forward declaration of LMI type More...

#include <lmi.hpp>

Inheritance diagram for convex::LMI< Meta, Child, MatIn >:

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

using	Mat = linalg::remove_cvref_t< MatIn >
	lifted matrix for P

Public Types inherited from convex::ConvexSet< Meta, LMI< Meta, Child, MatIn >, Child >
using	BaseT = Atom< Meta, ConvexSet< Meta, LMI< Meta, Child, MatIn >, 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	LMI (const linalg::Vector< Mat, N > &A_in, const Mat &B_in, const Child &child_in)
	CTOR for LMI A & B split out.

constexpr bool	contains_impl (const PointT &x, T) const
	contains function to see if x is in the LMI defined as

constexpr bool	is_well_formed () const
	is_well_formed to check if the set is valid

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

template<linalg::MatrixContainer Mat>
constexpr auto	transform_impl (const affine::AffineMap< Mat > &) const
	transform impl

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

Public Member Functions inherited from convex::ConvexSet< Meta, LMI< Meta, Child, MatIn >, 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
linalg::Vector< Mat, N >	A
	member vars for LMI

Mat	B
	B offset.

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

Static Public Attributes
static constexpr std::size_t	MatDim = linalg::mat_rows_v<Mat>

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, linalg::SquareMatrix MatIn>
struct convex::LMI< Meta, Child, MatIn >

forward declaration of LMI type

LMI (linear matrix inequality)

LMI solution set: 0 <= B + sum(x_i A_i).

Definition at line 33 of file lmi.hpp.

Member Typedef Documentation

◆ ConvexBase

template<typename Meta , typename Child , linalg::SquareMatrix MatIn>

using convex::LMI< Meta, Child, MatIn >::ConvexBase = ConvexSet<Meta, LMI<Meta, Child, MatIn>, Child>

bring into scope the type traits from the base class

Definition at line 35 of file lmi.hpp.

◆ Mat

template<typename Meta , typename Child , linalg::SquareMatrix MatIn>

using convex::LMI< Meta, Child, MatIn >::Mat = linalg::remove_cvref_t<MatIn>

lifted matrix for P

Definition at line 43 of file lmi.hpp.

Constructor & Destructor Documentation

◆ LMI()

template<typename Meta , typename Child , linalg::SquareMatrix MatIn>

constexpr convex::LMI< Meta, Child, MatIn >::LMI	(	const linalg::Vector< Mat, N > &	A_in,
		const Mat &	B_in,
		const Child &	child_in
	)

inlineexplicitconstexpr

CTOR for LMI A & B split out.

Parameters

A	vector of matrices
B	matrix

Definition at line 54 of file lmi.hpp.

Member Function Documentation

◆ canonicalize()

template<typename Meta , typename Child , linalg::SquareMatrix MatIn>

template<AtomType Type, conic::BuilderLike Builder>

constexpr auto convex::LMI< Meta, Child, MatIn >::canonicalize ( const Builder & builder ) const

inlineconstexpr

canonicalize impl

Apply P^{-1}(C) -> K and map K to cone block

a_i = svec(A_i) in R^k A_i in S^n where k = n(n+1)/2 b = svec(B) ...

B + sum(x_i A_i) >= 0 ... psd cone

Definition at line 124 of file lmi.hpp.

References convex::LMI< Meta, Child, MatIn >::A, convex::LMI< Meta, Child, MatIn >::B, convex::Atom< Meta, Derived, Cs >::children, convex::dom_size_v, convex::Atom< Meta, Derived, Cs >::M, convex::LMI< Meta, Child, MatIn >::MatDim, and convex::Atom< Meta, Derived, Cs >::N.

◆ contains_impl()

template<typename Meta , typename Child , linalg::SquareMatrix MatIn>

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

inlineconstexpr

contains function to see if x is in the LMI defined as

LMI (i) PSD: 0 <= B + A(x) (ii) PD: 0 < B + A(x)

Parameters

x	matrix with N vectors

Returns: T/F

Definition at line 69 of file lmi.hpp.

References convex::LMI< Meta, Child, MatIn >::A, convex::LMI< Meta, Child, MatIn >::B, convex::dom_size_v, and convex::Atom< Meta, Derived, Cs >::N.

◆ is_equal_impl()

template<typename Meta , typename Child , linalg::SquareMatrix MatIn>

template<typename Other >

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

inlineconstexpr

equality comparison

Parameters

convex set

Returns: T/F

Definition at line 94 of file lmi.hpp.

References convex::LMI< Meta, Child, MatIn >::A, convex::LMI< Meta, Child, MatIn >::B, convex::dom_size_v, and convex::Atom< Meta, Derived, Cs >::N.

◆ is_well_formed()

template<typename Meta , typename Child , linalg::SquareMatrix MatIn>

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

inlineconstexpr

is_well_formed to check if the set is valid

Cant really tell if B + sum(x_i A_i) >= 0 is valid until solve... so if construction passes well formed is fine

Returns: T/F

Definition at line 84 of file lmi.hpp.

◆ transform_impl()

template<typename Meta , typename Child , linalg::SquareMatrix MatIn>

template<linalg::MatrixContainer Mat>

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

inlineconstexpr

transform impl

Parameters

map

Returns: new set

Definition at line 109 of file lmi.hpp.

References convex::dom_size_v.

Member Data Documentation

◆ A

template<typename Meta , typename Child , linalg::SquareMatrix MatIn>

linalg::Vector<Mat, N> convex::LMI< Meta, Child, MatIn >::A

member vars for LMI

LMI of As

Definition at line 167 of file lmi.hpp.

Referenced by convex::LMI< Meta, Child, MatIn >::canonicalize(), convex::LMI< Meta, Child, MatIn >::contains_impl(), and convex::LMI< Meta, Child, MatIn >::is_equal_impl().

◆ B

template<typename Meta , typename Child , linalg::SquareMatrix MatIn>

Mat convex::LMI< Meta, Child, MatIn >::B

B offset.

Definition at line 168 of file lmi.hpp.

Referenced by convex::LMI< Meta, Child, MatIn >::canonicalize(), convex::LMI< Meta, Child, MatIn >::contains_impl(), and convex::LMI< Meta, Child, MatIn >::is_equal_impl().

◆ MatDim

template<typename Meta , typename Child , linalg::SquareMatrix MatIn>

constexpr std::size_t convex::LMI< Meta, Child, MatIn >::MatDim = linalg::mat_rows_v<Mat>

staticconstexpr

Definition at line 44 of file lmi.hpp.

Referenced by convex::LMI< Meta, Child, MatIn >::canonicalize().

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

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

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Member Typedef Documentation

◆ ConvexBase

◆ Mat

Constructor & Destructor Documentation

◆ LMI()

Member Function Documentation

◆ canonicalize()

◆ contains_impl()

◆ is_equal_impl()

◆ is_well_formed()

◆ transform_impl()

Member Data Documentation

◆ A

◆ B

◆ MatDim