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linalg_impl.py
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# Copyright 2017 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.
# ==============================================================================
"""Operations for linear algebra."""
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 gen_linalg_ops
from tensorflow.python.ops import math_ops
def logdet(matrix, name=None):
"""Computes log of the determinant of a hermitian positive definite matrix.
```python
# Compute the determinant of a matrix while reducing the chance of over- or
underflow:
A = ... # shape 10 x 10
det = tf.exp(tf.logdet(A)) # scalar
```
Args:
matrix: A `Tensor`. Must be `float32`, `float64`, `complex64`, or
`complex128` with shape `[..., M, M]`.
name: A name to give this `Op`. Defaults to `logdet`.
Returns:
The natural log of the determinant of `matrix`.
@compatibility(numpy)
Equivalent to numpy.linalg.slogdet, although no sign is returned since only
hermitian positive definite matrices are supported.
@end_compatibility
"""
# This uses the property that the log det(A) = 2*sum(log(real(diag(C))))
# where C is the cholesky decomposition of A.
with ops.name_scope(name, 'logdet', [matrix]):
chol = gen_linalg_ops.cholesky(matrix)
return 2.0 * math_ops.reduce_sum(
math_ops.log(math_ops.real(array_ops.matrix_diag_part(chol))),
reduction_indices=[-1])