def custom_exactsolve(A, params, B, E=None,
M=None, mparams=[], **options):
# A: (*BA, na, na)
# B: (*BB, na, ncols)
# E: (*BE, ncols)
# M: (*BM, na, na)
with A.uselinopparams(*params), M.uselinopparams(*mparams) if M is not None else dummy_context_manager():
return exactsolve(A, B, E, M)
def custom_exactsolve(A, B, E=None, M=None, **options):
# A: (*BA, na, na)
# B: (*BB, na, ncols)
# E: (*BE, ncols)
# M: (*BM, na, na)
return exactsolve(A, B, E, M)
def solve(A: LinearOperator,
B: torch.Tensor,
E: Union[torch.Tensor, None] = None,
M: Optional[LinearOperator] = None,
bck_options: Mapping[str, Any] = {},
method: Union[str, Callable, None] = None,
**fwd_options) -> torch.Tensor:
r"""
Performing iterative method to solve the equation
.. math::
\mathbf{AX=B}
or
.. math::
\mathbf{AX-MXE=B}
where :math:`\mathbf{E}` is a diagonal matrix.
This function can also solve batched multiple inverse equation at the
same time by applying :math:`\mathbf{A}` to a tensor :math:`\mathbf{X}`
with shape ``(...,na,ncols)``.
The applied :math:`\mathbf{E}` are not necessarily identical for each column.
Arguments
---------
A: xitorch.LinearOperator
A linear operator that takes an input ``X`` and produce the vectors in the same
space as ``B``.
It should have the shape of ``(*BA, na, na)``
B: torch.Tensor
The tensor on the right hand side with shape ``(*BB, na, ncols)``
E: torch.Tensor or None
If a tensor, it will solve :math:`\mathbf{AX-MXE = B}`.
It will be regarded as the diagonal of the matrix.
Otherwise, it just solves :math:`\mathbf{AX = B}` and ``M`` is ignored.
If it is a tensor, it should have shape of ``(*BE, ncols)``.
M: xitorch.LinearOperator or None
The transformation on the ``E`` side. If ``E`` is ``None``,
then this argument is ignored.
If E is not ``None`` and ``M`` is ``None``, then ``M=I``.
If LinearOperator, it must be Hermitian with shape ``(*BM, na, na)``.
bck_options: dict
Options of the iterative solver in the backward calculation.
method: str or callable or None
The method of linear equation solver. If ``None``, it will choose
``"cg"`` or ``"bicgstab"`` based on the matrices symmetry.
`Note`: default method will be changed quite frequently, so if you want
future compatibility, please specify a method.
**fwd_options
Method-specific options (see method below)
Returns
-------
torch.Tensor
The tensor :math:`\mathbf{X}` that satisfies :math:`\mathbf{AX-MXE=B}`.
"""
assert_runtime(A.shape[-1] == A.shape[-2],
"The linear operator A must have a square shape")
assert_runtime(
A.shape[-1] == B.shape[-2],
"Mismatch shape of A & B (A: %s, B: %s)" % (A.shape, B.shape))
assert_runtime(
not torch.is_grad_enabled() or A.is_getparamnames_implemented,
"The _getparamnames(self, prefix) of linear operator A must be "
"implemented if using solve with grad enabled")
if M is not None:
assert_runtime(M.shape[-1] == M.shape[-2],
"The linear operator M must have a square shape")
assert_runtime(
M.shape[-1] == A.shape[-1],
"The shape of A & M must match (A: %s, M: %s)" %
(A.shape, M.shape))
assert_runtime(M.is_hermitian,
"The linear operator M must be a Hermitian matrix")
assert_runtime(
not torch.is_grad_enabled() or M.is_getparamnames_implemented,
"The _getparamnames(self, prefix) of linear operator M must be "
"implemented if using solve with grad enabled")
if E is not None:
assert_runtime(
E.shape[-1] == B.shape[-1],
"The last dimension of E & B must match (E: %s, B: %s)" %
(E.shape, B.shape))
if E is None and M is not None:
warnings.warn(
"M is supplied but will be ignored because E is not supplied")
