[SOLVED] two dimensional fit with python

two dimensional fit with python

I need to fit a function

z(u,v) = C u v^p

That is, I have a two-dimensional data set, and I have to find two parameters, C and p. Is there something in numpy or scipy that can do this in a straightforward manner? I took a look at scipy.optimize.leastsq, but it's not clear to me how I would use it here.

Solution

def f(x,u,v,z_data):
  C = x[0]
  p = x[1]
  modelled_z = C*u*v**p
  diffs = modelled_z - z_data
  return diffs.flatten() # it expects a 1D array out. 
       # it doesn't matter that it's conceptually 2D, provided flatten it consistently

result = scipy.optimize.leastsq(f,[1.0,1.0], # initial guess at starting point
                        args = (u,v,z_data) # alternatively you can do this with closure variables in f if you like
                              )
# result is the best fit point

For your specific function you might be able to do it better - for example, for any given value of p there is one best value of C that can be determined by straightforward linear algebra.