forward declaration - harmonic mean fn More...

#include <harmonic_mean.hpp>

Inheritance diagram for convex::HarmonicMean< Meta, Child >:

Public Types
using	ConvexBase = Atom< Meta, HarmonicMean< Meta, Child >, Child >
	bring into scope the concave fn alias / helpers

using	Space = dom_space_t< meta_dom_t< Meta > >
	alias to extract space type

Public Types inherited from convex::Atom< Meta, HarmonicMean< Meta, Child >, Child >
using	Domain = meta_dom_t< Meta >
	Atom input domain.

using	Codomain = meta_codom_t< Meta >
	Atom output codomain.

using	ChildrenT = std::tuple< atom_decay_t< Cs >... >
	Tuple of decayed child atom types.

using	T = dom_type_t< Domain >
	Scalar field for the atom domain.

using	PointT = dom_point_t< Domain >
	Point type accepted by the atom domain.

Public Member Functions
constexpr	HarmonicMean (const Child &child_in)
	CTOR.

constexpr	HarmonicMean (const Child &child_in, const affine::AffineMap< LiftedVarMat< T > > &map_in)
	CTOR.

constexpr MonotonicityType	monotonicity () const
	mono

constexpr T	operator() (const PointT &x) const
	eval via operator overload

constexpr T	eval (const PointT &x) const
	eval impl

template<T Scalar>
constexpr auto	mul () const
	mul

constexpr auto	add (T beta) const
	add

template<AtomType Type, conic::BuilderLike Builder>
constexpr auto	canonicalize_impl (const Builder &builder) const
	canonicalization impl

Public Member Functions inherited from convex::Atom< Meta, HarmonicMean< Meta, Child >, Child >
constexpr	Atom ()
	Construct a leaf atom with no children.

constexpr	Atom (ChildrenT child_in)
	Construct an atom with normalized children.

constexpr void	validate_fn_domain (const auto &child) const
	Validate DCP composition for a function child.

constexpr void	validate_domain () const
	Validate child domains, signs, curvature, and composition rules.

constexpr auto	canonicalize (const Builder &builder) const
	Dispatch canonicalization to the derived atom.

constexpr const HarmonicMean< Meta, Child > &	self () const
	Return this object as the CRTP-derived atom type.

Public Attributes
affine::AffineMap< LiftedVarMat< T > >	lift_map
	member vars

const int	idx {-1}

Public Attributes inherited from convex::Atom< Meta, HarmonicMean< Meta, Child >, Child >
ChildrenT	children
	Tuple of normalized child atoms.

Static Public Attributes
static constexpr CurvatureType	Tag = meta_curv_v<Meta>
	curvature tag

Static Public Attributes inherited from convex::Atom< Meta, HarmonicMean< Meta, Child >, Child >
static constexpr std::size_t	N
	Domain dimension.

static constexpr std::size_t	M
	Codomain dimension.

static constexpr CurvatureType	Curvature
	Curvature declared by atom metadata.

static constexpr VarType	DomSign
	Domain sign declared by atom metadata.

static constexpr VarType	CodomSign
	Codomain sign declared by atom metadata.

Detailed Description

template<typename Meta, typename Child>
requires (dom_size_v<meta_dom_t<Meta>> == 2)
struct convex::HarmonicMean< Meta, Child >

forward declaration - harmonic mean fn

harmonic mean f(x) = 2xy / (x + y) is convex where dom f = R^2_++

Definition at line 46 of file harmonic_mean.hpp.

Member Typedef Documentation

◆ ConvexBase

template<typename Meta , typename Child >

using convex::HarmonicMean< Meta, Child >::ConvexBase = Atom<Meta, HarmonicMean<Meta, Child>, Child>

bring into scope the concave fn alias / helpers

Definition at line 48 of file harmonic_mean.hpp.

◆ Space

template<typename Meta , typename Child >

using convex::HarmonicMean< Meta, Child >::Space = dom_space_t<meta_dom_t<Meta> >

alias to extract space type

Definition at line 54 of file harmonic_mean.hpp.

Constructor & Destructor Documentation

◆ HarmonicMean() [1/2]

template<typename Meta , typename Child >

constexpr convex::HarmonicMean< Meta, Child >::HarmonicMean ( const Child & child_in )

inlineexplicitconstexpr

CTOR.

Parameters

child

Definition at line 64 of file harmonic_mean.hpp.

◆ HarmonicMean() [2/2]

template<typename Meta , typename Child >

constexpr convex::HarmonicMean< Meta, Child >::HarmonicMean	(	const Child &	child_in,
		const affine::AffineMap< LiftedVarMat< T > > &	map_in
	)

inlineexplicitconstexpr

CTOR.

