SummationByParts/utils/constmatrix/src/lib.rs

#![no_std]
#![feature(const_fn_floating_point_arithmetic)]

use float::Float;
use num_traits::identities::Zero;

/// A row-major matrix
#[derive(Debug, Clone, PartialEq, Eq, Hash)]
#[repr(transparent)]
pub struct Matrix<T, const M: usize, const N: usize> {
    pub data: [[T; N]; M],
}
pub type RowVector<T, const N: usize> = Matrix<T, 1, N>;
pub type ColVector<T, const N: usize> = Matrix<T, N, 1>;

impl<T: Copy + Default, const M: usize, const N: usize> Default for Matrix<T, M, N> {
    fn default() -> Self {
        Self {
            data: [[T::default(); N]; M],
        }
    }
}

impl<T: Copy + Zero + PartialEq, const M: usize, const N: usize> Zero for Matrix<T, M, N> {
    fn zero() -> Self {
        Self {
            data: [[T::zero(); N]; M],
        }
    }
    fn is_zero(&self) -> bool {
        self.iter().all(|x| x.is_zero())
    }
}

impl<T, const M: usize, const N: usize> core::ops::Index<(usize, usize)> for Matrix<T, M, N> {
    type Output = T;
    #[inline(always)]
    fn index(&self, (i, j): (usize, usize)) -> &Self::Output {
        &self.data[i][j]
    }
}

impl<T, const M: usize, const N: usize> core::ops::IndexMut<(usize, usize)> for Matrix<T, M, N> {
    #[inline(always)]
    fn index_mut(&mut self, (i, j): (usize, usize)) -> &mut Self::Output {
        &mut self.data[i][j]
    }
}

impl<T, const M: usize, const N: usize> core::ops::Index<usize> for Matrix<T, M, N> {
    type Output = [T; N];
    #[inline(always)]
    fn index(&self, i: usize) -> &Self::Output {
        &self.data[i]
    }
}

impl<T, const M: usize, const N: usize> core::ops::IndexMut<usize> for Matrix<T, M, N> {
    #[inline(always)]
    fn index_mut(&mut self, i: usize) -> &mut Self::Output {
        &mut self.data[i]
    }
}

impl<T, const M: usize, const N: usize> Matrix<T, M, N> {
    pub const fn new(data: [[T; N]; M]) -> Self {
        Self { data }
    }
    #[inline(always)]
    pub const fn nrows(&self) -> usize {
        M
    }
    #[inline(always)]
    pub const fn ncols(&self) -> usize {
        N
    }
    #[inline(always)]
    pub fn iter(&self) -> impl Iterator<Item = &T> {
        self.data.iter().flatten()
    }
    #[inline(always)]
    pub fn iter_mut(&mut self) -> impl Iterator<Item = &mut T> {
        self.data.iter_mut().flatten()
    }
    #[inline(always)]
    pub fn iter_rows(
        &self,
    ) -> impl ExactSizeIterator<Item = &[T; N]> + DoubleEndedIterator<Item = &[T; N]> {
        self.data.iter()
    }
    #[inline(always)]
    pub const fn row(&self, idx: usize) -> &[T; N] {
        &self.data[idx]
    }
}

impl<T, const N: usize> ColVector<T, N> {
    #[inline(always)]
    pub fn map_to_col(slice: &[T; N]) -> &ColVector<T, N> {
        unsafe { &*(slice.as_ptr().cast()) }
    }
    #[inline(always)]
    pub fn map_to_col_mut(slice: &mut [T; N]) -> &mut ColVector<T, N> {
        unsafe { &mut *(slice.as_mut_ptr().cast()) }
    }
}

impl<T, const N: usize> RowVector<T, N> {
    pub fn map_to_row(slice: &[T; N]) -> &Self {
        unsafe { &*(slice.as_ptr().cast()) }
    }
    pub fn map_to_row_mut(slice: &mut [T; N]) -> &mut Self {
        unsafe { &mut *(slice.as_mut_ptr().cast()) }
    }
}

impl<const M: usize, const P: usize> Matrix<Float, M, P> {
    /// A specialised matmul for Float, using fma
    pub fn matmul_float_into<const N: usize>(
        &mut self,
        lhs: &Matrix<Float, M, N>,
        rhs: &Matrix<Float, N, P>,
    ) {
        for i in 0..M {
            for j in 0..P {
                // Slightly cheaper to do first computation separately
                // rather than store zero and issue all ops as fma
                let mut t = if N == 0 {
                    0.0
                } else {
                    lhs[(i, 0)] * rhs[(0, j)]
                };
                for k in 1..N {
                    cfg_if::cfg_if!(
                        if #[cfg(any(target_feature="fma", target_feature="neon"))] {
                            t = Float::mul_add(lhs[(i, k)], rhs[(k, j)], t);
                        } else {
                            t = t + lhs[(i, k)]*rhs[(k, j)];
                        }
                    );
                }
                self[(i, j)] = t;
            }
        }
    }
}

