py_find_1st
===========

py_find_1st is a numpy extension that allows to find the first index
into an 1D-array that validates a boolean condition that can consist of
a comparison operator and a limit value.

Functionality
-------------

This extension solves the very frequent problem of finding first indices
without requiring to read the full array.

The call sequence

::

   import numpy as np
   import utils_find_1st as utf1st

   limit = 0.
   rr= np.random.randn(100)
   ind = utf1st.find_1st(rr < limit, True, utf1st.cmp_equal)

and more efficiently

::

   ind = utf1st.find_1st(rr, limit, utf1st.cmp_smaller)

is equivalent to

::

   import numpy as np
   limit = 0.
   rr= np.random.randn(100)
   ind = np.flatnonzero(rr < limit)
   if len(ind) :
       ret = ind[0]
   else:
       ret = -1

Implementation details
----------------------

py_find_1st is written as a numpy extension making use of a templated
implementation of the find_1st function that currently supports
operating on arrays of dtypes:

::

   [np.float64, np.float32, np.int64, np.int32, np.bool]

Comparison operators are selected using integer opcodes with the
following meaning:

::

   opcode == utils_find_1st.cmp_smaller    ->  comp op: <
   opcode == utils_find_1st.cmp_smaller_eq ->  comp op: <=
   opcode == utils_find_1st.cmp_equal      ->  comp op: ==
   opcode == utils_find_1st.cmp_not_equal  ->  comp op: !=
   opcode == utils_find_1st.cmp_larger     ->  comp op: <
   opcode == utils_find_1st.cmp_larger_eq  ->  comp op: <=

Performance
-----------

The runtime difference is strongly depending on the number of true cases
in the array. If the condition is never valid runtime is the same - both
implementations do not produce a valid index and need to compare the
full array - but on case that there are matches np.flatnonzero needs to
run through the full array and needs to create a result array with size
that depends o the number of matches while find_1st only produces a
scalar result and only needs to compare the array until the first match
is found.

Depending on the size of the array and the number of matches the speed
difference can be very significant (easily > factor 10)

test
----

run test/test_find_1st.py which should display "all tests passed!"

