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.linalg.logdet(A)) # scalar
```
Args:
matrix: A `Tensor`. Must be `float16`, `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))),
axis=[-1])
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 `float16`, `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])
def _RegularizedGramianCholesky(matrix, l2_regularizer, first_kind):
r"""Computes Cholesky factorization of regularized gramian matrix.
Below we will use the following notation for each pair of matrix and
right-hand sides in the batch:
`matrix`=\\(A \in \Re^{m \times n}\\),
`output`=\\(C \in \Re^{\min(m, n) \times \min(m,n)}\\),
`l2_regularizer`=\\(\lambda\\).
If `first_kind` is True, returns the Cholesky factorization \\(L\\) such that
\\(L L^H = A^H A + \lambda I\\).
If `first_kind` is False, returns the Cholesky factorization \\(L\\) such that
\\(L L^H = A A^H + \lambda I\\).
Args:
matrix: `Tensor` of shape `[..., M, N]`.
l2_regularizer: 0-D `double` `Tensor`. Ignored if `fast=False`.
first_kind: bool. Controls what gramian matrix to factor.
Returns:
output: `Tensor` of shape `[..., min(M,N), min(M,N)]` whose inner-most 2
dimensions contain the Cholesky factors \\(L\\) described above.
"""
gramian = math_ops.matmul(matrix,
matrix,
adjoint_a=first_kind,
adjoint_b=not first_kind)
if isinstance(l2_regularizer, ops.Tensor) or l2_regularizer != 0:
matrix_shape = array_ops.shape(matrix)
batch_shape = matrix_shape[:-2]
if first_kind:
small_dim = matrix_shape[-1]
else:
small_dim = matrix_shape[-2]
identity = eye(small_dim, batch_shape=batch_shape, dtype=matrix.dtype)
small_dim_static = matrix.shape[-1 if first_kind else -2]
identity.set_shape(matrix.shape[:-2].concatenate(
[small_dim_static, small_dim_static]))
gramian += l2_regularizer * identity
return gen_linalg_ops.cholesky(gramian)
def _RegularizedGramianCholesky(matrix, l2_regularizer, first_kind):
r"""Computes Cholesky factorization of regularized gramian matrix.
Below we will use the following notation for each pair of matrix and
right-hand sides in the batch:
`matrix`=\\(A \in \Re^{m \times n}\\),
`output`=\\(C \in \Re^{\min(m, n) \times \min(m,n)}\\),
`l2_regularizer`=\\(\lambda\\).
If `first_kind` is True, returns the Cholesky factorization \\(L\\) such that
\\(L L^H = A^H A + \lambda I\\).
If `first_kind` is False, returns the Cholesky factorization \\(L\\) such that
\\(L L^H = A A^H + \lambda I\\).
Args:
matrix: `Tensor` of shape `[..., M, N]`.
l2_regularizer: 0-D `double` `Tensor`. Ignored if `fast=False`.
first_kind: bool. Controls what gramian matrix to factor.
Returns:
output: `Tensor` of shape `[..., min(M,N), min(M,N)]` whose inner-most 2
dimensions contain the Cholesky factors \\(L\\) described above.
"""
gramian = math_ops.matmul(
matrix, matrix, adjoint_a=first_kind, adjoint_b=not first_kind)
if isinstance(l2_regularizer, ops.Tensor) or l2_regularizer != 0:
matrix_shape = array_ops.shape(matrix)
batch_shape = matrix_shape[:-2]
if first_kind:
small_dim = matrix_shape[-1]
else:
small_dim = matrix_shape[-2]
identity = eye(small_dim, batch_shape=batch_shape, dtype=matrix.dtype)
small_dim_static = matrix.shape[-1 if first_kind else -2]
identity.set_shape(
matrix.shape[:-2].concatenate([small_dim_static, small_dim_static]))
gramian += l2_regularizer * identity
return gen_linalg_ops.cholesky(gramian)
