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SparseSparse

SparseSparse is a Julia package for inverting sparse matrices with sparse inverses, or solving sparse linear problems with sparse right-hand-sides.

Installation

using Pkg; Pkg.add("SparseSparse")

Overview

A matrix $A$ is doubly sparse if both $A$ and $A^{-1}$ are sparse. The class of doubly sparse matrices includes all matrices of the form $P(\prod B_k) Q$ where $P,Q$ are permutations and $B_k$ are block diagonal.

With stock Julia, inverting a sparse matrix throws an error. SparseSparse provides functionality to invert sparse matrices and produce sparse inverses.

Basic Usage

using LinearAlgebra, SparseArrays, SparseSparse
A = sparse([2.0  3.0  0.0  0.0
             4.0  5.0  0.0  0.0
             0.0  0.0  6.0  7.0
             0.0  0.0  8.0  9.0])
inv(A)

Module reference

Types reference

SparseSparse.Factorization — Method
function Factorization(A::SparseMatrixCSC)

Compute a sparse factorization of the sparse matrix A. This returns a Factorization object F with fields F.L, F.U, F.p, F.q. The fields L and U are sparse lower and upper triangular matrices, and p and q are permutation vectors. Any of these fields can be replaced by the value missing.

source

Functions reference

Base.:\ — Method
function Base.:\(A::Factorization, B::SparseMatrixCSC)

Solve the problem A*X=B for the unknown X, where A is a Factorization object and B is sparse.

source
SparseSparse.solve — Method
function solve(L::SparseMatrixCSC{Tv,Ti},B::SparseMatrixCSC{Tv,Ti};solvemode=detect,numthreads=min(B.n,nthreads())) where {Tv,Ti<:Integer}

Solve L*X=B for the unknown X, where L and B are sparse matrices. L should be either lower or upper triangular. If numthreads>1 then multithreading is used. solvemode should be either lower, upper or detect.

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Index