crying 0.0.1

linear algebra utility library with generic matrix and vector types
Documentation 
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use std::{convert, ops};

use num_traits::identities;

use crate::gec::Gec;
use crate::scalar::{Scalar, ScalarFloat};

// Matrix
#[derive(Clone, Debug)]
pub struct Mat<S: Scalar, const NROWS: usize, const NCOLS: usize>([[S; NCOLS]; NROWS]);

impl<S: Scalar, const NROWS: usize, const NCOLS: usize> Mat<S, NROWS, NCOLS> {
    pub fn zeros() -> Self {
        Self::from([[identities::zero(); NCOLS]; NROWS])
    }
    pub fn ones() -> Self {
        Self::from([[identities::one(); NCOLS]; NROWS])
    }
}

// square matrices
impl<S: Scalar, const DIM: usize> Mat<S, DIM, DIM> {
    pub fn identity() -> Self {
        let mut res = Self::zeros();
        for i in 0..DIM {
            res[[i,i]] = identities::one();
        }
        res
    }

    // TODO: inverse, diagonal, ...
}

impl<S: Scalar, const NROWS: usize, const NCOLS: usize> convert::From<[[S; NCOLS]; NROWS]>
    for Mat<S, NROWS, NCOLS>
{
    fn from(value: [[S; NCOLS]; NROWS]) -> Self {
        Self(value)
    }
}

impl<S: Scalar, const NROWS: usize, const NCOLS: usize> ops::Index<[usize; 2]>
    for Mat<S, NROWS, NCOLS>
{
    type Output = S;
    fn index(&self, [row, col]: [usize; 2]) -> &Self::Output {
        &self.0[row][col]
    }
}
impl<S: Scalar, const NROWS: usize, const NCOLS: usize> ops::IndexMut<[usize; 2]>
    for Mat<S, NROWS, NCOLS>
{
    fn index_mut(&mut self, [row, col]: [usize; 2]) -> &mut Self::Output {
        &mut self.0[row][col]
    }
}

impl<S: Scalar, const NROWS: usize, const NCOLS: usize> ops::Mul<Gec<S, NCOLS>>
    for &Mat<S, NROWS, NCOLS>
{
    type Output = Gec<S, NROWS>;
    fn mul(self, rhs: Gec<S, NCOLS>) -> Self::Output {
        let mut res = Gec::zero();
        for row in 0..NROWS {
            for col in 0..NCOLS {
                res[row] = res[row] + self[[row, col]] * rhs[col];
            }
        }
        res
    }
}
// There's not actually a good way for us to reuse the memory of the matrix to
// hold the result. We could do it if we were able to treat the matrix contents
// as being continguous when iterating across rows (which it should be). Maybe
// there's an unsafe rust way to do this?
impl<S: Scalar, const NROWS: usize, const NCOLS: usize> ops::Mul<Gec<S, NCOLS>>
    for Mat<S, NROWS, NCOLS>
{
    type Output = Gec<S, NROWS>;
    fn mul(self, rhs: Gec<S, NCOLS>) -> Self::Output {
        &self * rhs
    }
}

// NOTE: This is a naive algorithm that is slow on large matrices. We should use
// blocks. TODO.
impl<S: Scalar, const DIM1: usize, const DIM2: usize, const DIM3: usize>
    ops::Mul<&Mat<S, DIM2, DIM3>> for &Mat<S, DIM1, DIM2>
{
    type Output = Mat<S,DIM1,DIM3>;
    fn mul(self, rhs: &Mat<S, DIM2, DIM3>) -> Self::Output {
        let mut res = Self::Output::from([[identities::zero(); DIM3]; DIM1]);
        for i in 0..DIM1 {
            for j in 0..DIM2 {
                for k in 0..DIM3 {
                    res[[i,k]] = res[[i,k]] + self[[i,j]]*rhs[[j,k]];
                }
            }
        }
        res
    }
}
// no in-place way to do this without assuming some structure, e.g.
// triangularity, of the matrices
impl<S: Scalar, const DIM1: usize, const DIM2: usize, const DIM3: usize>
    ops::Mul<&Mat<S, DIM2, DIM3>> for Mat<S, DIM1, DIM2>
{
    type Output = Mat<S,DIM1,DIM3>;
    fn mul(self, rhs: &Mat<S, DIM2, DIM3>) -> Self::Output {
        &self * rhs
    }
}
impl<S: Scalar, const DIM1: usize, const DIM2: usize, const DIM3: usize>
    ops::Mul<Mat<S, DIM2, DIM3>> for &Mat<S, DIM1, DIM2>
{
    type Output = Mat<S,DIM1,DIM3>;
    fn mul(self, rhs: Mat<S, DIM2, DIM3>) -> Self::Output {
        self * &rhs
    }
}
impl<S: Scalar, const DIM1: usize, const DIM2: usize, const DIM3: usize>
    ops::Mul<Mat<S, DIM2, DIM3>> for Mat<S, DIM1, DIM2>
{
    type Output = Mat<S,DIM1,DIM3>;
    fn mul(self, rhs: Mat<S, DIM2, DIM3>) -> Self::Output {
        &self * &rhs
    }
}

// Specific dimensions of matrices
impl<S: ScalarFloat> Mat<S,3,3> {
    pub fn rotate_xyz(rot_x: S, rot_y: S, rot_z: S) -> Self {
        let xcos = rot_x.cos();
        let ycos = rot_y.cos();
        let zcos = rot_z.cos();
        let xsin = rot_x.sin();
        let ysin = rot_y.sin();
        let zsin = rot_z.sin();

        let xsin_ysin = xsin * ysin;
        let xcos_ysin = xcos * ysin;

        Self::from([
            [ycos * zcos, xsin_ysin * zcos - xcos * zsin, xcos_ysin * zcos + xsin * zsin],
            [ycos * zsin, xsin_ysin * zsin - xcos * zcos, xcos_ysin * zsin - xsin * zcos],
            [      -ysin,                    xsin * ycos,                    xcos * ycos],
        ])
    }
}

impl<S: ScalarFloat> Mat<S,4,4> {
    pub fn rotate_xyz_translate(rot_x: S, rot_y: S, rot_z: S, translate: Gec<S,3>) -> Self {
        let xcos = rot_x.cos();
        let ycos = rot_y.cos();
        let zcos = rot_z.cos();
        let xsin = rot_x.sin();
        let ysin = rot_y.sin();
        let zsin = rot_z.sin();

        let xsin_ysin = xsin * ysin;
        let xcos_ysin = xcos * ysin;

        let zero = identities::zero();
        let one = identities::one();

        Self::from([
            [ycos * zcos, xsin_ysin * zcos - xcos * zsin, xcos_ysin * zcos + xsin * zsin, translate[0]],
            [ycos * zsin, xsin_ysin * zsin - xcos * zcos, xcos_ysin * zsin - xsin * zcos, translate[1]],
            [      -ysin,                    xsin * ycos,                    xcos * ycos, translate[2]],
            [       zero,                           zero,                           zero,          one],
        ])
    }
}