Krylov.jl
Krylov.jl: A Julia basket of hand-picked Krylov methods - Published in JOSS (2023)
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Published in Journal of Open Source Software
Keywords
Keywords from Contributors
Repository
A Julia Basket of Hand-Picked Krylov Methods
Basic Info
- Host: GitHub
- Owner: JuliaSmoothOptimizers
- License: other
- Language: Julia
- Default Branch: main
- Size: 23.6 MB
Statistics
- Stars: 424
- Watchers: 8
- Forks: 63
- Open Issues: 59
- Releases: 46
Topics
Metadata Files
README.md
Krylov.jl: A Julia basket of hand-picked Krylov methods
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How to Cite
If you use Krylov.jl in your work, please cite it using the metadata given in CITATION.cff.
BibTeX
@article{montoison-orban-2023,
author = {Montoison, Alexis and Orban, Dominique},
title = {{Krylov.jl: A Julia basket of hand-picked Krylov methods}},
journal = {Journal of Open Source Software},
volume = {8},
number = {89},
pages = {5187},
year = {2023},
doi = {10.21105/joss.05187}
}
Content
This package provides implementations of certain of the most useful Krylov method for a variety of problems:
- Square or rectangular full-rank systems
Ax = b
should be solved when b lies in the range space of A. This situation occurs when * A is square and nonsingular, * A is tall and has full column rank and b lies in the range of A.
- Linear least-squares problems
minimize ‖b - Ax‖
should be solved when b is not in the range of A (inconsistent systems), regardless of the shape and rank of A. This situation mainly occurs when * A is square and singular, * A is tall and thin.
Underdetermined systems are less common but also occur.
If there are infinitely many such x (because A is column rank-deficient), one with minimum norm is identified
minimize ‖x‖ subject to x ∈ argmin ‖b - Ax‖.
- Linear least-norm problems
minimize ‖x‖ subject to Ax = b
should be solved when A is column rank-deficient but b is in the range of A (consistent systems), regardless of the shape of A. This situation mainly occurs when * A is square and singular, * A is short and wide.
Overdetermined systems are less common but also occur.
- Adjoint systems
Ax = b and Aᴴy = c
where A can have any shape.
- Saddle-point and Hermitian quasi-definite systems
[M A] [x] = [b]
[Aᴴ -N] [y] [c]
where A can have any shape.
- Generalized saddle-point and non-Hermitian partitioned systems
[M A] [x] = [b]
[B N] [y] [c]
where A can have any shape and B has the shape of Aᴴ. A, B, b and c must be all nonzero.
Krylov solvers are particularly appropriate in situations where such problems must be solved but a factorization is not possible, either because: * A is not available explicitly, * A would be dense or would consume an excessive amount of memory if it were materialized, * factors would consume an excessive amount of memory.
Iterative methods are recommended in either of the following situations: * the problem is sufficiently large that a factorization is not feasible or would be slow, * an effective preconditioner is known in cases where the problem has unfavorable spectral structure, * the operator can be represented efficiently as a sparse matrix, * the operator is fast, i.e., can be applied with better complexity than if it were materialized as a matrix. Certain fast operators would materialize as dense matrices.
Features
All solvers in Krylov.jl have in-place version, are compatible with GPU and work in any floating-point data type.
How to Install
Krylov can be installed and tested through the Julia package manager:
julia
julia> ]
pkg> add Krylov
pkg> test Krylov
Bug reports and discussions
If you think you found a bug, feel free to open an issue. Focused suggestions and requests can also be opened as issues. Before opening a pull request, start an issue or a discussion on the topic, please.
If you want to ask a question not suited for a bug report, feel free to start a discussion here. This forum is for general discussion about this repository and the JuliaSmoothOptimizers organization, so questions about any of our packages are welcome.
