def __init__(self, *args):
args = list(args)
self.bc_mats = []
if isinstance(args[-1], (TPMatrix, SpectralMatrix)):
bc_mats = extract_bc_matrices([args])
self.tpmats = args
self.bc_mats = bc_mats
assert len(args) in (3, 6)
S, A, B = args[:3]
M = {d.get_key(): d for d in (S, A, B)}
self.S = M['SSBSBmat']
self.A = M['ASBSBmat']
self.B = M['BSBSBmat']
if len(args) == 3:
self.a0 = a0 = np.atleast_1d(self.S.scale).item()
self.alfa = alfa = self.A.scale
self.beta = beta = self.B.scale
if isinstance(self.S, TPMatrix):
self.S = self.S.pmat
self.A = self.A.pmat
self.B = self.B.pmat
self.alfa *= self.A.scale
self.beta *= self.B.scale
elif len(args) == 6:
self.a0 = a0 = args[3]
self.alfa = alfa = args[4]
self.beta = beta = args[5]
S, A, B = self.S, self.A, self.B
self.axis = S.axis
T = S.tensorproductspace
if T is None:
shape = [S[0].shape]
else:
shape = list(T.shape(True))
sii, siu, siuu = S[0], S[2], S[4]
ail, aii, aiu = A[-2], A[0], A[2]
bill, bil, bii, biu, biuu = B[-4], B[-2], B[0], B[2], B[4]
M = sii[::2].shape[0]
shape[S.axis] = M
ss = copy(shape)
ss.insert(0, 2)
self.u0 = np.zeros(ss)
self.u1 = np.zeros(ss)
self.u2 = np.zeros(ss)
self.l0 = np.zeros(ss)
self.l1 = np.zeros(ss)
self.ak = np.zeros(ss)
self.bk = np.zeros(ss)
self.LU_Biharmonic(a0, alfa, beta, sii, siu, siuu, ail, aii, aiu, bill,
bil, bii, biu, biuu, self.u0, self.u1, self.u2,
self.l0, self.l1, self.axis)
self.Biharmonic_factor_pr(self.ak, self.bk, self.l0, self.l1,
self.axis)
def __init__(self, *args):
args = list(args)
self.bc_mats = []
if isinstance(args[-1], (TPMatrix, SpectralMatrix)):
bc_mats = extract_bc_matrices([args])
self.tpmats = args
self.bc_mats = bc_mats
assert len(args) in (2, 4)
A, B = args[:2]
M = {d.get_key(): d for d in (A, B)}
self.A = A = M.get('ASDSDmat', M.get('ASNSNmat'))
self.B = B = M.get('BSDSDmat', M.get('BSNSNmat'))
if len(args) == 2:
self.alfa = self.A.scale
self.beta = self.B.scale
if isinstance(self.A, TPMatrix):
self.A = self.A.pmat
self.B = self.B.pmat
self.alfa *= self.A.scale
self.beta *= self.B.scale
elif len(args) == 4:
self.alfa = args[2]
self.beta = args[3]
A, B = self.A, self.B
B[2] = np.broadcast_to(B[2], A[2].shape)
B[-2] = np.broadcast_to(B[-2], A[2].shape)
v = A.testfunction[0]
neumann = self.neumann = self.A.testfunction[0].boundary_condition() == 'Neumann'
self.axis = A.axis
shape = [1]
T = A.tensorproductspace
if T is not None:
shape = list(T.shape(True))
shape[A.axis] = 1
self.alfa = np.atleast_1d(self.alfa)
self.beta = np.atleast_1d(self.beta)
if not self.alfa.shape == shape:
self.alfa = np.broadcast_to(self.alfa, shape).copy()
if not self.beta.shape == shape:
self.beta = np.broadcast_to(self.beta, shape).copy()
shape[self.axis] = A.shape[0] + 2
self.u0 = np.zeros(shape) # Diagonal entries of U
