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.
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| | Spectrahedron () |
| | Default constructor (yields the zero-dimensional nonempty set).
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| | Spectrahedron (const solvers::MathematicalProgram &prog) |
| | Constructs the spectrahedron from a MathematicalProgram.
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| | ~Spectrahedron () final |
| double | CalcVolume () const |
| bool | IsBounded (Parallelism parallelism=Parallelism::None()) const |
| | Spectrahedron uses the generic method for boundedness checking, which uses parallelism.
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| | Spectrahedron (const Spectrahedron &)=default |
| Spectrahedron & | operator= (const Spectrahedron &)=default |
| | Spectrahedron (Spectrahedron &&)=default |
| Spectrahedron & | operator= (Spectrahedron &&)=default |
| virtual | ~ConvexSet () |
| std::unique_ptr< ConvexSet > | Clone () const |
| | Creates a unique deep copy of this set.
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| int | ambient_dimension () const |
| | Returns the dimension of the vector space in which the elements of this set are evaluated.
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| bool | IntersectsWith (const ConvexSet &other) const |
| | Returns true iff the intersection between this and other is non-empty.
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| 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.
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| bool | IsEmpty () const |
| | Returns true iff the set is empty.
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| std::optional< Eigen::VectorXd > | MaybeGetPoint () const |
| | If this set trivially contains exactly one point, returns the value of that point.
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| std::optional< Eigen::VectorXd > | MaybeGetFeasiblePoint () const |
| | Returns a feasible point within this convex set if it is nonempty, and nullopt otherwise.
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| bool | PointInSet (const Eigen::Ref< const Eigen::VectorXd > &x, double tol=0) const |
| | Returns true iff the point x is contained in the set.
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| 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.
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| 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.
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| 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.
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| 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.
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| double | CalcVolume () const |
| | Computes the exact volume for the convex set.
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| 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.
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| 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.
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| bool | has_exact_volume () const |
| | Returns true if the exact volume can be computed for this convex set instance.
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