2017-08-03 01:37:44 +08:00
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use std::cmp;
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2017-08-14 01:52:46 +08:00
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use na::{DMatrix, Matrix2, Matrix3, Matrix4};
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2017-08-03 01:37:44 +08:00
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#[cfg(feature = "arbitrary")]
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quickcheck! {
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fn symmetric_eigen(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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2017-08-14 01:52:46 +08:00
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let eig = m.clone().symmetric_eigen();
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2017-08-03 01:37:44 +08:00
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let recomp = eig.recompose();
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println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
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relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
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}
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fn symmetric_eigen_singular(n: usize) -> bool {
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let n = cmp::max(1, cmp::min(n, 10));
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let mut m = DMatrix::<f64>::new_random(n, n);
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m.row_mut(n / 2).fill(0.0);
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m.column_mut(n / 2).fill(0.0);
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2017-08-14 01:52:46 +08:00
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let eig = m.clone().symmetric_eigen();
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2017-08-03 01:37:44 +08:00
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let recomp = eig.recompose();
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println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
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relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
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}
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fn symmetric_eigen_static_square_4x4(m: Matrix4<f64>) -> bool {
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2017-08-14 01:52:46 +08:00
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let eig = m.symmetric_eigen();
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2017-08-03 01:37:44 +08:00
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let recomp = eig.recompose();
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println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
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relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
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}
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fn symmetric_eigen_static_square_3x3(m: Matrix3<f64>) -> bool {
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2017-08-14 01:52:46 +08:00
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let eig = m.symmetric_eigen();
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2017-08-03 01:37:44 +08:00
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let recomp = eig.recompose();
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println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
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relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
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}
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fn symmetric_eigen_static_square_2x2(m: Matrix2<f64>) -> bool {
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2017-08-14 01:52:46 +08:00
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let eig = m.symmetric_eigen();
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2017-08-03 01:37:44 +08:00
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let recomp = eig.recompose();
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println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
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relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
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}
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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 symmetric_eigen_singular_24x24() {
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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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2017-08-14 01:52:46 +08:00
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let eig = m.clone().symmetric_eigen();
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2017-08-03 01:37:44 +08:00
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let recomp = eig.recompose();
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assert!(relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5));
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}
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// #[cfg(feature = "arbitrary")]
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// quickcheck! {
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// FIXME: full eigendecomposition is not implemented yet because of its complexity when some
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// eigenvalues have multiplicity > 1.
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//
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// /*
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// * NOTE: for the following tests, we use only upper-triangular matrices.
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// * Thes ensures the schur decomposition will work, and allows use to test the eigenvector
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// * computation.
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// */
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// fn eigen(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).upper_triangle();
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//
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// let eig = RealEigen::new(m.clone()).unwrap();
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// verify_eigenvectors(m, eig)
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// }
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//
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// fn eigen_with_adjascent_duplicate_diagonals(n: usize) -> bool {
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// let n = cmp::max(1, cmp::min(n, 10));
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// let mut m = DMatrix::<f64>::new_random(n, n).upper_triangle();
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//
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// // Suplicate some adjascent diagonal elements.
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// for i in 0 .. n / 2 {
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// m[(i * 2 + 1, i * 2 + 1)] = m[(i * 2, i * 2)];
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// }
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//
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// let eig = RealEigen::new(m.clone()).unwrap();
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// verify_eigenvectors(m, eig)
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// }
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//
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// fn eigen_with_nonadjascent_duplicate_diagonals(n: usize) -> bool {
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// let n = cmp::max(3, cmp::min(n, 10));
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// let mut m = DMatrix::<f64>::new_random(n, n).upper_triangle();
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//
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// // Suplicate some diagonal elements.
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// for i in n / 2 .. n {
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// m[(i, i)] = m[(i - n / 2, i - n / 2)];
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// }
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//
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// let eig = RealEigen::new(m.clone()).unwrap();
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// verify_eigenvectors(m, eig)
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// }
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//
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// fn eigen_static_square_4x4(m: Matrix4<f64>) -> bool {
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// let m = m.upper_triangle();
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// let eig = RealEigen::new(m.clone()).unwrap();
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// verify_eigenvectors(m, eig)
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// }
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//
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// fn eigen_static_square_3x3(m: Matrix3<f64>) -> bool {
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// let m = m.upper_triangle();
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// let eig = RealEigen::new(m.clone()).unwrap();
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// verify_eigenvectors(m, eig)
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// }
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//
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// fn eigen_static_square_2x2(m: Matrix2<f64>) -> bool {
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// let m = m.upper_triangle();
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// println!("{}", m);
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// let eig = RealEigen::new(m.clone()).unwrap();
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// verify_eigenvectors(m, eig)
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// }
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// }
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//
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// fn verify_eigenvectors<D: Dim>(m: MatrixN<f64, D>, mut eig: RealEigen<f64, D>) -> bool
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// where DefaultAllocator: Allocator<f64, D, D> +
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// Allocator<f64, D> +
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// Allocator<usize, D, D> +
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// Allocator<usize, D>,
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// MatrixN<f64, D>: Display,
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// VectorN<f64, D>: Display {
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// let mv = &m * &eig.eigenvectors;
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//
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// println!("eigenvalues: {}eigenvectors: {}", eig.eigenvalues, eig.eigenvectors);
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//
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// let dim = m.nrows();
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// for i in 0 .. dim {
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// let mut col = eig.eigenvectors.column_mut(i);
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// col *= eig.eigenvalues[i];
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// }
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//
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// println!("{}{:.5}{:.5}", m, mv, eig.eigenvectors);
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//
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// relative_eq!(eig.eigenvectors, mv, epsilon = 1.0e-5)
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// }
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