matplotlib Code

#!/usr/bin/env python
"""Simple data fitting and smoothing example"""

from numpy import exp,arange,array,linspace
from numpy.random import normal

from scipy.optimize import leastsq
from scipy.interpolate import splrep,splev


import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt

def func(pars):
    a, alpha, k = pars
    return a*exp(alpha*x_vals) + k

def errfunc(pars):
    """Return the error between the function func() evaluated""" 
    return y_noisy - func(pars)  #return the error

# Use globals for the x values and true parameters
pars_true = array([2.0, -.76, 0.1])
x_vals = linspace(0, 4, 1000)

# some pseudo data; add some noise
y_noisy = func(pars_true) + normal(0.0, 0.1, x_vals.shape)

# the intial guess of the params
guess = 1.0, -.4, 0.0

# now solve for the best fit paramters
best, mesg = leastsq(errfunc, guess)

print 'Least-squares fit to the data'
print 'true', pars_true
print 'best', best
print '|err|_l2 =',np.linalg.norm(pars_true-best)

# scipy's splrep uses FITPACK's curfit (B-spline interpolation)
print
print 'Spline smoothing of the data'
sp = splrep(x_vals,y_noisy)
smooth = splev(x_vals,sp)
print 'Spline information (see splrep and splev for details):',sp

# Polynomial fitting
def plot_polyfit(x,y,n,fignum=None):
    """ """
    if fignum is None:
        fignum = plt.figure().number
        plt.plot(x,y,label='Data')
        
    fit_coefs = np.polyfit(x,y,n)
    fit_val = np.polyval(fit_coefs,x)
    plt.plot(x,fit_val,label='Polynomial fit, $n=%d$' % n)
    plt.legend()
    return fignum

# Now use pylab to plot
plt.figure()
plt.plot(x_vals,y_noisy,label='Noisy data')
plt.plot(x_vals,func(best),lw=2,label='Least-squares fit')
plt.legend()
plt.figure()
plt.plot(x_vals,y_noisy,label='Noisy data')
plt.plot(x_vals,smooth,lw=2,label='Spline-smoothing')
plt.legend()

fignum = plot_polyfit(x_vals,y_noisy,1)
plot_polyfit(x_vals,y_noisy,2,fignum)
plot_polyfit(x_vals,y_noisy,3,fignum)

plt.show()