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 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)
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