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423 lines
11 KiB
Rust
423 lines
11 KiB
Rust
extern crate core;
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use index::Index2D;
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use std::cmp::min;
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use std::fmt::Debug;
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use std::iter::{zip, Flatten};
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use std::ops::{Index, IndexMut};
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pub mod decompose;
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mod identities;
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pub mod index;
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mod math;
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mod ops;
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mod util;
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/// A 2D array of values which can be operated upon.
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///
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/// Matrices have a fixed size known at compile time
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#[derive(Debug, Copy, Clone, PartialEq)]
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pub struct Matrix<T, const M: usize, const N: usize>
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where
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T: Copy,
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{
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data: [[T; N]; M], // Row-Major order
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}
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/// An alias for a [Matrix] with a single column
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pub type Vector<T, const N: usize> = Matrix<T, N, 1>;
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// CONSTRUCTORS
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// Default
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impl<T: Copy + Default, const M: usize, const N: usize> Default for Matrix<T, M, N> {
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fn default() -> Self {
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Matrix::fill(T::default())
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}
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}
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// Matrix constructors
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impl<T: Copy, const M: usize, const N: usize> Matrix<T, M, N> {
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/// Generate a new matrix from a 2D Array
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///
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/// # Arguments
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///
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/// * `data`: A 2D array of elements to copy into the new matrix
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///
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/// returns: Matrix<T, M, N>
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///
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/// # Examples
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///
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/// ```
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/// # use vector_victor::Matrix;
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/// let a = Matrix::mat([[1,2,3,4];4]);
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/// ```
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#[must_use]
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pub fn mat(data: [[T; N]; M]) -> Self {
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assert!(M > 0, "Matrix must have at least 1 row");
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assert!(N > 0, "Matrix must have at least 1 column");
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Matrix::<T, M, N> { data }
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}
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/// Generate a new matrix from a single scalar
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///
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/// # Arguments
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///
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/// * `scalar`: Scalar value to copy into the new matrix.
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///
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/// returns: Matrix<T, M, N>
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///
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/// # Examples
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///
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/// ```
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/// # use vector_victor::Matrix;
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/// let my_matrix = Matrix::<i32,4,4>::fill(5);
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/// // is equivalent to
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/// assert_eq!(my_matrix, Matrix::mat([[5;4];4]))
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/// ```
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#[must_use]
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pub fn fill(scalar: T) -> Matrix<T, M, N> {
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assert!(M > 0, "Matrix must have at least 1 row");
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assert!(N > 0, "Matrix must have at least 1 column");
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Matrix::<T, M, N> {
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data: [[scalar; N]; M],
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}
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}
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/// Create a matrix from an iterator of vectors
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///
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/// # Arguments
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///
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/// * `iter`: iterator of vectors to copy into rows
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///
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/// returns: Matrix<T, M, N>
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///
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/// # Examples
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///
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/// ```
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/// # use vector_victor::Matrix;
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/// let my_matrix = Matrix::mat([[1,2,3],[4,5,6]]);
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/// let transpose : Matrix<_,3,2>= Matrix::from_rows(my_matrix.cols());
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/// assert_eq!(transpose, Matrix::mat([[1,4],[2,5],[3,6]]))
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/// ```
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#[must_use]
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pub fn from_rows<I>(iter: I) -> Self
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where
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I: IntoIterator<Item = Vector<T, N>>,
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Self: Default,
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{
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let mut result = Self::default();
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for (m, row) in iter.into_iter().enumerate().take(M) {
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result.set_row(m, &row)
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}
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result
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}
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/// Create a matrix from an iterator of vectors
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///
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/// # Arguments
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///
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/// * `iter`: iterator of vectors to copy into columns
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///
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/// returns: Matrix<T, M, N>
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///
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/// # Examples
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///
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/// ```
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/// # use vector_victor::Matrix;
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/// let my_matrix = Matrix::mat([[1,2,3],[4,5,6]]);
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/// let transpose : Matrix<_,3,2>= Matrix::from_cols(my_matrix.rows());
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/// assert_eq!(transpose, Matrix::mat([[1,4],[2,5],[3,6]]))
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/// ```
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#[must_use]
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pub fn from_cols<I>(iter: I) -> Self
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where
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I: IntoIterator<Item = Vector<T, M>>,
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Self: Default,
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{
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let mut result = Self::default();
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for (n, col) in iter.into_iter().enumerate().take(N) {
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result.set_col(n, &col)
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}
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result
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}
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}
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// Vector constructor
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impl<T: Copy, const N: usize> Vector<T, N> {
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/// Create a vector from a 1D array.
