def map_unique_objs(self, uniqueobjs: List) -> List:
assert_runtime(
len(uniqueobjs) == self.num_unique,
"The uniqueobjs must have %d elements" % self.num_unique)
if self.all_unique:
return uniqueobjs
return [uniqueobjs[idx] for idx in self.nonunique_map_idxs]
def get_unique_objs(self, allobjs: Optional[List] = None) -> List:
if allobjs is None:
return self.unique_objs
assert_runtime(
len(allobjs) == self.nobjs,
"The allobjs must have %d elements" % self.nobjs)
if self.all_unique:
return allobjs
return [allobjs[i] for i in self.unique_idxs]
def solve_ivp(fcn: Union[Callable[..., torch.Tensor],
Callable[..., Sequence[torch.Tensor]]],
ts: torch.Tensor,
y0: torch.Tensor,
params: Sequence[Any] = [],
bck_options: Mapping[str, Any] = {},
method: Union[str, Callable, None] = None,
**fwd_options) -> Union[torch.Tensor, Sequence[torch.Tensor]]:
r"""
Solve the initial value problem (IVP) or also commonly known as ordinary
differential equations (ODE), where given the initial value :math:`\mathbf{y_0}`,
it then solves
.. math::
\mathbf{y}(t) = \mathbf{y_0} + \int_{t_0}^{t} \mathbf{f}(t', \mathbf{y}, \theta)\ \mathrm{d}t'
Arguments
---------
fcn: callable
The function that represents dy/dt. The function takes an input of a
single time ``t`` and tensor ``y`` with shape ``(*ny)`` and
produce :math:`\mathrm{d}\mathbf{y}/\mathrm{d}t` with shape ``(*ny)``.
The output of the function must be a tensor with shape ``(*ny)`` or
a list of tensors.
ts: torch.tensor
The time points where the value of `y` will be returned.
It must be monotonically increasing or decreasing.
It is a tensor with shape ``(nt,)``.
y0: torch.tensor
The initial value of ``y``, i.e. ``y(t[0]) == y0``.
It is a tensor with shape ``(*ny)`` or a list of tensors.
params: list
Sequence of other parameters required in the function.
bck_options: dict
Options for the backward solve_ivp method. If not specified, it will
take the same options as fwd_options.
method: str or callable or None
Initial value problem solver. If None, it will choose ``"rk45"``.
**fwd_options
Method-specific option (see method section below).
Returns
-------
torch.tensor or a list of tensors
The values of ``y`` for each time step in ``ts``.
It is a tensor with shape ``(nt,*ny)`` or a list of tensors
"""
if is_debug_enabled():
assert_fcn_params(fcn, (ts[0], y0, *params))
assert_runtime(len(ts.shape) == 1, "Argument ts must be a 1D tensor")
if method is None: # set the default method
method = "rk45"
fwd_options["method"] = method
# run once to see if the outputs is a tuple or a single tensor
is_y0_list = isinstance(y0, list) or isinstance(y0, tuple)
dydt = fcn(ts[0], y0, *params)
is_dydt_list = isinstance(dydt, list) or isinstance(dydt, tuple)
if is_y0_list != is_dydt_list:
raise RuntimeError(
"The y0 and output of fcn must both be tuple or a tensor")
pfcn = get_pure_function(fcn)
if is_y0_list:
nt = len(ts)
roller = TensorPacker(y0)
@make_sibling(pfcn)
def pfcn2(t, ytensor, *params):
ylist = roller.pack(ytensor)
res_list = pfcn(t, ylist, *params)
res = roller.flatten(res_list)
return res
y0 = roller.flatten(y0)
res = _SolveIVP.apply(pfcn2, ts, fwd_options, bck_options, len(params),
y0, *params, *pfcn.objparams())
return roller.pack(res)
else:
return _SolveIVP.apply(pfcn, ts, fwd_options, bck_options, len(params),
y0, *params, *pfcn.objparams())
def symeig(A: LinearOperator,
neig: Union[int, None] = None,
mode: str = "lowest",
M: Union[LinearOperator, None] = None,
fwd_options: Mapping[str, Any] = {},
bck_options: Mapping[str, Any] = {}):
"""
Obtain `neig` lowest eigenvalues and eigenvectors of a linear operator.
If M is specified, it solve the eigendecomposition Ax = eMx.
Arguments
---------
* A: xitorch.LinearOperator hermitian instance with shape (*BA, q, q)
The linear module object on which the eigenpairs are constructed.
