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/*! * Generic matrix type. * * Matrices are generic over some type `T`. If `T` is [Numeric](../numeric/index.html) then * the matrix can be used in a mathematical way. */ use std::ops::{Add, Sub, Mul, Neg, Div}; pub mod iterators; pub mod slices; use crate::matrices::iterators::{ ColumnIterator, RowIterator, ColumnMajorIterator, ColumnReferenceIterator, RowReferenceIterator, ColumnMajorReferenceIterator}; use crate::matrices::slices::Slice2D; use crate::numeric::{Numeric, NumericRef}; use crate::linear_algebra; /** * A general purpose matrix of some type. This type may implement * no traits, in which case the matrix will be rather useless. If the * type implements [`Clone`](https://doc.rust-lang.org/std/clone/trait.Clone.html) * most storage and accessor methods are defined and if the type implements * [`Numeric`](../numeric/index.html) then the matrix can be used in * a mathematical way. * * When doing numeric operations with Matrices you should be careful to not * consume a matrix by accidentally using it by value. All the operations are * also defined on references to matrices so you should favor `&x * &y` style * notation for matrices you intend to continue using. * * # Matrix size invariants * * Matrices must always be at least 1x1. You cannot construct a matrix with no rows or * no columns, and any function that resizes matrices will error if you try to use it * in a way that would construct a 0x1, 1x0, or 0x0 matrix. The maximum size of a matrix * is dependent on the platform's `std::usize::MAX` value. Matrices with dimensions NxM * such that N * M < `std::usize::MAX` should not cause any errors in this library, but * expanding their size further may cause panics and or errors. At the time of writing it * is theoretically possible to construct and use matrices where the product of their number * of rows and columns exceed `std::usize::MAX` but this should not be relied upon and may * become an error in the future. Concerned readers should note that on a 64 bit computer this * maximum value is 18,446,744,073,709,551,615 so running out of memory is likely to occur first. */ #[derive(Debug)] pub struct Matrix<T> { data: Vec<Vec<T>> } /// The maximum row and column lengths are usize, due to the internal storage being backed by /// nested Vecs pub type Row = usize; pub type Column = usize; /** * Methods for matrices of any type, including non numerical types such as bool. */ impl <T> Matrix<T> { /** * Creates a unit (1x1) matrix from some element */ pub fn unit(value: T) -> Matrix<T> { Matrix { data: vec![vec![value]] } } /** * Creates a row vector (1xN) from a list */ pub fn row(values: Vec<T>) -> Matrix<T> { Matrix { data: vec![values] } } /** * Creates a column vector (Nx1) from a list */ pub fn column(values: Vec<T>) -> Matrix<T> { Matrix { data: values.into_iter().map(|x| vec![x]).collect() } } /** * Creates a matrix from a nested array of values, each inner vector * being a row, and hence the outer vector containing all rows in sequence, the * same way as when writing matrices in mathematics. * * Example of a 2 x 3 matrix in both notations: * ```ignore * [ * 1, 2, 4 * 8, 9, 3 * ] * ``` * ``` * use easy_ml::matrices::Matrix; * Matrix::from(vec![ * vec![ 1, 2, 4 ], * vec![ 8, 9, 3 ]]); * ``` */ pub fn from(values: Vec<Vec<T>>) -> Matrix<T> { assert!(!values.is_empty(), "No rows defined"); // check length of first row is > 1 assert!(!values[0].is_empty(), "No column defined"); // check length of each row is the same assert!(values.iter().map(|x| x.len()).all(|x| x == values[0].len()), "Inconsistent size"); Matrix { data: values } } /** * Returns the dimensionality of this matrix in Row, Column format */ pub fn size(&self) -> (Row, Column) { (self.data.len(), self.data[0].len()) } /** * Gets the number of rows in this matrix. */ pub fn rows(&self) -> Row { self.data.len() } /** * Gets the number of columns in this matrix. */ pub fn columns(&self) -> Column { self.data[0].len() } /** * Gets a reference to the value at this row and column. Rows and Columns are 0 indexed. */ pub fn get_reference(&self, row: Row, column: Column) -> &T { assert!