Struct SquareMatrix 

pub struct SquareMatrix {
    pub entries: Vec<f64>,
    pub dim: usize,
}

A square matrix operator represented as a flat row-major array.

Fields

entries: Vec<f64>

Row-major entries.

dim: usize

Dimension (n x n).

Implementations

impl SquareMatrix

pub fn new(entries: Vec<f64>, dim: usize) -> Self

Create a new square matrix from row-major entries.

Panics if entries.len() != dim * dim.

pub fn identity(dim: usize) -> Self

The n x n identity matrix.

pub fn zero(dim: usize) -> Self

The n x n zero matrix.

pub fn get(&self, row: usize, col: usize) -> f64

Get entry at (row, col).

pub fn set(&mut self, row: usize, col: usize, val: f64)

Set entry at (row, col).

pub fn add(&self, other: &SquareMatrix) -> SquareMatrix

Matrix addition.

pub fn sub(&self, other: &SquareMatrix) -> SquareMatrix

Matrix subtraction.

pub fn scale(&self, s: f64) -> SquareMatrix

Scalar multiplication.

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

Matrix multiplication.

pub fn pow(&self, k: u32) -> SquareMatrix

Compute A^k (matrix exponentiation by repeated squaring).

pub fn operator_norm(&self) -> f64

The operator norm (approximated by the Frobenius norm).

pub fn frobenius_norm(&self) -> f64

The Frobenius norm: ||A||_F = sqrt(sum a_ij^2).

pub fn trace(&self) -> f64

The trace: sum of diagonal entries.

pub fn poly_eval(&self, poly: &Polynomial) -> SquareMatrix

Evaluate a polynomial at a matrix: p(A) = c_0 I + c_1 A + c_2 A^2 + …

Uses Horner’s method for efficiency: p(A) = (… ((c_n A + c_{n-1}) A + c_{n-2}) A + …) + c_0.

pub fn spectral_radius(&self, max_iter: u32) -> f64

Approximate spectral radius: r(A) = lim ||A^n||^{1/n}.

Computed by evaluating ||A^n||^{1/n} for increasing n and returning the value at max_iter.

pub fn resolvent_2x2(&self, lambda: f64) -> Option<SquareMatrix>

Compute the resolvent (lambda I - A)^{-1} for a 2x2 matrix using the explicit inverse formula.

Returns None if the matrix is not 2x2 or the determinant is zero (i.e., lambda is in the spectrum).

Trait Implementations

impl Clone for SquareMatrix

fn clone(&self) -> SquareMatrix

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SquareMatrix

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

Formats the value using the given formatter.