* neig: int or None
The number of eigenpairs to be retrieved. If None, all eigenpairs are
retrieved
* mode: str
"lowest" or "uppermost"/"uppest". If "lowest", it will take the lowest
`neig` eigenpairs. If "uppest", it will take the uppermost `neig`.
* M: xitorch.LinearOperator hermitian instance with shape (*BM, q, q) or None
The transformation on the right hand side. If None, then M=I.
* fwd_options: dict with str as key
Eigendecomposition iterative algorithm options.
* bck_options: dict with str as key
Conjugate gradient options to calculate the gradient in
backpropagation calculation.
Returns
-------
* eigvals: (*BAM, neig)
* eigvecs: (*BAM, na, neig)
The lowest eigenvalues and eigenvectors, where *BAM are the broadcasted
shape of *BA and *BM.
"""
assert_runtime(A.is_hermitian, "The linear operator A must be Hermitian")
if M is not None:
assert_runtime(M.is_hermitian,
"The linear operator M must be Hermitian")
assert_runtime(
M.shape[-1] == A.shape[-1],
"The shape of A & M must match (A: %s, M: %s)" %
(A.shape, M.shape))
mode = mode.lower()
if mode == "uppermost":
mode = "uppest"
# perform expensive check if debug mode is enabled
if is_debug_enabled():
A.check()
if M is not None:
M.check()
if "method" not in fwd_options or fwd_options["method"].lower(
) == "exacteig":
return exacteig(A, neig, mode, M)
else:
# get the unique parameters of A & M
params = A.getlinopparams()
mparams = M.getlinopparams() if M is not None else []
na = len(params)
return symeig_torchfcn.apply(A, neig, mode, M, fwd_options,
bck_options, na, *params, *mparams)
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 symeig(A: LinearOperator,
neig: Optional[int] = None,
mode: str = "lowest",
M: Optional[LinearOperator] = None,
bck_options: Mapping[str, Any] = {},
method: Union[str, Callable, None] = None,
**fwd_options) -> Tuple[torch.Tensor, torch.Tensor]:
r"""
Obtain ``neig`` lowest eigenvalues and eigenvectors of a linear operator,
.. math::
\mathbf{AX = MXE}
where :math:`\mathbf{A}, \mathbf{M}` are linear operators,
:math:`\mathbf{E}` is a diagonal matrix containing the eigenvalues, and
:math:`\mathbf{X}` is a matrix containing the eigenvectors.
Arguments
---------
A: xitorch.LinearOperator
The linear operator object on which the eigenpairs are constructed.
It must be a Hermitian linear operator with shape ``(*BA, q, q)``
neig: int or None
The number of eigenpairs to be retrieved. If ``None``, all eigenpairs are
retrieved
mode: str
``"lowest"`` or ``"uppermost"``/``"uppest"``. If ``"lowest"``,
it will take the lowest ``neig`` eigenpairs.
If ``"uppest"``, it will take the uppermost ``neig``.
M: xitorch.LinearOperator
The transformation on the right hand side. If ``None``, then ``M=I``.
If specified, it must be a Hermitian with shape ``(*BM, q, q)``.
bck_options: dict
Method-specific options for :func:`solve` which used in backpropagation
calculation.
method: str or callable or None
Method for the eigendecomposition. If ``None``, it will choose
``"exacteig"``.
**fwd_options
Method-specific options (see method section below).
Returns
-------
tuple of tensors (eigenvalues, eigenvectors)
It will return eigenvalues and eigenvectors with shapes respectively
``(*BAM, neig)`` and ``(*BAM, na, neig)``, where ``*BAM`` is the
broadcasted shape of ``*BA`` and ``*BM``.
"""
assert_runtime(A.is_hermitian, "The linear operator A must be Hermitian")
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 symeig with grad enabled")
if M is not None:
assert_runtime(M.is_hermitian,
"The linear operator M must be Hermitian")
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(
not torch.is_grad_enabled() or M.is_getparamnames_implemented,
"The _getparamnames(self, prefix) of linear operator M must be "
"implemented if using symeig with grad enabled")
mode = mode.lower()
if mode == "uppermost":
mode = "uppest"
if method is None:
if isinstance(A, MatrixLinearOperator) and \
(M is None or isinstance(M, MatrixLinearOperator)):
method = "exacteig"
else:
# TODO: implement robust LOBPCG and put it here
method = "exacteig"
if neig is None:
neig = A.shape[-1]
# perform expensive check if debug mode is enabled
if is_debug_enabled():
A.check()
if M is not None:
M.check()
if method == "exacteig":
return exacteig(A, neig, mode, M)
else:
fwd_options["method"] = method
# get the unique parameters of A & M
params = A.getlinopparams()
mparams = M.getlinopparams() if M is not None else []
na = len(params)
return symeig_torchfcn.apply(A, neig, mode, M, 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,
fwd_options: Mapping[str, Any] = {},
bck_options: Mapping[str, Any] = {}):
"""
Performing iterative method to solve the equation AX=B or
AX-MXE=B, where E is a diagonal matrix.
