# tfp.experimental.substrates.numpy.math.linalg.lu_matrix_inverse

Computes a matrix inverse given the matrix's LU decomposition.

``````tfp.experimental.substrates.numpy.math.linalg.lu_matrix_inverse(
lower_upper,
perm,
validate_args=False,
name=None
)
``````

This op is conceptually identical to,

``````inv_X = tf.lu_matrix_inverse(*tf.linalg.lu(X))
tf.assert_near(tf.matrix_inverse(X), inv_X)
# ==> True
``````

#### Args:

• `lower_upper`: `lu` as returned by `tf.linalg.lu`, i.e., if `matmul(P, matmul(L, U)) = X` then `lower_upper = L + U - eye`.
• `perm`: `p` as returned by `tf.linag.lu`, i.e., if `matmul(P, matmul(L, U)) = X` then `perm = argmax(P)`.
• `validate_args`: Python `bool` indicating whether arguments should be checked for correctness. Note: this function does not verify the implied matrix is actually invertible, even when `validate_args=True`. Default value: `False` (i.e., don't validate arguments).
• `name`: Python `str` name given to ops managed by this object. Default value: `None` (i.e., 'lu_matrix_inverse').

#### Returns:

• `inv_x`: The matrix_inv, i.e., `tf.matrix_inverse(tfp.math.lu_reconstruct(lu, perm))`.

#### Examples

``````import numpy as np
from tensorflow_probability.python.internal.backend import numpy as tf
import tensorflow_probability as tfp; tfp = tfp.experimental.substrates.numpy

x = [[[3., 4], [1, 2]],
[[7., 8], [3, 4]]]
inv_x = tfp.math.lu_matrix_inverse(*tf.linalg.lu(x))
tf.assert_near(tf.matrix_inverse(x), inv_x)
# ==> True
``````