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/// Note that vectors are always column vectors unless explicitly instantiated as row vectors
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///
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/// # Examples
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/// ```
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/// # use vector_victor::{Matrix, Vector};
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/// let my_vector = Vector::vec([1,2,3,4]);
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/// // is equivalent to
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/// assert_eq!(my_vector, Matrix::mat([[1],[2],[3],[4]]));
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/// ```
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pub fn vec(data: [T; N]) -> Self {
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assert!(N > 0, "Vector must have at least 1 element");
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return Vector::<T, N> {
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data: data.map(|e| [e]),
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};
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}
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}
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// ACCESSORS AND MUTATORS
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impl<T: Copy, const M: usize, const N: usize> Matrix<T, M, N> {
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/// Returns an iterator over the elements of the matrix in row-major order.
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///
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/// # Examples
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/// ```
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/// # use vector_victor::Matrix;
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/// let my_matrix = Matrix::mat([[1,2],[3,4]]);
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/// assert!(vec![1,2,3,4].iter().eq(my_matrix.elements()))
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/// ```
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#[must_use]
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pub fn elements<'a>(&'a self) -> impl Iterator<Item = &'a T> + 'a {
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self.data.iter().flatten()
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}
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/// Returns a mutable iterator over the elements of the matrix in row-major order.
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#[must_use]
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pub fn elements_mut<'a>(&'a mut self) -> impl Iterator<Item = &'a mut T> + 'a {
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self.data.iter_mut().flatten()
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}
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/// returns an iterator over the elements along the diagonal of a matrix
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#[must_use]
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pub fn diagonals<'s>(&'s self) -> impl Iterator<Item = T> + 's {
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(0..min(N, M)).map(|n| self[(n, n)])
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}
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/// Returns an iterator over the elements directly below the diagonal of a matrix
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#[must_use]
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pub fn subdiagonals<'s>(&'s self) -> impl Iterator<Item = T> + 's {
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(0..min(N, M) - 1).map(|n| self[(n, n + 1)])
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}
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/// Returns a reference to the element at that position in the matrix, or `None` if out of bounds.
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///
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/// # Examples
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///
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/// ```
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/// # use vector_victor::Matrix;
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/// let my_matrix = Matrix::mat([[1,2],[3,4]]);
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///
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/// // element at index 2 is the same as the element at (row 1, column 0).
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/// assert_eq!(my_matrix.get(2), my_matrix.get((1,0)));
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///
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/// // my_matrix.get() is equivalent to my_matrix[],
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/// // but returns an Option instead of panicking
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/// assert_eq!(my_matrix.get(2), Some(&my_matrix[2]));
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///
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/// // index 4 is out of range, so get(4) returns None.
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/// assert_eq!(my_matrix.get(4), None);
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/// ```
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#[inline]
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#[must_use]
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pub fn get(&self, index: impl Index2D) -> Option<&T> {
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let (m, n) = index.to_2d(M, N)?;
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Some(&self.data[m][n])
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}
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/// Returns a mutable reference to the element at that position in the matrix, or `None` if out of bounds.