This function can also solve batched multiple inverse equation at the
same time by applying A to a tensor X with shape (...,na,ncols).
The applied E are not necessarily identical for each column.
Arguments
---------
* A: xitorch.LinearOperator instance with shape (*BA, na, na)
A function that takes an input X and produce the vectors in the same
space as B.
* B: torch.tensor (*BB, na, ncols)
The tensor on the right hand side.
* E: torch.tensor (*BE, ncols) or None
If not None, it will solve AX-MXE = B. Otherwise, it just solves
AX = B and M is ignored. E would be applied to every column.
* M: xitorch.LinearOperator instance (*BM, na, na) or None
The transformation on the E side. If E is None,
then this argument is ignored. I E is not None and M is None, then M=I.
This LinearOperator must be Hermitian.
* fwd_options: dict
Options of the iterative solver in the forward calculation
* bck_options: dict
Options of the iterative solver in the backward calculation
"""
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" not in fwd_options or fwd_options["method"].lower(
) == "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, posdef, fwd_options,
bck_options, na, *params, *mparams)
def quad(fcn: Union[Callable[..., torch.Tensor], Callable[...,
List[torch.Tensor]]],
xl: Union[float, int, torch.Tensor],
xu: Union[float, int, torch.Tensor],
params: Sequence[Any] = [],
fwd_options: Mapping[str, Any] = {},
bck_options: Mapping[str, Any] = {}):
"""
Calculate the quadrature of the function `fcn` from `x0` to `xf`:
y = int_xl^xu fcn(x, *params)
Arguments
---------
* fcn: callable with output tensor with shape (*nout) or list of tensors
The function to be integrated.
* xl, xu: float, int, or 1-element torch.Tensor
The lower and upper bound of the integration.
* params: list
List of any other parameters for the function `fcn`.
* fwd_options: dict
Options for the forward quadrature method.
* bck_options: dict
Options for the backward quadrature method.
Returns
-------
* y: torch.tensor with shape (*nout) or list of tensors
The quadrature results.
"""
# perform implementation check if debug mode is enabled
if is_debug_enabled():
assert_fcn_params(fcn, (xl, *params))
if isinstance(xl, torch.Tensor):
assert_runtime(torch.numel(xl) == 1, "xl must be a 1-element tensors")
if isinstance(xu, torch.Tensor):
assert_runtime(torch.numel(xu) == 1, "xu must be a 1-element tensors")
out = fcn(xl, *params)
is_tuple_out = not isinstance(out, torch.Tensor)
if not is_tuple_out:
dtype = out.dtype
device = out.device
elif len(out) > 0:
dtype = out[0].dtype
device = out[0].device
else:
raise RuntimeError("The output of the fcn must be non-empty")
pfunc = get_pure_function(fcn)
nparams = len(params)
if is_tuple_out:
packer = TensorPacker(out)
@make_sibling(pfunc)
def pfunc2(x, *params):
y = fcn(x, *params)
return packer.flatten(y)
res = _Quadrature.apply(pfunc2, xl, xu, fwd_options, bck_options,
nparams, dtype, device, *params,
*pfunc.objparams())
return packer.pack(res)
else:
return _Quadrature.apply(pfunc, xl, xu, fwd_options, bck_options,
nparams, dtype, device, *params,
*pfunc.objparams())
def symeig(A: LinearOperator,
neig: Optional[int] = None,
mode: str = "lowest",
M: Optional[LinearOperator] = None,
bck_options: Mapping[str, Any] = {},
method: Union[str, Callable, None] = None,
**fwd_options) -> Tuple[torch.Tensor, torch.Tensor]:
r"""
Obtain ``neig`` lowest eigenvalues and eigenvectors of a linear operator,
.. math::
\mathbf{AX = MXE}
where :math:`\mathbf{A}, \mathbf{M}` are linear operators,
:math:`\mathbf{E}` is a diagonal matrix containing the eigenvalues, and
:math:`\mathbf{X}` is a matrix containing the eigenvectors.
