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mod imp; use crate::{ traits::{Real, Scalar}, utils::ConstVec, }; use imp::MatrixImpl; use std::{ cmp::PartialEq, fmt, ops::{Add, Div, Index, IndexMut, Mul, Sub}, }; fn mm_dot<'a, T: Scalar, const M: usize, const N: usize, const P: usize>( v: Row<'a, T, { M }, { N }>, u: Column<'a, T, { N }, { P }>, ) -> T { let mut out = T::ZERO; v.zip(u).for_each(|(&x, &y)| out += x * y); out } // ========================= Matrix /// An M * N column-major Matrix of scalar values backed by an array. Scalar /// refers to anything that implements the [`Scalar`] trait, which is any value /// that is [`Copy`] and has a notion of arithmetic. However, many operations, /// such as the determinant and Gaussian elimination may not be possible /// with integer values. #[derive(Clone)] pub struct Matrix<T: Scalar, const M: usize, const N: usize> { data: MatrixImpl<T, { M }, { N }>, } impl<T: Scalar, const M: usize, const N: usize> Matrix<T, { M }, { N }> { /// Constructs a matrix filled with all zero values. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let array = [[0.0, 0.0], [0.0, 0.0]]; /// let a = Matrix::<f64, 2, 2>::zero(); /// let b = Matrix::from_array(array); /// /// assert_eq!(a, b); /// ``` pub const fn zero() -> Self { Self { data: MatrixImpl::zero(), } } /// Constructs a matrix filled with all values equal to `t`. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let array = [[1.0, 1.0], [1.0, 1.0]]; /// let a = Matrix::<_, 2, 2>::from_val(1.0); /// let b = Matrix::from_array(array); /// /// assert_eq!(a, b); /// ``` pub const fn from_val(t: T) -> Self { Self { data: MatrixImpl::from_val(t), } } /// Constructs a matrix from a given 2 dimensional array. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let array = [[1.0, 2.0], [3.0, 4.0]]; /// let expected = [1.0, 2.0, 3.0, 4.0]; /// let m = Matrix::from_array(array); /// /// for (x, y) in m.column_iter().zip(expected.iter()) { /// assert_eq!(x, y) /// } /// ``` pub const fn from_array(array: [[T; M]; N]) -> Self { Self { data: MatrixImpl::from_array(array), } } /// Returns a reference to the backing array of the matrix. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let m = Matrix::<_, 2, 2>::from_val(1.0); /// let slice = m.as_array(); /// /// for a in slice { /// println!("{:?}", &a[..]); /// } /// ``` pub const fn as_array(&self) -> &[[T; M]; N] { self.data.as_array() } /// Returns a mutable reference to the backing array of the matrix. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let mut m = Matrix::<_, 2, 2>::from_val(1.0); /// let slice = m.as_mut_array(); /// /// for arr in slice { /// for elem in arr { /// *elem = 2.0; /// } /// } /// /// assert_eq!(m, Matrix::from_val(2.0)); /// ``` pub const fn as_mut_array(&mut self) -> &mut [[T; M]; N] { self.data.as_mut_array() } /// Returns a raw pointer to the first element in the array. Keep in mind that /// since the matrix is represented in column-major order, offsetting this /// pointer by `mem::size_of::<T>` bytes will cause it to point to the next /// element in the column. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let m = Matrix::<_, 2, 2>::from_val(1.0); /// let ptr = m.as_ptr(); /// /// unsafe { /// assert_eq!(*ptr, 1.0); /// } /// ``` pub const fn as_ptr(&self) -> *const T { self.as_array() as *const _ as _ } /// Returns a mutable raw pointer to the first element in the array. Keep in mind /// that since the matrix is represented in column-major order, offsetting this /// pointer by `mem::size_of::<T>` bytes will cause it to point to the next /// element in the column. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let mut m = Matrix::<_, 2, 2>::from_val(1.0); /// let ptr = m.as_mut_ptr(); /// /// unsafe { /// *ptr = 2.0; /// assert_ne!(*ptr, 1.0); /// } /// ``` pub const fn as_mut_ptr(&mut self) -> *mut T { self.as_mut_array() as *mut _ as _ } /// Returns the dimensions of the matrix, in the order (M, N). /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let m = Matrix::<_, 2, 3>::from_val(1.0); /// /// assert_eq!(m.dimensions(), (2, 3)) /// ``` pub const fn dimensions(&self) -> (usize, usize) { (M, N) } /// Returns a column-wise iterator of all elements in the matrix. