Detailed Description

Implements a spectrahedron (the feasible set of a semidefinite program).

The ambient dimension of the set is N(N+1)/2; the number of variables required to describe the N-by-N semidefinite matrix.

By convention, a zero-dimensional spectrahedron is considered nonempty.

#include <drake/geometry/optimization/spectrahedron.h>

Public Member Functions
	Spectrahedron ()
	Default constructor (yields the zero-dimensional nonempty set). More...

	Spectrahedron (const solvers::MathematicalProgram &prog)
	Constructs the spectrahedron from a MathematicalProgram. More...

	~Spectrahedron () final

double	CalcVolume () const

bool	IsBounded (Parallelism parallelism=Parallelism::None()) const
	Spectrahedron uses the generic method for boundedness checking, which uses `parallelism`. More...

Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable
	Spectrahedron (const Spectrahedron &)=default

Spectrahedron &	operator= (const Spectrahedron &)=default

	Spectrahedron (Spectrahedron &&)=default

Spectrahedron &	operator= (Spectrahedron &&)=default

Public Member Functions inherited from ConvexSet
virtual	~ConvexSet ()

std::unique_ptr< ConvexSet >	Clone () const
	Creates a unique deep copy of this set. More...

int	ambient_dimension () const
	Returns the dimension of the vector space in which the elements of this set are evaluated. More...

bool	IntersectsWith (const ConvexSet &other) const
	Returns true iff the intersection between `this` and `other` is non-empty. More...

bool	IsBounded (Parallelism parallelism=Parallelism::None()) const
	Returns true iff the set is bounded, e.g., there exists an element-wise finite lower and upper bound for the set. More...

bool	IsEmpty () const
	Returns true iff the set is empty. More...

std::optional< Eigen::VectorXd >	MaybeGetPoint () const
	If this set trivially contains exactly one point, returns the value of that point. More...

std::optional< Eigen::VectorXd >	MaybeGetFeasiblePoint () const
	Returns a feasible point within this convex set if it is nonempty, and nullopt otherwise. More...

bool	PointInSet (const Eigen::Ref< const Eigen::VectorXd > &x, double tol=0) const
	Returns true iff the point x is contained in the set. More...

std::pair< VectorX< symbolic::Variable >, std::vector< solvers::Binding< solvers::Constraint > > >	AddPointInSetConstraints (solvers::MathematicalProgram *prog, const Eigen::Ref< const solvers::VectorXDecisionVariable > &vars) const
	Adds a constraint to an existing MathematicalProgram enforcing that the point defined by vars is inside the set. More...

std::vector< solvers::Binding< solvers::Constraint > >	AddPointInNonnegativeScalingConstraints (solvers::MathematicalProgram *prog, const Eigen::Ref< const solvers::VectorXDecisionVariable > &x, const symbolic::Variable &t) const
	Let S be this convex set. More...

std::vector< solvers::Binding< solvers::Constraint > >	AddPointInNonnegativeScalingConstraints (solvers::MathematicalProgram *prog, const Eigen::Ref< const Eigen::MatrixXd > &A, const Eigen::Ref< const Eigen::VectorXd > &b, const Eigen::Ref< const Eigen::VectorXd > &c, double d, const Eigen::Ref< const solvers::VectorXDecisionVariable > &x, const Eigen::Ref< const solvers::VectorXDecisionVariable > &t) const
	Let S be this convex set. More...

std::pair< std::unique_ptr< Shape >, math::RigidTransformd >	ToShapeWithPose () const
	Constructs a Shape and a pose of the set in the world frame for use in the SceneGraph geometry ecosystem. More...

double	CalcVolume () const
	Computes the exact volume for the convex set. More...

SampledVolume	CalcVolumeViaSampling (RandomGenerator *generator, const double desired_rel_accuracy=1e-2, const int max_num_samples=1e4) const
	Calculates an estimate of the volume of the convex set using sampling and performing Monte Carlo integration. More...

std::optional< std::pair< std::vector< double >, Eigen::MatrixXd > >	Projection (const Eigen::Ref< const Eigen::MatrixXd > &points) const
	Computes in the L₂ norm the distance and the nearest point in this convex set to every column of `points`. More...

bool	has_exact_volume () const
	Returns true if the exact volume can be computed for this convex set instance. More...

Static Public Member Functions
static const solvers::ProgramAttributes &	supported_attributes ()
	Returns the list of solvers::ProgramAttributes supported by this class. More...