(row < self.rows(), "Row out of index"); assert!(column < self.columns(), "Column out of index"); &self.data[row][column] } /** * Sets a new value to this row and column. Rows and Columns are 0 indexed. */ pub fn set(&mut self, row: Row, column: Column, value: T) { assert!(row < self.rows(), "Row out of index"); assert!(column < self.columns(), "Column out of index"); self.data[row][column] = value; } /** * Removes a row from this Matrix, shifting all other rows to the left. * Rows are 0 indexed. * * This will panic if the row does not exist or the matrix only has * one row. */ pub fn remove_row(&mut self, row: Row) { assert!(self.rows() > 1); self.data.remove(row); } /** * Removes a column from this Matrix, shifting all other columns to the left. * Columns are 0 indexed. * * This will panic if the column does not exist or the matrix only has * one column. */ pub fn remove_column(&mut self, column: Column) { assert!(self.columns() > 1); for row in 0..self.rows() { self.data[row].remove(column); } } /** * Returns an iterator over references to a column vector in this matrix. * Columns are 0 indexed. */ pub fn column_reference_iter(&self, column: Column) -> ColumnReferenceIterator<T> { ColumnReferenceIterator::new(self, column) } /** * Returns an iterator over references to a row vector in this matrix. * Rows are 0 indexed. */ pub fn row_reference_iter(&self, row: Row) -> RowReferenceIterator<T> { RowReferenceIterator::new(self, row) } /** * Returns a column major iterator over references to all values in this matrix, * proceeding through each column in order. */ pub fn column_major_reference_iter(&self) -> ColumnMajorReferenceIterator<T> { ColumnMajorReferenceIterator::new(self) } /** * Shrinks this matrix down from its current MxN size down to * some new size OxP where O and P are determined by the kind of * slice given and 1 <= O <= M and 1 <= P <= N. * * Only rows and columns specified by the slice will be retained, so for * instance if the Slice is constructed by * `Slice2D::new().rows(Slice::Range(0..2)).columns(Slice::Range(0..3))` then the * modified matrix will be no bigger than 2x3 and contain up to the first two * rows and first three columns that it previously had. * * See [Slice](./slices/enum.Slice.html) for constructing slices. * * # Panics * * This function will panic if the slice would delete all rows or all columns * from this matrix, ie the resulting matrix must be at least 1x1. */ pub fn retain_mut(&mut self, slice: Slice2D) { // iterate through rows and columns backwards so removing entries doesn't // invalidate the index for row in (0..self.rows()).rev() { for column in (0..self.columns()).rev() { if !slice.accepts(row, column) { self.data[row].remove(column); } } // delete empty rows if self.data[row].is_empty() { self.data.remove(row); } } assert!( !self.data.is_empty(), "Provided slice must leave at least 1 row in the retained matrix"); assert!( !self.data[0].is_empty(), "Provided slice must leave at least 1 column in the retained matrix"); // By construction jagged slices should be impossible, if this // invariant later changes by accident it would be possible to break the // rectangle shape invariant on a matrix object // As Slice2D should prevent the construction of jagged slices no // check is here to detect if all rows are still the same length } } /** * Methods for matrices with types that can be copied, but still not neccessarily numerical. */ impl <T: Clone> Matrix<T> { /** * Computes and returns the transpose of this matrix * * ``` * use easy_ml::matrices::Matrix; * let x = Matrix::from(vec![ * vec![ 1, 2 ], * vec![ 3, 4 ]]); * let y = Matrix::from(vec![ * vec![ 1, 3 ], * vec![ 2, 4 ]]); * assert_eq!