def setUp(self):
mesh = dl.UnitSquareMesh(10, 10)
self.mpi_rank = dl.MPI.rank(mesh.mpi_comm())
self.mpi_size = dl.MPI.size(mesh.mpi_comm())
Vh1 = dl.FunctionSpace(mesh, 'Lagrange', 1)
uh, vh = dl.TrialFunction(Vh1), dl.TestFunction(Vh1)
mh, test_mh = dl.TrialFunction(Vh1), dl.TestFunction(Vh1)
## Set up B
ndim = 2
ntargets = 200
np.random.seed(seed=1)
targets = np.random.uniform(0.1, 0.9, [ntargets, ndim])
B = assemblePointwiseObservation(Vh1, targets)
## Set up Asolver
alpha = dl.Constant(1.0)
varfA = ufl.inner(ufl.grad(uh), ufl.grad(vh))*ufl.dx +\
alpha*ufl.inner(uh,vh)*ufl.dx
A = dl.assemble(varfA)
Asolver = PETScKrylovSolver(A.mpi_comm(), "cg", amg_method())
Asolver.set_operator(A)
Asolver.parameters["maximum_iterations"] = 100
Asolver.parameters["relative_tolerance"] = 1e-12
## Set up C
varfC = ufl.inner(mh, vh) * ufl.dx
C = dl.assemble(varfC)
self.Hop = Hop(B, Asolver, C)
## Set up RHS Matrix M.
varfM = ufl.inner(mh, test_mh) * ufl.dx
self.M = dl.assemble(varfM)
self.Minv = PETScKrylovSolver(self.M.mpi_comm(), "cg", amg_method())
self.Minv.set_operator(self.M)
self.Minv.parameters["maximum_iterations"] = 100
self.Minv.parameters["relative_tolerance"] = 1e-12
myRandom = Random(self.mpi_rank, self.mpi_size)
x_vec = dl.Vector(mesh.mpi_comm())
self.Hop.init_vector(x_vec, 1)
k_evec = 10
p_evec = 50
self.Omega = MultiVector(x_vec, k_evec + p_evec)
self.k_evec = k_evec
myRandom.normal(1., self.Omega)
class TestMultiVector(unittest.TestCase):
def setUp(self):
mesh = dl.UnitSquareMesh(10, 10)
self.mpi_rank = dl.MPI.rank(mesh.mpi_comm())
self.mpi_size = dl.MPI.size(mesh.mpi_comm())
Vh = dl.FunctionSpace(mesh, 'Lagrange', 1)
uh,vh = dl.TrialFunction(Vh),dl.TestFunction(Vh)
varfM = ufl.inner(uh,vh)*ufl.dx
self.M = dl.assemble(varfM)
x = dl.Vector( mesh.mpi_comm() )
self.M.init_vector(x,0)
k = 121
self.Q = MultiVector(x,k)
def testOrthogonalization(self):
myRandom = Random(self.mpi_rank, self.mpi_size)
myRandom.normal(1.,self.Q)
_ = self.Q.orthogonalize()
QtQ = self.Q.dot_mv(self.Q)
if self.mpi_rank == 0:
assert np.linalg.norm(QtQ - np.eye(QtQ.shape[0])) < 1e-8
def testBOrthogonalization(self):
myRandom = Random(self.mpi_rank, self.mpi_size)
myRandom.normal(1.,self.Q)
self.Q.Borthogonalize(self.M)
MQ = MultiVector(self.Q)
MQ.zero()
MatMvMult(self.M, self.Q, MQ)
QtMQ = self.Q.dot_mv(MQ)
if self.mpi_rank == 0:
assert np.linalg.norm(QtMQ - np.eye(QtMQ.shape[0])) < 1e-8
def testDoublePassG(self):
d, U = doublePassG(self.Hop,
self.M,
self.Minv,
self.Omega,
self.k_evec,
s=2)
nvec = U.nvec()
AU = MultiVector(U[0], nvec)
BU = MultiVector(U[0], nvec)
MatMvMult(self.Hop, U, AU)
MatMvMult(self.M, U, BU)
# Residual checks
diff = MultiVector(AU)
diff.axpy(-d, BU)
res_norms = diff.norm("l2")
# B-orthogonality
UtBU = BU.dot_mv(U)
err = UtBU - np.eye(nvec, dtype=UtBU.dtype)
err_Bortho = np.linalg.norm(err, 'fro')
# A-orthogonality
V = MultiVector(U)
scaling = np.power(np.abs(d), -0.5)
V.scale(scaling)
AU.scale(scaling)
VtAV = AU.dot_mv(V)
err = VtAV - np.diag(np.sign(d))
err_Aortho = np.linalg.norm(err, 'fro')
assert err_Bortho < 1e-8
assert err_Aortho < 1e-4
assert np.all(res_norms < 1e-4)