nalgebra/src/linalg/hessenberg.rs
2019-03-23 14:33:47 +01:00

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#[cfg(feature = "serde-serialize")]
use serde::{Deserialize, Serialize};
use alga::general::Complex;
use crate::allocator::Allocator;
use crate::base::{DefaultAllocator, MatrixMN, MatrixN, SquareMatrix, VectorN};
use crate::dimension::{DimDiff, DimSub, U1};
use crate::storage::Storage;
use crate::linalg::householder;
/// Hessenberg decomposition of a general matrix.
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
#[cfg_attr(
feature = "serde-serialize",
serde(bound(
serialize = "DefaultAllocator: Allocator<N, D, D> +
Allocator<N, DimDiff<D, U1>>,
MatrixN<N, D>: Serialize,
VectorN<N, DimDiff<D, U1>>: Serialize"
))
)]
#[cfg_attr(
feature = "serde-serialize",
serde(bound(
deserialize = "DefaultAllocator: Allocator<N, D, D> +
Allocator<N, DimDiff<D, U1>>,
MatrixN<N, D>: Deserialize<'de>,
VectorN<N, DimDiff<D, U1>>: Deserialize<'de>"
))
)]
#[derive(Clone, Debug)]
pub struct Hessenberg<N: Complex, 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: Complex, 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: Complex, 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 but its content does not have to be
/// initialized.
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>) {
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> {
let dim = self.hess.nrows();
self.hess.fill_lower_triangle(N::zero(), 2);
self.hess
.slice_mut((1, 0), (dim - 1, dim - 1))
.set_partial_diagonal(self.subdiag.iter().map(|e| N::from_real(e.modulus())));
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()` as it allocates a new matrix.
#[inline]
pub fn h(&self) -> MatrixN<N, D> {
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_partial_diagonal(self.subdiag.iter().map(|e| N::from_real(e.modulus())));
res
}
/// Computes the orthogonal matrix `Q` of this decomposition.
pub fn q(&self) -> MatrixN<N, D> {
householder::assemble_q(&self.hess, self.subdiag.as_slice())
}
#[doc(hidden)]
pub fn hess_internal(&self) -> &MatrixN<N, D> {
&self.hess
}
}
impl<N: Complex, 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())
}
}