def test_cg_DLORegularizedGram(self):
ATA = linop.DLORegularizedGram(self.A)
AAT = linop.DLORegularizedGram(self.A, transpose=True)
BBT = linop.DLORegularizedGram(self.B)
BTB = linop.DLORegularizedGram(self.B, transpose=False)
M_ATA = linop.DLODiagonal((1. / (self.rho + self.dATA)).persist())
M_AAT = linop.DLODiagonal((1. / (self.rho + self.dAAT)).persist())
M_BBT = linop.DLODiagonal((1. / (self.rho + self.dBBT)).persist())
M_BTB = linop.DLODiagonal((1. / (self.rho + self.dBTB)).persist())
for A, M in ((ATA, M_ATA), (AAT, M_AAT), (BBT, M_BBT), (BTB, M_BTB)):
assert cg_reduces_residuals(A)
assert cg_warmstart_reduces_iterations(A)
def jacobi_preconditioner(array, name=None):
name = 'jacobi-precond-' + array.name if name is None else name
m, n = array.shape
assert m == n, 'preconditioner expects square linear operator'
diag = da.diag(array)
return linop.DLODiagonal(da.core.map_blocks(da.reciprocal, diag,
name=name))
def test_cg_DLOGram(self):
ATA = linop.DLOGram(self.A)
AAT = linop.DLOGram(self.A, transpose=True)
BBT = linop.DLOGram(self.B)
BTB = linop.DLOGram(self.B, transpose=False)
M_ATA = linop.DLODiagonal(self.dATA)
M_BBT = linop.DLODiagonal(self.dBBT)
# skinny, full rank Gram
assert cg_reduces_residuals(ATA)
assert cg_warmstart_reduces_iterations(ATA)
# skinny, rank-deficient Gram
assert not cg_reduces_residuals(AAT)
# fat, full rank Gram
assert cg_reduces_residuals(BBT)
assert cg_warmstart_reduces_iterations(BBT)
# fat, rank-deficient Gram
assert not cg_reduces_residuals(BTB)
def test_DLODiag_ops(self):
D = linop.DLODiagonal(self.D)
Dx = self.D * self.x
assert operations_consistent(D, self.x, self.x, Dx, Dx)
def jacobi_preconditioner(linear_op, name=None):
name = 'jacobi-precond-' + linear_op.name if name is None else name
diag = atoms.diag_gram(linear_op)
return linop.DLODiagonal(da.core.map_blocks(da.reciprocal, diag,
name=name))