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
131
132
133
134
135
136
137

#[cfg(feature = "serde-serialize-no-std")]
use serde::{Deserialize, Serialize};

use crate::allocator::Allocator;
use crate::base::{DefaultAllocator, OMatrix, OVector};
use crate::dimension::{Const, DimDiff, DimSub, U1};
use crate::storage::Storage;
use simba::scalar::ComplexField;

use crate::linalg::householder;

/// Hessenberg decomposition of a general matrix.
#[cfg_attr(feature = "serde-serialize-no-std", derive(Serialize, Deserialize))]
#[cfg_attr(
    feature = "serde-serialize-no-std",
    serde(bound(serialize = "DefaultAllocator: Allocator<T, D, D> +
                           Allocator<T, DimDiff<D, U1>>,
         OMatrix<T, D, D>: Serialize,
         OVector<T, DimDiff<D, U1>>: Serialize"))
)]
#[cfg_attr(
    feature = "serde-serialize-no-std",
    serde(bound(deserialize = "DefaultAllocator: Allocator<T, D, D> +
                           Allocator<T, DimDiff<D, U1>>,
         OMatrix<T, D, D>: Deserialize<'de>,
         OVector<T, DimDiff<D, U1>>: Deserialize<'de>"))
)]
#[derive(Clone, Debug)]
pub struct Hessenberg<T: ComplexField, D: DimSub<U1>>
where
    DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimDiff<D, U1>>,
{
    hess: OMatrix<T, D, D>,
    subdiag: OVector<T, DimDiff<D, U1>>,
}

impl<T: ComplexField, D: DimSub<U1>> Copy for Hessenberg<T, D>
where
    DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimDiff<D, U1>>,
    OMatrix<T, D, D>: Copy,
    OVector<T, DimDiff<D, U1>>: Copy,
{
}

impl<T: ComplexField, D: DimSub<U1>> Hessenberg<T, D>
where
    DefaultAllocator: Allocator<T, D, D> + Allocator<T, D> + Allocator<T, DimDiff<D, U1>>,
{
    /// Computes the Hessenberg decomposition using householder reflections.
    pub fn new(hess: OMatrix<T, D, D>) -> Self {
        let mut work = unsafe {
            crate::unimplemented_or_uninitialized_generic!(hess.data.shape().0, Const::<1>)
        };
        Self::new_with_workspace(hess, &mut work)
    }

    /// Computes the Hessenberg decomposition using householder reflections.
    ///
    /// The workspace containing `D` elements must be provided but its content does not have to be
    /// initialized.
    pub fn new_with_workspace(mut hess: OMatrix<T, D, D>, work: &mut OVector<T, D>) -> Self {
        assert!(
            hess.is_square(),
            "Cannot compute the hessenberg decomposition of a non-square matrix."
        );

        let dim = hess.data.shape().0;

        assert!(
            dim.value() != 0,
            "Cannot compute the hessenberg decomposition of an empty matrix."
        );
        assert_eq!(
            dim.value(),
            work.len(),
            "Hessenberg: invalid workspace size."
        );

        let mut subdiag = unsafe {
            crate::unimplemented_or_uninitialized_generic!(dim.sub(Const::<1>), Const::<1>)
        };

        if dim.value() == 0 {
            return Hessenberg { hess, subdiag };
        }

        for ite in 0..dim.value() - 1 {
            householder::clear_column_unchecked(&mut hess, &mut subdiag[ite], ite, 1, Some(work));
        }

        Hessenberg { hess, subdiag }
    }

    /// Retrieves `(q, h)` with `q` the orthogonal matrix of this decomposition and `h` the
    /// hessenberg matrix.
    #[inline]
    pub fn unpack(self) -> (OMatrix<T, D, D>, OMatrix<T, D, D>) {
        let q = self.q();

        (q, self.unpack_h())
    }

    /// Retrieves the upper trapezoidal submatrix `H` of this decomposition.
    #[inline]
    pub fn unpack_h(mut self) -> OMatrix<T, D, D> {
        let dim = self.hess.nrows();
        self.hess.fill_lower_triangle(T::zero(), 2);
        self.hess
            .slice_mut((1, 0), (dim - 1, dim - 1))
            .set_partial_diagonal(self.subdiag.iter().map(|e| T::from_real(e.modulus())));
        self.hess
    }

    // TODO: add a h that moves out of self.
    /// Retrieves the upper trapezoidal submatrix `H` of this decomposition.
    ///
    /// This is less efficient than `.unpack_h()` as it allocates a new matrix.
    #[inline]
    pub fn h(&self) -> OMatrix<T, D, D> {
        let dim = self.hess.nrows();
        let mut res = self.hess.clone();
        res.fill_lower_triangle(T::zero(), 2);
        res.slice_mut((1, 0), (dim - 1, dim - 1))
            .set_partial_diagonal(self.subdiag.iter().map(|e| T::from_real(e.modulus())));
        res
    }

    /// Computes the orthogonal matrix `Q` of this decomposition.
    pub fn q(&self) -> OMatrix<T, D, D> {
        householder::assemble_q(&self.hess, self.subdiag.as_slice())
    }

    #[doc(hidden)]
    pub fn hess_internal(&self) -> &OMatrix<T, D, D> {
        &self.hess
    }
}