impl<T, const M: usize, const P: usize> Matrix<T, M, P> {
    pub fn matmul_into<const N: usize>(&mut self, lhs: &Matrix<T, M, N>, rhs: &Matrix<T, N, P>)
    where
        T: Default + Copy + core::ops::Mul<Output = T> + core::ops::Add<Output = T>,
        T: 'static,
    {
        for i in 0..M {
            for j in 0..P {
                let mut t = T::default();
                for k in 0..N {
                    t = t + lhs[(i, k)] * rhs[(k, j)];
                }
                self[(i, j)] = t;
            }
        }
    }
}

macro_rules! impl_op_mul_mul {
    ($lhs:ty, $rhs:ty) => {
        impl<T, const N: usize, const M: usize, const P: usize> core::ops::Mul<$rhs> for $lhs
        where
            T: Copy + Default + core::ops::Add<Output = T> + core::ops::Mul<Output = T>,
            T: 'static,
        {
            type Output = Matrix<T, M, P>;
            fn mul(self, lhs: $rhs) -> Self::Output {
                let mut out = Matrix::default();
                out.matmul_into(&self, &lhs);
                out
            }
        }
    };
}

impl_op_mul_mul! {  Matrix<T, M, N>,  Matrix<T, N, P> }
impl_op_mul_mul! { &Matrix<T, M, N>,  Matrix<T, N, P> }
impl_op_mul_mul! {  Matrix<T, M, N>, &Matrix<T, N, P> }
impl_op_mul_mul! { &Matrix<T, M, N>, &Matrix<T, N, P> }

impl<T, const M: usize, const N: usize> core::ops::MulAssign<T> for Matrix<T, M, N>
where
    T: Copy + core::ops::MulAssign<T>,
{
    #[inline(always)]
    fn mul_assign(&mut self, other: T) {
        self.iter_mut().for_each(|x| *x *= other)
    }
}

impl<T, const N: usize, const M: usize> core::ops::Add<Matrix<T, M, N>> for Matrix<T, M, N>
where
    T: Copy + Zero + core::ops::Add<Output = T> + PartialEq,
{
    type Output = Self;
    fn add(self, lhs: Self) -> Self::Output {
        let mut out = Matrix::zero();
        for i in 0..M {
            for j in 0..N {
                out[(i, j)] = self[(i, j)] + lhs[(i, j)];
            }
        }
        out
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    #[test]
    fn construct_copy_type() {
        let _m0 = Matrix::<i32, 4, 3>::default();
        let _m1: Matrix<u8, 8, 8> = Matrix::default();

        let _m2 = Matrix::new([[1, 2], [3, 4]]);
    }

    #[test]
    fn matmul() {
        let m1 = Matrix::new([[1_u8, 2, 3], [4, 5, 6]]);
        let m2 = Matrix::new([[7_u8, 8, 9, 10], [11, 12, 13, 14], [15, 16, 17, 18]]);

        let m3 = m1 * m2;
        assert_eq!(m3, Matrix::new([[74, 80, 86, 92], [173, 188, 203, 218]]));
    }
    #[test]
    fn iter() {
        let m = Matrix::new([[1_u8, 2, 3], [4, 5, 6]]);
        let mut iter = m.iter();
        assert_eq!(iter.next(), Some(&1));
        assert_eq!(iter.next(), Some(&2));
        assert_eq!(iter.next(), Some(&3));
        assert_eq!(iter.next(), Some(&4));
        assert_eq!(iter.next(), Some(&5));
        assert_eq!(iter.next(), Some(&6));
        assert_eq!(iter.next(), None);
    }
}

