linalg::Hessian< Mat, Type > Struct Template Reference

Hessian as a linear operator. More...

#include <hessian.hpp>

Inheritance diagram for linalg::Hessian< Mat, Type >:

Public Types
using	OperatorBase = Endomorphism< Mat, Hessian< Mat, Type > >
	alias from base class
using	Vec = linalg::Vector< T, N >
	alias to bring in vec
using	T = matrix_scalar_t< Mat >
	alias helpers for types
Public Types inherited from linalg::Endomorphism< Mat, Derived >
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	Hessian (const Mat &A)
	CTOR.
constexpr auto	operator() (std::size_t i, std::size_t j) const
	get element at (i,j)
template<MatrixContainer MatX> requires (N == mat_rows_v<MatX>)
constexpr auto	apply (const MatX &X) const
	apply
constexpr auto	apply (const Vec &x) const
	apply
constexpr auto	apply (const T &a) const
	apply
constexpr bool	is_pullback () const
	is pullback
Public Member Functions inherited from linalg::Endomorphism< Mat, Derived >
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 Derived &	self ()
	self
constexpr const Derived &	self () const
	self

Public Attributes
Mat	H
	member variables

Static Public Attributes
static constexpr std::size_t	N
	helper from base to get num rows
Static Public Attributes inherited from linalg::Endomorphism< Mat, Derived >
static constexpr std::size_t	N = mat_rows_v<Mat>
	helper to extract N

Detailed Description

template<SquareMatrix Mat, DifferentialType Type = DifferentialType::PUSHFORWARD>
struct linalg::Hessian< Mat, Type >

Hessian as a linear operator.

forward declaration of hessian

pushforward H: A(X) -> B, acts as a push-forward operator mapping primal / tangent vectors onto a change of gradient (i.e., F''(w)x -> s)

pullback H^{-1}: B(x) -> A, (i.e., F''(w)^{-1} s -> x) acts as a pull-back operator mapping gradient space vectors back to tangent / primal direction

Definition at line 25 of file hessian.hpp.

Member Typedef Documentation

OperatorBase

template<SquareMatrix Mat, DifferentialType Type = DifferentialType::PUSHFORWARD>

using linalg::Hessian< Mat, Type >::OperatorBase = Endomorphism<Mat, Hessian<Mat, Type> >

alias from base class

Definition at line 27 of file hessian.hpp.

T

template<SquareMatrix Mat, DifferentialType Type = DifferentialType::PUSHFORWARD>

using linalg::Endomorphism< Mat, Derived >::T = matrix_scalar_t<Mat>

alias helpers for types

Definition at line 18 of file endomorphism.hpp.

Vec

template<SquareMatrix Mat, DifferentialType Type = DifferentialType::PUSHFORWARD>

using linalg::Hessian< Mat, Type >::Vec = linalg::Vector<T, N>

alias to bring in vec

Definition at line 34 of file hessian.hpp.

Constructor & Destructor Documentation

Hessian()

template<SquareMatrix Mat, DifferentialType Type = DifferentialType::PUSHFORWARD>

constexpr linalg::Hessian< Mat, Type >::Hessian ( const Mat &  A )

inlineexplicitconstexpr

CTOR.

Parameters

A	in R^{n x n}

Definition at line 41 of file hessian.hpp.

Member Function Documentation

apply() [1/3]

template<SquareMatrix Mat, DifferentialType Type = DifferentialType::PUSHFORWARD>

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

constexpr auto linalg::Hessian< Mat, Type >::apply ( const MatX &  X ) const

inlineconstexpr

apply

H : A(X) -> B H^{-1} : B(X) -> A

Parameters

Mat

X

Returns

B or A pending on diffeomorphism

Definition at line 64 of file hessian.hpp.

References linalg::Hessian< Mat, Type >::H, and linalg::mat_rows_v.

apply() [2/3]

template<SquareMatrix Mat, DifferentialType Type = DifferentialType::PUSHFORWARD>

constexpr auto linalg::Hessian< Mat, Type >::apply ( const T &  a ) const

inlineconstexpr

apply

H : H(a) = aH (same for inv)

Parameters

a

scalar

Returns

scaled operator

Definition at line 89 of file hessian.hpp.

References linalg::Hessian< Mat, Type >::H, and linalg::mat_rows_v.

apply() [3/3]

template<SquareMatrix Mat, DifferentialType Type = DifferentialType::PUSHFORWARD>

constexpr auto linalg::Hessian< Mat, Type >::apply ( const Vec &  x ) const

inlineconstexpr

apply

H : A(x) -> b H^{-1} : A^{-1}(b) = x

Parameters

Vec

x

Returns

b or x pending on diffeomorphism

Definition at line 78 of file hessian.hpp.

References linalg::Hessian< Mat, Type >::H.

is_pullback()

template<SquareMatrix Mat, DifferentialType Type = DifferentialType::PUSHFORWARD>

constexpr bool linalg::Hessian< Mat, Type >::is_pullback ( ) const

inlineconstexpr

is pullback

Returns

T/F

Definition at line 96 of file hessian.hpp.

References linalg::mat_rows_v, and linalg::PULLBACK.

operator()()

template<SquareMatrix Mat, DifferentialType Type = DifferentialType::PUSHFORWARD>

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

inlineconstexpr

get element at (i,j)

Returns

element

Definition at line 48 of file hessian.hpp.

References linalg::Hessian< Mat, Type >::H, and linalg::mat_rows_v.

Member Data Documentation

H

template<SquareMatrix Mat, DifferentialType Type = DifferentialType::PUSHFORWARD>

Mat linalg::Hessian< Mat, Type >::H

member variables

hessian mat

Definition at line 101 of file hessian.hpp.

Referenced by linalg::Hessian< Mat, Type >::apply(), linalg::Hessian< Mat, Type >::apply(), linalg::Hessian< Mat, Type >::apply(), and linalg::Hessian< Mat, Type >::operator()().

N

template<SquareMatrix Mat, DifferentialType Type = DifferentialType::PUSHFORWARD>

constexpr std::size_t linalg::Endomorphism< Mat, Derived >::N

staticconstexpr

helper from base to get num rows

Definition at line 23 of file endomorphism.hpp.

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

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