nalgebra/nalgebra-lapack/tests/linalg/lu.rs

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use std::cmp;
use na::{DMatrix, DVector, Matrix4x3, Vector4};
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use nl::LU;
use crate::proptest::*;
use proptest::{prop_assert, proptest};
proptest! {
#[test]
fn lup(m in dmatrix()) {
let lup = LU::new(m.clone());
let l = lup.l();
let u = lup.u();
let mut computed1 = &l * &u;
lup.permute(&mut computed1);
let computed2 = lup.p() * l * u;
prop_assert!(relative_eq!(computed1, m, epsilon = 1.0e-7));
prop_assert!(relative_eq!(computed2, m, epsilon = 1.0e-7));
}
#[test]
fn lu_static(m in matrix3x5()) {
let lup = LU::new(m);
let l = lup.l();
let u = lup.u();
let mut computed1 = l * u;
lup.permute(&mut computed1);
let computed2 = lup.p() * l * u;
prop_assert!(relative_eq!(computed1, m, epsilon = 1.0e-7));
prop_assert!(relative_eq!(computed2, m, epsilon = 1.0e-7));
}
#[test]
fn lu_solve(n in PROPTEST_MATRIX_DIM, nb in PROPTEST_MATRIX_DIM) {
let n = cmp::min(n, 25); // To avoid slowing down the test too much.
let nb = cmp::min(nb, 25); // To avoid slowing down the test too much.
let m = DMatrix::<f64>::new_random(n, n);
let lup = LU::new(m.clone());
let b1 = DVector::new_random(n);
let b2 = DMatrix::new_random(n, nb);
let sol1 = lup.solve(&b1).unwrap();
let sol2 = lup.solve(&b2).unwrap();
let tr_sol1 = lup.solve_transpose(&b1).unwrap();
let tr_sol2 = lup.solve_transpose(&b2).unwrap();
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prop_assert!(relative_eq!(&m * sol1, b1, epsilon = 1.0e-5));
prop_assert!(relative_eq!(&m * sol2, b2, epsilon = 1.0e-5));
prop_assert!(relative_eq!(m.transpose() * tr_sol1, b1, epsilon = 1.0e-5));
prop_assert!(relative_eq!(m.transpose() * tr_sol2, b2, epsilon = 1.0e-5));
}
#[test]
fn lu_solve_static(m in matrix4()) {
let lup = LU::new(m);
let b1 = Vector4::new_random();
let b2 = Matrix4x3::new_random();
let sol1 = lup.solve(&b1).unwrap();
let sol2 = lup.solve(&b2).unwrap();
let tr_sol1 = lup.solve_transpose(&b1).unwrap();
let tr_sol2 = lup.solve_transpose(&b2).unwrap();
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prop_assert!(relative_eq!(m * sol1, b1, epsilon = 1.0e-5));
prop_assert!(relative_eq!(m * sol2, b2, epsilon = 1.0e-5));
prop_assert!(relative_eq!(m.transpose() * tr_sol1, b1, epsilon = 1.0e-5));
prop_assert!(relative_eq!(m.transpose() * tr_sol2, b2, epsilon = 1.0e-5));
}
#[test]
fn lu_inverse(n in PROPTEST_MATRIX_DIM) {
let n = cmp::min(n, 25); // To avoid slowing down the test too much.
let m = DMatrix::<f64>::new_random(n, n);
if let Some(m1) = LU::new(m.clone()).inverse() {
let id1 = &m * &m1;
let id2 = &m1 * &m;
prop_assert!(id1.is_identity(1.0e-7) && id2.is_identity(1.0e-7));
}
}
#[test]
fn lu_inverse_static(m in matrix4()) {
if let Some(m1) = LU::new(m.clone()).inverse() {
let id1 = &m * &m1;
let id2 = &m1 * &m;
prop_assert!(id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5))
}
}
}