Struct Matrix

pub struct Matrix { /* private fields */ }

Matrix with fractions as elements.

Implementations

impl Matrix

pub fn new() -> Self

Create a new matrix object.

pub fn create(row: usize, col: usize, value: Fraction) -> Self

Create a row x col matrix with all identical elements.

pub fn zeros(row: usize, col: usize) -> Self

Create a row x col matrix with all 0 elements.

pub fn ones(row: usize, col: usize) -> Self

Create a row x col matrix with all 1 elements.

pub fn identity(n: usize) -> Self

Generate an n-order identity matrix.

pub fn row_size(&self) -> usize

Return the number of rows in the matrix.

pub fn col_size(&self) -> usize

Return the number of columns in the matrix.

pub fn is_empty(&self) -> bool

Returns true if the matrix contains no elements.

pub fn is_symmetric(&self) -> bool

Returns true if the matrix is symmetric.

pub fn is_upper(&self) -> bool

Check if the matrix is upper triangular matrix.

pub fn is_lower(&self) -> bool

Check if the matrix is lower triangular matrix.

pub fn is_diagonal(&self) -> bool

Check if the matrix is diagonal matrix.

pub fn trace(&self) -> Fraction

Calculate the trace of the matrix.

pub fn transpose(&self) -> Self

Returns the transpose of the matrix.

pub fn row_echelon_form(&self) -> Self

Transform this matrix to general row echelon form.

pub fn row_canonical_form(&self) -> Self

Transform this matrix to reduced row echelon form.

pub fn det(&self) -> Fraction

Calculate the determinant of this matrix.

pub fn submatrix(&self, i: usize, j: usize) -> Self

Return the matrix that removed the i-th row and j-th column, 0 <= i, j < n.

pub fn minor(&self) -> Self

Return the minor matrix.

pub fn cofactor(&self) -> Self

Return the cofactor matrix.

pub fn adj(&self) -> Self

Return the adjugate matrix.

pub fn inv(&self) -> Option<Self>

Calculate the inverse of this matrix.

pub fn rank(&self) -> usize

Calculate the rank of this matrix.

pub fn lu_decomposition(&self) -> (Self, Self)

LU decomposition, use Doolittle algorithm.

pub fn split_row(&self, n: usize) -> (Self, Self)

Split this matrix by rows.

pub fn split_col(&self, n: usize) -> (Self, Self)

Split this matrix by columns.

pub fn expand_row(&mut self, matrix: Self) -> &Self

Expand this matrix by rows.

pub fn expand_col(&mut self, matrix: Self) -> &Self

Expand this matrix by columns.

pub fn e_row_swap(&mut self, i: usize, j: usize) -> &Self

Elementary Row Operations: Row Swap. (A[i] <=> A[j])

pub fn e_scalar_multiplication(&mut self, i: usize, k: Fraction) -> &Self

Elementary Row Operations: Scalar Multiplication. (A[i] *= k)

pub fn e_row_sum(&mut self, i: usize, j: usize, k: Fraction) -> &Self

Elementary Row Operations: Row Sum. (A[i] += A[j] * k)

Trait Implementations

impl Add<&Matrix> for &Matrix

type Output = Matrix

The resulting type after applying the + operator.

fn add(self, rhs: &Matrix) -> Self::Output

Performs the + operation.

impl Add<&Matrix> for Matrix

type Output = Matrix

The resulting type after applying the + operator.

fn add(self, rhs: &Matrix) -> Self::Output

Performs the + operation.

impl Add<Matrix> for &Matrix

type Output = Matrix

The resulting type after applying the + operator.

fn add(self, rhs: Matrix) -> Self::Output

Performs the + operation.

impl Add for Matrix

type Output = Matrix

The resulting type after applying the + operator.

fn add(self, rhs: Matrix) -> Self::Output

Performs the + operation.

impl AddAssign<&Matrix> for Matrix

fn add_assign(&mut self, rhs: &Matrix)

Performs the += operation.

impl AddAssign for Matrix

fn add_assign(&mut self, rhs: Matrix)

Performs the += operation.

