tempest/src/solver/NativeLinearEquationSolver.cpp

#include "src/solver/NativeLinearEquationSolver.h"

#include <utility>

#include "src/settings/SettingsManager.h"
#include "src/utility/vector.h"
#include "src/exceptions/InvalidStateException.h"

namespace storm {
    namespace solver {
        
        template<typename ValueType>
        NativeLinearEquationSolver<ValueType>::NativeLinearEquationSolver(storm::storage::SparseMatrix<ValueType> const& A, SolutionMethod method, double precision, uint_fast64_t maximalNumberOfIterations, bool relative) : A(A), method(method), precision(precision), relative(relative), maximalNumberOfIterations(maximalNumberOfIterations) {
            // Intentionally left empty.
        }
        
        template<typename ValueType>
        NativeLinearEquationSolver<ValueType>::NativeLinearEquationSolver(storm::storage::SparseMatrix<ValueType> const& A) : A(A) {
            // Get the settings object to customize linear solving.
            storm::settings::modules::NativeEquationSolverSettings const& settings = storm::settings::nativeEquationSolverSettings();
            
            // Get appropriate settings.
            maximalNumberOfIterations = settings.getMaximalIterationCount();
            precision = settings.getPrecision();
            relative = settings.getConvergenceCriterion() == storm::settings::modules::NativeEquationSolverSettings::ConvergenceCriterion::Relative;
            
            // Determine the method to be used.
            storm::settings::modules::NativeEquationSolverSettings::LinearEquationTechnique methodAsSetting = settings.getLinearEquationSystemTechnique();
            if (methodAsSetting == storm::settings::modules::NativeEquationSolverSettings::LinearEquationTechnique::Jacobi) {
                method = SolutionMethod::Jacobi;
            }
        }
                
        template<typename ValueType>
        void NativeLinearEquationSolver<ValueType>::solveEquationSystem(std::vector<ValueType>& x, std::vector<ValueType> const& b, std::vector<ValueType>* multiplyResult) const {
            // Get a Jacobi decomposition of the matrix A.
            std::pair<storm::storage::SparseMatrix<ValueType>, std::vector<ValueType>> jacobiDecomposition = A.getJacobiDecomposition();
            
            // To avoid copying the contents of the vector in the loop, we create a temporary x to swap with.
            bool multiplyResultProvided = true;
            std::vector<ValueType>* nextX = multiplyResult;
            if (nextX == nullptr) {
                nextX = new std::vector<ValueType>(x.size());
                multiplyResultProvided = false;
            }
            std::vector<ValueType> const* copyX = nextX;
            std::vector<ValueType>* currentX = &x;
            
            // Target vector for precision calculation.
            std::vector<ValueType> tmpX(x.size());
            
            // Set up additional environment variables.
            uint_fast64_t iterationCount = 0;
            bool converged = false;
            
            while (!converged && iterationCount < maximalNumberOfIterations) {
                // Compute D^-1 * (b - LU * x) and store result in nextX.
                jacobiDecomposition.first.multiplyWithVector(*currentX, tmpX);
                storm::utility::vector::subtractVectors(b, tmpX, tmpX);
                storm::utility::vector::multiplyVectorsPointwise(jacobiDecomposition.second, tmpX, *nextX);
                
                // Swap the two pointers as a preparation for the next iteration.
                std::swap(nextX, currentX);
                
                // Now check if the process already converged within our precision.
                converged = storm::utility::vector::equalModuloPrecision(*currentX, *nextX, precision, relative);
                
                // Increase iteration count so we can abort if convergence is too slow.
                ++iterationCount;
            }
            
            // If the last iteration did not write to the original x we have to swap the contents, because the
            // output has to be written to the input parameter x.
            if (currentX == copyX) {
                std::swap(x, *currentX);
            }
            
            // If the vector for the temporary multiplication result was not provided, we need to delete it.
            if (!multiplyResultProvided) {
                delete copyX;
            }
        }
        
        template<typename ValueType>
        void NativeLinearEquationSolver<ValueType>::performMatrixVectorMultiplication(std::vector<ValueType>& x, std::vector<ValueType> const* b, uint_fast64_t n, std::vector<ValueType>* multiplyResult) const {
            // Set up some temporary variables so that we can just swap pointers instead of copying the result after
            // each iteration.
            std::vector<ValueType>* currentX = &x;
            
            bool multiplyResultProvided = true;
            std::vector<ValueType>* nextX = multiplyResult;
            if (nextX == nullptr) {
                nextX = new std::vector<ValueType>(x.size());
                multiplyResultProvided = false;
            }
            std::vector<ValueType> const* copyX = nextX;
            
            // Now perform matrix-vector multiplication as long as we meet the bound.
            for (uint_fast64_t i = 0; i < n; ++i) {
                A.multiplyWithVector(*currentX, *nextX);
                std::swap(nextX, currentX);
                
                // If requested, add an offset to the current result vector.
                if (b != nullptr) {
                    storm::utility::vector::addVectors(*currentX, *b, *currentX);
                }
            }
            
            // If we performed an odd number of repetitions, we need to swap the contents of currentVector and x,
            // because the output is supposed to be stored in the input vector x.
            if (currentX == copyX) {
                std::swap(x, *currentX);
            }
            
            // If the vector for the temporary multiplication result was not provided, we need to delete it.
            if (!multiplyResultProvided) {
                delete copyX;
            }
        }


        template<typename ValueType>
        std::string NativeLinearEquationSolver<ValueType>::methodToString() const {
            switch (method) {
                case SolutionMethod::Jacobi: return "jacobi";
            }
        }
        
        // Explicitly instantiate the linear equation solver.
        template class NativeLinearEquationSolver<double>;
    }
}