main.rs

//! # examples::main
//!
//! A simple demonstration of using this library.

#![warn(missing_docs)]

use rmatrix_ks::{
    matrix::{
        complex::{is_hermitian_matrix, moore_penrose_inverse},
        matrix::Matrix,
    },
    number::instances::{complex::Complex, float::Float},
};

fn main() {
    // Properties that the Moore-Penrose inverse must satisfy.
    let rect = Matrix::<Complex<Float>>::of(
        2,
        3,
        &[
            (1.0, 2.0),
            (2.0, -1.0),
            (3.0, 0.0),
            (4.0, 0.0),
            (5.0, 1.0),
            (6.0, -2.0),
        ]
        .map(|(r, i)| Complex::of(Float::of(r), Float::of(i))),
    )
    .unwrap();
    let rectp = moore_penrose_inverse(&rect);
    // A . Ap . A = A
    assert_eq!(rect.clone() * rectp.clone() * rect.clone(), rect);
    // Ap . A . Ap = Ap
    assert_eq!(rectp.clone() * rect.clone() * rectp.clone(), rectp);
    // A . Ap is a hermitian matrix.
    assert!(is_hermitian_matrix(&(rect.clone() * rectp.clone())));
    // Ap . A is also a hermitian matrix.
    assert!(is_hermitian_matrix(&(rectp * rect)));
}