impl Clone for Matrix

fn clone(&self) -> Matrix

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Matrix

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

Formats the value using the given formatter.

impl Default for Matrix

fn default() -> Matrix

Returns the “default value” for a type.

impl Display for Matrix

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

Formats the value using the given formatter.

impl<const R: usize, const C: usize> From<[[Fraction; C]; R]> for Matrix

fn from(value: [[Fraction; C]; R]) -> Self

Converts to this type from the input type.

impl<const R: usize, const C: usize> From<[[i32; C]; R]> for Matrix

fn from(value: [[i32; C]; R]) -> Self

Converts to this type from the input type.

impl From<Vec<Vec<Fraction>>> for Matrix

fn from(value: Vec<Vec<Fraction>>) -> Self

Converts to this type from the input type.

impl From<Vec<Vec<i32>>> for Matrix

fn from(value: Vec<Vec<i32>>) -> Self

Converts to this type from the input type.

impl Hash for Matrix

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl Index<usize> for Matrix

type Output = Vector

The returned type after indexing.

fn index(&self, index: usize) -> &Self::Output

Performs the indexing (container[index]) operation.

impl IndexMut<usize> for Matrix

fn index_mut(&mut self, index: usize) -> &mut Self::Output

Performs the mutable indexing (container[index]) operation.

impl IntoIterator for Matrix

type Item = Vector

The type of the elements being iterated over.

type IntoIter = IntoIter<<Matrix as IntoIterator>::Item>

Which kind of iterator are we turning this into?

fn into_iter(self) -> Self::IntoIter

Creates an iterator from a value.

impl Mul<&Matrix> for &Matrix

type Output = Matrix

The resulting type after applying the * operator.

fn mul(self, rhs: &Matrix) -> Self::Output

Performs the * operation.

impl Mul<&Matrix> for Matrix

type Output = Matrix

The resulting type after applying the * operator.

fn mul(self, rhs: &Matrix) -> Self::Output

Performs the * operation.

impl Mul<Fraction> for Matrix

type Output = Matrix

The resulting type after applying the * operator.

fn mul(self, rhs: Fraction) -> Self::Output

Performs the * operation.

impl Mul<Matrix> for &Matrix

type Output = Matrix

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix) -> Self::Output

Performs the * operation.

impl Mul<Matrix> for Fraction

type Output = Matrix

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix) -> Self::Output

Performs the * operation.

impl Mul<Matrix> for i32

type Output = Matrix

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix) -> Self::Output

Performs the * operation.

impl Mul<i32> for Matrix

type Output = Matrix

The resulting type after applying the * operator.

fn mul(self, rhs: i32) -> Self::Output

Performs the * operation.

impl Mul for Matrix

type Output = Matrix

The resulting type after applying the * operator.

fn mul(self, rhs: Matrix) -> Self::Output

Performs the * operation.

impl MulAssign<Fraction> for Matrix

fn mul_assign(&mut self, rhs: Fraction)

Performs the *= operation.

impl MulAssign<i32> for Matrix

fn mul_assign(&mut self, rhs: i32)

Performs the *= operation.

impl PartialEq for Matrix

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl Sub<&Matrix> for &Matrix

type Output = Matrix

The resulting type after applying the - operator.

fn sub(self, rhs: &Matrix) -> Self::Output

Performs the - operation.

impl Sub<&Matrix> for Matrix

type Output = Matrix

The resulting type after applying the - operator.

fn sub(self, rhs: &Matrix) -> Self::Output

Performs the - operation.

impl Sub<Matrix> for &Matrix

type Output = Matrix

The resulting type after applying the - operator.

fn sub(self, rhs: Matrix) -> Self::Output

Performs the - operation.

impl Sub for Matrix

type Output = Matrix

The resulting type after applying the - operator.

fn sub(self, rhs: Matrix) -> Self::Output

Performs the - operation.

impl SubAssign<&Matrix> for Matrix

fn sub_assign(&mut self, rhs: &Matrix)

Performs the -= operation.

impl SubAssign for Matrix

fn sub_assign(&mut self, rhs: Matrix)

Performs the -= operation.

impl Eq for Matrix

impl StructuralPartialEq for Matrix