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let array = [[1.0, 2.0], [3.0, 4.0]]; /// let expected = [1.0, 2.0, 3.0, 4.0]; /// let m = Matrix::from_array(array); /// /// for (x, y) in m.column_iter().zip(expected.iter()) { /// assert_eq!(x, y) /// } /// ``` pub const fn column_iter(&self) -> ColumnIter<'_, T, { M }, { N }> { ColumnIter { matrix: self, row: 0, col: 0, } } /// Returns a column-wise iterator of mutable references to /// all elements in the matrix. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let array = [[1.0, 2.0], [3.0, 4.0]]; /// let expected = [2.0, 4.0, 6.0, 8.0]; /// let mut m = Matrix::from_array(array); /// /// for elem in m.column_iter_mut() { /// *elem *= 2.0; /// } /// /// for (x, y) in m.column_iter().zip(expected.iter()) { /// assert_eq!(x, y) /// } /// ``` pub const fn column_iter_mut(&mut self) -> ColumnIterMut<'_, T, { M }, { N }> { ColumnIterMut { matrix: self, row: 0, col: 0, } } /// Returns a row-wise iterator of all elements in the matrix. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let array = [[1.0, 2.0], [3.0, 4.0]]; /// let expected = [1.0, 3.0, 2.0, 4.0]; /// let m = Matrix::from_array(array); /// /// for (x, y) in m.row_iter().zip(expected.iter()) { /// assert_eq!(x, y) /// } /// ``` pub const fn row_iter(&self) -> RowIter<'_, T, { M }, { N }> { RowIter { matrix: self, row: 0, col: 0, } } /// Returns a row-wise iterator of mutable references to /// all elements in the matrix. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let array = [[1.0, 2.0], [3.0, 4.0]]; /// let expected = [2.0, 6.0, 4.0, 8.0]; /// let mut m = Matrix::from_array(array); /// /// for elem in m.row_iter_mut() { /// *elem *= 2.0; /// } /// /// for (x, y) in m.row_iter().zip(expected.iter()) { /// assert_eq!(x, y) /// } /// ``` pub const fn row_iter_mut(&mut self) -> RowIterMut<'_, T, { M }, { N }> { RowIterMut { matrix: self, row: 0, col: 0, } } /// Returns an iterator of elements over the specified column in /// the matrix, starting from the `n`th element. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let array = [[1.0, 2.0], [3.0, 4.0]]; /// let expected = [1.0, 2.0]; /// let m = Matrix::from_array(array); /// /// for (x, y) in m.column(0, 0).zip(expected.iter()) { /// assert_eq!(x, y) /// } /// ``` pub const fn column(&self, column: usize, n: usize) -> Column<'_, T, { M }, { N }> { Column { matrix: self, column, idx: n, } } /// Returns an iterator of mutable references over the specified column /// in the matrix, starting from the `n`th element. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let array = [[1.0, 2.0], [3.0, 4.0]]; /// let expected = [2.0, 4.0, 3.0, 4.0]; /// let mut m = Matrix::from_array(array); /// /// for elem in m.column_mut(0, 0) { /// *elem *= 2.0; /// } /// /// for (x, y) in m.column_iter().zip(expected.iter()) { /// assert_eq!(x, y) /// } /// ``` pub const fn column_mut(&mut self, column: usize, n: usize) -> ColumnMut<'_, T, { M }, { N }> { ColumnMut { matrix: self, column, idx: n, } } /// Returns an iterator of elements over the specified row in /// the matrix, starting from the `n`th element. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let array = [[1.0, 2.0], [3.0, 4.0]]; /// let expected = [1.0, 3.0]; /// let m = Matrix::from_array(array); /// /// for (x, y) in m.row(0, 0).zip(expected.iter()) { /// assert_eq!(x, y) /// } /// ``` pub const fn row(&self, row: usize, n: usize) -> Row<'_, T, { M }, { N }> { Row { matrix: self, row, idx: n, } } /// Returns an iterator of mutable references over the specified row /// in the matrix, starting from the `n`th element. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let array = [[1.0, 2.0], [3.0, 4.0]]; /// let expected = [2.0, 6.0, 2.0, 4.0]; /// let mut m = Matrix::from_array(array); /// /// for elem in m.row_mut(0, 0) { /// *elem *= 2.0; /// } /// /// for (x, y) in m.row_iter().zip(expected.iter()) { /// assert_eq!(x, y) /// } /// ``` pub const fn row_mut(&mut self, row: usize, n: usize) -> RowMut<'_, T, { M }, { N }> { RowMut { matrix: self, row, idx: n, } } /// Converts the provided matrix into one which holds [`f64`] /// values. This is required for some operations, such as /// computing the determinant of a matrix or putting the matrix /// into [row echelon form][1]. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let array = [[1, 2], [3, 4]]; /// let expected = [1.0, 2.0, 3.0, 4.0]; /// let m = Matrix::from_array(array).into_f64(); /// /// for (&x, &y) in m.column_iter().zip(expected.iter()) { /// assert_eq!