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https://github.com/eigenvivek/gershgorin.jl
Utility package for visualizing the Gerhsgorin discs of a matrix.
https://github.com/eigenvivek/gershgorin.jl
linear-algebra numerical-analysis
Last synced: 18 days ago
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Utility package for visualizing the Gerhsgorin discs of a matrix.
- Host: GitHub
- URL: https://github.com/eigenvivek/gershgorin.jl
- Owner: eigenvivek
- License: mit
- Created: 2022-05-24T20:16:54.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2022-08-05T01:54:10.000Z (over 2 years ago)
- Last Synced: 2024-10-11T00:27:42.781Z (about 1 month ago)
- Topics: linear-algebra, numerical-analysis
- Language: Julia
- Homepage:
- Size: 1.34 MB
- Stars: 2
- Watchers: 2
- Forks: 0
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Gershgorin
[](https://github.com/v715/Gershgorin.jl/actions/workflows/CI.yml?query=branch%3Amain)
Visualize the Gershgorin discs that bound the spectrum of a square matrix (see the [Gershgorin disc theorem](https://en.wikipedia.org/wiki/Gershgorin_circle_theorem)).
## Installation
Hit `]` in the Julia REPL to open the package manager, then use
```zsh
pkg> add Gershgorin
```
## Quickstart Guide
We can visualize the Gershgorin discs for a random complex matrix and its transpose.
Note that a matrix and its transpose have the same eigenvalues, so these eigenvalues will lie in the intersection of the Gershgorin regions of these two matrices.
```Julia
using LinearAlgebra
using Plots, LaTeXStrings
using Gershgorin
# Make a random (5,5) real matrix
M = randn(5, 5)
# Plot Gershgorin's discs
gershgorin(M; c=:blue, label=L"$M$")
λ = eigvals(M)
p1 = plot!(λ, seriestype=[:scatter], c=:black, label=L"$\lambda(M)$")
# Now do the same for the transpose
gershgorin(transpose(M); c=:red, label=L"$M^T$")
λ = eigvals(transpose(M))
p2 = plot!(λ, seriestype=[:scatter], c=:black, label=L"$\lambda(M^T)$")
# Plot the intersection between the two sets of regions
gershgorin(M; c=:blue)
gershgorin!(transpose(M); c=:red)
overlap(M, transpose(M), c=:black, alpha=1)
p3 = plot!(λ, seriestype=[:scatter], c=:black, label=L"$\lambda(M)$")
plot(p1, p2, p3, link=:all, dpi=300, layout=(1,3), size=(750,350))
```
Additionally, if you just want to get the Gershgorin discs for a matrix, you can use the `get_discs` function.
```Julia
discs = get_discs(M)
plot(discs, c=:blue, alpha=0.2, lw=0)
plot!(eigvals(M), seriestype=[:scatter], c=:black, label=L"$\lambda(M)$", aspect_ratio=1) |> display
```
