Static Math in Rust programming language

• This crate take advantage of the static arrays in Rust for fast operations in stack memory.

• This crate could be used in an no-std environment.

• The determinant of the matrixs are evaluated "in-place" without loops and code bifurcations

• The use cases can be: Robotics, Game programming, Simulations ...etc.

The matrix types Mnn (where n=2..6) implements the Methods from the LinearAlgebra trait:

• det(): Determinant of the matrix
• inverse(): Inverse of the matrix
• qr(): QR decomposition of the matrix
• norm2(): norm of the matrix
• transpose(): transpose of the matrix
• trace(): trace of the matrix
• shape(): shape of the matrix

Benchmarks

Using the criterion crate:

https://github.com/bheisler/criterion.rs

this are the results for one operation(6x6 matrix inverse):

```text inverse 6x6 time: [9.9747 us 9.9786 us 9.9827 us] change: [-0.0532% +0.3519% +1.0973%] (p = 0.44 > 0.05) No change in performance detected. Found 4 outliers among 100 measurements (4.00%) 1 (1.00%) high mild 3 (3.00%) high severe

inverse 4x4 time: [118.78 ns 118.97 ns 119.17 ns] change: [-0.3000% -0.0129% +0.2796%] (p = 0.93 > 0.05) No change in performance detected. ```

you can look the bench here: bench

The same Matrix and test but in Julia language:

```text BenchmarkTools.Trial: memory estimate: 33.48 KiB allocs estimate: 455

minimum time: 1.536 ms (0.00% GC) median time: 1.566 ms (0.00% GC) mean time: 1.643 ms (0.62% GC) maximum time: 20.027 ms (78.89% GC)

samples: 3040 evals/sample: 1 ```

TODOS:

• [ ] Quaternion type and methods
• [ ] expm(): Exponential matrix implementation
• [X] Eigenvalues
• [X] QR decomposition