A Port of LLDL to Julia. See https://github.com/optimizers/lldl.
Please cite this repository if you use LimitedLDLFactorizations.jl in your work: see
LimitedLDLFactorizations is a limited-memory LDLᵀ factorization for symmetric matrices. Given a symmetric matrix A, we search for a unit lower triangular L, a diagonal D and a diagonal ∆ such that LDLᵀ is an incomplete factorization of A+∆. The elements of the diagonal matrix ∆ have the form ±α, where α ≥ 0 is a shift.
It is possible to only supply the lower triangle of A and/or a prescribed permutation that attempts to diminish fill-in. AMD.jl and Metis.jl are recommended packages for computing fill-reducing orderings of sparse matrices.
julia> ] pkg> add LimitedLDLFactorizations
The only functions exported are
Supply a dense array or sparse matrix to
Dense arrays will be converted to sparse.
The strict lower triangle and diagonal of sparse matrices will be extracted.
Using a memory parameter larger than or equal to the size of A will yield an exact factorization provided one exists with the permutation supplied. In particular, the full factorization exists for any symmetric permutation of a symmetric quasi-definite matrix.
lldl returns a factorization in the form of a
ldiv! methods are implemented for objects of type
 C.-J. Lin and J. J. Moré. Incomplete Cholesky factorizations with limited
memory. SIAM Journal on Scientific Computing, 21(1):24--45, 1999.
 D. Orban. Limited-Memory LDLᵀ Factorization of Symmetric Quasi-Definite Matrices with Application to Constrained Optimization. Numerical Algorithms 70(1):9--41, 2015. DOI 10.1007/s11075-014-9933-x.
16 days ago