4- Parameter estimation (``estimation.py`` module).
---------------------------------------------------

The ``estimation.py`` module combines ODE solving with the DE
(differential evolution) genetic optimizer.

.. code:: python

    import matplotlib as mpl
    import stimator
    
    #To make sure we have always the same matplotlib settings
    #(the ones in comments are the ipython notebook settings)
    
    mpl.rcParams['figure.figsize']=(9.0,5.0)    #(6.0,4.0)
    mpl.rcParams['font.size']=14                #10 
    mpl.rcParams['savefig.dpi']=100             #72 

4.1. Example: glyoxalase system
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

An example with **two time courses**

.. code:: python

    mdl = """
    title Glyoxalase system in L. Infantum
    
    glx1 : HTA -> SDLTSH, V1*HTA/(Km1 + HTA)
    glx2 : SDLTSH ->,     V2*SDLTSH/(Km2 + SDLTSH)
    
    find V1  in [0.00001, 0.0001]
    find Km1 in [0.01, 1]
    find V2  in [0.00001, 0.0001]
    find Km2 in [0.01, 1]
    
    init : SDLTSH = 7.69231E-05, HTA = 0.1357
    """
    m1 = stimator.read_model(mdl)
    print mdl
    
    best = m1.estimate(['TSH2a.txt', 'TSH2b.txt'], names=['SDLTSH', 'HTA'])
    
    print best.info()
    best.plot()
    ## #save predicted timecourses to files
    ## redsols = solver.optimum.optimum_tcs
    ## redsols.saveTimeCoursesTo(['TSH2a_pred.txt', 'TSH2b_pred.txt'], verbose=True)

.. parsed-literal::

    
    title Glyoxalase system in L. Infantum
    
    glx1 : HTA -> SDLTSH, V1*HTA/(Km1 + HTA)
    glx2 : SDLTSH ->,     V2*SDLTSH/(Km2 + SDLTSH)
    
    find V1  in [0.00001, 0.0001]
    find Km1 in [0.01, 1]
    find V2  in [0.00001, 0.0001]
    find Km2 in [0.01, 1]
    
    init : SDLTSH = 7.69231E-05, HTA = 0.1357
    
    -- reading time courses -------------------------------
    file C:\Users\tonho\Desktop\stgit\doc\tutorial\TSH2a.txt:
    244 time points, 1 variables
    file C:\Users\tonho\Desktop\stgit\doc\tutorial\TSH2b.txt:
    347 time points, 2 variables
    
    Solving Glyoxalase system in L. Infantum...
    0   : 0.001590
    1   : 0.001590
    2   : 0.000133
    3   : 0.000133
    4   : 0.000133
    5   : 0.000133
    6   : 0.000133
    7   : 0.000133
    8   : 0.000133
    9   : 0.000133
    10  : 0.000133
    11  : 0.000133
    12  : 0.000133
    13  : 0.000133
    14  : 0.000133
    15  : 0.000133
    16  : 0.000133
    17  : 0.000133
    18  : 0.000133
    19  : 0.000133
    20  : 0.000133
    21  : 0.000133
    22  : 0.000133
    refining last solution ...
    
    Done!
    Too many generations with no improvement in 23 generations.
    best score = 0.000011
    best solution: [  2.57587430e-05   2.23315654e-05   9.80378174e-02   2.52514985e-01]
    Optimization took 2.018 s (00m 02.018s)
    
    --- PARAMETERS           -----------------------------
    V1	 2.57587e-05 +- 2.76715e-07
    V2	 2.23316e-05 +- 3.10525e-06
    Km2	   0.0980378 +- 0.0197222
    Km1	    0.252515 +- 0.00707576
    
    --- OPTIMIZATION         -----------------------------
    Final Score	1.06654e-05
    generations	23
    max generations	200
    population size	80
    Exit by	Too many generations with no improvement
    
    
    --- TIME COURSES         -----------------------------
    Name		Points		Score
    TSH2a.txt	244	4.1791e-06
    TSH2b.txt	347	6.48635e-06
    
    
    


.. image:: par_estimation_files/par_estimation_4_1.png


--------------

An example with an **unknown initial value**

.. code:: python

    m2 = m1.copy()
    
    # Assume init.HTA is uncertain
    m2.init.HTA.set_bounds((0.05,0.25))
    
    # do not estimate Km1 and Km2, just to help the analysis
    m2.parameters.Km1.set_bounds(None)
    m2.parameters.Km2.set_bounds(None)
    m2.parameters.Km1 = 0.252531
    m2.parameters.Km2 = 0.0980973
    
    
    # VERY IMPORTANT:
    # only one time course can be used: 
    # cannot fit one initial value using several timecourses!
    
    best = m2.estimate(['TSH2a.txt'], names=['SDLTSH', 'HTA'], opt_settings=dict(pop_size=60))
    
    print best.info()
    best.plot()

.. parsed-literal::

    -- reading time courses -------------------------------
    file C:\Users\tonho\Desktop\stgit\doc\tutorial\TSH2a.txt:
    244 time points, 1 variables
    
    Solving Glyoxalase system in L. Infantum...
    0   : 0.000146
    1   : 0.000146
    2   : 0.000025
    3   : 0.000025
    4   : 0.000025
    5   : 0.000021
    6   : 0.000021
    7   : 0.000021
    8   : 0.000021
    9   : 0.000021
    10  : 0.000021
    11  : 0.000021
    12  : 0.000021
    13  : 0.000021
    14  : 0.000021
    15  : 0.000008
    16  : 0.000008
    17  : 0.000008
    18  : 0.000008
    19  : 0.000008
    20  : 0.000008
    21  : 0.000008
    22  : 0.000008
    23  : 0.000008
    24  : 0.000008
    25  : 0.000008
    26  : 0.000008
    27  : 0.000008
    28  : 0.000008
    29  : 0.000008
    30  : 0.000008
    31  : 0.000008
    32  : 0.000008
    33  : 0.000008
    34  : 0.000008
    35  : 0.000008
    refining last solution ...
    
    Done!
    Too many generations with no improvement in 36 generations.
    best score = 0.000003
    best solution: [  3.36574664e-05   1.87056447e-05   9.25226437e-02]
    Optimization took 1.898 s (00m 01.898s)
    
    --- PARAMETERS           -----------------------------
    V1	 3.36575e-05 +- 1.02919e-05
    V2	 1.87056e-05 +- 5.94082e-06
    init.HTA	   0.0925226 +- 0.0400775
    
    --- OPTIMIZATION         -----------------------------
    Final Score	3.11054e-06
    generations	36
    max generations	200
    population size	60
    Exit by	Too many generations with no improvement
    
    
    --- TIME COURSES         -----------------------------
    Name		Points		Score
    TSH2a.txt	244	3.11054e-06
    
    
    


.. image:: par_estimation_files/par_estimation_6_1.png