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994 lines
77 KiB
994 lines
77 KiB
#include "storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.h"
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#include "storm/modelchecker/prctl/helper/SparseMdpPrctlHelper.h"
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#include "storm/models/sparse/StandardRewardModel.h"
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#include "storm/storage/StronglyConnectedComponentDecomposition.h"
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#include "storm/storage/MaximalEndComponentDecomposition.h"
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#include "storm/settings/SettingsManager.h"
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#include "storm/settings/modules/GeneralSettings.h"
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#include "storm/settings/modules/MinMaxEquationSolverSettings.h"
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#include "storm/settings/modules/MarkovAutomatonSettings.h"
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#include "storm/utility/macros.h"
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#include "storm/utility/vector.h"
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#include "storm/utility/graph.h"
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#include "storm/storage/expressions/Variable.h"
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#include "storm/storage/expressions/Expression.h"
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#include "storm/storage/expressions/ExpressionManager.h"
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#include "storm/utility/numerical.h"
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#include "storm/solver/MinMaxLinearEquationSolver.h"
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#include "storm/solver/LpSolver.h"
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#include "storm/exceptions/InvalidStateException.h"
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#include "storm/exceptions/InvalidPropertyException.h"
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#include "storm/exceptions/InvalidOperationException.h"
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#include "storm/exceptions/UncheckedRequirementException.h"
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namespace storm {
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namespace modelchecker {
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namespace helper {
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template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
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void SparseMarkovAutomatonCslHelper::computeBoundedReachabilityProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRates, storm::storage::BitVector const& goalStates, storm::storage::BitVector const& markovianNonGoalStates, storm::storage::BitVector const& probabilisticNonGoalStates, std::vector<ValueType>& markovianNonGoalValues, std::vector<ValueType>& probabilisticNonGoalValues, ValueType delta, uint64_t numberOfSteps, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
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// Start by computing four sparse matrices:
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// * a matrix aMarkovian with all (discretized) transitions from Markovian non-goal states to all Markovian non-goal states.
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// * a matrix aMarkovianToProbabilistic with all (discretized) transitions from Markovian non-goal states to all probabilistic non-goal states.
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// * a matrix aProbabilistic with all (non-discretized) transitions from probabilistic non-goal states to other probabilistic non-goal states.
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// * a matrix aProbabilisticToMarkovian with all (non-discretized) transitions from probabilistic non-goal states to all Markovian non-goal states.
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typename storm::storage::SparseMatrix<ValueType> aMarkovian = transitionMatrix.getSubmatrix(true, markovianNonGoalStates, markovianNonGoalStates, true);
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typename storm::storage::SparseMatrix<ValueType> aMarkovianToProbabilistic = transitionMatrix.getSubmatrix(true, markovianNonGoalStates, probabilisticNonGoalStates);
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typename storm::storage::SparseMatrix<ValueType> aProbabilistic = transitionMatrix.getSubmatrix(true, probabilisticNonGoalStates, probabilisticNonGoalStates);
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typename storm::storage::SparseMatrix<ValueType> aProbabilisticToMarkovian = transitionMatrix.getSubmatrix(true, probabilisticNonGoalStates, markovianNonGoalStates);
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// The matrices with transitions from Markovian states need to be digitized.
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// Digitize aMarkovian. Based on whether the transition is a self-loop or not, we apply the two digitization rules.
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uint64_t rowIndex = 0;
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for (auto state : markovianNonGoalStates) {
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for (auto& element : aMarkovian.getRow(rowIndex)) {
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ValueType eTerm = std::exp(-exitRates[state] * delta);
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if (element.getColumn() == rowIndex) {
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element.setValue((storm::utility::one<ValueType>() - eTerm) * element.getValue() + eTerm);
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} else {
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element.setValue((storm::utility::one<ValueType>() - eTerm) * element.getValue());
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}
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}
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++rowIndex;
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}
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// Digitize aMarkovianToProbabilistic. As there are no self-loops in this case, we only need to apply the digitization formula for regular successors.
