forward declaration of halfspace More...

#include <halfspace.hpp>

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

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

Public Types inherited from convex::ConvexSet< Meta, Halfspace< Meta, Child, Type >, Child >
using	BaseT = Atom< Meta, ConvexSet< Meta, Halfspace< 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	Halfspace (const PointT &a_in, T b_in, const Child &child_in)
	CTOR for halfspace set.

constexpr bool	contains_impl (const PointT &x, T) const
	contains function to see if x is in the halfspace a^T x <= b

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

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

template<typename Other >
constexpr bool	is_equal_impl (const Other &other) const
	is_equal implementation

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

Public Member Functions inherited from convex::ConvexSet< Meta, Halfspace< 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	a
	member variables in the halfspace

T	b

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, HalfspaceType Type>
struct convex::Halfspace< Meta, Child, Type >

forward declaration of halfspace

Halfspace defined on a valid vector space and one of the following type traits:

{x | a^T x <= b}... closed lower halfspace {x | a^T x < b}... open lower halfspace {x | a^T x >= b}... closed upper halfspace {x | a^T x > b}... open upper halfspace

Definition at line 35 of file halfspace.hpp.

Member Typedef Documentation

◆ ConvexBase

template<typename Meta , typename Child , HalfspaceType Type>

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

bring into scope the type traits from the base class

Definition at line 37 of file halfspace.hpp.

Constructor & Destructor Documentation

◆ Halfspace()

template<typename Meta , typename Child , HalfspaceType Type>

constexpr convex::Halfspace< Meta, Child, Type >::Halfspace	(	const PointT &	a_in,
		T	b_in,
		const Child &	child_in
	)

inlineexplicitconstexpr

CTOR for halfspace set.

Parameters

Point	(i.e., n-dim vector of type T)
b	bias scalar
child

Definition at line 51 of file halfspace.hpp.

Member Function Documentation

◆ canonicalize_set()

template<typename Meta , typename Child , HalfspaceType Type>

template<AtomType AType, conic::BuilderLike Builder>

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

inlineconstexpr

canonicalize impl

H = { x | a^T x <= b }

Direct cone map: -a^T x + b in R_+

Returns: cone block

Definition at line 138 of file halfspace.hpp.

References convex::Halfspace< Meta, Child, Type >::a, convex::Halfspace< Meta, Child, Type >::b, convex::Atom< Meta, Derived, Cs >::children, convex::dom_size_v, and convex::Atom< Meta, Derived, Cs >::N.

◆ contains_impl()

template<typename Meta , typename Child , HalfspaceType Type>

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

inlineconstexpr

contains function to see if x is in the halfspace a^T x <= b

Standard set: { x | a^T x <= b }... { x | a^T x - b <= 0 }

Parameters

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

Returns: T/F

Definition at line 65 of file halfspace.hpp.

References convex::Halfspace< Meta, Child, Type >::a, convex::Halfspace< Meta, Child, Type >::b, convex::LH, and convex::UH.

◆ is_equal_impl()

template<typename Meta , typename Child , HalfspaceType Type>

template<typename Other >

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

inlineconstexpr

is_equal implementation

Returns: T/F

Definition at line 123 of file halfspace.hpp.

References convex::Halfspace< Meta, Child, Type >::a, convex::Halfspace< Meta, Child, Type >::b, and convex::dom_size_v.

◆ is_well_formed()

template<typename Meta , typename Child , HalfspaceType Type>

constexpr bool convex::Halfspace< 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 81 of file halfspace.hpp.

References convex::Halfspace< Meta, Child, Type >::a, convex::Halfspace< Meta, Child, Type >::b, and convex::LH.

◆ transform_impl()

template<typename Meta , typename Child , HalfspaceType Type>

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

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

inlineconstexpr

transform halfspace by affine map

H = { x | a^T x <= b } f(H) = { y = f(x) | x in H}... image of halfspace under f mapping where affine map is: y = U x + t -> x = U^{-1} (y - t) so, a^T U^{-1} (y - t) <= b to a^T U^{-1} y <= b + a^T U^{-1} t we arrive at: f(H) = { y | a^T U^{-1} y <= b + a^T U^{-1} t }

Parameters

affine map