## Interpolation with splines

Posted February 27, 2013 at 02:43 PM | categories: interpolation | tags:

When you do not know the functional form of data to fit an equation, you can still fit/interpolate with splines.

# use splines to fit and interpolate data from scipy.interpolate import interp1d from scipy.optimize import fmin import numpy as np import matplotlib.pyplot as plt x = np.array([ 0, 1, 2, 3, 4 ]) y = np.array([ 0., 0.308, 0.55, 0.546, 0.44 ]) # create the interpolating function f = interp1d(x, y, kind='cubic', bounds_error=False) # to find the maximum, we minimize the negative of the function. We # cannot just multiply f by -1, so we create a new function here. f2 = interp1d(x, -y, kind='cubic') xmax = fmin(f2, 2.5) xfit = np.linspace(0,4) plt.plot(x,y,'bo') plt.plot(xfit, f(xfit),'r-') plt.plot(xmax, f(xmax),'g*') plt.legend(['data','fit','max'], loc='best', numpoints=1) plt.xlabel('x data') plt.ylabel('y data') plt.title('Max point = ({0:1.2f}, {1:1.2f})'.format(float(xmax), float(f(xmax)))) plt.savefig('images/splinefit.png')

Optimization terminated successfully. Current function value: -0.575712 Iterations: 12 Function evaluations: 24

There are other good examples at http://docs.scipy.org/doc/scipy/reference/tutorial/interpolate.html

Copyright (C) 2013 by John Kitchin. See the License for information about copying.