Curve fitting using least square technique (python)

least_square_fitting_recursive_function.py

#!/usr/bin/python -u
# -*- coding: utf-8 -*-

"""
Curve fitting using least square technique.
License: BSD
"""

__author__ = 'पुष्पक दगड़े (Pushpak Dagade) <guanidene@gmail.com>'
__date__ = 'Sun Sep 16 13:57:48 2012'

import matplotlib.pyplot as plt
from pylab import lstsq

# given data
X = [1, 2, 3, 4, 5, 6]
fx = [235, 130, 115, 105, 100, 99]
f = lambda x: fx[x - 1]

# solve for parameters using least square technique
A_list = []
B_list = []
for x in X[:-1]:
    A_list.append([f(x), 1])
    temp = (f(x + 1) - f(x))
    B_list.append(temp / abs(temp) * (abs(temp) ** (1.0 / 3)))
sol = lstsq(A_list, B_list)[0]

A = sol[0] ** 3
B = - sol[1] / sol[0]
print '(a,b):', sol
print '(A,B):', A, B


# defined the function since the parameters are now available
def f_curve(x, A, B):
    if x == 1:
        return 235
    else:
        return f_curve(x - 1, A, B) + A * ((f_curve(x - 1, A, B) - B) ** 3)

# another set of parameters (obtained using some fitting technique I don't know)
A2 = -1.1177e-5
B2 = 24
print '(A2,B2):', A2, B2

# create plots to compare
plt.plot(X, fx, '*--', label='Exp. Data', markersize=10)
plt.plot(X, [f_curve(x, A, B) for x in X], 'h-', label='Plot woth A, B', markersize=10)
plt.plot(X, [f_curve(x, A2, B2) for x in X], 'D-', markersize=6, label='Plot using A2, B2')
plt.legend()
plt.grid()
plt.show()