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# Poisson 2D constructors. Illustrate vectorization.
from pysparse import spmatrix
import numpy
def poisson2d_vec(n):
n2 = n*n
L = spmatrix.ll_mat(n2, n2, 5*n2-4*n)
d = numpy.arange(n2, dtype=numpy.int)
L.put(4.0, d)
L.put(-1.0, d[:-n], d[n:])
L.put(-1.0, d[n:], d[:-n])
for i in xrange(n):
di = d[i*n:(i+1)*n]
L.put(-1.0, di[1:], di[:-1])
L.put(-1.0, di[:-1], di[1:])
return L
def poisson2d_vec_sym(n):
n2 = n*n
L = spmatrix.ll_mat_sym(n2, 3*n2-2*n)
d = numpy.arange(n2, dtype=numpy.int)
L.put(4.0, d)
L.put(-1.0, d[n:], d[:-n])
for i in xrange(n):
di = d[i*n:(i+1)*n]
L.put(-1.0, di[:-1], di[1:])
return L
def poisson2d_vec_sym_blk(n):
n2 = n*n
L = spmatrix.ll_mat_sym(n2, 3*n2-2*n)
D = spmatrix.ll_mat_sym(n, 2*n-1)
d = numpy.arange(n, dtype=numpy.int)
D.put(4.0, d)
D.put(-1.0, d[1:], d[:-1])
P = spmatrix.ll_mat_sym(n, n-1)
P.put(-1,d)
for i in xrange(n-1):
L[i*n:(i+1)*n, i*n:(i+1)*n] = D
L[(i+1)*n:(i+2)*n, i*n:(i+1)*n] = P
# Last diagonal block
L[-n:,-n:] = D
return L
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