(x, y as f64); /// } /// ``` /// /// [1]: https://en.wikipedia.org/wiki/Row_echelon_form pub fn into_f64(self) -> Matrix<f64, { M }, { N }> { let mut out = Matrix::zero(); out.column_iter_mut() .zip(self.column_iter().map(|elem| elem.to_f64())) .for_each(|(x, y)| *x = y); out } /// Converts the provided matrix into one which holds [`f32`] /// values. This is required for some operations, such as /// computing the determinant of a matrix or putting the matrix /// into [row echelon form][1]. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let array = [[1, 2], [3, 4]]; /// let expected = [1.0, 2.0, 3.0, 4.0]; /// let m = Matrix::from_array(array).into_f32(); /// /// for (&x, &y) in m.column_iter().zip(expected.iter()) { /// assert_eq!(x, y as f32); /// } /// ``` /// /// [1]: https://en.wikipedia.org/wiki/Row_echelon_form pub fn into_f32(self) -> Matrix<f32, { M }, { N }> { let mut out = Matrix::zero(); out.column_iter_mut() .zip(self.column_iter().map(|elem| elem.to_f32())) .for_each(|(x, y)| *x = y); out } /// Returns the transpose of a matrix. This is a /// non-consuming operation, since the matrix needs /// to be copied anyways. /// /// # Examples /// /// ``` /// use const_linear::{matrix, Matrix}; /// /// let m = matrix![ /// 1.0, 2.0; /// 3.0, 4.0; /// 5.0, 6.0; /// ]; /// /// let m_t = m.transpose(); /// /// for (x, y) in m.column_iter().zip(m_t.row_iter()) { /// assert_eq!(x, y); /// } /// ``` pub fn transpose(&self) -> Matrix<T, { N }, { M }> { let mut out = Matrix::<T, { N }, { M }>::zero(); for row in 0..M { for col in 0..N { out[(col, row)] = self[(row, col)]; } } out } } // Methods that are only applicable when the matrix is square. impl<T: Scalar, const N: usize> Matrix<T, { N }, { N }> { /// Returns the N x N identity matrix. /// /// # Examples /// /// ``` /// use const_linear::Matrix; /// /// let array = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]; /// /// let m = Matrix::<usize, 3, 3>::id(); /// /// assert_eq!(m, Matrix::from_array(array)); /// ``` pub const fn id() -> Self { Self { data: MatrixImpl::id(), } } /// Returns the determinant of a given matrix. For N < 5, /// this is done manually, as matrices with dimensions of /// less than 5x5 are the most common ones encountered. For /// N >= 5, the matrix is first row reduced, and then the /// product of the main diagonal is returned. Note that /// this operation may not be 100% correct, as the matrix /// must first be converted into floating point /// representation, which may result in a loss of precision. /// /// # Examples /// /// ``` /// use const_linear::{matrix, Matrix}; /// /// let m = matrix![ /// 3, 3, 3; /// -2, -1, -2; /// 1, -2, -3; /// ]; /// /// assert_eq!(m.det(), -12.0); /// ``` pub fn det(&self) -> f64 { // For matrix dimensions 0 to 4, we do the determinant // manually in order to speed up computations. // For dimensions above 4, use gaussian elimination // and find the product of the diagonals. match N { 0 => 1.0, 1 => self[(0, 0)].to_f64(), 2 => { // | a b | // | c d | (self[(0, 0)] * self[(1, 1)] - self[(0, 1)] * self[(1, 0)]).to_f64() } 3 => { // This is horrible. // | a b c | // | d e f | // | g h i | let a = self[(0, 0)]; let b = self[(0, 1)]; let c = self[(0, 2)]; let d = self[(1, 0)]; let e = self[(1, 1)]; let f = self[(1, 2)]; let g = self[(2, 0)]; let h = self[(2, 1)]; let i = self[(2, 2)]; (a * (e * i - f * h) - b * (d * i - f * g) + c * (d * h - e * g)).to_f64() } 4 => { // And this is even worse. // | a b c d | // | e f g h | // | i j k l | // | m n o p | let a = self[(0, 0)]; let b = self[(0, 1)]; let c = self[(0, 2)]; let d = self[(0, 3)]; let e = self[(1, 0)]; let f = self[(1, 1)]; let g = self[(1, 2)]; let h = self[(1, 3)]; let i = self[(2, 0)]; let j = self[(2, 1)]; let k = self[(2, 2)]; let l = self[(2, 3)]; let m = self[(3, 0)]; let n = self[(3, 1)]; let o = self[(3, 2)]; let p = self[(3, 3)]; let x = a * (f * (k * p - l * o) - g * (j * p - l * n) + h * (j * o - k * n)); let y = b * (e * (k * p - l * o) - g * (i * p - l * m) + h * (i * o - k * m)); let z = c * (e * (j * p - l * n) - f * (i * p - l * m) + h * (i * n - j * m)); let w = d * (e * (j * o - k * n) - f * (i * o - k * m) + g * (i * n - j * m)); (x - y + z - w).to_f64() } _ => { let matrix = self.clone().into_f64().gauss(); let mut prod = 1.0; for i