(x.transpose(), y); * ``` */ pub fn transpose(&self) -> Matrix<T> { let mut result = Matrix::empty(self.get(0, 0), (self.columns(), self.rows())); for i in 0..self.columns() { for j in 0..self.rows() { result.set(i, j, self.get(j, i).clone()); } } result } /** * Transposes the matrix in place. * * ``` * use easy_ml::matrices::Matrix; * let mut x = Matrix::from(vec![ * vec![ 1, 2 ], * vec![ 3, 4 ]]); * x.transpose_mut(); * let y = Matrix::from(vec![ * vec![ 1, 3 ], * vec![ 2, 4 ]]); * assert_eq!(x, y); * ``` */ pub fn transpose_mut(&mut self) { for i in 0..self.rows() { for j in 0..self.columns() { if i > j { continue; } let temp = self.get(i, j); self.set(i, j, self.get(j, i)); self.set(j, i, temp); } } } /** * Returns an iterator over a column vector in this matrix. Columns are 0 indexed. * * If you have a matrix such as: * ```ignore * [ * 1, 2, 3 * 4, 5, 6 * 7, 8, 9 * ] * ``` * then a column of 0, 1, and 2 will yield [1, 4, 7], [2, 5, 8] and [3, 6, 9] * respectively. If you do not need to copy the elements use `column_reference_iter` * instead. */ pub fn column_iter(&self, column: Column) -> ColumnIterator<T> { ColumnIterator::new(self, column) } /** * Returns an iterator over a row vector in this matrix. Rows are 0 indexed. * * If you have a matrix such as: * ```ignore * [ * 1, 2, 3 * 4, 5, 6 * 7, 8, 9 * ] * ``` * then a row of 0, 1, and 2 will yield [1, 2, 3], [4, 5, 6] and [7, 8, 9] * respectively. If you do not need to copy the elements use `row_reference_iter` * instead. */ pub fn row_iter(&self, row: Row) -> RowIterator<T> { RowIterator::new(self, row) } /** * Returns a column major iterator over all values in this matrix, proceeding through each * column in order. * * If you have a matrix such as: * ```ignore * [ * 1, 2 * 3, 4 * ] * ``` * then the iterator will yield [1, 3, 2, 4]. If you do not need to copy the * elements use `column_major_reference_iter` instead. */ pub fn column_major_iter(&self) -> ColumnMajorIterator<T> { ColumnMajorIterator::new(self) } /** * Creates a matrix of the provided size with all elements initialised to the provided value */ pub fn empty(value: T, size: (Row, Column)) -> Matrix<T> { Matrix { data: vec![vec![value; size.1]; size.0] } } /** * Gets a copy of the value at this row and column. Rows and Columns are 0 indexed. */ pub fn get(&self, row: Row, column: Column) -> T { assert!(row < self.rows(), "Row out of index"); assert!(column < self.columns(), "Column out of index"); self.data[row][column].clone() } /** * Similar to matrix.get(0, 0) in that this returns the element in the first * row and first column, except that this method will panic if the matrix is * not 1x1. * * This is provided as a convenience function when you want to convert a unit matrix * to a scalar, such as after taking a dot product of two vectors. * * # Example * * ``` * use easy_ml::matrices::Matrix; * let x = Matrix::column(vec![ 1.0, 2.0, 3.0 ]); * let sum_of_squares: f64 = (x.transpose() * x).scalar(); * ``` */ pub fn scalar(&self) -> T { assert!(self.rows() == 1, "Cannot treat matrix as scalar as it has more than one row"); assert!(self.columns() == 1, "Cannot treat matrix as scalar as it has more than one column"); self.get(0, 0) } /** * Applies a function to all values in the matrix, modifying * the matrix in place. */ pub fn map_mut(&mut self, mapping_function: impl Fn(T) -> T) { for i in 0..self.rows() { for j in 0..self.columns() { self.set(i, j, mapping_function(self.get(i, j).clone())); } } } /** * Applies a function to all values and each value's index in the * matrix, modifying the matrix in place. */ pub fn map_mut_with_index(&mut self, mapping_function: impl Fn(T, Row, Column) -> T) { for i in 0..self.rows() { for j in 0..self.columns() { self.set(i, j, mapping_function(self.get(i, j).clone(), i, j)); } } } /** * Creates and returns a new matrix with all values from the original with the * function applied to each. This can be used to change the type of the matrix * such as creating a mask: * ``` * use easy_ml::matrices::Matrix; * let x = Matrix::from(vec![ * vec![ 0.0, 1.2 ], * vec![ 5.8, 6.9 ]]); * let y = x.map(|element| element > 2.0); * let result = Matrix::from(vec![ * vec![ false, false ], * vec![ true, true ]]); * assert_eq!