poissonTest.py
# -------------------------------------------------------------------------
#
# PYTHON for DUMMIES
# Problème 10
#
# Script de test
# Vincent Legat
#
# -------------------------------------------------------------------------
#
from numpy import *
from timeit import default_timer as timer
from numpy import *
from numpy.linalg import solve
#
# -1- Resolution du probleme de Poisson dans un domaine en "L"
#
# A MODIFIER [begin]
# - pour modifier le demaine de calcul en retirant
# le coin supérieur droit
# - pour tirer profit du caractère creux de la matrice
#
#
def poissonSolve(nCut):
n = 2*nCut + 1; m = n*n; h = 2/(n-1)
A = eye(m); B = zeros(m)
for i in range(1,n-1):
for j in range(1,n-1):
index = i + j*n
A[index,index] = 4
A[index,index-1] = -1
A[index,index+1] = -1
A[index,index+n] = -1
A[index,index-n] = -1
B[index] = 1
return solve(A/(h*h),B).reshape(n,n)
#
# A MODIFIER [end]
def main():
n = 20
tic = timer()
U = poissonSolve(n)
print(" Elapsed time : %f seconds" % (timer() - tic))
print(" ==== Maximum value of U : %10.8f " % amax(U))
print(" ==== Minimum value of U : %10.8f " % amin(U))
import matplotlib.pyplot as plt
import matplotlib
matplotlib.rcParams['toolbar'] = 'None'
plt.rcParams['figure.facecolor'] = 'lavender'
plt.rcParams['axes.facecolor'] = 'lavender'
myColorMap = matplotlib.cm.jet
X = linspace(-1,1,2*n+1); U = abs(U)
plt.figure("Python as Matlab clone...")
plt.contourf(X,X,U,10,cmap=myColorMap)
plt.contour(X,X,U,10,colors='k',linewidths=1)
plt.hlines(X,X.min(),X.max(),color='white',linewidths=0.5)
plt.vlines(X,X.min(),X.max(),color='white',linewidths=0.5)
plt.axis("off"); plt.axis("equal")
plt.show()
main()