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import spmatrix
def poisson1d(n):
L = spmatrix.ll_mat(n, n)
for i in range(n):
L[i,i] = 2
if i > 0:
L[i,i-1] = -1
if i < n-1:
L[i,i+1] = -1
return L
def poisson1d_sym(n):
L = spmatrix.ll_mat_sym(n)
for i in range(n):
L[i,i] = 2
if i > 0:
L[i,i-1] = -1
return L
def poisson2d(n):
L = spmatrix.ll_mat(n*n, n*n)
for i in range(n):
for j in range(n):
k = i + n*j
L[k,k] = 4
if i > 0:
L[k,k-1] = -1
if i < n-1:
L[k,k+1] = -1
if j > 0:
L[k,k-n] = -1
if j < n-1:
L[k,k+n] = -1
return L
def poisson2d_sym(n):
L = spmatrix.ll_mat_sym(n*n)
for i in range(n):
for j in range(n):
k = i + n*j
L[k,k] = 4
if i > 0:
L[k,k-1] = -1
if j > 0:
L[k,k-n] = -1
return L
def poisson2d_sym_blk(n):
L = spmatrix.ll_mat_sym(n*n)
I = spmatrix.ll_mat_sym(n)
for i in range(n):
I[i,i] = -1
P = spmatrix.ll_mat_sym(n)
for i in range(n):
P[i,i] = 4
if i > 0:
P[i,i-1] = -1
for i in range(0, n*n, n):
L[i:i+n,i:i+n] = P
if i > 0: L[i:i+n,i-n:i] = I
return L
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