How do I put a constraint on SciPy curve fit?

by

You can define your own residuals function, including a penalization parameter, like detailed in the code below, where it is known beforehand that the integral along the interval must be 2.. If you test without the penalization you will see that what your are getting is the conventional curve_fit:

enter image description here

import matplotlib.pyplot as plt
import scipy
from scipy.optimize import curve_fit, minimize, leastsq
from scipy.integrate import quad
from scipy import pi, sin

x = scipy.linspace(0, pi, 100)
y = scipy.sin(x) + (0. + scipy.rand(len(x))*0.4)
def func1(x, a0, a1, a2, a3):
    return a0 + a1*x + a2*x**2 + a3*x**3

# here you include the penalization factor
def residuals(p, x, y):
    integral = quad(func1, 0, pi, args=(p[0], p[1], p[2], p[3]))[0]
    penalization = abs(2.-integral)*10000
    return y - func1(x, p[0], p[1], p[2], p[3]) - penalization

popt1, pcov1 = curve_fit(func1, x, y)
popt2, pcov2 = leastsq(func=residuals, x0=(1., 1., 1., 1.), args=(x, y))
y_fit1 = func1(x, *popt1)
y_fit2 = func1(x, *popt2)
plt.scatter(x, y, marker=".")
plt.plot(x, y_fit1, color="g", label="curve_fit")
plt.plot(x, y_fit2, color="y", label="constrained")
plt.legend()
plt.xlim(-0.1, 3.5)
plt.ylim(0, 1.4)
print('Exact integral:', quad(sin, 0, pi)[0])
print('Approx integral1:', quad(func1, 0, pi, args=(popt1[0], popt1[1], popt1[2], popt1[3]))[0])
print('Approx integral2:', quad(func1, 0, pi, args=(popt2[0], popt2[1], popt2[2], popt2[3]))[0])
plt.show()

#Exact   integral: 2.0
#Approx integral1: 2.60068579748
#Approx integral2: 2.00001911981

Other related questions:

More Related Contents:

  1. How to do exponential and logarithmic curve fitting in Python? I found only polynomial fitting
  2. How to apply piecewise linear fit in Python?
  3. python numpy/scipy curve fitting
  4. Python curve_fit with multiple independent variables
  5. scipy curve_fit doesn’t like math module
  6. Most efficient way to calculate radial profile
  7. Fit a gaussian function
  8. scipy is not optimizing and returns “Desired error not necessarily achieved due to precision loss”
  9. Fitting a closed curve to a set of points
  10. scipy.curve_fit() returns multiple lines
  11. Python: Finding multiple roots of nonlinear equation
  12. scipy.optimize.leastsq with bound constraints
  13. Interpolating a closed curve using scipy
  14. A weighted version of random.choice
  15. Computing the correlation coefficient between two multi-dimensional arrays
  16. How do I fit a sine curve to my data with pylab and numpy?
  17. binning data in python with scipy/numpy
  18. Calculating Pearson correlation and significance in Python
  19. How to implement band-pass Butterworth filter with Scipy.signal.butter
  20. Sparse matrix slicing using list of int
  21. What do all the distributions available in scipy.stats look like?
  22. Processing time gets longer and longer after each iteration (TensorFlow)
  23. SciPy Create 2D Polygon Mask
  24. Multiplying a huge number times random() (Python)
  25. How to display progress of scipy.optimize function?
  26. Fitting a Weibull distribution using Scipy
  27. Is the order of a Python dictionary guaranteed over iterations?
  28. Is there a numpy/scipy dot product, calculating only the diagonal entries of the result?
  29. sampling random floats on a range in numpy
  30. Fast interpolation of grid data

Leave a Comment