Compute the least square fitting for a function of two variables and also the coefficient of determination (R**2).

least_sq_fit.py

from scipy import zeros, dot, linspace, linalg, array, sqrt, loadtxt, meshgrid
from scipy import shape, mean
from numpy.linalg import norm
from scipy.optimize import minimize

x = loadtxt('x.txt')
t = loadtxt('t.txt')
S = loadtxt('Syy.txt')

X, T = meshgrid(x,t)

def fun(x):
    S2 = x[0]*sqrt(T/X) + x[1]/sqrt(X) + x[2]
    return norm(S - S2)

def coeff_det(x):
    Savg = mean(S)  
    S2 = x[0]*sqrt(T/X) + x[1]/sqrt(X) + x[2]
    Serr = 0.0
    Stot = 0.0
    for i in range(0,shape(S)[0]):
        for j in range(0,shape(S)[1]):
            Serr = Serr + (S[i,j] - S2[i,j])**2
            Stot = Stot + (S[i,j] - Savg)**2

    return 1 - Serr/Stot


x0 = [0.37*sqrt(2.0),0.2214,-0.9608]
res = minimize(fun, x0, method='SLSQP')


print res.message
print "The solution found is: ", res.x
print "The relative error is: ", fun(res.x)/norm(S)
print "The coefficient of determination is (R**2): ", coeff_det(res.x)