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#[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;
#[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>>,
{
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)
}
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),
));
}
let subdiag = unsafe { subdiag.assume_init() };
Hessenberg { hess, subdiag }
}
#[inline]
pub fn unpack(self) -> (OMatrix<T, D, D>, OMatrix<T, D, D>) {
let q = self.q();
(q, self.unpack_h())
}
#[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
.slice_mut((1, 0), (dim - 1, dim - 1))
.set_partial_diagonal(
self.subdiag
.iter()
.map(|e| T::from_real(e.clone().modulus())),
);
self.hess
}
#[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.slice_mut((1, 0), (dim - 1, dim - 1))
.set_partial_diagonal(
self.subdiag
.iter()
.map(|e| T::from_real(e.clone().modulus())),
);
res
}
#[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
}
}