# perform expensive check if debug mode is enabled
if is_debug_enabled():
A.check()
if M is not None:
M.check()
if method is None:
if isinstance(A, MatrixLinearOperator) and \
(M is None or isinstance(M, MatrixLinearOperator)):
method = "exactsolve"
else:
is_hermit = A.is_hermitian and (M is None or M.is_hermitian)
method = "cg" if is_hermit else "bicgstab"
if method == "exactsolve":
return exactsolve(A, B, E, M)
else:
# get the unique parameters of A
params = A.getlinopparams()
mparams = M.getlinopparams() if M is not None else []
na = len(params)
return solve_torchfcn.apply(A, B, E, M, method, fwd_options,
bck_options, na, *params, *mparams)
def solve(A:LinearOperator, B:torch.Tensor, E:Union[torch.Tensor,None]=None,
M:Union[LinearOperator,None]=None, posdef=False,
bck_options:Mapping[str,Any]={},
method:Union[str,None]=None,
**fwd_options):
r"""
Performing iterative method to solve the equation
.. math::
\mathbf{AX=B}
or
.. math::
\mathbf{AX-MXE=B}
where :math:`\mathbf{E}` is a diagonal matrix.
This function can also solve batched multiple inverse equation at the
same time by applying :math:`\mathbf{A}` to a tensor :math:`\mathbf{X}`
with shape ``(...,na,ncols)``.
The applied :math:`\mathbf{E}` are not necessarily identical for each column.
Arguments
---------
A: xitorch.LinearOperator
A linear operator that takes an input ``X`` and produce the vectors in the same
space as ``B``.
It should have the shape of ``(*BA, na, na)``
B: torch.tensor
The tensor on the right hand side with shape ``(*BB, na, ncols)``
E: torch.tensor or None
If a tensor, it will solve :math:`\mathbf{AX-MXE = B}`.
It will be regarded as the diagonal of the matrix.
Otherwise, it just solves :math:`\mathbf{AX = B}` and ``M`` is ignored.
If it is a tensor, it should have shape of ``(*BE, ncols)``.
M: xitorch.LinearOperator or None
The transformation on the ``E`` side. If ``E`` is ``None``,
then this argument is ignored.
If E is not ``None`` and ``M`` is ``None``, then ``M=I``.
If LinearOperator, it must be Hermitian with shape ``(*BM, na, na)``.
bck_options: dict
Options of the iterative solver in the backward calculation.
method: str or None
Indicating the method of solve. If None, it will select ``exactsolve``.
**fwd_options
Method-specific options (see method below)
"""
assert_runtime(A.shape[-1] == A.shape[-2], "The linear operator A must have a square shape")
assert_runtime(A.shape[-1] == B.shape[-2], "Mismatch shape of A & B (A: %s, B: %s)" % (A.shape, B.shape))
if M is not None:
assert_runtime(M.shape[-1] == M.shape[-2], "The linear operator M must have a square shape")
assert_runtime(M.shape[-1] == A.shape[-1], "The shape of A & M must match (A: %s, M: %s)" % (A.shape, M.shape))
assert_runtime(M.is_hermitian, "The linear operator M must be a Hermitian matrix")
if E is not None:
assert_runtime(E.shape[-1] == B.shape[-1], "The last dimension of E & B must match (E: %s, B: %s)" % (E.shape, B.shape))
if E is None and M is not None:
warnings.warn("M is supplied but will be ignored because E is not supplied")
# perform expensive check if debug mode is enabled
if is_debug_enabled():
A.check()
if M is not None:
M.check()
if method is None:
method = "exactsolve" # TODO: do a proper method selection based on the size
if method == "exactsolve":
return exactsolve(A, B, E, M)
else:
fwd_options["method"] = method
# get the unique parameters of A
params = A.getlinopparams()
mparams = M.getlinopparams() if M is not None else []
na = len(params)
return solve_torchfcn.apply(
A, B, E, M, posdef,
fwd_options, bck_options,
na, *params, *mparams)