tfp.substrates.numpy.math.lu_solve

Solves systems of linear eqns A X = RHS, given LU factorizations.

tfp.substrates.numpy.math.lu_solve(
    lower_upper, perm, rhs, validate_args=False, name=None
)

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).
rhs Matrix-shaped float Tensor representing targets for which to solve; A X = RHS. To handle vector cases, use: lu_solve(..., rhs[..., tf.newaxis])[..., 0].
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_solve').

x The X in A @ X = RHS.

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