# Static L.A. (Linear Algebra)

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A fast minimal ultra type safe linear algebra library.

While [`ndarray`](https://docs.rs/ndarray/latest/ndarray/) offers no compile time type checking
 on dimensionality and [`nalgebra`](https://docs.rs/nalgebra/latest/nalgebra/) offers some
 finnicky checking, this offers the maximum possible checking.

When performing the addition of a `MatrixDxS` (a matrix with a known number of columns at
 compile time) and a `MatrixSxD` (a matrix with a known number of rows at compile time) you
 get a `MatrixSxS` (a matrix with a known number of rows and columns at compile time) since
 now both the number of rows and columns are known at compile time. This then allows this
 infomation to propagate through your program providing excellent compile time checking.

An example of how types will propagate through a program:
```rust
#![allow(incomplete_features)]
#![feature(generic_const_exprs)]
use static_la::*;
// MatrixSxS<i32,2,3>
let a = MatrixSxS::from([[1,2,3],[4,5,6]]);
// MatrixDxS<i32,3>
let b = MatrixDxS::from(vec![[2,2,2],[3,3,3]]);
// MatrixSxS<i32,2,3>
let c = (a.clone() + b.clone()) - a.clone();
// MatrixDxS<i32,3>
let d = c.add_rows(b);
// MatrixSxS<i32,4,3>
let e = MatrixSxS::from([[1,2,3],[4,5,6],[7,8,9],[10,11,12]]);
// MatrixSxS<i32,4,6>
let f = d.add_columns(e);
```

In this example the only operations which cannot be fully checked at compile time are:
1. `a.clone() + b.clone()`
2. `d.add_columns(e)`

 **You must include `#![feature(generic_const_exprs)]` when using this library otherwise you will get a compiler error.**

### Comparisons

In the comparison benchmarks we are using `static_la::MatrixDxD<f32>`, `ndarray::Array2<f32>` and `naglebra::DMatrix<f32>`.

We use specialization to call optimized BLAS functions for floating point types, this means this library will typically outperform standard ndarray and nalgebra with `f32` and `f64` operations but may underperformed with integer (`u32`,`i32`, etc.) operations.

The x axis refers to the size of the matrices e.g. 50 refers to 50x50 matrices.

<img src="https://github.com/JonathanWoollett-Light/static-la/blob/master/matmul.svg">

<table>
 <tr>
  <td><img src="https://github.com/JonathanWoollett-Light/static-la/blob/master/add.svg"></td>
  <td><img src="https://github.com/JonathanWoollett-Light/static-la/blob/master/sub.svg"></td>
 </tr>
 <tr></tr>
 <tr>
  <td><img src="https://github.com/JonathanWoollett-Light/static-la/blob/master/mul.svg"></td>
  <td><img src="https://github.com/JonathanWoollett-Light/static-la/blob/master/div.svg"></td>
 </tr>
 </tr>
</table>