* tmp = ((PyObject*)(r)); r = NULL; __Pyx_DECREF(tmp);}} while(0)

/* PyObjectGetAttrStr.proto */
#if CYTHON_USE_TYPE_SLOTS
static CYTHON_INLINE PyObject* __Pyx_PyObject_GetAttrStr(PyObject* obj, PyObject* attr_name) {
    PyTypeObject* tp = Py_TYPE(obj);
    if (likely(tp->tp_getattro))
        return tp->tp_getattro(obj, attr_name);
#if PY_MAJOR_VERSION < 3
    if (likely(tp->tp_getattr))
        return tp->tp_getattr(obj, PyString_AS_STRING(attr_name));
#endif
    return PyObject_GetAttr(obj, attr_name);
}
#else
#define __Pyx_PyObject_GetAttrStr(o,n) PyObject_GetAttr(o,n)
#endif

/* GetBuiltinName.proto */
static PyObject *__Pyx_GetBuiltinName(PyObject *name);

/* RaiseDoubleKeywords.proto */
static void __Pyx_RaiseDoubleKeywordsError(const char* func_name, PyObject* kw_name);

/* ParseKeywords.proto */
static int __Pyx_ParseOptionalKeywords(PyObject *kwds, PyObject **argnames[],\
    PyObject *kwds2, PyObject *values[], Py_ssize_t num_pos_args,\
    const char* function_name);

/* RaiseArgTupleInvalid.proto */
static void __Pyx_RaiseArgtupleInvalid(const char* func_name, int exact,
    Py_ssize_t num_min, Py_ssize_t num_max, Py_ssize_t num_found);

/* PyObjectSetAttrStr.proto */
#if CYTHON_USE_TYPE_SLOTS
#define __Pyx_PyObject_DelAttrStr(o,n) __Pyx_PyObject_SetAttrStr(o,n,NULL)
static CYTHON_INLINE int __Pyx_PyObject_SetAttrStr(PyObject* obj, PyObject* attr_name, PyObject* value) {
    PyTypeObject* tp = Py_TYPE(obj);
    if (likely(tp->tp_setattro))
        return tp->tp_setattro(obj, attr_name, value);
#if PY_MAJOR_VERSION < 3
    if (likely(tp->tp_setattr))
        return tp->tp_setattr(obj, PyString_AS_STRING(attr_name), value);
#endif
    return PyObject_SetAttr(obj, attr_name, value);
}
#else
#define __Pyx_PyObject_DelAttrStr(o,n)   PyObject_DelAttr(o,n)
#define __Pyx_PyObject_SetAttrStr(o,n,v) PyObject_SetAttr(o,n,v)
#endif

/* GetModuleGlobalName.proto */
static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name);

/* PyCFunctionFastCall.proto */
#if CYTHON_FAST_PYCCALL
static CYTHON_INLINE PyObject *__Pyx_PyCFunction_FastCall(PyObject *func, PyObject **args, Py_ssize_t nargs);
#else
#define __Pyx_PyCFunction_FastCall(func, args, nargs)  (assert(0), NULL)
#endif

/* PyFunctionFastCall.proto */
#if CYTHON_FAST_PYCALL
#define __Pyx_PyFunction_FastCall(func, args, nargs)\
    __Pyx_PyFunction_FastCallDict((func), (args), (nargs), NULL)
#if 1 || PY_VERSION_HEX < 0x030600B1
static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs);
#else
#define __Pyx_PyFunction_FastCallDict(func, args, nargs, kwargs) _PyFunction_FastCallDict(func, args, nargs, kwargs)
#endif
#endif

/* PyObjectCall.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw);
#else
#define __Pyx_PyObject_Call(func, arg, kw) PyObject_Call(func, arg, kw)
#endif

/* PyObjectCallMethO.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg);
#endif

/* PyObjectCallOneArg.proto */
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg);

/* ExtTypeTest.proto */
static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type);

/* IsLittleEndian.proto */
static CYTHON_INLINE int __Pyx_Is_Little_Endian(void);

/* BufferFormatCheck.proto */
static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts);
static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
                              __Pyx_BufFmt_StackElem* stack,
                              __Pyx_TypeInfo* type);

/* BufferGetAndValidate.proto */
#define __Pyx_GetBufferAndValidate(buf, obj, dtype, flags, nd, cast, stack)\
    ((obj == Py_None || obj == NULL) ?\
    (__Pyx_ZeroBuffer(buf), 0) :\
    __Pyx__GetBufferAndValidate(buf, obj, dtype, flags, nd, cast, stack))
static int  __Pyx__GetBufferAndValidate(Py_buffer* buf, PyObject* obj,
    __Pyx_TypeInfo* dtype, int flags, int nd, int cast, __Pyx_BufFmt_StackElem* stack);
static void __Pyx_ZeroBuffer(Py_buffer* buf);
static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info);
static Py_ssize_t __Pyx_minusones[] = { -1, -1, -1, -1, -1, -1, -1, -1 };
static Py_ssize_t __Pyx_zeros[] = { 0, 0, 0, 0, 0, 0, 0, 0 };

/* BufferFallbackError.proto */
static void __Pyx_RaiseBufferFallbackError(void);

/* PyObjectCallNoArg.proto */
#if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func);
#else
#define __Pyx_PyObject_CallNoArg(func) __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL)
#endif

/* RaiseTooManyValuesToUnpack.proto */
static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected);

/* RaiseNeedMoreValuesToUnpack.proto */
static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index);

/* IterFinish.proto */
static CYTHON_INLINE int __Pyx_IterFinish(void);

/* UnpackItemEndCheck.proto */
static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected);

/* BufferIndexError.proto */
static void __Pyx_RaiseBufferIndexError(int axis);

#define __Pyx_BufPtrStrided2d(type, buf, i0, s0, i1, s1) (type)((char*)buf + i0 * s0 + i1 * s1)
#define __Pyx_BufPtrStrided1d(type, buf, i0, s0) (type)((char*)buf + i0 * s0)
/* PyThreadStateGet.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_PyThreadState_declare  PyThreadState *__pyx_tstate;
#define __Pyx_PyErr_Occurred()  __pyx_tstate->curexc_type
#if PY_VERSION_HEX >= 0x03050000
  #define __Pyx_PyThreadState_assign  __pyx_tstate = _PyThreadState_UncheckedGet();
#elif PY_VERSION_HEX >= 0x03000000
  #define __Pyx_PyThreadState_assign  __pyx_tstate = PyThreadState_Get();
#elif PY_VERSION_HEX >= 0x02070000
  #define __Pyx_PyThreadState_assign  __pyx_tstate = _PyThreadState_Current;
#else
  #define __Pyx_PyThreadState_assign  __pyx_tstate = PyThreadState_Get();
#endif
#else
#define __Pyx_PyThreadState_declare
#define __Pyx_PyThreadState_assign
#define __Pyx_PyErr_Occurred()  PyErr_Occurred()
#endif

/* PyErrFetchRestore.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_PyErr_Clear() __Pyx_ErrRestore(NULL, NULL, NULL)
#define __Pyx_ErrRestoreWithState(type, value, tb)  __Pyx_ErrRestoreInState(PyThreadState_GET(), type, value, tb)
#define __Pyx_ErrFetchWithState(type, value, tb)    __Pyx_ErrFetchInState(PyThreadState_GET(), type, value, tb)
#define __Pyx_ErrRestore(type, value, tb)  __Pyx_ErrRestoreInState(__pyx_tstate, type, value, tb)
#define __Pyx_ErrFetch(type, value, tb)    __Pyx_ErrFetchInState(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
#if CYTHON_COMPILING_IN_CPYTHON
#define __Pyx_PyErr_SetNone(exc) (Py_INCREF(exc), __Pyx_ErrRestore((exc), NULL, NULL))
#else
#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
#endif
#else
#define __Pyx_PyErr_Clear() PyErr_Clear()
#define __Pyx_PyErr_SetNone(exc) PyErr_SetNone(exc)
#define __Pyx_ErrRestoreWithState(type, value, tb)  PyErr_Restore(type, value, tb)
#define __Pyx_ErrFetchWithState(type, value, tb)  PyErr_Fetch(type, value, tb)
#define __Pyx_ErrRestore(type, value, tb)  PyErr_Restore(type, value, tb)
#define __Pyx_ErrFetch(type, value, tb)  PyErr_Fetch(type, value, tb)
#endif

/* RaiseException.proto */
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause);

/* GetItemInt.proto */
#define __Pyx_GetItemInt(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
    __Pyx_GetItemInt_Fast(o, (Py_ssize_t)i, is_list, wraparound, boundscheck) :\
    (is_list ? (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL) :\
               __Pyx_GetItemInt_Generic(o, to_py_func(i))))
#define __Pyx_GetItemInt_List(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
    __Pyx_GetItemInt_List_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\
    (PyErr_SetString(PyExc_IndexError, "list index out of range"), (PyObject*)NULL))
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
                                                              int wraparound, int boundscheck);
#define __Pyx_GetItemInt_Tuple(o, i, type, is_signed, to_py_func, is_list, wraparound, boundscheck)\
    (__Pyx_fits_Py_ssize_t(i, type, is_signed) ?\
    __Pyx_GetItemInt_Tuple_Fast(o, (Py_ssize_t)i, wraparound, boundscheck) :\
    (PyErr_SetString(PyExc_IndexError, "tuple index out of range"), (PyObject*)NULL))
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
                                                              int wraparound, int boundscheck);
static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j);
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i,
                                                     int is_list, int wraparound, int boundscheck);

/* ListCompAppend.proto */
#if CYTHON_USE_PYLIST_INTERNALS && CYTHON_ASSUME_SAFE_MACROS
static CYTHON_INLINE int __Pyx_ListComp_Append(PyObject* list, PyObject* x) {
    PyListObject* L = (PyListObject*) list;
    Py_ssize_t len = Py_SIZE(list);
    if (likely(L->allocated > len)) {
        Py_INCREF(x);
        PyList_SET_ITEM(list, len, x);
        Py_SIZE(list) = len+1;
        return 0;
    }
    return PyList_Append(list, x);
}
#else
#define __Pyx_ListComp_Append(L,x) PyList_Append(L,x)
#endif

/* None.proto */
static CYTHON_INLINE void __Pyx_RaiseClosureNameError(const char *varname);

/* DictGetItem.proto */
#if PY_MAJOR_VERSION >= 3 && !CYTHON_COMPILING_IN_PYPY
static PyObject *__Pyx_PyDict_GetItem(PyObject *d, PyObject* key) {
    PyObject *value;
    value = PyDict_GetItemWithError(d, key);
    if (unlikely(!value)) {
        if (!PyErr_Occurred()) {
            PyObject* args = PyTuple_Pack(1, key);
            if (likely(args))
                PyErr_SetObject(PyExc_KeyError, args);
            Py_XDECREF(args);
        }
        return NULL;
    }
    Py_INCREF(value);
    return value;
}
#else
    #define __Pyx_PyDict_GetItem(d, key) PyObject_GetItem(d, key)
#endif

/* RaiseNoneIterError.proto */
static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void);

/* SaveResetException.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_ExceptionSave(type, value, tb)  __Pyx__ExceptionSave(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
#define __Pyx_ExceptionReset(type, value, tb)  __Pyx__ExceptionReset(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb);
#else
#define __Pyx_ExceptionSave(type, value, tb)   PyErr_GetExcInfo(type, value, tb)
#define __Pyx_ExceptionReset(type, value, tb)  PyErr_SetExcInfo(type, value, tb)
#endif

/* PyErrExceptionMatches.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_PyErr_ExceptionMatches(err) __Pyx_PyErr_ExceptionMatchesInState(__pyx_tstate, err)
static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err);
#else
#define __Pyx_PyErr_ExceptionMatches(err)  PyErr_ExceptionMatches(err)
#endif

/* GetException.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_GetException(type, value, tb)  __Pyx__GetException(__pyx_tstate, type, value, tb)
static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
#else
static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb);
#endif

/* IncludeStringH.proto */
#include <string.h>

/* Import.proto */
static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level);

/* ImportFrom.proto */
static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name);

/* CalculateMetaclass.proto */
static PyObject *__Pyx_CalculateMetaclass(PyTypeObject *metaclass, PyObject *bases);

/* FetchCommonType.proto */
static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type);

/* CythonFunction.proto */
#define __Pyx_CyFunction_USED 1
#include <structmember.h>
#define __Pyx_CYFUNCTION_STATICMETHOD  0x01
#define __Pyx_CYFUNCTION_CLASSMETHOD   0x02
#define __Pyx_CYFUNCTION_CCLASS        0x04
#define __Pyx_CyFunction_GetClosure(f)\
    (((__pyx_CyFunctionObject *) (f))->func_closure)
#define __Pyx_CyFunction_GetClassObj(f)\
    (((__pyx_CyFunctionObject *) (f))->func_classobj)
#define __Pyx_CyFunction_Defaults(type, f)\
    ((type *)(((__pyx_CyFunctionObject *) (f))->defaults))
#define __Pyx_CyFunction_SetDefaultsGetter(f, g)\
    ((__pyx_CyFunctionObject *) (f))->defaults_getter = (g)
typedef struct {
    PyCFunctionObject func;
#if PY_VERSION_HEX < 0x030500A0
    PyObject *func_weakreflist;
#endif
    PyObject *func_dict;
    PyObject *func_name;
    PyObject *func_qualname;
    PyObject *func_doc;
    PyObject *func_globals;
    PyObject *func_code;
    PyObject *func_closure;
    PyObject *func_classobj;
    void *defaults;
    int defaults_pyobjects;
    int flags;
    PyObject *defaults_tuple;
    PyObject *defaults_kwdict;
    PyObject *(*defaults_getter)(PyObject *);
    PyObject *func_annotations;
} __pyx_CyFunctionObject;
static PyTypeObject *__pyx_CyFunctionType = 0;
#define __Pyx_CyFunction_NewEx(ml, flags, qualname, self, module, globals, code)\
    __Pyx_CyFunction_New(__pyx_CyFunctionType, ml, flags, qualname, self, module, globals, code)
static PyObject *__Pyx_CyFunction_New(PyTypeObject *, PyMethodDef *ml,
                                      int flags, PyObject* qualname,
                                      PyObject *self,
                                      PyObject *module, PyObject *globals,
                                      PyObject* code);
static CYTHON_INLINE void *__Pyx_CyFunction_InitDefaults(PyObject *m,
                                                         size_t size,
                                                         int pyobjects);
static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsTuple(PyObject *m,
                                                            PyObject *tuple);
static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsKwDict(PyObject *m,
                                                             PyObject *dict);
static CYTHON_INLINE void __Pyx_CyFunction_SetAnnotationsDict(PyObject *m,
                                                              PyObject *dict);
static int __pyx_CyFunction_init(void);

/* Py3ClassCreate.proto */
static PyObject *__Pyx_Py3MetaclassPrepare(PyObject *metaclass, PyObject *bases, PyObject *name, PyObject *qualname,
                                           PyObject *mkw, PyObject *modname, PyObject *doc);
static PyObject *__Pyx_Py3ClassCreate(PyObject *metaclass, PyObject *name, PyObject *bases, PyObject *dict,
                                      PyObject *mkw, int calculate_metaclass, int allow_py2_metaclass);

/* CLineInTraceback.proto */
static int __Pyx_CLineForTraceback(int c_line);

/* CodeObjectCache.proto */
typedef struct {
    PyCodeObject* code_object;
    int code_line;
} __Pyx_CodeObjectCacheEntry;
struct __Pyx_CodeObjectCache {
    int count;
    int max_count;
    __Pyx_CodeObjectCacheEntry* entries;
};
static struct __Pyx_CodeObjectCache __pyx_code_cache = {0,0,NULL};
static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line);
static PyCodeObject *__pyx_find_code_object(int code_line);
static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object);

/* AddTraceback.proto */
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename);

/* BufferStructDeclare.proto */
typedef struct {
  Py_ssize_t shape, strides, suboffsets;
} __Pyx_Buf_DimInfo;
typedef struct {
  size_t refcount;
  Py_buffer pybuffer;
} __Pyx_Buffer;
typedef struct {
  __Pyx_Buffer *rcbuffer;
  char *data;
  __Pyx_Buf_DimInfo diminfo[8];
} __Pyx_LocalBuf_ND;

#if PY_MAJOR_VERSION < 3
    static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags);
    static void __Pyx_ReleaseBuffer(Py_buffer *view);
#else
    #define __Pyx_GetBuffer PyObject_GetBuffer
    #define __Pyx_ReleaseBuffer PyBuffer_Release
#endif


/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value);

/* RealImag.proto */
#if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    #define __Pyx_CREAL(z) ((z).real())
    #define __Pyx_CIMAG(z) ((z).imag())
  #else
    #define __Pyx_CREAL(z) (__real__(z))
    #define __Pyx_CIMAG(z) (__imag__(z))
  #endif
#else
    #define __Pyx_CREAL(z) ((z).real)
    #define __Pyx_CIMAG(z) ((z).imag)
#endif
#if defined(__cplusplus) && CYTHON_CCOMPLEX\
        && (defined(_WIN32) || defined(__clang__) || (defined(__GNUC__) && (__GNUC__ >= 5 || __GNUC__ == 4 && __GNUC_MINOR__ >= 4 )) || __cplusplus >= 201103)
    #define __Pyx_SET_CREAL(z,x) ((z).real(x))
    #define __Pyx_SET_CIMAG(z,y) ((z).imag(y))
#else
    #define __Pyx_SET_CREAL(z,x) __Pyx_CREAL(z) = (x)
    #define __Pyx_SET_CIMAG(z,y) __Pyx_CIMAG(z) = (y)
#endif

/* Arithmetic.proto */
#if CYTHON_CCOMPLEX
    #define __Pyx_c_eq_float(a, b)   ((a)==(b))
    #define __Pyx_c_sum_float(a, b)  ((a)+(b))
    #define __Pyx_c_diff_float(a, b) ((a)-(b))
    #define __Pyx_c_prod_float(a, b) ((a)*(b))
    #define __Pyx_c_quot_float(a, b) ((a)/(b))
    #define __Pyx_c_neg_float(a)     (-(a))
  #ifdef __cplusplus
    #define __Pyx_c_is_zero_float(z) ((z)==(float)0)
    #define __Pyx_c_conj_float(z)    (::std::conj(z))
    #if 1
        #define __Pyx_c_abs_float(z)     (::std::abs(z))
        #define __Pyx_c_pow_float(a, b)  (::std::pow(a, b))
    #endif
  #else
    #define __Pyx_c_is_zero_float(z) ((z)==0)
    #define __Pyx_c_conj_float(z)    (conjf(z))
    #if 1
        #define __Pyx_c_abs_float(z)     (cabsf(z))
        #define __Pyx_c_pow_float(a, b)  (cpowf(a, b))
    #endif
 #endif
#else
    static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex, __pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex);
    static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex);
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex);
    #if 1
        static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex);
        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex, __pyx_t_float_complex);
    #endif
#endif

/* Arithmetic.proto */
#if CYTHON_CCOMPLEX
    #define __Pyx_c_eq_double(a, b)   ((a)==(b))
    #define __Pyx_c_sum_double(a, b)  ((a)+(b))
    #define __Pyx_c_diff_double(a, b) ((a)-(b))
    #define __Pyx_c_prod_double(a, b) ((a)*(b))
    #define __Pyx_c_quot_double(a, b) ((a)/(b))
    #define __Pyx_c_neg_double(a)     (-(a))
  #ifdef __cplusplus
    #define __Pyx_c_is_zero_double(z) ((z)==(double)0)
    #define __Pyx_c_conj_double(z)    (::std::conj(z))
    #if 1
        #define __Pyx_c_abs_double(z)     (::std::abs(z))
        #define __Pyx_c_pow_double(a, b)  (::std::pow(a, b))
    #endif
  #else
    #define __Pyx_c_is_zero_double(z) ((z)==0)
    #define __Pyx_c_conj_double(z)    (conj(z))
    #if 1
        #define __Pyx_c_abs_double(z)     (cabs(z))
        #define __Pyx_c_pow_double(a, b)  (cpow(a, b))
    #endif
 #endif
#else
    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex, __pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex);
    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex);
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex);
    #if 1
        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex);
        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex, __pyx_t_double_complex);
    #endif
#endif

/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value);

/* CIntFromPy.proto */
static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *);

/* CIntToPy.proto */
static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value);

/* CIntFromPy.proto */
static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *);

/* FastTypeChecks.proto */
#if CYTHON_COMPILING_IN_CPYTHON
#define __Pyx_TypeCheck(obj, type) __Pyx_IsSubtype(Py_TYPE(obj), (PyTypeObject *)type)
static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b);
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject *type);
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *type1, PyObject *type2);
#else
#define __Pyx_TypeCheck(obj, type) PyObject_TypeCheck(obj, (PyTypeObject *)type)
#define __Pyx_PyErr_GivenExceptionMatches(err, type) PyErr_GivenExceptionMatches(err, type)
#define __Pyx_PyErr_GivenExceptionMatches2(err, type1, type2) (PyErr_GivenExceptionMatches(err, type1) || PyErr_GivenExceptionMatches(err, type2))
#endif

/* SwapException.proto */
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_ExceptionSwap(type, value, tb)  __Pyx__ExceptionSwap(__pyx_tstate, type, value, tb)
static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb);
#else
static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb);
#endif

/* PyObjectCallMethod1.proto */
static PyObject* __Pyx_PyObject_CallMethod1(PyObject* obj, PyObject* method_name, PyObject* arg);
static PyObject* __Pyx__PyObject_CallMethod1(PyObject* method, PyObject* arg);

/* CoroutineBase.proto */
typedef PyObject *(*__pyx_coroutine_body_t)(PyObject *, PyThreadState *, PyObject *);
typedef struct {
    PyObject_HEAD
    __pyx_coroutine_body_t body;
    PyObject *closure;
    PyObject *exc_type;
    PyObject *exc_value;
    PyObject *exc_traceback;
    PyObject *gi_weakreflist;
    PyObject *classobj;
    PyObject *yieldfrom;
    PyObject *gi_name;
    PyObject *gi_qualname;
    PyObject *gi_modulename;
    int resume_label;
    char is_running;
} __pyx_CoroutineObject;
static __pyx_CoroutineObject *__Pyx__Coroutine_New(
    PyTypeObject *type, __pyx_coroutine_body_t body, PyObject *closure,
    PyObject *name, PyObject *qualname, PyObject *module_name);
static __pyx_CoroutineObject *__Pyx__Coroutine_NewInit(
            __pyx_CoroutineObject *gen, __pyx_coroutine_body_t body, PyObject *closure,
            PyObject *name, PyObject *qualname, PyObject *module_name);
static int __Pyx_Coroutine_clear(PyObject *self);
static PyObject *__Pyx_Coroutine_Send(PyObject *self, PyObject *value);
static PyObject *__Pyx_Coroutine_Close(PyObject *self);
static PyObject *__Pyx_Coroutine_Throw(PyObject *gen, PyObject *args);
#define __Pyx_Coroutine_SwapException(self) {\
    __Pyx_ExceptionSwap(&(self)->exc_type, &(self)->exc_value, &(self)->exc_traceback);\
    __Pyx_Coroutine_ResetFrameBackpointer(self);\
    }
#define __Pyx_Coroutine_ResetAndClearException(self) {\
    __Pyx_ExceptionReset((self)->exc_type, (self)->exc_value, (self)->exc_traceback);\
    (self)->exc_type = (self)->exc_value = (self)->exc_traceback = NULL;\
    }
#if CYTHON_FAST_THREAD_STATE
#define __Pyx_PyGen_FetchStopIterationValue(pvalue)\
    __Pyx_PyGen__FetchStopIterationValue(__pyx_tstate, pvalue)
#else
#define __Pyx_PyGen_FetchStopIterationValue(pvalue)\
    __Pyx_PyGen__FetchStopIterationValue(__Pyx_PyThreadState_Current, pvalue)
#endif
static int __Pyx_PyGen__FetchStopIterationValue(PyThreadState *tstate, PyObject **pvalue);
static CYTHON_INLINE void __Pyx_Coroutine_ResetFrameBackpointer(__pyx_CoroutineObject *self);

/* PatchModuleWithCoroutine.proto */
static PyObject* __Pyx_Coroutine_patch_module(PyObject* module, const char* py_code);

/* PatchGeneratorABC.proto */
static int __Pyx_patch_abc(void);

/* Generator.proto */
#define __Pyx_Generator_USED
static PyTypeObject *__pyx_GeneratorType = 0;
#define __Pyx_Generator_CheckExact(obj) (Py_TYPE(obj) == __pyx_GeneratorType)
#define __Pyx_Generator_New(body, closure, name, qualname, module_name)\
    __Pyx__Coroutine_New(__pyx_GeneratorType, body, closure, name, qualname, module_name)
static PyObject *__Pyx_Generator_Next(PyObject *self);
static int __pyx_Generator_init(void);

/* CheckBinaryVersion.proto */
static int __Pyx_check_binary_version(void);

/* PyIdentifierFromString.proto */
#if !defined(__Pyx_PyIdentifier_FromString)
#if PY_MAJOR_VERSION < 3
  #define __Pyx_PyIdentifier_FromString(s) PyString_FromString(s)
#else
  #define __Pyx_PyIdentifier_FromString(s) PyUnicode_FromString(s)
#endif
#endif

/* ModuleImport.proto */
static PyObject *__Pyx_ImportModule(const char *name);

/* TypeImport.proto */
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name, size_t size, int strict);

/* InitStrings.proto */
static int __Pyx_InitStrings(__Pyx_StringTabEntry *t);


/* Module declarations from 'cpython.buffer' */

/* Module declarations from 'libc.string' */

/* Module declarations from 'libc.stdio' */

/* Module declarations from '__builtin__' */

/* Module declarations from 'cpython.type' */
static PyTypeObject *__pyx_ptype_7cpython_4type_type = 0;

/* Module declarations from 'cpython' */

/* Module declarations from 'cpython.object' */

/* Module declarations from 'cpython.ref' */

/* Module declarations from 'cpython.mem' */

/* Module declarations from 'numpy' */

/* Module declarations from 'numpy' */
static PyTypeObject *__pyx_ptype_5numpy_dtype = 0;
static PyTypeObject *__pyx_ptype_5numpy_flatiter = 0;
static PyTypeObject *__pyx_ptype_5numpy_broadcast = 0;
static PyTypeObject *__pyx_ptype_5numpy_ndarray = 0;
static PyTypeObject *__pyx_ptype_5numpy_ufunc = 0;
static CYTHON_INLINE char *__pyx_f_5numpy__util_dtypestring(PyArray_Descr *, char *, char *, int *); /*proto*/

/* Module declarations from 'surprise.prediction_algorithms.matrix_factorization' */
static PyTypeObject *__pyx_ptype_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate = 0;
static PyTypeObject *__pyx_ptype_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr = 0;
static __Pyx_TypeInfo __Pyx_TypeInfo_nn___pyx_t_5numpy_double_t = { "double_t", NULL, sizeof(__pyx_t_5numpy_double_t), { 0 }, 0, 'R', 0, 0 };
#define __Pyx_MODULE_NAME "surprise.prediction_algorithms.matrix_factorization"
int __pyx_module_is_main_surprise__prediction_algorithms__matrix_factorization = 0;

/* Implementation of 'surprise.prediction_algorithms.matrix_factorization' */
static PyObject *__pyx_builtin_print;
static PyObject *__pyx_builtin_sum;
static PyObject *__pyx_builtin_ValueError;
static PyObject *__pyx_builtin_range;
static PyObject *__pyx_builtin_RuntimeError;
static PyObject *__pyx_builtin_ImportError;
static const char __pyx_k_f[] = "f";
static const char __pyx_k_i[] = "i";
static const char __pyx_k_j[] = "j";
static const char __pyx_k_l[] = "l";
static const char __pyx_k_r[] = "r";
static const char __pyx_k_u[] = "u";
static const char __pyx_k_Iu[] = "Iu";
static const char __pyx_k_bi[] = "bi";
static const char __pyx_k_bu[] = "bu";
static const char __pyx_k_ir[] = "ir";
static const char __pyx_k_np[] = "np";
static const char __pyx_k_pu[] = "pu";
static const char __pyx_k_qi[] = "qi";
static const char __pyx_k_ur[] = "ur";
static const char __pyx_k_yj[] = "yj";
static const char __pyx_k_NMF[] = "NMF";
static const char __pyx_k_SVD[] = "SVD";
static const char __pyx_k__27[] = "_";
static const char __pyx_k_doc[] = "__doc__";
static const char __pyx_k_dot[] = "dot";
static const char __pyx_k_err[] = "err";
static const char __pyx_k_est[] = "est";
static const char __pyx_k_puf[] = "puf";
static const char __pyx_k_qif[] = "qif";
static const char __pyx_k_sgd[] = "sgd";
static const char __pyx_k_sum[] = "sum";
static const char __pyx_k_args[] = "args";
static const char __pyx_k_init[] = "__init__";
static const char __pyx_k_main[] = "__main__";
static const char __pyx_k_self[] = "self";
static const char __pyx_k_send[] = "send";
static const char __pyx_k_size[] = "size";
static const char __pyx_k_sqrt[] = "sqrt";
static const char __pyx_k_test[] = "__test__";
static const char __pyx_k_SVDpp[] = "SVDpp";
static const char __pyx_k_close[] = "close";
static const char __pyx_k_lr_bi[] = "lr_bi";
static const char __pyx_k_lr_bu[] = "lr_bu";
static const char __pyx_k_lr_pu[] = "lr_pu";
static const char __pyx_k_lr_qi[] = "lr_qi";
static const char __pyx_k_lr_yj[] = "lr_yj";
static const char __pyx_k_numpy[] = "numpy";
static const char __pyx_k_print[] = "print";
static const char __pyx_k_range[] = "range";
static const char __pyx_k_throw[] = "throw";
static const char __pyx_k_train[] = "train";
static const char __pyx_k_zeros[] = "zeros";
static const char __pyx_k_biased[] = "biased";
static const char __pyx_k_double[] = "double";
static const char __pyx_k_format[] = "format";
static const char __pyx_k_import[] = "__import__";
static const char __pyx_k_lr_all[] = "lr_all";
static const char __pyx_k_module[] = "__module__";
static const char __pyx_k_normal[] = "normal";
static const char __pyx_k_random[] = "random";
static const char __pyx_k_reg_bi[] = "reg_bi";
static const char __pyx_k_reg_bu[] = "reg_bu";
static const char __pyx_k_reg_pu[] = "reg_pu";
static const char __pyx_k_reg_qi[] = "reg_qi";
static const char __pyx_k_reg_yj[] = "reg_yj";
static const char __pyx_k_NMF_sgd[] = "NMF.sgd";
static const char __pyx_k_SVD_sgd[] = "SVD.sgd";
static const char __pyx_k_genexpr[] = "genexpr";
static const char __pyx_k_n_items[] = "n_items";
static const char __pyx_k_n_users[] = "n_users";
static const char __pyx_k_prepare[] = "__prepare__";
static const char __pyx_k_reg_all[] = "reg_all";
static const char __pyx_k_sqrt_Iu[] = "sqrt_Iu";
static const char __pyx_k_uniform[] = "uniform";
static const char __pyx_k_verbose[] = "verbose";
static const char __pyx_k_AlgoBase[] = "AlgoBase";
static const char __pyx_k_estimate[] = "estimate";
static const char __pyx_k_init_low[] = "init_low";
static const char __pyx_k_item_num[] = "item_num";
static const char __pyx_k_n_epochs[] = "n_epochs";
static const char __pyx_k_qualname[] = "__qualname__";
static const char __pyx_k_trainset[] = "trainset";
static const char __pyx_k_user_num[] = "user_num";
static const char __pyx_k_NMF_train[] = "NMF.train";
static const char __pyx_k_SVD_train[] = "SVD.train";
static const char __pyx_k_SVDpp_sgd[] = "SVDpp.sgd";
static const char __pyx_k_algo_base[] = "algo_base";
static const char __pyx_k_all_items[] = "all_items";
static const char __pyx_k_all_users[] = "all_users";
static const char __pyx_k_init_high[] = "init_high";
static const char __pyx_k_init_mean[] = "init_mean";
static const char __pyx_k_metaclass[] = "__metaclass__";
static const char __pyx_k_n_factors[] = "n_factors";
static const char __pyx_k_six_moves[] = "six.moves";
static const char __pyx_k_NMF___init[] = "NMF.__init__";
static const char __pyx_k_SVD___init[] = "SVD.__init__";
static const char __pyx_k_ValueError[] = "ValueError";
static const char __pyx_k_item_denom[] = "item_denom";
static const char __pyx_k_known_item[] = "known_item";
static const char __pyx_k_known_user[] = "known_user";
static const char __pyx_k_knows_item[] = "knows_item";
static const char __pyx_k_knows_user[] = "knows_user";
static const char __pyx_k_u_impl_fdb[] = "u_impl_fdb";
static const char __pyx_k_user_denom[] = "user_denom";
static const char __pyx_k_ImportError[] = "ImportError";
static const char __pyx_k_SVDpp_train[] = "SVDpp.train";
static const char __pyx_k_all_ratings[] = "all_ratings";
static const char __pyx_k_global_mean[] = "global_mean";
static const char __pyx_k_predictions[] = "predictions";
static const char __pyx_k_NMF_estimate[] = "NMF.estimate";
static const char __pyx_k_RuntimeError[] = "RuntimeError";
static const char __pyx_k_SVD_estimate[] = "SVD.estimate";
static const char __pyx_k_SVDpp___init[] = "SVDpp.__init__";
static const char __pyx_k_init_std_dev[] = "init_std_dev";
static const char __pyx_k_current_epoch[] = "current_epoch";
static const char __pyx_k_SVDpp_estimate[] = "SVDpp.estimate";
static const char __pyx_k_u_impl_feedback[] = "u_impl_feedback";
static const char __pyx_k_Processing_epoch[] = "Processing epoch {}";
static const char __pyx_k_processing_epoch[] = " processing epoch {}";
static const char __pyx_k_cline_in_traceback[] = "cline_in_traceback";
static const char __pyx_k_PredictionImpossible[] = "PredictionImpossible";
static const char __pyx_k_User_and_item_are_unkown[] = "User and item are unkown.";
static const char __pyx_k_ndarray_is_not_C_contiguous[] = "ndarray is not C contiguous";
static const char __pyx_k_SVDpp_estimate_locals_genexpr[] = "SVDpp.estimate.<locals>.genexpr";
static const char __pyx_k_init_low_should_be_greater_than[] = "init_low should be greater than zero";
static const char __pyx_k_numpy_core_multiarray_failed_to[] = "numpy.core.multiarray failed to import";
static const char __pyx_k_the_mod_matrix_factorization_mo[] = "\nthe :mod:`matrix_factorization` module includes some algorithms using matrix\nfactorization.\n";
static const char __pyx_k_unknown_dtype_code_in_numpy_pxd[] = "unknown dtype code in numpy.pxd (%d)";
static const char __pyx_k_A_collaborative_filtering_algori[] = "A collaborative filtering algorithm based on Non-negative Matrix\n    Factorization.\n\n    This algorithm is very similar to :class:`SVD`. The prediction\n    :math:`\\hat{r}_{ui}` is set as:\n\n    .. math::\n        \\hat{r}_{ui} = q_i^Tp_u,\n\n    where user and item factors are kept **positive**. Our implementation\n    follows that suggested in :cite:`NMF:2014`, which is equivalent to\n    :cite:`Zhang96` in its non-regularized form. Both are direct applications\n    of NMF for dense matrices :cite:`NMF_algo`.\n\n    The optimization procedure is a (regularized) stochastic gradient descent\n    with a specific choice of step size that ensures non-negativity of factors,\n    provided that their initial values are also positive.\n\n    At each step of the SGD procedure, the factors :math:`f` or user :math:`u`\n    and item :math:`i` are updated as follows:\n\n    .. math::\n        p_{uf} &\\leftarrow p_{uf} &\\cdot \\frac{\\sum_{i \\in I_u} q_{if}\n        \\cdot r_{ui}}{\\sum_{i \\in I_u} q_{if} \\cdot \\hat{r_{ui}} +\n        \\lambda_u |I_u| p_{uf}}\\\\\n        q_{if} &\\leftarrow q_{if} &\\cdot \\frac{\\sum_{u \\in U_i} p_{uf}\n        \\cdot r_{ui}}{\\sum_{u \\in U_i} p_{uf} \\cdot \\hat{r_{ui}} +\n        \\lambda_i |U_i| q_{if}}\\\\\n\n    where :math:`\\lambda_u` and :math:`\\lambda_i` are regularization\n    parameters.\n\n    This algorithm is highly dependent on initial values. User and item factors\n    are uniformly initialized between ``init_low`` and ``init_high``. Change\n    them at your own risks!\n\n    A biased version is available by setting the ``biased`` parameter to\n    ``True``. In this case, the prediction is set as\n\n    .. math::\n        \\hat{r}_{ui} = \\mu + b_u + b_i + q_i^Tp_u,\n\n    still ensuring positive factors. Baselines are optimized in the same way as\n    in the :class:`SVD` algorithm. While yielding better accuracy, the biased\n    version seems highly prone to overfitting so you may want to reduce the\n    number o""f factors (or increase regularization).\n\n    Args:\n        n_factors: The number of factors. Default is ``15``.\n        n_epochs: The number of iteration of the SGD procedure. Default is\n            ``50``.\n        biased(bool): Whether to use baselines (or biases). Default is\n            ``False``.\n        reg_pu: The regularization term for users :math:`\\lambda_u`. Default is\n            ``0.06``.\n        reg_qi: The regularization term for items :math:`\\lambda_i`. Default is\n            ``0.06``.\n        reg_bu: The regularization term for :math:`b_u`. Only relevant for\n            biased version. Default is ``0.02``.\n        reg_bi: The regularization term for :math:`b_i`. Only relevant for\n            biased version. Default is ``0.02``.\n        lr_bu: The learning rate for :math:`b_u`. Only relevant for biased\n            version. Default is ``0.005``.\n        lr_bi: The learning rate for :math:`b_i`. Only relevant for biased\n            version. Default is ``0.005``.\n        init_low: Lower bound for random initialization of factors. Must be\n            greater than ``0`` to ensure non-negative factors. Default is\n            ``0``.\n        init_high: Higher bound for random initialization of factors. Default\n            is ``1``.\n        verbose: If ``True``, prints the current epoch. Default is ``False``.\n    ";
static const char __pyx_k_Format_string_allocated_too_shor[] = "Format string allocated too short, see comment in numpy.pxd";
static const char __pyx_k_Non_native_byte_order_not_suppor[] = "Non-native byte order not supported";
static const char __pyx_k_The_SVD_algorithm_an_extension_o[] = "The *SVD++* algorithm, an extension of :class:`SVD` taking into account\n    implicit ratings.\n\n    The prediction :math:`\\hat{r}_{ui}` is set as:\n\n    .. math::\n        \\hat{r}_{ui} = \\mu + b_u + b_i + q_i^T\\left(p_u +\n        |I_u|^{-\\frac{1}{2}} \\sum_{j \\in I_u}y_j\\right)\n\n    Where the :math:`y_j` terms are a new set of item factors that capture\n    implicit ratings. Here, an implicit rating describes the fact that a user\n    :math:`u` rated an item :math:`j`, regardless of the rating value.\n\n    If user :math:`u` is unknown, then the bias :math:`b_u` and the factors\n    :math:`p_u` are assumed to be zero. The same applies for item :math:`i`\n    with :math:`b_i`, :math:`q_i` and :math:`y_i`.\n\n\n    For details, see section 4 of :cite:`Koren:2008:FMN`. See also\n    :cite:`Ricci:2010`, section 5.3.1.\n\n    Just as for :class:`SVD`, the parameters are learned using a SGD on the\n    regularized squared error objective.\n\n    Baselines are initialized to ``0``. User and item factors are randomly\n    initialized according to a normal distribution, which can be tuned using\n    the ``init_mean`` and ``init_std_dev`` parameters.\n\n    You have control over the learning rate :math:`\\gamma` and the\n    regularization term :math:`\\lambda`. Both can be different for each\n    kind of parameter (see below). By default, learning rates are set to\n    ``0.005`` and regularization terms are set to ``0.02``.\n\n    Args:\n        n_factors: The number of factors. Default is ``20``.\n        n_epochs: The number of iteration of the SGD procedure. Default is\n            ``20``.\n        init_mean: The mean of the normal distribution for factor vectors\n            initialization. Default is ``0``.\n        init_std_dev: The standard deviation of the normal distribution for\n            factor vectors initialization. Default is ``0.1``.\n        lr_all: The learning rate for all parameters. Default is ``0.007``.\n        reg_all: The regularization"" term for all parameters. Default is\n            ``0.02``.\n        lr_bu: The learning rate for :math:`b_u`. Takes precedence over\n            ``lr_all`` if set. Default is ``None``.\n        lr_bi: The learning rate for :math:`b_i`. Takes precedence over\n            ``lr_all`` if set. Default is ``None``.\n        lr_pu: The learning rate for :math:`p_u`. Takes precedence over\n            ``lr_all`` if set. Default is ``None``.\n        lr_qi: The learning rate for :math:`q_i`. Takes precedence over\n            ``lr_all`` if set. Default is ``None``.\n        lr_yj: The learning rate for :math:`y_j`. Takes precedence over\n            ``lr_all`` if set. Default is ``None``.\n        reg_bu: The regularization term for :math:`b_u`. Takes precedence\n            over ``reg_all`` if set. Default is ``None``.\n        reg_bi: The regularization term for :math:`b_i`. Takes precedence\n            over ``reg_all`` if set. Default is ``None``.\n        reg_pu: The regularization term for :math:`p_u`. Takes precedence\n            over ``reg_all`` if set. Default is ``None``.\n        reg_qi: The regularization term for :math:`q_i`. Takes precedence\n            over ``reg_all`` if set. Default is ``None``.\n        reg_yj: The regularization term for :math:`y_j`. Takes precedence\n            over ``reg_all`` if set. Default is ``None``.\n        verbose: If ``True``, prints the current epoch. Default is ``False``.\n    ";
static const char __pyx_k_The_famous_SVD_algorithm_as_popu[] = "The famous *SVD* algorithm, as popularized by `Simon Funk\n    <http://sifter.org/~simon/journal/20061211.html>`_ during the Netflix\n    Prize. When baselines are not used, this is equivalent to Probabilistic\n    Matrix Factorization :cite:`salakhutdinov2008a` (see :ref:`note\n    <unbiased_note>` below).\n\n    The prediction :math:`\\hat{r}_{ui}` is set as:\n\n    .. math::\n        \\hat{r}_{ui} = \\mu + b_u + b_i + q_i^Tp_u\n\n    If user :math:`u` is unknown, then the bias :math:`b_u` and the factors\n    :math:`p_u` are assumed to be zero. The same applies for item :math:`i`\n    with :math:`b_i` and :math:`q_i`.\n\n    For details, see equation (5) from :cite:`Koren:2009`. See also\n    :cite:`Ricci:2010`, section 5.3.1.\n\n    To estimate all the unknown, we minimize the following regularized squared\n    error:\n\n    .. math::\n        \\sum_{r_{ui} \\in R_{train}} \\left(r_{ui} - \\hat{r}_{ui} \\right)^2 +\n        \\lambda\\left(b_i^2 + b_u^2 + ||q_i||^2 + ||p_u||^2\\right)\n\n\n    The minimization is performed by a very straightforward stochastic gradient\n    descent:\n\n    .. math::\n        b_u &\\leftarrow b_u &+ \\gamma (e_{ui} - \\lambda b_u)\\\\\n        b_i &\\leftarrow b_i &+ \\gamma (e_{ui} - \\lambda b_i)\\\\\n        p_u &\\leftarrow p_u &+ \\gamma (e_{ui} \\cdot q_i - \\lambda p_u)\\\\\n        q_i &\\leftarrow q_i &+ \\gamma (e_{ui} \\cdot p_u - \\lambda q_i)\n\n    where :math:`e_{ui} = r_{ui} - \\hat{r}_{ui}`. These steps are performed\n    over all the ratings of the trainset and repeated ``n_epochs`` times.\n    Baselines are initialized to ``0``. User and item factors are randomly\n    initialized according to a normal distribution, which can be tuned using\n    the ``init_mean`` and ``init_std_dev`` parameters.\n\n    You also have control over the learning rate :math:`\\gamma` and the\n    regularization term :math:`\\lambda`. Both can be different for each\n    kind of parameter (see below). By default, learning rates are set t""o\n    ``0.005`` and regularization terms are set to ``0.02``.\n\n    .. _unbiased_note:\n\n    .. note::\n        You can choose to use an unbiased version of this algorithm, simply\n        predicting:\n\n        .. math::\n            \\hat{r}_{ui} = q_i^Tp_u\n\n        This is equivalent to Probabilistic Matrix Factorization\n        (:cite:`salakhutdinov2008a`, section 2) and can be achieved by setting\n        the ``biased`` parameter to ``False``.\n\n\n    Args:\n        n_factors: The number of factors. Default is ``100``.\n        n_epochs: The number of iteration of the SGD procedure. Default is\n            ``20``.\n        biased(bool): Whether to use baselines (or biases). See :ref:`note\n            <unbiased_note>` above.  Default is ``True``.\n        init_mean: The mean of the normal distribution for factor vectors\n            initialization. Default is ``0``.\n        init_std_dev: The standard deviation of the normal distribution for\n            factor vectors initialization. Default is ``0.1``.\n        lr_all: The learning rate for all parameters. Default is ``0.005``.\n        reg_all: The regularization term for all parameters. Default is\n            ``0.02``.\n        lr_bu: The learning rate for :math:`b_u`. Takes precedence over\n            ``lr_all`` if set. Default is ``None``.\n        lr_bi: The learning rate for :math:`b_i`. Takes precedence over\n            ``lr_all`` if set. Default is ``None``.\n        lr_pu: The learning rate for :math:`p_u`. Takes precedence over\n            ``lr_all`` if set. Default is ``None``.\n        lr_qi: The learning rate for :math:`q_i`. Takes precedence over\n            ``lr_all`` if set. Default is ``None``.\n        reg_bu: The regularization term for :math:`b_u`. Takes precedence\n            over ``reg_all`` if set. Default is ``None``.\n        reg_bi: The regularization term for :math:`b_i`. Takes precedence\n            over ``reg_all`` if set. Default is ``None``.\n        reg_pu: The re""gularization term for :math:`p_u`. Takes precedence\n            over ``reg_all`` if set. Default is ``None``.\n        reg_qi: The regularization term for :math:`q_i`. Takes precedence\n            over ``reg_all`` if set. Default is ``None``.\n        verbose: If ``True``, prints the current epoch. Default is ``False``.\n    ";
static const char __pyx_k_ndarray_is_not_Fortran_contiguou[] = "ndarray is not Fortran contiguous";
static const char __pyx_k_numpy_core_umath_failed_to_impor[] = "numpy.core.umath failed to import";
static const char __pyx_k_surprise_prediction_algorithms_m[] = "surprise.prediction_algorithms.matrix_factorization";
static const char __pyx_k_Format_string_allocated_too_shor_2[] = "Format string allocated too short.";
static const char __pyx_k_surprise_prediction_algorithms_m_2[] = "surprise/prediction_algorithms/matrix_factorization.pyx";
static PyObject *__pyx_kp_s_A_collaborative_filtering_algori;
static PyObject *__pyx_n_s_AlgoBase;
static PyObject *__pyx_kp_u_Format_string_allocated_too_shor;
static PyObject *__pyx_kp_u_Format_string_allocated_too_shor_2;
static PyObject *__pyx_n_s_ImportError;
static PyObject *__pyx_n_s_Iu;
static PyObject *__pyx_n_s_NMF;
static PyObject *__pyx_n_s_NMF___init;
static PyObject *__pyx_n_s_NMF_estimate;
static PyObject *__pyx_n_s_NMF_sgd;
static PyObject *__pyx_n_s_NMF_train;
static PyObject *__pyx_kp_u_Non_native_byte_order_not_suppor;
static PyObject *__pyx_n_s_PredictionImpossible;
static PyObject *__pyx_kp_u_Processing_epoch;
static PyObject *__pyx_n_s_RuntimeError;
static PyObject *__pyx_n_s_SVD;
static PyObject *__pyx_n_s_SVD___init;
static PyObject *__pyx_n_s_SVD_estimate;
static PyObject *__pyx_n_s_SVD_sgd;
static PyObject *__pyx_n_s_SVD_train;
static PyObject *__pyx_n_s_SVDpp;
static PyObject *__pyx_n_s_SVDpp___init;
static PyObject *__pyx_n_s_SVDpp_estimate;
static PyObject *__pyx_n_s_SVDpp_estimate_locals_genexpr;
static PyObject *__pyx_n_s_SVDpp_sgd;
static PyObject *__pyx_n_s_SVDpp_train;
static PyObject *__pyx_kp_s_The_SVD_algorithm_an_extension_o;
static PyObject *__pyx_kp_s_The_famous_SVD_algorithm_as_popu;
static PyObject *__pyx_kp_u_User_and_item_are_unkown;
static PyObject *__pyx_n_s_ValueError;
static PyObject *__pyx_n_s__27;
static PyObject *__pyx_n_s_algo_base;
static PyObject *__pyx_n_s_all_items;
static PyObject *__pyx_n_s_all_ratings;
static PyObject *__pyx_n_s_all_users;
static PyObject *__pyx_n_s_args;
static PyObject *__pyx_n_s_bi;
static PyObject *__pyx_n_s_biased;
static PyObject *__pyx_n_s_bu;
static PyObject *__pyx_n_s_cline_in_traceback;
static PyObject *__pyx_n_s_close;
static PyObject *__pyx_n_s_current_epoch;
static PyObject *__pyx_n_s_doc;
static PyObject *__pyx_n_s_dot;
static PyObject *__pyx_n_s_double;
static PyObject *__pyx_n_s_err;
static PyObject *__pyx_n_s_est;
static PyObject *__pyx_n_s_estimate;
static PyObject *__pyx_n_s_f;
static PyObject *__pyx_n_s_format;
static PyObject *__pyx_n_s_genexpr;
static PyObject *__pyx_n_s_global_mean;
static PyObject *__pyx_n_s_i;
static PyObject *__pyx_n_s_import;
static PyObject *__pyx_n_s_init;
static PyObject *__pyx_n_s_init_high;
static PyObject *__pyx_n_s_init_low;
static PyObject *__pyx_kp_u_init_low_should_be_greater_than;
static PyObject *__pyx_n_s_init_mean;
static PyObject *__pyx_n_s_init_std_dev;
static PyObject *__pyx_n_s_ir;
static PyObject *__pyx_n_s_item_denom;
static PyObject *__pyx_n_s_item_num;
static PyObject *__pyx_n_s_j;
static PyObject *__pyx_n_s_known_item;
static PyObject *__pyx_n_s_known_user;
static PyObject *__pyx_n_s_knows_item;
static PyObject *__pyx_n_s_knows_user;
static PyObject *__pyx_n_s_l;
static PyObject *__pyx_n_s_lr_all;
static PyObject *__pyx_n_s_lr_bi;
static PyObject *__pyx_n_s_lr_bu;
static PyObject *__pyx_n_s_lr_pu;
static PyObject *__pyx_n_s_lr_qi;
static PyObject *__pyx_n_s_lr_yj;
static PyObject *__pyx_n_s_main;
static PyObject *__pyx_n_s_metaclass;
static PyObject *__pyx_n_s_module;
static PyObject *__pyx_n_s_n_epochs;
static PyObject *__pyx_n_s_n_factors;
static PyObject *__pyx_n_s_n_items;
static PyObject *__pyx_n_s_n_users;
static PyObject *__pyx_kp_u_ndarray_is_not_C_contiguous;
static PyObject *__pyx_kp_u_ndarray_is_not_Fortran_contiguou;
static PyObject *__pyx_n_s_normal;
static PyObject *__pyx_n_s_np;
static PyObject *__pyx_n_s_numpy;
static PyObject *__pyx_kp_u_numpy_core_multiarray_failed_to;
static PyObject *__pyx_kp_u_numpy_core_umath_failed_to_impor;
static PyObject *__pyx_n_s_predictions;
static PyObject *__pyx_n_s_prepare;
static PyObject *__pyx_n_s_print;
static PyObject *__pyx_kp_u_processing_epoch;
static PyObject *__pyx_n_s_pu;
static PyObject *__pyx_n_s_puf;
static PyObject *__pyx_n_s_qi;
static PyObject *__pyx_n_s_qif;
static PyObject *__pyx_n_s_qualname;
static PyObject *__pyx_n_s_r;
static PyObject *__pyx_n_s_random;
static PyObject *__pyx_n_s_range;
static PyObject *__pyx_n_s_reg_all;
static PyObject *__pyx_n_s_reg_bi;
static PyObject *__pyx_n_s_reg_bu;
static PyObject *__pyx_n_s_reg_pu;
static PyObject *__pyx_n_s_reg_qi;
static PyObject *__pyx_n_s_reg_yj;
static PyObject *__pyx_n_s_self;
static PyObject *__pyx_n_s_send;
static PyObject *__pyx_n_s_sgd;
static PyObject *__pyx_n_s_six_moves;
static PyObject *__pyx_n_s_size;
static PyObject *__pyx_n_s_sqrt;
static PyObject *__pyx_n_s_sqrt_Iu;
static PyObject *__pyx_n_s_sum;
static PyObject *__pyx_n_s_surprise_prediction_algorithms_m;
static PyObject *__pyx_kp_s_surprise_prediction_algorithms_m_2;
static PyObject *__pyx_n_s_test;
static PyObject *__pyx_n_s_throw;
static PyObject *__pyx_n_s_train;
static PyObject *__pyx_n_s_trainset;
static PyObject *__pyx_n_s_u;
static PyObject *__pyx_n_s_u_impl_fdb;
static PyObject *__pyx_n_s_u_impl_feedback;
static PyObject *__pyx_n_s_uniform;
static PyObject *__pyx_kp_u_unknown_dtype_code_in_numpy_pxd;
static PyObject *__pyx_n_s_ur;
static PyObject *__pyx_n_s_user_denom;
static PyObject *__pyx_n_s_user_num;
static PyObject *__pyx_n_s_verbose;
static PyObject *__pyx_n_s_yj;
static PyObject *__pyx_n_s_zeros;
static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3SVD___init__(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_n_factors, PyObject *__pyx_v_n_epochs, PyObject *__pyx_v_biased, PyObject *__pyx_v_init_mean, PyObject *__pyx_v_init_std_dev, PyObject *__pyx_v_lr_all, PyObject *__pyx_v_reg_all, PyObject *__pyx_v_lr_bu, PyObject *__pyx_v_lr_bi, PyObject *__pyx_v_lr_pu, PyObject *__pyx_v_lr_qi, PyObject *__pyx_v_reg_bu, PyObject *__pyx_v_reg_bi, PyObject *__pyx_v_reg_pu, PyObject *__pyx_v_reg_qi, PyObject *__pyx_v_verbose); /* proto */
static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_2train(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_trainset); /* proto */
static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_4sgd(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_trainset); /* proto */
static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_6estimate(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_u, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp___init__(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_n_factors, PyObject *__pyx_v_n_epochs, PyObject *__pyx_v_init_mean, PyObject *__pyx_v_init_std_dev, PyObject *__pyx_v_lr_all, PyObject *__pyx_v_reg_all, PyObject *__pyx_v_lr_bu, PyObject *__pyx_v_lr_bi, PyObject *__pyx_v_lr_pu, PyObject *__pyx_v_lr_qi, PyObject *__pyx_v_lr_yj, PyObject *__pyx_v_reg_bu, PyObject *__pyx_v_reg_bi, PyObject *__pyx_v_reg_pu, PyObject *__pyx_v_reg_qi, PyObject *__pyx_v_reg_yj, PyObject *__pyx_v_verbose); /* proto */
static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_2train(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_trainset); /* proto */
static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_4sgd(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_trainset); /* proto */
static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_8estimate_genexpr(PyObject *__pyx_self); /* proto */
static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_6estimate(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_u, PyObject *__pyx_v_i); /* proto */
static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3NMF___init__(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_n_factors, PyObject *__pyx_v_n_epochs, PyObject *__pyx_v_biased, PyObject *__pyx_v_reg_pu, PyObject *__pyx_v_reg_qi, PyObject *__pyx_v_reg_bu, PyObject *__pyx_v_reg_bi, PyObject *__pyx_v_lr_bu, PyObject *__pyx_v_lr_bi, PyObject *__pyx_v_init_low, PyObject *__pyx_v_init_high, PyObject *__pyx_v_verbose); /* proto */
static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_2train(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_trainset); /* proto */
static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_4sgd(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_trainset); /* proto */
static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_6estimate(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_u, PyObject *__pyx_v_i); /* proto */
static int __pyx_pf_5numpy_7ndarray___getbuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /* proto */
static void __pyx_pf_5numpy_7ndarray_2__releasebuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info); /* proto */
static PyObject *__pyx_tp_new_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_tp_new_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr(PyTypeObject *t, PyObject *a, PyObject *k); /*proto*/
static PyObject *__pyx_float__1;
static PyObject *__pyx_float__02;
static PyObject *__pyx_float__06;
static PyObject *__pyx_float__005;
static PyObject *__pyx_float__007;
static PyObject *__pyx_int_0;
static PyObject *__pyx_int_1;
static PyObject *__pyx_int_15;
static PyObject *__pyx_int_20;
static PyObject *__pyx_int_50;
static PyObject *__pyx_int_100;
static PyObject *__pyx_tuple_;
static PyObject *__pyx_tuple__2;
static PyObject *__pyx_tuple__3;
static PyObject *__pyx_tuple__4;
static PyObject *__pyx_tuple__5;
static PyObject *__pyx_tuple__6;
static PyObject *__pyx_tuple__7;
static PyObject *__pyx_tuple__8;
static PyObject *__pyx_tuple__9;
static PyObject *__pyx_tuple__10;
static PyObject *__pyx_tuple__11;
static PyObject *__pyx_tuple__12;
static PyObject *__pyx_tuple__13;
static PyObject *__pyx_tuple__15;
static PyObject *__pyx_tuple__16;
static PyObject *__pyx_tuple__18;
static PyObject *__pyx_tuple__20;
static PyObject *__pyx_tuple__22;
static PyObject *__pyx_tuple__24;
static PyObject *__pyx_tuple__25;
static PyObject *__pyx_tuple__28;
static PyObject *__pyx_tuple__30;
static PyObject *__pyx_tuple__32;
static PyObject *__pyx_tuple__34;
static PyObject *__pyx_tuple__35;
static PyObject *__pyx_tuple__37;
static PyObject *__pyx_tuple__39;
static PyObject *__pyx_codeobj__14;
static PyObject *__pyx_codeobj__17;
static PyObject *__pyx_codeobj__19;
static PyObject *__pyx_codeobj__21;
static PyObject *__pyx_codeobj__23;
static PyObject *__pyx_codeobj__26;
static PyObject *__pyx_codeobj__29;
static PyObject *__pyx_codeobj__31;
static PyObject *__pyx_codeobj__33;
static PyObject *__pyx_codeobj__36;
static PyObject *__pyx_codeobj__38;
static PyObject *__pyx_codeobj__40;

/* "surprise/prediction_algorithms/matrix_factorization.pyx":110
 *     """
 * 
 *     def __init__(self, n_factors=100, n_epochs=20, biased=True, init_mean=0,             # <<<<<<<<<<<<<<
 *                  init_std_dev=.1, lr_all=.005,
 *                  reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None, lr_qi=None,
 */

/* Python wrapper */
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_1__init__(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static PyMethodDef __pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_1__init__ = {"__init__", (PyCFunction)__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_1__init__, METH_VARARGS|METH_KEYWORDS, 0};
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_1__init__(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
  PyObject *__pyx_v_self = 0;
  PyObject *__pyx_v_n_factors = 0;
  PyObject *__pyx_v_n_epochs = 0;
  PyObject *__pyx_v_biased = 0;
  PyObject *__pyx_v_init_mean = 0;
  PyObject *__pyx_v_init_std_dev = 0;
  PyObject *__pyx_v_lr_all = 0;
  PyObject *__pyx_v_reg_all = 0;
  PyObject *__pyx_v_lr_bu = 0;
  PyObject *__pyx_v_lr_bi = 0;
  PyObject *__pyx_v_lr_pu = 0;
  PyObject *__pyx_v_lr_qi = 0;
  PyObject *__pyx_v_reg_bu = 0;
  PyObject *__pyx_v_reg_bi = 0;
  PyObject *__pyx_v_reg_pu = 0;
  PyObject *__pyx_v_reg_qi = 0;
  PyObject *__pyx_v_verbose = 0;
  PyObject *__pyx_r = 0;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("__init__ (wrapper)", 0);
  {
    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_self,&__pyx_n_s_n_factors,&__pyx_n_s_n_epochs,&__pyx_n_s_biased,&__pyx_n_s_init_mean,&__pyx_n_s_init_std_dev,&__pyx_n_s_lr_all,&__pyx_n_s_reg_all,&__pyx_n_s_lr_bu,&__pyx_n_s_lr_bi,&__pyx_n_s_lr_pu,&__pyx_n_s_lr_qi,&__pyx_n_s_reg_bu,&__pyx_n_s_reg_bi,&__pyx_n_s_reg_pu,&__pyx_n_s_reg_qi,&__pyx_n_s_verbose,0};
    PyObject* values[17] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
    values[1] = ((PyObject *)((PyObject *)__pyx_int_100));
    values[2] = ((PyObject *)((PyObject *)__pyx_int_20));
    values[3] = ((PyObject *)((PyObject *)Py_True));
    values[4] = ((PyObject *)((PyObject *)__pyx_int_0));
    values[5] = ((PyObject *)((PyObject*)__pyx_float__1));
    values[6] = ((PyObject *)((PyObject*)__pyx_float__005));
    values[7] = ((PyObject *)((PyObject*)__pyx_float__02));

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":112
 *     def __init__(self, n_factors=100, n_epochs=20, biased=True, init_mean=0,
 *                  init_std_dev=.1, lr_all=.005,
 *                  reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None, lr_qi=None,             # <<<<<<<<<<<<<<
 *                  reg_bu=None, reg_bi=None, reg_pu=None, reg_qi=None,
 *                  verbose=False):
 */
    values[8] = ((PyObject *)((PyObject *)Py_None));
    values[9] = ((PyObject *)((PyObject *)Py_None));
    values[10] = ((PyObject *)((PyObject *)Py_None));
    values[11] = ((PyObject *)((PyObject *)Py_None));

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":113
 *                  init_std_dev=.1, lr_all=.005,
 *                  reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None, lr_qi=None,
 *                  reg_bu=None, reg_bi=None, reg_pu=None, reg_qi=None,             # <<<<<<<<<<<<<<
 *                  verbose=False):
 * 
 */
    values[12] = ((PyObject *)((PyObject *)Py_None));
    values[13] = ((PyObject *)((PyObject *)Py_None));
    values[14] = ((PyObject *)((PyObject *)Py_None));
    values[15] = ((PyObject *)((PyObject *)Py_None));

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":114
 *                  reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None, lr_qi=None,
 *                  reg_bu=None, reg_bi=None, reg_pu=None, reg_qi=None,
 *                  verbose=False):             # <<<<<<<<<<<<<<
 * 
 *         self.n_factors = n_factors
 */
    values[16] = ((PyObject *)((PyObject *)Py_False));
    if (unlikely(__pyx_kwds)) {
      Py_ssize_t kw_args;
      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
      switch (pos_args) {
        case 17: values[16] = PyTuple_GET_ITEM(__pyx_args, 16);
        CYTHON_FALLTHROUGH;
        case 16: values[15] = PyTuple_GET_ITEM(__pyx_args, 15);
        CYTHON_FALLTHROUGH;
        case 15: values[14] = PyTuple_GET_ITEM(__pyx_args, 14);
        CYTHON_FALLTHROUGH;
        case 14: values[13] = PyTuple_GET_ITEM(__pyx_args, 13);
        CYTHON_FALLTHROUGH;
        case 13: values[12] = PyTuple_GET_ITEM(__pyx_args, 12);
        CYTHON_FALLTHROUGH;
        case 12: values[11] = PyTuple_GET_ITEM(__pyx_args, 11);
        CYTHON_FALLTHROUGH;
        case 11: values[10] = PyTuple_GET_ITEM(__pyx_args, 10);
        CYTHON_FALLTHROUGH;
        case 10: values[9] = PyTuple_GET_ITEM(__pyx_args, 9);
        CYTHON_FALLTHROUGH;
        case  9: values[8] = PyTuple_GET_ITEM(__pyx_args, 8);
        CYTHON_FALLTHROUGH;
        case  8: values[7] = PyTuple_GET_ITEM(__pyx_args, 7);
        CYTHON_FALLTHROUGH;
        case  7: values[6] = PyTuple_GET_ITEM(__pyx_args, 6);
        CYTHON_FALLTHROUGH;
        case  6: values[5] = PyTuple_GET_ITEM(__pyx_args, 5);
        CYTHON_FALLTHROUGH;
        case  5: values[4] = PyTuple_GET_ITEM(__pyx_args, 4);
        CYTHON_FALLTHROUGH;
        case  4: values[3] = PyTuple_GET_ITEM(__pyx_args, 3);
        CYTHON_FALLTHROUGH;
        case  3: values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
        CYTHON_FALLTHROUGH;
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        CYTHON_FALLTHROUGH;
        case  0: break;
        default: goto __pyx_L5_argtuple_error;
      }
      kw_args = PyDict_Size(__pyx_kwds);
      switch (pos_args) {
        case  0:
        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_self)) != 0)) kw_args--;
        else goto __pyx_L5_argtuple_error;
        CYTHON_FALLTHROUGH;
        case  1:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_n_factors);
          if (value) { values[1] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  2:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_n_epochs);
          if (value) { values[2] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  3:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_biased);
          if (value) { values[3] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  4:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_init_mean);
          if (value) { values[4] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  5:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_init_std_dev);
          if (value) { values[5] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  6:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_lr_all);
          if (value) { values[6] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  7:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_all);
          if (value) { values[7] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  8:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_lr_bu);
          if (value) { values[8] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  9:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_lr_bi);
          if (value) { values[9] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 10:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_lr_pu);
          if (value) { values[10] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 11:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_lr_qi);
          if (value) { values[11] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 12:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_bu);
          if (value) { values[12] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 13:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_bi);
          if (value) { values[13] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 14:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_pu);
          if (value) { values[14] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 15:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_qi);
          if (value) { values[15] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 16:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_verbose);
          if (value) { values[16] = value; kw_args--; }
        }
      }
      if (unlikely(kw_args > 0)) {
        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "__init__") < 0)) __PYX_ERR(0, 110, __pyx_L3_error)
      }
    } else {
      switch (PyTuple_GET_SIZE(__pyx_args)) {
        case 17: values[16] = PyTuple_GET_ITEM(__pyx_args, 16);
        CYTHON_FALLTHROUGH;
        case 16: values[15] = PyTuple_GET_ITEM(__pyx_args, 15);
        CYTHON_FALLTHROUGH;
        case 15: values[14] = PyTuple_GET_ITEM(__pyx_args, 14);
        CYTHON_FALLTHROUGH;
        case 14: values[13] = PyTuple_GET_ITEM(__pyx_args, 13);
        CYTHON_FALLTHROUGH;
        case 13: values[12] = PyTuple_GET_ITEM(__pyx_args, 12);
        CYTHON_FALLTHROUGH;
        case 12: values[11] = PyTuple_GET_ITEM(__pyx_args, 11);
        CYTHON_FALLTHROUGH;
        case 11: values[10] = PyTuple_GET_ITEM(__pyx_args, 10);
        CYTHON_FALLTHROUGH;
        case 10: values[9] = PyTuple_GET_ITEM(__pyx_args, 9);
        CYTHON_FALLTHROUGH;
        case  9: values[8] = PyTuple_GET_ITEM(__pyx_args, 8);
        CYTHON_FALLTHROUGH;
        case  8: values[7] = PyTuple_GET_ITEM(__pyx_args, 7);
        CYTHON_FALLTHROUGH;
        case  7: values[6] = PyTuple_GET_ITEM(__pyx_args, 6);
        CYTHON_FALLTHROUGH;
        case  6: values[5] = PyTuple_GET_ITEM(__pyx_args, 5);
        CYTHON_FALLTHROUGH;
        case  5: values[4] = PyTuple_GET_ITEM(__pyx_args, 4);
        CYTHON_FALLTHROUGH;
        case  4: values[3] = PyTuple_GET_ITEM(__pyx_args, 3);
        CYTHON_FALLTHROUGH;
        case  3: values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
        CYTHON_FALLTHROUGH;
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        break;
        default: goto __pyx_L5_argtuple_error;
      }
    }
    __pyx_v_self = values[0];
    __pyx_v_n_factors = values[1];
    __pyx_v_n_epochs = values[2];
    __pyx_v_biased = values[3];
    __pyx_v_init_mean = values[4];
    __pyx_v_init_std_dev = values[5];
    __pyx_v_lr_all = values[6];
    __pyx_v_reg_all = values[7];
    __pyx_v_lr_bu = values[8];
    __pyx_v_lr_bi = values[9];
    __pyx_v_lr_pu = values[10];
    __pyx_v_lr_qi = values[11];
    __pyx_v_reg_bu = values[12];
    __pyx_v_reg_bi = values[13];
    __pyx_v_reg_pu = values[14];
    __pyx_v_reg_qi = values[15];
    __pyx_v_verbose = values[16];
  }
  goto __pyx_L4_argument_unpacking_done;
  __pyx_L5_argtuple_error:;
  __Pyx_RaiseArgtupleInvalid("__init__", 0, 1, 17, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 110, __pyx_L3_error)
  __pyx_L3_error:;
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVD.__init__", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __Pyx_RefNannyFinishContext();
  return NULL;
  __pyx_L4_argument_unpacking_done:;
  __pyx_r = __pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3SVD___init__(__pyx_self, __pyx_v_self, __pyx_v_n_factors, __pyx_v_n_epochs, __pyx_v_biased, __pyx_v_init_mean, __pyx_v_init_std_dev, __pyx_v_lr_all, __pyx_v_reg_all, __pyx_v_lr_bu, __pyx_v_lr_bi, __pyx_v_lr_pu, __pyx_v_lr_qi, __pyx_v_reg_bu, __pyx_v_reg_bi, __pyx_v_reg_pu, __pyx_v_reg_qi, __pyx_v_verbose);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":110
 *     """
 * 
 *     def __init__(self, n_factors=100, n_epochs=20, biased=True, init_mean=0,             # <<<<<<<<<<<<<<
 *                  init_std_dev=.1, lr_all=.005,
 *                  reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None, lr_qi=None,
 */

  /* function exit code */
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3SVD___init__(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_n_factors, PyObject *__pyx_v_n_epochs, PyObject *__pyx_v_biased, PyObject *__pyx_v_init_mean, PyObject *__pyx_v_init_std_dev, PyObject *__pyx_v_lr_all, PyObject *__pyx_v_reg_all, PyObject *__pyx_v_lr_bu, PyObject *__pyx_v_lr_bi, PyObject *__pyx_v_lr_pu, PyObject *__pyx_v_lr_qi, PyObject *__pyx_v_reg_bu, PyObject *__pyx_v_reg_bi, PyObject *__pyx_v_reg_pu, PyObject *__pyx_v_reg_qi, PyObject *__pyx_v_verbose) {
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  int __pyx_t_2;
  PyObject *__pyx_t_3 = NULL;
  PyObject *__pyx_t_4 = NULL;
  PyObject *__pyx_t_5 = NULL;
  __Pyx_RefNannySetupContext("__init__", 0);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":116
 *                  verbose=False):
 * 
 *         self.n_factors = n_factors             # <<<<<<<<<<<<<<
 *         self.n_epochs = n_epochs
 *         self.biased = biased
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_n_factors, __pyx_v_n_factors) < 0) __PYX_ERR(0, 116, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":117
 * 
 *         self.n_factors = n_factors
 *         self.n_epochs = n_epochs             # <<<<<<<<<<<<<<
 *         self.biased = biased
 *         self.init_mean = init_mean
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_n_epochs, __pyx_v_n_epochs) < 0) __PYX_ERR(0, 117, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":118
 *         self.n_factors = n_factors
 *         self.n_epochs = n_epochs
 *         self.biased = biased             # <<<<<<<<<<<<<<
 *         self.init_mean = init_mean
 *         self.init_std_dev = init_std_dev
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_biased, __pyx_v_biased) < 0) __PYX_ERR(0, 118, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":119
 *         self.n_epochs = n_epochs
 *         self.biased = biased
 *         self.init_mean = init_mean             # <<<<<<<<<<<<<<
 *         self.init_std_dev = init_std_dev
 *         self.lr_bu = lr_bu if lr_bu is not None else lr_all
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_init_mean, __pyx_v_init_mean) < 0) __PYX_ERR(0, 119, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":120
 *         self.biased = biased
 *         self.init_mean = init_mean
 *         self.init_std_dev = init_std_dev             # <<<<<<<<<<<<<<
 *         self.lr_bu = lr_bu if lr_bu is not None else lr_all
 *         self.lr_bi = lr_bi if lr_bi is not None else lr_all
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_init_std_dev, __pyx_v_init_std_dev) < 0) __PYX_ERR(0, 120, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":121
 *         self.init_mean = init_mean
 *         self.init_std_dev = init_std_dev
 *         self.lr_bu = lr_bu if lr_bu is not None else lr_all             # <<<<<<<<<<<<<<
 *         self.lr_bi = lr_bi if lr_bi is not None else lr_all
 *         self.lr_pu = lr_pu if lr_pu is not None else lr_all
 */
  __pyx_t_2 = (__pyx_v_lr_bu != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_lr_bu);
    __pyx_t_1 = __pyx_v_lr_bu;
  } else {
    __Pyx_INCREF(__pyx_v_lr_all);
    __pyx_t_1 = __pyx_v_lr_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_lr_bu, __pyx_t_1) < 0) __PYX_ERR(0, 121, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":122
 *         self.init_std_dev = init_std_dev
 *         self.lr_bu = lr_bu if lr_bu is not None else lr_all
 *         self.lr_bi = lr_bi if lr_bi is not None else lr_all             # <<<<<<<<<<<<<<
 *         self.lr_pu = lr_pu if lr_pu is not None else lr_all
 *         self.lr_qi = lr_qi if lr_qi is not None else lr_all
 */
  __pyx_t_2 = (__pyx_v_lr_bi != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_lr_bi);
    __pyx_t_1 = __pyx_v_lr_bi;
  } else {
    __Pyx_INCREF(__pyx_v_lr_all);
    __pyx_t_1 = __pyx_v_lr_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_lr_bi, __pyx_t_1) < 0) __PYX_ERR(0, 122, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":123
 *         self.lr_bu = lr_bu if lr_bu is not None else lr_all
 *         self.lr_bi = lr_bi if lr_bi is not None else lr_all
 *         self.lr_pu = lr_pu if lr_pu is not None else lr_all             # <<<<<<<<<<<<<<
 *         self.lr_qi = lr_qi if lr_qi is not None else lr_all
 *         self.reg_bu = reg_bu if reg_bu is not None else reg_all
 */
  __pyx_t_2 = (__pyx_v_lr_pu != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_lr_pu);
    __pyx_t_1 = __pyx_v_lr_pu;
  } else {
    __Pyx_INCREF(__pyx_v_lr_all);
    __pyx_t_1 = __pyx_v_lr_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_lr_pu, __pyx_t_1) < 0) __PYX_ERR(0, 123, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":124
 *         self.lr_bi = lr_bi if lr_bi is not None else lr_all
 *         self.lr_pu = lr_pu if lr_pu is not None else lr_all
 *         self.lr_qi = lr_qi if lr_qi is not None else lr_all             # <<<<<<<<<<<<<<
 *         self.reg_bu = reg_bu if reg_bu is not None else reg_all
 *         self.reg_bi = reg_bi if reg_bi is not None else reg_all
 */
  __pyx_t_2 = (__pyx_v_lr_qi != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_lr_qi);
    __pyx_t_1 = __pyx_v_lr_qi;
  } else {
    __Pyx_INCREF(__pyx_v_lr_all);
    __pyx_t_1 = __pyx_v_lr_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_lr_qi, __pyx_t_1) < 0) __PYX_ERR(0, 124, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":125
 *         self.lr_pu = lr_pu if lr_pu is not None else lr_all
 *         self.lr_qi = lr_qi if lr_qi is not None else lr_all
 *         self.reg_bu = reg_bu if reg_bu is not None else reg_all             # <<<<<<<<<<<<<<
 *         self.reg_bi = reg_bi if reg_bi is not None else reg_all
 *         self.reg_pu = reg_pu if reg_pu is not None else reg_all
 */
  __pyx_t_2 = (__pyx_v_reg_bu != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_reg_bu);
    __pyx_t_1 = __pyx_v_reg_bu;
  } else {
    __Pyx_INCREF(__pyx_v_reg_all);
    __pyx_t_1 = __pyx_v_reg_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_reg_bu, __pyx_t_1) < 0) __PYX_ERR(0, 125, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":126
 *         self.lr_qi = lr_qi if lr_qi is not None else lr_all
 *         self.reg_bu = reg_bu if reg_bu is not None else reg_all
 *         self.reg_bi = reg_bi if reg_bi is not None else reg_all             # <<<<<<<<<<<<<<
 *         self.reg_pu = reg_pu if reg_pu is not None else reg_all
 *         self.reg_qi = reg_qi if reg_qi is not None else reg_all
 */
  __pyx_t_2 = (__pyx_v_reg_bi != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_reg_bi);
    __pyx_t_1 = __pyx_v_reg_bi;
  } else {
    __Pyx_INCREF(__pyx_v_reg_all);
    __pyx_t_1 = __pyx_v_reg_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_reg_bi, __pyx_t_1) < 0) __PYX_ERR(0, 126, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":127
 *         self.reg_bu = reg_bu if reg_bu is not None else reg_all
 *         self.reg_bi = reg_bi if reg_bi is not None else reg_all
 *         self.reg_pu = reg_pu if reg_pu is not None else reg_all             # <<<<<<<<<<<<<<
 *         self.reg_qi = reg_qi if reg_qi is not None else reg_all
 *         self.verbose = verbose
 */
  __pyx_t_2 = (__pyx_v_reg_pu != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_reg_pu);
    __pyx_t_1 = __pyx_v_reg_pu;
  } else {
    __Pyx_INCREF(__pyx_v_reg_all);
    __pyx_t_1 = __pyx_v_reg_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_reg_pu, __pyx_t_1) < 0) __PYX_ERR(0, 127, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":128
 *         self.reg_bi = reg_bi if reg_bi is not None else reg_all
 *         self.reg_pu = reg_pu if reg_pu is not None else reg_all
 *         self.reg_qi = reg_qi if reg_qi is not None else reg_all             # <<<<<<<<<<<<<<
 *         self.verbose = verbose
 * 
 */
  __pyx_t_2 = (__pyx_v_reg_qi != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_reg_qi);
    __pyx_t_1 = __pyx_v_reg_qi;
  } else {
    __Pyx_INCREF(__pyx_v_reg_all);
    __pyx_t_1 = __pyx_v_reg_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_reg_qi, __pyx_t_1) < 0) __PYX_ERR(0, 128, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":129
 *         self.reg_pu = reg_pu if reg_pu is not None else reg_all
 *         self.reg_qi = reg_qi if reg_qi is not None else reg_all
 *         self.verbose = verbose             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.__init__(self)
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_verbose, __pyx_v_verbose) < 0) __PYX_ERR(0, 129, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":131
 *         self.verbose = verbose
 * 
 *         AlgoBase.__init__(self)             # <<<<<<<<<<<<<<
 * 
 *     def train(self, trainset):
 */
  __pyx_t_3 = __Pyx_GetModuleGlobalName(__pyx_n_s_AlgoBase); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 131, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_3, __pyx_n_s_init); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 131, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __pyx_t_3 = NULL;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_4))) {
    __pyx_t_3 = PyMethod_GET_SELF(__pyx_t_4);
    if (likely(__pyx_t_3)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_4);
      __Pyx_INCREF(__pyx_t_3);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_4, function);
    }
  }
  if (!__pyx_t_3) {
    __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_4, __pyx_v_self); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 131, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_4)) {
      PyObject *__pyx_temp[2] = {__pyx_t_3, __pyx_v_self};
      __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 131, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_4)) {
      PyObject *__pyx_temp[2] = {__pyx_t_3, __pyx_v_self};
      __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 131, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    {
      __pyx_t_5 = PyTuple_New(1+1); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 131, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_5);
      __Pyx_GIVEREF(__pyx_t_3); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_3); __pyx_t_3 = NULL;
      __Pyx_INCREF(__pyx_v_self);
      __Pyx_GIVEREF(__pyx_v_self);
      PyTuple_SET_ITEM(__pyx_t_5, 0+1, __pyx_v_self);
      __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_4, __pyx_t_5, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 131, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":110
 *     """
 * 
 *     def __init__(self, n_factors=100, n_epochs=20, biased=True, init_mean=0,             # <<<<<<<<<<<<<<
 *                  init_std_dev=.1, lr_all=.005,
 *                  reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None, lr_qi=None,
 */

  /* function exit code */
  __pyx_r = Py_None; __Pyx_INCREF(Py_None);
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_3);
  __Pyx_XDECREF(__pyx_t_4);
  __Pyx_XDECREF(__pyx_t_5);
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVD.__init__", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = NULL;
  __pyx_L0:;
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "surprise/prediction_algorithms/matrix_factorization.pyx":133
 *         AlgoBase.__init__(self)
 * 
 *     def train(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.train(self, trainset)
 */

/* Python wrapper */
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_3train(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static PyMethodDef __pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_3train = {"train", (PyCFunction)__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_3train, METH_VARARGS|METH_KEYWORDS, 0};
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_3train(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
  PyObject *__pyx_v_self = 0;
  PyObject *__pyx_v_trainset = 0;
  PyObject *__pyx_r = 0;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("train (wrapper)", 0);
  {
    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_self,&__pyx_n_s_trainset,0};
    PyObject* values[2] = {0,0};
    if (unlikely(__pyx_kwds)) {
      Py_ssize_t kw_args;
      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
      switch (pos_args) {
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        CYTHON_FALLTHROUGH;
        case  0: break;
        default: goto __pyx_L5_argtuple_error;
      }
      kw_args = PyDict_Size(__pyx_kwds);
      switch (pos_args) {
        case  0:
        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_self)) != 0)) kw_args--;
        else goto __pyx_L5_argtuple_error;
        CYTHON_FALLTHROUGH;
        case  1:
        if (likely((values[1] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_trainset)) != 0)) kw_args--;
        else {
          __Pyx_RaiseArgtupleInvalid("train", 1, 2, 2, 1); __PYX_ERR(0, 133, __pyx_L3_error)
        }
      }
      if (unlikely(kw_args > 0)) {
        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "train") < 0)) __PYX_ERR(0, 133, __pyx_L3_error)
      }
    } else if (PyTuple_GET_SIZE(__pyx_args) != 2) {
      goto __pyx_L5_argtuple_error;
    } else {
      values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
      values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
    }
    __pyx_v_self = values[0];
    __pyx_v_trainset = values[1];
  }
  goto __pyx_L4_argument_unpacking_done;
  __pyx_L5_argtuple_error:;
  __Pyx_RaiseArgtupleInvalid("train", 1, 2, 2, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 133, __pyx_L3_error)
  __pyx_L3_error:;
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVD.train", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __Pyx_RefNannyFinishContext();
  return NULL;
  __pyx_L4_argument_unpacking_done:;
  __pyx_r = __pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_2train(__pyx_self, __pyx_v_self, __pyx_v_trainset);

  /* function exit code */
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_2train(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_trainset) {
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  PyObject *__pyx_t_2 = NULL;
  PyObject *__pyx_t_3 = NULL;
  int __pyx_t_4;
  PyObject *__pyx_t_5 = NULL;
  __Pyx_RefNannySetupContext("train", 0);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":135
 *     def train(self, trainset):
 * 
 *         AlgoBase.train(self, trainset)             # <<<<<<<<<<<<<<
 *         self.sgd(trainset)
 * 
 */
  __pyx_t_2 = __Pyx_GetModuleGlobalName(__pyx_n_s_AlgoBase); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 135, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_t_2, __pyx_n_s_train); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 135, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_t_2 = NULL;
  __pyx_t_4 = 0;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_3))) {
    __pyx_t_2 = PyMethod_GET_SELF(__pyx_t_3);
    if (likely(__pyx_t_2)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
      __Pyx_INCREF(__pyx_t_2);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_3, function);
      __pyx_t_4 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_3)) {
    PyObject *__pyx_temp[3] = {__pyx_t_2, __pyx_v_self, __pyx_v_trainset};
    __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-__pyx_t_4, 2+__pyx_t_4); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 135, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_2); __pyx_t_2 = 0;
    __Pyx_GOTREF(__pyx_t_1);
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
    PyObject *__pyx_temp[3] = {__pyx_t_2, __pyx_v_self, __pyx_v_trainset};
    __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-__pyx_t_4, 2+__pyx_t_4); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 135, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_2); __pyx_t_2 = 0;
    __Pyx_GOTREF(__pyx_t_1);
  } else
  #endif
  {
    __pyx_t_5 = PyTuple_New(2+__pyx_t_4); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 135, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_5);
    if (__pyx_t_2) {
      __Pyx_GIVEREF(__pyx_t_2); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_2); __pyx_t_2 = NULL;
    }
    __Pyx_INCREF(__pyx_v_self);
    __Pyx_GIVEREF(__pyx_v_self);
    PyTuple_SET_ITEM(__pyx_t_5, 0+__pyx_t_4, __pyx_v_self);
    __Pyx_INCREF(__pyx_v_trainset);
    __Pyx_GIVEREF(__pyx_v_trainset);
    PyTuple_SET_ITEM(__pyx_t_5, 1+__pyx_t_4, __pyx_v_trainset);
    __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_5, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 135, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  }
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":136
 * 
 *         AlgoBase.train(self, trainset)
 *         self.sgd(trainset)             # <<<<<<<<<<<<<<
 * 
 *     def sgd(self, trainset):
 */
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_sgd); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 136, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __pyx_t_5 = NULL;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_3))) {
    __pyx_t_5 = PyMethod_GET_SELF(__pyx_t_3);
    if (likely(__pyx_t_5)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
      __Pyx_INCREF(__pyx_t_5);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_3, function);
    }
  }
  if (!__pyx_t_5) {
    __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_3, __pyx_v_trainset); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 136, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_3)) {
      PyObject *__pyx_temp[2] = {__pyx_t_5, __pyx_v_trainset};
      __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 136, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
      PyObject *__pyx_temp[2] = {__pyx_t_5, __pyx_v_trainset};
      __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 136, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    {
      __pyx_t_2 = PyTuple_New(1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 136, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_2, 0, __pyx_t_5); __pyx_t_5 = NULL;
      __Pyx_INCREF(__pyx_v_trainset);
      __Pyx_GIVEREF(__pyx_v_trainset);
      PyTuple_SET_ITEM(__pyx_t_2, 0+1, __pyx_v_trainset);
      __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_2, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 136, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":133
 *         AlgoBase.__init__(self)
 * 
 *     def train(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.train(self, trainset)
 */

  /* function exit code */
  __pyx_r = Py_None; __Pyx_INCREF(Py_None);
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_2);
  __Pyx_XDECREF(__pyx_t_3);
  __Pyx_XDECREF(__pyx_t_5);
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVD.train", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = NULL;
  __pyx_L0:;
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "surprise/prediction_algorithms/matrix_factorization.pyx":138
 *         self.sgd(trainset)
 * 
 *     def sgd(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         # OK, let's breath. I've seen so many different implementation of this
 */

/* Python wrapper */
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_5sgd(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static PyMethodDef __pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_5sgd = {"sgd", (PyCFunction)__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_5sgd, METH_VARARGS|METH_KEYWORDS, 0};
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_5sgd(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
  PyObject *__pyx_v_self = 0;
  PyObject *__pyx_v_trainset = 0;
  PyObject *__pyx_r = 0;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("sgd (wrapper)", 0);
  {
    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_self,&__pyx_n_s_trainset,0};
    PyObject* values[2] = {0,0};
    if (unlikely(__pyx_kwds)) {
      Py_ssize_t kw_args;
      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
      switch (pos_args) {
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        CYTHON_FALLTHROUGH;
        case  0: break;
        default: goto __pyx_L5_argtuple_error;
      }
      kw_args = PyDict_Size(__pyx_kwds);
      switch (pos_args) {
        case  0:
        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_self)) != 0)) kw_args--;
        else goto __pyx_L5_argtuple_error;
        CYTHON_FALLTHROUGH;
        case  1:
        if (likely((values[1] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_trainset)) != 0)) kw_args--;
        else {
          __Pyx_RaiseArgtupleInvalid("sgd", 1, 2, 2, 1); __PYX_ERR(0, 138, __pyx_L3_error)
        }
      }
      if (unlikely(kw_args > 0)) {
        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "sgd") < 0)) __PYX_ERR(0, 138, __pyx_L3_error)
      }
    } else if (PyTuple_GET_SIZE(__pyx_args) != 2) {
      goto __pyx_L5_argtuple_error;
    } else {
      values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
      values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
    }
    __pyx_v_self = values[0];
    __pyx_v_trainset = values[1];
  }
  goto __pyx_L4_argument_unpacking_done;
  __pyx_L5_argtuple_error:;
  __Pyx_RaiseArgtupleInvalid("sgd", 1, 2, 2, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 138, __pyx_L3_error)
  __pyx_L3_error:;
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVD.sgd", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __Pyx_RefNannyFinishContext();
  return NULL;
  __pyx_L4_argument_unpacking_done:;
  __pyx_r = __pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_4sgd(__pyx_self, __pyx_v_self, __pyx_v_trainset);

  /* function exit code */
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_4sgd(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_trainset) {
  PyArrayObject *__pyx_v_bu = 0;
  PyArrayObject *__pyx_v_bi = 0;
  PyArrayObject *__pyx_v_pu = 0;
  PyArrayObject *__pyx_v_qi = 0;
  int __pyx_v_u;
  int __pyx_v_i;
  int __pyx_v_f;
  double __pyx_v_r;
  double __pyx_v_err;
  double __pyx_v_dot;
  double __pyx_v_puf;
  double __pyx_v_qif;
  double __pyx_v_global_mean;
  double __pyx_v_lr_bu;
  double __pyx_v_lr_bi;
  double __pyx_v_lr_pu;
  double __pyx_v_lr_qi;
  double __pyx_v_reg_bu;
  double __pyx_v_reg_bi;
  double __pyx_v_reg_pu;
  double __pyx_v_reg_qi;
  PyObject *__pyx_v_current_epoch = NULL;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_bi;
  __Pyx_Buffer __pyx_pybuffer_bi;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_bu;
  __Pyx_Buffer __pyx_pybuffer_bu;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_pu;
  __Pyx_Buffer __pyx_pybuffer_pu;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_qi;
  __Pyx_Buffer __pyx_pybuffer_qi;
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  PyObject *__pyx_t_2 = NULL;
  double __pyx_t_3;
  PyObject *__pyx_t_4 = NULL;
  PyObject *__pyx_t_5 = NULL;
  PyObject *__pyx_t_6 = NULL;
  int __pyx_t_7;
  PyObject *__pyx_t_8 = NULL;
  PyArrayObject *__pyx_t_9 = NULL;
  PyObject *__pyx_t_10 = NULL;
  PyObject *__pyx_t_11 = NULL;
  PyObject *__pyx_t_12 = NULL;
  PyArrayObject *__pyx_t_13 = NULL;
  PyObject *__pyx_t_14 = NULL;
  PyArrayObject *__pyx_t_15 = NULL;
  PyArrayObject *__pyx_t_16 = NULL;
  int __pyx_t_17;
  int __pyx_t_18;
  Py_ssize_t __pyx_t_19;
  PyObject *(*__pyx_t_20)(PyObject *);
  Py_ssize_t __pyx_t_21;
  PyObject *(*__pyx_t_22)(PyObject *);
  PyObject *(*__pyx_t_23)(PyObject *);
  int __pyx_t_24;
  Py_ssize_t __pyx_t_25;
  PyObject *(*__pyx_t_26)(PyObject *);
  Py_ssize_t __pyx_t_27;
  Py_ssize_t __pyx_t_28;
  Py_ssize_t __pyx_t_29;
  Py_ssize_t __pyx_t_30;
  Py_ssize_t __pyx_t_31;
  Py_ssize_t __pyx_t_32;
  Py_ssize_t __pyx_t_33;
  Py_ssize_t __pyx_t_34;
  Py_ssize_t __pyx_t_35;
  Py_ssize_t __pyx_t_36;
  Py_ssize_t __pyx_t_37;
  Py_ssize_t __pyx_t_38;
  Py_ssize_t __pyx_t_39;
  Py_ssize_t __pyx_t_40;
  Py_ssize_t __pyx_t_41;
  Py_ssize_t __pyx_t_42;
  Py_ssize_t __pyx_t_43;
  Py_ssize_t __pyx_t_44;
  __Pyx_RefNannySetupContext("sgd", 0);
  __pyx_pybuffer_bu.pybuffer.buf = NULL;
  __pyx_pybuffer_bu.refcount = 0;
  __pyx_pybuffernd_bu.data = NULL;
  __pyx_pybuffernd_bu.rcbuffer = &__pyx_pybuffer_bu;
  __pyx_pybuffer_bi.pybuffer.buf = NULL;
  __pyx_pybuffer_bi.refcount = 0;
  __pyx_pybuffernd_bi.data = NULL;
  __pyx_pybuffernd_bi.rcbuffer = &__pyx_pybuffer_bi;
  __pyx_pybuffer_pu.pybuffer.buf = NULL;
  __pyx_pybuffer_pu.refcount = 0;
  __pyx_pybuffernd_pu.data = NULL;
  __pyx_pybuffernd_pu.rcbuffer = &__pyx_pybuffer_pu;
  __pyx_pybuffer_qi.pybuffer.buf = NULL;
  __pyx_pybuffer_qi.refcount = 0;
  __pyx_pybuffernd_qi.data = NULL;
  __pyx_pybuffernd_qi.rcbuffer = &__pyx_pybuffer_qi;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":183
 *         cdef int u, i, f
 *         cdef double r, err, dot, puf, qif
 *         cdef double global_mean = self.trainset.global_mean             # <<<<<<<<<<<<<<
 * 
 *         cdef double lr_bu = self.lr_bu
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 183, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_global_mean); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 183, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 183, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_global_mean = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":185
 *         cdef double global_mean = self.trainset.global_mean
 * 
 *         cdef double lr_bu = self.lr_bu             # <<<<<<<<<<<<<<
 *         cdef double lr_bi = self.lr_bi
 *         cdef double lr_pu = self.lr_pu
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_lr_bu); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 185, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 185, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_lr_bu = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":186
 * 
 *         cdef double lr_bu = self.lr_bu
 *         cdef double lr_bi = self.lr_bi             # <<<<<<<<<<<<<<
 *         cdef double lr_pu = self.lr_pu
 *         cdef double lr_qi = self.lr_qi
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_lr_bi); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 186, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 186, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_lr_bi = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":187
 *         cdef double lr_bu = self.lr_bu
 *         cdef double lr_bi = self.lr_bi
 *         cdef double lr_pu = self.lr_pu             # <<<<<<<<<<<<<<
 *         cdef double lr_qi = self.lr_qi
 * 
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_lr_pu); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 187, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 187, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_lr_pu = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":188
 *         cdef double lr_bi = self.lr_bi
 *         cdef double lr_pu = self.lr_pu
 *         cdef double lr_qi = self.lr_qi             # <<<<<<<<<<<<<<
 * 
 *         cdef double reg_bu = self.reg_bu
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_lr_qi); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 188, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 188, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_lr_qi = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":190
 *         cdef double lr_qi = self.lr_qi
 * 
 *         cdef double reg_bu = self.reg_bu             # <<<<<<<<<<<<<<
 *         cdef double reg_bi = self.reg_bi
 *         cdef double reg_pu = self.reg_pu
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_reg_bu); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 190, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 190, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_reg_bu = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":191
 * 
 *         cdef double reg_bu = self.reg_bu
 *         cdef double reg_bi = self.reg_bi             # <<<<<<<<<<<<<<
 *         cdef double reg_pu = self.reg_pu
 *         cdef double reg_qi = self.reg_qi
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_reg_bi); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 191, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 191, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_reg_bi = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":192
 *         cdef double reg_bu = self.reg_bu
 *         cdef double reg_bi = self.reg_bi
 *         cdef double reg_pu = self.reg_pu             # <<<<<<<<<<<<<<
 *         cdef double reg_qi = self.reg_qi
 * 
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_reg_pu); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 192, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 192, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_reg_pu = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":193
 *         cdef double reg_bi = self.reg_bi
 *         cdef double reg_pu = self.reg_pu
 *         cdef double reg_qi = self.reg_qi             # <<<<<<<<<<<<<<
 * 
 *         bu = np.zeros(trainset.n_users, np.double)
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_reg_qi); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 193, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 193, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_reg_qi = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":195
 *         cdef double reg_qi = self.reg_qi
 * 
 *         bu = np.zeros(trainset.n_users, np.double)             # <<<<<<<<<<<<<<
 *         bi = np.zeros(trainset.n_items, np.double)
 *         pu = np.random.normal(self.init_mean, self.init_std_dev,
 */
  __pyx_t_1 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 195, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_zeros); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 195, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_users); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 195, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_5 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 195, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_t_5, __pyx_n_s_double); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 195, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_6);
  __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  __pyx_t_5 = NULL;
  __pyx_t_7 = 0;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_4))) {
    __pyx_t_5 = PyMethod_GET_SELF(__pyx_t_4);
    if (likely(__pyx_t_5)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_4);
      __Pyx_INCREF(__pyx_t_5);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_4, function);
      __pyx_t_7 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_4)) {
    PyObject *__pyx_temp[3] = {__pyx_t_5, __pyx_t_1, __pyx_t_6};
    __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_4, __pyx_temp+1-__pyx_t_7, 2+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 195, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_4)) {
    PyObject *__pyx_temp[3] = {__pyx_t_5, __pyx_t_1, __pyx_t_6};
    __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_4, __pyx_temp+1-__pyx_t_7, 2+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 195, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  } else
  #endif
  {
    __pyx_t_8 = PyTuple_New(2+__pyx_t_7); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 195, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_8);
    if (__pyx_t_5) {
      __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_8, 0, __pyx_t_5); __pyx_t_5 = NULL;
    }
    __Pyx_GIVEREF(__pyx_t_1);
    PyTuple_SET_ITEM(__pyx_t_8, 0+__pyx_t_7, __pyx_t_1);
    __Pyx_GIVEREF(__pyx_t_6);
    PyTuple_SET_ITEM(__pyx_t_8, 1+__pyx_t_7, __pyx_t_6);
    __pyx_t_1 = 0;
    __pyx_t_6 = 0;
    __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_4, __pyx_t_8, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 195, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
  }
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  if (!(likely(((__pyx_t_2) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_2, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 195, __pyx_L1_error)
  __pyx_t_9 = ((PyArrayObject *)__pyx_t_2);
  {
    __Pyx_BufFmt_StackElem __pyx_stack[1];
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bu.rcbuffer->pybuffer);
    __pyx_t_7 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_bu.rcbuffer->pybuffer, (PyObject*)__pyx_t_9, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack);
    if (unlikely(__pyx_t_7 < 0)) {
      PyErr_Fetch(&__pyx_t_10, &__pyx_t_11, &__pyx_t_12);
      if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_bu.rcbuffer->pybuffer, (PyObject*)__pyx_v_bu, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack) == -1)) {
        Py_XDECREF(__pyx_t_10); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_12);
        __Pyx_RaiseBufferFallbackError();
      } else {
        PyErr_Restore(__pyx_t_10, __pyx_t_11, __pyx_t_12);
      }
      __pyx_t_10 = __pyx_t_11 = __pyx_t_12 = 0;
    }
    __pyx_pybuffernd_bu.diminfo[0].strides = __pyx_pybuffernd_bu.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_bu.diminfo[0].shape = __pyx_pybuffernd_bu.rcbuffer->pybuffer.shape[0];
    if (unlikely(__pyx_t_7 < 0)) __PYX_ERR(0, 195, __pyx_L1_error)
  }
  __pyx_t_9 = 0;
  __pyx_v_bu = ((PyArrayObject *)__pyx_t_2);
  __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":196
 * 
 *         bu = np.zeros(trainset.n_users, np.double)
 *         bi = np.zeros(trainset.n_items, np.double)             # <<<<<<<<<<<<<<
 *         pu = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_users, self.n_factors))
 */
  __pyx_t_4 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 196, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_8 = __Pyx_PyObject_GetAttrStr(__pyx_t_4, __pyx_n_s_zeros); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 196, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_items); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 196, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_6 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 196, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_6);
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_t_6, __pyx_n_s_double); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 196, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  __pyx_t_6 = NULL;
  __pyx_t_7 = 0;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_8))) {
    __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_8);
    if (likely(__pyx_t_6)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_8);
      __Pyx_INCREF(__pyx_t_6);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_8, function);
      __pyx_t_7 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_8)) {
    PyObject *__pyx_temp[3] = {__pyx_t_6, __pyx_t_4, __pyx_t_1};
    __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_8, __pyx_temp+1-__pyx_t_7, 2+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 196, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_8)) {
    PyObject *__pyx_temp[3] = {__pyx_t_6, __pyx_t_4, __pyx_t_1};
    __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_8, __pyx_temp+1-__pyx_t_7, 2+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 196, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  } else
  #endif
  {
    __pyx_t_5 = PyTuple_New(2+__pyx_t_7); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 196, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_5);
    if (__pyx_t_6) {
      __Pyx_GIVEREF(__pyx_t_6); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_6); __pyx_t_6 = NULL;
    }
    __Pyx_GIVEREF(__pyx_t_4);
    PyTuple_SET_ITEM(__pyx_t_5, 0+__pyx_t_7, __pyx_t_4);
    __Pyx_GIVEREF(__pyx_t_1);
    PyTuple_SET_ITEM(__pyx_t_5, 1+__pyx_t_7, __pyx_t_1);
    __pyx_t_4 = 0;
    __pyx_t_1 = 0;
    __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_8, __pyx_t_5, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 196, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  }
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
  if (!(likely(((__pyx_t_2) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_2, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 196, __pyx_L1_error)
  __pyx_t_13 = ((PyArrayObject *)__pyx_t_2);
  {
    __Pyx_BufFmt_StackElem __pyx_stack[1];
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bi.rcbuffer->pybuffer);
    __pyx_t_7 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_bi.rcbuffer->pybuffer, (PyObject*)__pyx_t_13, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack);
    if (unlikely(__pyx_t_7 < 0)) {
      PyErr_Fetch(&__pyx_t_12, &__pyx_t_11, &__pyx_t_10);
      if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_bi.rcbuffer->pybuffer, (PyObject*)__pyx_v_bi, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack) == -1)) {
        Py_XDECREF(__pyx_t_12); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_10);
        __Pyx_RaiseBufferFallbackError();
      } else {
        PyErr_Restore(__pyx_t_12, __pyx_t_11, __pyx_t_10);
      }
      __pyx_t_12 = __pyx_t_11 = __pyx_t_10 = 0;
    }
    __pyx_pybuffernd_bi.diminfo[0].strides = __pyx_pybuffernd_bi.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_bi.diminfo[0].shape = __pyx_pybuffernd_bi.rcbuffer->pybuffer.shape[0];
    if (unlikely(__pyx_t_7 < 0)) __PYX_ERR(0, 196, __pyx_L1_error)
  }
  __pyx_t_13 = 0;
  __pyx_v_bi = ((PyArrayObject *)__pyx_t_2);
  __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":197
 *         bu = np.zeros(trainset.n_users, np.double)
 *         bi = np.zeros(trainset.n_items, np.double)
 *         pu = np.random.normal(self.init_mean, self.init_std_dev,             # <<<<<<<<<<<<<<
 *                               (trainset.n_users, self.n_factors))
 *         qi = np.random.normal(self.init_mean, self.init_std_dev,
 */
  __pyx_t_8 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 197, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_t_8, __pyx_n_s_random); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 197, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
  __pyx_t_8 = __Pyx_PyObject_GetAttrStr(__pyx_t_5, __pyx_n_s_normal); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 197, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_mean); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 197, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_std_dev); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 197, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":198
 *         bi = np.zeros(trainset.n_items, np.double)
 *         pu = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_users, self.n_factors))             # <<<<<<<<<<<<<<
 *         qi = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_items, self.n_factors))
 */
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_users); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 198, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 198, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_6);
  __pyx_t_14 = PyTuple_New(2); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 198, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_14);
  __Pyx_GIVEREF(__pyx_t_4);
  PyTuple_SET_ITEM(__pyx_t_14, 0, __pyx_t_4);
  __Pyx_GIVEREF(__pyx_t_6);
  PyTuple_SET_ITEM(__pyx_t_14, 1, __pyx_t_6);
  __pyx_t_4 = 0;
  __pyx_t_6 = 0;
  __pyx_t_6 = NULL;
  __pyx_t_7 = 0;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_8))) {
    __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_8);
    if (likely(__pyx_t_6)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_8);
      __Pyx_INCREF(__pyx_t_6);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_8, function);
      __pyx_t_7 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_8)) {
    PyObject *__pyx_temp[4] = {__pyx_t_6, __pyx_t_5, __pyx_t_1, __pyx_t_14};
    __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_8, __pyx_temp+1-__pyx_t_7, 3+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 197, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_8)) {
    PyObject *__pyx_temp[4] = {__pyx_t_6, __pyx_t_5, __pyx_t_1, __pyx_t_14};
    __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_8, __pyx_temp+1-__pyx_t_7, 3+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 197, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
  } else
  #endif
  {
    __pyx_t_4 = PyTuple_New(3+__pyx_t_7); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 197, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_4);
    if (__pyx_t_6) {
      __Pyx_GIVEREF(__pyx_t_6); PyTuple_SET_ITEM(__pyx_t_4, 0, __pyx_t_6); __pyx_t_6 = NULL;
    }
    __Pyx_GIVEREF(__pyx_t_5);
    PyTuple_SET_ITEM(__pyx_t_4, 0+__pyx_t_7, __pyx_t_5);
    __Pyx_GIVEREF(__pyx_t_1);
    PyTuple_SET_ITEM(__pyx_t_4, 1+__pyx_t_7, __pyx_t_1);
    __Pyx_GIVEREF(__pyx_t_14);
    PyTuple_SET_ITEM(__pyx_t_4, 2+__pyx_t_7, __pyx_t_14);
    __pyx_t_5 = 0;
    __pyx_t_1 = 0;
    __pyx_t_14 = 0;
    __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_8, __pyx_t_4, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 197, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  }
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":197
 *         bu = np.zeros(trainset.n_users, np.double)
 *         bi = np.zeros(trainset.n_items, np.double)
 *         pu = np.random.normal(self.init_mean, self.init_std_dev,             # <<<<<<<<<<<<<<
 *                               (trainset.n_users, self.n_factors))
 *         qi = np.random.normal(self.init_mean, self.init_std_dev,
 */
  if (!(likely(((__pyx_t_2) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_2, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 197, __pyx_L1_error)
  __pyx_t_15 = ((PyArrayObject *)__pyx_t_2);
  {
    __Pyx_BufFmt_StackElem __pyx_stack[1];
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_pu.rcbuffer->pybuffer);
    __pyx_t_7 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_pu.rcbuffer->pybuffer, (PyObject*)__pyx_t_15, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack);
    if (unlikely(__pyx_t_7 < 0)) {
      PyErr_Fetch(&__pyx_t_10, &__pyx_t_11, &__pyx_t_12);
      if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_pu.rcbuffer->pybuffer, (PyObject*)__pyx_v_pu, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack) == -1)) {
        Py_XDECREF(__pyx_t_10); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_12);
        __Pyx_RaiseBufferFallbackError();
      } else {
        PyErr_Restore(__pyx_t_10, __pyx_t_11, __pyx_t_12);
      }
      __pyx_t_10 = __pyx_t_11 = __pyx_t_12 = 0;
    }
    __pyx_pybuffernd_pu.diminfo[0].strides = __pyx_pybuffernd_pu.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_pu.diminfo[0].shape = __pyx_pybuffernd_pu.rcbuffer->pybuffer.shape[0]; __pyx_pybuffernd_pu.diminfo[1].strides = __pyx_pybuffernd_pu.rcbuffer->pybuffer.strides[1]; __pyx_pybuffernd_pu.diminfo[1].shape = __pyx_pybuffernd_pu.rcbuffer->pybuffer.shape[1];
    if (unlikely(__pyx_t_7 < 0)) __PYX_ERR(0, 197, __pyx_L1_error)
  }
  __pyx_t_15 = 0;
  __pyx_v_pu = ((PyArrayObject *)__pyx_t_2);
  __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":199
 *         pu = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_users, self.n_factors))
 *         qi = np.random.normal(self.init_mean, self.init_std_dev,             # <<<<<<<<<<<<<<
 *                               (trainset.n_items, self.n_factors))
 * 
 */
  __pyx_t_8 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 199, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_8, __pyx_n_s_random); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 199, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
  __pyx_t_8 = __Pyx_PyObject_GetAttrStr(__pyx_t_4, __pyx_n_s_normal); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 199, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_mean); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 199, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_14 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_std_dev); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 199, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_14);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":200
 *                               (trainset.n_users, self.n_factors))
 *         qi = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_items, self.n_factors))             # <<<<<<<<<<<<<<
 * 
 *         if not self.biased:
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_items); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 200, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 200, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __pyx_t_6 = PyTuple_New(2); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 200, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_6);
  __Pyx_GIVEREF(__pyx_t_1);
  PyTuple_SET_ITEM(__pyx_t_6, 0, __pyx_t_1);
  __Pyx_GIVEREF(__pyx_t_5);
  PyTuple_SET_ITEM(__pyx_t_6, 1, __pyx_t_5);
  __pyx_t_1 = 0;
  __pyx_t_5 = 0;
  __pyx_t_5 = NULL;
  __pyx_t_7 = 0;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_8))) {
    __pyx_t_5 = PyMethod_GET_SELF(__pyx_t_8);
    if (likely(__pyx_t_5)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_8);
      __Pyx_INCREF(__pyx_t_5);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_8, function);
      __pyx_t_7 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_8)) {
    PyObject *__pyx_temp[4] = {__pyx_t_5, __pyx_t_4, __pyx_t_14, __pyx_t_6};
    __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_8, __pyx_temp+1-__pyx_t_7, 3+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 199, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_8)) {
    PyObject *__pyx_temp[4] = {__pyx_t_5, __pyx_t_4, __pyx_t_14, __pyx_t_6};
    __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_8, __pyx_temp+1-__pyx_t_7, 3+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 199, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  } else
  #endif
  {
    __pyx_t_1 = PyTuple_New(3+__pyx_t_7); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 199, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    if (__pyx_t_5) {
      __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_1, 0, __pyx_t_5); __pyx_t_5 = NULL;
    }
    __Pyx_GIVEREF(__pyx_t_4);
    PyTuple_SET_ITEM(__pyx_t_1, 0+__pyx_t_7, __pyx_t_4);
    __Pyx_GIVEREF(__pyx_t_14);
    PyTuple_SET_ITEM(__pyx_t_1, 1+__pyx_t_7, __pyx_t_14);
    __Pyx_GIVEREF(__pyx_t_6);
    PyTuple_SET_ITEM(__pyx_t_1, 2+__pyx_t_7, __pyx_t_6);
    __pyx_t_4 = 0;
    __pyx_t_14 = 0;
    __pyx_t_6 = 0;
    __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_8, __pyx_t_1, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 199, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  }
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":199
 *         pu = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_users, self.n_factors))
 *         qi = np.random.normal(self.init_mean, self.init_std_dev,             # <<<<<<<<<<<<<<
 *                               (trainset.n_items, self.n_factors))
 * 
 */
  if (!(likely(((__pyx_t_2) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_2, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 199, __pyx_L1_error)
  __pyx_t_16 = ((PyArrayObject *)__pyx_t_2);
  {
    __Pyx_BufFmt_StackElem __pyx_stack[1];
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_qi.rcbuffer->pybuffer);
    __pyx_t_7 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_qi.rcbuffer->pybuffer, (PyObject*)__pyx_t_16, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack);
    if (unlikely(__pyx_t_7 < 0)) {
      PyErr_Fetch(&__pyx_t_12, &__pyx_t_11, &__pyx_t_10);
      if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_qi.rcbuffer->pybuffer, (PyObject*)__pyx_v_qi, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack) == -1)) {
        Py_XDECREF(__pyx_t_12); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_10);
        __Pyx_RaiseBufferFallbackError();
      } else {
        PyErr_Restore(__pyx_t_12, __pyx_t_11, __pyx_t_10);
      }
      __pyx_t_12 = __pyx_t_11 = __pyx_t_10 = 0;
    }
    __pyx_pybuffernd_qi.diminfo[0].strides = __pyx_pybuffernd_qi.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_qi.diminfo[0].shape = __pyx_pybuffernd_qi.rcbuffer->pybuffer.shape[0]; __pyx_pybuffernd_qi.diminfo[1].strides = __pyx_pybuffernd_qi.rcbuffer->pybuffer.strides[1]; __pyx_pybuffernd_qi.diminfo[1].shape = __pyx_pybuffernd_qi.rcbuffer->pybuffer.shape[1];
    if (unlikely(__pyx_t_7 < 0)) __PYX_ERR(0, 199, __pyx_L1_error)
  }
  __pyx_t_16 = 0;
  __pyx_v_qi = ((PyArrayObject *)__pyx_t_2);
  __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":202
 *                               (trainset.n_items, self.n_factors))
 * 
 *         if not self.biased:             # <<<<<<<<<<<<<<
 *             global_mean = 0
 * 
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_biased); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 202, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_17 = __Pyx_PyObject_IsTrue(__pyx_t_2); if (unlikely(__pyx_t_17 < 0)) __PYX_ERR(0, 202, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_t_18 = ((!__pyx_t_17) != 0);
  if (__pyx_t_18) {

