"""
Curve fitting
=============

A curve fitting example
"""

import numpy as np
import scipy as sp
import matplotlib.pyplot as plt

np.random.seed(0)

# Our test function
def f(t, omega, phi):
    return np.cos(omega * t + phi)

# Our x and y data
x = np.linspace(0, 3, 50)
y = f(x, 1.5, 1) + .1*np.random.normal(size=50)

# Fit the model: the parameters omega and phi can be found in the
# `params` vector
params, params_cov = sp.optimize.curve_fit(f, x, y)

# plot the data and the fitted curve
t = np.linspace(0, 3, 1000)

plt.figure(1)
plt.clf()
plt.plot(x, y, 'bx')
plt.plot(t, f(t, *params), 'r-')
plt.show()