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# tfp.math.lu_matrix_inverse

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

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
``````

`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').

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

#### Examples

``````import numpy as np
import tensorflow as tf
import tensorflow_probability as tfp

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
``````
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