# -*- coding: UTF-8 -*-
# REGLA DE SIMPSON
# Abraham Teran
import numpy as np
def prod(A):
a = 1
for i in range(len(A)):
a = a*A[i]
return a
def lagrange(A,n):
results = []
lfun = np.arange((len(A[0]))**2,dtype=float)
lfun.shape = (len(A[0]),len(A[0]))\
for i in range(len(A[0])):
for j in range(len(lfun)):
if i == j: lfun[i,j] = 1
else: lfun[i,j] = (n-A[0][j])/(A[0][i]-A[0][j])\
for i in range(len(A[1])):
results.append(prod(lfun[i])*A[1][i])\
return sum(results)
def main():
cantPoints = input("Ingrese cantidad de puntos conocidos> ")\
if cantPoints < 2:
print "\nCANTIDAD DE PUNTOS CONOCIDOS >= 2\n"
main()\
integs = []
points = [[],[]]
midPoints = [[],[]]\
for i in range(cantPoints):
print "\n( x",i,",y",i,")"
x = float(input("Ingrese 'x'> ")) y = float(input("Ingrese 'y'> ")) points[0].append(x)
points[1].append(y)\
for i in range(len(points[0])-1):
midPoints[0].append((points[0][i+1]+points[0][i])/2)
midPoints[1].append(lagrange(points,midPoints[0][i]))\
for i in range(len(midPoints[0])):
intg = ((points[0][i+1]-points[0][i])/6)*\
(points[1][i]+(4*midPoints[1][i])+points[1][i+1])
integs.append(intg)\
print "\n\tIntegral: ",sum(integs)
raw_input()
print "\n\tREGLA DE SIMPSON\n\n"
main()
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