# tf.linalg.cholesky_solve

Solves systems of linear eqns `A X = RHS`

, given Cholesky factorizations.

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

# 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]

Args |

`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` . |

Returns |

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