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"""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 constant_op
from tensorflow.python.ops import linalg_ops
from tensorflow.python.ops import math_ops
@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.
Returns:
gradient
Args:
op: op
grad: grad
"""
a = op.inputs[0]
c = op.outputs[0]
ainv = linalg_ops.matrix_inverse(a)
return grad * c * array_ops.transpose(ainv)
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