def _applyToMatrix(self, A):
"""
Returns (preconditioning matrix, resulting matrix)
"""
return precon.jacobi(A), A.to_csr()
self.shape = A.shape
n = self.shape[0]
self.dinv = np.zeros(n, 'd')
for i in xrange(n):
self.dinv[i] = 1.0 / A[i,i]
def precon(self, x, y):
np.multiply(x, self.dinv, y)
def resid(A, b, x):
r = x.copy()
A.matvec(x, r)
r = b - r
return math.sqrt(np.dot(r, r))
K_diag = diag_prec(A)
K_jac = precon.jacobi(A, 1.0, 1)
K_ssor = precon.ssor(A, 1.0, 1)
# K_ilu = precon.ilutp(L)
n = L.shape[0];
b = np.arange(n).astype(np.Float)
x = np.zeros(n, 'd')
info, iter, relres = pcg(A, b, x, 1e-6, 1000)
print 'pcg, K_none: ', info, iter, relres, resid(A, b, x)
x = np.zeros(n, 'd')
info, iter, relres = pcg(A, b, x, 1e-6, 1000, K_diag)
print 'pcg, K_diag: ', info, iter, relres, resid(A, b, x)
x = np.zeros(n, 'd')
info, iter, relres = pcg(A, b, x, 1e-6, 1000, K_jac)
print 'pcg, K_jac: ', info, iter, relres, resid(A, b, x)
x = np.zeros(n, 'd')
for i in xrange(n):
self.dinv[i] = 1.0 / A[i, i]
def precon(self, x, y):
np.multiply(x, self.dinv, y)
def resid(A, b, x):
r = x.copy()
A.matvec(x, r)
r = b - r
return math.sqrt(np.dot(r, r))
K_diag = diag_prec(A)
K_jac = precon.jacobi(A, 1.0, 1)
K_ssor = precon.ssor(A, 1.0, 1)
# K_ilu = precon.ilutp(L)
n = L.shape[0]
b = np.arange(n).astype(np.Float)
x = np.zeros(n, 'd')
info, iter, relres = pcg(A, b, x, 1e-6, 1000)
print 'pcg, K_none: ', info, iter, relres, resid(A, b, x)
x = np.zeros(n, 'd')
info, iter, relres = pcg(A, b, x, 1e-6, 1000, K_diag)
print 'pcg, K_diag: ', info, iter, relres, resid(A, b, x)
x = np.zeros(n, 'd')
info, iter, relres = pcg(A, b, x, 1e-6, 1000, K_jac)
print 'pcg, K_jac: ', info, iter, relres, resid(A, b, x)
x = np.zeros(n, 'd')
def test_pcg(ProblemList, tol=1.0e-6):
if len(ProblemList) == 0:
usage()
sys.exit(1)
header1 = '%10s %6s %6s ' % ('Name', 'n', 'nnz')
header2 = '%6s %8s %8s %4s %6s %6s\n' % ('iter','relres','error','info','form M','solve')
dheader1 = '%10s %6d %6d '
dheader2 = '%6d %8.1e %8.1e %4d %6.2f %6.2f\n'
lhead1 = len(header1)
lhead2 = len(header2)
lhead = lhead1 + lhead2
sys.stderr.write('-' * lhead + '\n')
sys.stderr.write(header1)
sys.stderr.write(header2)
sys.stderr.write('-' * lhead + '\n')
# Record timings for each preconditioner
timings = { 'None' : [],
'Diagonal' : [],
'SSOR' : []
}
for problem in ProblemList:
A = spmatrix.ll_mat_from_mtx(problem)
(m, n) = A.shape
if m != n: break
prob = os.path.basename(problem)
if prob[-4:] == '.mtx': prob = prob[:-4]
# Right-hand side is Ae
e = np.ones(n, 'd')
b = np.empty(n, 'd')
A.matvec(e, b)
sys.stdout.write(dheader1 % (prob, n, A.nnz))
# No preconditioner
x = np.zeros(n, 'd')
t = cputime()
info, iter, relres = pcg(A, b, x, tol, 2*n)
t_noprec = cputime() - t
err = np.linalg.norm(x-e, ord=np.Inf)
sys.stdout.write(dheader2 % (iter, relres, err, info, 0.0, t_noprec))
timings['None'].append(t_noprec)
# Diagonal preconditioner
x = np.zeros(n, 'd')
t = cputime()
M = precon.jacobi(A, 1.0, 1)
t_getM_diag = cputime() - t
t = cputime()
info, iter, relres = pcg(A, b, x, tol, 2*n, M)
t_diag = cputime() - t
err = np.linalg.norm(x-e, ord=np.Inf)
sys.stdout.write(lhead1 * ' ')
sys.stdout.write(dheader2 % (iter,relres,err,info,t_getM_diag,t_diag))
timings['Diagonal'].append(t_diag)
# SSOR preconditioner
# It appears that steps=1 and omega=1.0 are nearly optimal in all cases
x = np.zeros(n, 'd')
t = cputime()
M = precon.ssor(A.to_sss(), 1.0, 1)
t_getM_ssor = cputime() - t
t = cputime()
info, iter, relres = pcg(A, b, x, tol, 2*n, M)
t_ssor = cputime() - t
err = np.linalg.norm(x-e, ord=np.Inf)
sys.stdout.write(lhead1 * ' ')
sys.stdout.write(dheader2 % (iter,relres,err,info,t_getM_ssor,t_ssor))
timings['SSOR'].append(t_ssor)
sys.stderr.write('-' * lhead + '\n')
return timings