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":203
 * 
 *         if not self.biased:
 *             global_mean = 0             # <<<<<<<<<<<<<<
 * 
 *         for current_epoch in range(self.n_epochs):
 */
    __pyx_v_global_mean = 0.0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":202
 *                               (trainset.n_items, self.n_factors))
 * 
 *         if not self.biased:             # <<<<<<<<<<<<<<
 *             global_mean = 0
 * 
 */
  }

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":205
 *             global_mean = 0
 * 
 *         for current_epoch in range(self.n_epochs):             # <<<<<<<<<<<<<<
 *             if self.verbose:
 *                 print("Processing epoch {}".format(current_epoch))
 */
  __pyx_t_8 = __Pyx_GetModuleGlobalName(__pyx_n_s_range); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 205, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_epochs); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 205, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_6 = NULL;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_8))) {
    __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_8);
    if (likely(__pyx_t_6)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_8);
      __Pyx_INCREF(__pyx_t_6);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_8, function);
    }
  }
  if (!__pyx_t_6) {
    __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_8, __pyx_t_1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 205, __pyx_L1_error)
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_GOTREF(__pyx_t_2);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_8)) {
      PyObject *__pyx_temp[2] = {__pyx_t_6, __pyx_t_1};
      __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_8, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 205, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_8)) {
      PyObject *__pyx_temp[2] = {__pyx_t_6, __pyx_t_1};
      __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_8, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 205, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    } else
    #endif
    {
      __pyx_t_14 = PyTuple_New(1+1); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 205, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_14);
      __Pyx_GIVEREF(__pyx_t_6); PyTuple_SET_ITEM(__pyx_t_14, 0, __pyx_t_6); __pyx_t_6 = NULL;
      __Pyx_GIVEREF(__pyx_t_1);
      PyTuple_SET_ITEM(__pyx_t_14, 0+1, __pyx_t_1);
      __pyx_t_1 = 0;
      __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_8, __pyx_t_14, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 205, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
  if (likely(PyList_CheckExact(__pyx_t_2)) || PyTuple_CheckExact(__pyx_t_2)) {
    __pyx_t_8 = __pyx_t_2; __Pyx_INCREF(__pyx_t_8); __pyx_t_19 = 0;
    __pyx_t_20 = NULL;
  } else {
    __pyx_t_19 = -1; __pyx_t_8 = PyObject_GetIter(__pyx_t_2); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 205, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_8);
    __pyx_t_20 = Py_TYPE(__pyx_t_8)->tp_iternext; if (unlikely(!__pyx_t_20)) __PYX_ERR(0, 205, __pyx_L1_error)
  }
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  for (;;) {
    if (likely(!__pyx_t_20)) {
      if (likely(PyList_CheckExact(__pyx_t_8))) {
        if (__pyx_t_19 >= PyList_GET_SIZE(__pyx_t_8)) break;
        #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
        __pyx_t_2 = PyList_GET_ITEM(__pyx_t_8, __pyx_t_19); __Pyx_INCREF(__pyx_t_2); __pyx_t_19++; if (unlikely(0 < 0)) __PYX_ERR(0, 205, __pyx_L1_error)
        #else
        __pyx_t_2 = PySequence_ITEM(__pyx_t_8, __pyx_t_19); __pyx_t_19++; if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 205, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_2);
        #endif
      } else {
        if (__pyx_t_19 >= PyTuple_GET_SIZE(__pyx_t_8)) break;
        #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
        __pyx_t_2 = PyTuple_GET_ITEM(__pyx_t_8, __pyx_t_19); __Pyx_INCREF(__pyx_t_2); __pyx_t_19++; if (unlikely(0 < 0)) __PYX_ERR(0, 205, __pyx_L1_error)
        #else
        __pyx_t_2 = PySequence_ITEM(__pyx_t_8, __pyx_t_19); __pyx_t_19++; if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 205, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_2);
        #endif
      }
    } else {
      __pyx_t_2 = __pyx_t_20(__pyx_t_8);
      if (unlikely(!__pyx_t_2)) {
        PyObject* exc_type = PyErr_Occurred();
        if (exc_type) {
          if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
          else __PYX_ERR(0, 205, __pyx_L1_error)
        }
        break;
      }
      __Pyx_GOTREF(__pyx_t_2);
    }
    __Pyx_XDECREF_SET(__pyx_v_current_epoch, __pyx_t_2);
    __pyx_t_2 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":206
 * 
 *         for current_epoch in range(self.n_epochs):
 *             if self.verbose:             # <<<<<<<<<<<<<<
 *                 print("Processing epoch {}".format(current_epoch))
 *             for u, i, r in trainset.all_ratings():
 */
    __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_verbose); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 206, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __pyx_t_18 = __Pyx_PyObject_IsTrue(__pyx_t_2); if (unlikely(__pyx_t_18 < 0)) __PYX_ERR(0, 206, __pyx_L1_error)
    __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    if (__pyx_t_18) {

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":207
 *         for current_epoch in range(self.n_epochs):
 *             if self.verbose:
 *                 print("Processing epoch {}".format(current_epoch))             # <<<<<<<<<<<<<<
 *             for u, i, r in trainset.all_ratings():
 * 
 */
      __pyx_t_14 = __Pyx_PyObject_GetAttrStr(__pyx_kp_u_Processing_epoch, __pyx_n_s_format); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 207, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_14);
      __pyx_t_1 = NULL;
      if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_14))) {
        __pyx_t_1 = PyMethod_GET_SELF(__pyx_t_14);
        if (likely(__pyx_t_1)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_14);
          __Pyx_INCREF(__pyx_t_1);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_14, function);
        }
      }
      if (!__pyx_t_1) {
        __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_14, __pyx_v_current_epoch); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 207, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_2);
      } else {
        #if CYTHON_FAST_PYCALL
        if (PyFunction_Check(__pyx_t_14)) {
          PyObject *__pyx_temp[2] = {__pyx_t_1, __pyx_v_current_epoch};
          __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_14, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 207, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
          __Pyx_GOTREF(__pyx_t_2);
        } else
        #endif
        #if CYTHON_FAST_PYCCALL
        if (__Pyx_PyFastCFunction_Check(__pyx_t_14)) {
          PyObject *__pyx_temp[2] = {__pyx_t_1, __pyx_v_current_epoch};
          __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_14, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 207, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
          __Pyx_GOTREF(__pyx_t_2);
        } else
        #endif
        {
          __pyx_t_6 = PyTuple_New(1+1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 207, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_6);
          __Pyx_GIVEREF(__pyx_t_1); PyTuple_SET_ITEM(__pyx_t_6, 0, __pyx_t_1); __pyx_t_1 = NULL;
          __Pyx_INCREF(__pyx_v_current_epoch);
          __Pyx_GIVEREF(__pyx_v_current_epoch);
          PyTuple_SET_ITEM(__pyx_t_6, 0+1, __pyx_v_current_epoch);
          __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_14, __pyx_t_6, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 207, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_2);
          __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
        }
      }
      __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
      __pyx_t_14 = PyTuple_New(1); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 207, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_14);
      __Pyx_GIVEREF(__pyx_t_2);
      PyTuple_SET_ITEM(__pyx_t_14, 0, __pyx_t_2);
      __pyx_t_2 = 0;
      __pyx_t_2 = __Pyx_PyObject_Call(__pyx_builtin_print, __pyx_t_14, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 207, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":206
 * 
 *         for current_epoch in range(self.n_epochs):
 *             if self.verbose:             # <<<<<<<<<<<<<<
 *                 print("Processing epoch {}".format(current_epoch))
 *             for u, i, r in trainset.all_ratings():
 */
    }

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":208
 *             if self.verbose:
 *                 print("Processing epoch {}".format(current_epoch))
 *             for u, i, r in trainset.all_ratings():             # <<<<<<<<<<<<<<
 * 
 *                 # compute current error
 */
    __pyx_t_14 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_all_ratings); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 208, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_14);
    __pyx_t_6 = NULL;
    if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_14))) {
      __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_14);
      if (likely(__pyx_t_6)) {
        PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_14);
        __Pyx_INCREF(__pyx_t_6);
        __Pyx_INCREF(function);
        __Pyx_DECREF_SET(__pyx_t_14, function);
      }
    }
    if (__pyx_t_6) {
      __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_14, __pyx_t_6); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 208, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
    } else {
      __pyx_t_2 = __Pyx_PyObject_CallNoArg(__pyx_t_14); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 208, __pyx_L1_error)
    }
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
    if (likely(PyList_CheckExact(__pyx_t_2)) || PyTuple_CheckExact(__pyx_t_2)) {
      __pyx_t_14 = __pyx_t_2; __Pyx_INCREF(__pyx_t_14); __pyx_t_21 = 0;
      __pyx_t_22 = NULL;
    } else {
      __pyx_t_21 = -1; __pyx_t_14 = PyObject_GetIter(__pyx_t_2); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 208, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_14);
      __pyx_t_22 = Py_TYPE(__pyx_t_14)->tp_iternext; if (unlikely(!__pyx_t_22)) __PYX_ERR(0, 208, __pyx_L1_error)
    }
    __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    for (;;) {
      if (likely(!__pyx_t_22)) {
        if (likely(PyList_CheckExact(__pyx_t_14))) {
          if (__pyx_t_21 >= PyList_GET_SIZE(__pyx_t_14)) break;
          #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
          __pyx_t_2 = PyList_GET_ITEM(__pyx_t_14, __pyx_t_21); __Pyx_INCREF(__pyx_t_2); __pyx_t_21++; if (unlikely(0 < 0)) __PYX_ERR(0, 208, __pyx_L1_error)
          #else
          __pyx_t_2 = PySequence_ITEM(__pyx_t_14, __pyx_t_21); __pyx_t_21++; if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 208, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_2);
          #endif
        } else {
          if (__pyx_t_21 >= PyTuple_GET_SIZE(__pyx_t_14)) break;
          #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
          __pyx_t_2 = PyTuple_GET_ITEM(__pyx_t_14, __pyx_t_21); __Pyx_INCREF(__pyx_t_2); __pyx_t_21++; if (unlikely(0 < 0)) __PYX_ERR(0, 208, __pyx_L1_error)
          #else
          __pyx_t_2 = PySequence_ITEM(__pyx_t_14, __pyx_t_21); __pyx_t_21++; if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 208, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_2);
          #endif
        }
      } else {
        __pyx_t_2 = __pyx_t_22(__pyx_t_14);
        if (unlikely(!__pyx_t_2)) {
          PyObject* exc_type = PyErr_Occurred();
          if (exc_type) {
            if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
            else __PYX_ERR(0, 208, __pyx_L1_error)
          }
          break;
        }
        __Pyx_GOTREF(__pyx_t_2);
      }
      if ((likely(PyTuple_CheckExact(__pyx_t_2))) || (PyList_CheckExact(__pyx_t_2))) {
        PyObject* sequence = __pyx_t_2;
        #if !CYTHON_COMPILING_IN_PYPY
        Py_ssize_t size = Py_SIZE(sequence);
        #else
        Py_ssize_t size = PySequence_Size(sequence);
        #endif
        if (unlikely(size != 3)) {
          if (size > 3) __Pyx_RaiseTooManyValuesError(3);
          else if (size >= 0) __Pyx_RaiseNeedMoreValuesError(size);
          __PYX_ERR(0, 208, __pyx_L1_error)
        }
        #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
        if (likely(PyTuple_CheckExact(sequence))) {
          __pyx_t_6 = PyTuple_GET_ITEM(sequence, 0); 
          __pyx_t_1 = PyTuple_GET_ITEM(sequence, 1); 
          __pyx_t_4 = PyTuple_GET_ITEM(sequence, 2); 
        } else {
          __pyx_t_6 = PyList_GET_ITEM(sequence, 0); 
          __pyx_t_1 = PyList_GET_ITEM(sequence, 1); 
          __pyx_t_4 = PyList_GET_ITEM(sequence, 2); 
        }
        __Pyx_INCREF(__pyx_t_6);
        __Pyx_INCREF(__pyx_t_1);
        __Pyx_INCREF(__pyx_t_4);
        #else
        __pyx_t_6 = PySequence_ITEM(sequence, 0); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 208, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_6);
        __pyx_t_1 = PySequence_ITEM(sequence, 1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 208, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        __pyx_t_4 = PySequence_ITEM(sequence, 2); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 208, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_4);
        #endif
        __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
      } else {
        Py_ssize_t index = -1;
        __pyx_t_5 = PyObject_GetIter(__pyx_t_2); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 208, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_5);
        __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
        __pyx_t_23 = Py_TYPE(__pyx_t_5)->tp_iternext;
        index = 0; __pyx_t_6 = __pyx_t_23(__pyx_t_5); if (unlikely(!__pyx_t_6)) goto __pyx_L9_unpacking_failed;
        __Pyx_GOTREF(__pyx_t_6);
        index = 1; __pyx_t_1 = __pyx_t_23(__pyx_t_5); if (unlikely(!__pyx_t_1)) goto __pyx_L9_unpacking_failed;
        __Pyx_GOTREF(__pyx_t_1);
        index = 2; __pyx_t_4 = __pyx_t_23(__pyx_t_5); if (unlikely(!__pyx_t_4)) goto __pyx_L9_unpacking_failed;
        __Pyx_GOTREF(__pyx_t_4);
        if (__Pyx_IternextUnpackEndCheck(__pyx_t_23(__pyx_t_5), 3) < 0) __PYX_ERR(0, 208, __pyx_L1_error)
        __pyx_t_23 = NULL;
        __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        goto __pyx_L10_unpacking_done;
        __pyx_L9_unpacking_failed:;
        __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        __pyx_t_23 = NULL;
        if (__Pyx_IterFinish() == 0) __Pyx_RaiseNeedMoreValuesError(index);
        __PYX_ERR(0, 208, __pyx_L1_error)
        __pyx_L10_unpacking_done:;
      }
      __pyx_t_7 = __Pyx_PyInt_As_int(__pyx_t_6); if (unlikely((__pyx_t_7 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 208, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      __pyx_t_24 = __Pyx_PyInt_As_int(__pyx_t_1); if (unlikely((__pyx_t_24 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 208, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_4); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 208, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_v_u = __pyx_t_7;
      __pyx_v_i = __pyx_t_24;
      __pyx_v_r = __pyx_t_3;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":211
 * 
 *                 # compute current error
 *                 dot = 0  # <q_i, p_u>             # <<<<<<<<<<<<<<
 *                 for f in range(self.n_factors):
 *                     dot += qi[i, f] * pu[u, f]
 */
      __pyx_v_dot = 0.0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":212
 *                 # compute current error
 *                 dot = 0  # <q_i, p_u>
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     dot += qi[i, f] * pu[u, f]
 *                 err = r - (global_mean + bu[u] + bi[i] + dot)
 */
      __pyx_t_4 = __Pyx_GetModuleGlobalName(__pyx_n_s_range); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 212, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 212, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __pyx_t_6 = NULL;
      if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_4))) {
        __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_4);
        if (likely(__pyx_t_6)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_4);
          __Pyx_INCREF(__pyx_t_6);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_4, function);
        }
      }
      if (!__pyx_t_6) {
        __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_4, __pyx_t_1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 212, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
        __Pyx_GOTREF(__pyx_t_2);
      } else {
        #if CYTHON_FAST_PYCALL
        if (PyFunction_Check(__pyx_t_4)) {
          PyObject *__pyx_temp[2] = {__pyx_t_6, __pyx_t_1};
          __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 212, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
          __Pyx_GOTREF(__pyx_t_2);
          __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
        } else
        #endif
        #if CYTHON_FAST_PYCCALL
        if (__Pyx_PyFastCFunction_Check(__pyx_t_4)) {
          PyObject *__pyx_temp[2] = {__pyx_t_6, __pyx_t_1};
          __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 212, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
          __Pyx_GOTREF(__pyx_t_2);
          __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
        } else
        #endif
        {
          __pyx_t_5 = PyTuple_New(1+1); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 212, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_5);
          __Pyx_GIVEREF(__pyx_t_6); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_6); __pyx_t_6 = NULL;
          __Pyx_GIVEREF(__pyx_t_1);
          PyTuple_SET_ITEM(__pyx_t_5, 0+1, __pyx_t_1);
          __pyx_t_1 = 0;
          __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_4, __pyx_t_5, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 212, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_2);
          __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        }
      }
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      if (likely(PyList_CheckExact(__pyx_t_2)) || PyTuple_CheckExact(__pyx_t_2)) {
        __pyx_t_4 = __pyx_t_2; __Pyx_INCREF(__pyx_t_4); __pyx_t_25 = 0;
        __pyx_t_26 = NULL;
      } else {
        __pyx_t_25 = -1; __pyx_t_4 = PyObject_GetIter(__pyx_t_2); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 212, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_4);
        __pyx_t_26 = Py_TYPE(__pyx_t_4)->tp_iternext; if (unlikely(!__pyx_t_26)) __PYX_ERR(0, 212, __pyx_L1_error)
      }
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
      for (;;) {
        if (likely(!__pyx_t_26)) {
          if (likely(PyList_CheckExact(__pyx_t_4))) {
            if (__pyx_t_25 >= PyList_GET_SIZE(__pyx_t_4)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_2 = PyList_GET_ITEM(__pyx_t_4, __pyx_t_25); __Pyx_INCREF(__pyx_t_2); __pyx_t_25++; if (unlikely(0 < 0)) __PYX_ERR(0, 212, __pyx_L1_error)
            #else
            __pyx_t_2 = PySequence_ITEM(__pyx_t_4, __pyx_t_25); __pyx_t_25++; if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 212, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_2);
            #endif
          } else {
            if (__pyx_t_25 >= PyTuple_GET_SIZE(__pyx_t_4)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_2 = PyTuple_GET_ITEM(__pyx_t_4, __pyx_t_25); __Pyx_INCREF(__pyx_t_2); __pyx_t_25++; if (unlikely(0 < 0)) __PYX_ERR(0, 212, __pyx_L1_error)
            #else
            __pyx_t_2 = PySequence_ITEM(__pyx_t_4, __pyx_t_25); __pyx_t_25++; if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 212, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_2);
            #endif
          }
        } else {
          __pyx_t_2 = __pyx_t_26(__pyx_t_4);
          if (unlikely(!__pyx_t_2)) {
            PyObject* exc_type = PyErr_Occurred();
            if (exc_type) {
              if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
              else __PYX_ERR(0, 212, __pyx_L1_error)
            }
            break;
          }
          __Pyx_GOTREF(__pyx_t_2);
        }
        __pyx_t_24 = __Pyx_PyInt_As_int(__pyx_t_2); if (unlikely((__pyx_t_24 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 212, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
        __pyx_v_f = __pyx_t_24;

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":213
 *                 dot = 0  # <q_i, p_u>
 *                 for f in range(self.n_factors):
 *                     dot += qi[i, f] * pu[u, f]             # <<<<<<<<<<<<<<
 *                 err = r - (global_mean + bu[u] + bi[i] + dot)
 * 
 */
        __pyx_t_27 = __pyx_v_i;
        __pyx_t_28 = __pyx_v_f;
        __pyx_t_24 = -1;
        if (__pyx_t_27 < 0) {
          __pyx_t_27 += __pyx_pybuffernd_qi.diminfo[0].shape;
          if (unlikely(__pyx_t_27 < 0)) __pyx_t_24 = 0;
        } else if (unlikely(__pyx_t_27 >= __pyx_pybuffernd_qi.diminfo[0].shape)) __pyx_t_24 = 0;
        if (__pyx_t_28 < 0) {
          __pyx_t_28 += __pyx_pybuffernd_qi.diminfo[1].shape;
          if (unlikely(__pyx_t_28 < 0)) __pyx_t_24 = 1;
        } else if (unlikely(__pyx_t_28 >= __pyx_pybuffernd_qi.diminfo[1].shape)) __pyx_t_24 = 1;
        if (unlikely(__pyx_t_24 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_24);
          __PYX_ERR(0, 213, __pyx_L1_error)
        }
        __pyx_t_29 = __pyx_v_u;
        __pyx_t_30 = __pyx_v_f;
        __pyx_t_24 = -1;
        if (__pyx_t_29 < 0) {
          __pyx_t_29 += __pyx_pybuffernd_pu.diminfo[0].shape;
          if (unlikely(__pyx_t_29 < 0)) __pyx_t_24 = 0;
        } else if (unlikely(__pyx_t_29 >= __pyx_pybuffernd_pu.diminfo[0].shape)) __pyx_t_24 = 0;
        if (__pyx_t_30 < 0) {
          __pyx_t_30 += __pyx_pybuffernd_pu.diminfo[1].shape;
          if (unlikely(__pyx_t_30 < 0)) __pyx_t_24 = 1;
        } else if (unlikely(__pyx_t_30 >= __pyx_pybuffernd_pu.diminfo[1].shape)) __pyx_t_24 = 1;
        if (unlikely(__pyx_t_24 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_24);
          __PYX_ERR(0, 213, __pyx_L1_error)
        }
        __pyx_v_dot = (__pyx_v_dot + ((*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_qi.rcbuffer->pybuffer.buf, __pyx_t_27, __pyx_pybuffernd_qi.diminfo[0].strides, __pyx_t_28, __pyx_pybuffernd_qi.diminfo[1].strides)) * (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_pu.rcbuffer->pybuffer.buf, __pyx_t_29, __pyx_pybuffernd_pu.diminfo[0].strides, __pyx_t_30, __pyx_pybuffernd_pu.diminfo[1].strides))));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":212
 *                 # compute current error
 *                 dot = 0  # <q_i, p_u>
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     dot += qi[i, f] * pu[u, f]
 *                 err = r - (global_mean + bu[u] + bi[i] + dot)
 */
      }
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":214
 *                 for f in range(self.n_factors):
 *                     dot += qi[i, f] * pu[u, f]
 *                 err = r - (global_mean + bu[u] + bi[i] + dot)             # <<<<<<<<<<<<<<
 * 
 *                 # update biases
 */
      __pyx_t_31 = __pyx_v_u;
      __pyx_t_24 = -1;
      if (__pyx_t_31 < 0) {
        __pyx_t_31 += __pyx_pybuffernd_bu.diminfo[0].shape;
        if (unlikely(__pyx_t_31 < 0)) __pyx_t_24 = 0;
      } else if (unlikely(__pyx_t_31 >= __pyx_pybuffernd_bu.diminfo[0].shape)) __pyx_t_24 = 0;
      if (unlikely(__pyx_t_24 != -1)) {
        __Pyx_RaiseBufferIndexError(__pyx_t_24);
        __PYX_ERR(0, 214, __pyx_L1_error)
      }
      __pyx_t_32 = __pyx_v_i;
      __pyx_t_24 = -1;
      if (__pyx_t_32 < 0) {
        __pyx_t_32 += __pyx_pybuffernd_bi.diminfo[0].shape;
        if (unlikely(__pyx_t_32 < 0)) __pyx_t_24 = 0;
      } else if (unlikely(__pyx_t_32 >= __pyx_pybuffernd_bi.diminfo[0].shape)) __pyx_t_24 = 0;
      if (unlikely(__pyx_t_24 != -1)) {
        __Pyx_RaiseBufferIndexError(__pyx_t_24);
        __PYX_ERR(0, 214, __pyx_L1_error)
      }
      __pyx_v_err = (__pyx_v_r - (((__pyx_v_global_mean + (*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bu.rcbuffer->pybuffer.buf, __pyx_t_31, __pyx_pybuffernd_bu.diminfo[0].strides))) + (*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bi.rcbuffer->pybuffer.buf, __pyx_t_32, __pyx_pybuffernd_bi.diminfo[0].strides))) + __pyx_v_dot));

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":217
 * 
 *                 # update biases
 *                 if self.biased:             # <<<<<<<<<<<<<<
 *                     bu[u] += lr_bu * (err - reg_bu * bu[u])
 *                     bi[i] += lr_bi * (err - reg_bi * bi[i])
 */
      __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_biased); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 217, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_18 = __Pyx_PyObject_IsTrue(__pyx_t_4); if (unlikely(__pyx_t_18 < 0)) __PYX_ERR(0, 217, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      if (__pyx_t_18) {

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":218
 *                 # update biases
 *                 if self.biased:
 *                     bu[u] += lr_bu * (err - reg_bu * bu[u])             # <<<<<<<<<<<<<<
 *                     bi[i] += lr_bi * (err - reg_bi * bi[i])
 * 
 */
        __pyx_t_33 = __pyx_v_u;
        __pyx_t_24 = -1;
        if (__pyx_t_33 < 0) {
          __pyx_t_33 += __pyx_pybuffernd_bu.diminfo[0].shape;
          if (unlikely(__pyx_t_33 < 0)) __pyx_t_24 = 0;
        } else if (unlikely(__pyx_t_33 >= __pyx_pybuffernd_bu.diminfo[0].shape)) __pyx_t_24 = 0;
        if (unlikely(__pyx_t_24 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_24);
          __PYX_ERR(0, 218, __pyx_L1_error)
        }
        __pyx_t_34 = __pyx_v_u;
        __pyx_t_24 = -1;
        if (__pyx_t_34 < 0) {
          __pyx_t_34 += __pyx_pybuffernd_bu.diminfo[0].shape;
          if (unlikely(__pyx_t_34 < 0)) __pyx_t_24 = 0;
        } else if (unlikely(__pyx_t_34 >= __pyx_pybuffernd_bu.diminfo[0].shape)) __pyx_t_24 = 0;
        if (unlikely(__pyx_t_24 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_24);
          __PYX_ERR(0, 218, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bu.rcbuffer->pybuffer.buf, __pyx_t_34, __pyx_pybuffernd_bu.diminfo[0].strides) += (__pyx_v_lr_bu * (__pyx_v_err - (__pyx_v_reg_bu * (*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bu.rcbuffer->pybuffer.buf, __pyx_t_33, __pyx_pybuffernd_bu.diminfo[0].strides)))));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":219
 *                 if self.biased:
 *                     bu[u] += lr_bu * (err - reg_bu * bu[u])
 *                     bi[i] += lr_bi * (err - reg_bi * bi[i])             # <<<<<<<<<<<<<<
 * 
 *                 # update factors
 */
        __pyx_t_35 = __pyx_v_i;
        __pyx_t_24 = -1;
        if (__pyx_t_35 < 0) {
          __pyx_t_35 += __pyx_pybuffernd_bi.diminfo[0].shape;
          if (unlikely(__pyx_t_35 < 0)) __pyx_t_24 = 0;
        } else if (unlikely(__pyx_t_35 >= __pyx_pybuffernd_bi.diminfo[0].shape)) __pyx_t_24 = 0;
        if (unlikely(__pyx_t_24 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_24);
          __PYX_ERR(0, 219, __pyx_L1_error)
        }
        __pyx_t_36 = __pyx_v_i;
        __pyx_t_24 = -1;
        if (__pyx_t_36 < 0) {
          __pyx_t_36 += __pyx_pybuffernd_bi.diminfo[0].shape;
          if (unlikely(__pyx_t_36 < 0)) __pyx_t_24 = 0;
        } else if (unlikely(__pyx_t_36 >= __pyx_pybuffernd_bi.diminfo[0].shape)) __pyx_t_24 = 0;
        if (unlikely(__pyx_t_24 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_24);
          __PYX_ERR(0, 219, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bi.rcbuffer->pybuffer.buf, __pyx_t_36, __pyx_pybuffernd_bi.diminfo[0].strides) += (__pyx_v_lr_bi * (__pyx_v_err - (__pyx_v_reg_bi * (*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bi.rcbuffer->pybuffer.buf, __pyx_t_35, __pyx_pybuffernd_bi.diminfo[0].strides)))));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":217
 * 
 *                 # update biases
 *                 if self.biased:             # <<<<<<<<<<<<<<
 *                     bu[u] += lr_bu * (err - reg_bu * bu[u])
 *                     bi[i] += lr_bi * (err - reg_bi * bi[i])
 */
      }

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":222
 * 
 *                 # update factors
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     puf = pu[u, f]
 *                     qif = qi[i, f]
 */
      __pyx_t_2 = __Pyx_GetModuleGlobalName(__pyx_n_s_range); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 222, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 222, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_5);
      __pyx_t_1 = NULL;
      if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_2))) {
        __pyx_t_1 = PyMethod_GET_SELF(__pyx_t_2);
        if (likely(__pyx_t_1)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_2);
          __Pyx_INCREF(__pyx_t_1);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_2, function);
        }
      }
      if (!__pyx_t_1) {
        __pyx_t_4 = __Pyx_PyObject_CallOneArg(__pyx_t_2, __pyx_t_5); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 222, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        __Pyx_GOTREF(__pyx_t_4);
      } else {
        #if CYTHON_FAST_PYCALL
        if (PyFunction_Check(__pyx_t_2)) {
          PyObject *__pyx_temp[2] = {__pyx_t_1, __pyx_t_5};
          __pyx_t_4 = __Pyx_PyFunction_FastCall(__pyx_t_2, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 222, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
          __Pyx_GOTREF(__pyx_t_4);
          __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        } else
        #endif
        #if CYTHON_FAST_PYCCALL
        if (__Pyx_PyFastCFunction_Check(__pyx_t_2)) {
          PyObject *__pyx_temp[2] = {__pyx_t_1, __pyx_t_5};
          __pyx_t_4 = __Pyx_PyCFunction_FastCall(__pyx_t_2, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 222, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
          __Pyx_GOTREF(__pyx_t_4);
          __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        } else
        #endif
        {
          __pyx_t_6 = PyTuple_New(1+1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 222, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_6);
          __Pyx_GIVEREF(__pyx_t_1); PyTuple_SET_ITEM(__pyx_t_6, 0, __pyx_t_1); __pyx_t_1 = NULL;
          __Pyx_GIVEREF(__pyx_t_5);
          PyTuple_SET_ITEM(__pyx_t_6, 0+1, __pyx_t_5);
          __pyx_t_5 = 0;
          __pyx_t_4 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_t_6, NULL); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 222, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_4);
          __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
        }
      }
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
      if (likely(PyList_CheckExact(__pyx_t_4)) || PyTuple_CheckExact(__pyx_t_4)) {
        __pyx_t_2 = __pyx_t_4; __Pyx_INCREF(__pyx_t_2); __pyx_t_25 = 0;
        __pyx_t_26 = NULL;
      } else {
        __pyx_t_25 = -1; __pyx_t_2 = PyObject_GetIter(__pyx_t_4); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 222, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_2);
        __pyx_t_26 = Py_TYPE(__pyx_t_2)->tp_iternext; if (unlikely(!__pyx_t_26)) __PYX_ERR(0, 222, __pyx_L1_error)
      }
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      for (;;) {
        if (likely(!__pyx_t_26)) {
          if (likely(PyList_CheckExact(__pyx_t_2))) {
            if (__pyx_t_25 >= PyList_GET_SIZE(__pyx_t_2)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_4 = PyList_GET_ITEM(__pyx_t_2, __pyx_t_25); __Pyx_INCREF(__pyx_t_4); __pyx_t_25++; if (unlikely(0 < 0)) __PYX_ERR(0, 222, __pyx_L1_error)
            #else
            __pyx_t_4 = PySequence_ITEM(__pyx_t_2, __pyx_t_25); __pyx_t_25++; if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 222, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_4);
            #endif
          } else {
            if (__pyx_t_25 >= PyTuple_GET_SIZE(__pyx_t_2)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_4 = PyTuple_GET_ITEM(__pyx_t_2, __pyx_t_25); __Pyx_INCREF(__pyx_t_4); __pyx_t_25++; if (unlikely(0 < 0)) __PYX_ERR(0, 222, __pyx_L1_error)
            #else
            __pyx_t_4 = PySequence_ITEM(__pyx_t_2, __pyx_t_25); __pyx_t_25++; if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 222, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_4);
            #endif
          }
        } else {
          __pyx_t_4 = __pyx_t_26(__pyx_t_2);
          if (unlikely(!__pyx_t_4)) {
            PyObject* exc_type = PyErr_Occurred();
            if (exc_type) {
              if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
              else __PYX_ERR(0, 222, __pyx_L1_error)
            }
            break;
          }
          __Pyx_GOTREF(__pyx_t_4);
        }
        __pyx_t_24 = __Pyx_PyInt_As_int(__pyx_t_4); if (unlikely((__pyx_t_24 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 222, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
        __pyx_v_f = __pyx_t_24;

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":223
 *                 # update factors
 *                 for f in range(self.n_factors):
 *                     puf = pu[u, f]             # <<<<<<<<<<<<<<
 *                     qif = qi[i, f]
 *                     pu[u, f] += lr_pu * (err * qif - reg_pu * puf)
 */
        __pyx_t_37 = __pyx_v_u;
        __pyx_t_38 = __pyx_v_f;
        __pyx_t_24 = -1;
        if (__pyx_t_37 < 0) {
          __pyx_t_37 += __pyx_pybuffernd_pu.diminfo[0].shape;
          if (unlikely(__pyx_t_37 < 0)) __pyx_t_24 = 0;
        } else if (unlikely(__pyx_t_37 >= __pyx_pybuffernd_pu.diminfo[0].shape)) __pyx_t_24 = 0;
        if (__pyx_t_38 < 0) {
          __pyx_t_38 += __pyx_pybuffernd_pu.diminfo[1].shape;
          if (unlikely(__pyx_t_38 < 0)) __pyx_t_24 = 1;
        } else if (unlikely(__pyx_t_38 >= __pyx_pybuffernd_pu.diminfo[1].shape)) __pyx_t_24 = 1;
        if (unlikely(__pyx_t_24 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_24);
          __PYX_ERR(0, 223, __pyx_L1_error)
        }
        __pyx_v_puf = (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_pu.rcbuffer->pybuffer.buf, __pyx_t_37, __pyx_pybuffernd_pu.diminfo[0].strides, __pyx_t_38, __pyx_pybuffernd_pu.diminfo[1].strides));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":224
 *                 for f in range(self.n_factors):
 *                     puf = pu[u, f]
 *                     qif = qi[i, f]             # <<<<<<<<<<<<<<
 *                     pu[u, f] += lr_pu * (err * qif - reg_pu * puf)
 *                     qi[i, f] += lr_qi * (err * puf - reg_qi * qif)
 */
        __pyx_t_39 = __pyx_v_i;
        __pyx_t_40 = __pyx_v_f;
        __pyx_t_24 = -1;
        if (__pyx_t_39 < 0) {
          __pyx_t_39 += __pyx_pybuffernd_qi.diminfo[0].shape;
          if (unlikely(__pyx_t_39 < 0)) __pyx_t_24 = 0;
        } else if (unlikely(__pyx_t_39 >= __pyx_pybuffernd_qi.diminfo[0].shape)) __pyx_t_24 = 0;
        if (__pyx_t_40 < 0) {
          __pyx_t_40 += __pyx_pybuffernd_qi.diminfo[1].shape;
          if (unlikely(__pyx_t_40 < 0)) __pyx_t_24 = 1;
        } else if (unlikely(__pyx_t_40 >= __pyx_pybuffernd_qi.diminfo[1].shape)) __pyx_t_24 = 1;
        if (unlikely(__pyx_t_24 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_24);
          __PYX_ERR(0, 224, __pyx_L1_error)
        }
        __pyx_v_qif = (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_qi.rcbuffer->pybuffer.buf, __pyx_t_39, __pyx_pybuffernd_qi.diminfo[0].strides, __pyx_t_40, __pyx_pybuffernd_qi.diminfo[1].strides));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":225
 *                     puf = pu[u, f]
 *                     qif = qi[i, f]
 *                     pu[u, f] += lr_pu * (err * qif - reg_pu * puf)             # <<<<<<<<<<<<<<
 *                     qi[i, f] += lr_qi * (err * puf - reg_qi * qif)
 * 
 */
        __pyx_t_41 = __pyx_v_u;
        __pyx_t_42 = __pyx_v_f;
        __pyx_t_24 = -1;
        if (__pyx_t_41 < 0) {
          __pyx_t_41 += __pyx_pybuffernd_pu.diminfo[0].shape;
          if (unlikely(__pyx_t_41 < 0)) __pyx_t_24 = 0;
        } else if (unlikely(__pyx_t_41 >= __pyx_pybuffernd_pu.diminfo[0].shape)) __pyx_t_24 = 0;
        if (__pyx_t_42 < 0) {
          __pyx_t_42 += __pyx_pybuffernd_pu.diminfo[1].shape;
          if (unlikely(__pyx_t_42 < 0)) __pyx_t_24 = 1;
        } else if (unlikely(__pyx_t_42 >= __pyx_pybuffernd_pu.diminfo[1].shape)) __pyx_t_24 = 1;
        if (unlikely(__pyx_t_24 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_24);
          __PYX_ERR(0, 225, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_pu.rcbuffer->pybuffer.buf, __pyx_t_41, __pyx_pybuffernd_pu.diminfo[0].strides, __pyx_t_42, __pyx_pybuffernd_pu.diminfo[1].strides) += (__pyx_v_lr_pu * ((__pyx_v_err * __pyx_v_qif) - (__pyx_v_reg_pu * __pyx_v_puf)));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":226
 *                     qif = qi[i, f]
 *                     pu[u, f] += lr_pu * (err * qif - reg_pu * puf)
 *                     qi[i, f] += lr_qi * (err * puf - reg_qi * qif)             # <<<<<<<<<<<<<<
 * 
 *         self.bu = bu
 */
        __pyx_t_43 = __pyx_v_i;
        __pyx_t_44 = __pyx_v_f;
        __pyx_t_24 = -1;
        if (__pyx_t_43 < 0) {
          __pyx_t_43 += __pyx_pybuffernd_qi.diminfo[0].shape;
          if (unlikely(__pyx_t_43 < 0)) __pyx_t_24 = 0;
        } else if (unlikely(__pyx_t_43 >= __pyx_pybuffernd_qi.diminfo[0].shape)) __pyx_t_24 = 0;
        if (__pyx_t_44 < 0) {
          __pyx_t_44 += __pyx_pybuffernd_qi.diminfo[1].shape;
          if (unlikely(__pyx_t_44 < 0)) __pyx_t_24 = 1;
        } else if (unlikely(__pyx_t_44 >= __pyx_pybuffernd_qi.diminfo[1].shape)) __pyx_t_24 = 1;
        if (unlikely(__pyx_t_24 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_24);
          __PYX_ERR(0, 226, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_qi.rcbuffer->pybuffer.buf, __pyx_t_43, __pyx_pybuffernd_qi.diminfo[0].strides, __pyx_t_44, __pyx_pybuffernd_qi.diminfo[1].strides) += (__pyx_v_lr_qi * ((__pyx_v_err * __pyx_v_puf) - (__pyx_v_reg_qi * __pyx_v_qif)));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":222
 * 
 *                 # update factors
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     puf = pu[u, f]
 *                     qif = qi[i, f]
 */
      }
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":208
 *             if self.verbose:
 *                 print("Processing epoch {}".format(current_epoch))
 *             for u, i, r in trainset.all_ratings():             # <<<<<<<<<<<<<<
 * 
 *                 # compute current error
 */
    }
    __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":205
 *             global_mean = 0
 * 
 *         for current_epoch in range(self.n_epochs):             # <<<<<<<<<<<<<<
 *             if self.verbose:
 *                 print("Processing epoch {}".format(current_epoch))
 */
  }
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":228
 *                     qi[i, f] += lr_qi * (err * puf - reg_qi * qif)
 * 
 *         self.bu = bu             # <<<<<<<<<<<<<<
 *         self.bi = bi
 *         self.pu = pu
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_bu, ((PyObject *)__pyx_v_bu)) < 0) __PYX_ERR(0, 228, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":229
 * 
 *         self.bu = bu
 *         self.bi = bi             # <<<<<<<<<<<<<<
 *         self.pu = pu
 *         self.qi = qi
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_bi, ((PyObject *)__pyx_v_bi)) < 0) __PYX_ERR(0, 229, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":230
 *         self.bu = bu
 *         self.bi = bi
 *         self.pu = pu             # <<<<<<<<<<<<<<
 *         self.qi = qi
 * 
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_pu, ((PyObject *)__pyx_v_pu)) < 0) __PYX_ERR(0, 230, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":231
 *         self.bi = bi
 *         self.pu = pu
 *         self.qi = qi             # <<<<<<<<<<<<<<
 * 
 *     def estimate(self, u, i):
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_qi, ((PyObject *)__pyx_v_qi)) < 0) __PYX_ERR(0, 231, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":138
 *         self.sgd(trainset)
 * 
 *     def sgd(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         # OK, let's breath. I've seen so many different implementation of this
 */

  /* function exit code */
  __pyx_r = Py_None; __Pyx_INCREF(Py_None);
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_2);
  __Pyx_XDECREF(__pyx_t_4);
  __Pyx_XDECREF(__pyx_t_5);
  __Pyx_XDECREF(__pyx_t_6);
  __Pyx_XDECREF(__pyx_t_8);
  __Pyx_XDECREF(__pyx_t_14);
  { PyObject *__pyx_type, *__pyx_value, *__pyx_tb;
    __Pyx_PyThreadState_declare
    __Pyx_PyThreadState_assign
    __Pyx_ErrFetch(&__pyx_type, &__pyx_value, &__pyx_tb);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bi.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bu.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_pu.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_qi.rcbuffer->pybuffer);
  __Pyx_ErrRestore(__pyx_type, __pyx_value, __pyx_tb);}
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVD.sgd", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = NULL;
  goto __pyx_L2;
  __pyx_L0:;
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bi.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bu.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_pu.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_qi.rcbuffer->pybuffer);
  __pyx_L2:;
  __Pyx_XDECREF((PyObject *)__pyx_v_bu);
  __Pyx_XDECREF((PyObject *)__pyx_v_bi);
  __Pyx_XDECREF((PyObject *)__pyx_v_pu);
  __Pyx_XDECREF((PyObject *)__pyx_v_qi);
  __Pyx_XDECREF(__pyx_v_current_epoch);
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "surprise/prediction_algorithms/matrix_factorization.pyx":233
 *         self.qi = qi
 * 
 *     def estimate(self, u, i):             # <<<<<<<<<<<<<<
 *         # Should we cythonize this as well?
 * 
 */

/* Python wrapper */
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_7estimate(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static PyMethodDef __pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_7estimate = {"estimate", (PyCFunction)__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_7estimate, METH_VARARGS|METH_KEYWORDS, 0};
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_7estimate(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
  PyObject *__pyx_v_self = 0;
  PyObject *__pyx_v_u = 0;
  PyObject *__pyx_v_i = 0;
  PyObject *__pyx_r = 0;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("estimate (wrapper)", 0);
  {
    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_self,&__pyx_n_s_u,&__pyx_n_s_i,0};
    PyObject* values[3] = {0,0,0};
    if (unlikely(__pyx_kwds)) {
      Py_ssize_t kw_args;
      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
      switch (pos_args) {
        case  3: values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
        CYTHON_FALLTHROUGH;
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        CYTHON_FALLTHROUGH;
        case  0: break;
        default: goto __pyx_L5_argtuple_error;
      }
      kw_args = PyDict_Size(__pyx_kwds);
      switch (pos_args) {
        case  0:
        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_self)) != 0)) kw_args--;
        else goto __pyx_L5_argtuple_error;
        CYTHON_FALLTHROUGH;
        case  1:
        if (likely((values[1] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_u)) != 0)) kw_args--;
        else {
          __Pyx_RaiseArgtupleInvalid("estimate", 1, 3, 3, 1); __PYX_ERR(0, 233, __pyx_L3_error)
        }
        CYTHON_FALLTHROUGH;
        case  2:
        if (likely((values[2] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_i)) != 0)) kw_args--;
        else {
          __Pyx_RaiseArgtupleInvalid("estimate", 1, 3, 3, 2); __PYX_ERR(0, 233, __pyx_L3_error)
        }
      }
      if (unlikely(kw_args > 0)) {
        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "estimate") < 0)) __PYX_ERR(0, 233, __pyx_L3_error)
      }
    } else if (PyTuple_GET_SIZE(__pyx_args) != 3) {
      goto __pyx_L5_argtuple_error;
    } else {
      values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
      values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
      values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
    }
    __pyx_v_self = values[0];
    __pyx_v_u = values[1];
    __pyx_v_i = values[2];
  }
  goto __pyx_L4_argument_unpacking_done;
  __pyx_L5_argtuple_error:;
  __Pyx_RaiseArgtupleInvalid("estimate", 1, 3, 3, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 233, __pyx_L3_error)
  __pyx_L3_error:;
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVD.estimate", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __Pyx_RefNannyFinishContext();
  return NULL;
  __pyx_L4_argument_unpacking_done:;
  __pyx_r = __pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_6estimate(__pyx_self, __pyx_v_self, __pyx_v_u, __pyx_v_i);

  /* function exit code */
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_6estimate(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_u, PyObject *__pyx_v_i) {
  PyObject *__pyx_v_known_user = NULL;
  PyObject *__pyx_v_known_item = NULL;
  PyObject *__pyx_v_est = NULL;
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  PyObject *__pyx_t_2 = NULL;
  PyObject *__pyx_t_3 = NULL;
  PyObject *__pyx_t_4 = NULL;
  int __pyx_t_5;
  int __pyx_t_6;
  PyObject *__pyx_t_7 = NULL;
  int __pyx_t_8;
  PyObject *__pyx_t_9 = NULL;
  __Pyx_RefNannySetupContext("estimate", 0);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":236
 *         # Should we cythonize this as well?
 * 
 *         known_user = self.trainset.knows_user(u)             # <<<<<<<<<<<<<<
 *         known_item = self.trainset.knows_item(i)
 * 
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 236, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_t_2, __pyx_n_s_knows_user); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 236, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_t_2 = NULL;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_3))) {
    __pyx_t_2 = PyMethod_GET_SELF(__pyx_t_3);
    if (likely(__pyx_t_2)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
      __Pyx_INCREF(__pyx_t_2);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_3, function);
    }
  }
  if (!__pyx_t_2) {
    __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_3, __pyx_v_u); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 236, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_3)) {
      PyObject *__pyx_temp[2] = {__pyx_t_2, __pyx_v_u};
      __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 236, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_2); __pyx_t_2 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
      PyObject *__pyx_temp[2] = {__pyx_t_2, __pyx_v_u};
      __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 236, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_2); __pyx_t_2 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    {
      __pyx_t_4 = PyTuple_New(1+1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 236, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __Pyx_GIVEREF(__pyx_t_2); PyTuple_SET_ITEM(__pyx_t_4, 0, __pyx_t_2); __pyx_t_2 = NULL;
      __Pyx_INCREF(__pyx_v_u);
      __Pyx_GIVEREF(__pyx_v_u);
      PyTuple_SET_ITEM(__pyx_t_4, 0+1, __pyx_v_u);
      __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_4, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 236, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __pyx_v_known_user = __pyx_t_1;
  __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":237
 * 
 *         known_user = self.trainset.knows_user(u)
 *         known_item = self.trainset.knows_item(i)             # <<<<<<<<<<<<<<
 * 
 *         if self.biased:
 */
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 237, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_3, __pyx_n_s_knows_item); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 237, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __pyx_t_3 = NULL;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_4))) {
    __pyx_t_3 = PyMethod_GET_SELF(__pyx_t_4);
    if (likely(__pyx_t_3)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_4);
      __Pyx_INCREF(__pyx_t_3);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_4, function);
    }
  }
  if (!__pyx_t_3) {
    __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_4, __pyx_v_i); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 237, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_4)) {
      PyObject *__pyx_temp[2] = {__pyx_t_3, __pyx_v_i};
      __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 237, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_4)) {
      PyObject *__pyx_temp[2] = {__pyx_t_3, __pyx_v_i};
      __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 237, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    {
      __pyx_t_2 = PyTuple_New(1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 237, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_GIVEREF(__pyx_t_3); PyTuple_SET_ITEM(__pyx_t_2, 0, __pyx_t_3); __pyx_t_3 = NULL;
      __Pyx_INCREF(__pyx_v_i);
      __Pyx_GIVEREF(__pyx_v_i);
      PyTuple_SET_ITEM(__pyx_t_2, 0+1, __pyx_v_i);
      __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_4, __pyx_t_2, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 237, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __pyx_v_known_item = __pyx_t_1;
  __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":239
 *         known_item = self.trainset.knows_item(i)
 * 
 *         if self.biased:             # <<<<<<<<<<<<<<
 *             est = self.trainset.global_mean
 * 
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_biased); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 239, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_5 = __Pyx_PyObject_IsTrue(__pyx_t_1); if (unlikely(__pyx_t_5 < 0)) __PYX_ERR(0, 239, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  if (__pyx_t_5) {

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":240
 * 
 *         if self.biased:
 *             est = self.trainset.global_mean             # <<<<<<<<<<<<<<
 * 
 *             if known_user:
 */
    __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 240, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_global_mean); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 240, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_4);
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __pyx_v_est = __pyx_t_4;
    __pyx_t_4 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":242
 *             est = self.trainset.global_mean
 * 
 *             if known_user:             # <<<<<<<<<<<<<<
 *                 est += self.bu[u]
 * 
 */
    __pyx_t_5 = __Pyx_PyObject_IsTrue(__pyx_v_known_user); if (unlikely(__pyx_t_5 < 0)) __PYX_ERR(0, 242, __pyx_L1_error)
    if (__pyx_t_5) {

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":243
 * 
 *             if known_user:
 *                 est += self.bu[u]             # <<<<<<<<<<<<<<
 * 
 *             if known_item:
 */
      __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_bu); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 243, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_1 = PyObject_GetItem(__pyx_t_4, __pyx_v_u); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 243, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_4 = PyNumber_InPlaceAdd(__pyx_v_est, __pyx_t_1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 243, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __Pyx_DECREF_SET(__pyx_v_est, __pyx_t_4);
      __pyx_t_4 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":242
 *             est = self.trainset.global_mean
 * 
 *             if known_user:             # <<<<<<<<<<<<<<
 *                 est += self.bu[u]
 * 
 */
    }

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":245
 *                 est += self.bu[u]
 * 
 *             if known_item:             # <<<<<<<<<<<<<<
 *                 est += self.bi[i]
 * 
 */
    __pyx_t_5 = __Pyx_PyObject_IsTrue(__pyx_v_known_item); if (unlikely(__pyx_t_5 < 0)) __PYX_ERR(0, 245, __pyx_L1_error)
    if (__pyx_t_5) {

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":246
 * 
 *             if known_item:
 *                 est += self.bi[i]             # <<<<<<<<<<<<<<
 * 
 *             if known_user and known_item:
 */
      __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_bi); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 246, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_1 = PyObject_GetItem(__pyx_t_4, __pyx_v_i); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 246, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_4 = PyNumber_InPlaceAdd(__pyx_v_est, __pyx_t_1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 246, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __Pyx_DECREF_SET(__pyx_v_est, __pyx_t_4);
      __pyx_t_4 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":245
 *                 est += self.bu[u]
 * 
 *             if known_item:             # <<<<<<<<<<<<<<
 *                 est += self.bi[i]
 * 
 */
    }

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":248
 *                 est += self.bi[i]
 * 
 *             if known_user and known_item:             # <<<<<<<<<<<<<<
 *                 est += np.dot(self.qi[i], self.pu[u])
 * 
 */
    __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_v_known_user); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(0, 248, __pyx_L1_error)
    if (__pyx_t_6) {
    } else {
      __pyx_t_5 = __pyx_t_6;
      goto __pyx_L7_bool_binop_done;
    }
    __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_v_known_item); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(0, 248, __pyx_L1_error)
    __pyx_t_5 = __pyx_t_6;
    __pyx_L7_bool_binop_done:;
    if (__pyx_t_5) {

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":249
 * 
 *             if known_user and known_item:
 *                 est += np.dot(self.qi[i], self.pu[u])             # <<<<<<<<<<<<<<
 * 
 *         else:
 */
      __pyx_t_1 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 249, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_dot); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 249, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_qi); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 249, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __pyx_t_3 = PyObject_GetItem(__pyx_t_1, __pyx_v_i); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 249, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_pu); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 249, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __pyx_t_7 = PyObject_GetItem(__pyx_t_1, __pyx_v_u); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 249, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_7);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __pyx_t_1 = NULL;
      __pyx_t_8 = 0;
      if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_2))) {
        __pyx_t_1 = PyMethod_GET_SELF(__pyx_t_2);
        if (likely(__pyx_t_1)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_2);
          __Pyx_INCREF(__pyx_t_1);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_2, function);
          __pyx_t_8 = 1;
        }
      }
      #if CYTHON_FAST_PYCALL
      if (PyFunction_Check(__pyx_t_2)) {
        PyObject *__pyx_temp[3] = {__pyx_t_1, __pyx_t_3, __pyx_t_7};
        __pyx_t_4 = __Pyx_PyFunction_FastCall(__pyx_t_2, __pyx_temp+1-__pyx_t_8, 2+__pyx_t_8); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 249, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
        __Pyx_GOTREF(__pyx_t_4);
        __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
        __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
      } else
      #endif
      #if CYTHON_FAST_PYCCALL
      if (__Pyx_PyFastCFunction_Check(__pyx_t_2)) {
        PyObject *__pyx_temp[3] = {__pyx_t_1, __pyx_t_3, __pyx_t_7};
        __pyx_t_4 = __Pyx_PyCFunction_FastCall(__pyx_t_2, __pyx_temp+1-__pyx_t_8, 2+__pyx_t_8); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 249, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
        __Pyx_GOTREF(__pyx_t_4);
        __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
        __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
      } else
      #endif
      {
        __pyx_t_9 = PyTuple_New(2+__pyx_t_8); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 249, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_9);
        if (__pyx_t_1) {
          __Pyx_GIVEREF(__pyx_t_1); PyTuple_SET_ITEM(__pyx_t_9, 0, __pyx_t_1); __pyx_t_1 = NULL;
        }
        __Pyx_GIVEREF(__pyx_t_3);
        PyTuple_SET_ITEM(__pyx_t_9, 0+__pyx_t_8, __pyx_t_3);
        __Pyx_GIVEREF(__pyx_t_7);
        PyTuple_SET_ITEM(__pyx_t_9, 1+__pyx_t_8, __pyx_t_7);
        __pyx_t_3 = 0;
        __pyx_t_7 = 0;
        __pyx_t_4 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_t_9, NULL); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 249, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_4);
        __Pyx_DECREF(__pyx_t_9); __pyx_t_9 = 0;
      }
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
      __pyx_t_2 = PyNumber_InPlaceAdd(__pyx_v_est, __pyx_t_4); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 249, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __Pyx_DECREF_SET(__pyx_v_est, __pyx_t_2);
      __pyx_t_2 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":248
 *                 est += self.bi[i]
 * 
 *             if known_user and known_item:             # <<<<<<<<<<<<<<
 *                 est += np.dot(self.qi[i], self.pu[u])
 * 
 */
    }

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":239
 *         known_item = self.trainset.knows_item(i)
 * 
 *         if self.biased:             # <<<<<<<<<<<<<<
 *             est = self.trainset.global_mean
 * 
 */
    goto __pyx_L3;
  }

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":252
 * 
 *         else:
 *             if known_user and known_item:             # <<<<<<<<<<<<<<
 *                 est = np.dot(self.qi[i], self.pu[u])
 *             else:
 */
  /*else*/ {
    __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_v_known_user); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(0, 252, __pyx_L1_error)
    if (__pyx_t_6) {
    } else {
      __pyx_t_5 = __pyx_t_6;
      goto __pyx_L10_bool_binop_done;
    }
    __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_v_known_item); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(0, 252, __pyx_L1_error)
    __pyx_t_5 = __pyx_t_6;
    __pyx_L10_bool_binop_done:;
    if (__pyx_t_5) {

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":253
 *         else:
 *             if known_user and known_item:
 *                 est = np.dot(self.qi[i], self.pu[u])             # <<<<<<<<<<<<<<
 *             else:
 *                 raise PredictionImpossible('User and item are unkown.')
 */
      __pyx_t_4 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 253, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_9 = __Pyx_PyObject_GetAttrStr(__pyx_t_4, __pyx_n_s_dot); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 253, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_9);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_qi); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 253, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_7 = PyObject_GetItem(__pyx_t_4, __pyx_v_i); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 253, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_7);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_pu); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 253, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_3 = PyObject_GetItem(__pyx_t_4, __pyx_v_u); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 253, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_4 = NULL;
      __pyx_t_8 = 0;
      if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_9))) {
        __pyx_t_4 = PyMethod_GET_SELF(__pyx_t_9);
        if (likely(__pyx_t_4)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_9);
          __Pyx_INCREF(__pyx_t_4);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_9, function);
          __pyx_t_8 = 1;
        }
      }
      #if CYTHON_FAST_PYCALL
      if (PyFunction_Check(__pyx_t_9)) {
        PyObject *__pyx_temp[3] = {__pyx_t_4, __pyx_t_7, __pyx_t_3};
        __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_9, __pyx_temp+1-__pyx_t_8, 2+__pyx_t_8); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 253, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
        __Pyx_GOTREF(__pyx_t_2);
        __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
        __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      } else
      #endif
      #if CYTHON_FAST_PYCCALL
      if (__Pyx_PyFastCFunction_Check(__pyx_t_9)) {
        PyObject *__pyx_temp[3] = {__pyx_t_4, __pyx_t_7, __pyx_t_3};
        __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_9, __pyx_temp+1-__pyx_t_8, 2+__pyx_t_8); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 253, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
        __Pyx_GOTREF(__pyx_t_2);
        __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
        __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      } else
      #endif
      {
        __pyx_t_1 = PyTuple_New(2+__pyx_t_8); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 253, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        if (__pyx_t_4) {
          __Pyx_GIVEREF(__pyx_t_4); PyTuple_SET_ITEM(__pyx_t_1, 0, __pyx_t_4); __pyx_t_4 = NULL;
        }
        __Pyx_GIVEREF(__pyx_t_7);
        PyTuple_SET_ITEM(__pyx_t_1, 0+__pyx_t_8, __pyx_t_7);
        __Pyx_GIVEREF(__pyx_t_3);
        PyTuple_SET_ITEM(__pyx_t_1, 1+__pyx_t_8, __pyx_t_3);
        __pyx_t_7 = 0;
        __pyx_t_3 = 0;
        __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_9, __pyx_t_1, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 253, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_2);
        __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      }
      __Pyx_DECREF(__pyx_t_9); __pyx_t_9 = 0;
      __pyx_v_est = __pyx_t_2;
      __pyx_t_2 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":252
 * 
 *         else:
 *             if known_user and known_item:             # <<<<<<<<<<<<<<
 *                 est = np.dot(self.qi[i], self.pu[u])
 *             else:
 */
      goto __pyx_L9;
    }

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":255
 *                 est = np.dot(self.qi[i], self.pu[u])
 *             else:
 *                 raise PredictionImpossible('User and item are unkown.')             # <<<<<<<<<<<<<<
 * 
 *         return est
 */
    /*else*/ {
      __pyx_t_2 = __Pyx_GetModuleGlobalName(__pyx_n_s_PredictionImpossible); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 255, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __pyx_t_9 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_tuple_, NULL); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 255, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_9);
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
      __Pyx_Raise(__pyx_t_9, 0, 0, 0);
      __Pyx_DECREF(__pyx_t_9); __pyx_t_9 = 0;
      __PYX_ERR(0, 255, __pyx_L1_error)
    }
    __pyx_L9:;
  }
  __pyx_L3:;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":257
 *                 raise PredictionImpossible('User and item are unkown.')
 * 
 *         return est             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __Pyx_XDECREF(__pyx_r);
  __Pyx_INCREF(__pyx_v_est);
  __pyx_r = __pyx_v_est;
  goto __pyx_L0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":233
 *         self.qi = qi
 * 
 *     def estimate(self, u, i):             # <<<<<<<<<<<<<<
 *         # Should we cythonize this as well?
 * 
 */

  /* function exit code */
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_2);
  __Pyx_XDECREF(__pyx_t_3);
  __Pyx_XDECREF(__pyx_t_4);
  __Pyx_XDECREF(__pyx_t_7);
  __Pyx_XDECREF(__pyx_t_9);
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVD.estimate", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = NULL;
  __pyx_L0:;
  __Pyx_XDECREF(__pyx_v_known_user);
  __Pyx_XDECREF(__pyx_v_known_item);
  __Pyx_XDECREF(__pyx_v_est);
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "surprise/prediction_algorithms/matrix_factorization.pyx":328
 *     """
 * 
 *     def __init__(self, n_factors=20, n_epochs=20, init_mean=0, init_std_dev=.1,             # <<<<<<<<<<<<<<
 *                  lr_all=.007, reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None,
 *                  lr_qi=None, lr_yj=None, reg_bu=None, reg_bi=None, reg_pu=None,
 */

/* Python wrapper */
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_1__init__(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static PyMethodDef __pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_1__init__ = {"__init__", (PyCFunction)__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_1__init__, METH_VARARGS|METH_KEYWORDS, 0};
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_1__init__(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
  PyObject *__pyx_v_self = 0;
  PyObject *__pyx_v_n_factors = 0;
  PyObject *__pyx_v_n_epochs = 0;
  PyObject *__pyx_v_init_mean = 0;
  PyObject *__pyx_v_init_std_dev = 0;
  PyObject *__pyx_v_lr_all = 0;
  PyObject *__pyx_v_reg_all = 0;
  PyObject *__pyx_v_lr_bu = 0;
  PyObject *__pyx_v_lr_bi = 0;
  PyObject *__pyx_v_lr_pu = 0;
  PyObject *__pyx_v_lr_qi = 0;
  PyObject *__pyx_v_lr_yj = 0;
  PyObject *__pyx_v_reg_bu = 0;
  PyObject *__pyx_v_reg_bi = 0;
  PyObject *__pyx_v_reg_pu = 0;
  PyObject *__pyx_v_reg_qi = 0;
  PyObject *__pyx_v_reg_yj = 0;
  PyObject *__pyx_v_verbose = 0;
  PyObject *__pyx_r = 0;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("__init__ (wrapper)", 0);
  {
    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_self,&__pyx_n_s_n_factors,&__pyx_n_s_n_epochs,&__pyx_n_s_init_mean,&__pyx_n_s_init_std_dev,&__pyx_n_s_lr_all,&__pyx_n_s_reg_all,&__pyx_n_s_lr_bu,&__pyx_n_s_lr_bi,&__pyx_n_s_lr_pu,&__pyx_n_s_lr_qi,&__pyx_n_s_lr_yj,&__pyx_n_s_reg_bu,&__pyx_n_s_reg_bi,&__pyx_n_s_reg_pu,&__pyx_n_s_reg_qi,&__pyx_n_s_reg_yj,&__pyx_n_s_verbose,0};
    PyObject* values[18] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
    values[1] = ((PyObject *)((PyObject *)__pyx_int_20));
    values[2] = ((PyObject *)((PyObject *)__pyx_int_20));
    values[3] = ((PyObject *)((PyObject *)__pyx_int_0));
    values[4] = ((PyObject *)((PyObject*)__pyx_float__1));
    values[5] = ((PyObject *)((PyObject*)__pyx_float__007));
    values[6] = ((PyObject *)((PyObject*)__pyx_float__02));

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":329
 * 
 *     def __init__(self, n_factors=20, n_epochs=20, init_mean=0, init_std_dev=.1,
 *                  lr_all=.007, reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None,             # <<<<<<<<<<<<<<
 *                  lr_qi=None, lr_yj=None, reg_bu=None, reg_bi=None, reg_pu=None,
 *                  reg_qi=None, reg_yj=None, verbose=False):
 */
    values[7] = ((PyObject *)((PyObject *)Py_None));
    values[8] = ((PyObject *)((PyObject *)Py_None));
    values[9] = ((PyObject *)((PyObject *)Py_None));

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":330
 *     def __init__(self, n_factors=20, n_epochs=20, init_mean=0, init_std_dev=.1,
 *                  lr_all=.007, reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None,
 *                  lr_qi=None, lr_yj=None, reg_bu=None, reg_bi=None, reg_pu=None,             # <<<<<<<<<<<<<<
 *                  reg_qi=None, reg_yj=None, verbose=False):
 * 
 */
    values[10] = ((PyObject *)((PyObject *)Py_None));
    values[11] = ((PyObject *)((PyObject *)Py_None));
    values[12] = ((PyObject *)((PyObject *)Py_None));
    values[13] = ((PyObject *)((PyObject *)Py_None));
    values[14] = ((PyObject *)((PyObject *)Py_None));

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":331
 *                  lr_all=.007, reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None,
 *                  lr_qi=None, lr_yj=None, reg_bu=None, reg_bi=None, reg_pu=None,
 *                  reg_qi=None, reg_yj=None, verbose=False):             # <<<<<<<<<<<<<<
 * 
 *         self.n_factors = n_factors
 */
    values[15] = ((PyObject *)((PyObject *)Py_None));
    values[16] = ((PyObject *)((PyObject *)Py_None));
    values[17] = ((PyObject *)((PyObject *)Py_False));
    if (unlikely(__pyx_kwds)) {
      Py_ssize_t kw_args;
      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
      switch (pos_args) {
        case 18: values[17] = PyTuple_GET_ITEM(__pyx_args, 17);
        CYTHON_FALLTHROUGH;
        case 17: values[16] = PyTuple_GET_ITEM(__pyx_args, 16);
        CYTHON_FALLTHROUGH;
        case 16: values[15] = PyTuple_GET_ITEM(__pyx_args, 15);
        CYTHON_FALLTHROUGH;
        case 15: values[14] = PyTuple_GET_ITEM(__pyx_args, 14);
        CYTHON_FALLTHROUGH;
        case 14: values[13] = PyTuple_GET_ITEM(__pyx_args, 13);
        CYTHON_FALLTHROUGH;
        case 13: values[12] = PyTuple_GET_ITEM(__pyx_args, 12);
        CYTHON_FALLTHROUGH;
        case 12: values[11] = PyTuple_GET_ITEM(__pyx_args, 11);
        CYTHON_FALLTHROUGH;
        case 11: values[10] = PyTuple_GET_ITEM(__pyx_args, 10);
        CYTHON_FALLTHROUGH;
        case 10: values[9] = PyTuple_GET_ITEM(__pyx_args, 9);
        CYTHON_FALLTHROUGH;
        case  9: values[8] = PyTuple_GET_ITEM(__pyx_args, 8);
        CYTHON_FALLTHROUGH;
        case  8: values[7] = PyTuple_GET_ITEM(__pyx_args, 7);
        CYTHON_FALLTHROUGH;
        case  7: values[6] = PyTuple_GET_ITEM(__pyx_args, 6);
        CYTHON_FALLTHROUGH;
        case  6: values[5] = PyTuple_GET_ITEM(__pyx_args, 5);
        CYTHON_FALLTHROUGH;
        case  5: values[4] = PyTuple_GET_ITEM(__pyx_args, 4);
        CYTHON_FALLTHROUGH;
        case  4: values[3] = PyTuple_GET_ITEM(__pyx_args, 3);
        CYTHON_FALLTHROUGH;
        case  3: values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
        CYTHON_FALLTHROUGH;
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        CYTHON_FALLTHROUGH;
        case  0: break;
        default: goto __pyx_L5_argtuple_error;
      }
      kw_args = PyDict_Size(__pyx_kwds);
      switch (pos_args) {
        case  0:
        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_self)) != 0)) kw_args--;
        else goto __pyx_L5_argtuple_error;
        CYTHON_FALLTHROUGH;
        case  1:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_n_factors);
          if (value) { values[1] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  2:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_n_epochs);
          if (value) { values[2] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  3:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_init_mean);
          if (value) { values[3] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  4:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_init_std_dev);
          if (value) { values[4] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  5:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_lr_all);
          if (value) { values[5] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  6:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_all);
          if (value) { values[6] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  7:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_lr_bu);
          if (value) { values[7] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  8:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_lr_bi);
          if (value) { values[8] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  9:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_lr_pu);
          if (value) { values[9] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 10:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_lr_qi);
          if (value) { values[10] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 11:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_lr_yj);
          if (value) { values[11] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 12:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_bu);
          if (value) { values[12] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 13:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_bi);
          if (value) { values[13] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 14:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_pu);
          if (value) { values[14] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 15:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_qi);
          if (value) { values[15] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 16:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_yj);
          if (value) { values[16] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 17:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_verbose);
          if (value) { values[17] = value; kw_args--; }
        }
      }
      if (unlikely(kw_args > 0)) {
        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "__init__") < 0)) __PYX_ERR(0, 328, __pyx_L3_error)
      }
    } else {
      switch (PyTuple_GET_SIZE(__pyx_args)) {
        case 18: values[17] = PyTuple_GET_ITEM(__pyx_args, 17);
        CYTHON_FALLTHROUGH;
        case 17: values[16] = PyTuple_GET_ITEM(__pyx_args, 16);
        CYTHON_FALLTHROUGH;
        case 16: values[15] = PyTuple_GET_ITEM(__pyx_args, 15);
        CYTHON_FALLTHROUGH;
        case 15: values[14] = PyTuple_GET_ITEM(__pyx_args, 14);
        CYTHON_FALLTHROUGH;
        case 14: values[13] = PyTuple_GET_ITEM(__pyx_args, 13);
        CYTHON_FALLTHROUGH;
        case 13: values[12] = PyTuple_GET_ITEM(__pyx_args, 12);
        CYTHON_FALLTHROUGH;
        case 12: values[11] = PyTuple_GET_ITEM(__pyx_args, 11);
        CYTHON_FALLTHROUGH;
        case 11: values[10] = PyTuple_GET_ITEM(__pyx_args, 10);
        CYTHON_FALLTHROUGH;
        case 10: values[9] = PyTuple_GET_ITEM(__pyx_args, 9);
        CYTHON_FALLTHROUGH;
        case  9: values[8] = PyTuple_GET_ITEM(__pyx_args, 8);
        CYTHON_FALLTHROUGH;
        case  8: values[7] = PyTuple_GET_ITEM(__pyx_args, 7);
        CYTHON_FALLTHROUGH;
        case  7: values[6] = PyTuple_GET_ITEM(__pyx_args, 6);
        CYTHON_FALLTHROUGH;
        case  6: values[5] = PyTuple_GET_ITEM(__pyx_args, 5);
        CYTHON_FALLTHROUGH;
        case  5: values[4] = PyTuple_GET_ITEM(__pyx_args, 4);
        CYTHON_FALLTHROUGH;
        case  4: values[3] = PyTuple_GET_ITEM(__pyx_args, 3);
        CYTHON_FALLTHROUGH;
        case  3: values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
        CYTHON_FALLTHROUGH;
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        break;
        default: goto __pyx_L5_argtuple_error;
      }
    }
    __pyx_v_self = values[0];
    __pyx_v_n_factors = values[1];
    __pyx_v_n_epochs = values[2];
    __pyx_v_init_mean = values[3];
    __pyx_v_init_std_dev = values[4];
    __pyx_v_lr_all = values[5];
    __pyx_v_reg_all = values[6];
    __pyx_v_lr_bu = values[7];
    __pyx_v_lr_bi = values[8];
    __pyx_v_lr_pu = values[9];
    __pyx_v_lr_qi = values[10];
    __pyx_v_lr_yj = values[11];
    __pyx_v_reg_bu = values[12];
    __pyx_v_reg_bi = values[13];
    __pyx_v_reg_pu = values[14];
    __pyx_v_reg_qi = values[15];
    __pyx_v_reg_yj = values[16];
    __pyx_v_verbose = values[17];
  }
  goto __pyx_L4_argument_unpacking_done;
  __pyx_L5_argtuple_error:;
  __Pyx_RaiseArgtupleInvalid("__init__", 0, 1, 18, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 328, __pyx_L3_error)
  __pyx_L3_error:;
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVDpp.__init__", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __Pyx_RefNannyFinishContext();
  return NULL;
  __pyx_L4_argument_unpacking_done:;
  __pyx_r = __pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp___init__(__pyx_self, __pyx_v_self, __pyx_v_n_factors, __pyx_v_n_epochs, __pyx_v_init_mean, __pyx_v_init_std_dev, __pyx_v_lr_all, __pyx_v_reg_all, __pyx_v_lr_bu, __pyx_v_lr_bi, __pyx_v_lr_pu, __pyx_v_lr_qi, __pyx_v_lr_yj, __pyx_v_reg_bu, __pyx_v_reg_bi, __pyx_v_reg_pu, __pyx_v_reg_qi, __pyx_v_reg_yj, __pyx_v_verbose);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":328
 *     """
 * 
 *     def __init__(self, n_factors=20, n_epochs=20, init_mean=0, init_std_dev=.1,             # <<<<<<<<<<<<<<
 *                  lr_all=.007, reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None,
 *                  lr_qi=None, lr_yj=None, reg_bu=None, reg_bi=None, reg_pu=None,
 */

  /* function exit code */
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp___init__(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_n_factors, PyObject *__pyx_v_n_epochs, PyObject *__pyx_v_init_mean, PyObject *__pyx_v_init_std_dev, PyObject *__pyx_v_lr_all, PyObject *__pyx_v_reg_all, PyObject *__pyx_v_lr_bu, PyObject *__pyx_v_lr_bi, PyObject *__pyx_v_lr_pu, PyObject *__pyx_v_lr_qi, PyObject *__pyx_v_lr_yj, PyObject *__pyx_v_reg_bu, PyObject *__pyx_v_reg_bi, PyObject *__pyx_v_reg_pu, PyObject *__pyx_v_reg_qi, PyObject *__pyx_v_reg_yj, PyObject *__pyx_v_verbose) {
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  int __pyx_t_2;
  PyObject *__pyx_t_3 = NULL;
  PyObject *__pyx_t_4 = NULL;
  PyObject *__pyx_t_5 = NULL;
  __Pyx_RefNannySetupContext("__init__", 0);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":333
 *                  reg_qi=None, reg_yj=None, verbose=False):
 * 
 *         self.n_factors = n_factors             # <<<<<<<<<<<<<<
 *         self.n_epochs = n_epochs
 *         self.init_mean = init_mean
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_n_factors, __pyx_v_n_factors) < 0) __PYX_ERR(0, 333, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":334
 * 
 *         self.n_factors = n_factors
 *         self.n_epochs = n_epochs             # <<<<<<<<<<<<<<
 *         self.init_mean = init_mean
 *         self.init_std_dev = init_std_dev
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_n_epochs, __pyx_v_n_epochs) < 0) __PYX_ERR(0, 334, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":335
 *         self.n_factors = n_factors
 *         self.n_epochs = n_epochs
 *         self.init_mean = init_mean             # <<<<<<<<<<<<<<
 *         self.init_std_dev = init_std_dev
 *         self.lr_bu = lr_bu if lr_bu is not None else lr_all
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_init_mean, __pyx_v_init_mean) < 0) __PYX_ERR(0, 335, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":336
 *         self.n_epochs = n_epochs
 *         self.init_mean = init_mean
 *         self.init_std_dev = init_std_dev             # <<<<<<<<<<<<<<
 *         self.lr_bu = lr_bu if lr_bu is not None else lr_all
 *         self.lr_bi = lr_bi if lr_bi is not None else lr_all
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_init_std_dev, __pyx_v_init_std_dev) < 0) __PYX_ERR(0, 336, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":337
 *         self.init_mean = init_mean
 *         self.init_std_dev = init_std_dev
 *         self.lr_bu = lr_bu if lr_bu is not None else lr_all             # <<<<<<<<<<<<<<
 *         self.lr_bi = lr_bi if lr_bi is not None else lr_all
 *         self.lr_pu = lr_pu if lr_pu is not None else lr_all
 */
  __pyx_t_2 = (__pyx_v_lr_bu != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_lr_bu);
    __pyx_t_1 = __pyx_v_lr_bu;
  } else {
    __Pyx_INCREF(__pyx_v_lr_all);
    __pyx_t_1 = __pyx_v_lr_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_lr_bu, __pyx_t_1) < 0) __PYX_ERR(0, 337, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":338
 *         self.init_std_dev = init_std_dev
 *         self.lr_bu = lr_bu if lr_bu is not None else lr_all
 *         self.lr_bi = lr_bi if lr_bi is not None else lr_all             # <<<<<<<<<<<<<<
 *         self.lr_pu = lr_pu if lr_pu is not None else lr_all
 *         self.lr_qi = lr_qi if lr_qi is not None else lr_all
 */
  __pyx_t_2 = (__pyx_v_lr_bi != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_lr_bi);
    __pyx_t_1 = __pyx_v_lr_bi;
  } else {
    __Pyx_INCREF(__pyx_v_lr_all);
    __pyx_t_1 = __pyx_v_lr_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_lr_bi, __pyx_t_1) < 0) __PYX_ERR(0, 338, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":339
 *         self.lr_bu = lr_bu if lr_bu is not None else lr_all
 *         self.lr_bi = lr_bi if lr_bi is not None else lr_all
 *         self.lr_pu = lr_pu if lr_pu is not None else lr_all             # <<<<<<<<<<<<<<
 *         self.lr_qi = lr_qi if lr_qi is not None else lr_all
 *         self.lr_yj = lr_yj if lr_yj is not None else lr_all
 */
  __pyx_t_2 = (__pyx_v_lr_pu != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_lr_pu);
    __pyx_t_1 = __pyx_v_lr_pu;
  } else {
    __Pyx_INCREF(__pyx_v_lr_all);
    __pyx_t_1 = __pyx_v_lr_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_lr_pu, __pyx_t_1) < 0) __PYX_ERR(0, 339, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":340
 *         self.lr_bi = lr_bi if lr_bi is not None else lr_all
 *         self.lr_pu = lr_pu if lr_pu is not None else lr_all
 *         self.lr_qi = lr_qi if lr_qi is not None else lr_all             # <<<<<<<<<<<<<<
 *         self.lr_yj = lr_yj if lr_yj is not None else lr_all
 *         self.reg_bu = reg_bu if reg_bu is not None else reg_all
 */
  __pyx_t_2 = (__pyx_v_lr_qi != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_lr_qi);
    __pyx_t_1 = __pyx_v_lr_qi;
  } else {
    __Pyx_INCREF(__pyx_v_lr_all);
    __pyx_t_1 = __pyx_v_lr_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_lr_qi, __pyx_t_1) < 0) __PYX_ERR(0, 340, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":341
 *         self.lr_pu = lr_pu if lr_pu is not None else lr_all
 *         self.lr_qi = lr_qi if lr_qi is not None else lr_all
 *         self.lr_yj = lr_yj if lr_yj is not None else lr_all             # <<<<<<<<<<<<<<
 *         self.reg_bu = reg_bu if reg_bu is not None else reg_all
 *         self.reg_bi = reg_bi if reg_bi is not None else reg_all
 */
  __pyx_t_2 = (__pyx_v_lr_yj != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_lr_yj);
    __pyx_t_1 = __pyx_v_lr_yj;
  } else {
    __Pyx_INCREF(__pyx_v_lr_all);
    __pyx_t_1 = __pyx_v_lr_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_lr_yj, __pyx_t_1) < 0) __PYX_ERR(0, 341, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":342
 *         self.lr_qi = lr_qi if lr_qi is not None else lr_all
 *         self.lr_yj = lr_yj if lr_yj is not None else lr_all
 *         self.reg_bu = reg_bu if reg_bu is not None else reg_all             # <<<<<<<<<<<<<<
 *         self.reg_bi = reg_bi if reg_bi is not None else reg_all
 *         self.reg_pu = reg_pu if reg_pu is not None else reg_all
 */
  __pyx_t_2 = (__pyx_v_reg_bu != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_reg_bu);
    __pyx_t_1 = __pyx_v_reg_bu;
  } else {
    __Pyx_INCREF(__pyx_v_reg_all);
    __pyx_t_1 = __pyx_v_reg_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_reg_bu, __pyx_t_1) < 0) __PYX_ERR(0, 342, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":343
 *         self.lr_yj = lr_yj if lr_yj is not None else lr_all
 *         self.reg_bu = reg_bu if reg_bu is not None else reg_all
 *         self.reg_bi = reg_bi if reg_bi is not None else reg_all             # <<<<<<<<<<<<<<
 *         self.reg_pu = reg_pu if reg_pu is not None else reg_all
 *         self.reg_qi = reg_qi if reg_qi is not None else reg_all
 */
  __pyx_t_2 = (__pyx_v_reg_bi != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_reg_bi);
    __pyx_t_1 = __pyx_v_reg_bi;
  } else {
    __Pyx_INCREF(__pyx_v_reg_all);
    __pyx_t_1 = __pyx_v_reg_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_reg_bi, __pyx_t_1) < 0) __PYX_ERR(0, 343, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":344
 *         self.reg_bu = reg_bu if reg_bu is not None else reg_all
 *         self.reg_bi = reg_bi if reg_bi is not None else reg_all
 *         self.reg_pu = reg_pu if reg_pu is not None else reg_all             # <<<<<<<<<<<<<<
 *         self.reg_qi = reg_qi if reg_qi is not None else reg_all
 *         self.reg_yj = reg_yj if reg_yj is not None else reg_all
 */
  __pyx_t_2 = (__pyx_v_reg_pu != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_reg_pu);
    __pyx_t_1 = __pyx_v_reg_pu;
  } else {
    __Pyx_INCREF(__pyx_v_reg_all);
    __pyx_t_1 = __pyx_v_reg_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_reg_pu, __pyx_t_1) < 0) __PYX_ERR(0, 344, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":345
 *         self.reg_bi = reg_bi if reg_bi is not None else reg_all
 *         self.reg_pu = reg_pu if reg_pu is not None else reg_all
 *         self.reg_qi = reg_qi if reg_qi is not None else reg_all             # <<<<<<<<<<<<<<
 *         self.reg_yj = reg_yj if reg_yj is not None else reg_all
 *         self.verbose = verbose
 */
  __pyx_t_2 = (__pyx_v_reg_qi != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_reg_qi);
    __pyx_t_1 = __pyx_v_reg_qi;
  } else {
    __Pyx_INCREF(__pyx_v_reg_all);
    __pyx_t_1 = __pyx_v_reg_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_reg_qi, __pyx_t_1) < 0) __PYX_ERR(0, 345, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":346
 *         self.reg_pu = reg_pu if reg_pu is not None else reg_all
 *         self.reg_qi = reg_qi if reg_qi is not None else reg_all
 *         self.reg_yj = reg_yj if reg_yj is not None else reg_all             # <<<<<<<<<<<<<<
 *         self.verbose = verbose
 * 
 */
  __pyx_t_2 = (__pyx_v_reg_yj != Py_None);
  if ((__pyx_t_2 != 0)) {
    __Pyx_INCREF(__pyx_v_reg_yj);
    __pyx_t_1 = __pyx_v_reg_yj;
  } else {
    __Pyx_INCREF(__pyx_v_reg_all);
    __pyx_t_1 = __pyx_v_reg_all;
  }
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_reg_yj, __pyx_t_1) < 0) __PYX_ERR(0, 346, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":347
 *         self.reg_qi = reg_qi if reg_qi is not None else reg_all
 *         self.reg_yj = reg_yj if reg_yj is not None else reg_all
 *         self.verbose = verbose             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.__init__(self)
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_verbose, __pyx_v_verbose) < 0) __PYX_ERR(0, 347, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":349
 *         self.verbose = verbose
 * 
 *         AlgoBase.__init__(self)             # <<<<<<<<<<<<<<
 * 
 *     def train(self, trainset):
 */
  __pyx_t_3 = __Pyx_GetModuleGlobalName(__pyx_n_s_AlgoBase); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 349, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_3, __pyx_n_s_init); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 349, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __pyx_t_3 = NULL;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_4))) {
    __pyx_t_3 = PyMethod_GET_SELF(__pyx_t_4);
    if (likely(__pyx_t_3)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_4);
      __Pyx_INCREF(__pyx_t_3);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_4, function);
    }
  }
  if (!__pyx_t_3) {
    __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_4, __pyx_v_self); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 349, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_4)) {
      PyObject *__pyx_temp[2] = {__pyx_t_3, __pyx_v_self};
      __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 349, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_4)) {
      PyObject *__pyx_temp[2] = {__pyx_t_3, __pyx_v_self};
      __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 349, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    {
      __pyx_t_5 = PyTuple_New(1+1); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 349, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_5);
      __Pyx_GIVEREF(__pyx_t_3); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_3); __pyx_t_3 = NULL;
      __Pyx_INCREF(__pyx_v_self);
      __Pyx_GIVEREF(__pyx_v_self);
      PyTuple_SET_ITEM(__pyx_t_5, 0+1, __pyx_v_self);
      __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_4, __pyx_t_5, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 349, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":328
 *     """
 * 
 *     def __init__(self, n_factors=20, n_epochs=20, init_mean=0, init_std_dev=.1,             # <<<<<<<<<<<<<<
 *                  lr_all=.007, reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None,
 *                  lr_qi=None, lr_yj=None, reg_bu=None, reg_bi=None, reg_pu=None,
 */

  /* function exit code */
  __pyx_r = Py_None; __Pyx_INCREF(Py_None);
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_3);
  __Pyx_XDECREF(__pyx_t_4);
  __Pyx_XDECREF(__pyx_t_5);
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVDpp.__init__", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = NULL;
  __pyx_L0:;
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "surprise/prediction_algorithms/matrix_factorization.pyx":351
 *         AlgoBase.__init__(self)
 * 
 *     def train(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.train(self, trainset)
 */

/* Python wrapper */
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_3train(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static PyMethodDef __pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_3train = {"train", (PyCFunction)__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_3train, METH_VARARGS|METH_KEYWORDS, 0};
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_3train(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
  PyObject *__pyx_v_self = 0;
  PyObject *__pyx_v_trainset = 0;
  PyObject *__pyx_r = 0;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("train (wrapper)", 0);
  {
    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_self,&__pyx_n_s_trainset,0};
    PyObject* values[2] = {0,0};
    if (unlikely(__pyx_kwds)) {
      Py_ssize_t kw_args;
      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
      switch (pos_args) {
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        CYTHON_FALLTHROUGH;
        case  0: break;
        default: goto __pyx_L5_argtuple_error;
      }
      kw_args = PyDict_Size(__pyx_kwds);
      switch (pos_args) {
        case  0:
        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_self)) != 0)) kw_args--;
        else goto __pyx_L5_argtuple_error;
        CYTHON_FALLTHROUGH;
        case  1:
        if (likely((values[1] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_trainset)) != 0)) kw_args--;
        else {
          __Pyx_RaiseArgtupleInvalid("train", 1, 2, 2, 1); __PYX_ERR(0, 351, __pyx_L3_error)
        }
      }
      if (unlikely(kw_args > 0)) {
        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "train") < 0)) __PYX_ERR(0, 351, __pyx_L3_error)
      }
    } else if (PyTuple_GET_SIZE(__pyx_args) != 2) {
      goto __pyx_L5_argtuple_error;
    } else {
      values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
      values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
    }
    __pyx_v_self = values[0];
    __pyx_v_trainset = values[1];
  }
  goto __pyx_L4_argument_unpacking_done;
  __pyx_L5_argtuple_error:;
  __Pyx_RaiseArgtupleInvalid("train", 1, 2, 2, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 351, __pyx_L3_error)
  __pyx_L3_error:;
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVDpp.train", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __Pyx_RefNannyFinishContext();
  return NULL;
  __pyx_L4_argument_unpacking_done:;
  __pyx_r = __pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_2train(__pyx_self, __pyx_v_self, __pyx_v_trainset);

  /* function exit code */
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_2train(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_trainset) {
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  PyObject *__pyx_t_2 = NULL;
  PyObject *__pyx_t_3 = NULL;
  int __pyx_t_4;
  PyObject *__pyx_t_5 = NULL;
  __Pyx_RefNannySetupContext("train", 0);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":353
 *     def train(self, trainset):
 * 
 *         AlgoBase.train(self, trainset)             # <<<<<<<<<<<<<<
 *         self.sgd(trainset)
 * 
 */
  __pyx_t_2 = __Pyx_GetModuleGlobalName(__pyx_n_s_AlgoBase); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 353, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_t_2, __pyx_n_s_train); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 353, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_t_2 = NULL;
  __pyx_t_4 = 0;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_3))) {
    __pyx_t_2 = PyMethod_GET_SELF(__pyx_t_3);
    if (likely(__pyx_t_2)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
      __Pyx_INCREF(__pyx_t_2);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_3, function);
      __pyx_t_4 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_3)) {
    PyObject *__pyx_temp[3] = {__pyx_t_2, __pyx_v_self, __pyx_v_trainset};
    __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-__pyx_t_4, 2+__pyx_t_4); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 353, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_2); __pyx_t_2 = 0;
    __Pyx_GOTREF(__pyx_t_1);
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
    PyObject *__pyx_temp[3] = {__pyx_t_2, __pyx_v_self, __pyx_v_trainset};
    __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-__pyx_t_4, 2+__pyx_t_4); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 353, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_2); __pyx_t_2 = 0;
    __Pyx_GOTREF(__pyx_t_1);
  } else
  #endif
  {
    __pyx_t_5 = PyTuple_New(2+__pyx_t_4); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 353, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_5);
    if (__pyx_t_2) {
      __Pyx_GIVEREF(__pyx_t_2); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_2); __pyx_t_2 = NULL;
    }
    __Pyx_INCREF(__pyx_v_self);
    __Pyx_GIVEREF(__pyx_v_self);
    PyTuple_SET_ITEM(__pyx_t_5, 0+__pyx_t_4, __pyx_v_self);
    __Pyx_INCREF(__pyx_v_trainset);
    __Pyx_GIVEREF(__pyx_v_trainset);
    PyTuple_SET_ITEM(__pyx_t_5, 1+__pyx_t_4, __pyx_v_trainset);
    __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_5, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 353, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  }
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":354
 * 
 *         AlgoBase.train(self, trainset)
 *         self.sgd(trainset)             # <<<<<<<<<<<<<<
 * 
 *     def sgd(self, trainset):
 */
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_sgd); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 354, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __pyx_t_5 = NULL;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_3))) {
    __pyx_t_5 = PyMethod_GET_SELF(__pyx_t_3);
    if (likely(__pyx_t_5)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
      __Pyx_INCREF(__pyx_t_5);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_3, function);
    }
  }
  if (!__pyx_t_5) {
    __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_3, __pyx_v_trainset); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 354, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_3)) {
      PyObject *__pyx_temp[2] = {__pyx_t_5, __pyx_v_trainset};
      __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 354, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
      PyObject *__pyx_temp[2] = {__pyx_t_5, __pyx_v_trainset};
      __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 354, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    {
      __pyx_t_2 = PyTuple_New(1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 354, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_2, 0, __pyx_t_5); __pyx_t_5 = NULL;
      __Pyx_INCREF(__pyx_v_trainset);
      __Pyx_GIVEREF(__pyx_v_trainset);
      PyTuple_SET_ITEM(__pyx_t_2, 0+1, __pyx_v_trainset);
      __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_2, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 354, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":351
 *         AlgoBase.__init__(self)
 * 
 *     def train(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.train(self, trainset)
 */

  /* function exit code */
  __pyx_r = Py_None; __Pyx_INCREF(Py_None);
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_2);
  __Pyx_XDECREF(__pyx_t_3);
  __Pyx_XDECREF(__pyx_t_5);
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVDpp.train", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = NULL;
  __pyx_L0:;
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "surprise/prediction_algorithms/matrix_factorization.pyx":356
 *         self.sgd(trainset)
 * 
 *     def sgd(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         # user biases
 */

/* Python wrapper */
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_5sgd(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static PyMethodDef __pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_5sgd = {"sgd", (PyCFunction)__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_5sgd, METH_VARARGS|METH_KEYWORDS, 0};
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_5sgd(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
  PyObject *__pyx_v_self = 0;
  PyObject *__pyx_v_trainset = 0;
  PyObject *__pyx_r = 0;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("sgd (wrapper)", 0);
  {
    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_self,&__pyx_n_s_trainset,0};
    PyObject* values[2] = {0,0};
    if (unlikely(__pyx_kwds)) {
      Py_ssize_t kw_args;
      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
      switch (pos_args) {
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        CYTHON_FALLTHROUGH;
        case  0: break;
        default: goto __pyx_L5_argtuple_error;
      }
      kw_args = PyDict_Size(__pyx_kwds);
      switch (pos_args) {
        case  0:
        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_self)) != 0)) kw_args--;
        else goto __pyx_L5_argtuple_error;
        CYTHON_FALLTHROUGH;
        case  1:
        if (likely((values[1] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_trainset)) != 0)) kw_args--;
        else {
          __Pyx_RaiseArgtupleInvalid("sgd", 1, 2, 2, 1); __PYX_ERR(0, 356, __pyx_L3_error)
        }
      }
      if (unlikely(kw_args > 0)) {
        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "sgd") < 0)) __PYX_ERR(0, 356, __pyx_L3_error)
      }
    } else if (PyTuple_GET_SIZE(__pyx_args) != 2) {
      goto __pyx_L5_argtuple_error;
    } else {
      values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
      values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
    }
    __pyx_v_self = values[0];
    __pyx_v_trainset = values[1];
  }
  goto __pyx_L4_argument_unpacking_done;
  __pyx_L5_argtuple_error:;
  __Pyx_RaiseArgtupleInvalid("sgd", 1, 2, 2, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 356, __pyx_L3_error)
  __pyx_L3_error:;
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVDpp.sgd", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __Pyx_RefNannyFinishContext();
  return NULL;
  __pyx_L4_argument_unpacking_done:;
  __pyx_r = __pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_4sgd(__pyx_self, __pyx_v_self, __pyx_v_trainset);

