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https://github.com/juliasparse/metis.jl
Julia interface to Metis graph partitioning
https://github.com/juliasparse/metis.jl
Last synced: about 2 months ago
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Julia interface to Metis graph partitioning
- Host: GitHub
- URL: https://github.com/juliasparse/metis.jl
- Owner: JuliaSparse
- License: other
- Created: 2013-04-30T17:46:17.000Z (over 11 years ago)
- Default Branch: master
- Last Pushed: 2024-09-19T16:24:03.000Z (4 months ago)
- Last Synced: 2024-09-21T07:07:31.357Z (3 months ago)
- Language: Julia
- Homepage:
- Size: 4.09 MB
- Stars: 54
- Watchers: 12
- Forks: 20
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- License: LICENSE.md
Awesome Lists containing this project
README
# Metis
| **Build Status** |
|:--------------------------------------------------------------------- |
| [![][gh-actions-img]][gh-actions-url] [![][codecov-img]][codecov-url] |
*Metis.jl* is a Julia wrapper to the [Metis library][metis-url] which is a
library for partitioning unstructured graphs, partitioning meshes, and
computing fill-reducing orderings of sparse matrices.
## Graph partitioning
`Metis.partition` calculates graph partitions. As an example, here we partition
a small graph into two, three and four parts, and visualize the result:
| ![][partition2-url] | ![][partition3-url] | ![][partition4-url] |
|:----------------------- |:----------------------- |:----------------------- |
| `Metis.partition(g, 2)` | `Metis.partition(g, 3)` | `Metis.partition(g, 4)` |
`Metis.partition` calls `METIS_PartGraphKway` or `METIS_PartGraphRecursive` from the Metis
C API, depending on the optional keyword argument `alg`:
- `alg = :KWAY`: multilevel k-way partitioning (`METIS_PartGraphKway`).
- `alg = :RECURSIVE`: multilevel recursive bisection (`METIS_PartGraphRecursive`).
## Vertex separator
`Metis.separator` calculates a [vertex separator](https://en.wikipedia.org/wiki/Vertex_separator)
of a graph. `Metis.separator` calls `METIS_ComputeVertexSeparator` from the Metis C API.
As an example, here we calculate a vertex separator (green) of a small graph:
| ![][separator-url] |
|:-------------------- |
| `Metis.separator(g)` |
## Fill reducing permutation
`Metis.permutation` calculates the fill reducing permutation
for a sparse matrices. `Metis.permutation` calls `METIS_NodeND` from the Metis
C API. As an example, we calculate the fill reducing permutation
for a sparse matrix `S` originating from a typical (small) FEM problem, and