(&y, &result); * ``` */ pub fn map<U>(&self, mapping_function: impl Fn(T) -> U) -> Matrix<U> where U: Clone { // compute the first mapped value so we have a value of type U // to initialise the mapped matrix with let first_value: U = mapping_function(self.get(0, 0)); let mut mapped = Matrix::empty(first_value, self.size()); for i in 0..self.rows() { for j in 0..self.columns() { mapped.set(i, j, mapping_function(self.get(i, j).clone())); } } mapped } /** * Creates and returns a new matrix with all values from the original * and the index of each value mapped by a function. This can be used * to perform elementwise operations that are not defined on the * Matrix type itself. * * # Exmples * * Matrix elementwise division: * * ``` * use easy_ml::matrices::Matrix; * let x = Matrix::from(vec![ * vec![ 9.0, 2.0 ], * vec![ 4.0, 3.0 ]]); * let y = Matrix::from(vec![ * vec![ 3.0, 2.0 ], * vec![ 1.0, 3.0 ]]); * let z = x.map_with_index(|x, row, column| x / y.get(row, column)); * let result = Matrix::from(vec![ * vec![ 3.0, 1.0 ], * vec![ 4.0, 1.0 ]]); * assert_eq!(&z, &result); * ``` */ pub fn map_with_index<U>(&self, mapping_function: impl Fn(T, Row, Column) -> U) -> Matrix<U> where U: Clone { // compute the first mapped value so we have a value of type U // to initialise the mapped matrix with let first_value: U = mapping_function(self.get(0, 0), 0, 0); let mut mapped = Matrix::empty(first_value, self.size()); for i in 0..self.rows() { for j in 0..self.columns() { mapped.set(i, j, mapping_function(self.get(i, j).clone(), i, j)); } } mapped } /** * Inserts a new row into the Matrix at the provided index, * shifting other rows to the right and filling all entries with the * provided value. Rows are 0 indexed. * * This will panic if the row is greater than the number of rows in the matrix. */ pub fn insert_row(&mut self, row: Row, value: T) { let new_row = vec![value; self.columns()]; self.data.insert(row, new_row); } /** * Inserts a new row into the Matrix at the provided index, shifting other rows * to the right and filling all entries with the values from the iterator in sequence. * Rows are 0 indexed. * * This will panic if the row is greater than the number of rows in the matrix, * or if the iterator has fewer elements than `self.columns()`. * * Example of duplicating a row: * ``` * use easy_ml::matrices::Matrix; * let x: Matrix<u8> = Matrix::row(vec![ 1, 2, 3 ]); * let mut y = x.clone(); * // duplicate the first row as the second row * y.insert_row_with(1, x.row_iter(0)); * assert_eq!((2, 3), y.size()); * let mut values = y.column_major_iter(); * assert_eq!(Some(1), values.next()); * assert_eq!(Some(1), values.next()); * assert_eq!(Some(2), values.next()); * assert_eq!(Some(2), values.next()); * assert_eq!(Some(3), values.next()); * assert_eq!(Some(3), values.next()); * assert_eq!(None, values.next()); * ``` */ pub fn insert_row_with<I>(&mut self, row: Row, values: I) where I: Iterator<Item = T> { let new_row = values.take(self.columns()).collect(); self.data.insert(row, new_row); } /** * Inserts a new column into the Matrix at the provided index, shifting other * columns to the right and filling all entries with the provided value. * Columns are 0 indexed. * * This will panic if the column is greater than the number of columns in the matrix. */ pub fn insert_column(&mut self, column: Column, value: T) { for row in 0..self.rows() { self.data[row].insert(column, value.clone()); } } /** * Inserts a new column into the Matrix at the provided index, shifting other columns * to the right and filling all entries with the values from the iterator in sequence. * Columns are 0 indexed. * * This will panic if the column is greater than the number of columns in the matrix, * or if the iterator has fewer elements than `self.rows()`. * * Example of duplicating a column: * ``` * use easy_ml::matrices::Matrix; * let x: Matrix<u8> = Matrix::column(vec![ 1, 2, 3 ]); * let mut y = x.clone(); * // duplicate the first column as the second column * y.insert_column_with(1, x.column_iter(0)); * assert_eq!