  /* function exit code */
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_4sgd(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_trainset) {
  PyArrayObject *__pyx_v_bu = 0;
  PyArrayObject *__pyx_v_bi = 0;
  PyArrayObject *__pyx_v_pu = 0;
  PyArrayObject *__pyx_v_qi = 0;
  PyArrayObject *__pyx_v_yj = 0;
  int __pyx_v_u;
  int __pyx_v_i;
  int __pyx_v_j;
  int __pyx_v_f;
  double __pyx_v_r;
  double __pyx_v_err;
  double __pyx_v_dot;
  double __pyx_v_puf;
  double __pyx_v_qif;
  double __pyx_v_sqrt_Iu;
  CYTHON_UNUSED double __pyx_v__;
  double __pyx_v_global_mean;
  PyArrayObject *__pyx_v_u_impl_fdb = 0;
  double __pyx_v_lr_bu;
  double __pyx_v_lr_bi;
  double __pyx_v_lr_pu;
  double __pyx_v_lr_qi;
  double __pyx_v_lr_yj;
  double __pyx_v_reg_bu;
  double __pyx_v_reg_bi;
  double __pyx_v_reg_pu;
  double __pyx_v_reg_qi;
  double __pyx_v_reg_yj;
  PyObject *__pyx_v_current_epoch = NULL;
  PyObject *__pyx_v_Iu = NULL;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_bi;
  __Pyx_Buffer __pyx_pybuffer_bi;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_bu;
  __Pyx_Buffer __pyx_pybuffer_bu;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_pu;
  __Pyx_Buffer __pyx_pybuffer_pu;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_qi;
  __Pyx_Buffer __pyx_pybuffer_qi;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_u_impl_fdb;
  __Pyx_Buffer __pyx_pybuffer_u_impl_fdb;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_yj;
  __Pyx_Buffer __pyx_pybuffer_yj;
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  PyObject *__pyx_t_2 = NULL;
  double __pyx_t_3;
  PyObject *__pyx_t_4 = NULL;
  PyObject *__pyx_t_5 = NULL;
  PyObject *__pyx_t_6 = NULL;
  int __pyx_t_7;
  PyObject *__pyx_t_8 = NULL;
  PyArrayObject *__pyx_t_9 = NULL;
  PyObject *__pyx_t_10 = NULL;
  PyObject *__pyx_t_11 = NULL;
  PyObject *__pyx_t_12 = NULL;
  PyArrayObject *__pyx_t_13 = NULL;
  PyObject *__pyx_t_14 = NULL;
  PyArrayObject *__pyx_t_15 = NULL;
  PyArrayObject *__pyx_t_16 = NULL;
  PyArrayObject *__pyx_t_17 = NULL;
  PyArrayObject *__pyx_t_18 = NULL;
  Py_ssize_t __pyx_t_19;
  PyObject *(*__pyx_t_20)(PyObject *);
  int __pyx_t_21;
  Py_ssize_t __pyx_t_22;
  PyObject *(*__pyx_t_23)(PyObject *);
  PyObject *(*__pyx_t_24)(PyObject *);
  int __pyx_t_25;
  Py_ssize_t __pyx_t_26;
  PyObject *(*__pyx_t_27)(PyObject *);
  PyObject *__pyx_t_28 = NULL;
  Py_ssize_t __pyx_t_29;
  Py_ssize_t __pyx_t_30;
  Py_ssize_t __pyx_t_31;
  __pyx_t_5numpy_double_t __pyx_t_32;
  Py_ssize_t __pyx_t_33;
  Py_ssize_t __pyx_t_34;
  Py_ssize_t __pyx_t_35;
  Py_ssize_t __pyx_t_36;
  Py_ssize_t __pyx_t_37;
  Py_ssize_t __pyx_t_38;
  Py_ssize_t __pyx_t_39;
  Py_ssize_t __pyx_t_40;
  Py_ssize_t __pyx_t_41;
  Py_ssize_t __pyx_t_42;
  Py_ssize_t __pyx_t_43;
  Py_ssize_t __pyx_t_44;
  Py_ssize_t __pyx_t_45;
  Py_ssize_t __pyx_t_46;
  Py_ssize_t __pyx_t_47;
  Py_ssize_t __pyx_t_48;
  Py_ssize_t __pyx_t_49;
  Py_ssize_t __pyx_t_50;
  Py_ssize_t __pyx_t_51;
  Py_ssize_t __pyx_t_52;
  Py_ssize_t __pyx_t_53;
  Py_ssize_t __pyx_t_54;
  Py_ssize_t __pyx_t_55;
  Py_ssize_t __pyx_t_56;
  Py_ssize_t __pyx_t_57;
  __Pyx_RefNannySetupContext("sgd", 0);
  __pyx_pybuffer_bu.pybuffer.buf = NULL;
  __pyx_pybuffer_bu.refcount = 0;
  __pyx_pybuffernd_bu.data = NULL;
  __pyx_pybuffernd_bu.rcbuffer = &__pyx_pybuffer_bu;
  __pyx_pybuffer_bi.pybuffer.buf = NULL;
  __pyx_pybuffer_bi.refcount = 0;
  __pyx_pybuffernd_bi.data = NULL;
  __pyx_pybuffernd_bi.rcbuffer = &__pyx_pybuffer_bi;
  __pyx_pybuffer_pu.pybuffer.buf = NULL;
  __pyx_pybuffer_pu.refcount = 0;
  __pyx_pybuffernd_pu.data = NULL;
  __pyx_pybuffernd_pu.rcbuffer = &__pyx_pybuffer_pu;
  __pyx_pybuffer_qi.pybuffer.buf = NULL;
  __pyx_pybuffer_qi.refcount = 0;
  __pyx_pybuffernd_qi.data = NULL;
  __pyx_pybuffernd_qi.rcbuffer = &__pyx_pybuffer_qi;
  __pyx_pybuffer_yj.pybuffer.buf = NULL;
  __pyx_pybuffer_yj.refcount = 0;
  __pyx_pybuffernd_yj.data = NULL;
  __pyx_pybuffernd_yj.rcbuffer = &__pyx_pybuffer_yj;
  __pyx_pybuffer_u_impl_fdb.pybuffer.buf = NULL;
  __pyx_pybuffer_u_impl_fdb.refcount = 0;
  __pyx_pybuffernd_u_impl_fdb.data = NULL;
  __pyx_pybuffernd_u_impl_fdb.rcbuffer = &__pyx_pybuffer_u_impl_fdb;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":371
 *         cdef int u, i, j, f
 *         cdef double r, err, dot, puf, qif, sqrt_Iu, _
 *         cdef double global_mean = self.trainset.global_mean             # <<<<<<<<<<<<<<
 *         cdef np.ndarray[np.double_t] u_impl_fdb
 * 
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 371, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_global_mean); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 371, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 371, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_global_mean = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":374
 *         cdef np.ndarray[np.double_t] u_impl_fdb
 * 
 *         cdef double lr_bu = self.lr_bu             # <<<<<<<<<<<<<<
 *         cdef double lr_bi = self.lr_bi
 *         cdef double lr_pu = self.lr_pu
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_lr_bu); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 374, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 374, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_lr_bu = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":375
 * 
 *         cdef double lr_bu = self.lr_bu
 *         cdef double lr_bi = self.lr_bi             # <<<<<<<<<<<<<<
 *         cdef double lr_pu = self.lr_pu
 *         cdef double lr_qi = self.lr_qi
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_lr_bi); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 375, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 375, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_lr_bi = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":376
 *         cdef double lr_bu = self.lr_bu
 *         cdef double lr_bi = self.lr_bi
 *         cdef double lr_pu = self.lr_pu             # <<<<<<<<<<<<<<
 *         cdef double lr_qi = self.lr_qi
 *         cdef double lr_yj = self.lr_yj
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_lr_pu); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 376, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 376, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_lr_pu = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":377
 *         cdef double lr_bi = self.lr_bi
 *         cdef double lr_pu = self.lr_pu
 *         cdef double lr_qi = self.lr_qi             # <<<<<<<<<<<<<<
 *         cdef double lr_yj = self.lr_yj
 * 
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_lr_qi); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 377, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 377, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_lr_qi = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":378
 *         cdef double lr_pu = self.lr_pu
 *         cdef double lr_qi = self.lr_qi
 *         cdef double lr_yj = self.lr_yj             # <<<<<<<<<<<<<<
 * 
 *         cdef double reg_bu = self.reg_bu
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_lr_yj); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 378, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 378, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_lr_yj = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":380
 *         cdef double lr_yj = self.lr_yj
 * 
 *         cdef double reg_bu = self.reg_bu             # <<<<<<<<<<<<<<
 *         cdef double reg_bi = self.reg_bi
 *         cdef double reg_pu = self.reg_pu
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_reg_bu); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 380, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 380, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_reg_bu = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":381
 * 
 *         cdef double reg_bu = self.reg_bu
 *         cdef double reg_bi = self.reg_bi             # <<<<<<<<<<<<<<
 *         cdef double reg_pu = self.reg_pu
 *         cdef double reg_qi = self.reg_qi
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_reg_bi); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 381, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 381, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_reg_bi = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":382
 *         cdef double reg_bu = self.reg_bu
 *         cdef double reg_bi = self.reg_bi
 *         cdef double reg_pu = self.reg_pu             # <<<<<<<<<<<<<<
 *         cdef double reg_qi = self.reg_qi
 *         cdef double reg_yj = self.reg_yj
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_reg_pu); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 382, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 382, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_reg_pu = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":383
 *         cdef double reg_bi = self.reg_bi
 *         cdef double reg_pu = self.reg_pu
 *         cdef double reg_qi = self.reg_qi             # <<<<<<<<<<<<<<
 *         cdef double reg_yj = self.reg_yj
 * 
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_reg_qi); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 383, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 383, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_reg_qi = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":384
 *         cdef double reg_pu = self.reg_pu
 *         cdef double reg_qi = self.reg_qi
 *         cdef double reg_yj = self.reg_yj             # <<<<<<<<<<<<<<
 * 
 *         bu = np.zeros(trainset.n_users, np.double)
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_reg_yj); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 384, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 384, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_reg_yj = __pyx_t_3;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":386
 *         cdef double reg_yj = self.reg_yj
 * 
 *         bu = np.zeros(trainset.n_users, np.double)             # <<<<<<<<<<<<<<
 *         bi = np.zeros(trainset.n_items, np.double)
 * 
 */
  __pyx_t_1 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 386, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_zeros); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 386, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_users); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 386, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_5 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 386, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_t_5, __pyx_n_s_double); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 386, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_6);
  __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  __pyx_t_5 = NULL;
  __pyx_t_7 = 0;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_4))) {
    __pyx_t_5 = PyMethod_GET_SELF(__pyx_t_4);
    if (likely(__pyx_t_5)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_4);
      __Pyx_INCREF(__pyx_t_5);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_4, function);
      __pyx_t_7 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_4)) {
    PyObject *__pyx_temp[3] = {__pyx_t_5, __pyx_t_1, __pyx_t_6};
    __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_4, __pyx_temp+1-__pyx_t_7, 2+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 386, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_4)) {
    PyObject *__pyx_temp[3] = {__pyx_t_5, __pyx_t_1, __pyx_t_6};
    __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_4, __pyx_temp+1-__pyx_t_7, 2+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 386, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  } else
  #endif
  {
    __pyx_t_8 = PyTuple_New(2+__pyx_t_7); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 386, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_8);
    if (__pyx_t_5) {
      __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_8, 0, __pyx_t_5); __pyx_t_5 = NULL;
    }
    __Pyx_GIVEREF(__pyx_t_1);
    PyTuple_SET_ITEM(__pyx_t_8, 0+__pyx_t_7, __pyx_t_1);
    __Pyx_GIVEREF(__pyx_t_6);
    PyTuple_SET_ITEM(__pyx_t_8, 1+__pyx_t_7, __pyx_t_6);
    __pyx_t_1 = 0;
    __pyx_t_6 = 0;
    __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_4, __pyx_t_8, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 386, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
  }
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  if (!(likely(((__pyx_t_2) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_2, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 386, __pyx_L1_error)
  __pyx_t_9 = ((PyArrayObject *)__pyx_t_2);
  {
    __Pyx_BufFmt_StackElem __pyx_stack[1];
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bu.rcbuffer->pybuffer);
    __pyx_t_7 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_bu.rcbuffer->pybuffer, (PyObject*)__pyx_t_9, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack);
    if (unlikely(__pyx_t_7 < 0)) {
      PyErr_Fetch(&__pyx_t_10, &__pyx_t_11, &__pyx_t_12);
      if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_bu.rcbuffer->pybuffer, (PyObject*)__pyx_v_bu, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack) == -1)) {
        Py_XDECREF(__pyx_t_10); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_12);
        __Pyx_RaiseBufferFallbackError();
      } else {
        PyErr_Restore(__pyx_t_10, __pyx_t_11, __pyx_t_12);
      }
      __pyx_t_10 = __pyx_t_11 = __pyx_t_12 = 0;
    }
    __pyx_pybuffernd_bu.diminfo[0].strides = __pyx_pybuffernd_bu.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_bu.diminfo[0].shape = __pyx_pybuffernd_bu.rcbuffer->pybuffer.shape[0];
    if (unlikely(__pyx_t_7 < 0)) __PYX_ERR(0, 386, __pyx_L1_error)
  }
  __pyx_t_9 = 0;
  __pyx_v_bu = ((PyArrayObject *)__pyx_t_2);
  __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":387
 * 
 *         bu = np.zeros(trainset.n_users, np.double)
 *         bi = np.zeros(trainset.n_items, np.double)             # <<<<<<<<<<<<<<
 * 
 *         pu = np.random.normal(self.init_mean, self.init_std_dev,
 */
  __pyx_t_4 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 387, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_8 = __Pyx_PyObject_GetAttrStr(__pyx_t_4, __pyx_n_s_zeros); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 387, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_items); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 387, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_6 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 387, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_6);
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_t_6, __pyx_n_s_double); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 387, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  __pyx_t_6 = NULL;
  __pyx_t_7 = 0;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_8))) {
    __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_8);
    if (likely(__pyx_t_6)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_8);
      __Pyx_INCREF(__pyx_t_6);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_8, function);
      __pyx_t_7 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_8)) {
    PyObject *__pyx_temp[3] = {__pyx_t_6, __pyx_t_4, __pyx_t_1};
    __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_8, __pyx_temp+1-__pyx_t_7, 2+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 387, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_8)) {
    PyObject *__pyx_temp[3] = {__pyx_t_6, __pyx_t_4, __pyx_t_1};
    __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_8, __pyx_temp+1-__pyx_t_7, 2+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 387, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  } else
  #endif
  {
    __pyx_t_5 = PyTuple_New(2+__pyx_t_7); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 387, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_5);
    if (__pyx_t_6) {
      __Pyx_GIVEREF(__pyx_t_6); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_6); __pyx_t_6 = NULL;
    }
    __Pyx_GIVEREF(__pyx_t_4);
    PyTuple_SET_ITEM(__pyx_t_5, 0+__pyx_t_7, __pyx_t_4);
    __Pyx_GIVEREF(__pyx_t_1);
    PyTuple_SET_ITEM(__pyx_t_5, 1+__pyx_t_7, __pyx_t_1);
    __pyx_t_4 = 0;
    __pyx_t_1 = 0;
    __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_8, __pyx_t_5, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 387, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  }
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
  if (!(likely(((__pyx_t_2) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_2, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 387, __pyx_L1_error)
  __pyx_t_13 = ((PyArrayObject *)__pyx_t_2);
  {
    __Pyx_BufFmt_StackElem __pyx_stack[1];
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bi.rcbuffer->pybuffer);
    __pyx_t_7 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_bi.rcbuffer->pybuffer, (PyObject*)__pyx_t_13, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack);
    if (unlikely(__pyx_t_7 < 0)) {
      PyErr_Fetch(&__pyx_t_12, &__pyx_t_11, &__pyx_t_10);
      if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_bi.rcbuffer->pybuffer, (PyObject*)__pyx_v_bi, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack) == -1)) {
        Py_XDECREF(__pyx_t_12); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_10);
        __Pyx_RaiseBufferFallbackError();
      } else {
        PyErr_Restore(__pyx_t_12, __pyx_t_11, __pyx_t_10);
      }
      __pyx_t_12 = __pyx_t_11 = __pyx_t_10 = 0;
    }
    __pyx_pybuffernd_bi.diminfo[0].strides = __pyx_pybuffernd_bi.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_bi.diminfo[0].shape = __pyx_pybuffernd_bi.rcbuffer->pybuffer.shape[0];
    if (unlikely(__pyx_t_7 < 0)) __PYX_ERR(0, 387, __pyx_L1_error)
  }
  __pyx_t_13 = 0;
  __pyx_v_bi = ((PyArrayObject *)__pyx_t_2);
  __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":389
 *         bi = np.zeros(trainset.n_items, np.double)
 * 
 *         pu = np.random.normal(self.init_mean, self.init_std_dev,             # <<<<<<<<<<<<<<
 *                               (trainset.n_users, self.n_factors))
 *         qi = np.random.normal(self.init_mean, self.init_std_dev,
 */
  __pyx_t_8 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 389, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_t_8, __pyx_n_s_random); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 389, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
  __pyx_t_8 = __Pyx_PyObject_GetAttrStr(__pyx_t_5, __pyx_n_s_normal); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 389, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_mean); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 389, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_std_dev); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 389, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":390
 * 
 *         pu = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_users, self.n_factors))             # <<<<<<<<<<<<<<
 *         qi = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_items, self.n_factors))
 */
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_users); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 390, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 390, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_6);
  __pyx_t_14 = PyTuple_New(2); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 390, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_14);
  __Pyx_GIVEREF(__pyx_t_4);
  PyTuple_SET_ITEM(__pyx_t_14, 0, __pyx_t_4);
  __Pyx_GIVEREF(__pyx_t_6);
  PyTuple_SET_ITEM(__pyx_t_14, 1, __pyx_t_6);
  __pyx_t_4 = 0;
  __pyx_t_6 = 0;
  __pyx_t_6 = NULL;
  __pyx_t_7 = 0;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_8))) {
    __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_8);
    if (likely(__pyx_t_6)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_8);
      __Pyx_INCREF(__pyx_t_6);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_8, function);
      __pyx_t_7 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_8)) {
    PyObject *__pyx_temp[4] = {__pyx_t_6, __pyx_t_5, __pyx_t_1, __pyx_t_14};
    __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_8, __pyx_temp+1-__pyx_t_7, 3+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 389, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_8)) {
    PyObject *__pyx_temp[4] = {__pyx_t_6, __pyx_t_5, __pyx_t_1, __pyx_t_14};
    __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_8, __pyx_temp+1-__pyx_t_7, 3+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 389, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
  } else
  #endif
  {
    __pyx_t_4 = PyTuple_New(3+__pyx_t_7); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 389, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_4);
    if (__pyx_t_6) {
      __Pyx_GIVEREF(__pyx_t_6); PyTuple_SET_ITEM(__pyx_t_4, 0, __pyx_t_6); __pyx_t_6 = NULL;
    }
    __Pyx_GIVEREF(__pyx_t_5);
    PyTuple_SET_ITEM(__pyx_t_4, 0+__pyx_t_7, __pyx_t_5);
    __Pyx_GIVEREF(__pyx_t_1);
    PyTuple_SET_ITEM(__pyx_t_4, 1+__pyx_t_7, __pyx_t_1);
    __Pyx_GIVEREF(__pyx_t_14);
    PyTuple_SET_ITEM(__pyx_t_4, 2+__pyx_t_7, __pyx_t_14);
    __pyx_t_5 = 0;
    __pyx_t_1 = 0;
    __pyx_t_14 = 0;
    __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_8, __pyx_t_4, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 389, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  }
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":389
 *         bi = np.zeros(trainset.n_items, np.double)
 * 
 *         pu = np.random.normal(self.init_mean, self.init_std_dev,             # <<<<<<<<<<<<<<
 *                               (trainset.n_users, self.n_factors))
 *         qi = np.random.normal(self.init_mean, self.init_std_dev,
 */
  if (!(likely(((__pyx_t_2) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_2, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 389, __pyx_L1_error)
  __pyx_t_15 = ((PyArrayObject *)__pyx_t_2);
  {
    __Pyx_BufFmt_StackElem __pyx_stack[1];
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_pu.rcbuffer->pybuffer);
    __pyx_t_7 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_pu.rcbuffer->pybuffer, (PyObject*)__pyx_t_15, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack);
    if (unlikely(__pyx_t_7 < 0)) {
      PyErr_Fetch(&__pyx_t_10, &__pyx_t_11, &__pyx_t_12);
      if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_pu.rcbuffer->pybuffer, (PyObject*)__pyx_v_pu, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack) == -1)) {
        Py_XDECREF(__pyx_t_10); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_12);
        __Pyx_RaiseBufferFallbackError();
      } else {
        PyErr_Restore(__pyx_t_10, __pyx_t_11, __pyx_t_12);
      }
      __pyx_t_10 = __pyx_t_11 = __pyx_t_12 = 0;
    }
    __pyx_pybuffernd_pu.diminfo[0].strides = __pyx_pybuffernd_pu.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_pu.diminfo[0].shape = __pyx_pybuffernd_pu.rcbuffer->pybuffer.shape[0]; __pyx_pybuffernd_pu.diminfo[1].strides = __pyx_pybuffernd_pu.rcbuffer->pybuffer.strides[1]; __pyx_pybuffernd_pu.diminfo[1].shape = __pyx_pybuffernd_pu.rcbuffer->pybuffer.shape[1];
    if (unlikely(__pyx_t_7 < 0)) __PYX_ERR(0, 389, __pyx_L1_error)
  }
  __pyx_t_15 = 0;
  __pyx_v_pu = ((PyArrayObject *)__pyx_t_2);
  __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":391
 *         pu = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_users, self.n_factors))
 *         qi = np.random.normal(self.init_mean, self.init_std_dev,             # <<<<<<<<<<<<<<
 *                               (trainset.n_items, self.n_factors))
 *         yj = np.random.normal(self.init_mean, self.init_std_dev,
 */
  __pyx_t_8 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 391, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_8, __pyx_n_s_random); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 391, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
  __pyx_t_8 = __Pyx_PyObject_GetAttrStr(__pyx_t_4, __pyx_n_s_normal); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 391, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_mean); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 391, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_14 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_std_dev); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 391, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_14);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":392
 *                               (trainset.n_users, self.n_factors))
 *         qi = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_items, self.n_factors))             # <<<<<<<<<<<<<<
 *         yj = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_items, self.n_factors))
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_items); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 392, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 392, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __pyx_t_6 = PyTuple_New(2); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 392, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_6);
  __Pyx_GIVEREF(__pyx_t_1);
  PyTuple_SET_ITEM(__pyx_t_6, 0, __pyx_t_1);
  __Pyx_GIVEREF(__pyx_t_5);
  PyTuple_SET_ITEM(__pyx_t_6, 1, __pyx_t_5);
  __pyx_t_1 = 0;
  __pyx_t_5 = 0;
  __pyx_t_5 = NULL;
  __pyx_t_7 = 0;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_8))) {
    __pyx_t_5 = PyMethod_GET_SELF(__pyx_t_8);
    if (likely(__pyx_t_5)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_8);
      __Pyx_INCREF(__pyx_t_5);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_8, function);
      __pyx_t_7 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_8)) {
    PyObject *__pyx_temp[4] = {__pyx_t_5, __pyx_t_4, __pyx_t_14, __pyx_t_6};
    __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_8, __pyx_temp+1-__pyx_t_7, 3+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 391, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_8)) {
    PyObject *__pyx_temp[4] = {__pyx_t_5, __pyx_t_4, __pyx_t_14, __pyx_t_6};
    __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_8, __pyx_temp+1-__pyx_t_7, 3+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 391, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  } else
  #endif
  {
    __pyx_t_1 = PyTuple_New(3+__pyx_t_7); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 391, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    if (__pyx_t_5) {
      __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_1, 0, __pyx_t_5); __pyx_t_5 = NULL;
    }
    __Pyx_GIVEREF(__pyx_t_4);
    PyTuple_SET_ITEM(__pyx_t_1, 0+__pyx_t_7, __pyx_t_4);
    __Pyx_GIVEREF(__pyx_t_14);
    PyTuple_SET_ITEM(__pyx_t_1, 1+__pyx_t_7, __pyx_t_14);
    __Pyx_GIVEREF(__pyx_t_6);
    PyTuple_SET_ITEM(__pyx_t_1, 2+__pyx_t_7, __pyx_t_6);
    __pyx_t_4 = 0;
    __pyx_t_14 = 0;
    __pyx_t_6 = 0;
    __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_8, __pyx_t_1, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 391, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  }
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":391
 *         pu = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_users, self.n_factors))
 *         qi = np.random.normal(self.init_mean, self.init_std_dev,             # <<<<<<<<<<<<<<
 *                               (trainset.n_items, self.n_factors))
 *         yj = np.random.normal(self.init_mean, self.init_std_dev,
 */
  if (!(likely(((__pyx_t_2) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_2, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 391, __pyx_L1_error)
  __pyx_t_16 = ((PyArrayObject *)__pyx_t_2);
  {
    __Pyx_BufFmt_StackElem __pyx_stack[1];
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_qi.rcbuffer->pybuffer);
    __pyx_t_7 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_qi.rcbuffer->pybuffer, (PyObject*)__pyx_t_16, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack);
    if (unlikely(__pyx_t_7 < 0)) {
      PyErr_Fetch(&__pyx_t_12, &__pyx_t_11, &__pyx_t_10);
      if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_qi.rcbuffer->pybuffer, (PyObject*)__pyx_v_qi, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack) == -1)) {
        Py_XDECREF(__pyx_t_12); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_10);
        __Pyx_RaiseBufferFallbackError();
      } else {
        PyErr_Restore(__pyx_t_12, __pyx_t_11, __pyx_t_10);
      }
      __pyx_t_12 = __pyx_t_11 = __pyx_t_10 = 0;
    }
    __pyx_pybuffernd_qi.diminfo[0].strides = __pyx_pybuffernd_qi.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_qi.diminfo[0].shape = __pyx_pybuffernd_qi.rcbuffer->pybuffer.shape[0]; __pyx_pybuffernd_qi.diminfo[1].strides = __pyx_pybuffernd_qi.rcbuffer->pybuffer.strides[1]; __pyx_pybuffernd_qi.diminfo[1].shape = __pyx_pybuffernd_qi.rcbuffer->pybuffer.shape[1];
    if (unlikely(__pyx_t_7 < 0)) __PYX_ERR(0, 391, __pyx_L1_error)
  }
  __pyx_t_16 = 0;
  __pyx_v_qi = ((PyArrayObject *)__pyx_t_2);
  __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":393
 *         qi = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_items, self.n_factors))
 *         yj = np.random.normal(self.init_mean, self.init_std_dev,             # <<<<<<<<<<<<<<
 *                               (trainset.n_items, self.n_factors))
 *         u_impl_fdb = np.zeros(self.n_factors, np.double)
 */
  __pyx_t_8 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 393, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_t_8, __pyx_n_s_random); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 393, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
  __pyx_t_8 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_normal); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 393, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_mean); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 393, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_std_dev); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 393, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_6);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":394
 *                               (trainset.n_items, self.n_factors))
 *         yj = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_items, self.n_factors))             # <<<<<<<<<<<<<<
 *         u_impl_fdb = np.zeros(self.n_factors, np.double)
 * 
 */
  __pyx_t_14 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_items); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 394, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_14);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 394, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_5 = PyTuple_New(2); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 394, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __Pyx_GIVEREF(__pyx_t_14);
  PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_14);
  __Pyx_GIVEREF(__pyx_t_4);
  PyTuple_SET_ITEM(__pyx_t_5, 1, __pyx_t_4);
  __pyx_t_14 = 0;
  __pyx_t_4 = 0;
  __pyx_t_4 = NULL;
  __pyx_t_7 = 0;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_8))) {
    __pyx_t_4 = PyMethod_GET_SELF(__pyx_t_8);
    if (likely(__pyx_t_4)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_8);
      __Pyx_INCREF(__pyx_t_4);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_8, function);
      __pyx_t_7 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_8)) {
    PyObject *__pyx_temp[4] = {__pyx_t_4, __pyx_t_1, __pyx_t_6, __pyx_t_5};
    __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_8, __pyx_temp+1-__pyx_t_7, 3+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 393, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_8)) {
    PyObject *__pyx_temp[4] = {__pyx_t_4, __pyx_t_1, __pyx_t_6, __pyx_t_5};
    __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_8, __pyx_temp+1-__pyx_t_7, 3+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 393, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  } else
  #endif
  {
    __pyx_t_14 = PyTuple_New(3+__pyx_t_7); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 393, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_14);
    if (__pyx_t_4) {
      __Pyx_GIVEREF(__pyx_t_4); PyTuple_SET_ITEM(__pyx_t_14, 0, __pyx_t_4); __pyx_t_4 = NULL;
    }
    __Pyx_GIVEREF(__pyx_t_1);
    PyTuple_SET_ITEM(__pyx_t_14, 0+__pyx_t_7, __pyx_t_1);
    __Pyx_GIVEREF(__pyx_t_6);
    PyTuple_SET_ITEM(__pyx_t_14, 1+__pyx_t_7, __pyx_t_6);
    __Pyx_GIVEREF(__pyx_t_5);
    PyTuple_SET_ITEM(__pyx_t_14, 2+__pyx_t_7, __pyx_t_5);
    __pyx_t_1 = 0;
    __pyx_t_6 = 0;
    __pyx_t_5 = 0;
    __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_8, __pyx_t_14, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 393, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
  }
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":393
 *         qi = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_items, self.n_factors))
 *         yj = np.random.normal(self.init_mean, self.init_std_dev,             # <<<<<<<<<<<<<<
 *                               (trainset.n_items, self.n_factors))
 *         u_impl_fdb = np.zeros(self.n_factors, np.double)
 */
  if (!(likely(((__pyx_t_2) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_2, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 393, __pyx_L1_error)
  __pyx_t_17 = ((PyArrayObject *)__pyx_t_2);
  {
    __Pyx_BufFmt_StackElem __pyx_stack[1];
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_yj.rcbuffer->pybuffer);
    __pyx_t_7 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_yj.rcbuffer->pybuffer, (PyObject*)__pyx_t_17, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack);
    if (unlikely(__pyx_t_7 < 0)) {
      PyErr_Fetch(&__pyx_t_10, &__pyx_t_11, &__pyx_t_12);
      if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_yj.rcbuffer->pybuffer, (PyObject*)__pyx_v_yj, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack) == -1)) {
        Py_XDECREF(__pyx_t_10); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_12);
        __Pyx_RaiseBufferFallbackError();
      } else {
        PyErr_Restore(__pyx_t_10, __pyx_t_11, __pyx_t_12);
      }
      __pyx_t_10 = __pyx_t_11 = __pyx_t_12 = 0;
    }
    __pyx_pybuffernd_yj.diminfo[0].strides = __pyx_pybuffernd_yj.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_yj.diminfo[0].shape = __pyx_pybuffernd_yj.rcbuffer->pybuffer.shape[0]; __pyx_pybuffernd_yj.diminfo[1].strides = __pyx_pybuffernd_yj.rcbuffer->pybuffer.strides[1]; __pyx_pybuffernd_yj.diminfo[1].shape = __pyx_pybuffernd_yj.rcbuffer->pybuffer.shape[1];
    if (unlikely(__pyx_t_7 < 0)) __PYX_ERR(0, 393, __pyx_L1_error)
  }
  __pyx_t_17 = 0;
  __pyx_v_yj = ((PyArrayObject *)__pyx_t_2);
  __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":395
 *         yj = np.random.normal(self.init_mean, self.init_std_dev,
 *                               (trainset.n_items, self.n_factors))
 *         u_impl_fdb = np.zeros(self.n_factors, np.double)             # <<<<<<<<<<<<<<
 * 
 *         for current_epoch in range(self.n_epochs):
 */
  __pyx_t_8 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 395, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __pyx_t_14 = __Pyx_PyObject_GetAttrStr(__pyx_t_8, __pyx_n_s_zeros); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 395, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_14);
  __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
  __pyx_t_8 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 395, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_8);
  __pyx_t_5 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 395, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_t_5, __pyx_n_s_double); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 395, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_6);
  __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  __pyx_t_5 = NULL;
  __pyx_t_7 = 0;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_14))) {
    __pyx_t_5 = PyMethod_GET_SELF(__pyx_t_14);
    if (likely(__pyx_t_5)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_14);
      __Pyx_INCREF(__pyx_t_5);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_14, function);
      __pyx_t_7 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_14)) {
    PyObject *__pyx_temp[3] = {__pyx_t_5, __pyx_t_8, __pyx_t_6};
    __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_14, __pyx_temp+1-__pyx_t_7, 2+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 395, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_14)) {
    PyObject *__pyx_temp[3] = {__pyx_t_5, __pyx_t_8, __pyx_t_6};
    __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_14, __pyx_temp+1-__pyx_t_7, 2+__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 395, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  } else
  #endif
  {
    __pyx_t_1 = PyTuple_New(2+__pyx_t_7); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 395, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    if (__pyx_t_5) {
      __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_1, 0, __pyx_t_5); __pyx_t_5 = NULL;
    }
    __Pyx_GIVEREF(__pyx_t_8);
    PyTuple_SET_ITEM(__pyx_t_1, 0+__pyx_t_7, __pyx_t_8);
    __Pyx_GIVEREF(__pyx_t_6);
    PyTuple_SET_ITEM(__pyx_t_1, 1+__pyx_t_7, __pyx_t_6);
    __pyx_t_8 = 0;
    __pyx_t_6 = 0;
    __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_14, __pyx_t_1, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 395, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  }
  __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
  if (!(likely(((__pyx_t_2) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_2, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 395, __pyx_L1_error)
  __pyx_t_18 = ((PyArrayObject *)__pyx_t_2);
  {
    __Pyx_BufFmt_StackElem __pyx_stack[1];
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer);
    __pyx_t_7 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer, (PyObject*)__pyx_t_18, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack);
    if (unlikely(__pyx_t_7 < 0)) {
      PyErr_Fetch(&__pyx_t_12, &__pyx_t_11, &__pyx_t_10);
      if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer, (PyObject*)__pyx_v_u_impl_fdb, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack) == -1)) {
        Py_XDECREF(__pyx_t_12); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_10);
        __Pyx_RaiseBufferFallbackError();
      } else {
        PyErr_Restore(__pyx_t_12, __pyx_t_11, __pyx_t_10);
      }
      __pyx_t_12 = __pyx_t_11 = __pyx_t_10 = 0;
    }
    __pyx_pybuffernd_u_impl_fdb.diminfo[0].strides = __pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_u_impl_fdb.diminfo[0].shape = __pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer.shape[0];
    if (unlikely(__pyx_t_7 < 0)) __PYX_ERR(0, 395, __pyx_L1_error)
  }
  __pyx_t_18 = 0;
  __pyx_v_u_impl_fdb = ((PyArrayObject *)__pyx_t_2);
  __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":397
 *         u_impl_fdb = np.zeros(self.n_factors, np.double)
 * 
 *         for current_epoch in range(self.n_epochs):             # <<<<<<<<<<<<<<
 *             if self.verbose:
 *                 print(" processing epoch {}".format(current_epoch))
 */
  __pyx_t_14 = __Pyx_GetModuleGlobalName(__pyx_n_s_range); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 397, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_14);
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_epochs); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 397, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_6 = NULL;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_14))) {
    __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_14);
    if (likely(__pyx_t_6)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_14);
      __Pyx_INCREF(__pyx_t_6);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_14, function);
    }
  }
  if (!__pyx_t_6) {
    __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_14, __pyx_t_1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 397, __pyx_L1_error)
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_GOTREF(__pyx_t_2);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_14)) {
      PyObject *__pyx_temp[2] = {__pyx_t_6, __pyx_t_1};
      __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_14, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 397, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_14)) {
      PyObject *__pyx_temp[2] = {__pyx_t_6, __pyx_t_1};
      __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_14, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 397, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    } else
    #endif
    {
      __pyx_t_8 = PyTuple_New(1+1); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 397, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_8);
      __Pyx_GIVEREF(__pyx_t_6); PyTuple_SET_ITEM(__pyx_t_8, 0, __pyx_t_6); __pyx_t_6 = NULL;
      __Pyx_GIVEREF(__pyx_t_1);
      PyTuple_SET_ITEM(__pyx_t_8, 0+1, __pyx_t_1);
      __pyx_t_1 = 0;
      __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_14, __pyx_t_8, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 397, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;
  if (likely(PyList_CheckExact(__pyx_t_2)) || PyTuple_CheckExact(__pyx_t_2)) {
    __pyx_t_14 = __pyx_t_2; __Pyx_INCREF(__pyx_t_14); __pyx_t_19 = 0;
    __pyx_t_20 = NULL;
  } else {
    __pyx_t_19 = -1; __pyx_t_14 = PyObject_GetIter(__pyx_t_2); if (unlikely(!__pyx_t_14)) __PYX_ERR(0, 397, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_14);
    __pyx_t_20 = Py_TYPE(__pyx_t_14)->tp_iternext; if (unlikely(!__pyx_t_20)) __PYX_ERR(0, 397, __pyx_L1_error)
  }
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  for (;;) {
    if (likely(!__pyx_t_20)) {
      if (likely(PyList_CheckExact(__pyx_t_14))) {
        if (__pyx_t_19 >= PyList_GET_SIZE(__pyx_t_14)) break;
        #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
        __pyx_t_2 = PyList_GET_ITEM(__pyx_t_14, __pyx_t_19); __Pyx_INCREF(__pyx_t_2); __pyx_t_19++; if (unlikely(0 < 0)) __PYX_ERR(0, 397, __pyx_L1_error)
        #else
        __pyx_t_2 = PySequence_ITEM(__pyx_t_14, __pyx_t_19); __pyx_t_19++; if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 397, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_2);
        #endif
      } else {
        if (__pyx_t_19 >= PyTuple_GET_SIZE(__pyx_t_14)) break;
        #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
        __pyx_t_2 = PyTuple_GET_ITEM(__pyx_t_14, __pyx_t_19); __Pyx_INCREF(__pyx_t_2); __pyx_t_19++; if (unlikely(0 < 0)) __PYX_ERR(0, 397, __pyx_L1_error)
        #else
        __pyx_t_2 = PySequence_ITEM(__pyx_t_14, __pyx_t_19); __pyx_t_19++; if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 397, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_2);
        #endif
      }
    } else {
      __pyx_t_2 = __pyx_t_20(__pyx_t_14);
      if (unlikely(!__pyx_t_2)) {
        PyObject* exc_type = PyErr_Occurred();
        if (exc_type) {
          if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
          else __PYX_ERR(0, 397, __pyx_L1_error)
        }
        break;
      }
      __Pyx_GOTREF(__pyx_t_2);
    }
    __Pyx_XDECREF_SET(__pyx_v_current_epoch, __pyx_t_2);
    __pyx_t_2 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":398
 * 
 *         for current_epoch in range(self.n_epochs):
 *             if self.verbose:             # <<<<<<<<<<<<<<
 *                 print(" processing epoch {}".format(current_epoch))
 *             for u, i, r in trainset.all_ratings():
 */
    __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_verbose); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 398, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __pyx_t_21 = __Pyx_PyObject_IsTrue(__pyx_t_2); if (unlikely(__pyx_t_21 < 0)) __PYX_ERR(0, 398, __pyx_L1_error)
    __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    if (__pyx_t_21) {

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":399
 *         for current_epoch in range(self.n_epochs):
 *             if self.verbose:
 *                 print(" processing epoch {}".format(current_epoch))             # <<<<<<<<<<<<<<
 *             for u, i, r in trainset.all_ratings():
 * 
 */
      __pyx_t_8 = __Pyx_PyObject_GetAttrStr(__pyx_kp_u_processing_epoch, __pyx_n_s_format); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 399, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_8);
      __pyx_t_1 = NULL;
      if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_8))) {
        __pyx_t_1 = PyMethod_GET_SELF(__pyx_t_8);
        if (likely(__pyx_t_1)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_8);
          __Pyx_INCREF(__pyx_t_1);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_8, function);
        }
      }
      if (!__pyx_t_1) {
        __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_8, __pyx_v_current_epoch); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 399, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_2);
      } else {
        #if CYTHON_FAST_PYCALL
        if (PyFunction_Check(__pyx_t_8)) {
          PyObject *__pyx_temp[2] = {__pyx_t_1, __pyx_v_current_epoch};
          __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_8, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 399, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
          __Pyx_GOTREF(__pyx_t_2);
        } else
        #endif
        #if CYTHON_FAST_PYCCALL
        if (__Pyx_PyFastCFunction_Check(__pyx_t_8)) {
          PyObject *__pyx_temp[2] = {__pyx_t_1, __pyx_v_current_epoch};
          __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_8, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 399, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
          __Pyx_GOTREF(__pyx_t_2);
        } else
        #endif
        {
          __pyx_t_6 = PyTuple_New(1+1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 399, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_6);
          __Pyx_GIVEREF(__pyx_t_1); PyTuple_SET_ITEM(__pyx_t_6, 0, __pyx_t_1); __pyx_t_1 = NULL;
          __Pyx_INCREF(__pyx_v_current_epoch);
          __Pyx_GIVEREF(__pyx_v_current_epoch);
          PyTuple_SET_ITEM(__pyx_t_6, 0+1, __pyx_v_current_epoch);
          __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_8, __pyx_t_6, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 399, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_2);
          __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
        }
      }
      __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
      __pyx_t_8 = PyTuple_New(1); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 399, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_8);
      __Pyx_GIVEREF(__pyx_t_2);
      PyTuple_SET_ITEM(__pyx_t_8, 0, __pyx_t_2);
      __pyx_t_2 = 0;
      __pyx_t_2 = __Pyx_PyObject_Call(__pyx_builtin_print, __pyx_t_8, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 399, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":398
 * 
 *         for current_epoch in range(self.n_epochs):
 *             if self.verbose:             # <<<<<<<<<<<<<<
 *                 print(" processing epoch {}".format(current_epoch))
 *             for u, i, r in trainset.all_ratings():
 */
    }

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":400
 *             if self.verbose:
 *                 print(" processing epoch {}".format(current_epoch))
 *             for u, i, r in trainset.all_ratings():             # <<<<<<<<<<<<<<
 * 
 *                 # items rated by u. This is COSTLY
 */
    __pyx_t_8 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_all_ratings); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 400, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_8);
    __pyx_t_6 = NULL;
    if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_8))) {
      __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_8);
      if (likely(__pyx_t_6)) {
        PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_8);
        __Pyx_INCREF(__pyx_t_6);
        __Pyx_INCREF(function);
        __Pyx_DECREF_SET(__pyx_t_8, function);
      }
    }
    if (__pyx_t_6) {
      __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_8, __pyx_t_6); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 400, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
    } else {
      __pyx_t_2 = __Pyx_PyObject_CallNoArg(__pyx_t_8); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 400, __pyx_L1_error)
    }
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
    if (likely(PyList_CheckExact(__pyx_t_2)) || PyTuple_CheckExact(__pyx_t_2)) {
      __pyx_t_8 = __pyx_t_2; __Pyx_INCREF(__pyx_t_8); __pyx_t_22 = 0;
      __pyx_t_23 = NULL;
    } else {
      __pyx_t_22 = -1; __pyx_t_8 = PyObject_GetIter(__pyx_t_2); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 400, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_8);
      __pyx_t_23 = Py_TYPE(__pyx_t_8)->tp_iternext; if (unlikely(!__pyx_t_23)) __PYX_ERR(0, 400, __pyx_L1_error)
    }
    __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    for (;;) {
      if (likely(!__pyx_t_23)) {
        if (likely(PyList_CheckExact(__pyx_t_8))) {
          if (__pyx_t_22 >= PyList_GET_SIZE(__pyx_t_8)) break;
          #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
          __pyx_t_2 = PyList_GET_ITEM(__pyx_t_8, __pyx_t_22); __Pyx_INCREF(__pyx_t_2); __pyx_t_22++; if (unlikely(0 < 0)) __PYX_ERR(0, 400, __pyx_L1_error)
          #else
          __pyx_t_2 = PySequence_ITEM(__pyx_t_8, __pyx_t_22); __pyx_t_22++; if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 400, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_2);
          #endif
        } else {
          if (__pyx_t_22 >= PyTuple_GET_SIZE(__pyx_t_8)) break;
          #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
          __pyx_t_2 = PyTuple_GET_ITEM(__pyx_t_8, __pyx_t_22); __Pyx_INCREF(__pyx_t_2); __pyx_t_22++; if (unlikely(0 < 0)) __PYX_ERR(0, 400, __pyx_L1_error)
          #else
          __pyx_t_2 = PySequence_ITEM(__pyx_t_8, __pyx_t_22); __pyx_t_22++; if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 400, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_2);
          #endif
        }
      } else {
        __pyx_t_2 = __pyx_t_23(__pyx_t_8);
        if (unlikely(!__pyx_t_2)) {
          PyObject* exc_type = PyErr_Occurred();
          if (exc_type) {
            if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
            else __PYX_ERR(0, 400, __pyx_L1_error)
          }
          break;
        }
        __Pyx_GOTREF(__pyx_t_2);
      }
      if ((likely(PyTuple_CheckExact(__pyx_t_2))) || (PyList_CheckExact(__pyx_t_2))) {
        PyObject* sequence = __pyx_t_2;
        #if !CYTHON_COMPILING_IN_PYPY
        Py_ssize_t size = Py_SIZE(sequence);
        #else
        Py_ssize_t size = PySequence_Size(sequence);
        #endif
        if (unlikely(size != 3)) {
          if (size > 3) __Pyx_RaiseTooManyValuesError(3);
          else if (size >= 0) __Pyx_RaiseNeedMoreValuesError(size);
          __PYX_ERR(0, 400, __pyx_L1_error)
        }
        #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
        if (likely(PyTuple_CheckExact(sequence))) {
          __pyx_t_6 = PyTuple_GET_ITEM(sequence, 0); 
          __pyx_t_1 = PyTuple_GET_ITEM(sequence, 1); 
          __pyx_t_5 = PyTuple_GET_ITEM(sequence, 2); 
        } else {
          __pyx_t_6 = PyList_GET_ITEM(sequence, 0); 
          __pyx_t_1 = PyList_GET_ITEM(sequence, 1); 
          __pyx_t_5 = PyList_GET_ITEM(sequence, 2); 
        }
        __Pyx_INCREF(__pyx_t_6);
        __Pyx_INCREF(__pyx_t_1);
        __Pyx_INCREF(__pyx_t_5);
        #else
        __pyx_t_6 = PySequence_ITEM(sequence, 0); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 400, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_6);
        __pyx_t_1 = PySequence_ITEM(sequence, 1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 400, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        __pyx_t_5 = PySequence_ITEM(sequence, 2); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 400, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_5);
        #endif
        __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
      } else {
        Py_ssize_t index = -1;
        __pyx_t_4 = PyObject_GetIter(__pyx_t_2); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 400, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_4);
        __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
        __pyx_t_24 = Py_TYPE(__pyx_t_4)->tp_iternext;
        index = 0; __pyx_t_6 = __pyx_t_24(__pyx_t_4); if (unlikely(!__pyx_t_6)) goto __pyx_L8_unpacking_failed;
        __Pyx_GOTREF(__pyx_t_6);
        index = 1; __pyx_t_1 = __pyx_t_24(__pyx_t_4); if (unlikely(!__pyx_t_1)) goto __pyx_L8_unpacking_failed;
        __Pyx_GOTREF(__pyx_t_1);
        index = 2; __pyx_t_5 = __pyx_t_24(__pyx_t_4); if (unlikely(!__pyx_t_5)) goto __pyx_L8_unpacking_failed;
        __Pyx_GOTREF(__pyx_t_5);
        if (__Pyx_IternextUnpackEndCheck(__pyx_t_24(__pyx_t_4), 3) < 0) __PYX_ERR(0, 400, __pyx_L1_error)
        __pyx_t_24 = NULL;
        __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
        goto __pyx_L9_unpacking_done;
        __pyx_L8_unpacking_failed:;
        __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
        __pyx_t_24 = NULL;
        if (__Pyx_IterFinish() == 0) __Pyx_RaiseNeedMoreValuesError(index);
        __PYX_ERR(0, 400, __pyx_L1_error)
        __pyx_L9_unpacking_done:;
      }
      __pyx_t_7 = __Pyx_PyInt_As_int(__pyx_t_6); if (unlikely((__pyx_t_7 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 400, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      __pyx_t_25 = __Pyx_PyInt_As_int(__pyx_t_1); if (unlikely((__pyx_t_25 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 400, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_5); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 400, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
      __pyx_v_u = __pyx_t_7;
      __pyx_v_i = __pyx_t_25;
      __pyx_v_r = __pyx_t_3;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":403
 * 
 *                 # items rated by u. This is COSTLY
 *                 Iu = [j for (j, _) in trainset.ur[u]]             # <<<<<<<<<<<<<<
 *                 sqrt_Iu = np.sqrt(len(Iu))
 * 
 */
      __pyx_t_2 = PyList_New(0); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 403, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_ur); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 403, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_5);
      __pyx_t_1 = __Pyx_GetItemInt(__pyx_t_5, __pyx_v_u, int, 1, __Pyx_PyInt_From_int, 0, 1, 1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 403, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
      if (likely(PyList_CheckExact(__pyx_t_1)) || PyTuple_CheckExact(__pyx_t_1)) {
        __pyx_t_5 = __pyx_t_1; __Pyx_INCREF(__pyx_t_5); __pyx_t_26 = 0;
        __pyx_t_27 = NULL;
      } else {
        __pyx_t_26 = -1; __pyx_t_5 = PyObject_GetIter(__pyx_t_1); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 403, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_5);
        __pyx_t_27 = Py_TYPE(__pyx_t_5)->tp_iternext; if (unlikely(!__pyx_t_27)) __PYX_ERR(0, 403, __pyx_L1_error)
      }
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      for (;;) {
        if (likely(!__pyx_t_27)) {
          if (likely(PyList_CheckExact(__pyx_t_5))) {
            if (__pyx_t_26 >= PyList_GET_SIZE(__pyx_t_5)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_1 = PyList_GET_ITEM(__pyx_t_5, __pyx_t_26); __Pyx_INCREF(__pyx_t_1); __pyx_t_26++; if (unlikely(0 < 0)) __PYX_ERR(0, 403, __pyx_L1_error)
            #else
            __pyx_t_1 = PySequence_ITEM(__pyx_t_5, __pyx_t_26); __pyx_t_26++; if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 403, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_1);
            #endif
          } else {
            if (__pyx_t_26 >= PyTuple_GET_SIZE(__pyx_t_5)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_1 = PyTuple_GET_ITEM(__pyx_t_5, __pyx_t_26); __Pyx_INCREF(__pyx_t_1); __pyx_t_26++; if (unlikely(0 < 0)) __PYX_ERR(0, 403, __pyx_L1_error)
            #else
            __pyx_t_1 = PySequence_ITEM(__pyx_t_5, __pyx_t_26); __pyx_t_26++; if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 403, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_1);
            #endif
          }
        } else {
          __pyx_t_1 = __pyx_t_27(__pyx_t_5);
          if (unlikely(!__pyx_t_1)) {
            PyObject* exc_type = PyErr_Occurred();
            if (exc_type) {
              if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
              else __PYX_ERR(0, 403, __pyx_L1_error)
            }
            break;
          }
          __Pyx_GOTREF(__pyx_t_1);
        }
        if ((likely(PyTuple_CheckExact(__pyx_t_1))) || (PyList_CheckExact(__pyx_t_1))) {
          PyObject* sequence = __pyx_t_1;
          #if !CYTHON_COMPILING_IN_PYPY
          Py_ssize_t size = Py_SIZE(sequence);
          #else
          Py_ssize_t size = PySequence_Size(sequence);
          #endif
          if (unlikely(size != 2)) {
            if (size > 2) __Pyx_RaiseTooManyValuesError(2);
            else if (size >= 0) __Pyx_RaiseNeedMoreValuesError(size);
            __PYX_ERR(0, 403, __pyx_L1_error)
          }
          #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
          if (likely(PyTuple_CheckExact(sequence))) {
            __pyx_t_6 = PyTuple_GET_ITEM(sequence, 0); 
            __pyx_t_4 = PyTuple_GET_ITEM(sequence, 1); 
          } else {
            __pyx_t_6 = PyList_GET_ITEM(sequence, 0); 
            __pyx_t_4 = PyList_GET_ITEM(sequence, 1); 
          }
          __Pyx_INCREF(__pyx_t_6);
          __Pyx_INCREF(__pyx_t_4);
          #else
          __pyx_t_6 = PySequence_ITEM(sequence, 0); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 403, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_6);
          __pyx_t_4 = PySequence_ITEM(sequence, 1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 403, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_4);
          #endif
          __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
        } else {
          Py_ssize_t index = -1;
          __pyx_t_28 = PyObject_GetIter(__pyx_t_1); if (unlikely(!__pyx_t_28)) __PYX_ERR(0, 403, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_28);
          __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
          __pyx_t_24 = Py_TYPE(__pyx_t_28)->tp_iternext;
          index = 0; __pyx_t_6 = __pyx_t_24(__pyx_t_28); if (unlikely(!__pyx_t_6)) goto __pyx_L12_unpacking_failed;
          __Pyx_GOTREF(__pyx_t_6);
          index = 1; __pyx_t_4 = __pyx_t_24(__pyx_t_28); if (unlikely(!__pyx_t_4)) goto __pyx_L12_unpacking_failed;
          __Pyx_GOTREF(__pyx_t_4);
          if (__Pyx_IternextUnpackEndCheck(__pyx_t_24(__pyx_t_28), 2) < 0) __PYX_ERR(0, 403, __pyx_L1_error)
          __pyx_t_24 = NULL;
          __Pyx_DECREF(__pyx_t_28); __pyx_t_28 = 0;
          goto __pyx_L13_unpacking_done;
          __pyx_L12_unpacking_failed:;
          __Pyx_DECREF(__pyx_t_28); __pyx_t_28 = 0;
          __pyx_t_24 = NULL;
          if (__Pyx_IterFinish() == 0) __Pyx_RaiseNeedMoreValuesError(index);
          __PYX_ERR(0, 403, __pyx_L1_error)
          __pyx_L13_unpacking_done:;
        }
        __pyx_t_25 = __Pyx_PyInt_As_int(__pyx_t_6); if (unlikely((__pyx_t_25 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 403, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
        __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_4); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 403, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
        __pyx_v_j = __pyx_t_25;
        __pyx_v__ = __pyx_t_3;
        __pyx_t_1 = __Pyx_PyInt_From_int(__pyx_v_j); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 403, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        if (unlikely(__Pyx_ListComp_Append(__pyx_t_2, (PyObject*)__pyx_t_1))) __PYX_ERR(0, 403, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      }
      __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
      __Pyx_XDECREF_SET(__pyx_v_Iu, ((PyObject*)__pyx_t_2));
      __pyx_t_2 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":404
 *                 # items rated by u. This is COSTLY
 *                 Iu = [j for (j, _) in trainset.ur[u]]
 *                 sqrt_Iu = np.sqrt(len(Iu))             # <<<<<<<<<<<<<<
 * 
 *                 # compute user implicit feedback
 */
      __pyx_t_5 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 404, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_5);
      __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_t_5, __pyx_n_s_sqrt); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 404, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
      __pyx_t_26 = PyList_GET_SIZE(__pyx_v_Iu); if (unlikely(__pyx_t_26 == -1)) __PYX_ERR(0, 404, __pyx_L1_error)
      __pyx_t_5 = PyInt_FromSsize_t(__pyx_t_26); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 404, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_5);
      __pyx_t_4 = NULL;
      if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_1))) {
        __pyx_t_4 = PyMethod_GET_SELF(__pyx_t_1);
        if (likely(__pyx_t_4)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_1);
          __Pyx_INCREF(__pyx_t_4);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_1, function);
        }
      }
      if (!__pyx_t_4) {
        __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_1, __pyx_t_5); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 404, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        __Pyx_GOTREF(__pyx_t_2);
      } else {
        #if CYTHON_FAST_PYCALL
        if (PyFunction_Check(__pyx_t_1)) {
          PyObject *__pyx_temp[2] = {__pyx_t_4, __pyx_t_5};
          __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_1, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 404, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
          __Pyx_GOTREF(__pyx_t_2);
          __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        } else
        #endif
        #if CYTHON_FAST_PYCCALL
        if (__Pyx_PyFastCFunction_Check(__pyx_t_1)) {
          PyObject *__pyx_temp[2] = {__pyx_t_4, __pyx_t_5};
          __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_1, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 404, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
          __Pyx_GOTREF(__pyx_t_2);
          __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        } else
        #endif
        {
          __pyx_t_6 = PyTuple_New(1+1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 404, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_6);
          __Pyx_GIVEREF(__pyx_t_4); PyTuple_SET_ITEM(__pyx_t_6, 0, __pyx_t_4); __pyx_t_4 = NULL;
          __Pyx_GIVEREF(__pyx_t_5);
          PyTuple_SET_ITEM(__pyx_t_6, 0+1, __pyx_t_5);
          __pyx_t_5 = 0;
          __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_1, __pyx_t_6, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 404, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_2);
          __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
        }
      }
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __pyx_t_3 = __pyx_PyFloat_AsDouble(__pyx_t_2); if (unlikely((__pyx_t_3 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 404, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
      __pyx_v_sqrt_Iu = __pyx_t_3;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":407
 * 
 *                 # compute user implicit feedback
 *                 u_impl_fdb = np.zeros(self.n_factors, np.double)             # <<<<<<<<<<<<<<
 *                 for j in Iu:
 *                     for f in range(self.n_factors):
 */
      __pyx_t_1 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 407, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_zeros); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 407, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_6);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 407, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __pyx_t_5 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 407, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_5);
      __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_5, __pyx_n_s_double); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 407, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
      __pyx_t_5 = NULL;
      __pyx_t_25 = 0;
      if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_6))) {
        __pyx_t_5 = PyMethod_GET_SELF(__pyx_t_6);
        if (likely(__pyx_t_5)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_6);
          __Pyx_INCREF(__pyx_t_5);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_6, function);
          __pyx_t_25 = 1;
        }
      }
      #if CYTHON_FAST_PYCALL
      if (PyFunction_Check(__pyx_t_6)) {
        PyObject *__pyx_temp[3] = {__pyx_t_5, __pyx_t_1, __pyx_t_4};
        __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_6, __pyx_temp+1-__pyx_t_25, 2+__pyx_t_25); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 407, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
        __Pyx_GOTREF(__pyx_t_2);
        __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
        __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      } else
      #endif
      #if CYTHON_FAST_PYCCALL
      if (__Pyx_PyFastCFunction_Check(__pyx_t_6)) {
        PyObject *__pyx_temp[3] = {__pyx_t_5, __pyx_t_1, __pyx_t_4};
        __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_6, __pyx_temp+1-__pyx_t_25, 2+__pyx_t_25); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 407, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
        __Pyx_GOTREF(__pyx_t_2);
        __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
        __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      } else
      #endif
      {
        __pyx_t_28 = PyTuple_New(2+__pyx_t_25); if (unlikely(!__pyx_t_28)) __PYX_ERR(0, 407, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_28);
        if (__pyx_t_5) {
          __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_28, 0, __pyx_t_5); __pyx_t_5 = NULL;
        }
        __Pyx_GIVEREF(__pyx_t_1);
        PyTuple_SET_ITEM(__pyx_t_28, 0+__pyx_t_25, __pyx_t_1);
        __Pyx_GIVEREF(__pyx_t_4);
        PyTuple_SET_ITEM(__pyx_t_28, 1+__pyx_t_25, __pyx_t_4);
        __pyx_t_1 = 0;
        __pyx_t_4 = 0;
        __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_6, __pyx_t_28, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 407, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_2);
        __Pyx_DECREF(__pyx_t_28); __pyx_t_28 = 0;
      }
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      if (!(likely(((__pyx_t_2) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_2, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 407, __pyx_L1_error)
      __pyx_t_18 = ((PyArrayObject *)__pyx_t_2);
      {
        __Pyx_BufFmt_StackElem __pyx_stack[1];
        __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer);
        __pyx_t_25 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer, (PyObject*)__pyx_t_18, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack);
        if (unlikely(__pyx_t_25 < 0)) {
          PyErr_Fetch(&__pyx_t_10, &__pyx_t_11, &__pyx_t_12);
          if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer, (PyObject*)__pyx_v_u_impl_fdb, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack) == -1)) {
            Py_XDECREF(__pyx_t_10); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_12);
            __Pyx_RaiseBufferFallbackError();
          } else {
            PyErr_Restore(__pyx_t_10, __pyx_t_11, __pyx_t_12);
          }
          __pyx_t_10 = __pyx_t_11 = __pyx_t_12 = 0;
        }
        __pyx_pybuffernd_u_impl_fdb.diminfo[0].strides = __pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_u_impl_fdb.diminfo[0].shape = __pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer.shape[0];
        if (unlikely(__pyx_t_25 < 0)) __PYX_ERR(0, 407, __pyx_L1_error)
      }
      __pyx_t_18 = 0;
      __Pyx_DECREF_SET(__pyx_v_u_impl_fdb, ((PyArrayObject *)__pyx_t_2));
      __pyx_t_2 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":408
 *                 # compute user implicit feedback
 *                 u_impl_fdb = np.zeros(self.n_factors, np.double)
 *                 for j in Iu:             # <<<<<<<<<<<<<<
 *                     for f in range(self.n_factors):
 *                         u_impl_fdb[f] += yj[j, f] / sqrt_Iu
 */
      __pyx_t_2 = __pyx_v_Iu; __Pyx_INCREF(__pyx_t_2); __pyx_t_26 = 0;
      for (;;) {
        if (__pyx_t_26 >= PyList_GET_SIZE(__pyx_t_2)) break;
        #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
        __pyx_t_6 = PyList_GET_ITEM(__pyx_t_2, __pyx_t_26); __Pyx_INCREF(__pyx_t_6); __pyx_t_26++; if (unlikely(0 < 0)) __PYX_ERR(0, 408, __pyx_L1_error)
        #else
        __pyx_t_6 = PySequence_ITEM(__pyx_t_2, __pyx_t_26); __pyx_t_26++; if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 408, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_6);
        #endif
        __pyx_t_25 = __Pyx_PyInt_As_int(__pyx_t_6); if (unlikely((__pyx_t_25 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 408, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
        __pyx_v_j = __pyx_t_25;

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":409
 *                 u_impl_fdb = np.zeros(self.n_factors, np.double)
 *                 for j in Iu:
 *                     for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                         u_impl_fdb[f] += yj[j, f] / sqrt_Iu
 * 
 */
        __pyx_t_28 = __Pyx_GetModuleGlobalName(__pyx_n_s_range); if (unlikely(!__pyx_t_28)) __PYX_ERR(0, 409, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_28);
        __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 409, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_4);
        __pyx_t_1 = NULL;
        if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_28))) {
          __pyx_t_1 = PyMethod_GET_SELF(__pyx_t_28);
          if (likely(__pyx_t_1)) {
            PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_28);
            __Pyx_INCREF(__pyx_t_1);
            __Pyx_INCREF(function);
            __Pyx_DECREF_SET(__pyx_t_28, function);
          }
        }
        if (!__pyx_t_1) {
          __pyx_t_6 = __Pyx_PyObject_CallOneArg(__pyx_t_28, __pyx_t_4); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 409, __pyx_L1_error)
          __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
          __Pyx_GOTREF(__pyx_t_6);
        } else {
          #if CYTHON_FAST_PYCALL
          if (PyFunction_Check(__pyx_t_28)) {
            PyObject *__pyx_temp[2] = {__pyx_t_1, __pyx_t_4};
            __pyx_t_6 = __Pyx_PyFunction_FastCall(__pyx_t_28, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 409, __pyx_L1_error)
            __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
            __Pyx_GOTREF(__pyx_t_6);
            __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
          } else
          #endif
          #if CYTHON_FAST_PYCCALL
          if (__Pyx_PyFastCFunction_Check(__pyx_t_28)) {
            PyObject *__pyx_temp[2] = {__pyx_t_1, __pyx_t_4};
            __pyx_t_6 = __Pyx_PyCFunction_FastCall(__pyx_t_28, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 409, __pyx_L1_error)
            __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
            __Pyx_GOTREF(__pyx_t_6);
            __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
          } else
          #endif
          {
            __pyx_t_5 = PyTuple_New(1+1); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 409, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_5);
            __Pyx_GIVEREF(__pyx_t_1); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_1); __pyx_t_1 = NULL;
            __Pyx_GIVEREF(__pyx_t_4);
            PyTuple_SET_ITEM(__pyx_t_5, 0+1, __pyx_t_4);
            __pyx_t_4 = 0;
            __pyx_t_6 = __Pyx_PyObject_Call(__pyx_t_28, __pyx_t_5, NULL); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 409, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_6);
            __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
          }
        }
        __Pyx_DECREF(__pyx_t_28); __pyx_t_28 = 0;
        if (likely(PyList_CheckExact(__pyx_t_6)) || PyTuple_CheckExact(__pyx_t_6)) {
          __pyx_t_28 = __pyx_t_6; __Pyx_INCREF(__pyx_t_28); __pyx_t_29 = 0;
          __pyx_t_27 = NULL;
        } else {
          __pyx_t_29 = -1; __pyx_t_28 = PyObject_GetIter(__pyx_t_6); if (unlikely(!__pyx_t_28)) __PYX_ERR(0, 409, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_28);
          __pyx_t_27 = Py_TYPE(__pyx_t_28)->tp_iternext; if (unlikely(!__pyx_t_27)) __PYX_ERR(0, 409, __pyx_L1_error)
        }
        __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
        for (;;) {
          if (likely(!__pyx_t_27)) {
            if (likely(PyList_CheckExact(__pyx_t_28))) {
              if (__pyx_t_29 >= PyList_GET_SIZE(__pyx_t_28)) break;
              #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
              __pyx_t_6 = PyList_GET_ITEM(__pyx_t_28, __pyx_t_29); __Pyx_INCREF(__pyx_t_6); __pyx_t_29++; if (unlikely(0 < 0)) __PYX_ERR(0, 409, __pyx_L1_error)
              #else
              __pyx_t_6 = PySequence_ITEM(__pyx_t_28, __pyx_t_29); __pyx_t_29++; if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 409, __pyx_L1_error)
              __Pyx_GOTREF(__pyx_t_6);
              #endif
            } else {
              if (__pyx_t_29 >= PyTuple_GET_SIZE(__pyx_t_28)) break;
              #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
              __pyx_t_6 = PyTuple_GET_ITEM(__pyx_t_28, __pyx_t_29); __Pyx_INCREF(__pyx_t_6); __pyx_t_29++; if (unlikely(0 < 0)) __PYX_ERR(0, 409, __pyx_L1_error)
              #else
              __pyx_t_6 = PySequence_ITEM(__pyx_t_28, __pyx_t_29); __pyx_t_29++; if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 409, __pyx_L1_error)
              __Pyx_GOTREF(__pyx_t_6);
              #endif
            }
          } else {
            __pyx_t_6 = __pyx_t_27(__pyx_t_28);
            if (unlikely(!__pyx_t_6)) {
              PyObject* exc_type = PyErr_Occurred();
              if (exc_type) {
                if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
                else __PYX_ERR(0, 409, __pyx_L1_error)
              }
              break;
            }
            __Pyx_GOTREF(__pyx_t_6);
          }
          __pyx_t_25 = __Pyx_PyInt_As_int(__pyx_t_6); if (unlikely((__pyx_t_25 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 409, __pyx_L1_error)
          __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
          __pyx_v_f = __pyx_t_25;

          /* "surprise/prediction_algorithms/matrix_factorization.pyx":410
 *                 for j in Iu:
 *                     for f in range(self.n_factors):
 *                         u_impl_fdb[f] += yj[j, f] / sqrt_Iu             # <<<<<<<<<<<<<<
 * 
 *                 # compute current error
 */
          __pyx_t_30 = __pyx_v_j;
          __pyx_t_31 = __pyx_v_f;
          __pyx_t_25 = -1;
          if (__pyx_t_30 < 0) {
            __pyx_t_30 += __pyx_pybuffernd_yj.diminfo[0].shape;
            if (unlikely(__pyx_t_30 < 0)) __pyx_t_25 = 0;
          } else if (unlikely(__pyx_t_30 >= __pyx_pybuffernd_yj.diminfo[0].shape)) __pyx_t_25 = 0;
          if (__pyx_t_31 < 0) {
            __pyx_t_31 += __pyx_pybuffernd_yj.diminfo[1].shape;
            if (unlikely(__pyx_t_31 < 0)) __pyx_t_25 = 1;
          } else if (unlikely(__pyx_t_31 >= __pyx_pybuffernd_yj.diminfo[1].shape)) __pyx_t_25 = 1;
          if (unlikely(__pyx_t_25 != -1)) {
            __Pyx_RaiseBufferIndexError(__pyx_t_25);
            __PYX_ERR(0, 410, __pyx_L1_error)
          }
          __pyx_t_32 = (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_yj.rcbuffer->pybuffer.buf, __pyx_t_30, __pyx_pybuffernd_yj.diminfo[0].strides, __pyx_t_31, __pyx_pybuffernd_yj.diminfo[1].strides));
          if (unlikely(__pyx_v_sqrt_Iu == 0)) {
            PyErr_SetString(PyExc_ZeroDivisionError, "float division");
            __PYX_ERR(0, 410, __pyx_L1_error)
          }
          __pyx_t_33 = __pyx_v_f;
          __pyx_t_25 = -1;
          if (__pyx_t_33 < 0) {
            __pyx_t_33 += __pyx_pybuffernd_u_impl_fdb.diminfo[0].shape;
            if (unlikely(__pyx_t_33 < 0)) __pyx_t_25 = 0;
          } else if (unlikely(__pyx_t_33 >= __pyx_pybuffernd_u_impl_fdb.diminfo[0].shape)) __pyx_t_25 = 0;
          if (unlikely(__pyx_t_25 != -1)) {
            __Pyx_RaiseBufferIndexError(__pyx_t_25);
            __PYX_ERR(0, 410, __pyx_L1_error)
          }
          *__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer.buf, __pyx_t_33, __pyx_pybuffernd_u_impl_fdb.diminfo[0].strides) += (__pyx_t_32 / ((__pyx_t_5numpy_double_t)__pyx_v_sqrt_Iu));

          /* "surprise/prediction_algorithms/matrix_factorization.pyx":409
 *                 u_impl_fdb = np.zeros(self.n_factors, np.double)
 *                 for j in Iu:
 *                     for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                         u_impl_fdb[f] += yj[j, f] / sqrt_Iu
 * 
 */
        }
        __Pyx_DECREF(__pyx_t_28); __pyx_t_28 = 0;

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":408
 *                 # compute user implicit feedback
 *                 u_impl_fdb = np.zeros(self.n_factors, np.double)
 *                 for j in Iu:             # <<<<<<<<<<<<<<
 *                     for f in range(self.n_factors):
 *                         u_impl_fdb[f] += yj[j, f] / sqrt_Iu
 */
      }
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":413
 * 
 *                 # compute current error
 *                 dot = 0  # <q_i, (p_u + sum_{jin Iu} y_j / sqrt{Iu}>             # <<<<<<<<<<<<<<
 *                 for f in range(self.n_factors):
 *                     dot += qi[i, f] * (pu[u, f] + u_impl_fdb[f])
 */
      __pyx_v_dot = 0.0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":414
 *                 # compute current error
 *                 dot = 0  # <q_i, (p_u + sum_{jin Iu} y_j / sqrt{Iu}>
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     dot += qi[i, f] * (pu[u, f] + u_impl_fdb[f])
 * 
 */
      __pyx_t_28 = __Pyx_GetModuleGlobalName(__pyx_n_s_range); if (unlikely(!__pyx_t_28)) __PYX_ERR(0, 414, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_28);
      __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 414, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_6);
      __pyx_t_5 = NULL;
      if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_28))) {
        __pyx_t_5 = PyMethod_GET_SELF(__pyx_t_28);
        if (likely(__pyx_t_5)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_28);
          __Pyx_INCREF(__pyx_t_5);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_28, function);
        }
      }
      if (!__pyx_t_5) {
        __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_28, __pyx_t_6); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 414, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
        __Pyx_GOTREF(__pyx_t_2);
      } else {
        #if CYTHON_FAST_PYCALL
        if (PyFunction_Check(__pyx_t_28)) {
          PyObject *__pyx_temp[2] = {__pyx_t_5, __pyx_t_6};
          __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_28, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 414, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
          __Pyx_GOTREF(__pyx_t_2);
          __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
        } else
        #endif
        #if CYTHON_FAST_PYCCALL
        if (__Pyx_PyFastCFunction_Check(__pyx_t_28)) {
          PyObject *__pyx_temp[2] = {__pyx_t_5, __pyx_t_6};
          __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_28, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 414, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
          __Pyx_GOTREF(__pyx_t_2);
          __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
        } else
        #endif
        {
          __pyx_t_4 = PyTuple_New(1+1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 414, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_4);
          __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_4, 0, __pyx_t_5); __pyx_t_5 = NULL;
          __Pyx_GIVEREF(__pyx_t_6);
          PyTuple_SET_ITEM(__pyx_t_4, 0+1, __pyx_t_6);
          __pyx_t_6 = 0;
          __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_28, __pyx_t_4, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 414, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_2);
          __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
        }
      }
      __Pyx_DECREF(__pyx_t_28); __pyx_t_28 = 0;
      if (likely(PyList_CheckExact(__pyx_t_2)) || PyTuple_CheckExact(__pyx_t_2)) {
        __pyx_t_28 = __pyx_t_2; __Pyx_INCREF(__pyx_t_28); __pyx_t_26 = 0;
        __pyx_t_27 = NULL;
      } else {
        __pyx_t_26 = -1; __pyx_t_28 = PyObject_GetIter(__pyx_t_2); if (unlikely(!__pyx_t_28)) __PYX_ERR(0, 414, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_28);
        __pyx_t_27 = Py_TYPE(__pyx_t_28)->tp_iternext; if (unlikely(!__pyx_t_27)) __PYX_ERR(0, 414, __pyx_L1_error)
      }
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
      for (;;) {
        if (likely(!__pyx_t_27)) {
          if (likely(PyList_CheckExact(__pyx_t_28))) {
            if (__pyx_t_26 >= PyList_GET_SIZE(__pyx_t_28)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_2 = PyList_GET_ITEM(__pyx_t_28, __pyx_t_26); __Pyx_INCREF(__pyx_t_2); __pyx_t_26++; if (unlikely(0 < 0)) __PYX_ERR(0, 414, __pyx_L1_error)
            #else
            __pyx_t_2 = PySequence_ITEM(__pyx_t_28, __pyx_t_26); __pyx_t_26++; if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 414, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_2);
            #endif
          } else {
            if (__pyx_t_26 >= PyTuple_GET_SIZE(__pyx_t_28)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_2 = PyTuple_GET_ITEM(__pyx_t_28, __pyx_t_26); __Pyx_INCREF(__pyx_t_2); __pyx_t_26++; if (unlikely(0 < 0)) __PYX_ERR(0, 414, __pyx_L1_error)
            #else
            __pyx_t_2 = PySequence_ITEM(__pyx_t_28, __pyx_t_26); __pyx_t_26++; if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 414, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_2);
            #endif
          }
        } else {
          __pyx_t_2 = __pyx_t_27(__pyx_t_28);
          if (unlikely(!__pyx_t_2)) {
            PyObject* exc_type = PyErr_Occurred();
            if (exc_type) {
              if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
              else __PYX_ERR(0, 414, __pyx_L1_error)
            }
            break;
          }
          __Pyx_GOTREF(__pyx_t_2);
        }
        __pyx_t_25 = __Pyx_PyInt_As_int(__pyx_t_2); if (unlikely((__pyx_t_25 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 414, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
        __pyx_v_f = __pyx_t_25;

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":415
 *                 dot = 0  # <q_i, (p_u + sum_{jin Iu} y_j / sqrt{Iu}>
 *                 for f in range(self.n_factors):
 *                     dot += qi[i, f] * (pu[u, f] + u_impl_fdb[f])             # <<<<<<<<<<<<<<
 * 
 *                 err = r - (global_mean + bu[u] + bi[i] + dot)
 */
        __pyx_t_34 = __pyx_v_i;
        __pyx_t_35 = __pyx_v_f;
        __pyx_t_25 = -1;
        if (__pyx_t_34 < 0) {
          __pyx_t_34 += __pyx_pybuffernd_qi.diminfo[0].shape;
          if (unlikely(__pyx_t_34 < 0)) __pyx_t_25 = 0;
        } else if (unlikely(__pyx_t_34 >= __pyx_pybuffernd_qi.diminfo[0].shape)) __pyx_t_25 = 0;
        if (__pyx_t_35 < 0) {
          __pyx_t_35 += __pyx_pybuffernd_qi.diminfo[1].shape;
          if (unlikely(__pyx_t_35 < 0)) __pyx_t_25 = 1;
        } else if (unlikely(__pyx_t_35 >= __pyx_pybuffernd_qi.diminfo[1].shape)) __pyx_t_25 = 1;
        if (unlikely(__pyx_t_25 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_25);
          __PYX_ERR(0, 415, __pyx_L1_error)
        }
        __pyx_t_36 = __pyx_v_u;
        __pyx_t_37 = __pyx_v_f;
        __pyx_t_25 = -1;
        if (__pyx_t_36 < 0) {
          __pyx_t_36 += __pyx_pybuffernd_pu.diminfo[0].shape;
          if (unlikely(__pyx_t_36 < 0)) __pyx_t_25 = 0;
        } else if (unlikely(__pyx_t_36 >= __pyx_pybuffernd_pu.diminfo[0].shape)) __pyx_t_25 = 0;
        if (__pyx_t_37 < 0) {
          __pyx_t_37 += __pyx_pybuffernd_pu.diminfo[1].shape;
          if (unlikely(__pyx_t_37 < 0)) __pyx_t_25 = 1;
        } else if (unlikely(__pyx_t_37 >= __pyx_pybuffernd_pu.diminfo[1].shape)) __pyx_t_25 = 1;
        if (unlikely(__pyx_t_25 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_25);
          __PYX_ERR(0, 415, __pyx_L1_error)
        }
        __pyx_t_38 = __pyx_v_f;
        __pyx_t_25 = -1;
        if (__pyx_t_38 < 0) {
          __pyx_t_38 += __pyx_pybuffernd_u_impl_fdb.diminfo[0].shape;
          if (unlikely(__pyx_t_38 < 0)) __pyx_t_25 = 0;
        } else if (unlikely(__pyx_t_38 >= __pyx_pybuffernd_u_impl_fdb.diminfo[0].shape)) __pyx_t_25 = 0;
        if (unlikely(__pyx_t_25 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_25);
          __PYX_ERR(0, 415, __pyx_L1_error)
        }
        __pyx_v_dot = (__pyx_v_dot + ((*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_qi.rcbuffer->pybuffer.buf, __pyx_t_34, __pyx_pybuffernd_qi.diminfo[0].strides, __pyx_t_35, __pyx_pybuffernd_qi.diminfo[1].strides)) * ((*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_pu.rcbuffer->pybuffer.buf, __pyx_t_36, __pyx_pybuffernd_pu.diminfo[0].strides, __pyx_t_37, __pyx_pybuffernd_pu.diminfo[1].strides)) + (*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer.buf, __pyx_t_38, __pyx_pybuffernd_u_impl_fdb.diminfo[0].strides)))));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":414
 *                 # compute current error
 *                 dot = 0  # <q_i, (p_u + sum_{jin Iu} y_j / sqrt{Iu}>
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     dot += qi[i, f] * (pu[u, f] + u_impl_fdb[f])
 * 
 */
      }
      __Pyx_DECREF(__pyx_t_28); __pyx_t_28 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":417
 *                     dot += qi[i, f] * (pu[u, f] + u_impl_fdb[f])
 * 
 *                 err = r - (global_mean + bu[u] + bi[i] + dot)             # <<<<<<<<<<<<<<
 * 
 *                 # update biases
 */
      __pyx_t_39 = __pyx_v_u;
      __pyx_t_25 = -1;
      if (__pyx_t_39 < 0) {
        __pyx_t_39 += __pyx_pybuffernd_bu.diminfo[0].shape;
        if (unlikely(__pyx_t_39 < 0)) __pyx_t_25 = 0;
      } else if (unlikely(__pyx_t_39 >= __pyx_pybuffernd_bu.diminfo[0].shape)) __pyx_t_25 = 0;
      if (unlikely(__pyx_t_25 != -1)) {
        __Pyx_RaiseBufferIndexError(__pyx_t_25);
        __PYX_ERR(0, 417, __pyx_L1_error)
      }
      __pyx_t_40 = __pyx_v_i;
      __pyx_t_25 = -1;
      if (__pyx_t_40 < 0) {
        __pyx_t_40 += __pyx_pybuffernd_bi.diminfo[0].shape;
        if (unlikely(__pyx_t_40 < 0)) __pyx_t_25 = 0;
      } else if (unlikely(__pyx_t_40 >= __pyx_pybuffernd_bi.diminfo[0].shape)) __pyx_t_25 = 0;
      if (unlikely(__pyx_t_25 != -1)) {
        __Pyx_RaiseBufferIndexError(__pyx_t_25);
        __PYX_ERR(0, 417, __pyx_L1_error)
      }
      __pyx_v_err = (__pyx_v_r - (((__pyx_v_global_mean + (*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bu.rcbuffer->pybuffer.buf, __pyx_t_39, __pyx_pybuffernd_bu.diminfo[0].strides))) + (*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bi.rcbuffer->pybuffer.buf, __pyx_t_40, __pyx_pybuffernd_bi.diminfo[0].strides))) + __pyx_v_dot));

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":420
 * 
 *                 # update biases
 *                 bu[u] += lr_bu * (err - reg_bu * bu[u])             # <<<<<<<<<<<<<<
 *                 bi[i] += lr_bi * (err - reg_bi * bi[i])
 * 
 */
      __pyx_t_41 = __pyx_v_u;
      __pyx_t_25 = -1;
      if (__pyx_t_41 < 0) {
        __pyx_t_41 += __pyx_pybuffernd_bu.diminfo[0].shape;
        if (unlikely(__pyx_t_41 < 0)) __pyx_t_25 = 0;
      } else if (unlikely(__pyx_t_41 >= __pyx_pybuffernd_bu.diminfo[0].shape)) __pyx_t_25 = 0;
      if (unlikely(__pyx_t_25 != -1)) {
        __Pyx_RaiseBufferIndexError(__pyx_t_25);
        __PYX_ERR(0, 420, __pyx_L1_error)
      }
      __pyx_t_42 = __pyx_v_u;
      __pyx_t_25 = -1;
      if (__pyx_t_42 < 0) {
        __pyx_t_42 += __pyx_pybuffernd_bu.diminfo[0].shape;
        if (unlikely(__pyx_t_42 < 0)) __pyx_t_25 = 0;
      } else if (unlikely(__pyx_t_42 >= __pyx_pybuffernd_bu.diminfo[0].shape)) __pyx_t_25 = 0;
      if (unlikely(__pyx_t_25 != -1)) {
        __Pyx_RaiseBufferIndexError(__pyx_t_25);
        __PYX_ERR(0, 420, __pyx_L1_error)
      }
      *__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bu.rcbuffer->pybuffer.buf, __pyx_t_42, __pyx_pybuffernd_bu.diminfo[0].strides) += (__pyx_v_lr_bu * (__pyx_v_err - (__pyx_v_reg_bu * (*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bu.rcbuffer->pybuffer.buf, __pyx_t_41, __pyx_pybuffernd_bu.diminfo[0].strides)))));

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":421
 *                 # update biases
 *                 bu[u] += lr_bu * (err - reg_bu * bu[u])
 *                 bi[i] += lr_bi * (err - reg_bi * bi[i])             # <<<<<<<<<<<<<<
 * 
 *                 # update factors
 */
      __pyx_t_43 = __pyx_v_i;
      __pyx_t_25 = -1;
      if (__pyx_t_43 < 0) {
        __pyx_t_43 += __pyx_pybuffernd_bi.diminfo[0].shape;
        if (unlikely(__pyx_t_43 < 0)) __pyx_t_25 = 0;
      } else if (unlikely(__pyx_t_43 >= __pyx_pybuffernd_bi.diminfo[0].shape)) __pyx_t_25 = 0;
      if (unlikely(__pyx_t_25 != -1)) {
        __Pyx_RaiseBufferIndexError(__pyx_t_25);
        __PYX_ERR(0, 421, __pyx_L1_error)
      }
      __pyx_t_44 = __pyx_v_i;
      __pyx_t_25 = -1;
      if (__pyx_t_44 < 0) {
        __pyx_t_44 += __pyx_pybuffernd_bi.diminfo[0].shape;
        if (unlikely(__pyx_t_44 < 0)) __pyx_t_25 = 0;
      } else if (unlikely(__pyx_t_44 >= __pyx_pybuffernd_bi.diminfo[0].shape)) __pyx_t_25 = 0;
      if (unlikely(__pyx_t_25 != -1)) {
        __Pyx_RaiseBufferIndexError(__pyx_t_25);
        __PYX_ERR(0, 421, __pyx_L1_error)
      }
      *__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bi.rcbuffer->pybuffer.buf, __pyx_t_44, __pyx_pybuffernd_bi.diminfo[0].strides) += (__pyx_v_lr_bi * (__pyx_v_err - (__pyx_v_reg_bi * (*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bi.rcbuffer->pybuffer.buf, __pyx_t_43, __pyx_pybuffernd_bi.diminfo[0].strides)))));

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":424
 * 
 *                 # update factors
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     puf = pu[u, f]
 *                     qif = qi[i, f]
 */
      __pyx_t_2 = __Pyx_GetModuleGlobalName(__pyx_n_s_range); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 424, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 424, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_6 = NULL;
      if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_2))) {
        __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_2);
        if (likely(__pyx_t_6)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_2);
          __Pyx_INCREF(__pyx_t_6);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_2, function);
        }
      }
      if (!__pyx_t_6) {
        __pyx_t_28 = __Pyx_PyObject_CallOneArg(__pyx_t_2, __pyx_t_4); if (unlikely(!__pyx_t_28)) __PYX_ERR(0, 424, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
        __Pyx_GOTREF(__pyx_t_28);
      } else {
        #if CYTHON_FAST_PYCALL
        if (PyFunction_Check(__pyx_t_2)) {
          PyObject *__pyx_temp[2] = {__pyx_t_6, __pyx_t_4};
          __pyx_t_28 = __Pyx_PyFunction_FastCall(__pyx_t_2, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_28)) __PYX_ERR(0, 424, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
          __Pyx_GOTREF(__pyx_t_28);
          __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
        } else
        #endif
        #if CYTHON_FAST_PYCCALL
        if (__Pyx_PyFastCFunction_Check(__pyx_t_2)) {
          PyObject *__pyx_temp[2] = {__pyx_t_6, __pyx_t_4};
          __pyx_t_28 = __Pyx_PyCFunction_FastCall(__pyx_t_2, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_28)) __PYX_ERR(0, 424, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
          __Pyx_GOTREF(__pyx_t_28);
          __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
        } else
        #endif
        {
          __pyx_t_5 = PyTuple_New(1+1); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 424, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_5);
          __Pyx_GIVEREF(__pyx_t_6); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_6); __pyx_t_6 = NULL;
          __Pyx_GIVEREF(__pyx_t_4);
          PyTuple_SET_ITEM(__pyx_t_5, 0+1, __pyx_t_4);
          __pyx_t_4 = 0;
          __pyx_t_28 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_t_5, NULL); if (unlikely(!__pyx_t_28)) __PYX_ERR(0, 424, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_28);
          __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        }
      }
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
      if (likely(PyList_CheckExact(__pyx_t_28)) || PyTuple_CheckExact(__pyx_t_28)) {
        __pyx_t_2 = __pyx_t_28; __Pyx_INCREF(__pyx_t_2); __pyx_t_26 = 0;
        __pyx_t_27 = NULL;
      } else {
        __pyx_t_26 = -1; __pyx_t_2 = PyObject_GetIter(__pyx_t_28); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 424, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_2);
        __pyx_t_27 = Py_TYPE(__pyx_t_2)->tp_iternext; if (unlikely(!__pyx_t_27)) __PYX_ERR(0, 424, __pyx_L1_error)
      }
      __Pyx_DECREF(__pyx_t_28); __pyx_t_28 = 0;
      for (;;) {
        if (likely(!__pyx_t_27)) {
          if (likely(PyList_CheckExact(__pyx_t_2))) {
            if (__pyx_t_26 >= PyList_GET_SIZE(__pyx_t_2)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_28 = PyList_GET_ITEM(__pyx_t_2, __pyx_t_26); __Pyx_INCREF(__pyx_t_28); __pyx_t_26++; if (unlikely(0 < 0)) __PYX_ERR(0, 424, __pyx_L1_error)
            #else
            __pyx_t_28 = PySequence_ITEM(__pyx_t_2, __pyx_t_26); __pyx_t_26++; if (unlikely(!__pyx_t_28)) __PYX_ERR(0, 424, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_28);
            #endif
          } else {
            if (__pyx_t_26 >= PyTuple_GET_SIZE(__pyx_t_2)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_28 = PyTuple_GET_ITEM(__pyx_t_2, __pyx_t_26); __Pyx_INCREF(__pyx_t_28); __pyx_t_26++; if (unlikely(0 < 0)) __PYX_ERR(0, 424, __pyx_L1_error)
            #else
            __pyx_t_28 = PySequence_ITEM(__pyx_t_2, __pyx_t_26); __pyx_t_26++; if (unlikely(!__pyx_t_28)) __PYX_ERR(0, 424, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_28);
            #endif
          }
        } else {
          __pyx_t_28 = __pyx_t_27(__pyx_t_2);
          if (unlikely(!__pyx_t_28)) {
            PyObject* exc_type = PyErr_Occurred();
            if (exc_type) {
              if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
              else __PYX_ERR(0, 424, __pyx_L1_error)
            }
            break;
          }
          __Pyx_GOTREF(__pyx_t_28);
        }
        __pyx_t_25 = __Pyx_PyInt_As_int(__pyx_t_28); if (unlikely((__pyx_t_25 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 424, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_28); __pyx_t_28 = 0;
        __pyx_v_f = __pyx_t_25;

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":425
 *                 # update factors
 *                 for f in range(self.n_factors):
 *                     puf = pu[u, f]             # <<<<<<<<<<<<<<
 *                     qif = qi[i, f]
 *                     pu[u, f] += lr_pu * (err * qif - reg_pu * puf)
 */
        __pyx_t_45 = __pyx_v_u;
        __pyx_t_46 = __pyx_v_f;
        __pyx_t_25 = -1;
        if (__pyx_t_45 < 0) {
          __pyx_t_45 += __pyx_pybuffernd_pu.diminfo[0].shape;
          if (unlikely(__pyx_t_45 < 0)) __pyx_t_25 = 0;
        } else if (unlikely(__pyx_t_45 >= __pyx_pybuffernd_pu.diminfo[0].shape)) __pyx_t_25 = 0;
        if (__pyx_t_46 < 0) {
          __pyx_t_46 += __pyx_pybuffernd_pu.diminfo[1].shape;
          if (unlikely(__pyx_t_46 < 0)) __pyx_t_25 = 1;
        } else if (unlikely(__pyx_t_46 >= __pyx_pybuffernd_pu.diminfo[1].shape)) __pyx_t_25 = 1;
        if (unlikely(__pyx_t_25 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_25);
          __PYX_ERR(0, 425, __pyx_L1_error)
        }
        __pyx_v_puf = (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_pu.rcbuffer->pybuffer.buf, __pyx_t_45, __pyx_pybuffernd_pu.diminfo[0].strides, __pyx_t_46, __pyx_pybuffernd_pu.diminfo[1].strides));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":426
 *                 for f in range(self.n_factors):
 *                     puf = pu[u, f]
 *                     qif = qi[i, f]             # <<<<<<<<<<<<<<
 *                     pu[u, f] += lr_pu * (err * qif - reg_pu * puf)
 *                     qi[i, f] += lr_qi * (err * (puf + u_impl_fdb[f]) -
 */
        __pyx_t_47 = __pyx_v_i;
        __pyx_t_48 = __pyx_v_f;
        __pyx_t_25 = -1;
        if (__pyx_t_47 < 0) {
          __pyx_t_47 += __pyx_pybuffernd_qi.diminfo[0].shape;
          if (unlikely(__pyx_t_47 < 0)) __pyx_t_25 = 0;
        } else if (unlikely(__pyx_t_47 >= __pyx_pybuffernd_qi.diminfo[0].shape)) __pyx_t_25 = 0;
        if (__pyx_t_48 < 0) {
          __pyx_t_48 += __pyx_pybuffernd_qi.diminfo[1].shape;
          if (unlikely(__pyx_t_48 < 0)) __pyx_t_25 = 1;
        } else if (unlikely(__pyx_t_48 >= __pyx_pybuffernd_qi.diminfo[1].shape)) __pyx_t_25 = 1;
        if (unlikely(__pyx_t_25 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_25);
          __PYX_ERR(0, 426, __pyx_L1_error)
        }
        __pyx_v_qif = (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_qi.rcbuffer->pybuffer.buf, __pyx_t_47, __pyx_pybuffernd_qi.diminfo[0].strides, __pyx_t_48, __pyx_pybuffernd_qi.diminfo[1].strides));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":427
 *                     puf = pu[u, f]
 *                     qif = qi[i, f]
 *                     pu[u, f] += lr_pu * (err * qif - reg_pu * puf)             # <<<<<<<<<<<<<<
 *                     qi[i, f] += lr_qi * (err * (puf + u_impl_fdb[f]) -
 *                                          reg_qi * qif)
 */
        __pyx_t_49 = __pyx_v_u;
        __pyx_t_50 = __pyx_v_f;
        __pyx_t_25 = -1;
        if (__pyx_t_49 < 0) {
          __pyx_t_49 += __pyx_pybuffernd_pu.diminfo[0].shape;
          if (unlikely(__pyx_t_49 < 0)) __pyx_t_25 = 0;
        } else if (unlikely(__pyx_t_49 >= __pyx_pybuffernd_pu.diminfo[0].shape)) __pyx_t_25 = 0;
        if (__pyx_t_50 < 0) {
          __pyx_t_50 += __pyx_pybuffernd_pu.diminfo[1].shape;
          if (unlikely(__pyx_t_50 < 0)) __pyx_t_25 = 1;
        } else if (unlikely(__pyx_t_50 >= __pyx_pybuffernd_pu.diminfo[1].shape)) __pyx_t_25 = 1;
        if (unlikely(__pyx_t_25 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_25);
          __PYX_ERR(0, 427, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_pu.rcbuffer->pybuffer.buf, __pyx_t_49, __pyx_pybuffernd_pu.diminfo[0].strides, __pyx_t_50, __pyx_pybuffernd_pu.diminfo[1].strides) += (__pyx_v_lr_pu * ((__pyx_v_err * __pyx_v_qif) - (__pyx_v_reg_pu * __pyx_v_puf)));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":428
 *                     qif = qi[i, f]
 *                     pu[u, f] += lr_pu * (err * qif - reg_pu * puf)
 *                     qi[i, f] += lr_qi * (err * (puf + u_impl_fdb[f]) -             # <<<<<<<<<<<<<<
 *                                          reg_qi * qif)
 *                     for j in Iu:
 */
        __pyx_t_51 = __pyx_v_f;
        __pyx_t_25 = -1;
        if (__pyx_t_51 < 0) {
          __pyx_t_51 += __pyx_pybuffernd_u_impl_fdb.diminfo[0].shape;
          if (unlikely(__pyx_t_51 < 0)) __pyx_t_25 = 0;
        } else if (unlikely(__pyx_t_51 >= __pyx_pybuffernd_u_impl_fdb.diminfo[0].shape)) __pyx_t_25 = 0;
        if (unlikely(__pyx_t_25 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_25);
          __PYX_ERR(0, 428, __pyx_L1_error)
        }

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":429
 *                     pu[u, f] += lr_pu * (err * qif - reg_pu * puf)
 *                     qi[i, f] += lr_qi * (err * (puf + u_impl_fdb[f]) -
 *                                          reg_qi * qif)             # <<<<<<<<<<<<<<
 *                     for j in Iu:
 *                         yj[j, f] += lr_yj * (err * qif / sqrt_Iu -
 */
        __pyx_t_52 = __pyx_v_i;
        __pyx_t_53 = __pyx_v_f;
        __pyx_t_25 = -1;
        if (__pyx_t_52 < 0) {
          __pyx_t_52 += __pyx_pybuffernd_qi.diminfo[0].shape;
          if (unlikely(__pyx_t_52 < 0)) __pyx_t_25 = 0;
        } else if (unlikely(__pyx_t_52 >= __pyx_pybuffernd_qi.diminfo[0].shape)) __pyx_t_25 = 0;
        if (__pyx_t_53 < 0) {
          __pyx_t_53 += __pyx_pybuffernd_qi.diminfo[1].shape;
          if (unlikely(__pyx_t_53 < 0)) __pyx_t_25 = 1;
        } else if (unlikely(__pyx_t_53 >= __pyx_pybuffernd_qi.diminfo[1].shape)) __pyx_t_25 = 1;
        if (unlikely(__pyx_t_25 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_25);
          __PYX_ERR(0, 428, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_qi.rcbuffer->pybuffer.buf, __pyx_t_52, __pyx_pybuffernd_qi.diminfo[0].strides, __pyx_t_53, __pyx_pybuffernd_qi.diminfo[1].strides) += (__pyx_v_lr_qi * ((__pyx_v_err * (__pyx_v_puf + (*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer.buf, __pyx_t_51, __pyx_pybuffernd_u_impl_fdb.diminfo[0].strides)))) - (__pyx_v_reg_qi * __pyx_v_qif)));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":430
 *                     qi[i, f] += lr_qi * (err * (puf + u_impl_fdb[f]) -
 *                                          reg_qi * qif)
 *                     for j in Iu:             # <<<<<<<<<<<<<<
 *                         yj[j, f] += lr_yj * (err * qif / sqrt_Iu -
 *                                              reg_yj * yj[j, f])
 */
        __pyx_t_28 = __pyx_v_Iu; __Pyx_INCREF(__pyx_t_28); __pyx_t_29 = 0;
        for (;;) {
          if (__pyx_t_29 >= PyList_GET_SIZE(__pyx_t_28)) break;
          #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
          __pyx_t_5 = PyList_GET_ITEM(__pyx_t_28, __pyx_t_29); __Pyx_INCREF(__pyx_t_5); __pyx_t_29++; if (unlikely(0 < 0)) __PYX_ERR(0, 430, __pyx_L1_error)
          #else
          __pyx_t_5 = PySequence_ITEM(__pyx_t_28, __pyx_t_29); __pyx_t_29++; if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 430, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_5);
          #endif
          __pyx_t_25 = __Pyx_PyInt_As_int(__pyx_t_5); if (unlikely((__pyx_t_25 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 430, __pyx_L1_error)
          __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
          __pyx_v_j = __pyx_t_25;

          /* "surprise/prediction_algorithms/matrix_factorization.pyx":431
 *                                          reg_qi * qif)
 *                     for j in Iu:
 *                         yj[j, f] += lr_yj * (err * qif / sqrt_Iu -             # <<<<<<<<<<<<<<
 *                                              reg_yj * yj[j, f])
 * 
 */
          __pyx_t_3 = (__pyx_v_err * __pyx_v_qif);
          if (unlikely(__pyx_v_sqrt_Iu == 0)) {
            PyErr_SetString(PyExc_ZeroDivisionError, "float division");
            __PYX_ERR(0, 431, __pyx_L1_error)
          }

          /* "surprise/prediction_algorithms/matrix_factorization.pyx":432
 *                     for j in Iu:
 *                         yj[j, f] += lr_yj * (err * qif / sqrt_Iu -
 *                                              reg_yj * yj[j, f])             # <<<<<<<<<<<<<<
 * 
 *         self.bu = bu
 */
          __pyx_t_54 = __pyx_v_j;
          __pyx_t_55 = __pyx_v_f;
          __pyx_t_25 = -1;
          if (__pyx_t_54 < 0) {
            __pyx_t_54 += __pyx_pybuffernd_yj.diminfo[0].shape;
            if (unlikely(__pyx_t_54 < 0)) __pyx_t_25 = 0;
          } else if (unlikely(__pyx_t_54 >= __pyx_pybuffernd_yj.diminfo[0].shape)) __pyx_t_25 = 0;
          if (__pyx_t_55 < 0) {
            __pyx_t_55 += __pyx_pybuffernd_yj.diminfo[1].shape;
            if (unlikely(__pyx_t_55 < 0)) __pyx_t_25 = 1;
          } else if (unlikely(__pyx_t_55 >= __pyx_pybuffernd_yj.diminfo[1].shape)) __pyx_t_25 = 1;
          if (unlikely(__pyx_t_25 != -1)) {
            __Pyx_RaiseBufferIndexError(__pyx_t_25);
            __PYX_ERR(0, 432, __pyx_L1_error)
          }

          /* "surprise/prediction_algorithms/matrix_factorization.pyx":431
 *                                          reg_qi * qif)
 *                     for j in Iu:
 *                         yj[j, f] += lr_yj * (err * qif / sqrt_Iu -             # <<<<<<<<<<<<<<
 *                                              reg_yj * yj[j, f])
 * 
 */
          __pyx_t_56 = __pyx_v_j;
          __pyx_t_57 = __pyx_v_f;
          __pyx_t_25 = -1;
          if (__pyx_t_56 < 0) {
            __pyx_t_56 += __pyx_pybuffernd_yj.diminfo[0].shape;
            if (unlikely(__pyx_t_56 < 0)) __pyx_t_25 = 0;
          } else if (unlikely(__pyx_t_56 >= __pyx_pybuffernd_yj.diminfo[0].shape)) __pyx_t_25 = 0;
          if (__pyx_t_57 < 0) {
            __pyx_t_57 += __pyx_pybuffernd_yj.diminfo[1].shape;
            if (unlikely(__pyx_t_57 < 0)) __pyx_t_25 = 1;
          } else if (unlikely(__pyx_t_57 >= __pyx_pybuffernd_yj.diminfo[1].shape)) __pyx_t_25 = 1;
          if (unlikely(__pyx_t_25 != -1)) {
            __Pyx_RaiseBufferIndexError(__pyx_t_25);
            __PYX_ERR(0, 431, __pyx_L1_error)
          }
          *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_yj.rcbuffer->pybuffer.buf, __pyx_t_56, __pyx_pybuffernd_yj.diminfo[0].strides, __pyx_t_57, __pyx_pybuffernd_yj.diminfo[1].strides) += (__pyx_v_lr_yj * ((__pyx_t_3 / __pyx_v_sqrt_Iu) - (__pyx_v_reg_yj * (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_yj.rcbuffer->pybuffer.buf, __pyx_t_54, __pyx_pybuffernd_yj.diminfo[0].strides, __pyx_t_55, __pyx_pybuffernd_yj.diminfo[1].strides)))));

          /* "surprise/prediction_algorithms/matrix_factorization.pyx":430
 *                     qi[i, f] += lr_qi * (err * (puf + u_impl_fdb[f]) -
 *                                          reg_qi * qif)
 *                     for j in Iu:             # <<<<<<<<<<<<<<
 *                         yj[j, f] += lr_yj * (err * qif / sqrt_Iu -
 *                                              reg_yj * yj[j, f])
 */
        }
        __Pyx_DECREF(__pyx_t_28); __pyx_t_28 = 0;

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":424
 * 
 *                 # update factors
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     puf = pu[u, f]
 *                     qif = qi[i, f]
 */
      }
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":400
 *             if self.verbose:
 *                 print(" processing epoch {}".format(current_epoch))
 *             for u, i, r in trainset.all_ratings():             # <<<<<<<<<<<<<<
 * 
 *                 # items rated by u. This is COSTLY
 */
    }
    __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":397
 *         u_impl_fdb = np.zeros(self.n_factors, np.double)
 * 
 *         for current_epoch in range(self.n_epochs):             # <<<<<<<<<<<<<<
 *             if self.verbose:
 *                 print(" processing epoch {}".format(current_epoch))
 */
  }
  __Pyx_DECREF(__pyx_t_14); __pyx_t_14 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":434
 *                                              reg_yj * yj[j, f])
 * 
 *         self.bu = bu             # <<<<<<<<<<<<<<
 *         self.bi = bi
 *         self.pu = pu
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_bu, ((PyObject *)__pyx_v_bu)) < 0) __PYX_ERR(0, 434, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":435
 * 
 *         self.bu = bu
 *         self.bi = bi             # <<<<<<<<<<<<<<
 *         self.pu = pu
 *         self.qi = qi
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_bi, ((PyObject *)__pyx_v_bi)) < 0) __PYX_ERR(0, 435, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":436
 *         self.bu = bu
 *         self.bi = bi
 *         self.pu = pu             # <<<<<<<<<<<<<<
 *         self.qi = qi
 *         self.yj = yj
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_pu, ((PyObject *)__pyx_v_pu)) < 0) __PYX_ERR(0, 436, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":437
 *         self.bi = bi
 *         self.pu = pu
 *         self.qi = qi             # <<<<<<<<<<<<<<
 *         self.yj = yj
 * 
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_qi, ((PyObject *)__pyx_v_qi)) < 0) __PYX_ERR(0, 437, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":438
 *         self.pu = pu
 *         self.qi = qi
 *         self.yj = yj             # <<<<<<<<<<<<<<
 * 
 *     def estimate(self, u, i):
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_yj, ((PyObject *)__pyx_v_yj)) < 0) __PYX_ERR(0, 438, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":356
 *         self.sgd(trainset)
 * 
 *     def sgd(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         # user biases
 */

  /* function exit code */
  __pyx_r = Py_None; __Pyx_INCREF(Py_None);
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_2);
  __Pyx_XDECREF(__pyx_t_4);
  __Pyx_XDECREF(__pyx_t_5);
  __Pyx_XDECREF(__pyx_t_6);
  __Pyx_XDECREF(__pyx_t_8);
  __Pyx_XDECREF(__pyx_t_14);
  __Pyx_XDECREF(__pyx_t_28);
  { PyObject *__pyx_type, *__pyx_value, *__pyx_tb;
    __Pyx_PyThreadState_declare
    __Pyx_PyThreadState_assign
    __Pyx_ErrFetch(&__pyx_type, &__pyx_value, &__pyx_tb);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bi.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bu.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_pu.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_qi.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_yj.rcbuffer->pybuffer);
  __Pyx_ErrRestore(__pyx_type, __pyx_value, __pyx_tb);}
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVDpp.sgd", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = NULL;
  goto __pyx_L2;
  __pyx_L0:;
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bi.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bu.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_pu.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_qi.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_u_impl_fdb.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_yj.rcbuffer->pybuffer);
  __pyx_L2:;
  __Pyx_XDECREF((PyObject *)__pyx_v_bu);
  __Pyx_XDECREF((PyObject *)__pyx_v_bi);
  __Pyx_XDECREF((PyObject *)__pyx_v_pu);
  __Pyx_XDECREF((PyObject *)__pyx_v_qi);
  __Pyx_XDECREF((PyObject *)__pyx_v_yj);
  __Pyx_XDECREF((PyObject *)__pyx_v_u_impl_fdb);
  __Pyx_XDECREF(__pyx_v_current_epoch);
  __Pyx_XDECREF(__pyx_v_Iu);
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "surprise/prediction_algorithms/matrix_factorization.pyx":440
 *         self.yj = yj
 * 
 *     def estimate(self, u, i):             # <<<<<<<<<<<<<<
 * 
 *         est = self.trainset.global_mean
 */

/* Python wrapper */
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_7estimate(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static PyMethodDef __pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_7estimate = {"estimate", (PyCFunction)__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_7estimate, METH_VARARGS|METH_KEYWORDS, 0};
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_7estimate(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
  PyObject *__pyx_v_self = 0;
  PyObject *__pyx_v_u = 0;
  PyObject *__pyx_v_i = 0;
  PyObject *__pyx_r = 0;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("estimate (wrapper)", 0);
  {
    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_self,&__pyx_n_s_u,&__pyx_n_s_i,0};
    PyObject* values[3] = {0,0,0};
    if (unlikely(__pyx_kwds)) {
      Py_ssize_t kw_args;
      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
      switch (pos_args) {
        case  3: values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
        CYTHON_FALLTHROUGH;
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        CYTHON_FALLTHROUGH;
        case  0: break;
        default: goto __pyx_L5_argtuple_error;
      }
      kw_args = PyDict_Size(__pyx_kwds);
      switch (pos_args) {
        case  0:
        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_self)) != 0)) kw_args--;
        else goto __pyx_L5_argtuple_error;
        CYTHON_FALLTHROUGH;
        case  1:
        if (likely((values[1] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_u)) != 0)) kw_args--;
        else {
          __Pyx_RaiseArgtupleInvalid("estimate", 1, 3, 3, 1); __PYX_ERR(0, 440, __pyx_L3_error)
        }
        CYTHON_FALLTHROUGH;
        case  2:
        if (likely((values[2] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_i)) != 0)) kw_args--;
        else {
          __Pyx_RaiseArgtupleInvalid("estimate", 1, 3, 3, 2); __PYX_ERR(0, 440, __pyx_L3_error)
        }
      }
      if (unlikely(kw_args > 0)) {
        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "estimate") < 0)) __PYX_ERR(0, 440, __pyx_L3_error)
      }
    } else if (PyTuple_GET_SIZE(__pyx_args) != 3) {
      goto __pyx_L5_argtuple_error;
    } else {
      values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
      values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
      values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
    }
    __pyx_v_self = values[0];
    __pyx_v_u = values[1];
    __pyx_v_i = values[2];
  }
  goto __pyx_L4_argument_unpacking_done;
  __pyx_L5_argtuple_error:;
  __Pyx_RaiseArgtupleInvalid("estimate", 1, 3, 3, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 440, __pyx_L3_error)
  __pyx_L3_error:;
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVDpp.estimate", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __Pyx_RefNannyFinishContext();
  return NULL;
  __pyx_L4_argument_unpacking_done:;
  __pyx_r = __pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_6estimate(__pyx_self, __pyx_v_self, __pyx_v_u, __pyx_v_i);

  /* function exit code */
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}
static PyObject *__pyx_gb_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_8estimate_2generator(__pyx_CoroutineObject *__pyx_generator, CYTHON_UNUSED PyThreadState *__pyx_tstate, PyObject *__pyx_sent_value); /* proto */

/* "surprise/prediction_algorithms/matrix_factorization.pyx":452
 *         if self.trainset.knows_user(u) and self.trainset.knows_item(i):
 *             Iu = len(self.trainset.ur[u])  # nb of items rated by u
 *             u_impl_feedback = (sum(self.yj[j] for (j, _)             # <<<<<<<<<<<<<<
 *                                in self.trainset.ur[u]) / np.sqrt(Iu))
 *             est += np.dot(self.qi[i], self.pu[u] + u_impl_feedback)
 */

static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_8estimate_genexpr(PyObject *__pyx_self) {
  struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr *__pyx_cur_scope;
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("genexpr", 0);
  __pyx_cur_scope = (struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr *)__pyx_tp_new_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr(__pyx_ptype_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr, __pyx_empty_tuple, NULL);
  if (unlikely(!__pyx_cur_scope)) {
    __pyx_cur_scope = ((struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr *)Py_None);
    __Pyx_INCREF(Py_None);
    __PYX_ERR(0, 452, __pyx_L1_error)
  } else {
    __Pyx_GOTREF(__pyx_cur_scope);
  }
  __pyx_cur_scope->__pyx_outer_scope = (struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate *) __pyx_self;
  __Pyx_INCREF(((PyObject *)__pyx_cur_scope->__pyx_outer_scope));
  __Pyx_GIVEREF(__pyx_cur_scope->__pyx_outer_scope);
  {
    __pyx_CoroutineObject *gen = __Pyx_Generator_New((__pyx_coroutine_body_t) __pyx_gb_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_8estimate_2generator, (PyObject *) __pyx_cur_scope, __pyx_n_s_genexpr, __pyx_n_s_SVDpp_estimate_locals_genexpr, __pyx_n_s_surprise_prediction_algorithms_m); if (unlikely(!gen)) __PYX_ERR(0, 452, __pyx_L1_error)
    __Pyx_DECREF(__pyx_cur_scope);
    __Pyx_RefNannyFinishContext();
    return (PyObject *) gen;
  }

