TensorFlow 2.0 Beta is available

# tf.linalg.lu

Defined in generated file: `python/ops/gen_linalg_ops.py`

Computes the LU decomposition of one or more square matrices.

### Aliases:

• `tf.compat.v1.linalg.lu`
• `tf.compat.v2.linalg.lu`
``````tf.linalg.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`.