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# tf.cholesky_solve

### Aliases:

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

See the guide: Math > Matrix Math Functions

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.cholesky(A)  # shape 10 x 2 x 2
X = tf.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]
```

#### Args:

• `chol`: A `Tensor`. Must be `float32` or `float64`, shape is `[..., M, M]`. Cholesky factorization of `A`, e.g. `chol = tf.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`.

#### Returns:

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

© 2018 The TensorFlow Authors. All rights reserved.
Licensed under the Creative Commons Attribution License 3.0.
Code samples licensed under the Apache 2.0 License.
https://www.tensorflow.org/api_docs/python/tf/cholesky_solve