|---| | [ View source on GitHub](https://github.com/tensorflow/probability/blob/v0.25.0/tensorflow_probability/python/math/linalg.py#L111-L217) | Returns cholesky of chol @ chol.T + multiplier \* u @ u.T. tfp.math.cholesky_update( chol, update_vector, multiplier=1.0, name=None ) Given a (batch of) lower triangular cholesky factor(s) `chol`, along with a (batch of) vector(s) `update_vector`, compute the lower triangular cholesky factor of the rank-1 update `chol @ chol.T + multiplier * u @ u.T`, where `multiplier` is a (batch of) scalar(s). If `chol` has shape `[L, L]`, this has complexity `O(L^2)` compared to the naive algorithm which has complexity `O(L^3)`.


| ## Args || |---|---|---| | `chol` | Floating-point `Tensor` with shape `[B1, ..., Bn, L, L]`. Cholesky decomposition of `mat = chol @ chol.T`. Batch dimensions must be broadcastable with `update_vector` and `multiplier`. | | `update_vector` | Floating-point `Tensor` with shape `[B1, ... Bn, L]`. Vector defining rank-one update. Batch dimensions must be broadcastable with `chol` and `multiplier`. | | `multiplier` | Floating-point `Tensor` with shape `[B1, ..., Bn]. Scalar multiplier to rank-one update. Batch dimensions must be broadcastable with`chol`and`update_vector`. Note that updates where`multiplier`is positive are numerically stable, while when`multiplier`is negative (downdating), the update will only work if the new resulting matrix is still positive definite. `name\` | Optional name for this op. |
#### References \[1\] Oswin Krause. Christian Igel. A More Efficient Rank-one Covariance Matrix Update for Evolution Strategies. 2015 ACM Conference.