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|
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
withcholandupdate_vector. Note that updates wheremultiplieris
positive are numerically stable, while whenmultiplieris negative
(downdating), the update will only work if the new resulting matrix is
still positive definite.
</td>
</tr><tr>
<td>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. https://www.researchgate.net/publication/300581419_A_More_Efficient_Rank-one_Covariance_Matrix_Update_for_Evolution_Strategies