This function can handle derivatives for degenerate cases by setting non-zero
``degen_atol`` and ``degen_rtol`` in the backward option using the expressions
in [1]_.
Arguments
---------
A: xitorch.LinearOperator
The linear operator object on which the eigenpairs are constructed.
It must be a Hermitian linear operator with shape ``(*BA, q, q)``
neig: int or None
The number of eigenpairs to be retrieved. If ``None``, all eigenpairs are
retrieved
mode: str
``"lowest"`` or ``"uppermost"``/``"uppest"``. If ``"lowest"``,
it will take the lowest ``neig`` eigenpairs.
If ``"uppest"``, it will take the uppermost ``neig``.
M: xitorch.LinearOperator
The transformation on the right hand side. If ``None``, then ``M=I``.
If specified, it must be a Hermitian with shape ``(*BM, q, q)``.
bck_options: dict
Method-specific options for :func:`solve` which used in backpropagation
calculation with some additional arguments for computing the backward
derivatives:
* ``degen_atol`` (``float`` or None): Minimum absolute difference between
two eigenvalues to be treated as degenerate. If None, it is
``torch.finfo(dtype).eps**0.6``. If 0.0, no special treatment on
degeneracy is applied. (default: None)
* ``degen_rtol`` (``float`` or None): Minimum relative difference between
two eigenvalues to be treated as degenerate. If None, it is
``torch.finfo(dtype).eps**0.4``. If 0.0, no special treatment on
degeneracy is applied. (default: None)
Note: the default values of ``degen_atol`` and ``degen_rtol`` are going
to change in the future. So, for future compatibility, please specify
the specific values.
method: str or callable or None
Method for the eigendecomposition. If ``None``, it will choose
``"exacteig"``.
**fwd_options
Method-specific options (see method section below).
Returns
-------
tuple of tensors (eigenvalues, eigenvectors)
It will return eigenvalues and eigenvectors with shapes respectively
``(*BAM, neig)`` and ``(*BAM, na, neig)``, where ``*BAM`` is the
broadcasted shape of ``*BA`` and ``*BM``.
References
----------
.. [1] Muhammad F. Kasim,
"Derivatives of partial eigendecomposition of a real symmetric matrix for degenerate cases".
arXiv:2011.04366 (2020)
`https://arxiv.org/abs/2011.04366 <https://arxiv.org/abs/2011.04366>`_
"""
assert_runtime(A.is_hermitian, "The linear operator A must be Hermitian")
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 symeig with grad enabled")
if M is not None:
assert_runtime(M.is_hermitian,
"The linear operator M must be Hermitian")
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(
not torch.is_grad_enabled() or M.is_getparamnames_implemented,
"The _getparamnames(self, prefix) of linear operator M must be "
"implemented if using symeig with grad enabled")
mode = mode.lower()
if mode == "uppermost":
mode = "uppest"
if method is None:
if isinstance(A, MatrixLinearOperator) and \
(M is None or isinstance(M, MatrixLinearOperator)):
method = "exacteig"
else:
# TODO: implement robust LOBPCG and put it here
method = "exacteig"
if neig is None:
neig = A.shape[-1]
# perform expensive check if debug mode is enabled
if is_debug_enabled():
A.check()
if M is not None:
M.check()
if method == "exacteig":
return exacteig(A, neig, mode, M)
else:
fwd_options["method"] = method
# get the unique parameters of A & M
params = A.getlinopparams()
mparams = M.getlinopparams() if M is not None else []
na = len(params)
return symeig_torchfcn.apply(A, neig, mode, M, fwd_options,
bck_options, na, *params, *mparams)
def solve_ivp(fcn: Callable[..., torch.Tensor],
ts: torch.Tensor,
y0: torch.Tensor,
params: Sequence[Any] = [],
fwd_options: Mapping[str, Any] = {},
bck_options: Mapping[str, Any] = {}) -> torch.Tensor:
"""
Solve the initial value problem (IVP) which given the initial value `y0`,
the function is then solve
y(t) = y0 + int_t0^t f(t', y, *params) dt'
Arguments
---------
* fcn: callable with output a tensor with shape (*ny) or a list of tensors
The function that represents dy/dt. The function takes an input of a
single time `t` and `y` with shape (*ny) and produce dydt with shape (*ny).
