def IC(self): # Incomplete Cholesky decomposition
matrix = loadMatrix('identity')
pcwrap = preconditioner.ICPreconditioner()
pc = pcwrap.create_preconditioner(matrix)
saveMatrix(pc.unfactored(), 'matrix.out')
self.assert_(
fp_file_compare('matrix.out', os.path.join(datadir, 'identity'),
1.e-8))
## NOTE: The reference matrices were generated by this
## program, not SparseLib++, because the SparseLib++ IC
## preconditioner seems to be broken...
matrix = loadMatrix('small_sym_sparse2.mat')
pc = pcwrap.create_preconditioner(matrix)
# Save the *upper* triangle, even though the lower one is more
# natural for the ICPreconditioner class. The reference file
# generated by SparseLib++ contains the upper triangle.
saveMatrix(pc.upper(), 'matrix.out')
self.assert_(
fp_file_compare('matrix.out',
os.path.join(datadir, 'small_sym_upper2.out'),
1.e-8))
matrix = loadMatrix('small_sym_sparse.mat')
pc = pcwrap.create_preconditioner(matrix)
# Save the *upper* triangle, even though the lower one is more
# natural for the ICPreconditioner class. The reference file
# generated by SparseLib++ contains the upper triangle.
saveMatrix(pc.upper(), 'matrix.out')
self.assert_(
fp_file_compare('matrix.out',
os.path.join(datadir, 'small_sym_upper.out'),
1.e-8))
# Big matrices from Matrix Market. 'bcsstk07' has been
# removed. It can't be factored, apparently due to a pathology
# of the matrix or the algorithm. It passes the complete
# Cholesky test.
for mtxname in (
's1rmq4m1',
'bcsstk01',
):
print >> sys.stderr, mtxname + '.mtx'
matrix = loadMatrix(mtxname + '.mtx', fortran=True, symmetric=True)
pc = pcwrap.create_preconditioner(matrix)
self.assert_(pc.upper().unique_indices())
saveMatrix(pc.upper(), 'matrix.out')
self.assert_(
fp_file_compare('matrix.out',
os.path.join(datadir, mtxname + '_upper.out'),
1.e-8))
file_utils.remove('matrix.out')
def Cholesky(self):
# Cholesky decomposition of dense symmetric positive definite matrices.
matrix = loadMatrix('identity-full')
pcwrap = preconditioner.ICPreconditioner()
pc = pcwrap.create_preconditioner(matrix)
saveMatrix(pc.unfactored(), 'matrix.out')
self.assert_(fp_file_compare('matrix.out',
os.path.join(datadir, 'identity-full'),
1.e-8))
matrix = loadMatrix('small_sym_dense.mat')
pc = pcwrap.create_preconditioner(matrix)
saveMatrix(pc.unfactored(), 'matrix.out')
self.assert_(fp_file_compare(
'matrix.out', os.path.join(datadir, 'small_sym_dense.mat'),
1.e-8))
# Check preconditioner solutions
for vecname in ('rhs0', 'rhs1'):
vec = loadVector(vecname)
result = pc.solve(vec)
result.save('vector.out')
self.assert_(fp_file_compare('vector.out',
os.path.join(datadir,
vecname+'_ic.out'),
1.e-8))
resid = matrix*result - vec
self.assertAlmostEqual(resid.norm(), 0.0, 8)
matrix = loadMatrix('small_sym_dense2.mat')
pc = pcwrap.create_preconditioner(matrix)
saveMatrix(pc.unfactored(), 'matrix.out')
self.assert_(fp_file_compare(
'matrix.out', os.path.join(datadir, 'small_sym_dense2.mat'),
1.e-8))
for vecname in ('rhs2.1', 'rhs2.2', 'rhs2.3'):
vec = loadVector(vecname)
result = pc.solve(vec)
result.save('vector.out')
self.assert_(fp_file_compare('vector.out',
os.path.join(datadir,
vecname+'_ic.out'),
1.e-8))
resid = matrix*result - vec
self.assertAlmostEqual(resid.norm(), 0.0, 8)
saveMatrix(pc.upper(), 'matrix.out')
self.assert_(fp_file_compare(
'matrix.out', os.path.join(datadir,
'small_sym_dense2_lower.out'),
1.e-8))
# Hilbert matrix, which is notoriously badly conditioned.
size = 12 # test fails for size > 12!
matrix = sparsemat.SparseMat(size, size)
for i in range(size):
for j in range(size):
matrix.insert(i, j, 1./(i+j+1.0))
matrix.consolidate()
norm = 1.0/matrix.norm()
pc = pcwrap.create_preconditioner(matrix)
resid = pc.unfactored() - matrix
for i,j,x in resid:
self.assertAlmostEqual(x*norm, 0.0, 8)
# Large Matrix market matrices
for mtxname in ('bcsstk01.mtx', 'bcsstk07.mtx'):
print >> sys.stderr, mtxname
matrix = loadMatrix(mtxname, fortran=True, symmetric=True)
fillMatrix(matrix)
matrix.consolidate()
pc = pcwrap.create_preconditioner(matrix)
unf = pc.unfactored()
resid = matrix - unf
resid.consolidate()
norm = 1./matrix.norm()
for i,j,x in resid:
self.assertAlmostEqual(x*norm, 0.0, 8)
file_utils.remove('matrix.out')
file_utils.remove('vector.out')