1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130

/*!

## Auxiliar functions to manipulate arrays

 */

use nalgebra as na;

use approx::relative_eq;
use na::linalg::SymmetricEigen;
use na::Dynamic;
use na::{DMatrix, DVector};

/// Generate a random highly diagonal symmetric matrix
pub fn generate_diagonal_dominant(dim: usize, sparsity: f64) -> DMatrix<f64> {
    let xs = 1..=dim;
    let it = xs.map(|x: usize| x as f64);
    let vs = DVector::<f64>::from_iterator(dim, it);
    let mut arr = DMatrix::<f64>::new_random(dim, dim);
    arr += &arr.transpose();
    arr *= sparsity;
    arr.set_diagonal(&vs);
    arr
}

/// Random symmetric matrix
pub fn generate_random_symmetric(dim: usize, magnitude: f64) -> DMatrix<f64> {
    let arr = DMatrix::<f64>::new_random(dim, dim) * magnitude;
    &arr * arr.transpose()
}

/// Random Sparse matrix
pub fn generate_random_sparse_symmetric(dim: usize, lim: usize, sparsity: f64) -> DMatrix<f64> {
    let arr = generate_diagonal_dominant(dim, sparsity);
    let lambda = |i, j| {
        if j > i + lim && i > j + lim {
            0.0
        } else {
            arr[(i, j)]
        }
    };
    DMatrix::<f64>::from_fn(dim, dim, lambda)
}

/// Sort the eigenvalues and their corresponding eigenvectors in ascending order
pub fn sort_eigenpairs(
    eig: SymmetricEigen<f64, Dynamic>,
    ascending: bool,
) -> SymmetricEigen<f64, Dynamic> {
    // Sort the eigenvalues
    let mut vs: Vec<(f64, usize)> = eig
        .eigenvalues
        .iter()
        .enumerate()
        .map(|(idx, &x)| (x, idx))
        .collect();
    sort_vector(&mut vs, ascending);

    // Sorted eigenvalues
    let eigenvalues = DVector::<f64>::from_iterator(vs.len(), vs.iter().map(|t| t.0));

    // Indices of the sorted eigenvalues
    let indices: Vec<_> = vs.iter().map(|t| t.1).collect();

    // Create sorted eigenvectors
    let dim_rows = eig.eigenvectors.nrows();
    let dim_cols = eig.eigenvectors.ncols();
    let mut eigenvectors = DMatrix::<f64>::zeros(dim_rows, dim_cols);

    for (k, i) in indices.iter().enumerate() {
        eigenvectors.set_column(k, &eig.eigenvectors.column(*i));
    }
    SymmetricEigen {
        eigenvalues,
        eigenvectors,
    }
}

pub fn sort_vector<T: PartialOrd>(vs: &mut Vec<T>, ascending: bool) {
    if ascending {
        vs.sort_unstable_by(|a, b| a.partial_cmp(b).unwrap());
    } else {
        vs.sort_unstable_by(|a, b| b.partial_cmp(a).unwrap());
    }
}

pub fn test_eigenpairs(
    reference: &na::linalg::SymmetricEigen<f64, na::Dynamic>,
    eigenpair: (na::DVector<f64>, na::DMatrix<f64>),
    number: usize,
) {
    let (dav_eigenvalues, dav_eigenvectors) = eigenpair;
    for i in 0..number {
        // Test Eigenvalues
        assert!(relative_eq!(
            reference.eigenvalues[i],
            dav_eigenvalues[i],
            epsilon = 1e-6
        ));
        // Test Eigenvectors
        let x = reference.eigenvectors.column(i);
        let y = dav_eigenvectors.column(i);
        // The autovectors may different in their sign
        // They should be either parallel or antiparallel
        let dot = x.dot(&y).abs();
        assert!(relative_eq!(dot, 1.0, epsilon = 1e-6));
    }
}

#[cfg(test)]
mod test {
    use nalgebra as na;
    use std::f64;

    #[test]
    fn test_random_symmetric() {
        let matrix = super::generate_random_symmetric(10, 2.5);
        test_symmetric(matrix);
    }
    #[test]
    fn test_diagonal_dominant() {
        let matrix = super::generate_diagonal_dominant(10, 0.005);
        test_symmetric(matrix);
    }

    fn test_symmetric(matrix: na::DMatrix<f64>) {
        let rs = &matrix - &matrix.transpose();
        assert!(rs.sum() < f64::EPSILON);
    }
}