hessenberg.rs - source
Description: Source of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/nalgebra-0.32.1/src/linalg/hessenberg.rs`.
Keywords: rust, rustlang, rust-lang

    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
    138
    139
    140
    141
    142
    143
    144
    145
    146
    147
    148
    149
    150
    151
    152
    153
    154

    #[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 simba::scalar::ComplexField;

    use crate::linalg::householder;
    use crate::Matrix;
    use std::mem::MaybeUninit;

    /// 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 = Matrix::zeros_generic(hess.shape_generic().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.shape_generic().0;

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

            if dim.value() == 0 {
                return Hessenberg {
                    hess,
                    subdiag: Matrix::zeros_generic(dim.sub(Const::<1>), Const::<1>),
                };
            }

            let mut subdiag = Matrix::uninit(dim.sub(Const::<1>), Const::<1>);

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

            // Safety: subdiag is now fully initialized.
            let subdiag = unsafe { subdiag.assume_init() };
            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
                .view_mut((1, 0), (dim - 1, dim - 1))
                .set_partial_diagonal(
                    self.subdiag
                        .iter()
                        .map(|e| T::from_real(e.clone().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]
        #[must_use]
        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.view_mut((1, 0), (dim - 1, dim - 1))
                .set_partial_diagonal(
                    self.subdiag
                        .iter()
                        .map(|e| T::from_real(e.clone().modulus())),
                );
            res
        }

        /// Computes the orthogonal matrix `Q` of this decomposition.
        #[must_use]
        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
        }
    }