self.u1 = np.zeros(shape) # Diagonal+2 entries of U
self.u2 = np.zeros(shape) # Diagonal+4 entries of U
self.L = np.zeros(shape) # The single nonzero row of L
self.LU_Helmholtz(A, B, self.alfa, self.beta, neumann, self.u0,
self.u1, self.u2, self.L, self.axis)
def __init__(self, A, test):
assert isinstance(A, (SparseMatrix, list))
self.s = test.slice()
self.bc_mats = []
if isinstance(A, list):
bc_mats = extract_bc_matrices([A])
self.A = np.sum(np.array(A, dtype=object))
self.bc_mats = bc_mats
else:
self.A = A
self.test = test
assert self.A.shape[0] == self.A.shape[1]
def __init__(self, mats):
assert isinstance(mats, list)
naxes = set()
for tpmat in mats:
if not tpmat._issimplified:
tpmat.simplify_diagonal_matrices()
naxes.update(tpmat.naxes)
assert len(naxes) == 1
self.naxes = naxes.pop()
bc_mats = extract_bc_matrices([mats])
self.mats = mats
self.bc_mats = bc_mats
# For time-dependent solver, store all generated matrices and reuse
# This takes a lot of memory, so for now it's only implemented for 2D
self.MM = None
def __init__(self, tpmats, fixed_gauge=None):
bc_mats = extract_bc_matrices([tpmats])
self.tpmats = tpmats
self.bc_mats = bc_mats
self._lu = None
m = tpmats[0]
self.T = T = m.space # test space
ndim = T.dimensions
assert ndim == 3
assert np.atleast_1d(
m.scale).size == 1, "Use level = 2 with :func:`.inner`"
A0 = m.mats[0].diags('csc')
A1 = m.mats[1].diags('csc')
A2 = m.mats[2].diags('csc')
M0 = scp.kron(scp.kron(A0, A1, 'csc'), A2, 'csc')
M0 *= np.atleast_1d(m.scale).item()
for m in tpmats[1:]:
A0 = m.mats[0].diags('csc')
A1 = m.mats[1].diags('csc')
A2 = m.mats[2].diags('csc')
M1 = scp.kron(scp.kron(A0, A1, 'csc'), A2, 'csc')
assert np.atleast_1d(
m.scale).size == 1, "Use level = 2 with :func:`.inner`"
M1 *= np.atleast_1d(m.scale).item()
M0 = M0 + M1
# Check if we need to fix gauge. This is required if we are solving
# a pure Neumann Poisson problem.
if fixed_gauge:
# Ident first row
z0 = M0[0].nonzero()
if len(z0[0]) == 0 or z0[1][0] > 0:
M0 = M0.tolil()
zerorow = M0[0].nonzero()[1]
M0[(0, zerorow)] = 0
M0[0, 0] = 1
M0 = M0.tocsc()
self.M = M0
def __init__(self, *args):
args = list(args)
self.bc_mats = []
if isinstance(args[-1], (TPMatrix, SpectralMatrix)):
bc_mats = extract_bc_matrices([args])
self.tpmats = args
self.bc_mats = bc_mats
#assert len(args) in (3, 6)
S, A, B = args[:3]
M = {d.get_key(): d for d in (S, A, B)}
self.S = M['SSBSBmat']
self.A = M['ASBSBmat']
self.B = M['BSBSBmat']
if len(args) == 3:
S_scale = self.S.scale
A_scale = self.A.scale
B_scale = self.B.scale
if isinstance(self.S, TPMatrix):
S = self.S.mats[self.A.naxes[0]]
A = self.A.pmat
B = self.B.pmat
A_scale *= A.scale
B_scale *= B.scale
S_scale *= S.scale
elif len(args) == 6:
S_scale = np.asscalar(args[3])
A_scale = args[4]
B_scale = args[5]
v = S.testfunction[0]
