Fitting only one parameter of a function with many parameters in python

In python I have a function which has many parameters. I want to fit this function to a data set, but using only one parameter, the rest of the parameters I want to supply on on my own. Here is an example:

def func(x,a,b):
   return a*x*x + b

for b in xrange(10):
   popt,pcov = curve_fit(func,x1,x2)

In this I want that the fitting is done only for a and the parameter b takes the value of the loop variable. How can this be done?

You can wrap func in a lambda, as follows:

def func(x,a,b):
   return a*x*x + b

for b in xrange(10):
   popt,pcov = curve_fit(lambda x, a: func(x, a, b), x1, x2)

A lambda is an anonymous function, which in Python can only be used for simple one line functions. Basically, it's normally used to reduce the amount of code when don't need to assign a name to the function. A more detailed description is given in the official documentation: http://docs.python.org/tutorial/controlflow.html#lambda-forms

In this case, a lambda is used to fix one of the arguments of func. The newly created function accepts only two arguments: x and a, whereas b is fixed to the value taken from the local b variable. This new function is then passed into curve_fit as an argument.

A better approach would use lmfit, which provides a higher level interface to curve-fitting. Among other features, Lmfit makes fitting parameters be first-class objects that can have bounds or be explicitly fixed (among other features).

Using lmfit, this problem might be solved as:

from lmfit import Model
def func(x,a,b):
   return a*x*x + b

# create model
fmodel = Model(func)
# create parameters -- these are named from the function arguments --
# giving initial values
params = fmodel.make_params(a=1, b=0)

# fix b:
params['b'].vary = False

# fit parameters to data with various *static* values of b:
for b in range(10):
   params['b'].value = b
   result = fmodel.fit(ydata, params, x=x)
   print(": b=%f, a=%f+/-%f, chi-square=%f" % (b, result.params['a'].value, 
                                             result.params['a'].stderr,
                                             result.chisqr))