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https://github.com/planetis-m/manu
Nim MAtrix NUmeric package
https://github.com/planetis-m/manu
decomposition determinants linear-algebra matrices matrix-decompositions matrix-functions nim nim-library scientific simultaneous-linear-equations
Last synced: 3 months ago
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Nim MAtrix NUmeric package
- Host: GitHub
- URL: https://github.com/planetis-m/manu
- Owner: planetis-m
- License: mit
- Created: 2019-06-16T08:05:48.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2024-03-21T21:09:58.000Z (8 months ago)
- Last Synced: 2024-05-18T15:40:02.803Z (6 months ago)
- Topics: decomposition, determinants, linear-algebra, matrices, matrix-decompositions, matrix-functions, nim, nim-library, scientific, simultaneous-linear-equations
- Language: Nim
- Size: 474 KB
- Stars: 42
- Watchers: 3
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
- awesome-nim - manu - Nim MAtrix NUmeric package - a port of JAMA, adapted to Nim. (Algorithms / Math)
README
# Manu — Nim Matrix Numeric library
Manu is a pure Nim library, no external dependencies to BLAS frameworks.
Supports constructing and manipulating only real, dense matrices.
It started as a port of [JAMA](https://math.nist.gov/javanumerics/jama/)
library, and is adapted to Nim programming paradigm and specific performace considerations.
What is supported:
- Compute solutions of simultaneous linear equations, determinants, inverses and other matrix functions.
- Generics allow matrices of ``SomeFloat`` only.
- Arithmetic operators are overloaded to support matrices.
* Broadcast scalars, column and row vectors to work with matrices.
- Destructors, with sink annotations, copies can be avoided in some cases.
API [documentation](https://planetis-m.github.io/manu/)
## Examples
In the examples directory you will find the following:
1. [two layer neural network](https://github.com/planetis-m/manu/blob/master/examples/neural.nim)
2. [stress state analysis script](https://github.com/planetis-m/manu/blob/master/examples/mohr.nim)
showcasing what can already be done.
### example2.nim
```nim
import manu
# Solve a linear system A x = b and compute the residual norm, ||b - A x||.
let vals = @[@[1.0, 2, 3], @[4.0, 5, 6], @[7.0, 8, 10]]
let A = matrix(vals)
let b = randMatrix64(3, 1)
let x = A.solve(b)
let r = A * x - b
let rnorm = r.normInf()
echo("x =\n", x)
echo("residual norm = ", rnorm)
```
Output:
```
x =
⎡-918.9217543597e-3⎤
⎢ 2.1952979104⎥
⎣ -1.0796593055⎦
residual norm = 1.554312234475219e-15
```
## Matrix decompositions
Five matrix decompositions are used to compute solutions of simultaneous linear equations,
determinants, inverses and other matrix functions. Theses are:
- Cholesky Decomposition of symmetric, positive definite matrices
- LU Decomposition (Gaussian elimination) of rectangular matrices
- QR Decomposition of rectangular matrices
- Eigenvalue Decomposition of both symmetric and nonsymmetric square matrices
- Singular Value Decomposition of rectangular matrices
## Broadcasting
It is implemented with the help of two ``distinct`` types ``RowVector[T]`` and ``ColVector[T]``.
You can cast any compatible matrix to these and when performing matrix operations,
it will be broadcasted to the correct dimensions:
```nim
var a = matrix(1, 5, 2.0)
let b = ones64(2, 1)
echo ColVector64(b) + RowVector64(a)
echo 2.0 + a # matrix-scalar ops are implicit
```
Results in:
```
⎡3 3 3 3 3⎤
⎣3 3 3 3 3⎦
⎡4 4 4 4 4⎤
```
If the matrices are not broadcastable an ``AssertionDefect`` will be thrown at runtime.
The correct paradigm of usage is to first initialize a matrix, i.e ``let a = ones64(1, 5)``
and cast it to ``RowVector64`` where broadcasting is needed: ``RowVector64(a) + zeros64(5, 5)``.
This system is designed to be more explicit, and since it is type-checked,
work well with ``sink`` optimizations.
## Feature improvements / contributions
- Add more tests
- Incorporate usefull additions from [Apache Commons Math](https://github.com/apache/commons-math)
## License
This library is distributed under the [MIT license](LICENSE).