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//! This crate provides a stack-allocated, constant-size [`Matrix<T, M, N>`]
//! type implemented using const generics.
//!
//! # 🚀 Getting started
//!
//! Add this crate to your Cargo manifest.
//!
//! ```sh
//! cargo add vectrix
//! ```
//!
//! `no_std` is also supported by disabling the default std feature.
//!
//! ```sh
//! cargo add vectrix --no-default-features --features=macro
//! ```
//!
//! # 🤸 Usage
//!
//! ## Types
//!
//! The base [`Matrix<T, M, N>`] type represents a matrix with `M` rows and `N`
//! columns. This type is a backed by an array of arrays. The data is stored in
//! column-major order. Some convenient aliases are provided for common
//! matrices, like vectors.
//!
//! - [`Matrix<T, M, N>`] → a generic matrix type with `M` rows and `N` columns.
//! - [`Vector<T, M>`] → a column vector with `M` rows.
//! - [`RowVector<T, N>`] → a row vector with `N` columns.
//!
//! ## Macros
//!
//! Macros are provided for easy construction of the provided types. These
//! macros will also work in `const` contexts.
//!
//! - The [`matrix!`] macro can be used to construct a new [`Matrix`] of any
//! size.
//! ```
//! # use vectrix::*;
//! #
//! let m = matrix![
//! 1, 3, 5;
//! 2, 4, 6;
//! ];
//! ```
//!
//! In the above example `matrix` is a `Matrix<_, 2, 3>` type, having 2 rows and
//! 3 columns.
//!
//! - The [`vector!`] and [`row_vector!`] macros can be used to to construct
//! column and row vectors respectively.
//! ```
//! # use vectrix::*;
//! #
//! let v = vector![1, 3, 3, 7];
//! // ^ type `Vector<_, 4>`
//! assert_eq!(v, matrix![1; 3; 3; 7]);
//!
//! let v = row_vector![1, 3, 3, 7];
//! // ^^^^^^ type `RowVector<_, 4>`
//! assert_eq!(v, matrix![1, 3, 3, 7]);
//! ```
//!
//! ## Constructors
//!
//! Commonly used constructors are listed below.
//!
//! - [`::zero()`][`Matrix::zero()`] → constructs a new matrix filled with
//! [`T::zero()`][`Zero::zero()`].
//! - [`::identity()`][`Matrix::identity()`] → constructs a new identity matrix.
//! - [`::repeat(..)`][`Matrix::repeat()`] → constructs a new matrix filled with
//! the provided value.
//! - [`::repeat_with(..)`][`Matrix::repeat_with()`] → constructs a new matrix
//! filled with values computed by the provided closure.
//! - [`::from_iter(..)`][`core::iter::FromIterator::from_iter`] → constructs a
//! new matrix from an iterator.
//! - [`::new(..)`][`Matrix::new()`] → constructs a new vector using the
//! provided components.
//!
//! ## Accessing elements
//!
//! Three types of element access are available.
//!
//! - `usize` indexing selects the nth element in the matrix as viewed in
//! column-major order.
//! ```
//! # use vectrix::*;
//! #
//! let m = matrix![
//! 1, 2, 3;
//! 4, 5, 6;
//! ];
//! assert_eq!(m[1], 4);
//! ```
//!
//! - `(usize, usize)` indexing selects the element at a particular row and
//! column position.
//! ```
//! # use vectrix::*;
//! #
//! let m = matrix![
//! 1, 2, 3;
//! 4, 5, 6;
//! ];
//! assert_eq!(m[(1, 0)], 4);
//! ```
//!
//! - Component accessors are available for small vectors using traditional
//! names.
//! ```
//! # use vectrix::*;
//! #
//! let mut v = vector![1, 2, 3, 4, 0, 0];
//! v.y = 3;
//! v.w = 7;
//! assert_eq!(v.x, 1);
//! assert_eq!(v.y, 3);
//! assert_eq!(v.z, 3);
//! assert_eq!(v.w, 7);
//! assert_eq!(v.a, 0);
//! assert_eq!(v.b, 0);
//! ```
//!
//! ## Accessing a row or column
//!
//! You can get a reference to particular row or column using the
//! [`.row()`][`Matrix::row`] or [`.column()`][`Matrix::column`] methods. You
//! can get a mutable reference using the `_mut` variants.
//!
