nalgebra/tests/linalg/qr.rs

#![cfg(feature = "arbitrary")]

macro_rules! gen_tests(
    ($module: ident, $scalar: ty) => {
        mod $module {
            use na::{DMatrix, DVector, Matrix3x5, Matrix4, Matrix4x3, Matrix5x3, Vector4};
            use std::cmp;
            #[allow(unused_imports)]
            use crate::core::helper::{RandScalar, RandComplex};

            quickcheck! {
                fn qr(m: DMatrix<$scalar>) -> bool {
                    let m = m.map(|e| e.0);
                    let qr = m.clone().qr();
                    let q  = qr.q();
                    let r  = qr.r();

                    println!("m: {}", m);
                    println!("qr: {}", &q * &r);

                    relative_eq!(m, &q * r, epsilon = 1.0e-7) &&
                    q.is_orthogonal(1.0e-7)
                }

                fn qr_static_5_3(m: Matrix5x3<$scalar>) -> bool {
                    let m = m.map(|e| e.0);
                    let qr = m.qr();
                    let q  = qr.q();
                    let r  = qr.r();

                    relative_eq!(m, q * r, epsilon = 1.0e-7) &&
                    q.is_orthogonal(1.0e-7)
                }

                fn qr_static_3_5(m: Matrix3x5<$scalar>) -> bool {
                    let m = m.map(|e| e.0);
                    let qr = m.qr();
                    let q  = qr.q();
                    let r  = qr.r();

                    relative_eq!(m, q * r, epsilon = 1.0e-7) &&
                    q.is_orthogonal(1.0e-7)
                }

                fn qr_static_square(m: Matrix4<$scalar>) -> bool {
                    let m = m.map(|e| e.0);
                    let qr = m.qr();
                    let q  = qr.q();
                    let r  = qr.r();

                    println!("{}{}{}{}", q, r, q * r, m);

                    relative_eq!(m, q * r, epsilon = 1.0e-7) &&
                    q.is_orthogonal(1.0e-7)
                }

                fn qr_solve(n: usize, nb: usize) -> bool {
                    if n != 0 && nb != 0 {
                        let n  = cmp::min(n, 50);  // To avoid slowing down the test too much.
                        let nb = cmp::min(nb, 50); // To avoid slowing down the test too much.
                        let m  = DMatrix::<$scalar>::new_random(n, n).map(|e| e.0);

                        let qr = m.clone().qr();
                        let b1 = DVector::<$scalar>::new_random(n).map(|e| e.0);
                        let b2 = DMatrix::<$scalar>::new_random(n, nb).map(|e| e.0);

                        if qr.is_invertible() {
                            let sol1 = qr.solve(&b1).unwrap();
                            let sol2 = qr.solve(&b2).unwrap();

                            return relative_eq!(&m * sol1, b1, epsilon = 1.0e-6) &&
                                relative_eq!(&m * sol2, b2, epsilon = 1.0e-6)
                        }
                    }

                    return true;
                }

                fn qr_solve_static(m: Matrix4<$scalar>) -> bool {
                     let m = m.map(|e| e.0);
                     let qr = m.qr();
                     let b1 = Vector4::<$scalar>::new_random().map(|e| e.0);
                     let b2 = Matrix4x3::<$scalar>::new_random().map(|e| e.0);

                     if qr.is_invertible() {
                         let sol1 = qr.solve(&b1).unwrap();
                         let sol2 = qr.solve(&b2).unwrap();

                         relative_eq!(m * sol1, b1, epsilon = 1.0e-6) &&
                         relative_eq!(m * sol2, b2, epsilon = 1.0e-6)
                     }
                     else {
                         false
                     }
                }

                fn qr_inverse(n: usize) -> bool {
                    let n = cmp::max(1, cmp::min(n, 15)); // To avoid slowing down the test too much.
                    let m = DMatrix::<$scalar>::new_random(n, n).map(|e| e.0);

                    if let Some(m1) = m.clone().qr().try_inverse() {
                        let id1 = &m  * &m1;
                        let id2 = &m1 * &m;

                        id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5)
                    }
                    else {
                        true
                    }
                }

                fn qr_inverse_static(m: Matrix4<$scalar>) -> bool {
                    let m  = m.map(|e| e.0);
                    let qr = m.qr();

                    if let Some(m1) = qr.try_inverse() {
                        let id1 = &m  * &m1;
                        let id2 = &m1 * &m;

                        id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5)
                    }
                    else {
                        true
                    }
                }
            }
        }
    }
);

gen_tests!(complex, RandComplex<f64>);
gen_tests!(f64, RandScalar<f64>);