* ts: torch.tensor with shape (nt,)
The time points where the value of `y` is returned.
It must be monotonically increasing or decreasing.
* y0: torch.tensor with shape (*ny) or a list of tensors
The initial value of y, i.e. y(t[0]) == y0
* params: list
List of other parameters required in the function.
* fwd_options: dict
Options for the forward solve_ivp method.
* bck_options: dict
Options for the backward solve_ivp method.
Returns
-------
* yt: torch.tensor with shape (nt,*ny) or a list of tensors
The values of `y` for each time step in `ts`.
"""
if is_debug_enabled():
assert_fcn_params(fcn, (ts[0], y0, *params))
assert_runtime(len(ts.shape) == 1, "Argument ts must be a 1D tensor")
# run once to see if the outputs is a tuple or a single tensor
is_y0_list = isinstance(y0, list) or isinstance(y0, tuple)
dydt = fcn(ts[0], y0, *params)
is_dydt_list = isinstance(dydt, list) or isinstance(dydt, tuple)
if is_y0_list != is_dydt_list:
raise RuntimeError(
"The y0 and output of fcn must both be tuple or a tensor")
pfcn = get_pure_function(fcn)
if is_y0_list:
nt = len(ts)
roller = TensorPacker(y0)
@make_sibling(pfcn)
def pfcn2(t, ytensor, *params):
ylist = roller.pack(ytensor)
res_list = pfcn(t, ylist, *params)
res = roller.flatten(res_list)
return res
y0 = roller.flatten(y0)
res = _SolveIVP.apply(pfcn2, ts, fwd_options, bck_options, len(params),
y0, *params, *pfcn.objparams())
return roller.pack(res)
else:
return _SolveIVP.apply(pfcn, ts, fwd_options, bck_options, len(params),
y0, *params, *pfcn.objparams())
def quad(fcn: Union[Callable[..., torch.Tensor],
Callable[..., Sequence[torch.Tensor]]],
xl: Union[float, int, torch.Tensor],
xu: Union[float, int, torch.Tensor],
params: Sequence[Any] = [],
bck_options: Mapping[str, Any] = {},
method: Union[str, Callable, None] = None,
**fwd_options) -> Union[torch.Tensor, Sequence[torch.Tensor]]:
r"""
Calculate the quadrature:
.. math::
y = \int_{x_l}^{x_u} f(x, \theta)\ \mathrm{d}x
Arguments
---------
fcn: callable
The function to be integrated. Its output must be a tensor with
shape ``(*nout)`` or list of tensors.
xl: float, int or 1-element torch.Tensor
The lower bound of the integration.
xu: float, int or 1-element torch.Tensor
The upper bound of the integration.
params: list
Sequence of any other parameters for the function ``fcn``.
bck_options: dict
Options for the backward quadrature method.
method: str or callable or None
Quadrature method. If None, it will choose ``"leggauss"``.
**fwd_options
Method-specific options (see method section).
Returns
-------
torch.tensor or a list of tensors
The quadrature results with shape ``(*nout)`` or list of tensors.
"""
# perform implementation check if debug mode is enabled
if is_debug_enabled():
assert_fcn_params(fcn, (xl, *params))
if isinstance(xl, torch.Tensor):
assert_runtime(torch.numel(xl) == 1, "xl must be a 1-element tensors")
if isinstance(xu, torch.Tensor):
assert_runtime(torch.numel(xu) == 1, "xu must be a 1-element tensors")
if method is None:
method = "leggauss"
fwd_options["method"] = method
out = fcn(xl, *params)
if isinstance(out, torch.Tensor):
dtype = out.dtype
device = out.device
is_tuple_out = False
elif len(out) > 0:
dtype = out[0].dtype
device = out[0].device
is_tuple_out = True
else:
raise RuntimeError("The output of the fcn must be non-empty")
pfunc = get_pure_function(fcn)
nparams = len(params)
if is_tuple_out:
packer = TensorPacker(out)
@make_sibling(pfunc)
def pfunc2(x, *params):
y = fcn(x, *params)
return packer.flatten(y)
res = _Quadrature.apply(pfunc2, xl, xu, fwd_options, bck_options,
nparams, dtype, device, *params,
*pfunc.objparams())
return packer.pack(res)
else:
return _Quadrature.apply(pfunc, xl, xu, fwd_options, bck_options,
nparams, dtype, device, *params,
*pfunc.objparams())
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)
