forward declaration of polyhedron set More...

#include <polyhedron.hpp>

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

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

using	Mat = linalg::Matrix< T, M, N >
	bring into scope type traits from MatA

using	Bias = linalg::Vector< T, M >

using	Space = linalg::Matrix< T, 1, N >

Public Types inherited from convex::ConvexSet< Meta, Polyhedron< Meta, Child >, Child >
using	BaseT = Atom< Meta, ConvexSet< Meta, Polyhedron< Meta, Child >, 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	Polyhedron (const Mat &A_in, const Bias &b_in, const Child &child_in)
	CTOR for polyhedron set.

constexpr bool	is_well_formed () const
	is_well_formed implementation

constexpr bool	contains_impl (const PointT &x, T tol) const
	check if candidate vector is in the 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 polyhedron by affine map

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

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

Public Member Functions inherited from convex::ConvexSet< Meta, Polyhedron< Meta, Child >, 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
Mat	A
	member variables in the polyhedron

Bias	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>
struct convex::Polyhedron< Meta, Child >

forward declaration of polyhedron set

Polyhedron convex set.

P = { x | A x <= b }... deprecating Cx = d in favor of a separate intersection with an affine subspace or additional constraint to be added in the problem space

Definition at line 35 of file polyhedron.hpp.

Member Typedef Documentation

◆ Bias

template<typename Meta , typename Child >

using convex::Polyhedron< Meta, Child >::Bias = linalg::Vector<T, M>

Definition at line 45 of file polyhedron.hpp.

◆ ConvexBase

template<typename Meta , typename Child >

using convex::Polyhedron< Meta, Child >::ConvexBase = ConvexSet<Meta, Polyhedron<Meta, Child>, Child>

bring into scope the type traits from the base class

Definition at line 37 of file polyhedron.hpp.

◆ Mat

template<typename Meta , typename Child >

using convex::Polyhedron< Meta, Child >::Mat = linalg::Matrix<T, M, N>

bring into scope type traits from MatA

Definition at line 44 of file polyhedron.hpp.

◆ Space

template<typename Meta , typename Child >

using convex::Polyhedron< Meta, Child >::Space = linalg::Matrix<T, 1, N>

Definition at line 46 of file polyhedron.hpp.

Constructor & Destructor Documentation

◆ Polyhedron()

template<typename Meta , typename Child >

constexpr convex::Polyhedron< Meta, Child >::Polyhedron	(	const Mat &	A_in,
		const Bias &	b_in,
		const Child &	child_in
	)

inlineexplicitconstexpr

CTOR for polyhedron set.

Parameters

A	basis of vectors describing linear combinations with x to form halfspace
b	vector describing halfspace inequality (per row vec in A)
child

Definition at line 56 of file polyhedron.hpp.

Member Function Documentation

◆ canonicalize_set()

template<typename Meta , typename Child >

template<AtomType Type, conic::BuilderLike Builder>

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

inlineconstexpr

canonicalize impl

C = { x | A x <= b }

Direct cone map: -A x + b in R_+^m

Returns: cone block

Definition at line 144 of file polyhedron.hpp.

References convex::Polyhedron< Meta, Child >::A, convex::Polyhedron< Meta, Child >::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 >

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

inlineconstexpr

check if candidate vector is in the set

Parameters

Vec	X of type T with N elements

Returns: T/F

Definition at line 81 of file polyhedron.hpp.

References convex::Polyhedron< Meta, Child >::A, convex::Polyhedron< Meta, Child >::b, convex::Atom< Meta, Derived, Cs >::children, convex::dom_size_v, convex::LH, and convex::Atom< Meta, Derived, Cs >::M.

◆ is_equal_impl()

template<typename Meta , typename Child >

template<typename Other >

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

inlineconstexpr

equality comparison

Parameters

convex set

Returns: T/F

Definition at line 129 of file polyhedron.hpp.

References convex::Polyhedron< Meta, Child >::A, convex::Polyhedron< Meta, Child >::b, and convex::dom_size_v.

◆ is_well_formed()

template<typename Meta , typename Child >

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

inlineconstexpr

is_well_formed implementation

Returns: T/F

Definition at line 65 of file polyhedron.hpp.

References convex::Polyhedron< Meta, Child >::A, convex::Polyhedron< Meta, Child >::b, convex::Atom< Meta, Derived, Cs >::children, convex::dom_size_v, convex::Polyhedron< Meta, Child >::is_well_formed(), convex::LH, and convex::Atom< Meta, Derived, Cs >::M.

Referenced by convex::Polyhedron< Meta, Child >::is_well_formed().

◆ transform_impl()

template<typename Meta , typename Child >

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

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

inlineconstexpr

transform polyhedron by affine map

P = { x | Ax <= b, Cx = d } f(x) = U x + t

P' = { y = f(x) | x in P } y = U x + t to x = U^{-1}(y - t)

constraints become: A U^{-1} (y - t) <= b & C U^{-1} (y - t) = d (i) A U^{-1} y <= b + A U^{-1} t (ii) C U^{-1} y = d + C U^{-1} t

Returns: T/F

Definition at line 109 of file polyhedron.hpp.

References convex::Polyhedron< Meta, Child >::A, convex::Polyhedron< Meta, Child >::b, convex::Atom< Meta, Derived, Cs >::children, and convex::dom_size_v.

Member Data Documentation

◆ A

template<typename Meta , typename Child >

Mat convex::Polyhedron< Meta, Child >::A

member variables in the polyhedron

Definition at line 166 of file polyhedron.hpp.

Referenced by convex::Polyhedron< Meta, Child >::canonicalize_set(), convex::Polyhedron< Meta, Child >::contains_impl(), convex::Polyhedron< Meta, Child >::is_equal_impl(), convex::Polyhedron< Meta, Child >::is_well_formed(), and convex::Polyhedron< Meta, Child >::transform_impl().

◆ b

template<typename Meta , typename Child >

Bias convex::Polyhedron< Meta, Child >::b

Definition at line 167 of file polyhedron.hpp.

Referenced by convex::Polyhedron< Meta, Child >::canonicalize_set(), convex::Polyhedron< Meta, Child >::contains_impl(), convex::Polyhedron< Meta, Child >::is_equal_impl(), convex::Polyhedron< Meta, Child >::is_well_formed(), and convex::Polyhedron< Meta, Child >::transform_impl().

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

include/akreon/convex/convex_traits.hpp
include/akreon/convex/sets/polyhedron.hpp

Public Types

Public Member Functions

Public Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ Bias

◆ ConvexBase

◆ Mat

◆ Space

Constructor & Destructor Documentation

◆ Polyhedron()

Member Function Documentation

◆ canonicalize_set()

◆ contains_impl()

◆ is_equal_impl()

◆ is_well_formed()

◆ transform_impl()

Member Data Documentation

◆ A

◆ b