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# Copyright 2015 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Gradients for operators defined in linalg_ops.py.
Useful reference for derivative formulas is
An extended collection of matrix derivative results for forward and reverse
mode algorithmic differentiation by Mike Giles:
http://eprints.maths.ox.ac.uk/1079/1/NA-08-01.pdf
"""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
from tensorflow.python.framework import ops
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import control_flow_ops
from tensorflow.python.ops import linalg_ops
from tensorflow.python.ops import math_ops
ops.NoGradient("CholeskyGrad")
ops.NoGradient("BatchCholeskyGrad")
ops.NoGradient("SelfAdjointEig")
ops.NoGradient("BatchSelfAdjointEig")
ops.NoGradient("SelfAdjointEigV2")
ops.NoGradient("BatchSelfAdjointEigV2")
ops.NoGradient("Svd")
ops.NoGradient("BatchSvd")
@ops.RegisterGradient("MatrixInverse")
def _MatrixInverseGrad(op, grad):
"""Gradient for MatrixInverse."""
ainv = op.outputs[0]
return -math_ops.matmul(ainv,
math_ops.matmul(grad,
ainv,
transpose_b=True),
transpose_a=True)
@ops.RegisterGradient("BatchMatrixInverse")
def _BatchMatrixInverseGrad(op, grad):
"""Gradient for BatchMatrixInverse."""
ainv = op.outputs[0]
return -math_ops.batch_matmul(ainv,
math_ops.batch_matmul(grad,
ainv,
adj_y=True),
adj_x=True)
@ops.RegisterGradient("MatrixDeterminant")
def _MatrixDeterminantGrad(op, grad):
"""Gradient for MatrixDeterminant."""
a = op.inputs[0]
c = op.outputs[0]
a_adj_inv = linalg_ops.matrix_inverse(a, adjoint=True)
return grad * c * a_adj_inv
@ops.RegisterGradient("BatchMatrixDeterminant")
def _BatchMatrixDeterminantGrad(op, grad):
"""Gradient for BatchMatrixDeterminant."""
a = op.inputs[0]
c = op.outputs[0]
a_adj_inv = linalg_ops.batch_matrix_inverse(a, adjoint=True)
multipliers = array_ops.reshape(
grad * c, array_ops.concat(0, [array_ops.shape(c), [1, 1]]))
return multipliers * a_adj_inv
@ops.RegisterGradient("Cholesky")
def _CholeskyGrad(op, grad):
"""Gradient for Cholesky."""
return linalg_ops.cholesky_grad(op.outputs[0], grad)
@ops.RegisterGradient("BatchCholesky")
def _BatchCholeskyGrad(op, grad):
"""Gradient for BatchCholesky."""
return linalg_ops.batch_cholesky_grad(op.outputs[0], grad)
@ops.RegisterGradient("MatrixSolve")
def _MatrixSolveGrad(op, grad):
"""Gradients for MatrixSolve."""
a = op.inputs[0]
adjoint_a = op.get_attr("adjoint")
c = op.outputs[0]
grad_b = linalg_ops.matrix_solve(a, grad, adjoint=not adjoint_a)
if adjoint_a:
grad_a = -math_ops.matmul(c, grad_b, transpose_b=True)
else:
grad_a = -math_ops.matmul(grad_b, c, transpose_b=True)
return (grad_a, grad_b)
@ops.RegisterGradient("BatchMatrixSolve")
def _BatchMatrixSolveGrad(op, grad):
"""Gradient for BatchMatrixSolve."""
a = op.inputs[0]
adjoint_a = op.get_attr("adjoint")
c = op.outputs[0]
grad_b = linalg_ops.batch_matrix_solve(a, grad, adjoint=not adjoint_a)
if adjoint_a:
grad_a = -math_ops.batch_matmul(c, grad_b, adj_y=True)
else:
grad_a = -math_ops.batch_matmul(grad_b, c, adj_y=True)
return (grad_a, grad_b)
@ops.RegisterGradient("MatrixTriangularSolve")
def _MatrixTriangularSolveGrad(op, grad):
"""Gradients for MatrixTriangularSolve."""
a = op.inputs[0]
adjoint_a = op.get_attr("adjoint")
lower_a = op.get_attr("lower")
c = op.outputs[0]
grad_b = linalg_ops.matrix_triangular_solve(a,
grad,
lower=lower_a,
adjoint=not adjoint_a)
if adjoint_a:
grad_a = -math_ops.matmul(c, grad_b, transpose_b=True)
else:
grad_a = -math_ops.matmul(grad_b, c, transpose_b=True)
if lower_a:
grad_a = array_ops.batch_matrix_band_part(grad_a, -1, 0)
else:
grad_a = array_ops.batch_matrix_band_part(grad_a, 0, -1)
return (grad_a, grad_b)
@ops.RegisterGradient("BatchMatrixTriangularSolve")
def _BatchMatrixTriangularSolveGrad(op, grad):
"""Gradient for BatchMatrixTriangularSolve."""
a = op.inputs[0]
adjoint_a = op.get_attr("adjoint")
lower_a = op.get_attr("lower")
c = op.outputs[0]
grad_b = linalg_ops.batch_matrix_triangular_solve(a,
grad,
lower=lower_a,
adjoint=not adjoint_a)
if adjoint_a:
grad_a = -math_ops.batch_matmul(c, grad_b, adj_y=True)
else:
grad_a = -math_ops.batch_matmul(grad_b, c, adj_y=True)
if lower_a:
grad_a = array_ops.batch_matrix_band_part(grad_a, -1, 0)
else:
grad_a = array_ops.batch_matrix_band_part(grad_a, 0, -1)
return (grad_a, grad_b)