def test_on_diagonal_matrix(self):
a = spmatrix.ll_mat(3, 3)
a.put([1, 2, 3])
r = jdsym.jdsym(a, None, None, 3, 1, 1e-9, 100, krylov.qmrs)
self.assertEqual(r[0], 3)
self.assertTrue(numpy.allclose(r[1], [1, 2, 3]))
self.assertTrue(numpy.allclose(numpy.abs(r[2]), numpy.identity(3)))
def test_on_diagonal_matrix(self):
a = spmatrix.ll_mat(3, 3)
a.put([1, 2, 3])
r = jdsym.jdsym(a, None, None, 3, 1, 1e-9, 100, krylov.qmrs)
self.assertEqual(r[0], 3)
self.assertTrue(numpy.allclose(r[1], [1, 2, 3]))
self.assertTrue(numpy.allclose(numpy.abs(r[2]), numpy.identity(3)))
print "norm(x) = %g" % np.linalg.norm(x) r = np.empty(n * n, "d") A.matvec(x, r) r = b - r print "norm(b - A*x) = %g" % np.linalg.norm(r) # ----------------------------------------------------------------------------- K_ssor = precon.ssor(S, 1.9) t1 = time.clock() x = np.empty(n * n, "d") info, iter, relres = pcg(S, b, x, tol, 2000, K_ssor) print "info=%d, iter=%d, relres=%e" % (info, iter, relres) print "Solve time using SSS matrix and SSOR preconditioner: %8.2f sec" % (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) # ----------------------------------------------------------------------------- from pysparse.eigen import jdsym jdsym.jdsym(S, None, None, 5, 0.0, 1e-8, 100, qmrs, clvl=1)
from pysparse.precon import precon
from pysparse.eigen import jdsym
import time
def poisson2d_sym_blk(n):
L = spmatrix.ll_mat_sym(n*n)
I = spmatrix.ll_mat_sym(n)
P = spmatrix.ll_mat_sym(n)
for i in range(n):
I[i,i] = -1
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
n = 200
t1 = time.clock()
L = poisson2d_sym_blk(n)
print 'Time for constructing the matrix: %8.2f sec' % (time.clock() - t1)
print L.nnz
# -----------------------------------------------------------------------------
t1 = time.clock()
jdsym.jdsym(L.to_sss(), None, None, 5, 0.0, 1e-8, 100, qmrs, clvl=1)
print 'Time spend in jdsym: %8.2f sec' % (time.clock() - t1)
Ms = M.to_sss()
normM = M[n-1,n-1]
K = diagPrecShifted(A, M, 0.006)
#-------------------------------------------------------------------------------
# Test 1: M = K = None
print 'Test 1'
lmbd_exact = zeros(ncv, 'd')
for k in xrange(ncv):
lmbd_exact[k] = A[k,k]
kconv, lmbd, Q, it, it_inner = jdsym.jdsym(As, None, None, ncv,
0.0, tol, 150, qmrs,
jmin=5, jmax=10, eps_tr=1e-4, clvl=1)
assert ncv == kconv
assert allclose(computeResiduals(As, None, lmbd, Q), zeros(kconv), 0.0, tol)
assert allclose(lmbd, lmbd_exact, tol*tol, 0.0)
print 'OK'
#-------------------------------------------------------------------------------
# Test 2: K = None
print 'Test 2',
lmbd_exact = zeros(ncv, 'd')
for k in xrange(ncv):
#-------------------------------------------------------------------------------
# Test 1: M = K = None
print 'Test 1'
lmbd_exact = zeros(ncv, 'd')
for k in xrange(ncv):
lmbd_exact[k] = A[k, k]
kconv, lmbd, Q, it, it_inner = jdsym.jdsym(As,
None,
None,
ncv,
0.0,
tol,
150,
qmrs,
jmin=5,
jmax=10,
eps_tr=1e-4,
clvl=1)
assert ncv == kconv
assert allclose(computeResiduals(As, None, lmbd, Q), zeros(kconv), 0.0, tol)
assert allclose(lmbd, lmbd_exact, tol * tol, 0.0)
print 'OK'
#-------------------------------------------------------------------------------
# Test 2: K = None
print 'norm(x) = %g' % np.linalg.norm(x)
r = np.empty(n * n, 'd')
A.matvec(x, r)
r = b - r
print 'norm(b - A*x) = %g' % np.linalg.norm(r)
# -----------------------------------------------------------------------------
K_ssor = precon.ssor(S, 1.9)
t1 = time.clock()
x = np.empty(n * n, 'd')
info, iter, relres = pcg(S, b, x, tol, 2000, K_ssor)
print 'info=%d, iter=%d, relres=%e' % (info, iter, relres)
print 'Solve time using SSS matrix and SSOR preconditioner: %8.2f sec' % (
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)
# -----------------------------------------------------------------------------
from pysparse.eigen import jdsym
jdsym.jdsym(S, None, None, 5, 0.0, 1e-8, 100, qmrs, clvl=1)
import time
def poisson2d_sym_blk(n):
L = spmatrix.ll_mat_sym(n * n)
I = spmatrix.ll_mat_sym(n)
P = spmatrix.ll_mat_sym(n)
for i in range(n):
I[i, i] = -1
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
n = 200
t1 = time.clock()
L = poisson2d_sym_blk(n)
print 'Time for constructing the matrix: %8.2f sec' % (time.clock() - t1)
print L.nnz
# -----------------------------------------------------------------------------
t1 = time.clock()
jdsym.jdsym(L.to_sss(), None, None, 5, 0.0, 1e-8, 100, qmrs, clvl=1)
print 'Time spend in jdsym: %8.2f sec' % (time.clock() - t1)