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rowIndex = 0;
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for (auto state : markovianNonGoalStates) {
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for (auto& element : aMarkovianToProbabilistic.getRow(rowIndex)) {
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element.setValue((1 - std::exp(-exitRates[state] * delta)) * element.getValue());
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}
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++rowIndex;
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}
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// Initialize the two vectors that hold the variable one-step probabilities to all target states for probabilistic and Markovian (non-goal) states.
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std::vector<ValueType> bProbabilistic(aProbabilistic.getRowCount());
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std::vector<ValueType> bMarkovian(markovianNonGoalStates.getNumberOfSetBits());
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// Compute the two fixed right-hand side vectors, one for Markovian states and one for the probabilistic ones.
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std::vector<ValueType> bProbabilisticFixed = transitionMatrix.getConstrainedRowGroupSumVector(probabilisticNonGoalStates, goalStates);
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std::vector<ValueType> bMarkovianFixed;
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bMarkovianFixed.reserve(markovianNonGoalStates.getNumberOfSetBits());
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for (auto state : markovianNonGoalStates) {
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bMarkovianFixed.push_back(storm::utility::zero<ValueType>());
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for (auto& element : transitionMatrix.getRowGroup(state)) {
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if (goalStates.get(element.getColumn())) {
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bMarkovianFixed.back() += (1 - std::exp(-exitRates[state] * delta)) * element.getValue();
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}
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}
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}
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// Check for requirements of the solver.
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// The solution is unique as we assume non-zeno MAs.
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storm::solver::MinMaxLinearEquationSolverRequirements requirements = minMaxLinearEquationSolverFactory.getRequirements(true, dir);
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requirements.clearBounds();
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STORM_LOG_THROW(requirements.empty(), storm::exceptions::UncheckedRequirementException, "Cannot establish requirements for solver.");
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std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = minMaxLinearEquationSolverFactory.create(aProbabilistic);
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solver->setHasUniqueSolution();
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solver->setBounds(storm::utility::zero<ValueType>(), storm::utility::one<ValueType>());
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solver->setRequirementsChecked();
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solver->setCachingEnabled(true);
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// Perform the actual value iteration
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// * loop until the step bound has been reached
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// * in the loop:
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// * perform value iteration using A_PSwG, v_PS and the vector b where b = (A * 1_G)|PS + A_PStoMS * v_MS
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// and 1_G being the characteristic vector for all goal states.
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// * perform one timed-step using v_MS := A_MSwG * v_MS + A_MStoPS * v_PS + (A * 1_G)|MS
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std::vector<ValueType> markovianNonGoalValuesSwap(markovianNonGoalValues);
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for (uint64_t currentStep = 0; currentStep < numberOfSteps; ++currentStep) {
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// Start by (re-)computing bProbabilistic = bProbabilisticFixed + aProbabilisticToMarkovian * vMarkovian.
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aProbabilisticToMarkovian.multiplyWithVector(markovianNonGoalValues, bProbabilistic);
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storm::utility::vector::addVectors(bProbabilistic, bProbabilisticFixed, bProbabilistic);
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// Now perform the inner value iteration for probabilistic states.
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solver->solveEquations(dir, probabilisticNonGoalValues, bProbabilistic);
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// (Re-)compute bMarkovian = bMarkovianFixed + aMarkovianToProbabilistic * vProbabilistic.
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aMarkovianToProbabilistic.multiplyWithVector(probabilisticNonGoalValues, bMarkovian);
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storm::utility::vector::addVectors(bMarkovian, bMarkovianFixed, bMarkovian);
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aMarkovian.multiplyWithVector(markovianNonGoalValues, markovianNonGoalValuesSwap);
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std::swap(markovianNonGoalValues, markovianNonGoalValuesSwap);
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storm::utility::vector::addVectors(markovianNonGoalValues, bMarkovian, markovianNonGoalValues);
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}
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// After the loop, perform one more step of the value iteration for PS states.
