How do I put a constraint on SciPy curve fit?

Question

I\'m trying to fit the distribution of some experimental values with a custom probability density function. Obviously, the integral of the resulting function should always b

Answer 1

Here is an almost-identical snippet which makes only use of curve_fit.

import matplotlib.pyplot as plt
import numpy as np
import scipy.optimize as opt
import scipy.integrate as integr


x = np.linspace(0, np.pi, 100)
y = np.sin(x) + (0. + np.random.rand(len(x))*0.4)

def Func(x, a0, a1, a2, a3):
    return a0 + a1*x + a2*x**2 + a3*x**3

# modified function definition with Penalization
def FuncPen(x, a0, a1, a2, a3):
    integral = integr.quad( Func, 0, np.pi, args=(a0,a1,a2,a3))[0]
    penalization = abs(2.-integral)*10000
    return a0 + a1*x + a2*x**2 + a3*x**3 + penalization


popt1, pcov1 = opt.curve_fit( Func, x, y )
popt2, pcov2 = opt.curve_fit( FuncPen, x, y )

y_fit1 = Func(x, *popt1)
y_fit2 = Func(x, *popt2)

plt.scatter(x,y, marker='.')
plt.plot(x,y_fit2, color='y', label='constrained')
plt.plot(x,y_fit1, color='g', label='curve_fit')
plt.legend(); plt.xlim(-0.1,3.5); plt.ylim(0,1.4)
print 'Exact   integral:',integr.quad(np.sin ,0,np.pi)[0]
print 'Approx integral1:',integr.quad(Func,0,np.pi,args=(popt1[0],popt1[1],
                                                popt1[2],popt1[3]))[0]
print 'Approx integral2:',integr.quad(Func,0,np.pi,args=(popt2[0],popt2[1],
                                                popt2[2],popt2[3]))[0]
plt.show()

#Exact   integral: 2.0
#Approx integral1: 2.66485028754
#Approx integral2: 2.00002116217