linalg::Hessenberg< Mat > Struct Template Reference

Reduces A to upper Hessenberg form H = U^* A U. More...

#include <hessenberg.hpp>

Inheritance diagram for linalg::Hessenberg< Mat >:

Public Types
using	OperatorBase = Endomorphism< Mat, Hessenberg< Mat > >
	alias from base class
Public Types inherited from linalg::Endomorphism< Mat, Hessenberg< Mat > >
using	T = matrix_scalar_t< Mat >
	alias helpers for types
using	ScalarT = real_type_t< T >
using	ComplexT = std::complex< ScalarT >

Public Member Functions
constexpr	Hessenberg (const Mat &A)
	Reduce A by two-sided Householder similarities.
constexpr auto	H () const
	Extract the upper Hessenberg matrix.
constexpr auto	U () const
	Reconstruct the orthogonal or unitary similarity basis.
constexpr auto	operator() (std::size_t i, std::size_t j) const
	Read an entry of the Hessenberg matrix.
Public Member Functions inherited from linalg::Endomorphism< Mat, Hessenberg< Mat > >
constexpr const T &	operator() (std::size_t i, std::size_t j) const
	get element at (i,j) index
constexpr T &	operator() (std::size_t i, std::size_t j)
	get element at (i,j) index
constexpr Hessenberg< Mat > &	self ()
	self
constexpr const Hessenberg< Mat > &	self () const
	self

Public Attributes
Vector< T, N >	beta
	Vector member variables.

Additional Inherited Members
Static Public Attributes inherited from linalg::Endomorphism< Mat, Hessenberg< Mat > >
static constexpr std::size_t	N
	helper to extract N

Detailed Description

template<SquareMatrix Mat>
struct linalg::Hessenberg< Mat >

Reduces A to upper Hessenberg form H = U^* A U.

forward declaration of hessenberg matrix

Householder similarities eliminate entries below the first subdiagonal. Packed reflector tails reconstruct the orthogonal or unitary basis U.

Template Parameters

Mat	Square real or complex matrix type.

Definition at line 21 of file hessenberg.hpp.

Member Typedef Documentation

OperatorBase

template<SquareMatrix Mat>

using linalg::Hessenberg< Mat >::OperatorBase = Endomorphism<Mat, Hessenberg<Mat> >

alias from base class

Definition at line 23 of file hessenberg.hpp.

Constructor & Destructor Documentation

Hessenberg()

template<SquareMatrix Mat>

constexpr linalg::Hessenberg< Mat >::Hessenberg ( const Mat &  A )

inlineexplicitconstexpr

Reduce A by two-sided Householder similarities.

Parameters

[in]

A

Square input matrix to reduce to upper Hessenberg form.

Definition at line 34 of file hessenberg.hpp.

References linalg::as_col_vector(), linalg::Hessenberg< Mat >::beta, linalg::conjugate_transpose(), linalg::constexpr_for(), linalg::get_col(), linalg::mat_rows_v, linalg::Endomorphism< Mat, Hessenberg< Mat > >::N, and linalg::transpose().

Member Function Documentation

H()

template<SquareMatrix Mat>

constexpr auto linalg::Hessenberg< Mat >::H ( ) const

inlineconstexpr

Extract the upper Hessenberg matrix.

Returns

Matrix<T, N, N> with zeros below the first subdiagonal.

Definition at line 80 of file hessenberg.hpp.

References linalg::mat_rows_v, and linalg::Endomorphism< Mat, Hessenberg< Mat > >::N.

operator()()

template<SquareMatrix Mat>

constexpr auto linalg::Hessenberg< Mat >::operator() ( std::size_t  i, std::size_t  j  ) const

inlineconstexpr

Read an entry of the Hessenberg matrix.

Parameters

[in]	i	Zero-based row index.
[in]	j	Zero-based column index.

Returns

Scalar T; zero below the first subdiagonal.

Definition at line 128 of file hessenberg.hpp.

References linalg::mat_rows_v.

U()

template<SquareMatrix Mat>

constexpr auto linalg::Hessenberg< Mat >::U ( ) const

inlineconstexpr

Reconstruct the orthogonal or unitary similarity basis.

Returns

Matrix<T, N, N> containing U such that H = U^* A U.

Definition at line 96 of file hessenberg.hpp.

References linalg::as_col_vector(), linalg::Hessenberg< Mat >::beta, linalg::conjugate_transpose(), linalg::constexpr_for(), linalg::mat_rows_v, linalg::Endomorphism< Mat, Hessenberg< Mat > >::N, linalg::transpose(), and linalg::Hessenberg< Mat >::U().

Referenced by linalg::Hessenberg< Mat >::U().

Member Data Documentation

beta

template<SquareMatrix Mat>

Vector<T, N> linalg::Hessenberg< Mat >::beta

Vector member variables.

beta vector from householder reflections

Definition at line 134 of file hessenberg.hpp.

Referenced by linalg::Hessenberg< Mat >::Hessenberg(), and linalg::Hessenberg< Mat >::U().

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The documentation for this struct was generated from the following file:

• include/akreon/linalg/operator/hessenberg.hpp