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 :ballot_box_with_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

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)

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