e301dda113
Also register `linop.solve(identity_linop) = linop.inverse()`. This is useful for families like ScaledIdentity that are closed under inversion. PiperOrigin-RevId: 272530839
191 lines
7.5 KiB
Python
191 lines
7.5 KiB
Python
# Copyright 2019 The TensorFlow Authors. All Rights Reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# ==============================================================================
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"""Registrations for LinearOperator.solve."""
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from __future__ import absolute_import
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from __future__ import division
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from __future__ import print_function
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from tensorflow.python.ops.linalg import linear_operator
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from tensorflow.python.ops.linalg import linear_operator_algebra
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from tensorflow.python.ops.linalg import linear_operator_circulant
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from tensorflow.python.ops.linalg import linear_operator_composition
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from tensorflow.python.ops.linalg import linear_operator_diag
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from tensorflow.python.ops.linalg import linear_operator_identity
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from tensorflow.python.ops.linalg import linear_operator_inversion
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from tensorflow.python.ops.linalg import linear_operator_lower_triangular
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from tensorflow.python.ops.linalg import registrations_util
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# By default, use a LinearOperatorComposition to delay the computation.
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@linear_operator_algebra.RegisterSolve(
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linear_operator.LinearOperator, linear_operator.LinearOperator)
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def _solve_linear_operator(linop_a, linop_b):
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"""Generic solve of two `LinearOperator`s."""
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is_square = registrations_util.is_square(linop_a, linop_b)
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is_non_singular = None
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is_self_adjoint = None
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is_positive_definite = None
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if is_square:
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is_non_singular = registrations_util.combined_non_singular_hint(
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linop_a, linop_b)
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elif is_square is False: # pylint:disable=g-bool-id-comparison
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is_non_singular = False
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is_self_adjoint = False
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is_positive_definite = False
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return linear_operator_composition.LinearOperatorComposition(
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operators=[
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linear_operator_inversion.LinearOperatorInversion(linop_a),
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linop_b
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],
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is_non_singular=is_non_singular,
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is_self_adjoint=is_self_adjoint,
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is_positive_definite=is_positive_definite,
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is_square=is_square,
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)
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@linear_operator_algebra.RegisterSolve(
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linear_operator_inversion.LinearOperatorInversion,
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linear_operator.LinearOperator)
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def _solve_inverse_linear_operator(linop_a, linop_b):
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"""Solve inverse of generic `LinearOperator`s."""
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return linop_a.operator.matmul(linop_b)
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# Identity
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@linear_operator_algebra.RegisterSolve(
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linear_operator_identity.LinearOperatorIdentity,
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linear_operator.LinearOperator)
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def _solve_linear_operator_identity_left(identity, linop):
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del identity
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return linop
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@linear_operator_algebra.RegisterSolve(
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linear_operator.LinearOperator,
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linear_operator_identity.LinearOperatorIdentity)
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def _solve_linear_operator_identity_right(linop, identity):
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del identity
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return linop.inverse()
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@linear_operator_algebra.RegisterSolve(
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linear_operator_identity.LinearOperatorScaledIdentity,
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linear_operator_identity.LinearOperatorScaledIdentity)
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def _solve_linear_operator_scaled_identity(linop_a, linop_b):
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"""Solve of two ScaledIdentity `LinearOperators`."""
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return linear_operator_identity.LinearOperatorScaledIdentity(
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num_rows=linop_a.domain_dimension_tensor(),
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multiplier=linop_b.multiplier / linop_a.multiplier,
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is_non_singular=registrations_util.combined_non_singular_hint(
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linop_a, linop_b),
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is_self_adjoint=registrations_util.combined_commuting_self_adjoint_hint(
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linop_a, linop_b),
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is_positive_definite=(
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registrations_util.combined_commuting_positive_definite_hint(
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linop_a, linop_b)),
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is_square=True)
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# Diag.
