Static Math in Rust programming language

"Simple things should be simple, complex things should be possible" Alan Kay.

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

• We use a tuple to indexing elements: m[(i, j)] allowing nice interface with the match feature of Rust

• No unsafe code :ballotboxwith_check:

• Could be optimize more with the use of SIMD

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

• You can visualize the matrices

text inverse: |-0.54 0.58 0.67 -0.08 -0.17 -1.18| |2.16 -1.53 -2.44 0.44 0.32 3.77| |0.21 -0.42 -0.39 0.15 0.20 0.62| |0.70 -0.24 -0.53 0.20 -0.21 0.73| |0.85 -0.47 -0.83 0.11 0.11 1.20| |-3.91 2.47 4.17 -0.87 -0.31 -6.08|

• The determinant of the matrices 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 matrixs inverse operations(in a very old machine)

```text inverse 6x6 time: [9.6090 us 9.6128 us 9.6172 us] change: [-3.2723% -3.0278% -2.8038%] (p = 0.00 < 0.05) Performance has improved. Found 5 outliers among 100 measurements (5.00%) 1 (1.00%) low mild 1 (1.00%) high mild 3 (3.00%) high severe

inverse 4x4 time: [98.560 ns 98.605 ns 98.677 ns] change: [-5.4359% -3.2101% -1.4680%] (p = 0.00 < 0.05) Performance has improved. Found 15 outliers among 100 measurements (15.00%) 5 (5.00%) high mild 10 (10.00%) high severe ```

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