  /* function exit code */
  __pyx_L1_error:;
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVDpp.estimate.genexpr", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = NULL;
  __Pyx_DECREF(((PyObject *)__pyx_cur_scope));
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

static PyObject *__pyx_gb_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_8estimate_2generator(__pyx_CoroutineObject *__pyx_generator, CYTHON_UNUSED PyThreadState *__pyx_tstate, PyObject *__pyx_sent_value) /* generator body */
{
  struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr *__pyx_cur_scope = ((struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr *)__pyx_generator->closure);
  PyObject *__pyx_r = NULL;
  PyObject *__pyx_t_1 = NULL;
  PyObject *__pyx_t_2 = NULL;
  Py_ssize_t __pyx_t_3;
  PyObject *(*__pyx_t_4)(PyObject *);
  PyObject *__pyx_t_5 = NULL;
  PyObject *__pyx_t_6 = NULL;
  PyObject *__pyx_t_7 = NULL;
  PyObject *(*__pyx_t_8)(PyObject *);
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("genexpr", 0);
  switch (__pyx_generator->resume_label) {
    case 0: goto __pyx_L3_first_run;
    case 1: goto __pyx_L8_resume_from_yield;
    default: /* CPython raises the right error here */
    __Pyx_RefNannyFinishContext();
    return NULL;
  }
  __pyx_L3_first_run:;
  if (unlikely(!__pyx_sent_value)) __PYX_ERR(0, 452, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":453
 *             Iu = len(self.trainset.ur[u])  # nb of items rated by u
 *             u_impl_feedback = (sum(self.yj[j] for (j, _)
 *                                in self.trainset.ur[u]) / np.sqrt(Iu))             # <<<<<<<<<<<<<<
 *             est += np.dot(self.qi[i], self.pu[u] + u_impl_feedback)
 * 
 */
  if (unlikely(!__pyx_cur_scope->__pyx_outer_scope->__pyx_v_self)) { __Pyx_RaiseClosureNameError("self"); __PYX_ERR(0, 453, __pyx_L1_error) }
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_cur_scope->__pyx_outer_scope->__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 453, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_ur); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 453, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  if (unlikely(!__pyx_cur_scope->__pyx_outer_scope->__pyx_v_u)) { __Pyx_RaiseClosureNameError("u"); __PYX_ERR(0, 453, __pyx_L1_error) }
  __pyx_t_1 = PyObject_GetItem(__pyx_t_2, __pyx_cur_scope->__pyx_outer_scope->__pyx_v_u); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 453, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  if (likely(PyList_CheckExact(__pyx_t_1)) || PyTuple_CheckExact(__pyx_t_1)) {
    __pyx_t_2 = __pyx_t_1; __Pyx_INCREF(__pyx_t_2); __pyx_t_3 = 0;
    __pyx_t_4 = NULL;
  } else {
    __pyx_t_3 = -1; __pyx_t_2 = PyObject_GetIter(__pyx_t_1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 453, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __pyx_t_4 = Py_TYPE(__pyx_t_2)->tp_iternext; if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 453, __pyx_L1_error)
  }
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  for (;;) {
    if (likely(!__pyx_t_4)) {
      if (likely(PyList_CheckExact(__pyx_t_2))) {
        if (__pyx_t_3 >= PyList_GET_SIZE(__pyx_t_2)) break;
        #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
        __pyx_t_1 = PyList_GET_ITEM(__pyx_t_2, __pyx_t_3); __Pyx_INCREF(__pyx_t_1); __pyx_t_3++; if (unlikely(0 < 0)) __PYX_ERR(0, 453, __pyx_L1_error)
        #else
        __pyx_t_1 = PySequence_ITEM(__pyx_t_2, __pyx_t_3); __pyx_t_3++; if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 453, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        #endif
      } else {
        if (__pyx_t_3 >= PyTuple_GET_SIZE(__pyx_t_2)) break;
        #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
        __pyx_t_1 = PyTuple_GET_ITEM(__pyx_t_2, __pyx_t_3); __Pyx_INCREF(__pyx_t_1); __pyx_t_3++; if (unlikely(0 < 0)) __PYX_ERR(0, 453, __pyx_L1_error)
        #else
        __pyx_t_1 = PySequence_ITEM(__pyx_t_2, __pyx_t_3); __pyx_t_3++; if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 453, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        #endif
      }
    } else {
      __pyx_t_1 = __pyx_t_4(__pyx_t_2);
      if (unlikely(!__pyx_t_1)) {
        PyObject* exc_type = PyErr_Occurred();
        if (exc_type) {
          if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
          else __PYX_ERR(0, 453, __pyx_L1_error)
        }
        break;
      }
      __Pyx_GOTREF(__pyx_t_1);
    }
    if ((likely(PyTuple_CheckExact(__pyx_t_1))) || (PyList_CheckExact(__pyx_t_1))) {
      PyObject* sequence = __pyx_t_1;
      #if !CYTHON_COMPILING_IN_PYPY
      Py_ssize_t size = Py_SIZE(sequence);
      #else
      Py_ssize_t size = PySequence_Size(sequence);
      #endif
      if (unlikely(size != 2)) {
        if (size > 2) __Pyx_RaiseTooManyValuesError(2);
        else if (size >= 0) __Pyx_RaiseNeedMoreValuesError(size);
        __PYX_ERR(0, 452, __pyx_L1_error)
      }
      #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
      if (likely(PyTuple_CheckExact(sequence))) {
        __pyx_t_5 = PyTuple_GET_ITEM(sequence, 0); 
        __pyx_t_6 = PyTuple_GET_ITEM(sequence, 1); 
      } else {
        __pyx_t_5 = PyList_GET_ITEM(sequence, 0); 
        __pyx_t_6 = PyList_GET_ITEM(sequence, 1); 
      }
      __Pyx_INCREF(__pyx_t_5);
      __Pyx_INCREF(__pyx_t_6);
      #else
      __pyx_t_5 = PySequence_ITEM(sequence, 0); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 452, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_5);
      __pyx_t_6 = PySequence_ITEM(sequence, 1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 452, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_6);
      #endif
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    } else {
      Py_ssize_t index = -1;
      __pyx_t_7 = PyObject_GetIter(__pyx_t_1); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 452, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_7);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __pyx_t_8 = Py_TYPE(__pyx_t_7)->tp_iternext;
      index = 0; __pyx_t_5 = __pyx_t_8(__pyx_t_7); if (unlikely(!__pyx_t_5)) goto __pyx_L6_unpacking_failed;
      __Pyx_GOTREF(__pyx_t_5);
      index = 1; __pyx_t_6 = __pyx_t_8(__pyx_t_7); if (unlikely(!__pyx_t_6)) goto __pyx_L6_unpacking_failed;
      __Pyx_GOTREF(__pyx_t_6);
      if (__Pyx_IternextUnpackEndCheck(__pyx_t_8(__pyx_t_7), 2) < 0) __PYX_ERR(0, 452, __pyx_L1_error)
      __pyx_t_8 = NULL;
      __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
      goto __pyx_L7_unpacking_done;
      __pyx_L6_unpacking_failed:;
      __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
      __pyx_t_8 = NULL;
      if (__Pyx_IterFinish() == 0) __Pyx_RaiseNeedMoreValuesError(index);
      __PYX_ERR(0, 452, __pyx_L1_error)
      __pyx_L7_unpacking_done:;
    }

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":452
 *         if self.trainset.knows_user(u) and self.trainset.knows_item(i):
 *             Iu = len(self.trainset.ur[u])  # nb of items rated by u
 *             u_impl_feedback = (sum(self.yj[j] for (j, _)             # <<<<<<<<<<<<<<
 *                                in self.trainset.ur[u]) / np.sqrt(Iu))
 *             est += np.dot(self.qi[i], self.pu[u] + u_impl_feedback)
 */
    __Pyx_XGOTREF(__pyx_cur_scope->__pyx_v_j);
    __Pyx_XDECREF_SET(__pyx_cur_scope->__pyx_v_j, __pyx_t_5);
    __Pyx_GIVEREF(__pyx_t_5);
    __pyx_t_5 = 0;
    __Pyx_XGOTREF(__pyx_cur_scope->__pyx_v__);
    __Pyx_XDECREF_SET(__pyx_cur_scope->__pyx_v__, __pyx_t_6);
    __Pyx_GIVEREF(__pyx_t_6);
    __pyx_t_6 = 0;
    if (unlikely(!__pyx_cur_scope->__pyx_outer_scope->__pyx_v_self)) { __Pyx_RaiseClosureNameError("self"); __PYX_ERR(0, 452, __pyx_L1_error) }
    __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_cur_scope->__pyx_outer_scope->__pyx_v_self, __pyx_n_s_yj); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 452, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    __pyx_t_6 = PyObject_GetItem(__pyx_t_1, __pyx_cur_scope->__pyx_v_j); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 452, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_6);
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __pyx_r = __pyx_t_6;
    __pyx_t_6 = 0;
    __Pyx_XGIVEREF(__pyx_t_2);
    __pyx_cur_scope->__pyx_t_0 = __pyx_t_2;
    __pyx_cur_scope->__pyx_t_1 = __pyx_t_3;
    __pyx_cur_scope->__pyx_t_2 = __pyx_t_4;
    __Pyx_XGIVEREF(__pyx_r);
    __Pyx_RefNannyFinishContext();
    __Pyx_Coroutine_ResetAndClearException(__pyx_generator);
    /* return from generator, yielding value */
    __pyx_generator->resume_label = 1;
    return __pyx_r;
    __pyx_L8_resume_from_yield:;
    __pyx_t_2 = __pyx_cur_scope->__pyx_t_0;
    __pyx_cur_scope->__pyx_t_0 = 0;
    __Pyx_XGOTREF(__pyx_t_2);
    __pyx_t_3 = __pyx_cur_scope->__pyx_t_1;
    __pyx_t_4 = __pyx_cur_scope->__pyx_t_2;
    if (unlikely(!__pyx_sent_value)) __PYX_ERR(0, 452, __pyx_L1_error)
  }
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  CYTHON_MAYBE_UNUSED_VAR(__pyx_cur_scope);

  /* function exit code */
  PyErr_SetNone(PyExc_StopIteration);
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_2);
  __Pyx_XDECREF(__pyx_t_5);
  __Pyx_XDECREF(__pyx_t_6);
  __Pyx_XDECREF(__pyx_t_7);
  __Pyx_AddTraceback("genexpr", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_L0:;
  __Pyx_XDECREF(__pyx_r); __pyx_r = 0;
  __Pyx_Coroutine_ResetAndClearException(__pyx_generator);
  __pyx_generator->resume_label = -1;
  __Pyx_Coroutine_clear((PyObject*)__pyx_generator);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "surprise/prediction_algorithms/matrix_factorization.pyx":440
 *         self.yj = yj
 * 
 *     def estimate(self, u, i):             # <<<<<<<<<<<<<<
 * 
 *         est = self.trainset.global_mean
 */

static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_6estimate(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_u, PyObject *__pyx_v_i) {
  struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate *__pyx_cur_scope;
  PyObject *__pyx_v_est = NULL;
  PyObject *__pyx_v_Iu = NULL;
  PyObject *__pyx_v_u_impl_feedback = NULL;
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  PyObject *__pyx_t_2 = NULL;
  PyObject *__pyx_t_3 = NULL;
  PyObject *__pyx_t_4 = NULL;
  int __pyx_t_5;
  int __pyx_t_6;
  Py_ssize_t __pyx_t_7;
  PyObject *__pyx_t_8 = NULL;
  int __pyx_t_9;
  PyObject *__pyx_t_10 = NULL;
  __Pyx_RefNannySetupContext("estimate", 0);
  __pyx_cur_scope = (struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate *)__pyx_tp_new_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate(__pyx_ptype_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate, __pyx_empty_tuple, NULL);
  if (unlikely(!__pyx_cur_scope)) {
    __pyx_cur_scope = ((struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate *)Py_None);
    __Pyx_INCREF(Py_None);
    __PYX_ERR(0, 440, __pyx_L1_error)
  } else {
    __Pyx_GOTREF(__pyx_cur_scope);
  }
  __pyx_cur_scope->__pyx_v_self = __pyx_v_self;
  __Pyx_INCREF(__pyx_cur_scope->__pyx_v_self);
  __Pyx_GIVEREF(__pyx_cur_scope->__pyx_v_self);
  __pyx_cur_scope->__pyx_v_u = __pyx_v_u;
  __Pyx_INCREF(__pyx_cur_scope->__pyx_v_u);
  __Pyx_GIVEREF(__pyx_cur_scope->__pyx_v_u);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":442
 *     def estimate(self, u, i):
 * 
 *         est = self.trainset.global_mean             # <<<<<<<<<<<<<<
 * 
 *         if self.trainset.knows_user(u):
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_cur_scope->__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 442, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_global_mean); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 442, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_v_est = __pyx_t_2;
  __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":444
 *         est = self.trainset.global_mean
 * 
 *         if self.trainset.knows_user(u):             # <<<<<<<<<<<<<<
 *             est += self.bu[u]
 * 
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_cur_scope->__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 444, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_knows_user); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 444, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_1 = NULL;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_3))) {
    __pyx_t_1 = PyMethod_GET_SELF(__pyx_t_3);
    if (likely(__pyx_t_1)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
      __Pyx_INCREF(__pyx_t_1);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_3, function);
    }
  }
  if (!__pyx_t_1) {
    __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_3, __pyx_cur_scope->__pyx_v_u); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 444, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_3)) {
      PyObject *__pyx_temp[2] = {__pyx_t_1, __pyx_cur_scope->__pyx_v_u};
      __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 444, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
      __Pyx_GOTREF(__pyx_t_2);
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
      PyObject *__pyx_temp[2] = {__pyx_t_1, __pyx_cur_scope->__pyx_v_u};
      __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 444, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
      __Pyx_GOTREF(__pyx_t_2);
    } else
    #endif
    {
      __pyx_t_4 = PyTuple_New(1+1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 444, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __Pyx_GIVEREF(__pyx_t_1); PyTuple_SET_ITEM(__pyx_t_4, 0, __pyx_t_1); __pyx_t_1 = NULL;
      __Pyx_INCREF(__pyx_cur_scope->__pyx_v_u);
      __Pyx_GIVEREF(__pyx_cur_scope->__pyx_v_u);
      PyTuple_SET_ITEM(__pyx_t_4, 0+1, __pyx_cur_scope->__pyx_v_u);
      __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_4, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 444, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __pyx_t_5 = __Pyx_PyObject_IsTrue(__pyx_t_2); if (unlikely(__pyx_t_5 < 0)) __PYX_ERR(0, 444, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  if (__pyx_t_5) {

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":445
 * 
 *         if self.trainset.knows_user(u):
 *             est += self.bu[u]             # <<<<<<<<<<<<<<
 * 
 *         if self.trainset.knows_item(i):
 */
    __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_cur_scope->__pyx_v_self, __pyx_n_s_bu); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 445, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __pyx_t_3 = PyObject_GetItem(__pyx_t_2, __pyx_cur_scope->__pyx_v_u); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 445, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    __pyx_t_2 = PyNumber_InPlaceAdd(__pyx_v_est, __pyx_t_3); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 445, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    __Pyx_DECREF_SET(__pyx_v_est, __pyx_t_2);
    __pyx_t_2 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":444
 *         est = self.trainset.global_mean
 * 
 *         if self.trainset.knows_user(u):             # <<<<<<<<<<<<<<
 *             est += self.bu[u]
 * 
 */
  }

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":447
 *             est += self.bu[u]
 * 
 *         if self.trainset.knows_item(i):             # <<<<<<<<<<<<<<
 *             est += self.bi[i]
 * 
 */
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_cur_scope->__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 447, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_3, __pyx_n_s_knows_item); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 447, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __pyx_t_3 = NULL;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_4))) {
    __pyx_t_3 = PyMethod_GET_SELF(__pyx_t_4);
    if (likely(__pyx_t_3)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_4);
      __Pyx_INCREF(__pyx_t_3);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_4, function);
    }
  }
  if (!__pyx_t_3) {
    __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_4, __pyx_v_i); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 447, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_4)) {
      PyObject *__pyx_temp[2] = {__pyx_t_3, __pyx_v_i};
      __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 447, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
      __Pyx_GOTREF(__pyx_t_2);
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_4)) {
      PyObject *__pyx_temp[2] = {__pyx_t_3, __pyx_v_i};
      __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 447, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
      __Pyx_GOTREF(__pyx_t_2);
    } else
    #endif
    {
      __pyx_t_1 = PyTuple_New(1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 447, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_GIVEREF(__pyx_t_3); PyTuple_SET_ITEM(__pyx_t_1, 0, __pyx_t_3); __pyx_t_3 = NULL;
      __Pyx_INCREF(__pyx_v_i);
      __Pyx_GIVEREF(__pyx_v_i);
      PyTuple_SET_ITEM(__pyx_t_1, 0+1, __pyx_v_i);
      __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_4, __pyx_t_1, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 447, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __pyx_t_5 = __Pyx_PyObject_IsTrue(__pyx_t_2); if (unlikely(__pyx_t_5 < 0)) __PYX_ERR(0, 447, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  if (__pyx_t_5) {

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":448
 * 
 *         if self.trainset.knows_item(i):
 *             est += self.bi[i]             # <<<<<<<<<<<<<<
 * 
 *         if self.trainset.knows_user(u) and self.trainset.knows_item(i):
 */
    __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_cur_scope->__pyx_v_self, __pyx_n_s_bi); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 448, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __pyx_t_4 = PyObject_GetItem(__pyx_t_2, __pyx_v_i); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 448, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_4);
    __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    __pyx_t_2 = PyNumber_InPlaceAdd(__pyx_v_est, __pyx_t_4); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 448, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    __Pyx_DECREF_SET(__pyx_v_est, __pyx_t_2);
    __pyx_t_2 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":447
 *             est += self.bu[u]
 * 
 *         if self.trainset.knows_item(i):             # <<<<<<<<<<<<<<
 *             est += self.bi[i]
 * 
 */
  }

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":450
 *             est += self.bi[i]
 * 
 *         if self.trainset.knows_user(u) and self.trainset.knows_item(i):             # <<<<<<<<<<<<<<
 *             Iu = len(self.trainset.ur[u])  # nb of items rated by u
 *             u_impl_feedback = (sum(self.yj[j] for (j, _)
 */
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_cur_scope->__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 450, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_t_4, __pyx_n_s_knows_user); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 450, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __pyx_t_4 = NULL;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_1))) {
    __pyx_t_4 = PyMethod_GET_SELF(__pyx_t_1);
    if (likely(__pyx_t_4)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_1);
      __Pyx_INCREF(__pyx_t_4);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_1, function);
    }
  }
  if (!__pyx_t_4) {
    __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_1, __pyx_cur_scope->__pyx_v_u); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 450, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_1)) {
      PyObject *__pyx_temp[2] = {__pyx_t_4, __pyx_cur_scope->__pyx_v_u};
      __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_1, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 450, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
      __Pyx_GOTREF(__pyx_t_2);
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_1)) {
      PyObject *__pyx_temp[2] = {__pyx_t_4, __pyx_cur_scope->__pyx_v_u};
      __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_1, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 450, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
      __Pyx_GOTREF(__pyx_t_2);
    } else
    #endif
    {
      __pyx_t_3 = PyTuple_New(1+1); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 450, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __Pyx_GIVEREF(__pyx_t_4); PyTuple_SET_ITEM(__pyx_t_3, 0, __pyx_t_4); __pyx_t_4 = NULL;
      __Pyx_INCREF(__pyx_cur_scope->__pyx_v_u);
      __Pyx_GIVEREF(__pyx_cur_scope->__pyx_v_u);
      PyTuple_SET_ITEM(__pyx_t_3, 0+1, __pyx_cur_scope->__pyx_v_u);
      __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_1, __pyx_t_3, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 450, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_2); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(0, 450, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  if (__pyx_t_6) {
  } else {
    __pyx_t_5 = __pyx_t_6;
    goto __pyx_L6_bool_binop_done;
  }
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_cur_scope->__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 450, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_knows_item); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 450, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_1 = NULL;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_3))) {
    __pyx_t_1 = PyMethod_GET_SELF(__pyx_t_3);
    if (likely(__pyx_t_1)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
      __Pyx_INCREF(__pyx_t_1);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_3, function);
    }
  }
  if (!__pyx_t_1) {
    __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_3, __pyx_v_i); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 450, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_3)) {
      PyObject *__pyx_temp[2] = {__pyx_t_1, __pyx_v_i};
      __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 450, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
      __Pyx_GOTREF(__pyx_t_2);
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
      PyObject *__pyx_temp[2] = {__pyx_t_1, __pyx_v_i};
      __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 450, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
      __Pyx_GOTREF(__pyx_t_2);
    } else
    #endif
    {
      __pyx_t_4 = PyTuple_New(1+1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 450, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __Pyx_GIVEREF(__pyx_t_1); PyTuple_SET_ITEM(__pyx_t_4, 0, __pyx_t_1); __pyx_t_1 = NULL;
      __Pyx_INCREF(__pyx_v_i);
      __Pyx_GIVEREF(__pyx_v_i);
      PyTuple_SET_ITEM(__pyx_t_4, 0+1, __pyx_v_i);
      __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_4, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 450, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_2); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(0, 450, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_t_5 = __pyx_t_6;
  __pyx_L6_bool_binop_done:;
  if (__pyx_t_5) {

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":451
 * 
 *         if self.trainset.knows_user(u) and self.trainset.knows_item(i):
 *             Iu = len(self.trainset.ur[u])  # nb of items rated by u             # <<<<<<<<<<<<<<
 *             u_impl_feedback = (sum(self.yj[j] for (j, _)
 *                                in self.trainset.ur[u]) / np.sqrt(Iu))
 */
    __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_cur_scope->__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 451, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_t_2, __pyx_n_s_ur); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 451, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    __pyx_t_2 = PyObject_GetItem(__pyx_t_3, __pyx_cur_scope->__pyx_v_u); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 451, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    __pyx_t_7 = PyObject_Length(__pyx_t_2); if (unlikely(__pyx_t_7 == -1)) __PYX_ERR(0, 451, __pyx_L1_error)
    __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    __pyx_t_2 = PyInt_FromSsize_t(__pyx_t_7); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 451, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __pyx_v_Iu = __pyx_t_2;
    __pyx_t_2 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":452
 *         if self.trainset.knows_user(u) and self.trainset.knows_item(i):
 *             Iu = len(self.trainset.ur[u])  # nb of items rated by u
 *             u_impl_feedback = (sum(self.yj[j] for (j, _)             # <<<<<<<<<<<<<<
 *                                in self.trainset.ur[u]) / np.sqrt(Iu))
 *             est += np.dot(self.qi[i], self.pu[u] + u_impl_feedback)
 */
    __pyx_t_2 = __pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_8estimate_genexpr(((PyObject*)__pyx_cur_scope)); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 452, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __pyx_t_3 = PyTuple_New(1); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 452, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __Pyx_GIVEREF(__pyx_t_2);
    PyTuple_SET_ITEM(__pyx_t_3, 0, __pyx_t_2);
    __pyx_t_2 = 0;
    __pyx_t_2 = __Pyx_PyObject_Call(__pyx_builtin_sum, __pyx_t_3, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 452, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":453
 *             Iu = len(self.trainset.ur[u])  # nb of items rated by u
 *             u_impl_feedback = (sum(self.yj[j] for (j, _)
 *                                in self.trainset.ur[u]) / np.sqrt(Iu))             # <<<<<<<<<<<<<<
 *             est += np.dot(self.qi[i], self.pu[u] + u_impl_feedback)
 * 
 */
    __pyx_t_4 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 453, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_4);
    __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_t_4, __pyx_n_s_sqrt); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 453, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    __pyx_t_4 = NULL;
    if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_1))) {
      __pyx_t_4 = PyMethod_GET_SELF(__pyx_t_1);
      if (likely(__pyx_t_4)) {
        PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_1);
        __Pyx_INCREF(__pyx_t_4);
        __Pyx_INCREF(function);
        __Pyx_DECREF_SET(__pyx_t_1, function);
      }
    }
    if (!__pyx_t_4) {
      __pyx_t_3 = __Pyx_PyObject_CallOneArg(__pyx_t_1, __pyx_v_Iu); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 453, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
    } else {
      #if CYTHON_FAST_PYCALL
      if (PyFunction_Check(__pyx_t_1)) {
        PyObject *__pyx_temp[2] = {__pyx_t_4, __pyx_v_Iu};
        __pyx_t_3 = __Pyx_PyFunction_FastCall(__pyx_t_1, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 453, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
        __Pyx_GOTREF(__pyx_t_3);
      } else
      #endif
      #if CYTHON_FAST_PYCCALL
      if (__Pyx_PyFastCFunction_Check(__pyx_t_1)) {
        PyObject *__pyx_temp[2] = {__pyx_t_4, __pyx_v_Iu};
        __pyx_t_3 = __Pyx_PyCFunction_FastCall(__pyx_t_1, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 453, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
        __Pyx_GOTREF(__pyx_t_3);
      } else
      #endif
      {
        __pyx_t_8 = PyTuple_New(1+1); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 453, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_8);
        __Pyx_GIVEREF(__pyx_t_4); PyTuple_SET_ITEM(__pyx_t_8, 0, __pyx_t_4); __pyx_t_4 = NULL;
        __Pyx_INCREF(__pyx_v_Iu);
        __Pyx_GIVEREF(__pyx_v_Iu);
        PyTuple_SET_ITEM(__pyx_t_8, 0+1, __pyx_v_Iu);
        __pyx_t_3 = __Pyx_PyObject_Call(__pyx_t_1, __pyx_t_8, NULL); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 453, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_3);
        __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
      }
    }
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __pyx_t_1 = __Pyx_PyNumber_Divide(__pyx_t_2, __pyx_t_3); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 453, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    __pyx_v_u_impl_feedback = __pyx_t_1;
    __pyx_t_1 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":454
 *             u_impl_feedback = (sum(self.yj[j] for (j, _)
 *                                in self.trainset.ur[u]) / np.sqrt(Iu))
 *             est += np.dot(self.qi[i], self.pu[u] + u_impl_feedback)             # <<<<<<<<<<<<<<
 * 
 *         return est
 */
    __pyx_t_3 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 454, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_t_3, __pyx_n_s_dot); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 454, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_cur_scope->__pyx_v_self, __pyx_n_s_qi); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 454, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __pyx_t_8 = PyObject_GetItem(__pyx_t_3, __pyx_v_i); if (unlikely(!__pyx_t_8)) __PYX_ERR(0, 454, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_8);
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_cur_scope->__pyx_v_self, __pyx_n_s_pu); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 454, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __pyx_t_4 = PyObject_GetItem(__pyx_t_3, __pyx_cur_scope->__pyx_v_u); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 454, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_4);
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    __pyx_t_3 = PyNumber_Add(__pyx_t_4, __pyx_v_u_impl_feedback); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 454, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    __pyx_t_4 = NULL;
    __pyx_t_9 = 0;
    if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_2))) {
      __pyx_t_4 = PyMethod_GET_SELF(__pyx_t_2);
      if (likely(__pyx_t_4)) {
        PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_2);
        __Pyx_INCREF(__pyx_t_4);
        __Pyx_INCREF(function);
        __Pyx_DECREF_SET(__pyx_t_2, function);
        __pyx_t_9 = 1;
      }
    }
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_2)) {
      PyObject *__pyx_temp[3] = {__pyx_t_4, __pyx_t_8, __pyx_t_3};
      __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_2, __pyx_temp+1-__pyx_t_9, 2+__pyx_t_9); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 454, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_2)) {
      PyObject *__pyx_temp[3] = {__pyx_t_4, __pyx_t_8, __pyx_t_3};
      __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_2, __pyx_temp+1-__pyx_t_9, 2+__pyx_t_9); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 454, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    } else
    #endif
    {
      __pyx_t_10 = PyTuple_New(2+__pyx_t_9); if (unlikely(!__pyx_t_10)) __PYX_ERR(0, 454, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_10);
      if (__pyx_t_4) {
        __Pyx_GIVEREF(__pyx_t_4); PyTuple_SET_ITEM(__pyx_t_10, 0, __pyx_t_4); __pyx_t_4 = NULL;
      }
      __Pyx_GIVEREF(__pyx_t_8);
      PyTuple_SET_ITEM(__pyx_t_10, 0+__pyx_t_9, __pyx_t_8);
      __Pyx_GIVEREF(__pyx_t_3);
      PyTuple_SET_ITEM(__pyx_t_10, 1+__pyx_t_9, __pyx_t_3);
      __pyx_t_8 = 0;
      __pyx_t_3 = 0;
      __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_t_10, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 454, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_10); __pyx_t_10 = 0;
    }
    __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    __pyx_t_2 = PyNumber_InPlaceAdd(__pyx_v_est, __pyx_t_1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 454, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_DECREF_SET(__pyx_v_est, __pyx_t_2);
    __pyx_t_2 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":450
 *             est += self.bi[i]
 * 
 *         if self.trainset.knows_user(u) and self.trainset.knows_item(i):             # <<<<<<<<<<<<<<
 *             Iu = len(self.trainset.ur[u])  # nb of items rated by u
 *             u_impl_feedback = (sum(self.yj[j] for (j, _)
 */
  }

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":456
 *             est += np.dot(self.qi[i], self.pu[u] + u_impl_feedback)
 * 
 *         return est             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __Pyx_XDECREF(__pyx_r);
  __Pyx_INCREF(__pyx_v_est);
  __pyx_r = __pyx_v_est;
  goto __pyx_L0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":440
 *         self.yj = yj
 * 
 *     def estimate(self, u, i):             # <<<<<<<<<<<<<<
 * 
 *         est = self.trainset.global_mean
 */

  /* function exit code */
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_2);
  __Pyx_XDECREF(__pyx_t_3);
  __Pyx_XDECREF(__pyx_t_4);
  __Pyx_XDECREF(__pyx_t_8);
  __Pyx_XDECREF(__pyx_t_10);
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.SVDpp.estimate", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = NULL;
  __pyx_L0:;
  __Pyx_XDECREF(__pyx_v_est);
  __Pyx_XDECREF(__pyx_v_Iu);
  __Pyx_XDECREF(__pyx_v_u_impl_feedback);
  __Pyx_DECREF(((PyObject *)__pyx_cur_scope));
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "surprise/prediction_algorithms/matrix_factorization.pyx":533
 *     """
 * 
 *     def __init__(self, n_factors=15, n_epochs=50, biased=False, reg_pu=.06,             # <<<<<<<<<<<<<<
 *                  reg_qi=.06, reg_bu=.02, reg_bi=.02, lr_bu=.005, lr_bi=.005,
 *                  init_low=0, init_high=1, verbose=False):
 */

/* Python wrapper */
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_1__init__(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static PyMethodDef __pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_1__init__ = {"__init__", (PyCFunction)__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_1__init__, METH_VARARGS|METH_KEYWORDS, 0};
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_1__init__(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
  PyObject *__pyx_v_self = 0;
  PyObject *__pyx_v_n_factors = 0;
  PyObject *__pyx_v_n_epochs = 0;
  PyObject *__pyx_v_biased = 0;
  PyObject *__pyx_v_reg_pu = 0;
  PyObject *__pyx_v_reg_qi = 0;
  PyObject *__pyx_v_reg_bu = 0;
  PyObject *__pyx_v_reg_bi = 0;
  PyObject *__pyx_v_lr_bu = 0;
  PyObject *__pyx_v_lr_bi = 0;
  PyObject *__pyx_v_init_low = 0;
  PyObject *__pyx_v_init_high = 0;
  PyObject *__pyx_v_verbose = 0;
  PyObject *__pyx_r = 0;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("__init__ (wrapper)", 0);
  {
    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_self,&__pyx_n_s_n_factors,&__pyx_n_s_n_epochs,&__pyx_n_s_biased,&__pyx_n_s_reg_pu,&__pyx_n_s_reg_qi,&__pyx_n_s_reg_bu,&__pyx_n_s_reg_bi,&__pyx_n_s_lr_bu,&__pyx_n_s_lr_bi,&__pyx_n_s_init_low,&__pyx_n_s_init_high,&__pyx_n_s_verbose,0};
    PyObject* values[13] = {0,0,0,0,0,0,0,0,0,0,0,0,0};
    values[1] = ((PyObject *)((PyObject *)__pyx_int_15));
    values[2] = ((PyObject *)((PyObject *)__pyx_int_50));
    values[3] = ((PyObject *)((PyObject *)Py_False));
    values[4] = ((PyObject *)((PyObject*)__pyx_float__06));
    values[5] = ((PyObject *)((PyObject*)__pyx_float__06));
    values[6] = ((PyObject *)((PyObject*)__pyx_float__02));
    values[7] = ((PyObject *)((PyObject*)__pyx_float__02));
    values[8] = ((PyObject *)((PyObject*)__pyx_float__005));
    values[9] = ((PyObject *)((PyObject*)__pyx_float__005));
    values[10] = ((PyObject *)((PyObject *)__pyx_int_0));
    values[11] = ((PyObject *)((PyObject *)__pyx_int_1));

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":535
 *     def __init__(self, n_factors=15, n_epochs=50, biased=False, reg_pu=.06,
 *                  reg_qi=.06, reg_bu=.02, reg_bi=.02, lr_bu=.005, lr_bi=.005,
 *                  init_low=0, init_high=1, verbose=False):             # <<<<<<<<<<<<<<
 * 
 *         self.n_factors = n_factors
 */
    values[12] = ((PyObject *)((PyObject *)Py_False));
    if (unlikely(__pyx_kwds)) {
      Py_ssize_t kw_args;
      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
      switch (pos_args) {
        case 13: values[12] = PyTuple_GET_ITEM(__pyx_args, 12);
        CYTHON_FALLTHROUGH;
        case 12: values[11] = PyTuple_GET_ITEM(__pyx_args, 11);
        CYTHON_FALLTHROUGH;
        case 11: values[10] = PyTuple_GET_ITEM(__pyx_args, 10);
        CYTHON_FALLTHROUGH;
        case 10: values[9] = PyTuple_GET_ITEM(__pyx_args, 9);
        CYTHON_FALLTHROUGH;
        case  9: values[8] = PyTuple_GET_ITEM(__pyx_args, 8);
        CYTHON_FALLTHROUGH;
        case  8: values[7] = PyTuple_GET_ITEM(__pyx_args, 7);
        CYTHON_FALLTHROUGH;
        case  7: values[6] = PyTuple_GET_ITEM(__pyx_args, 6);
        CYTHON_FALLTHROUGH;
        case  6: values[5] = PyTuple_GET_ITEM(__pyx_args, 5);
        CYTHON_FALLTHROUGH;
        case  5: values[4] = PyTuple_GET_ITEM(__pyx_args, 4);
        CYTHON_FALLTHROUGH;
        case  4: values[3] = PyTuple_GET_ITEM(__pyx_args, 3);
        CYTHON_FALLTHROUGH;
        case  3: values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
        CYTHON_FALLTHROUGH;
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        CYTHON_FALLTHROUGH;
        case  0: break;
        default: goto __pyx_L5_argtuple_error;
      }
      kw_args = PyDict_Size(__pyx_kwds);
      switch (pos_args) {
        case  0:
        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_self)) != 0)) kw_args--;
        else goto __pyx_L5_argtuple_error;
        CYTHON_FALLTHROUGH;
        case  1:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_n_factors);
          if (value) { values[1] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  2:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_n_epochs);
          if (value) { values[2] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  3:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_biased);
          if (value) { values[3] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  4:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_pu);
          if (value) { values[4] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  5:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_qi);
          if (value) { values[5] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  6:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_bu);
          if (value) { values[6] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  7:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_reg_bi);
          if (value) { values[7] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  8:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_lr_bu);
          if (value) { values[8] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case  9:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_lr_bi);
          if (value) { values[9] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 10:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_init_low);
          if (value) { values[10] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 11:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_init_high);
          if (value) { values[11] = value; kw_args--; }
        }
        CYTHON_FALLTHROUGH;
        case 12:
        if (kw_args > 0) {
          PyObject* value = PyDict_GetItem(__pyx_kwds, __pyx_n_s_verbose);
          if (value) { values[12] = value; kw_args--; }
        }
      }
      if (unlikely(kw_args > 0)) {
        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "__init__") < 0)) __PYX_ERR(0, 533, __pyx_L3_error)
      }
    } else {
      switch (PyTuple_GET_SIZE(__pyx_args)) {
        case 13: values[12] = PyTuple_GET_ITEM(__pyx_args, 12);
        CYTHON_FALLTHROUGH;
        case 12: values[11] = PyTuple_GET_ITEM(__pyx_args, 11);
        CYTHON_FALLTHROUGH;
        case 11: values[10] = PyTuple_GET_ITEM(__pyx_args, 10);
        CYTHON_FALLTHROUGH;
        case 10: values[9] = PyTuple_GET_ITEM(__pyx_args, 9);
        CYTHON_FALLTHROUGH;
        case  9: values[8] = PyTuple_GET_ITEM(__pyx_args, 8);
        CYTHON_FALLTHROUGH;
        case  8: values[7] = PyTuple_GET_ITEM(__pyx_args, 7);
        CYTHON_FALLTHROUGH;
        case  7: values[6] = PyTuple_GET_ITEM(__pyx_args, 6);
        CYTHON_FALLTHROUGH;
        case  6: values[5] = PyTuple_GET_ITEM(__pyx_args, 5);
        CYTHON_FALLTHROUGH;
        case  5: values[4] = PyTuple_GET_ITEM(__pyx_args, 4);
        CYTHON_FALLTHROUGH;
        case  4: values[3] = PyTuple_GET_ITEM(__pyx_args, 3);
        CYTHON_FALLTHROUGH;
        case  3: values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
        CYTHON_FALLTHROUGH;
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        break;
        default: goto __pyx_L5_argtuple_error;
      }
    }
    __pyx_v_self = values[0];
    __pyx_v_n_factors = values[1];
    __pyx_v_n_epochs = values[2];
    __pyx_v_biased = values[3];
    __pyx_v_reg_pu = values[4];
    __pyx_v_reg_qi = values[5];
    __pyx_v_reg_bu = values[6];
    __pyx_v_reg_bi = values[7];
    __pyx_v_lr_bu = values[8];
    __pyx_v_lr_bi = values[9];
    __pyx_v_init_low = values[10];
    __pyx_v_init_high = values[11];
    __pyx_v_verbose = values[12];
  }
  goto __pyx_L4_argument_unpacking_done;
  __pyx_L5_argtuple_error:;
  __Pyx_RaiseArgtupleInvalid("__init__", 0, 1, 13, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 533, __pyx_L3_error)
  __pyx_L3_error:;
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.NMF.__init__", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __Pyx_RefNannyFinishContext();
  return NULL;
  __pyx_L4_argument_unpacking_done:;
  __pyx_r = __pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3NMF___init__(__pyx_self, __pyx_v_self, __pyx_v_n_factors, __pyx_v_n_epochs, __pyx_v_biased, __pyx_v_reg_pu, __pyx_v_reg_qi, __pyx_v_reg_bu, __pyx_v_reg_bi, __pyx_v_lr_bu, __pyx_v_lr_bi, __pyx_v_init_low, __pyx_v_init_high, __pyx_v_verbose);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":533
 *     """
 * 
 *     def __init__(self, n_factors=15, n_epochs=50, biased=False, reg_pu=.06,             # <<<<<<<<<<<<<<
 *                  reg_qi=.06, reg_bu=.02, reg_bi=.02, lr_bu=.005, lr_bi=.005,
 *                  init_low=0, init_high=1, verbose=False):
 */

  /* function exit code */
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3NMF___init__(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_n_factors, PyObject *__pyx_v_n_epochs, PyObject *__pyx_v_biased, PyObject *__pyx_v_reg_pu, PyObject *__pyx_v_reg_qi, PyObject *__pyx_v_reg_bu, PyObject *__pyx_v_reg_bi, PyObject *__pyx_v_lr_bu, PyObject *__pyx_v_lr_bi, PyObject *__pyx_v_init_low, PyObject *__pyx_v_init_high, PyObject *__pyx_v_verbose) {
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  PyObject *__pyx_t_2 = NULL;
  int __pyx_t_3;
  PyObject *__pyx_t_4 = NULL;
  PyObject *__pyx_t_5 = NULL;
  __Pyx_RefNannySetupContext("__init__", 0);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":537
 *                  init_low=0, init_high=1, verbose=False):
 * 
 *         self.n_factors = n_factors             # <<<<<<<<<<<<<<
 *         self.n_epochs = n_epochs
 *         self.biased = biased
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_n_factors, __pyx_v_n_factors) < 0) __PYX_ERR(0, 537, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":538
 * 
 *         self.n_factors = n_factors
 *         self.n_epochs = n_epochs             # <<<<<<<<<<<<<<
 *         self.biased = biased
 *         self.reg_pu = reg_pu
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_n_epochs, __pyx_v_n_epochs) < 0) __PYX_ERR(0, 538, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":539
 *         self.n_factors = n_factors
 *         self.n_epochs = n_epochs
 *         self.biased = biased             # <<<<<<<<<<<<<<
 *         self.reg_pu = reg_pu
 *         self.reg_qi = reg_qi
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_biased, __pyx_v_biased) < 0) __PYX_ERR(0, 539, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":540
 *         self.n_epochs = n_epochs
 *         self.biased = biased
 *         self.reg_pu = reg_pu             # <<<<<<<<<<<<<<
 *         self.reg_qi = reg_qi
 *         self.lr_bu = lr_bu
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_reg_pu, __pyx_v_reg_pu) < 0) __PYX_ERR(0, 540, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":541
 *         self.biased = biased
 *         self.reg_pu = reg_pu
 *         self.reg_qi = reg_qi             # <<<<<<<<<<<<<<
 *         self.lr_bu = lr_bu
 *         self.lr_bi = lr_bi
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_reg_qi, __pyx_v_reg_qi) < 0) __PYX_ERR(0, 541, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":542
 *         self.reg_pu = reg_pu
 *         self.reg_qi = reg_qi
 *         self.lr_bu = lr_bu             # <<<<<<<<<<<<<<
 *         self.lr_bi = lr_bi
 *         self.reg_bu = reg_bu
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_lr_bu, __pyx_v_lr_bu) < 0) __PYX_ERR(0, 542, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":543
 *         self.reg_qi = reg_qi
 *         self.lr_bu = lr_bu
 *         self.lr_bi = lr_bi             # <<<<<<<<<<<<<<
 *         self.reg_bu = reg_bu
 *         self.reg_bi = reg_bi
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_lr_bi, __pyx_v_lr_bi) < 0) __PYX_ERR(0, 543, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":544
 *         self.lr_bu = lr_bu
 *         self.lr_bi = lr_bi
 *         self.reg_bu = reg_bu             # <<<<<<<<<<<<<<
 *         self.reg_bi = reg_bi
 *         self.init_low = init_low
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_reg_bu, __pyx_v_reg_bu) < 0) __PYX_ERR(0, 544, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":545
 *         self.lr_bi = lr_bi
 *         self.reg_bu = reg_bu
 *         self.reg_bi = reg_bi             # <<<<<<<<<<<<<<
 *         self.init_low = init_low
 *         self.init_high = init_high
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_reg_bi, __pyx_v_reg_bi) < 0) __PYX_ERR(0, 545, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":546
 *         self.reg_bu = reg_bu
 *         self.reg_bi = reg_bi
 *         self.init_low = init_low             # <<<<<<<<<<<<<<
 *         self.init_high = init_high
 *         self.verbose = verbose
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_init_low, __pyx_v_init_low) < 0) __PYX_ERR(0, 546, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":547
 *         self.reg_bi = reg_bi
 *         self.init_low = init_low
 *         self.init_high = init_high             # <<<<<<<<<<<<<<
 *         self.verbose = verbose
 * 
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_init_high, __pyx_v_init_high) < 0) __PYX_ERR(0, 547, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":548
 *         self.init_low = init_low
 *         self.init_high = init_high
 *         self.verbose = verbose             # <<<<<<<<<<<<<<
 * 
 *         if self.init_low < 0:
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_verbose, __pyx_v_verbose) < 0) __PYX_ERR(0, 548, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":550
 *         self.verbose = verbose
 * 
 *         if self.init_low < 0:             # <<<<<<<<<<<<<<
 *             raise ValueError('init_low should be greater than zero')
 * 
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_low); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 550, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_2 = PyObject_RichCompare(__pyx_t_1, __pyx_int_0, Py_LT); __Pyx_XGOTREF(__pyx_t_2); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 550, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_3 = __Pyx_PyObject_IsTrue(__pyx_t_2); if (unlikely(__pyx_t_3 < 0)) __PYX_ERR(0, 550, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  if (__pyx_t_3) {

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":551
 * 
 *         if self.init_low < 0:
 *             raise ValueError('init_low should be greater than zero')             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.__init__(self)
 */
    __pyx_t_2 = __Pyx_PyObject_Call(__pyx_builtin_ValueError, __pyx_tuple__2, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 551, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
    __Pyx_Raise(__pyx_t_2, 0, 0, 0);
    __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    __PYX_ERR(0, 551, __pyx_L1_error)

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":550
 *         self.verbose = verbose
 * 
 *         if self.init_low < 0:             # <<<<<<<<<<<<<<
 *             raise ValueError('init_low should be greater than zero')
 * 
 */
  }

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":553
 *             raise ValueError('init_low should be greater than zero')
 * 
 *         AlgoBase.__init__(self)             # <<<<<<<<<<<<<<
 * 
 *     def train(self, trainset):
 */
  __pyx_t_1 = __Pyx_GetModuleGlobalName(__pyx_n_s_AlgoBase); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 553, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_init); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 553, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_1 = NULL;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_4))) {
    __pyx_t_1 = PyMethod_GET_SELF(__pyx_t_4);
    if (likely(__pyx_t_1)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_4);
      __Pyx_INCREF(__pyx_t_1);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_4, function);
    }
  }
  if (!__pyx_t_1) {
    __pyx_t_2 = __Pyx_PyObject_CallOneArg(__pyx_t_4, __pyx_v_self); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 553, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_2);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_4)) {
      PyObject *__pyx_temp[2] = {__pyx_t_1, __pyx_v_self};
      __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 553, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
      __Pyx_GOTREF(__pyx_t_2);
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_4)) {
      PyObject *__pyx_temp[2] = {__pyx_t_1, __pyx_v_self};
      __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 553, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
      __Pyx_GOTREF(__pyx_t_2);
    } else
    #endif
    {
      __pyx_t_5 = PyTuple_New(1+1); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 553, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_5);
      __Pyx_GIVEREF(__pyx_t_1); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_1); __pyx_t_1 = NULL;
      __Pyx_INCREF(__pyx_v_self);
      __Pyx_GIVEREF(__pyx_v_self);
      PyTuple_SET_ITEM(__pyx_t_5, 0+1, __pyx_v_self);
      __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_4, __pyx_t_5, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 553, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":533
 *     """
 * 
 *     def __init__(self, n_factors=15, n_epochs=50, biased=False, reg_pu=.06,             # <<<<<<<<<<<<<<
 *                  reg_qi=.06, reg_bu=.02, reg_bi=.02, lr_bu=.005, lr_bi=.005,
 *                  init_low=0, init_high=1, verbose=False):
 */

  /* function exit code */
  __pyx_r = Py_None; __Pyx_INCREF(Py_None);
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_2);
  __Pyx_XDECREF(__pyx_t_4);
  __Pyx_XDECREF(__pyx_t_5);
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.NMF.__init__", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = NULL;
  __pyx_L0:;
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "surprise/prediction_algorithms/matrix_factorization.pyx":555
 *         AlgoBase.__init__(self)
 * 
 *     def train(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.train(self, trainset)
 */

/* Python wrapper */
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_3train(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static PyMethodDef __pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_3train = {"train", (PyCFunction)__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_3train, METH_VARARGS|METH_KEYWORDS, 0};
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_3train(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
  PyObject *__pyx_v_self = 0;
  PyObject *__pyx_v_trainset = 0;
  PyObject *__pyx_r = 0;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("train (wrapper)", 0);
  {
    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_self,&__pyx_n_s_trainset,0};
    PyObject* values[2] = {0,0};
    if (unlikely(__pyx_kwds)) {
      Py_ssize_t kw_args;
      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
      switch (pos_args) {
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        CYTHON_FALLTHROUGH;
        case  0: break;
        default: goto __pyx_L5_argtuple_error;
      }
      kw_args = PyDict_Size(__pyx_kwds);
      switch (pos_args) {
        case  0:
        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_self)) != 0)) kw_args--;
        else goto __pyx_L5_argtuple_error;
        CYTHON_FALLTHROUGH;
        case  1:
        if (likely((values[1] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_trainset)) != 0)) kw_args--;
        else {
          __Pyx_RaiseArgtupleInvalid("train", 1, 2, 2, 1); __PYX_ERR(0, 555, __pyx_L3_error)
        }
      }
      if (unlikely(kw_args > 0)) {
        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "train") < 0)) __PYX_ERR(0, 555, __pyx_L3_error)
      }
    } else if (PyTuple_GET_SIZE(__pyx_args) != 2) {
      goto __pyx_L5_argtuple_error;
    } else {
      values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
      values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
    }
    __pyx_v_self = values[0];
    __pyx_v_trainset = values[1];
  }
  goto __pyx_L4_argument_unpacking_done;
  __pyx_L5_argtuple_error:;
  __Pyx_RaiseArgtupleInvalid("train", 1, 2, 2, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 555, __pyx_L3_error)
  __pyx_L3_error:;
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.NMF.train", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __Pyx_RefNannyFinishContext();
  return NULL;
  __pyx_L4_argument_unpacking_done:;
  __pyx_r = __pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_2train(__pyx_self, __pyx_v_self, __pyx_v_trainset);

  /* function exit code */
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_2train(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_trainset) {
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  PyObject *__pyx_t_2 = NULL;
  PyObject *__pyx_t_3 = NULL;
  int __pyx_t_4;
  PyObject *__pyx_t_5 = NULL;
  __Pyx_RefNannySetupContext("train", 0);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":557
 *     def train(self, trainset):
 * 
 *         AlgoBase.train(self, trainset)             # <<<<<<<<<<<<<<
 *         self.sgd(trainset)
 * 
 */
  __pyx_t_2 = __Pyx_GetModuleGlobalName(__pyx_n_s_AlgoBase); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 557, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_t_2, __pyx_n_s_train); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 557, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_t_2 = NULL;
  __pyx_t_4 = 0;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_3))) {
    __pyx_t_2 = PyMethod_GET_SELF(__pyx_t_3);
    if (likely(__pyx_t_2)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
      __Pyx_INCREF(__pyx_t_2);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_3, function);
      __pyx_t_4 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_3)) {
    PyObject *__pyx_temp[3] = {__pyx_t_2, __pyx_v_self, __pyx_v_trainset};
    __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-__pyx_t_4, 2+__pyx_t_4); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 557, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_2); __pyx_t_2 = 0;
    __Pyx_GOTREF(__pyx_t_1);
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
    PyObject *__pyx_temp[3] = {__pyx_t_2, __pyx_v_self, __pyx_v_trainset};
    __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-__pyx_t_4, 2+__pyx_t_4); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 557, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_2); __pyx_t_2 = 0;
    __Pyx_GOTREF(__pyx_t_1);
  } else
  #endif
  {
    __pyx_t_5 = PyTuple_New(2+__pyx_t_4); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 557, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_5);
    if (__pyx_t_2) {
      __Pyx_GIVEREF(__pyx_t_2); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_2); __pyx_t_2 = NULL;
    }
    __Pyx_INCREF(__pyx_v_self);
    __Pyx_GIVEREF(__pyx_v_self);
    PyTuple_SET_ITEM(__pyx_t_5, 0+__pyx_t_4, __pyx_v_self);
    __Pyx_INCREF(__pyx_v_trainset);
    __Pyx_GIVEREF(__pyx_v_trainset);
    PyTuple_SET_ITEM(__pyx_t_5, 1+__pyx_t_4, __pyx_v_trainset);
    __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_5, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 557, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  }
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":558
 * 
 *         AlgoBase.train(self, trainset)
 *         self.sgd(trainset)             # <<<<<<<<<<<<<<
 * 
 *     def sgd(self, trainset):
 */
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_sgd); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 558, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __pyx_t_5 = NULL;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_3))) {
    __pyx_t_5 = PyMethod_GET_SELF(__pyx_t_3);
    if (likely(__pyx_t_5)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
      __Pyx_INCREF(__pyx_t_5);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_3, function);
    }
  }
  if (!__pyx_t_5) {
    __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_3, __pyx_v_trainset); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 558, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_3)) {
      PyObject *__pyx_temp[2] = {__pyx_t_5, __pyx_v_trainset};
      __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 558, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
      PyObject *__pyx_temp[2] = {__pyx_t_5, __pyx_v_trainset};
      __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 558, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    {
      __pyx_t_2 = PyTuple_New(1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 558, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_2, 0, __pyx_t_5); __pyx_t_5 = NULL;
      __Pyx_INCREF(__pyx_v_trainset);
      __Pyx_GIVEREF(__pyx_v_trainset);
      PyTuple_SET_ITEM(__pyx_t_2, 0+1, __pyx_v_trainset);
      __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_2, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 558, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":555
 *         AlgoBase.__init__(self)
 * 
 *     def train(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.train(self, trainset)
 */

  /* function exit code */
  __pyx_r = Py_None; __Pyx_INCREF(Py_None);
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_2);
  __Pyx_XDECREF(__pyx_t_3);
  __Pyx_XDECREF(__pyx_t_5);
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.NMF.train", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = NULL;
  __pyx_L0:;
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "surprise/prediction_algorithms/matrix_factorization.pyx":560
 *         self.sgd(trainset)
 * 
 *     def sgd(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         # user and item factors
 */

/* Python wrapper */
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_5sgd(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static PyMethodDef __pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_5sgd = {"sgd", (PyCFunction)__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_5sgd, METH_VARARGS|METH_KEYWORDS, 0};
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_5sgd(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
  PyObject *__pyx_v_self = 0;
  PyObject *__pyx_v_trainset = 0;
  PyObject *__pyx_r = 0;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("sgd (wrapper)", 0);
  {
    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_self,&__pyx_n_s_trainset,0};
    PyObject* values[2] = {0,0};
    if (unlikely(__pyx_kwds)) {
      Py_ssize_t kw_args;
      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
      switch (pos_args) {
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        CYTHON_FALLTHROUGH;
        case  0: break;
        default: goto __pyx_L5_argtuple_error;
      }
      kw_args = PyDict_Size(__pyx_kwds);
      switch (pos_args) {
        case  0:
        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_self)) != 0)) kw_args--;
        else goto __pyx_L5_argtuple_error;
        CYTHON_FALLTHROUGH;
        case  1:
        if (likely((values[1] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_trainset)) != 0)) kw_args--;
        else {
          __Pyx_RaiseArgtupleInvalid("sgd", 1, 2, 2, 1); __PYX_ERR(0, 560, __pyx_L3_error)
        }
      }
      if (unlikely(kw_args > 0)) {
        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "sgd") < 0)) __PYX_ERR(0, 560, __pyx_L3_error)
      }
    } else if (PyTuple_GET_SIZE(__pyx_args) != 2) {
      goto __pyx_L5_argtuple_error;
    } else {
      values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
      values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
    }
    __pyx_v_self = values[0];
    __pyx_v_trainset = values[1];
  }
  goto __pyx_L4_argument_unpacking_done;
  __pyx_L5_argtuple_error:;
  __Pyx_RaiseArgtupleInvalid("sgd", 1, 2, 2, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 560, __pyx_L3_error)
  __pyx_L3_error:;
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.NMF.sgd", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __Pyx_RefNannyFinishContext();
  return NULL;
  __pyx_L4_argument_unpacking_done:;
  __pyx_r = __pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_4sgd(__pyx_self, __pyx_v_self, __pyx_v_trainset);

  /* function exit code */
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_4sgd(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_trainset) {
  PyArrayObject *__pyx_v_pu = 0;
  PyArrayObject *__pyx_v_qi = 0;
  PyArrayObject *__pyx_v_bu = 0;
  PyArrayObject *__pyx_v_bi = 0;
  PyArrayObject *__pyx_v_user_num = 0;
  PyArrayObject *__pyx_v_user_denom = 0;
  PyArrayObject *__pyx_v_item_num = 0;
  PyArrayObject *__pyx_v_item_denom = 0;
  int __pyx_v_u;
  int __pyx_v_i;
  int __pyx_v_f;
  double __pyx_v_r;
  double __pyx_v_est;
  double __pyx_v_l;
  double __pyx_v_dot;
  double __pyx_v_err;
  double __pyx_v_reg_pu;
  double __pyx_v_reg_qi;
  double __pyx_v_reg_bu;
  double __pyx_v_reg_bi;
  double __pyx_v_lr_bu;
  double __pyx_v_lr_bi;
  double __pyx_v_global_mean;
  PyObject *__pyx_v_current_epoch = NULL;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_bi;
  __Pyx_Buffer __pyx_pybuffer_bi;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_bu;
  __Pyx_Buffer __pyx_pybuffer_bu;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_item_denom;
  __Pyx_Buffer __pyx_pybuffer_item_denom;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_item_num;
  __Pyx_Buffer __pyx_pybuffer_item_num;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_pu;
  __Pyx_Buffer __pyx_pybuffer_pu;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_qi;
  __Pyx_Buffer __pyx_pybuffer_qi;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_user_denom;
  __Pyx_Buffer __pyx_pybuffer_user_denom;
  __Pyx_LocalBuf_ND __pyx_pybuffernd_user_num;
  __Pyx_Buffer __pyx_pybuffer_user_num;
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  double __pyx_t_2;
  PyObject *__pyx_t_3 = NULL;
  PyObject *__pyx_t_4 = NULL;
  PyObject *__pyx_t_5 = NULL;
  PyObject *__pyx_t_6 = NULL;
  PyObject *__pyx_t_7 = NULL;
  PyArrayObject *__pyx_t_8 = NULL;
  int __pyx_t_9;
  PyObject *__pyx_t_10 = NULL;
  PyObject *__pyx_t_11 = NULL;
  PyObject *__pyx_t_12 = NULL;
  PyArrayObject *__pyx_t_13 = NULL;
  PyArrayObject *__pyx_t_14 = NULL;
  PyArrayObject *__pyx_t_15 = NULL;
  int __pyx_t_16;
  int __pyx_t_17;
  Py_ssize_t __pyx_t_18;
  PyObject *(*__pyx_t_19)(PyObject *);
  PyArrayObject *__pyx_t_20 = NULL;
  PyArrayObject *__pyx_t_21 = NULL;
  PyArrayObject *__pyx_t_22 = NULL;
  PyArrayObject *__pyx_t_23 = NULL;
  Py_ssize_t __pyx_t_24;
  PyObject *(*__pyx_t_25)(PyObject *);
  PyObject *__pyx_t_26 = NULL;
  PyObject *(*__pyx_t_27)(PyObject *);
  int __pyx_t_28;
  Py_ssize_t __pyx_t_29;
  PyObject *(*__pyx_t_30)(PyObject *);
  Py_ssize_t __pyx_t_31;
  Py_ssize_t __pyx_t_32;
  Py_ssize_t __pyx_t_33;
  Py_ssize_t __pyx_t_34;
  Py_ssize_t __pyx_t_35;
  Py_ssize_t __pyx_t_36;
  Py_ssize_t __pyx_t_37;
  Py_ssize_t __pyx_t_38;
  Py_ssize_t __pyx_t_39;
  Py_ssize_t __pyx_t_40;
  Py_ssize_t __pyx_t_41;
  Py_ssize_t __pyx_t_42;
  Py_ssize_t __pyx_t_43;
  Py_ssize_t __pyx_t_44;
  Py_ssize_t __pyx_t_45;
  Py_ssize_t __pyx_t_46;
  Py_ssize_t __pyx_t_47;
  Py_ssize_t __pyx_t_48;
  Py_ssize_t __pyx_t_49;
  Py_ssize_t __pyx_t_50;
  Py_ssize_t __pyx_t_51;
  Py_ssize_t __pyx_t_52;
  Py_ssize_t __pyx_t_53;
  Py_ssize_t __pyx_t_54;
  Py_ssize_t __pyx_t_55;
  Py_ssize_t __pyx_t_56;
  Py_ssize_t __pyx_t_57;
  Py_ssize_t __pyx_t_58;
  Py_ssize_t __pyx_t_59;
  Py_ssize_t __pyx_t_60;
  Py_ssize_t __pyx_t_61;
  Py_ssize_t __pyx_t_62;
  __pyx_t_5numpy_double_t __pyx_t_63;
  Py_ssize_t __pyx_t_64;
  Py_ssize_t __pyx_t_65;
  __pyx_t_5numpy_double_t __pyx_t_66;
  Py_ssize_t __pyx_t_67;
  Py_ssize_t __pyx_t_68;
  Py_ssize_t __pyx_t_69;
  Py_ssize_t __pyx_t_70;
  Py_ssize_t __pyx_t_71;
  Py_ssize_t __pyx_t_72;
  Py_ssize_t __pyx_t_73;
  Py_ssize_t __pyx_t_74;
  Py_ssize_t __pyx_t_75;
  Py_ssize_t __pyx_t_76;
  Py_ssize_t __pyx_t_77;
  Py_ssize_t __pyx_t_78;
  __Pyx_RefNannySetupContext("sgd", 0);
  __pyx_pybuffer_pu.pybuffer.buf = NULL;
  __pyx_pybuffer_pu.refcount = 0;
  __pyx_pybuffernd_pu.data = NULL;
  __pyx_pybuffernd_pu.rcbuffer = &__pyx_pybuffer_pu;
  __pyx_pybuffer_qi.pybuffer.buf = NULL;
  __pyx_pybuffer_qi.refcount = 0;
  __pyx_pybuffernd_qi.data = NULL;
  __pyx_pybuffernd_qi.rcbuffer = &__pyx_pybuffer_qi;
  __pyx_pybuffer_bu.pybuffer.buf = NULL;
  __pyx_pybuffer_bu.refcount = 0;
  __pyx_pybuffernd_bu.data = NULL;
  __pyx_pybuffernd_bu.rcbuffer = &__pyx_pybuffer_bu;
  __pyx_pybuffer_bi.pybuffer.buf = NULL;
  __pyx_pybuffer_bi.refcount = 0;
  __pyx_pybuffernd_bi.data = NULL;
  __pyx_pybuffernd_bi.rcbuffer = &__pyx_pybuffer_bi;
  __pyx_pybuffer_user_num.pybuffer.buf = NULL;
  __pyx_pybuffer_user_num.refcount = 0;
  __pyx_pybuffernd_user_num.data = NULL;
  __pyx_pybuffernd_user_num.rcbuffer = &__pyx_pybuffer_user_num;
  __pyx_pybuffer_user_denom.pybuffer.buf = NULL;
  __pyx_pybuffer_user_denom.refcount = 0;
  __pyx_pybuffernd_user_denom.data = NULL;
  __pyx_pybuffernd_user_denom.rcbuffer = &__pyx_pybuffer_user_denom;
  __pyx_pybuffer_item_num.pybuffer.buf = NULL;
  __pyx_pybuffer_item_num.refcount = 0;
  __pyx_pybuffernd_item_num.data = NULL;
  __pyx_pybuffernd_item_num.rcbuffer = &__pyx_pybuffer_item_num;
  __pyx_pybuffer_item_denom.pybuffer.buf = NULL;
  __pyx_pybuffer_item_denom.refcount = 0;
  __pyx_pybuffernd_item_denom.data = NULL;
  __pyx_pybuffernd_item_denom.rcbuffer = &__pyx_pybuffer_item_denom;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":578
 *         cdef int u, i, f
 *         cdef double r, est, l, dot, err
 *         cdef double reg_pu = self.reg_pu             # <<<<<<<<<<<<<<
 *         cdef double reg_qi = self.reg_qi
 *         cdef double reg_bu = self.reg_bu
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_reg_pu); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 578, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_2 = __pyx_PyFloat_AsDouble(__pyx_t_1); if (unlikely((__pyx_t_2 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 578, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_v_reg_pu = __pyx_t_2;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":579
 *         cdef double r, est, l, dot, err
 *         cdef double reg_pu = self.reg_pu
 *         cdef double reg_qi = self.reg_qi             # <<<<<<<<<<<<<<
 *         cdef double reg_bu = self.reg_bu
 *         cdef double reg_bi = self.reg_bi
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_reg_qi); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 579, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_2 = __pyx_PyFloat_AsDouble(__pyx_t_1); if (unlikely((__pyx_t_2 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 579, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_v_reg_qi = __pyx_t_2;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":580
 *         cdef double reg_pu = self.reg_pu
 *         cdef double reg_qi = self.reg_qi
 *         cdef double reg_bu = self.reg_bu             # <<<<<<<<<<<<<<
 *         cdef double reg_bi = self.reg_bi
 *         cdef double lr_bu = self.lr_bu
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_reg_bu); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 580, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_2 = __pyx_PyFloat_AsDouble(__pyx_t_1); if (unlikely((__pyx_t_2 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 580, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_v_reg_bu = __pyx_t_2;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":581
 *         cdef double reg_qi = self.reg_qi
 *         cdef double reg_bu = self.reg_bu
 *         cdef double reg_bi = self.reg_bi             # <<<<<<<<<<<<<<
 *         cdef double lr_bu = self.lr_bu
 *         cdef double lr_bi = self.lr_bi
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_reg_bi); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 581, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_2 = __pyx_PyFloat_AsDouble(__pyx_t_1); if (unlikely((__pyx_t_2 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 581, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_v_reg_bi = __pyx_t_2;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":582
 *         cdef double reg_bu = self.reg_bu
 *         cdef double reg_bi = self.reg_bi
 *         cdef double lr_bu = self.lr_bu             # <<<<<<<<<<<<<<
 *         cdef double lr_bi = self.lr_bi
 *         cdef double global_mean = self.trainset.global_mean
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_lr_bu); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 582, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_2 = __pyx_PyFloat_AsDouble(__pyx_t_1); if (unlikely((__pyx_t_2 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 582, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_v_lr_bu = __pyx_t_2;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":583
 *         cdef double reg_bi = self.reg_bi
 *         cdef double lr_bu = self.lr_bu
 *         cdef double lr_bi = self.lr_bi             # <<<<<<<<<<<<<<
 *         cdef double global_mean = self.trainset.global_mean
 * 
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_lr_bi); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 583, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_2 = __pyx_PyFloat_AsDouble(__pyx_t_1); if (unlikely((__pyx_t_2 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 583, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_v_lr_bi = __pyx_t_2;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":584
 *         cdef double lr_bu = self.lr_bu
 *         cdef double lr_bi = self.lr_bi
 *         cdef double global_mean = self.trainset.global_mean             # <<<<<<<<<<<<<<
 * 
 *         # Randomly initialize user and item factors
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 584, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_global_mean); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 584, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_2 = __pyx_PyFloat_AsDouble(__pyx_t_3); if (unlikely((__pyx_t_2 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 584, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __pyx_v_global_mean = __pyx_t_2;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":587
 * 
 *         # Randomly initialize user and item factors
 *         pu = np.random.uniform(self.init_low, self.init_high,             # <<<<<<<<<<<<<<
 *                                size=(trainset.n_users, self.n_factors))
 *         qi = np.random.uniform(self.init_low, self.init_high,
 */
  __pyx_t_3 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 587, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_t_3, __pyx_n_s_random); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 587, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_uniform); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 587, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_low); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 587, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_high); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 587, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_5 = PyTuple_New(2); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 587, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __Pyx_GIVEREF(__pyx_t_1);
  PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_1);
  __Pyx_GIVEREF(__pyx_t_4);
  PyTuple_SET_ITEM(__pyx_t_5, 1, __pyx_t_4);
  __pyx_t_1 = 0;
  __pyx_t_4 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":588
 *         # Randomly initialize user and item factors
 *         pu = np.random.uniform(self.init_low, self.init_high,
 *                                size=(trainset.n_users, self.n_factors))             # <<<<<<<<<<<<<<
 *         qi = np.random.uniform(self.init_low, self.init_high,
 *                                size=(trainset.n_items, self.n_factors))
 */
  __pyx_t_4 = __Pyx_PyDict_NewPresized(1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 588, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_users); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 588, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 588, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_6);
  __pyx_t_7 = PyTuple_New(2); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 588, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_7);
  __Pyx_GIVEREF(__pyx_t_1);
  PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_t_1);
  __Pyx_GIVEREF(__pyx_t_6);
  PyTuple_SET_ITEM(__pyx_t_7, 1, __pyx_t_6);
  __pyx_t_1 = 0;
  __pyx_t_6 = 0;
  if (PyDict_SetItem(__pyx_t_4, __pyx_n_s_size, __pyx_t_7) < 0) __PYX_ERR(0, 588, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":587
 * 
 *         # Randomly initialize user and item factors
 *         pu = np.random.uniform(self.init_low, self.init_high,             # <<<<<<<<<<<<<<
 *                                size=(trainset.n_users, self.n_factors))
 *         qi = np.random.uniform(self.init_low, self.init_high,
 */
  __pyx_t_7 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_5, __pyx_t_4); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 587, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_7);
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  if (!(likely(((__pyx_t_7) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_7, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 587, __pyx_L1_error)
  __pyx_t_8 = ((PyArrayObject *)__pyx_t_7);
  {
    __Pyx_BufFmt_StackElem __pyx_stack[1];
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_pu.rcbuffer->pybuffer);
    __pyx_t_9 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_pu.rcbuffer->pybuffer, (PyObject*)__pyx_t_8, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack);
    if (unlikely(__pyx_t_9 < 0)) {
      PyErr_Fetch(&__pyx_t_10, &__pyx_t_11, &__pyx_t_12);
      if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_pu.rcbuffer->pybuffer, (PyObject*)__pyx_v_pu, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack) == -1)) {
        Py_XDECREF(__pyx_t_10); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_12);
        __Pyx_RaiseBufferFallbackError();
      } else {
        PyErr_Restore(__pyx_t_10, __pyx_t_11, __pyx_t_12);
      }
      __pyx_t_10 = __pyx_t_11 = __pyx_t_12 = 0;
    }
    __pyx_pybuffernd_pu.diminfo[0].strides = __pyx_pybuffernd_pu.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_pu.diminfo[0].shape = __pyx_pybuffernd_pu.rcbuffer->pybuffer.shape[0]; __pyx_pybuffernd_pu.diminfo[1].strides = __pyx_pybuffernd_pu.rcbuffer->pybuffer.strides[1]; __pyx_pybuffernd_pu.diminfo[1].shape = __pyx_pybuffernd_pu.rcbuffer->pybuffer.shape[1];
    if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 587, __pyx_L1_error)
  }
  __pyx_t_8 = 0;
  __pyx_v_pu = ((PyArrayObject *)__pyx_t_7);
  __pyx_t_7 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":589
 *         pu = np.random.uniform(self.init_low, self.init_high,
 *                                size=(trainset.n_users, self.n_factors))
 *         qi = np.random.uniform(self.init_low, self.init_high,             # <<<<<<<<<<<<<<
 *                                size=(trainset.n_items, self.n_factors))
 * 
 */
  __pyx_t_7 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 589, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_7);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_7, __pyx_n_s_random); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 589, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
  __pyx_t_7 = __Pyx_PyObject_GetAttrStr(__pyx_t_4, __pyx_n_s_uniform); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 589, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_7);
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_low); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 589, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_init_high); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 589, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __pyx_t_3 = PyTuple_New(2); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 589, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __Pyx_GIVEREF(__pyx_t_4);
  PyTuple_SET_ITEM(__pyx_t_3, 0, __pyx_t_4);
  __Pyx_GIVEREF(__pyx_t_5);
  PyTuple_SET_ITEM(__pyx_t_3, 1, __pyx_t_5);
  __pyx_t_4 = 0;
  __pyx_t_5 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":590
 *                                size=(trainset.n_users, self.n_factors))
 *         qi = np.random.uniform(self.init_low, self.init_high,
 *                                size=(trainset.n_items, self.n_factors))             # <<<<<<<<<<<<<<
 * 
 *         bu = np.zeros(trainset.n_users, np.double)
 */
  __pyx_t_5 = __Pyx_PyDict_NewPresized(1); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 590, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_items); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 590, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 590, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_6);
  __pyx_t_1 = PyTuple_New(2); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 590, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __Pyx_GIVEREF(__pyx_t_4);
  PyTuple_SET_ITEM(__pyx_t_1, 0, __pyx_t_4);
  __Pyx_GIVEREF(__pyx_t_6);
  PyTuple_SET_ITEM(__pyx_t_1, 1, __pyx_t_6);
  __pyx_t_4 = 0;
  __pyx_t_6 = 0;
  if (PyDict_SetItem(__pyx_t_5, __pyx_n_s_size, __pyx_t_1) < 0) __PYX_ERR(0, 590, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":589
 *         pu = np.random.uniform(self.init_low, self.init_high,
 *                                size=(trainset.n_users, self.n_factors))
 *         qi = np.random.uniform(self.init_low, self.init_high,             # <<<<<<<<<<<<<<
 *                                size=(trainset.n_items, self.n_factors))
 * 
 */
  __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_7, __pyx_t_3, __pyx_t_5); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 589, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  if (!(likely(((__pyx_t_1) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_1, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 589, __pyx_L1_error)
  __pyx_t_13 = ((PyArrayObject *)__pyx_t_1);
  {
    __Pyx_BufFmt_StackElem __pyx_stack[1];
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_qi.rcbuffer->pybuffer);
    __pyx_t_9 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_qi.rcbuffer->pybuffer, (PyObject*)__pyx_t_13, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack);
    if (unlikely(__pyx_t_9 < 0)) {
      PyErr_Fetch(&__pyx_t_12, &__pyx_t_11, &__pyx_t_10);
      if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_qi.rcbuffer->pybuffer, (PyObject*)__pyx_v_qi, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack) == -1)) {
        Py_XDECREF(__pyx_t_12); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_10);
        __Pyx_RaiseBufferFallbackError();
      } else {
        PyErr_Restore(__pyx_t_12, __pyx_t_11, __pyx_t_10);
      }
      __pyx_t_12 = __pyx_t_11 = __pyx_t_10 = 0;
    }
    __pyx_pybuffernd_qi.diminfo[0].strides = __pyx_pybuffernd_qi.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_qi.diminfo[0].shape = __pyx_pybuffernd_qi.rcbuffer->pybuffer.shape[0]; __pyx_pybuffernd_qi.diminfo[1].strides = __pyx_pybuffernd_qi.rcbuffer->pybuffer.strides[1]; __pyx_pybuffernd_qi.diminfo[1].shape = __pyx_pybuffernd_qi.rcbuffer->pybuffer.shape[1];
    if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 589, __pyx_L1_error)
  }
  __pyx_t_13 = 0;
  __pyx_v_qi = ((PyArrayObject *)__pyx_t_1);
  __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":592
 *                                size=(trainset.n_items, self.n_factors))
 * 
 *         bu = np.zeros(trainset.n_users, np.double)             # <<<<<<<<<<<<<<
 *         bi = np.zeros(trainset.n_items, np.double)
 * 
 */
  __pyx_t_5 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 592, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_t_5, __pyx_n_s_zeros); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 592, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_users); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 592, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __pyx_t_7 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 592, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_7);
  __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_t_7, __pyx_n_s_double); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 592, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_6);
  __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
  __pyx_t_7 = NULL;
  __pyx_t_9 = 0;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_3))) {
    __pyx_t_7 = PyMethod_GET_SELF(__pyx_t_3);
    if (likely(__pyx_t_7)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
      __Pyx_INCREF(__pyx_t_7);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_3, function);
      __pyx_t_9 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_3)) {
    PyObject *__pyx_temp[3] = {__pyx_t_7, __pyx_t_5, __pyx_t_6};
    __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-__pyx_t_9, 2+__pyx_t_9); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 592, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_7); __pyx_t_7 = 0;
    __Pyx_GOTREF(__pyx_t_1);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
    PyObject *__pyx_temp[3] = {__pyx_t_7, __pyx_t_5, __pyx_t_6};
    __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-__pyx_t_9, 2+__pyx_t_9); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 592, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_7); __pyx_t_7 = 0;
    __Pyx_GOTREF(__pyx_t_1);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  } else
  #endif
  {
    __pyx_t_4 = PyTuple_New(2+__pyx_t_9); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 592, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_4);
    if (__pyx_t_7) {
      __Pyx_GIVEREF(__pyx_t_7); PyTuple_SET_ITEM(__pyx_t_4, 0, __pyx_t_7); __pyx_t_7 = NULL;
    }
    __Pyx_GIVEREF(__pyx_t_5);
    PyTuple_SET_ITEM(__pyx_t_4, 0+__pyx_t_9, __pyx_t_5);
    __Pyx_GIVEREF(__pyx_t_6);
    PyTuple_SET_ITEM(__pyx_t_4, 1+__pyx_t_9, __pyx_t_6);
    __pyx_t_5 = 0;
    __pyx_t_6 = 0;
    __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_4, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 592, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  }
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  if (!(likely(((__pyx_t_1) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_1, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 592, __pyx_L1_error)
  __pyx_t_14 = ((PyArrayObject *)__pyx_t_1);
  {
    __Pyx_BufFmt_StackElem __pyx_stack[1];
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bu.rcbuffer->pybuffer);
    __pyx_t_9 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_bu.rcbuffer->pybuffer, (PyObject*)__pyx_t_14, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack);
    if (unlikely(__pyx_t_9 < 0)) {
      PyErr_Fetch(&__pyx_t_10, &__pyx_t_11, &__pyx_t_12);
      if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_bu.rcbuffer->pybuffer, (PyObject*)__pyx_v_bu, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack) == -1)) {
        Py_XDECREF(__pyx_t_10); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_12);
        __Pyx_RaiseBufferFallbackError();
      } else {
        PyErr_Restore(__pyx_t_10, __pyx_t_11, __pyx_t_12);
      }
      __pyx_t_10 = __pyx_t_11 = __pyx_t_12 = 0;
    }
    __pyx_pybuffernd_bu.diminfo[0].strides = __pyx_pybuffernd_bu.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_bu.diminfo[0].shape = __pyx_pybuffernd_bu.rcbuffer->pybuffer.shape[0];
    if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 592, __pyx_L1_error)
  }
  __pyx_t_14 = 0;
  __pyx_v_bu = ((PyArrayObject *)__pyx_t_1);
  __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":593
 * 
 *         bu = np.zeros(trainset.n_users, np.double)
 *         bi = np.zeros(trainset.n_items, np.double)             # <<<<<<<<<<<<<<
 * 
 *         if not self.biased:
 */
  __pyx_t_3 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 593, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_3, __pyx_n_s_zeros); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 593, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_items); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 593, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __pyx_t_6 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 593, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_6);
  __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_t_6, __pyx_n_s_double); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 593, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_5);
  __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
  __pyx_t_6 = NULL;
  __pyx_t_9 = 0;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_4))) {
    __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_4);
    if (likely(__pyx_t_6)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_4);
      __Pyx_INCREF(__pyx_t_6);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_4, function);
      __pyx_t_9 = 1;
    }
  }
  #if CYTHON_FAST_PYCALL
  if (PyFunction_Check(__pyx_t_4)) {
    PyObject *__pyx_temp[3] = {__pyx_t_6, __pyx_t_3, __pyx_t_5};
    __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_4, __pyx_temp+1-__pyx_t_9, 2+__pyx_t_9); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 593, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
    __Pyx_GOTREF(__pyx_t_1);
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  } else
  #endif
  #if CYTHON_FAST_PYCCALL
  if (__Pyx_PyFastCFunction_Check(__pyx_t_4)) {
    PyObject *__pyx_temp[3] = {__pyx_t_6, __pyx_t_3, __pyx_t_5};
    __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_4, __pyx_temp+1-__pyx_t_9, 2+__pyx_t_9); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 593, __pyx_L1_error)
    __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
    __Pyx_GOTREF(__pyx_t_1);
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
  } else
  #endif
  {
    __pyx_t_7 = PyTuple_New(2+__pyx_t_9); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 593, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_7);
    if (__pyx_t_6) {
      __Pyx_GIVEREF(__pyx_t_6); PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_t_6); __pyx_t_6 = NULL;
    }
    __Pyx_GIVEREF(__pyx_t_3);
    PyTuple_SET_ITEM(__pyx_t_7, 0+__pyx_t_9, __pyx_t_3);
    __Pyx_GIVEREF(__pyx_t_5);
    PyTuple_SET_ITEM(__pyx_t_7, 1+__pyx_t_9, __pyx_t_5);
    __pyx_t_3 = 0;
    __pyx_t_5 = 0;
    __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_4, __pyx_t_7, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 593, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
  }
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  if (!(likely(((__pyx_t_1) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_1, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 593, __pyx_L1_error)
  __pyx_t_15 = ((PyArrayObject *)__pyx_t_1);
  {
    __Pyx_BufFmt_StackElem __pyx_stack[1];
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bi.rcbuffer->pybuffer);
    __pyx_t_9 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_bi.rcbuffer->pybuffer, (PyObject*)__pyx_t_15, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack);
    if (unlikely(__pyx_t_9 < 0)) {
      PyErr_Fetch(&__pyx_t_12, &__pyx_t_11, &__pyx_t_10);
      if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_bi.rcbuffer->pybuffer, (PyObject*)__pyx_v_bi, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 1, 0, __pyx_stack) == -1)) {
        Py_XDECREF(__pyx_t_12); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_10);
        __Pyx_RaiseBufferFallbackError();
      } else {
        PyErr_Restore(__pyx_t_12, __pyx_t_11, __pyx_t_10);
      }
      __pyx_t_12 = __pyx_t_11 = __pyx_t_10 = 0;
    }
    __pyx_pybuffernd_bi.diminfo[0].strides = __pyx_pybuffernd_bi.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_bi.diminfo[0].shape = __pyx_pybuffernd_bi.rcbuffer->pybuffer.shape[0];
    if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 593, __pyx_L1_error)
  }
  __pyx_t_15 = 0;
  __pyx_v_bi = ((PyArrayObject *)__pyx_t_1);
  __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":595
 *         bi = np.zeros(trainset.n_items, np.double)
 * 
 *         if not self.biased:             # <<<<<<<<<<<<<<
 *             global_mean = 0
 * 
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_biased); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 595, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_16 = __Pyx_PyObject_IsTrue(__pyx_t_1); if (unlikely(__pyx_t_16 < 0)) __PYX_ERR(0, 595, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_17 = ((!__pyx_t_16) != 0);
  if (__pyx_t_17) {

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":596
 * 
 *         if not self.biased:
 *             global_mean = 0             # <<<<<<<<<<<<<<
 * 
 *         for current_epoch in range(self.n_epochs):
 */
    __pyx_v_global_mean = 0.0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":595
 *         bi = np.zeros(trainset.n_items, np.double)
 * 
 *         if not self.biased:             # <<<<<<<<<<<<<<
 *             global_mean = 0
 * 
 */
  }

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":598
 *             global_mean = 0
 * 
 *         for current_epoch in range(self.n_epochs):             # <<<<<<<<<<<<<<
 * 
 *             if self.verbose:
 */
  __pyx_t_4 = __Pyx_GetModuleGlobalName(__pyx_n_s_range); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 598, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __pyx_t_7 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_epochs); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 598, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_7);
  __pyx_t_5 = NULL;
  if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_4))) {
    __pyx_t_5 = PyMethod_GET_SELF(__pyx_t_4);
    if (likely(__pyx_t_5)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_4);
      __Pyx_INCREF(__pyx_t_5);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_4, function);
    }
  }
  if (!__pyx_t_5) {
    __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_4, __pyx_t_7); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 598, __pyx_L1_error)
    __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
    __Pyx_GOTREF(__pyx_t_1);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_4)) {
      PyObject *__pyx_temp[2] = {__pyx_t_5, __pyx_t_7};
      __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 598, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_4)) {
      PyObject *__pyx_temp[2] = {__pyx_t_5, __pyx_t_7};
      __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 598, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
    } else
    #endif
    {
      __pyx_t_3 = PyTuple_New(1+1); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 598, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_3, 0, __pyx_t_5); __pyx_t_5 = NULL;
      __Pyx_GIVEREF(__pyx_t_7);
      PyTuple_SET_ITEM(__pyx_t_3, 0+1, __pyx_t_7);
      __pyx_t_7 = 0;
      __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_4, __pyx_t_3, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 598, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  if (likely(PyList_CheckExact(__pyx_t_1)) || PyTuple_CheckExact(__pyx_t_1)) {
    __pyx_t_4 = __pyx_t_1; __Pyx_INCREF(__pyx_t_4); __pyx_t_18 = 0;
    __pyx_t_19 = NULL;
  } else {
    __pyx_t_18 = -1; __pyx_t_4 = PyObject_GetIter(__pyx_t_1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 598, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_4);
    __pyx_t_19 = Py_TYPE(__pyx_t_4)->tp_iternext; if (unlikely(!__pyx_t_19)) __PYX_ERR(0, 598, __pyx_L1_error)
  }
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  for (;;) {
    if (likely(!__pyx_t_19)) {
      if (likely(PyList_CheckExact(__pyx_t_4))) {
        if (__pyx_t_18 >= PyList_GET_SIZE(__pyx_t_4)) break;
        #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
        __pyx_t_1 = PyList_GET_ITEM(__pyx_t_4, __pyx_t_18); __Pyx_INCREF(__pyx_t_1); __pyx_t_18++; if (unlikely(0 < 0)) __PYX_ERR(0, 598, __pyx_L1_error)
        #else
        __pyx_t_1 = PySequence_ITEM(__pyx_t_4, __pyx_t_18); __pyx_t_18++; if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 598, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        #endif
      } else {
        if (__pyx_t_18 >= PyTuple_GET_SIZE(__pyx_t_4)) break;
        #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
        __pyx_t_1 = PyTuple_GET_ITEM(__pyx_t_4, __pyx_t_18); __Pyx_INCREF(__pyx_t_1); __pyx_t_18++; if (unlikely(0 < 0)) __PYX_ERR(0, 598, __pyx_L1_error)
        #else
        __pyx_t_1 = PySequence_ITEM(__pyx_t_4, __pyx_t_18); __pyx_t_18++; if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 598, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        #endif
      }
    } else {
      __pyx_t_1 = __pyx_t_19(__pyx_t_4);
      if (unlikely(!__pyx_t_1)) {
        PyObject* exc_type = PyErr_Occurred();
        if (exc_type) {
          if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
          else __PYX_ERR(0, 598, __pyx_L1_error)
        }
        break;
      }
      __Pyx_GOTREF(__pyx_t_1);
    }
    __Pyx_XDECREF_SET(__pyx_v_current_epoch, __pyx_t_1);
    __pyx_t_1 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":600
 *         for current_epoch in range(self.n_epochs):
 * 
 *             if self.verbose:             # <<<<<<<<<<<<<<
 *                 print("Processing epoch {}".format(current_epoch))
 * 
 */
    __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_verbose); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 600, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    __pyx_t_17 = __Pyx_PyObject_IsTrue(__pyx_t_1); if (unlikely(__pyx_t_17 < 0)) __PYX_ERR(0, 600, __pyx_L1_error)
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    if (__pyx_t_17) {

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":601
 * 
 *             if self.verbose:
 *                 print("Processing epoch {}".format(current_epoch))             # <<<<<<<<<<<<<<
 * 
 *             # (re)initialize nums and denoms to zero
 */
      __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_kp_u_Processing_epoch, __pyx_n_s_format); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 601, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_7 = NULL;
      if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_3))) {
        __pyx_t_7 = PyMethod_GET_SELF(__pyx_t_3);
        if (likely(__pyx_t_7)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
          __Pyx_INCREF(__pyx_t_7);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_3, function);
        }
      }
      if (!__pyx_t_7) {
        __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_3, __pyx_v_current_epoch); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 601, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
      } else {
        #if CYTHON_FAST_PYCALL
        if (PyFunction_Check(__pyx_t_3)) {
          PyObject *__pyx_temp[2] = {__pyx_t_7, __pyx_v_current_epoch};
          __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 601, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_7); __pyx_t_7 = 0;
          __Pyx_GOTREF(__pyx_t_1);
        } else
        #endif
        #if CYTHON_FAST_PYCCALL
        if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
          PyObject *__pyx_temp[2] = {__pyx_t_7, __pyx_v_current_epoch};
          __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 601, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_7); __pyx_t_7 = 0;
          __Pyx_GOTREF(__pyx_t_1);
        } else
        #endif
        {
          __pyx_t_5 = PyTuple_New(1+1); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 601, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_5);
          __Pyx_GIVEREF(__pyx_t_7); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_7); __pyx_t_7 = NULL;
          __Pyx_INCREF(__pyx_v_current_epoch);
          __Pyx_GIVEREF(__pyx_v_current_epoch);
          PyTuple_SET_ITEM(__pyx_t_5, 0+1, __pyx_v_current_epoch);
          __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_5, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 601, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_1);
          __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        }
      }
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __pyx_t_3 = PyTuple_New(1); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 601, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __Pyx_GIVEREF(__pyx_t_1);
      PyTuple_SET_ITEM(__pyx_t_3, 0, __pyx_t_1);
      __pyx_t_1 = 0;
      __pyx_t_1 = __Pyx_PyObject_Call(__pyx_builtin_print, __pyx_t_3, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 601, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":600
 *         for current_epoch in range(self.n_epochs):
 * 
 *             if self.verbose:             # <<<<<<<<<<<<<<
 *                 print("Processing epoch {}".format(current_epoch))
 * 
 */
    }

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":604
 * 
 *             # (re)initialize nums and denoms to zero
 *             user_num = np.zeros((trainset.n_users, self.n_factors))             # <<<<<<<<<<<<<<
 *             user_denom = np.zeros((trainset.n_users, self.n_factors))
 *             item_num = np.zeros((trainset.n_items, self.n_factors))
 */
    __pyx_t_3 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 604, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_t_3, __pyx_n_s_zeros); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 604, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_5);
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_users); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 604, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __pyx_t_7 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 604, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_7);
    __pyx_t_6 = PyTuple_New(2); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 604, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_6);
    __Pyx_GIVEREF(__pyx_t_3);
    PyTuple_SET_ITEM(__pyx_t_6, 0, __pyx_t_3);
    __Pyx_GIVEREF(__pyx_t_7);
    PyTuple_SET_ITEM(__pyx_t_6, 1, __pyx_t_7);
    __pyx_t_3 = 0;
    __pyx_t_7 = 0;
    __pyx_t_7 = NULL;
    if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_5))) {
      __pyx_t_7 = PyMethod_GET_SELF(__pyx_t_5);
      if (likely(__pyx_t_7)) {
        PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_5);
        __Pyx_INCREF(__pyx_t_7);
        __Pyx_INCREF(function);
        __Pyx_DECREF_SET(__pyx_t_5, function);
      }
    }
    if (!__pyx_t_7) {
      __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_5, __pyx_t_6); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 604, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else {
      #if CYTHON_FAST_PYCALL
      if (PyFunction_Check(__pyx_t_5)) {
        PyObject *__pyx_temp[2] = {__pyx_t_7, __pyx_t_6};
        __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_5, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 604, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_7); __pyx_t_7 = 0;
        __Pyx_GOTREF(__pyx_t_1);
        __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      } else
      #endif
      #if CYTHON_FAST_PYCCALL
      if (__Pyx_PyFastCFunction_Check(__pyx_t_5)) {
        PyObject *__pyx_temp[2] = {__pyx_t_7, __pyx_t_6};
        __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_5, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 604, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_7); __pyx_t_7 = 0;
        __Pyx_GOTREF(__pyx_t_1);
        __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      } else
      #endif
      {
        __pyx_t_3 = PyTuple_New(1+1); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 604, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_3);
        __Pyx_GIVEREF(__pyx_t_7); PyTuple_SET_ITEM(__pyx_t_3, 0, __pyx_t_7); __pyx_t_7 = NULL;
        __Pyx_GIVEREF(__pyx_t_6);
        PyTuple_SET_ITEM(__pyx_t_3, 0+1, __pyx_t_6);
        __pyx_t_6 = 0;
        __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_5, __pyx_t_3, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 604, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      }
    }
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    if (!(likely(((__pyx_t_1) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_1, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 604, __pyx_L1_error)
    __pyx_t_20 = ((PyArrayObject *)__pyx_t_1);
    {
      __Pyx_BufFmt_StackElem __pyx_stack[1];
      __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_user_num.rcbuffer->pybuffer);
      __pyx_t_9 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_user_num.rcbuffer->pybuffer, (PyObject*)__pyx_t_20, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack);
      if (unlikely(__pyx_t_9 < 0)) {
        PyErr_Fetch(&__pyx_t_10, &__pyx_t_11, &__pyx_t_12);
        if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_user_num.rcbuffer->pybuffer, (PyObject*)__pyx_v_user_num, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack) == -1)) {
          Py_XDECREF(__pyx_t_10); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_12);
          __Pyx_RaiseBufferFallbackError();
        } else {
          PyErr_Restore(__pyx_t_10, __pyx_t_11, __pyx_t_12);
        }
        __pyx_t_10 = __pyx_t_11 = __pyx_t_12 = 0;
      }
      __pyx_pybuffernd_user_num.diminfo[0].strides = __pyx_pybuffernd_user_num.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_user_num.diminfo[0].shape = __pyx_pybuffernd_user_num.rcbuffer->pybuffer.shape[0]; __pyx_pybuffernd_user_num.diminfo[1].strides = __pyx_pybuffernd_user_num.rcbuffer->pybuffer.strides[1]; __pyx_pybuffernd_user_num.diminfo[1].shape = __pyx_pybuffernd_user_num.rcbuffer->pybuffer.shape[1];
      if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 604, __pyx_L1_error)
    }
    __pyx_t_20 = 0;
    __Pyx_XDECREF_SET(__pyx_v_user_num, ((PyArrayObject *)__pyx_t_1));
    __pyx_t_1 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":605
 *             # (re)initialize nums and denoms to zero
 *             user_num = np.zeros((trainset.n_users, self.n_factors))
 *             user_denom = np.zeros((trainset.n_users, self.n_factors))             # <<<<<<<<<<<<<<
 *             item_num = np.zeros((trainset.n_items, self.n_factors))
 *             item_denom = np.zeros((trainset.n_items, self.n_factors))
 */
    __pyx_t_5 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 605, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_5);
    __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_t_5, __pyx_n_s_zeros); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 605, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_users); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 605, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_5);
    __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 605, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_6);
    __pyx_t_7 = PyTuple_New(2); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 605, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_7);
    __Pyx_GIVEREF(__pyx_t_5);
    PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_t_5);
    __Pyx_GIVEREF(__pyx_t_6);
    PyTuple_SET_ITEM(__pyx_t_7, 1, __pyx_t_6);
    __pyx_t_5 = 0;
    __pyx_t_6 = 0;
    __pyx_t_6 = NULL;
    if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_3))) {
      __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_3);
      if (likely(__pyx_t_6)) {
        PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
        __Pyx_INCREF(__pyx_t_6);
        __Pyx_INCREF(function);
        __Pyx_DECREF_SET(__pyx_t_3, function);
      }
    }
    if (!__pyx_t_6) {
      __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_3, __pyx_t_7); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 605, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else {
      #if CYTHON_FAST_PYCALL
      if (PyFunction_Check(__pyx_t_3)) {
        PyObject *__pyx_temp[2] = {__pyx_t_6, __pyx_t_7};
        __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 605, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
        __Pyx_GOTREF(__pyx_t_1);
        __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
      } else
      #endif
      #if CYTHON_FAST_PYCCALL
      if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
        PyObject *__pyx_temp[2] = {__pyx_t_6, __pyx_t_7};
        __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 605, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
        __Pyx_GOTREF(__pyx_t_1);
        __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
      } else
      #endif
      {
        __pyx_t_5 = PyTuple_New(1+1); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 605, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_5);
        __Pyx_GIVEREF(__pyx_t_6); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_6); __pyx_t_6 = NULL;
        __Pyx_GIVEREF(__pyx_t_7);
        PyTuple_SET_ITEM(__pyx_t_5, 0+1, __pyx_t_7);
        __pyx_t_7 = 0;
        __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_5, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 605, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
      }
    }
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    if (!(likely(((__pyx_t_1) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_1, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 605, __pyx_L1_error)
    __pyx_t_21 = ((PyArrayObject *)__pyx_t_1);
    {
      __Pyx_BufFmt_StackElem __pyx_stack[1];
      __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_user_denom.rcbuffer->pybuffer);
      __pyx_t_9 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_user_denom.rcbuffer->pybuffer, (PyObject*)__pyx_t_21, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack);
      if (unlikely(__pyx_t_9 < 0)) {
        PyErr_Fetch(&__pyx_t_12, &__pyx_t_11, &__pyx_t_10);
        if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_user_denom.rcbuffer->pybuffer, (PyObject*)__pyx_v_user_denom, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack) == -1)) {
          Py_XDECREF(__pyx_t_12); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_10);
          __Pyx_RaiseBufferFallbackError();
        } else {
          PyErr_Restore(__pyx_t_12, __pyx_t_11, __pyx_t_10);
        }
        __pyx_t_12 = __pyx_t_11 = __pyx_t_10 = 0;
      }
      __pyx_pybuffernd_user_denom.diminfo[0].strides = __pyx_pybuffernd_user_denom.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_user_denom.diminfo[0].shape = __pyx_pybuffernd_user_denom.rcbuffer->pybuffer.shape[0]; __pyx_pybuffernd_user_denom.diminfo[1].strides = __pyx_pybuffernd_user_denom.rcbuffer->pybuffer.strides[1]; __pyx_pybuffernd_user_denom.diminfo[1].shape = __pyx_pybuffernd_user_denom.rcbuffer->pybuffer.shape[1];
      if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 605, __pyx_L1_error)
    }
    __pyx_t_21 = 0;
    __Pyx_XDECREF_SET(__pyx_v_user_denom, ((PyArrayObject *)__pyx_t_1));
    __pyx_t_1 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":606
 *             user_num = np.zeros((trainset.n_users, self.n_factors))
 *             user_denom = np.zeros((trainset.n_users, self.n_factors))
 *             item_num = np.zeros((trainset.n_items, self.n_factors))             # <<<<<<<<<<<<<<
 *             item_denom = np.zeros((trainset.n_items, self.n_factors))
 * 
 */
    __pyx_t_3 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 606, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_t_3, __pyx_n_s_zeros); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 606, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_5);
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_items); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 606, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __pyx_t_7 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 606, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_7);
    __pyx_t_6 = PyTuple_New(2); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 606, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_6);
    __Pyx_GIVEREF(__pyx_t_3);
    PyTuple_SET_ITEM(__pyx_t_6, 0, __pyx_t_3);
    __Pyx_GIVEREF(__pyx_t_7);
    PyTuple_SET_ITEM(__pyx_t_6, 1, __pyx_t_7);
    __pyx_t_3 = 0;
    __pyx_t_7 = 0;
    __pyx_t_7 = NULL;
    if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_5))) {
      __pyx_t_7 = PyMethod_GET_SELF(__pyx_t_5);
      if (likely(__pyx_t_7)) {
        PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_5);
        __Pyx_INCREF(__pyx_t_7);
        __Pyx_INCREF(function);
        __Pyx_DECREF_SET(__pyx_t_5, function);
      }
    }
    if (!__pyx_t_7) {
      __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_5, __pyx_t_6); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 606, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else {
      #if CYTHON_FAST_PYCALL
      if (PyFunction_Check(__pyx_t_5)) {
        PyObject *__pyx_temp[2] = {__pyx_t_7, __pyx_t_6};
        __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_5, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 606, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_7); __pyx_t_7 = 0;
        __Pyx_GOTREF(__pyx_t_1);
        __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      } else
      #endif
      #if CYTHON_FAST_PYCCALL
      if (__Pyx_PyFastCFunction_Check(__pyx_t_5)) {
        PyObject *__pyx_temp[2] = {__pyx_t_7, __pyx_t_6};
        __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_5, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 606, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_7); __pyx_t_7 = 0;
        __Pyx_GOTREF(__pyx_t_1);
        __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      } else
      #endif
      {
        __pyx_t_3 = PyTuple_New(1+1); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 606, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_3);
        __Pyx_GIVEREF(__pyx_t_7); PyTuple_SET_ITEM(__pyx_t_3, 0, __pyx_t_7); __pyx_t_7 = NULL;
        __Pyx_GIVEREF(__pyx_t_6);
        PyTuple_SET_ITEM(__pyx_t_3, 0+1, __pyx_t_6);
        __pyx_t_6 = 0;
        __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_5, __pyx_t_3, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 606, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      }
    }
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    if (!(likely(((__pyx_t_1) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_1, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 606, __pyx_L1_error)
    __pyx_t_22 = ((PyArrayObject *)__pyx_t_1);
    {
      __Pyx_BufFmt_StackElem __pyx_stack[1];
      __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_item_num.rcbuffer->pybuffer);
      __pyx_t_9 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_item_num.rcbuffer->pybuffer, (PyObject*)__pyx_t_22, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack);
      if (unlikely(__pyx_t_9 < 0)) {
        PyErr_Fetch(&__pyx_t_10, &__pyx_t_11, &__pyx_t_12);
        if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_item_num.rcbuffer->pybuffer, (PyObject*)__pyx_v_item_num, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack) == -1)) {
          Py_XDECREF(__pyx_t_10); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_12);
          __Pyx_RaiseBufferFallbackError();
        } else {
          PyErr_Restore(__pyx_t_10, __pyx_t_11, __pyx_t_12);
        }
        __pyx_t_10 = __pyx_t_11 = __pyx_t_12 = 0;
      }
      __pyx_pybuffernd_item_num.diminfo[0].strides = __pyx_pybuffernd_item_num.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_item_num.diminfo[0].shape = __pyx_pybuffernd_item_num.rcbuffer->pybuffer.shape[0]; __pyx_pybuffernd_item_num.diminfo[1].strides = __pyx_pybuffernd_item_num.rcbuffer->pybuffer.strides[1]; __pyx_pybuffernd_item_num.diminfo[1].shape = __pyx_pybuffernd_item_num.rcbuffer->pybuffer.shape[1];
      if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 606, __pyx_L1_error)
    }
    __pyx_t_22 = 0;
    __Pyx_XDECREF_SET(__pyx_v_item_num, ((PyArrayObject *)__pyx_t_1));
    __pyx_t_1 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":607
 *             user_denom = np.zeros((trainset.n_users, self.n_factors))
 *             item_num = np.zeros((trainset.n_items, self.n_factors))
 *             item_denom = np.zeros((trainset.n_items, self.n_factors))             # <<<<<<<<<<<<<<
 * 
 *             # Compute numerators and denominators for users and items factors
 */
    __pyx_t_5 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 607, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_5);
    __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_t_5, __pyx_n_s_zeros); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 607, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_n_items); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 607, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_5);
    __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 607, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_6);
    __pyx_t_7 = PyTuple_New(2); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 607, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_7);
    __Pyx_GIVEREF(__pyx_t_5);
    PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_t_5);
    __Pyx_GIVEREF(__pyx_t_6);
    PyTuple_SET_ITEM(__pyx_t_7, 1, __pyx_t_6);
    __pyx_t_5 = 0;
    __pyx_t_6 = 0;
    __pyx_t_6 = NULL;
    if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_3))) {
      __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_3);
      if (likely(__pyx_t_6)) {
        PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
        __Pyx_INCREF(__pyx_t_6);
        __Pyx_INCREF(function);
        __Pyx_DECREF_SET(__pyx_t_3, function);
      }
    }
    if (!__pyx_t_6) {
      __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_3, __pyx_t_7); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 607, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else {
      #if CYTHON_FAST_PYCALL
      if (PyFunction_Check(__pyx_t_3)) {
        PyObject *__pyx_temp[2] = {__pyx_t_6, __pyx_t_7};
        __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 607, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
        __Pyx_GOTREF(__pyx_t_1);
        __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
      } else
      #endif
      #if CYTHON_FAST_PYCCALL
      if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
        PyObject *__pyx_temp[2] = {__pyx_t_6, __pyx_t_7};
        __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 607, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_6); __pyx_t_6 = 0;
        __Pyx_GOTREF(__pyx_t_1);
        __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
      } else
      #endif
      {
        __pyx_t_5 = PyTuple_New(1+1); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 607, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_5);
        __Pyx_GIVEREF(__pyx_t_6); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_6); __pyx_t_6 = NULL;
        __Pyx_GIVEREF(__pyx_t_7);
        PyTuple_SET_ITEM(__pyx_t_5, 0+1, __pyx_t_7);
        __pyx_t_7 = 0;
        __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_5, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 607, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
      }
    }
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    if (!(likely(((__pyx_t_1) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_1, __pyx_ptype_5numpy_ndarray))))) __PYX_ERR(0, 607, __pyx_L1_error)
    __pyx_t_23 = ((PyArrayObject *)__pyx_t_1);
    {
      __Pyx_BufFmt_StackElem __pyx_stack[1];
      __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_item_denom.rcbuffer->pybuffer);
      __pyx_t_9 = __Pyx_GetBufferAndValidate(&__pyx_pybuffernd_item_denom.rcbuffer->pybuffer, (PyObject*)__pyx_t_23, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack);
      if (unlikely(__pyx_t_9 < 0)) {
        PyErr_Fetch(&__pyx_t_12, &__pyx_t_11, &__pyx_t_10);
        if (unlikely(__Pyx_GetBufferAndValidate(&__pyx_pybuffernd_item_denom.rcbuffer->pybuffer, (PyObject*)__pyx_v_item_denom, &__Pyx_TypeInfo_nn___pyx_t_5numpy_double_t, PyBUF_FORMAT| PyBUF_STRIDES| PyBUF_WRITABLE, 2, 0, __pyx_stack) == -1)) {
          Py_XDECREF(__pyx_t_12); Py_XDECREF(__pyx_t_11); Py_XDECREF(__pyx_t_10);
          __Pyx_RaiseBufferFallbackError();
        } else {
          PyErr_Restore(__pyx_t_12, __pyx_t_11, __pyx_t_10);
        }
        __pyx_t_12 = __pyx_t_11 = __pyx_t_10 = 0;
      }
      __pyx_pybuffernd_item_denom.diminfo[0].strides = __pyx_pybuffernd_item_denom.rcbuffer->pybuffer.strides[0]; __pyx_pybuffernd_item_denom.diminfo[0].shape = __pyx_pybuffernd_item_denom.rcbuffer->pybuffer.shape[0]; __pyx_pybuffernd_item_denom.diminfo[1].strides = __pyx_pybuffernd_item_denom.rcbuffer->pybuffer.strides[1]; __pyx_pybuffernd_item_denom.diminfo[1].shape = __pyx_pybuffernd_item_denom.rcbuffer->pybuffer.shape[1];
      if (unlikely(__pyx_t_9 < 0)) __PYX_ERR(0, 607, __pyx_L1_error)
    }
    __pyx_t_23 = 0;
    __Pyx_XDECREF_SET(__pyx_v_item_denom, ((PyArrayObject *)__pyx_t_1));
    __pyx_t_1 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":610
 * 
 *             # Compute numerators and denominators for users and items factors
 *             for u, i, r in trainset.all_ratings():             # <<<<<<<<<<<<<<
 * 
 *                 # compute current estimation and error
 */
    __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_all_ratings); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 610, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __pyx_t_5 = NULL;
    if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_3))) {
      __pyx_t_5 = PyMethod_GET_SELF(__pyx_t_3);
      if (likely(__pyx_t_5)) {
        PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
        __Pyx_INCREF(__pyx_t_5);
        __Pyx_INCREF(function);
        __Pyx_DECREF_SET(__pyx_t_3, function);
      }
    }
    if (__pyx_t_5) {
      __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_3, __pyx_t_5); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 610, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
    } else {
      __pyx_t_1 = __Pyx_PyObject_CallNoArg(__pyx_t_3); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 610, __pyx_L1_error)
    }
    __Pyx_GOTREF(__pyx_t_1);
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    if (likely(PyList_CheckExact(__pyx_t_1)) || PyTuple_CheckExact(__pyx_t_1)) {
      __pyx_t_3 = __pyx_t_1; __Pyx_INCREF(__pyx_t_3); __pyx_t_24 = 0;
      __pyx_t_25 = NULL;
    } else {
      __pyx_t_24 = -1; __pyx_t_3 = PyObject_GetIter(__pyx_t_1); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 610, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_25 = Py_TYPE(__pyx_t_3)->tp_iternext; if (unlikely(!__pyx_t_25)) __PYX_ERR(0, 610, __pyx_L1_error)
    }
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    for (;;) {
      if (likely(!__pyx_t_25)) {
        if (likely(PyList_CheckExact(__pyx_t_3))) {
          if (__pyx_t_24 >= PyList_GET_SIZE(__pyx_t_3)) break;
          #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
          __pyx_t_1 = PyList_GET_ITEM(__pyx_t_3, __pyx_t_24); __Pyx_INCREF(__pyx_t_1); __pyx_t_24++; if (unlikely(0 < 0)) __PYX_ERR(0, 610, __pyx_L1_error)
          #else
          __pyx_t_1 = PySequence_ITEM(__pyx_t_3, __pyx_t_24); __pyx_t_24++; if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 610, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_1);
          #endif
        } else {
          if (__pyx_t_24 >= PyTuple_GET_SIZE(__pyx_t_3)) break;
          #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
          __pyx_t_1 = PyTuple_GET_ITEM(__pyx_t_3, __pyx_t_24); __Pyx_INCREF(__pyx_t_1); __pyx_t_24++; if (unlikely(0 < 0)) __PYX_ERR(0, 610, __pyx_L1_error)
          #else
          __pyx_t_1 = PySequence_ITEM(__pyx_t_3, __pyx_t_24); __pyx_t_24++; if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 610, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_1);
          #endif
        }
      } else {
        __pyx_t_1 = __pyx_t_25(__pyx_t_3);
        if (unlikely(!__pyx_t_1)) {
          PyObject* exc_type = PyErr_Occurred();
          if (exc_type) {
            if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
            else __PYX_ERR(0, 610, __pyx_L1_error)
          }
          break;
        }
        __Pyx_GOTREF(__pyx_t_1);
      }
      if ((likely(PyTuple_CheckExact(__pyx_t_1))) || (PyList_CheckExact(__pyx_t_1))) {
        PyObject* sequence = __pyx_t_1;
        #if !CYTHON_COMPILING_IN_PYPY
        Py_ssize_t size = Py_SIZE(sequence);
        #else
        Py_ssize_t size = PySequence_Size(sequence);
        #endif
        if (unlikely(size != 3)) {
          if (size > 3) __Pyx_RaiseTooManyValuesError(3);
          else if (size >= 0) __Pyx_RaiseNeedMoreValuesError(size);
          __PYX_ERR(0, 610, __pyx_L1_error)
        }
        #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
        if (likely(PyTuple_CheckExact(sequence))) {
          __pyx_t_5 = PyTuple_GET_ITEM(sequence, 0); 
          __pyx_t_7 = PyTuple_GET_ITEM(sequence, 1); 
          __pyx_t_6 = PyTuple_GET_ITEM(sequence, 2); 
        } else {
          __pyx_t_5 = PyList_GET_ITEM(sequence, 0); 
          __pyx_t_7 = PyList_GET_ITEM(sequence, 1); 
          __pyx_t_6 = PyList_GET_ITEM(sequence, 2); 
        }
        __Pyx_INCREF(__pyx_t_5);
        __Pyx_INCREF(__pyx_t_7);
        __Pyx_INCREF(__pyx_t_6);
        #else
        __pyx_t_5 = PySequence_ITEM(sequence, 0); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 610, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_5);
        __pyx_t_7 = PySequence_ITEM(sequence, 1); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 610, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_7);
        __pyx_t_6 = PySequence_ITEM(sequence, 2); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 610, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_6);
        #endif
        __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      } else {
        Py_ssize_t index = -1;
        __pyx_t_26 = PyObject_GetIter(__pyx_t_1); if (unlikely(!__pyx_t_26)) __PYX_ERR(0, 610, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_26);
        __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
        __pyx_t_27 = Py_TYPE(__pyx_t_26)->tp_iternext;
        index = 0; __pyx_t_5 = __pyx_t_27(__pyx_t_26); if (unlikely(!__pyx_t_5)) goto __pyx_L9_unpacking_failed;
        __Pyx_GOTREF(__pyx_t_5);
        index = 1; __pyx_t_7 = __pyx_t_27(__pyx_t_26); if (unlikely(!__pyx_t_7)) goto __pyx_L9_unpacking_failed;
        __Pyx_GOTREF(__pyx_t_7);
        index = 2; __pyx_t_6 = __pyx_t_27(__pyx_t_26); if (unlikely(!__pyx_t_6)) goto __pyx_L9_unpacking_failed;
        __Pyx_GOTREF(__pyx_t_6);
        if (__Pyx_IternextUnpackEndCheck(__pyx_t_27(__pyx_t_26), 3) < 0) __PYX_ERR(0, 610, __pyx_L1_error)
        __pyx_t_27 = NULL;
        __Pyx_DECREF(__pyx_t_26); __pyx_t_26 = 0;
        goto __pyx_L10_unpacking_done;
        __pyx_L9_unpacking_failed:;
        __Pyx_DECREF(__pyx_t_26); __pyx_t_26 = 0;
        __pyx_t_27 = NULL;
        if (__Pyx_IterFinish() == 0) __Pyx_RaiseNeedMoreValuesError(index);
        __PYX_ERR(0, 610, __pyx_L1_error)
        __pyx_L10_unpacking_done:;
      }
      __pyx_t_9 = __Pyx_PyInt_As_int(__pyx_t_5); if (unlikely((__pyx_t_9 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 610, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
      __pyx_t_28 = __Pyx_PyInt_As_int(__pyx_t_7); if (unlikely((__pyx_t_28 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 610, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
      __pyx_t_2 = __pyx_PyFloat_AsDouble(__pyx_t_6); if (unlikely((__pyx_t_2 == (double)-1) && PyErr_Occurred())) __PYX_ERR(0, 610, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      __pyx_v_u = __pyx_t_9;
      __pyx_v_i = __pyx_t_28;
      __pyx_v_r = __pyx_t_2;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":613
 * 
 *                 # compute current estimation and error
 *                 dot = 0  # <q_i, p_u>             # <<<<<<<<<<<<<<
 *                 for f in range(self.n_factors):
 *                     dot += qi[i, f] * pu[u, f]
 */
      __pyx_v_dot = 0.0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":614
 *                 # compute current estimation and error
 *                 dot = 0  # <q_i, p_u>
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     dot += qi[i, f] * pu[u, f]
 *                 est = global_mean + bu[u] + bi[i] + dot
 */
      __pyx_t_6 = __Pyx_GetModuleGlobalName(__pyx_n_s_range); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 614, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_6);
      __pyx_t_7 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 614, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_7);
      __pyx_t_5 = NULL;
      if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_6))) {
        __pyx_t_5 = PyMethod_GET_SELF(__pyx_t_6);
        if (likely(__pyx_t_5)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_6);
          __Pyx_INCREF(__pyx_t_5);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_6, function);
        }
      }
      if (!__pyx_t_5) {
        __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_6, __pyx_t_7); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 614, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
        __Pyx_GOTREF(__pyx_t_1);
      } else {
        #if CYTHON_FAST_PYCALL
        if (PyFunction_Check(__pyx_t_6)) {
          PyObject *__pyx_temp[2] = {__pyx_t_5, __pyx_t_7};
          __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_6, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 614, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
          __Pyx_GOTREF(__pyx_t_1);
          __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
        } else
        #endif
        #if CYTHON_FAST_PYCCALL
        if (__Pyx_PyFastCFunction_Check(__pyx_t_6)) {
          PyObject *__pyx_temp[2] = {__pyx_t_5, __pyx_t_7};
          __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_6, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 614, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
          __Pyx_GOTREF(__pyx_t_1);
          __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
        } else
        #endif
        {
          __pyx_t_26 = PyTuple_New(1+1); if (unlikely(!__pyx_t_26)) __PYX_ERR(0, 614, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_26);
          __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_26, 0, __pyx_t_5); __pyx_t_5 = NULL;
          __Pyx_GIVEREF(__pyx_t_7);
          PyTuple_SET_ITEM(__pyx_t_26, 0+1, __pyx_t_7);
          __pyx_t_7 = 0;
          __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_6, __pyx_t_26, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 614, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_1);
          __Pyx_DECREF(__pyx_t_26); __pyx_t_26 = 0;
        }
      }
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      if (likely(PyList_CheckExact(__pyx_t_1)) || PyTuple_CheckExact(__pyx_t_1)) {
        __pyx_t_6 = __pyx_t_1; __Pyx_INCREF(__pyx_t_6); __pyx_t_29 = 0;
        __pyx_t_30 = NULL;
      } else {
        __pyx_t_29 = -1; __pyx_t_6 = PyObject_GetIter(__pyx_t_1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 614, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_6);
        __pyx_t_30 = Py_TYPE(__pyx_t_6)->tp_iternext; if (unlikely(!__pyx_t_30)) __PYX_ERR(0, 614, __pyx_L1_error)
      }
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      for (;;) {
        if (likely(!__pyx_t_30)) {
          if (likely(PyList_CheckExact(__pyx_t_6))) {
            if (__pyx_t_29 >= PyList_GET_SIZE(__pyx_t_6)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_1 = PyList_GET_ITEM(__pyx_t_6, __pyx_t_29); __Pyx_INCREF(__pyx_t_1); __pyx_t_29++; if (unlikely(0 < 0)) __PYX_ERR(0, 614, __pyx_L1_error)
            #else
            __pyx_t_1 = PySequence_ITEM(__pyx_t_6, __pyx_t_29); __pyx_t_29++; if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 614, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_1);
            #endif
          } else {
            if (__pyx_t_29 >= PyTuple_GET_SIZE(__pyx_t_6)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_1 = PyTuple_GET_ITEM(__pyx_t_6, __pyx_t_29); __Pyx_INCREF(__pyx_t_1); __pyx_t_29++; if (unlikely(0 < 0)) __PYX_ERR(0, 614, __pyx_L1_error)
            #else
            __pyx_t_1 = PySequence_ITEM(__pyx_t_6, __pyx_t_29); __pyx_t_29++; if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 614, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_1);
            #endif
          }
        } else {
          __pyx_t_1 = __pyx_t_30(__pyx_t_6);
          if (unlikely(!__pyx_t_1)) {
            PyObject* exc_type = PyErr_Occurred();
            if (exc_type) {
              if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
              else __PYX_ERR(0, 614, __pyx_L1_error)
            }
            break;
          }
          __Pyx_GOTREF(__pyx_t_1);
        }
        __pyx_t_28 = __Pyx_PyInt_As_int(__pyx_t_1); if (unlikely((__pyx_t_28 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 614, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
        __pyx_v_f = __pyx_t_28;

