https://github.com/wildart/smithnormalform.jl

Smith normal form (SNF) decomposition
https://github.com/wildart/smithnormalform.jl

Last synced: 20 days ago
JSON representation

Smith normal form (SNF) decomposition

• Host: GitHub
• URL: https://github.com/wildart/smithnormalform.jl
• Owner: wildart
• License: other
• Created: 2017-05-24T21:47:45.000Z (over 7 years ago)
• Default Branch: master
• Last Pushed: 2023-01-02T17:20:40.000Z (almost 2 years ago)
• Last Synced: 2023-03-25T22:02:30.594Z (over 1 year ago)
• Language: Julia
• Homepage:
• Size: 31.3 KB
• Stars: 5
• Watchers: 3
• Forks: 4
• Open Issues: 4
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

Awesome Lists containing this project

README

        
# Smith Normal Form

[![Build Status](https://travis-ci.org/wildart/SmithNormalForm.jl.svg?branch=master)](https://travis-ci.org/wildart/SmithNormalForm.jl)

[![Coverage Status](https://coveralls.io/repos/wildart/SmithNormalForm.jl/badge.svg?branch=master&service=github)](https://coveralls.io/github/wildart/SmithNormalForm.jl?branch=master)

The [Smith normal form](https://en.wikipedia.org/wiki/Smith_normal_form) decomposition over integer domain implementation in Julia.

## Installation

For Julia 1.1+, add [BoffinStuff](https://github.com/wildart/BoffinStuff.git) registry in the package manager, and proceed with the installation:

```

pkg> registry add https://github.com/wildart/BoffinStuff.git

pkg> add SmithNormalForm

```

## Example

```julia

julia> using SmithNormalForm, LinearAlgebra

julia> M = [2 4 4; -6 6 12; 10 -4 -16]

3×3 Array{Int64,2}:

  2   4    4

 -6   6   12

 10  -4  -16

julia> F = smith(M)

Smith normal form:

[2 0 0; 0 6 0; 0 0 12]

julia> F.S

3×3 Array{Int64,2}:

  1   0  0

 -3   1  0

  5  -2  1

julia> F.T

3×3 Array{Int64,2}:

 1  2  2

 0  3  4

 0  1  1

julia> diagm(F)

3×3 Array{Int64,2}:

 2  0   0

 0  6   0

 0  0  12

julia> F.S*diagm(F)*F.T

3×3 Array{Int64,2}:

  2   4    4

 -6   6   12

 10  -4  -16

```