.. _performance-howto:

=========================
How to optimize for speed
=========================

The following gives some practical guidelines to help you write efficient
code for the scikit-learn project.

.. note::

  While it is always useful to profile your code so as to **check
  performance assumptions**, it is also highly recommended
  to **review the literature** to ensure that the implemented algorithm
  is the state of the art for the task before investing into costly
  implementation optimization.

  Times and times, hours of efforts invested in optimizing complicated
  implementation details have been rendered irrelevant by the subsequent
  discovery of simple **algorithmic tricks**, or by using another algorithm
  altogether that is better suited to the problem.

  The section :ref:`warm-restarts` gives an example of such a trick.


Python, Cython or C/C++?
========================

.. currentmodule:: sklearn

In general, the scikit-learn project emphasizes the **readability** of
the source code to make it easy for the project users to dive into the
source code so as to understand how the algorithm behaves on their data
but also for ease of maintanability (by the developers).

When implementing a new algorithm is thus recommended to **start
implementing it in Python using Numpy and Scipy** by taking care of avoiding
looping code using the vectorized idioms of those libraries. In practice
this means trying to **replace any nested for loops by calls to equivalent
Numpy array methods**. The goal is to avoid the CPU wasting time in the
Python interpreter rather than crunching numbers to fit your statistical
model. It's generally a good idea to consider NumPy and SciPy performance tips:
http://wiki.scipy.org/PerformanceTips

Sometimes however an algorithm cannot be expressed efficiently in simple
vectorized Numpy code. In this case, the recommended strategy is the
following:

  1. **Profile** the Python implementation to find the main bottleneck and
     isolate it in a **dedicated module level function**. This function
     will be reimplemented as a compiled extension module.

  2. If there exists a well maintained BSD or MIT **C/C++** implementation
     of the same algorithm that is not too big, you can write a
     **Cython wrapper** for it and include a copy of the source code
     of the library in the scikit-learn source tree: this strategy is
     used for the classes :class:`svm.LinearSVC`, :class:`svm.SVC` and
     :class:`linear_model.LogisticRegression` (wrappers for liblinear
     and libsvm).

  3. Otherwise, write an optimized version of your Python function using
     **Cython** directly. This strategy is used
     for the :class:`linear_model.ElasticNet` and
     :class:`linear_model.SGDClassifier` classes for instance.

  4. **Move the Python version of the function in the tests** and use
     it to check that the results of the compiled extension are consistent
     with the gold standard, easy to debug Python version.

  5. Once the code is optimized (not simple bottleneck spottable by
     profiling), check whether it is possible to have **coarse grained
     parallelism** that is amenable to **multi-processing** by using the
     ``joblib.Parallel`` class.

When using Cython, include the generated C source code alongside with
the Cython source code. The goal is to make it possible to install the
scikit on any machine with Python, Numpy, Scipy and C/C++ compiler.

Fast matrix multiplications
===========================

Matrix multiplications (matrix-matrix and matrix-vector) are usually handled
using the NumPy function ``np.dot``, but in versions of NumPy before 1.7.2
this function is suboptimal when the inputs are not both in the C (row-major)
layout; in that case, the inputs may be implicitly copied to obtain the right
layout. This obviously consumes memory and takes time.

The function ``fast_dot`` in ``sklearn.utils.extmath`` offers a fast
replacement for ``np.dot`` that prevents copies from being made in some cases.
In all other cases, it dispatches to ``np.dot`` and when the NumPy version is
new enough, it is in fact an alias for that function, making it a drop-in
replacement. Example usage of ``fast_dot``::

  >>> import numpy as np
  >>> from sklearn.utils.extmath import fast_dot
  >>> X = np.random.random_sample([2, 10])
  >>> np.allclose(np.dot(X, X.T), fast_dot(X, X.T))
  True

This function operates optimally on 2-dimensional arrays, both of the same
dtype, which should be either single or double precision float. If these
requirements aren't met or the BLAS package is not available, the call is
silently dispatched to ``numpy.dot``. If you want to be sure when the original
``numpy.dot`` has been invoked in a situation where it is suboptimal, you can
activate the related warning::

  >>> import warnings
  >>> from sklearn.utils.validation import NonBLASDotWarning
  >>> warnings.simplefilter('always', NonBLASDotWarning) # doctest: +SKIP

.. _profiling-python-code:

Profiling Python code
=====================

In order to profile Python code we recommend to write a script that
loads and prepare you data and then use the IPython integrated profiler
for interactively exploring the relevant part for the code.

