tempest/src/storm/storage/geometry/NativePolytope.h

#ifndef STORM_STORAGE_GEOMETRY_NATIVEPOLYTOPE_H_
#define STORM_STORAGE_GEOMETRY_NATIVEPOLYTOPE_H_

#include "storm/storage/geometry/Polytope.h"
#include "storm/storage/expressions/Expressions.h"
#include "storm/adapters/EigenAdapter.h"

namespace storm {
    namespace storage {
        namespace geometry {
            
            template <typename ValueType>
            class NativePolytope : public Polytope<ValueType> {
            public:

                typedef StormEigen::Matrix<ValueType, StormEigen::Dynamic, StormEigen::Dynamic> EigenMatrix;
                typedef StormEigen::Matrix<ValueType, StormEigen::Dynamic, 1> EigenVector;

                enum class EmptyStatus{
                    Unknown, //It is unknown whether the polytope is empty or not
                    Empty, //The polytope is empty
                    Nonempty //the polytope is not empty
                };


                typedef typename Polytope<ValueType>::Point Point;


                /*!
                 * Creates a NativePolytope from the given halfspaces or points.
                 * If both representations are given, one of them might be ignored
                 */
                static std::shared_ptr<Polytope<ValueType>> create(boost::optional<std::vector<Halfspace<ValueType>>> const& halfspaces,
                                                                   boost::optional<std::vector<Point>> const& points);
                
                /*!
                 * Creates a NativePolytope from the given halfspaces
                 * The resulting polytope is defined as the intersection of the halfspaces.
                 */
                NativePolytope(std::vector<Halfspace<ValueType>> const& halfspaces);
                
                /*!
                 * Creates a NativePolytope from the given points.
                 * The resulting polytope is defined as the convex hull of the points'
                 */
                NativePolytope(std::vector<Point> const& points);
                
                /*!
                 * Copy and move constructors
                 */
                NativePolytope(NativePolytope<ValueType> const& other);
                NativePolytope(NativePolytope<ValueType>&& other);

                /*!
                * Construction from intern data
                */
                NativePolytope(EmptyStatus const& emptyStatus, EigenMatrix const& halfspaceMatrix, EigenVector const& halfspaceVector);
                NativePolytope(EmptyStatus&& emptyStatus, EigenMatrix&& halfspaceMatrix, EigenVector&& halfspaceVector);
                

                virtual ~NativePolytope();

                /*!
                 * Returns the vertices of this polytope.
                 */
                virtual std::vector<Point> getVertices() const override;
                
                /*!
                 * Returns the halfspaces of this polytope.
                 */
                virtual std::vector<Halfspace<ValueType>> getHalfspaces() const override;
                
                
                /*!
                 * Returns whether this polytope is the empty set.
                 */
                virtual bool isEmpty() const override;
                
                /*!
                 * Returns whether this polytope is universal (i.e., equals R^n).
                 */
                virtual bool isUniversal() const override;
                
                /*!
                 * Returns true iff the given point is inside of the polytope.
                 */
                virtual bool contains(Point const& point) const override;
                
                /*!
                 * Returns true iff the given polytope is a subset of this polytope.
                 */
                virtual bool contains(std::shared_ptr<Polytope<ValueType>> const& other) const override;
                
                /*!
                 * Intersects this polytope with rhs and returns the result.
                 */
                virtual std::shared_ptr<Polytope<ValueType>> intersection(std::shared_ptr<Polytope<ValueType>> const& rhs) const override;
                virtual std::shared_ptr<Polytope<ValueType>> intersection(Halfspace<ValueType> const& halfspace) const override;
                
                /*!
                 * Returns the convex union of this polytope and rhs.
                 */
                virtual std::shared_ptr<Polytope<ValueType>> convexUnion(std::shared_ptr<Polytope<ValueType>> const& rhs) const override;
                
                /*!
                 * Returns the minkowskiSum of this polytope and rhs.
                 */
                virtual std::shared_ptr<Polytope<ValueType>> minkowskiSum(std::shared_ptr<Polytope<ValueType>> const& rhs) const override;
                
                /*!
                 * Returns the affine transformation of this polytope P w.r.t. the given matrix A and vector b.
                 * The result is the set {A*x+b | x \in P}
                 * 
                 * @param matrix the transformation matrix, given as vector of rows
                 * @param vector the transformation offset
                 */
                virtual std::shared_ptr<Polytope<ValueType>> affineTransformation(std::vector<Point> const& matrix, Point const& vector) const override;
                
                /*!
                 * Finds an optimal point inside this polytope w.r.t. the given direction, i.e.,
                 * a point that maximizes dotPorduct(point, direction).
                 * If such a point does not exist, the returned bool is false. There are two reasons for this:
                 * - The polytope is empty
                 * - The polytope is not bounded in the given direction
                 */
                virtual std::pair<Point, bool> optimize(Point const& direction) const override;

                virtual bool isNativePolytope() const override;
                
            private:

                // returns the vertices of this polytope as EigenVectors
                std::vector<EigenVector> getEigenVertices() const;

                // As optimize(..) but with EigenVectors
                std::pair<EigenVector, bool> optimize(EigenVector const& direction) const;


                // declares one variable for each constraint and returns the obtained variables.
                std::vector<storm::expressions::Variable> declareVariables(storm::expressions::ExpressionManager& manager, std::string const& namePrefix) const;

                // returns the constrains defined by this polytope as an expresseion
                std::vector<storm::expressions::Expression> getConstraints(storm::expressions::ExpressionManager const& manager, std::vector<storm::expressions::Variable> const& variables) const;


                //Stores whether the polytope is empty or not
                mutable EmptyStatus emptyStatus;

                // Intern representation of the polytope as { x | Ax<=b }
                EigenMatrix A;
                EigenVector b;



            };
            
        }
    }
}

#endif /* STORM_STORAGE_GEOMETRY_NATIVEPOLYTOPE_H_ */