nalgebra/tests/linalg/qr.rs

#![cfg(feature = "proptest-support")]

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

            proptest! {
                #[test]
                fn qr(m in dmatrix_($scalar)) {
                    let qr = m.clone().qr();
                    let q  = qr.q();
                    let r  = qr.r();

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

                #[test]
                fn qr_static_5_3(m in matrix5x3_($scalar)) {
                    let qr = m.qr();
                    let q  = qr.q();
                    let r  = qr.r();

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

                #[test]
                fn qr_static_3_5(m in matrix3x5_($scalar)) {
                    let qr = m.qr();
                    let q  = qr.q();
                    let r  = qr.r();

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

                #[test]
                fn qr_static_square(m in matrix4_($scalar)) {
                    let qr = m.qr();
                    let q  = qr.q();
                    let r  = qr.r();

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

                #[test]
                fn qr_solve(n in PROPTEST_MATRIX_DIM, nb in PROPTEST_MATRIX_DIM) {
                    let m  = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0);

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

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

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

                #[test]
                fn qr_solve_static(m in matrix4_($scalar)) {
                     let qr = m.qr();
                     let b1 = Vector4::<$scalar_type>::new_random().map(|e| e.0);
                     let b2 = Matrix4x3::<$scalar_type>::new_random().map(|e| e.0);

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

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

                #[test]
                fn qr_inverse(n in PROPTEST_MATRIX_DIM) {
                    let n = cmp::max(1, cmp::min(n, 15)); // To avoid slowing down the test too much.
                    let m = DMatrix::<$scalar_type>::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;

                        prop_assert!(id1.is_identity(1.0e-5));
                        prop_assert!(id2.is_identity(1.0e-5));
                    }
                }

                #[test]
                fn qr_inverse_static(m in matrix4_($scalar)) {
                    let qr = m.qr();

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

                        prop_assert!(id1.is_identity(1.0e-5));
                        prop_assert!(id2.is_identity(1.0e-5));
                    }
                }
            }
        }
    }
);

gen_tests!(complex, complex_f64(), RandComplex<f64>);
gen_tests!(f64, PROPTEST_F64, RandScalar<f64>);