from numpy import *
x = arange(0,6e-2,6e-2/30)
A,k,theta = 10, 1.0/3e-2, pi/6
y_true = A*sin(2*pi*k*x+theta)
y_meas = y_true + 2*random.randn(len(x))

def residuals(p, y, x):
    A,k,theta = p
    err = y-A*sin(2*pi*k*x+theta)
    return err

def peval(x, p):
    return p[0]*sin(2*pi*p[1]*x+p[2])

p0 = [8, 1/2.3e-2, pi/3]
print array(p0)
# [  8.      43.4783   1.0472]

from scipy.optimize import leastsq
plsq = leastsq(residuals, p0, args=(y_meas, x))
print plsq[0]
# [ 10.9437  33.3605   0.5834]

print array([A, k, theta])
# [ 10.      33.3333   0.5236]

import matplotlib.pyplot as plt
plt.plot(x,peval(x,plsq[0]),x,y_meas,'o',x,y_true)
plt.title('Least-squares fit to noisy data')
plt.legend(['Fit', 'Noisy', 'True'])
plt.show()