forward declaration of norm ball set More...

#include <norm_ball.hpp>

Inheritance diagram for convex::NormBall< Meta, Child, Type >:

Public Types
using	ConvexBase = ConvexSet< Meta, NormBall< Meta, Child, Type >, Child >
	bring into scope the type traits from the base class

Public Types inherited from convex::ConvexSet< Meta, NormBall< Meta, Child, Type >, Child >
using	BaseT = Atom< Meta, ConvexSet< Meta, NormBall< Meta, Child, Type >, Child >, Child >
	alias to extract type traits from Domain convex set

Public Types inherited from convex::Atom< Meta, Derived, Cs >
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	NormBall (const PointT &c_in, T r_in, const Child &child_in)
	CTOR for NormBall set.

constexpr bool	contains_impl (const PointT &x, T) const
	contains function to see if x is in the norm ball (norm(x - c) <= r)

constexpr bool	is_well_formed () const
	is_well_formed checks to see if underlying set is a valid convex set

template<typename Other >
constexpr bool	is_equal_impl (const Other &other) const
	equality comparison

template<linalg::SquareMatrix Mat> requires (linalg::mat_cols_v<Mat> == N && std::same_as<T, linalg::matrix_scalar_t<Mat>>)
constexpr auto	transform_impl (const affine::AffineMap< Mat > &map) const
	transform norm ball by affine map

template<AtomType AType, conic::BuilderLike Builder>
constexpr auto	canonicalize_set (const Builder &builder) const
	canonicalize impl

Public Member Functions inherited from convex::ConvexSet< Meta, NormBall< Meta, Child, Type >, Child >
constexpr	ConvexSet (const Child &child_in)
	CTOR.

constexpr void	validate_domain_impl () const
	is_well_formed

constexpr bool	contains (const PointT &x, T tol=1e-8) const
	contains to check if the point lies in the convex set

constexpr auto	transform (const affine::AffineMap< Mat > &map) const
	transform convex set by affine map

constexpr bool	operator== (const ConvexSet< Meta, OtherDerived, OtherChild > &other) const
	equality comparison overload

constexpr bool	operator!= (const ConvexSet< Meta, OtherDerived, OtherChild > &other) const
	inequality comparison overload

constexpr auto	canonicalize_impl (const Builder &builder) const
	canonicalize

constexpr auto	self () const
	self function which returns a const ref to the derived object

Public Member Functions inherited from convex::Atom< Meta, Derived, Cs >
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.

template<AtomType Type, conic::BuilderLike Builder>
constexpr auto	canonicalize (const Builder &builder) const
	Dispatch canonicalization to the derived atom.

constexpr const Derived &	self () const
	Return this object as the CRTP-derived atom type.

Public Attributes
PointT	c
	member variables in the norm ball

T	r

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

Additional Inherited Members
Static Public Attributes inherited from convex::Atom< Meta, Derived, Cs >
static constexpr std::size_t	N = dom_size_v<Domain>
	Domain dimension.

static constexpr std::size_t	M = dom_size_v<Codomain>
	Codomain dimension.

static constexpr CurvatureType	Curvature = meta_curv_v<Meta>
	Curvature declared by atom metadata.

static constexpr VarType	DomSign = dom_vartype_v<Domain>
	Domain sign declared by atom metadata.

static constexpr VarType	CodomSign = dom_vartype_v<Codomain>
	Codomain sign declared by atom metadata.

Detailed Description

template<typename Meta, typename Child, NormBallType Type>
struct convex::NormBall< Meta, Child, Type >

forward declaration of norm ball set

Norm ball defined on valid vector space and one of the following type traits.

{ x | norm(x - c) <= r }... closed norm (L2, L1, Linf) ball that lies within radius { x | norm(x - c) < r}... open "" ball that ""

Definition at line 35 of file norm_ball.hpp.

Member Typedef Documentation

◆ ConvexBase

template<typename Meta , typename Child , NormBallType Type>

using convex::NormBall< Meta, Child, Type >::ConvexBase = ConvexSet<Meta, NormBall<Meta, Child, Type>, Child>

bring into scope the type traits from the base class

Definition at line 37 of file norm_ball.hpp.

