Python curve_fit with multiple independent variables

Question

Python's curve_fit calculates the best-fit parameters for a function with a single independent variable, but is there a way, using curve_fit or something else, to fit for a function with multiple independent variables? For example:

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

where x and y are the independent variable and we would like to fit for a, b, and c.

Answer 1

You can pass curve_fit a multi-dimensional array for the independent variables, but then your func must accept the same thing. For example, calling this array X and unpacking it to x, y for clarity:

import numpy as np
from scipy.optimize import curve_fit

def func(X, a, b, c):
    x,y = X
    return np.log(a) + b*np.log(x) + c*np.log(y)

# some artificially noisy data to fit
x = np.linspace(0.1,1.1,101)
y = np.linspace(1.,2., 101)
a, b, c = 10., 4., 6.
z = func((x,y), a, b, c) * 1 + np.random.random(101) / 100

# initial guesses for a,b,c:
p0 = 8., 2., 7.
print curve_fit(func, (x,y), z, p0)

Gives the fit:

(array([ 9.99933937,  3.99710083,  6.00875164]), array([[  1.75295644e-03,   9.34724308e-05,  -2.90150983e-04],
   [  9.34724308e-05,   5.09079478e-06,  -1.53939905e-05],
   [ -2.90150983e-04,  -1.53939905e-05,   4.84935731e-05]]))