nalgebra/tests/linalg/eigen.rs

204 lines
10 KiB
Rust

use na::DMatrix;
#[cfg(feature = "proptest-support")]
mod proptest_tests {
macro_rules! gen_tests(
($module: ident, $scalar: expr, $scalar_type: ty) => {
mod $module {
use na::DMatrix;
#[allow(unused_imports)]
use crate::core::helper::{RandScalar, RandComplex};
use std::cmp;
use crate::proptest::*;
use proptest::{prop_assert, proptest};
proptest! {
#[test]
fn symmetric_eigen(n in PROPTEST_MATRIX_DIM) {
let n = cmp::max(1, cmp::min(n, 10));
let m = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0).hermitian_part();
let eig = m.clone().symmetric_eigen();
let recomp = eig.recompose();
prop_assert!(relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5))
}
#[test]
fn symmetric_eigen_singular(n in PROPTEST_MATRIX_DIM) {
let n = cmp::max(1, cmp::min(n, 10));
let mut m = DMatrix::<$scalar_type>::new_random(n, n).map(|e| e.0).hermitian_part();
m.row_mut(n / 2).fill(na::zero());
m.column_mut(n / 2).fill(na::zero());
let eig = m.clone().symmetric_eigen();
let recomp = eig.recompose();
prop_assert!(relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5))
}
#[test]
fn symmetric_eigen_static_square_4x4(m in matrix4_($scalar)) {
let m = m.hermitian_part();
let eig = m.symmetric_eigen();
let recomp = eig.recompose();
prop_assert!(relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5))
}
#[test]
fn symmetric_eigen_static_square_3x3(m in matrix3_($scalar)) {
let m = m.hermitian_part();
let eig = m.symmetric_eigen();
let recomp = eig.recompose();
prop_assert!(relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5))
}
#[test]
fn symmetric_eigen_static_square_2x2(m in matrix2_($scalar)) {
let m = m.hermitian_part();
let eig = m.symmetric_eigen();
let recomp = eig.recompose();
prop_assert!(relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5))
}
}
}
}
);
gen_tests!(complex, complex_f64(), RandComplex<f64>);
gen_tests!(f64, PROPTEST_F64, RandScalar<f64>);
}
// Test proposed on the issue #176 of rulinalg.
#[test]
#[rustfmt::skip]
fn symmetric_eigen_singular_24x24() {
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 eig = m.clone().symmetric_eigen();
let recomp = eig.recompose();
assert_relative_eq!(
m.lower_triangle(),
recomp.lower_triangle(),
epsilon = 1.0e-5
);
}
// #[cfg(feature = "arbitrary")]
// quickcheck! {
// TODO: full eigendecomposition is not implemented yet because of its complexity when some
// eigenvalues have multiplicity > 1.
//
// /*
// * NOTE: for the following tests, we use only upper-triangular matrices.
// * Thes ensures the schur decomposition will work, and allows use to test the eigenvector
// * computation.
// */
// fn eigen(n: usize) -> bool {
// let n = cmp::max(1, cmp::min(n, 10));
// let m = DMatrix::<f64>::new_random(n, n).upper_triangle();
//
// let eig = RealEigen::new(m.clone()).unwrap();
// verify_eigenvectors(m, eig)
// }
//
// fn eigen_with_adjascent_duplicate_diagonals(n: usize) -> bool {
// let n = cmp::max(1, cmp::min(n, 10));
// let mut m = DMatrix::<f64>::new_random(n, n).upper_triangle();
//
// // Suplicate some adjascent diagonal elements.
// for i in 0 .. n / 2 {
// m[(i * 2 + 1, i * 2 + 1)] = m[(i * 2, i * 2)];
// }
//
// let eig = RealEigen::new(m.clone()).unwrap();
// verify_eigenvectors(m, eig)
// }
//
// fn eigen_with_nonadjascent_duplicate_diagonals(n: usize) -> bool {
// let n = cmp::max(3, cmp::min(n, 10));
// let mut m = DMatrix::<f64>::new_random(n, n).upper_triangle();
//
// // Suplicate some diagonal elements.
// for i in n / 2 .. n {
// m[(i, i)] = m[(i - n / 2, i - n / 2)];
// }
//
// let eig = RealEigen::new(m.clone()).unwrap();
// verify_eigenvectors(m, eig)
// }
//
// fn eigen_static_square_4x4(m: Matrix4<f64>) -> bool {
// let m = m.upper_triangle();
// let eig = RealEigen::new(m.clone()).unwrap();
// verify_eigenvectors(m, eig)
// }
//
// fn eigen_static_square_3x3(m: Matrix3<f64>) -> bool {
// let m = m.upper_triangle();
// let eig = RealEigen::new(m.clone()).unwrap();
// verify_eigenvectors(m, eig)
// }
//
// fn eigen_static_square_2x2(m: Matrix2<f64>) -> bool {
// let m = m.upper_triangle();
// println!("{}", m);
// let eig = RealEigen::new(m.clone()).unwrap();
// verify_eigenvectors(m, eig)
// }
// }
//
// fn verify_eigenvectors<D: Dim>(m: MatrixN<f64, D>, mut eig: RealEigen<f64, D>) -> bool
// where DefaultAllocator: Allocator<f64, D, D> +
// Allocator<f64, D> +
// Allocator<usize, D, D> +
// Allocator<usize, D>,
// MatrixN<f64, D>: Display,
// VectorN<f64, D>: Display {
// let mv = &m * &eig.eigenvectors;
//
// println!("eigenvalues: {}eigenvectors: {}", eig.eigenvalues, eig.eigenvectors);
//
// let dim = m.nrows();
// for i in 0 .. dim {
// let mut col = eig.eigenvectors.column_mut(i);
// col *= eig.eigenvalues[i];
// }
//
// println!("{}{:.5}{:.5}", m, mv, eig.eigenvectors);
//
// relative_eq!(eig.eigenvectors, mv, epsilon = 1.0e-5)
// }