in 0..N { prod *= matrix[(i, i)]; } prod } } } /// Returns the determinant of a given matrix. For N < 5, /// this is done manually, as matrices with dimensions of /// less than 5x5 are the most common ones encountered. For /// N >= 5, the matrix is first row reduced, and then the /// product of the main diagonal is returned. Note that /// this operation may not be 100% correct, as the matrix /// must first be converted into floating point /// representation, which may result in a loss of precision. /// /// # Examples /// /// ``` /// use const_linear::{matrix, Matrix}; /// /// let m = matrix![ /// 3, 3, 3; /// -2, -1, -2; /// 1, -2, -3; /// ]; /// /// assert_eq!(m.det_f32(), -12.0); /// ``` pub fn det_f32(&self) -> f32 { match N { 0 => 1.0, 1 => self[(0, 0)].to_f32(), 2 => (self[(0, 0)] * self[(1, 1)] - self[(0, 1)] * self[(1, 0)]).to_f32(), 3 => { let a = self[(0, 0)]; let b = self[(0, 1)]; let c = self[(0, 2)]; let d = self[(1, 0)]; let e = self[(1, 1)]; let f = self[(1, 2)]; let g = self[(2, 0)]; let h = self[(2, 1)]; let i = self[(2, 2)]; (a * (e * i - f * h) - b * (d * i - f * g) + c * (d * h - e * g)).to_f32() } 4 => { let a = self[(0, 0)]; let b = self[(0, 1)]; let c = self[(0, 2)]; let d = self[(0, 3)]; let e = self[(1, 0)]; let f = self[(1, 1)]; let g = self[(1, 2)]; let h = self[(1, 3)]; let i = self[(2, 0)]; let j = self[(2, 1)]; let k = self[(2, 2)]; let l = self[(2, 3)]; let m = self[(3, 0)]; let n = self[(3, 1)]; let o = self[(3, 2)]; let p = self[(3, 3)]; let x = a * (f * (k * p - l * o) - g * (j * p - l * n) + h * (j * o - k * n)); let y = b * (e * (k * p - l * o) - g * (i * p - l * m) + h * (i * o - k * m)); let z = c * (e * (j * p - l * n) - f * (i * p - l * m) + h * (i * n - j * m)); let w = d * (e * (j * o - k * n) - f * (i * o - k * m) + g * (i * n - j * m)); (x - y + z - w).to_f32() } _ => { let matrix = self.clone().into_f32().gauss(); let mut prod = 1.0; for i in 0..N { prod *= matrix[(i, i)]; } prod } } } } // Methods that are only applicable when the matrix contains floating point // values. impl<T: Real, const M: usize, const N: usize> Matrix<T, { M }, { N }> { /// Reduces the provided matrix to [row echelon form][1], /// consuming the original matrix in the process. /// /// # Examples /// /// ``` /// use const_linear::{matrix, Matrix}; /// /// let m = matrix![ /// 3, 3, 3; /// -2, -1, -2; /// 1, -2, -3; /// ].into_f64().gauss(); /// /// let rows = m.dimensions().0; /// /// for i in 0..rows { /// println!("{:?}", m[(i, i)]); /// } /// /// ``` /// /// [1]: https://en.wikipedia.org/wiki/Row_echelon_form pub fn gauss(mut self) -> Self { self.gauss_in_place(); self } /// Reduces the provided matrix to [row echelon form][1] without /// consuming the original matrix. /// /// # Examples /// /// ``` /// use const_linear::{matrix, Matrix}; /// /// let mut m = matrix![ /// 3, 3, 3; /// -2, -1, -2; /// 1, -2, -3; /// ].into_f64(); /// /// m.gauss_in_place(); /// let rows = m.dimensions().0; /// /// for i in 0..rows { /// println!("{:?}", m[(i, i)]); /// } /// /// ``` /// /// [1]: https://en.wikipedia.org/wiki/Row_echelon_form pub fn gauss_in_place(&mut self) { for pivot_idx in 0..M - 1 { if self[(pivot_idx, pivot_idx)] != T::ZERO { let mut pivot = ConstVec::<_, { N }>::new(); self.row(pivot_idx, pivot_idx) .for_each(|&val| pivot.push(val).ok().unwrap()); for row_idx in pivot_idx + 1..M { // Find the ratio needed to remove the elements below the // pivot. let ratio = self[(row_idx, pivot_idx)] / pivot[0]; // subtract a multiple of the pivot row from this row. self.row_mut(row_idx, pivot_idx) .zip(pivot.iter()) .for_each(|(val, &sub)| *val -= ratio * sub); } } } } } // ========================= Iterators /// A column-wise iterator over the elements of a matrix. pub struct ColumnIter<'a, T: Scalar + 'a, const M: usize, const N: usize> { matrix: &'a Matrix<T, { M }, { N }>, row: usize, col: usize, } impl<'a, T: Scalar + 'a, const M: usize, const N: usize> Iterator for ColumnIter<'a, T, { M }, { N }> { type Item = &'a T; fn next(&mut self) -> Option<&'a T> { if self.col == N { None } else { let ret = &self.matrix.index((self.row, self.col)); if self.row == M - 1 { self.row = 0; self.col += 1; } else { self.row += 1; } Some(ret) } } fn size_hint(&self) -> (usize, Option<usize>) { (M * N, Some(M * N)) } } impl<'a, T: Scalar + 'a, const M: usize, const N: usize> ExactSizeIterator