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#!/usr/bin/python | |
import math | |
import numpy as np | |
from numpy import linalg as LA | |
# Function to approximate | |
def f(x): | |
return math.exp(x * math.cos(3.0 * math.pi * x)) - 1.0 | |
# Radial basis function (Gaussian with epsilon 3.05048) | |
def phi(r): | |
return math.exp(-math.pow(3.05048 * r, 2.0)) | |
# Discrete points | |
X = np.array([x / 14.0 for x in range(0, 15)]) | |
# Data values (right hand side) | |
V = np.array([f(x) for x in X]) | |
# Matrix containing interpolation values | |
# with phi(||xi - xj||) at each Mij | |
M = np.array([[phi(abs(x - y)) for x in X] for y in X]) | |
print('X: %s' % X) | |
print('V: %s' % V) | |
print('M: %s' % M) | |
# Solve M*W=V | |
W = LA.solve(M, V) | |
print('W: %s' % W) | |
# Compute intepolated values | |
S = np.array([sum([w * phi(abs(x - y)) for w, y in zip(W, X)]) for x in X]) | |
print('S: %s' % S) | |
# Maximum error | |
print('Error: %s' % max(np.array([abs(x - y) for x, y in zip(S, V)]))) |
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