======================================
Scipy : boite à outils d'algorithmes
======================================

.. 
   >>> import numpy as np
   >>> import scipy as sp
   >>> import pylab as pl

Optimisation
============

    >>> def f(x):
    ...     return x**3 - x**2 - 10
    >>> from scipy import optimize
    >>> optimize.fsolve(f, 1)
    2.5445115283877615

Statistiques et nombre aleatoires
===================================

    >>> a = np.random.random(size=1000)
    >>> bins = np.arange(-4, 5)
    >>> bins
    array([-4, -3, -2, -1,  0,  1,  2,  3,  4])
    >>> histogram = np.histogram(a, bins=bins)
    >>> bins = 0.5*(bins[1:] + bins[:-1])
    >>> bins
    array([-3.5, -2.5, -1.5, -0.5,  0.5,  1.5,  2.5,  3.5])
    >>> from scipy import stats
    >>> b = stats.norm.pdf(bins)

.. sourcecode:: ipython

    In [1]: pl.plot(bins, histogram)
    In [2]: pl.plot(bins, b)

.. plot:: normal_distribution.py
    :align: center
    :scale: 75


Manipulation d'images
======================

::

    from scipy import ndimage
    l = sp.lena()
    pl.imshow(ndimage.gaussian_filter(l, 5), cmap=pl.cm.gray)

.. plot:: lena_ndimage.py
    :align: center

Interpolation
==============

::

    x = np.arange(10)
    y = np.sin(x)

    pl.plot(x, y, '+', markersize=10)

    from scipy import interpolate

    f = interpolate.interp1d(x, y)
    X = np.linspace(0, 9, 100)
    pl.plot(X, f(X), '--')

    f = interpolate.interp1d(x, y, kind='cubic')
    X = np.linspace(0, 9, 100)
    pl.plot(X, f(X), '--')


.. plot:: demo_interpolate.py
    :align: center
    :scale: 75

Interlude
==========

.. |tarek| image:: tarek.jpg
    :scale: 150

.. |lena| image:: lena.png
    :scale: 45

.. htmlonly::

    |tarek| |lena|

.. literalinclude:: interlude_displayed.py
    :lines: 5-

.. plot:: interlude.py
   :align: center

Algebre Lineaire
================

"blanchissement" de Lena::

    rows, weight, columns = np.linalg.svd(l, full_matrices=False)
    l_ = np.dot(rows, columns)

.. plot:: lena_whitened.py
    :align: center