Suppose we want to profile the Non Negative Matrix Factorization module
of the scikit. Let us setup a new IPython session and load the digits
dataset and as in the :ref:`example_plot_digits_classification.py` example::

  In [1]: from sklearn.decomposition import NMF

  In [2]: from sklearn.datasets import load_digits

  In [3]: X = load_digits().data

Before starting the profiling session and engaging in tentative
optimization iterations, it is important to measure the total execution
time of the function we want to optimize without any kind of profiler
overhead and save it somewhere for later reference::

  In [4]: %timeit NMF(n_components=16, tol=1e-2).fit(X)
  1 loops, best of 3: 1.7 s per loop

To have have a look at the overall performance profile using the ``%prun``
magic command::

  In [5]: %prun -l nmf.py NMF(n_components=16, tol=1e-2).fit(X)
           14496 function calls in 1.682 CPU seconds

     Ordered by: internal time
     List reduced from 90 to 9 due to restriction <'nmf.py'>

     ncalls  tottime  percall  cumtime  percall filename:lineno(function)
         36    0.609    0.017    1.499    0.042 nmf.py:151(_nls_subproblem)
       1263    0.157    0.000    0.157    0.000 nmf.py:18(_pos)
          1    0.053    0.053    1.681    1.681 nmf.py:352(fit_transform)
        673    0.008    0.000    0.057    0.000 nmf.py:28(norm)
          1    0.006    0.006    0.047    0.047 nmf.py:42(_initialize_nmf)
         36    0.001    0.000    0.010    0.000 nmf.py:36(_sparseness)
         30    0.001    0.000    0.001    0.000 nmf.py:23(_neg)
          1    0.000    0.000    0.000    0.000 nmf.py:337(__init__)
          1    0.000    0.000    1.681    1.681 nmf.py:461(fit)

The ``tottime`` column is the most interesting: it gives to total time spent
executing the code of a given function ignoring the time spent in executing the
sub-functions. The real total time (local code + sub-function calls) is given by
the ``cumtime`` column.

Note the use of the ``-l nmf.py`` that restricts the output to lines that
contains the "nmf.py" string. This is useful to have a quick look at the hotspot
of the nmf Python module it-self ignoring anything else.

Here is the beginning of the output of the same command without the ``-l nmf.py``
filter::

  In [5] %prun NMF(n_components=16, tol=1e-2).fit(X)
           16159 function calls in 1.840 CPU seconds

     Ordered by: internal time

     ncalls  tottime  percall  cumtime  percall filename:lineno(function)
       2833    0.653    0.000    0.653    0.000 {numpy.core._dotblas.dot}
         46    0.651    0.014    1.636    0.036 nmf.py:151(_nls_subproblem)
       1397    0.171    0.000    0.171    0.000 nmf.py:18(_pos)
       2780    0.167    0.000    0.167    0.000 {method 'sum' of 'numpy.ndarray' objects}
          1    0.064    0.064    1.840    1.840 nmf.py:352(fit_transform)
       1542    0.043    0.000    0.043    0.000 {method 'flatten' of 'numpy.ndarray' objects}
        337    0.019    0.000    0.019    0.000 {method 'all' of 'numpy.ndarray' objects}
       2734    0.011    0.000    0.181    0.000 fromnumeric.py:1185(sum)
          2    0.010    0.005    0.010    0.005 {numpy.linalg.lapack_lite.dgesdd}
        748    0.009    0.000    0.065    0.000 nmf.py:28(norm)
  ...

The above results show that the execution is largely dominated by
dot products operations (delegated to blas). Hence there is probably
no huge gain to expect by rewriting this code in Cython or C/C++: in
this case out of the 1.7s total execution time, almost 0.7s are spent
in compiled code we can consider optimal. By rewriting the rest of the
Python code and assuming we could achieve a 1000% boost on this portion
(which is highly unlikely given the shallowness of the Python loops),
we would not gain more than a 2.4x speed-up globally.

Hence major improvements can only be achieved by **algorithmic
improvements** in this particular example (e.g. trying to find operation
that are both costly and useless to avoid computing then rather than
trying to optimize their implementation).