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#[inline]
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#[must_use]
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pub fn get_mut(&mut self, index: impl Index2D) -> Option<&mut T> {
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let (m, n) = index.to_2d(M, N)?;
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Some(&mut self.data[m][n])
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}
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/// Returns a row of the matrix. or [None] if index is out of bounds
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///
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/// # Examples
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///
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/// ```
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/// # use vector_victor::{Matrix, Vector};
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/// let my_matrix = Matrix::mat([[1,2],[3,4]]);
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///
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/// // row at index 1
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/// assert_eq!(my_matrix.row(1), Vector::vec([3,4]));
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/// ```
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#[inline]
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#[must_use]
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pub fn row(&self, m: usize) -> Vector<T, N> {
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assert!(
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m < M,
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"Row index {} out of bounds for {}x{} matrix",
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m,
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M,
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N
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);
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Vector::<T, N>::vec(self.data[m])
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}
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#[inline]
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pub fn set_row(&mut self, m: usize, val: &Vector<T, N>) {
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assert!(
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m < M,
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"Row index {} out of bounds for {}x{} matrix",
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m,
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M,
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N
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);
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for n in 0..N {
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self.data[m][n] = val.data[n][0];
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}
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}
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pub fn pivot_row(&mut self, m1: usize, m2: usize) {
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let tmp = self.row(m2);
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self.set_row(m2, &self.row(m1));
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self.set_row(m1, &tmp);
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}
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#[inline]
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#[must_use]
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pub fn col(&self, n: usize) -> Vector<T, M> {
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assert!(
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n < N,
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"Column index {} out of bounds for {}x{} matrix",
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n,
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M,
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N
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);
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Vector::<T, M>::vec(self.data.map(|r| r[n]))
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}
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#[inline]
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pub fn set_col(&mut self, n: usize, val: &Vector<T, M>) {
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assert!(
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n < N,
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"Column index {} out of bounds for {}x{} matrix",
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n,
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M,
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N
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);
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for m in 0..M {
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self.data[m][n] = val.data[m][0];
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}
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}
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pub fn pivot_col(&mut self, n1: usize, n2: usize) {
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let tmp = self.col(n2);
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self.set_col(n2, &self.col(n1));
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self.set_col(n1, &tmp);
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}
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#[must_use]
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pub fn rows<'a>(&'a self) -> impl Iterator<Item = Vector<T, N>> + 'a {
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(0..M).map(|m| self.row(m))
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}
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#[must_use]
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pub fn cols<'a>(&'a self) -> impl Iterator<Item = Vector<T, M>> + 'a {
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(0..N).map(|n| self.col(n))
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}
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#[must_use]
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pub fn permute_rows(&self, ms: &Vector<usize, M>) -> Self
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where
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T: Default,
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{
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Self::from_rows(ms.elements().map(|&m| self.row(m)))
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}
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#[must_use]
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pub fn permute_cols(&self, ns: &Vector<usize, N>) -> Self
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where
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T: Default,
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{
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Self::from_cols(ns.elements().map(|&n| self.col(n)))
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}
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pub fn transpose(&self) -> Matrix<T, N, M>
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where
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Matrix<T, N, M>: Default,
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{
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Matrix::<T, N, M>::from_rows(self.cols())
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}
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}
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// Index
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impl<I, T, const M: usize, const N: usize> Index<I> for Matrix<T, M, N>
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where
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I: Index2D,
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T: Copy,
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{
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type Output = T;
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#[inline(always)]
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fn index(&self, index: I) -> &Self::Output {
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self.get(index).expect(&*format!(
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"index {:?} out of range for {}x{} Matrix",
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index, M, N
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))
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}
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}
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// IndexMut
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impl<I, T, const M: usize, const N: usize> IndexMut<I> for Matrix<T, M, N>
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where
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I: Index2D,
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T: Copy,
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{
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#[inline(always)]
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fn index_mut(&mut self, index: I) -> &mut Self::Output {
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self.get_mut(index).expect(&*format!(
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"index {:?} out of range for {}x{} Matrix",
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index, M, N
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))
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}
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}
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// CONVERSIONS
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// Convert from 2D Array (equivalent to new)
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impl<T: Copy, const M: usize, const N: usize> From<[[T; N]; M]> for Matrix<T, M, N> {
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fn from(data: [[T; N]; M]) -> Self {
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Self::mat(data)
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}
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}
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// Convert from 1D Array (equivalent to vec)
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impl<T: Copy, const M: usize> From<[T; M]> for Vector<T, M> {
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fn from(data: [T; M]) -> Self {
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Self::vec(data)
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}
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}
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// Convert from scalar (equivalent to fill)
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impl<T: Copy, const M: usize, const N: usize> From<T> for Matrix<T, M, N> {
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fn from(scalar: T) -> Self {
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Self::fill(scalar)
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}
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}
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// IntoIter
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impl<T: Copy, const M: usize, const N: usize> IntoIterator for Matrix<T, M, N> {
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type Item = T;
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type IntoIter = Flatten<std::array::IntoIter<[T; N], M>>;
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fn into_iter(self) -> Self::IntoIter {
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self.data.into_iter().flatten()
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}
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}
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// FromIterator
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impl<T: Copy, const M: usize, const N: usize> FromIterator<T> for Matrix<T, M, N>
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where
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Self: Default,
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{
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fn from_iter<I: IntoIterator<Item = T>>(iter: I) -> Self {
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let mut result: Self = Default::default();
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for (l, r) in zip(result.elements_mut(), iter) {
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*l = r;
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}
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result
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}
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}
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