Parameters

child
map

Definition at line 74 of file harmonic_mean.hpp.

Member Function Documentation

◆ add()

template<typename Meta , typename Child >

constexpr auto convex::HarmonicMean< Meta, Child >::add ( T beta ) const

inlineconstexpr

add

Parameters

scalar

Returns: harmonic mean fn

Definition at line 149 of file harmonic_mean.hpp.

References convex::dom_size_v.

◆ canonicalize_impl()

template<typename Meta , typename Child >

template<AtomType Type, conic::BuilderLike Builder>

constexpr auto convex::HarmonicMean< Meta, Child >::canonicalize_impl ( const Builder & builder ) const

inlineconstexpr

canonicalization impl

(1) f(x) = 2 x y / (x + y) C = { (x, y, t) | 2 x y / (x + y) >= t, x > 0, y > 0 } 2xy >= t(x + y)

RSOC let u = t / sqrt(2), v = x - t/2, w = y - t/2 t^2 / 2 <= 2(x - t/2)(y - t/2) t^2 <= 4[xy - xt/2 - yt/2 + t^2/4] 0 <= 4xy - 2t(x + y) + t^2... 2xy >= t(x + t)

[ 0 0 1/sqrt(2) ] [ x; y; t ] + [ 0; b; b ] -> (u, v, w) [ a0 0 -1/2 ] [ 0 a1 -1/2 ]

(2) -f(x) = -2 x y / (x + y) RSOC let u = -t/sqrt(2), v = x + t/2, w = y + t/2

[ 0 0 -1/sqrt(2) ] [ x; y; t ] + [ 0; b; b ] -> (u, v, w) [ a0 0 1/2 ] [ 0 a1 1/2 ]

Parameters

builder

Returns: new builder

Definition at line 183 of file harmonic_mean.hpp.

References convex::CONCAVE, and convex::dom_size_v.

◆ eval()

template<typename Meta , typename Child >

constexpr T convex::HarmonicMean< Meta, Child >::eval ( const PointT & x ) const

inlineconstexpr

eval impl

Parameters

x in dom f

Returns: y in R_++ or R_–

Definition at line 105 of file harmonic_mean.hpp.

References convex::CONCAVE, and convex::dom_size_v.

◆ monotonicity()

template<typename Meta , typename Child >

constexpr MonotonicityType convex::HarmonicMean< Meta, Child >::monotonicity ( ) const

inlineconstexpr

mono

Returns: monotonicity

Definition at line 83 of file harmonic_mean.hpp.

References convex::CONCAVE, convex::NONDEC, and convex::NONINC.

◆ mul()

template<typename Meta , typename Child >

template<T Scalar>

constexpr auto convex::HarmonicMean< Meta, Child >::mul ( ) const

inlineconstexpr

mul

Returns: harmonic mean fn

Definition at line 122 of file harmonic_mean.hpp.

References convex::CONVEX, and convex::dom_size_v.

◆ operator()()

template<typename Meta , typename Child >

constexpr T convex::HarmonicMean< Meta, Child >::operator() ( const PointT & x ) const

inlineconstexpr

eval via operator overload

Parameters

point x

Returns: result

Definition at line 96 of file harmonic_mean.hpp.

Member Data Documentation

◆ idx

template<typename Meta , typename Child >

const int convex::HarmonicMean< Meta, Child >::idx {-1}

Definition at line 226 of file harmonic_mean.hpp.

◆ lift_map

template<typename Meta , typename Child >

affine::AffineMap<LiftedVarMat<T> > convex::HarmonicMean< Meta, Child >::lift_map

member vars

Definition at line 225 of file harmonic_mean.hpp.

◆ Tag

template<typename Meta , typename Child >

constexpr CurvatureType convex::HarmonicMean< Meta, Child >::Tag = meta_curv_v<Meta>

staticconstexpr

curvature tag

Definition at line 57 of file harmonic_mean.hpp.

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

include/akreon/convex/convex_traits.hpp
include/akreon/convex/functions/harmonic_mean.hpp

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ ConvexBase

◆ Space

Constructor & Destructor Documentation

◆ HarmonicMean() [1/2]

◆ HarmonicMean() [2/2]

Member Function Documentation

◆ add()

◆ canonicalize_impl()

◆ eval()

◆ monotonicity()

◆ mul()

◆ operator()()

Member Data Documentation

◆ idx

◆ lift_map

◆ Tag