lecture 8-3

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Tue Oct  2 22:47:57 2018

@author: cdibble
"""

from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
import numpy as np

plt.figure(figsize=[10, 6])


#define the function
f = lambda x,a,b,c: (a*np.exp(x) + b*np.exp(-x) + c)

#define the paramters for the plot
x_min, x_max = 0, 1
npoints = 100
a = float(input("enter a coefficient for a:"))
b = float(input("enter a coefficient for b:"))
c = float(input("enter a coefficient for c:"))


x = np.linspace(x_min, x_max, npoints)
y = f(x,a,b,c) + np.random.rand(npoints) + a*b*c

#do the curve fit
params, extras = curve_fit(f, x, y)

plt.plot(x,f(x,a,b,c), '--', label='ideal function')
plt.plot(x,y, 'o', label='noisy data')
plt.plot(x,f(x,params[0],params[1],params[2]), label='curve_fit')

plt.xlabel('x')
plt.ylabel('$f(x)$')
plt.xlim([x_min, x_max])
plt.legend(fontsize=12)
plt.show()
print('original coefficients: %6.3f, %6.3f, %6.3f' %(a,b,c))
print('fitted   coefficients: %6.3f, %6.3f, %6.3f' %(params[0], params[1], params[2]))