//! ```
//! # use vectrix::*;
//! #
//! let mut m = matrix![
//! 1, 2, 3;
//! 4, 7, 6;
//! ];
//! let row = m.row_mut(1);
//! row[1] = 5;
//! assert_eq!(m.column(1), &[2, 5]);
//! ```
//!
//! ## Iteration
//!
//! Element-wise, column-major order iteration is provided using the following
//! methods.
//!
//! - [`.into_iter()`][`Matrix::into_iter()`] → consumes the matrix and returns
//! an owned iterator over each element.
//! - [`.iter()`][`Matrix::iter()`] → returns an iterator over a reference to
//! each element.
//! - [`.iter_mut()`][`Matrix::iter_mut()`] → returns an iterator over a mutable
//! reference to each element.
//!
//! Iteration over rows and columns is provide using the following methods.
//!
//! - [`.iter_rows()`][`Matrix::iter_rows()`] → returns an iterator over a
//! reference to each row.
//! - [`.iter_rows_mut()`][`Matrix::iter_rows_mut()`] → returns an iterator over
//! mutable reference to each row.
//! - [`.iter_columns()`][`Matrix::iter_columns()`] → returns an iterator over a
//! reference to each column.
//! - [`.iter_columns_mut()`][`Matrix::iter_columns_mut()`] → returns an
//! iterator over a mutable reference to each column.
//!
//! ### Slice representation
//!
//! A slice view of the underlying data is provided using
//! [`.as_slice()`][`Matrix::as_slice`] and
//! [`.as_mut_slice()`][`Matrix::as_mut_slice`].
//! ```
//! # use vectrix::*;
//! #
//! let mut m = matrix![
//! 1, 3, 5;
//! 2, 3, 6;
//! ];
//! m.as_mut_slice()[3] = 4;
//! assert_eq!(m.as_slice(), &[1, 2, 3, 4, 5, 6]);
//! ```
//!
//! ## Debug
//!
//! The [`Debug`][`core::fmt::Debug`] implementation will print out vectors as
//! lists and matrices as a list of lists in column-major order.
//!
//! ```
//! # use vectrix::*;
//! #
//! let v = vector![1.1, 2.0];
//! let m = matrix![1, 2; 3, 4];
//! println!("vector: {:.2?}", v);
//! println!("matrix: {:?}", m);
//! ```
//!
//! This will output:
//!
//! ```text
//! vector: [1.10, 2.00]
//! matrix: [[1, 3], [2, 4]]
//! ```
//!
//! ## Display
//!
//! The [`Display`][`core::fmt::Display`] implementation will print out the
//! matrix in the traditional box bracket format. Precision is supported as well
//! as most of the other formatting traits like
//! [`LowerHex`][`core::fmt::LowerHex`].
//!
//! ```
//! # use vectrix::*;
//! #
//! let cv = vector![1.1, 2.0];
//! let rv = row_vector![1.1, 2.0];
//! let m = matrix![1, 2; 3, 4];
//! println!("column vector: {:.2}", cv);
//! println!("row vector: {:.1}", rv);
//! println!("matrix: {:b}", m);
//! ```
//!
//! This will output:
//!
//! ```text
//! column vector:
//! ┌ ┐
//! │ 1.10 │
//! │ 2.00 │
//! └ ┘
//!
//! row vector:
//! ┌ ┐
//! │ 1.1 2.0 │
//! └ ┘
//!
//! matrix:
//! ┌ ┐
//! │ 1 10 │
//! │ 11 100 │
//! └ ┘
//! ```
//!
//! ## Operations
//!
//! [`Matrix`] implements many built-in operators. With scalar operands almost
//! all operators are implemented and they simply apply the operation to each
//! element in the matrix. Unary operators will do the equivalent. In the
//! following example each element in the matrix is multiplied by 2.
//!
//! ```
//! # use vectrix::*;
//! #
//! let m = matrix![
//! 1, -3;
//! 3, -7;
//! ];
//! let exp = matrix![
//! 2, -6;
//! 6, -14;
//! ];
//! assert_eq!(m * 2, exp);
//! ```
//!
//! [`Matrix`] supports addition and subtraction with same size matrices for
//! element-wise addition and subtraction. In the following example a matrix
//! is added to itself.
//!