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":615
 *                 dot = 0  # <q_i, p_u>
 *                 for f in range(self.n_factors):
 *                     dot += qi[i, f] * pu[u, f]             # <<<<<<<<<<<<<<
 *                 est = global_mean + bu[u] + bi[i] + dot
 *                 err = r - est
 */
        __pyx_t_31 = __pyx_v_i;
        __pyx_t_32 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_31 < 0) {
          __pyx_t_31 += __pyx_pybuffernd_qi.diminfo[0].shape;
          if (unlikely(__pyx_t_31 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_31 >= __pyx_pybuffernd_qi.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_32 < 0) {
          __pyx_t_32 += __pyx_pybuffernd_qi.diminfo[1].shape;
          if (unlikely(__pyx_t_32 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_32 >= __pyx_pybuffernd_qi.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 615, __pyx_L1_error)
        }
        __pyx_t_33 = __pyx_v_u;
        __pyx_t_34 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_33 < 0) {
          __pyx_t_33 += __pyx_pybuffernd_pu.diminfo[0].shape;
          if (unlikely(__pyx_t_33 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_33 >= __pyx_pybuffernd_pu.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_34 < 0) {
          __pyx_t_34 += __pyx_pybuffernd_pu.diminfo[1].shape;
          if (unlikely(__pyx_t_34 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_34 >= __pyx_pybuffernd_pu.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 615, __pyx_L1_error)
        }
        __pyx_v_dot = (__pyx_v_dot + ((*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_qi.rcbuffer->pybuffer.buf, __pyx_t_31, __pyx_pybuffernd_qi.diminfo[0].strides, __pyx_t_32, __pyx_pybuffernd_qi.diminfo[1].strides)) * (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_pu.rcbuffer->pybuffer.buf, __pyx_t_33, __pyx_pybuffernd_pu.diminfo[0].strides, __pyx_t_34, __pyx_pybuffernd_pu.diminfo[1].strides))));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":614
 *                 # compute current estimation and error
 *                 dot = 0  # <q_i, p_u>
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     dot += qi[i, f] * pu[u, f]
 *                 est = global_mean + bu[u] + bi[i] + dot
 */
      }
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":616
 *                 for f in range(self.n_factors):
 *                     dot += qi[i, f] * pu[u, f]
 *                 est = global_mean + bu[u] + bi[i] + dot             # <<<<<<<<<<<<<<
 *                 err = r - est
 * 
 */
      __pyx_t_35 = __pyx_v_u;
      __pyx_t_28 = -1;
      if (__pyx_t_35 < 0) {
        __pyx_t_35 += __pyx_pybuffernd_bu.diminfo[0].shape;
        if (unlikely(__pyx_t_35 < 0)) __pyx_t_28 = 0;
      } else if (unlikely(__pyx_t_35 >= __pyx_pybuffernd_bu.diminfo[0].shape)) __pyx_t_28 = 0;
      if (unlikely(__pyx_t_28 != -1)) {
        __Pyx_RaiseBufferIndexError(__pyx_t_28);
        __PYX_ERR(0, 616, __pyx_L1_error)
      }
      __pyx_t_36 = __pyx_v_i;
      __pyx_t_28 = -1;
      if (__pyx_t_36 < 0) {
        __pyx_t_36 += __pyx_pybuffernd_bi.diminfo[0].shape;
        if (unlikely(__pyx_t_36 < 0)) __pyx_t_28 = 0;
      } else if (unlikely(__pyx_t_36 >= __pyx_pybuffernd_bi.diminfo[0].shape)) __pyx_t_28 = 0;
      if (unlikely(__pyx_t_28 != -1)) {
        __Pyx_RaiseBufferIndexError(__pyx_t_28);
        __PYX_ERR(0, 616, __pyx_L1_error)
      }
      __pyx_v_est = (((__pyx_v_global_mean + (*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bu.rcbuffer->pybuffer.buf, __pyx_t_35, __pyx_pybuffernd_bu.diminfo[0].strides))) + (*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bi.rcbuffer->pybuffer.buf, __pyx_t_36, __pyx_pybuffernd_bi.diminfo[0].strides))) + __pyx_v_dot);

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":617
 *                     dot += qi[i, f] * pu[u, f]
 *                 est = global_mean + bu[u] + bi[i] + dot
 *                 err = r - est             # <<<<<<<<<<<<<<
 * 
 *                 # update biases
 */
      __pyx_v_err = (__pyx_v_r - __pyx_v_est);

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":620
 * 
 *                 # update biases
 *                 if self.biased:             # <<<<<<<<<<<<<<
 *                     bu[u] += lr_bu * (err - reg_bu * bu[u])
 *                     bi[i] += lr_bi * (err - reg_bi * bi[i])
 */
      __pyx_t_6 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_biased); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 620, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_6);
      __pyx_t_17 = __Pyx_PyObject_IsTrue(__pyx_t_6); if (unlikely(__pyx_t_17 < 0)) __PYX_ERR(0, 620, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      if (__pyx_t_17) {

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":621
 *                 # update biases
 *                 if self.biased:
 *                     bu[u] += lr_bu * (err - reg_bu * bu[u])             # <<<<<<<<<<<<<<
 *                     bi[i] += lr_bi * (err - reg_bi * bi[i])
 * 
 */
        __pyx_t_37 = __pyx_v_u;
        __pyx_t_28 = -1;
        if (__pyx_t_37 < 0) {
          __pyx_t_37 += __pyx_pybuffernd_bu.diminfo[0].shape;
          if (unlikely(__pyx_t_37 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_37 >= __pyx_pybuffernd_bu.diminfo[0].shape)) __pyx_t_28 = 0;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 621, __pyx_L1_error)
        }
        __pyx_t_38 = __pyx_v_u;
        __pyx_t_28 = -1;
        if (__pyx_t_38 < 0) {
          __pyx_t_38 += __pyx_pybuffernd_bu.diminfo[0].shape;
          if (unlikely(__pyx_t_38 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_38 >= __pyx_pybuffernd_bu.diminfo[0].shape)) __pyx_t_28 = 0;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 621, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bu.rcbuffer->pybuffer.buf, __pyx_t_38, __pyx_pybuffernd_bu.diminfo[0].strides) += (__pyx_v_lr_bu * (__pyx_v_err - (__pyx_v_reg_bu * (*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bu.rcbuffer->pybuffer.buf, __pyx_t_37, __pyx_pybuffernd_bu.diminfo[0].strides)))));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":622
 *                 if self.biased:
 *                     bu[u] += lr_bu * (err - reg_bu * bu[u])
 *                     bi[i] += lr_bi * (err - reg_bi * bi[i])             # <<<<<<<<<<<<<<
 * 
 *                 # compute numerators and denominators
 */
        __pyx_t_39 = __pyx_v_i;
        __pyx_t_28 = -1;
        if (__pyx_t_39 < 0) {
          __pyx_t_39 += __pyx_pybuffernd_bi.diminfo[0].shape;
          if (unlikely(__pyx_t_39 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_39 >= __pyx_pybuffernd_bi.diminfo[0].shape)) __pyx_t_28 = 0;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 622, __pyx_L1_error)
        }
        __pyx_t_40 = __pyx_v_i;
        __pyx_t_28 = -1;
        if (__pyx_t_40 < 0) {
          __pyx_t_40 += __pyx_pybuffernd_bi.diminfo[0].shape;
          if (unlikely(__pyx_t_40 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_40 >= __pyx_pybuffernd_bi.diminfo[0].shape)) __pyx_t_28 = 0;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 622, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bi.rcbuffer->pybuffer.buf, __pyx_t_40, __pyx_pybuffernd_bi.diminfo[0].strides) += (__pyx_v_lr_bi * (__pyx_v_err - (__pyx_v_reg_bi * (*__Pyx_BufPtrStrided1d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_bi.rcbuffer->pybuffer.buf, __pyx_t_39, __pyx_pybuffernd_bi.diminfo[0].strides)))));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":620
 * 
 *                 # update biases
 *                 if self.biased:             # <<<<<<<<<<<<<<
 *                     bu[u] += lr_bu * (err - reg_bu * bu[u])
 *                     bi[i] += lr_bi * (err - reg_bi * bi[i])
 */
      }

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":625
 * 
 *                 # compute numerators and denominators
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     user_num[u, f] += qi[i, f] * r
 *                     user_denom[u, f] += qi[i, f] * est
 */
      __pyx_t_1 = __Pyx_GetModuleGlobalName(__pyx_n_s_range); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 625, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __pyx_t_26 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_26)) __PYX_ERR(0, 625, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_26);
      __pyx_t_7 = NULL;
      if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_1))) {
        __pyx_t_7 = PyMethod_GET_SELF(__pyx_t_1);
        if (likely(__pyx_t_7)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_1);
          __Pyx_INCREF(__pyx_t_7);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_1, function);
        }
      }
      if (!__pyx_t_7) {
        __pyx_t_6 = __Pyx_PyObject_CallOneArg(__pyx_t_1, __pyx_t_26); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 625, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_26); __pyx_t_26 = 0;
        __Pyx_GOTREF(__pyx_t_6);
      } else {
        #if CYTHON_FAST_PYCALL
        if (PyFunction_Check(__pyx_t_1)) {
          PyObject *__pyx_temp[2] = {__pyx_t_7, __pyx_t_26};
          __pyx_t_6 = __Pyx_PyFunction_FastCall(__pyx_t_1, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 625, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_7); __pyx_t_7 = 0;
          __Pyx_GOTREF(__pyx_t_6);
          __Pyx_DECREF(__pyx_t_26); __pyx_t_26 = 0;
        } else
        #endif
        #if CYTHON_FAST_PYCCALL
        if (__Pyx_PyFastCFunction_Check(__pyx_t_1)) {
          PyObject *__pyx_temp[2] = {__pyx_t_7, __pyx_t_26};
          __pyx_t_6 = __Pyx_PyCFunction_FastCall(__pyx_t_1, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 625, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_7); __pyx_t_7 = 0;
          __Pyx_GOTREF(__pyx_t_6);
          __Pyx_DECREF(__pyx_t_26); __pyx_t_26 = 0;
        } else
        #endif
        {
          __pyx_t_5 = PyTuple_New(1+1); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 625, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_5);
          __Pyx_GIVEREF(__pyx_t_7); PyTuple_SET_ITEM(__pyx_t_5, 0, __pyx_t_7); __pyx_t_7 = NULL;
          __Pyx_GIVEREF(__pyx_t_26);
          PyTuple_SET_ITEM(__pyx_t_5, 0+1, __pyx_t_26);
          __pyx_t_26 = 0;
          __pyx_t_6 = __Pyx_PyObject_Call(__pyx_t_1, __pyx_t_5, NULL); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 625, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_6);
          __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        }
      }
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      if (likely(PyList_CheckExact(__pyx_t_6)) || PyTuple_CheckExact(__pyx_t_6)) {
        __pyx_t_1 = __pyx_t_6; __Pyx_INCREF(__pyx_t_1); __pyx_t_29 = 0;
        __pyx_t_30 = NULL;
      } else {
        __pyx_t_29 = -1; __pyx_t_1 = PyObject_GetIter(__pyx_t_6); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 625, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        __pyx_t_30 = Py_TYPE(__pyx_t_1)->tp_iternext; if (unlikely(!__pyx_t_30)) __PYX_ERR(0, 625, __pyx_L1_error)
      }
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      for (;;) {
        if (likely(!__pyx_t_30)) {
          if (likely(PyList_CheckExact(__pyx_t_1))) {
            if (__pyx_t_29 >= PyList_GET_SIZE(__pyx_t_1)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_6 = PyList_GET_ITEM(__pyx_t_1, __pyx_t_29); __Pyx_INCREF(__pyx_t_6); __pyx_t_29++; if (unlikely(0 < 0)) __PYX_ERR(0, 625, __pyx_L1_error)
            #else
            __pyx_t_6 = PySequence_ITEM(__pyx_t_1, __pyx_t_29); __pyx_t_29++; if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 625, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_6);
            #endif
          } else {
            if (__pyx_t_29 >= PyTuple_GET_SIZE(__pyx_t_1)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_6 = PyTuple_GET_ITEM(__pyx_t_1, __pyx_t_29); __Pyx_INCREF(__pyx_t_6); __pyx_t_29++; if (unlikely(0 < 0)) __PYX_ERR(0, 625, __pyx_L1_error)
            #else
            __pyx_t_6 = PySequence_ITEM(__pyx_t_1, __pyx_t_29); __pyx_t_29++; if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 625, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_6);
            #endif
          }
        } else {
          __pyx_t_6 = __pyx_t_30(__pyx_t_1);
          if (unlikely(!__pyx_t_6)) {
            PyObject* exc_type = PyErr_Occurred();
            if (exc_type) {
              if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
              else __PYX_ERR(0, 625, __pyx_L1_error)
            }
            break;
          }
          __Pyx_GOTREF(__pyx_t_6);
        }
        __pyx_t_28 = __Pyx_PyInt_As_int(__pyx_t_6); if (unlikely((__pyx_t_28 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 625, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
        __pyx_v_f = __pyx_t_28;

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":626
 *                 # compute numerators and denominators
 *                 for f in range(self.n_factors):
 *                     user_num[u, f] += qi[i, f] * r             # <<<<<<<<<<<<<<
 *                     user_denom[u, f] += qi[i, f] * est
 *                     item_num[i, f] += pu[u, f] * r
 */
        __pyx_t_41 = __pyx_v_i;
        __pyx_t_42 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_41 < 0) {
          __pyx_t_41 += __pyx_pybuffernd_qi.diminfo[0].shape;
          if (unlikely(__pyx_t_41 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_41 >= __pyx_pybuffernd_qi.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_42 < 0) {
          __pyx_t_42 += __pyx_pybuffernd_qi.diminfo[1].shape;
          if (unlikely(__pyx_t_42 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_42 >= __pyx_pybuffernd_qi.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 626, __pyx_L1_error)
        }
        __pyx_t_43 = __pyx_v_u;
        __pyx_t_44 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_43 < 0) {
          __pyx_t_43 += __pyx_pybuffernd_user_num.diminfo[0].shape;
          if (unlikely(__pyx_t_43 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_43 >= __pyx_pybuffernd_user_num.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_44 < 0) {
          __pyx_t_44 += __pyx_pybuffernd_user_num.diminfo[1].shape;
          if (unlikely(__pyx_t_44 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_44 >= __pyx_pybuffernd_user_num.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 626, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_user_num.rcbuffer->pybuffer.buf, __pyx_t_43, __pyx_pybuffernd_user_num.diminfo[0].strides, __pyx_t_44, __pyx_pybuffernd_user_num.diminfo[1].strides) += ((*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_qi.rcbuffer->pybuffer.buf, __pyx_t_41, __pyx_pybuffernd_qi.diminfo[0].strides, __pyx_t_42, __pyx_pybuffernd_qi.diminfo[1].strides)) * __pyx_v_r);

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":627
 *                 for f in range(self.n_factors):
 *                     user_num[u, f] += qi[i, f] * r
 *                     user_denom[u, f] += qi[i, f] * est             # <<<<<<<<<<<<<<
 *                     item_num[i, f] += pu[u, f] * r
 *                     item_denom[i, f] += pu[u, f] * est
 */
        __pyx_t_45 = __pyx_v_i;
        __pyx_t_46 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_45 < 0) {
          __pyx_t_45 += __pyx_pybuffernd_qi.diminfo[0].shape;
          if (unlikely(__pyx_t_45 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_45 >= __pyx_pybuffernd_qi.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_46 < 0) {
          __pyx_t_46 += __pyx_pybuffernd_qi.diminfo[1].shape;
          if (unlikely(__pyx_t_46 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_46 >= __pyx_pybuffernd_qi.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 627, __pyx_L1_error)
        }
        __pyx_t_47 = __pyx_v_u;
        __pyx_t_48 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_47 < 0) {
          __pyx_t_47 += __pyx_pybuffernd_user_denom.diminfo[0].shape;
          if (unlikely(__pyx_t_47 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_47 >= __pyx_pybuffernd_user_denom.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_48 < 0) {
          __pyx_t_48 += __pyx_pybuffernd_user_denom.diminfo[1].shape;
          if (unlikely(__pyx_t_48 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_48 >= __pyx_pybuffernd_user_denom.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 627, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_user_denom.rcbuffer->pybuffer.buf, __pyx_t_47, __pyx_pybuffernd_user_denom.diminfo[0].strides, __pyx_t_48, __pyx_pybuffernd_user_denom.diminfo[1].strides) += ((*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_qi.rcbuffer->pybuffer.buf, __pyx_t_45, __pyx_pybuffernd_qi.diminfo[0].strides, __pyx_t_46, __pyx_pybuffernd_qi.diminfo[1].strides)) * __pyx_v_est);

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":628
 *                     user_num[u, f] += qi[i, f] * r
 *                     user_denom[u, f] += qi[i, f] * est
 *                     item_num[i, f] += pu[u, f] * r             # <<<<<<<<<<<<<<
 *                     item_denom[i, f] += pu[u, f] * est
 * 
 */
        __pyx_t_49 = __pyx_v_u;
        __pyx_t_50 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_49 < 0) {
          __pyx_t_49 += __pyx_pybuffernd_pu.diminfo[0].shape;
          if (unlikely(__pyx_t_49 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_49 >= __pyx_pybuffernd_pu.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_50 < 0) {
          __pyx_t_50 += __pyx_pybuffernd_pu.diminfo[1].shape;
          if (unlikely(__pyx_t_50 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_50 >= __pyx_pybuffernd_pu.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 628, __pyx_L1_error)
        }
        __pyx_t_51 = __pyx_v_i;
        __pyx_t_52 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_51 < 0) {
          __pyx_t_51 += __pyx_pybuffernd_item_num.diminfo[0].shape;
          if (unlikely(__pyx_t_51 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_51 >= __pyx_pybuffernd_item_num.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_52 < 0) {
          __pyx_t_52 += __pyx_pybuffernd_item_num.diminfo[1].shape;
          if (unlikely(__pyx_t_52 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_52 >= __pyx_pybuffernd_item_num.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 628, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_item_num.rcbuffer->pybuffer.buf, __pyx_t_51, __pyx_pybuffernd_item_num.diminfo[0].strides, __pyx_t_52, __pyx_pybuffernd_item_num.diminfo[1].strides) += ((*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_pu.rcbuffer->pybuffer.buf, __pyx_t_49, __pyx_pybuffernd_pu.diminfo[0].strides, __pyx_t_50, __pyx_pybuffernd_pu.diminfo[1].strides)) * __pyx_v_r);

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":629
 *                     user_denom[u, f] += qi[i, f] * est
 *                     item_num[i, f] += pu[u, f] * r
 *                     item_denom[i, f] += pu[u, f] * est             # <<<<<<<<<<<<<<
 * 
 *             # Update user factors
 */
        __pyx_t_53 = __pyx_v_u;
        __pyx_t_54 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_53 < 0) {
          __pyx_t_53 += __pyx_pybuffernd_pu.diminfo[0].shape;
          if (unlikely(__pyx_t_53 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_53 >= __pyx_pybuffernd_pu.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_54 < 0) {
          __pyx_t_54 += __pyx_pybuffernd_pu.diminfo[1].shape;
          if (unlikely(__pyx_t_54 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_54 >= __pyx_pybuffernd_pu.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 629, __pyx_L1_error)
        }
        __pyx_t_55 = __pyx_v_i;
        __pyx_t_56 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_55 < 0) {
          __pyx_t_55 += __pyx_pybuffernd_item_denom.diminfo[0].shape;
          if (unlikely(__pyx_t_55 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_55 >= __pyx_pybuffernd_item_denom.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_56 < 0) {
          __pyx_t_56 += __pyx_pybuffernd_item_denom.diminfo[1].shape;
          if (unlikely(__pyx_t_56 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_56 >= __pyx_pybuffernd_item_denom.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 629, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_item_denom.rcbuffer->pybuffer.buf, __pyx_t_55, __pyx_pybuffernd_item_denom.diminfo[0].strides, __pyx_t_56, __pyx_pybuffernd_item_denom.diminfo[1].strides) += ((*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_pu.rcbuffer->pybuffer.buf, __pyx_t_53, __pyx_pybuffernd_pu.diminfo[0].strides, __pyx_t_54, __pyx_pybuffernd_pu.diminfo[1].strides)) * __pyx_v_est);

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":625
 * 
 *                 # compute numerators and denominators
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     user_num[u, f] += qi[i, f] * r
 *                     user_denom[u, f] += qi[i, f] * est
 */
      }
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":610
 * 
 *             # Compute numerators and denominators for users and items factors
 *             for u, i, r in trainset.all_ratings():             # <<<<<<<<<<<<<<
 * 
 *                 # compute current estimation and error
 */
    }
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":632
 * 
 *             # Update user factors
 *             for u in trainset.all_users():             # <<<<<<<<<<<<<<
 *                 l = len(trainset.ur[u])
 *                 for f in range(self.n_factors):
 */
    __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_all_users); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 632, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    __pyx_t_6 = NULL;
    if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_1))) {
      __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_1);
      if (likely(__pyx_t_6)) {
        PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_1);
        __Pyx_INCREF(__pyx_t_6);
        __Pyx_INCREF(function);
        __Pyx_DECREF_SET(__pyx_t_1, function);
      }
    }
    if (__pyx_t_6) {
      __pyx_t_3 = __Pyx_PyObject_CallOneArg(__pyx_t_1, __pyx_t_6); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 632, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
    } else {
      __pyx_t_3 = __Pyx_PyObject_CallNoArg(__pyx_t_1); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 632, __pyx_L1_error)
    }
    __Pyx_GOTREF(__pyx_t_3);
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    if (likely(PyList_CheckExact(__pyx_t_3)) || PyTuple_CheckExact(__pyx_t_3)) {
      __pyx_t_1 = __pyx_t_3; __Pyx_INCREF(__pyx_t_1); __pyx_t_24 = 0;
      __pyx_t_25 = NULL;
    } else {
      __pyx_t_24 = -1; __pyx_t_1 = PyObject_GetIter(__pyx_t_3); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 632, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __pyx_t_25 = Py_TYPE(__pyx_t_1)->tp_iternext; if (unlikely(!__pyx_t_25)) __PYX_ERR(0, 632, __pyx_L1_error)
    }
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    for (;;) {
      if (likely(!__pyx_t_25)) {
        if (likely(PyList_CheckExact(__pyx_t_1))) {
          if (__pyx_t_24 >= PyList_GET_SIZE(__pyx_t_1)) break;
          #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
          __pyx_t_3 = PyList_GET_ITEM(__pyx_t_1, __pyx_t_24); __Pyx_INCREF(__pyx_t_3); __pyx_t_24++; if (unlikely(0 < 0)) __PYX_ERR(0, 632, __pyx_L1_error)
          #else
          __pyx_t_3 = PySequence_ITEM(__pyx_t_1, __pyx_t_24); __pyx_t_24++; if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 632, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_3);
          #endif
        } else {
          if (__pyx_t_24 >= PyTuple_GET_SIZE(__pyx_t_1)) break;
          #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
          __pyx_t_3 = PyTuple_GET_ITEM(__pyx_t_1, __pyx_t_24); __Pyx_INCREF(__pyx_t_3); __pyx_t_24++; if (unlikely(0 < 0)) __PYX_ERR(0, 632, __pyx_L1_error)
          #else
          __pyx_t_3 = PySequence_ITEM(__pyx_t_1, __pyx_t_24); __pyx_t_24++; if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 632, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_3);
          #endif
        }
      } else {
        __pyx_t_3 = __pyx_t_25(__pyx_t_1);
        if (unlikely(!__pyx_t_3)) {
          PyObject* exc_type = PyErr_Occurred();
          if (exc_type) {
            if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
            else __PYX_ERR(0, 632, __pyx_L1_error)
          }
          break;
        }
        __Pyx_GOTREF(__pyx_t_3);
      }
      __pyx_t_28 = __Pyx_PyInt_As_int(__pyx_t_3); if (unlikely((__pyx_t_28 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 632, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __pyx_v_u = __pyx_t_28;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":633
 *             # Update user factors
 *             for u in trainset.all_users():
 *                 l = len(trainset.ur[u])             # <<<<<<<<<<<<<<
 *                 for f in range(self.n_factors):
 *                     user_denom[u, f] += l * reg_pu * pu[u, f]
 */
      __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_ur); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 633, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_6 = __Pyx_GetItemInt(__pyx_t_3, __pyx_v_u, int, 1, __Pyx_PyInt_From_int, 0, 1, 1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 633, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_6);
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __pyx_t_29 = PyObject_Length(__pyx_t_6); if (unlikely(__pyx_t_29 == -1)) __PYX_ERR(0, 633, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      __pyx_v_l = __pyx_t_29;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":634
 *             for u in trainset.all_users():
 *                 l = len(trainset.ur[u])
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     user_denom[u, f] += l * reg_pu * pu[u, f]
 *                     pu[u, f] *= user_num[u, f] / user_denom[u, f]
 */
      __pyx_t_3 = __Pyx_GetModuleGlobalName(__pyx_n_s_range); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 634, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_5 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_5)) __PYX_ERR(0, 634, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_5);
      __pyx_t_26 = NULL;
      if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_3))) {
        __pyx_t_26 = PyMethod_GET_SELF(__pyx_t_3);
        if (likely(__pyx_t_26)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
          __Pyx_INCREF(__pyx_t_26);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_3, function);
        }
      }
      if (!__pyx_t_26) {
        __pyx_t_6 = __Pyx_PyObject_CallOneArg(__pyx_t_3, __pyx_t_5); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 634, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        __Pyx_GOTREF(__pyx_t_6);
      } else {
        #if CYTHON_FAST_PYCALL
        if (PyFunction_Check(__pyx_t_3)) {
          PyObject *__pyx_temp[2] = {__pyx_t_26, __pyx_t_5};
          __pyx_t_6 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 634, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_26); __pyx_t_26 = 0;
          __Pyx_GOTREF(__pyx_t_6);
          __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        } else
        #endif
        #if CYTHON_FAST_PYCCALL
        if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
          PyObject *__pyx_temp[2] = {__pyx_t_26, __pyx_t_5};
          __pyx_t_6 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 634, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_26); __pyx_t_26 = 0;
          __Pyx_GOTREF(__pyx_t_6);
          __Pyx_DECREF(__pyx_t_5); __pyx_t_5 = 0;
        } else
        #endif
        {
          __pyx_t_7 = PyTuple_New(1+1); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 634, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_7);
          __Pyx_GIVEREF(__pyx_t_26); PyTuple_SET_ITEM(__pyx_t_7, 0, __pyx_t_26); __pyx_t_26 = NULL;
          __Pyx_GIVEREF(__pyx_t_5);
          PyTuple_SET_ITEM(__pyx_t_7, 0+1, __pyx_t_5);
          __pyx_t_5 = 0;
          __pyx_t_6 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_7, NULL); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 634, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_6);
          __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
        }
      }
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      if (likely(PyList_CheckExact(__pyx_t_6)) || PyTuple_CheckExact(__pyx_t_6)) {
        __pyx_t_3 = __pyx_t_6; __Pyx_INCREF(__pyx_t_3); __pyx_t_29 = 0;
        __pyx_t_30 = NULL;
      } else {
        __pyx_t_29 = -1; __pyx_t_3 = PyObject_GetIter(__pyx_t_6); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 634, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_3);
        __pyx_t_30 = Py_TYPE(__pyx_t_3)->tp_iternext; if (unlikely(!__pyx_t_30)) __PYX_ERR(0, 634, __pyx_L1_error)
      }
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      for (;;) {
        if (likely(!__pyx_t_30)) {
          if (likely(PyList_CheckExact(__pyx_t_3))) {
            if (__pyx_t_29 >= PyList_GET_SIZE(__pyx_t_3)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_6 = PyList_GET_ITEM(__pyx_t_3, __pyx_t_29); __Pyx_INCREF(__pyx_t_6); __pyx_t_29++; if (unlikely(0 < 0)) __PYX_ERR(0, 634, __pyx_L1_error)
            #else
            __pyx_t_6 = PySequence_ITEM(__pyx_t_3, __pyx_t_29); __pyx_t_29++; if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 634, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_6);
            #endif
          } else {
            if (__pyx_t_29 >= PyTuple_GET_SIZE(__pyx_t_3)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_6 = PyTuple_GET_ITEM(__pyx_t_3, __pyx_t_29); __Pyx_INCREF(__pyx_t_6); __pyx_t_29++; if (unlikely(0 < 0)) __PYX_ERR(0, 634, __pyx_L1_error)
            #else
            __pyx_t_6 = PySequence_ITEM(__pyx_t_3, __pyx_t_29); __pyx_t_29++; if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 634, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_6);
            #endif
          }
        } else {
          __pyx_t_6 = __pyx_t_30(__pyx_t_3);
          if (unlikely(!__pyx_t_6)) {
            PyObject* exc_type = PyErr_Occurred();
            if (exc_type) {
              if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
              else __PYX_ERR(0, 634, __pyx_L1_error)
            }
            break;
          }
          __Pyx_GOTREF(__pyx_t_6);
        }
        __pyx_t_28 = __Pyx_PyInt_As_int(__pyx_t_6); if (unlikely((__pyx_t_28 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 634, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
        __pyx_v_f = __pyx_t_28;

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":635
 *                 l = len(trainset.ur[u])
 *                 for f in range(self.n_factors):
 *                     user_denom[u, f] += l * reg_pu * pu[u, f]             # <<<<<<<<<<<<<<
 *                     pu[u, f] *= user_num[u, f] / user_denom[u, f]
 * 
 */
        __pyx_t_57 = __pyx_v_u;
        __pyx_t_58 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_57 < 0) {
          __pyx_t_57 += __pyx_pybuffernd_pu.diminfo[0].shape;
          if (unlikely(__pyx_t_57 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_57 >= __pyx_pybuffernd_pu.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_58 < 0) {
          __pyx_t_58 += __pyx_pybuffernd_pu.diminfo[1].shape;
          if (unlikely(__pyx_t_58 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_58 >= __pyx_pybuffernd_pu.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 635, __pyx_L1_error)
        }
        __pyx_t_59 = __pyx_v_u;
        __pyx_t_60 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_59 < 0) {
          __pyx_t_59 += __pyx_pybuffernd_user_denom.diminfo[0].shape;
          if (unlikely(__pyx_t_59 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_59 >= __pyx_pybuffernd_user_denom.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_60 < 0) {
          __pyx_t_60 += __pyx_pybuffernd_user_denom.diminfo[1].shape;
          if (unlikely(__pyx_t_60 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_60 >= __pyx_pybuffernd_user_denom.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 635, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_user_denom.rcbuffer->pybuffer.buf, __pyx_t_59, __pyx_pybuffernd_user_denom.diminfo[0].strides, __pyx_t_60, __pyx_pybuffernd_user_denom.diminfo[1].strides) += ((__pyx_v_l * __pyx_v_reg_pu) * (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_pu.rcbuffer->pybuffer.buf, __pyx_t_57, __pyx_pybuffernd_pu.diminfo[0].strides, __pyx_t_58, __pyx_pybuffernd_pu.diminfo[1].strides)));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":636
 *                 for f in range(self.n_factors):
 *                     user_denom[u, f] += l * reg_pu * pu[u, f]
 *                     pu[u, f] *= user_num[u, f] / user_denom[u, f]             # <<<<<<<<<<<<<<
 * 
 *             # Update item factors
 */
        __pyx_t_61 = __pyx_v_u;
        __pyx_t_62 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_61 < 0) {
          __pyx_t_61 += __pyx_pybuffernd_user_num.diminfo[0].shape;
          if (unlikely(__pyx_t_61 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_61 >= __pyx_pybuffernd_user_num.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_62 < 0) {
          __pyx_t_62 += __pyx_pybuffernd_user_num.diminfo[1].shape;
          if (unlikely(__pyx_t_62 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_62 >= __pyx_pybuffernd_user_num.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 636, __pyx_L1_error)
        }
        __pyx_t_63 = (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_user_num.rcbuffer->pybuffer.buf, __pyx_t_61, __pyx_pybuffernd_user_num.diminfo[0].strides, __pyx_t_62, __pyx_pybuffernd_user_num.diminfo[1].strides));
        __pyx_t_64 = __pyx_v_u;
        __pyx_t_65 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_64 < 0) {
          __pyx_t_64 += __pyx_pybuffernd_user_denom.diminfo[0].shape;
          if (unlikely(__pyx_t_64 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_64 >= __pyx_pybuffernd_user_denom.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_65 < 0) {
          __pyx_t_65 += __pyx_pybuffernd_user_denom.diminfo[1].shape;
          if (unlikely(__pyx_t_65 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_65 >= __pyx_pybuffernd_user_denom.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 636, __pyx_L1_error)
        }
        __pyx_t_66 = (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_user_denom.rcbuffer->pybuffer.buf, __pyx_t_64, __pyx_pybuffernd_user_denom.diminfo[0].strides, __pyx_t_65, __pyx_pybuffernd_user_denom.diminfo[1].strides));
        if (unlikely(__pyx_t_66 == 0)) {
          PyErr_SetString(PyExc_ZeroDivisionError, "float division");
          __PYX_ERR(0, 636, __pyx_L1_error)
        }
        __pyx_t_67 = __pyx_v_u;
        __pyx_t_68 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_67 < 0) {
          __pyx_t_67 += __pyx_pybuffernd_pu.diminfo[0].shape;
          if (unlikely(__pyx_t_67 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_67 >= __pyx_pybuffernd_pu.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_68 < 0) {
          __pyx_t_68 += __pyx_pybuffernd_pu.diminfo[1].shape;
          if (unlikely(__pyx_t_68 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_68 >= __pyx_pybuffernd_pu.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 636, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_pu.rcbuffer->pybuffer.buf, __pyx_t_67, __pyx_pybuffernd_pu.diminfo[0].strides, __pyx_t_68, __pyx_pybuffernd_pu.diminfo[1].strides) *= (__pyx_t_63 / __pyx_t_66);

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":634
 *             for u in trainset.all_users():
 *                 l = len(trainset.ur[u])
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     user_denom[u, f] += l * reg_pu * pu[u, f]
 *                     pu[u, f] *= user_num[u, f] / user_denom[u, f]
 */
      }
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":632
 * 
 *             # Update user factors
 *             for u in trainset.all_users():             # <<<<<<<<<<<<<<
 *                 l = len(trainset.ur[u])
 *                 for f in range(self.n_factors):
 */
    }
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":639
 * 
 *             # Update item factors
 *             for i in trainset.all_items():             # <<<<<<<<<<<<<<
 *                 l = len(trainset.ir[i])
 *                 for f in range(self.n_factors):
 */
    __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_all_items); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 639, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __pyx_t_6 = NULL;
    if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_3))) {
      __pyx_t_6 = PyMethod_GET_SELF(__pyx_t_3);
      if (likely(__pyx_t_6)) {
        PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
        __Pyx_INCREF(__pyx_t_6);
        __Pyx_INCREF(function);
        __Pyx_DECREF_SET(__pyx_t_3, function);
      }
    }
    if (__pyx_t_6) {
      __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_3, __pyx_t_6); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 639, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
    } else {
      __pyx_t_1 = __Pyx_PyObject_CallNoArg(__pyx_t_3); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 639, __pyx_L1_error)
    }
    __Pyx_GOTREF(__pyx_t_1);
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    if (likely(PyList_CheckExact(__pyx_t_1)) || PyTuple_CheckExact(__pyx_t_1)) {
      __pyx_t_3 = __pyx_t_1; __Pyx_INCREF(__pyx_t_3); __pyx_t_24 = 0;
      __pyx_t_25 = NULL;
    } else {
      __pyx_t_24 = -1; __pyx_t_3 = PyObject_GetIter(__pyx_t_1); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 639, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_25 = Py_TYPE(__pyx_t_3)->tp_iternext; if (unlikely(!__pyx_t_25)) __PYX_ERR(0, 639, __pyx_L1_error)
    }
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    for (;;) {
      if (likely(!__pyx_t_25)) {
        if (likely(PyList_CheckExact(__pyx_t_3))) {
          if (__pyx_t_24 >= PyList_GET_SIZE(__pyx_t_3)) break;
          #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
          __pyx_t_1 = PyList_GET_ITEM(__pyx_t_3, __pyx_t_24); __Pyx_INCREF(__pyx_t_1); __pyx_t_24++; if (unlikely(0 < 0)) __PYX_ERR(0, 639, __pyx_L1_error)
          #else
          __pyx_t_1 = PySequence_ITEM(__pyx_t_3, __pyx_t_24); __pyx_t_24++; if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 639, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_1);
          #endif
        } else {
          if (__pyx_t_24 >= PyTuple_GET_SIZE(__pyx_t_3)) break;
          #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
          __pyx_t_1 = PyTuple_GET_ITEM(__pyx_t_3, __pyx_t_24); __Pyx_INCREF(__pyx_t_1); __pyx_t_24++; if (unlikely(0 < 0)) __PYX_ERR(0, 639, __pyx_L1_error)
          #else
          __pyx_t_1 = PySequence_ITEM(__pyx_t_3, __pyx_t_24); __pyx_t_24++; if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 639, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_1);
          #endif
        }
      } else {
        __pyx_t_1 = __pyx_t_25(__pyx_t_3);
        if (unlikely(!__pyx_t_1)) {
          PyObject* exc_type = PyErr_Occurred();
          if (exc_type) {
            if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
            else __PYX_ERR(0, 639, __pyx_L1_error)
          }
          break;
        }
        __Pyx_GOTREF(__pyx_t_1);
      }
      __pyx_t_28 = __Pyx_PyInt_As_int(__pyx_t_1); if (unlikely((__pyx_t_28 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 639, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __pyx_v_i = __pyx_t_28;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":640
 *             # Update item factors
 *             for i in trainset.all_items():
 *                 l = len(trainset.ir[i])             # <<<<<<<<<<<<<<
 *                 for f in range(self.n_factors):
 *                     item_denom[i, f] += l * reg_qi * qi[i, f]
 */
      __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_trainset, __pyx_n_s_ir); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 640, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __pyx_t_6 = __Pyx_GetItemInt(__pyx_t_1, __pyx_v_i, int, 1, __Pyx_PyInt_From_int, 0, 1, 1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 640, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_6);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __pyx_t_29 = PyObject_Length(__pyx_t_6); if (unlikely(__pyx_t_29 == -1)) __PYX_ERR(0, 640, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      __pyx_v_l = __pyx_t_29;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":641
 *             for i in trainset.all_items():
 *                 l = len(trainset.ir[i])
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     item_denom[i, f] += l * reg_qi * qi[i, f]
 *                     qi[i, f] *= item_num[i, f] / item_denom[i, f]
 */
      __pyx_t_1 = __Pyx_GetModuleGlobalName(__pyx_n_s_range); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 641, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __pyx_t_7 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_n_factors); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 641, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_7);
      __pyx_t_5 = NULL;
      if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_1))) {
        __pyx_t_5 = PyMethod_GET_SELF(__pyx_t_1);
        if (likely(__pyx_t_5)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_1);
          __Pyx_INCREF(__pyx_t_5);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_1, function);
        }
      }
      if (!__pyx_t_5) {
        __pyx_t_6 = __Pyx_PyObject_CallOneArg(__pyx_t_1, __pyx_t_7); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 641, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
        __Pyx_GOTREF(__pyx_t_6);
      } else {
        #if CYTHON_FAST_PYCALL
        if (PyFunction_Check(__pyx_t_1)) {
          PyObject *__pyx_temp[2] = {__pyx_t_5, __pyx_t_7};
          __pyx_t_6 = __Pyx_PyFunction_FastCall(__pyx_t_1, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 641, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
          __Pyx_GOTREF(__pyx_t_6);
          __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
        } else
        #endif
        #if CYTHON_FAST_PYCCALL
        if (__Pyx_PyFastCFunction_Check(__pyx_t_1)) {
          PyObject *__pyx_temp[2] = {__pyx_t_5, __pyx_t_7};
          __pyx_t_6 = __Pyx_PyCFunction_FastCall(__pyx_t_1, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 641, __pyx_L1_error)
          __Pyx_XDECREF(__pyx_t_5); __pyx_t_5 = 0;
          __Pyx_GOTREF(__pyx_t_6);
          __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
        } else
        #endif
        {
          __pyx_t_26 = PyTuple_New(1+1); if (unlikely(!__pyx_t_26)) __PYX_ERR(0, 641, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_26);
          __Pyx_GIVEREF(__pyx_t_5); PyTuple_SET_ITEM(__pyx_t_26, 0, __pyx_t_5); __pyx_t_5 = NULL;
          __Pyx_GIVEREF(__pyx_t_7);
          PyTuple_SET_ITEM(__pyx_t_26, 0+1, __pyx_t_7);
          __pyx_t_7 = 0;
          __pyx_t_6 = __Pyx_PyObject_Call(__pyx_t_1, __pyx_t_26, NULL); if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 641, __pyx_L1_error)
          __Pyx_GOTREF(__pyx_t_6);
          __Pyx_DECREF(__pyx_t_26); __pyx_t_26 = 0;
        }
      }
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      if (likely(PyList_CheckExact(__pyx_t_6)) || PyTuple_CheckExact(__pyx_t_6)) {
        __pyx_t_1 = __pyx_t_6; __Pyx_INCREF(__pyx_t_1); __pyx_t_29 = 0;
        __pyx_t_30 = NULL;
      } else {
        __pyx_t_29 = -1; __pyx_t_1 = PyObject_GetIter(__pyx_t_6); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 641, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        __pyx_t_30 = Py_TYPE(__pyx_t_1)->tp_iternext; if (unlikely(!__pyx_t_30)) __PYX_ERR(0, 641, __pyx_L1_error)
      }
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      for (;;) {
        if (likely(!__pyx_t_30)) {
          if (likely(PyList_CheckExact(__pyx_t_1))) {
            if (__pyx_t_29 >= PyList_GET_SIZE(__pyx_t_1)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_6 = PyList_GET_ITEM(__pyx_t_1, __pyx_t_29); __Pyx_INCREF(__pyx_t_6); __pyx_t_29++; if (unlikely(0 < 0)) __PYX_ERR(0, 641, __pyx_L1_error)
            #else
            __pyx_t_6 = PySequence_ITEM(__pyx_t_1, __pyx_t_29); __pyx_t_29++; if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 641, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_6);
            #endif
          } else {
            if (__pyx_t_29 >= PyTuple_GET_SIZE(__pyx_t_1)) break;
            #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
            __pyx_t_6 = PyTuple_GET_ITEM(__pyx_t_1, __pyx_t_29); __Pyx_INCREF(__pyx_t_6); __pyx_t_29++; if (unlikely(0 < 0)) __PYX_ERR(0, 641, __pyx_L1_error)
            #else
            __pyx_t_6 = PySequence_ITEM(__pyx_t_1, __pyx_t_29); __pyx_t_29++; if (unlikely(!__pyx_t_6)) __PYX_ERR(0, 641, __pyx_L1_error)
            __Pyx_GOTREF(__pyx_t_6);
            #endif
          }
        } else {
          __pyx_t_6 = __pyx_t_30(__pyx_t_1);
          if (unlikely(!__pyx_t_6)) {
            PyObject* exc_type = PyErr_Occurred();
            if (exc_type) {
              if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) PyErr_Clear();
              else __PYX_ERR(0, 641, __pyx_L1_error)
            }
            break;
          }
          __Pyx_GOTREF(__pyx_t_6);
        }
        __pyx_t_28 = __Pyx_PyInt_As_int(__pyx_t_6); if (unlikely((__pyx_t_28 == (int)-1) && PyErr_Occurred())) __PYX_ERR(0, 641, __pyx_L1_error)
        __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
        __pyx_v_f = __pyx_t_28;

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":642
 *                 l = len(trainset.ir[i])
 *                 for f in range(self.n_factors):
 *                     item_denom[i, f] += l * reg_qi * qi[i, f]             # <<<<<<<<<<<<<<
 *                     qi[i, f] *= item_num[i, f] / item_denom[i, f]
 * 
 */
        __pyx_t_69 = __pyx_v_i;
        __pyx_t_70 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_69 < 0) {
          __pyx_t_69 += __pyx_pybuffernd_qi.diminfo[0].shape;
          if (unlikely(__pyx_t_69 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_69 >= __pyx_pybuffernd_qi.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_70 < 0) {
          __pyx_t_70 += __pyx_pybuffernd_qi.diminfo[1].shape;
          if (unlikely(__pyx_t_70 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_70 >= __pyx_pybuffernd_qi.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 642, __pyx_L1_error)
        }
        __pyx_t_71 = __pyx_v_i;
        __pyx_t_72 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_71 < 0) {
          __pyx_t_71 += __pyx_pybuffernd_item_denom.diminfo[0].shape;
          if (unlikely(__pyx_t_71 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_71 >= __pyx_pybuffernd_item_denom.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_72 < 0) {
          __pyx_t_72 += __pyx_pybuffernd_item_denom.diminfo[1].shape;
          if (unlikely(__pyx_t_72 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_72 >= __pyx_pybuffernd_item_denom.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 642, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_item_denom.rcbuffer->pybuffer.buf, __pyx_t_71, __pyx_pybuffernd_item_denom.diminfo[0].strides, __pyx_t_72, __pyx_pybuffernd_item_denom.diminfo[1].strides) += ((__pyx_v_l * __pyx_v_reg_qi) * (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_qi.rcbuffer->pybuffer.buf, __pyx_t_69, __pyx_pybuffernd_qi.diminfo[0].strides, __pyx_t_70, __pyx_pybuffernd_qi.diminfo[1].strides)));

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":643
 *                 for f in range(self.n_factors):
 *                     item_denom[i, f] += l * reg_qi * qi[i, f]
 *                     qi[i, f] *= item_num[i, f] / item_denom[i, f]             # <<<<<<<<<<<<<<
 * 
 *         self.bu = bu
 */
        __pyx_t_73 = __pyx_v_i;
        __pyx_t_74 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_73 < 0) {
          __pyx_t_73 += __pyx_pybuffernd_item_num.diminfo[0].shape;
          if (unlikely(__pyx_t_73 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_73 >= __pyx_pybuffernd_item_num.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_74 < 0) {
          __pyx_t_74 += __pyx_pybuffernd_item_num.diminfo[1].shape;
          if (unlikely(__pyx_t_74 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_74 >= __pyx_pybuffernd_item_num.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 643, __pyx_L1_error)
        }
        __pyx_t_66 = (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_item_num.rcbuffer->pybuffer.buf, __pyx_t_73, __pyx_pybuffernd_item_num.diminfo[0].strides, __pyx_t_74, __pyx_pybuffernd_item_num.diminfo[1].strides));
        __pyx_t_75 = __pyx_v_i;
        __pyx_t_76 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_75 < 0) {
          __pyx_t_75 += __pyx_pybuffernd_item_denom.diminfo[0].shape;
          if (unlikely(__pyx_t_75 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_75 >= __pyx_pybuffernd_item_denom.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_76 < 0) {
          __pyx_t_76 += __pyx_pybuffernd_item_denom.diminfo[1].shape;
          if (unlikely(__pyx_t_76 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_76 >= __pyx_pybuffernd_item_denom.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 643, __pyx_L1_error)
        }
        __pyx_t_63 = (*__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_item_denom.rcbuffer->pybuffer.buf, __pyx_t_75, __pyx_pybuffernd_item_denom.diminfo[0].strides, __pyx_t_76, __pyx_pybuffernd_item_denom.diminfo[1].strides));
        if (unlikely(__pyx_t_63 == 0)) {
          PyErr_SetString(PyExc_ZeroDivisionError, "float division");
          __PYX_ERR(0, 643, __pyx_L1_error)
        }
        __pyx_t_77 = __pyx_v_i;
        __pyx_t_78 = __pyx_v_f;
        __pyx_t_28 = -1;
        if (__pyx_t_77 < 0) {
          __pyx_t_77 += __pyx_pybuffernd_qi.diminfo[0].shape;
          if (unlikely(__pyx_t_77 < 0)) __pyx_t_28 = 0;
        } else if (unlikely(__pyx_t_77 >= __pyx_pybuffernd_qi.diminfo[0].shape)) __pyx_t_28 = 0;
        if (__pyx_t_78 < 0) {
          __pyx_t_78 += __pyx_pybuffernd_qi.diminfo[1].shape;
          if (unlikely(__pyx_t_78 < 0)) __pyx_t_28 = 1;
        } else if (unlikely(__pyx_t_78 >= __pyx_pybuffernd_qi.diminfo[1].shape)) __pyx_t_28 = 1;
        if (unlikely(__pyx_t_28 != -1)) {
          __Pyx_RaiseBufferIndexError(__pyx_t_28);
          __PYX_ERR(0, 643, __pyx_L1_error)
        }
        *__Pyx_BufPtrStrided2d(__pyx_t_5numpy_double_t *, __pyx_pybuffernd_qi.rcbuffer->pybuffer.buf, __pyx_t_77, __pyx_pybuffernd_qi.diminfo[0].strides, __pyx_t_78, __pyx_pybuffernd_qi.diminfo[1].strides) *= (__pyx_t_66 / __pyx_t_63);

        /* "surprise/prediction_algorithms/matrix_factorization.pyx":641
 *             for i in trainset.all_items():
 *                 l = len(trainset.ir[i])
 *                 for f in range(self.n_factors):             # <<<<<<<<<<<<<<
 *                     item_denom[i, f] += l * reg_qi * qi[i, f]
 *                     qi[i, f] *= item_num[i, f] / item_denom[i, f]
 */
      }
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":639
 * 
 *             # Update item factors
 *             for i in trainset.all_items():             # <<<<<<<<<<<<<<
 *                 l = len(trainset.ir[i])
 *                 for f in range(self.n_factors):
 */
    }
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":598
 *             global_mean = 0
 * 
 *         for current_epoch in range(self.n_epochs):             # <<<<<<<<<<<<<<
 * 
 *             if self.verbose:
 */
  }
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":645
 *                     qi[i, f] *= item_num[i, f] / item_denom[i, f]
 * 
 *         self.bu = bu             # <<<<<<<<<<<<<<
 *         self.bi = bi
 *         self.pu = pu
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_bu, ((PyObject *)__pyx_v_bu)) < 0) __PYX_ERR(0, 645, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":646
 * 
 *         self.bu = bu
 *         self.bi = bi             # <<<<<<<<<<<<<<
 *         self.pu = pu
 *         self.qi = qi
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_bi, ((PyObject *)__pyx_v_bi)) < 0) __PYX_ERR(0, 646, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":647
 *         self.bu = bu
 *         self.bi = bi
 *         self.pu = pu             # <<<<<<<<<<<<<<
 *         self.qi = qi
 * 
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_pu, ((PyObject *)__pyx_v_pu)) < 0) __PYX_ERR(0, 647, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":648
 *         self.bi = bi
 *         self.pu = pu
 *         self.qi = qi             # <<<<<<<<<<<<<<
 * 
 *     def estimate(self, u, i):
 */
  if (__Pyx_PyObject_SetAttrStr(__pyx_v_self, __pyx_n_s_qi, ((PyObject *)__pyx_v_qi)) < 0) __PYX_ERR(0, 648, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":560
 *         self.sgd(trainset)
 * 
 *     def sgd(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         # user and item factors
 */

  /* function exit code */
  __pyx_r = Py_None; __Pyx_INCREF(Py_None);
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_3);
  __Pyx_XDECREF(__pyx_t_4);
  __Pyx_XDECREF(__pyx_t_5);
  __Pyx_XDECREF(__pyx_t_6);
  __Pyx_XDECREF(__pyx_t_7);
  __Pyx_XDECREF(__pyx_t_26);
  { PyObject *__pyx_type, *__pyx_value, *__pyx_tb;
    __Pyx_PyThreadState_declare
    __Pyx_PyThreadState_assign
    __Pyx_ErrFetch(&__pyx_type, &__pyx_value, &__pyx_tb);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bi.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bu.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_item_denom.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_item_num.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_pu.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_qi.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_user_denom.rcbuffer->pybuffer);
    __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_user_num.rcbuffer->pybuffer);
  __Pyx_ErrRestore(__pyx_type, __pyx_value, __pyx_tb);}
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.NMF.sgd", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = NULL;
  goto __pyx_L2;
  __pyx_L0:;
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bi.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_bu.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_item_denom.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_item_num.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_pu.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_qi.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_user_denom.rcbuffer->pybuffer);
  __Pyx_SafeReleaseBuffer(&__pyx_pybuffernd_user_num.rcbuffer->pybuffer);
  __pyx_L2:;
  __Pyx_XDECREF((PyObject *)__pyx_v_pu);
  __Pyx_XDECREF((PyObject *)__pyx_v_qi);
  __Pyx_XDECREF((PyObject *)__pyx_v_bu);
  __Pyx_XDECREF((PyObject *)__pyx_v_bi);
  __Pyx_XDECREF((PyObject *)__pyx_v_user_num);
  __Pyx_XDECREF((PyObject *)__pyx_v_user_denom);
  __Pyx_XDECREF((PyObject *)__pyx_v_item_num);
  __Pyx_XDECREF((PyObject *)__pyx_v_item_denom);
  __Pyx_XDECREF(__pyx_v_current_epoch);
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "surprise/prediction_algorithms/matrix_factorization.pyx":650
 *         self.qi = qi
 * 
 *     def estimate(self, u, i):             # <<<<<<<<<<<<<<
 *         # Should we cythonize this as well?
 * 
 */

/* Python wrapper */
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_7estimate(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds); /*proto*/
static PyMethodDef __pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_7estimate = {"estimate", (PyCFunction)__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_7estimate, METH_VARARGS|METH_KEYWORDS, 0};
static PyObject *__pyx_pw_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_7estimate(PyObject *__pyx_self, PyObject *__pyx_args, PyObject *__pyx_kwds) {
  PyObject *__pyx_v_self = 0;
  PyObject *__pyx_v_u = 0;
  PyObject *__pyx_v_i = 0;
  PyObject *__pyx_r = 0;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("estimate (wrapper)", 0);
  {
    static PyObject **__pyx_pyargnames[] = {&__pyx_n_s_self,&__pyx_n_s_u,&__pyx_n_s_i,0};
    PyObject* values[3] = {0,0,0};
    if (unlikely(__pyx_kwds)) {
      Py_ssize_t kw_args;
      const Py_ssize_t pos_args = PyTuple_GET_SIZE(__pyx_args);
      switch (pos_args) {
        case  3: values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
        CYTHON_FALLTHROUGH;
        case  2: values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
        CYTHON_FALLTHROUGH;
        case  1: values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
        CYTHON_FALLTHROUGH;
        case  0: break;
        default: goto __pyx_L5_argtuple_error;
      }
      kw_args = PyDict_Size(__pyx_kwds);
      switch (pos_args) {
        case  0:
        if (likely((values[0] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_self)) != 0)) kw_args--;
        else goto __pyx_L5_argtuple_error;
        CYTHON_FALLTHROUGH;
        case  1:
        if (likely((values[1] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_u)) != 0)) kw_args--;
        else {
          __Pyx_RaiseArgtupleInvalid("estimate", 1, 3, 3, 1); __PYX_ERR(0, 650, __pyx_L3_error)
        }
        CYTHON_FALLTHROUGH;
        case  2:
        if (likely((values[2] = PyDict_GetItem(__pyx_kwds, __pyx_n_s_i)) != 0)) kw_args--;
        else {
          __Pyx_RaiseArgtupleInvalid("estimate", 1, 3, 3, 2); __PYX_ERR(0, 650, __pyx_L3_error)
        }
      }
      if (unlikely(kw_args > 0)) {
        if (unlikely(__Pyx_ParseOptionalKeywords(__pyx_kwds, __pyx_pyargnames, 0, values, pos_args, "estimate") < 0)) __PYX_ERR(0, 650, __pyx_L3_error)
      }
    } else if (PyTuple_GET_SIZE(__pyx_args) != 3) {
      goto __pyx_L5_argtuple_error;
    } else {
      values[0] = PyTuple_GET_ITEM(__pyx_args, 0);
      values[1] = PyTuple_GET_ITEM(__pyx_args, 1);
      values[2] = PyTuple_GET_ITEM(__pyx_args, 2);
    }
    __pyx_v_self = values[0];
    __pyx_v_u = values[1];
    __pyx_v_i = values[2];
  }
  goto __pyx_L4_argument_unpacking_done;
  __pyx_L5_argtuple_error:;
  __Pyx_RaiseArgtupleInvalid("estimate", 1, 3, 3, PyTuple_GET_SIZE(__pyx_args)); __PYX_ERR(0, 650, __pyx_L3_error)
  __pyx_L3_error:;
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.NMF.estimate", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __Pyx_RefNannyFinishContext();
  return NULL;
  __pyx_L4_argument_unpacking_done:;
  __pyx_r = __pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_6estimate(__pyx_self, __pyx_v_self, __pyx_v_u, __pyx_v_i);

  /* function exit code */
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

static PyObject *__pyx_pf_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_6estimate(CYTHON_UNUSED PyObject *__pyx_self, PyObject *__pyx_v_self, PyObject *__pyx_v_u, PyObject *__pyx_v_i) {
  PyObject *__pyx_v_known_user = NULL;
  PyObject *__pyx_v_known_item = NULL;
  PyObject *__pyx_v_est = NULL;
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  PyObject *__pyx_t_2 = NULL;
  PyObject *__pyx_t_3 = NULL;
  PyObject *__pyx_t_4 = NULL;
  int __pyx_t_5;
  int __pyx_t_6;
  PyObject *__pyx_t_7 = NULL;
  int __pyx_t_8;
  PyObject *__pyx_t_9 = NULL;
  __Pyx_RefNannySetupContext("estimate", 0);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":653
 *         # Should we cythonize this as well?
 * 
 *         known_user = self.trainset.knows_user(u)             # <<<<<<<<<<<<<<
 *         known_item = self.trainset.knows_item(i)
 * 
 */
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 653, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_t_2, __pyx_n_s_knows_user); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 653, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_t_2 = NULL;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_3))) {
    __pyx_t_2 = PyMethod_GET_SELF(__pyx_t_3);
    if (likely(__pyx_t_2)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_3);
      __Pyx_INCREF(__pyx_t_2);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_3, function);
    }
  }
  if (!__pyx_t_2) {
    __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_3, __pyx_v_u); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 653, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_3)) {
      PyObject *__pyx_temp[2] = {__pyx_t_2, __pyx_v_u};
      __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 653, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_2); __pyx_t_2 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_3)) {
      PyObject *__pyx_temp[2] = {__pyx_t_2, __pyx_v_u};
      __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_3, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 653, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_2); __pyx_t_2 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    {
      __pyx_t_4 = PyTuple_New(1+1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 653, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __Pyx_GIVEREF(__pyx_t_2); PyTuple_SET_ITEM(__pyx_t_4, 0, __pyx_t_2); __pyx_t_2 = NULL;
      __Pyx_INCREF(__pyx_v_u);
      __Pyx_GIVEREF(__pyx_v_u);
      PyTuple_SET_ITEM(__pyx_t_4, 0+1, __pyx_v_u);
      __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_3, __pyx_t_4, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 653, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __pyx_v_known_user = __pyx_t_1;
  __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":654
 * 
 *         known_user = self.trainset.knows_user(u)
 *         known_item = self.trainset.knows_item(i)             # <<<<<<<<<<<<<<
 * 
 *         if self.biased:
 */
  __pyx_t_3 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 654, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);
  __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_3, __pyx_n_s_knows_item); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 654, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __pyx_t_3 = NULL;
  if (CYTHON_UNPACK_METHODS && likely(PyMethod_Check(__pyx_t_4))) {
    __pyx_t_3 = PyMethod_GET_SELF(__pyx_t_4);
    if (likely(__pyx_t_3)) {
      PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_4);
      __Pyx_INCREF(__pyx_t_3);
      __Pyx_INCREF(function);
      __Pyx_DECREF_SET(__pyx_t_4, function);
    }
  }
  if (!__pyx_t_3) {
    __pyx_t_1 = __Pyx_PyObject_CallOneArg(__pyx_t_4, __pyx_v_i); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 654, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
  } else {
    #if CYTHON_FAST_PYCALL
    if (PyFunction_Check(__pyx_t_4)) {
      PyObject *__pyx_temp[2] = {__pyx_t_3, __pyx_v_i};
      __pyx_t_1 = __Pyx_PyFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 654, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    #if CYTHON_FAST_PYCCALL
    if (__Pyx_PyFastCFunction_Check(__pyx_t_4)) {
      PyObject *__pyx_temp[2] = {__pyx_t_3, __pyx_v_i};
      __pyx_t_1 = __Pyx_PyCFunction_FastCall(__pyx_t_4, __pyx_temp+1-1, 1+1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 654, __pyx_L1_error)
      __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
      __Pyx_GOTREF(__pyx_t_1);
    } else
    #endif
    {
      __pyx_t_2 = PyTuple_New(1+1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 654, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_GIVEREF(__pyx_t_3); PyTuple_SET_ITEM(__pyx_t_2, 0, __pyx_t_3); __pyx_t_3 = NULL;
      __Pyx_INCREF(__pyx_v_i);
      __Pyx_GIVEREF(__pyx_v_i);
      PyTuple_SET_ITEM(__pyx_t_2, 0+1, __pyx_v_i);
      __pyx_t_1 = __Pyx_PyObject_Call(__pyx_t_4, __pyx_t_2, NULL); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 654, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
    }
  }
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __pyx_v_known_item = __pyx_t_1;
  __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":656
 *         known_item = self.trainset.knows_item(i)
 * 
 *         if self.biased:             # <<<<<<<<<<<<<<
 *             est = self.trainset.global_mean
 * 
 */
  __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_biased); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 656, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_5 = __Pyx_PyObject_IsTrue(__pyx_t_1); if (unlikely(__pyx_t_5 < 0)) __PYX_ERR(0, 656, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  if (__pyx_t_5) {

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":657
 * 
 *         if self.biased:
 *             est = self.trainset.global_mean             # <<<<<<<<<<<<<<
 * 
 *             if known_user:
 */
    __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_trainset); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 657, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_1);
    __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_global_mean); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 657, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_4);
    __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
    __pyx_v_est = __pyx_t_4;
    __pyx_t_4 = 0;

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":659
 *             est = self.trainset.global_mean
 * 
 *             if known_user:             # <<<<<<<<<<<<<<
 *                 est += self.bu[u]
 * 
 */
    __pyx_t_5 = __Pyx_PyObject_IsTrue(__pyx_v_known_user); if (unlikely(__pyx_t_5 < 0)) __PYX_ERR(0, 659, __pyx_L1_error)
    if (__pyx_t_5) {

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":660
 * 
 *             if known_user:
 *                 est += self.bu[u]             # <<<<<<<<<<<<<<
 * 
 *             if known_item:
 */
      __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_bu); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 660, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_1 = PyObject_GetItem(__pyx_t_4, __pyx_v_u); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 660, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_4 = PyNumber_InPlaceAdd(__pyx_v_est, __pyx_t_1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 660, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __Pyx_DECREF_SET(__pyx_v_est, __pyx_t_4);
      __pyx_t_4 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":659
 *             est = self.trainset.global_mean
 * 
 *             if known_user:             # <<<<<<<<<<<<<<
 *                 est += self.bu[u]
 * 
 */
    }

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":662
 *                 est += self.bu[u]
 * 
 *             if known_item:             # <<<<<<<<<<<<<<
 *                 est += self.bi[i]
 * 
 */
    __pyx_t_5 = __Pyx_PyObject_IsTrue(__pyx_v_known_item); if (unlikely(__pyx_t_5 < 0)) __PYX_ERR(0, 662, __pyx_L1_error)
    if (__pyx_t_5) {

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":663
 * 
 *             if known_item:
 *                 est += self.bi[i]             # <<<<<<<<<<<<<<
 * 
 *             if known_user and known_item:
 */
      __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_bi); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 663, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_1 = PyObject_GetItem(__pyx_t_4, __pyx_v_i); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 663, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_4 = PyNumber_InPlaceAdd(__pyx_v_est, __pyx_t_1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 663, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __Pyx_DECREF_SET(__pyx_v_est, __pyx_t_4);
      __pyx_t_4 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":662
 *                 est += self.bu[u]
 * 
 *             if known_item:             # <<<<<<<<<<<<<<
 *                 est += self.bi[i]
 * 
 */
    }

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":665
 *                 est += self.bi[i]
 * 
 *             if known_user and known_item:             # <<<<<<<<<<<<<<
 *                 est += np.dot(self.qi[i], self.pu[u])
 * 
 */
    __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_v_known_user); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(0, 665, __pyx_L1_error)
    if (__pyx_t_6) {
    } else {
      __pyx_t_5 = __pyx_t_6;
      goto __pyx_L7_bool_binop_done;
    }
    __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_v_known_item); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(0, 665, __pyx_L1_error)
    __pyx_t_5 = __pyx_t_6;
    __pyx_L7_bool_binop_done:;
    if (__pyx_t_5) {

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":666
 * 
 *             if known_user and known_item:
 *                 est += np.dot(self.qi[i], self.pu[u])             # <<<<<<<<<<<<<<
 * 
 *         else:
 */
      __pyx_t_1 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 666, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_t_1, __pyx_n_s_dot); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 666, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_qi); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 666, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __pyx_t_3 = PyObject_GetItem(__pyx_t_1, __pyx_v_i); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 666, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __pyx_t_1 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_pu); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 666, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_1);
      __pyx_t_7 = PyObject_GetItem(__pyx_t_1, __pyx_v_u); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 666, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_7);
      __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      __pyx_t_1 = NULL;
      __pyx_t_8 = 0;
      if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_2))) {
        __pyx_t_1 = PyMethod_GET_SELF(__pyx_t_2);
        if (likely(__pyx_t_1)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_2);
          __Pyx_INCREF(__pyx_t_1);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_2, function);
          __pyx_t_8 = 1;
        }
      }
      #if CYTHON_FAST_PYCALL
      if (PyFunction_Check(__pyx_t_2)) {
        PyObject *__pyx_temp[3] = {__pyx_t_1, __pyx_t_3, __pyx_t_7};
        __pyx_t_4 = __Pyx_PyFunction_FastCall(__pyx_t_2, __pyx_temp+1-__pyx_t_8, 2+__pyx_t_8); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 666, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
        __Pyx_GOTREF(__pyx_t_4);
        __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
        __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
      } else
      #endif
      #if CYTHON_FAST_PYCCALL
      if (__Pyx_PyFastCFunction_Check(__pyx_t_2)) {
        PyObject *__pyx_temp[3] = {__pyx_t_1, __pyx_t_3, __pyx_t_7};
        __pyx_t_4 = __Pyx_PyCFunction_FastCall(__pyx_t_2, __pyx_temp+1-__pyx_t_8, 2+__pyx_t_8); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 666, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
        __Pyx_GOTREF(__pyx_t_4);
        __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
        __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
      } else
      #endif
      {
        __pyx_t_9 = PyTuple_New(2+__pyx_t_8); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 666, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_9);
        if (__pyx_t_1) {
          __Pyx_GIVEREF(__pyx_t_1); PyTuple_SET_ITEM(__pyx_t_9, 0, __pyx_t_1); __pyx_t_1 = NULL;
        }
        __Pyx_GIVEREF(__pyx_t_3);
        PyTuple_SET_ITEM(__pyx_t_9, 0+__pyx_t_8, __pyx_t_3);
        __Pyx_GIVEREF(__pyx_t_7);
        PyTuple_SET_ITEM(__pyx_t_9, 1+__pyx_t_8, __pyx_t_7);
        __pyx_t_3 = 0;
        __pyx_t_7 = 0;
        __pyx_t_4 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_t_9, NULL); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 666, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_4);
        __Pyx_DECREF(__pyx_t_9); __pyx_t_9 = 0;
      }
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
      __pyx_t_2 = PyNumber_InPlaceAdd(__pyx_v_est, __pyx_t_4); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 666, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __Pyx_DECREF_SET(__pyx_v_est, __pyx_t_2);
      __pyx_t_2 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":665
 *                 est += self.bi[i]
 * 
 *             if known_user and known_item:             # <<<<<<<<<<<<<<
 *                 est += np.dot(self.qi[i], self.pu[u])
 * 
 */
    }

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":656
 *         known_item = self.trainset.knows_item(i)
 * 
 *         if self.biased:             # <<<<<<<<<<<<<<
 *             est = self.trainset.global_mean
 * 
 */
    goto __pyx_L3;
  }

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":669
 * 
 *         else:
 *             if known_user and known_item:             # <<<<<<<<<<<<<<
 *                 est = np.dot(self.qi[i], self.pu[u])
 *             else:
 */
  /*else*/ {
    __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_v_known_user); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(0, 669, __pyx_L1_error)
    if (__pyx_t_6) {
    } else {
      __pyx_t_5 = __pyx_t_6;
      goto __pyx_L10_bool_binop_done;
    }
    __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_v_known_item); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(0, 669, __pyx_L1_error)
    __pyx_t_5 = __pyx_t_6;
    __pyx_L10_bool_binop_done:;
    if (__pyx_t_5) {

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":670
 *         else:
 *             if known_user and known_item:
 *                 est = np.dot(self.qi[i], self.pu[u])             # <<<<<<<<<<<<<<
 *             else:
 *                 raise PredictionImpossible('User and item are unkown.')
 */
      __pyx_t_4 = __Pyx_GetModuleGlobalName(__pyx_n_s_np); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 670, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_9 = __Pyx_PyObject_GetAttrStr(__pyx_t_4, __pyx_n_s_dot); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 670, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_9);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_qi); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 670, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_7 = PyObject_GetItem(__pyx_t_4, __pyx_v_i); if (unlikely(!__pyx_t_7)) __PYX_ERR(0, 670, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_7);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_4 = __Pyx_PyObject_GetAttrStr(__pyx_v_self, __pyx_n_s_pu); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 670, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_3 = PyObject_GetItem(__pyx_t_4, __pyx_v_u); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 670, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_4 = NULL;
      __pyx_t_8 = 0;
      if (CYTHON_UNPACK_METHODS && unlikely(PyMethod_Check(__pyx_t_9))) {
        __pyx_t_4 = PyMethod_GET_SELF(__pyx_t_9);
        if (likely(__pyx_t_4)) {
          PyObject* function = PyMethod_GET_FUNCTION(__pyx_t_9);
          __Pyx_INCREF(__pyx_t_4);
          __Pyx_INCREF(function);
          __Pyx_DECREF_SET(__pyx_t_9, function);
          __pyx_t_8 = 1;
        }
      }
      #if CYTHON_FAST_PYCALL
      if (PyFunction_Check(__pyx_t_9)) {
        PyObject *__pyx_temp[3] = {__pyx_t_4, __pyx_t_7, __pyx_t_3};
        __pyx_t_2 = __Pyx_PyFunction_FastCall(__pyx_t_9, __pyx_temp+1-__pyx_t_8, 2+__pyx_t_8); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 670, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
        __Pyx_GOTREF(__pyx_t_2);
        __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
        __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      } else
      #endif
      #if CYTHON_FAST_PYCCALL
      if (__Pyx_PyFastCFunction_Check(__pyx_t_9)) {
        PyObject *__pyx_temp[3] = {__pyx_t_4, __pyx_t_7, __pyx_t_3};
        __pyx_t_2 = __Pyx_PyCFunction_FastCall(__pyx_t_9, __pyx_temp+1-__pyx_t_8, 2+__pyx_t_8); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 670, __pyx_L1_error)
        __Pyx_XDECREF(__pyx_t_4); __pyx_t_4 = 0;
        __Pyx_GOTREF(__pyx_t_2);
        __Pyx_DECREF(__pyx_t_7); __pyx_t_7 = 0;
        __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      } else
      #endif
      {
        __pyx_t_1 = PyTuple_New(2+__pyx_t_8); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 670, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_1);
        if (__pyx_t_4) {
          __Pyx_GIVEREF(__pyx_t_4); PyTuple_SET_ITEM(__pyx_t_1, 0, __pyx_t_4); __pyx_t_4 = NULL;
        }
        __Pyx_GIVEREF(__pyx_t_7);
        PyTuple_SET_ITEM(__pyx_t_1, 0+__pyx_t_8, __pyx_t_7);
        __Pyx_GIVEREF(__pyx_t_3);
        PyTuple_SET_ITEM(__pyx_t_1, 1+__pyx_t_8, __pyx_t_3);
        __pyx_t_7 = 0;
        __pyx_t_3 = 0;
        __pyx_t_2 = __Pyx_PyObject_Call(__pyx_t_9, __pyx_t_1, NULL); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 670, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_2);
        __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
      }
      __Pyx_DECREF(__pyx_t_9); __pyx_t_9 = 0;
      __pyx_v_est = __pyx_t_2;
      __pyx_t_2 = 0;

      /* "surprise/prediction_algorithms/matrix_factorization.pyx":669
 * 
 *         else:
 *             if known_user and known_item:             # <<<<<<<<<<<<<<
 *                 est = np.dot(self.qi[i], self.pu[u])
 *             else:
 */
      goto __pyx_L9;
    }

    /* "surprise/prediction_algorithms/matrix_factorization.pyx":672
 *                 est = np.dot(self.qi[i], self.pu[u])
 *             else:
 *                 raise PredictionImpossible('User and item are unkown.')             # <<<<<<<<<<<<<<
 * 
 *         return est
 */
    /*else*/ {
      __pyx_t_2 = __Pyx_GetModuleGlobalName(__pyx_n_s_PredictionImpossible); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 672, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_2);
      __pyx_t_9 = __Pyx_PyObject_Call(__pyx_t_2, __pyx_tuple__3, NULL); if (unlikely(!__pyx_t_9)) __PYX_ERR(0, 672, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_9);
      __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
      __Pyx_Raise(__pyx_t_9, 0, 0, 0);
      __Pyx_DECREF(__pyx_t_9); __pyx_t_9 = 0;
      __PYX_ERR(0, 672, __pyx_L1_error)
    }
    __pyx_L9:;
  }
  __pyx_L3:;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":674
 *                 raise PredictionImpossible('User and item are unkown.')
 * 
 *         return est             # <<<<<<<<<<<<<<
 */
  __Pyx_XDECREF(__pyx_r);
  __Pyx_INCREF(__pyx_v_est);
  __pyx_r = __pyx_v_est;
  goto __pyx_L0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":650
 *         self.qi = qi
 * 
 *     def estimate(self, u, i):             # <<<<<<<<<<<<<<
 *         # Should we cythonize this as well?
 * 
 */

  /* function exit code */
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_2);
  __Pyx_XDECREF(__pyx_t_3);
  __Pyx_XDECREF(__pyx_t_4);
  __Pyx_XDECREF(__pyx_t_7);
  __Pyx_XDECREF(__pyx_t_9);
  __Pyx_AddTraceback("surprise.prediction_algorithms.matrix_factorization.NMF.estimate", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = NULL;
  __pyx_L0:;
  __Pyx_XDECREF(__pyx_v_known_user);
  __Pyx_XDECREF(__pyx_v_known_item);
  __Pyx_XDECREF(__pyx_v_est);
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":214
 *         # experimental exception made for __getbuffer__ and __releasebuffer__
 *         # -- the details of this may change.
 *         def __getbuffer__(ndarray self, Py_buffer* info, int flags):             # <<<<<<<<<<<<<<
 *             # This implementation of getbuffer is geared towards Cython
 *             # requirements, and does not yet fullfill the PEP.
 */

/* Python wrapper */
static CYTHON_UNUSED int __pyx_pw_5numpy_7ndarray_1__getbuffer__(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags); /*proto*/
static CYTHON_UNUSED int __pyx_pw_5numpy_7ndarray_1__getbuffer__(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags) {
  int __pyx_r;
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("__getbuffer__ (wrapper)", 0);
  __pyx_r = __pyx_pf_5numpy_7ndarray___getbuffer__(((PyArrayObject *)__pyx_v_self), ((Py_buffer *)__pyx_v_info), ((int)__pyx_v_flags));

  /* function exit code */
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

static int __pyx_pf_5numpy_7ndarray___getbuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info, int __pyx_v_flags) {
  int __pyx_v_copy_shape;
  int __pyx_v_i;
  int __pyx_v_ndim;
  int __pyx_v_endian_detector;
  int __pyx_v_little_endian;
  int __pyx_v_t;
  char *__pyx_v_f;
  PyArray_Descr *__pyx_v_descr = 0;
  int __pyx_v_offset;
  int __pyx_v_hasfields;
  int __pyx_r;
  __Pyx_RefNannyDeclarations
  int __pyx_t_1;
  int __pyx_t_2;
  PyObject *__pyx_t_3 = NULL;
  int __pyx_t_4;
  int __pyx_t_5;
  PyObject *__pyx_t_6 = NULL;
  char *__pyx_t_7;
  __Pyx_RefNannySetupContext("__getbuffer__", 0);
  if (__pyx_v_info != NULL) {
    __pyx_v_info->obj = Py_None; __Pyx_INCREF(Py_None);
    __Pyx_GIVEREF(__pyx_v_info->obj);
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":220
 *             # of flags
 * 
 *             if info == NULL: return             # <<<<<<<<<<<<<<
 * 
 *             cdef int copy_shape, i, ndim
 */
  __pyx_t_1 = ((__pyx_v_info == NULL) != 0);
  if (__pyx_t_1) {
    __pyx_r = 0;
    goto __pyx_L0;
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":223
 * 
 *             cdef int copy_shape, i, ndim
 *             cdef int endian_detector = 1             # <<<<<<<<<<<<<<
 *             cdef bint little_endian = ((<char*>&endian_detector)[0] != 0)
 * 
 */
  __pyx_v_endian_detector = 1;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":224
 *             cdef int copy_shape, i, ndim
 *             cdef int endian_detector = 1
 *             cdef bint little_endian = ((<char*>&endian_detector)[0] != 0)             # <<<<<<<<<<<<<<
 * 
 *             ndim = PyArray_NDIM(self)
 */
  __pyx_v_little_endian = ((((char *)(&__pyx_v_endian_detector))[0]) != 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":226
 *             cdef bint little_endian = ((<char*>&endian_detector)[0] != 0)
 * 
 *             ndim = PyArray_NDIM(self)             # <<<<<<<<<<<<<<
 * 
 *             if sizeof(npy_intp) != sizeof(Py_ssize_t):
 */
  __pyx_v_ndim = PyArray_NDIM(__pyx_v_self);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":228
 *             ndim = PyArray_NDIM(self)
 * 
 *             if sizeof(npy_intp) != sizeof(Py_ssize_t):             # <<<<<<<<<<<<<<
 *                 copy_shape = 1
 *             else:
 */
  __pyx_t_1 = (((sizeof(npy_intp)) != (sizeof(Py_ssize_t))) != 0);
  if (__pyx_t_1) {

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":229
 * 
 *             if sizeof(npy_intp) != sizeof(Py_ssize_t):
 *                 copy_shape = 1             # <<<<<<<<<<<<<<
 *             else:
 *                 copy_shape = 0
 */
    __pyx_v_copy_shape = 1;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":228
 *             ndim = PyArray_NDIM(self)
 * 
 *             if sizeof(npy_intp) != sizeof(Py_ssize_t):             # <<<<<<<<<<<<<<
 *                 copy_shape = 1
 *             else:
 */
    goto __pyx_L4;
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":231
 *                 copy_shape = 1
 *             else:
 *                 copy_shape = 0             # <<<<<<<<<<<<<<
 * 
 *             if ((flags & pybuf.PyBUF_C_CONTIGUOUS == pybuf.PyBUF_C_CONTIGUOUS)
 */
  /*else*/ {
    __pyx_v_copy_shape = 0;
  }
  __pyx_L4:;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":233
 *                 copy_shape = 0
 * 
 *             if ((flags & pybuf.PyBUF_C_CONTIGUOUS == pybuf.PyBUF_C_CONTIGUOUS)             # <<<<<<<<<<<<<<
 *                 and not PyArray_CHKFLAGS(self, NPY_C_CONTIGUOUS)):
 *                 raise ValueError(u"ndarray is not C contiguous")
 */
  __pyx_t_2 = (((__pyx_v_flags & PyBUF_C_CONTIGUOUS) == PyBUF_C_CONTIGUOUS) != 0);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L6_bool_binop_done;
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":234
 * 
 *             if ((flags & pybuf.PyBUF_C_CONTIGUOUS == pybuf.PyBUF_C_CONTIGUOUS)
 *                 and not PyArray_CHKFLAGS(self, NPY_C_CONTIGUOUS)):             # <<<<<<<<<<<<<<
 *                 raise ValueError(u"ndarray is not C contiguous")
 * 
 */
  __pyx_t_2 = ((!(PyArray_CHKFLAGS(__pyx_v_self, NPY_C_CONTIGUOUS) != 0)) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L6_bool_binop_done:;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":233
 *                 copy_shape = 0
 * 
 *             if ((flags & pybuf.PyBUF_C_CONTIGUOUS == pybuf.PyBUF_C_CONTIGUOUS)             # <<<<<<<<<<<<<<
 *                 and not PyArray_CHKFLAGS(self, NPY_C_CONTIGUOUS)):
 *                 raise ValueError(u"ndarray is not C contiguous")
 */
  if (__pyx_t_1) {

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":235
 *             if ((flags & pybuf.PyBUF_C_CONTIGUOUS == pybuf.PyBUF_C_CONTIGUOUS)
 *                 and not PyArray_CHKFLAGS(self, NPY_C_CONTIGUOUS)):
 *                 raise ValueError(u"ndarray is not C contiguous")             # <<<<<<<<<<<<<<
 * 
 *             if ((flags & pybuf.PyBUF_F_CONTIGUOUS == pybuf.PyBUF_F_CONTIGUOUS)
 */
    __pyx_t_3 = __Pyx_PyObject_Call(__pyx_builtin_ValueError, __pyx_tuple__4, NULL); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 235, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __Pyx_Raise(__pyx_t_3, 0, 0, 0);
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    __PYX_ERR(1, 235, __pyx_L1_error)

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":233
 *                 copy_shape = 0
 * 
 *             if ((flags & pybuf.PyBUF_C_CONTIGUOUS == pybuf.PyBUF_C_CONTIGUOUS)             # <<<<<<<<<<<<<<
 *                 and not PyArray_CHKFLAGS(self, NPY_C_CONTIGUOUS)):
 *                 raise ValueError(u"ndarray is not C contiguous")
 */
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":237
 *                 raise ValueError(u"ndarray is not C contiguous")
 * 
 *             if ((flags & pybuf.PyBUF_F_CONTIGUOUS == pybuf.PyBUF_F_CONTIGUOUS)             # <<<<<<<<<<<<<<
 *                 and not PyArray_CHKFLAGS(self, NPY_F_CONTIGUOUS)):
 *                 raise ValueError(u"ndarray is not Fortran contiguous")
 */
  __pyx_t_2 = (((__pyx_v_flags & PyBUF_F_CONTIGUOUS) == PyBUF_F_CONTIGUOUS) != 0);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L9_bool_binop_done;
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":238
 * 
 *             if ((flags & pybuf.PyBUF_F_CONTIGUOUS == pybuf.PyBUF_F_CONTIGUOUS)
 *                 and not PyArray_CHKFLAGS(self, NPY_F_CONTIGUOUS)):             # <<<<<<<<<<<<<<
 *                 raise ValueError(u"ndarray is not Fortran contiguous")
 * 
 */
  __pyx_t_2 = ((!(PyArray_CHKFLAGS(__pyx_v_self, NPY_F_CONTIGUOUS) != 0)) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L9_bool_binop_done:;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":237
 *                 raise ValueError(u"ndarray is not C contiguous")
 * 
 *             if ((flags & pybuf.PyBUF_F_CONTIGUOUS == pybuf.PyBUF_F_CONTIGUOUS)             # <<<<<<<<<<<<<<
 *                 and not PyArray_CHKFLAGS(self, NPY_F_CONTIGUOUS)):
 *                 raise ValueError(u"ndarray is not Fortran contiguous")
 */
  if (__pyx_t_1) {

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":239
 *             if ((flags & pybuf.PyBUF_F_CONTIGUOUS == pybuf.PyBUF_F_CONTIGUOUS)
 *                 and not PyArray_CHKFLAGS(self, NPY_F_CONTIGUOUS)):
 *                 raise ValueError(u"ndarray is not Fortran contiguous")             # <<<<<<<<<<<<<<
 * 
 *             info.buf = PyArray_DATA(self)
 */
    __pyx_t_3 = __Pyx_PyObject_Call(__pyx_builtin_ValueError, __pyx_tuple__5, NULL); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 239, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __Pyx_Raise(__pyx_t_3, 0, 0, 0);
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    __PYX_ERR(1, 239, __pyx_L1_error)

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":237
 *                 raise ValueError(u"ndarray is not C contiguous")
 * 
 *             if ((flags & pybuf.PyBUF_F_CONTIGUOUS == pybuf.PyBUF_F_CONTIGUOUS)             # <<<<<<<<<<<<<<
 *                 and not PyArray_CHKFLAGS(self, NPY_F_CONTIGUOUS)):
 *                 raise ValueError(u"ndarray is not Fortran contiguous")
 */
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":241
 *                 raise ValueError(u"ndarray is not Fortran contiguous")
 * 
 *             info.buf = PyArray_DATA(self)             # <<<<<<<<<<<<<<
 *             info.ndim = ndim
 *             if copy_shape:
 */
  __pyx_v_info->buf = PyArray_DATA(__pyx_v_self);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":242
 * 
 *             info.buf = PyArray_DATA(self)
 *             info.ndim = ndim             # <<<<<<<<<<<<<<
 *             if copy_shape:
 *                 # Allocate new buffer for strides and shape info.
 */
  __pyx_v_info->ndim = __pyx_v_ndim;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":243
 *             info.buf = PyArray_DATA(self)
 *             info.ndim = ndim
 *             if copy_shape:             # <<<<<<<<<<<<<<
 *                 # Allocate new buffer for strides and shape info.
 *                 # This is allocated as one block, strides first.
 */
  __pyx_t_1 = (__pyx_v_copy_shape != 0);
  if (__pyx_t_1) {

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":246
 *                 # Allocate new buffer for strides and shape info.
 *                 # This is allocated as one block, strides first.
 *                 info.strides = <Py_ssize_t*>PyObject_Malloc(sizeof(Py_ssize_t) * 2 * <size_t>ndim)             # <<<<<<<<<<<<<<
 *                 info.shape = info.strides + ndim
 *                 for i in range(ndim):
 */
    __pyx_v_info->strides = ((Py_ssize_t *)PyObject_Malloc((((sizeof(Py_ssize_t)) * 2) * ((size_t)__pyx_v_ndim))));

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":247
 *                 # This is allocated as one block, strides first.
 *                 info.strides = <Py_ssize_t*>PyObject_Malloc(sizeof(Py_ssize_t) * 2 * <size_t>ndim)
 *                 info.shape = info.strides + ndim             # <<<<<<<<<<<<<<
 *                 for i in range(ndim):
 *                     info.strides[i] = PyArray_STRIDES(self)[i]
 */
    __pyx_v_info->shape = (__pyx_v_info->strides + __pyx_v_ndim);

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":248
 *                 info.strides = <Py_ssize_t*>PyObject_Malloc(sizeof(Py_ssize_t) * 2 * <size_t>ndim)
 *                 info.shape = info.strides + ndim
 *                 for i in range(ndim):             # <<<<<<<<<<<<<<
 *                     info.strides[i] = PyArray_STRIDES(self)[i]
 *                     info.shape[i] = PyArray_DIMS(self)[i]
 */
    __pyx_t_4 = __pyx_v_ndim;
    for (__pyx_t_5 = 0; __pyx_t_5 < __pyx_t_4; __pyx_t_5+=1) {
      __pyx_v_i = __pyx_t_5;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":249
 *                 info.shape = info.strides + ndim
 *                 for i in range(ndim):
 *                     info.strides[i] = PyArray_STRIDES(self)[i]             # <<<<<<<<<<<<<<
 *                     info.shape[i] = PyArray_DIMS(self)[i]
 *             else:
 */
      (__pyx_v_info->strides[__pyx_v_i]) = (PyArray_STRIDES(__pyx_v_self)[__pyx_v_i]);

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":250
 *                 for i in range(ndim):
 *                     info.strides[i] = PyArray_STRIDES(self)[i]
 *                     info.shape[i] = PyArray_DIMS(self)[i]             # <<<<<<<<<<<<<<
 *             else:
 *                 info.strides = <Py_ssize_t*>PyArray_STRIDES(self)
 */
      (__pyx_v_info->shape[__pyx_v_i]) = (PyArray_DIMS(__pyx_v_self)[__pyx_v_i]);
    }

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":243
 *             info.buf = PyArray_DATA(self)
 *             info.ndim = ndim
 *             if copy_shape:             # <<<<<<<<<<<<<<
 *                 # Allocate new buffer for strides and shape info.
 *                 # This is allocated as one block, strides first.
 */
    goto __pyx_L11;
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":252
 *                     info.shape[i] = PyArray_DIMS(self)[i]
 *             else:
 *                 info.strides = <Py_ssize_t*>PyArray_STRIDES(self)             # <<<<<<<<<<<<<<
 *                 info.shape = <Py_ssize_t*>PyArray_DIMS(self)
 *             info.suboffsets = NULL
 */
  /*else*/ {
    __pyx_v_info->strides = ((Py_ssize_t *)PyArray_STRIDES(__pyx_v_self));

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":253
 *             else:
 *                 info.strides = <Py_ssize_t*>PyArray_STRIDES(self)
 *                 info.shape = <Py_ssize_t*>PyArray_DIMS(self)             # <<<<<<<<<<<<<<
 *             info.suboffsets = NULL
 *             info.itemsize = PyArray_ITEMSIZE(self)
 */
    __pyx_v_info->shape = ((Py_ssize_t *)PyArray_DIMS(__pyx_v_self));
  }
  __pyx_L11:;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":254
 *                 info.strides = <Py_ssize_t*>PyArray_STRIDES(self)
 *                 info.shape = <Py_ssize_t*>PyArray_DIMS(self)
 *             info.suboffsets = NULL             # <<<<<<<<<<<<<<
 *             info.itemsize = PyArray_ITEMSIZE(self)
 *             info.readonly = not PyArray_ISWRITEABLE(self)
 */
  __pyx_v_info->suboffsets = NULL;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":255
 *                 info.shape = <Py_ssize_t*>PyArray_DIMS(self)
 *             info.suboffsets = NULL
 *             info.itemsize = PyArray_ITEMSIZE(self)             # <<<<<<<<<<<<<<
 *             info.readonly = not PyArray_ISWRITEABLE(self)
 * 
 */
  __pyx_v_info->itemsize = PyArray_ITEMSIZE(__pyx_v_self);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":256
 *             info.suboffsets = NULL
 *             info.itemsize = PyArray_ITEMSIZE(self)
 *             info.readonly = not PyArray_ISWRITEABLE(self)             # <<<<<<<<<<<<<<
 * 
 *             cdef int t
 */
  __pyx_v_info->readonly = (!(PyArray_ISWRITEABLE(__pyx_v_self) != 0));

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":259
 * 
 *             cdef int t
 *             cdef char* f = NULL             # <<<<<<<<<<<<<<
 *             cdef dtype descr = self.descr
 *             cdef int offset
 */
  __pyx_v_f = NULL;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":260
 *             cdef int t
 *             cdef char* f = NULL
 *             cdef dtype descr = self.descr             # <<<<<<<<<<<<<<
 *             cdef int offset
 * 
 */
  __pyx_t_3 = ((PyObject *)__pyx_v_self->descr);
  __Pyx_INCREF(__pyx_t_3);
  __pyx_v_descr = ((PyArray_Descr *)__pyx_t_3);
  __pyx_t_3 = 0;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":263
 *             cdef int offset
 * 
 *             cdef bint hasfields = PyDataType_HASFIELDS(descr)             # <<<<<<<<<<<<<<
 * 
 *             if not hasfields and not copy_shape:
 */
  __pyx_v_hasfields = PyDataType_HASFIELDS(__pyx_v_descr);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":265
 *             cdef bint hasfields = PyDataType_HASFIELDS(descr)
 * 
 *             if not hasfields and not copy_shape:             # <<<<<<<<<<<<<<
 *                 # do not call releasebuffer
 *                 info.obj = None
 */
  __pyx_t_2 = ((!(__pyx_v_hasfields != 0)) != 0);
  if (__pyx_t_2) {
  } else {
    __pyx_t_1 = __pyx_t_2;
    goto __pyx_L15_bool_binop_done;
  }
  __pyx_t_2 = ((!(__pyx_v_copy_shape != 0)) != 0);
  __pyx_t_1 = __pyx_t_2;
  __pyx_L15_bool_binop_done:;
  if (__pyx_t_1) {

