nalgebra/nalgebra-lapack/src/hessenberg.rs

use num::Zero;
use num_complex::Complex;

use ::ComplexHelper;
use na::{Scalar, Matrix, DefaultAllocator, VectorN, MatrixN};
use na::dimension::{DimSub, DimDiff, U1};
use na::storage::Storage;
use na::allocator::Allocator;

use lapack::fortran as interface;


/// The Hessenberg decomposition of a general matrix.
pub struct Hessenberg<N: Scalar, D: DimSub<U1>>
    where DefaultAllocator: Allocator<N, D, D> +
                            Allocator<N, DimDiff<D, U1>> {
    h:   MatrixN<N, D>,
    tau: VectorN<N, DimDiff<D, U1>>
}


impl<N: HessenbergScalar + Zero, D: DimSub<U1>> Hessenberg<N, D>
        where DefaultAllocator: Allocator<N, D, D> +
                                Allocator<N, DimDiff<D, U1>> {
    /// Computes the hessenberg decomposition of the matrix `m`.
    pub fn new(mut m: MatrixN<N, D>) -> Hessenberg<N, D> {
        let nrows = m.data.shape().0;
        let n     = nrows.value() as i32;

        assert!(m.is_square(), "Unable to compute the hessenberg decomposition of a non-square matrix.");
        assert!(!m.is_empty(), "Unable to compute the hessenberg decomposition of an empty matrix.");

        let mut tau = unsafe { Matrix::new_uninitialized_generic(nrows.sub(U1), U1) };

        let mut info  = 0;
        let lwork = N::xgehrd_work_size(n, 1, n, m.as_mut_slice(), n, tau.as_mut_slice(), &mut info);
        let mut work = unsafe { ::uninitialized_vec(lwork as usize) };

        lapack_panic!(info);

        N::xgehrd(n, 1, n, m.as_mut_slice(), n, tau.as_mut_slice(), &mut work, lwork, &mut info);
        lapack_panic!(info);

        Hessenberg { h: m, tau: tau }
    }

    /// Computes the hessenberg matrix of this decomposition.
    #[inline]
    pub fn h(&self) -> MatrixN<N, D> {
        let mut h = self.h.clone_owned();
        h.fill_lower_triangle(N::zero(), 2);

        h
    }
}

impl<N: HessenbergReal + Zero, D: DimSub<U1>> Hessenberg<N, D>
        where DefaultAllocator: Allocator<N, D, D> +
                                Allocator<N, DimDiff<D, U1>> {
    /// Computes the matrices `(Q, H)` of this decomposition.
    #[inline]
    pub fn unpack(self) -> (MatrixN<N, D>, MatrixN<N, D>) {
        (self.q(), self.h())
    }

    /// Computes the unitary matrix `Q` of this decomposition.
    #[inline]
    pub fn q(&self) -> MatrixN<N, D> {
        let n = self.h.nrows() as i32;
        let mut q = self.h.clone_owned();
        let mut info  = 0;

        let lwork = N::xorghr_work_size(n, 1, n, q.as_mut_slice(), n, self.tau.as_slice(), &mut info);
        let mut work = vec![ N::zero(); lwork as usize ];

        N::xorghr(n, 1, n, q.as_mut_slice(), n, self.tau.as_slice(), &mut work, lwork, &mut info);

        q
    }
}




/*
 *
 * Lapack functions dispatch.
 *
 */
pub trait HessenbergScalar: Scalar {
    fn xgehrd(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32, 
              tau: &mut [Self], work: &mut [Self], lwork: i32, info: &mut i32);
    fn xgehrd_work_size(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32, 
                        tau: &mut [Self], info: &mut i32) -> i32;
}

/// Trait implemented by scalars for which Lapack implements the hessenberg decomposition.
pub trait HessenbergReal: HessenbergScalar {
    #[allow(missing_docs)]
    fn xorghr(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32, tau: &[Self],
              work: &mut [Self], lwork: i32, info: &mut i32);
    #[allow(missing_docs)]
    fn xorghr_work_size(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32,
                        tau: &[Self], info: &mut i32) -> i32;
}

macro_rules! hessenberg_scalar_impl(
    ($N: ty, $xgehrd: path) => (
        impl HessenbergScalar for $N {
            #[inline]
            fn xgehrd(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32, 
                      tau: &mut [Self], work: &mut [Self], lwork: i32, info: &mut i32) {
                $xgehrd(n, ilo, ihi, a, lda, tau, work, lwork, info)
            }

            #[inline]
            fn xgehrd_work_size(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32, 
                                tau: &mut [Self], info: &mut i32) -> i32 {
                let mut work = [ Zero::zero() ];
                let lwork = -1 as i32;

                $xgehrd(n, ilo, ihi, a, lda, tau, &mut work, lwork, info);
                ComplexHelper::real_part(work[0]) as i32
            }
        }
    )
);

macro_rules! hessenberg_real_impl(
    ($N: ty, $xorghr: path) => (
        impl HessenbergReal for $N {
            #[inline]
            fn xorghr(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32, tau: &[Self],
                      work: &mut [Self], lwork: i32, info: &mut i32) {
                $xorghr(n, ilo, ihi, a, lda, tau, work, lwork, info)
            }

            #[inline]
            fn xorghr_work_size(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32,
                                tau: &[Self], info: &mut i32) -> i32 {
                let mut work = [ Zero::zero() ];
                let lwork = -1 as i32;

                $xorghr(n, ilo, ihi, a, lda, tau, &mut work, lwork, info);
                ComplexHelper::real_part(work[0]) as i32
            }
        }
    )
);

hessenberg_scalar_impl!(f32, interface::sgehrd);
hessenberg_scalar_impl!(f64, interface::dgehrd);
hessenberg_scalar_impl!(Complex<f32>, interface::cgehrd);
hessenberg_scalar_impl!(Complex<f64>, interface::zgehrd);

hessenberg_real_impl!(f32, interface::sorghr);
hessenberg_real_impl!(f64, interface::dorghr);