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https://github.com/jagot/weirdmatrices.jl

Last synced: 6 days ago
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Host: GitHub
URL: https://github.com/jagot/weirdmatrices.jl
Owner: jagot
License: mit
Created: 2020-07-13T11:37:32.000Z (over 4 years ago)
Default Branch: master
Last Pushed: 2023-10-04T01:01:59.000Z (over 1 year ago)
Last Synced: 2024-11-15T18:34:52.802Z (2 months ago)
Language: Julia
Size: 125 KB
Stars: 2
Watchers: 2
Forks: 1
Open Issues: 1
Metadata Files:
- Readme: README.md
- License: LICENSE

Awesome Lists containing this project

README

# WeirdMatrices.jl

[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://jagot.github.io/WeirdMatrices.jl/stable)
[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://jagot.github.io/WeirdMatrices.jl/dev)
[![Build Status](https://github.com/jagot/WeirdMatrices.jl/workflows/CI/badge.svg)](https://github.com/jagot/WeirdMatrices.jl/actions)
[![Coverage](https://codecov.io/gh/jagot/WeirdMatrices.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/jagot/WeirdMatrices.jl)

A home for weird matrices that do not fit in anywhere else.

```julia
julia> SkewTridiagonal(1:10)
11×11 SkewTridiagonal{Int64,UnitRange{Int64}}:
⋅ -1 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
1 ⋅ -2 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ 2 ⋅ -3 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ 3 ⋅ -4 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ 4 ⋅ -5 ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ 5 ⋅ -6 ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ 6 ⋅ -7 ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 7 ⋅ -8 ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 8 ⋅ -9 ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 9 ⋅ -10
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ 10 ⋅

julia> OneBlockMatrix(Matrix(reshape(1:15, 5, 3)), 10, 20)
10×20 OneBlockMatrix{Int64,Array{Int64,2}}:
1 6 11 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
2 7 12 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
3 8 13 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
4 9 14 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
5 10 15 ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
```

`OneBlockMatrix` are also closed under some operations:

```julia
julia> N = 7
7

julia> A = OneBlockMatrix(Matrix(reshape(1:16, 4,4)), N, N)
7×7 OneBlockMatrix{Int64,Array{Int64,2}}:
1 5 9 13 ⋅ ⋅ ⋅
2 6 10 14 ⋅ ⋅ ⋅
3 7 11 15 ⋅ ⋅ ⋅
4 8 12 16 ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅

julia> o = ones(Int, N)
7-element Array{Int64,1}:
1
1
1
1
1
1
1

julia> T = Tridiagonal(o[2:end], 2o, 3o[2:end])
7×7 Tridiagonal{Int64,Array{Int64,1}}:
2 3 ⋅ ⋅ ⋅ ⋅ ⋅
1 2 3 ⋅ ⋅ ⋅ ⋅
⋅ 1 2 3 ⋅ ⋅ ⋅
⋅ ⋅ 1 2 3 ⋅ ⋅
⋅ ⋅ ⋅ 1 2 3 ⋅
⋅ ⋅ ⋅ ⋅ 1 2 3
⋅ ⋅ ⋅ ⋅ ⋅ 1 2

julia> T*A
7×7 OneBlockMatrix{Int64,Array{Int64,2}}:
8 28 48 68 ⋅ ⋅ ⋅
14 38 62 86 ⋅ ⋅ ⋅
20 44 68 92 ⋅ ⋅ ⋅
11 23 35 47 ⋅ ⋅ ⋅
4 8 12 16 ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅

julia> A^2
7×7 OneBlockMatrix{Int64,Array{Int64,2}}:
90 202 314 426 ⋅ ⋅ ⋅
100 228 356 484 ⋅ ⋅ ⋅
110 254 398 542 ⋅ ⋅ ⋅
120 280 440 600 ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅
```