229 lines
10 KiB
Rust
229 lines
10 KiB
Rust
use na::{DMatrix, Matrix3};
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#[cfg(feature = "proptest-support")]
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mod proptest_tests {
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macro_rules! gen_tests(
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($module: ident, $scalar: expr, $scalar_type: ty) => {
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mod $module {
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use na::DMatrix;
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#[allow(unused_imports)]
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use crate::core::helper::{RandScalar, RandComplex};
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use std::cmp;
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use crate::proptest::*;
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use proptest::{prop_assert, proptest};
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proptest! {
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#[test]
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fn symmetric_eigen(n in PROPTEST_MATRIX_DIM) {
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let n = cmp::max(1, cmp::min(n, 10));
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let m = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0).hermitian_part();
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let eig = m.clone().symmetric_eigen();
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let recomp = eig.recompose();
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prop_assert!(relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5))
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}
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#[test]
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fn symmetric_eigen_singular(n in PROPTEST_MATRIX_DIM) {
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let n = cmp::max(1, cmp::min(n, 10));
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let mut m = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0).hermitian_part();
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m.row_mut(n / 2).fill(na::zero());
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m.column_mut(n / 2).fill(na::zero());
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let eig = m.clone().symmetric_eigen();
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let recomp = eig.recompose();
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prop_assert!(relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5))
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}
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#[test]
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fn symmetric_eigen_static_square_4x4(m in matrix4_($scalar)) {
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let m = m.hermitian_part();
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let eig = m.symmetric_eigen();
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let recomp = eig.recompose();
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prop_assert!(relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5))
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}
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#[test]
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fn symmetric_eigen_static_square_3x3(m in matrix3_($scalar)) {
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let m = m.hermitian_part();
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let eig = m.symmetric_eigen();
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let recomp = eig.recompose();
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prop_assert!(relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5))
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}
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#[test]
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fn symmetric_eigen_static_square_2x2(m in matrix2_($scalar)) {
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let m = m.hermitian_part();
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let eig = m.symmetric_eigen();
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let recomp = eig.recompose();
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prop_assert!(relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5))
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}
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}
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}
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}
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);
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gen_tests!(complex, complex_f64(), RandComplex<f64>);
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gen_tests!(f64, PROPTEST_F64, RandScalar<f64>);
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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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#[rustfmt::skip]
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fn symmetric_eigen_singular_24x24() {
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let m = DMatrix::from_row_slice(
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24,
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24,
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&[
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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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],
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);
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let eig = m.clone().symmetric_eigen();
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let recomp = eig.recompose();
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assert_relative_eq!(
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m.lower_triangle(),
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recomp.lower_triangle(),
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epsilon = 1.0e-5
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);
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}
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// Regression test for #1368
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#[test]
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fn very_small_deviation_from_identity_issue_1368() {
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let m = Matrix3::<f32>::new(
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1.0,
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3.1575704e-23,
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8.1146196e-23,
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3.1575704e-23,
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1.0,
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1.7471054e-22,
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8.1146196e-23,
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1.7471054e-22,
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1.0,
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);
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for v in m
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.try_symmetric_eigen(f32::EPSILON, 0)
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.unwrap()
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.eigenvalues
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.into_iter()
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{
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assert_relative_eq!(*v, 1.);
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}
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}
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// #[cfg(feature = "arbitrary")]
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// quickcheck! {
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// TODO: 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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// * This 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_adjacent_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 adjacent 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_nonadjacent_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: OMatrix<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<D, D> +
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// Allocator<D>,
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// OMatrix<f64, D>: Display,
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// OVector<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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