Additional Inherited Members
Protected Member Functions inherited from ConvexSet
	ConvexSet (int ambient_dimension, bool has_exact_volume)
	For use by derived classes to construct a ConvexSet. More...

template<typename Archive >
void	Serialize (Archive *a)
	Implements non-virtual base class serialization. More...

virtual std::optional< bool >	DoIsBoundedShortcutParallel (Parallelism) const
	Non-virtual interface implementation for DoIsBoundedShortcutParallel(). More...

virtual std::vector< std::optional< double > >	DoProjectionShortcut (const Eigen::Ref< const Eigen::MatrixXd > &points, EigenPtr< Eigen::MatrixXd > projected_points) const
	Non-virtual interface implementation for DoProjectionShortcut(). More...

virtual bool	DoIsEmpty () const
	Non-virtual interface implementation for IsEmpty(). More...

virtual std::optional< Eigen::VectorXd >	DoMaybeGetPoint () const
	Non-virtual interface implementation for MaybeGetPoint(). More...

virtual std::optional< Eigen::VectorXd >	DoMaybeGetFeasiblePoint () const
	Non-virtual interface implementation for MaybeGetFeasiblePoint(). More...

virtual bool	DoPointInSet (const Eigen::Ref< const Eigen::VectorXd > &x, double tol) const
	Non-virtual interface implementation for PointInSet(). More...

virtual double	DoCalcVolume () const
	Non-virtual interface implementation for CalcVolume(). More...

std::optional< symbolic::Variable >	HandleZeroAmbientDimensionConstraints (solvers::MathematicalProgram prog, const ConvexSet &set, std::vector< solvers::Binding< solvers::Constraint >> constraints) const
	Instances of subclasses such as CartesianProduct and MinkowskiSum can have constituent sets with zero ambient dimension, which much be handled in a special manner when calling methods such as DoAddPointInSetConstraints. More...

virtual std::unique_ptr< ConvexSet >	DoAffineHullShortcut (std::optional< double > tol) const
	NVI implementation of DoAffineHullShortcut, which trivially returns null. More...

	ConvexSet (const ConvexSet &)=default

ConvexSet &	operator= (const ConvexSet &)=default

	ConvexSet (ConvexSet &&)=default

ConvexSet &	operator= (ConvexSet &&)=default

Static Protected Member Functions inherited from ConvexSet
static std::unique_ptr< ConvexSet >	AffineHullShortcut (const ConvexSet &self, std::optional< double > tol)
	When there is a more efficient strategy to compute the affine hull of this set, returns affine hull as an AffineSubspace. More...

Constructor & Destructor Documentation

◆ Spectrahedron() [1/4]

Spectrahedron ( const Spectrahedron & )

default

◆ Spectrahedron() [2/4]

Spectrahedron ( Spectrahedron && )

default

◆ Spectrahedron() [3/4]

Spectrahedron ( )

Default constructor (yields the zero-dimensional nonempty set).

◆ Spectrahedron() [4/4]

Spectrahedron ( const solvers::MathematicalProgram & prog )

explicit

Constructs the spectrahedron from a MathematicalProgram.

Exceptions

std::exception if prog.required_capabilities() is not a subset of supported_attributes().

◆ ~Spectrahedron()

~Spectrahedron ( )

final

Member Function Documentation

◆ CalcVolume()

double CalcVolume

Exceptions

Not	implemented.

◆ IsBounded()

bool IsBounded

Spectrahedron uses the generic method for boundedness checking, which uses parallelism.

Parameters

parallelism The maximum number of threads to use.

Note: See parent class's documentation for more details.

◆ operator=() [1/2]

Spectrahedron& operator= ( Spectrahedron && )

default

◆ operator=() [2/2]

Spectrahedron& operator= ( const Spectrahedron & )

default

◆ supported_attributes()

static const solvers::ProgramAttributes& supported_attributes ( )

static

Returns the list of solvers::ProgramAttributes supported by this class.

The documentation for this class was generated from the following file:

drake/geometry/optimization/spectrahedron.h

Detailed Description

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ Spectrahedron() [1/4]

◆ Spectrahedron() [2/4]

◆ Spectrahedron() [3/4]

◆ Spectrahedron() [4/4]

◆ ~Spectrahedron()

Member Function Documentation

◆ CalcVolume()

◆ IsBounded()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ supported_attributes()