Struct Matrix

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pub struct Matrix<D: EuclideanDomain> { /* private fields */ }

Expand description

A dense matrix with elements from a EuclideanDomain.

Elements are stored in row-major order.

§Example

use ocas_domain::{EuclideanDomain, IntegerDomain, Integer};
use ocas_poly::matrix::Matrix;

let d = IntegerDomain;
let a = Matrix::from_rows(vec![
    vec![Integer::from(1), Integer::from(1)],
    vec![Integer::from(1), Integer::from(-1)],
], d);
let b = vec![Integer::from(3), Integer::from(-1)];
let x = a.solve(&b).unwrap();
assert_eq!(x, vec![Integer::from(1), Integer::from(2)]);

Implementations§

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impl<D: EuclideanDomain> Matrix<D>

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pub fn new(nrows: usize, ncols: usize, data: Vec<D::Element>, domain: D) -> Self

Create a matrix from row-major data.

Panics if data.len() != nrows * ncols.

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pub fn zeros(nrows: usize, ncols: usize, domain: D) -> Self

Create a zero matrix of the given shape.

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pub fn identity(n: usize, domain: D) -> Self

Create an identity matrix of size n.

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pub fn from_rows(rows: Vec<Vec<D::Element>>, domain: D) -> Self

Create a matrix from nested row vectors.

Returns None if rows have inconsistent lengths.

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pub fn nrows(&self) -> usize

Return the number of rows.

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pub fn ncols(&self) -> usize

Return the number of columns.

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pub fn domain(&self) -> &D

Return a reference to the domain.

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

Swap two rows, starting from column start_col.

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pub fn augment(&self, other: &Matrix<D>) -> Result<Matrix<D>, MatrixError>

Horizontally concatenate self with other.

Both must have the same number of rows.

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pub fn row_echelon(&mut self, max_col: usize) -> usize

Perform fraction-free Gaussian elimination on the first max_col columns, putting the matrix in row echelon form. Returns the rank.

This mirrors Symbolica’s partial_row_reduce_fraction_free.

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pub fn back_substitution(&mut self, max_col: usize)

Perform fraction-free back substitution on a matrix already in row echelon form (mutating the first max_col columns).

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pub fn solve(&self, b: &[D::Element]) -> Result<Vec<D::Element>, MatrixError>

Solve the linear system Ax = b where A is self and b is a column vector represented as a slice.

Returns the solution vector x on success.

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pub fn into_rows(self) -> Vec<Vec<D::Element>>

Convert the matrix into a nested vector of rows.

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pub fn data(&self) -> &[D::Element]

Return a reference to the underlying row-major data.

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pub fn row(&self, i: usize) -> Vec<D::Element>

Return a copy of a single row as a vector.

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pub fn column(&self, j: usize) -> Vec<D::Element>

Return a copy of a single column as a vector.

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pub fn transpose(&self) -> Matrix<D>

Return the transpose of the matrix.

§Example

use ocas_domain::{Integer, IntegerDomain};
use ocas_poly::matrix::Matrix;

let d = IntegerDomain;
let a = Matrix::from_rows(vec![vec![Integer::from(1), Integer::from(2)]], d);
let t = a.transpose();
assert_eq!(t.nrows(), 2);
assert_eq!(t.ncols(), 1);
assert_eq!(t[(0, 0)], Integer::from(1));
assert_eq!(t[(1, 0)], Integer::from(2));

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pub fn trace(&self) -> Result<D::Element, MatrixError>

Return the trace (sum of the diagonal) of a square matrix.

Returns an error if the matrix is not square.

§Example

use ocas_domain::{Integer, IntegerDomain};
use ocas_poly::matrix::Matrix;

let d = IntegerDomain;
let a = Matrix::from_rows(
    vec![vec![Integer::from(1), Integer::from(2)], vec![Integer::from(3), Integer::from(4)]],
    d,
);
assert_eq!(a.trace().unwrap(), Integer::from(5));

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pub fn matmul(&self, other: &Matrix<D>) -> Result<Matrix<D>, MatrixError>

Compute the matrix product self * other.

Returns an error if self.ncols != other.nrows.

§Example

use ocas_domain::{Integer, IntegerDomain};
use ocas_poly::matrix::Matrix;

let d = IntegerDomain;
let a = Matrix::from_rows(vec![vec![Integer::from(1), Integer::from(2)]], d);
let b = Matrix::from_rows(vec![vec![Integer::from(3)], vec![Integer::from(4)]], d);
let c = a.matmul(&b).unwrap();
assert_eq!(c[(0, 0)], Integer::from(11));

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pub fn rank(&self) -> usize

Compute the rank of the matrix via fraction-free Gaussian elimination.

§Example

use ocas_domain::{Integer, IntegerDomain};
use ocas_poly::matrix::Matrix;

let d = IntegerDomain;
let a = Matrix::from_rows(
    vec![vec![Integer::from(1), Integer::from(2)], vec![Integer::from(2), Integer::from(4)]],
    d,
);
assert_eq!(a.rank(), 1);

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pub fn determinant(&self) -> Result<D::Element, MatrixError>

Compute the determinant of a square matrix using the Bareiss fraction-free algorithm with partial pivoting.

Returns an error if the matrix is not square.

§Example

use ocas_domain::{Integer, IntegerDomain};
use ocas_poly::matrix::Matrix;

let d = IntegerDomain;
let a = Matrix::from_rows(
    vec![vec![Integer::from(1), Integer::from(2)], vec![Integer::from(3), Integer::from(4)]],
    d,
);
assert_eq!(a.determinant().unwrap(), Integer::from(-2));

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pub fn inverse(&self) -> Result<Matrix<D>, MatrixError>

Compute the inverse of a square non-singular matrix.

Returns an error if the matrix is not square or is singular over the coefficient domain.

§Example

use ocas_domain::{Integer, IntegerDomain};
use ocas_poly::matrix::Matrix;

let d = IntegerDomain;
// Unimodular matrix: determinant 1, integer inverse exists.
let a = Matrix::from_rows(
    vec![vec![Integer::from(1), Integer::from(2)], vec![Integer::from(0), Integer::from(1)]],
    d,
);
let inv = a.inverse().unwrap();
assert_eq!(inv[(0, 0)], Integer::from(1));
assert_eq!(inv[(0, 1)], Integer::from(-2));
assert_eq!(inv[(1, 0)], Integer::from(0));
assert_eq!(inv[(1, 1)], Integer::from(1));