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

• You could index the rows of the matrix with simply: m[i]

• 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.

  by enabling the feature no-std, for example in your Cargo.toml:

  [dependencies.static-math]
  default-features = false
  version = "0.2.0"
  features = ["no-std"]
  

• 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

• We have implemented Quaternions (and all the most used methods)

• We have implemented DualQuaternions (and all the most used methods in Robotics and graphics like Screw Linear Interpolation)

• We have implemented in the transformations.rs module a wide variety of functions used in Robotics (which conforms to the screw theory)

Benchmarks

Using the criterion crate:

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

run with: cargo bench

Others benches comparing the performance with others crates are in this repo: https://github.com/bitshifter/mathbench-rs

NOTE: this is the only crate that not have unsafe code

with the following results:

TODOS:

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