tfp.substrates.numpy.math.lu_matrix_inverse

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

tfp.substrates.numpy.math.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

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
from tensorflow_probability.python.internal.backend import numpy as tf
import tensorflow_probability as tfp; tfp = tfp.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