SciPy comes with a least squares Levenberg-Marquardt implementation. This allows you to minimize functions. By defining your function as the difference between some measurements and your model function, you can fit a model to those measurements.

Sometimes your model contains multiple functions. You can also minimize for all functions using this approach:

- Define your functions that you like to minimize A(p0), B(P1), ...

their cumulative paramaters will be a tuple (p0, p1, ...). - Define your function to be minimized as f(x0), where x0 is expanded to the parameter tuple.
- The function f returns a vector of differences between discrete measured sample and the individual functions A, B etc.
- Let SciPy minimize this function, starting with a reasonably selected initial parameter vector.

This is an example implementation:

import math import scipy.optimize measured = { 1: [ 0, 0.02735, 0.47265 ], 6: [ 0.0041, 0.09335, 0.40255 ], 10: [ 0.0133, 0.14555, 0.34115 ], 20: [ 0.0361, 0.205, 0.2589 ], 30: [ 0.06345, 0.23425, 0.20225 ], 60: [ 0.132, 0.25395, 0.114 ], 90: [ 0.2046, 0.23445, 0.06095 ], 120: [ 0.2429, 0.20815, 0.04895 ], 180: [ 0.31755, 0.1618, 0.02065 ], 240: [ 0.3648, 0.121, 0.0142 ], 315: [ 0.3992, 0.0989, 0.00195 ] } def A( x, a, k ): return a * math.exp( -x * k ) def B( x, a, k, l ): return k * a / ( l - k ) * ( math.exp( -k * x ) - math.exp( -l * x ) ) def C( x, a, k, l ): return a * ( 1 - l / ( l - k ) * math.exp( -x * k ) + k / ( l - k ) * math.exp( -x * l ) ) def f( x0 ): a, k, l = x0 error = [] for x in measured: error += [ C( x, a, k, l ) - measured[ x ][ 0 ], B( x, a, k, l ) - measured[ x ][ 1 ], A( x, a, k ) - measured[ x ][ 2 ] ] return error def main(): x0 = ( 0.46, 0.01, 0.001 ) # initial parameters for a, k and l x, cov, infodict, mesg, ier = scipy.optimize.leastsq( f, x0, full_output = True, epsfcn = 1.0e-2 ) print x if __name__ == "__main__": main()SciPy returns a lot more information, not only the final parameters. See their documentation for details. You also may want to tweak epsfcn for a better fit. This depends on your functions shape and properties.

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