Struct Matrix

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pub struct Matrix { /* private fields */ }

Expand description

A dense matrix stored in row-major order.

Implementations§

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impl Matrix

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pub fn zeros(rows: usize, cols: usize) -> Self

Creates a new matrix with the given dimensions, initialized to zero.

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pub fn identity(size: usize) -> Self

Creates a new identity matrix of the given size.

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pub fn from_rows(rows: Vec<Vec<Rational64>>) -> Self

Creates a new matrix from a Vec of row vectors.

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pub fn from_vec(rows: usize, cols: usize, data: Vec<Rational64>) -> Self

Creates a new matrix from a flat array in row-major order.

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pub fn nrows(&self) -> usize

Returns the number of rows.

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pub fn ncols(&self) -> usize

Returns the number of columns.

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pub fn get(&self, row: usize, col: usize) -> Rational64

Gets the element at position (row, col).

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pub fn set(&mut self, row: usize, col: usize, value: Rational64)

Sets the element at position (row, col).

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pub fn row(&self, row: usize) -> &[Rational64] ⓘ

Gets a reference to a row.

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pub fn swap_rows(&mut self, i: usize, j: usize)

Swaps two rows.

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pub fn add_row_multiple(&mut self, i: usize, j: usize, scalar: Rational64)

Adds a scalar multiple of one row to another: row_i += scalar * row_j

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pub fn scale_row(&mut self, row: usize, scalar: Rational64)

Multiplies a row by a scalar.

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pub fn mul_vec(&self, v: &[Rational64]) -> Vec<Rational64> ⓘ

Matrix-vector multiplication: returns A * v

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pub fn mul(&self, other: &Matrix) -> Matrix

Matrix-matrix multiplication: returns A * B

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pub fn transpose(&self) -> Matrix

Transposes the matrix.

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pub fn gaussian_elimination(&self) -> (Matrix, usize)

Performs Gaussian elimination with partial pivoting. Returns the row-echelon form and the rank of the matrix.

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pub fn lu_decomposition(&self) -> Option<(Matrix, Matrix, Vec<usize>)>

Performs LU decomposition with partial pivoting. Returns (L, U, P) where P is a permutation vector.

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pub fn solve(&self, b: &[Rational64]) -> Option<Vec<Rational64>>

Solves a linear system Ax = b using Gaussian elimination with back substitution. Returns None if the system has no unique solution.

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pub fn determinant(&self) -> Option<Rational64>

Computes the determinant using LU decomposition.

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pub fn qr_decomposition(&self) -> Option<(Matrix, Matrix)>

Performs QR decomposition using the modified Gram-Schmidt process. Returns (Q, R) where Q has orthogonal columns and R is upper triangular such that QR = A.

§Note

Since we’re working with exact rational arithmetic and can’t compute square roots, Q will not be orthonormal in the traditional sense. Instead, Q contains unnormalized orthogonal vectors, and R is adjusted accordingly so that QR = A holds exactly.

Specifically: R[j,j] = 1 and the j-th column of Q has squared norm stored implicitly.

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pub fn cholesky_decomposition(&self) -> Option<Matrix>

Performs Cholesky decomposition for symmetric positive definite matrices. Returns L where A = L * L^T and L is lower triangular.

§Returns

None if the matrix is not square, symmetric, or positive definite.

§Note

This requires taking square roots, which may not be exact for rationals. The function will fail (return None) if any diagonal element during decomposition is not a perfect rational square.

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pub fn inverse(&self) -> Option<Matrix>

Computes the inverse of a square matrix using LU decomposition. Returns None if the matrix is singular (non-invertible).

§Algorithm

Uses LU decomposition with partial pivoting to solve AX = I, where I is the identity matrix. Each column of the inverse is computed by solving a system with the corresponding column of I.

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