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":267
 *             if not hasfields and not copy_shape:
 *                 # do not call releasebuffer
 *                 info.obj = None             # <<<<<<<<<<<<<<
 *             else:
 *                 # need to call releasebuffer
 */
    __Pyx_INCREF(Py_None);
    __Pyx_GIVEREF(Py_None);
    __Pyx_GOTREF(__pyx_v_info->obj);
    __Pyx_DECREF(__pyx_v_info->obj);
    __pyx_v_info->obj = Py_None;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":265
 *             cdef bint hasfields = PyDataType_HASFIELDS(descr)
 * 
 *             if not hasfields and not copy_shape:             # <<<<<<<<<<<<<<
 *                 # do not call releasebuffer
 *                 info.obj = None
 */
    goto __pyx_L14;
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":270
 *             else:
 *                 # need to call releasebuffer
 *                 info.obj = self             # <<<<<<<<<<<<<<
 * 
 *             if not hasfields:
 */
  /*else*/ {
    __Pyx_INCREF(((PyObject *)__pyx_v_self));
    __Pyx_GIVEREF(((PyObject *)__pyx_v_self));
    __Pyx_GOTREF(__pyx_v_info->obj);
    __Pyx_DECREF(__pyx_v_info->obj);
    __pyx_v_info->obj = ((PyObject *)__pyx_v_self);
  }
  __pyx_L14:;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":272
 *                 info.obj = self
 * 
 *             if not hasfields:             # <<<<<<<<<<<<<<
 *                 t = descr.type_num
 *                 if ((descr.byteorder == c'>' and little_endian) or
 */
  __pyx_t_1 = ((!(__pyx_v_hasfields != 0)) != 0);
  if (__pyx_t_1) {

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":273
 * 
 *             if not hasfields:
 *                 t = descr.type_num             # <<<<<<<<<<<<<<
 *                 if ((descr.byteorder == c'>' and little_endian) or
 *                     (descr.byteorder == c'<' and not little_endian)):
 */
    __pyx_t_4 = __pyx_v_descr->type_num;
    __pyx_v_t = __pyx_t_4;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":274
 *             if not hasfields:
 *                 t = descr.type_num
 *                 if ((descr.byteorder == c'>' and little_endian) or             # <<<<<<<<<<<<<<
 *                     (descr.byteorder == c'<' and not little_endian)):
 *                     raise ValueError(u"Non-native byte order not supported")
 */
    __pyx_t_2 = ((__pyx_v_descr->byteorder == '>') != 0);
    if (!__pyx_t_2) {
      goto __pyx_L20_next_or;
    } else {
    }
    __pyx_t_2 = (__pyx_v_little_endian != 0);
    if (!__pyx_t_2) {
    } else {
      __pyx_t_1 = __pyx_t_2;
      goto __pyx_L19_bool_binop_done;
    }
    __pyx_L20_next_or:;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":275
 *                 t = descr.type_num
 *                 if ((descr.byteorder == c'>' and little_endian) or
 *                     (descr.byteorder == c'<' and not little_endian)):             # <<<<<<<<<<<<<<
 *                     raise ValueError(u"Non-native byte order not supported")
 *                 if   t == NPY_BYTE:        f = "b"
 */
    __pyx_t_2 = ((__pyx_v_descr->byteorder == '<') != 0);
    if (__pyx_t_2) {
    } else {
      __pyx_t_1 = __pyx_t_2;
      goto __pyx_L19_bool_binop_done;
    }
    __pyx_t_2 = ((!(__pyx_v_little_endian != 0)) != 0);
    __pyx_t_1 = __pyx_t_2;
    __pyx_L19_bool_binop_done:;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":274
 *             if not hasfields:
 *                 t = descr.type_num
 *                 if ((descr.byteorder == c'>' and little_endian) or             # <<<<<<<<<<<<<<
 *                     (descr.byteorder == c'<' and not little_endian)):
 *                     raise ValueError(u"Non-native byte order not supported")
 */
    if (__pyx_t_1) {

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":276
 *                 if ((descr.byteorder == c'>' and little_endian) or
 *                     (descr.byteorder == c'<' and not little_endian)):
 *                     raise ValueError(u"Non-native byte order not supported")             # <<<<<<<<<<<<<<
 *                 if   t == NPY_BYTE:        f = "b"
 *                 elif t == NPY_UBYTE:       f = "B"
 */
      __pyx_t_3 = __Pyx_PyObject_Call(__pyx_builtin_ValueError, __pyx_tuple__6, NULL); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 276, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __Pyx_Raise(__pyx_t_3, 0, 0, 0);
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __PYX_ERR(1, 276, __pyx_L1_error)

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":274
 *             if not hasfields:
 *                 t = descr.type_num
 *                 if ((descr.byteorder == c'>' and little_endian) or             # <<<<<<<<<<<<<<
 *                     (descr.byteorder == c'<' and not little_endian)):
 *                     raise ValueError(u"Non-native byte order not supported")
 */
    }

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":277
 *                     (descr.byteorder == c'<' and not little_endian)):
 *                     raise ValueError(u"Non-native byte order not supported")
 *                 if   t == NPY_BYTE:        f = "b"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_UBYTE:       f = "B"
 *                 elif t == NPY_SHORT:       f = "h"
 */
    switch (__pyx_v_t) {
      case NPY_BYTE:
      __pyx_v_f = ((char *)"b");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":278
 *                     raise ValueError(u"Non-native byte order not supported")
 *                 if   t == NPY_BYTE:        f = "b"
 *                 elif t == NPY_UBYTE:       f = "B"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_SHORT:       f = "h"
 *                 elif t == NPY_USHORT:      f = "H"
 */
      case NPY_UBYTE:
      __pyx_v_f = ((char *)"B");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":279
 *                 if   t == NPY_BYTE:        f = "b"
 *                 elif t == NPY_UBYTE:       f = "B"
 *                 elif t == NPY_SHORT:       f = "h"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_USHORT:      f = "H"
 *                 elif t == NPY_INT:         f = "i"
 */
      case NPY_SHORT:
      __pyx_v_f = ((char *)"h");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":280
 *                 elif t == NPY_UBYTE:       f = "B"
 *                 elif t == NPY_SHORT:       f = "h"
 *                 elif t == NPY_USHORT:      f = "H"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_INT:         f = "i"
 *                 elif t == NPY_UINT:        f = "I"
 */
      case NPY_USHORT:
      __pyx_v_f = ((char *)"H");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":281
 *                 elif t == NPY_SHORT:       f = "h"
 *                 elif t == NPY_USHORT:      f = "H"
 *                 elif t == NPY_INT:         f = "i"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_UINT:        f = "I"
 *                 elif t == NPY_LONG:        f = "l"
 */
      case NPY_INT:
      __pyx_v_f = ((char *)"i");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":282
 *                 elif t == NPY_USHORT:      f = "H"
 *                 elif t == NPY_INT:         f = "i"
 *                 elif t == NPY_UINT:        f = "I"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_LONG:        f = "l"
 *                 elif t == NPY_ULONG:       f = "L"
 */
      case NPY_UINT:
      __pyx_v_f = ((char *)"I");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":283
 *                 elif t == NPY_INT:         f = "i"
 *                 elif t == NPY_UINT:        f = "I"
 *                 elif t == NPY_LONG:        f = "l"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_ULONG:       f = "L"
 *                 elif t == NPY_LONGLONG:    f = "q"
 */
      case NPY_LONG:
      __pyx_v_f = ((char *)"l");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":284
 *                 elif t == NPY_UINT:        f = "I"
 *                 elif t == NPY_LONG:        f = "l"
 *                 elif t == NPY_ULONG:       f = "L"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_LONGLONG:    f = "q"
 *                 elif t == NPY_ULONGLONG:   f = "Q"
 */
      case NPY_ULONG:
      __pyx_v_f = ((char *)"L");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":285
 *                 elif t == NPY_LONG:        f = "l"
 *                 elif t == NPY_ULONG:       f = "L"
 *                 elif t == NPY_LONGLONG:    f = "q"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_ULONGLONG:   f = "Q"
 *                 elif t == NPY_FLOAT:       f = "f"
 */
      case NPY_LONGLONG:
      __pyx_v_f = ((char *)"q");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":286
 *                 elif t == NPY_ULONG:       f = "L"
 *                 elif t == NPY_LONGLONG:    f = "q"
 *                 elif t == NPY_ULONGLONG:   f = "Q"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_FLOAT:       f = "f"
 *                 elif t == NPY_DOUBLE:      f = "d"
 */
      case NPY_ULONGLONG:
      __pyx_v_f = ((char *)"Q");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":287
 *                 elif t == NPY_LONGLONG:    f = "q"
 *                 elif t == NPY_ULONGLONG:   f = "Q"
 *                 elif t == NPY_FLOAT:       f = "f"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_DOUBLE:      f = "d"
 *                 elif t == NPY_LONGDOUBLE:  f = "g"
 */
      case NPY_FLOAT:
      __pyx_v_f = ((char *)"f");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":288
 *                 elif t == NPY_ULONGLONG:   f = "Q"
 *                 elif t == NPY_FLOAT:       f = "f"
 *                 elif t == NPY_DOUBLE:      f = "d"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_LONGDOUBLE:  f = "g"
 *                 elif t == NPY_CFLOAT:      f = "Zf"
 */
      case NPY_DOUBLE:
      __pyx_v_f = ((char *)"d");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":289
 *                 elif t == NPY_FLOAT:       f = "f"
 *                 elif t == NPY_DOUBLE:      f = "d"
 *                 elif t == NPY_LONGDOUBLE:  f = "g"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_CFLOAT:      f = "Zf"
 *                 elif t == NPY_CDOUBLE:     f = "Zd"
 */
      case NPY_LONGDOUBLE:
      __pyx_v_f = ((char *)"g");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":290
 *                 elif t == NPY_DOUBLE:      f = "d"
 *                 elif t == NPY_LONGDOUBLE:  f = "g"
 *                 elif t == NPY_CFLOAT:      f = "Zf"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_CDOUBLE:     f = "Zd"
 *                 elif t == NPY_CLONGDOUBLE: f = "Zg"
 */
      case NPY_CFLOAT:
      __pyx_v_f = ((char *)"Zf");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":291
 *                 elif t == NPY_LONGDOUBLE:  f = "g"
 *                 elif t == NPY_CFLOAT:      f = "Zf"
 *                 elif t == NPY_CDOUBLE:     f = "Zd"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_CLONGDOUBLE: f = "Zg"
 *                 elif t == NPY_OBJECT:      f = "O"
 */
      case NPY_CDOUBLE:
      __pyx_v_f = ((char *)"Zd");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":292
 *                 elif t == NPY_CFLOAT:      f = "Zf"
 *                 elif t == NPY_CDOUBLE:     f = "Zd"
 *                 elif t == NPY_CLONGDOUBLE: f = "Zg"             # <<<<<<<<<<<<<<
 *                 elif t == NPY_OBJECT:      f = "O"
 *                 else:
 */
      case NPY_CLONGDOUBLE:
      __pyx_v_f = ((char *)"Zg");
      break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":293
 *                 elif t == NPY_CDOUBLE:     f = "Zd"
 *                 elif t == NPY_CLONGDOUBLE: f = "Zg"
 *                 elif t == NPY_OBJECT:      f = "O"             # <<<<<<<<<<<<<<
 *                 else:
 *                     raise ValueError(u"unknown dtype code in numpy.pxd (%d)" % t)
 */
      case NPY_OBJECT:
      __pyx_v_f = ((char *)"O");
      break;
      default:

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":295
 *                 elif t == NPY_OBJECT:      f = "O"
 *                 else:
 *                     raise ValueError(u"unknown dtype code in numpy.pxd (%d)" % t)             # <<<<<<<<<<<<<<
 *                 info.format = f
 *                 return
 */
      __pyx_t_3 = __Pyx_PyInt_From_int(__pyx_v_t); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 295, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_6 = PyUnicode_Format(__pyx_kp_u_unknown_dtype_code_in_numpy_pxd, __pyx_t_3); if (unlikely(!__pyx_t_6)) __PYX_ERR(1, 295, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_6);
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __pyx_t_3 = PyTuple_New(1); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 295, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __Pyx_GIVEREF(__pyx_t_6);
      PyTuple_SET_ITEM(__pyx_t_3, 0, __pyx_t_6);
      __pyx_t_6 = 0;
      __pyx_t_6 = __Pyx_PyObject_Call(__pyx_builtin_ValueError, __pyx_t_3, NULL); if (unlikely(!__pyx_t_6)) __PYX_ERR(1, 295, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_6);
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __Pyx_Raise(__pyx_t_6, 0, 0, 0);
      __Pyx_DECREF(__pyx_t_6); __pyx_t_6 = 0;
      __PYX_ERR(1, 295, __pyx_L1_error)
      break;
    }

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":296
 *                 else:
 *                     raise ValueError(u"unknown dtype code in numpy.pxd (%d)" % t)
 *                 info.format = f             # <<<<<<<<<<<<<<
 *                 return
 *             else:
 */
    __pyx_v_info->format = __pyx_v_f;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":297
 *                     raise ValueError(u"unknown dtype code in numpy.pxd (%d)" % t)
 *                 info.format = f
 *                 return             # <<<<<<<<<<<<<<
 *             else:
 *                 info.format = <char*>PyObject_Malloc(_buffer_format_string_len)
 */
    __pyx_r = 0;
    goto __pyx_L0;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":272
 *                 info.obj = self
 * 
 *             if not hasfields:             # <<<<<<<<<<<<<<
 *                 t = descr.type_num
 *                 if ((descr.byteorder == c'>' and little_endian) or
 */
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":299
 *                 return
 *             else:
 *                 info.format = <char*>PyObject_Malloc(_buffer_format_string_len)             # <<<<<<<<<<<<<<
 *                 info.format[0] = c'^' # Native data types, manual alignment
 *                 offset = 0
 */
  /*else*/ {
    __pyx_v_info->format = ((char *)PyObject_Malloc(0xFF));

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":300
 *             else:
 *                 info.format = <char*>PyObject_Malloc(_buffer_format_string_len)
 *                 info.format[0] = c'^' # Native data types, manual alignment             # <<<<<<<<<<<<<<
 *                 offset = 0
 *                 f = _util_dtypestring(descr, info.format + 1,
 */
    (__pyx_v_info->format[0]) = '^';

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":301
 *                 info.format = <char*>PyObject_Malloc(_buffer_format_string_len)
 *                 info.format[0] = c'^' # Native data types, manual alignment
 *                 offset = 0             # <<<<<<<<<<<<<<
 *                 f = _util_dtypestring(descr, info.format + 1,
 *                                       info.format + _buffer_format_string_len,
 */
    __pyx_v_offset = 0;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":302
 *                 info.format[0] = c'^' # Native data types, manual alignment
 *                 offset = 0
 *                 f = _util_dtypestring(descr, info.format + 1,             # <<<<<<<<<<<<<<
 *                                       info.format + _buffer_format_string_len,
 *                                       &offset)
 */
    __pyx_t_7 = __pyx_f_5numpy__util_dtypestring(__pyx_v_descr, (__pyx_v_info->format + 1), (__pyx_v_info->format + 0xFF), (&__pyx_v_offset)); if (unlikely(__pyx_t_7 == NULL)) __PYX_ERR(1, 302, __pyx_L1_error)
    __pyx_v_f = __pyx_t_7;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":305
 *                                       info.format + _buffer_format_string_len,
 *                                       &offset)
 *                 f[0] = c'\0' # Terminate format string             # <<<<<<<<<<<<<<
 * 
 *         def __releasebuffer__(ndarray self, Py_buffer* info):
 */
    (__pyx_v_f[0]) = '\x00';
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":214
 *         # experimental exception made for __getbuffer__ and __releasebuffer__
 *         # -- the details of this may change.
 *         def __getbuffer__(ndarray self, Py_buffer* info, int flags):             # <<<<<<<<<<<<<<
 *             # This implementation of getbuffer is geared towards Cython
 *             # requirements, and does not yet fullfill the PEP.
 */

  /* function exit code */
  __pyx_r = 0;
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_3);
  __Pyx_XDECREF(__pyx_t_6);
  __Pyx_AddTraceback("numpy.ndarray.__getbuffer__", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = -1;
  if (__pyx_v_info != NULL && __pyx_v_info->obj != NULL) {
    __Pyx_GOTREF(__pyx_v_info->obj);
    __Pyx_DECREF(__pyx_v_info->obj); __pyx_v_info->obj = NULL;
  }
  goto __pyx_L2;
  __pyx_L0:;
  if (__pyx_v_info != NULL && __pyx_v_info->obj == Py_None) {
    __Pyx_GOTREF(Py_None);
    __Pyx_DECREF(Py_None); __pyx_v_info->obj = NULL;
  }
  __pyx_L2:;
  __Pyx_XDECREF((PyObject *)__pyx_v_descr);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":307
 *                 f[0] = c'\0' # Terminate format string
 * 
 *         def __releasebuffer__(ndarray self, Py_buffer* info):             # <<<<<<<<<<<<<<
 *             if PyArray_HASFIELDS(self):
 *                 PyObject_Free(info.format)
 */

/* Python wrapper */
static CYTHON_UNUSED void __pyx_pw_5numpy_7ndarray_3__releasebuffer__(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info); /*proto*/
static CYTHON_UNUSED void __pyx_pw_5numpy_7ndarray_3__releasebuffer__(PyObject *__pyx_v_self, Py_buffer *__pyx_v_info) {
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("__releasebuffer__ (wrapper)", 0);
  __pyx_pf_5numpy_7ndarray_2__releasebuffer__(((PyArrayObject *)__pyx_v_self), ((Py_buffer *)__pyx_v_info));

  /* function exit code */
  __Pyx_RefNannyFinishContext();
}

static void __pyx_pf_5numpy_7ndarray_2__releasebuffer__(PyArrayObject *__pyx_v_self, Py_buffer *__pyx_v_info) {
  __Pyx_RefNannyDeclarations
  int __pyx_t_1;
  __Pyx_RefNannySetupContext("__releasebuffer__", 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":308
 * 
 *         def __releasebuffer__(ndarray self, Py_buffer* info):
 *             if PyArray_HASFIELDS(self):             # <<<<<<<<<<<<<<
 *                 PyObject_Free(info.format)
 *             if sizeof(npy_intp) != sizeof(Py_ssize_t):
 */
  __pyx_t_1 = (PyArray_HASFIELDS(__pyx_v_self) != 0);
  if (__pyx_t_1) {

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":309
 *         def __releasebuffer__(ndarray self, Py_buffer* info):
 *             if PyArray_HASFIELDS(self):
 *                 PyObject_Free(info.format)             # <<<<<<<<<<<<<<
 *             if sizeof(npy_intp) != sizeof(Py_ssize_t):
 *                 PyObject_Free(info.strides)
 */
    PyObject_Free(__pyx_v_info->format);

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":308
 * 
 *         def __releasebuffer__(ndarray self, Py_buffer* info):
 *             if PyArray_HASFIELDS(self):             # <<<<<<<<<<<<<<
 *                 PyObject_Free(info.format)
 *             if sizeof(npy_intp) != sizeof(Py_ssize_t):
 */
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":310
 *             if PyArray_HASFIELDS(self):
 *                 PyObject_Free(info.format)
 *             if sizeof(npy_intp) != sizeof(Py_ssize_t):             # <<<<<<<<<<<<<<
 *                 PyObject_Free(info.strides)
 *                 # info.shape was stored after info.strides in the same block
 */
  __pyx_t_1 = (((sizeof(npy_intp)) != (sizeof(Py_ssize_t))) != 0);
  if (__pyx_t_1) {

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":311
 *                 PyObject_Free(info.format)
 *             if sizeof(npy_intp) != sizeof(Py_ssize_t):
 *                 PyObject_Free(info.strides)             # <<<<<<<<<<<<<<
 *                 # info.shape was stored after info.strides in the same block
 * 
 */
    PyObject_Free(__pyx_v_info->strides);

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":310
 *             if PyArray_HASFIELDS(self):
 *                 PyObject_Free(info.format)
 *             if sizeof(npy_intp) != sizeof(Py_ssize_t):             # <<<<<<<<<<<<<<
 *                 PyObject_Free(info.strides)
 *                 # info.shape was stored after info.strides in the same block
 */
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":307
 *                 f[0] = c'\0' # Terminate format string
 * 
 *         def __releasebuffer__(ndarray self, Py_buffer* info):             # <<<<<<<<<<<<<<
 *             if PyArray_HASFIELDS(self):
 *                 PyObject_Free(info.format)
 */

  /* function exit code */
  __Pyx_RefNannyFinishContext();
}

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":788
 * ctypedef npy_cdouble     complex_t
 * 
 * cdef inline object PyArray_MultiIterNew1(a):             # <<<<<<<<<<<<<<
 *     return PyArray_MultiIterNew(1, <void*>a)
 * 
 */

static CYTHON_INLINE PyObject *__pyx_f_5numpy_PyArray_MultiIterNew1(PyObject *__pyx_v_a) {
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  __Pyx_RefNannySetupContext("PyArray_MultiIterNew1", 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":789
 * 
 * cdef inline object PyArray_MultiIterNew1(a):
 *     return PyArray_MultiIterNew(1, <void*>a)             # <<<<<<<<<<<<<<
 * 
 * cdef inline object PyArray_MultiIterNew2(a, b):
 */
  __Pyx_XDECREF(__pyx_r);
  __pyx_t_1 = PyArray_MultiIterNew(1, ((void *)__pyx_v_a)); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 789, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_r = __pyx_t_1;
  __pyx_t_1 = 0;
  goto __pyx_L0;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":788
 * ctypedef npy_cdouble     complex_t
 * 
 * cdef inline object PyArray_MultiIterNew1(a):             # <<<<<<<<<<<<<<
 *     return PyArray_MultiIterNew(1, <void*>a)
 * 
 */

  /* function exit code */
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_AddTraceback("numpy.PyArray_MultiIterNew1", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = 0;
  __pyx_L0:;
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":791
 *     return PyArray_MultiIterNew(1, <void*>a)
 * 
 * cdef inline object PyArray_MultiIterNew2(a, b):             # <<<<<<<<<<<<<<
 *     return PyArray_MultiIterNew(2, <void*>a, <void*>b)
 * 
 */

static CYTHON_INLINE PyObject *__pyx_f_5numpy_PyArray_MultiIterNew2(PyObject *__pyx_v_a, PyObject *__pyx_v_b) {
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  __Pyx_RefNannySetupContext("PyArray_MultiIterNew2", 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":792
 * 
 * cdef inline object PyArray_MultiIterNew2(a, b):
 *     return PyArray_MultiIterNew(2, <void*>a, <void*>b)             # <<<<<<<<<<<<<<
 * 
 * cdef inline object PyArray_MultiIterNew3(a, b, c):
 */
  __Pyx_XDECREF(__pyx_r);
  __pyx_t_1 = PyArray_MultiIterNew(2, ((void *)__pyx_v_a), ((void *)__pyx_v_b)); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 792, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_r = __pyx_t_1;
  __pyx_t_1 = 0;
  goto __pyx_L0;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":791
 *     return PyArray_MultiIterNew(1, <void*>a)
 * 
 * cdef inline object PyArray_MultiIterNew2(a, b):             # <<<<<<<<<<<<<<
 *     return PyArray_MultiIterNew(2, <void*>a, <void*>b)
 * 
 */

  /* function exit code */
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_AddTraceback("numpy.PyArray_MultiIterNew2", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = 0;
  __pyx_L0:;
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":794
 *     return PyArray_MultiIterNew(2, <void*>a, <void*>b)
 * 
 * cdef inline object PyArray_MultiIterNew3(a, b, c):             # <<<<<<<<<<<<<<
 *     return PyArray_MultiIterNew(3, <void*>a, <void*>b, <void*> c)
 * 
 */

static CYTHON_INLINE PyObject *__pyx_f_5numpy_PyArray_MultiIterNew3(PyObject *__pyx_v_a, PyObject *__pyx_v_b, PyObject *__pyx_v_c) {
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  __Pyx_RefNannySetupContext("PyArray_MultiIterNew3", 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":795
 * 
 * cdef inline object PyArray_MultiIterNew3(a, b, c):
 *     return PyArray_MultiIterNew(3, <void*>a, <void*>b, <void*> c)             # <<<<<<<<<<<<<<
 * 
 * cdef inline object PyArray_MultiIterNew4(a, b, c, d):
 */
  __Pyx_XDECREF(__pyx_r);
  __pyx_t_1 = PyArray_MultiIterNew(3, ((void *)__pyx_v_a), ((void *)__pyx_v_b), ((void *)__pyx_v_c)); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 795, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_r = __pyx_t_1;
  __pyx_t_1 = 0;
  goto __pyx_L0;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":794
 *     return PyArray_MultiIterNew(2, <void*>a, <void*>b)
 * 
 * cdef inline object PyArray_MultiIterNew3(a, b, c):             # <<<<<<<<<<<<<<
 *     return PyArray_MultiIterNew(3, <void*>a, <void*>b, <void*> c)
 * 
 */

  /* function exit code */
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_AddTraceback("numpy.PyArray_MultiIterNew3", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = 0;
  __pyx_L0:;
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":797
 *     return PyArray_MultiIterNew(3, <void*>a, <void*>b, <void*> c)
 * 
 * cdef inline object PyArray_MultiIterNew4(a, b, c, d):             # <<<<<<<<<<<<<<
 *     return PyArray_MultiIterNew(4, <void*>a, <void*>b, <void*>c, <void*> d)
 * 
 */

static CYTHON_INLINE PyObject *__pyx_f_5numpy_PyArray_MultiIterNew4(PyObject *__pyx_v_a, PyObject *__pyx_v_b, PyObject *__pyx_v_c, PyObject *__pyx_v_d) {
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  __Pyx_RefNannySetupContext("PyArray_MultiIterNew4", 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":798
 * 
 * cdef inline object PyArray_MultiIterNew4(a, b, c, d):
 *     return PyArray_MultiIterNew(4, <void*>a, <void*>b, <void*>c, <void*> d)             # <<<<<<<<<<<<<<
 * 
 * cdef inline object PyArray_MultiIterNew5(a, b, c, d, e):
 */
  __Pyx_XDECREF(__pyx_r);
  __pyx_t_1 = PyArray_MultiIterNew(4, ((void *)__pyx_v_a), ((void *)__pyx_v_b), ((void *)__pyx_v_c), ((void *)__pyx_v_d)); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 798, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_r = __pyx_t_1;
  __pyx_t_1 = 0;
  goto __pyx_L0;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":797
 *     return PyArray_MultiIterNew(3, <void*>a, <void*>b, <void*> c)
 * 
 * cdef inline object PyArray_MultiIterNew4(a, b, c, d):             # <<<<<<<<<<<<<<
 *     return PyArray_MultiIterNew(4, <void*>a, <void*>b, <void*>c, <void*> d)
 * 
 */

  /* function exit code */
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_AddTraceback("numpy.PyArray_MultiIterNew4", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = 0;
  __pyx_L0:;
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":800
 *     return PyArray_MultiIterNew(4, <void*>a, <void*>b, <void*>c, <void*> d)
 * 
 * cdef inline object PyArray_MultiIterNew5(a, b, c, d, e):             # <<<<<<<<<<<<<<
 *     return PyArray_MultiIterNew(5, <void*>a, <void*>b, <void*>c, <void*> d, <void*> e)
 * 
 */

static CYTHON_INLINE PyObject *__pyx_f_5numpy_PyArray_MultiIterNew5(PyObject *__pyx_v_a, PyObject *__pyx_v_b, PyObject *__pyx_v_c, PyObject *__pyx_v_d, PyObject *__pyx_v_e) {
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  __Pyx_RefNannySetupContext("PyArray_MultiIterNew5", 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":801
 * 
 * cdef inline object PyArray_MultiIterNew5(a, b, c, d, e):
 *     return PyArray_MultiIterNew(5, <void*>a, <void*>b, <void*>c, <void*> d, <void*> e)             # <<<<<<<<<<<<<<
 * 
 * cdef inline tuple PyDataType_SHAPE(dtype d):
 */
  __Pyx_XDECREF(__pyx_r);
  __pyx_t_1 = PyArray_MultiIterNew(5, ((void *)__pyx_v_a), ((void *)__pyx_v_b), ((void *)__pyx_v_c), ((void *)__pyx_v_d), ((void *)__pyx_v_e)); if (unlikely(!__pyx_t_1)) __PYX_ERR(1, 801, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_r = __pyx_t_1;
  __pyx_t_1 = 0;
  goto __pyx_L0;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":800
 *     return PyArray_MultiIterNew(4, <void*>a, <void*>b, <void*>c, <void*> d)
 * 
 * cdef inline object PyArray_MultiIterNew5(a, b, c, d, e):             # <<<<<<<<<<<<<<
 *     return PyArray_MultiIterNew(5, <void*>a, <void*>b, <void*>c, <void*> d, <void*> e)
 * 
 */

  /* function exit code */
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_AddTraceback("numpy.PyArray_MultiIterNew5", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = 0;
  __pyx_L0:;
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":803
 *     return PyArray_MultiIterNew(5, <void*>a, <void*>b, <void*>c, <void*> d, <void*> e)
 * 
 * cdef inline tuple PyDataType_SHAPE(dtype d):             # <<<<<<<<<<<<<<
 *     if PyDataType_HASSUBARRAY(d):
 *         return <tuple>d.subarray.shape
 */

static CYTHON_INLINE PyObject *__pyx_f_5numpy_PyDataType_SHAPE(PyArray_Descr *__pyx_v_d) {
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  int __pyx_t_1;
  __Pyx_RefNannySetupContext("PyDataType_SHAPE", 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":804
 * 
 * cdef inline tuple PyDataType_SHAPE(dtype d):
 *     if PyDataType_HASSUBARRAY(d):             # <<<<<<<<<<<<<<
 *         return <tuple>d.subarray.shape
 *     else:
 */
  __pyx_t_1 = (PyDataType_HASSUBARRAY(__pyx_v_d) != 0);
  if (__pyx_t_1) {

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":805
 * cdef inline tuple PyDataType_SHAPE(dtype d):
 *     if PyDataType_HASSUBARRAY(d):
 *         return <tuple>d.subarray.shape             # <<<<<<<<<<<<<<
 *     else:
 *         return ()
 */
    __Pyx_XDECREF(__pyx_r);
    __Pyx_INCREF(((PyObject*)__pyx_v_d->subarray->shape));
    __pyx_r = ((PyObject*)__pyx_v_d->subarray->shape);
    goto __pyx_L0;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":804
 * 
 * cdef inline tuple PyDataType_SHAPE(dtype d):
 *     if PyDataType_HASSUBARRAY(d):             # <<<<<<<<<<<<<<
 *         return <tuple>d.subarray.shape
 *     else:
 */
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":807
 *         return <tuple>d.subarray.shape
 *     else:
 *         return ()             # <<<<<<<<<<<<<<
 * 
 * cdef inline char* _util_dtypestring(dtype descr, char* f, char* end, int* offset) except NULL:
 */
  /*else*/ {
    __Pyx_XDECREF(__pyx_r);
    __Pyx_INCREF(__pyx_empty_tuple);
    __pyx_r = __pyx_empty_tuple;
    goto __pyx_L0;
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":803
 *     return PyArray_MultiIterNew(5, <void*>a, <void*>b, <void*>c, <void*> d, <void*> e)
 * 
 * cdef inline tuple PyDataType_SHAPE(dtype d):             # <<<<<<<<<<<<<<
 *     if PyDataType_HASSUBARRAY(d):
 *         return <tuple>d.subarray.shape
 */

  /* function exit code */
  __pyx_L0:;
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":809
 *         return ()
 * 
 * cdef inline char* _util_dtypestring(dtype descr, char* f, char* end, int* offset) except NULL:             # <<<<<<<<<<<<<<
 *     # Recursive utility function used in __getbuffer__ to get format
 *     # string. The new location in the format string is returned.
 */

static CYTHON_INLINE char *__pyx_f_5numpy__util_dtypestring(PyArray_Descr *__pyx_v_descr, char *__pyx_v_f, char *__pyx_v_end, int *__pyx_v_offset) {
  PyArray_Descr *__pyx_v_child = 0;
  int __pyx_v_endian_detector;
  int __pyx_v_little_endian;
  PyObject *__pyx_v_fields = 0;
  PyObject *__pyx_v_childname = NULL;
  PyObject *__pyx_v_new_offset = NULL;
  PyObject *__pyx_v_t = NULL;
  char *__pyx_r;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  Py_ssize_t __pyx_t_2;
  PyObject *__pyx_t_3 = NULL;
  PyObject *__pyx_t_4 = NULL;
  int __pyx_t_5;
  int __pyx_t_6;
  int __pyx_t_7;
  long __pyx_t_8;
  char *__pyx_t_9;
  __Pyx_RefNannySetupContext("_util_dtypestring", 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":814
 * 
 *     cdef dtype child
 *     cdef int endian_detector = 1             # <<<<<<<<<<<<<<
 *     cdef bint little_endian = ((<char*>&endian_detector)[0] != 0)
 *     cdef tuple fields
 */
  __pyx_v_endian_detector = 1;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":815
 *     cdef dtype child
 *     cdef int endian_detector = 1
 *     cdef bint little_endian = ((<char*>&endian_detector)[0] != 0)             # <<<<<<<<<<<<<<
 *     cdef tuple fields
 * 
 */
  __pyx_v_little_endian = ((((char *)(&__pyx_v_endian_detector))[0]) != 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":818
 *     cdef tuple fields
 * 
 *     for childname in descr.names:             # <<<<<<<<<<<<<<
 *         fields = descr.fields[childname]
 *         child, new_offset = fields
 */
  if (unlikely(__pyx_v_descr->names == Py_None)) {
    PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable");
    __PYX_ERR(1, 818, __pyx_L1_error)
  }
  __pyx_t_1 = __pyx_v_descr->names; __Pyx_INCREF(__pyx_t_1); __pyx_t_2 = 0;
  for (;;) {
    if (__pyx_t_2 >= PyTuple_GET_SIZE(__pyx_t_1)) break;
    #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
    __pyx_t_3 = PyTuple_GET_ITEM(__pyx_t_1, __pyx_t_2); __Pyx_INCREF(__pyx_t_3); __pyx_t_2++; if (unlikely(0 < 0)) __PYX_ERR(1, 818, __pyx_L1_error)
    #else
    __pyx_t_3 = PySequence_ITEM(__pyx_t_1, __pyx_t_2); __pyx_t_2++; if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 818, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    #endif
    __Pyx_XDECREF_SET(__pyx_v_childname, __pyx_t_3);
    __pyx_t_3 = 0;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":819
 * 
 *     for childname in descr.names:
 *         fields = descr.fields[childname]             # <<<<<<<<<<<<<<
 *         child, new_offset = fields
 * 
 */
    if (unlikely(__pyx_v_descr->fields == Py_None)) {
      PyErr_SetString(PyExc_TypeError, "'NoneType' object is not subscriptable");
      __PYX_ERR(1, 819, __pyx_L1_error)
    }
    __pyx_t_3 = __Pyx_PyDict_GetItem(__pyx_v_descr->fields, __pyx_v_childname); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 819, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    if (!(likely(PyTuple_CheckExact(__pyx_t_3))||((__pyx_t_3) == Py_None)||(PyErr_Format(PyExc_TypeError, "Expected %.16s, got %.200s", "tuple", Py_TYPE(__pyx_t_3)->tp_name), 0))) __PYX_ERR(1, 819, __pyx_L1_error)
    __Pyx_XDECREF_SET(__pyx_v_fields, ((PyObject*)__pyx_t_3));
    __pyx_t_3 = 0;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":820
 *     for childname in descr.names:
 *         fields = descr.fields[childname]
 *         child, new_offset = fields             # <<<<<<<<<<<<<<
 * 
 *         if (end - f) - <int>(new_offset - offset[0]) < 15:
 */
    if (likely(__pyx_v_fields != Py_None)) {
      PyObject* sequence = __pyx_v_fields;
      #if !CYTHON_COMPILING_IN_PYPY
      Py_ssize_t size = Py_SIZE(sequence);
      #else
      Py_ssize_t size = PySequence_Size(sequence);
      #endif
      if (unlikely(size != 2)) {
        if (size > 2) __Pyx_RaiseTooManyValuesError(2);
        else if (size >= 0) __Pyx_RaiseNeedMoreValuesError(size);
        __PYX_ERR(1, 820, __pyx_L1_error)
      }
      #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
      __pyx_t_3 = PyTuple_GET_ITEM(sequence, 0); 
      __pyx_t_4 = PyTuple_GET_ITEM(sequence, 1); 
      __Pyx_INCREF(__pyx_t_3);
      __Pyx_INCREF(__pyx_t_4);
      #else
      __pyx_t_3 = PySequence_ITEM(sequence, 0); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 820, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_4 = PySequence_ITEM(sequence, 1); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 820, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      #endif
    } else {
      __Pyx_RaiseNoneNotIterableError(); __PYX_ERR(1, 820, __pyx_L1_error)
    }
    if (!(likely(((__pyx_t_3) == Py_None) || likely(__Pyx_TypeTest(__pyx_t_3, __pyx_ptype_5numpy_dtype))))) __PYX_ERR(1, 820, __pyx_L1_error)
    __Pyx_XDECREF_SET(__pyx_v_child, ((PyArray_Descr *)__pyx_t_3));
    __pyx_t_3 = 0;
    __Pyx_XDECREF_SET(__pyx_v_new_offset, __pyx_t_4);
    __pyx_t_4 = 0;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":822
 *         child, new_offset = fields
 * 
 *         if (end - f) - <int>(new_offset - offset[0]) < 15:             # <<<<<<<<<<<<<<
 *             raise RuntimeError(u"Format string allocated too short, see comment in numpy.pxd")
 * 
 */
    __pyx_t_4 = __Pyx_PyInt_From_int((__pyx_v_offset[0])); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 822, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_4);
    __pyx_t_3 = PyNumber_Subtract(__pyx_v_new_offset, __pyx_t_4); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 822, __pyx_L1_error)
    __Pyx_GOTREF(__pyx_t_3);
    __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
    __pyx_t_5 = __Pyx_PyInt_As_int(__pyx_t_3); if (unlikely((__pyx_t_5 == (int)-1) && PyErr_Occurred())) __PYX_ERR(1, 822, __pyx_L1_error)
    __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
    __pyx_t_6 = ((((__pyx_v_end - __pyx_v_f) - ((int)__pyx_t_5)) < 15) != 0);
    if (__pyx_t_6) {

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":823
 * 
 *         if (end - f) - <int>(new_offset - offset[0]) < 15:
 *             raise RuntimeError(u"Format string allocated too short, see comment in numpy.pxd")             # <<<<<<<<<<<<<<
 * 
 *         if ((child.byteorder == c'>' and little_endian) or
 */
      __pyx_t_3 = __Pyx_PyObject_Call(__pyx_builtin_RuntimeError, __pyx_tuple__7, NULL); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 823, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __Pyx_Raise(__pyx_t_3, 0, 0, 0);
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __PYX_ERR(1, 823, __pyx_L1_error)

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":822
 *         child, new_offset = fields
 * 
 *         if (end - f) - <int>(new_offset - offset[0]) < 15:             # <<<<<<<<<<<<<<
 *             raise RuntimeError(u"Format string allocated too short, see comment in numpy.pxd")
 * 
 */
    }

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":825
 *             raise RuntimeError(u"Format string allocated too short, see comment in numpy.pxd")
 * 
 *         if ((child.byteorder == c'>' and little_endian) or             # <<<<<<<<<<<<<<
 *             (child.byteorder == c'<' and not little_endian)):
 *             raise ValueError(u"Non-native byte order not supported")
 */
    __pyx_t_7 = ((__pyx_v_child->byteorder == '>') != 0);
    if (!__pyx_t_7) {
      goto __pyx_L8_next_or;
    } else {
    }
    __pyx_t_7 = (__pyx_v_little_endian != 0);
    if (!__pyx_t_7) {
    } else {
      __pyx_t_6 = __pyx_t_7;
      goto __pyx_L7_bool_binop_done;
    }
    __pyx_L8_next_or:;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":826
 * 
 *         if ((child.byteorder == c'>' and little_endian) or
 *             (child.byteorder == c'<' and not little_endian)):             # <<<<<<<<<<<<<<
 *             raise ValueError(u"Non-native byte order not supported")
 *             # One could encode it in the format string and have Cython
 */
    __pyx_t_7 = ((__pyx_v_child->byteorder == '<') != 0);
    if (__pyx_t_7) {
    } else {
      __pyx_t_6 = __pyx_t_7;
      goto __pyx_L7_bool_binop_done;
    }
    __pyx_t_7 = ((!(__pyx_v_little_endian != 0)) != 0);
    __pyx_t_6 = __pyx_t_7;
    __pyx_L7_bool_binop_done:;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":825
 *             raise RuntimeError(u"Format string allocated too short, see comment in numpy.pxd")
 * 
 *         if ((child.byteorder == c'>' and little_endian) or             # <<<<<<<<<<<<<<
 *             (child.byteorder == c'<' and not little_endian)):
 *             raise ValueError(u"Non-native byte order not supported")
 */
    if (__pyx_t_6) {

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":827
 *         if ((child.byteorder == c'>' and little_endian) or
 *             (child.byteorder == c'<' and not little_endian)):
 *             raise ValueError(u"Non-native byte order not supported")             # <<<<<<<<<<<<<<
 *             # One could encode it in the format string and have Cython
 *             # complain instead, BUT: < and > in format strings also imply
 */
      __pyx_t_3 = __Pyx_PyObject_Call(__pyx_builtin_ValueError, __pyx_tuple__8, NULL); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 827, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __Pyx_Raise(__pyx_t_3, 0, 0, 0);
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __PYX_ERR(1, 827, __pyx_L1_error)

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":825
 *             raise RuntimeError(u"Format string allocated too short, see comment in numpy.pxd")
 * 
 *         if ((child.byteorder == c'>' and little_endian) or             # <<<<<<<<<<<<<<
 *             (child.byteorder == c'<' and not little_endian)):
 *             raise ValueError(u"Non-native byte order not supported")
 */
    }

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":837
 * 
 *         # Output padding bytes
 *         while offset[0] < new_offset:             # <<<<<<<<<<<<<<
 *             f[0] = 120 # "x"; pad byte
 *             f += 1
 */
    while (1) {
      __pyx_t_3 = __Pyx_PyInt_From_int((__pyx_v_offset[0])); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 837, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_4 = PyObject_RichCompare(__pyx_t_3, __pyx_v_new_offset, Py_LT); __Pyx_XGOTREF(__pyx_t_4); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 837, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_4); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 837, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      if (!__pyx_t_6) break;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":838
 *         # Output padding bytes
 *         while offset[0] < new_offset:
 *             f[0] = 120 # "x"; pad byte             # <<<<<<<<<<<<<<
 *             f += 1
 *             offset[0] += 1
 */
      (__pyx_v_f[0]) = 0x78;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":839
 *         while offset[0] < new_offset:
 *             f[0] = 120 # "x"; pad byte
 *             f += 1             # <<<<<<<<<<<<<<
 *             offset[0] += 1
 * 
 */
      __pyx_v_f = (__pyx_v_f + 1);

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":840
 *             f[0] = 120 # "x"; pad byte
 *             f += 1
 *             offset[0] += 1             # <<<<<<<<<<<<<<
 * 
 *         offset[0] += child.itemsize
 */
      __pyx_t_8 = 0;
      (__pyx_v_offset[__pyx_t_8]) = ((__pyx_v_offset[__pyx_t_8]) + 1);
    }

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":842
 *             offset[0] += 1
 * 
 *         offset[0] += child.itemsize             # <<<<<<<<<<<<<<
 * 
 *         if not PyDataType_HASFIELDS(child):
 */
    __pyx_t_8 = 0;
    (__pyx_v_offset[__pyx_t_8]) = ((__pyx_v_offset[__pyx_t_8]) + __pyx_v_child->elsize);

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":844
 *         offset[0] += child.itemsize
 * 
 *         if not PyDataType_HASFIELDS(child):             # <<<<<<<<<<<<<<
 *             t = child.type_num
 *             if end - f < 5:
 */
    __pyx_t_6 = ((!(PyDataType_HASFIELDS(__pyx_v_child) != 0)) != 0);
    if (__pyx_t_6) {

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":845
 * 
 *         if not PyDataType_HASFIELDS(child):
 *             t = child.type_num             # <<<<<<<<<<<<<<
 *             if end - f < 5:
 *                 raise RuntimeError(u"Format string allocated too short.")
 */
      __pyx_t_4 = __Pyx_PyInt_From_int(__pyx_v_child->type_num); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 845, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __Pyx_XDECREF_SET(__pyx_v_t, __pyx_t_4);
      __pyx_t_4 = 0;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":846
 *         if not PyDataType_HASFIELDS(child):
 *             t = child.type_num
 *             if end - f < 5:             # <<<<<<<<<<<<<<
 *                 raise RuntimeError(u"Format string allocated too short.")
 * 
 */
      __pyx_t_6 = (((__pyx_v_end - __pyx_v_f) < 5) != 0);
      if (__pyx_t_6) {

        /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":847
 *             t = child.type_num
 *             if end - f < 5:
 *                 raise RuntimeError(u"Format string allocated too short.")             # <<<<<<<<<<<<<<
 * 
 *             # Until ticket #99 is fixed, use integers to avoid warnings
 */
        __pyx_t_4 = __Pyx_PyObject_Call(__pyx_builtin_RuntimeError, __pyx_tuple__9, NULL); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 847, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_4);
        __Pyx_Raise(__pyx_t_4, 0, 0, 0);
        __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
        __PYX_ERR(1, 847, __pyx_L1_error)

        /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":846
 *         if not PyDataType_HASFIELDS(child):
 *             t = child.type_num
 *             if end - f < 5:             # <<<<<<<<<<<<<<
 *                 raise RuntimeError(u"Format string allocated too short.")
 * 
 */
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":850
 * 
 *             # Until ticket #99 is fixed, use integers to avoid warnings
 *             if   t == NPY_BYTE:        f[0] =  98 #"b"             # <<<<<<<<<<<<<<
 *             elif t == NPY_UBYTE:       f[0] =  66 #"B"
 *             elif t == NPY_SHORT:       f[0] = 104 #"h"
 */
      __pyx_t_4 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_BYTE); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 850, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_3 = PyObject_RichCompare(__pyx_v_t, __pyx_t_4, Py_EQ); __Pyx_XGOTREF(__pyx_t_3); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 850, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_3); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 850, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 98;
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":851
 *             # Until ticket #99 is fixed, use integers to avoid warnings
 *             if   t == NPY_BYTE:        f[0] =  98 #"b"
 *             elif t == NPY_UBYTE:       f[0] =  66 #"B"             # <<<<<<<<<<<<<<
 *             elif t == NPY_SHORT:       f[0] = 104 #"h"
 *             elif t == NPY_USHORT:      f[0] =  72 #"H"
 */
      __pyx_t_3 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_UBYTE); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 851, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_4 = PyObject_RichCompare(__pyx_v_t, __pyx_t_3, Py_EQ); __Pyx_XGOTREF(__pyx_t_4); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 851, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_4); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 851, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 66;
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":852
 *             if   t == NPY_BYTE:        f[0] =  98 #"b"
 *             elif t == NPY_UBYTE:       f[0] =  66 #"B"
 *             elif t == NPY_SHORT:       f[0] = 104 #"h"             # <<<<<<<<<<<<<<
 *             elif t == NPY_USHORT:      f[0] =  72 #"H"
 *             elif t == NPY_INT:         f[0] = 105 #"i"
 */
      __pyx_t_4 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_SHORT); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 852, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_3 = PyObject_RichCompare(__pyx_v_t, __pyx_t_4, Py_EQ); __Pyx_XGOTREF(__pyx_t_3); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 852, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_3); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 852, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 0x68;
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":853
 *             elif t == NPY_UBYTE:       f[0] =  66 #"B"
 *             elif t == NPY_SHORT:       f[0] = 104 #"h"
 *             elif t == NPY_USHORT:      f[0] =  72 #"H"             # <<<<<<<<<<<<<<
 *             elif t == NPY_INT:         f[0] = 105 #"i"
 *             elif t == NPY_UINT:        f[0] =  73 #"I"
 */
      __pyx_t_3 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_USHORT); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 853, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_4 = PyObject_RichCompare(__pyx_v_t, __pyx_t_3, Py_EQ); __Pyx_XGOTREF(__pyx_t_4); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 853, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_4); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 853, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 72;
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":854
 *             elif t == NPY_SHORT:       f[0] = 104 #"h"
 *             elif t == NPY_USHORT:      f[0] =  72 #"H"
 *             elif t == NPY_INT:         f[0] = 105 #"i"             # <<<<<<<<<<<<<<
 *             elif t == NPY_UINT:        f[0] =  73 #"I"
 *             elif t == NPY_LONG:        f[0] = 108 #"l"
 */
      __pyx_t_4 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_INT); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 854, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_3 = PyObject_RichCompare(__pyx_v_t, __pyx_t_4, Py_EQ); __Pyx_XGOTREF(__pyx_t_3); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 854, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_3); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 854, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 0x69;
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":855
 *             elif t == NPY_USHORT:      f[0] =  72 #"H"
 *             elif t == NPY_INT:         f[0] = 105 #"i"
 *             elif t == NPY_UINT:        f[0] =  73 #"I"             # <<<<<<<<<<<<<<
 *             elif t == NPY_LONG:        f[0] = 108 #"l"
 *             elif t == NPY_ULONG:       f[0] = 76  #"L"
 */
      __pyx_t_3 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_UINT); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 855, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_4 = PyObject_RichCompare(__pyx_v_t, __pyx_t_3, Py_EQ); __Pyx_XGOTREF(__pyx_t_4); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 855, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_4); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 855, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 73;
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":856
 *             elif t == NPY_INT:         f[0] = 105 #"i"
 *             elif t == NPY_UINT:        f[0] =  73 #"I"
 *             elif t == NPY_LONG:        f[0] = 108 #"l"             # <<<<<<<<<<<<<<
 *             elif t == NPY_ULONG:       f[0] = 76  #"L"
 *             elif t == NPY_LONGLONG:    f[0] = 113 #"q"
 */
      __pyx_t_4 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_LONG); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 856, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_3 = PyObject_RichCompare(__pyx_v_t, __pyx_t_4, Py_EQ); __Pyx_XGOTREF(__pyx_t_3); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 856, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_3); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 856, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 0x6C;
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":857
 *             elif t == NPY_UINT:        f[0] =  73 #"I"
 *             elif t == NPY_LONG:        f[0] = 108 #"l"
 *             elif t == NPY_ULONG:       f[0] = 76  #"L"             # <<<<<<<<<<<<<<
 *             elif t == NPY_LONGLONG:    f[0] = 113 #"q"
 *             elif t == NPY_ULONGLONG:   f[0] = 81  #"Q"
 */
      __pyx_t_3 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_ULONG); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 857, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_4 = PyObject_RichCompare(__pyx_v_t, __pyx_t_3, Py_EQ); __Pyx_XGOTREF(__pyx_t_4); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 857, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_4); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 857, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 76;
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":858
 *             elif t == NPY_LONG:        f[0] = 108 #"l"
 *             elif t == NPY_ULONG:       f[0] = 76  #"L"
 *             elif t == NPY_LONGLONG:    f[0] = 113 #"q"             # <<<<<<<<<<<<<<
 *             elif t == NPY_ULONGLONG:   f[0] = 81  #"Q"
 *             elif t == NPY_FLOAT:       f[0] = 102 #"f"
 */
      __pyx_t_4 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_LONGLONG); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 858, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_3 = PyObject_RichCompare(__pyx_v_t, __pyx_t_4, Py_EQ); __Pyx_XGOTREF(__pyx_t_3); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 858, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_3); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 858, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 0x71;
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":859
 *             elif t == NPY_ULONG:       f[0] = 76  #"L"
 *             elif t == NPY_LONGLONG:    f[0] = 113 #"q"
 *             elif t == NPY_ULONGLONG:   f[0] = 81  #"Q"             # <<<<<<<<<<<<<<
 *             elif t == NPY_FLOAT:       f[0] = 102 #"f"
 *             elif t == NPY_DOUBLE:      f[0] = 100 #"d"
 */
      __pyx_t_3 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_ULONGLONG); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 859, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_4 = PyObject_RichCompare(__pyx_v_t, __pyx_t_3, Py_EQ); __Pyx_XGOTREF(__pyx_t_4); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 859, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_4); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 859, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 81;
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":860
 *             elif t == NPY_LONGLONG:    f[0] = 113 #"q"
 *             elif t == NPY_ULONGLONG:   f[0] = 81  #"Q"
 *             elif t == NPY_FLOAT:       f[0] = 102 #"f"             # <<<<<<<<<<<<<<
 *             elif t == NPY_DOUBLE:      f[0] = 100 #"d"
 *             elif t == NPY_LONGDOUBLE:  f[0] = 103 #"g"
 */
      __pyx_t_4 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_FLOAT); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 860, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_3 = PyObject_RichCompare(__pyx_v_t, __pyx_t_4, Py_EQ); __Pyx_XGOTREF(__pyx_t_3); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 860, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_3); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 860, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 0x66;
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":861
 *             elif t == NPY_ULONGLONG:   f[0] = 81  #"Q"
 *             elif t == NPY_FLOAT:       f[0] = 102 #"f"
 *             elif t == NPY_DOUBLE:      f[0] = 100 #"d"             # <<<<<<<<<<<<<<
 *             elif t == NPY_LONGDOUBLE:  f[0] = 103 #"g"
 *             elif t == NPY_CFLOAT:      f[0] = 90; f[1] = 102; f += 1 # Zf
 */
      __pyx_t_3 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_DOUBLE); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 861, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_4 = PyObject_RichCompare(__pyx_v_t, __pyx_t_3, Py_EQ); __Pyx_XGOTREF(__pyx_t_4); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 861, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_4); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 861, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 0x64;
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":862
 *             elif t == NPY_FLOAT:       f[0] = 102 #"f"
 *             elif t == NPY_DOUBLE:      f[0] = 100 #"d"
 *             elif t == NPY_LONGDOUBLE:  f[0] = 103 #"g"             # <<<<<<<<<<<<<<
 *             elif t == NPY_CFLOAT:      f[0] = 90; f[1] = 102; f += 1 # Zf
 *             elif t == NPY_CDOUBLE:     f[0] = 90; f[1] = 100; f += 1 # Zd
 */
      __pyx_t_4 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_LONGDOUBLE); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 862, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_3 = PyObject_RichCompare(__pyx_v_t, __pyx_t_4, Py_EQ); __Pyx_XGOTREF(__pyx_t_3); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 862, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_3); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 862, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 0x67;
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":863
 *             elif t == NPY_DOUBLE:      f[0] = 100 #"d"
 *             elif t == NPY_LONGDOUBLE:  f[0] = 103 #"g"
 *             elif t == NPY_CFLOAT:      f[0] = 90; f[1] = 102; f += 1 # Zf             # <<<<<<<<<<<<<<
 *             elif t == NPY_CDOUBLE:     f[0] = 90; f[1] = 100; f += 1 # Zd
 *             elif t == NPY_CLONGDOUBLE: f[0] = 90; f[1] = 103; f += 1 # Zg
 */
      __pyx_t_3 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_CFLOAT); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 863, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_4 = PyObject_RichCompare(__pyx_v_t, __pyx_t_3, Py_EQ); __Pyx_XGOTREF(__pyx_t_4); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 863, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_4); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 863, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 90;
        (__pyx_v_f[1]) = 0x66;
        __pyx_v_f = (__pyx_v_f + 1);
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":864
 *             elif t == NPY_LONGDOUBLE:  f[0] = 103 #"g"
 *             elif t == NPY_CFLOAT:      f[0] = 90; f[1] = 102; f += 1 # Zf
 *             elif t == NPY_CDOUBLE:     f[0] = 90; f[1] = 100; f += 1 # Zd             # <<<<<<<<<<<<<<
 *             elif t == NPY_CLONGDOUBLE: f[0] = 90; f[1] = 103; f += 1 # Zg
 *             elif t == NPY_OBJECT:      f[0] = 79 #"O"
 */
      __pyx_t_4 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_CDOUBLE); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 864, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_3 = PyObject_RichCompare(__pyx_v_t, __pyx_t_4, Py_EQ); __Pyx_XGOTREF(__pyx_t_3); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 864, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_3); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 864, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 90;
        (__pyx_v_f[1]) = 0x64;
        __pyx_v_f = (__pyx_v_f + 1);
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":865
 *             elif t == NPY_CFLOAT:      f[0] = 90; f[1] = 102; f += 1 # Zf
 *             elif t == NPY_CDOUBLE:     f[0] = 90; f[1] = 100; f += 1 # Zd
 *             elif t == NPY_CLONGDOUBLE: f[0] = 90; f[1] = 103; f += 1 # Zg             # <<<<<<<<<<<<<<
 *             elif t == NPY_OBJECT:      f[0] = 79 #"O"
 *             else:
 */
      __pyx_t_3 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_CLONGDOUBLE); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 865, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_3);
      __pyx_t_4 = PyObject_RichCompare(__pyx_v_t, __pyx_t_3, Py_EQ); __Pyx_XGOTREF(__pyx_t_4); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 865, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_4); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 865, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 90;
        (__pyx_v_f[1]) = 0x67;
        __pyx_v_f = (__pyx_v_f + 1);
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":866
 *             elif t == NPY_CDOUBLE:     f[0] = 90; f[1] = 100; f += 1 # Zd
 *             elif t == NPY_CLONGDOUBLE: f[0] = 90; f[1] = 103; f += 1 # Zg
 *             elif t == NPY_OBJECT:      f[0] = 79 #"O"             # <<<<<<<<<<<<<<
 *             else:
 *                 raise ValueError(u"unknown dtype code in numpy.pxd (%d)" % t)
 */
      __pyx_t_4 = __Pyx_PyInt_From_enum__NPY_TYPES(NPY_OBJECT); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 866, __pyx_L1_error)
      __Pyx_GOTREF(__pyx_t_4);
      __pyx_t_3 = PyObject_RichCompare(__pyx_v_t, __pyx_t_4, Py_EQ); __Pyx_XGOTREF(__pyx_t_3); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 866, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
      __pyx_t_6 = __Pyx_PyObject_IsTrue(__pyx_t_3); if (unlikely(__pyx_t_6 < 0)) __PYX_ERR(1, 866, __pyx_L1_error)
      __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
      if (__pyx_t_6) {
        (__pyx_v_f[0]) = 79;
        goto __pyx_L15;
      }

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":868
 *             elif t == NPY_OBJECT:      f[0] = 79 #"O"
 *             else:
 *                 raise ValueError(u"unknown dtype code in numpy.pxd (%d)" % t)             # <<<<<<<<<<<<<<
 *             f += 1
 *         else:
 */
      /*else*/ {
        __pyx_t_3 = PyUnicode_Format(__pyx_kp_u_unknown_dtype_code_in_numpy_pxd, __pyx_v_t); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 868, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_3);
        __pyx_t_4 = PyTuple_New(1); if (unlikely(!__pyx_t_4)) __PYX_ERR(1, 868, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_4);
        __Pyx_GIVEREF(__pyx_t_3);
        PyTuple_SET_ITEM(__pyx_t_4, 0, __pyx_t_3);
        __pyx_t_3 = 0;
        __pyx_t_3 = __Pyx_PyObject_Call(__pyx_builtin_ValueError, __pyx_t_4, NULL); if (unlikely(!__pyx_t_3)) __PYX_ERR(1, 868, __pyx_L1_error)
        __Pyx_GOTREF(__pyx_t_3);
        __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
        __Pyx_Raise(__pyx_t_3, 0, 0, 0);
        __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
        __PYX_ERR(1, 868, __pyx_L1_error)
      }
      __pyx_L15:;

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":869
 *             else:
 *                 raise ValueError(u"unknown dtype code in numpy.pxd (%d)" % t)
 *             f += 1             # <<<<<<<<<<<<<<
 *         else:
 *             # Cython ignores struct boundary information ("T{...}"),
 */
      __pyx_v_f = (__pyx_v_f + 1);

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":844
 *         offset[0] += child.itemsize
 * 
 *         if not PyDataType_HASFIELDS(child):             # <<<<<<<<<<<<<<
 *             t = child.type_num
 *             if end - f < 5:
 */
      goto __pyx_L13;
    }

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":873
 *             # Cython ignores struct boundary information ("T{...}"),
 *             # so don't output it
 *             f = _util_dtypestring(child, f, end, offset)             # <<<<<<<<<<<<<<
 *     return f
 * 
 */
    /*else*/ {
      __pyx_t_9 = __pyx_f_5numpy__util_dtypestring(__pyx_v_child, __pyx_v_f, __pyx_v_end, __pyx_v_offset); if (unlikely(__pyx_t_9 == NULL)) __PYX_ERR(1, 873, __pyx_L1_error)
      __pyx_v_f = __pyx_t_9;
    }
    __pyx_L13:;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":818
 *     cdef tuple fields
 * 
 *     for childname in descr.names:             # <<<<<<<<<<<<<<
 *         fields = descr.fields[childname]
 *         child, new_offset = fields
 */
  }
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":874
 *             # so don't output it
 *             f = _util_dtypestring(child, f, end, offset)
 *     return f             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __pyx_r = __pyx_v_f;
  goto __pyx_L0;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":809
 *         return ()
 * 
 * cdef inline char* _util_dtypestring(dtype descr, char* f, char* end, int* offset) except NULL:             # <<<<<<<<<<<<<<
 *     # Recursive utility function used in __getbuffer__ to get format
 *     # string. The new location in the format string is returned.
 */

  /* function exit code */
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_3);
  __Pyx_XDECREF(__pyx_t_4);
  __Pyx_AddTraceback("numpy._util_dtypestring", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = NULL;
  __pyx_L0:;
  __Pyx_XDECREF((PyObject *)__pyx_v_child);
  __Pyx_XDECREF(__pyx_v_fields);
  __Pyx_XDECREF(__pyx_v_childname);
  __Pyx_XDECREF(__pyx_v_new_offset);
  __Pyx_XDECREF(__pyx_v_t);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":990
 * 
 * 
 * cdef inline void set_array_base(ndarray arr, object base):             # <<<<<<<<<<<<<<
 *      cdef PyObject* baseptr
 *      if base is None:
 */

static CYTHON_INLINE void __pyx_f_5numpy_set_array_base(PyArrayObject *__pyx_v_arr, PyObject *__pyx_v_base) {
  PyObject *__pyx_v_baseptr;
  __Pyx_RefNannyDeclarations
  int __pyx_t_1;
  int __pyx_t_2;
  __Pyx_RefNannySetupContext("set_array_base", 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":992
 * cdef inline void set_array_base(ndarray arr, object base):
 *      cdef PyObject* baseptr
 *      if base is None:             # <<<<<<<<<<<<<<
 *          baseptr = NULL
 *      else:
 */
  __pyx_t_1 = (__pyx_v_base == Py_None);
  __pyx_t_2 = (__pyx_t_1 != 0);
  if (__pyx_t_2) {

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":993
 *      cdef PyObject* baseptr
 *      if base is None:
 *          baseptr = NULL             # <<<<<<<<<<<<<<
 *      else:
 *          Py_INCREF(base) # important to do this before decref below!
 */
    __pyx_v_baseptr = NULL;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":992
 * cdef inline void set_array_base(ndarray arr, object base):
 *      cdef PyObject* baseptr
 *      if base is None:             # <<<<<<<<<<<<<<
 *          baseptr = NULL
 *      else:
 */
    goto __pyx_L3;
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":995
 *          baseptr = NULL
 *      else:
 *          Py_INCREF(base) # important to do this before decref below!             # <<<<<<<<<<<<<<
 *          baseptr = <PyObject*>base
 *      Py_XDECREF(arr.base)
 */
  /*else*/ {
    Py_INCREF(__pyx_v_base);

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":996
 *      else:
 *          Py_INCREF(base) # important to do this before decref below!
 *          baseptr = <PyObject*>base             # <<<<<<<<<<<<<<
 *      Py_XDECREF(arr.base)
 *      arr.base = baseptr
 */
    __pyx_v_baseptr = ((PyObject *)__pyx_v_base);
  }
  __pyx_L3:;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":997
 *          Py_INCREF(base) # important to do this before decref below!
 *          baseptr = <PyObject*>base
 *      Py_XDECREF(arr.base)             # <<<<<<<<<<<<<<
 *      arr.base = baseptr
 * 
 */
  Py_XDECREF(__pyx_v_arr->base);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":998
 *          baseptr = <PyObject*>base
 *      Py_XDECREF(arr.base)
 *      arr.base = baseptr             # <<<<<<<<<<<<<<
 * 
 * cdef inline object get_array_base(ndarray arr):
 */
  __pyx_v_arr->base = __pyx_v_baseptr;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":990
 * 
 * 
 * cdef inline void set_array_base(ndarray arr, object base):             # <<<<<<<<<<<<<<
 *      cdef PyObject* baseptr
 *      if base is None:
 */

  /* function exit code */
  __Pyx_RefNannyFinishContext();
}

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1000
 *      arr.base = baseptr
 * 
 * cdef inline object get_array_base(ndarray arr):             # <<<<<<<<<<<<<<
 *     if arr.base is NULL:
 *         return None
 */

static CYTHON_INLINE PyObject *__pyx_f_5numpy_get_array_base(PyArrayObject *__pyx_v_arr) {
  PyObject *__pyx_r = NULL;
  __Pyx_RefNannyDeclarations
  int __pyx_t_1;
  __Pyx_RefNannySetupContext("get_array_base", 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1001
 * 
 * cdef inline object get_array_base(ndarray arr):
 *     if arr.base is NULL:             # <<<<<<<<<<<<<<
 *         return None
 *     else:
 */
  __pyx_t_1 = ((__pyx_v_arr->base == NULL) != 0);
  if (__pyx_t_1) {

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1002
 * cdef inline object get_array_base(ndarray arr):
 *     if arr.base is NULL:
 *         return None             # <<<<<<<<<<<<<<
 *     else:
 *         return <object>arr.base
 */
    __Pyx_XDECREF(__pyx_r);
    __Pyx_INCREF(Py_None);
    __pyx_r = Py_None;
    goto __pyx_L0;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1001
 * 
 * cdef inline object get_array_base(ndarray arr):
 *     if arr.base is NULL:             # <<<<<<<<<<<<<<
 *         return None
 *     else:
 */
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1004
 *         return None
 *     else:
 *         return <object>arr.base             # <<<<<<<<<<<<<<
 * 
 * 
 */
  /*else*/ {
    __Pyx_XDECREF(__pyx_r);
    __Pyx_INCREF(((PyObject *)__pyx_v_arr->base));
    __pyx_r = ((PyObject *)__pyx_v_arr->base);
    goto __pyx_L0;
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1000
 *      arr.base = baseptr
 * 
 * cdef inline object get_array_base(ndarray arr):             # <<<<<<<<<<<<<<
 *     if arr.base is NULL:
 *         return None
 */

  /* function exit code */
  __pyx_L0:;
  __Pyx_XGIVEREF(__pyx_r);
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1009
 * # Versions of the import_* functions which are more suitable for
 * # Cython code.
 * cdef inline int import_array() except -1:             # <<<<<<<<<<<<<<
 *     try:
 *         _import_array()
 */

static CYTHON_INLINE int __pyx_f_5numpy_import_array(void) {
  int __pyx_r;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  PyObject *__pyx_t_2 = NULL;
  PyObject *__pyx_t_3 = NULL;
  int __pyx_t_4;
  PyObject *__pyx_t_5 = NULL;
  PyObject *__pyx_t_6 = NULL;
  PyObject *__pyx_t_7 = NULL;
  PyObject *__pyx_t_8 = NULL;
  __Pyx_RefNannySetupContext("import_array", 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1010
 * # Cython code.
 * cdef inline int import_array() except -1:
 *     try:             # <<<<<<<<<<<<<<
 *         _import_array()
 *     except Exception:
 */
  {
    __Pyx_PyThreadState_declare
    __Pyx_PyThreadState_assign
    __Pyx_ExceptionSave(&__pyx_t_1, &__pyx_t_2, &__pyx_t_3);
    __Pyx_XGOTREF(__pyx_t_1);
    __Pyx_XGOTREF(__pyx_t_2);
    __Pyx_XGOTREF(__pyx_t_3);
    /*try:*/ {

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1011
 * cdef inline int import_array() except -1:
 *     try:
 *         _import_array()             # <<<<<<<<<<<<<<
 *     except Exception:
 *         raise ImportError("numpy.core.multiarray failed to import")
 */
      __pyx_t_4 = _import_array(); if (unlikely(__pyx_t_4 == -1)) __PYX_ERR(1, 1011, __pyx_L3_error)

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1010
 * # Cython code.
 * cdef inline int import_array() except -1:
 *     try:             # <<<<<<<<<<<<<<
 *         _import_array()
 *     except Exception:
 */
    }
    __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_XDECREF(__pyx_t_2); __pyx_t_2 = 0;
    __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
    goto __pyx_L8_try_end;
    __pyx_L3_error:;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1012
 *     try:
 *         _import_array()
 *     except Exception:             # <<<<<<<<<<<<<<
 *         raise ImportError("numpy.core.multiarray failed to import")
 * 
 */
    __pyx_t_4 = __Pyx_PyErr_ExceptionMatches(((PyObject *)(&((PyTypeObject*)PyExc_Exception)[0])));
    if (__pyx_t_4) {
      __Pyx_AddTraceback("numpy.import_array", __pyx_clineno, __pyx_lineno, __pyx_filename);
      if (__Pyx_GetException(&__pyx_t_5, &__pyx_t_6, &__pyx_t_7) < 0) __PYX_ERR(1, 1012, __pyx_L5_except_error)
      __Pyx_GOTREF(__pyx_t_5);
      __Pyx_GOTREF(__pyx_t_6);
      __Pyx_GOTREF(__pyx_t_7);

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1013
 *         _import_array()
 *     except Exception:
 *         raise ImportError("numpy.core.multiarray failed to import")             # <<<<<<<<<<<<<<
 * 
 * cdef inline int import_umath() except -1:
 */
      __pyx_t_8 = __Pyx_PyObject_Call(__pyx_builtin_ImportError, __pyx_tuple__10, NULL); if (unlikely(!__pyx_t_8)) __PYX_ERR(1, 1013, __pyx_L5_except_error)
      __Pyx_GOTREF(__pyx_t_8);
      __Pyx_Raise(__pyx_t_8, 0, 0, 0);
      __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
      __PYX_ERR(1, 1013, __pyx_L5_except_error)
    }
    goto __pyx_L5_except_error;
    __pyx_L5_except_error:;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1010
 * # Cython code.
 * cdef inline int import_array() except -1:
 *     try:             # <<<<<<<<<<<<<<
 *         _import_array()
 *     except Exception:
 */
    __Pyx_XGIVEREF(__pyx_t_1);
    __Pyx_XGIVEREF(__pyx_t_2);
    __Pyx_XGIVEREF(__pyx_t_3);
    __Pyx_ExceptionReset(__pyx_t_1, __pyx_t_2, __pyx_t_3);
    goto __pyx_L1_error;
    __pyx_L8_try_end:;
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1009
 * # Versions of the import_* functions which are more suitable for
 * # Cython code.
 * cdef inline int import_array() except -1:             # <<<<<<<<<<<<<<
 *     try:
 *         _import_array()
 */

  /* function exit code */
  __pyx_r = 0;
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_5);
  __Pyx_XDECREF(__pyx_t_6);
  __Pyx_XDECREF(__pyx_t_7);
  __Pyx_XDECREF(__pyx_t_8);
  __Pyx_AddTraceback("numpy.import_array", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = -1;
  __pyx_L0:;
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1015
 *         raise ImportError("numpy.core.multiarray failed to import")
 * 
 * cdef inline int import_umath() except -1:             # <<<<<<<<<<<<<<
 *     try:
 *         _import_umath()
 */

static CYTHON_INLINE int __pyx_f_5numpy_import_umath(void) {
  int __pyx_r;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  PyObject *__pyx_t_2 = NULL;
  PyObject *__pyx_t_3 = NULL;
  int __pyx_t_4;
  PyObject *__pyx_t_5 = NULL;
  PyObject *__pyx_t_6 = NULL;
  PyObject *__pyx_t_7 = NULL;
  PyObject *__pyx_t_8 = NULL;
  __Pyx_RefNannySetupContext("import_umath", 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1016
 * 
 * cdef inline int import_umath() except -1:
 *     try:             # <<<<<<<<<<<<<<
 *         _import_umath()
 *     except Exception:
 */
  {
    __Pyx_PyThreadState_declare
    __Pyx_PyThreadState_assign
    __Pyx_ExceptionSave(&__pyx_t_1, &__pyx_t_2, &__pyx_t_3);
    __Pyx_XGOTREF(__pyx_t_1);
    __Pyx_XGOTREF(__pyx_t_2);
    __Pyx_XGOTREF(__pyx_t_3);
    /*try:*/ {

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1017
 * cdef inline int import_umath() except -1:
 *     try:
 *         _import_umath()             # <<<<<<<<<<<<<<
 *     except Exception:
 *         raise ImportError("numpy.core.umath failed to import")
 */
      __pyx_t_4 = _import_umath(); if (unlikely(__pyx_t_4 == -1)) __PYX_ERR(1, 1017, __pyx_L3_error)

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1016
 * 
 * cdef inline int import_umath() except -1:
 *     try:             # <<<<<<<<<<<<<<
 *         _import_umath()
 *     except Exception:
 */
    }
    __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_XDECREF(__pyx_t_2); __pyx_t_2 = 0;
    __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
    goto __pyx_L8_try_end;
    __pyx_L3_error:;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1018
 *     try:
 *         _import_umath()
 *     except Exception:             # <<<<<<<<<<<<<<
 *         raise ImportError("numpy.core.umath failed to import")
 * 
 */
    __pyx_t_4 = __Pyx_PyErr_ExceptionMatches(((PyObject *)(&((PyTypeObject*)PyExc_Exception)[0])));
    if (__pyx_t_4) {
      __Pyx_AddTraceback("numpy.import_umath", __pyx_clineno, __pyx_lineno, __pyx_filename);
      if (__Pyx_GetException(&__pyx_t_5, &__pyx_t_6, &__pyx_t_7) < 0) __PYX_ERR(1, 1018, __pyx_L5_except_error)
      __Pyx_GOTREF(__pyx_t_5);
      __Pyx_GOTREF(__pyx_t_6);
      __Pyx_GOTREF(__pyx_t_7);

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1019
 *         _import_umath()
 *     except Exception:
 *         raise ImportError("numpy.core.umath failed to import")             # <<<<<<<<<<<<<<
 * 
 * cdef inline int import_ufunc() except -1:
 */
      __pyx_t_8 = __Pyx_PyObject_Call(__pyx_builtin_ImportError, __pyx_tuple__11, NULL); if (unlikely(!__pyx_t_8)) __PYX_ERR(1, 1019, __pyx_L5_except_error)
      __Pyx_GOTREF(__pyx_t_8);
      __Pyx_Raise(__pyx_t_8, 0, 0, 0);
      __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
      __PYX_ERR(1, 1019, __pyx_L5_except_error)
    }
    goto __pyx_L5_except_error;
    __pyx_L5_except_error:;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1016
 * 
 * cdef inline int import_umath() except -1:
 *     try:             # <<<<<<<<<<<<<<
 *         _import_umath()
 *     except Exception:
 */
    __Pyx_XGIVEREF(__pyx_t_1);
    __Pyx_XGIVEREF(__pyx_t_2);
    __Pyx_XGIVEREF(__pyx_t_3);
    __Pyx_ExceptionReset(__pyx_t_1, __pyx_t_2, __pyx_t_3);
    goto __pyx_L1_error;
    __pyx_L8_try_end:;
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1015
 *         raise ImportError("numpy.core.multiarray failed to import")
 * 
 * cdef inline int import_umath() except -1:             # <<<<<<<<<<<<<<
 *     try:
 *         _import_umath()
 */

  /* function exit code */
  __pyx_r = 0;
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_5);
  __Pyx_XDECREF(__pyx_t_6);
  __Pyx_XDECREF(__pyx_t_7);
  __Pyx_XDECREF(__pyx_t_8);
  __Pyx_AddTraceback("numpy.import_umath", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = -1;
  __pyx_L0:;
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

/* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1021
 *         raise ImportError("numpy.core.umath failed to import")
 * 
 * cdef inline int import_ufunc() except -1:             # <<<<<<<<<<<<<<
 *     try:
 *         _import_umath()
 */

static CYTHON_INLINE int __pyx_f_5numpy_import_ufunc(void) {
  int __pyx_r;
  __Pyx_RefNannyDeclarations
  PyObject *__pyx_t_1 = NULL;
  PyObject *__pyx_t_2 = NULL;
  PyObject *__pyx_t_3 = NULL;
  int __pyx_t_4;
  PyObject *__pyx_t_5 = NULL;
  PyObject *__pyx_t_6 = NULL;
  PyObject *__pyx_t_7 = NULL;
  PyObject *__pyx_t_8 = NULL;
  __Pyx_RefNannySetupContext("import_ufunc", 0);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1022
 * 
 * cdef inline int import_ufunc() except -1:
 *     try:             # <<<<<<<<<<<<<<
 *         _import_umath()
 *     except Exception:
 */
  {
    __Pyx_PyThreadState_declare
    __Pyx_PyThreadState_assign
    __Pyx_ExceptionSave(&__pyx_t_1, &__pyx_t_2, &__pyx_t_3);
    __Pyx_XGOTREF(__pyx_t_1);
    __Pyx_XGOTREF(__pyx_t_2);
    __Pyx_XGOTREF(__pyx_t_3);
    /*try:*/ {

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1023
 * cdef inline int import_ufunc() except -1:
 *     try:
 *         _import_umath()             # <<<<<<<<<<<<<<
 *     except Exception:
 *         raise ImportError("numpy.core.umath failed to import")
 */
      __pyx_t_4 = _import_umath(); if (unlikely(__pyx_t_4 == -1)) __PYX_ERR(1, 1023, __pyx_L3_error)

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1022
 * 
 * cdef inline int import_ufunc() except -1:
 *     try:             # <<<<<<<<<<<<<<
 *         _import_umath()
 *     except Exception:
 */
    }
    __Pyx_XDECREF(__pyx_t_1); __pyx_t_1 = 0;
    __Pyx_XDECREF(__pyx_t_2); __pyx_t_2 = 0;
    __Pyx_XDECREF(__pyx_t_3); __pyx_t_3 = 0;
    goto __pyx_L8_try_end;
    __pyx_L3_error:;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1024
 *     try:
 *         _import_umath()
 *     except Exception:             # <<<<<<<<<<<<<<
 *         raise ImportError("numpy.core.umath failed to import")
 */
    __pyx_t_4 = __Pyx_PyErr_ExceptionMatches(((PyObject *)(&((PyTypeObject*)PyExc_Exception)[0])));
    if (__pyx_t_4) {
      __Pyx_AddTraceback("numpy.import_ufunc", __pyx_clineno, __pyx_lineno, __pyx_filename);
      if (__Pyx_GetException(&__pyx_t_5, &__pyx_t_6, &__pyx_t_7) < 0) __PYX_ERR(1, 1024, __pyx_L5_except_error)
      __Pyx_GOTREF(__pyx_t_5);
      __Pyx_GOTREF(__pyx_t_6);
      __Pyx_GOTREF(__pyx_t_7);

      /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1025
 *         _import_umath()
 *     except Exception:
 *         raise ImportError("numpy.core.umath failed to import")             # <<<<<<<<<<<<<<
 */
      __pyx_t_8 = __Pyx_PyObject_Call(__pyx_builtin_ImportError, __pyx_tuple__12, NULL); if (unlikely(!__pyx_t_8)) __PYX_ERR(1, 1025, __pyx_L5_except_error)
      __Pyx_GOTREF(__pyx_t_8);
      __Pyx_Raise(__pyx_t_8, 0, 0, 0);
      __Pyx_DECREF(__pyx_t_8); __pyx_t_8 = 0;
      __PYX_ERR(1, 1025, __pyx_L5_except_error)
    }
    goto __pyx_L5_except_error;
    __pyx_L5_except_error:;

    /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1022
 * 
 * cdef inline int import_ufunc() except -1:
 *     try:             # <<<<<<<<<<<<<<
 *         _import_umath()
 *     except Exception:
 */
    __Pyx_XGIVEREF(__pyx_t_1);
    __Pyx_XGIVEREF(__pyx_t_2);
    __Pyx_XGIVEREF(__pyx_t_3);
    __Pyx_ExceptionReset(__pyx_t_1, __pyx_t_2, __pyx_t_3);
    goto __pyx_L1_error;
    __pyx_L8_try_end:;
  }

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1021
 *         raise ImportError("numpy.core.umath failed to import")
 * 
 * cdef inline int import_ufunc() except -1:             # <<<<<<<<<<<<<<
 *     try:
 *         _import_umath()
 */

  /* function exit code */
  __pyx_r = 0;
  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_5);
  __Pyx_XDECREF(__pyx_t_6);
  __Pyx_XDECREF(__pyx_t_7);
  __Pyx_XDECREF(__pyx_t_8);
  __Pyx_AddTraceback("numpy.import_ufunc", __pyx_clineno, __pyx_lineno, __pyx_filename);
  __pyx_r = -1;
  __pyx_L0:;
  __Pyx_RefNannyFinishContext();
  return __pyx_r;
}

static struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate *__pyx_freelist_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate[8];
static int __pyx_freecount_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate = 0;

static PyObject *__pyx_tp_new_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate(PyTypeObject *t, CYTHON_UNUSED PyObject *a, CYTHON_UNUSED PyObject *k) {
  PyObject *o;
  if (CYTHON_COMPILING_IN_CPYTHON && likely((__pyx_freecount_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate > 0) & (t->tp_basicsize == sizeof(struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate)))) {
    o = (PyObject*)__pyx_freelist_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate[--__pyx_freecount_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate];
    memset(o, 0, sizeof(struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate));
    (void) PyObject_INIT(o, t);
    PyObject_GC_Track(o);
  } else {
    o = (*t->tp_alloc)(t, 0);
    if (unlikely(!o)) return 0;
  }
  return o;
}

static void __pyx_tp_dealloc_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate(PyObject *o) {
  struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate *p = (struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate *)o;
  PyObject_GC_UnTrack(o);
  Py_CLEAR(p->__pyx_v_self);
  Py_CLEAR(p->__pyx_v_u);
  if (CYTHON_COMPILING_IN_CPYTHON && ((__pyx_freecount_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate < 8) & (Py_TYPE(o)->tp_basicsize == sizeof(struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate)))) {
    __pyx_freelist_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate[__pyx_freecount_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate++] = ((struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate *)o);
  } else {
    (*Py_TYPE(o)->tp_free)(o);
  }
}

static int __pyx_tp_traverse_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate *p = (struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate *)o;
  if (p->__pyx_v_self) {
    e = (*v)(p->__pyx_v_self, a); if (e) return e;
  }
  if (p->__pyx_v_u) {
    e = (*v)(p->__pyx_v_u, a); if (e) return e;
  }
  return 0;
}

static int __pyx_tp_clear_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate(PyObject *o) {
  PyObject* tmp;
  struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate *p = (struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate *)o;
  tmp = ((PyObject*)p->__pyx_v_self);
  p->__pyx_v_self = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  tmp = ((PyObject*)p->__pyx_v_u);
  p->__pyx_v_u = Py_None; Py_INCREF(Py_None);
  Py_XDECREF(tmp);
  return 0;
}

static PyTypeObject __pyx_type_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate = {
  PyVarObject_HEAD_INIT(0, 0)
  "surprise.prediction_algorithms.matrix_factorization.__pyx_scope_struct__estimate", /*tp_name*/
  sizeof(struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate, /*tp_dealloc*/
  0, /*tp_print*/
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
  #endif
  #if PY_MAJOR_VERSION >= 3
  0, /*tp_as_async*/
  #endif
  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  0, /*tp_doc*/
  __pyx_tp_traverse_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate, /*tp_traverse*/
  __pyx_tp_clear_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  0, /*tp_methods*/
  0, /*tp_members*/
  0, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  0, /*tp_dictoffset*/
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};

static struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr *__pyx_freelist_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr[8];
static int __pyx_freecount_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr = 0;

static PyObject *__pyx_tp_new_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr(PyTypeObject *t, CYTHON_UNUSED PyObject *a, CYTHON_UNUSED PyObject *k) {
  PyObject *o;
  if (CYTHON_COMPILING_IN_CPYTHON && likely((__pyx_freecount_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr > 0) & (t->tp_basicsize == sizeof(struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr)))) {
    o = (PyObject*)__pyx_freelist_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr[--__pyx_freecount_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr];
    memset(o, 0, sizeof(struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr));
    (void) PyObject_INIT(o, t);
    PyObject_GC_Track(o);
  } else {
    o = (*t->tp_alloc)(t, 0);
    if (unlikely(!o)) return 0;
  }
  return o;
}

static void __pyx_tp_dealloc_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr(PyObject *o) {
  struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr *p = (struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr *)o;
  PyObject_GC_UnTrack(o);
  Py_CLEAR(p->__pyx_outer_scope);
  Py_CLEAR(p->__pyx_v__);
  Py_CLEAR(p->__pyx_v_j);
  Py_CLEAR(p->__pyx_t_0);
  if (CYTHON_COMPILING_IN_CPYTHON && ((__pyx_freecount_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr < 8) & (Py_TYPE(o)->tp_basicsize == sizeof(struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr)))) {
    __pyx_freelist_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr[__pyx_freecount_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr++] = ((struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr *)o);
  } else {
    (*Py_TYPE(o)->tp_free)(o);
  }
}

static int __pyx_tp_traverse_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr(PyObject *o, visitproc v, void *a) {
  int e;
  struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr *p = (struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr *)o;
  if (p->__pyx_outer_scope) {
    e = (*v)(((PyObject *)p->__pyx_outer_scope), a); if (e) return e;
  }
  if (p->__pyx_v__) {
    e = (*v)(p->__pyx_v__, a); if (e) return e;
  }
  if (p->__pyx_v_j) {
    e = (*v)(p->__pyx_v_j, a); if (e) return e;
  }
  if (p->__pyx_t_0) {
    e = (*v)(p->__pyx_t_0, a); if (e) return e;
  }
  return 0;
}

static PyTypeObject __pyx_type_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr = {
  PyVarObject_HEAD_INIT(0, 0)
  "surprise.prediction_algorithms.matrix_factorization.__pyx_scope_struct_1_genexpr", /*tp_name*/
  sizeof(struct __pyx_obj_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr), /*tp_basicsize*/
  0, /*tp_itemsize*/
  __pyx_tp_dealloc_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr, /*tp_dealloc*/
  0, /*tp_print*/
  0, /*tp_getattr*/
  0, /*tp_setattr*/
  #if PY_MAJOR_VERSION < 3
  0, /*tp_compare*/
  #endif
  #if PY_MAJOR_VERSION >= 3
  0, /*tp_as_async*/
  #endif
  0, /*tp_repr*/
  0, /*tp_as_number*/
  0, /*tp_as_sequence*/
  0, /*tp_as_mapping*/
  0, /*tp_hash*/
  0, /*tp_call*/
  0, /*tp_str*/
  0, /*tp_getattro*/
  0, /*tp_setattro*/
  0, /*tp_as_buffer*/
  Py_TPFLAGS_DEFAULT|Py_TPFLAGS_HAVE_VERSION_TAG|Py_TPFLAGS_CHECKTYPES|Py_TPFLAGS_HAVE_NEWBUFFER|Py_TPFLAGS_HAVE_GC, /*tp_flags*/
  0, /*tp_doc*/
  __pyx_tp_traverse_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr, /*tp_traverse*/
  0, /*tp_clear*/
  0, /*tp_richcompare*/
  0, /*tp_weaklistoffset*/
  0, /*tp_iter*/
  0, /*tp_iternext*/
  0, /*tp_methods*/
  0, /*tp_members*/
  0, /*tp_getset*/
  0, /*tp_base*/
  0, /*tp_dict*/
  0, /*tp_descr_get*/
  0, /*tp_descr_set*/
  0, /*tp_dictoffset*/
  0, /*tp_init*/
  0, /*tp_alloc*/
  __pyx_tp_new_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr, /*tp_new*/
  0, /*tp_free*/
  0, /*tp_is_gc*/
  0, /*tp_bases*/
  0, /*tp_mro*/
  0, /*tp_cache*/
  0, /*tp_subclasses*/
  0, /*tp_weaklist*/
  0, /*tp_del*/
  0, /*tp_version_tag*/
  #if PY_VERSION_HEX >= 0x030400a1
  0, /*tp_finalize*/
  #endif
};

static PyMethodDef __pyx_methods[] = {
  {0, 0, 0, 0}
};

#if PY_MAJOR_VERSION >= 3
#if CYTHON_PEP489_MULTI_PHASE_INIT
static PyObject* __pyx_pymod_create(PyObject *spec, PyModuleDef *def); /*proto*/
static int __pyx_pymod_exec_matrix_factorization(PyObject* module); /*proto*/
static PyModuleDef_Slot __pyx_moduledef_slots[] = {
  {Py_mod_create, (void*)__pyx_pymod_create},
  {Py_mod_exec, (void*)__pyx_pymod_exec_matrix_factorization},
  {0, NULL}
};
#endif

static struct PyModuleDef __pyx_moduledef = {
    PyModuleDef_HEAD_INIT,
    "matrix_factorization",
    __pyx_k_the_mod_matrix_factorization_mo, /* m_doc */
  #if CYTHON_PEP489_MULTI_PHASE_INIT
    0, /* m_size */
  #else
    -1, /* m_size */
  #endif
    __pyx_methods /* m_methods */,
  #if CYTHON_PEP489_MULTI_PHASE_INIT
    __pyx_moduledef_slots, /* m_slots */
  #else
    NULL, /* m_reload */
  #endif
    NULL, /* m_traverse */
    NULL, /* m_clear */
    NULL /* m_free */
};
#endif

static __Pyx_StringTabEntry __pyx_string_tab[] = {
  {&__pyx_kp_s_A_collaborative_filtering_algori, __pyx_k_A_collaborative_filtering_algori, sizeof(__pyx_k_A_collaborative_filtering_algori), 0, 0, 1, 0},
  {&__pyx_n_s_AlgoBase, __pyx_k_AlgoBase, sizeof(__pyx_k_AlgoBase), 0, 0, 1, 1},
  {&__pyx_kp_u_Format_string_allocated_too_shor, __pyx_k_Format_string_allocated_too_shor, sizeof(__pyx_k_Format_string_allocated_too_shor), 0, 1, 0, 0},
  {&__pyx_kp_u_Format_string_allocated_too_shor_2, __pyx_k_Format_string_allocated_too_shor_2, sizeof(__pyx_k_Format_string_allocated_too_shor_2), 0, 1, 0, 0},
  {&__pyx_n_s_ImportError, __pyx_k_ImportError, sizeof(__pyx_k_ImportError), 0, 0, 1, 1},
  {&__pyx_n_s_Iu, __pyx_k_Iu, sizeof(__pyx_k_Iu), 0, 0, 1, 1},
  {&__pyx_n_s_NMF, __pyx_k_NMF, sizeof(__pyx_k_NMF), 0, 0, 1, 1},
  {&__pyx_n_s_NMF___init, __pyx_k_NMF___init, sizeof(__pyx_k_NMF___init), 0, 0, 1, 1},
  {&__pyx_n_s_NMF_estimate, __pyx_k_NMF_estimate, sizeof(__pyx_k_NMF_estimate), 0, 0, 1, 1},
  {&__pyx_n_s_NMF_sgd, __pyx_k_NMF_sgd, sizeof(__pyx_k_NMF_sgd), 0, 0, 1, 1},
  {&__pyx_n_s_NMF_train, __pyx_k_NMF_train, sizeof(__pyx_k_NMF_train), 0, 0, 1, 1},
  {&__pyx_kp_u_Non_native_byte_order_not_suppor, __pyx_k_Non_native_byte_order_not_suppor, sizeof(__pyx_k_Non_native_byte_order_not_suppor), 0, 1, 0, 0},
  {&__pyx_n_s_PredictionImpossible, __pyx_k_PredictionImpossible, sizeof(__pyx_k_PredictionImpossible), 0, 0, 1, 1},
  {&__pyx_kp_u_Processing_epoch, __pyx_k_Processing_epoch, sizeof(__pyx_k_Processing_epoch), 0, 1, 0, 0},
  {&__pyx_n_s_RuntimeError, __pyx_k_RuntimeError, sizeof(__pyx_k_RuntimeError), 0, 0, 1, 1},
  {&__pyx_n_s_SVD, __pyx_k_SVD, sizeof(__pyx_k_SVD), 0, 0, 1, 1},
  {&__pyx_n_s_SVD___init, __pyx_k_SVD___init, sizeof(__pyx_k_SVD___init), 0, 0, 1, 1},
  {&__pyx_n_s_SVD_estimate, __pyx_k_SVD_estimate, sizeof(__pyx_k_SVD_estimate), 0, 0, 1, 1},
  {&__pyx_n_s_SVD_sgd, __pyx_k_SVD_sgd, sizeof(__pyx_k_SVD_sgd), 0, 0, 1, 1},
  {&__pyx_n_s_SVD_train, __pyx_k_SVD_train, sizeof(__pyx_k_SVD_train), 0, 0, 1, 1},
  {&__pyx_n_s_SVDpp, __pyx_k_SVDpp, sizeof(__pyx_k_SVDpp), 0, 0, 1, 1},
  {&__pyx_n_s_SVDpp___init, __pyx_k_SVDpp___init, sizeof(__pyx_k_SVDpp___init), 0, 0, 1, 1},
  {&__pyx_n_s_SVDpp_estimate, __pyx_k_SVDpp_estimate, sizeof(__pyx_k_SVDpp_estimate), 0, 0, 1, 1},
  {&__pyx_n_s_SVDpp_estimate_locals_genexpr, __pyx_k_SVDpp_estimate_locals_genexpr, sizeof(__pyx_k_SVDpp_estimate_locals_genexpr), 0, 0, 1, 1},
  {&__pyx_n_s_SVDpp_sgd, __pyx_k_SVDpp_sgd, sizeof(__pyx_k_SVDpp_sgd), 0, 0, 1, 1},
  {&__pyx_n_s_SVDpp_train, __pyx_k_SVDpp_train, sizeof(__pyx_k_SVDpp_train), 0, 0, 1, 1},
  {&__pyx_kp_s_The_SVD_algorithm_an_extension_o, __pyx_k_The_SVD_algorithm_an_extension_o, sizeof(__pyx_k_The_SVD_algorithm_an_extension_o), 0, 0, 1, 0},
  {&__pyx_kp_s_The_famous_SVD_algorithm_as_popu, __pyx_k_The_famous_SVD_algorithm_as_popu, sizeof(__pyx_k_The_famous_SVD_algorithm_as_popu), 0, 0, 1, 0},
  {&__pyx_kp_u_User_and_item_are_unkown, __pyx_k_User_and_item_are_unkown, sizeof(__pyx_k_User_and_item_are_unkown), 0, 1, 0, 0},
  {&__pyx_n_s_ValueError, __pyx_k_ValueError, sizeof(__pyx_k_ValueError), 0, 0, 1, 1},
  {&__pyx_n_s__27, __pyx_k__27, sizeof(__pyx_k__27), 0, 0, 1, 1},
  {&__pyx_n_s_algo_base, __pyx_k_algo_base, sizeof(__pyx_k_algo_base), 0, 0, 1, 1},
  {&__pyx_n_s_all_items, __pyx_k_all_items, sizeof(__pyx_k_all_items), 0, 0, 1, 1},
  {&__pyx_n_s_all_ratings, __pyx_k_all_ratings, sizeof(__pyx_k_all_ratings), 0, 0, 1, 1},
  {&__pyx_n_s_all_users, __pyx_k_all_users, sizeof(__pyx_k_all_users), 0, 0, 1, 1},
  {&__pyx_n_s_args, __pyx_k_args, sizeof(__pyx_k_args), 0, 0, 1, 1},
  {&__pyx_n_s_bi, __pyx_k_bi, sizeof(__pyx_k_bi), 0, 0, 1, 1},
  {&__pyx_n_s_biased, __pyx_k_biased, sizeof(__pyx_k_biased), 0, 0, 1, 1},
  {&__pyx_n_s_bu, __pyx_k_bu, sizeof(__pyx_k_bu), 0, 0, 1, 1},
  {&__pyx_n_s_cline_in_traceback, __pyx_k_cline_in_traceback, sizeof(__pyx_k_cline_in_traceback), 0, 0, 1, 1},
  {&__pyx_n_s_close, __pyx_k_close, sizeof(__pyx_k_close), 0, 0, 1, 1},
  {&__pyx_n_s_current_epoch, __pyx_k_current_epoch, sizeof(__pyx_k_current_epoch), 0, 0, 1, 1},
  {&__pyx_n_s_doc, __pyx_k_doc, sizeof(__pyx_k_doc), 0, 0, 1, 1},
  {&__pyx_n_s_dot, __pyx_k_dot, sizeof(__pyx_k_dot), 0, 0, 1, 1},
  {&__pyx_n_s_double, __pyx_k_double, sizeof(__pyx_k_double), 0, 0, 1, 1},
  {&__pyx_n_s_err, __pyx_k_err, sizeof(__pyx_k_err), 0, 0, 1, 1},
  {&__pyx_n_s_est, __pyx_k_est, sizeof(__pyx_k_est), 0, 0, 1, 1},
  {&__pyx_n_s_estimate, __pyx_k_estimate, sizeof(__pyx_k_estimate), 0, 0, 1, 1},
  {&__pyx_n_s_f, __pyx_k_f, sizeof(__pyx_k_f), 0, 0, 1, 1},
  {&__pyx_n_s_format, __pyx_k_format, sizeof(__pyx_k_format), 0, 0, 1, 1},
  {&__pyx_n_s_genexpr, __pyx_k_genexpr, sizeof(__pyx_k_genexpr), 0, 0, 1, 1},
  {&__pyx_n_s_global_mean, __pyx_k_global_mean, sizeof(__pyx_k_global_mean), 0, 0, 1, 1},
  {&__pyx_n_s_i, __pyx_k_i, sizeof(__pyx_k_i), 0, 0, 1, 1},
  {&__pyx_n_s_import, __pyx_k_import, sizeof(__pyx_k_import), 0, 0, 1, 1},
  {&__pyx_n_s_init, __pyx_k_init, sizeof(__pyx_k_init), 0, 0, 1, 1},
  {&__pyx_n_s_init_high, __pyx_k_init_high, sizeof(__pyx_k_init_high), 0, 0, 1, 1},
  {&__pyx_n_s_init_low, __pyx_k_init_low, sizeof(__pyx_k_init_low), 0, 0, 1, 1},
  {&__pyx_kp_u_init_low_should_be_greater_than, __pyx_k_init_low_should_be_greater_than, sizeof(__pyx_k_init_low_should_be_greater_than), 0, 1, 0, 0},
  {&__pyx_n_s_init_mean, __pyx_k_init_mean, sizeof(__pyx_k_init_mean), 0, 0, 1, 1},
  {&__pyx_n_s_init_std_dev, __pyx_k_init_std_dev, sizeof(__pyx_k_init_std_dev), 0, 0, 1, 1},
  {&__pyx_n_s_ir, __pyx_k_ir, sizeof(__pyx_k_ir), 0, 0, 1, 1},
  {&__pyx_n_s_item_denom, __pyx_k_item_denom, sizeof(__pyx_k_item_denom), 0, 0, 1, 1},
  {&__pyx_n_s_item_num, __pyx_k_item_num, sizeof(__pyx_k_item_num), 0, 0, 1, 1},
  {&__pyx_n_s_j, __pyx_k_j, sizeof(__pyx_k_j), 0, 0, 1, 1},
  {&__pyx_n_s_known_item, __pyx_k_known_item, sizeof(__pyx_k_known_item), 0, 0, 1, 1},
  {&__pyx_n_s_known_user, __pyx_k_known_user, sizeof(__pyx_k_known_user), 0, 0, 1, 1},
  {&__pyx_n_s_knows_item, __pyx_k_knows_item, sizeof(__pyx_k_knows_item), 0, 0, 1, 1},
  {&__pyx_n_s_knows_user, __pyx_k_knows_user, sizeof(__pyx_k_knows_user), 0, 0, 1, 1},
  {&__pyx_n_s_l, __pyx_k_l, sizeof(__pyx_k_l), 0, 0, 1, 1},
  {&__pyx_n_s_lr_all, __pyx_k_lr_all, sizeof(__pyx_k_lr_all), 0, 0, 1, 1},
  {&__pyx_n_s_lr_bi, __pyx_k_lr_bi, sizeof(__pyx_k_lr_bi), 0, 0, 1, 1},
  {&__pyx_n_s_lr_bu, __pyx_k_lr_bu, sizeof(__pyx_k_lr_bu), 0, 0, 1, 1},
  {&__pyx_n_s_lr_pu, __pyx_k_lr_pu, sizeof(__pyx_k_lr_pu), 0, 0, 1, 1},
  {&__pyx_n_s_lr_qi, __pyx_k_lr_qi, sizeof(__pyx_k_lr_qi), 0, 0, 1, 1},
  {&__pyx_n_s_lr_yj, __pyx_k_lr_yj, sizeof(__pyx_k_lr_yj), 0, 0, 1, 1},
  {&__pyx_n_s_main, __pyx_k_main, sizeof(__pyx_k_main), 0, 0, 1, 1},
  {&__pyx_n_s_metaclass, __pyx_k_metaclass, sizeof(__pyx_k_metaclass), 0, 0, 1, 1},
  {&__pyx_n_s_module, __pyx_k_module, sizeof(__pyx_k_module), 0, 0, 1, 1},
  {&__pyx_n_s_n_epochs, __pyx_k_n_epochs, sizeof(__pyx_k_n_epochs), 0, 0, 1, 1},
  {&__pyx_n_s_n_factors, __pyx_k_n_factors, sizeof(__pyx_k_n_factors), 0, 0, 1, 1},
  {&__pyx_n_s_n_items, __pyx_k_n_items, sizeof(__pyx_k_n_items), 0, 0, 1, 1},
  {&__pyx_n_s_n_users, __pyx_k_n_users, sizeof(__pyx_k_n_users), 0, 0, 1, 1},
  {&__pyx_kp_u_ndarray_is_not_C_contiguous, __pyx_k_ndarray_is_not_C_contiguous, sizeof(__pyx_k_ndarray_is_not_C_contiguous), 0, 1, 0, 0},
  {&__pyx_kp_u_ndarray_is_not_Fortran_contiguou, __pyx_k_ndarray_is_not_Fortran_contiguou, sizeof(__pyx_k_ndarray_is_not_Fortran_contiguou), 0, 1, 0, 0},
  {&__pyx_n_s_normal, __pyx_k_normal, sizeof(__pyx_k_normal), 0, 0, 1, 1},
  {&__pyx_n_s_np, __pyx_k_np, sizeof(__pyx_k_np), 0, 0, 1, 1},
  {&__pyx_n_s_numpy, __pyx_k_numpy, sizeof(__pyx_k_numpy), 0, 0, 1, 1},
  {&__pyx_kp_u_numpy_core_multiarray_failed_to, __pyx_k_numpy_core_multiarray_failed_to, sizeof(__pyx_k_numpy_core_multiarray_failed_to), 0, 1, 0, 0},
  {&__pyx_kp_u_numpy_core_umath_failed_to_impor, __pyx_k_numpy_core_umath_failed_to_impor, sizeof(__pyx_k_numpy_core_umath_failed_to_impor), 0, 1, 0, 0},
  {&__pyx_n_s_predictions, __pyx_k_predictions, sizeof(__pyx_k_predictions), 0, 0, 1, 1},
  {&__pyx_n_s_prepare, __pyx_k_prepare, sizeof(__pyx_k_prepare), 0, 0, 1, 1},
  {&__pyx_n_s_print, __pyx_k_print, sizeof(__pyx_k_print), 0, 0, 1, 1},
  {&__pyx_kp_u_processing_epoch, __pyx_k_processing_epoch, sizeof(__pyx_k_processing_epoch), 0, 1, 0, 0},
  {&__pyx_n_s_pu, __pyx_k_pu, sizeof(__pyx_k_pu), 0, 0, 1, 1},
  {&__pyx_n_s_puf, __pyx_k_puf, sizeof(__pyx_k_puf), 0, 0, 1, 1},
  {&__pyx_n_s_qi, __pyx_k_qi, sizeof(__pyx_k_qi), 0, 0, 1, 1},
  {&__pyx_n_s_qif, __pyx_k_qif, sizeof(__pyx_k_qif), 0, 0, 1, 1},
  {&__pyx_n_s_qualname, __pyx_k_qualname, sizeof(__pyx_k_qualname), 0, 0, 1, 1},
  {&__pyx_n_s_r, __pyx_k_r, sizeof(__pyx_k_r), 0, 0, 1, 1},
  {&__pyx_n_s_random, __pyx_k_random, sizeof(__pyx_k_random), 0, 0, 1, 1},
  {&__pyx_n_s_range, __pyx_k_range, sizeof(__pyx_k_range), 0, 0, 1, 1},
  {&__pyx_n_s_reg_all, __pyx_k_reg_all, sizeof(__pyx_k_reg_all), 0, 0, 1, 1},
  {&__pyx_n_s_reg_bi, __pyx_k_reg_bi, sizeof(__pyx_k_reg_bi), 0, 0, 1, 1},
  {&__pyx_n_s_reg_bu, __pyx_k_reg_bu, sizeof(__pyx_k_reg_bu), 0, 0, 1, 1},
  {&__pyx_n_s_reg_pu, __pyx_k_reg_pu, sizeof(__pyx_k_reg_pu), 0, 0, 1, 1},
  {&__pyx_n_s_reg_qi, __pyx_k_reg_qi, sizeof(__pyx_k_reg_qi), 0, 0, 1, 1},
  {&__pyx_n_s_reg_yj, __pyx_k_reg_yj, sizeof(__pyx_k_reg_yj), 0, 0, 1, 1},
  {&__pyx_n_s_self, __pyx_k_self, sizeof(__pyx_k_self), 0, 0, 1, 1},
  {&__pyx_n_s_send, __pyx_k_send, sizeof(__pyx_k_send), 0, 0, 1, 1},
  {&__pyx_n_s_sgd, __pyx_k_sgd, sizeof(__pyx_k_sgd), 0, 0, 1, 1},
  {&__pyx_n_s_six_moves, __pyx_k_six_moves, sizeof(__pyx_k_six_moves), 0, 0, 1, 1},
  {&__pyx_n_s_size, __pyx_k_size, sizeof(__pyx_k_size), 0, 0, 1, 1},
  {&__pyx_n_s_sqrt, __pyx_k_sqrt, sizeof(__pyx_k_sqrt), 0, 0, 1, 1},
  {&__pyx_n_s_sqrt_Iu, __pyx_k_sqrt_Iu, sizeof(__pyx_k_sqrt_Iu), 0, 0, 1, 1},
  {&__pyx_n_s_sum, __pyx_k_sum, sizeof(__pyx_k_sum), 0, 0, 1, 1},
  {&__pyx_n_s_surprise_prediction_algorithms_m, __pyx_k_surprise_prediction_algorithms_m, sizeof(__pyx_k_surprise_prediction_algorithms_m), 0, 0, 1, 1},
  {&__pyx_kp_s_surprise_prediction_algorithms_m_2, __pyx_k_surprise_prediction_algorithms_m_2, sizeof(__pyx_k_surprise_prediction_algorithms_m_2), 0, 0, 1, 0},
  {&__pyx_n_s_test, __pyx_k_test, sizeof(__pyx_k_test), 0, 0, 1, 1},
  {&__pyx_n_s_throw, __pyx_k_throw, sizeof(__pyx_k_throw), 0, 0, 1, 1},
  {&__pyx_n_s_train, __pyx_k_train, sizeof(__pyx_k_train), 0, 0, 1, 1},
  {&__pyx_n_s_trainset, __pyx_k_trainset, sizeof(__pyx_k_trainset), 0, 0, 1, 1},
  {&__pyx_n_s_u, __pyx_k_u, sizeof(__pyx_k_u), 0, 0, 1, 1},
  {&__pyx_n_s_u_impl_fdb, __pyx_k_u_impl_fdb, sizeof(__pyx_k_u_impl_fdb), 0, 0, 1, 1},
  {&__pyx_n_s_u_impl_feedback, __pyx_k_u_impl_feedback, sizeof(__pyx_k_u_impl_feedback), 0, 0, 1, 1},
  {&__pyx_n_s_uniform, __pyx_k_uniform, sizeof(__pyx_k_uniform), 0, 0, 1, 1},
  {&__pyx_kp_u_unknown_dtype_code_in_numpy_pxd, __pyx_k_unknown_dtype_code_in_numpy_pxd, sizeof(__pyx_k_unknown_dtype_code_in_numpy_pxd), 0, 1, 0, 0},
  {&__pyx_n_s_ur, __pyx_k_ur, sizeof(__pyx_k_ur), 0, 0, 1, 1},
  {&__pyx_n_s_user_denom, __pyx_k_user_denom, sizeof(__pyx_k_user_denom), 0, 0, 1, 1},
  {&__pyx_n_s_user_num, __pyx_k_user_num, sizeof(__pyx_k_user_num), 0, 0, 1, 1},
  {&__pyx_n_s_verbose, __pyx_k_verbose, sizeof(__pyx_k_verbose), 0, 0, 1, 1},
  {&__pyx_n_s_yj, __pyx_k_yj, sizeof(__pyx_k_yj), 0, 0, 1, 1},
  {&__pyx_n_s_zeros, __pyx_k_zeros, sizeof(__pyx_k_zeros), 0, 0, 1, 1},
  {0, 0, 0, 0, 0, 0, 0}
};
static int __Pyx_InitCachedBuiltins(void) {
  __pyx_builtin_print = __Pyx_GetBuiltinName(__pyx_n_s_print); if (!__pyx_builtin_print) __PYX_ERR(0, 207, __pyx_L1_error)
  __pyx_builtin_sum = __Pyx_GetBuiltinName(__pyx_n_s_sum); if (!__pyx_builtin_sum) __PYX_ERR(0, 452, __pyx_L1_error)
  __pyx_builtin_ValueError = __Pyx_GetBuiltinName(__pyx_n_s_ValueError); if (!__pyx_builtin_ValueError) __PYX_ERR(0, 551, __pyx_L1_error)
  __pyx_builtin_range = __Pyx_GetBuiltinName(__pyx_n_s_range); if (!__pyx_builtin_range) __PYX_ERR(1, 248, __pyx_L1_error)
  __pyx_builtin_RuntimeError = __Pyx_GetBuiltinName(__pyx_n_s_RuntimeError); if (!__pyx_builtin_RuntimeError) __PYX_ERR(1, 823, __pyx_L1_error)
  __pyx_builtin_ImportError = __Pyx_GetBuiltinName(__pyx_n_s_ImportError); if (!__pyx_builtin_ImportError) __PYX_ERR(1, 1013, __pyx_L1_error)
  return 0;
  __pyx_L1_error:;
  return -1;
}

static int __Pyx_InitCachedConstants(void) {
  __Pyx_RefNannyDeclarations
  __Pyx_RefNannySetupContext("__Pyx_InitCachedConstants", 0);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":255
 *                 est = np.dot(self.qi[i], self.pu[u])
 *             else:
 *                 raise PredictionImpossible('User and item are unkown.')             # <<<<<<<<<<<<<<
 * 
 *         return est
 */
  __pyx_tuple_ = PyTuple_Pack(1, __pyx_kp_u_User_and_item_are_unkown); if (unlikely(!__pyx_tuple_)) __PYX_ERR(0, 255, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple_);
  __Pyx_GIVEREF(__pyx_tuple_);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":551
 * 
 *         if self.init_low < 0:
 *             raise ValueError('init_low should be greater than zero')             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.__init__(self)
 */
  __pyx_tuple__2 = PyTuple_Pack(1, __pyx_kp_u_init_low_should_be_greater_than); if (unlikely(!__pyx_tuple__2)) __PYX_ERR(0, 551, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__2);
  __Pyx_GIVEREF(__pyx_tuple__2);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":672
 *                 est = np.dot(self.qi[i], self.pu[u])
 *             else:
 *                 raise PredictionImpossible('User and item are unkown.')             # <<<<<<<<<<<<<<
 * 
 *         return est
 */
  __pyx_tuple__3 = PyTuple_Pack(1, __pyx_kp_u_User_and_item_are_unkown); if (unlikely(!__pyx_tuple__3)) __PYX_ERR(0, 672, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__3);
  __Pyx_GIVEREF(__pyx_tuple__3);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":235
 *             if ((flags & pybuf.PyBUF_C_CONTIGUOUS == pybuf.PyBUF_C_CONTIGUOUS)
 *                 and not PyArray_CHKFLAGS(self, NPY_C_CONTIGUOUS)):
 *                 raise ValueError(u"ndarray is not C contiguous")             # <<<<<<<<<<<<<<
 * 
 *             if ((flags & pybuf.PyBUF_F_CONTIGUOUS == pybuf.PyBUF_F_CONTIGUOUS)
 */
  __pyx_tuple__4 = PyTuple_Pack(1, __pyx_kp_u_ndarray_is_not_C_contiguous); if (unlikely(!__pyx_tuple__4)) __PYX_ERR(1, 235, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__4);
  __Pyx_GIVEREF(__pyx_tuple__4);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":239
 *             if ((flags & pybuf.PyBUF_F_CONTIGUOUS == pybuf.PyBUF_F_CONTIGUOUS)
 *                 and not PyArray_CHKFLAGS(self, NPY_F_CONTIGUOUS)):
 *                 raise ValueError(u"ndarray is not Fortran contiguous")             # <<<<<<<<<<<<<<
 * 
 *             info.buf = PyArray_DATA(self)
 */
  __pyx_tuple__5 = PyTuple_Pack(1, __pyx_kp_u_ndarray_is_not_Fortran_contiguou); if (unlikely(!__pyx_tuple__5)) __PYX_ERR(1, 239, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__5);
  __Pyx_GIVEREF(__pyx_tuple__5);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":276
 *                 if ((descr.byteorder == c'>' and little_endian) or
 *                     (descr.byteorder == c'<' and not little_endian)):
 *                     raise ValueError(u"Non-native byte order not supported")             # <<<<<<<<<<<<<<
 *                 if   t == NPY_BYTE:        f = "b"
 *                 elif t == NPY_UBYTE:       f = "B"
 */
  __pyx_tuple__6 = PyTuple_Pack(1, __pyx_kp_u_Non_native_byte_order_not_suppor); if (unlikely(!__pyx_tuple__6)) __PYX_ERR(1, 276, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__6);
  __Pyx_GIVEREF(__pyx_tuple__6);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":823
 * 
 *         if (end - f) - <int>(new_offset - offset[0]) < 15:
 *             raise RuntimeError(u"Format string allocated too short, see comment in numpy.pxd")             # <<<<<<<<<<<<<<
 * 
 *         if ((child.byteorder == c'>' and little_endian) or
 */
  __pyx_tuple__7 = PyTuple_Pack(1, __pyx_kp_u_Format_string_allocated_too_shor); if (unlikely(!__pyx_tuple__7)) __PYX_ERR(1, 823, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__7);
  __Pyx_GIVEREF(__pyx_tuple__7);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":827
 *         if ((child.byteorder == c'>' and little_endian) or
 *             (child.byteorder == c'<' and not little_endian)):
 *             raise ValueError(u"Non-native byte order not supported")             # <<<<<<<<<<<<<<
 *             # One could encode it in the format string and have Cython
 *             # complain instead, BUT: < and > in format strings also imply
 */
  __pyx_tuple__8 = PyTuple_Pack(1, __pyx_kp_u_Non_native_byte_order_not_suppor); if (unlikely(!__pyx_tuple__8)) __PYX_ERR(1, 827, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__8);
  __Pyx_GIVEREF(__pyx_tuple__8);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":847
 *             t = child.type_num
 *             if end - f < 5:
 *                 raise RuntimeError(u"Format string allocated too short.")             # <<<<<<<<<<<<<<
 * 
 *             # Until ticket #99 is fixed, use integers to avoid warnings
 */
  __pyx_tuple__9 = PyTuple_Pack(1, __pyx_kp_u_Format_string_allocated_too_shor_2); if (unlikely(!__pyx_tuple__9)) __PYX_ERR(1, 847, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__9);
  __Pyx_GIVEREF(__pyx_tuple__9);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1013
 *         _import_array()
 *     except Exception:
 *         raise ImportError("numpy.core.multiarray failed to import")             # <<<<<<<<<<<<<<
 * 
 * cdef inline int import_umath() except -1:
 */
  __pyx_tuple__10 = PyTuple_Pack(1, __pyx_kp_u_numpy_core_multiarray_failed_to); if (unlikely(!__pyx_tuple__10)) __PYX_ERR(1, 1013, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__10);
  __Pyx_GIVEREF(__pyx_tuple__10);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1019
 *         _import_umath()
 *     except Exception:
 *         raise ImportError("numpy.core.umath failed to import")             # <<<<<<<<<<<<<<
 * 
 * cdef inline int import_ufunc() except -1:
 */
  __pyx_tuple__11 = PyTuple_Pack(1, __pyx_kp_u_numpy_core_umath_failed_to_impor); if (unlikely(!__pyx_tuple__11)) __PYX_ERR(1, 1019, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__11);
  __Pyx_GIVEREF(__pyx_tuple__11);

