lapackFailedAt
Translates a LAPACK info return into a failedAt position. A positive info is the 1-based pivot index; a negative one is an illegal-argument report and maps to NOT_SINGULAR.
NOT_SINGULAR
The failedAt value of a factorization that succeeded, dense or sparse.
SINGULAR_POSITION_UNKNOWN
A failedAt meaning "singular, but this backend cannot say where". Exists so a host solver like UMFPACK, which counts zero pivots without locating them, need not invent a position or report NOT_SINGULAR.