nalgebra/nalgebra-lapack/src/hessenberg.rs

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use num::Zero;
use num_complex::Complex;
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use crate::ComplexHelper;
use na::allocator::Allocator;
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use na::dimension::{DimDiff, DimSub, U1};
use na::storage::Storage;
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use na::{DefaultAllocator, Matrix, OMatrix, OVector, Scalar};
use lapack;
/// The Hessenberg decomposition of a general matrix.
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
#[cfg_attr(
feature = "serde-serialize",
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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",
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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)]
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pub struct Hessenberg<T: Scalar, D: DimSub<U1>>
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where
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DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimDiff<D, U1>>,
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{
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h: OMatrix<T, D, D>,
tau: OVector<T, DimDiff<D, U1>>,
}
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impl<T: Scalar + Copy, D: DimSub<U1>> Copy for Hessenberg<T, D>
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where
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DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimDiff<D, U1>>,
OMatrix<T, D, D>: Copy,
OVector<T, DimDiff<D, U1>>: Copy,
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{
}
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impl<T: HessenbergScalar + Zero, D: DimSub<U1>> Hessenberg<T, D>
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where
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DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimDiff<D, U1>>,
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{
/// Computes the hessenberg decomposition of the matrix `m`.
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pub fn new(mut m: OMatrix<T, D, D>) -> Self {
let nrows = m.data.shape().0;
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let n = nrows.value() as i32;
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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).assume_init() };
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let mut info = 0;
let lwork =
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T::xgehrd_work_size(n, 1, n, m.as_mut_slice(), n, tau.as_mut_slice(), &mut info);
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let mut work = unsafe { crate::uninitialized_vec(lwork as usize) };
lapack_panic!(info);
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T::xgehrd(
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n,
1,
n,
m.as_mut_slice(),
n,
tau.as_mut_slice(),
&mut work,
lwork,
&mut info,
);
lapack_panic!(info);
Self { h: m, tau: tau }
}
/// Computes the hessenberg matrix of this decomposition.
#[inline]
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pub fn h(&self) -> OMatrix<T, D, D> {
let mut h = self.h.clone_owned();
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h.fill_lower_triangle(T::zero(), 2);
h
}
}
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impl<T: HessenbergReal + Zero, D: DimSub<U1>> Hessenberg<T, D>
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where
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DefaultAllocator: Allocator<T, D, D> + Allocator<T, DimDiff<D, U1>>,
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{
/// Computes the matrices `(Q, H)` of this decomposition.
#[inline]
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pub fn unpack(self) -> (OMatrix<T, D, D>, OMatrix<T, D, D>) {
(self.q(), self.h())
}
/// Computes the unitary matrix `Q` of this decomposition.
#[inline]
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pub fn q(&self) -> OMatrix<T, D, D> {
let n = self.h.nrows() as i32;
let mut q = self.h.clone_owned();
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let mut info = 0;
let lwork =
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T::xorghr_work_size(n, 1, n, q.as_mut_slice(), n, self.tau.as_slice(), &mut info);
let mut work = vec![T::zero(); lwork as usize];
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T::xorghr(
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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 + Copy {
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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)]
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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)]
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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]
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fn xgehrd(n: i32, ilo: i32, ihi: i32, a: &mut [Self], lda: i32,
tau: &mut [Self], work: &mut [Self], lwork: i32, info: &mut i32) {
unsafe { $xgehrd(n, ilo, ihi, a, lda, tau, work, lwork, info) }
}
#[inline]
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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;
unsafe { $xgehrd(n, ilo, ihi, a, lda, tau, &mut work, lwork, info) };
ComplexHelper::real_part(work[0]) as i32
}
}
)
);
macro_rules! hessenberg_real_impl(
($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) {
unsafe { $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;
unsafe { $xorghr(n, ilo, ihi, a, lda, tau, &mut work, lwork, info) };
ComplexHelper::real_part(work[0]) as i32
}
}
)
);
hessenberg_scalar_impl!(f32, lapack::sgehrd);
hessenberg_scalar_impl!(f64, lapack::dgehrd);
hessenberg_scalar_impl!(Complex<f32>, lapack::cgehrd);
hessenberg_scalar_impl!(Complex<f64>, lapack::zgehrd);
hessenberg_real_impl!(f32, lapack::sorghr);
hessenberg_real_impl!(f64, lapack::dorghr);