self.s = v.sl[v.slice()]
self.bc = v.bc
if np.ndim(B_scale) > 1:
shape = list(B_scale.shape)
self.axis = S.axis
shape[S.axis] = v.N
self.d0 = np.zeros(shape)
self.d1 = np.zeros(shape)
self.d2 = np.zeros(shape)
S0 = v.broadcast_to_ndims(np.atleast_1d(S[0]))
A0 = v.broadcast_to_ndims(A[0])
B0 = v.broadcast_to_ndims(B[0])
A2 = v.broadcast_to_ndims(A[2])
B2 = v.broadcast_to_ndims(B[2])
B4 = v.broadcast_to_ndims(B[4])
ss = [slice(None)] * self.d0.ndim
ss[S.axis] = slice(0, A[0].shape[0])
self.d0[tuple(ss)] = S0 * S_scale + A0 * A_scale + B0 * B_scale
ss[S.axis] = slice(0, A[2].shape[0])
self.d1[tuple(ss)] = A2 * A_scale + B2 * B_scale
ss[S.axis] = slice(0, B[4].shape[0])
self.d2[tuple(ss)] = B4 * B_scale
self.PDMA_SymLU_VC(self.d0, self.d1, self.d2, S.axis)
else:
self.d0 = S[0] * S_scale + A[0] * A_scale + B[0] * B_scale
self.d1 = A[2] * A_scale + B[2] * B_scale
self.d2 = B[4] * B_scale
self.axis = 0
la.PDMA_SymLU(self.d0, self.d1, self.d2)
def __init__(self, *args, **kwargs):
args = list(args)
self.bc_mats = []
if isinstance(args[-1], (TPMatrix, SpectralMatrix)):
bc_mats = extract_bc_matrices([args])
self.tpmats = args
self.bc_mats = bc_mats
A, B = args[:2]
M = {d.get_key(): d for d in (A, B)}
self.A = A = M.get('ASDSDmat', M.get('ASNSNmat'))
self.B = B = M.get('BSDSDmat', M.get('BSNSNmat'))
naxes = B.naxes[0] if isinstance(B, TPMatrix) else B.axis
if len(args) == 2:
A_scale = self.A.scale
B_scale = self.B.scale
if isinstance(self.A, TPMatrix):
A = self.A.mats[naxes]
B = self.B.mats[naxes]
A_scale *= A.scale
B_scale *= B.scale
else:
A_scale = args[2]
B_scale = args[3]
v = A.testfunction[0]
self.s = v.sl[v.slice()]
neumann = self.neumann = v.boundary_condition() == 'Neumann'
if not neumann:
self.bc = v.bc
self.scaled = v.is_scaled()
self.axis = A.axis
shape = [1]
T = A.tensorproductspace
if T is not None:
shape = list(T.shape(True))
shape[A.axis] = 1
if np.ndim(B_scale) > 1:
if len(shape) == 2:
if neumann and B_scale[0, 0] == 0:
B_scale[0, 0] = 1.
elif len(shape) == 3:
if neumann and B_scale[0, 0, 0] == 0:
B_scale[0, 0, 0] = 1.
A[0] = np.atleast_1d(A[0])
if A[0].shape[0] == 1:
A[0] = np.ones(A.shape[0]) * A[0]
A0 = v.broadcast_to_ndims(A[0])
B0 = v.broadcast_to_ndims(B[0])
B2 = v.broadcast_to_ndims(B[2])
shape[A.axis] = v.N
self.d0 = np.zeros(shape)
self.d1 = np.zeros(shape)
ss = [slice(None)] * self.d0.ndim
ss[self.axis] = slice(0, A.shape[0])
self.d0[tuple(ss)] = A0 * A_scale + B0 * B_scale
ss[self.axis] = slice(0, A.shape[0] - 2)
self.d1[tuple(ss)] = B2 * B_scale
self.L = np.zeros_like(self.d0)
self.TDMA_SymLU_VC(self.d0, self.d1, self.L, self.axis)
else:
self.d0 = A[0] * A_scale + B[0] * B_scale
self.d1 = B[2] * B_scale
self.L = np.zeros_like(self.d1)
self.bc = A.testfunction[0].bc
self.axis = 0
self.TDMA_SymLU(self.d0, self.d1, self.L)