Source code for linear_operator.operators.chol_linear_operator

#!/usr/bin/env python3

from __future__ import annotations

import warnings
from typing import Callable, Optional, Tuple

import torch

from ..utils.memoize import cached
from ._linear_operator import LinearOperator
from .root_linear_operator import RootLinearOperator
from .triangular_linear_operator import TriangularLinearOperator, _TriangularLinearOperatorBase

[docs]class CholLinearOperator(RootLinearOperator): r""" A LinearOperator 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 :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: _TriangularLinearOperatorBase, 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) -> torch.Tensor: return self.root._diagonal() @cached(name="cholesky") def _cholesky(self, upper: bool = False) -> TriangularLinearOperator: if upper == self.upper: return self.root else: return self.root._transpose_nonbatch() @cached def _diagonal(self) -> torch.Tensor: # TODO: Can we be smarter here? return (self.root.to_dense() ** 2).sum(-1) def _solve(self, rhs: torch.Tensor, preconditioner: Callable, num_tridiag: int = 0) -> torch.Tensor: 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) -> torch.Tensor: 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) -> "CholLinearOperator": """ 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, tensor: torch.Tensor, reduce_inv_quad: bool = True) -> torch.Tensor: if self.upper: R = self.root._transpose_nonbatch().solve(tensor) else: R = self.root.solve(tensor) 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, inv_quad_rhs: Optional[torch.Tensor] = None, logdet: bool = False, reduce_inv_quad: bool = True ) -> Tuple[torch.Tensor, torch.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, initial_vectors: Optional[torch.Tensor] = None, test_vectors: Optional[torch.Tensor] = None, method: Optional[str] = None, ) -> LinearOperator: inv_root = self.root.inverse() return RootLinearOperator(inv_root._transpose_nonbatch()) def solve(self, right_tensor: torch.Tensor, left_tensor: Optional[torch.Tensor] = None) -> torch.Tensor: 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