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)
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