((3, 2), y.size()); * let mut values = y.column_major_iter(); * assert_eq!(Some(1), values.next()); * assert_eq!(Some(2), values.next()); * assert_eq!(Some(3), values.next()); * assert_eq!(Some(1), values.next()); * assert_eq!(Some(2), values.next()); * assert_eq!(Some(3), values.next()); * assert_eq!(None, values.next()); * ``` */ pub fn insert_column_with<I>(&mut self, column: Column, mut values: I) where I: Iterator<Item = T> { for row in 0..self.rows() { self.data[row].insert(column, values.next().unwrap()); } } /** * Makes a copy of this matrix shrunk down in size according to the slice. See * [retain_mut](#method.retain_mut). */ pub fn retain(&self, slice: Slice2D) -> Matrix<T> { let mut retained = self.clone(); retained.retain_mut(slice); retained } } /** * Any matrix of a Cloneable type implements Clone. */ impl <T: Clone> Clone for Matrix<T> { fn clone(&self) -> Self { self.map(|element| element) } } // FIXME: conflicting implementations of trait `std::convert::TryInto<_>` for type `matrices::Matrix<_>` // /** // * An error indicating failure to convert a matrix to a scalar because it is not a unit matrix. // */ // pub struct ScalarConversionError; // // impl <T: Clone> std::convert::TryInto<T> for Matrix<T> { // /** // * Attempts to convert a unit matrix into a scalar. If the matrix is not 1x1 then // * an error is returned. // */ // fn try_into(&self) -> Result<T, ScalarConversionError> { // if self.rows() == 1 && self.columns() == 1 { // Ok(self.get(0, 0)) // } else { // Err(ScalarConversionError) // } // } // } /** * Methods for matrices with numerical types, such as f32 or f64. * * Note that unsigned integers are not Numeric because they do not * implement [Neg](https://doc.rust-lang.org/std/ops/trait.Neg.html). You must first * wrap unsigned integers via [Wrapping](https://doc.rust-lang.org/std/num/struct.Wrapping.html). * * While these methods will all be defined on signed integer types as well, such as i16 or i32, * in many cases integers cannot be used sensibly in these computations. If you * have a matrix of type i8 for example, you should consider mapping it into a floating * type before doing heavy linear algebra maths on it. * * Determinants can be computed without loss of precision using sufficiently large signed * integers because the only operations performed on the elements are addition, subtraction * and mulitplication. However the inverse of a matrix such as * * ```ignore * [ * 4, 7 * 2, 8 * ] * ``` * * is * * ```ignore * [ * 0.6, -0.7, * -0.2, 0.4 * ] * ``` * * which requires a type that supports decimals to accurately represent. * * Mapping matrix type example: * ``` * use easy_ml::matrices::Matrix; * use std::num::Wrapping; * * let matrix: Matrix<u8> = Matrix::from(vec![ * vec![ 2, 3 ], * vec![ 6, 0 ] * ]); * // determinant is not defined on this matrix because u8 is not Numeric * // println!("{:?}", matrix.determinant()); // won't compile * // however Wrapping<u8> is numeric * let matrix = matrix.map(|element| Wrapping(element)); * println!("{:?}", matrix.determinant()); // -> 238 (overflow) * println!("{:?}", matrix.map(|element| element.0 as i16).determinant()); // -> -18 * println!("{:?