It is however still interesting to check what's happening inside the
``_nls_subproblem`` function which is the hotspot if we only consider
Python code: it takes around 100% of the cumulated time of the module. In
order to better understand the profile of this specific function, let
us install ``line-prof`` and wire it to IPython::

  $ pip install line-profiler

- **Under IPython <= 0.10**, edit ``~/.ipython/ipy_user_conf.py`` and
  ensure the following lines are present::

    import IPython.ipapi
    ip = IPython.ipapi.get()

  Towards the end of the file, define the ``%lprun`` magic::

    import line_profiler
    ip.expose_magic('lprun', line_profiler.magic_lprun)

- **Under IPython 0.11+**, first create a configuration profile::

    $ ipython profile create

  Then create a file named ``~/.ipython/extensions/line_profiler_ext.py`` with
  the following content::

    import line_profiler

    def load_ipython_extension(ip):
        ip.define_magic('lprun', line_profiler.magic_lprun)

  Then register it in ``~/.ipython/profile_default/ipython_config.py``::

    c.TerminalIPythonApp.extensions = [
        'line_profiler_ext',
    ]
    c.InteractiveShellApp.extensions = [
        'line_profiler_ext',
    ]

  This will register the ``%lprun`` magic command in the IPython terminal
  application and the other frontends such as qtconsole and notebook.

Now restart IPython and let us use this new toy::

  In [1]: from sklearn.datasets import load_digits

  In [2]: from sklearn.decomposition.nmf import _nls_subproblem, NMF

  In [3]: X = load_digits().data

  In [4]: %lprun -f _nls_subproblem NMF(n_components=16, tol=1e-2).fit(X)
  Timer unit: 1e-06 s

  File: sklearn/decomposition/nmf.py
  Function: _nls_subproblem at line 137
  Total time: 1.73153 s

  Line #      Hits         Time  Per Hit   % Time  Line Contents
  ==============================================================
     137                                           def _nls_subproblem(V, W, H_init, tol, max_iter):
     138                                               """Non-negative least square solver
     ...
     170                                               """
     171        48         5863    122.1      0.3      if (H_init < 0).any():
     172                                                   raise ValueError("Negative values in H_init passed to NLS solver.")
     173
     174        48          139      2.9      0.0      H = H_init
     175        48       112141   2336.3      5.8      WtV = np.dot(W.T, V)
     176        48        16144    336.3      0.8      WtW = np.dot(W.T, W)
     177
     178                                               # values justified in the paper
     179        48          144      3.0      0.0      alpha = 1
     180        48          113      2.4      0.0      beta = 0.1
     181       638         1880      2.9      0.1      for n_iter in xrange(1, max_iter + 1):
     182       638       195133    305.9     10.2          grad = np.dot(WtW, H) - WtV
     183       638       495761    777.1     25.9          proj_gradient = norm(grad[np.logical_or(grad < 0, H > 0)])
     184       638         2449      3.8      0.1          if proj_gradient < tol:
     185        48          130      2.7      0.0              break
     186
     187      1474         4474      3.0      0.2          for inner_iter in xrange(1, 20):
     188      1474        83833     56.9      4.4              Hn = H - alpha * grad
     189                                                       # Hn = np.where(Hn > 0, Hn, 0)
     190      1474       194239    131.8     10.1              Hn = _pos(Hn)
     191      1474        48858     33.1      2.5              d = Hn - H
     192      1474       150407    102.0      7.8              gradd = np.sum(grad * d)
     193      1474       515390    349.7     26.9              dQd = np.sum(np.dot(WtW, d) * d)
     ...

By looking at the top values of the ``% Time`` column it is really easy to
pin-point the most expensive expressions that would deserve additional care.


Memory usage profiling
======================

You can analyze in detail the memory usage of any Python code with the help of
`memory_profiler <http://pypi.python.org/pypi/memory_profiler>`_. First,
install the latest version::

    $ pip install -U memory_profiler

Then, setup the magics in a manner similar to ``line_profiler``.

