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# tf.linalg.cholesky_solve

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

``````# 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]`.

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