}", matrix.map(|element| element.0 as f32).determinant()); // -> -18.0 * ``` */ impl <T: Numeric> Matrix<T> where for<'a> &'a T: NumericRef<T> { /** * Returns the determinant of this square matrix, or None if the matrix * does not have a determinant. See [`linear_algebra`](../linear_algebra/fn.determinant.html) */ pub fn determinant(&self) -> Option<T> { linear_algebra::determinant(self) } /** * Computes the inverse of a matrix provided that it exists. To have an inverse a * matrix must be square (same number of rows and columns) and it must also have a * non zero determinant. See [`linear_algebra`](../linear_algebra/fn.inverse.html) */ pub fn inverse(&self) -> Option<Matrix<T>> where T: Add<Output = T> + Mul<Output = T> + Sub<Output = T> + Div<Output = T> { linear_algebra::inverse(self) } /** * Computes the covariance matrix for this NxM feature matrix, in which * each N'th row has M features to find the covariance and variance of. See * [`linear_algebra`](../linear_algebra/fn.covariance_column_features.html) */ pub fn covariance_column_features(&self) -> Matrix<T> { linear_algebra::covariance_column_features(self) } /** * Computes the covariance matrix for this NxM feature matrix, in which * each M'th column has N features to find the covariance and variance of. See * [`linear_algebra`](../linear_algebra/fn.covariance_row_features.html) */ pub fn covariance_row_features(&self) -> Matrix<T> { linear_algebra::covariance_row_features(self) } } // FIXME: want this to be callable in the main numeric impl block impl <T: Numeric> Matrix<T> { /** * Creates a diagonal matrix of the provided size with the diagonal elements * set to the provided value and all other elements in the matrix set to 0. * A diagonal matrix is always square. * * The size is still taken as a tuple to facilitate creating a diagonal matrix * from the dimensionality of an existing one. If the provided value is 1 then * this will create an identity matrix. * * A 3 x 3 identity matrix: * ```ignore * [ * 1, 0, 0 * 0, 1, 0 * 0, 0, 1 * ] * ``` */ pub fn diagonal(value: T, size: (Row, Column)) -> Matrix<T> { assert!(size.0 == size.1); let mut matrix = Matrix { data: vec![vec![T::zero(); size.1]; size.0] }; for i in 0..size.0 { matrix.set(i, i, value.clone()); } matrix } } /** * PartialEq is implemented as two matrices are equal if and only if all their elements * are equal and they have the same size. */ impl <T: PartialEq> PartialEq for Matrix<T> { fn eq(&self, other: &Self) -> bool { if self.rows() != other.rows() { return false; } if self.columns() != other.columns() { return false; } // perform elementwise check, return true only if every element in // each matrix is the same self.data.iter() .zip(other.data.iter()) .all(|(x, y)| x.iter().zip(y.iter()).all(|(a, b)| a == b)) } } /** * Matrix multiplication for two referenced matrices. * * This is matrix multiplication such that a matrix of dimensionality (LxM) multiplied with * a matrix of dimensionality (MxN) yields a new matrix of dimensionality (LxN) with each element * corresponding to the sum of products of the ith row in the first matrix and the jth column in * the second matrix. * * Matrices of the wrong sizes will result in a panic. No broadcasting is performed, ie you cannot * multiply a (NxM) matrix by a (Nx1) column vector, you must transpose one of the arguments so * that the operation is valid. */ impl <T: Numeric> Mul for &Matrix<T> where for<'a> &'a T: NumericRef<T> { // Tell the compiler our output type is another matrix of type T type Output = Matrix<T>; fn mul(self, rhs: Self) -> Self::Output { // LxM * MxN -> LxN assert!