tf.linalg.cholesky_solve

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

tf.linalg.cholesky_solve(
    chol, rhs, name=None
)

Used in the notebooks

Used in the tutorials

Specifically, returns X from A X = RHS, where A = L L^T, L is the chol arg and RHS is the rhs arg.

# Solve 10 separate 2x2 linear systems:
A = ... # shape 10 x 2 x 2
RHS = ... # shape 10 x 2 x 1
chol = tf.linalg.cholesky(A)  # shape 10 x 2 x 2
X = tf.linalg.cholesky_solve(chol, RHS)  # shape 10 x 2 x 1
# tf.matmul(A, X) ~ RHS
X[3, :, 0]  # Solution to the linear system A[3, :, :] x = RHS[3, :, 0]

# Solve five linear systems (K = 5) for every member of the length 10 batch.
A = ... # shape 10 x 2 x 2
RHS = ... # shape 10 x 2 x 5
...
X[3, :, 2]  # Solution to the linear system A[3, :, :] x = RHS[3, :, 2]

chol A Tensor. Must be float32 or float64, shape is [..., M, M]. Cholesky factorization of A, e.g. chol = tf.linalg.cholesky(A). For that reason, only the lower triangular parts (including the diagonal) of the last two dimensions of chol are used. The strictly upper part is assumed to be zero and not accessed.
rhs A Tensor, same type as chol, shape is [..., M, K].
name A name to give this Op. Defaults to cholesky_solve.

Solution to A x = rhs, shape [..., M, K].