Drake
Drake C++ Documentation

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
 
Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable
 Spectrahedron (const Spectrahedron &)=default
 
Spectrahedronoperator= (const Spectrahedron &)=default
 
 Spectrahedron (Spectrahedron &&)=default
 
Spectrahedronoperator= (Spectrahedron &&)=default
 
- Public Member Functions inherited from ConvexSet
virtual ~ConvexSet ()
 
std::unique_ptr< ConvexSetClone () 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 () 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...
 
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::ProgramAttributessupported_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 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 double DoCalcVolume () const
 Non-virtual interface implementation for CalcVolume(). More...
 
std::optional< symbolic::VariableHandleZeroAmbientDimensionConstraints (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...
 
 ConvexSet (const ConvexSet &)=default
 
ConvexSetoperator= (const ConvexSet &)=default
 
 ConvexSet (ConvexSet &&)=default
 
ConvexSetoperator= (ConvexSet &&)=default
 

Constructor & Destructor Documentation

◆ Spectrahedron() [1/4]

Spectrahedron ( const Spectrahedron )
default

◆ Spectrahedron() [2/4]

Spectrahedron ( Spectrahedron &&  )
default

◆ Spectrahedron() [3/4]

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::exceptionif prog.required_capabilities() is not a subset of supported_attributes().

◆ ~Spectrahedron()

~Spectrahedron ( )
final

Member Function Documentation

◆ CalcVolume()

double CalcVolume
Exceptions
Notimplemented.

◆ 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: