nalgebra 0.18.0

Linear algebra library with transformations and statically-sized or dynamically-sized matrices.
Documentation 
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#![cfg_attr(rustfmt, rustfmt_skip)]

use na::DMatrix;

#[cfg(feature = "arbitrary")]
mod quickcheck_tests {
    macro_rules! gen_tests(
        ($module: ident, $scalar: ty) => {
            mod $module {
                use na::{DMatrix, Matrix2, Matrix3, Matrix4};
                #[allow(unused_imports)]
                use crate::core::helper::{RandScalar, RandComplex};
                use std::cmp;

                quickcheck! {
                    fn symmetric_eigen(n: usize) -> bool {
                        let n      = cmp::max(1, cmp::min(n, 10));
                        let m      = DMatrix::<$scalar>::new_random(n, n).map(|e| e.0).hermitian_part();
                        let eig    = m.clone().symmetric_eigen();
                        let recomp = eig.recompose();

                        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::<$scalar>::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();

                        relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
                    }

                    fn symmetric_eigen_static_square_4x4(m: Matrix4<$scalar>) -> bool {
                        let m      = m.map(|e| e.0).hermitian_part();
                        let eig    = m.symmetric_eigen();
                        let recomp = eig.recompose();

                        relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
                    }

                    fn symmetric_eigen_static_square_3x3(m: Matrix3<$scalar>) -> bool {
                        let m      = m.map(|e| e.0).hermitian_part();
                        let eig    = m.symmetric_eigen();
                        let recomp = eig.recompose();

                        relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
                    }

                    fn symmetric_eigen_static_square_2x2(m: Matrix2<$scalar>) -> bool {
                        let m      = m.map(|e| e.0).hermitian_part();
                        let eig    = m.symmetric_eigen();
                        let recomp = eig.recompose();

                        relative_eq!(m.lower_triangle(), recomp.lower_triangle(), epsilon = 1.0e-5)
                    }
                }
            }
        }
    );

    gen_tests!(complex, RandComplex<f64>);
    gen_tests!(f64, RandScalar<f64>);
}

// 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)
// }