for ColumnIter<'a, T, { M }, { N }> { } /// A column-wise iterator over mutable references to the elements of a matrix. pub struct ColumnIterMut<'a, T: Scalar + 'a, const M: usize, const N: usize> { matrix: &'a mut Matrix<T, { M }, { N }>, row: usize, col: usize, } impl<'a, T: Scalar + 'a, const M: usize, const N: usize> Iterator for ColumnIterMut<'a, T, { M }, { N }> { type Item = &'a mut T; fn next(&mut self) -> Option<&'a mut T> { if self.col == N { None } else { let ret = self.matrix.index_mut((self.row, self.col)) as *mut T; if self.row == M - 1 { self.row = 0; self.col += 1; } else { self.row += 1; } // SAFETY: // 1. The pointer can never be invalid, since the Matrix can not // be dropped due to it being mutably borrowed. // 2. The code above only ever gets one mutable borrow to each // element, so there is no pointer aliasing. unsafe { Some(&mut *ret) } } } fn size_hint(&self) -> (usize, Option<usize>) { (M * N, Some(M * N)) } } impl<'a, T: Scalar + 'a, const M: usize, const N: usize> ExactSizeIterator for ColumnIterMut<'a, T, { M }, { N }> { } /// A row-wise iterator over the elements of a matrix. pub struct RowIter<'a, T: Scalar + 'a, const M: usize, const N: usize> { matrix: &'a Matrix<T, { M }, { N }>, row: usize, col: usize, } impl<'a, T: Scalar + 'a, const M: usize, const N: usize> Iterator for RowIter<'a, T, { M }, { N }> { type Item = &'a T; fn next(&mut self) -> Option<&'a T> { if self.row == M { None } else { let ret = &self.matrix.index((self.row, self.col)); if self.col == N - 1 { self.col = 0; self.row += 1; } else { self.col += 1; } Some(ret) } } fn size_hint(&self) -> (usize, Option<usize>) { (M * N, Some(M * N)) } } impl<'a, T: Scalar + 'a, const M: usize, const N: usize> ExactSizeIterator for RowIter<'a, T, { M }, { N }> { } /// A row-wise iterator over mutable references to the elements of a matrix. pub struct RowIterMut<'a, T: Scalar + 'a, const M: usize, const N: usize> { matrix: &'a mut Matrix<T, { M }, { N }>, row: usize, col: usize, } impl<'a, T: Scalar + 'a, const M: usize, const N: usize> Iterator for RowIterMut<'a, T, { M }, { N }> { type Item = &'a mut T; fn next(&mut self) -> Option<&'a mut T> { if self.row == M { None } else { let ret = self.matrix.index_mut((self.row, self.col)) as *mut T; if self.col == N - 1 { self.col = 0; self.row += 1; } else { self.col += 1; } // SAFETY: // 1. The pointer can never be invalid, since the Matrix can not // be dropped due to it being mutably borrowed. // 2. The code above only ever gets one mutable borrow to each // element, so there is no pointer aliasing. unsafe { Some(&mut *ret) } } } fn size_hint(&self) -> (usize, Option<usize>) { (M * N, Some(M * N)) } } impl<'a, T: Scalar, const M: usize, const N: usize> ExactSizeIterator for RowIterMut<'a, T, { M }, { N }> { } /// An iterator over elements in one column of a matrix. pub struct Column<'a, T: Scalar + 'a, const M: usize, const N: usize> { matrix: &'a Matrix<T, { M }, { N }>, column: usize, idx: usize, } impl<'a, T: Scalar + 'a, const M: usize, const N: usize> Iterator for Column<'a, T, { M }, { N }> { type Item = &'a T; fn next(&mut self) -> Option<&'a T> { if self.idx == M { None } else { let ret = &self.matrix.index((self.idx, self.column)); self.idx += 1; Some(ret) } } fn size_hint(&self) -> (usize, Option<usize>) { (M, Some(M)) } } /// An iterator over mutable references to elements in one column of a matrix. pub struct ColumnMut<'a, T: Scalar + 'a, const M: usize, const N: usize> { matrix: &'a mut Matrix<T, { M }, { N }>, column: usize, idx: usize, } impl<'a, T: Scalar + 'a, const M: usize, const N: usize> Iterator for ColumnMut<'a, T, { M }, { N }> { type Item = &'a mut T; fn next(&mut self) -> Option<&'a mut T> { if self.idx == M { None } else { let ret = self.matrix.index_mut((self.idx, self.column)) as *mut T; self.idx += 1; unsafe { Some(&mut *ret) } } } fn size_hint(&self) -> (usize, Option<usize>) { (M, Some(M)) } } /// An iterator over elements in one row of a matrix. pub struct Row<'a, T: Scalar + 'a, const M: usize, const N: usize> { matrix: &'a Matrix<T, { M }, { N }>, row: usize, idx: usize, } impl<'a, T: Scalar + 'a, const M: usize, const N: usize> Iterator for Row<'a, T, { M }, { N }> { type Item = &'a T; fn next(&mut self) -> Option<&'a T> { if self.idx == N { None } else { let ret = &self.matrix.index((self.row, self.idx)); self.idx += 1; Some(ret) } } fn size_hint(&self) -> (usize, Option<usize>) { (N, Some(N)) } } /// An iterator over mutable references to elements in one row of a matrix. pub struct RowMut<'a, T: Scalar + 'a, const M: usize, const N: usize> { matrix: &'a mut Matrix<T, { M }, { N }>, row: usize, idx: usize, } impl<'a, T: Scalar + 'a, const M: usize, const N: usize> Iterator for RowMut<'a, T, { M }, { N }> { type Item = &'a mut T; fn next(&mut self) -> Option<&'a mut T> { if self.idx == N { None } else { let ret = self.matrix.index_mut((self.row, self.idx)) as *mut T; self.idx += 1; unsafe { Some(&mut *ret) } } } fn size_hint(&self) -> (usize, Option<usize>) { (N, Some(N)) } } // ========================= Matrix Trait Impls impl<T: Scalar, const M: usize, const N: usize> fmt::Debug for Matrix<T, { M }, { N }> { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { writeln!(f, "Matrix {{")?; writeln!(f, " [")?; for col in self.as_array().iter() { writeln!(f, " {:?},", &col[..])?; } writeln!(f, " ],")?; writeln!(f, "}}") } } impl<T: Scalar, const M: usize, const N: usize> PartialEq for Matrix<T, { M }, { N }> { fn eq(&self, other: &Self) -> bool { self.column_iter() .zip(other.column_iter()) .all(|(x, y)| x == y) } } impl<T: Scalar + Eq, const M: usize, const N: usize> Eq for Matrix<T, { M }, { N }> {} impl<T: Scalar, const M: usize, const N: usize> Index<(usize, usize)> for Matrix<T, { M }, { N }> { type Output = T; fn index(&self, index: (usize, usize)) -> &T { &self.as_array()[index.1][index.0] } } impl<T: Scalar, const M: usize, const N: usize> IndexMut<(usize, usize)> for Matrix<T, { M }, { N }> { fn index_mut(&mut self, index: (usize, usize)) -> &mut Self::Output { &mut self.as_mut_array()[index.1][index.0] } } impl<T: Scalar, const M: usize, const N: usize> Add for Matrix<T, { M }, { N }> { type Output = Self; fn add(mut self, rhs: Self) -> Self::Output { self.column_iter_mut() .zip(rhs.column_iter()) .for_each(|(self_val, &rhs_val)| *self_val += rhs_val); self } } impl<T: Scalar, const M: usize, const N: usize> Sub for Matrix<T, { M }, { N }> { type Output = Self; fn sub(mut self, rhs: Self) -> Self::Output { self.column_iter_mut() .zip(rhs.column_iter()) .for_each(|(self_val, &rhs_val)| *self_val -= rhs_val); self } } impl<T: Scalar, const M: usize, const N: usize, const P: usize> Mul<Matrix<T, { N }, { P }>> for Matrix<T, { M }, { N }> { type Output = Matrix<T, { M }, { P }>; fn mul(self, rhs: Matrix<T, { N }, { P }>) -> Self::Output { let mut out = Self::Output::zero(); for i in 0..M { for j in 0..P { let row = self.row(i, 0); let column = rhs.column(j, 0); out[(i, j)] = mm_dot(row, column); } } out } } impl<T: Scalar, const R: usize, const C: usize> Mul<T> for Matrix<T, { R }, { C }> { type Output = Self; fn mul(mut self, rhs: T) -> Self { for elem in self.column_iter_mut() { *elem *= rhs; } self } } // ========================= Vectors (Special case of Matrix) /// An N dimensional vector, represented as a matrix /// with dimensions N x 1. pub type Vector<T, const N: usize> = Matrix<T, { N }, 1>; /// An N dimensional vector of f64 values. pub type VectorF64<const N: usize> = Vector<f64, { N }>; /// An N dimensional vector of f32 values. pub type VectorF32<const N: usize> = Vector<f32, { N }>; impl<T: Scalar, const N: usize> Vector<T, { N }> { /// Returns the length of the vector as an [`f64`]. /// /// # Examples /// /// ``` /// use const_linear::{vector, Vector}; /// /// let v = vector![1, 1, 1]; /// /// assert_eq!(v.length(), f64::sqrt(3.0)); /// ``` pub fn length(&self) -> f64 { f64::sqrt(self.squared_sum().to_f64()) } /// Returns the length of the vector as an [`f32`]. /// /// # Examples /// /// ``` /// use const_linear::{vector, Vector}; /// /// let v = vector![1, 1, 1]; /// /// assert_eq!(v.length(), f64::sqrt(3.0)); /// ``` /// pub fn length_f32(&self) -> f32 { f32::sqrt(self.squared_sum().to_f32()) } /// Consumes and normalizes the vector, returning the /// unit vector of [`f64`] values in the same direction /// as the original vector. /// /// # Examples /// /// ``` /// use const_linear::{vector, Vector}; /// /// let v = vector![1, 1, 1].normalize(); /// /// assert_eq!