forward declaration of ellipsoid set More...

#include <ellipsoid.hpp>

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

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

using	Mat = linalg::Matrix< T, N, N >
	common mat type for P

Public Types inherited from convex::ConvexSet< Meta, Ellipsoid< Meta, Child >, Child >
using	BaseT = Atom< Meta, ConvexSet< Meta, Ellipsoid< 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	Ellipsoid (const PointT &c_in, const Mat &P_in, const Child &child_in)
	CTOR for ellipsoidal set.

constexpr bool	contains_impl (const PointT &x, T) const
	contains function to see if x is in the ellipsoid (x - c)^T P^{-1} (x - c) <= 1

constexpr bool	is_well_formed () const
	is_well_formed implementation checks to see if set is valid

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 set from an 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, Ellipsoid< 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
PointT	c
	member variables in the ellipsoid

Mat	P

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::Ellipsoid< Meta, Child >

forward declaration of ellipsoid set

Ellipsoid defined as the following.

E = { x | (x - c)^T P (x - c) <= 1 } s.t. P in S^n_+

Definition at line 32 of file ellipsoid.hpp.

Member Typedef Documentation

◆ ConvexBase

template<typename Meta , typename Child >

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

bring into scope the type traits from the base class

Definition at line 34 of file ellipsoid.hpp.

◆ Mat

template<typename Meta , typename Child >

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

common mat type for P

Definition at line 42 of file ellipsoid.hpp.

Constructor & Destructor Documentation

◆ Ellipsoid()

template<typename Meta , typename Child >

constexpr convex::Ellipsoid< Meta, Child >::Ellipsoid	(	const PointT &	c_in,
		const Mat &	P_in,
		const Child &	child_in
	)

inlineexplicitconstexpr

CTOR for ellipsoidal set.

Parameters

center	point (i.e., n-dim vector of type T)
P	in S^n_+
child

Definition at line 51 of file ellipsoid.hpp.

Member Function Documentation

◆ canonicalize_set()

template<typename Meta , typename Child >

template<AtomType Type, conic::BuilderLike Builder>

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

inlineconstexpr

canonicalize impl

E = { x | (x - c)^T P (x - c) <= 1, P in S^n_+ }

Eigen decomposition: P = V D V^T (x - c)^T V D V^T (x - c) <= 1 let u = V^T (x - c), u^T = (x-c)^T V

Let w = D^{1/2} V^T (x - c). Then (x - c)^T P (x - c) <= 1 <=> ||w||_2 <= 1.

Direct cone map: [ D^{1/2} V^T ] x + [ -D^{1/2} V^T c ] [ 0 ] [ 1 ] in K_soc

Returns: cone block

Definition at line 144 of file ellipsoid.hpp.

References convex::Ellipsoid< Meta, Child >::c, convex::Atom< Meta, Derived, Cs >::children, convex::dom_size_v, convex::Atom< Meta, Derived, Cs >::N, and convex::Ellipsoid< Meta, Child >::P.

◆ contains_impl()

template<typename Meta , typename Child >

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

inlineconstexpr

contains function to see if x is in the ellipsoid (x - c)^T P^{-1} (x - c) <= 1

Parameters

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

Returns: T/F

Definition at line 64 of file ellipsoid.hpp.

References convex::Ellipsoid< Meta, Child >::c, convex::dom_size_v, and convex::Ellipsoid< Meta, Child >::P.

◆ is_equal_impl()

template<typename Meta , typename Child >

template<typename Other >

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

inlineconstexpr

equality comparison

Parameters

convex set

Returns: T/F

Definition at line 120 of file ellipsoid.hpp.

References convex::Ellipsoid< Meta, Child >::c, convex::dom_size_v, and convex::Ellipsoid< Meta, Child >::P.

◆ is_well_formed()

template<typename Meta , typename Child >

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

inlineconstexpr

is_well_formed implementation checks to see if set is valid

Returns: T/F

Definition at line 79 of file ellipsoid.hpp.

References convex::dom_size_v, and convex::Ellipsoid< Meta, Child >::P.

◆ transform_impl()

template<typename Meta , typename Child >

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

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

inlineconstexpr

transform set from an affine map

E = {x | (x - c)^T P (x - c) <= 1} f(x) = U x + t -> { y = f(x) | x in E } x = U^{-1}(y - t), sub back in we get... E' = {y | (U^{-1}(y - t) - c)^T P (U^{-1}(y - t) - c) <= 1} ... U^{-1}(y - t) - c to U^{-1}(y - (U c + t) E' = { y | (y - (U c + t))^T U^{-T} P U^{-1} (y - (U c + t)) <= 1

c' = U c + t P' = U^{-T} P u

Parameters

Affine map