Static Math in Rust programming language

• 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

• Could be optimize more with the use of SIMD

• 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 matrixs inverse operations(in a very old machine)

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:

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
• Eigenvalues
• QR decomposition