Analyzing results
=================

To analyze the results the numpy and scipy packages of Python are used. For 
even more functionality the statistical package
`pandas  <http://pandas.pydata.org/>`_ can be used, but 
that is not included in this documentation.

In all examples at this page a typical VanDerPol simulation is assumed to be 
run first: 

.. code-block:: python

    from pysim.simulation import Sim
    from pysim.systems import VanDerPol
    import matplotlib.pyplot as plt
    import numpy as np
    
    sim = Sim()
    sys = VanDerPol()
    sys.store("x")
    sim.addSys(sys)
    
    sim.simulate(20,0.1)
    time = np.arange(0,20,0.1)

    x = sys.res.x

The stored values are saved as 
`numpy arrays <http://docs.scipy.org/doc/numpy/reference/arrays.ndarray.html>`_
so all methods that can be used on numpy arrays can be used on the results.
It is for example possible, and often useful, to
`slice <http://docs.scipy.org/doc/numpy/reference/arrays.indexing.html>`_
an array to efficiently get a subset of it. 

Say that you have an result x then you can get the first five values of that
array by slicing it

    >>> x[:5]
    array([ 1. , 1.0994475 , 1.19490544, 1.28069498, 1.34919295])

It is also possible to get the last five values

    >>> x[-5:]
    array([ 1.56819423, 1.74261745, 1.93952537, 2.15280207, 2.3669469 ])

To get the maximum or minimum of an array you can use its max and min function

    >>> x.max()
    2.6762298217379024
    >>> x.min()
    -2.6780402033754451

To get the index of the max value use 
`argmax <http://docs.scipy.org/doc/numpy/reference/generated/numpy.argmax.html#numpy.argmax>`_ 
   
    >>> x.argmax()
    135
    >>> x[135]
    2.6762298217379024
    >>> time[135]
    13.5

Plotting
--------
To plot a graph use the `matplotlib <http://matplotlib.org/>`_ plot function. 

    >>> plt.plot(time,x)
    >>> plt.show()

.. image:: /images/VanDerPolPlot.png

It is also possible to plot a subset of the values by using slicing.

    >>> plt.plot(time[40:100],x[40:100])
    >>> plt.show()
    
.. image:: /images/VanDerPolPlot_40_100.png

Finally, lets att some more information to the plot
    >>> plt.plot(time,x)
    >>> plt.xlabel('time')
    >>> plt.ylabel('x')
    >>> plt.title('Van Der Pol Oscillations')
    >>> plt.grid()
    >>> plt.show()
    
.. image:: /images/VanDerPolPlot_with_grid.png

This is just an introduction to the matplotlib. To proceed from here have a look
at their 
`tutorial <http://matplotlib.org/1.3.1/users/pyplot_tutorial.html>`_.