- **Under IPython <= 0.10**, edit ``~/.ipython/ipy_user_conf.py`` and
  ensure the following lines are present::

    import IPython.ipapi
    ip = IPython.ipapi.get()

  Towards the end of the file, define the ``%memit`` and ``%mprun`` magics::

    import memory_profiler
    ip.expose_magic('memit', memory_profiler.magic_memit)
    ip.expose_magic('mprun', memory_profiler.magic_mprun)

- **Under IPython 0.11+**, first create a configuration profile::

    $ ipython profile create

  Then create a file named ``~/.ipython/extensions/memory_profiler_ext.py``
  with the following content::

    import memory_profiler

    def load_ipython_extension(ip):
        ip.define_magic('memit', memory_profiler.magic_memit)
        ip.define_magic('mprun', memory_profiler.magic_mprun)

  Then register it in ``~/.ipython/profile_default/ipython_config.py``::

    c.TerminalIPythonApp.extensions = [
        'memory_profiler_ext',
    ]
    c.InteractiveShellApp.extensions = [
        'memory_profiler_ext',
    ]

  This will register the ``%memit`` and ``%mprun`` magic commands in the
  IPython terminal application and the other frontends such as qtconsole and
  notebook.

``%mprun`` is useful to examine, line-by-line, the memory usage of key
functions in your program. It is very similar to ``%lprun``, discussed in the
previous section. For example, from the ``memory_profiler`` ``examples``
directory::

    In [1] from example import my_func

    In [2] %mprun -f my_func my_func()
    Filename: example.py

    Line #    Mem usage  Increment   Line Contents
    ==============================================
         3                           @profile
         4      5.97 MB    0.00 MB   def my_func():
         5     13.61 MB    7.64 MB       a = [1] * (10 ** 6)
         6    166.20 MB  152.59 MB       b = [2] * (2 * 10 ** 7)
         7     13.61 MB -152.59 MB       del b
         8     13.61 MB    0.00 MB       return a

Another useful magic that ``memory_profiler`` defines is `%memit`, which is
analogous to `%timeit`. It can be used as follows::

    In [1]: import numpy as np

    In [2]: %memit np.zeros(1e7)
    maximum of 3: 76.402344 MB per loop

For more details, see the docstrings of the magics, using ``%memit?`` and
``%mprun?``.


Performance tips for the Cython developer
=========================================

If profiling of the Python code reveals that the Python interpreter
overhead is larger by one order of magnitude or more than the cost of the
actual numerical computation (e.g. ``for`` loops over vector components,
nested evaluation of conditional expression, scalar arithmetic...), it
is probably adequate to extract the hotspot portion of the code as a
standalone function in a ``.pyx`` file, add static type declarations and
then use Cython to generate a C program suitable to be compiled as a
Python extension module.

The official documentation available at http://docs.cython.org/ contains
a tutorial and reference guide for developing such a module. In the
following we will just highlight a couple of tricks that we found
important in practice on the existing cython codebase in the scikit-learn
project.

TODO: html report, type declarations, bound checks, division by zero checks,
memory alignment, direct blas calls...

- http://www.euroscipy.org/file/3696?vid=download
- http://conference.scipy.org/proceedings/SciPy2009/paper_1/
- http://conference.scipy.org/proceedings/SciPy2009/paper_2/


.. _profiling-compiled-extension:

Profiling compiled extensions
=============================

When working with compiled extensions (written in C/C++ with a wrapper or
directly as Cython extension), the default Python profiler is useless:
we need a dedicated tool to introspect what's happening inside the
compiled extension it-self.

Using yep and google-perftools
--------------------------------

Easy profiling without special compilation options use yep:

- http://pypi.python.org/pypi/yep
- http://fseoane.net/blog/2011/a-profiler-for-python-extensions/

.. note::

  google-perftools provides a nice 'line by line' report mode that
  can be triggered with the ``--lines`` option. However this
  does not seem to work correctly at the time of writing. This
  issue can be tracked on the `project issue tracker
  <https://code.google.com/p/google-perftools/issues/detail?id=326>`_.



Using gprof
-------------

In order to profile compiled Python extensions one could use ``gprof``
after having recompiled the project with ``gcc -pg`` and using the
``python-dbg`` variant of the interpreter on debian / ubuntu: however
this approach requires to also have ``numpy`` and ``scipy`` recompiled
with ``-pg`` which is rather complicated to get working.

Fortunately there exist two alternative profilers that don't require you to
recompile everything.


Using valgrind / callgrind / kcachegrind
----------------------------------------

TODO


Multi-core parallelism using ``joblib.Parallel``
================================================

TODO: give a simple teaser example here.

Checkout the official joblib documentation:

- http://packages.python.org/joblib/


.. _warm-restarts:

A sample algorithmic trick: warm restarts for cross validation
==============================================================

TODO: demonstrate the warm restart tricks for cross validation of linear
regression with Coordinate Descent.