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1025
 *         _import_umath()
 *     except Exception:
 *         raise ImportError("numpy.core.umath failed to import")             # <<<<<<<<<<<<<<
 */
  __pyx_tuple__12 = PyTuple_Pack(1, __pyx_kp_u_numpy_core_umath_failed_to_impor); if (unlikely(!__pyx_tuple__12)) __PYX_ERR(1, 1025, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__12);
  __Pyx_GIVEREF(__pyx_tuple__12);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":110
 *     """
 * 
 *     def __init__(self, n_factors=100, n_epochs=20, biased=True, init_mean=0,             # <<<<<<<<<<<<<<
 *                  init_std_dev=.1, lr_all=.005,
 *                  reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None, lr_qi=None,
 */
  __pyx_tuple__13 = PyTuple_Pack(17, __pyx_n_s_self, __pyx_n_s_n_factors, __pyx_n_s_n_epochs, __pyx_n_s_biased, __pyx_n_s_init_mean, __pyx_n_s_init_std_dev, __pyx_n_s_lr_all, __pyx_n_s_reg_all, __pyx_n_s_lr_bu, __pyx_n_s_lr_bi, __pyx_n_s_lr_pu, __pyx_n_s_lr_qi, __pyx_n_s_reg_bu, __pyx_n_s_reg_bi, __pyx_n_s_reg_pu, __pyx_n_s_reg_qi, __pyx_n_s_verbose); if (unlikely(!__pyx_tuple__13)) __PYX_ERR(0, 110, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__13);
  __Pyx_GIVEREF(__pyx_tuple__13);
  __pyx_codeobj__14 = (PyObject*)__Pyx_PyCode_New(17, 0, 17, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__13, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_surprise_prediction_algorithms_m_2, __pyx_n_s_init, 110, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__14)) __PYX_ERR(0, 110, __pyx_L1_error)
  __pyx_tuple__15 = PyTuple_Pack(16, ((PyObject *)__pyx_int_100), ((PyObject *)__pyx_int_20), ((PyObject *)Py_True), ((PyObject *)__pyx_int_0), ((PyObject*)__pyx_float__1), ((PyObject*)__pyx_float__005), ((PyObject*)__pyx_float__02), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_False)); if (unlikely(!__pyx_tuple__15)) __PYX_ERR(0, 110, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__15);
  __Pyx_GIVEREF(__pyx_tuple__15);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":133
 *         AlgoBase.__init__(self)
 * 
 *     def train(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.train(self, trainset)
 */
  __pyx_tuple__16 = PyTuple_Pack(2, __pyx_n_s_self, __pyx_n_s_trainset); if (unlikely(!__pyx_tuple__16)) __PYX_ERR(0, 133, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__16);
  __Pyx_GIVEREF(__pyx_tuple__16);
  __pyx_codeobj__17 = (PyObject*)__Pyx_PyCode_New(2, 0, 2, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__16, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_surprise_prediction_algorithms_m_2, __pyx_n_s_train, 133, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__17)) __PYX_ERR(0, 133, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":138
 *         self.sgd(trainset)
 * 
 *     def sgd(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         # OK, let's breath. I've seen so many different implementation of this
 */
  __pyx_tuple__18 = PyTuple_Pack(24, __pyx_n_s_self, __pyx_n_s_trainset, __pyx_n_s_bu, __pyx_n_s_bi, __pyx_n_s_pu, __pyx_n_s_qi, __pyx_n_s_u, __pyx_n_s_i, __pyx_n_s_f, __pyx_n_s_r, __pyx_n_s_err, __pyx_n_s_dot, __pyx_n_s_puf, __pyx_n_s_qif, __pyx_n_s_global_mean, __pyx_n_s_lr_bu, __pyx_n_s_lr_bi, __pyx_n_s_lr_pu, __pyx_n_s_lr_qi, __pyx_n_s_reg_bu, __pyx_n_s_reg_bi, __pyx_n_s_reg_pu, __pyx_n_s_reg_qi, __pyx_n_s_current_epoch); if (unlikely(!__pyx_tuple__18)) __PYX_ERR(0, 138, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__18);
  __Pyx_GIVEREF(__pyx_tuple__18);
  __pyx_codeobj__19 = (PyObject*)__Pyx_PyCode_New(2, 0, 24, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__18, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_surprise_prediction_algorithms_m_2, __pyx_n_s_sgd, 138, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__19)) __PYX_ERR(0, 138, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":233
 *         self.qi = qi
 * 
 *     def estimate(self, u, i):             # <<<<<<<<<<<<<<
 *         # Should we cythonize this as well?
 * 
 */
  __pyx_tuple__20 = PyTuple_Pack(6, __pyx_n_s_self, __pyx_n_s_u, __pyx_n_s_i, __pyx_n_s_known_user, __pyx_n_s_known_item, __pyx_n_s_est); if (unlikely(!__pyx_tuple__20)) __PYX_ERR(0, 233, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__20);
  __Pyx_GIVEREF(__pyx_tuple__20);
  __pyx_codeobj__21 = (PyObject*)__Pyx_PyCode_New(3, 0, 6, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__20, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_surprise_prediction_algorithms_m_2, __pyx_n_s_estimate, 233, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__21)) __PYX_ERR(0, 233, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":328
 *     """
 * 
 *     def __init__(self, n_factors=20, n_epochs=20, init_mean=0, init_std_dev=.1,             # <<<<<<<<<<<<<<
 *                  lr_all=.007, reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None,
 *                  lr_qi=None, lr_yj=None, reg_bu=None, reg_bi=None, reg_pu=None,
 */
  __pyx_tuple__22 = PyTuple_Pack(18, __pyx_n_s_self, __pyx_n_s_n_factors, __pyx_n_s_n_epochs, __pyx_n_s_init_mean, __pyx_n_s_init_std_dev, __pyx_n_s_lr_all, __pyx_n_s_reg_all, __pyx_n_s_lr_bu, __pyx_n_s_lr_bi, __pyx_n_s_lr_pu, __pyx_n_s_lr_qi, __pyx_n_s_lr_yj, __pyx_n_s_reg_bu, __pyx_n_s_reg_bi, __pyx_n_s_reg_pu, __pyx_n_s_reg_qi, __pyx_n_s_reg_yj, __pyx_n_s_verbose); if (unlikely(!__pyx_tuple__22)) __PYX_ERR(0, 328, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__22);
  __Pyx_GIVEREF(__pyx_tuple__22);
  __pyx_codeobj__23 = (PyObject*)__Pyx_PyCode_New(18, 0, 18, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__22, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_surprise_prediction_algorithms_m_2, __pyx_n_s_init, 328, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__23)) __PYX_ERR(0, 328, __pyx_L1_error)
  __pyx_tuple__24 = PyTuple_Pack(17, ((PyObject *)__pyx_int_20), ((PyObject *)__pyx_int_20), ((PyObject *)__pyx_int_0), ((PyObject*)__pyx_float__1), ((PyObject*)__pyx_float__007), ((PyObject*)__pyx_float__02), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_None), ((PyObject *)Py_False)); if (unlikely(!__pyx_tuple__24)) __PYX_ERR(0, 328, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__24);
  __Pyx_GIVEREF(__pyx_tuple__24);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":351
 *         AlgoBase.__init__(self)
 * 
 *     def train(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.train(self, trainset)
 */
  __pyx_tuple__25 = PyTuple_Pack(2, __pyx_n_s_self, __pyx_n_s_trainset); if (unlikely(!__pyx_tuple__25)) __PYX_ERR(0, 351, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__25);
  __Pyx_GIVEREF(__pyx_tuple__25);
  __pyx_codeobj__26 = (PyObject*)__Pyx_PyCode_New(2, 0, 2, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__25, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_surprise_prediction_algorithms_m_2, __pyx_n_s_train, 351, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__26)) __PYX_ERR(0, 351, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":356
 *         self.sgd(trainset)
 * 
 *     def sgd(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         # user biases
 */
  __pyx_tuple__28 = PyTuple_Pack(32, __pyx_n_s_self, __pyx_n_s_trainset, __pyx_n_s_bu, __pyx_n_s_bi, __pyx_n_s_pu, __pyx_n_s_qi, __pyx_n_s_yj, __pyx_n_s_u, __pyx_n_s_i, __pyx_n_s_j, __pyx_n_s_f, __pyx_n_s_r, __pyx_n_s_err, __pyx_n_s_dot, __pyx_n_s_puf, __pyx_n_s_qif, __pyx_n_s_sqrt_Iu, __pyx_n_s__27, __pyx_n_s_global_mean, __pyx_n_s_u_impl_fdb, __pyx_n_s_lr_bu, __pyx_n_s_lr_bi, __pyx_n_s_lr_pu, __pyx_n_s_lr_qi, __pyx_n_s_lr_yj, __pyx_n_s_reg_bu, __pyx_n_s_reg_bi, __pyx_n_s_reg_pu, __pyx_n_s_reg_qi, __pyx_n_s_reg_yj, __pyx_n_s_current_epoch, __pyx_n_s_Iu); if (unlikely(!__pyx_tuple__28)) __PYX_ERR(0, 356, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__28);
  __Pyx_GIVEREF(__pyx_tuple__28);
  __pyx_codeobj__29 = (PyObject*)__Pyx_PyCode_New(2, 0, 32, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__28, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_surprise_prediction_algorithms_m_2, __pyx_n_s_sgd, 356, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__29)) __PYX_ERR(0, 356, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":440
 *         self.yj = yj
 * 
 *     def estimate(self, u, i):             # <<<<<<<<<<<<<<
 * 
 *         est = self.trainset.global_mean
 */
  __pyx_tuple__30 = PyTuple_Pack(8, __pyx_n_s_self, __pyx_n_s_u, __pyx_n_s_i, __pyx_n_s_est, __pyx_n_s_Iu, __pyx_n_s_u_impl_feedback, __pyx_n_s_genexpr, __pyx_n_s_genexpr); if (unlikely(!__pyx_tuple__30)) __PYX_ERR(0, 440, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__30);
  __Pyx_GIVEREF(__pyx_tuple__30);
  __pyx_codeobj__31 = (PyObject*)__Pyx_PyCode_New(3, 0, 8, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__30, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_surprise_prediction_algorithms_m_2, __pyx_n_s_estimate, 440, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__31)) __PYX_ERR(0, 440, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":533
 *     """
 * 
 *     def __init__(self, n_factors=15, n_epochs=50, biased=False, reg_pu=.06,             # <<<<<<<<<<<<<<
 *                  reg_qi=.06, reg_bu=.02, reg_bi=.02, lr_bu=.005, lr_bi=.005,
 *                  init_low=0, init_high=1, verbose=False):
 */
  __pyx_tuple__32 = PyTuple_Pack(13, __pyx_n_s_self, __pyx_n_s_n_factors, __pyx_n_s_n_epochs, __pyx_n_s_biased, __pyx_n_s_reg_pu, __pyx_n_s_reg_qi, __pyx_n_s_reg_bu, __pyx_n_s_reg_bi, __pyx_n_s_lr_bu, __pyx_n_s_lr_bi, __pyx_n_s_init_low, __pyx_n_s_init_high, __pyx_n_s_verbose); if (unlikely(!__pyx_tuple__32)) __PYX_ERR(0, 533, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__32);
  __Pyx_GIVEREF(__pyx_tuple__32);
  __pyx_codeobj__33 = (PyObject*)__Pyx_PyCode_New(13, 0, 13, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__32, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_surprise_prediction_algorithms_m_2, __pyx_n_s_init, 533, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__33)) __PYX_ERR(0, 533, __pyx_L1_error)
  __pyx_tuple__34 = PyTuple_Pack(12, ((PyObject *)__pyx_int_15), ((PyObject *)__pyx_int_50), ((PyObject *)Py_False), ((PyObject*)__pyx_float__06), ((PyObject*)__pyx_float__06), ((PyObject*)__pyx_float__02), ((PyObject*)__pyx_float__02), ((PyObject*)__pyx_float__005), ((PyObject*)__pyx_float__005), ((PyObject *)__pyx_int_0), ((PyObject *)__pyx_int_1), ((PyObject *)Py_False)); if (unlikely(!__pyx_tuple__34)) __PYX_ERR(0, 533, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__34);
  __Pyx_GIVEREF(__pyx_tuple__34);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":555
 *         AlgoBase.__init__(self)
 * 
 *     def train(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.train(self, trainset)
 */
  __pyx_tuple__35 = PyTuple_Pack(2, __pyx_n_s_self, __pyx_n_s_trainset); if (unlikely(!__pyx_tuple__35)) __PYX_ERR(0, 555, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__35);
  __Pyx_GIVEREF(__pyx_tuple__35);
  __pyx_codeobj__36 = (PyObject*)__Pyx_PyCode_New(2, 0, 2, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__35, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_surprise_prediction_algorithms_m_2, __pyx_n_s_train, 555, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__36)) __PYX_ERR(0, 555, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":560
 *         self.sgd(trainset)
 * 
 *     def sgd(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         # user and item factors
 */
  __pyx_tuple__37 = PyTuple_Pack(26, __pyx_n_s_self, __pyx_n_s_trainset, __pyx_n_s_pu, __pyx_n_s_qi, __pyx_n_s_bu, __pyx_n_s_bi, __pyx_n_s_user_num, __pyx_n_s_user_denom, __pyx_n_s_item_num, __pyx_n_s_item_denom, __pyx_n_s_u, __pyx_n_s_i, __pyx_n_s_f, __pyx_n_s_r, __pyx_n_s_est, __pyx_n_s_l, __pyx_n_s_dot, __pyx_n_s_err, __pyx_n_s_reg_pu, __pyx_n_s_reg_qi, __pyx_n_s_reg_bu, __pyx_n_s_reg_bi, __pyx_n_s_lr_bu, __pyx_n_s_lr_bi, __pyx_n_s_global_mean, __pyx_n_s_current_epoch); if (unlikely(!__pyx_tuple__37)) __PYX_ERR(0, 560, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__37);
  __Pyx_GIVEREF(__pyx_tuple__37);
  __pyx_codeobj__38 = (PyObject*)__Pyx_PyCode_New(2, 0, 26, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__37, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_surprise_prediction_algorithms_m_2, __pyx_n_s_sgd, 560, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__38)) __PYX_ERR(0, 560, __pyx_L1_error)

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":650
 *         self.qi = qi
 * 
 *     def estimate(self, u, i):             # <<<<<<<<<<<<<<
 *         # Should we cythonize this as well?
 * 
 */
  __pyx_tuple__39 = PyTuple_Pack(6, __pyx_n_s_self, __pyx_n_s_u, __pyx_n_s_i, __pyx_n_s_known_user, __pyx_n_s_known_item, __pyx_n_s_est); if (unlikely(!__pyx_tuple__39)) __PYX_ERR(0, 650, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_tuple__39);
  __Pyx_GIVEREF(__pyx_tuple__39);
  __pyx_codeobj__40 = (PyObject*)__Pyx_PyCode_New(3, 0, 6, 0, CO_OPTIMIZED|CO_NEWLOCALS, __pyx_empty_bytes, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_tuple__39, __pyx_empty_tuple, __pyx_empty_tuple, __pyx_kp_s_surprise_prediction_algorithms_m_2, __pyx_n_s_estimate, 650, __pyx_empty_bytes); if (unlikely(!__pyx_codeobj__40)) __PYX_ERR(0, 650, __pyx_L1_error)
  __Pyx_RefNannyFinishContext();
  return 0;
  __pyx_L1_error:;
  __Pyx_RefNannyFinishContext();
  return -1;
}

static int __Pyx_InitGlobals(void) {
  if (__Pyx_InitStrings(__pyx_string_tab) < 0) __PYX_ERR(0, 1, __pyx_L1_error);
  __pyx_float__1 = PyFloat_FromDouble(.1); if (unlikely(!__pyx_float__1)) __PYX_ERR(0, 1, __pyx_L1_error)
  __pyx_float__02 = PyFloat_FromDouble(.02); if (unlikely(!__pyx_float__02)) __PYX_ERR(0, 1, __pyx_L1_error)
  __pyx_float__06 = PyFloat_FromDouble(.06); if (unlikely(!__pyx_float__06)) __PYX_ERR(0, 1, __pyx_L1_error)
  __pyx_float__005 = PyFloat_FromDouble(.005); if (unlikely(!__pyx_float__005)) __PYX_ERR(0, 1, __pyx_L1_error)
  __pyx_float__007 = PyFloat_FromDouble(.007); if (unlikely(!__pyx_float__007)) __PYX_ERR(0, 1, __pyx_L1_error)
  __pyx_int_0 = PyInt_FromLong(0); if (unlikely(!__pyx_int_0)) __PYX_ERR(0, 1, __pyx_L1_error)
  __pyx_int_1 = PyInt_FromLong(1); if (unlikely(!__pyx_int_1)) __PYX_ERR(0, 1, __pyx_L1_error)
  __pyx_int_15 = PyInt_FromLong(15); if (unlikely(!__pyx_int_15)) __PYX_ERR(0, 1, __pyx_L1_error)
  __pyx_int_20 = PyInt_FromLong(20); if (unlikely(!__pyx_int_20)) __PYX_ERR(0, 1, __pyx_L1_error)
  __pyx_int_50 = PyInt_FromLong(50); if (unlikely(!__pyx_int_50)) __PYX_ERR(0, 1, __pyx_L1_error)
  __pyx_int_100 = PyInt_FromLong(100); if (unlikely(!__pyx_int_100)) __PYX_ERR(0, 1, __pyx_L1_error)
  return 0;
  __pyx_L1_error:;
  return -1;
}

#if PY_MAJOR_VERSION < 3
PyMODINIT_FUNC initmatrix_factorization(void); /*proto*/
PyMODINIT_FUNC initmatrix_factorization(void)
#else
PyMODINIT_FUNC PyInit_matrix_factorization(void); /*proto*/
PyMODINIT_FUNC PyInit_matrix_factorization(void)
#if CYTHON_PEP489_MULTI_PHASE_INIT
{
  return PyModuleDef_Init(&__pyx_moduledef);
}
static int __Pyx_copy_spec_to_module(PyObject *spec, PyObject *moddict, const char* from_name, const char* to_name) {
    PyObject *value = PyObject_GetAttrString(spec, from_name);
    int result = 0;
    if (likely(value)) {
        result = PyDict_SetItemString(moddict, to_name, value);
        Py_DECREF(value);
    } else if (PyErr_ExceptionMatches(PyExc_AttributeError)) {
        PyErr_Clear();
    } else {
        result = -1;
    }
    return result;
}
static PyObject* __pyx_pymod_create(PyObject *spec, CYTHON_UNUSED PyModuleDef *def) {
    PyObject *module = NULL, *moddict, *modname;
    modname = PyObject_GetAttrString(spec, "name");
    if (unlikely(!modname)) goto bad;
    module = PyModule_NewObject(modname);
    Py_DECREF(modname);
    if (unlikely(!module)) goto bad;
    moddict = PyModule_GetDict(module);
    if (unlikely(!moddict)) goto bad;
    if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "loader", "__loader__") < 0)) goto bad;
    if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "origin", "__file__") < 0)) goto bad;
    if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "parent", "__package__") < 0)) goto bad;
    if (unlikely(__Pyx_copy_spec_to_module(spec, moddict, "submodule_search_locations", "__path__") < 0)) goto bad;
    return module;
bad:
    Py_XDECREF(module);
    return NULL;
}


static int __pyx_pymod_exec_matrix_factorization(PyObject *__pyx_pyinit_module)
#endif
#endif
{
  PyObject *__pyx_t_1 = NULL;
  PyObject *__pyx_t_2 = NULL;
  PyObject *__pyx_t_3 = NULL;
  PyObject *__pyx_t_4 = NULL;
  __Pyx_RefNannyDeclarations
  #if CYTHON_REFNANNY
  __Pyx_RefNanny = __Pyx_RefNannyImportAPI("refnanny");
  if (!__Pyx_RefNanny) {
      PyErr_Clear();
      __Pyx_RefNanny = __Pyx_RefNannyImportAPI("Cython.Runtime.refnanny");
      if (!__Pyx_RefNanny)
          Py_FatalError("failed to import 'refnanny' module");
  }
  #endif
  __Pyx_RefNannySetupContext("PyMODINIT_FUNC PyInit_matrix_factorization(void)", 0);
  if (__Pyx_check_binary_version() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
  __pyx_empty_tuple = PyTuple_New(0); if (unlikely(!__pyx_empty_tuple)) __PYX_ERR(0, 1, __pyx_L1_error)
  __pyx_empty_bytes = PyBytes_FromStringAndSize("", 0); if (unlikely(!__pyx_empty_bytes)) __PYX_ERR(0, 1, __pyx_L1_error)
  __pyx_empty_unicode = PyUnicode_FromStringAndSize("", 0); if (unlikely(!__pyx_empty_unicode)) __PYX_ERR(0, 1, __pyx_L1_error)
  #ifdef __Pyx_CyFunction_USED
  if (__pyx_CyFunction_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
  #endif
  #ifdef __Pyx_FusedFunction_USED
  if (__pyx_FusedFunction_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
  #endif
  #ifdef __Pyx_Coroutine_USED
  if (__pyx_Coroutine_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
  #endif
  #ifdef __Pyx_Generator_USED
  if (__pyx_Generator_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
  #endif
  #ifdef __Pyx_AsyncGen_USED
  if (__pyx_AsyncGen_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
  #endif
  #ifdef __Pyx_StopAsyncIteration_USED
  if (__pyx_StopAsyncIteration_init() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
  #endif
  /*--- Library function declarations ---*/
  /*--- Threads initialization code ---*/
  #if defined(__PYX_FORCE_INIT_THREADS) && __PYX_FORCE_INIT_THREADS
  #ifdef WITH_THREAD /* Python build with threading support? */
  PyEval_InitThreads();
  #endif
  #endif
  /*--- Module creation code ---*/
  #if CYTHON_PEP489_MULTI_PHASE_INIT
  __pyx_m = __pyx_pyinit_module;
  Py_INCREF(__pyx_m);
  #else
  #if PY_MAJOR_VERSION < 3
  __pyx_m = Py_InitModule4("matrix_factorization", __pyx_methods, __pyx_k_the_mod_matrix_factorization_mo, 0, PYTHON_API_VERSION); Py_XINCREF(__pyx_m);
  #else
  __pyx_m = PyModule_Create(&__pyx_moduledef);
  #endif
  if (unlikely(!__pyx_m)) __PYX_ERR(0, 1, __pyx_L1_error)
  #endif
  __pyx_d = PyModule_GetDict(__pyx_m); if (unlikely(!__pyx_d)) __PYX_ERR(0, 1, __pyx_L1_error)
  Py_INCREF(__pyx_d);
  __pyx_b = PyImport_AddModule(__Pyx_BUILTIN_MODULE_NAME); if (unlikely(!__pyx_b)) __PYX_ERR(0, 1, __pyx_L1_error)
  __pyx_cython_runtime = PyImport_AddModule((char *) "cython_runtime"); if (unlikely(!__pyx_cython_runtime)) __PYX_ERR(0, 1, __pyx_L1_error)
  #if CYTHON_COMPILING_IN_PYPY
  Py_INCREF(__pyx_b);
  #endif
  if (PyObject_SetAttrString(__pyx_m, "__builtins__", __pyx_b) < 0) __PYX_ERR(0, 1, __pyx_L1_error);
  /*--- Initialize various global constants etc. ---*/
  if (__Pyx_InitGlobals() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
  #if PY_MAJOR_VERSION < 3 && (__PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT)
  if (__Pyx_init_sys_getdefaultencoding_params() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
  #endif
  if (__pyx_module_is_main_surprise__prediction_algorithms__matrix_factorization) {
    if (PyObject_SetAttrString(__pyx_m, "__name__", __pyx_n_s_main) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
  }
  #if PY_MAJOR_VERSION >= 3
  {
    PyObject *modules = PyImport_GetModuleDict(); if (unlikely(!modules)) __PYX_ERR(0, 1, __pyx_L1_error)
    if (!PyDict_GetItemString(modules, "surprise.prediction_algorithms.matrix_factorization")) {
      if (unlikely(PyDict_SetItemString(modules, "surprise.prediction_algorithms.matrix_factorization", __pyx_m) < 0)) __PYX_ERR(0, 1, __pyx_L1_error)
    }
  }
  #endif
  /*--- Builtin init code ---*/
  if (__Pyx_InitCachedBuiltins() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
  /*--- Constants init code ---*/
  if (__Pyx_InitCachedConstants() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
  /*--- Global init code ---*/
  /*--- Variable export code ---*/
  /*--- Function export code ---*/
  /*--- Type init code ---*/
  if (PyType_Ready(&__pyx_type_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate) < 0) __PYX_ERR(0, 440, __pyx_L1_error)
  __pyx_type_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate.tp_print = 0;
  __pyx_ptype_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate = &__pyx_type_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct__estimate;
  if (PyType_Ready(&__pyx_type_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr) < 0) __PYX_ERR(0, 452, __pyx_L1_error)
  __pyx_type_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr.tp_print = 0;
  __pyx_ptype_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr = &__pyx_type_8surprise_21prediction_algorithms_20matrix_factorization___pyx_scope_struct_1_genexpr;
  /*--- Type import code ---*/
  __pyx_ptype_7cpython_4type_type = __Pyx_ImportType(__Pyx_BUILTIN_MODULE_NAME, "type", 
  #if CYTHON_COMPILING_IN_PYPY
  sizeof(PyTypeObject),
  #else
  sizeof(PyHeapTypeObject),
  #endif
  0); if (unlikely(!__pyx_ptype_7cpython_4type_type)) __PYX_ERR(2, 9, __pyx_L1_error)
  __pyx_ptype_5numpy_dtype = __Pyx_ImportType("numpy", "dtype", sizeof(PyArray_Descr), 0); if (unlikely(!__pyx_ptype_5numpy_dtype)) __PYX_ERR(1, 163, __pyx_L1_error)
  __pyx_ptype_5numpy_flatiter = __Pyx_ImportType("numpy", "flatiter", sizeof(PyArrayIterObject), 0); if (unlikely(!__pyx_ptype_5numpy_flatiter)) __PYX_ERR(1, 185, __pyx_L1_error)
  __pyx_ptype_5numpy_broadcast = __Pyx_ImportType("numpy", "broadcast", sizeof(PyArrayMultiIterObject), 0); if (unlikely(!__pyx_ptype_5numpy_broadcast)) __PYX_ERR(1, 189, __pyx_L1_error)
  __pyx_ptype_5numpy_ndarray = __Pyx_ImportType("numpy", "ndarray", sizeof(PyArrayObject), 0); if (unlikely(!__pyx_ptype_5numpy_ndarray)) __PYX_ERR(1, 198, __pyx_L1_error)
  __pyx_ptype_5numpy_ufunc = __Pyx_ImportType("numpy", "ufunc", sizeof(PyUFuncObject), 0); if (unlikely(!__pyx_ptype_5numpy_ufunc)) __PYX_ERR(1, 885, __pyx_L1_error)
  /*--- Variable import code ---*/
  /*--- Function import code ---*/
  /*--- Execution code ---*/
  #if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
  if (__Pyx_patch_abc() < 0) __PYX_ERR(0, 1, __pyx_L1_error)
  #endif

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":10
 * 
 * cimport numpy as np  # noqa
 * import numpy as np             # <<<<<<<<<<<<<<
 * from six.moves import range
 * 
 */
  __pyx_t_1 = __Pyx_Import(__pyx_n_s_numpy, 0, 0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 10, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  if (PyDict_SetItem(__pyx_d, __pyx_n_s_np, __pyx_t_1) < 0) __PYX_ERR(0, 10, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":11
 * cimport numpy as np  # noqa
 * import numpy as np
 * from six.moves import range             # <<<<<<<<<<<<<<
 * 
 * from .algo_base import AlgoBase
 */
  __pyx_t_1 = PyList_New(1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 11, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __Pyx_INCREF(__pyx_n_s_range);
  __Pyx_GIVEREF(__pyx_n_s_range);
  PyList_SET_ITEM(__pyx_t_1, 0, __pyx_n_s_range);
  __pyx_t_2 = __Pyx_Import(__pyx_n_s_six_moves, __pyx_t_1, 0); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 11, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_1 = __Pyx_ImportFrom(__pyx_t_2, __pyx_n_s_range); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 11, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  if (PyDict_SetItem(__pyx_d, __pyx_n_s_range, __pyx_t_1) < 0) __PYX_ERR(0, 11, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":13
 * from six.moves import range
 * 
 * from .algo_base import AlgoBase             # <<<<<<<<<<<<<<
 * from .predictions import PredictionImpossible
 * 
 */
  __pyx_t_2 = PyList_New(1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 13, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __Pyx_INCREF(__pyx_n_s_AlgoBase);
  __Pyx_GIVEREF(__pyx_n_s_AlgoBase);
  PyList_SET_ITEM(__pyx_t_2, 0, __pyx_n_s_AlgoBase);
  __pyx_t_1 = __Pyx_Import(__pyx_n_s_algo_base, __pyx_t_2, 1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 13, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_t_2 = __Pyx_ImportFrom(__pyx_t_1, __pyx_n_s_AlgoBase); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 13, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  if (PyDict_SetItem(__pyx_d, __pyx_n_s_AlgoBase, __pyx_t_2) < 0) __PYX_ERR(0, 13, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":14
 * 
 * from .algo_base import AlgoBase
 * from .predictions import PredictionImpossible             # <<<<<<<<<<<<<<
 * 
 * 
 */
  __pyx_t_1 = PyList_New(1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 14, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __Pyx_INCREF(__pyx_n_s_PredictionImpossible);
  __Pyx_GIVEREF(__pyx_n_s_PredictionImpossible);
  PyList_SET_ITEM(__pyx_t_1, 0, __pyx_n_s_PredictionImpossible);
  __pyx_t_2 = __Pyx_Import(__pyx_n_s_predictions, __pyx_t_1, 1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 14, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_t_1 = __Pyx_ImportFrom(__pyx_t_2, __pyx_n_s_PredictionImpossible); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 14, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  if (PyDict_SetItem(__pyx_d, __pyx_n_s_PredictionImpossible, __pyx_t_1) < 0) __PYX_ERR(0, 14, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":17
 * 
 * 
 * class SVD(AlgoBase):             # <<<<<<<<<<<<<<
 *     """The famous *SVD* algorithm, as popularized by `Simon Funk
 *     <http://sifter.org/~simon/journal/20061211.html>`_ during the Netflix
 */
  __pyx_t_2 = __Pyx_GetModuleGlobalName(__pyx_n_s_AlgoBase); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 17, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_1 = PyTuple_New(1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 17, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __Pyx_GIVEREF(__pyx_t_2);
  PyTuple_SET_ITEM(__pyx_t_1, 0, __pyx_t_2);
  __pyx_t_2 = 0;
  __pyx_t_2 = __Pyx_CalculateMetaclass(NULL, __pyx_t_1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 17, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __Pyx_Py3MetaclassPrepare(__pyx_t_2, __pyx_t_1, __pyx_n_s_SVD, __pyx_n_s_SVD, (PyObject *) NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_kp_s_The_famous_SVD_algorithm_as_popu); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 17, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":110
 *     """
 * 
 *     def __init__(self, n_factors=100, n_epochs=20, biased=True, init_mean=0,             # <<<<<<<<<<<<<<
 *                  init_std_dev=.1, lr_all=.005,
 *                  reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None, lr_qi=None,
 */
  __pyx_t_4 = __Pyx_CyFunction_NewEx(&__pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_1__init__, 0, __pyx_n_s_SVD___init, NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_d, ((PyObject *)__pyx_codeobj__14)); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 110, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_CyFunction_SetDefaultsTuple(__pyx_t_4, __pyx_tuple__15);
  if (PyObject_SetItem(__pyx_t_3, __pyx_n_s_init, __pyx_t_4) < 0) __PYX_ERR(0, 110, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":133
 *         AlgoBase.__init__(self)
 * 
 *     def train(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.train(self, trainset)
 */
  __pyx_t_4 = __Pyx_CyFunction_NewEx(&__pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_3train, 0, __pyx_n_s_SVD_train, NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_d, ((PyObject *)__pyx_codeobj__17)); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 133, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  if (PyObject_SetItem(__pyx_t_3, __pyx_n_s_train, __pyx_t_4) < 0) __PYX_ERR(0, 133, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":138
 *         self.sgd(trainset)
 * 
 *     def sgd(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         # OK, let's breath. I've seen so many different implementation of this
 */
  __pyx_t_4 = __Pyx_CyFunction_NewEx(&__pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_5sgd, 0, __pyx_n_s_SVD_sgd, NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_d, ((PyObject *)__pyx_codeobj__19)); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 138, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  if (PyObject_SetItem(__pyx_t_3, __pyx_n_s_sgd, __pyx_t_4) < 0) __PYX_ERR(0, 138, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":233
 *         self.qi = qi
 * 
 *     def estimate(self, u, i):             # <<<<<<<<<<<<<<
 *         # Should we cythonize this as well?
 * 
 */
  __pyx_t_4 = __Pyx_CyFunction_NewEx(&__pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3SVD_7estimate, 0, __pyx_n_s_SVD_estimate, NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_d, ((PyObject *)__pyx_codeobj__21)); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 233, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  if (PyObject_SetItem(__pyx_t_3, __pyx_n_s_estimate, __pyx_t_4) < 0) __PYX_ERR(0, 233, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":17
 * 
 * 
 * class SVD(AlgoBase):             # <<<<<<<<<<<<<<
 *     """The famous *SVD* algorithm, as popularized by `Simon Funk
 *     <http://sifter.org/~simon/journal/20061211.html>`_ during the Netflix
 */
  __pyx_t_4 = __Pyx_Py3ClassCreate(__pyx_t_2, __pyx_n_s_SVD, __pyx_t_1, __pyx_t_3, NULL, 0, 1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 17, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  if (PyDict_SetItem(__pyx_d, __pyx_n_s_SVD, __pyx_t_4) < 0) __PYX_ERR(0, 17, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":260
 * 
 * 
 * class SVDpp(AlgoBase):             # <<<<<<<<<<<<<<
 *     """The *SVD++* algorithm, an extension of :class:`SVD` taking into account
 *     implicit ratings.
 */
  __pyx_t_1 = __Pyx_GetModuleGlobalName(__pyx_n_s_AlgoBase); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 260, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_2 = PyTuple_New(1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 260, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __Pyx_GIVEREF(__pyx_t_1);
  PyTuple_SET_ITEM(__pyx_t_2, 0, __pyx_t_1);
  __pyx_t_1 = 0;
  __pyx_t_1 = __Pyx_CalculateMetaclass(NULL, __pyx_t_2); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 260, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __pyx_t_3 = __Pyx_Py3MetaclassPrepare(__pyx_t_1, __pyx_t_2, __pyx_n_s_SVDpp, __pyx_n_s_SVDpp, (PyObject *) NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_kp_s_The_SVD_algorithm_an_extension_o); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 260, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":328
 *     """
 * 
 *     def __init__(self, n_factors=20, n_epochs=20, init_mean=0, init_std_dev=.1,             # <<<<<<<<<<<<<<
 *                  lr_all=.007, reg_all=.02, lr_bu=None, lr_bi=None, lr_pu=None,
 *                  lr_qi=None, lr_yj=None, reg_bu=None, reg_bi=None, reg_pu=None,
 */
  __pyx_t_4 = __Pyx_CyFunction_NewEx(&__pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_1__init__, 0, __pyx_n_s_SVDpp___init, NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_d, ((PyObject *)__pyx_codeobj__23)); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 328, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_CyFunction_SetDefaultsTuple(__pyx_t_4, __pyx_tuple__24);
  if (PyObject_SetItem(__pyx_t_3, __pyx_n_s_init, __pyx_t_4) < 0) __PYX_ERR(0, 328, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":351
 *         AlgoBase.__init__(self)
 * 
 *     def train(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.train(self, trainset)
 */
  __pyx_t_4 = __Pyx_CyFunction_NewEx(&__pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_3train, 0, __pyx_n_s_SVDpp_train, NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_d, ((PyObject *)__pyx_codeobj__26)); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 351, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  if (PyObject_SetItem(__pyx_t_3, __pyx_n_s_train, __pyx_t_4) < 0) __PYX_ERR(0, 351, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":356
 *         self.sgd(trainset)
 * 
 *     def sgd(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         # user biases
 */
  __pyx_t_4 = __Pyx_CyFunction_NewEx(&__pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_5sgd, 0, __pyx_n_s_SVDpp_sgd, NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_d, ((PyObject *)__pyx_codeobj__29)); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 356, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  if (PyObject_SetItem(__pyx_t_3, __pyx_n_s_sgd, __pyx_t_4) < 0) __PYX_ERR(0, 356, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":440
 *         self.yj = yj
 * 
 *     def estimate(self, u, i):             # <<<<<<<<<<<<<<
 * 
 *         est = self.trainset.global_mean
 */
  __pyx_t_4 = __Pyx_CyFunction_NewEx(&__pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_5SVDpp_7estimate, 0, __pyx_n_s_SVDpp_estimate, NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_d, ((PyObject *)__pyx_codeobj__31)); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 440, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  if (PyObject_SetItem(__pyx_t_3, __pyx_n_s_estimate, __pyx_t_4) < 0) __PYX_ERR(0, 440, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":260
 * 
 * 
 * class SVDpp(AlgoBase):             # <<<<<<<<<<<<<<
 *     """The *SVD++* algorithm, an extension of :class:`SVD` taking into account
 *     implicit ratings.
 */
  __pyx_t_4 = __Pyx_Py3ClassCreate(__pyx_t_1, __pyx_n_s_SVDpp, __pyx_t_2, __pyx_t_3, NULL, 0, 1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 260, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  if (PyDict_SetItem(__pyx_d, __pyx_n_s_SVDpp, __pyx_t_4) < 0) __PYX_ERR(0, 260, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":459
 * 
 * 
 * class NMF(AlgoBase):             # <<<<<<<<<<<<<<
 *     """A collaborative filtering algorithm based on Non-negative Matrix
 *     Factorization.
 */
  __pyx_t_2 = __Pyx_GetModuleGlobalName(__pyx_n_s_AlgoBase); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 459, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_1 = PyTuple_New(1); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 459, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  __Pyx_GIVEREF(__pyx_t_2);
  PyTuple_SET_ITEM(__pyx_t_1, 0, __pyx_t_2);
  __pyx_t_2 = 0;
  __pyx_t_2 = __Pyx_CalculateMetaclass(NULL, __pyx_t_1); if (unlikely(!__pyx_t_2)) __PYX_ERR(0, 459, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_3 = __Pyx_Py3MetaclassPrepare(__pyx_t_2, __pyx_t_1, __pyx_n_s_NMF, __pyx_n_s_NMF, (PyObject *) NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_kp_s_A_collaborative_filtering_algori); if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 459, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_3);

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":533
 *     """
 * 
 *     def __init__(self, n_factors=15, n_epochs=50, biased=False, reg_pu=.06,             # <<<<<<<<<<<<<<
 *                  reg_qi=.06, reg_bu=.02, reg_bi=.02, lr_bu=.005, lr_bi=.005,
 *                  init_low=0, init_high=1, verbose=False):
 */
  __pyx_t_4 = __Pyx_CyFunction_NewEx(&__pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_1__init__, 0, __pyx_n_s_NMF___init, NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_d, ((PyObject *)__pyx_codeobj__33)); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 533, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  __Pyx_CyFunction_SetDefaultsTuple(__pyx_t_4, __pyx_tuple__34);
  if (PyObject_SetItem(__pyx_t_3, __pyx_n_s_init, __pyx_t_4) < 0) __PYX_ERR(0, 533, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":555
 *         AlgoBase.__init__(self)
 * 
 *     def train(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         AlgoBase.train(self, trainset)
 */
  __pyx_t_4 = __Pyx_CyFunction_NewEx(&__pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_3train, 0, __pyx_n_s_NMF_train, NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_d, ((PyObject *)__pyx_codeobj__36)); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 555, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  if (PyObject_SetItem(__pyx_t_3, __pyx_n_s_train, __pyx_t_4) < 0) __PYX_ERR(0, 555, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":560
 *         self.sgd(trainset)
 * 
 *     def sgd(self, trainset):             # <<<<<<<<<<<<<<
 * 
 *         # user and item factors
 */
  __pyx_t_4 = __Pyx_CyFunction_NewEx(&__pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_5sgd, 0, __pyx_n_s_NMF_sgd, NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_d, ((PyObject *)__pyx_codeobj__38)); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 560, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  if (PyObject_SetItem(__pyx_t_3, __pyx_n_s_sgd, __pyx_t_4) < 0) __PYX_ERR(0, 560, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":650
 *         self.qi = qi
 * 
 *     def estimate(self, u, i):             # <<<<<<<<<<<<<<
 *         # Should we cythonize this as well?
 * 
 */
  __pyx_t_4 = __Pyx_CyFunction_NewEx(&__pyx_mdef_8surprise_21prediction_algorithms_20matrix_factorization_3NMF_7estimate, 0, __pyx_n_s_NMF_estimate, NULL, __pyx_n_s_surprise_prediction_algorithms_m, __pyx_d, ((PyObject *)__pyx_codeobj__40)); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 650, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  if (PyObject_SetItem(__pyx_t_3, __pyx_n_s_estimate, __pyx_t_4) < 0) __PYX_ERR(0, 650, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":459
 * 
 * 
 * class NMF(AlgoBase):             # <<<<<<<<<<<<<<
 *     """A collaborative filtering algorithm based on Non-negative Matrix
 *     Factorization.
 */
  __pyx_t_4 = __Pyx_Py3ClassCreate(__pyx_t_2, __pyx_n_s_NMF, __pyx_t_1, __pyx_t_3, NULL, 0, 1); if (unlikely(!__pyx_t_4)) __PYX_ERR(0, 459, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_4);
  if (PyDict_SetItem(__pyx_d, __pyx_n_s_NMF, __pyx_t_4) < 0) __PYX_ERR(0, 459, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_4); __pyx_t_4 = 0;
  __Pyx_DECREF(__pyx_t_3); __pyx_t_3 = 0;
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "surprise/prediction_algorithms/matrix_factorization.pyx":1
 * """             # <<<<<<<<<<<<<<
 * the :mod:`matrix_factorization` module includes some algorithms using matrix
 * factorization.
 */
  __pyx_t_1 = __Pyx_PyDict_NewPresized(0); if (unlikely(!__pyx_t_1)) __PYX_ERR(0, 1, __pyx_L1_error)
  __Pyx_GOTREF(__pyx_t_1);
  if (PyDict_SetItem(__pyx_d, __pyx_n_s_test, __pyx_t_1) < 0) __PYX_ERR(0, 1, __pyx_L1_error)
  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;

  /* "../../.virtualenvs/tmp-29abb9dd64191e3/lib/python3.6/site-packages/Cython/Includes/numpy/__init__.pxd":1021
 *         raise ImportError("numpy.core.umath failed to import")
 * 
 * cdef inline int import_ufunc() except -1:             # <<<<<<<<<<<<<<
 *     try:
 *         _import_umath()
 */

  /*--- Wrapped vars code ---*/

  goto __pyx_L0;
  __pyx_L1_error:;
  __Pyx_XDECREF(__pyx_t_1);
  __Pyx_XDECREF(__pyx_t_2);
  __Pyx_XDECREF(__pyx_t_3);
  __Pyx_XDECREF(__pyx_t_4);
  if (__pyx_m) {
    if (__pyx_d) {
      __Pyx_AddTraceback("init surprise.prediction_algorithms.matrix_factorization", 0, __pyx_lineno, __pyx_filename);
    }
    Py_DECREF(__pyx_m); __pyx_m = 0;
  } else if (!PyErr_Occurred()) {
    PyErr_SetString(PyExc_ImportError, "init surprise.prediction_algorithms.matrix_factorization");
  }
  __pyx_L0:;
  __Pyx_RefNannyFinishContext();
  #if CYTHON_PEP489_MULTI_PHASE_INIT
  return (__pyx_m != NULL) ? 0 : -1;
  #elif PY_MAJOR_VERSION >= 3
  return __pyx_m;
  #else
  return;
  #endif
}

/* --- Runtime support code --- */
/* Refnanny */
#if CYTHON_REFNANNY
static __Pyx_RefNannyAPIStruct *__Pyx_RefNannyImportAPI(const char *modname) {
    PyObject *m = NULL, *p = NULL;
    void *r = NULL;
    m = PyImport_ImportModule((char *)modname);
    if (!m) goto end;
    p = PyObject_GetAttrString(m, (char *)"RefNannyAPI");
    if (!p) goto end;
    r = PyLong_AsVoidPtr(p);
end:
    Py_XDECREF(p);
    Py_XDECREF(m);
    return (__Pyx_RefNannyAPIStruct *)r;
}
#endif

/* GetBuiltinName */
static PyObject *__Pyx_GetBuiltinName(PyObject *name) {
    PyObject* result = __Pyx_PyObject_GetAttrStr(__pyx_b, name);
    if (unlikely(!result)) {
        PyErr_Format(PyExc_NameError,
#if PY_MAJOR_VERSION >= 3
            "name '%U' is not defined", name);
#else
            "name '%.200s' is not defined", PyString_AS_STRING(name));
#endif
    }
    return result;
}

/* RaiseDoubleKeywords */
static void __Pyx_RaiseDoubleKeywordsError(
    const char* func_name,
    PyObject* kw_name)
{
    PyErr_Format(PyExc_TypeError,
        #if PY_MAJOR_VERSION >= 3
        "%s() got multiple values for keyword argument '%U'", func_name, kw_name);
        #else
        "%s() got multiple values for keyword argument '%s'", func_name,
        PyString_AsString(kw_name));
        #endif
}

/* ParseKeywords */
static int __Pyx_ParseOptionalKeywords(
    PyObject *kwds,
    PyObject **argnames[],
    PyObject *kwds2,
    PyObject *values[],
    Py_ssize_t num_pos_args,
    const char* function_name)
{
    PyObject *key = 0, *value = 0;
    Py_ssize_t pos = 0;
    PyObject*** name;
    PyObject*** first_kw_arg = argnames + num_pos_args;
    while (PyDict_Next(kwds, &pos, &key, &value)) {
        name = first_kw_arg;
        while (*name && (**name != key)) name++;
        if (*name) {
            values[name-argnames] = value;
            continue;
        }
        name = first_kw_arg;
        #if PY_MAJOR_VERSION < 3
        if (likely(PyString_CheckExact(key)) || likely(PyString_Check(key))) {
            while (*name) {
                if ((CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**name) == PyString_GET_SIZE(key))
                        && _PyString_Eq(**name, key)) {
                    values[name-argnames] = value;
                    break;
                }
                name++;
            }
            if (*name) continue;
            else {
                PyObject*** argname = argnames;
                while (argname != first_kw_arg) {
                    if ((**argname == key) || (
                            (CYTHON_COMPILING_IN_PYPY || PyString_GET_SIZE(**argname) == PyString_GET_SIZE(key))
                             && _PyString_Eq(**argname, key))) {
                        goto arg_passed_twice;
                    }
                    argname++;
                }
            }
        } else
        #endif
        if (likely(PyUnicode_Check(key))) {
            while (*name) {
                int cmp = (**name == key) ? 0 :
                #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                    (PyUnicode_GET_SIZE(**name) != PyUnicode_GET_SIZE(key)) ? 1 :
                #endif
                    PyUnicode_Compare(**name, key);
                if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
                if (cmp == 0) {
                    values[name-argnames] = value;
                    break;
                }
                name++;
            }
            if (*name) continue;
            else {
                PyObject*** argname = argnames;
                while (argname != first_kw_arg) {
                    int cmp = (**argname == key) ? 0 :
                    #if !CYTHON_COMPILING_IN_PYPY && PY_MAJOR_VERSION >= 3
                        (PyUnicode_GET_SIZE(**argname) != PyUnicode_GET_SIZE(key)) ? 1 :
                    #endif
                        PyUnicode_Compare(**argname, key);
                    if (cmp < 0 && unlikely(PyErr_Occurred())) goto bad;
                    if (cmp == 0) goto arg_passed_twice;
                    argname++;
                }
            }
        } else
            goto invalid_keyword_type;
        if (kwds2) {
            if (unlikely(PyDict_SetItem(kwds2, key, value))) goto bad;
        } else {
            goto invalid_keyword;
        }
    }
    return 0;
arg_passed_twice:
    __Pyx_RaiseDoubleKeywordsError(function_name, key);
    goto bad;
invalid_keyword_type:
    PyErr_Format(PyExc_TypeError,
        "%.200s() keywords must be strings", function_name);
    goto bad;
invalid_keyword:
    PyErr_Format(PyExc_TypeError,
    #if PY_MAJOR_VERSION < 3
        "%.200s() got an unexpected keyword argument '%.200s'",
        function_name, PyString_AsString(key));
    #else
        "%s() got an unexpected keyword argument '%U'",
        function_name, key);
    #endif
bad:
    return -1;
}

/* RaiseArgTupleInvalid */
static void __Pyx_RaiseArgtupleInvalid(
    const char* func_name,
    int exact,
    Py_ssize_t num_min,
    Py_ssize_t num_max,
    Py_ssize_t num_found)
{
    Py_ssize_t num_expected;
    const char *more_or_less;
    if (num_found < num_min) {
        num_expected = num_min;
        more_or_less = "at least";
    } else {
        num_expected = num_max;
        more_or_less = "at most";
    }
    if (exact) {
        more_or_less = "exactly";
    }
    PyErr_Format(PyExc_TypeError,
                 "%.200s() takes %.8s %" CYTHON_FORMAT_SSIZE_T "d positional argument%.1s (%" CYTHON_FORMAT_SSIZE_T "d given)",
                 func_name, more_or_less, num_expected,
                 (num_expected == 1) ? "" : "s", num_found);
}

/* GetModuleGlobalName */
static CYTHON_INLINE PyObject *__Pyx_GetModuleGlobalName(PyObject *name) {
    PyObject *result;
#if !CYTHON_AVOID_BORROWED_REFS
    result = PyDict_GetItem(__pyx_d, name);
    if (likely(result)) {
        Py_INCREF(result);
    } else {
#else
    result = PyObject_GetItem(__pyx_d, name);
    if (!result) {
        PyErr_Clear();
#endif
        result = __Pyx_GetBuiltinName(name);
    }
    return result;
}

/* PyCFunctionFastCall */
  #if CYTHON_FAST_PYCCALL
static CYTHON_INLINE PyObject * __Pyx_PyCFunction_FastCall(PyObject *func_obj, PyObject **args, Py_ssize_t nargs) {
    PyCFunctionObject *func = (PyCFunctionObject*)func_obj;
    PyCFunction meth = PyCFunction_GET_FUNCTION(func);
    PyObject *self = PyCFunction_GET_SELF(func);
    int flags = PyCFunction_GET_FLAGS(func);
    assert(PyCFunction_Check(func));
    assert(METH_FASTCALL == (flags & ~(METH_CLASS | METH_STATIC | METH_COEXIST | METH_KEYWORDS)));
    assert(nargs >= 0);
    assert(nargs == 0 || args != NULL);
    /* _PyCFunction_FastCallDict() must not be called with an exception set,
       because it may clear it (directly or indirectly) and so the
       caller loses its exception */
    assert(!PyErr_Occurred());
    if ((PY_VERSION_HEX < 0x030700A0) || unlikely(flags & METH_KEYWORDS)) {
        return (*((__Pyx_PyCFunctionFastWithKeywords)meth)) (self, args, nargs, NULL);
    } else {
        return (*((__Pyx_PyCFunctionFast)meth)) (self, args, nargs);
    }
}
#endif

/* PyFunctionFastCall */
  #if CYTHON_FAST_PYCALL
#include "frameobject.h"
static PyObject* __Pyx_PyFunction_FastCallNoKw(PyCodeObject *co, PyObject **args, Py_ssize_t na,
                                               PyObject *globals) {
    PyFrameObject *f;
    PyThreadState *tstate = __Pyx_PyThreadState_Current;
    PyObject **fastlocals;
    Py_ssize_t i;
    PyObject *result;
    assert(globals != NULL);
    /* XXX Perhaps we should create a specialized
       PyFrame_New() that doesn't take locals, but does
       take builtins without sanity checking them.
       */
    assert(tstate != NULL);
    f = PyFrame_New(tstate, co, globals, NULL);
    if (f == NULL) {
        return NULL;
    }
    fastlocals = f->f_localsplus;
    for (i = 0; i < na; i++) {
        Py_INCREF(*args);
        fastlocals[i] = *args++;
    }
    result = PyEval_EvalFrameEx(f,0);
    ++tstate->recursion_depth;
    Py_DECREF(f);
    --tstate->recursion_depth;
    return result;
}
#if 1 || PY_VERSION_HEX < 0x030600B1
static PyObject *__Pyx_PyFunction_FastCallDict(PyObject *func, PyObject **args, int nargs, PyObject *kwargs) {
    PyCodeObject *co = (PyCodeObject *)PyFunction_GET_CODE(func);
    PyObject *globals = PyFunction_GET_GLOBALS(func);
    PyObject *argdefs = PyFunction_GET_DEFAULTS(func);
    PyObject *closure;
#if PY_MAJOR_VERSION >= 3
    PyObject *kwdefs;
#endif
    PyObject *kwtuple, **k;
    PyObject **d;
    Py_ssize_t nd;
    Py_ssize_t nk;
    PyObject *result;
    assert(kwargs == NULL || PyDict_Check(kwargs));
    nk = kwargs ? PyDict_Size(kwargs) : 0;
    if (Py_EnterRecursiveCall((char*)" while calling a Python object")) {
        return NULL;
    }
    if (
#if PY_MAJOR_VERSION >= 3
            co->co_kwonlyargcount == 0 &&
#endif
            likely(kwargs == NULL || nk == 0) &&
            co->co_flags == (CO_OPTIMIZED | CO_NEWLOCALS | CO_NOFREE)) {
        if (argdefs == NULL && co->co_argcount == nargs) {
            result = __Pyx_PyFunction_FastCallNoKw(co, args, nargs, globals);
            goto done;
        }
        else if (nargs == 0 && argdefs != NULL
                 && co->co_argcount == Py_SIZE(argdefs)) {
            /* function called with no arguments, but all parameters have
               a default value: use default values as arguments .*/
            args = &PyTuple_GET_ITEM(argdefs, 0);
            result =__Pyx_PyFunction_FastCallNoKw(co, args, Py_SIZE(argdefs), globals);
            goto done;
        }
    }
    if (kwargs != NULL) {
        Py_ssize_t pos, i;
        kwtuple = PyTuple_New(2 * nk);
        if (kwtuple == NULL) {
            result = NULL;
            goto done;
        }
        k = &PyTuple_GET_ITEM(kwtuple, 0);
        pos = i = 0;
        while (PyDict_Next(kwargs, &pos, &k[i], &k[i+1])) {
            Py_INCREF(k[i]);
            Py_INCREF(k[i+1]);
            i += 2;
        }
        nk = i / 2;
    }
    else {
        kwtuple = NULL;
        k = NULL;
    }
    closure = PyFunction_GET_CLOSURE(func);
#if PY_MAJOR_VERSION >= 3
    kwdefs = PyFunction_GET_KW_DEFAULTS(func);
#endif
    if (argdefs != NULL) {
        d = &PyTuple_GET_ITEM(argdefs, 0);
        nd = Py_SIZE(argdefs);
    }
    else {
        d = NULL;
        nd = 0;
    }
#if PY_MAJOR_VERSION >= 3
    result = PyEval_EvalCodeEx((PyObject*)co, globals, (PyObject *)NULL,
                               args, nargs,
                               k, (int)nk,
                               d, (int)nd, kwdefs, closure);
#else
    result = PyEval_EvalCodeEx(co, globals, (PyObject *)NULL,
                               args, nargs,
                               k, (int)nk,
                               d, (int)nd, closure);
#endif
    Py_XDECREF(kwtuple);
done:
    Py_LeaveRecursiveCall();
    return result;
}
#endif
#endif

/* PyObjectCall */
  #if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_Call(PyObject *func, PyObject *arg, PyObject *kw) {
    PyObject *result;
    ternaryfunc call = func->ob_type->tp_call;
    if (unlikely(!call))
        return PyObject_Call(func, arg, kw);
    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
        return NULL;
    result = (*call)(func, arg, kw);
    Py_LeaveRecursiveCall();
    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
        PyErr_SetString(
            PyExc_SystemError,
            "NULL result without error in PyObject_Call");
    }
    return result;
}
#endif

/* PyObjectCallMethO */
  #if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallMethO(PyObject *func, PyObject *arg) {
    PyObject *self, *result;
    PyCFunction cfunc;
    cfunc = PyCFunction_GET_FUNCTION(func);
    self = PyCFunction_GET_SELF(func);
    if (unlikely(Py_EnterRecursiveCall((char*)" while calling a Python object")))
        return NULL;
    result = cfunc(self, arg);
    Py_LeaveRecursiveCall();
    if (unlikely(!result) && unlikely(!PyErr_Occurred())) {
        PyErr_SetString(
            PyExc_SystemError,
            "NULL result without error in PyObject_Call");
    }
    return result;
}
#endif

/* PyObjectCallOneArg */
  #if CYTHON_COMPILING_IN_CPYTHON
static PyObject* __Pyx__PyObject_CallOneArg(PyObject *func, PyObject *arg) {
    PyObject *result;
    PyObject *args = PyTuple_New(1);
    if (unlikely(!args)) return NULL;
    Py_INCREF(arg);
    PyTuple_SET_ITEM(args, 0, arg);
    result = __Pyx_PyObject_Call(func, args, NULL);
    Py_DECREF(args);
    return result;
}
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
#if CYTHON_FAST_PYCALL
    if (PyFunction_Check(func)) {
        return __Pyx_PyFunction_FastCall(func, &arg, 1);
    }
#endif
    if (likely(PyCFunction_Check(func))) {
        if (likely(PyCFunction_GET_FLAGS(func) & METH_O)) {
            return __Pyx_PyObject_CallMethO(func, arg);
#if CYTHON_FAST_PYCCALL
        } else if (PyCFunction_GET_FLAGS(func) & METH_FASTCALL) {
            return __Pyx_PyCFunction_FastCall(func, &arg, 1);
#endif
        }
    }
    return __Pyx__PyObject_CallOneArg(func, arg);
}
#else
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallOneArg(PyObject *func, PyObject *arg) {
    PyObject *result;
    PyObject *args = PyTuple_Pack(1, arg);
    if (unlikely(!args)) return NULL;
    result = __Pyx_PyObject_Call(func, args, NULL);
    Py_DECREF(args);
    return result;
}
#endif

/* ExtTypeTest */
  static CYTHON_INLINE int __Pyx_TypeTest(PyObject *obj, PyTypeObject *type) {
    if (unlikely(!type)) {
        PyErr_SetString(PyExc_SystemError, "Missing type object");
        return 0;
    }
    if (likely(__Pyx_TypeCheck(obj, type)))
        return 1;
    PyErr_Format(PyExc_TypeError, "Cannot convert %.200s to %.200s",
                 Py_TYPE(obj)->tp_name, type->tp_name);
    return 0;
}

/* IsLittleEndian */
  static CYTHON_INLINE int __Pyx_Is_Little_Endian(void)
{
  union {
    uint32_t u32;
    uint8_t u8[4];
  } S;
  S.u32 = 0x01020304;
  return S.u8[0] == 4;
}

/* BufferFormatCheck */
  static void __Pyx_BufFmt_Init(__Pyx_BufFmt_Context* ctx,
                              __Pyx_BufFmt_StackElem* stack,
                              __Pyx_TypeInfo* type) {
  stack[0].field = &ctx->root;
  stack[0].parent_offset = 0;
  ctx->root.type = type;
  ctx->root.name = "buffer dtype";
  ctx->root.offset = 0;
  ctx->head = stack;
  ctx->head->field = &ctx->root;
  ctx->fmt_offset = 0;
  ctx->head->parent_offset = 0;
  ctx->new_packmode = '@';
  ctx->enc_packmode = '@';
  ctx->new_count = 1;
  ctx->enc_count = 0;
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  ctx->is_valid_array = 0;
  ctx->struct_alignment = 0;
  while (type->typegroup == 'S') {
    ++ctx->head;
    ctx->head->field = type->fields;
    ctx->head->parent_offset = 0;
    type = type->fields->type;
  }
}
static int __Pyx_BufFmt_ParseNumber(const char** ts) {
    int count;
    const char* t = *ts;
    if (*t < '0' || *t > '9') {
      return -1;
    } else {
        count = *t++ - '0';
        while (*t >= '0' && *t < '9') {
            count *= 10;
            count += *t++ - '0';
        }
    }
    *ts = t;
    return count;
}
static int __Pyx_BufFmt_ExpectNumber(const char **ts) {
    int number = __Pyx_BufFmt_ParseNumber(ts);
    if (number == -1)
        PyErr_Format(PyExc_ValueError,\
                     "Does not understand character buffer dtype format string ('%c')", **ts);
    return number;
}
static void __Pyx_BufFmt_RaiseUnexpectedChar(char ch) {
  PyErr_Format(PyExc_ValueError,
               "Unexpected format string character: '%c'", ch);
}
static const char* __Pyx_BufFmt_DescribeTypeChar(char ch, int is_complex) {
  switch (ch) {
    case 'c': return "'char'";
    case 'b': return "'signed char'";
    case 'B': return "'unsigned char'";
    case 'h': return "'short'";
    case 'H': return "'unsigned short'";
    case 'i': return "'int'";
    case 'I': return "'unsigned int'";
    case 'l': return "'long'";
    case 'L': return "'unsigned long'";
    case 'q': return "'long long'";
    case 'Q': return "'unsigned long long'";
    case 'f': return (is_complex ? "'complex float'" : "'float'");
    case 'd': return (is_complex ? "'complex double'" : "'double'");
    case 'g': return (is_complex ? "'complex long double'" : "'long double'");
    case 'T': return "a struct";
    case 'O': return "Python object";
    case 'P': return "a pointer";
    case 's': case 'p': return "a string";
    case 0: return "end";
    default: return "unparseable format string";
  }
}
static size_t __Pyx_BufFmt_TypeCharToStandardSize(char ch, int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return 2;
    case 'i': case 'I': case 'l': case 'L': return 4;
    case 'q': case 'Q': return 8;
    case 'f': return (is_complex ? 8 : 4);
    case 'd': return (is_complex ? 16 : 8);
    case 'g': {
      PyErr_SetString(PyExc_ValueError, "Python does not define a standard format string size for long double ('g')..");
      return 0;
    }
    case 'O': case 'P': return sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static size_t __Pyx_BufFmt_TypeCharToNativeSize(char ch, int is_complex) {
  switch (ch) {
    case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(short);
    case 'i': case 'I': return sizeof(int);
    case 'l': case 'L': return sizeof(long);
    #ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(PY_LONG_LONG);
    #endif
    case 'f': return sizeof(float) * (is_complex ? 2 : 1);
    case 'd': return sizeof(double) * (is_complex ? 2 : 1);
    case 'g': return sizeof(long double) * (is_complex ? 2 : 1);
    case 'O': case 'P': return sizeof(void*);
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
  }
}
typedef struct { char c; short x; } __Pyx_st_short;
typedef struct { char c; int x; } __Pyx_st_int;
typedef struct { char c; long x; } __Pyx_st_long;
typedef struct { char c; float x; } __Pyx_st_float;
typedef struct { char c; double x; } __Pyx_st_double;
typedef struct { char c; long double x; } __Pyx_st_longdouble;
typedef struct { char c; void *x; } __Pyx_st_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { char c; PY_LONG_LONG x; } __Pyx_st_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToAlignment(char ch, CYTHON_UNUSED int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_st_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_st_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_st_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_st_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_st_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_st_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_st_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_st_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
/* These are for computing the padding at the end of the struct to align
   on the first member of the struct. This will probably the same as above,
   but we don't have any guarantees.
 */
typedef struct { short x; char c; } __Pyx_pad_short;
typedef struct { int x; char c; } __Pyx_pad_int;
typedef struct { long x; char c; } __Pyx_pad_long;
typedef struct { float x; char c; } __Pyx_pad_float;
typedef struct { double x; char c; } __Pyx_pad_double;
typedef struct { long double x; char c; } __Pyx_pad_longdouble;
typedef struct { void *x; char c; } __Pyx_pad_void_p;
#ifdef HAVE_LONG_LONG
typedef struct { PY_LONG_LONG x; char c; } __Pyx_pad_longlong;
#endif
static size_t __Pyx_BufFmt_TypeCharToPadding(char ch, CYTHON_UNUSED int is_complex) {
  switch (ch) {
    case '?': case 'c': case 'b': case 'B': case 's': case 'p': return 1;
    case 'h': case 'H': return sizeof(__Pyx_pad_short) - sizeof(short);
    case 'i': case 'I': return sizeof(__Pyx_pad_int) - sizeof(int);
    case 'l': case 'L': return sizeof(__Pyx_pad_long) - sizeof(long);
#ifdef HAVE_LONG_LONG
    case 'q': case 'Q': return sizeof(__Pyx_pad_longlong) - sizeof(PY_LONG_LONG);
#endif
    case 'f': return sizeof(__Pyx_pad_float) - sizeof(float);
    case 'd': return sizeof(__Pyx_pad_double) - sizeof(double);
    case 'g': return sizeof(__Pyx_pad_longdouble) - sizeof(long double);
    case 'P': case 'O': return sizeof(__Pyx_pad_void_p) - sizeof(void*);
    default:
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
}
static char __Pyx_BufFmt_TypeCharToGroup(char ch, int is_complex) {
  switch (ch) {
    case 'c':
        return 'H';
    case 'b': case 'h': case 'i':
    case 'l': case 'q': case 's': case 'p':
        return 'I';
    case 'B': case 'H': case 'I': case 'L': case 'Q':
        return 'U';
    case 'f': case 'd': case 'g':
        return (is_complex ? 'C' : 'R');
    case 'O':
        return 'O';
    case 'P':
        return 'P';
    default: {
      __Pyx_BufFmt_RaiseUnexpectedChar(ch);
      return 0;
    }
  }
}
static void __Pyx_BufFmt_RaiseExpected(__Pyx_BufFmt_Context* ctx) {
  if (ctx->head == NULL || ctx->head->field == &ctx->root) {
    const char* expected;
    const char* quote;
    if (ctx->head == NULL) {
      expected = "end";
      quote = "";
    } else {
      expected = ctx->head->field->type->name;
      quote = "'";
    }
    PyErr_Format(PyExc_ValueError,
                 "Buffer dtype mismatch, expected %s%s%s but got %s",
                 quote, expected, quote,
                 __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex));
  } else {
    __Pyx_StructField* field = ctx->head->field;
    __Pyx_StructField* parent = (ctx->head - 1)->field;
    PyErr_Format(PyExc_ValueError,
                 "Buffer dtype mismatch, expected '%s' but got %s in '%s.%s'",
                 field->type->name, __Pyx_BufFmt_DescribeTypeChar(ctx->enc_type, ctx->is_complex),
                 parent->type->name, field->name);
  }
}
static int __Pyx_BufFmt_ProcessTypeChunk(__Pyx_BufFmt_Context* ctx) {
  char group;
  size_t size, offset, arraysize = 1;
  if (ctx->enc_type == 0) return 0;
  if (ctx->head->field->type->arraysize[0]) {
    int i, ndim = 0;
    if (ctx->enc_type == 's' || ctx->enc_type == 'p') {
        ctx->is_valid_array = ctx->head->field->type->ndim == 1;
        ndim = 1;
        if (ctx->enc_count != ctx->head->field->type->arraysize[0]) {
            PyErr_Format(PyExc_ValueError,
                         "Expected a dimension of size %zu, got %zu",
                         ctx->head->field->type->arraysize[0], ctx->enc_count);
            return -1;
        }
    }
    if (!ctx->is_valid_array) {
      PyErr_Format(PyExc_ValueError, "Expected %d dimensions, got %d",
                   ctx->head->field->type->ndim, ndim);
      return -1;
    }
    for (i = 0; i < ctx->head->field->type->ndim; i++) {
      arraysize *= ctx->head->field->type->arraysize[i];
    }
    ctx->is_valid_array = 0;
    ctx->enc_count = 1;
  }
  group = __Pyx_BufFmt_TypeCharToGroup(ctx->enc_type, ctx->is_complex);
  do {
    __Pyx_StructField* field = ctx->head->field;
    __Pyx_TypeInfo* type = field->type;
    if (ctx->enc_packmode == '@' || ctx->enc_packmode == '^') {
      size = __Pyx_BufFmt_TypeCharToNativeSize(ctx->enc_type, ctx->is_complex);
    } else {
      size = __Pyx_BufFmt_TypeCharToStandardSize(ctx->enc_type, ctx->is_complex);
    }
    if (ctx->enc_packmode == '@') {
      size_t align_at = __Pyx_BufFmt_TypeCharToAlignment(ctx->enc_type, ctx->is_complex);
      size_t align_mod_offset;
      if (align_at == 0) return -1;
      align_mod_offset = ctx->fmt_offset % align_at;
      if (align_mod_offset > 0) ctx->fmt_offset += align_at - align_mod_offset;
      if (ctx->struct_alignment == 0)
          ctx->struct_alignment = __Pyx_BufFmt_TypeCharToPadding(ctx->enc_type,
                                                                 ctx->is_complex);
    }
    if (type->size != size || type->typegroup != group) {
      if (type->typegroup == 'C' && type->fields != NULL) {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        ++ctx->head;
        ctx->head->field = type->fields;
        ctx->head->parent_offset = parent_offset;
        continue;
      }
      if ((type->typegroup == 'H' || group == 'H') && type->size == size) {
      } else {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
      }
    }
    offset = ctx->head->parent_offset + field->offset;
    if (ctx->fmt_offset != offset) {
      PyErr_Format(PyExc_ValueError,
                   "Buffer dtype mismatch; next field is at offset %" CYTHON_FORMAT_SSIZE_T "d but %" CYTHON_FORMAT_SSIZE_T "d expected",
                   (Py_ssize_t)ctx->fmt_offset, (Py_ssize_t)offset);
      return -1;
    }
    ctx->fmt_offset += size;
    if (arraysize)
      ctx->fmt_offset += (arraysize - 1) * size;
    --ctx->enc_count;
    while (1) {
      if (field == &ctx->root) {
        ctx->head = NULL;
        if (ctx->enc_count != 0) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return -1;
        }
        break;
      }
      ctx->head->field = ++field;
      if (field->type == NULL) {
        --ctx->head;
        field = ctx->head->field;
        continue;
      } else if (field->type->typegroup == 'S') {
        size_t parent_offset = ctx->head->parent_offset + field->offset;
        if (field->type->fields->type == NULL) continue;
        field = field->type->fields;
        ++ctx->head;
        ctx->head->field = field;
        ctx->head->parent_offset = parent_offset;
        break;
      } else {
        break;
      }
    }
  } while (ctx->enc_count);
  ctx->enc_type = 0;
  ctx->is_complex = 0;
  return 0;
}
static PyObject *
__pyx_buffmt_parse_array(__Pyx_BufFmt_Context* ctx, const char** tsp)
{
    const char *ts = *tsp;
    int i = 0, number;
    int ndim = ctx->head->field->type->ndim;
;
    ++ts;
    if (ctx->new_count != 1) {
        PyErr_SetString(PyExc_ValueError,
                        "Cannot handle repeated arrays in format string");
        return NULL;
    }
    if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
    while (*ts && *ts != ')') {
        switch (*ts) {
            case ' ': case '\f': case '\r': case '\n': case '\t': case '\v':  continue;
            default:  break;
        }
        number = __Pyx_BufFmt_ExpectNumber(&ts);
        if (number == -1) return NULL;
        if (i < ndim && (size_t) number != ctx->head->field->type->arraysize[i])
            return PyErr_Format(PyExc_ValueError,
                        "Expected a dimension of size %zu, got %d",
                        ctx->head->field->type->arraysize[i], number);
        if (*ts != ',' && *ts != ')')
            return PyErr_Format(PyExc_ValueError,
                                "Expected a comma in format string, got '%c'", *ts);
        if (*ts == ',') ts++;
        i++;
    }
    if (i != ndim)
        return PyErr_Format(PyExc_ValueError, "Expected %d dimension(s), got %d",
                            ctx->head->field->type->ndim, i);
    if (!*ts) {
        PyErr_SetString(PyExc_ValueError,
                        "Unexpected end of format string, expected ')'");
        return NULL;
    }
    ctx->is_valid_array = 1;
    ctx->new_count = 1;
    *tsp = ++ts;
    return Py_None;
}
static const char* __Pyx_BufFmt_CheckString(__Pyx_BufFmt_Context* ctx, const char* ts) {
  int got_Z = 0;
  while (1) {
    switch(*ts) {
      case 0:
        if (ctx->enc_type != 0 && ctx->head == NULL) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return NULL;
        }
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        if (ctx->head != NULL) {
          __Pyx_BufFmt_RaiseExpected(ctx);
          return NULL;
        }
        return ts;
      case ' ':
      case '\r':
      case '\n':
        ++ts;
        break;
      case '<':
        if (!__Pyx_Is_Little_Endian()) {
          PyErr_SetString(PyExc_ValueError, "Little-endian buffer not supported on big-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '>':
      case '!':
        if (__Pyx_Is_Little_Endian()) {
          PyErr_SetString(PyExc_ValueError, "Big-endian buffer not supported on little-endian compiler");
          return NULL;
        }
        ctx->new_packmode = '=';
        ++ts;
        break;
      case '=':
      case '@':
      case '^':
        ctx->new_packmode = *ts++;
        break;
      case 'T':
        {
          const char* ts_after_sub;
          size_t i, struct_count = ctx->new_count;
          size_t struct_alignment = ctx->struct_alignment;
          ctx->new_count = 1;
          ++ts;
          if (*ts != '{') {
            PyErr_SetString(PyExc_ValueError, "Buffer acquisition: Expected '{' after 'T'");
            return NULL;
          }
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->enc_type = 0;
          ctx->enc_count = 0;
          ctx->struct_alignment = 0;
          ++ts;
          ts_after_sub = ts;
          for (i = 0; i != struct_count; ++i) {
            ts_after_sub = __Pyx_BufFmt_CheckString(ctx, ts);
            if (!ts_after_sub) return NULL;
          }
          ts = ts_after_sub;
          if (struct_alignment) ctx->struct_alignment = struct_alignment;
        }
        break;
      case '}':
        {
          size_t alignment = ctx->struct_alignment;
          ++ts;
          if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
          ctx->enc_type = 0;
          if (alignment && ctx->fmt_offset % alignment) {
            ctx->fmt_offset += alignment - (ctx->fmt_offset % alignment);
          }
        }
        return ts;
      case 'x':
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        ctx->fmt_offset += ctx->new_count;
        ctx->new_count = 1;
        ctx->enc_count = 0;
        ctx->enc_type = 0;
        ctx->enc_packmode = ctx->new_packmode;
        ++ts;
        break;
      case 'Z':
        got_Z = 1;
        ++ts;
        if (*ts != 'f' && *ts != 'd' && *ts != 'g') {
          __Pyx_BufFmt_RaiseUnexpectedChar('Z');
          return NULL;
        }
      case 'c': case 'b': case 'B': case 'h': case 'H': case 'i': case 'I':
      case 'l': case 'L': case 'q': case 'Q':
      case 'f': case 'd': case 'g':
      case 'O': case 'p':
        if (ctx->enc_type == *ts && got_Z == ctx->is_complex &&
            ctx->enc_packmode == ctx->new_packmode) {
          ctx->enc_count += ctx->new_count;
          ctx->new_count = 1;
          got_Z = 0;
          ++ts;
          break;
        }
      case 's':
        if (__Pyx_BufFmt_ProcessTypeChunk(ctx) == -1) return NULL;
        ctx->enc_count = ctx->new_count;
        ctx->enc_packmode = ctx->new_packmode;
        ctx->enc_type = *ts;
        ctx->is_complex = got_Z;
        ++ts;
        ctx->new_count = 1;
        got_Z = 0;
        break;
      case ':':
        ++ts;
        while(*ts != ':') ++ts;
        ++ts;
        break;
      case '(':
        if (!__pyx_buffmt_parse_array(ctx, &ts)) return NULL;
        break;
      default:
        {
          int number = __Pyx_BufFmt_ExpectNumber(&ts);
          if (number == -1) return NULL;
          ctx->new_count = (size_t)number;
        }
    }
  }
}

/* BufferGetAndValidate */
    static CYTHON_INLINE void __Pyx_SafeReleaseBuffer(Py_buffer* info) {
  if (unlikely(info->buf == NULL)) return;
  if (info->suboffsets == __Pyx_minusones) info->suboffsets = NULL;
  __Pyx_ReleaseBuffer(info);
}
static void __Pyx_ZeroBuffer(Py_buffer* buf) {
  buf->buf = NULL;
  buf->obj = NULL;
  buf->strides = __Pyx_zeros;
  buf->shape = __Pyx_zeros;
  buf->suboffsets = __Pyx_minusones;
}
static int __Pyx__GetBufferAndValidate(
        Py_buffer* buf, PyObject* obj,  __Pyx_TypeInfo* dtype, int flags,
        int nd, int cast, __Pyx_BufFmt_StackElem* stack)
{
  buf->buf = NULL;
  if (unlikely(__Pyx_GetBuffer(obj, buf, flags) == -1)) {
    __Pyx_ZeroBuffer(buf);
    return -1;
  }
  if (unlikely(buf->ndim != nd)) {
    PyErr_Format(PyExc_ValueError,
                 "Buffer has wrong number of dimensions (expected %d, got %d)",
                 nd, buf->ndim);
    goto fail;
  }
  if (!cast) {
    __Pyx_BufFmt_Context ctx;
    __Pyx_BufFmt_Init(&ctx, stack, dtype);
    if (!__Pyx_BufFmt_CheckString(&ctx, buf->format)) goto fail;
  }
  if (unlikely((unsigned)buf->itemsize != dtype->size)) {
    PyErr_Format(PyExc_ValueError,
      "Item size of buffer (%" CYTHON_FORMAT_SSIZE_T "d byte%s) does not match size of '%s' (%" CYTHON_FORMAT_SSIZE_T "d byte%s)",
      buf->itemsize, (buf->itemsize > 1) ? "s" : "",
      dtype->name, (Py_ssize_t)dtype->size, (dtype->size > 1) ? "s" : "");
    goto fail;
  }
  if (buf->suboffsets == NULL) buf->suboffsets = __Pyx_minusones;
  return 0;
fail:;
  __Pyx_SafeReleaseBuffer(buf);
  return -1;
}

/* BufferFallbackError */
    static void __Pyx_RaiseBufferFallbackError(void) {
  PyErr_SetString(PyExc_ValueError,
     "Buffer acquisition failed on assignment; and then reacquiring the old buffer failed too!");
}

/* PyObjectCallNoArg */
    #if CYTHON_COMPILING_IN_CPYTHON
static CYTHON_INLINE PyObject* __Pyx_PyObject_CallNoArg(PyObject *func) {
#if CYTHON_FAST_PYCALL
    if (PyFunction_Check(func)) {
        return __Pyx_PyFunction_FastCall(func, NULL, 0);
    }
#endif
#ifdef __Pyx_CyFunction_USED
    if (likely(PyCFunction_Check(func) || __Pyx_TypeCheck(func, __pyx_CyFunctionType))) {
#else
    if (likely(PyCFunction_Check(func))) {
#endif
        if (likely(PyCFunction_GET_FLAGS(func) & METH_NOARGS)) {
            return __Pyx_PyObject_CallMethO(func, NULL);
        }
    }
    return __Pyx_PyObject_Call(func, __pyx_empty_tuple, NULL);
}
#endif

/* RaiseTooManyValuesToUnpack */
      static CYTHON_INLINE void __Pyx_RaiseTooManyValuesError(Py_ssize_t expected) {
    PyErr_Format(PyExc_ValueError,
                 "too many values to unpack (expected %" CYTHON_FORMAT_SSIZE_T "d)", expected);
}

/* RaiseNeedMoreValuesToUnpack */
      static CYTHON_INLINE void __Pyx_RaiseNeedMoreValuesError(Py_ssize_t index) {
    PyErr_Format(PyExc_ValueError,
                 "need more than %" CYTHON_FORMAT_SSIZE_T "d value%.1s to unpack",
                 index, (index == 1) ? "" : "s");
}

/* IterFinish */
      static CYTHON_INLINE int __Pyx_IterFinish(void) {
#if CYTHON_FAST_THREAD_STATE
    PyThreadState *tstate = __Pyx_PyThreadState_Current;
    PyObject* exc_type = tstate->curexc_type;
    if (unlikely(exc_type)) {
        if (likely(__Pyx_PyErr_GivenExceptionMatches(exc_type, PyExc_StopIteration))) {
            PyObject *exc_value, *exc_tb;
            exc_value = tstate->curexc_value;
            exc_tb = tstate->curexc_traceback;
            tstate->curexc_type = 0;
            tstate->curexc_value = 0;
            tstate->curexc_traceback = 0;
            Py_DECREF(exc_type);
            Py_XDECREF(exc_value);
            Py_XDECREF(exc_tb);
            return 0;
        } else {
            return -1;
        }
    }
    return 0;
#else
    if (unlikely(PyErr_Occurred())) {
        if (likely(PyErr_ExceptionMatches(PyExc_StopIteration))) {
            PyErr_Clear();
            return 0;
        } else {
            return -1;
        }
    }
    return 0;
#endif
}

/* UnpackItemEndCheck */
      static int __Pyx_IternextUnpackEndCheck(PyObject *retval, Py_ssize_t expected) {
    if (unlikely(retval)) {
        Py_DECREF(retval);
        __Pyx_RaiseTooManyValuesError(expected);
        return -1;
    } else {
        return __Pyx_IterFinish();
    }
    return 0;
}

/* BufferIndexError */
      static void __Pyx_RaiseBufferIndexError(int axis) {
  PyErr_Format(PyExc_IndexError,
     "Out of bounds on buffer access (axis %d)", axis);
}

/* PyErrFetchRestore */
      #if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE void __Pyx_ErrRestoreInState(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    tmp_type = tstate->curexc_type;
    tmp_value = tstate->curexc_value;
    tmp_tb = tstate->curexc_traceback;
    tstate->curexc_type = type;
    tstate->curexc_value = value;
    tstate->curexc_traceback = tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
}
static CYTHON_INLINE void __Pyx_ErrFetchInState(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
    *type = tstate->curexc_type;
    *value = tstate->curexc_value;
    *tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
}
#endif

/* RaiseException */
      #if PY_MAJOR_VERSION < 3
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb,
                        CYTHON_UNUSED PyObject *cause) {
    __Pyx_PyThreadState_declare
    Py_XINCREF(type);
    if (!value || value == Py_None)
        value = NULL;
    else
        Py_INCREF(value);
    if (!tb || tb == Py_None)
        tb = NULL;
    else {
        Py_INCREF(tb);
        if (!PyTraceBack_Check(tb)) {
            PyErr_SetString(PyExc_TypeError,
                "raise: arg 3 must be a traceback or None");
            goto raise_error;
        }
    }
    if (PyType_Check(type)) {
#if CYTHON_COMPILING_IN_PYPY
        if (!value) {
            Py_INCREF(Py_None);
            value = Py_None;
        }
#endif
        PyErr_NormalizeException(&type, &value, &tb);
    } else {
        if (value) {
            PyErr_SetString(PyExc_TypeError,
                "instance exception may not have a separate value");
            goto raise_error;
        }
        value = type;
        type = (PyObject*) Py_TYPE(type);
        Py_INCREF(type);
        if (!PyType_IsSubtype((PyTypeObject *)type, (PyTypeObject *)PyExc_BaseException)) {
            PyErr_SetString(PyExc_TypeError,
                "raise: exception class must be a subclass of BaseException");
            goto raise_error;
        }
    }
    __Pyx_PyThreadState_assign
    __Pyx_ErrRestore(type, value, tb);
    return;
raise_error:
    Py_XDECREF(value);
    Py_XDECREF(type);
    Py_XDECREF(tb);
    return;
}
#else
static void __Pyx_Raise(PyObject *type, PyObject *value, PyObject *tb, PyObject *cause) {
    PyObject* owned_instance = NULL;
    if (tb == Py_None) {
        tb = 0;
    } else if (tb && !PyTraceBack_Check(tb)) {
        PyErr_SetString(PyExc_TypeError,
            "raise: arg 3 must be a traceback or None");
        goto bad;
    }
    if (value == Py_None)
        value = 0;
    if (PyExceptionInstance_Check(type)) {
        if (value) {
            PyErr_SetString(PyExc_TypeError,
                "instance exception may not have a separate value");
            goto bad;
        }
        value = type;
        type = (PyObject*) Py_TYPE(value);
    } else if (PyExceptionClass_Check(type)) {
        PyObject *instance_class = NULL;
        if (value && PyExceptionInstance_Check(value)) {
            instance_class = (PyObject*) Py_TYPE(value);
            if (instance_class != type) {
                int is_subclass = PyObject_IsSubclass(instance_class, type);
                if (!is_subclass) {
                    instance_class = NULL;
                } else if (unlikely(is_subclass == -1)) {
                    goto bad;
                } else {
                    type = instance_class;
                }
            }
        }
        if (!instance_class) {
            PyObject *args;
            if (!value)
                args = PyTuple_New(0);
            else if (PyTuple_Check(value)) {
                Py_INCREF(value);
                args = value;
            } else
                args = PyTuple_Pack(1, value);
            if (!args)
                goto bad;
            owned_instance = PyObject_Call(type, args, NULL);
            Py_DECREF(args);
            if (!owned_instance)
                goto bad;
            value = owned_instance;
            if (!PyExceptionInstance_Check(value)) {
                PyErr_Format(PyExc_TypeError,
                             "calling %R should have returned an instance of "
                             "BaseException, not %R",
                             type, Py_TYPE(value));
                goto bad;
            }
        }
    } else {
        PyErr_SetString(PyExc_TypeError,
            "raise: exception class must be a subclass of BaseException");
        goto bad;
    }
    if (cause) {
        PyObject *fixed_cause;
        if (cause == Py_None) {
            fixed_cause = NULL;
        } else if (PyExceptionClass_Check(cause)) {
            fixed_cause = PyObject_CallObject(cause, NULL);
            if (fixed_cause == NULL)
                goto bad;
        } else if (PyExceptionInstance_Check(cause)) {
            fixed_cause = cause;
            Py_INCREF(fixed_cause);
        } else {
            PyErr_SetString(PyExc_TypeError,
                            "exception causes must derive from "
                            "BaseException");
            goto bad;
        }
        PyException_SetCause(value, fixed_cause);
    }
    PyErr_SetObject(type, value);
    if (tb) {
#if CYTHON_COMPILING_IN_PYPY
        PyObject *tmp_type, *tmp_value, *tmp_tb;
        PyErr_Fetch(&tmp_type, &tmp_value, &tmp_tb);
        Py_INCREF(tb);
        PyErr_Restore(tmp_type, tmp_value, tb);
        Py_XDECREF(tmp_tb);
#else
        PyThreadState *tstate = __Pyx_PyThreadState_Current;
        PyObject* tmp_tb = tstate->curexc_traceback;
        if (tb != tmp_tb) {
            Py_INCREF(tb);
            tstate->curexc_traceback = tb;
            Py_XDECREF(tmp_tb);
        }
#endif
    }
bad:
    Py_XDECREF(owned_instance);
    return;
}
#endif

/* GetItemInt */
      static PyObject *__Pyx_GetItemInt_Generic(PyObject *o, PyObject* j) {
    PyObject *r;
    if (!j) return NULL;
    r = PyObject_GetItem(o, j);
    Py_DECREF(j);
    return r;
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_List_Fast(PyObject *o, Py_ssize_t i,
                                                              CYTHON_NCP_UNUSED int wraparound,
                                                              CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
    Py_ssize_t wrapped_i = i;
    if (wraparound & unlikely(i < 0)) {
        wrapped_i += PyList_GET_SIZE(o);
    }
    if ((!boundscheck) || likely((0 <= wrapped_i) & (wrapped_i < PyList_GET_SIZE(o)))) {
        PyObject *r = PyList_GET_ITEM(o, wrapped_i);
        Py_INCREF(r);
        return r;
    }
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
#else
    return PySequence_GetItem(o, i);
#endif
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Tuple_Fast(PyObject *o, Py_ssize_t i,
                                                              CYTHON_NCP_UNUSED int wraparound,
                                                              CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
    Py_ssize_t wrapped_i = i;
    if (wraparound & unlikely(i < 0)) {
        wrapped_i += PyTuple_GET_SIZE(o);
    }
    if ((!boundscheck) || likely((0 <= wrapped_i) & (wrapped_i < PyTuple_GET_SIZE(o)))) {
        PyObject *r = PyTuple_GET_ITEM(o, wrapped_i);
        Py_INCREF(r);
        return r;
    }
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
#else
    return PySequence_GetItem(o, i);
#endif
}
static CYTHON_INLINE PyObject *__Pyx_GetItemInt_Fast(PyObject *o, Py_ssize_t i, int is_list,
                                                     CYTHON_NCP_UNUSED int wraparound,
                                                     CYTHON_NCP_UNUSED int boundscheck) {
#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS && CYTHON_USE_TYPE_SLOTS
    if (is_list || PyList_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyList_GET_SIZE(o);
        if ((!boundscheck) || (likely((n >= 0) & (n < PyList_GET_SIZE(o))))) {
            PyObject *r = PyList_GET_ITEM(o, n);
            Py_INCREF(r);
            return r;
        }
    }
    else if (PyTuple_CheckExact(o)) {
        Py_ssize_t n = ((!wraparound) | likely(i >= 0)) ? i : i + PyTuple_GET_SIZE(o);
        if ((!boundscheck) || likely((n >= 0) & (n < PyTuple_GET_SIZE(o)))) {
            PyObject *r = PyTuple_GET_ITEM(o, n);
            Py_INCREF(r);
            return r;
        }
    } else {
        PySequenceMethods *m = Py_TYPE(o)->tp_as_sequence;
        if (likely(m && m->sq_item)) {
            if (wraparound && unlikely(i < 0) && likely(m->sq_length)) {
                Py_ssize_t l = m->sq_length(o);
                if (likely(l >= 0)) {
                    i += l;
                } else {
                    if (!PyErr_ExceptionMatches(PyExc_OverflowError))
                        return NULL;
                    PyErr_Clear();
                }
            }
            return m->sq_item(o, i);
        }
    }
#else
    if (is_list || PySequence_Check(o)) {
        return PySequence_GetItem(o, i);
    }
#endif
    return __Pyx_GetItemInt_Generic(o, PyInt_FromSsize_t(i));
}

/* None */
      static CYTHON_INLINE void __Pyx_RaiseClosureNameError(const char *varname) {
    PyErr_Format(PyExc_NameError, "free variable '%s' referenced before assignment in enclosing scope", varname);
}

/* RaiseNoneIterError */
      static CYTHON_INLINE void __Pyx_RaiseNoneNotIterableError(void) {
    PyErr_SetString(PyExc_TypeError, "'NoneType' object is not iterable");
}

/* SaveResetException */
      #if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE void __Pyx__ExceptionSave(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
    *type = tstate->exc_type;
    *value = tstate->exc_value;
    *tb = tstate->exc_traceback;
    Py_XINCREF(*type);
    Py_XINCREF(*value);
    Py_XINCREF(*tb);
}
static CYTHON_INLINE void __Pyx__ExceptionReset(PyThreadState *tstate, PyObject *type, PyObject *value, PyObject *tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = type;
    tstate->exc_value = value;
    tstate->exc_traceback = tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
}
#endif

/* PyErrExceptionMatches */
      #if CYTHON_FAST_THREAD_STATE
static int __Pyx_PyErr_ExceptionMatchesTuple(PyObject *exc_type, PyObject *tuple) {
    Py_ssize_t i, n;
    n = PyTuple_GET_SIZE(tuple);
#if PY_MAJOR_VERSION >= 3
    for (i=0; i<n; i++) {
        if (exc_type == PyTuple_GET_ITEM(tuple, i)) return 1;
    }
#endif
    for (i=0; i<n; i++) {
        if (__Pyx_PyErr_GivenExceptionMatches(exc_type, PyTuple_GET_ITEM(tuple, i))) return 1;
    }
    return 0;
}
static CYTHON_INLINE int __Pyx_PyErr_ExceptionMatchesInState(PyThreadState* tstate, PyObject* err) {
    PyObject *exc_type = tstate->curexc_type;
    if (exc_type == err) return 1;
    if (unlikely(!exc_type)) return 0;
    if (unlikely(PyTuple_Check(err)))
        return __Pyx_PyErr_ExceptionMatchesTuple(exc_type, err);
    return __Pyx_PyErr_GivenExceptionMatches(exc_type, err);
}
#endif

/* GetException */
      #if CYTHON_FAST_THREAD_STATE
static int __Pyx__GetException(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
#else
static int __Pyx_GetException(PyObject **type, PyObject **value, PyObject **tb) {
#endif
    PyObject *local_type, *local_value, *local_tb;
#if CYTHON_FAST_THREAD_STATE
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    local_type = tstate->curexc_type;
    local_value = tstate->curexc_value;
    local_tb = tstate->curexc_traceback;
    tstate->curexc_type = 0;
    tstate->curexc_value = 0;
    tstate->curexc_traceback = 0;
#else
    PyErr_Fetch(&local_type, &local_value, &local_tb);
#endif
    PyErr_NormalizeException(&local_type, &local_value, &local_tb);
#if CYTHON_FAST_THREAD_STATE
    if (unlikely(tstate->curexc_type))
#else
    if (unlikely(PyErr_Occurred()))
#endif
        goto bad;
    #if PY_MAJOR_VERSION >= 3
    if (local_tb) {
        if (unlikely(PyException_SetTraceback(local_value, local_tb) < 0))
            goto bad;
    }
    #endif
    Py_XINCREF(local_tb);
    Py_XINCREF(local_type);
    Py_XINCREF(local_value);
    *type = local_type;
    *value = local_value;
    *tb = local_tb;
#if CYTHON_FAST_THREAD_STATE
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = local_type;
    tstate->exc_value = local_value;
    tstate->exc_traceback = local_tb;
    Py_XDECREF(tmp_type);
    Py_XDECREF(tmp_value);
    Py_XDECREF(tmp_tb);
#else
    PyErr_SetExcInfo(local_type, local_value, local_tb);
#endif
    return 0;
bad:
    *type = 0;
    *value = 0;
    *tb = 0;
    Py_XDECREF(local_type);
    Py_XDECREF(local_value);
    Py_XDECREF(local_tb);
    return -1;
}

/* Import */
        static PyObject *__Pyx_Import(PyObject *name, PyObject *from_list, int level) {
    PyObject *empty_list = 0;
    PyObject *module = 0;
    PyObject *global_dict = 0;
    PyObject *empty_dict = 0;
    PyObject *list;
    #if PY_MAJOR_VERSION < 3
    PyObject *py_import;
    py_import = __Pyx_PyObject_GetAttrStr(__pyx_b, __pyx_n_s_import);
    if (!py_import)
        goto bad;
    #endif
    if (from_list)
        list = from_list;
    else {
        empty_list = PyList_New(0);
        if (!empty_list)
            goto bad;
        list = empty_list;
    }
    global_dict = PyModule_GetDict(__pyx_m);
    if (!global_dict)
        goto bad;
    empty_dict = PyDict_New();
    if (!empty_dict)
        goto bad;
    {
        #if PY_MAJOR_VERSION >= 3
        if (level == -1) {
            if (strchr(__Pyx_MODULE_NAME, '.')) {
                module = PyImport_ImportModuleLevelObject(
                    name, global_dict, empty_dict, list, 1);
                if (!module) {
                    if (!PyErr_ExceptionMatches(PyExc_ImportError))
                        goto bad;
                    PyErr_Clear();
                }
            }
            level = 0;
        }
        #endif
        if (!module) {
            #if PY_MAJOR_VERSION < 3
            PyObject *py_level = PyInt_FromLong(level);
            if (!py_level)
                goto bad;
            module = PyObject_CallFunctionObjArgs(py_import,
                name, global_dict, empty_dict, list, py_level, NULL);
            Py_DECREF(py_level);
            #else
            module = PyImport_ImportModuleLevelObject(
                name, global_dict, empty_dict, list, level);
            #endif
        }
    }
bad:
    #if PY_MAJOR_VERSION < 3
    Py_XDECREF(py_import);
    #endif
    Py_XDECREF(empty_list);
    Py_XDECREF(empty_dict);
    return module;
}

