Sparse Linear Algebra

Sparse matrix solvers call functions from SuiteSparse. The following factorizations are available:

Type	Description
`SuiteSparse.CHOLMOD.Factor`	Cholesky factorization
`SuiteSparse.UMFPACK.UmfpackLU`	LU factorization
`SuiteSparse.SPQR.QRSparse`	QR factorization

Other solvers such as Pardiso.jl are as external packages. Arpack.jl provides eigs and svds for iterative solution of eigensystems and singular value decompositions.

These factorizations are described in the Linear Algebra section of the manual:

SuiteSparse.CHOLMOD.lowrankupdate — Function

lowrankupdate(F::CHOLMOD.Factor, C::AbstractArray) -> FF::CHOLMOD.Factor

Get an LDLt Factorization of A + C*C' given an LDLt or LLt factorization F of A.

The returned factor is always an LDLt factorization.

source

SuiteSparse.CHOLMOD.lowrankupdate! — Function

lowrankupdate!(F::CHOLMOD.Factor, C::AbstractArray)

Update an LDLt or LLt Factorization F of A to a factorization of A + C*C'.

LLt factorizations are converted to LDLt.

source

SuiteSparse.CHOLMOD.lowrankdowndate — Function

lowrankupdate(F::CHOLMOD.Factor, C::AbstractArray) -> FF::CHOLMOD.Factor

Get an LDLt Factorization of A + C*C' given an LDLt or LLt factorization F of A.

The returned factor is always an LDLt factorization.

source

SuiteSparse.CHOLMOD.lowrankdowndate! — Function

lowrankdowndate!(F::CHOLMOD.Factor, C::AbstractArray)

Update an LDLt or LLt Factorization F of A to a factorization of A - C*C'.

LLt factorizations are converted to LDLt.

source

SuiteSparse.CHOLMOD.lowrankupdowndate! — Function

lowrankupdowndate!(F::CHOLMOD.Factor, C::Sparse, update::Cint)

Update an LDLt or LLt Factorization F of A to a factorization of A ± C*C'.

If sparsity preserving factorization is used, i.e. L*L' == P*A*P' then the new factor will be L*L' == P*A*P' + C'*C

update: Cint(1) for A + CC', Cint(0) for A - CC'

source