#[cfg(feature = "approx")]
mod approx {
    use super::Matrix;
    use ::approx::{AbsDiffEq, RelativeEq, UlpsEq};

    impl<T, const M: usize, const N: usize> AbsDiffEq for Matrix<T, M, N>
    where
        T: AbsDiffEq,
    {
        type Epsilon = T::Epsilon;
        fn default_epsilon() -> Self::Epsilon {
            T::default_epsilon()
        }
        fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
            self.iter()
                .zip(other.iter())
                .all(|(r, l)| r.abs_diff_eq(l, T::default_epsilon()))
        }
    }
    impl<T, const M: usize, const N: usize> RelativeEq for Matrix<T, M, N>
    where
        T: RelativeEq,
        Self::Epsilon: Copy,
    {
        fn default_max_relative() -> Self::Epsilon {
            T::default_max_relative()
        }
        fn relative_eq(
            &self,
            other: &Self,
            epsilon: Self::Epsilon,
            max_relative: Self::Epsilon,
        ) -> bool {
            self.iter()
                .zip(other.iter())
                .all(|(r, l)| r.relative_eq(l, epsilon, max_relative))
        }
    }
    impl<T, const M: usize, const N: usize> UlpsEq for Matrix<T, M, N>
    where
        T: UlpsEq,
        Self::Epsilon: Copy,
    {
        fn default_max_ulps() -> u32 {
            T::default_max_ulps()
        }
        fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool {
            self.iter()
                .zip(other.iter())
                .all(|(r, l)| r.ulps_eq(l, epsilon, max_ulps))
        }
    }
}

impl<const M: usize, const N: usize> Matrix<Float, M, N> {
    pub const fn flip_ud(&self) -> Self {
        let mut m = Self::new([[0.0; N]; M]);
        let mut i = 0;
        while i < M {
            m.data[M - 1 - i] = self.data[i];
            i += 1;
        }
        m
    }

    pub const fn flip_lr(&self) -> Self {
        let mut m = Self::new([[0.0; N]; M]);
        let mut i = 0;
        while i < M {
            let mut j = 0;
            while j < N {
                m.data[i][N - 1 - j] = self.data[i][j];
                j += 1;
            }
            i += 1;
        }
        m
    }

    /// Flip all sign bits
    pub const fn flip_sign(&self) -> Self {
        let mut m = Self::new([[0.0; N]; M]);
        let mut i = 0;
        while i < M {
            let mut j = 0;
            while j < N {
                m.data[i][j] = -self.data[i][j];
                j += 1;
            }
            i += 1;
        }
        m
    }

    /// Zero extends if larger than self
    pub const fn resize<const M2: usize, const N2: usize>(&self) -> Matrix<Float, M2, N2> {
        let mut m = Matrix::new([[0.0; N2]; M2]);

        let m_min = if M < M2 { M } else { M2 };
        let n_min = if N < N2 { N } else { N2 };

        let mut i = 0;
        while i < m_min {
            let mut j = 0;
            while j < n_min {
                m.data[i][j] = self.data[i][j];
                j += 1;
            }
            i += 1;
        }

        m
    }
}

#[cfg(test)]
mod flipping {
    use super::*;

    #[test]
    fn flip_lr_test() {
        let m = Matrix::new([[1.0, 2.0, 3.0, 4.0]]);
        let flipped = m.flip_lr();
        assert_eq!(flipped, Matrix::new([[4.0, 3.0, 2.0, 1.0]]));
        let m = Matrix::new([[1.0, 2.0, 3.0, 4.0, 5.0]]);
        let flipped = m.flip_lr();
        assert_eq!(flipped, Matrix::new([[5.0, 4.0, 3.0, 2.0, 1.0]]));
    }
    #[test]
    fn flip_ud_test() {
        let m = Matrix::new([[1.0], [2.0], [3.0], [4.0]]);
        let flipped = m.flip_ud();
        assert_eq!(flipped, Matrix::new([[4.0], [3.0], [2.0], [1.0]]));
        let m = Matrix::new([[1.0], [2.0], [3.0], [4.0], [5.0]]);
        let flipped = m.flip_ud();
        assert_eq!(flipped, Matrix::new([[5.0], [4.0], [3.0], [2.0], [1.0]]));
    }

    #[test]
    fn assert_castability_of_alignment() {
        let m = Matrix::new([[1.0], [2.0], [3.0], [4.0_f64]]);
        assert_eq!(core::mem::align_of_val(&m), core::mem::align_of::<f64>());
        let m = Matrix::new([[1.0], [2.0], [3.0], [4.0_f32]]);
        assert_eq!(core::mem::align_of_val(&m), core::mem::align_of::<f32>());
        let m = Matrix::new([[1], [2], [3], [4_i32]]);
        assert_eq!(core::mem::align_of_val(&m), core::mem::align_of::<i32>());
        let m = Matrix::new([[1], [2], [3], [4_u64]]);
        assert_eq!(core::mem::align_of_val(&m), core::mem::align_of::<u64>());
        let m = Matrix::new([[1], [2], [3], [4_u128]]);
        assert_eq!(core::mem::align_of_val(&m), core::mem::align_of::<u128>());
    }
}