92 lines
3.4 KiB
Python
92 lines
3.4 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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"""Common utilities for registering LinearOperator methods."""
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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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# Note: only use this method in the commuting case.
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def combined_commuting_self_adjoint_hint(operator_a, operator_b):
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"""Get combined hint for self-adjoint-ness."""
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# The property is preserved under composition when the operators commute.
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if operator_a.is_self_adjoint and operator_b.is_self_adjoint:
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return True
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# The property is not preserved when an operator with the property is composed
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# with an operator without the property.
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# pylint:disable=g-bool-id-comparison
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if ((operator_a.is_self_adjoint is True and
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operator_b.is_self_adjoint is False) or
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(operator_a.is_self_adjoint is False and
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operator_b.is_self_adjoint is True)):
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return False
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# pylint:enable=g-bool-id-comparison
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# The property is not known when operators are not known to have the property
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# or both operators don't have the property (the property for the complement
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# class is not closed under composition).
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return None
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def is_square(operator_a, operator_b):
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"""Return a hint to whether the composition is square."""
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if operator_a.is_square and operator_b.is_square:
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return True
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if operator_a.is_square is False and operator_b.is_square is False: # pylint:disable=g-bool-id-comparison
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# Let A have shape [B, M, N], B have shape [B, N, L].
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m = operator_a.range_dimension
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l = operator_b.domain_dimension
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if m is not None and l is not None:
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return m == l
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if (operator_a.is_square != operator_b.is_square) and (
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operator_a.is_square is not None and operator_a.is_square is not None):
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return False
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return None
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# Note: Positive definiteness is only guaranteed to be preserved
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# when the operators commute and are symmetric. Only use this method in
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# commuting cases.
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def combined_commuting_positive_definite_hint(operator_a, operator_b):
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"""Get combined PD hint for compositions."""
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# pylint:disable=g-bool-id-comparison
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if (operator_a.is_positive_definite is True and
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operator_a.is_self_adjoint is True and
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operator_b.is_positive_definite is True and
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operator_b.is_self_adjoint is True):
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return True
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# pylint:enable=g-bool-id-comparison
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return None
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def combined_non_singular_hint(operator_a, operator_b):
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"""Get combined hint for when ."""
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# If either operator is not-invertible the composition isn't.
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# pylint:disable=g-bool-id-comparison
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if (operator_a.is_non_singular is False or
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operator_b.is_non_singular is False):
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return False
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# pylint:enable=g-bool-id-comparison
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return operator_a.is_non_singular and operator_b.is_non_singular
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