splineSoluce.py
# -------------------------------------------------------------------------
#
# PYTHON for DUMMIES
#
# Homework 2 : Splines cubiques périodiques
#
# Solution detaillée préliminaire :-)
# Si y a des trucs géniaux des tuteurs, je la mettrai à jour :-)
#
# Vincent Legat
# Nathan Coppin
#
# -------------------------------------------------------------------------
from numpy import *
from numpy.linalg import solve
def spline(x,h,U):
#
# -0- On crée les abscisses
#
n = size(U)
X = arange(0,n+1)*h
#
# -1- Résolution du système linéaire
#
A = zeros((n,n))
b = zeros(n)
for i in range(-1,n-1):
A[i,[i-1,i,i+1]] = [1,4,1]
b[i] = 6*(U[i-1] - 2*U[i] + U[i+1])/(h*h)
ddU = solve(A,b)
#
# -2- Evaluation des cubiques
#
i = zeros(len(x),dtype=int)
for j in range(1,n):
i[X[j]<=x] = j
U = append(U,U[0])
ddU = append(ddU,ddU[0])
s1 = x - X[i]
s2 = X[i+1] - x
return s2 * ((U[i]/h - (ddU[i]*h)/6)
+ (ddU[i]/(6*h)) * (s2**2)) + \
s1 * ((U[i+1]/h - (ddU[i+1]*h)/6)
+ (ddU[i+1]/(6*h)) * (s1**2))