//! ```
//! # use vectrix::*;
//! #
//! let m = matrix![
//! 1, -3;
//! 3, -7;
//! ];
//! let exp = matrix![
//! 2, -6;
//! 6, -14;
//! ];
//! assert_eq!(m + m, exp);
//! ```
#![no_std]
#![warn(unsafe_op_in_unsafe_fn)]
#[cfg(feature = "std")]
extern crate std;
mod fmt;
mod index;
mod iter;
mod new;
mod ops;
mod traits;
mod vector;
mod view;
use core::iter::Sum;
use core::ops::*;
use core::slice;
#[doc(hidden)]
#[cfg(feature = "macro")]
pub use vectrix_macro as proc_macro;
pub use crate::index::MatrixIndex;
pub use crate::iter::{IntoIter, IterColumns, IterColumnsMut, IterRows, IterRowsMut};
pub use crate::traits::{Abs, One, Zero};
pub use crate::view::{Column, Row};
/// Represents a matrix with constant `M` rows and constant `N` columns.
///
/// The underlying data is represented as an array and is always stored in
/// column-major order.
///
/// See the [crate root][crate] for usage examples.
#[derive(Clone, Copy, PartialEq, Eq, Hash, PartialOrd, Ord)]
#[repr(transparent)]
pub struct Matrix<T, const M: usize, const N: usize> {
data: [[T; M]; N],
}
/// A matrix with one row and `N` columns.
pub type RowVector<T, const N: usize> = Matrix<T, 1, N>;
/// A matrix with one column and `M` rows.
pub type Vector<T, const M: usize> = Matrix<T, M, 1>;
////////////////////////////////////////////////////////////////////////////////
// Matrix<T, M, N> methods
////////////////////////////////////////////////////////////////////////////////
impl<T, const M: usize, const N: usize> Matrix<T, M, N> {
/// Create a new matrix from an array of arrays in column-major order.
#[doc(hidden)]
#[inline]
pub const fn from_column_major_order(data: [[T; M]; N]) -> Self {
Self { data }
}
/// Returns a zero matrix.
#[must_use]
#[inline]
pub fn zero() -> Self
where
T: Copy + Zero,
{
Self::repeat(T::zero())
}
/// Create a new matrix filled with the given element.
#[must_use]
#[inline]
pub fn repeat(element: T) -> Self
where
T: Copy,
{
Self {
data: [[element; M]; N],
}
}
/// Create a new matrix filled with computed elements.
///
/// Elements will be filled in column-major order.
#[must_use]
#[inline]
pub fn repeat_with<F>(f: F) -> Self
where
F: FnMut() -> T,
{
// SAFETY: the iterator will yield forever.
unsafe { new::collect_unchecked(core::iter::repeat_with(f)) }
}
/// Returns a raw pointer to the underlying data.
#[inline]
fn as_ptr(&self) -> *const T {
self.data.as_ptr() as *const T
}
/// Returns an unsafe mutable pointer to the underlying data.
#[inline]
fn as_mut_ptr(&mut self) -> *mut T {
self.data.as_mut_ptr() as *mut T
}
/// Views the underlying data as a contiguous slice.
#[inline]
pub fn as_slice(&self) -> &[T] {
unsafe { slice::from_raw_parts(self.as_ptr(), M * N) }
}
/// Views the underlying data as a contiguous mutable slice.
#[inline]
pub fn as_mut_slice(&mut self) -> &mut [T] {
unsafe { slice::from_raw_parts_mut(self.as_mut_ptr(), M * N) }
}
/// Returns a reference to an element in the matrix or `None` if out of
/// bounds.
#[inline]
pub fn get<I>(&self, i: I) -> Option<&I::Output>
where
I: MatrixIndex<Self>,
{
i.get(self)
}
/// Returns a mutable reference to an element in the matrix or `None` if out
/// of bounds.
#[inline]
pub fn get_mut<I>(&mut self, i: I) -> Option<&mut I::Output>
where
I: MatrixIndex<Self>,
{
i.get_mut(self)
}
/// Returns a reference to an element in the matrix without doing any bounds
/// checking.
///
/// # Safety
///
/// Calling this method with an out-of-bounds index is
/// *[undefined behavior]* even if the resulting reference is not used.
///
/// [undefined behavior]: https://doc.rust-lang.org/reference/behavior-considered-undefined.html
#[inline]
pub unsafe fn get_unchecked<I>(&self, i: I) -> &I::Output
where
I: MatrixIndex<Self>,
{
unsafe { &*i.get_unchecked(self) }
}
/// Returns a mutable reference to an element in the matrix without doing
/// any bounds checking.