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@linear_operator_algebra.RegisterSolve(
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linear_operator_diag.LinearOperatorDiag,
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linear_operator_diag.LinearOperatorDiag)
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def _solve_linear_operator_diag(linop_a, linop_b):
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return linear_operator_diag.LinearOperatorDiag(
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diag=linop_b.diag / linop_a.diag,
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is_non_singular=registrations_util.combined_non_singular_hint(
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linop_a, linop_b),
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is_self_adjoint=registrations_util.combined_commuting_self_adjoint_hint(
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linop_a, linop_b),
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is_positive_definite=(
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registrations_util.combined_commuting_positive_definite_hint(
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linop_a, linop_b)),
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is_square=True)
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@linear_operator_algebra.RegisterSolve(
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linear_operator_diag.LinearOperatorDiag,
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linear_operator_identity.LinearOperatorScaledIdentity)
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def _solve_linear_operator_diag_scaled_identity_right(
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linop_diag, linop_scaled_identity):
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return linear_operator_diag.LinearOperatorDiag(
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diag=linop_scaled_identity.multiplier / linop_diag.diag,
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is_non_singular=registrations_util.combined_non_singular_hint(
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linop_diag, linop_scaled_identity),
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is_self_adjoint=registrations_util.combined_commuting_self_adjoint_hint(
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linop_diag, linop_scaled_identity),
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is_positive_definite=(
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registrations_util.combined_commuting_positive_definite_hint(
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linop_diag, linop_scaled_identity)),
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is_square=True)
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@linear_operator_algebra.RegisterSolve(
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linear_operator_identity.LinearOperatorScaledIdentity,
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linear_operator_diag.LinearOperatorDiag)
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def _solve_linear_operator_diag_scaled_identity_left(
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linop_scaled_identity, linop_diag):
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return linear_operator_diag.LinearOperatorDiag(
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diag=linop_diag.diag / linop_scaled_identity.multiplier,
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is_non_singular=registrations_util.combined_non_singular_hint(
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linop_diag, linop_scaled_identity),
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is_self_adjoint=registrations_util.combined_commuting_self_adjoint_hint(
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linop_diag, linop_scaled_identity),
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is_positive_definite=(
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registrations_util.combined_commuting_positive_definite_hint(
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linop_diag, linop_scaled_identity)),
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is_square=True)
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@linear_operator_algebra.RegisterSolve(
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linear_operator_diag.LinearOperatorDiag,
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linear_operator_lower_triangular.LinearOperatorLowerTriangular)
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def _solve_linear_operator_diag_tril(linop_diag, linop_triangular):
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return linear_operator_lower_triangular.LinearOperatorLowerTriangular(
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tril=linop_triangular.to_dense() / linop_diag.diag[..., None],
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is_non_singular=registrations_util.combined_non_singular_hint(
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linop_diag, linop_triangular),
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# This is safe to do since the Triangular matrix is only self-adjoint
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# when it is a diagonal matrix, and hence commutes.
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is_self_adjoint=registrations_util.combined_commuting_self_adjoint_hint(
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linop_diag, linop_triangular),
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is_positive_definite=None,
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is_square=True)
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# Circulant.
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@linear_operator_algebra.RegisterSolve(
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linear_operator_circulant.LinearOperatorCirculant,
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linear_operator_circulant.LinearOperatorCirculant)
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def _solve_linear_operator_circulant_circulant(linop_a, linop_b):
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return linear_operator_circulant.LinearOperatorCirculant(
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spectrum=linop_b.spectrum / linop_a.spectrum,
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is_non_singular=registrations_util.combined_non_singular_hint(
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linop_a, linop_b),
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is_self_adjoint=registrations_util.combined_commuting_self_adjoint_hint(
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linop_a, linop_b),
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is_positive_definite=(
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registrations_util.combined_commuting_positive_definite_hint(
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linop_a, linop_b)),
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is_square=True)
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