nalgebra/nalgebra-lapack/src/hessenberg.rs

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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;
}
pub trait HessenbergReal: HessenbergScalar {
fn xorghr(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32, tau: &[Self],
work: &mut [Self], lwork: i32, info: &mut i32);
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);