downdate

CholeskyFactor.downdate(C)

Multiple-rank downdate of a sparse LDL factorization.

Compute a downdate to the factorization of a sparse matrix A [1]:

\[L' D' L'^{\top} = P (A - C C^{\top}) P^{\top}\]

where L is a lower triangular matrix with unit diagonal, and D is a diagonal matrix. The input C is a sparse matrix representing the downdate to the factorization. The fill-reducing permutation is not recomputed from the original A.

Parameters:

C ((N, K) csc_array) – The sparse matrix representing the rank-k update or downdate to the matrix.

Returns:

CholeskyFactor – The current object, for method chaining.

References

[1]

cholmod_updown.c - CHOLMOD up/downdate function https://github.com/DrTimothyAldenDavis/SuiteSparse/blob/dev/CHOLMOD/Modify/cholmod_updown.c

Added in version 0.5.0.