Question

I am doing some data fitting using the pyminuit Python bindings for the minuit minimisation code (http://code.google.com/p/pyminuit/). The minimiser accepts a function and uses introspection to extract the parameters to be minimised. In general, I want to minimise the chi squared value for a dataset given a particular function to describe the dataset.

My question: Is there a way to define a chi squared function which, given an arbitrary function with varying numbers of parameters, returns a function which gives the chi squared value for that function and only contains the parameters to be minimised in the function argument specification?

Example:

from scipy import *
import minuit
# Generate some data to fit
data_x = arange(50)
noise = 0.3
data_y = data_x**3 + normal(0.0, noise)
# Fit function, e.g. a cubic
fit_func = lambda x, a1, a2, a3, a4: a1 + a2*x + a3*x**2 + a4*x**3

# Minimisation function e.g. chi squared
# Note this has only the parameters to be minimised in the definition (eg not data_x)
min_func = lambda a1, a2, a3, a4: sum( (fit_func(data_x, a1, a2, a3, a4) - data_y)**2 / noise**2 )

THIS is where I’d like to write something like min_func = make_chi2(fit_func). I don’t know what to do as data_x and data_y are only defined outside of the function. The rest of the minimisation routine, for completeness, looks like:

# Initialise minimiser object with initial values
m = minuit.Minuit(min_func, {'a1': 1.0, 'a2': 1.0, 'a3': 1.0, 'a4': 1.0})
# Run minimiser
m.migrad()
# Print minimised values - example output
print m.values
>>> {'a1': 0.000, 'a2': 0.000, 'a3': 0.000, 'a4': 1.000}

Thanks for your help in advance!

Answer 1

Since PyMinuit uses introspection, you have to use introspection, too. make_chi_squared() could be implemented like this:

import inspect

chi_squared_template = """
def chi_squared(%(params)s):
    return (((f(data_x, %(params)s) - data_y) / errors) ** 2).sum()
"""

def make_chi_squared(f, data_x, data_y, errors):
    params = ", ".join(inspect.getargspec(f).args[1:])
    exec chi_squared_template % {"params": params}
    return chi_squared

Example usage:

import numpy

def f(x, a1, a2, a3, a4):
    return a1 + a2*x + a3*x**2 + a4*x**3

data_x = numpy.arange(50)
errors = numpy.random.randn(50) * 0.3
data_y = data_x**3 + errors

chi_squared = make_chi_squared(f, data_x, data_y, errors)
print inspect.getargspec(chi_squared).args

printing

['a1', 'a2', 'a3', 'a4']