nalgebra/tests/linalg/col_piv_qr.rs

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#[cfg_attr(rustfmt, rustfmt_skip)]
use na::Matrix4;
#[test]
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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
));
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let (q, r, p) = col_piv_qr.unpack();
let mut qr = q * r;
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p.inv_permute_columns(&mut qr);
assert!(relative_eq!(m, qr, epsilon = 1.0e-7));
}
#[cfg(feature = "arbitrary")]
mod quickcheck_tests {
macro_rules! gen_tests(
($module: ident, $scalar: ty) => {
mod $module {
use na::{DMatrix, DVector, Matrix3x5, Matrix4, Matrix4x3, Matrix5x3, Vector4};
use std::cmp;
#[allow(unused_imports)]
use crate::core::helper::{RandScalar, RandComplex};
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quickcheck! {
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fn col_piv_qr(m: DMatrix<$scalar>) -> bool {
let m = m.map(|e| e.0);
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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);
println!("m: {}", m);
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println!("col_piv_qr: {}", &q * &r);
relative_eq!(m, &qr, epsilon = 1.0e-7) &&
q.is_orthogonal(1.0e-7)
}
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fn col_piv_qr_static_5_3(m: Matrix5x3<$scalar>) -> bool {
let m = m.map(|e| e.0);
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let col_piv_qr = m.col_piv_qr();
let (q, r, p) = col_piv_qr.unpack();
let mut qr = q * r;
p.inv_permute_columns(&mut qr);
relative_eq!(m, qr, epsilon = 1.0e-7) &&
q.is_orthogonal(1.0e-7)
}
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fn col_piv_qr_static_3_5(m: Matrix3x5<$scalar>) -> bool {
let m = m.map(|e| e.0);
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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);
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relative_eq!(m, qr, epsilon = 1.0e-7) &&
q.is_orthogonal(1.0e-7)
}
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fn col_piv_qr_static_square(m: Matrix4<$scalar>) -> bool {
let m = m.map(|e| e.0);
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let col_piv_qr = m.col_piv_qr();
let (q, r, p) = col_piv_qr.unpack();
let mut qr = q * r;
p.inv_permute_columns(&mut qr);
println!("{}{}{}{}", q, r, qr, m);
relative_eq!(m, qr, epsilon = 1.0e-7) &&
q.is_orthogonal(1.0e-7)
}
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fn col_piv_qr_solve(n: usize, nb: usize) -> bool {
if n != 0 && nb != 0 {
let n = cmp::min(n, 50); // To avoid slowing down the test too much.
let nb = cmp::min(nb, 50); // To avoid slowing down the test too much.
let m = DMatrix::<$scalar>::new_random(n, n).map(|e| e.0);
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let col_piv_qr = m.clone().col_piv_qr();
let b1 = DVector::<$scalar>::new_random(n).map(|e| e.0);
let b2 = DMatrix::<$scalar>::new_random(n, nb).map(|e| e.0);
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if col_piv_qr.is_invertible() {
let sol1 = col_piv_qr.solve(&b1).unwrap();
let sol2 = col_piv_qr.solve(&b2).unwrap();
return relative_eq!(&m * sol1, b1, epsilon = 1.0e-6) &&
relative_eq!(&m * sol2, b2, epsilon = 1.0e-6)
}
}
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return true;
}
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fn col_piv_qr_solve_static(m: Matrix4<$scalar>) -> bool {
let m = m.map(|e| e.0);
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let col_piv_qr = m.col_piv_qr();
let b1 = Vector4::<$scalar>::new_random().map(|e| e.0);
let b2 = Matrix4x3::<$scalar>::new_random().map(|e| e.0);
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if col_piv_qr.is_invertible() {
let sol1 = col_piv_qr.solve(&b1).unwrap();
let sol2 = col_piv_qr.solve(&b2).unwrap();
relative_eq!(m * sol1, b1, epsilon = 1.0e-6) &&
relative_eq!(m * sol2, b2, epsilon = 1.0e-6)
}
else {
false
}
}
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fn col_piv_qr_inverse(n: usize) -> bool {
let n = cmp::max(1, cmp::min(n, 15)); // To avoid slowing down the test too much.
let m = DMatrix::<$scalar>::new_random(n, n).map(|e| e.0);
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if let Some(m1) = m.clone().col_piv_qr().try_inverse() {
let id1 = &m * &m1;
let id2 = &m1 * &m;
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id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5)
}
else {
true
}
}
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fn col_piv_qr_inverse_static(m: Matrix4<$scalar>) -> bool {
let m = m.map(|e| e.0);
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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;
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id1.is_identity(1.0e-5) && id2.is_identity(1.0e-5)
}
else {
true
}
}
}
}
}
);
gen_tests!(complex, RandComplex<f64>);
gen_tests!(f64, RandScalar<f64>);
}