Constructor & Destructor Documentation

◆ NormBall()

template<typename Meta , typename Child , NormBallType Type>

constexpr convex::NormBall< Meta, Child, Type >::NormBall	(	const PointT &	c_in,
		T	r_in,
		const Child &	child_in
	)

inlineexplicitconstexpr

CTOR for NormBall set.

Parameters

Point (i.e., n-dim vector of type T)

Definition at line 47 of file norm_ball.hpp.

Member Function Documentation

◆ canonicalize_set()

template<typename Meta , typename Child , NormBallType Type>

template<AtomType AType, conic::BuilderLike Builder>

constexpr auto convex::NormBall< Meta, Child, Type >::canonicalize_set ( const Builder & builder ) const

inlineconstexpr

canonicalize impl

C = { x | ||x - c|| <= r }

let y = x - c

L2 Direct SOC map: [ I ] x + [ -c ] [ 0 ] [ r ] so that (y, r) in K_soc.

Linf Direct nonnegative-cone map: [ I ] x + [ -c + r 1 ] [ -I ] [ c + r 1 ]

L1 Introduce u >= |y| with 1^T u <= r. The direct nonnegative-cone map is built over (x, u) without any homogeneous lift.

Definition at line 264 of file norm_ball.hpp.

References convex::NormBall< Meta, Child, Type >::c, convex::Atom< Meta, Derived, Cs >::children, convex::dom_size_v, convex::L2, convex::Linf, convex::Atom< Meta, Derived, Cs >::N, and convex::NormBall< Meta, Child, Type >::r.

◆ contains_impl()

template<typename Meta , typename Child , NormBallType Type>

constexpr bool convex::NormBall< Meta, Child, Type >::contains_impl	(	const PointT &	x,
		T
	)		const

inlineconstexpr

contains function to see if x is in the norm ball (norm(x - c) <= r)

Parameters

Point	x of type T with n elements
tolerance	of type T (ignored)

Returns: T/F

Definition at line 58 of file norm_ball.hpp.

References convex::NormBall< Meta, Child, Type >::c, convex::L1, convex::L2, convex::Linf, and convex::NormBall< Meta, Child, Type >::r.

◆ is_equal_impl()

template<typename Meta , typename Child , NormBallType Type>

template<typename Other >

constexpr bool convex::NormBall< Meta, Child, Type >::is_equal_impl ( const Other & other ) const

inlineconstexpr

equality comparison

Parameters

convex set

Returns: T/F

Definition at line 85 of file norm_ball.hpp.

References convex::NormBall< Meta, Child, Type >::c, convex::dom_size_v, and convex::NormBall< Meta, Child, Type >::r.

◆ is_well_formed()

template<typename Meta , typename Child , NormBallType Type>

constexpr bool convex::NormBall< Meta, Child, Type >::is_well_formed ( ) const

inlineconstexpr

is_well_formed checks to see if underlying set is a valid convex set

Returns: T/F

Definition at line 75 of file norm_ball.hpp.

References convex::NormBall< Meta, Child, Type >::r.

◆ transform_impl()

template<typename Meta , typename Child , NormBallType Type>

template<linalg::SquareMatrix Mat>
requires (linalg::mat_cols_v<Mat> == N && std::same_as<T, linalg::matrix_scalar_t<Mat>>)

constexpr auto convex::NormBall< Meta, Child, Type >::transform_impl ( const affine::AffineMap< Mat > & map ) const

inlineconstexpr

transform norm ball by affine map

Br(c) = ||x - c|| < r or B = {x | ||x - c|| < r} f(B) = {y = f(x) | x in B}... y = Ux + t -> U^{-1}(y - t) = x Br'(c) = ||U^{-1}(y - t) - c|| < r -> U^{-1}(y - (U c + t))

Above is a polyhedron represented in Ax <= b and Cx = d by projecting onto y-coordinates

Parameters

affine map