nalgebra/tests/linalg/col_piv_qr.rs

153 lines
6.1 KiB
Rust

#[cfg_attr(rustfmt, rustfmt_skip)]
use na::Matrix4;
#[test]
fn col_piv_qr() {
let m = Matrix4::new(
1.0, -1.0, 2.0, 1.0, -1.0, 3.0, -1.0, -1.0, 3.0, -5.0, 5.0, 3.0, 1.0, 2.0, 1.0, -2.0,
);
let col_piv_qr = m.col_piv_qr();
assert!(relative_eq!(
col_piv_qr.determinant(),
0.0,
epsilon = 1.0e-7
));
let (q, r, p) = col_piv_qr.unpack();
let mut qr = q * r;
p.inv_permute_columns(&mut qr);
assert!(relative_eq!(m, qr, epsilon = 1.0e-7));
}
#[cfg(feature = "proptest-support")]
mod proptest_tests {
macro_rules! gen_tests(
($module: ident, $scalar: expr ,$scalar_type: ty) => {
mod $module {
use na::{DMatrix, DVector, Matrix4x3, Vector4};
use std::cmp;
#[allow(unused_imports)]
use crate::core::helper::{RandComplex, RandScalar};
use crate::proptest::*;
use proptest::{prop_assert, proptest};
proptest! {
#[test]
fn col_piv_qr(m in dmatrix_($scalar)) {
let col_piv_qr = m.clone().col_piv_qr();
let (q, r, p) = col_piv_qr.unpack();
let mut qr = &q * &r;
p.inv_permute_columns(&mut qr);
prop_assert!(relative_eq!(m, &qr, epsilon = 1.0e-7));
prop_assert!(q.is_orthogonal(1.0e-7));
}
#[test]
fn col_piv_qr_static_5_3(m in matrix5x3_($scalar)) {
let col_piv_qr = m.col_piv_qr();
let (q, r, p) = col_piv_qr.unpack();
let mut qr = q * r;
p.inv_permute_columns(&mut qr);
prop_assert!(relative_eq!(m, qr, epsilon = 1.0e-7));
prop_assert!(q.is_orthogonal(1.0e-7));
}
#[test]
fn col_piv_qr_static_3_5(m in matrix3x5_($scalar)) {
let col_piv_qr = m.col_piv_qr();
let (q, r, p) = col_piv_qr.unpack();
let mut qr = q * r;
p.inv_permute_columns(&mut qr);
prop_assert!(relative_eq!(m, qr, epsilon = 1.0e-7));
prop_assert!(q.is_orthogonal(1.0e-7));
}
#[test]
fn col_piv_qr_static_square(m in matrix4_($scalar)) {
let col_piv_qr = m.col_piv_qr();
let (q, r, p) = col_piv_qr.unpack();
let mut qr = q * r;
p.inv_permute_columns(&mut qr);
prop_assert!(relative_eq!(m, qr, epsilon = 1.0e-7));
prop_assert!(q.is_orthogonal(1.0e-7));
}
#[test]
fn col_piv_qr_solve(n in PROPTEST_MATRIX_DIM, nb in PROPTEST_MATRIX_DIM) {
if n != 0 && nb != 0 {
let n = cmp::min(n, 50); // To avoid slowing down the test too much.
let nb = cmp::min(nb, 50); // To avoid slowing down the test too much.
let m = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0);
let col_piv_qr = m.clone().col_piv_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 col_piv_qr.is_invertible() {
let sol1 = col_piv_qr.solve(&b1).unwrap();
let sol2 = col_piv_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 col_piv_qr_solve_static(m in matrix4_($scalar)) {
let col_piv_qr = m.col_piv_qr();
let b1 = Vector4::<$scalar_type>::new_random().map(|e| e.0);
let b2 = Matrix4x3::<$scalar_type>::new_random().map(|e| e.0);
if col_piv_qr.is_invertible() {
let sol1 = col_piv_qr.solve(&b1).unwrap();
let sol2 = col_piv_qr.solve(&b2).unwrap();
prop_assert!(relative_eq!(m * sol1, b1, epsilon = 1.0e-6));
prop_assert!(relative_eq!(m * sol2, b2, epsilon = 1.0e-6));
}
}
#[test]
fn col_piv_qr_inverse(n in PROPTEST_MATRIX_DIM) {
let n = cmp::max(1, cmp::min(n, 15)); // To avoid slowing down the test too much.
let m = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0);
if let Some(m1) = m.clone().col_piv_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 col_piv_qr_inverse_static(m in matrix4_($scalar)) {
let col_piv_qr = m.col_piv_qr();
if let Some(m1) = col_piv_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>);
}