ldl_factor_ex

→LD, pivots : Tensor

ldl_factor_ex(A: Tensor, hermitian: bool = False, check_errors: bool = False)

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LDL factorization with an explicit status.

Variant of ldl_factor that returns the factors of a matrix whose $D$ is singular too, with an info code following LAPACK sytrf:

info == 0 — $D$ is non-singular.
info == k > 0 — $D_{kk}$ , a $1 \times 1$ block, is the first one that is exactly zero (or NaN), 1-based. The factorization is complete, but ldl_solve would divide by that block.

Parameters

ATensor

Symmetric / Hermitian matrix of shape (*, n, n).

hermitian(bool, keyword - only)= False

As ldl_factor. Default False.

check_errors(bool, keyword - only)= False

If True, raise LinAlgError for the first failed matrix instead of reporting it through info.

Returns

LD, pivots : Tensor

The packed factor (*, n, n) and int32 pivots (*, n), as ldl_factor returns them.

Notes

LD differentiates as ldl_factor's does — the reference framework does not differentiate it. A matrix whose info is non-zero receives no gradient, as a failed matrix of the other *_ex variants does.

Examples

>>> import lucid
>>> from lucid.linalg import ldl_factor_ex
>>> LD, piv, info = ldl_factor_ex(lucid.zeros(2, 2))
>>> int(info)
1

Used by 1

lucid.linalg