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:

  1. cholesky
  2. ldlt
  3. lu
  4. qr

SuiteSparse.CHOLMOD.lowrankupdateFunction 

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.

See also lowrankupdate!, lowrankdowndate, lowrankdowndate!.

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.

See also lowrankupdate, lowrankdowndate, lowrankdowndate!.

source

SuiteSparse.CHOLMOD.lowrankdowndateFunction 

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.

See also lowrankdowndate!, lowrankupdate, lowrankupdate!.

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.

See also lowrankdowndate, lowrankupdate, lowrankupdate!.

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'

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© 2009–2021 Jeff Bezanson, Stefan Karpinski, Viral B. Shah, and other contributors
Licensed under the MIT License.
https://docs.julialang.org/en/v1.6.0/stdlib/SuiteSparse/