visualize the sparsity pattern for the original matrix and the permuted matrix:
```julia
perm, iperm = Metis.permutation(S)
```
|
⠛⣤⢠⠄⠀⣌⠃⢠⠀⠐⠈⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠔⠀
⠀⠖⠻⣦⡅⠘⡁⠀⠀⠀⠀⠐⠀⠁⠀⢂⠀⠀⠠⠀⠀⠀⠁⢀⠀⢀⠀⠀⠄⢣
⡀⢤⣁⠉⠛⣤⡡⢀⠀⠂⠂⠀⠂⠃⢰⣀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀
⠉⣀⠁⠈⠁⢊⠱⢆⡰⠀⠈⠀⠀⠀⠀⢈⠉⡂⠀⠐⢀⡞⠐⠂⠀⠄⡀⠠⠂⠀
⢀⠀⠀⠀⠠⠀⠐⠊⠛⣤⡔⠘⠰⠒⠠⠀⡈⠀⠀⠀⠉⠉⠘⠂⠀⠀⠀⡐⢈⠀
⠂⠀⢀⠀⠈⠀⠂⠀⣐⠉⢑⣴⡉⡈⠁⡂⠒⠀⠁⢠⡄⠀⠐⠀⠠⠄⠀⠁⢀⡀
⠀⠀⠄⠀⠬⠀⠀⠀⢰⠂⡃⠨⣿⣿⡕⠂⠀⠨⠌⠈⠆⠀⠄⡀⠑⠀⠀⠘⠀⠀
⡄⠀⠠⢀⠐⢲⡀⢀⠀⠂⠡⠠⠱⠉⢱⢖⡀⠀⡈⠃⠀⠀⠀⢁⠄⢀⣐⠢⠀⠀
⠉⠀⠀⠀⢀⠄⠣⠠⠂⠈⠘⠀⡀⡀⠀⠈⠱⢆⣰⠠⠰⠐⠐⢀⠀⢀⢀⠀⠌⠀
⠀⠀⠀⠂⠀⠀⢀⠀⠀⠀⠁⣀⡂⠁⠦⠈⠐⡚⠱⢆⢀⢀⠡⠌⡀⡈⠸⠁⠂⠀
⠀⠀⠀⠀⠀⠀⣠⠴⡇⠀⠀⠉⠈⠁⠀⠀⢐⠂⠀⢐⣻⣾⠡⠀⠈⠀⠄⠀⡉⠄
⠀⠀⠁⢀⠀⠀⠰⠀⠲⠀⠐⠀⠀⠡⠄⢀⠐⢀⡁⠆⠁⠂⠱⢆⡀⣀⠠⠁⠉⠇
⣀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠆⠑⠀⠀⢁⠀⢀⡀⠨⠂⠀⠀⢨⠿⢇⠀⡸⠀⢀
⠠⠀⠀⠀⠀⠄⠀⡈⢀⠠⠄⠀⣀⠀⠰⡘⠀⠐⠖⠂⠀⠁⠄⠂⣀⡠⠻⢆⠄⠃
⠐⠁⠤⣁⠀⠁⠈⠀⠂⠐⠀⠰⠀⠀⠀⠀⠂⠁⠈⠀⠃⠌⠧⠄⠀⢀⠤⠁⠱⢆
| ⣕⢝⠀⠀⢸⠔⡵⢊⡀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠑
⠀⠀⠑⢄⠀⠳⠡⢡⣒⣃⢣⠯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌
⢒⠖⢤⡀⠑⢄⢶⡈⣂⠎⢎⠉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡱⢋⠅⣂⡘⠳⠻⢆⡥⣈⠆⡨⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀
⠠⠈⠼⢸⡨⠜⡁⢫⣻⢞⢔⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠
⠀⠀⡭⡖⡎⠑⡈⡡⠐⠑⠵⣧⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠁⠈⠁⠃⠂⠃⠊⠀⠘⠒⠙⠛⢄⠀⠀⢄⠀⠤⢠⠀⢄⢀⢀⠀⡀⠀⠀⢄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠊⠀⣂⠅⢓⣤⡄⠢⠠⠀⠌⠉⢀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠑⢄⠁⣋⠀⢀⢰⢄⢔⢠⡖⢥⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⠌⠜⡥⢠⠛⣤⠐⣂⡀⠀⡀⡁⠍⠤⠒⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠙⣴⠀⢀⠰⢠⠿⣧⡅⠁⠂⢂⠂⠋⢃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⡉⠐⢖⠀⠈⠅⠉⢕⢕⠝⠘⡒⠠⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠐⣑⠄⠨⠨⢀⣓⠁⣕⢝⡥⢉⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠜⣍⠃⡅⡬⠀⠘⡈⡅⢋⠛⣤⡅⠒
⢕⠘⡂⠄⠀⠀⠁⠀⠀⡂⠀⢠⠀⢕⠄⢐⠄⠀⠘⠀⠉⢐⠀⠀⠁⡀⢡⠉⢟⣵
|
|:---------------------- |:--------------------------------- |
| `S` (5% stored values) | `S[perm,perm]` (5% stored values) |
We can also visualize the sparsity pattern of the Cholesky factorization of
the same matrix. It is here clear that using the fill reducing permutation
results in a sparser factorization:
|
⠙⢤⢠⡄⠀⣜⠃⢠⠀⠐⠘⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⡔⠀
⠀⠀⠙⢦⡇⠾⡃⠰⠀⠀⠀⠐⠀⠃⠀⢂⠀⠀⠠⠀⠀⠀⠃⢀⠀⢀⠀⠀⠆⢣
⠀⠀⠀⠀⠙⢼⣣⢠⠀⣂⣂⢘⡂⡃⢰⣋⡀⣔⢠⠀⠀⠀⡃⠈⠀⢈⠀⡄⣄⡋
⠀⠀⠀⠀⠀⠀⠑⢖⡰⠉⠉⠈⠁⠁⢘⢙⠉⡊⢐⢐⢀⣞⠱⠎⠀⠌⡀⡣⡊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣴⢸⣴⡖⢠⣤⡜⢣⠀⠀⠛⠛⡜⠂⠀⢢⠀⡔⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⣛⣛⣛⣛⣓⣚⡃⢠⣖⣒⣓⢐⢠⣜⠀⡃⢘⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣾⣿⣿⠀⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣒⣿⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿
| ⠑⢝⠀⠀⢸⠔⡵⢊⡀⡂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣕⢕
⠀⠀⠑⢄⠀⠳⠡⢡⣒⣃⢣⠯⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌
⠀⠀⠀⠀⠑⢄⢶⡘⣂⡎⢎⡭⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠴
⠀⠀⠀⠀⠀⠀⠙⢎⣷⣏⢷⣯⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢼⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⢄⠀⠤⢠⠀⢄⢀⢀⠀⡀⠀⠀⢟⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠊⠀⣂⠅⢓⣤⡄⠢⠠⠀⠌⠉⢀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠉⣋⠀⢁⢰⢔⢔⢠⡖⢥⠁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠘⣶⡂⠠⡀⣡⠭⣤⢓⢗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡇⡇⣢⣢⠂⣯⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢕⢟⢝⣒⠭⠭⡭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢝⣿⣿⡭⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿
|
|:----------------------------- |:--------------------------------------- |
| `chol(S)` (16% stored values) | `chol(S[perm,perm])` (6% stored values) |
## Direct access to the Metis C API
For more fine tuned usage of Metis consider calling the C API directly.
The following functions are currently exposed:
- `METIS_PartGraphRecursive`
- `METIS_PartGraphKway`
- `METIS_ComputeVertexSeparator`
- `METIS_NodeND`
all with the same arguments and argument order as described in the
[Metis manual][metis-manual-url].
[gh-actions-img]: https://github.com/JuliaSparse/Metis.jl/workflows/CI/badge.svg
[gh-actions-url]: https://github.com/JuliaSparse/Metis.jl/actions?query=workflow%3ACI
[codecov-img]: http://codecov.io/github/JuliaSparse/Metis.jl/coverage.svg?branch=master
[codecov-url]: http://codecov.io/github/JuliaSparse/Metis.jl?branch=master
[metis-url]: http://glaros.dtc.umn.edu/gkhome/metis/metis/overview
[metis-manual-url]: http://glaros.dtc.umn.edu/gkhome/fetch/sw/metis/manual.pdf
[S-url]: https://user-images.githubusercontent.com/11698744/38196722-dd9877c2-3684-11e8-8c02-a767604824d1.png
[Spp-url]: https://user-images.githubusercontent.com/11698744/38196723-ddb62fba-3684-11e8-89ff-181128644294.png
[C-url]: https://user-images.githubusercontent.com/11698744/38196720-dd5dd748-3684-11e8-8413-a52d336abe49.png
[Cpp-url]: https://user-images.githubusercontent.com/11698744/38196721-dd7ac16e-3684-11e8-8a35-761e97d11235.png
[partition2-url]: https://user-images.githubusercontent.com/11698744/38196819-65950f1e-3685-11e8-8db4-6aa9563bbd62.png
[partition3-url]: https://user-images.githubusercontent.com/11698744/38196820-65b11c9a-3685-11e8-95a0-b3b280359b31.png
[partition4-url]: https://user-images.githubusercontent.com/11698744/38196821-65ddc1dc-3685-11e8-8eb1-ce44ef1646f3.png
[separator-url]: https://user-images.githubusercontent.com/11698744/38196822-65fffc34-3685-11e8-9575-4dba41faec41.png
[vertex-separator-url]: https://en.wikipedia.org/wiki/Vertex_separator