Owner
- Name: JuliaSmoothOptimizers
- Login: JuliaSmoothOptimizers
- Kind: organization
- Location: DOI: 10.5281/zenodo.2655082
- Website: https://juliasmoothoptimizers.github.io
- Repositories: 63
- Profile: https://github.com/JuliaSmoothOptimizers
Infrastructure and Solvers for Continuous Optimization in Julia
JOSS Publication
Krylov.jl: A Julia basket of hand-picked Krylov methods
Authors
GERAD and Department of Mathematics and Industrial Engineering, Polytechnique Montréal, QC, Canada.
GERAD and Department of Mathematics and Industrial Engineering, Polytechnique Montréal, QC, Canada.
Editor
Jed Brown
Tags
linear algebra Krylov methods Krylov processes sparse linear systems GPU computingCitation (CITATION.cff)
cff-version: "1.2.0"
title: "Krylov.jl: A Julia basket of hand-picked Krylov methods"
message: "If you use this software, please cite our article in the Journal of Open Source Software."
type: software
authors:
- given-names: Alexis
family-names: Montoison
orcid: "https://orcid.org/0000-0002-3403-5450"
affiliation: "GERAD and Department of Mathematics and Industrial Engineering, Polytechnique Montréal, QC, Canada."
- given-names: Dominique
family-names: Orban
orcid: "https://orcid.org/0000-0002-8017-7687"
affiliation: "GERAD and Department of Mathematics and Industrial Engineering, Polytechnique Montréal, QC, Canada."
- given-names: contributors
contact:
- given-names: Alexis
family-names: Montoison
email: alexis.montoison@gerad.ca
orcid: "https://orcid.org/0000-0002-3403-5450"
identifiers:
- description: Zenodo archive
type: doi
value: 10.5281/zenodo.822073
- description: JOSS paper
type: doi
value: 10.21105/joss.05187
keywords:
- Julia
- linear algebra
- Krylov methods
- Krylov processes
- sparse linear systems
- GPU computing
license: MPL-2.0
repository-code: "https://github.com/JuliaSmoothOptimizers/Krylov.jl"
preferred-citation:
authors:
- given-names: Alexis
family-names: Montoison
orcid: "https://orcid.org/0000-0002-3403-5450"
- given-names: Dominique
family-names: Orban
orcid: "https://orcid.org/0000-0002-8017-7687"
date-published: "2023-09-26"
doi: 10.21105/joss.05187
issn: 2475-9066
issue: 89
journal: Journal of Open Source Software
publisher:
name: Open Journals
start: 5187
title: "Krylov.jl: A Julia basket of hand-picked Krylov methods"
type: article
url: "https://joss.theoj.org/papers/10.21105/joss.05187"
volume: 8
GitHub Events
Total
- Create event: 29
- Commit comment event: 12
- Release event: 6
- Issues event: 83
- Watch event: 68
- Delete event: 47
- Issue comment event: 255
- Push event: 291
- Pull request review event: 113
- Pull request review comment event: 190
- Pull request event: 151
- Fork event: 11
Last Year
- Create event: 29
- Commit comment event: 12
- Release event: 6
- Issues event: 83
- Watch event: 68
- Delete event: 47
- Issue comment event: 255
- Push event: 291
- Pull request review event: 113
- Pull request review comment event: 190
- Pull request event: 151
- Fork event: 11
Committers
Last synced: 5 months ago
Top Committers
| Name | Commits | |
|---|---|---|
| Alexis Montoison | a****n@p****a | 946 |
| Dominique Orban | d****n@g****m | 220 |
| Geoffroy Leconte | g****0@g****m | 77 |
| tmigot | t****t@g****m | 37 |
| Abel Soares Siqueira | a****a@g****m | 30 |
| farhadrclass | 3****s | 11 |
| Xx-Alexis-xX | a****n@e****r | 9 |
