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AMD

Approximate Minimum Degree Ordering in Julia

https://github.com/juliasmoothoptimizers/amd.jl

Science Score: 67.0%

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    Found 12 DOI reference(s) in README
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Keywords

amd factorization julia julia-language linear-algebra permutation sparse-matrices sparse-matrix

Keywords from Contributors

nlpmodels ampl krylov linear-systems nonlinear-programming ipopt fluxes particles number-theory discrete-mathematics
Last synced: 4 months ago · JSON representation ·

Repository

Approximate Minimum Degree Ordering in Julia

Basic Info
  • Host: GitHub
  • Owner: JuliaSmoothOptimizers
  • License: other
  • Language: Julia
  • Default Branch: main
  • Size: 816 KB
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Topics
amd factorization julia julia-language linear-algebra permutation sparse-matrices sparse-matrix
Created over 10 years ago · Last pushed about 1 year ago
Metadata Files
Readme License Citation Zenodo

README.md

AMD

DOI Stable Dev CI Build Status codecov.io

Given a square sparse matrix, compute an approximate minimum degree ordering. This package is an interface to the AMD library (Amestoy, Davis and Duff) and COLAMD library (Liromore, Davis, Gilberg an Ng).

Installing

julia julia> ] pkg> add AMD pkg> test AMD

Algorithms

amd: an approximate minimum degree ordering algorithm for the sparse factorization of square matrices.

symamd: an approximate minimum degree ordering algorithm for the sparse factorization of symmetric matrices.

colamd: an approximate minimum degree column ordering algorithm for the sparse factorization of arbitrary, square or rectangular, matrices.

Examples

In the simplest case:

julia using AMD A = sprand(10, 10, .5) p_amd = amd(A) p_symamd = symamd(A) p_colamd = colamd(A)

If statistics on the permutation are of interest and/or for changing the default control parameters:

julia julia> meta = Amd{Clong}(); # because A's index type is Int64 on my platform julia> # optionally change meta.control: ?Amd julia> p = amd(A, meta) julia> print(meta) Control: dense row parameter: 10.0 aggressive absorption: 1.0 Info: status: ok matrix size: 10.0 number of nonzeros: 54.0 pattern symmetry: 0.5 number of nonzeros on diagonal: 6.0 number of nonzeros in A + A': 72.0 number of dense columns: 0.0 memory used: 1408.0 number of garbage collections: 0.0 approx number of nonzers in factor: 38.0 number of float divides: 38.0 number of float * or - for LDL: 114.0 number of float * or - for LU: 190.0 max nonzeros in any column of factor: 8.0

The amd algorithm computes a fill-reducing permutation based on the sparsity pattern of A + A. The input pattern can be anything: diagonal entries will be ignored and the rest will be used to implicitly work on the pattern of A + A. Thus if A is symmetric, it is sufficient to supply the strict lower or upper triangle only.

References

  1. P. R. Amestoy, T. A. Davis and I. S. Duff. An Approximate Minimum Degree Ordering Algorithm. SIAM Journal on Matrix Analysis and Applications, 17(4), pp. 886–905, 1996. DOI 10.1137/S0895479894278952
  2. P. R. Amestoy, T. A. Davis, and I. S. Duff. Algorithm 837: An approximate minimum degree ordering algorithm. ACM Transactions on Mathematical Software, 30(3), pp. 381–388, 2004. DOI 10.1145/1024074.1024081
  3. T. A. Davis, J. R. Gilbert, S. Larimore, E. Ng. Algorithm 836: COLAMD, an approximate column minimum degree ordering algorithm, ACM Transactions on Mathematical Software, 30(3), pp. 377–380, 2004. DOI 10.1145/1024074.1024080

Owner

  • Name: JuliaSmoothOptimizers
  • Login: JuliaSmoothOptimizers
  • Kind: organization
  • Location: DOI: 10.5281/zenodo.2655082

Infrastructure and Solvers for Continuous Optimization in Julia

Citation (CITATION.cff) 

cff-version: 1.2.0
message: "If you use this software, please cite it as below."
authors:
  - family-names: Montoison
    given-names: Alexis
    orcid: https://orcid.org/0000-0002-3403-5450
  - family-names: Orban
    given-names: Dominique
    orcid: https://orcid.org/0000-0002-8017-7687
  - family-names: Siqueira
    given-names: Abel S.
    orcid: https://orcid.org/0000-0003-4451-281X
  - name: "contributors"
title: "AMD.jl: A Julia interface to the AMD library of Amestoy, Davis and Duff"
identifiers:
  - description: "The concept DOI of the work."
    type: doi
    value: 10.5281/zenodo.3381898
  - description: "The versioned DOI for version 0.4.0 of the work."
    type: doi
    value: 10.5281/zenodo.3783808
doi: 10.5281/zenodo.3381898
date-released: "2020-05-03"
license: MPL-2.0
repository-code: "https://github.com/JuliaSmoothOptimizers/AMD.jl"

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  • Total versions: 7
juliahub.com: AMD

Approximate Minimum Degree Ordering in Julia

  • Versions: 7
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Rankings
Dependent repos count: 6.9%
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Forks count: 11.4%
Average: 12.5%
Stargazers count: 24.7%
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