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https://github.com/SciML/LinearSolve.jl

LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.
https://github.com/SciML/LinearSolve.jl

amg differential-equations distributed-computing factorization gpu julia krylov-methods linear-algebra linear-solvers multigrid newton-krylov preconditioners scientific-machine-learning sciml

Last synced: 3 months ago
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LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.

Host: GitHub
URL: https://github.com/SciML/LinearSolve.jl
Owner: SciML
License: other
Created: 2021-07-02T19:56:38.000Z (over 3 years ago)
Default Branch: main
Last Pushed: 2024-04-08T12:28:27.000Z (7 months ago)
Last Synced: 2024-04-14T01:46:57.368Z (7 months ago)
Topics: amg, differential-equations, distributed-computing, factorization, gpu, julia, krylov-methods, linear-algebra, linear-solvers, multigrid, newton-krylov, preconditioners, scientific-machine-learning, sciml
Language: Julia
Homepage: https://docs.sciml.ai/LinearSolve/stable/
Size: 4.06 MB
Stars: 220
Watchers: 12
Forks: 46
Open Issues: 67
Metadata Files:
- Readme: README.md
- License: LICENSE

Awesome Lists containing this project

awesome-sciml - SciML/LinearSolve.jl: LinearSolve.jl: High-Performance Unified Linear Solvers

README

        # LinearSolve.jl

[![Join the chat at https://julialang.zulipchat.com #sciml-bridged](https://img.shields.io/static/v1?label=Zulip&message=chat&color=9558b2&labelColor=389826)](https://julialang.zulipchat.com/#narrow/stream/279055-sciml-bridged)

[![Global Docs](https://img.shields.io/badge/docs-SciML-blue.svg)](https://docs.sciml.ai/LinearSolve/stable/)

[![codecov](https://codecov.io/gh/SciML/LinearSolve.jl/branch/main/graph/badge.svg)](https://app.codecov.io/gh/SciML/LinearSolve.jl)

[![Build Status](https://github.com/SciML/LinearSolvers.jl/workflows/CI/badge.svg)](https://github.com/SciML/LinearSolvers.jl/actions?query=workflow%3ACI)

[![Build status](https://badge.buildkite.com/74699764ce224514c9632e2750e08f77c6d174c5ba7cd38297.svg?branch=main)](https://buildkite.com/julialang/linearsolve-dot-jl)

[![ColPrac: Contributor's Guide on Collaborative Practices for Community Packages](https://img.shields.io/badge/ColPrac-Contributor%27s%20Guide-blueviolet)](https://github.com/SciML/ColPrac)

[![SciML Code Style](https://img.shields.io/static/v1?label=code%20style&message=SciML&color=9558b2&labelColor=389826)](https://github.com/SciML/SciMLStyle)

Fast implementations of linear solving algorithms in Julia that satisfy the SciML

common interface. LinearSolve.jl makes it easy to define high level algorithms

which allow for swapping out the linear solver that is used while maintaining

maximum efficiency. Specifically, LinearSolve.jl includes:

  - Fast pure Julia LU factorizations which outperform standard BLAS

  - KLU for faster sparse LU factorization on unstructured matrices

  - UMFPACK for faster sparse LU factorization on matrices with some repeated structure

  - MKLPardiso wrappers for handling many sparse matrices faster than SuiteSparse (KLU, UMFPACK) methods

  - Sparspak.jl for sparse LU factorization in pure Julia for generic number types and for non-GPL distributions

  - GPU-offloading for large dense matrices

  - Wrappers to all of the Krylov implementations (Krylov.jl, IterativeSolvers.jl, KrylovKit.jl) for easy

    testing of all of them. LinearSolve.jl handles the API differences, especially with the preconditioner

    definitions

  - A polyalgorithm that smartly chooses between these methods

  - A caching interface which automates caching of symbolic factorizations and numerical factorizations

    as optimally as possible

For information on using the package,

[see the stable documentation](https://docs.sciml.ai/LinearSolve/stable/). Use the

[in-development documentation](https://docs.sciml.ai/LinearSolve/dev/) for the version of

the documentation which contains the unreleased features.

## High Level Examples

```julia

n = 4

A = rand(n, n)

b1 = rand(n);

b2 = rand(n);

prob = LinearProblem(A, b1)

linsolve = init(prob)

sol1 = solve(linsolve)

sol1.u

#=

4-element Vector{Float64}:

 -0.9247817429364165

 -0.0972021708185121

  0.6839050402960025

  1.8385599677530706

=#

linsolve = LinearSolve.set_b(linsolve, b2)

sol2 = solve(linsolve)

sol2.u

#=

4-element Vector{Float64}:

  1.0321556637762768

  0.49724400693338083

 -1.1696540870182406

 -0.4998342686003478

=#

linsolve = LinearSolve.set_b(linsolve, b2)

sol2 = solve(linsolve, IterativeSolversJL_GMRES()) # Switch to GMRES

sol2.u

#=

4-element Vector{Float64}:

  1.0321556637762768

  0.49724400693338083

 -1.1696540870182406

 -0.4998342686003478

=#

A2 = rand(n, n)

linsolve = LinearSolve.set_A(linsolve, A2)

sol3 = solve(linsolve)

sol3.u

#=

4-element Vector{Float64}:

 -6.793605395935224

  2.8673042300837466

  1.1665136934977371

 -0.4097250749016653

=#

```