///
/// # Safety
///
/// Calling this method with an out-of-bounds index is
/// *[undefined behavior]* even if the resulting reference is not used.
///
/// [undefined behavior]: https://doc.rust-lang.org/reference/behavior-considered-undefined.html
#[inline]
pub unsafe fn get_unchecked_mut<I>(&mut self, i: I) -> &mut I::Output
where
I: MatrixIndex<Self>,
{
unsafe { &mut *i.get_unchecked_mut(self) }
}
/// Returns a reference to the `i`-th row of this matrix.
#[inline]
pub fn row(&self, i: usize) -> &Row<T, M, N> {
Row::new(&self.as_slice()[i..])
}
/// Returns a mutable reference to the `i`-th row of this matrix.
#[inline]
pub fn row_mut(&mut self, i: usize) -> &mut Row<T, M, N> {
Row::new_mut(&mut self.as_mut_slice()[i..])
}
/// Returns a reference to the `i`-th column of this matrix.
#[inline]
pub fn column(&self, i: usize) -> &Column<T, M, N> {
Column::new(&self.data[i])
}
/// Returns a mutable reference to the `i`-th column of this matrix.
#[inline]
pub fn column_mut(&mut self, i: usize) -> &mut Column<T, M, N> {
Column::new_mut(&mut self.data[i])
}
/// Returns an iterator over the underlying data.
#[inline]
pub fn iter(&self) -> slice::Iter<'_, T> {
self.as_slice().iter()
}
/// Returns a mutable iterator over the underlying data.
#[inline]
pub fn iter_mut(&mut self) -> slice::IterMut<'_, T> {
self.as_mut_slice().iter_mut()
}
/// Returns an iterator over the rows in this matrix.
#[inline]
pub fn iter_rows(&self) -> IterRows<'_, T, M, N> {
IterRows::new(self)
}
/// Returns a mutable iterator over the rows in this matrix.
#[inline]
pub fn iter_rows_mut(&mut self) -> IterRowsMut<'_, T, M, N> {
IterRowsMut::new(self)
}
/// Returns an iterator over the columns in this matrix.
#[inline]
pub fn iter_columns(&self) -> IterColumns<'_, T, M, N> {
IterColumns::new(self)
}
/// Returns a mutable iterator over the columns in this matrix.
#[inline]
pub fn iter_columns_mut(&mut self) -> IterColumnsMut<'_, T, M, N> {
IterColumnsMut::new(self)
}
/// Returns a matrix of the same size as self, with function `f` applied to
/// each element in column-major order.
#[inline]
pub fn map<F, U>(self, f: F) -> Matrix<U, M, N>
where
F: FnMut(T) -> U,
{
// SAFETY: the iterator has the exact number of elements required.
unsafe { new::collect_unchecked(self.into_iter().map(f)) }
}
/// Returns the L1 norm of the matrix.
///
/// Also known as *Manhattan Distance* or *Taxicab norm*. L1 Norm is the sum
/// of the magnitudes of the vectors in a space.
///
/// # Note
///
/// If the matrix is a *row vector* this method might not do what you what
/// you expect. For example:
///
/// ```
/// # use vectrix::matrix;
/// #
/// let row_vector = matrix![1, 2, 3];
/// assert_eq!(row_vector.l1_norm(), 3);
///
/// let column_vector = matrix![1; 2; 3];
/// assert_eq!(column_vector.l1_norm(), 6);
/// ```
pub fn l1_norm(&self) -> T
where
T: Copy + Ord + Abs + Zero + Sum<T>,
{
(0..N)
.map(|i| self.data[i].iter().copied().map(Abs::abs).sum())
.max()
.unwrap_or_else(Zero::zero)
}
}
////////////////////////////////////////////////////////////////////////////////
// Matrix<T, N, N> methods
////////////////////////////////////////////////////////////////////////////////
impl<T, const N: usize> Matrix<T, N, N> {
/// Returns an identity matrix.
#[must_use]
#[inline]
pub fn identity() -> Self
where
T: Copy + One + Zero,
{
let mut matrix = Self::zero();
for i in 0..N {
matrix[(i, i)] = T::one();
}
matrix
}
/// Returns the diagonal of the matrix.
pub fn diagonal(&self) -> Vector<T, N>
where
T: Copy + Zero,
{
let mut vector = Vector::zero();
for i in 0..N {
vector[i] = self[(i, i)];
}
vector
}
}