(v.length(), 1.0); /// ``` pub fn normalize(self) -> VectorF64<{ N }> { let len = self.length(); // A vector's length is zero iff it is the zero vector. if len == f64::ZERO { VectorF64::<{ N }>::zero() } else { self.into_f64() / len } } /// Consumes and normalizes the vector, returning the /// unit vector of [`f32`] values in the same direction /// as the original vector. /// /// # Examples /// /// ``` /// use const_linear::{ /// traits::Real, /// vector, Vector, /// }; /// /// let v = vector![1, 1, 1].normalize_f32(); /// /// // Relative equality is needed here, since /// // the value doesn't come out as *exactly* /// // 1.0f32. /// let epsilon = std::f32::EPSILON; /// let relative = 1.0E-7f32; /// /// assert!(v.length_f32().approx_eq(1.0f32, epsilon, relative)); /// ``` pub fn normalize_f32(self) -> VectorF32<{ N }> { let len = self.length_f32(); if len == f32::ZERO { VectorF32::<{ N }>::zero() } else { self.into_f32() / len } } pub fn dot(&self, rhs: &Self) -> T { self.column_iter() .zip(rhs.column_iter()) .fold(T::ZERO, |acc, (&x, &y)| acc + (x * y)) } /// Returns the sum of every elements squared. fn squared_sum(&self) -> T { let mut sum = T::ZERO; for &x in self.column_iter() { sum += x * x; } sum } } impl<T: Scalar> Vector<T, { 3 }> { pub fn cross(&self, rhs: &Self) -> Self { vector![ self[(1, 0)] * rhs[(2, 0)] - self[(2, 0)] * rhs[(1, 0)], self[(2, 0)] * rhs[(0, 0)] - self[(0, 0)] * rhs[(2, 0)], self[(0, 0)] * rhs[(1, 0)] - self[(1, 0)] * rhs[(0, 0)], ] } } // ========================= Vector Trait Impls impl<T: Scalar, const N: usize> Add<T> for Vector<T, { N }> { type Output = Self; fn add(mut self, rhs: T) -> Self::Output { for elem in self.column_iter_mut() { *elem += rhs; } self } } impl<T: Scalar, const N: usize> Sub<T> for Vector<T, { N }> { type Output = Self; fn sub(mut self, rhs: T) -> Self::Output { for elem in self.column_iter_mut() { *elem -= rhs; } self } } /// Note that this impl will do *integer* division if `T` /// happens to be an integer. If you want a floating point /// representation, call [`Matrix::into_f64`] or /// [`Matrix::into_f32`] before dividing. impl<T: Scalar, const N: usize> Div<T> for Vector<T, { N }> { type Output = Vector<T, { N }>; fn div(mut self, rhs: T) -> Self::Output { for elem in self.column_iter_mut() { *elem /= rhs } self } } #[cfg(test)] mod tests { use super::*; use std::time::Instant; #[test] fn index() { const ARRAY: [[f64; 2]; 3] = [[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]; let matrix = Matrix::from_array(ARRAY); assert_eq!(matrix[(1, 2)], 6.0); } #[test] fn iter() { const ARRAY: [[f64; 2]; 3] = [[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]; const COLUMN_FLATTENED: [f64; 6] = [1.0, 2.0, 3.0, 4.0, 5.0, 6.0]; const ROW_FLATTENED: [f64; 6] = [1.0, 3.0, 5.0, 2.0, 4.0, 6.0]; let matrix = Matrix::from_array(ARRAY); // Check that column_iter() is indeed a column-wise iterator. for (i, &matrix_elem) in matrix.column_iter().enumerate() { assert_eq!(COLUMN_FLATTENED[i], matrix_elem); } // And likewise for row_iter() for (i, &matrix_elem) in matrix.row_iter().enumerate() { assert_eq!(ROW_FLATTENED[i], matrix_elem); } // The below code shows that `matrix` can not be dropped // as it is mutably borrowed. This is just a test two ensure // that the unsafe code works as intended. // let mut mut_col_iter = matrix.column_iter_mut(); // // let mut_borrowed = mut_col_iter.next().unwrap(); // // drop(mut_col_iter); // drop(matrix); // // *mut_borrowed = 0.0; } #[test] fn transpose() { const ARRAY: [[f64; 2]; 3] = [[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]]; const ITER_TRANSPOSED: [f64; 6] = [1.0, 3.0, 5.0, 2.0, 4.0, 6.0]; let matrix = Matrix::from_array(ARRAY).transpose(); // Ensure we get the expected results. for (i, &matrix_elem) in matrix.column_iter().enumerate() { // eprintln!("{}", matrix_elem); assert_eq!(ITER_TRANSPOSED[i], matrix_elem); } // Check that (Matrix^T)^T is the same as the original // matrix. assert!(matrix .column_iter() .zip(matrix.transpose().transpose().column_iter()) .all(|(x, y)| x == y)); // Four times? assert!(matrix .column_iter() .zip( matrix .transpose() .transpose() .transpose() .transpose() .column_iter() ) .all(|(x, y)| x == y)); } #[test] fn matrix_matrix_mul() { let first = [[1usize, 2], [3, 4]]; let second = [[1, 2], [3, 4], [5, 6]]; let expected = [7usize, 10, 15, 22, 23, 34]; let multiplied = Matrix::from_array(first) * Matrix::from_array(second); // Check each element is correct. for (i, &elem) in multiplied.column_iter().enumerate() { assert_eq!