linalg::HouseholderVector< T, N > Struct Template Reference

Compact representation of a real or complex Householder reflector. More...

#include <householder.hpp>

Public Member Functions
constexpr	HouseholderVector (const Vector< T, N > &x)
	Construct a compact Householder reflector for x.

Public Attributes
Vector< T, N >	v
	Reflector direction vector.
real_type_t< T >	beta
	Real coefficient in I - beta * v * v^*.

Detailed Description

template<typename T, std::size_t N>
requires (Field<T> && N > 0)
struct linalg::HouseholderVector< T, N >

Compact representation of a real or complex Householder reflector.

The stored v and real coefficient beta represent P = I - beta * v * v^T over a real field and P = I - beta * v * v^* over a complex field. Construction follows the Golub and Van Loan algorithm and selects a numerically stable leading coordinate. Applying the reflector maps the input toward a multiple of the first coordinate vector. For a non-axis real input, that multiple has the opposite sign to the leading input coordinate to avoid cancellation.

For N == 1, the representation is the identity reflector (v = [1], beta = 0). A zero complex input similarly requires no reflector.

Template Parameters

T	Real or complex field scalar.
N	Positive compile-time vector dimension.

Definition at line 35 of file householder.hpp.

Constructor & Destructor Documentation

HouseholderVector()

template<typename T , std::size_t N>

constexpr linalg::HouseholderVector< T, N >::HouseholderVector ( const Vector< T, N > &  x )

inlineconstexpr

Construct a compact Householder reflector for x.

Parameters

[in]

x

Vector to reduce toward the first coordinate axis.

Definition at line 41 of file householder.hpp.

Member Data Documentation

beta

template<typename T , std::size_t N>

real_type_t<T> linalg::HouseholderVector< T, N >::beta

Real coefficient in I - beta * v * v^*.

Definition at line 46 of file householder.hpp.

v

template<typename T , std::size_t N>

Vector<T, N> linalg::HouseholderVector< T, N >::v

Reflector direction vector.

Definition at line 45 of file householder.hpp.

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

• include/akreon/linalg/vector/householder.hpp