Struct matrix_basic::Matrix

pub struct Matrix<T: Mul + Add + Sub> { /* private fields */ }

A generic matrix struct (over any type with addition, substraction and multiplication defined on it). Look at from to see examples.

Implementations

impl<T: Mul + Add + Sub> Matrix<T>

pub fn from(entries: Vec<Vec<T>>) -> Result<Matrix<T>, &'static str>

Creates a matrix from given 2D “array” in a Vec<Vec<T>> form. It’ll throw an error if all the given rows aren’t of the same size.

Example

use matrix_basic::Matrix;
let m = Matrix::from(vec![vec![1,2,3], vec![4,5,6]]);

will create the following matrix:
⌈1,2,3⌉
⌊4,5,6⌋

pub fn height(&self) -> usize

Return the height of a matrix.

pub fn width(&self) -> usize

Return the width of a matrix.

pub fn transpose(&self) -> Selfwhere T: Copy,

Return the transpose of a matrix.

pub fn rows(&self) -> &Vec<Vec<T>>

Return a reference to the rows of a matrix as &Vec<Vec<T>>.

pub fn columns(&self) -> Vec<Vec<T>>where T: Copy,

Return the columns of a matrix as Vec<Vec<T>>.

pub fn is_square(&self) -> bool

Return true if a matrix is square and false otherwise.

pub fn submatrix(&self, row: usize, col: usize) -> Selfwhere T: Copy,

Return a matrix after removing the provided row and column from it. Note: Row and column numbers are 0-indexed.

Example

use matrix_basic::Matrix;
let m = Matrix::from(vec![vec![1,2,3],vec![4,5,6]]).unwrap();
let n = Matrix::from(vec![vec![5,6]]).unwrap();
assert_eq!(m.submatrix(0,0),n);

pub fn det(&self) -> Result<T, &'static str>where T: Copy + Mul<Output = T> + Sub<Output = T> + Zero,

Return the determinant of a square matrix. This method additionally requires Zero, One and Copy traits. Also, we need that the Mul and Add operations return the same type T. This uses basic recursive algorithm using cofactor-minor. See det_in_field for faster determinant calculation in fields. It’ll throw an error if the provided matrix isn’t square.

Example

use matrix_basic::Matrix;
let m = Matrix::from(vec![vec![1,2],vec![3,4]]).unwrap();
assert_eq!(m.det(),Ok(-2));

pub fn det_in_field(&self) -> Result<T, &'static str>where T: Copy + Mul<Output = T> + Sub<Output = T> + Zero + One + PartialEq + Div<Output = T>,

Return the determinant of a square matrix over a field i.e. needs One and Div traits. See det for determinants in rings. This method uses row reduction as is much faster. It’ll throw an error if the provided matrix isn’t square.

Example

use matrix_basic::Matrix;
let m = Matrix::from(vec![vec![1.0,2.0],vec![3.0,4.0]]).unwrap();
assert_eq!(m.det(),Ok(-2.0));

pub fn row_echelon(&self) -> Selfwhere T: Copy + Mul<Output = T> + Sub<Output = T> + Zero + One + PartialEq + Div<Output = T>,

Returns the row echelon form of a matrix over a field i.e. needs One and Div traits.

Example

use matrix_basic::Matrix;
let m = Matrix::from(vec![vec![1.0,2.0,3.0],vec![3.0,4.0,5.0]]).unwrap();
let n = Matrix::from(vec![vec![1.0,2.0,3.0], vec![0.0,-2.0,-4.0]]).unwrap();
assert_eq!(m.row_echelon(),n);

pub fn column_echelon(&self) -> Selfwhere T: Copy + Mul<Output = T> + Sub<Output = T> + Zero + One + PartialEq + Div<Output = T>,

Returns the column echelon form of a matrix over a field i.e. needs One and Div traits. It’s just the transpose of the row echelon form of the transpose. See row_echelon and transpose.

pub fn reduced_row_echelon(&self) -> Selfwhere T: Copy + Mul<Output = T> + Sub<Output = T> + Zero + One + PartialEq + Div<Output = T> + Display + Debug,

Returns the reduced row echelon form of a matrix over a field i.e. needs One and Div traits.

Example

use matrix_basic::Matrix;
let m = Matrix::from(vec![vec![1.0,2.0,3.0],vec![3.0,4.0,5.0]]).unwrap();
let n = Matrix::from(vec![vec![1.0,2.0,3.0], vec![0.0,1.0,2.0]]).unwrap();
assert_eq!(m.reduced_row_echelon(),n);

pub fn zero(height: usize, width: usize) -> Selfwhere T: Zero,

Creates a zero matrix of a given size.

pub fn identity(size: usize) -> Selfwhere T: Zero + One,

Creates an identity matrix of a given size.

Trait Implementations

impl<T: Add<Output = T> + Sub + Mul + Copy + Zero> Add<Matrix<T>> for Matrix<T>

type Output = Matrix<T>

The resulting type after applying the + operator.

fn add(self, other: Self) -> Self

Performs the + operation.

impl<T: Clone + Mul + Add + Sub> Clone for Matrix<T>

fn clone(&self) -> Matrix<T>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<T: Debug + Mul + Add + Sub> Debug for Matrix<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Debug + Mul + Add + Sub> Display for Matrix<T>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<T: Mul<Output = T> + Add + Sub + Copy + Zero> Mul<Matrix<T>> for Matrix<T>

type Output = Matrix<T>

The resulting type after applying the * operator.

fn mul(self, other: Self) -> Self

Performs the * operation.

impl<T: PartialEq + Mul + Add + Sub> PartialEq<Matrix<T>> for Matrix<T>

fn eq(&self, other: &Matrix<T>) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<T: Add + Sub<Output = T> + Mul + Copy + Zero> Sub<Matrix<T>> for Matrix<T>

type Output = Matrix<T>

The resulting type after applying the - operator.

fn sub(self, other: Self) -> Self

Performs the - operation.

impl<T: Mul + Add + Sub> StructuralPartialEq for Matrix<T>