Write a program in python 2.7 that implements the n-point Lagrange interpolation

Question

Write a program in python 2.7 that implements the n-point Lagrange interpolation. Treat n as an input
parameter.
Use your program to calculate values of following functions in n uniform points in the
[0.0,10.0] interval.
f (x) = exp(sin(ax))
Consider the values a = 12, 1, and 1.5. For a = 1, Comment on how the number of the base
points affects the quality of interpolation.
In a separate write-up, list in a table the result of evaluating the interpolating function for f(x)
for at least 5 values of x between 0 and 10. Do this for each of the above values of a.

Explanation / Answer

import numpy as np

import matplotlib.pyplot as plt

import sys

def main():

if len(sys.argv) == 1 or "-h" in sys.argv or "--help" in sys.argv:

print "python lagrange.py <x1.y1> .. <x_k.y_k>"

print "Example:"

print "python lagrange.py 0.1 2.4 4.5 3.2"

exit()

points = []

for i in xrange(len(sys.argv)):

if i != 0:

points.append((int(sys.argv[i].split(".")[0]),int(sys.argv[i].split(".")[1])))

#points =[(0,0),(25,30),(50,10), (57,0)]

P = lagrange(points)

nr = 2

print "(" + str(points[nr][0]) + ", " + str(points[nr][1]) +") P(" + str(points[nr][0]) +")= " +str(P(points[nr][0]))

plot(P, points)

def plot(f, points):

x = range(-10, 100)

y = map(f, x)

print y

plt.plot( x, y, linewidth=2.0)

x_list = []

y_list = []

for x_p, y_p in points:

x_list.append(x_p)

y_list.append(y_p)

print x_list

print y_list

plt.plot(x_list, y_list, 'ro')

plt.show()

def lagrange(points):

def P(x):

total = 0

n = len(points)

for i in xrange(n):

xi, yi = points[i]

def g(i, n):

tot_mul = 1

for j in xrange(n):

if i == j:

continue

xj, yj = points[j]

tot_mul *= (x - xj) / float(xi - xj)

return tot_mul

total += yi * g(i, n)

return total

return P

if __name__ == "__main__":

main()

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