print "Time for constructing the matrix using poisson2d : %8.2f sec" % (time.clock() - t1,) A = L.to_csr() S = L.to_sss() print L.nnz print S.nnz print A.nnz b = np.ones(n * n, "d") # ----------------------------------------------------------------------------- t1 = time.clock() x = np.empty(n * n, "d") info, iter, relres = pcg(S, b, x, tol, 2000) print "info=%d, iter=%d, relres=%e" % (info, iter, relres) print "Solve time using SSS matrix: %8.2f s" % (time.clock() - t1) print "norm(x) = %g" % np.linalg.norm(x) r = np.empty(n * n, "d") S.matvec(x, r) r = b - r print "norm(b - A*x) = %g" % np.linalg.norm(r) print x[0:10] # -----------------------------------------------------------------------------
L = poisson2d_vec_sym_blk(N)
S = L.to_sss()
b = np.ones(N*N, 'd')
print 'Solving 2D-Laplace equation using PCG and SSOR preconditioner with variable omega'
print
print 'omega nit time resid'
print '--------------------------------'
for omega in [0.1*(i+1) for i in range(20)]:
K_ssor = precon.ssor(S, omega, SSOR_STEPS)
t1 = time.clock()
x = np.empty(N*N, 'd')
info, iter, relres = pcg(S, b, x, TOL, MAXIT, K_ssor)
elapsed_time = time.clock() - t1
r = np.zeros(N*N, 'd')
S.matvec(x, r)
r = b - r
res_nrm2 = np.linalg.norm(r)
if info == 0:
iter_str = str(iter)
else:
iter_str = '---'
print '%5.1f %5s %6.2f %10.3e' % (omega, iter_str, elapsed_time, res_nrm2)
A.matvec(x, y)
print y
print 'norm(y) = ', math.sqrt(np.add.reduce(y))
##A.matvec_transp(x, z)
##print z
##print 'norm(z) = ', math.sqrt(np.add.reduce(z))
L = spmatrix.ll_mat(10, 10)
for i in range(10):
L[i, i] = float(i + 1)
A = L.to_csr()
print A
x = np.zeros(10, 'd')
b = np.ones(10, 'd')
info, iter, relres = pcg(A, b, x, 1e-8, 100)
print info, iter, relres
print x
if (info != 0):
print >> sys.stderr, 'cg not converged'
L2 = L.copy()
x = np.zeros(10, 'd')
info, iter, relres = pcg(A, b, x, 1e-8, 100)
print info, iter, relres
# -----------------------------------------------------------
print 'remove test'
n = 100
L = spmatrix.ll_mat(n, n)
def pcg(*args, **kwargs):
return krylov.pcg(*args, **kwargs)
def pcg(*args, **kwargs):
return krylov.pcg(*args, **kwargs)
print 'Time for constructing the matrix using poisson2d : %8.2f sec' % (
time.clock() - t1, )
A = L.to_csr()
S = L.to_sss()
print L.nnz
print S.nnz
print A.nnz
b = np.ones(n * n, 'd')
# -----------------------------------------------------------------------------
t1 = time.clock()
x = np.empty(n * n, 'd')
info, iter, relres = pcg(S, b, x, tol, 2000)
print 'info=%d, iter=%d, relres=%e' % (info, iter, relres)
print 'Solve time using SSS matrix: %8.2f s' % (time.clock() - t1)
print 'norm(x) = %g' % np.linalg.norm(x)
r = np.empty(n * n, 'd')
S.matvec(x, r)
r = b - r
print 'norm(b - A*x) = %g' % np.linalg.norm(r)
print x[0:10]
# -----------------------------------------------------------------------------
A.matvec(x, y)
print y
print 'norm(y) = ', math.sqrt(np.add.reduce(y))
##A.matvec_transp(x, z)
##print z
##print 'norm(z) = ', math.sqrt(np.add.reduce(z))
L = spmatrix.ll_mat(10,10)
for i in range(10):
L[i,i] = float(i+1)
A = L.to_csr()
print A
x = np.zeros(10, 'd')
b = np.ones(10, 'd')
info, iter, relres = pcg(A, b, x, 1e-8, 100)
print info, iter, relres
print x
if (info != 0):
print >> sys.stderr, 'cg not converged'
L2 = L.copy()
x = np.zeros(10, 'd')
info, iter, relres = pcg(A, b, x, 1e-8, 100)
print info, iter, relres
# -----------------------------------------------------------
print 'remove test'
n = 100
L = spmatrix.ll_mat(n, n)
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
S = L.to_sss()
b = np.ones(N * N, 'd')
print 'Solving 2D-Laplace equation using PCG and SSOR preconditioner with variable omega'
print
print 'omega nit time resid'
print '--------------------------------'
for omega in [0.1 * (i + 1) for i in range(20)]:
K_ssor = precon.ssor(S, omega, SSOR_STEPS)
t1 = time.clock()
x = np.empty(N * N, 'd')
info, iter, relres = pcg(S, b, x, TOL, MAXIT, K_ssor)
elapsed_time = time.clock() - t1
r = np.zeros(N * N, 'd')
S.matvec(x, r)
r = b - r
res_nrm2 = np.linalg.norm(r)
if info == 0:
iter_str = str(iter)
else:
iter_str = '---'
print '%5.1f %5s %6.2f %10.3e' % (omega, iter_str, elapsed_time,
res_nrm2)
