141 lines
7.6 KiB
Rust
141 lines
7.6 KiB
Rust
#![cfg_attr(rustfmt, rustfmt_skip)]
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use na::{DMatrix, Matrix3, Matrix4};
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#[test]
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fn schur_simpl_mat3() {
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let m = Matrix3::new(-2.0, -4.0, 2.0,
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-2.0, 1.0, 2.0,
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4.0, 2.0, 5.0);
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let schur = m.real_schur();
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let (vecs, vals) = schur.unpack();
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assert!(relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7));
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}
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#[cfg(feature = "arbitrary")]
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mod quickcheck_tests {
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use std::cmp;
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use na::{DMatrix, Matrix2, Matrix3, Matrix4};
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quickcheck! {
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fn schur(n: usize) -> bool {
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let n = cmp::max(1, cmp::min(n, 10));
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let m = DMatrix::<f64>::new_random(n, n);
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let (vecs, vals) = m.clone().real_schur().unpack();
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if !relative_eq!(&vecs * &vals * vecs.transpose(), m, epsilon = 1.0e-7) {
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println!("{:.5}{:.5}", m, &vecs * &vals * vecs.transpose());
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}
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relative_eq!(&vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7)
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}
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fn schur_static_mat2(m: Matrix2<f64>) -> bool {
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let (vecs, vals) = m.clone().real_schur().unpack();
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let ok = relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7);
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if !ok {
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println!("{:.5}{:.5}", vecs, vals);
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println!("Reconstruction:{}{}", m, &vecs * &vals * vecs.transpose());
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}
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ok
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}
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fn schur_static_mat3(m: Matrix3<f64>) -> bool {
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let (vecs, vals) = m.clone().real_schur().unpack();
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let ok = relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7);
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if !ok {
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println!("{:.5}{:.5}", m, &vecs * &vals * vecs.transpose());
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}
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ok
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}
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fn schur_static_mat4(m: Matrix4<f64>) -> bool {
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let (vecs, vals) = m.clone().real_schur().unpack();
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let ok = relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7);
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if !ok {
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println!("{:.5}{:.5}", m, &vecs * &vals * vecs.transpose());
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}
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ok
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}
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}
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}
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#[test]
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fn schur_static_mat4_fail() {
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let m = Matrix4::new(
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33.32699857679677, 46.794945978960044, -20.792148817005838, 84.73945485997737,
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-53.04896234480401, -4.031523330630989, 19.022858300892366, -93.2258351951158,
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-94.61793793643038, -18.64216213611094, 88.32376703241675, -99.30169870309795,
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90.62661897246733, 96.74200696130146, 34.7421322611369, 84.86773307198098);
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let (vecs, vals) = m.clone().real_schur().unpack();
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println!("{:.6}{:.6}", m, &vecs * &vals * vecs.transpose());
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assert!(relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7))
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}
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#[test]
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fn schur_static_mat4_fail2() {
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let m = Matrix4::new(
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14.623586538485966, 7.646156622760756, -52.11923331576265, -97.50030223503413,
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53.829398131426785, -33.40560799661168, 70.31168286972388, -81.25248138434173,
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27.932377940728202, 82.94220150938, -35.5898884705951, 67.56447552434219,
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55.66754906908682, -42.14328890569226, -20.684709585152206, -87.9456949841046);
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let (vecs, vals) = m.clone().real_schur().unpack();
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println!("{:.6}{:.6}", m, &vecs * &vals * vecs.transpose());
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assert!(relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7))
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}
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#[test]
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fn schur_static_mat3_fail() {
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let m = Matrix3::new(
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-21.58457553143394, -67.3881542667948, -14.619829849784338,
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-7.525423104386547, -17.827350599642287, 11.297377444555849,
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38.080736654870464, -84.27428302131528, -95.88198590331922);
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let (vecs, vals) = m.clone().real_schur().unpack();
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println!("{:.6}{:.6}", m, &vecs * &vals * vecs.transpose());
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assert!(relative_eq!(vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7))
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}
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// Test proposed on the issue #176 of rulinalg.
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#[test]
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fn schur_singular() {
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let m = DMatrix::from_row_slice(24, 24, &[
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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,
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-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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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,
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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]);
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let (vecs, vals) = m.clone().real_schur().unpack();
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println!("{:.6}{:.6}", m, &vecs * &vals * vecs.transpose());
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assert!(relative_eq!(&vecs * vals * vecs.transpose(), m, epsilon = 1.0e-7))
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}
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