"""
=====================================
Sparse matrices (:mod:`scipy.sparse`)
=====================================

.. currentmodule:: scipy.sparse

SciPy 2-D sparse matrix package for numeric data.

Contents
========

Sparse matrix classes
---------------------

.. autosummary::
   :toctree: generated/

   bsr_matrix - Block Sparse Row matrix
   coo_matrix - A sparse matrix in COOrdinate format
   csc_matrix - Compressed Sparse Column matrix
   csr_matrix - Compressed Sparse Row matrix
   dia_matrix - Sparse matrix with DIAgonal storage
   dok_matrix - Dictionary Of Keys based sparse matrix
   lil_matrix - Row-based linked list sparse matrix

Functions
---------

Building sparse matrices:

.. autosummary::
   :toctree: generated/

   eye - Sparse MxN matrix whose k-th diagonal is all ones
   identity - Identity matrix in sparse format
   kron - kronecker product of two sparse matrices
   kronsum - kronecker sum of sparse matrices
   diags - Return a sparse matrix from diagonals
   spdiags - Return a sparse matrix from diagonals
   block_diag - Build a block diagonal sparse matrix
   tril - Lower triangular portion of a matrix in sparse format
   triu - Upper triangular portion of a matrix in sparse format
   bmat - Build a sparse matrix from sparse sub-blocks
   hstack - Stack sparse matrices horizontally (column wise)
   vstack - Stack sparse matrices vertically (row wise)
   rand - Random values in a given shape

Identifying sparse matrices:

.. autosummary::
   :toctree: generated/

   issparse
   isspmatrix
   isspmatrix_csc
   isspmatrix_csr
   isspmatrix_bsr
   isspmatrix_lil
   isspmatrix_dok
   isspmatrix_coo
   isspmatrix_dia

Submodules
----------

.. autosummary::
   :toctree: generated/

   csgraph - Compressed sparse graph routines
   linalg - sparse linear algebra routines

Exceptions
----------

.. autosummary::
   :toctree: generated/

   SparseEfficiencyWarning
   SparseWarning


Usage information
=================

There are seven available sparse matrix types:

    1. csc_matrix: Compressed Sparse Column format
    2. csr_matrix: Compressed Sparse Row format
    3. bsr_matrix: Block Sparse Row format
    4. lil_matrix: List of Lists format
    5. dok_matrix: Dictionary of Keys format
    6. coo_matrix: COOrdinate format (aka IJV, triplet format)
    7. dia_matrix: DIAgonal format

To construct a matrix efficiently, use either lil_matrix (recommended) or
dok_matrix. The lil_matrix class supports basic slicing and fancy
indexing with a similar syntax to NumPy arrays.  As illustrated below,
the COO format may also be used to efficiently construct matrices.

To perform manipulations such as multiplication or inversion, first
convert the matrix to either CSC or CSR format. The lil_matrix format is
row-based, so conversion to CSR is efficient, whereas conversion to CSC
is less so.

All conversions among the CSR, CSC, and COO formats are efficient,
linear-time operations.

Matrix vector product
---------------------
To do a vector product between a sparse matrix and a vector simply use
the matrix `dot` method, as described in its docstring:

>>> import numpy as np
>>> from scipy.sparse import csr_matrix
>>> A = csr_matrix([[1, 2, 0], [0, 0, 3], [4, 0, 5]])
>>> v = np.array([1, 0, -1])
>>> A.dot(v)
array([ 1, -3, -1], dtype=int64)

.. warning:: As of NumPy 1.7, `np.dot` is not aware of sparse matrices,
  therefore using it will result on unexpected results or errors.
  The corresponding dense matrix should be obtained first instead:

  >>> np.dot(A.todense(), v)
  matrix([[ 1, -3, -1]], dtype=int64)

  but then all the performance advantages would be lost.
  Notice that it returned a matrix, because `todense` returns a matrix.

The CSR format is specially suitable for fast matrix vector products.

Example 1
---------
Construct a 1000x1000 lil_matrix and add some values to it:

>>> from scipy.sparse import lil_matrix
>>> from scipy.sparse.linalg import spsolve
>>> from numpy.linalg import solve, norm
>>> from numpy.random import rand

>>> A = lil_matrix((1000, 1000))
>>> A[0, :100] = rand(100)
>>> A[1, 100:200] = A[0, :100]
>>> A.setdiag(rand(1000))

Now convert it to CSR format and solve A x = b for x:

>>> A = A.tocsr()
>>> b = rand(1000)
>>> x = spsolve(A, b)

Convert it to a dense matrix and solve, and check that the result
is the same:

>>> x_ = solve(A.todense(), b)

Now we can compute norm of the error with:

>>> err = norm(x-x_)
>>> err < 1e-10
True

It should be small :)


Example 2
---------

Construct a matrix in COO format:

>>> from scipy import sparse
>>> from numpy import array
>>> I = array([0,3,1,0])
>>> J = array([0,3,1,2])
>>> V = array([4,5,7,9])
>>> A = sparse.coo_matrix((V,(I,J)),shape=(4,4))

Notice that the indices do not need to be sorted.

Duplicate (i,j) entries are summed when converting to CSR or CSC.

>>> I = array([0,0,1,3,1,0,0])
>>> J = array([0,2,1,3,1,0,0])
>>> V = array([1,1,1,1,1,1,1])
>>> B = sparse.coo_matrix((V,(I,J)),shape=(4,4)).tocsr()

This is useful for constructing finite-element stiffness and mass matrices.

Further Details
---------------

CSR column indices are not necessarily sorted.  Likewise for CSC row
indices.  Use the .sorted_indices() and .sort_indices() methods when
sorted indices are required (e.g. when passing data to other libraries).

"""

from __future__ import division, print_function, absolute_import

# Original code by Travis Oliphant.
# Modified and extended by Ed Schofield, Robert Cimrman,
# Nathan Bell, and Jake Vanderplas.

from .base import *
from .csr import *
from .csc import *
from .lil import *
from .dok import *
from .coo import *
from .dia import *
from .bsr import *
from .construct import *
from .extract import *

# for backward compatibility with v0.10.  This function is marked as deprecated
from .csgraph import cs_graph_components

#from spfuncs import *

__all__ = [s for s in dir() if not s.startswith('_')]
from numpy.testing import Tester
test = Tester().test
bench = Tester().bench