Benchmarking
~~~~~~~~~~~~

We can easily compare the runtime for the setup displayed before
executing the three lines

.. raw:: html

   <pre><code>In [6]: timeit ind = np.flatnonzero(rr < limit)[0]
   1.69&mu;s &plusmn; 24.5ns per loop (mean &plusmn; std. dev. of 7 runs, 1000000 loops each)
       
   In [4]: timeit ind = utf1st.find_1st(rr limit, True, utf1st.cmp_equal)
   1.13&mu;s &plusmn; 18.9ns per loop (mean &plusmn; std. dev. of 7 runs, 1000000 loops each)
       
   In [5]: timeit ind = utf1st.find_1st(rr, limit, utf1st.cmp_smaller)
   270ns &plusmn; 5.57ns per loop (mean &plusmn; std. dev. of 7 runs, 1000000 loops each)
   </code></pre>

It shows the rather significant improvement obtained by the last version
that does not require to perform all comparisons of the 100 elements. In
the above case the second element is tested positive. In the worst case,
where no valid element is present all comparisons have to be performed
and flatnonzero does not need to create a results array, and therefore
performance should be similar. We can benchmark this case by means of
changing the limit such that it does never fit. For the small array
sizes we used so far the overhead of np.flanonzero is dominating the
costs as can be seen in the following.

.. raw:: html

   <pre><code>In [9]: limit = -1000.
   In [10]: timeit ind = np.flatnonzero(rr < limit)
   1.56&mu;s &plusmn; 13.8ns per loop (mean &plusmn; std. dev. of 7 runs, 1000000 loops each)

   In [11]: timeit ind = utf1st.find_1st(rr < limit, True, utf1st.cmp_equal)
   1.16&mu;s &plusmn; 7.07ns per loop (mean &plusmn; std. dev. of 7 runs, 1000000 loops each)

   In [12]: timeit ind = utf1st.find_1st(rr, limit, utf1st.cmp_smaller)
   314ns &plusmn; 3.36ns per loop (mean &plusmn; std. dev. of 7 runs, 1000000 loops each)
   </code></pre>

For a significantly larger array size costs become more comparable

.. raw:: html

   <pre><code>rr= np.random.randn(10000)
   In [13]: timeit ind = np.flatnonzero(rr < limit)
   4.87&mu;s &plusmn; 101ns per loop (mean &plusmn; std. dev. of 7 runs, 100000 loops each)

   In [14]: timeit ind = utf1st.find_1st(rr < limit, True, utf1st.cmp_equal)
   8.95&mu;s &plusmn; 497ns per loop (mean &plusmn; std. dev. of 7 runs 100000 loops each)

   In [15]: timeit ind = utf1st.find_1st(rr, limit, utf1st.cmp_smaller)
   4.4&mu;s &plusmn; 47.9ns per loop (mean &plusmn; std. dev. of 7 runs, 100000 loops each)
   </code></pre>

Which demonstrates that even in this case the find_1st extension is more
efficient besides if the boolean intermediate array is used in line 14.
In that case the comparison of the full array is actually performed
twice.

This result is nevertheless a bit higher than expected from the sum of
the simple boolean comparison

.. raw:: html

   <pre><code>In [35]: timeit ind = rr < limit
   3.31&mu;s &plusmn; 47.3ns per loop (mean &plusmn; std. dev. of 7 runs, 100000 loops each)
   </code></pre>

and the find_1st operation in line 15 above, which would result in
7.7μs. The clarification of this remaining issue needs further
investigation. Any comments are welcome.

Changes
-------

Version 1.1.7 (2025-01-01)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  Updated build system to support numpy 2.0 and to avoid running
   setup.py directly.
-  Fixed math display in README.

Version 1.1.6 (2023-10-28)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  fixed test script for numpy > 1.20
-  fixed Makefile under macosx ARM64

Version 1.1.5 (2021-02-02)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  fixed problems with numpy dependency handling (thanks to xmatthias).
   Now use oldest-supported-numpy instead of using the most recent
   numpy.

Version 1.1.4 (2019-08-04)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  added support for automatic installation of requirements
-  add and support pre-release tags in the version number
-  use hashlib to calculate the README checksum.
-  support testing via ``make check``

Version 1.1.3 (2018-10-05)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  Removed setting stdlib for clang in setup.py - the default should do
   just fine.

Version 1.1.2 (2018-09-28)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  Removed ez_setup.py that seems to be no longer maintained by
   setuptools maintainers.

Version 1.1.1 (2017-09-19)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  Use NPY_INT64/NPY_INT32 instead of NPY_INT/NPY_LONG such that the
   test does not rely on the compiler specific int sizes.

Version 1.1.0 (2017-09-18)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  fixed bug in cmp operator values that were not coherent on the python
   and C++ side
-  support arbitrary strides for one dimensional arrays
-  Added test script

Version 1.0.7 (2017-09-18)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  Changed compiler test to hopefully work for MSVC under windows.

Version 1.0.6 (2017-05-31)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  Removed more non ascii elements in README.

Version 1.0.5 (2017-05-31)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  Fixed non ascii elements in README that led to problems with some
   python configurations.

Version 1.0.4 (2017-05-31)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  Fixed setup.py problems: on the fly generation of LONG_DESCRIPTION
   file.

Version 1.0.3 (2017-05-31)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  Moved to github

Version 1.0.2 (2017-05-31)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  Force using c++ compiler

Version 1.0.1 (2017-05-31)
~~~~~~~~~~~~~~~~~~~~~~~~~~

-  initial release

Copyright
---------

Copyright (C) 2017 IRCAM

License
-------

GPL see file Copying.txt

Author
------

Axel Roebel
