# 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.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.

See also `lowrankupdate!`, `lowrankdowndate`, `lowrankdowndate!`.

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`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.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.

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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This document was generated with Documenter.jl version 0.27.17 on Friday 27 May 2022. Using Julia version 1.8.0-rc1.