#!/usr/bin/env python3
from __future__ import annotations
import warnings
from typing import Callable, Optional, Tuple, Union
import torch
from jaxtyping import Float
from torch import Tensor
from ..utils.memoize import cached
from ._linear_operator import LinearOperator
from .root_linear_operator import RootLinearOperator
from .triangular_linear_operator import _TriangularLinearOperatorBase, TriangularLinearOperator
[docs]class CholLinearOperator(RootLinearOperator):
r"""
A LinearOperator (... x N x N) that represents a positive definite matrix given
a lower trinagular Cholesky factor :math:`\mathbf L`
(or upper triangular Cholesky factor :math:`\mathbf R`).
:param chol: The Cholesky factor :math:`\mathbf L` (or :math:`\mathbf R`).
:type chol: TriangularLinearOperator (... x N x N)
:param upper: If the orientation of the cholesky factor is an upper triangular matrix
(i.e. :math:`\mathbf R^\top \mathbf R`).
If false, then the orientation is assumed to be a lower triangular matrix
(i.e. :math:`\mathbf L \mathbf L^\top`).
"""
def __init__(self, chol: Float[_TriangularLinearOperatorBase, "*#batch N N"], upper: bool = False):
if not isinstance(chol, _TriangularLinearOperatorBase):
warnings.warn(
"chol argument to CholLinearOperator should be a TriangularLinearOperator. "
"Passing a dense tensor will cause errors in future versions.",
DeprecationWarning,
)
if torch.all(torch.tril(chol) == chol):
chol = TriangularLinearOperator(chol, upper=False)
elif torch.all(torch.triu(chol) == chol):
chol = TriangularLinearOperator(chol, upper=True)
else:
raise ValueError("chol must be either lower or upper triangular")
super().__init__(chol)
self.upper = upper
@property
def _chol_diag(self: Float[LinearOperator, "*batch N N"]) -> Float[torch.Tensor, "... N"]:
return self.root._diagonal()
@cached(name="cholesky")
def _cholesky(
self: Float[LinearOperator, "*batch N N"], upper: Optional[bool] = False
) -> Float[LinearOperator, "*batch N N"]:
if upper == self.upper:
return self.root
else:
return self.root._transpose_nonbatch()
@cached
def _diagonal(self: Float[LinearOperator, "... M N"]) -> Float[torch.Tensor, "... N"]:
# TODO: Can we be smarter here?
return (self.root.to_dense() ** 2).sum(-1)
def _solve(
self: Float[LinearOperator, "... N N"],
rhs: Float[torch.Tensor, "... N C"],
preconditioner: Optional[Callable[[Float[torch.Tensor, "... N C"]], Float[torch.Tensor, "... N C"]]] = None,
num_tridiag: Optional[int] = 0,
) -> Union[
Float[torch.Tensor, "... N C"],
Tuple[
Float[torch.Tensor, "... N C"],
Float[torch.Tensor, "..."], # Note that in case of a tuple the second term size depends on num_tridiag
],
]:
if num_tridiag:
return super()._solve(rhs, preconditioner, num_tridiag=num_tridiag)
return self.root._cholesky_solve(rhs, upper=self.upper)
@cached
def to_dense(self: Float[LinearOperator, "*batch M N"]) -> Float[Tensor, "*batch M N"]:
root = self.root
if self.upper:
res = root._transpose_nonbatch() @ root
else:
res = root @ root._transpose_nonbatch()
return res.to_dense()
[docs] @cached
def inverse(self: Float[LinearOperator, "*batch N N"]) -> Float[LinearOperator, "*batch N N"]:
"""
Returns the inverse of the CholLinearOperator.
"""
Linv = self.root.inverse() # this could be slow in some cases w/ structured lazies
return CholLinearOperator(TriangularLinearOperator(Linv, upper=not self.upper), upper=not self.upper)
def inv_quad(
self: Float[LinearOperator, "*batch N N"],
inv_quad_rhs: Union[Float[Tensor, "*batch N M"], Float[Tensor, "*batch N"]],
reduce_inv_quad: bool = True,
) -> Union[Float[Tensor, "*batch M"], Float[Tensor, " *batch"]]:
if self.upper:
R = self.root._transpose_nonbatch().solve(inv_quad_rhs)
else:
R = self.root.solve(inv_quad_rhs)
inv_quad_term = (R**2).sum(dim=-2)
if inv_quad_term.numel() and reduce_inv_quad:
inv_quad_term = inv_quad_term.sum(-1)
return inv_quad_term
def inv_quad_logdet(
self: Float[LinearOperator, "*batch N N"],
inv_quad_rhs: Optional[Union[Float[Tensor, "*batch N M"], Float[Tensor, "*batch N"]]] = None,
logdet: Optional[bool] = False,
reduce_inv_quad: Optional[bool] = True,
) -> Tuple[
Optional[Union[Float[Tensor, "*batch M"], Float[Tensor, " *batch"], Float[Tensor, " 0"]]],
Optional[Float[Tensor, "..."]],
]:
if not self.is_square:
raise RuntimeError(
"inv_quad_logdet only operates on (batches of) square (positive semi-definite) LinearOperators. "
"Got a {} of size {}.".format(self.__class__.__name__, self.size())
)
if inv_quad_rhs is not None:
if self.dim() == 2 and inv_quad_rhs.dim() == 1:
if self.shape[-1] != inv_quad_rhs.numel():
raise RuntimeError(
"LinearOperator (size={}) cannot be multiplied with right-hand-side Tensor (size={}).".format(
self.shape, inv_quad_rhs.shape
)
)
elif self.dim() != inv_quad_rhs.dim():
raise RuntimeError(
"LinearOperator (size={}) and right-hand-side Tensor (size={}) should have the same number "
"of dimensions.".format(self.shape, inv_quad_rhs.shape)
)
elif self.shape[-1] != inv_quad_rhs.shape[-2]:
raise RuntimeError(
"LinearOperator (size={}) cannot be multiplied with right-hand-side Tensor (size={}).".format(
self.shape, inv_quad_rhs.shape
)
)
inv_quad_term = None
logdet_term = None
if inv_quad_rhs is not None:
inv_quad_term = self.inv_quad(inv_quad_rhs, reduce_inv_quad=reduce_inv_quad)
if logdet:
logdet_term = self._chol_diag.pow(2).log().sum(-1)
return inv_quad_term, logdet_term
def root_inv_decomposition(
self: Float[LinearOperator, "*batch N N"],
initial_vectors: Optional[torch.Tensor] = None,
test_vectors: Optional[torch.Tensor] = None,
method: Optional[str] = None,
) -> Union[Float[LinearOperator, "... N N"], Float[Tensor, "... N N"]]:
inv_root = self.root.inverse()
return RootLinearOperator(inv_root._transpose_nonbatch())
def solve(
self: Float[LinearOperator, "... N N"],
right_tensor: Union[Float[Tensor, "... N P"], Float[Tensor, " N"]],
left_tensor: Optional[Float[Tensor, "... O N"]] = None,
) -> Union[Float[Tensor, "... N P"], Float[Tensor, "... N"], Float[Tensor, "... O P"], Float[Tensor, "... O"]]:
is_vector = right_tensor.ndim == 1
if is_vector:
right_tensor = right_tensor.unsqueeze(-1)
res = self.root._cholesky_solve(right_tensor, upper=self.upper)
if is_vector:
res = res.squeeze(-1)
if left_tensor is not None:
res = left_tensor @ res
return res