Computes the LU decomposition of one or more square matrices.
tf.raw_ops.Lu(
input, output_idx_type=tf.dtypes.int32, name=None
)
The input is a tensor of shape [..., M, M] whose inner-most 2 dimensions
form square matrices.
The input has to be invertible.
The output consists of two tensors LU and P containing the LU decomposition
of all input submatrices [..., :, :]. LU encodes the lower triangular and
upper triangular factors.
For each input submatrix of shape [M, M], L is a lower triangular matrix of
shape [M, M] with unit diagonal whose entries correspond to the strictly lower
triangular part of LU. U is a upper triangular matrix of shape [M, M] whose
entries correspond to the upper triangular part, including the diagonal, of LU.
P represents a permutation matrix encoded as a list of indices each between 0
and M-1, inclusive. If P_mat denotes the permutation matrix corresponding to
P, then the L, U and P satisfies P_mat * input = L * U.
Args | |
|---|---|
input
|
A Tensor. Must be one of the following types: float64, float32, half, complex64, complex128.
A tensor of shape [..., M, M] whose inner-most 2 dimensions form matrices of
size [M, M].
|
output_idx_type
|
An optional tf.DType from: tf.int32, tf.int64. Defaults to tf.int32.
|
name
|
A name for the operation (optional). |
Returns | |
|---|---|
A tuple of Tensor objects (lu, p).
|
|
lu
|
A Tensor. Has the same type as input.
|
p
|
A Tensor of type output_idx_type.
|