| DahitoMA | m****o@p****a | 8 |
| Pawel Latawiec | p****l@m****m | 4 |
| Monssaf Toukal | t****f@g****m | 4 |
| AntoninKns | 4****s | 4 |
| Michael Friedlander | m****l@f****o | 2 |
| Alexander Seiler | s****x@g****m | 1 |
| Christopher Rackauckas | a****s@c****m | 1 |
| Jaroslav Lobačevski | j****b@g****m | 1 |
| Julia TagBot | 5****t | 1 |
| Mathieu Besançon | m****n@g****m | 1 |
| Tim Besard | t****d@g****m | 1 |
| dependabot[bot] | 4****] | 1 |
| fpacaud | f****8@g****m | 1 |
| github-actions[bot] | 4****] | 1 |
| pricklypointer | 1****r | 1 |
| Jean-Pierre Dussault | d****1@d****a | 1 |
| restrin | r****6@g****m | 1 |
| vepiteski | v****i@g****m | 1 |
Committer Domains (Top 20 + Academic)
Issues and Pull Requests
Last synced: 4 months ago
All Time
- Total issues: 123
- Total pull requests: 308
- Average time to close issues: 5 months
- Average time to close pull requests: 22 days
- Total issue authors: 31
- Total pull request authors: 17
- Average comments per issue: 2.28
- Average comments per pull request: 2.26
- Merged pull requests: 250
- Bot issues: 0
- Bot pull requests: 0
Past Year
- Issues: 49
- Pull requests: 137
- Average time to close issues: 30 days
- Average time to close pull requests: 6 days
- Issue authors: 12
- Pull request authors: 7
- Average comments per issue: 1.04
- Average comments per pull request: 1.77
- Merged pull requests: 120
- Bot issues: 0
- Bot pull requests: 0
Top Authors
Issue Authors
- amontoison (81)
- gdalle (7)
- rveltz (4)
- albertomercurio (3)
- farhadrclass (2)
- loiseaujc (1)
- JuliaTagBot (1)
- charleskawczynski (1)
- KlausC (1)
- abelsiqueira (1)
- alexQueue (1)
- lijas (1)
- ZhangFengshun (1)
- jonas-schulze (1)
- packquickly (1)
Pull Request Authors
- amontoison (293)
- abelsiqueira (22)
- farhadrclass (13)
- tmigot (9)
- gdalle (4)
- glwagner (2)
- dpo (2)
- oscardssmith (2)
- mpf (2)
- ChrisRackauckas (2)
- dependabot[bot] (1)
- pricklypointer (1)
- geoffroyleconte (1)
- goggle (1)
- paraynaud (1)
Top Labels
Issue Labels
Pull Request Labels
Packages
- Total packages: 1
-
Total downloads:
- julia 5,505 total
- Total dependent packages: 26
- Total dependent repositories: 13
- Total versions: 45
juliahub.com: Krylov
A Julia Basket of Hand-Picked Krylov Methods
- Documentation: https://docs.juliahub.com/General/Krylov/stable/
- License: MPL-2.0
-
Latest release: 0.10.1
published 8 months ago
Rankings
Dependencies
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- julia-actions/setup-julia latest composite
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- julia-actions/julia-buildpkg v1 composite
- julia-actions/setup-julia v1 composite
- actions/github-script v3.1.0 composite
- actions/github-script v6 composite
- julia-actions/setup-julia v1 composite
- actions/checkout v3 composite
- julia-actions/setup-julia latest composite
- actions/checkout v3 composite
- julia-actions/julia-buildpkg v1 composite
- julia-actions/julia-invalidations v1 composite
- julia-actions/setup-julia v1 composite
- JuliaRegistries/TagBot v1 composite
- actions/cache v3 composite
- actions/checkout v3 composite
- codecov/codecov-action v3 composite
- julia-actions/julia-buildpkg v1 composite
- julia-actions/julia-processcoverage v1 composite
- julia-actions/julia-runtest v1 composite
- julia-actions/setup-julia v1 composite