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nalgebra/tests/linalg/eigen.rs
sebcrozet fc24db8ff3 Merge branch 'master-public' into sparse 
# Conflicts:
#	Cargo.toml
#	examples/matrix_construction.rs
#	nalgebra-glm/src/constructors.rs
#	nalgebra-glm/src/ext/matrix_clip_space.rs
#	nalgebra-glm/src/ext/matrix_transform.rs
#	nalgebra-glm/src/ext/mod.rs
#	nalgebra-glm/src/ext/quaternion_common.rs
#	nalgebra-glm/src/gtx/quaternion.rs
#	nalgebra-glm/src/gtx/rotate_vector.rs
#	nalgebra-glm/src/lib.rs
#	nalgebra-glm/src/traits.rs
#	nalgebra-lapack/src/cholesky.rs
#	nalgebra-lapack/src/eigen.rs
#	nalgebra-lapack/src/hessenberg.rs
#	nalgebra-lapack/src/lu.rs
#	nalgebra-lapack/src/qr.rs
#	nalgebra-lapack/src/schur.rs
#	nalgebra-lapack/src/svd.rs
#	nalgebra-lapack/src/symmetric_eigen.rs
#	rustfmt.toml
#	src/base/array_storage.rs
#	src/base/blas.rs
#	src/base/cg.rs
#	src/base/default_allocator.rs
#	src/base/edition.rs
#	src/base/iter.rs
#	src/base/matrix.rs
#	src/base/swizzle.rs
#	src/base/vec_storage.rs
#	src/geometry/mod.rs
#	src/geometry/point_construction.rs
#	src/geometry/quaternion.rs
#	src/geometry/similarity.rs
#	src/geometry/translation.rs
#	src/geometry/unit_complex_construction.rs
#	src/linalg/bidiagonal.rs
#	src/linalg/cholesky.rs
#	src/linalg/full_piv_lu.rs
#	src/linalg/hessenberg.rs
#	src/linalg/lu.rs
#	src/linalg/permutation_sequence.rs
#	src/linalg/qr.rs
#	src/linalg/schur.rs
#	src/linalg/svd.rs
#	src/linalg/symmetric_eigen.rs
#	src/linalg/symmetric_tridiagonal.rs
#	tests/geometry/point.rs
#	tests/geometry/quaternion.rs
#	tests/lib.rs
#	tests/linalg/eigen.rs
#	tests/linalg/svd.rs
2019-02-03 12:53:41 +01:00

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#![cfg_attr(rustfmt, rustfmt_skip)]
use na::DMatrix;
#[cfg(feature = "arbitrary")]
mod quickcheck_tests {
use na::{DMatrix, Matrix2, Matrix3, Matrix4};
use std::cmp;
quickcheck! {
fn symmetric_eigen(n: usize) -> bool {
let n = cmp::max(1, cmp::min(n, 10));
let m = DMatrix::<f64>::new_random(n, n);
let eig = m.clone().symmetric_eigen();
let recomp = eig.recompose();
println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
}
fn symmetric_eigen_singular(n: usize) -> bool {
let n = cmp::max(1, cmp::min(n, 10));
let mut m = DMatrix::<f64>::new_random(n, n);
m.row_mut(n / 2).fill(0.0);
m.column_mut(n / 2).fill(0.0);
let eig = m.clone().symmetric_eigen();
let recomp = eig.recompose();
println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
}
fn symmetric_eigen_static_square_4x4(m: Matrix4<f64>) -> bool {
let eig = m.symmetric_eigen();
let recomp = eig.recompose();
println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
}
fn symmetric_eigen_static_square_3x3(m: Matrix3<f64>) -> bool {
let eig = m.symmetric_eigen();
let recomp = eig.recompose();
println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
}
fn symmetric_eigen_static_square_2x2(m: Matrix2<f64>) -> bool {
let eig = m.symmetric_eigen();
let recomp = eig.recompose();
println!("{}{}", m.lower_triangle(), recomp.lower_triangle());
relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
}
}
}
// Test proposed on the issue #176 of rulinalg.
#[test]
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! {
// FIXME: 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)
// }
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