forward declaration - abs fn More...

#include <abs.hpp>

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

Public Types
using	ConvexBase = Atom< Meta, Abs< Meta, Child >, Child >
	bring into scope convex fn alias / helpers

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

Public Types inherited from convex::Atom< Meta, Abs< 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	Abs (const Child &child_in)
	CTOR.

constexpr	Abs (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
	canonicalize_impl

Public Member Functions inherited from convex::Atom< Meta, Abs< 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 Abs< 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, Abs< 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, Abs< 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>> == 1)
struct convex::Abs< Meta, Child >

forward declaration - abs fn

abs function

f(x) = |x|, x in R

Definition at line 45 of file abs.hpp.

Member Typedef Documentation

◆ ConvexBase

template<typename Meta , typename Child >

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

bring into scope convex fn alias / helpers

Definition at line 47 of file abs.hpp.

◆ Space

template<typename Meta , typename Child >

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

alias to extract space type

Definition at line 53 of file abs.hpp.

Constructor & Destructor Documentation

◆ Abs() [1/2]

template<typename Meta , typename Child >

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

inlineexplicitconstexpr

CTOR.

Parameters

child

Definition at line 63 of file abs.hpp.

◆ Abs() [2/2]

template<typename Meta , typename Child >

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

inlineexplicitconstexpr

CTOR.

Parameters

child
map

Definition at line 73 of file abs.hpp.

Member Function Documentation

◆ add()

template<typename Meta , typename Child >

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

inlineconstexpr

add

Parameters

scalar

Returns: abs fn (updated map)

Definition at line 159 of file abs.hpp.

References convex::dom_size_v.

◆ canonicalize_impl()

template<typename Meta , typename Child >

template<AtomType Type, conic::BuilderLike Builder>

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

inlineconstexpr

canonicalize_impl

(1) abs(x) -> epi -> cones f(x) = |x| K_epi = { (x,t) | |x| <= t }

let u >= |x|... first convex constraint 0 <= t - u... second convex constraint u >= 0... third convex constraint t >= 0... fourth convex constraint

-u <= x <= u 0 <= u + x... nonneg orthant cone 0 <= u - x... nonneg orthant cone 0 <= t - u... nonneg orthant cone u >= 0... nonneg orthant cone t >= 0... nonneg orthant cone

[ a^T 1 0 ] [ x; u; t ] + [ b; -b; 0; 0; 0 ] [ -a^T 1 0 ] [ 0 -1 1 ] [ 0 1 0 ] [ 0 0 1 ]

(2) -abs(x) -> hypo -> cones f(x) = - |x| K_hypo = { (x,t) | -|x| >= t, t <= 0}

let u >= |x|... first convex constraint let t <= -u... second convex constraint u >= 0... third convex constraint t <= 0... fourth convex constraint

0 <= u + x... nonneg orthant cone 0 <= u - x... nonneg orthant cone 0 <= -u - t... nonneg orthant cone u >= 0... nonneg orthant cone -t >= 0... nonneg orthant cone

[ a^T 1 0 ] [ x; u; t ] + [ b; -b; 0; 0; 0 ] [ -a^T 1 0 ] [ 0 -1 -1 ] [ 0 1 0 ] [ 0 0 -1 ]

Parameters

cone	block builder

Returns: cone block builder

Definition at line 216 of file abs.hpp.

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

◆ eval()

template<typename Meta , typename Child >

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

inlineconstexpr

eval impl

Parameters

x in R

Returns: abs(x) in R

Definition at line 120 of file abs.hpp.

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

◆ monotonicity()

template<typename Meta , typename Child >

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

inlineconstexpr

mono

Returns: monotonicity

Definition at line 82 of file abs.hpp.

References convex::CONVEX, convex::dom_size_v, convex::NONDEC, convex::NONINC, convex::NONNEG, convex::NONPOS, and convex::UNKNOWN.

◆ mul()

template<typename Meta , typename Child >

template<T Scalar>

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

inlineconstexpr

mul

Returns: abs fn (updated map)

Definition at line 134 of file abs.hpp.

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

◆ operator()()

template<typename Meta , typename Child >

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

inlineconstexpr

eval via operator overload

Parameters

point x

Returns: result

Definition at line 111 of file abs.hpp.

Member Data Documentation

◆ idx

template<typename Meta , typename Child >

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

Definition at line 259 of file abs.hpp.

◆ lift_map

template<typename Meta , typename Child >

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

member vars

Definition at line 258 of file abs.hpp.

◆ Tag

template<typename Meta , typename Child >

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

staticconstexpr

curvature tag

Definition at line 56 of file abs.hpp.

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

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

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ ConvexBase

◆ Space

Constructor & Destructor Documentation

◆ Abs() [1/2]

◆ Abs() [2/2]

Member Function Documentation

◆ add()

◆ canonicalize_impl()

◆ eval()

◆ monotonicity()

◆ mul()

◆ operator()()

Member Data Documentation

◆ idx

◆ lift_map

◆ Tag