Struct matrix_basic::Matrix

pub struct Matrix<T: ToMatrix> { /* private fields */ }

A generic matrix struct (over any type with Add, Sub, Mul, Zero, Neg and Copy implemented). Look at from to see examples.

Implementations

impl<T: ToMatrix> 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

Returns the height of a matrix.

pub fn width(&self) -> usize

Returns the width of a matrix.

pub fn transpose(&self) -> Self

Returns the transpose of a matrix.

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

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

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

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) -> Self

Returns 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>

Returns the determinant of a square matrix. 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: One + PartialEq + Div<Output = T>,

Returns 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_in_field(), Ok(-2.0));

pub fn row_echelon(&self) -> Selfwhere T: PartialEq + Div<Output = T>,

Returns the row echelon form of a matrix over a field i.e. needs the Div trait.

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: PartialEq + Div<Output = T>,

Returns the column echelon form of a matrix over a field i.e. needs the Div trait. 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: PartialEq + Div<Output = T>,

Returns the reduced row echelon form of a matrix over a field i.e. needs the Div] trait.

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) -> Self

Creates a zero matrix of a given size.

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

Creates an identity matrix of a given size. It needs the One trait.

pub fn trace(self) -> Result<T, &'static str>

Returns the trace of a square matrix. 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.trace(), Ok(5));

pub fn diagonal_matrix(diag: Vec<T>) -> Self

Returns a diagonal matrix with a given diagonal.

Example

use matrix_basic::Matrix;
let m = Matrix::diagonal_matrix(vec![1, 2, 3]);
let n = Matrix::from(vec![vec![1, 0, 0], vec![0, 2, 0], vec![0, 0, 3]]).unwrap();

assert_eq!(m, n);

pub fn mul_scalar(&mut self, scalar: T)

Multiplies all entries of a matrix by a scalar. Note that it modifies the supplied matrix.

Example

use matrix_basic::Matrix;
let mut m = Matrix::from(vec![vec![1, 2, 0], vec![0, 2, 5], vec![0, 0, 3]]).unwrap();
let n = Matrix::from(vec![vec![2, 4, 0], vec![0, 4, 10], vec![0, 0, 6]]).unwrap();
m.mul_scalar(2);

assert_eq!(m, n);

pub fn inverse(&self) -> Result<Self, &'static str>where T: Div<Output = T> + One + PartialEq,

Returns the inverse of a square matrix. Throws an error if the 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();
let n = Matrix::from(vec![vec![-2.0, 1.0], vec![1.5, -0.5]]).unwrap();
assert_eq!(m.inverse(), Ok(n));

Trait Implementations

impl<T: Mul<Output = T> + ToMatrix> Add<Matrix<T>> for Matrix<T>

type Output = Matrix<T>

The resulting type after applying the + operator.

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

Performs the + operation.

impl<T: Clone + ToMatrix> 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 + ToMatrix> Debug for Matrix<T>

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

Formats the value using the given formatter.

impl<T: Debug + ToMatrix> Display for Matrix<T>

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

Formats the value using the given formatter.

impl<T: MatrixInto<S>, S: ToMatrix> MatrixFrom<T> for Matrix<S>

Blanket implementation of MatrixFrom for Matrix<S> whenever T (which is actually some)Matrix<U> implements MatrixInto<S>.

fn matrix_from(input: T) -> Self

Method for getting a matrix from another matrix of type Matrix<T>.

impl<T: ToMatrix, S: ToMatrix + Into<T>> MatrixInto<T> for Matrix<S>

Blanket implementation of MatrixInto for converting Matrix<S> to Matrix<T> whenever S implements [Into(T)]. Look at matrix_into.

fn matrix_into(self) -> Matrix<T>

Method for converting a matrix into a matrix of type Matrix<T>.

impl<T: Mul<Output = T> + ToMatrix> Mul<Matrix<T>> for Matrix<T>

type Output = Matrix<T>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: ToMatrix> Neg for Matrix<T>

type Output = Matrix<T>

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl<T: PartialEq + ToMatrix> 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: ToMatrix> Sub<Matrix<T>> for Matrix<T>

type Output = Matrix<T>

The resulting type after applying the - operator.

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

Performs the - operation.

impl<T: ToMatrix> StructuralPartialEq for Matrix<T>