(expected[i], elem); } // Sanity check for square matrices, as Matrix::<N, N> * Matrix<N, N> -> Matrix<N, N> let m = Matrix::<usize, 5, 5>::from_val(1); let n = Matrix::<usize, 5, 5>::from_val(1); for arr in m.as_array() { for elem in arr { eprint!("{:?}, ", elem) } } let square_matrix = m * n; let expected = [5; 25]; for (i, &elem) in square_matrix.column_iter().enumerate() { assert_eq!(expected[i], elem); } } #[test] fn gauss_elim() { let array = [[2, -3, -2], [1, -1, 1], [-1, 2, 2]]; let expected = [[2.0, 0.0, 0.0], [1.0, 0.5, 0.0], [-1.0, 0.5, -1.0]]; let matrix = Matrix::from_array(array).into_f64().gauss(); let eliminated = Matrix::from_array(expected).into_f64(); // For this matrix, all of these turn out to be completely equal, // but approx_eq is used as a safety measure, since this may not // always be the case. dbg!(matrix.as_array()); dbg!(eliminated.as_array()); for (x, y) in matrix.column_iter().zip(eliminated.column_iter()) { assert!(x.approx_eq(*y, std::f64::EPSILON, 1.0E-10)); } } #[test] fn matrix_macro() { let first = [1usize, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]; let second = [1usize; 16]; let third = [1usize, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1]; let mat_one = matrix![ 1usize, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12; 13, 14, 15, 16; ]; let mat_two = matrix![1usize; 4, 4]; let mat_three = matrix![usize; 4]; for (i, &elem) in mat_one.column_iter().enumerate() { assert_eq!(first[i], elem); } for (i, &elem) in mat_two.column_iter().enumerate() { assert_eq!(second[i], elem); } for (i, &elem) in mat_three.column_iter().enumerate() { assert_eq!(third[i], elem); } } #[test] fn vector_macro() { let first = [1, 2, 3]; let second = [1, 1, 1]; let vec_one = vector![1, 2, 3]; let vec_two = vector![1; 3]; for (i, &elem) in vec_one.column_iter().enumerate() { assert_eq!(first[i], elem); } for (i, &elem) in vec_two.column_iter().enumerate() { assert_eq!(second[i], elem); } } #[test] fn vector_length() { use crate::traits::Real as _; let expected_f64 = std::f64::consts::SQRT_2; let expected_f32 = std::f32::consts::SQRT_2; let vec_one = vector![1.0f64; 2]; let vec_two = vector![1.0f32; 2]; // eprintln!("{}, {}", vec_one.length(), expected_f64); // eprintln!("{}, {}", vec_two.length_f32(), expected_f32); assert!(vec_one .length() .approx_eq(expected_f64, std::f64::EPSILON, 1.0e-6)); assert!(vec_two .length_f32() .approx_eq(expected_f32, std::f32::EPSILON, 1.0e-6)); } #[test] fn normalize() { use crate::traits::Real as _; let vector = vector![1, 2, 3]; let normalized = vector.normalize(); // eprintln!("{}", normalized.length()); // eprintln!("{:?}", normalized.as_array()); assert!(normalized .length() .approx_eq(1.0f64, std::f64::EPSILON, 1.0e-15)); } #[test] fn cross() { let v = vector![0, 4, -2]; let w = vector![3, -1, 5]; let expected = vector![18, -6, -12]; assert!(v.cross(&w) == expected); } #[test] #[ignore] fn large_matrix_time() { // let m1 = matrix![1.0; 16, 16]; // let n1 = matrix![1.0; 16, 16]; // let m2 = matrix![1; 32, 32]; // let n2 = matrix![1; 32, 32]; // let m3 = matrix![1; 64, 64]; // let n3 = matrix![1; 64, 64]; // let m4 = matrix![1; 128, 128]; // let n4 = matrix![1; 128, 128]; // let m5 = matrix![1; 4, 4]; // let n5 = matrix![1; 4, 4]; // // let n2 = n.clone(); // // let n3 = n.clone(); // // let n4 = n.clone(); // // let n5 = n.clone(); // // let start = Instant::now(); // let _ = m5 * n5; // eprintln!("4: {:?}", start.elapsed()); // // let start = Instant::now(); // let _ = m1 * n1; // eprintln!("16: {:?}", start.elapsed()); // // let start = Instant::now(); // let _ = m2 * n2; // eprintln!("32: {:?}", start.elapsed()); // // let start = Instant::now(); // let _ = m3 * n3; // eprintln!("64: {:?}", start.elapsed()); // // let start = Instant::now(); // let _ = m4 * n4; // eprintln!("128: {:?}", start.elapsed()); let mut a = matrix![ 1.0, -2.0, 5.0, 2.0; 5.0, 3.0, 1.0, 3.0; 4.0, 6.0, 0.0, -4.0; 2.0, 4.0, -1.0, 0.0; ]; let b = a.clone(); let c = a.clone(); let start_gauss = Instant::now(); a.gauss_in_place(); eprintln!("gauss: {:?}", start_gauss.elapsed()); let start_mm = Instant::now(); let _ = b * c; eprintln!("mm: {:?}", start_mm.elapsed()); let start_det = Instant::now(); let _ = a.det(); eprintln!("det: {:?}", start_det.elapsed()); } #[test] #[ignore] fn debug() { let m = matrix![usize; 16]; dbg!(m); } }