/* ImportFrom */
        static PyObject* __Pyx_ImportFrom(PyObject* module, PyObject* name) {
    PyObject* value = __Pyx_PyObject_GetAttrStr(module, name);
    if (unlikely(!value) && PyErr_ExceptionMatches(PyExc_AttributeError)) {
        PyErr_Format(PyExc_ImportError,
        #if PY_MAJOR_VERSION < 3
            "cannot import name %.230s", PyString_AS_STRING(name));
        #else
            "cannot import name %S", name);
        #endif
    }
    return value;
}

/* CalculateMetaclass */
        static PyObject *__Pyx_CalculateMetaclass(PyTypeObject *metaclass, PyObject *bases) {
    Py_ssize_t i, nbases = PyTuple_GET_SIZE(bases);
    for (i=0; i < nbases; i++) {
        PyTypeObject *tmptype;
        PyObject *tmp = PyTuple_GET_ITEM(bases, i);
        tmptype = Py_TYPE(tmp);
#if PY_MAJOR_VERSION < 3
        if (tmptype == &PyClass_Type)
            continue;
#endif
        if (!metaclass) {
            metaclass = tmptype;
            continue;
        }
        if (PyType_IsSubtype(metaclass, tmptype))
            continue;
        if (PyType_IsSubtype(tmptype, metaclass)) {
            metaclass = tmptype;
            continue;
        }
        PyErr_SetString(PyExc_TypeError,
                        "metaclass conflict: "
                        "the metaclass of a derived class "
                        "must be a (non-strict) subclass "
                        "of the metaclasses of all its bases");
        return NULL;
    }
    if (!metaclass) {
#if PY_MAJOR_VERSION < 3
        metaclass = &PyClass_Type;
#else
        metaclass = &PyType_Type;
#endif
    }
    Py_INCREF((PyObject*) metaclass);
    return (PyObject*) metaclass;
}

/* FetchCommonType */
        static PyTypeObject* __Pyx_FetchCommonType(PyTypeObject* type) {
    PyObject* fake_module;
    PyTypeObject* cached_type = NULL;
    fake_module = PyImport_AddModule((char*) "_cython_" CYTHON_ABI);
    if (!fake_module) return NULL;
    Py_INCREF(fake_module);
    cached_type = (PyTypeObject*) PyObject_GetAttrString(fake_module, type->tp_name);
    if (cached_type) {
        if (!PyType_Check((PyObject*)cached_type)) {
            PyErr_Format(PyExc_TypeError,
                "Shared Cython type %.200s is not a type object",
                type->tp_name);
            goto bad;
        }
        if (cached_type->tp_basicsize != type->tp_basicsize) {
            PyErr_Format(PyExc_TypeError,
                "Shared Cython type %.200s has the wrong size, try recompiling",
                type->tp_name);
            goto bad;
        }
    } else {
        if (!PyErr_ExceptionMatches(PyExc_AttributeError)) goto bad;
        PyErr_Clear();
        if (PyType_Ready(type) < 0) goto bad;
        if (PyObject_SetAttrString(fake_module, type->tp_name, (PyObject*) type) < 0)
            goto bad;
        Py_INCREF(type);
        cached_type = type;
    }
done:
    Py_DECREF(fake_module);
    return cached_type;
bad:
    Py_XDECREF(cached_type);
    cached_type = NULL;
    goto done;
}

/* CythonFunction */
        static PyObject *
__Pyx_CyFunction_get_doc(__pyx_CyFunctionObject *op, CYTHON_UNUSED void *closure)
{
    if (unlikely(op->func_doc == NULL)) {
        if (op->func.m_ml->ml_doc) {
#if PY_MAJOR_VERSION >= 3
            op->func_doc = PyUnicode_FromString(op->func.m_ml->ml_doc);
#else
            op->func_doc = PyString_FromString(op->func.m_ml->ml_doc);
#endif
            if (unlikely(op->func_doc == NULL))
                return NULL;
        } else {
            Py_INCREF(Py_None);
            return Py_None;
        }
    }
    Py_INCREF(op->func_doc);
    return op->func_doc;
}
static int
__Pyx_CyFunction_set_doc(__pyx_CyFunctionObject *op, PyObject *value)
{
    PyObject *tmp = op->func_doc;
    if (value == NULL) {
        value = Py_None;
    }
    Py_INCREF(value);
    op->func_doc = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_name(__pyx_CyFunctionObject *op)
{
    if (unlikely(op->func_name == NULL)) {
#if PY_MAJOR_VERSION >= 3
        op->func_name = PyUnicode_InternFromString(op->func.m_ml->ml_name);
#else
        op->func_name = PyString_InternFromString(op->func.m_ml->ml_name);
#endif
        if (unlikely(op->func_name == NULL))
            return NULL;
    }
    Py_INCREF(op->func_name);
    return op->func_name;
}
static int
__Pyx_CyFunction_set_name(__pyx_CyFunctionObject *op, PyObject *value)
{
    PyObject *tmp;
#if PY_MAJOR_VERSION >= 3
    if (unlikely(value == NULL || !PyUnicode_Check(value))) {
#else
    if (unlikely(value == NULL || !PyString_Check(value))) {
#endif
        PyErr_SetString(PyExc_TypeError,
                        "__name__ must be set to a string object");
        return -1;
    }
    tmp = op->func_name;
    Py_INCREF(value);
    op->func_name = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_qualname(__pyx_CyFunctionObject *op)
{
    Py_INCREF(op->func_qualname);
    return op->func_qualname;
}
static int
__Pyx_CyFunction_set_qualname(__pyx_CyFunctionObject *op, PyObject *value)
{
    PyObject *tmp;
#if PY_MAJOR_VERSION >= 3
    if (unlikely(value == NULL || !PyUnicode_Check(value))) {
#else
    if (unlikely(value == NULL || !PyString_Check(value))) {
#endif
        PyErr_SetString(PyExc_TypeError,
                        "__qualname__ must be set to a string object");
        return -1;
    }
    tmp = op->func_qualname;
    Py_INCREF(value);
    op->func_qualname = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_self(__pyx_CyFunctionObject *m, CYTHON_UNUSED void *closure)
{
    PyObject *self;
    self = m->func_closure;
    if (self == NULL)
        self = Py_None;
    Py_INCREF(self);
    return self;
}
static PyObject *
__Pyx_CyFunction_get_dict(__pyx_CyFunctionObject *op)
{
    if (unlikely(op->func_dict == NULL)) {
        op->func_dict = PyDict_New();
        if (unlikely(op->func_dict == NULL))
            return NULL;
    }
    Py_INCREF(op->func_dict);
    return op->func_dict;
}
static int
__Pyx_CyFunction_set_dict(__pyx_CyFunctionObject *op, PyObject *value)
{
    PyObject *tmp;
    if (unlikely(value == NULL)) {
        PyErr_SetString(PyExc_TypeError,
               "function's dictionary may not be deleted");
        return -1;
    }
    if (unlikely(!PyDict_Check(value))) {
        PyErr_SetString(PyExc_TypeError,
               "setting function's dictionary to a non-dict");
        return -1;
    }
    tmp = op->func_dict;
    Py_INCREF(value);
    op->func_dict = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_globals(__pyx_CyFunctionObject *op)
{
    Py_INCREF(op->func_globals);
    return op->func_globals;
}
static PyObject *
__Pyx_CyFunction_get_closure(CYTHON_UNUSED __pyx_CyFunctionObject *op)
{
    Py_INCREF(Py_None);
    return Py_None;
}
static PyObject *
__Pyx_CyFunction_get_code(__pyx_CyFunctionObject *op)
{
    PyObject* result = (op->func_code) ? op->func_code : Py_None;
    Py_INCREF(result);
    return result;
}
static int
__Pyx_CyFunction_init_defaults(__pyx_CyFunctionObject *op) {
    int result = 0;
    PyObject *res = op->defaults_getter((PyObject *) op);
    if (unlikely(!res))
        return -1;
    #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
    op->defaults_tuple = PyTuple_GET_ITEM(res, 0);
    Py_INCREF(op->defaults_tuple);
    op->defaults_kwdict = PyTuple_GET_ITEM(res, 1);
    Py_INCREF(op->defaults_kwdict);
    #else
    op->defaults_tuple = PySequence_ITEM(res, 0);
    if (unlikely(!op->defaults_tuple)) result = -1;
    else {
        op->defaults_kwdict = PySequence_ITEM(res, 1);
        if (unlikely(!op->defaults_kwdict)) result = -1;
    }
    #endif
    Py_DECREF(res);
    return result;
}
static int
__Pyx_CyFunction_set_defaults(__pyx_CyFunctionObject *op, PyObject* value) {
    PyObject* tmp;
    if (!value) {
        value = Py_None;
    } else if (value != Py_None && !PyTuple_Check(value)) {
        PyErr_SetString(PyExc_TypeError,
                        "__defaults__ must be set to a tuple object");
        return -1;
    }
    Py_INCREF(value);
    tmp = op->defaults_tuple;
    op->defaults_tuple = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_defaults(__pyx_CyFunctionObject *op) {
    PyObject* result = op->defaults_tuple;
    if (unlikely(!result)) {
        if (op->defaults_getter) {
            if (__Pyx_CyFunction_init_defaults(op) < 0) return NULL;
            result = op->defaults_tuple;
        } else {
            result = Py_None;
        }
    }
    Py_INCREF(result);
    return result;
}
static int
__Pyx_CyFunction_set_kwdefaults(__pyx_CyFunctionObject *op, PyObject* value) {
    PyObject* tmp;
    if (!value) {
        value = Py_None;
    } else if (value != Py_None && !PyDict_Check(value)) {
        PyErr_SetString(PyExc_TypeError,
                        "__kwdefaults__ must be set to a dict object");
        return -1;
    }
    Py_INCREF(value);
    tmp = op->defaults_kwdict;
    op->defaults_kwdict = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_kwdefaults(__pyx_CyFunctionObject *op) {
    PyObject* result = op->defaults_kwdict;
    if (unlikely(!result)) {
        if (op->defaults_getter) {
            if (__Pyx_CyFunction_init_defaults(op) < 0) return NULL;
            result = op->defaults_kwdict;
        } else {
            result = Py_None;
        }
    }
    Py_INCREF(result);
    return result;
}
static int
__Pyx_CyFunction_set_annotations(__pyx_CyFunctionObject *op, PyObject* value) {
    PyObject* tmp;
    if (!value || value == Py_None) {
        value = NULL;
    } else if (!PyDict_Check(value)) {
        PyErr_SetString(PyExc_TypeError,
                        "__annotations__ must be set to a dict object");
        return -1;
    }
    Py_XINCREF(value);
    tmp = op->func_annotations;
    op->func_annotations = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_CyFunction_get_annotations(__pyx_CyFunctionObject *op) {
    PyObject* result = op->func_annotations;
    if (unlikely(!result)) {
        result = PyDict_New();
        if (unlikely(!result)) return NULL;
        op->func_annotations = result;
    }
    Py_INCREF(result);
    return result;
}
static PyGetSetDef __pyx_CyFunction_getsets[] = {
    {(char *) "func_doc", (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0},
    {(char *) "__doc__",  (getter)__Pyx_CyFunction_get_doc, (setter)__Pyx_CyFunction_set_doc, 0, 0},
    {(char *) "func_name", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0},
    {(char *) "__name__", (getter)__Pyx_CyFunction_get_name, (setter)__Pyx_CyFunction_set_name, 0, 0},
    {(char *) "__qualname__", (getter)__Pyx_CyFunction_get_qualname, (setter)__Pyx_CyFunction_set_qualname, 0, 0},
    {(char *) "__self__", (getter)__Pyx_CyFunction_get_self, 0, 0, 0},
    {(char *) "func_dict", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0},
    {(char *) "__dict__", (getter)__Pyx_CyFunction_get_dict, (setter)__Pyx_CyFunction_set_dict, 0, 0},
    {(char *) "func_globals", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0},
    {(char *) "__globals__", (getter)__Pyx_CyFunction_get_globals, 0, 0, 0},
    {(char *) "func_closure", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0},
    {(char *) "__closure__", (getter)__Pyx_CyFunction_get_closure, 0, 0, 0},
    {(char *) "func_code", (getter)__Pyx_CyFunction_get_code, 0, 0, 0},
    {(char *) "__code__", (getter)__Pyx_CyFunction_get_code, 0, 0, 0},
    {(char *) "func_defaults", (getter)__Pyx_CyFunction_get_defaults, (setter)__Pyx_CyFunction_set_defaults, 0, 0},
    {(char *) "__defaults__", (getter)__Pyx_CyFunction_get_defaults, (setter)__Pyx_CyFunction_set_defaults, 0, 0},
    {(char *) "__kwdefaults__", (getter)__Pyx_CyFunction_get_kwdefaults, (setter)__Pyx_CyFunction_set_kwdefaults, 0, 0},
    {(char *) "__annotations__", (getter)__Pyx_CyFunction_get_annotations, (setter)__Pyx_CyFunction_set_annotations, 0, 0},
    {0, 0, 0, 0, 0}
};
static PyMemberDef __pyx_CyFunction_members[] = {
    {(char *) "__module__", T_OBJECT, offsetof(__pyx_CyFunctionObject, func.m_module), PY_WRITE_RESTRICTED, 0},
    {0, 0, 0,  0, 0}
};
static PyObject *
__Pyx_CyFunction_reduce(__pyx_CyFunctionObject *m, CYTHON_UNUSED PyObject *args)
{
#if PY_MAJOR_VERSION >= 3
    return PyUnicode_FromString(m->func.m_ml->ml_name);
#else
    return PyString_FromString(m->func.m_ml->ml_name);
#endif
}
static PyMethodDef __pyx_CyFunction_methods[] = {
    {"__reduce__", (PyCFunction)__Pyx_CyFunction_reduce, METH_VARARGS, 0},
    {0, 0, 0, 0}
};
#if PY_VERSION_HEX < 0x030500A0
#define __Pyx_CyFunction_weakreflist(cyfunc) ((cyfunc)->func_weakreflist)
#else
#define __Pyx_CyFunction_weakreflist(cyfunc) ((cyfunc)->func.m_weakreflist)
#endif
static PyObject *__Pyx_CyFunction_New(PyTypeObject *type, PyMethodDef *ml, int flags, PyObject* qualname,
                                      PyObject *closure, PyObject *module, PyObject* globals, PyObject* code) {
    __pyx_CyFunctionObject *op = PyObject_GC_New(__pyx_CyFunctionObject, type);
    if (op == NULL)
        return NULL;
    op->flags = flags;
    __Pyx_CyFunction_weakreflist(op) = NULL;
    op->func.m_ml = ml;
    op->func.m_self = (PyObject *) op;
    Py_XINCREF(closure);
    op->func_closure = closure;
    Py_XINCREF(module);
    op->func.m_module = module;
    op->func_dict = NULL;
    op->func_name = NULL;
    Py_INCREF(qualname);
    op->func_qualname = qualname;
    op->func_doc = NULL;
    op->func_classobj = NULL;
    op->func_globals = globals;
    Py_INCREF(op->func_globals);
    Py_XINCREF(code);
    op->func_code = code;
    op->defaults_pyobjects = 0;
    op->defaults = NULL;
    op->defaults_tuple = NULL;
    op->defaults_kwdict = NULL;
    op->defaults_getter = NULL;
    op->func_annotations = NULL;
    PyObject_GC_Track(op);
    return (PyObject *) op;
}
static int
__Pyx_CyFunction_clear(__pyx_CyFunctionObject *m)
{
    Py_CLEAR(m->func_closure);
    Py_CLEAR(m->func.m_module);
    Py_CLEAR(m->func_dict);
    Py_CLEAR(m->func_name);
    Py_CLEAR(m->func_qualname);
    Py_CLEAR(m->func_doc);
    Py_CLEAR(m->func_globals);
    Py_CLEAR(m->func_code);
    Py_CLEAR(m->func_classobj);
    Py_CLEAR(m->defaults_tuple);
    Py_CLEAR(m->defaults_kwdict);
    Py_CLEAR(m->func_annotations);
    if (m->defaults) {
        PyObject **pydefaults = __Pyx_CyFunction_Defaults(PyObject *, m);
        int i;
        for (i = 0; i < m->defaults_pyobjects; i++)
            Py_XDECREF(pydefaults[i]);
        PyObject_Free(m->defaults);
        m->defaults = NULL;
    }
    return 0;
}
static void __Pyx_CyFunction_dealloc(__pyx_CyFunctionObject *m)
{
    PyObject_GC_UnTrack(m);
    if (__Pyx_CyFunction_weakreflist(m) != NULL)
        PyObject_ClearWeakRefs((PyObject *) m);
    __Pyx_CyFunction_clear(m);
    PyObject_GC_Del(m);
}
static int __Pyx_CyFunction_traverse(__pyx_CyFunctionObject *m, visitproc visit, void *arg)
{
    Py_VISIT(m->func_closure);
    Py_VISIT(m->func.m_module);
    Py_VISIT(m->func_dict);
    Py_VISIT(m->func_name);
    Py_VISIT(m->func_qualname);
    Py_VISIT(m->func_doc);
    Py_VISIT(m->func_globals);
    Py_VISIT(m->func_code);
    Py_VISIT(m->func_classobj);
    Py_VISIT(m->defaults_tuple);
    Py_VISIT(m->defaults_kwdict);
    if (m->defaults) {
        PyObject **pydefaults = __Pyx_CyFunction_Defaults(PyObject *, m);
        int i;
        for (i = 0; i < m->defaults_pyobjects; i++)
            Py_VISIT(pydefaults[i]);
    }
    return 0;
}
static PyObject *__Pyx_CyFunction_descr_get(PyObject *func, PyObject *obj, PyObject *type)
{
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    if (m->flags & __Pyx_CYFUNCTION_STATICMETHOD) {
        Py_INCREF(func);
        return func;
    }
    if (m->flags & __Pyx_CYFUNCTION_CLASSMETHOD) {
        if (type == NULL)
            type = (PyObject *)(Py_TYPE(obj));
        return __Pyx_PyMethod_New(func, type, (PyObject *)(Py_TYPE(type)));
    }
    if (obj == Py_None)
        obj = NULL;
    return __Pyx_PyMethod_New(func, obj, type);
}
static PyObject*
__Pyx_CyFunction_repr(__pyx_CyFunctionObject *op)
{
#if PY_MAJOR_VERSION >= 3
    return PyUnicode_FromFormat("<cyfunction %U at %p>",
                                op->func_qualname, (void *)op);
#else
    return PyString_FromFormat("<cyfunction %s at %p>",
                               PyString_AsString(op->func_qualname), (void *)op);
#endif
}
static PyObject * __Pyx_CyFunction_CallMethod(PyObject *func, PyObject *self, PyObject *arg, PyObject *kw) {
    PyCFunctionObject* f = (PyCFunctionObject*)func;
    PyCFunction meth = f->m_ml->ml_meth;
    Py_ssize_t size;
    switch (f->m_ml->ml_flags & (METH_VARARGS | METH_KEYWORDS | METH_NOARGS | METH_O)) {
    case METH_VARARGS:
        if (likely(kw == NULL || PyDict_Size(kw) == 0))
            return (*meth)(self, arg);
        break;
    case METH_VARARGS | METH_KEYWORDS:
        return (*(PyCFunctionWithKeywords)meth)(self, arg, kw);
    case METH_NOARGS:
        if (likely(kw == NULL || PyDict_Size(kw) == 0)) {
            size = PyTuple_GET_SIZE(arg);
            if (likely(size == 0))
                return (*meth)(self, NULL);
            PyErr_Format(PyExc_TypeError,
                "%.200s() takes no arguments (%" CYTHON_FORMAT_SSIZE_T "d given)",
                f->m_ml->ml_name, size);
            return NULL;
        }
        break;
    case METH_O:
        if (likely(kw == NULL || PyDict_Size(kw) == 0)) {
            size = PyTuple_GET_SIZE(arg);
            if (likely(size == 1)) {
                PyObject *result, *arg0;
                #if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
                arg0 = PyTuple_GET_ITEM(arg, 0);
                #else
                arg0 = PySequence_ITEM(arg, 0); if (unlikely(!arg0)) return NULL;
                #endif
                result = (*meth)(self, arg0);
                #if !(CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS)
                Py_DECREF(arg0);
                #endif
                return result;
            }
            PyErr_Format(PyExc_TypeError,
                "%.200s() takes exactly one argument (%" CYTHON_FORMAT_SSIZE_T "d given)",
                f->m_ml->ml_name, size);
            return NULL;
        }
        break;
    default:
        PyErr_SetString(PyExc_SystemError, "Bad call flags in "
                        "__Pyx_CyFunction_Call. METH_OLDARGS is no "
                        "longer supported!");
        return NULL;
    }
    PyErr_Format(PyExc_TypeError, "%.200s() takes no keyword arguments",
                 f->m_ml->ml_name);
    return NULL;
}
static CYTHON_INLINE PyObject *__Pyx_CyFunction_Call(PyObject *func, PyObject *arg, PyObject *kw) {
    return __Pyx_CyFunction_CallMethod(func, ((PyCFunctionObject*)func)->m_self, arg, kw);
}
static PyObject *__Pyx_CyFunction_CallAsMethod(PyObject *func, PyObject *args, PyObject *kw) {
    PyObject *result;
    __pyx_CyFunctionObject *cyfunc = (__pyx_CyFunctionObject *) func;
    if ((cyfunc->flags & __Pyx_CYFUNCTION_CCLASS) && !(cyfunc->flags & __Pyx_CYFUNCTION_STATICMETHOD)) {
        Py_ssize_t argc;
        PyObject *new_args;
        PyObject *self;
        argc = PyTuple_GET_SIZE(args);
        new_args = PyTuple_GetSlice(args, 1, argc);
        if (unlikely(!new_args))
            return NULL;
        self = PyTuple_GetItem(args, 0);
        if (unlikely(!self)) {
            Py_DECREF(new_args);
            return NULL;
        }
        result = __Pyx_CyFunction_CallMethod(func, self, new_args, kw);
        Py_DECREF(new_args);
    } else {
        result = __Pyx_CyFunction_Call(func, args, kw);
    }
    return result;
}
static PyTypeObject __pyx_CyFunctionType_type = {
    PyVarObject_HEAD_INIT(0, 0)
    "cython_function_or_method",
    sizeof(__pyx_CyFunctionObject),
    0,
    (destructor) __Pyx_CyFunction_dealloc,
    0,
    0,
    0,
#if PY_MAJOR_VERSION < 3
    0,
#else
    0,
#endif
    (reprfunc) __Pyx_CyFunction_repr,
    0,
    0,
    0,
    0,
    __Pyx_CyFunction_CallAsMethod,
    0,
    0,
    0,
    0,
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC,
    0,
    (traverseproc) __Pyx_CyFunction_traverse,
    (inquiry) __Pyx_CyFunction_clear,
    0,
#if PY_VERSION_HEX < 0x030500A0
    offsetof(__pyx_CyFunctionObject, func_weakreflist),
#else
    offsetof(PyCFunctionObject, m_weakreflist),
#endif
    0,
    0,
    __pyx_CyFunction_methods,
    __pyx_CyFunction_members,
    __pyx_CyFunction_getsets,
    0,
    0,
    __Pyx_CyFunction_descr_get,
    0,
    offsetof(__pyx_CyFunctionObject, func_dict),
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
#if PY_VERSION_HEX >= 0x030400a1
    0,
#endif
};
static int __pyx_CyFunction_init(void) {
    __pyx_CyFunctionType = __Pyx_FetchCommonType(&__pyx_CyFunctionType_type);
    if (unlikely(__pyx_CyFunctionType == NULL)) {
        return -1;
    }
    return 0;
}
static CYTHON_INLINE void *__Pyx_CyFunction_InitDefaults(PyObject *func, size_t size, int pyobjects) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->defaults = PyObject_Malloc(size);
    if (unlikely(!m->defaults))
        return PyErr_NoMemory();
    memset(m->defaults, 0, size);
    m->defaults_pyobjects = pyobjects;
    return m->defaults;
}
static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsTuple(PyObject *func, PyObject *tuple) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->defaults_tuple = tuple;
    Py_INCREF(tuple);
}
static CYTHON_INLINE void __Pyx_CyFunction_SetDefaultsKwDict(PyObject *func, PyObject *dict) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->defaults_kwdict = dict;
    Py_INCREF(dict);
}
static CYTHON_INLINE void __Pyx_CyFunction_SetAnnotationsDict(PyObject *func, PyObject *dict) {
    __pyx_CyFunctionObject *m = (__pyx_CyFunctionObject *) func;
    m->func_annotations = dict;
    Py_INCREF(dict);
}

/* Py3ClassCreate */
            static PyObject *__Pyx_Py3MetaclassPrepare(PyObject *metaclass, PyObject *bases, PyObject *name,
                                           PyObject *qualname, PyObject *mkw, PyObject *modname, PyObject *doc) {
    PyObject *ns;
    if (metaclass) {
        PyObject *prep = __Pyx_PyObject_GetAttrStr(metaclass, __pyx_n_s_prepare);
        if (prep) {
            PyObject *pargs = PyTuple_Pack(2, name, bases);
            if (unlikely(!pargs)) {
                Py_DECREF(prep);
                return NULL;
            }
            ns = PyObject_Call(prep, pargs, mkw);
            Py_DECREF(prep);
            Py_DECREF(pargs);
        } else {
            if (unlikely(!PyErr_ExceptionMatches(PyExc_AttributeError)))
                return NULL;
            PyErr_Clear();
            ns = PyDict_New();
        }
    } else {
        ns = PyDict_New();
    }
    if (unlikely(!ns))
        return NULL;
    if (unlikely(PyObject_SetItem(ns, __pyx_n_s_module, modname) < 0)) goto bad;
    if (unlikely(PyObject_SetItem(ns, __pyx_n_s_qualname, qualname) < 0)) goto bad;
    if (unlikely(doc && PyObject_SetItem(ns, __pyx_n_s_doc, doc) < 0)) goto bad;
    return ns;
bad:
    Py_DECREF(ns);
    return NULL;
}
static PyObject *__Pyx_Py3ClassCreate(PyObject *metaclass, PyObject *name, PyObject *bases,
                                      PyObject *dict, PyObject *mkw,
                                      int calculate_metaclass, int allow_py2_metaclass) {
    PyObject *result, *margs;
    PyObject *owned_metaclass = NULL;
    if (allow_py2_metaclass) {
        owned_metaclass = PyObject_GetItem(dict, __pyx_n_s_metaclass);
        if (owned_metaclass) {
            metaclass = owned_metaclass;
        } else if (likely(PyErr_ExceptionMatches(PyExc_KeyError))) {
            PyErr_Clear();
        } else {
            return NULL;
        }
    }
    if (calculate_metaclass && (!metaclass || PyType_Check(metaclass))) {
        metaclass = __Pyx_CalculateMetaclass((PyTypeObject*) metaclass, bases);
        Py_XDECREF(owned_metaclass);
        if (unlikely(!metaclass))
            return NULL;
        owned_metaclass = metaclass;
    }
    margs = PyTuple_Pack(3, name, bases, dict);
    if (unlikely(!margs)) {
        result = NULL;
    } else {
        result = PyObject_Call(metaclass, margs, mkw);
        Py_DECREF(margs);
    }
    Py_XDECREF(owned_metaclass);
    return result;
}

/* CLineInTraceback */
            static int __Pyx_CLineForTraceback(int c_line) {
#ifdef CYTHON_CLINE_IN_TRACEBACK
    return ((CYTHON_CLINE_IN_TRACEBACK)) ? c_line : 0;
#else
    PyObject *use_cline;
#if CYTHON_COMPILING_IN_CPYTHON
    PyObject **cython_runtime_dict = _PyObject_GetDictPtr(__pyx_cython_runtime);
    if (likely(cython_runtime_dict)) {
      use_cline = PyDict_GetItem(*cython_runtime_dict, __pyx_n_s_cline_in_traceback);
    } else
#endif
    {
      PyObject *ptype, *pvalue, *ptraceback;
      PyObject *use_cline_obj;
      PyErr_Fetch(&ptype, &pvalue, &ptraceback);
      use_cline_obj = __Pyx_PyObject_GetAttrStr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback);
      if (use_cline_obj) {
        use_cline = PyObject_Not(use_cline_obj) ? Py_False : Py_True;
        Py_DECREF(use_cline_obj);
      } else {
        use_cline = NULL;
      }
      PyErr_Restore(ptype, pvalue, ptraceback);
    }
    if (!use_cline) {
        c_line = 0;
        PyObject_SetAttr(__pyx_cython_runtime, __pyx_n_s_cline_in_traceback, Py_False);
    }
    else if (PyObject_Not(use_cline) != 0) {
        c_line = 0;
    }
    return c_line;
#endif
}

/* CodeObjectCache */
            static int __pyx_bisect_code_objects(__Pyx_CodeObjectCacheEntry* entries, int count, int code_line) {
    int start = 0, mid = 0, end = count - 1;
    if (end >= 0 && code_line > entries[end].code_line) {
        return count;
    }
    while (start < end) {
        mid = start + (end - start) / 2;
        if (code_line < entries[mid].code_line) {
            end = mid;
        } else if (code_line > entries[mid].code_line) {
             start = mid + 1;
        } else {
            return mid;
        }
    }
    if (code_line <= entries[mid].code_line) {
        return mid;
    } else {
        return mid + 1;
    }
}
static PyCodeObject *__pyx_find_code_object(int code_line) {
    PyCodeObject* code_object;
    int pos;
    if (unlikely(!code_line) || unlikely(!__pyx_code_cache.entries)) {
        return NULL;
    }
    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
    if (unlikely(pos >= __pyx_code_cache.count) || unlikely(__pyx_code_cache.entries[pos].code_line != code_line)) {
        return NULL;
    }
    code_object = __pyx_code_cache.entries[pos].code_object;
    Py_INCREF(code_object);
    return code_object;
}
static void __pyx_insert_code_object(int code_line, PyCodeObject* code_object) {
    int pos, i;
    __Pyx_CodeObjectCacheEntry* entries = __pyx_code_cache.entries;
    if (unlikely(!code_line)) {
        return;
    }
    if (unlikely(!entries)) {
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Malloc(64*sizeof(__Pyx_CodeObjectCacheEntry));
        if (likely(entries)) {
            __pyx_code_cache.entries = entries;
            __pyx_code_cache.max_count = 64;
            __pyx_code_cache.count = 1;
            entries[0].code_line = code_line;
            entries[0].code_object = code_object;
            Py_INCREF(code_object);
        }
        return;
    }
    pos = __pyx_bisect_code_objects(__pyx_code_cache.entries, __pyx_code_cache.count, code_line);
    if ((pos < __pyx_code_cache.count) && unlikely(__pyx_code_cache.entries[pos].code_line == code_line)) {
        PyCodeObject* tmp = entries[pos].code_object;
        entries[pos].code_object = code_object;
        Py_DECREF(tmp);
        return;
    }
    if (__pyx_code_cache.count == __pyx_code_cache.max_count) {
        int new_max = __pyx_code_cache.max_count + 64;
        entries = (__Pyx_CodeObjectCacheEntry*)PyMem_Realloc(
            __pyx_code_cache.entries, (size_t)new_max*sizeof(__Pyx_CodeObjectCacheEntry));
        if (unlikely(!entries)) {
            return;
        }
        __pyx_code_cache.entries = entries;
        __pyx_code_cache.max_count = new_max;
    }
    for (i=__pyx_code_cache.count; i>pos; i--) {
        entries[i] = entries[i-1];
    }
    entries[pos].code_line = code_line;
    entries[pos].code_object = code_object;
    __pyx_code_cache.count++;
    Py_INCREF(code_object);
}

/* AddTraceback */
            #include "compile.h"
#include "frameobject.h"
#include "traceback.h"
static PyCodeObject* __Pyx_CreateCodeObjectForTraceback(
            const char *funcname, int c_line,
            int py_line, const char *filename) {
    PyCodeObject *py_code = 0;
    PyObject *py_srcfile = 0;
    PyObject *py_funcname = 0;
    #if PY_MAJOR_VERSION < 3
    py_srcfile = PyString_FromString(filename);
    #else
    py_srcfile = PyUnicode_FromString(filename);
    #endif
    if (!py_srcfile) goto bad;
    if (c_line) {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        #else
        py_funcname = PyUnicode_FromFormat( "%s (%s:%d)", funcname, __pyx_cfilenm, c_line);
        #endif
    }
    else {
        #if PY_MAJOR_VERSION < 3
        py_funcname = PyString_FromString(funcname);
        #else
        py_funcname = PyUnicode_FromString(funcname);
        #endif
    }
    if (!py_funcname) goto bad;
    py_code = __Pyx_PyCode_New(
        0,
        0,
        0,
        0,
        0,
        __pyx_empty_bytes, /*PyObject *code,*/
        __pyx_empty_tuple, /*PyObject *consts,*/
        __pyx_empty_tuple, /*PyObject *names,*/
        __pyx_empty_tuple, /*PyObject *varnames,*/
        __pyx_empty_tuple, /*PyObject *freevars,*/
        __pyx_empty_tuple, /*PyObject *cellvars,*/
        py_srcfile,   /*PyObject *filename,*/
        py_funcname,  /*PyObject *name,*/
        py_line,
        __pyx_empty_bytes  /*PyObject *lnotab*/
    );
    Py_DECREF(py_srcfile);
    Py_DECREF(py_funcname);
    return py_code;
bad:
    Py_XDECREF(py_srcfile);
    Py_XDECREF(py_funcname);
    return NULL;
}
static void __Pyx_AddTraceback(const char *funcname, int c_line,
                               int py_line, const char *filename) {
    PyCodeObject *py_code = 0;
    PyFrameObject *py_frame = 0;
    if (c_line) {
        c_line = __Pyx_CLineForTraceback(c_line);
    }
    py_code = __pyx_find_code_object(c_line ? -c_line : py_line);
    if (!py_code) {
        py_code = __Pyx_CreateCodeObjectForTraceback(
            funcname, c_line, py_line, filename);
        if (!py_code) goto bad;
        __pyx_insert_code_object(c_line ? -c_line : py_line, py_code);
    }
    py_frame = PyFrame_New(
        __Pyx_PyThreadState_Current, /*PyThreadState *tstate,*/
        py_code,                     /*PyCodeObject *code,*/
        __pyx_d,              /*PyObject *globals,*/
        0                            /*PyObject *locals*/
    );
    if (!py_frame) goto bad;
    __Pyx_PyFrame_SetLineNumber(py_frame, py_line);
    PyTraceBack_Here(py_frame);
bad:
    Py_XDECREF(py_code);
    Py_XDECREF(py_frame);
}

#if PY_MAJOR_VERSION < 3
static int __Pyx_GetBuffer(PyObject *obj, Py_buffer *view, int flags) {
    if (PyObject_CheckBuffer(obj)) return PyObject_GetBuffer(obj, view, flags);
        if (__Pyx_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) return __pyx_pw_5numpy_7ndarray_1__getbuffer__(obj, view, flags);
    PyErr_Format(PyExc_TypeError, "'%.200s' does not have the buffer interface", Py_TYPE(obj)->tp_name);
    return -1;
}
static void __Pyx_ReleaseBuffer(Py_buffer *view) {
    PyObject *obj = view->obj;
    if (!obj) return;
    if (PyObject_CheckBuffer(obj)) {
        PyBuffer_Release(view);
        return;
    }
    if ((0)) {}
        else if (__Pyx_TypeCheck(obj, __pyx_ptype_5numpy_ndarray)) __pyx_pw_5numpy_7ndarray_3__releasebuffer__(obj, view);
    view->obj = NULL;
    Py_DECREF(obj);
}
#endif


            /* CIntFromPyVerify */
            #define __PYX_VERIFY_RETURN_INT(target_type, func_type, func_value)\
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 0)
#define __PYX_VERIFY_RETURN_INT_EXC(target_type, func_type, func_value)\
    __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, 1)
#define __PYX__VERIFY_RETURN_INT(target_type, func_type, func_value, exc)\
    {\
        func_type value = func_value;\
        if (sizeof(target_type) < sizeof(func_type)) {\
            if (unlikely(value != (func_type) (target_type) value)) {\
                func_type zero = 0;\
                if (exc && unlikely(value == (func_type)-1 && PyErr_Occurred()))\
                    return (target_type) -1;\
                if (is_unsigned && unlikely(value < zero))\
                    goto raise_neg_overflow;\
                else\
                    goto raise_overflow;\
            }\
        }\
        return (target_type) value;\
    }

/* CIntToPy */
            static CYTHON_INLINE PyObject* __Pyx_PyInt_From_int(int value) {
    const int neg_one = (int) -1, const_zero = (int) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(int) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(int) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(int) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(int),
                                     little, !is_unsigned);
    }
}

/* Declarations */
            #if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
      return ::std::complex< float >(x, y);
    }
  #else
    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
      return x + y*(__pyx_t_float_complex)_Complex_I;
    }
  #endif
#else
    static CYTHON_INLINE __pyx_t_float_complex __pyx_t_float_complex_from_parts(float x, float y) {
      __pyx_t_float_complex z;
      z.real = x;
      z.imag = y;
      return z;
    }
#endif

/* Arithmetic */
            #if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eq_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
       return (a.real == b.real) && (a.imag == b.imag);
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_sum_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        z.real = a.real + b.real;
        z.imag = a.imag + b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_diff_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        z.real = a.real - b.real;
        z.imag = a.imag - b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_prod_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        __pyx_t_float_complex z;
        z.real = a.real * b.real - a.imag * b.imag;
        z.imag = a.real * b.imag + a.imag * b.real;
        return z;
    }
    #if 1
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        if (b.imag == 0) {
            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else if (fabsf(b.real) >= fabsf(b.imag)) {
            if (b.real == 0 && b.imag == 0) {
                return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.imag);
            } else {
                float r = b.imag / b.real;
                float s = 1.0 / (b.real + b.imag * r);
                return __pyx_t_float_complex_from_parts(
                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
            }
        } else {
            float r = b.real / b.imag;
            float s = 1.0 / (b.imag + b.real * r);
            return __pyx_t_float_complex_from_parts(
                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
        }
    }
    #else
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_quot_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
        if (b.imag == 0) {
            return __pyx_t_float_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else {
            float denom = b.real * b.real + b.imag * b.imag;
            return __pyx_t_float_complex_from_parts(
                (a.real * b.real + a.imag * b.imag) / denom,
                (a.imag * b.real - a.real * b.imag) / denom);
        }
    }
    #endif
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_neg_float(__pyx_t_float_complex a) {
        __pyx_t_float_complex z;
        z.real = -a.real;
        z.imag = -a.imag;
        return z;
    }
    static CYTHON_INLINE int __Pyx_c_is_zero_float(__pyx_t_float_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_conj_float(__pyx_t_float_complex a) {
        __pyx_t_float_complex z;
        z.real =  a.real;
        z.imag = -a.imag;
        return z;
    }
    #if 1
        static CYTHON_INLINE float __Pyx_c_abs_float(__pyx_t_float_complex z) {
          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
            return sqrtf(z.real*z.real + z.imag*z.imag);
          #else
            return hypotf(z.real, z.imag);
          #endif
        }
        static CYTHON_INLINE __pyx_t_float_complex __Pyx_c_pow_float(__pyx_t_float_complex a, __pyx_t_float_complex b) {
            __pyx_t_float_complex z;
            float r, lnr, theta, z_r, z_theta;
            if (b.imag == 0 && b.real == (int)b.real) {
                if (b.real < 0) {
                    float denom = a.real * a.real + a.imag * a.imag;
                    a.real = a.real / denom;
                    a.imag = -a.imag / denom;
                    b.real = -b.real;
                }
                switch ((int)b.real) {
                    case 0:
                        z.real = 1;
                        z.imag = 0;
                        return z;
                    case 1:
                        return a;
                    case 2:
                        z = __Pyx_c_prod_float(a, a);
                        return __Pyx_c_prod_float(a, a);
                    case 3:
                        z = __Pyx_c_prod_float(a, a);
                        return __Pyx_c_prod_float(z, a);
                    case 4:
                        z = __Pyx_c_prod_float(a, a);
                        return __Pyx_c_prod_float(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                } else if (b.imag == 0) {
                    z.real = powf(a.real, b.real);
                    z.imag = 0;
                    return z;
                } else if (a.real > 0) {
                    r = a.real;
                    theta = 0;
                } else {
                    r = -a.real;
                    theta = atan2f(0, -1);
                }
            } else {
                r = __Pyx_c_abs_float(a);
                theta = atan2f(a.imag, a.real);
            }
            lnr = logf(r);
            z_r = expf(lnr * b.real - theta * b.imag);
            z_theta = theta * b.real + lnr * b.imag;
            z.real = z_r * cosf(z_theta);
            z.imag = z_r * sinf(z_theta);
            return z;
        }
    #endif
#endif

/* Declarations */
            #if CYTHON_CCOMPLEX
  #ifdef __cplusplus
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      return ::std::complex< double >(x, y);
    }
  #else
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      return x + y*(__pyx_t_double_complex)_Complex_I;
    }
  #endif
#else
    static CYTHON_INLINE __pyx_t_double_complex __pyx_t_double_complex_from_parts(double x, double y) {
      __pyx_t_double_complex z;
      z.real = x;
      z.imag = y;
      return z;
    }
#endif

/* Arithmetic */
            #if CYTHON_CCOMPLEX
#else
    static CYTHON_INLINE int __Pyx_c_eq_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
       return (a.real == b.real) && (a.imag == b.imag);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_sum_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real + b.real;
        z.imag = a.imag + b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_diff_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real - b.real;
        z.imag = a.imag - b.imag;
        return z;
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_prod_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        __pyx_t_double_complex z;
        z.real = a.real * b.real - a.imag * b.imag;
        z.imag = a.real * b.imag + a.imag * b.real;
        return z;
    }
    #if 1
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        if (b.imag == 0) {
            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else if (fabs(b.real) >= fabs(b.imag)) {
            if (b.real == 0 && b.imag == 0) {
                return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.imag);
            } else {
                double r = b.imag / b.real;
                double s = 1.0 / (b.real + b.imag * r);
                return __pyx_t_double_complex_from_parts(
                    (a.real + a.imag * r) * s, (a.imag - a.real * r) * s);
            }
        } else {
            double r = b.real / b.imag;
            double s = 1.0 / (b.imag + b.real * r);
            return __pyx_t_double_complex_from_parts(
                (a.real * r + a.imag) * s, (a.imag * r - a.real) * s);
        }
    }
    #else
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_quot_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
        if (b.imag == 0) {
            return __pyx_t_double_complex_from_parts(a.real / b.real, a.imag / b.real);
        } else {
            double denom = b.real * b.real + b.imag * b.imag;
            return __pyx_t_double_complex_from_parts(
                (a.real * b.real + a.imag * b.imag) / denom,
                (a.imag * b.real - a.real * b.imag) / denom);
        }
    }
    #endif
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_neg_double(__pyx_t_double_complex a) {
        __pyx_t_double_complex z;
        z.real = -a.real;
        z.imag = -a.imag;
        return z;
    }
    static CYTHON_INLINE int __Pyx_c_is_zero_double(__pyx_t_double_complex a) {
       return (a.real == 0) && (a.imag == 0);
    }
    static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_conj_double(__pyx_t_double_complex a) {
        __pyx_t_double_complex z;
        z.real =  a.real;
        z.imag = -a.imag;
        return z;
    }
    #if 1
        static CYTHON_INLINE double __Pyx_c_abs_double(__pyx_t_double_complex z) {
          #if !defined(HAVE_HYPOT) || defined(_MSC_VER)
            return sqrt(z.real*z.real + z.imag*z.imag);
          #else
            return hypot(z.real, z.imag);
          #endif
        }
        static CYTHON_INLINE __pyx_t_double_complex __Pyx_c_pow_double(__pyx_t_double_complex a, __pyx_t_double_complex b) {
            __pyx_t_double_complex z;
            double r, lnr, theta, z_r, z_theta;
            if (b.imag == 0 && b.real == (int)b.real) {
                if (b.real < 0) {
                    double denom = a.real * a.real + a.imag * a.imag;
                    a.real = a.real / denom;
                    a.imag = -a.imag / denom;
                    b.real = -b.real;
                }
                switch ((int)b.real) {
                    case 0:
                        z.real = 1;
                        z.imag = 0;
                        return z;
                    case 1:
                        return a;
                    case 2:
                        z = __Pyx_c_prod_double(a, a);
                        return __Pyx_c_prod_double(a, a);
                    case 3:
                        z = __Pyx_c_prod_double(a, a);
                        return __Pyx_c_prod_double(z, a);
                    case 4:
                        z = __Pyx_c_prod_double(a, a);
                        return __Pyx_c_prod_double(z, z);
                }
            }
            if (a.imag == 0) {
                if (a.real == 0) {
                    return a;
                } else if (b.imag == 0) {
                    z.real = pow(a.real, b.real);
                    z.imag = 0;
                    return z;
                } else if (a.real > 0) {
                    r = a.real;
                    theta = 0;
                } else {
                    r = -a.real;
                    theta = atan2(0, -1);
                }
            } else {
                r = __Pyx_c_abs_double(a);
                theta = atan2(a.imag, a.real);
            }
            lnr = log(r);
            z_r = exp(lnr * b.real - theta * b.imag);
            z_theta = theta * b.real + lnr * b.imag;
            z.real = z_r * cos(z_theta);
            z.imag = z_r * sin(z_theta);
            return z;
        }
    #endif
#endif

/* CIntToPy */
            static CYTHON_INLINE PyObject* __Pyx_PyInt_From_enum__NPY_TYPES(enum NPY_TYPES value) {
    const enum NPY_TYPES neg_one = (enum NPY_TYPES) -1, const_zero = (enum NPY_TYPES) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(enum NPY_TYPES) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(enum NPY_TYPES) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(enum NPY_TYPES) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(enum NPY_TYPES) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(enum NPY_TYPES),
                                     little, !is_unsigned);
    }
}

/* CIntFromPy */
            static CYTHON_INLINE int __Pyx_PyInt_As_int(PyObject *x) {
    const int neg_one = (int) -1, const_zero = (int) 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(int) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(int, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (int) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (int) 0;
                case  1: __PYX_VERIFY_RETURN_INT(int, digit, digits[0])
                case 2:
                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) >= 2 * PyLong_SHIFT) {
                            return (int) (((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) >= 3 * PyLong_SHIFT) {
                            return (int) (((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) >= 4 * PyLong_SHIFT) {
                            return (int) (((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0]));
                        }
                    }
                    break;
            }
#endif
#if CYTHON_COMPILING_IN_CPYTHON
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
#else
            {
                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
                if (unlikely(result < 0))
                    return (int) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(int) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(int) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (int) 0;
                case -1: __PYX_VERIFY_RETURN_INT(int, sdigit, (sdigit) (-(sdigit)digits[0]))
                case  1: __PYX_VERIFY_RETURN_INT(int,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(int) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                            return (int) (((int)-1)*(((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(int) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                            return (int) ((((((int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(int) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                            return (int) (((int)-1)*(((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(int) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                            return (int) ((((((((int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(int) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
                            return (int) (((int)-1)*(((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(int) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(int, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(int) - 1 > 4 * PyLong_SHIFT) {
                            return (int) ((((((((((int)digits[3]) << PyLong_SHIFT) | (int)digits[2]) << PyLong_SHIFT) | (int)digits[1]) << PyLong_SHIFT) | (int)digits[0])));
                        }
                    }
                    break;
            }
#endif
            if (sizeof(int) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(int) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(int, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            int val;
            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (int) -1;
        }
    } else {
        int val;
        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
        if (!tmp) return (int) -1;
        val = __Pyx_PyInt_As_int(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to int");
    return (int) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to int");
    return (int) -1;
}

/* CIntToPy */
            static CYTHON_INLINE PyObject* __Pyx_PyInt_From_long(long value) {
    const long neg_one = (long) -1, const_zero = (long) 0;
    const int is_unsigned = neg_one > const_zero;
    if (is_unsigned) {
        if (sizeof(long) < sizeof(long)) {
            return PyInt_FromLong((long) value);
        } else if (sizeof(long) <= sizeof(unsigned long)) {
            return PyLong_FromUnsignedLong((unsigned long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
            return PyLong_FromUnsignedLongLong((unsigned PY_LONG_LONG) value);
#endif
        }
    } else {
        if (sizeof(long) <= sizeof(long)) {
            return PyInt_FromLong((long) value);
#ifdef HAVE_LONG_LONG
        } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
            return PyLong_FromLongLong((PY_LONG_LONG) value);
#endif
        }
    }
    {
        int one = 1; int little = (int)*(unsigned char *)&one;
        unsigned char *bytes = (unsigned char *)&value;
        return _PyLong_FromByteArray(bytes, sizeof(long),
                                     little, !is_unsigned);
    }
}

/* CIntFromPy */
            static CYTHON_INLINE long __Pyx_PyInt_As_long(PyObject *x) {
    const long neg_one = (long) -1, const_zero = (long) 0;
    const int is_unsigned = neg_one > const_zero;
#if PY_MAJOR_VERSION < 3
    if (likely(PyInt_Check(x))) {
        if (sizeof(long) < sizeof(long)) {
            __PYX_VERIFY_RETURN_INT(long, long, PyInt_AS_LONG(x))
        } else {
            long val = PyInt_AS_LONG(x);
            if (is_unsigned && unlikely(val < 0)) {
                goto raise_neg_overflow;
            }
            return (long) val;
        }
    } else
#endif
    if (likely(PyLong_Check(x))) {
        if (is_unsigned) {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (long) 0;
                case  1: __PYX_VERIFY_RETURN_INT(long, digit, digits[0])
                case 2:
                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) >= 2 * PyLong_SHIFT) {
                            return (long) (((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) >= 3 * PyLong_SHIFT) {
                            return (long) (((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) >= 4 * PyLong_SHIFT) {
                            return (long) (((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0]));
                        }
                    }
                    break;
            }
#endif
#if CYTHON_COMPILING_IN_CPYTHON
            if (unlikely(Py_SIZE(x) < 0)) {
                goto raise_neg_overflow;
            }
#else
            {
                int result = PyObject_RichCompareBool(x, Py_False, Py_LT);
                if (unlikely(result < 0))
                    return (long) -1;
                if (unlikely(result == 1))
                    goto raise_neg_overflow;
            }
#endif
            if (sizeof(long) <= sizeof(unsigned long)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned long, PyLong_AsUnsignedLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(long) <= sizeof(unsigned PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, unsigned PY_LONG_LONG, PyLong_AsUnsignedLongLong(x))
#endif
            }
        } else {
#if CYTHON_USE_PYLONG_INTERNALS
            const digit* digits = ((PyLongObject*)x)->ob_digit;
            switch (Py_SIZE(x)) {
                case  0: return (long) 0;
                case -1: __PYX_VERIFY_RETURN_INT(long, sdigit, (sdigit) (-(sdigit)digits[0]))
                case  1: __PYX_VERIFY_RETURN_INT(long,  digit, +digits[0])
                case -2:
                    if (8 * sizeof(long) - 1 > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                            return (long) (((long)-1)*(((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 2:
                    if (8 * sizeof(long) > 1 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 2 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                            return (long) ((((((long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case -3:
                    if (8 * sizeof(long) - 1 > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                            return (long) (((long)-1)*(((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 3:
                    if (8 * sizeof(long) > 2 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 3 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                            return (long) ((((((((long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case -4:
                    if (8 * sizeof(long) - 1 > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, long, -(long) (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                            return (long) (((long)-1)*(((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
                case 4:
                    if (8 * sizeof(long) > 3 * PyLong_SHIFT) {
                        if (8 * sizeof(unsigned long) > 4 * PyLong_SHIFT) {
                            __PYX_VERIFY_RETURN_INT(long, unsigned long, (((((((((unsigned long)digits[3]) << PyLong_SHIFT) | (unsigned long)digits[2]) << PyLong_SHIFT) | (unsigned long)digits[1]) << PyLong_SHIFT) | (unsigned long)digits[0])))
                        } else if (8 * sizeof(long) - 1 > 4 * PyLong_SHIFT) {
                            return (long) ((((((((((long)digits[3]) << PyLong_SHIFT) | (long)digits[2]) << PyLong_SHIFT) | (long)digits[1]) << PyLong_SHIFT) | (long)digits[0])));
                        }
                    }
                    break;
            }
#endif
            if (sizeof(long) <= sizeof(long)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, long, PyLong_AsLong(x))
#ifdef HAVE_LONG_LONG
            } else if (sizeof(long) <= sizeof(PY_LONG_LONG)) {
                __PYX_VERIFY_RETURN_INT_EXC(long, PY_LONG_LONG, PyLong_AsLongLong(x))
#endif
            }
        }
        {
#if CYTHON_COMPILING_IN_PYPY && !defined(_PyLong_AsByteArray)
            PyErr_SetString(PyExc_RuntimeError,
                            "_PyLong_AsByteArray() not available in PyPy, cannot convert large numbers");
#else
            long val;
            PyObject *v = __Pyx_PyNumber_IntOrLong(x);
 #if PY_MAJOR_VERSION < 3
            if (likely(v) && !PyLong_Check(v)) {
                PyObject *tmp = v;
                v = PyNumber_Long(tmp);
                Py_DECREF(tmp);
            }
 #endif
            if (likely(v)) {
                int one = 1; int is_little = (int)*(unsigned char *)&one;
                unsigned char *bytes = (unsigned char *)&val;
                int ret = _PyLong_AsByteArray((PyLongObject *)v,
                                              bytes, sizeof(val),
                                              is_little, !is_unsigned);
                Py_DECREF(v);
                if (likely(!ret))
                    return val;
            }
#endif
            return (long) -1;
        }
    } else {
        long val;
        PyObject *tmp = __Pyx_PyNumber_IntOrLong(x);
        if (!tmp) return (long) -1;
        val = __Pyx_PyInt_As_long(tmp);
        Py_DECREF(tmp);
        return val;
    }
raise_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "value too large to convert to long");
    return (long) -1;
raise_neg_overflow:
    PyErr_SetString(PyExc_OverflowError,
        "can't convert negative value to long");
    return (long) -1;
}

/* FastTypeChecks */
            #if CYTHON_COMPILING_IN_CPYTHON
static int __Pyx_InBases(PyTypeObject *a, PyTypeObject *b) {
    while (a) {
        a = a->tp_base;
        if (a == b)
            return 1;
    }
    return b == &PyBaseObject_Type;
}
static CYTHON_INLINE int __Pyx_IsSubtype(PyTypeObject *a, PyTypeObject *b) {
    PyObject *mro;
    if (a == b) return 1;
    mro = a->tp_mro;
    if (likely(mro)) {
        Py_ssize_t i, n;
        n = PyTuple_GET_SIZE(mro);
        for (i = 0; i < n; i++) {
            if (PyTuple_GET_ITEM(mro, i) == (PyObject *)b)
                return 1;
        }
        return 0;
    }
    return __Pyx_InBases(a, b);
}
#if PY_MAJOR_VERSION == 2
static int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject* exc_type2) {
    PyObject *exception, *value, *tb;
    int res;
    __Pyx_PyThreadState_declare
    __Pyx_PyThreadState_assign
    __Pyx_ErrFetch(&exception, &value, &tb);
    res = exc_type1 ? PyObject_IsSubclass(err, exc_type1) : 0;
    if (unlikely(res == -1)) {
        PyErr_WriteUnraisable(err);
        res = 0;
    }
    if (!res) {
        res = PyObject_IsSubclass(err, exc_type2);
        if (unlikely(res == -1)) {
            PyErr_WriteUnraisable(err);
            res = 0;
        }
    }
    __Pyx_ErrRestore(exception, value, tb);
    return res;
}
#else
static CYTHON_INLINE int __Pyx_inner_PyErr_GivenExceptionMatches2(PyObject *err, PyObject* exc_type1, PyObject *exc_type2) {
    int res = exc_type1 ? __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type1) : 0;
    if (!res) {
        res = __Pyx_IsSubtype((PyTypeObject*)err, (PyTypeObject*)exc_type2);
    }
    return res;
}
#endif
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches(PyObject *err, PyObject* exc_type) {
    if (likely(err == exc_type)) return 1;
    if (likely(PyExceptionClass_Check(err))) {
        return __Pyx_inner_PyErr_GivenExceptionMatches2(err, NULL, exc_type);
    }
    return PyErr_GivenExceptionMatches(err, exc_type);
}
static CYTHON_INLINE int __Pyx_PyErr_GivenExceptionMatches2(PyObject *err, PyObject *exc_type1, PyObject *exc_type2) {
    if (likely(err == exc_type1 || err == exc_type2)) return 1;
    if (likely(PyExceptionClass_Check(err))) {
        return __Pyx_inner_PyErr_GivenExceptionMatches2(err, exc_type1, exc_type2);
    }
    return (PyErr_GivenExceptionMatches(err, exc_type1) || PyErr_GivenExceptionMatches(err, exc_type2));
}
#endif

/* SwapException */
            #if CYTHON_FAST_THREAD_STATE
static CYTHON_INLINE void __Pyx__ExceptionSwap(PyThreadState *tstate, PyObject **type, PyObject **value, PyObject **tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    tmp_type = tstate->exc_type;
    tmp_value = tstate->exc_value;
    tmp_tb = tstate->exc_traceback;
    tstate->exc_type = *type;
    tstate->exc_value = *value;
    tstate->exc_traceback = *tb;
    *type = tmp_type;
    *value = tmp_value;
    *tb = tmp_tb;
}
#else
static CYTHON_INLINE void __Pyx_ExceptionSwap(PyObject **type, PyObject **value, PyObject **tb) {
    PyObject *tmp_type, *tmp_value, *tmp_tb;
    PyErr_GetExcInfo(&tmp_type, &tmp_value, &tmp_tb);
    PyErr_SetExcInfo(*type, *value, *tb);
    *type = tmp_type;
    *value = tmp_value;
    *tb = tmp_tb;
}
#endif

/* PyObjectCallMethod1 */
            static PyObject* __Pyx__PyObject_CallMethod1(PyObject* method, PyObject* arg) {
    PyObject *result = NULL;
#if CYTHON_UNPACK_METHODS
    if (likely(PyMethod_Check(method))) {
        PyObject *self = PyMethod_GET_SELF(method);
        if (likely(self)) {
            PyObject *args;
            PyObject *function = PyMethod_GET_FUNCTION(method);
            #if CYTHON_FAST_PYCALL
            if (PyFunction_Check(function)) {
                PyObject *args[2] = {self, arg};
                result = __Pyx_PyFunction_FastCall(function, args, 2);
                goto done;
            }
            #endif
            #if CYTHON_FAST_PYCCALL
            if (__Pyx_PyFastCFunction_Check(function)) {
                PyObject *args[2] = {self, arg};
                result = __Pyx_PyCFunction_FastCall(function, args, 2);
                goto done;
            }
            #endif
            args = PyTuple_New(2);
            if (unlikely(!args)) goto done;
            Py_INCREF(self);
            PyTuple_SET_ITEM(args, 0, self);
            Py_INCREF(arg);
            PyTuple_SET_ITEM(args, 1, arg);
            Py_INCREF(function);
            result = __Pyx_PyObject_Call(function, args, NULL);
            Py_DECREF(args);
            Py_DECREF(function);
            return result;
        }
    }
#endif
    result = __Pyx_PyObject_CallOneArg(method, arg);
    goto done;
done:
    return result;
}
static PyObject* __Pyx_PyObject_CallMethod1(PyObject* obj, PyObject* method_name, PyObject* arg) {
    PyObject *method, *result = NULL;
    method = __Pyx_PyObject_GetAttrStr(obj, method_name);
    if (unlikely(!method)) goto done;
    result = __Pyx__PyObject_CallMethod1(method, arg);
done:
    Py_XDECREF(method);
    return result;
}

/* CoroutineBase */
            #include <structmember.h>
#include <frameobject.h>
#define __Pyx_Coroutine_Undelegate(gen) Py_CLEAR((gen)->yieldfrom)
static int __Pyx_PyGen__FetchStopIterationValue(CYTHON_UNUSED PyThreadState *__pyx_tstate, PyObject **pvalue) {
    PyObject *et, *ev, *tb;
    PyObject *value = NULL;
    __Pyx_ErrFetch(&et, &ev, &tb);
    if (!et) {
        Py_XDECREF(tb);
        Py_XDECREF(ev);
        Py_INCREF(Py_None);
        *pvalue = Py_None;
        return 0;
    }
    if (likely(et == PyExc_StopIteration)) {
        if (!ev) {
            Py_INCREF(Py_None);
            value = Py_None;
        }
#if PY_VERSION_HEX >= 0x030300A0
        else if (Py_TYPE(ev) == (PyTypeObject*)PyExc_StopIteration) {
            value = ((PyStopIterationObject *)ev)->value;
            Py_INCREF(value);
            Py_DECREF(ev);
        }
#endif
        else if (unlikely(PyTuple_Check(ev))) {
            if (PyTuple_GET_SIZE(ev) >= 1) {
#if CYTHON_ASSUME_SAFE_MACROS && !CYTHON_AVOID_BORROWED_REFS
                value = PyTuple_GET_ITEM(ev, 0);
                Py_INCREF(value);
#else
                value = PySequence_ITEM(ev, 0);
#endif
            } else {
                Py_INCREF(Py_None);
                value = Py_None;
            }
            Py_DECREF(ev);
        }
        else if (!__Pyx_TypeCheck(ev, (PyTypeObject*)PyExc_StopIteration)) {
            value = ev;
        }
        if (likely(value)) {
            Py_XDECREF(tb);
            Py_DECREF(et);
            *pvalue = value;
            return 0;
        }
    } else if (!__Pyx_PyErr_GivenExceptionMatches(et, PyExc_StopIteration)) {
        __Pyx_ErrRestore(et, ev, tb);
        return -1;
    }
    PyErr_NormalizeException(&et, &ev, &tb);
    if (unlikely(!PyObject_TypeCheck(ev, (PyTypeObject*)PyExc_StopIteration))) {
        __Pyx_ErrRestore(et, ev, tb);
        return -1;
    }
    Py_XDECREF(tb);
    Py_DECREF(et);
#if PY_VERSION_HEX >= 0x030300A0
    value = ((PyStopIterationObject *)ev)->value;
    Py_INCREF(value);
    Py_DECREF(ev);
#else
    {
        PyObject* args = __Pyx_PyObject_GetAttrStr(ev, __pyx_n_s_args);
        Py_DECREF(ev);
        if (likely(args)) {
            value = PySequence_GetItem(args, 0);
            Py_DECREF(args);
        }
        if (unlikely(!value)) {
            __Pyx_ErrRestore(NULL, NULL, NULL);
            Py_INCREF(Py_None);
            value = Py_None;
        }
    }
#endif
    *pvalue = value;
    return 0;
}
static CYTHON_INLINE
void __Pyx_Coroutine_ExceptionClear(__pyx_CoroutineObject *self) {
    PyObject *exc_type = self->exc_type;
    PyObject *exc_value = self->exc_value;
    PyObject *exc_traceback = self->exc_traceback;
    self->exc_type = NULL;
    self->exc_value = NULL;
    self->exc_traceback = NULL;
    Py_XDECREF(exc_type);
    Py_XDECREF(exc_value);
    Py_XDECREF(exc_traceback);
}
#define __Pyx_Coroutine_AlreadyRunningError(gen)  (__Pyx__Coroutine_AlreadyRunningError(gen), (PyObject*)NULL)
static void __Pyx__Coroutine_AlreadyRunningError(CYTHON_UNUSED __pyx_CoroutineObject *gen) {
    const char *msg;
    if (0) {
    #ifdef __Pyx_Coroutine_USED
    } else if (__Pyx_Coroutine_CheckExact((PyObject*)gen)) {
        msg = "coroutine already executing";
    #endif
    #ifdef __Pyx_AsyncGen_USED
    } else if (__Pyx_AsyncGen_CheckExact((PyObject*)gen)) {
        msg = "async generator already executing";
    #endif
    } else {
        msg = "generator already executing";
    }
    PyErr_SetString(PyExc_ValueError, msg);
}
#define __Pyx_Coroutine_NotStartedError(gen)  (__Pyx__Coroutine_NotStartedError(gen), (PyObject*)NULL)
static void __Pyx__Coroutine_NotStartedError(CYTHON_UNUSED PyObject *gen) {
    const char *msg;
    if (0) {
    #ifdef __Pyx_Coroutine_USED
    } else if (__Pyx_Coroutine_CheckExact(gen)) {
        msg = "can't send non-None value to a just-started coroutine";
    #endif
    #ifdef __Pyx_AsyncGen_USED
    } else if (__Pyx_AsyncGen_CheckExact(gen)) {
        msg = "can't send non-None value to a just-started async generator";
    #endif
    } else {
        msg = "can't send non-None value to a just-started generator";
    }
    PyErr_SetString(PyExc_TypeError, msg);
}
#define __Pyx_Coroutine_AlreadyTerminatedError(gen, value, closing)  (__Pyx__Coroutine_AlreadyTerminatedError(gen, value, closing), (PyObject*)NULL)
static void __Pyx__Coroutine_AlreadyTerminatedError(CYTHON_UNUSED PyObject *gen, PyObject *value, CYTHON_UNUSED int closing) {
    #ifdef __Pyx_Coroutine_USED
    if (!closing && __Pyx_Coroutine_CheckExact(gen)) {
        PyErr_SetString(PyExc_RuntimeError, "cannot reuse already awaited coroutine");
    } else
    #endif
    if (value) {
        #ifdef __Pyx_AsyncGen_USED
        if (__Pyx_AsyncGen_CheckExact(gen))
            PyErr_SetNone(__Pyx_PyExc_StopAsyncIteration);
        else
        #endif
        PyErr_SetNone(PyExc_StopIteration);
    }
}
static
PyObject *__Pyx_Coroutine_SendEx(__pyx_CoroutineObject *self, PyObject *value, int closing) {
    __Pyx_PyThreadState_declare
    PyThreadState *tstate;
    PyObject *retval;
    assert(!self->is_running);
    if (unlikely(self->resume_label == 0)) {
        if (unlikely(value && value != Py_None)) {
            return __Pyx_Coroutine_NotStartedError((PyObject*)self);
        }
    }
    if (unlikely(self->resume_label == -1)) {
        return __Pyx_Coroutine_AlreadyTerminatedError((PyObject*)self, value, closing);
    }
#if CYTHON_FAST_THREAD_STATE
    __Pyx_PyThreadState_assign
    tstate = __pyx_tstate;
#else
    tstate = __Pyx_PyThreadState_Current;
#endif
    if (self->exc_type) {
#if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_PYSTON
#else
        if (self->exc_traceback) {
            PyTracebackObject *tb = (PyTracebackObject *) self->exc_traceback;
            PyFrameObject *f = tb->tb_frame;
            Py_XINCREF(tstate->frame);
            assert(f->f_back == NULL);
            f->f_back = tstate->frame;
        }
#endif
        __Pyx_ExceptionSwap(&self->exc_type, &self->exc_value,
                            &self->exc_traceback);
    } else {
        __Pyx_Coroutine_ExceptionClear(self);
        __Pyx_ExceptionSave(&self->exc_type, &self->exc_value, &self->exc_traceback);
    }
    self->is_running = 1;
    retval = self->body((PyObject *) self, tstate, value);
    self->is_running = 0;
    return retval;
}
static CYTHON_INLINE void __Pyx_Coroutine_ResetFrameBackpointer(__pyx_CoroutineObject *self) {
    if (likely(self->exc_traceback)) {
#if CYTHON_COMPILING_IN_PYPY || CYTHON_COMPILING_IN_PYSTON
#else
        PyTracebackObject *tb = (PyTracebackObject *) self->exc_traceback;
        PyFrameObject *f = tb->tb_frame;
        Py_CLEAR(f->f_back);
#endif
    }
}
static CYTHON_INLINE
PyObject *__Pyx_Coroutine_MethodReturn(CYTHON_UNUSED PyObject* gen, PyObject *retval) {
    if (unlikely(!retval)) {
        __Pyx_PyThreadState_declare
        __Pyx_PyThreadState_assign
        if (!__Pyx_PyErr_Occurred()) {
            PyObject *exc = PyExc_StopIteration;
            #ifdef __Pyx_AsyncGen_USED
            if (__Pyx_AsyncGen_CheckExact(gen))
                exc = __Pyx_PyExc_StopAsyncIteration;
            #endif
            __Pyx_PyErr_SetNone(exc);
        }
    }
    return retval;
}
static CYTHON_INLINE
PyObject *__Pyx_Coroutine_FinishDelegation(__pyx_CoroutineObject *gen) {
    PyObject *ret;
    PyObject *val = NULL;
    __Pyx_Coroutine_Undelegate(gen);
    __Pyx_PyGen__FetchStopIterationValue(__Pyx_PyThreadState_Current, &val);
    ret = __Pyx_Coroutine_SendEx(gen, val, 0);
    Py_XDECREF(val);
    return ret;
}
static PyObject *__Pyx_Coroutine_Send(PyObject *self, PyObject *value) {
    PyObject *retval;
    __pyx_CoroutineObject *gen = (__pyx_CoroutineObject*) self;
    PyObject *yf = gen->yieldfrom;
    if (unlikely(gen->is_running))
        return __Pyx_Coroutine_AlreadyRunningError(gen);
    if (yf) {
        PyObject *ret;
        gen->is_running = 1;
        #ifdef __Pyx_Generator_USED
        if (__Pyx_Generator_CheckExact(yf)) {
            ret = __Pyx_Coroutine_Send(yf, value);
        } else
        #endif
        #ifdef __Pyx_Coroutine_USED
        if (__Pyx_Coroutine_CheckExact(yf)) {
            ret = __Pyx_Coroutine_Send(yf, value);
        } else
        #endif
        #ifdef __Pyx_AsyncGen_USED
        if (__pyx_PyAsyncGenASend_CheckExact(yf)) {
            ret = __Pyx_async_gen_asend_send(yf, value);
        } else
        #endif
        #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03030000 && (!defined(_MSC_VER) || PY_VERSION_HEX >= 0x03060000)
        if (PyGen_CheckExact(yf)) {
            ret = _PyGen_Send((PyGenObject*)yf, value == Py_None ? NULL : value);
        } else
        #endif
        #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03050000 && defined(PyCoro_CheckExact) && (!defined(_MSC_VER) || PY_VERSION_HEX >= 0x03060000)
        if (PyCoro_CheckExact(yf)) {
            ret = _PyGen_Send((PyGenObject*)yf, value == Py_None ? NULL : value);
        } else
        #endif
        {
            if (value == Py_None)
                ret = Py_TYPE(yf)->tp_iternext(yf);
            else
                ret = __Pyx_PyObject_CallMethod1(yf, __pyx_n_s_send, value);
        }
        gen->is_running = 0;
        if (likely(ret)) {
            return ret;
        }
        retval = __Pyx_Coroutine_FinishDelegation(gen);
    } else {
        retval = __Pyx_Coroutine_SendEx(gen, value, 0);
    }
    return __Pyx_Coroutine_MethodReturn(self, retval);
}
static int __Pyx_Coroutine_CloseIter(__pyx_CoroutineObject *gen, PyObject *yf) {
    PyObject *retval = NULL;
    int err = 0;
    #ifdef __Pyx_Generator_USED
    if (__Pyx_Generator_CheckExact(yf)) {
        retval = __Pyx_Coroutine_Close(yf);
        if (!retval)
            return -1;
    } else
    #endif
    #ifdef __Pyx_Coroutine_USED
    if (__Pyx_Coroutine_CheckExact(yf)) {
        retval = __Pyx_Coroutine_Close(yf);
        if (!retval)
            return -1;
    } else
    if (__Pyx_CoroutineAwait_CheckExact(yf)) {
        retval = __Pyx_CoroutineAwait_Close((__pyx_CoroutineAwaitObject*)yf);
        if (!retval)
            return -1;
    } else
    #endif
    #ifdef __Pyx_AsyncGen_USED
    if (__pyx_PyAsyncGenASend_CheckExact(yf)) {
        retval = __Pyx_async_gen_asend_close(yf, NULL);
    } else
    if (__pyx_PyAsyncGenAThrow_CheckExact(yf)) {
        retval = __Pyx_async_gen_athrow_close(yf, NULL);
    } else
    #endif
    {
        PyObject *meth;
        gen->is_running = 1;
        meth = __Pyx_PyObject_GetAttrStr(yf, __pyx_n_s_close);
        if (unlikely(!meth)) {
            if (!PyErr_ExceptionMatches(PyExc_AttributeError)) {
                PyErr_WriteUnraisable(yf);
            }
            PyErr_Clear();
        } else {
            retval = PyObject_CallFunction(meth, NULL);
            Py_DECREF(meth);
            if (!retval)
                err = -1;
        }
        gen->is_running = 0;
    }
    Py_XDECREF(retval);
    return err;
}
static PyObject *__Pyx_Generator_Next(PyObject *self) {
    __pyx_CoroutineObject *gen = (__pyx_CoroutineObject*) self;
    PyObject *yf = gen->yieldfrom;
    if (unlikely(gen->is_running))
        return __Pyx_Coroutine_AlreadyRunningError(gen);
    if (yf) {
        PyObject *ret;
        gen->is_running = 1;
        #ifdef __Pyx_Generator_USED
        if (__Pyx_Generator_CheckExact(yf)) {
            ret = __Pyx_Generator_Next(yf);
        } else
        #endif
        #if CYTHON_COMPILING_IN_CPYTHON && PY_VERSION_HEX >= 0x03030000 && (!defined(_MSC_VER) || PY_VERSION_HEX >= 0x03060000)
        if (PyGen_CheckExact(yf)) {
            ret = _PyGen_Send((PyGenObject*)yf, NULL);
        } else
        #endif
            ret = Py_TYPE(yf)->tp_iternext(yf);
        gen->is_running = 0;
        if (likely(ret)) {
            return ret;
        }
        return __Pyx_Coroutine_FinishDelegation(gen);
    }
    return __Pyx_Coroutine_SendEx(gen, Py_None, 0);
}
static PyObject *__Pyx_Coroutine_Close(PyObject *self) {
    __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
    PyObject *retval, *raised_exception;
    PyObject *yf = gen->yieldfrom;
    int err = 0;
    if (unlikely(gen->is_running))
        return __Pyx_Coroutine_AlreadyRunningError(gen);
    if (yf) {
        Py_INCREF(yf);
        err = __Pyx_Coroutine_CloseIter(gen, yf);
        __Pyx_Coroutine_Undelegate(gen);
        Py_DECREF(yf);
    }
    if (err == 0)
        PyErr_SetNone(PyExc_GeneratorExit);
    retval = __Pyx_Coroutine_SendEx(gen, NULL, 1);
    if (unlikely(retval)) {
        const char *msg;
        Py_DECREF(retval);
        if ((0)) {
        #ifdef __Pyx_Coroutine_USED
        } else if (__Pyx_Coroutine_CheckExact(self)) {
            msg = "coroutine ignored GeneratorExit";
        #endif
        #ifdef __Pyx_AsyncGen_USED
        } else if (__Pyx_AsyncGen_CheckExact(self)) {
#if PY_VERSION_HEX < 0x03060000
            msg = "async generator ignored GeneratorExit - might require Python 3.6+ finalisation (PEP 525)";
#else
            msg = "async generator ignored GeneratorExit";
#endif
        #endif
        } else {
            msg = "generator ignored GeneratorExit";
        }
        PyErr_SetString(PyExc_RuntimeError, msg);
        return NULL;
    }
    raised_exception = PyErr_Occurred();
    if (likely(!raised_exception || __Pyx_PyErr_GivenExceptionMatches2(raised_exception, PyExc_GeneratorExit, PyExc_StopIteration))) {
        if (raised_exception) PyErr_Clear();
        Py_INCREF(Py_None);
        return Py_None;
    }
    return NULL;
}
static PyObject *__Pyx__Coroutine_Throw(PyObject *self, PyObject *typ, PyObject *val, PyObject *tb,
                                        PyObject *args, int close_on_genexit) {
    __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
    PyObject *yf = gen->yieldfrom;
    if (unlikely(gen->is_running))
        return __Pyx_Coroutine_AlreadyRunningError(gen);
    if (yf) {
        PyObject *ret;
        Py_INCREF(yf);
        if (__Pyx_PyErr_GivenExceptionMatches(typ, PyExc_GeneratorExit) && close_on_genexit) {
            int err = __Pyx_Coroutine_CloseIter(gen, yf);
            Py_DECREF(yf);
            __Pyx_Coroutine_Undelegate(gen);
            if (err < 0)
                return __Pyx_Coroutine_MethodReturn(self, __Pyx_Coroutine_SendEx(gen, NULL, 0));
            goto throw_here;
        }
        gen->is_running = 1;
        if (0
        #ifdef __Pyx_Generator_USED
            || __Pyx_Generator_CheckExact(yf)
        #endif
        #ifdef __Pyx_Coroutine_USED
            || __Pyx_Coroutine_CheckExact(yf)
        #endif
            ) {
            ret = __Pyx__Coroutine_Throw(yf, typ, val, tb, args, close_on_genexit);
        #ifdef __Pyx_Coroutine_USED
        } else if (__Pyx_CoroutineAwait_CheckExact(yf)) {
            ret = __Pyx__Coroutine_Throw(((__pyx_CoroutineAwaitObject*)yf)->coroutine, typ, val, tb, args, close_on_genexit);
        #endif
        } else {
            PyObject *meth = __Pyx_PyObject_GetAttrStr(yf, __pyx_n_s_throw);
            if (unlikely(!meth)) {
                Py_DECREF(yf);
                if (!PyErr_ExceptionMatches(PyExc_AttributeError)) {
                    gen->is_running = 0;
                    return NULL;
                }
                PyErr_Clear();
                __Pyx_Coroutine_Undelegate(gen);
                gen->is_running = 0;
                goto throw_here;
            }
            if (likely(args)) {
                ret = PyObject_CallObject(meth, args);
            } else {
                ret = PyObject_CallFunctionObjArgs(meth, typ, val, tb, NULL);
            }
            Py_DECREF(meth);
        }
        gen->is_running = 0;
        Py_DECREF(yf);
        if (!ret) {
            ret = __Pyx_Coroutine_FinishDelegation(gen);
        }
        return __Pyx_Coroutine_MethodReturn(self, ret);
    }
throw_here:
    __Pyx_Raise(typ, val, tb, NULL);
    return __Pyx_Coroutine_MethodReturn(self, __Pyx_Coroutine_SendEx(gen, NULL, 0));
}
static PyObject *__Pyx_Coroutine_Throw(PyObject *self, PyObject *args) {
    PyObject *typ;
    PyObject *val = NULL;
    PyObject *tb = NULL;
    if (!PyArg_UnpackTuple(args, (char *)"throw", 1, 3, &typ, &val, &tb))
        return NULL;
    return __Pyx__Coroutine_Throw(self, typ, val, tb, args, 1);
}
static int __Pyx_Coroutine_traverse(__pyx_CoroutineObject *gen, visitproc visit, void *arg) {
    Py_VISIT(gen->closure);
    Py_VISIT(gen->classobj);
    Py_VISIT(gen->yieldfrom);
    Py_VISIT(gen->exc_type);
    Py_VISIT(gen->exc_value);
    Py_VISIT(gen->exc_traceback);
    return 0;
}
static int __Pyx_Coroutine_clear(PyObject *self) {
    __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
    Py_CLEAR(gen->closure);
    Py_CLEAR(gen->classobj);
    Py_CLEAR(gen->yieldfrom);
    Py_CLEAR(gen->exc_type);
    Py_CLEAR(gen->exc_value);
    Py_CLEAR(gen->exc_traceback);
#ifdef __Pyx_AsyncGen_USED
    if (__Pyx_AsyncGen_CheckExact(self)) {
        Py_CLEAR(((__pyx_PyAsyncGenObject*)gen)->ag_finalizer);
    }
#endif
    Py_CLEAR(gen->gi_name);
    Py_CLEAR(gen->gi_qualname);
    return 0;
}
static void __Pyx_Coroutine_dealloc(PyObject *self) {
    __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
    PyObject_GC_UnTrack(gen);
    if (gen->gi_weakreflist != NULL)
        PyObject_ClearWeakRefs(self);
    if (gen->resume_label >= 0) {
        PyObject_GC_Track(self);
#if PY_VERSION_HEX >= 0x030400a1
        if (PyObject_CallFinalizerFromDealloc(self))
#else
        Py_TYPE(gen)->tp_del(self);
        if (self->ob_refcnt > 0)
#endif
        {
            return;
        }
        PyObject_GC_UnTrack(self);
    }
#ifdef __Pyx_AsyncGen_USED
    if (__Pyx_AsyncGen_CheckExact(self)) {
        /* We have to handle this case for asynchronous generators
           right here, because this code has to be between UNTRACK
           and GC_Del. */
        Py_CLEAR(((__pyx_PyAsyncGenObject*)self)->ag_finalizer);
    }
#endif
    __Pyx_Coroutine_clear(self);
    PyObject_GC_Del(gen);
}
static void __Pyx_Coroutine_del(PyObject *self) {
    PyObject *error_type, *error_value, *error_traceback;
    __pyx_CoroutineObject *gen = (__pyx_CoroutineObject *) self;
    __Pyx_PyThreadState_declare
    if (gen->resume_label < 0) {
        return;
    }
#if PY_VERSION_HEX < 0x030400a1
    assert(self->ob_refcnt == 0);
    self->ob_refcnt = 1;
#endif
    __Pyx_PyThreadState_assign
    __Pyx_ErrFetch(&error_type, &error_value, &error_traceback);
#ifdef __Pyx_AsyncGen_USED
    if (__Pyx_AsyncGen_CheckExact(self)) {
        __pyx_PyAsyncGenObject *agen = (__pyx_PyAsyncGenObject*)self;
        PyObject *finalizer = agen->ag_finalizer;
        if (finalizer && !agen->ag_closed) {
            PyObject *res = __Pyx_PyObject_CallOneArg(finalizer, self);
            if (unlikely(!res)) {
                PyErr_WriteUnraisable(self);
            } else {
                Py_DECREF(res);
            }
            __Pyx_ErrRestore(error_type, error_value, error_traceback);
            return;
        }
    }
#endif
    if (unlikely(gen->resume_label == 0 && !error_value)) {
#ifdef __Pyx_Coroutine_USED
#ifdef __Pyx_Generator_USED
    if (!__Pyx_Generator_CheckExact(self))
#endif
        {
        PyObject_GC_UnTrack(self);
#if PY_MAJOR_VERSION >= 3  || defined(PyErr_WarnFormat)
        if (unlikely(PyErr_WarnFormat(PyExc_RuntimeWarning, 1, "coroutine '%.50S' was never awaited", gen->gi_qualname) < 0))
            PyErr_WriteUnraisable(self);
#else
        {PyObject *msg;
        char *cmsg;
        #if CYTHON_COMPILING_IN_PYPY
        msg = NULL;
        cmsg = (char*) "coroutine was never awaited";
        #else
        char *cname;
        PyObject *qualname;
        qualname = gen->gi_qualname;
        cname = PyString_AS_STRING(qualname);
        msg = PyString_FromFormat("coroutine '%.50s' was never awaited", cname);
        if (unlikely(!msg)) {
            PyErr_Clear();
            cmsg = (char*) "coroutine was never awaited";
        } else {
            cmsg = PyString_AS_STRING(msg);
        }
        #endif
        if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning, cmsg, 1) < 0))
            PyErr_WriteUnraisable(self);
        Py_XDECREF(msg);}
#endif
        PyObject_GC_Track(self);
        }
#endif
    } else {
        PyObject *res = __Pyx_Coroutine_Close(self);
        if (unlikely(!res)) {
            if (PyErr_Occurred())
                PyErr_WriteUnraisable(self);
        } else {
            Py_DECREF(res);
        }
    }
    __Pyx_ErrRestore(error_type, error_value, error_traceback);
#if PY_VERSION_HEX < 0x030400a1
    assert(self->ob_refcnt > 0);
    if (--self->ob_refcnt == 0) {
        return;
    }
    {
        Py_ssize_t refcnt = self->ob_refcnt;
        _Py_NewReference(self);
        self->ob_refcnt = refcnt;
    }
#if CYTHON_COMPILING_IN_CPYTHON
    assert(PyType_IS_GC(self->ob_type) &&
           _Py_AS_GC(self)->gc.gc_refs != _PyGC_REFS_UNTRACKED);
    _Py_DEC_REFTOTAL;
#endif
#ifdef COUNT_ALLOCS
    --Py_TYPE(self)->tp_frees;
    --Py_TYPE(self)->tp_allocs;
#endif
#endif
}
static PyObject *
__Pyx_Coroutine_get_name(__pyx_CoroutineObject *self)
{
    PyObject *name = self->gi_name;
    if (unlikely(!name)) name = Py_None;
    Py_INCREF(name);
    return name;
}
static int
__Pyx_Coroutine_set_name(__pyx_CoroutineObject *self, PyObject *value)
{
    PyObject *tmp;
#if PY_MAJOR_VERSION >= 3
    if (unlikely(value == NULL || !PyUnicode_Check(value))) {
#else
    if (unlikely(value == NULL || !PyString_Check(value))) {
#endif
        PyErr_SetString(PyExc_TypeError,
                        "__name__ must be set to a string object");
        return -1;
    }
    tmp = self->gi_name;
    Py_INCREF(value);
    self->gi_name = value;
    Py_XDECREF(tmp);
    return 0;
}
static PyObject *
__Pyx_Coroutine_get_qualname(__pyx_CoroutineObject *self)
{
    PyObject *name = self->gi_qualname;
    if (unlikely(!name)) name = Py_None;
    Py_INCREF(name);
    return name;
}
static int
__Pyx_Coroutine_set_qualname(__pyx_CoroutineObject *self, PyObject *value)
{
    PyObject *tmp;
#if PY_MAJOR_VERSION >= 3
    if (unlikely(value == NULL || !PyUnicode_Check(value))) {
#else
    if (unlikely(value == NULL || !PyString_Check(value))) {
#endif
        PyErr_SetString(PyExc_TypeError,
                        "__qualname__ must be set to a string object");
        return -1;
    }
    tmp = self->gi_qualname;
    Py_INCREF(value);
    self->gi_qualname = value;
    Py_XDECREF(tmp);
    return 0;
}
static __pyx_CoroutineObject *__Pyx__Coroutine_New(
            PyTypeObject* type, __pyx_coroutine_body_t body, PyObject *closure,
            PyObject *name, PyObject *qualname, PyObject *module_name) {
    __pyx_CoroutineObject *gen = PyObject_GC_New(__pyx_CoroutineObject, type);
    if (unlikely(!gen))
        return NULL;
    return __Pyx__Coroutine_NewInit(gen, body, closure, name, qualname, module_name);
}
static __pyx_CoroutineObject *__Pyx__Coroutine_NewInit(
            __pyx_CoroutineObject *gen, __pyx_coroutine_body_t body, PyObject *closure,
            PyObject *name, PyObject *qualname, PyObject *module_name) {
    gen->body = body;
    gen->closure = closure;
    Py_XINCREF(closure);
    gen->is_running = 0;
    gen->resume_label = 0;
    gen->classobj = NULL;
    gen->yieldfrom = NULL;
    gen->exc_type = NULL;
    gen->exc_value = NULL;
    gen->exc_traceback = NULL;
    gen->gi_weakreflist = NULL;
    Py_XINCREF(qualname);
    gen->gi_qualname = qualname;
    Py_XINCREF(name);
    gen->gi_name = name;
    Py_XINCREF(module_name);
    gen->gi_modulename = module_name;
    PyObject_GC_Track(gen);
    return gen;
}

/* PatchModuleWithCoroutine */
                static PyObject* __Pyx_Coroutine_patch_module(PyObject* module, const char* py_code) {
#if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
    int result;
    PyObject *globals, *result_obj;
    globals = PyDict_New();  if (unlikely(!globals)) goto ignore;
    result = PyDict_SetItemString(globals, "_cython_coroutine_type",
    #ifdef __Pyx_Coroutine_USED
        (PyObject*)__pyx_CoroutineType);
    #else
        Py_None);
    #endif
    if (unlikely(result < 0)) goto ignore;
    result = PyDict_SetItemString(globals, "_cython_generator_type",
    #ifdef __Pyx_Generator_USED
        (PyObject*)__pyx_GeneratorType);
    #else
        Py_None);
    #endif
    if (unlikely(result < 0)) goto ignore;
    if (unlikely(PyDict_SetItemString(globals, "_module", module) < 0)) goto ignore;
    if (unlikely(PyDict_SetItemString(globals, "__builtins__", __pyx_b) < 0)) goto ignore;
    result_obj = PyRun_String(py_code, Py_file_input, globals, globals);
    if (unlikely(!result_obj)) goto ignore;
    Py_DECREF(result_obj);
    Py_DECREF(globals);
    return module;
ignore:
    Py_XDECREF(globals);
    PyErr_WriteUnraisable(module);
    if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning, "Cython module failed to patch module with custom type", 1) < 0)) {
        Py_DECREF(module);
        module = NULL;
    }
#else
    py_code++;
#endif
    return module;
}

/* PatchGeneratorABC */
                #ifndef CYTHON_REGISTER_ABCS
#define CYTHON_REGISTER_ABCS 1
#endif
#if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
static PyObject* __Pyx_patch_abc_module(PyObject *module);
static PyObject* __Pyx_patch_abc_module(PyObject *module) {
    module = __Pyx_Coroutine_patch_module(
        module, ""
"if _cython_generator_type is not None:\n"
"    try: Generator = _module.Generator\n"
"    except AttributeError: pass\n"
"    else: Generator.register(_cython_generator_type)\n"
"if _cython_coroutine_type is not None:\n"
"    try: Coroutine = _module.Coroutine\n"
"    except AttributeError: pass\n"
"    else: Coroutine.register(_cython_coroutine_type)\n"
    );
    return module;
}
#endif
static int __Pyx_patch_abc(void) {
#if defined(__Pyx_Generator_USED) || defined(__Pyx_Coroutine_USED)
    static int abc_patched = 0;
    if (CYTHON_REGISTER_ABCS && !abc_patched) {
        PyObject *module;
        module = PyImport_ImportModule((PY_MAJOR_VERSION >= 3) ? "collections.abc" : "collections");
        if (!module) {
            PyErr_WriteUnraisable(NULL);
            if (unlikely(PyErr_WarnEx(PyExc_RuntimeWarning,
                    ((PY_MAJOR_VERSION >= 3) ?
                        "Cython module failed to register with collections.abc module" :
                        "Cython module failed to register with collections module"), 1) < 0)) {
                return -1;
            }
        } else {
            module = __Pyx_patch_abc_module(module);
            abc_patched = 1;
            if (unlikely(!module))
                return -1;
            Py_DECREF(module);
        }
        module = PyImport_ImportModule("backports_abc");
        if (module) {
            module = __Pyx_patch_abc_module(module);
            Py_XDECREF(module);
        }
        if (!module) {
            PyErr_Clear();
        }
    }
#else
    if ((0)) __Pyx_Coroutine_patch_module(NULL, NULL);
#endif
    return 0;
}

/* Generator */
                static PyMethodDef __pyx_Generator_methods[] = {
    {"send", (PyCFunction) __Pyx_Coroutine_Send, METH_O,
     (char*) PyDoc_STR("send(arg) -> send 'arg' into generator,\nreturn next yielded value or raise StopIteration.")},
    {"throw", (PyCFunction) __Pyx_Coroutine_Throw, METH_VARARGS,
     (char*) PyDoc_STR("throw(typ[,val[,tb]]) -> raise exception in generator,\nreturn next yielded value or raise StopIteration.")},
    {"close", (PyCFunction) __Pyx_Coroutine_Close, METH_NOARGS,
     (char*) PyDoc_STR("close() -> raise GeneratorExit inside generator.")},
    {0, 0, 0, 0}
};
static PyMemberDef __pyx_Generator_memberlist[] = {
    {(char *) "gi_running", T_BOOL, offsetof(__pyx_CoroutineObject, is_running), READONLY, NULL},
    {(char*) "gi_yieldfrom", T_OBJECT, offsetof(__pyx_CoroutineObject, yieldfrom), READONLY,
     (char*) PyDoc_STR("object being iterated by 'yield from', or None")},
    {0, 0, 0, 0, 0}
};
static PyGetSetDef __pyx_Generator_getsets[] = {
    {(char *) "__name__", (getter)__Pyx_Coroutine_get_name, (setter)__Pyx_Coroutine_set_name,
     (char*) PyDoc_STR("name of the generator"), 0},
    {(char *) "__qualname__", (getter)__Pyx_Coroutine_get_qualname, (setter)__Pyx_Coroutine_set_qualname,
     (char*) PyDoc_STR("qualified name of the generator"), 0},
    {0, 0, 0, 0, 0}
};
static PyTypeObject __pyx_GeneratorType_type = {
    PyVarObject_HEAD_INIT(0, 0)
    "generator",
    sizeof(__pyx_CoroutineObject),
    0,
    (destructor) __Pyx_Coroutine_dealloc,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    Py_TPFLAGS_DEFAULT | Py_TPFLAGS_HAVE_GC | Py_TPFLAGS_HAVE_FINALIZE,
    0,
    (traverseproc) __Pyx_Coroutine_traverse,
    0,
    0,
    offsetof(__pyx_CoroutineObject, gi_weakreflist),
    0,
    (iternextfunc) __Pyx_Generator_Next,
    __pyx_Generator_methods,
    __pyx_Generator_memberlist,
    __pyx_Generator_getsets,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
    0,
#if CYTHON_USE_TP_FINALIZE
    0,
#else
    __Pyx_Coroutine_del,
#endif
    0,
#if CYTHON_USE_TP_FINALIZE
    __Pyx_Coroutine_del,
#endif
};
static int __pyx_Generator_init(void) {
    __pyx_GeneratorType_type.tp_getattro = PyObject_GenericGetAttr;
    __pyx_GeneratorType_type.tp_iter = PyObject_SelfIter;
    __pyx_GeneratorType = __Pyx_FetchCommonType(&__pyx_GeneratorType_type);
    if (unlikely(!__pyx_GeneratorType)) {
        return -1;
    }
    return 0;
}

/* CheckBinaryVersion */
                static int __Pyx_check_binary_version(void) {
    char ctversion[4], rtversion[4];
    PyOS_snprintf(ctversion, 4, "%d.%d", PY_MAJOR_VERSION, PY_MINOR_VERSION);
    PyOS_snprintf(rtversion, 4, "%s", Py_GetVersion());
    if (ctversion[0] != rtversion[0] || ctversion[2] != rtversion[2]) {
        char message[200];
        PyOS_snprintf(message, sizeof(message),
                      "compiletime version %s of module '%.100s' "
                      "does not match runtime version %s",
                      ctversion, __Pyx_MODULE_NAME, rtversion);
        return PyErr_WarnEx(NULL, message, 1);
    }
    return 0;
}

/* ModuleImport */
                #ifndef __PYX_HAVE_RT_ImportModule
#define __PYX_HAVE_RT_ImportModule
static PyObject *__Pyx_ImportModule(const char *name) {
    PyObject *py_name = 0;
    PyObject *py_module = 0;
    py_name = __Pyx_PyIdentifier_FromString(name);
    if (!py_name)
        goto bad;
    py_module = PyImport_Import(py_name);
    Py_DECREF(py_name);
    return py_module;
bad:
    Py_XDECREF(py_name);
    return 0;
}
#endif

/* TypeImport */
                #ifndef __PYX_HAVE_RT_ImportType
#define __PYX_HAVE_RT_ImportType
static PyTypeObject *__Pyx_ImportType(const char *module_name, const char *class_name,
    size_t size, int strict)
{
    PyObject *py_module = 0;
    PyObject *result = 0;
    PyObject *py_name = 0;
    char warning[200];
    Py_ssize_t basicsize;
#ifdef Py_LIMITED_API
    PyObject *py_basicsize;
#endif
    py_module = __Pyx_ImportModule(module_name);
    if (!py_module)
        goto bad;
    py_name = __Pyx_PyIdentifier_FromString(class_name);
    if (!py_name)
        goto bad;
    result = PyObject_GetAttr(py_module, py_name);
    Py_DECREF(py_name);
    py_name = 0;
    Py_DECREF(py_module);
    py_module = 0;
    if (!result)
        goto bad;
    if (!PyType_Check(result)) {
        PyErr_Format(PyExc_TypeError,
            "%.200s.%.200s is not a type object",
            module_name, class_name);
        goto bad;
    }
#ifndef Py_LIMITED_API
    basicsize = ((PyTypeObject *)result)->tp_basicsize;
#else
    py_basicsize = PyObject_GetAttrString(result, "__basicsize__");
    if (!py_basicsize)
        goto bad;
    basicsize = PyLong_AsSsize_t(py_basicsize);
    Py_DECREF(py_basicsize);
    py_basicsize = 0;
    if (basicsize == (Py_ssize_t)-1 && PyErr_Occurred())
        goto bad;
#endif
    if (!strict && (size_t)basicsize > size) {
        PyOS_snprintf(warning, sizeof(warning),
            "%s.%s size changed, may indicate binary incompatibility. Expected %zd, got %zd",
            module_name, class_name, basicsize, size);
        if (PyErr_WarnEx(NULL, warning, 0) < 0) goto bad;
    }
    else if ((size_t)basicsize != size) {
        PyErr_Format(PyExc_ValueError,
            "%.200s.%.200s has the wrong size, try recompiling. Expected %zd, got %zd",
            module_name, class_name, basicsize, size);
        goto bad;
    }
    return (PyTypeObject *)result;
bad:
    Py_XDECREF(py_module);
    Py_XDECREF(result);
    return NULL;
}
#endif

/* InitStrings */
                static int __Pyx_InitStrings(__Pyx_StringTabEntry *t) {
    while (t->p) {
        #if PY_MAJOR_VERSION < 3
        if (t->is_unicode) {
            *t->p = PyUnicode_DecodeUTF8(t->s, t->n - 1, NULL);
        } else if (t->intern) {
            *t->p = PyString_InternFromString(t->s);
        } else {
            *t->p = PyString_FromStringAndSize(t->s, t->n - 1);
        }
        #else
        if (t->is_unicode | t->is_str) {
            if (t->intern) {
                *t->p = PyUnicode_InternFromString(t->s);
            } else if (t->encoding) {
                *t->p = PyUnicode_Decode(t->s, t->n - 1, t->encoding, NULL);
            } else {
                *t->p = PyUnicode_FromStringAndSize(t->s, t->n - 1);
            }
        } else {
            *t->p = PyBytes_FromStringAndSize(t->s, t->n - 1);
        }
        #endif
        if (!*t->p)
            return -1;
        if (PyObject_Hash(*t->p) == -1)
            PyErr_Clear();
        ++t;
    }
    return 0;
}

static CYTHON_INLINE PyObject* __Pyx_PyUnicode_FromString(const char* c_str) {
    return __Pyx_PyUnicode_FromStringAndSize(c_str, (Py_ssize_t)strlen(c_str));
}
static CYTHON_INLINE const char* __Pyx_PyObject_AsString(PyObject* o) {
    Py_ssize_t ignore;
    return __Pyx_PyObject_AsStringAndSize(o, &ignore);
}
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
#if !CYTHON_PEP393_ENABLED
static const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
    char* defenc_c;
    PyObject* defenc = _PyUnicode_AsDefaultEncodedString(o, NULL);
    if (!defenc) return NULL;
    defenc_c = PyBytes_AS_STRING(defenc);
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
    {
        char* end = defenc_c + PyBytes_GET_SIZE(defenc);
        char* c;
        for (c = defenc_c; c < end; c++) {
            if ((unsigned char) (*c) >= 128) {
                PyUnicode_AsASCIIString(o);
                return NULL;
            }
        }
    }
#endif
    *length = PyBytes_GET_SIZE(defenc);
    return defenc_c;
}
#else
static CYTHON_INLINE const char* __Pyx_PyUnicode_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
    if (unlikely(__Pyx_PyUnicode_READY(o) == -1)) return NULL;
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
    if (likely(PyUnicode_IS_ASCII(o))) {
        *length = PyUnicode_GET_LENGTH(o);
        return PyUnicode_AsUTF8(o);
    } else {
        PyUnicode_AsASCIIString(o);
        return NULL;
    }
#else
    return PyUnicode_AsUTF8AndSize(o, length);
#endif
}
#endif
#endif
static CYTHON_INLINE const char* __Pyx_PyObject_AsStringAndSize(PyObject* o, Py_ssize_t *length) {
#if __PYX_DEFAULT_STRING_ENCODING_IS_ASCII || __PYX_DEFAULT_STRING_ENCODING_IS_DEFAULT
    if (
#if PY_MAJOR_VERSION < 3 && __PYX_DEFAULT_STRING_ENCODING_IS_ASCII
            __Pyx_sys_getdefaultencoding_not_ascii &&
#endif
            PyUnicode_Check(o)) {
        return __Pyx_PyUnicode_AsStringAndSize(o, length);
    } else
#endif
#if (!CYTHON_COMPILING_IN_PYPY) || (defined(PyByteArray_AS_STRING) && defined(PyByteArray_GET_SIZE))
    if (PyByteArray_Check(o)) {
        *length = PyByteArray_GET_SIZE(o);
        return PyByteArray_AS_STRING(o);
    } else
#endif
    {
        char* result;
        int r = PyBytes_AsStringAndSize(o, &result, length);
        if (unlikely(r < 0)) {
            return NULL;
        } else {
            return result;
        }
    }
}
static CYTHON_INLINE int __Pyx_PyObject_IsTrue(PyObject* x) {
   int is_true = x == Py_True;
   if (is_true | (x == Py_False) | (x == Py_None)) return is_true;
   else return PyObject_IsTrue(x);
}
static PyObject* __Pyx_PyNumber_IntOrLongWrongResultType(PyObject* result, const char* type_name) {
#if PY_MAJOR_VERSION >= 3
    if (PyLong_Check(result)) {
        if (PyErr_WarnFormat(PyExc_DeprecationWarning, 1,
                "__int__ returned non-int (type %.200s).  "
                "The ability to return an instance of a strict subclass of int "
                "is deprecated, and may be removed in a future version of Python.",
                Py_TYPE(result)->tp_name)) {
            Py_DECREF(result);
            return NULL;
        }
        return result;
    }
#endif
    PyErr_Format(PyExc_TypeError,
                 "__%.4s__ returned non-%.4s (type %.200s)",
                 type_name, type_name, Py_TYPE(result)->tp_name);
    Py_DECREF(result);
    return NULL;
}
static CYTHON_INLINE PyObject* __Pyx_PyNumber_IntOrLong(PyObject* x) {
#if CYTHON_USE_TYPE_SLOTS
  PyNumberMethods *m;
#endif
  const char *name = NULL;
  PyObject *res = NULL;
#if PY_MAJOR_VERSION < 3
  if (likely(PyInt_Check(x) || PyLong_Check(x)))
#else
  if (likely(PyLong_Check(x)))
#endif
    return __Pyx_NewRef(x);
#if CYTHON_USE_TYPE_SLOTS
  m = Py_TYPE(x)->tp_as_number;
  #if PY_MAJOR_VERSION < 3
  if (m && m->nb_int) {
    name = "int";
    res = m->nb_int(x);
  }
  else if (m && m->nb_long) {
    name = "long";
    res = m->nb_long(x);
  }
  #else
  if (likely(m && m->nb_int)) {
    name = "int";
    res = m->nb_int(x);
  }
  #endif
#else
  if (!PyBytes_CheckExact(x) && !PyUnicode_CheckExact(x)) {
    res = PyNumber_Int(x);
  }
#endif
  if (likely(res)) {
#if PY_MAJOR_VERSION < 3
    if (unlikely(!PyInt_Check(res) && !PyLong_Check(res))) {
#else
    if (unlikely(!PyLong_CheckExact(res))) {
#endif
        return __Pyx_PyNumber_IntOrLongWrongResultType(res, name);
    }
  }
  else if (!PyErr_Occurred()) {
    PyErr_SetString(PyExc_TypeError,
                    "an integer is required");
  }
  return res;
}
static CYTHON_INLINE Py_ssize_t __Pyx_PyIndex_AsSsize_t(PyObject* b) {
  Py_ssize_t ival;
  PyObject *x;
#if PY_MAJOR_VERSION < 3
  if (likely(PyInt_CheckExact(b))) {
    if (sizeof(Py_ssize_t) >= sizeof(long))
        return PyInt_AS_LONG(b);
    else
        return PyInt_AsSsize_t(x);
  }
#endif
  if (likely(PyLong_CheckExact(b))) {
    #if CYTHON_USE_PYLONG_INTERNALS
    const digit* digits = ((PyLongObject*)b)->ob_digit;
    const Py_ssize_t size = Py_SIZE(b);
    if (likely(__Pyx_sst_abs(size) <= 1)) {
        ival = likely(size) ? digits[0] : 0;
        if (size == -1) ival = -ival;
        return ival;
    } else {
      switch (size) {
         case 2:
           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -2:
           if (8 * sizeof(Py_ssize_t) > 2 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case 3:
           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -3:
           if (8 * sizeof(Py_ssize_t) > 3 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((((size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case 4:
           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
             return (Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
         case -4:
           if (8 * sizeof(Py_ssize_t) > 4 * PyLong_SHIFT) {
             return -(Py_ssize_t) (((((((((size_t)digits[3]) << PyLong_SHIFT) | (size_t)digits[2]) << PyLong_SHIFT) | (size_t)digits[1]) << PyLong_SHIFT) | (size_t)digits[0]));
           }
           break;
      }
    }
    #endif
    return PyLong_AsSsize_t(b);
  }
  x = PyNumber_Index(b);
  if (!x) return -1;
  ival = PyInt_AsSsize_t(x);
  Py_DECREF(x);
  return ival;
}
static CYTHON_INLINE PyObject * __Pyx_PyInt_FromSize_t(size_t ival) {
    return PyInt_FromSize_t(ival);
}


#endif /* Py_PYTHON_H */
