使用lmfit在Python中进行卡方最小化

Question

I'm trying to carry out a multi-parameter fit using python and the lmfit module. I've been following the example shown here as the basis for my code. As far as I understand the code, I should be able to carry out a least-squares fit, provided I properly define my objective function (gives the residuals) and supply it with the right arguments.

This is my current objective function:

# Define objective function: each data point has a different
# objective function which is defined by the model method
# the objective function returns the array to be minimized
def objfunc(params,trans,sum_in,sum_out,data):
    """ model fit using branching ratios and resonance strength
        then subtract data """
    model = fit_model(params,trans,sum_in,sum_out)

    return model - data

where the fit_model(args*) method is defined by

def fit_model(params,trans,sum_in,sum_out):
    """ model the transition based upon the input string trans
        using parameter convention for the branching """
    model = []

    # The amplitude: technically the resonance strength term
    # here it gives the number of resonant decays
    amp = params['amp'].value

    # For each transition we want to retrieve the parameter values
    # for the branching ratios and evaluate the new value for
    # the fit (of that transition). The easiest way to do this is
    # to store the braching ratios with the same notation used
    # previously, and to explicity call those values using the
    # 'params.['']value' method
    for i in range(len(trans)):

        # Employs the termvalue() method to evalueate the branching
        # and efficiency values
        model.append( str(amp * termValue(trans[i]) + amp * termValue(sum_in[i]) - amp * termValue(sum_out[i])))

    return np.array(model,dtype='float64')

This gives me what I expect to get: a numpy.ndarray the length of my data. The problem I'm having is that when I try to minimize the chi-squared fit with

result = minimize(objfunc,params,args=(trans,sum_in,sum_out,data)) 

I get the error message:

File "path/chisquare.py", line 94, in <module>
    result = minimize(objfunc,params,args=(trans,sum_in,sum_out,data))
  File "/usr/local/lib/python2.7/dist-packages/lmfit-0.7-py2.7.egg/lmfit/minimizer.py", line 498, in minimize
    fitter.leastsq()
  File "/usr/local/lib/python2.7/dist-packages/lmfit-0.7-py2.7.egg/lmfit/minimizer.py", line 369, in leastsq
    lsout = scipy_leastsq(self.__residual, self.vars, **lskws)
  File "/usr/lib/python2.7/dist-packages/scipy/optimize/minpack.py", line 278, in leastsq
    raise TypeError('Improper input: N=%s must not exceed M=%s' % (n,m))
TypeError: Improper input: N=26 must not exceed M=25

I've tried to figure out what this means from the lmfit source code, but it's a bit beyond my understanding. Does anyone know how I can resolve this error?

Thanks

Answer 1

This problem seems to be caused by having more parameters than data points. Checked my inputs and resolved the problem!