linalg::QuadraticRep< JxJ, Circ > Struct Template Reference

forward declaration of P(x) / P(x^{-1}) More...

#include <quadratic_rep.hpp>

Public Types
using	T = matrix_scalar_t< JxJ >
	extract type & sizes
using	J = Vector< T, N >

Public Member Functions
constexpr	QuadraticRep (const J &x_in)
	CTOR.
constexpr auto	apply (const J &y) const
	apply
template<MatrixContainer MatX> requires (N == mat_rows_v<MatX>)
constexpr auto	apply (const MatX &Y) const
	apply column-wise to a matrix

Public Attributes
J	x
	member var

Static Public Attributes
static constexpr std::size_t	N = mat_rows_v<JxJ>

Detailed Description

template<SquareMatrix JxJ, typename Circ>
struct linalg::QuadraticRep< JxJ, Circ >

forward declaration of P(x) / P(x^{-1})

P(x) : J -> J.

Quadratic rep of Jordan Algebra as a hessian

P(x)^{-1} = P(x^{-1})... valid automorphism

P(x) -> 2L(x)^2 - L(x)^2 P(x) : J -> J... (linear op / automorphism of the cone) L(x) : J -> J... (linear op) x circ y -> J x J -> J... (bilinear map)

Definition at line 27 of file quadratic_rep.hpp.

Member Typedef Documentation

J

template<SquareMatrix JxJ, typename Circ >

using linalg::QuadraticRep< JxJ, Circ >::J = Vector<T, N>

Definition at line 31 of file quadratic_rep.hpp.

T

template<SquareMatrix JxJ, typename Circ >

using linalg::QuadraticRep< JxJ, Circ >::T = matrix_scalar_t<JxJ>

extract type & sizes

Definition at line 29 of file quadratic_rep.hpp.

Constructor & Destructor Documentation

QuadraticRep()

template<SquareMatrix JxJ, typename Circ >

constexpr linalg::QuadraticRep< JxJ, Circ >::QuadraticRep ( const J &  x_in )

inlineexplicitconstexpr

CTOR.

Parameters

x

in J

Definition at line 38 of file quadratic_rep.hpp.

Member Function Documentation

apply() [1/2]

template<SquareMatrix JxJ, typename Circ >

constexpr auto linalg::QuadraticRep< JxJ, Circ >::apply ( const J &  y ) const

inlineconstexpr

apply

P(x)y = 2L(x)^2y - L(x^2)y = 2 L(x) L(x) y - L(x^2) y = 2 x circ (x circ y) - (x circ x) circ y

Parameters

y

in J

Returns

P(x)y

Definition at line 51 of file quadratic_rep.hpp.

References linalg::mat_rows_v, and linalg::QuadraticRep< JxJ, Circ >::x.

Referenced by linalg::QuadraticRep< JxJ, Circ >::apply().

apply() [2/2]

template<SquareMatrix JxJ, typename Circ >

template<MatrixContainer MatX>
requires (N == mat_rows_v<MatX>)

constexpr auto linalg::QuadraticRep< JxJ, Circ >::apply ( const MatX &  Y ) const

inlineconstexpr

apply column-wise to a matrix

P(x)Y = [P(x)y_1 ... P(x)y_m]

Parameters

Y	matrix with columns in J

Returns

P(x)Y

Definition at line 67 of file quadratic_rep.hpp.

References linalg::QuadraticRep< JxJ, Circ >::apply(), linalg::get_col(), linalg::mat_rows_v, and linalg::QuadraticRep< JxJ, Circ >::N.

Member Data Documentation

N

template<SquareMatrix JxJ, typename Circ >

constexpr std::size_t linalg::QuadraticRep< JxJ, Circ >::N = mat_rows_v<JxJ>

staticconstexpr

Definition at line 30 of file quadratic_rep.hpp.

Referenced by linalg::QuadraticRep< JxJ, Circ >::apply().

x

template<SquareMatrix JxJ, typename Circ >

J linalg::QuadraticRep< JxJ, Circ >::x

member var

x in domain of P (i.e., P(x))

Definition at line 79 of file quadratic_rep.hpp.

Referenced by linalg::QuadraticRep< JxJ, Circ >::apply().

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

• include/akreon/linalg/operator/operator_traits.hpp
• include/akreon/linalg/operator/quadratic_rep.hpp