use na::{DMatrix, Matrix3, Matrix4};
#[test]
#[rustfmt::skip]
fn schur_simpl_mat3() {
let m = Matrix3::new(-2.0, -4.0, 2.0,
-2.0, 1.0, 2.0,
4.0, 2.0, 5.0);
let schur = m.schur();
let (vecs, vals) = schur.unpack();
assert!(relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7));
}
#[cfg(feature = "proptest-support")]
mod proptest_tests {
macro_rules! gen_tests(
($module: ident, $scalar: expr, $scalar_type: ty) => {
mod $module {
use na::DMatrix;
#[allow(unused_imports)]
use crate::core::helper::{RandScalar, RandComplex};
use crate::proptest::*;
use proptest::{prop_assert, proptest};
proptest! {
#[test]
fn schur(n in PROPTEST_MATRIX_DIM) {
let m = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0);
let (vecs, vals) = m.clone().schur().unpack();
prop_assert!(relative_eq!(&vecs * vals * vecs.adjoint(), m, epsilon = 1.0e-7));
}
#[test]
fn schur_static_mat2(m in matrix2_($scalar)) {
let (vecs, vals) = m.clone().schur().unpack();
prop_assert!(relative_eq!(vecs * vals * vecs.adjoint(), m, epsilon = 1.0e-7));
}
#[test]
fn schur_static_mat3(m in matrix3_($scalar)) {
let (vecs, vals) = m.clone().schur().unpack();
prop_assert!(relative_eq!(vecs * vals * vecs.adjoint(), m, epsilon = 1.0e-7));
}
#[test]
fn schur_static_mat4(m in matrix4_($scalar)) {
let (vecs, vals) = m.clone().schur().unpack();
prop_assert!(relative_eq!(vecs * vals * vecs.adjoint(), m, epsilon = 1.0e-7));
}
}
}
}
);
gen_tests!(complex, complex_f64(), RandComplex<f64>);
gen_tests!(f64, PROPTEST_F64, RandScalar<f64>);
}
#[test]
#[rustfmt::skip]
fn schur_static_mat4_fail() {
let m = Matrix4::new(
33.32699857679677, 46.794945978960044, -20.792148817005838, 84.73945485997737,
-53.04896234480401, -4.031523330630989, 19.022858300892366, -93.2258351951158,
-94.61793793643038, -18.64216213611094, 88.32376703241675, -99.30169870309795,
90.62661897246733, 96.74200696130146, 34.7421322611369, 84.86773307198098);
let (vecs, vals) = m.clone().schur().unpack();
assert!(relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7))
}
#[test]
#[rustfmt::skip]
fn schur_static_mat4_fail2() {
let m = Matrix4::new(
14.623586538485966, 7.646156622760756, -52.11923331576265, -97.50030223503413,
53.829398131426785, -33.40560799661168, 70.31168286972388, -81.25248138434173,
27.932377940728202, 82.94220150938, -35.5898884705951, 67.56447552434219,
55.66754906908682, -42.14328890569226, -20.684709585152206, -87.9456949841046);
let (vecs, vals) = m.clone().schur().unpack();
assert!(relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7))
}
#[test]
#[rustfmt::skip]
fn schur_static_mat3_fail() {
let m = Matrix3::new(
-21.58457553143394, -67.3881542667948, -14.619829849784338,
-7.525423104386547, -17.827350599642287, 11.297377444555849,
38.080736654870464, -84.27428302131528, -95.88198590331922);
let (vecs, vals) = m.clone().schur().unpack();
assert!(relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7))
}
#[test]
#[rustfmt::skip]
fn schur_singular() {
let m = DMatrix::from_row_slice(24, 24, &[
1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-1.0, -1.0, -1.0, -1.0, -1.0, 0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 0.0, 1.0, 1.0, 1.0,
0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 4.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 4.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, -4.0, 0.0, 0.0, 0.0, 0.0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0]);
let (vecs, vals) = m.clone().schur().unpack();
assert!(relative_eq!(&vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7))
}