[SciPy-User] scipy.optimize: fitting multiple data arrays with the same function methodological and general problems

[Luca Codutti]

Dear Scipy users,
I'm wondering if you can help me with an optimization problem I'm  
stuck for quite some time.
I need to fit several experimental data arrays using a common function  
in order to determine common "global" parameters. Each dataset has  
further known constants depending on each dataset that need to be feed  
to the fitting function.
Till now I've figured out, browsing into the scipy mailing list, that  
a good strategy might be in creating a one-dimensional least-square  
differences array to be minimized using optmize.leastsq or curve_fit  
algorithms.
The problem is that I'm working with sums and products of exponential  
decays which possibly are difficult to optimize (I observe many times  
NaN during the optimization) and I can't obtain valid or robust output  
from the optimization.

I'm wondering if I understood correctly how to solve my global  
optimization problem or if I'm doing things untidily.

Being more specific in a pseudo code way:

function_to_be_fit = (K*e^(-a)*e^(-b))/(K*e^(-c) + e^(-b))
to be optimized : a, b, and c
x_data = list(numpy.arrayX1, numpy.arrayX2 ...)
y_data = list(numpy.arrayY1, numpy.arrayY2 ...)  *experimental data
known_constants = list(k1, k2,...)
starting optimization values = Opt = [a = Float1, b = Float2, c= Float3]

def Fitter ( Opt, constants, x_data, y_data):
    s = []
    def func = lambda Opt, k, x = log  
((K*e^(-Opt[0])*e^(-Opt[1]))/(K*e^(-Opt[2]) + e^(-Opt[1])) )
    for i in xrange(len(constants)):
        for j in xrange(len(x_data)):
           X_theor = func(Opt, constants[i], x[i][j])
           Difference = X_theor - log (y_data[i][j])
           s.append(Difference)
    return s

fit = scipy.optimize.leastsq(Fitter, Opt, args = {known_constants,  
x_data, y_data})

While this method seems to work fine while fitting e.g. parabolas  
sharing the same amplitude but having different heights, for my  
function I'm stuck every time into local minima which depend  
substantially on the initial guessing parameters. So here I'm pretty  
lost and I could not manage to find any working protocol in order to  
obtain a global minima. Do you have any suggestions?

Thank you in advance.












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