tempest/src/storm/solver/SymbolicNativeLinearEquationSolver.h

#pragma once

#include "storm/solver/SymbolicLinearEquationSolver.h"
#include "storm/solver/SolverStatus.h"
#include "storm/solver/SolverSelectionOptions.h"

#include "storm/utility/NumberTraits.h"

namespace storm {
    namespace solver {

        /*!
         * An interface that represents an abstract symbolic linear equation solver. In addition to solving a system of
         * linear equations, the functionality to repeatedly multiply a matrix with a given vector is provided.
         */
        template<storm::dd::DdType DdType, typename ValueType = double>
        class SymbolicNativeLinearEquationSolver : public SymbolicLinearEquationSolver<DdType, ValueType> {
        public:
            /*!
             * Constructs a symbolic linear equation solver.
             *
             * @param settings The settings to use.
             */
            SymbolicNativeLinearEquationSolver();
            
            /*!
             * Constructs a symbolic linear equation solver with the given meta variable sets and pairs.
             *
             * @param A The matrix defining the coefficients of the linear equation system.
             * @param diagonal An ADD characterizing the elements on the diagonal of the matrix.
             * @param allRows A BDD characterizing all rows of the equation system.
             * @param rowMetaVariables The meta variables used to encode the rows of the matrix.
             * @param columnMetaVariables The meta variables used to encode the columns of the matrix.
             * @param rowColumnMetaVariablePairs The pairs of row meta variables and the corresponding column meta
             * variables.
             * @param settings The settings to use.
             */
            SymbolicNativeLinearEquationSolver(storm::dd::Add<DdType, ValueType> const& A, storm::dd::Bdd<DdType> const& allRows, std::set<storm::expressions::Variable> const& rowMetaVariables, std::set<storm::expressions::Variable> const& columnMetaVariables, std::vector<std::pair<storm::expressions::Variable, storm::expressions::Variable>> const& rowColumnMetaVariablePairs);

            /*!
             * Constructs a symbolic linear equation solver with the given meta variable sets and pairs.
             *
             * @param diagonal An ADD characterizing the elements on the diagonal of the matrix.
             * @param allRows A BDD characterizing all rows of the equation system.
             * @param rowMetaVariables The meta variables used to encode the rows of the matrix.
             * @param columnMetaVariables The meta variables used to encode the columns of the matrix.
             * @param rowColumnMetaVariablePairs The pairs of row meta variables and the corresponding column meta
             * variables.
             * @param settings The settings to use.
             */
            SymbolicNativeLinearEquationSolver(storm::dd::Bdd<DdType> const& allRows, std::set<storm::expressions::Variable> const& rowMetaVariables, std::set<storm::expressions::Variable> const& columnMetaVariables, std::vector<std::pair<storm::expressions::Variable, storm::expressions::Variable>> const& rowColumnMetaVariablePairs);

            /*!
             * Solves the equation system A*x = b. The matrix A is required to be square and have a unique solution.
             * The solution of the set of linear equations will be written to the vector x. Note that the matrix A has
             * to be given upon construction time of the solver object.
             *
             * @param x The initial guess for the solution vector. Its length must be equal to the number of rows of A.
             * @param b The right-hand side of the equation system. Its length must be equal to the number of rows of A.
             * @return The solution of the equation system.
             */
            virtual storm::dd::Add<DdType, ValueType> solveEquations(Environment const& env, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const override;
            
            virtual LinearEquationSolverProblemFormat getEquationProblemFormat(Environment const& env) const override;
            virtual LinearEquationSolverRequirements getRequirements(Environment const& env) const override;
            
        private:
            NativeLinearEquationSolverMethod getMethod(Environment const& env, bool isExactMode) const;
            
            storm::dd::Add<DdType, ValueType> solveEquationsJacobi(Environment const& env, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;
            storm::dd::Add<DdType, ValueType> solveEquationsPower(Environment const& env, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;
            storm::dd::Add<DdType, ValueType> solveEquationsRationalSearch(Environment const& env, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;
            
            /*!
             * Determines whether the given vector x satisfies x = Ax + b.
             */
            bool isSolutionFixedPoint(storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;
            
            template<typename RationalType, typename ImpreciseType>
            static storm::dd::Add<DdType, RationalType> sharpen(uint64_t precision, SymbolicNativeLinearEquationSolver<DdType, RationalType> const& rationalSolver, storm::dd::Add<DdType, ImpreciseType> const& x, storm::dd::Add<DdType, RationalType> const& rationalB, bool& isSolution);
            
            template<typename RationalType, typename ImpreciseType>
            storm::dd::Add<DdType, RationalType> solveEquationsRationalSearchHelper(Environment const& env, SymbolicNativeLinearEquationSolver<DdType, RationalType> const& rationalSolver, SymbolicNativeLinearEquationSolver<DdType, ImpreciseType> const& impreciseSolver, storm::dd::Add<DdType, RationalType> const& rationalB, storm::dd::Add<DdType, ImpreciseType> const& x, storm::dd::Add<DdType, ImpreciseType> const& b) const;
            template<typename ImpreciseType>
            typename std::enable_if<std::is_same<ValueType, ImpreciseType>::value && storm::NumberTraits<ValueType>::IsExact, storm::dd::Add<DdType, ValueType>>::type solveEquationsRationalSearchHelper(Environment const& env, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;
            template<typename ImpreciseType>
            typename std::enable_if<std::is_same<ValueType, ImpreciseType>::value && !storm::NumberTraits<ValueType>::IsExact, storm::dd::Add<DdType, ValueType>>::type solveEquationsRationalSearchHelper(Environment const& env, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;
            template<typename ImpreciseType>
            typename std::enable_if<!std::is_same<ValueType, ImpreciseType>::value, storm::dd::Add<DdType, ValueType>>::type solveEquationsRationalSearchHelper(Environment const& env, storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b) const;

            template<storm::dd::DdType DdTypePrime, typename ValueTypePrime>
            friend class SymbolicNativeLinearEquationSolver;

            struct PowerIterationResult {
                PowerIterationResult(SolverStatus status, uint64_t iterations, storm::dd::Add<DdType, ValueType> const& values) : status(status), iterations(iterations), values(values) {
                    // Intentionally left empty.
                }
                
                SolverStatus status;
                uint64_t iterations;
                storm::dd::Add<DdType, ValueType> values;
            };
            
            PowerIterationResult performPowerIteration(storm::dd::Add<DdType, ValueType> const& x, storm::dd::Add<DdType, ValueType> const& b, ValueType const& precision, bool relativeTerminationCriterion, uint64_t maximalIterations) const;

        };
        
        template<storm::dd::DdType DdType, typename ValueType>
        class SymbolicNativeLinearEquationSolverFactory : SymbolicLinearEquationSolverFactory<DdType, ValueType> {
        public:
            using SymbolicLinearEquationSolverFactory<DdType, ValueType>::create;
            
            virtual std::unique_ptr<storm::solver::SymbolicLinearEquationSolver<DdType, ValueType>> create(Environment const& env) const override;
            
        };
        
    } // namespace solver
} // namespace storm