(self.columns() == rhs.rows(), "Mismatched Matrices, left is {}x{}, right is {}x{}, * is only defined for MxN * NxL", self.rows(), self.columns(), rhs.rows(), rhs.columns()); let mut result = Matrix::empty(self.get(0, 0), (self.rows(), rhs.columns())); for i in 0..self.rows() { for j in 0..rhs.columns() { // compute dot product for each element in the new matrix result.set(i, j, self.row_reference_iter(i) .zip(rhs.column_reference_iter(j)) .map(|(x, y)| x * y) .sum()); } } result } } /** * Matrix multiplication for two matrices. */ impl <T: Numeric> Mul for Matrix<T> where for<'a> &'a T: NumericRef<T> { type Output = Matrix<T>; fn mul(self, rhs: Self) -> Self::Output { &self * &rhs } } /** * Matrix multiplication for two matrices with one referenced. */ impl <T: Numeric> Mul<&Matrix<T>> for Matrix<T> where for<'a> &'a T: NumericRef<T> { type Output = Matrix<T>; fn mul(self, rhs: &Self) -> Self::Output { &self * rhs } } /** * Matrix multiplication for two matrices with one referenced. */ impl <T: Numeric> Mul<Matrix<T>> for &Matrix<T> where for<'a> &'a T: NumericRef<T> { type Output = Matrix<T>; fn mul(self, rhs: Matrix<T>) -> Self::Output { self * &rhs } } /** * Elementwise addition for two referenced matrices. */ impl <T: Numeric> Add for &Matrix<T> where for<'a> &'a T: NumericRef<T> { // Tell the compiler our output type is another matrix of type T type Output = Matrix<T>; fn add(self, rhs: Self) -> Self::Output { // LxM + LxM -> LxM assert!(self.size() == rhs.size(), "Mismatched Matrices, left is {}x{}, right is {}x{}, + is only defined for MxN + MxN", self.rows(), self.columns(), rhs.rows(), rhs.columns()); let mut result = Matrix::empty(self.get(0, 0), self.size()); for i in 0..self.rows() { for j in 0..self.columns() { result.set(i, j, self.get_reference(i, j) + rhs.get_reference(i, j)); } } result } } /** * Elementwise addition for two matrices. */ impl <T: Numeric> Add for Matrix<T> where for<'a> &'a T: NumericRef<T> { type Output = Matrix<T>; fn add(self, rhs: Self) -> Self::Output { &self + &rhs } } /** * Elementwise addition for two matrices with one referenced. */ impl <T: Numeric> Add<&Matrix<T>> for Matrix<T> where for<'a> &'a T: NumericRef<T> { type Output = Matrix<T>; fn add(self, rhs: &Self) -> Self::Output { &self + rhs } } /** * Elementwise addition for two matrices with one referenced. */ impl <T: Numeric> Add<Matrix<T>> for &Matrix<T> where for<'a> &'a T: NumericRef<T> { type Output = Matrix<T>; fn add(self, rhs: Matrix<T>) -> Self::Output { self + &rhs } } /** * Elementwise subtraction for two referenced matrices. */ impl <T: Numeric> Sub for &Matrix<T> where for<'a> &'a T: NumericRef<T> { // Tell the compiler our output type is another matrix of type T type Output = Matrix<T>; fn sub(self, rhs: Self) -> Self::Output { // LxM - LxM -> LxM assert!(self.size() == rhs.size(), "Mismatched Matrices, left is {}x{}, right is {}x{}, - is only defined for MxN - MxN", self.rows(), self.columns(), rhs.rows(), rhs.columns()); let mut result = Matrix::empty(self.get(0, 0), self.size()); for i in 0..self.rows() { for j in 0..self.columns() { result.set(i, j, self.get_reference(i, j) - rhs.get_reference(i, j)); } } result } } /** * Elementwise subtraction for two matrices. */ impl <T: Numeric> Sub for Matrix<T> where for<'a> &'a T: NumericRef<T> { type Output = Matrix<T>; fn sub(self, rhs: Self) -> Self::Output { &self - &rhs } } /** * Elementwise subtraction for two matrices with one referenced. */ impl <T: Numeric> Sub<&Matrix<T>> for Matrix<T> where for<'a> &'a T: NumericRef<T> { type Output = Matrix<T>; fn sub(self, rhs: &Self) -> Self::Output { &self - rhs } } /** * Elementwise subtraction for two matrices with one referenced. */ impl <T: Numeric> Sub<Matrix<T>> for &Matrix<T> where for<'a> &'a T: NumericRef<T> { type Output = Matrix<T>; fn sub(self, rhs: Matrix<T>) -> Self::Output { self - &rhs } } /** * Elementwise negation for a referenced matrix. */ impl <T: Numeric> Neg for &Matrix<T> where for<'a> &'a T: NumericRef<T> { // Tell the compiler our output type is another matrix of type T type Output = Matrix<T>; fn neg(self) -> Self::Output { self.map(|v| -v) } } /** * Elementwise negation for a matrix. */ impl <T: Numeric> Neg for Matrix<T> where for<'a> &'a T: NumericRef<T> { // Tell the compiler our output type is another matrix of type T type Output = Matrix<T>; fn neg(self) -> Self::Output { - &self } }