nalgebra/src/linalg/hessenberg.rs

use alga::general::Real;
use core::{SquareMatrix, MatrixN, MatrixMN, VectorN, DefaultAllocator};
use dimension::{DimSub, DimDiff, Dynamic, U1};
use storage::Storage;
use allocator::Allocator;
use constraint::{ShapeConstraint, DimEq};

use linalg::householder;

/// The Hessenberg decomposition of a general matrix.
#[derive(Clone, Debug)]
pub struct Hessenberg<N: Real, D: DimSub<U1>>
    where DefaultAllocator: Allocator<N, D, D> +
                            Allocator<N, DimDiff<D, U1>> {

    hess:    MatrixN<N, D>,
    subdiag: VectorN<N, DimDiff<D, U1>>
}

impl<N: Real, D: DimSub<U1>> Copy for Hessenberg<N, D>
    where DefaultAllocator: Allocator<N, D, D> +
                            Allocator<N, DimDiff<D, U1>>,
          MatrixN<N, D>: Copy,
          VectorN<N, DimDiff<D, U1>>: Copy { }

impl<N: Real, D: DimSub<U1>> Hessenberg<N, D>
    where DefaultAllocator: Allocator<N, D, D> +
                            Allocator<N, D>    +
                            Allocator<N, DimDiff<D, U1>> {

    /// Computes the Hessenberg decomposition using householder reflections.
    pub fn new(hess: MatrixN<N, D>) -> Self {
        let mut work = unsafe { MatrixMN::new_uninitialized_generic(hess.data.shape().0, U1) };
        Self::new_with_workspace(hess, &mut work)
    }

    /// Computes the Hessenberg decomposition using householder reflections.
    ///
    /// The workspace containing `D` elements must be provided and may be uninitialized.
    pub fn new_with_workspace(mut hess: MatrixN<N, D>, work: &mut VectorN<N, 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 { MatrixMN::new_uninitialized_generic(dim.sub(U1), U1) };

        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) -> (MatrixN<N, D>, MatrixN<N, D>)
        where ShapeConstraint: DimEq<Dynamic, DimDiff<D, U1>> {
        let q = self.q();

        (q, self.unpack_h())
    }

    /// Retrieves the upper trapezoidal submatrix `H` of this decomposition.
    #[inline]
    pub fn unpack_h(mut self) -> MatrixN<N, D>
        where ShapeConstraint: DimEq<Dynamic, DimDiff<D, U1>> {
        let dim = self.hess.nrows();
        self.hess.fill_lower_triangle(N::zero(), 2);
        self.hess.slice_mut((1, 0), (dim - 1, dim - 1)).set_diagonal(&self.subdiag);
        self.hess
    }

    // FIXME: add a h that moves out of self.
    /// Retrieves the upper trapezoidal submatrix `H` of this decomposition.
    ///
    /// This is less efficient than `.unpack_h()`.
    #[inline]
    pub fn h(&self) -> MatrixN<N, D>
        where ShapeConstraint: DimEq<Dynamic, DimDiff<D, U1>> {
        let dim = self.hess.nrows();
        let mut res = self.hess.clone();
        res.fill_lower_triangle(N::zero(), 2);
        res.slice_mut((1, 0), (dim - 1, dim - 1)).set_diagonal(&self.subdiag);
        res
    }

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

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


impl<N: Real, D: DimSub<U1>, S: Storage<N, D, D>> SquareMatrix<N, D, S>
    where DefaultAllocator: Allocator<N, D, D> +
                            Allocator<N, D>    +
                            Allocator<N, DimDiff<D, U1>> {
    /// Computes the Hessenberg decomposition of this matrix using householder reflections.
    pub fn hessenberg(self) -> Hessenberg<N, D> {
        Hessenberg::new(self.into_owned())
    }
}