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aProbabilisticToMarkovian.multiplyWithVector(markovianNonGoalValues, bProbabilistic);
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storm::utility::vector::addVectors(bProbabilistic, bProbabilisticFixed, bProbabilistic);
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solver->solveEquations(dir, probabilisticNonGoalValues, bProbabilistic);
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}
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template <typename ValueType, typename std::enable_if<!storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
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void SparseMarkovAutomatonCslHelper::computeBoundedReachabilityProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRates, storm::storage::BitVector const& goalStates, storm::storage::BitVector const& markovianNonGoalStates, storm::storage::BitVector const& probabilisticNonGoalStates, std::vector<ValueType>& markovianNonGoalValues, std::vector<ValueType>& probabilisticNonGoalValues, ValueType delta, uint64_t numberOfSteps, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
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STORM_LOG_THROW(false, storm::exceptions::InvalidOperationException, "Computing bounded reachability probabilities is unsupported for this value type.");
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}
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template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
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void SparseMarkovAutomatonCslHelper::printTransitions(std::vector<ValueType> const& exitRateVector, storm::storage::SparseMatrix<ValueType> const& fullTransitionMatrix, storm::storage::BitVector const& markovianStates, std::vector<std::vector<ValueType>>& vd, std::vector<std::vector<ValueType>>& vu, std::vector<std::vector<ValueType>>& wu){
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std::ofstream logfile("U+logfile.txt", std::ios::app);
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auto const& rowGroupIndices = fullTransitionMatrix.getRowGroupIndices();
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auto numberOfStates = fullTransitionMatrix.getRowGroupCount();
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logfile << "number of states = num of row group count " << numberOfStates << "\n";
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for (uint_fast64_t i = 0; i < fullTransitionMatrix.getRowGroupCount(); i++) {
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logfile << " from node " << i << " ";
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auto from = rowGroupIndices[i];
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auto to = rowGroupIndices[i+1];
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for (auto j = from ; j < to; j++){
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for (auto &v : fullTransitionMatrix.getRow(j)) {
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if (markovianStates[i]){
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logfile << v.getValue() *exitRateVector[i] << " -> "<< v.getColumn() << "\t";
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} else {
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logfile << v.getValue() << " -> "<< v.getColumn() << "\t";
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}
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}
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logfile << "\n";
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}
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}
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logfile << "\n";
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logfile << "vd: \n";
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for (uint_fast64_t i =0 ; i<vd.size(); i++){
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for(uint_fast64_t j=0; j<fullTransitionMatrix.getRowGroupCount(); j++){
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logfile << vd[i][j] << "\t" ;
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}
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logfile << "\n";
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}
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logfile << "\nvu:\n";
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for (uint_fast64_t i =0 ; i<vu.size(); i++){
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for(uint_fast64_t j=0; j<fullTransitionMatrix.getRowGroupCount(); j++){
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logfile << vu[i][j] << "\t" ;
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}
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logfile << "\n";
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}
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logfile << "\nwu\n";
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for (uint_fast64_t i =0 ; i<wu.size(); i++){
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for(uint_fast64_t j=0; j<fullTransitionMatrix.getRowGroupCount(); j++){
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logfile << wu[i][j] << "\t" ;
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}
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logfile << "\n";
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}
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logfile.close();
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}
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template<typename ValueType>
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ValueType SparseMarkovAutomatonCslHelper::poisson(ValueType lambda, uint64_t i) {
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ValueType res = pow(lambda, i);
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ValueType fac = 1;
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for (long j = i ; j>0 ; j--){
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fac = fac *j;
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}
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res = res / fac ;
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res = res * exp(-lambda);
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return res;
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}
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template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
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void SparseMarkovAutomatonCslHelper::calculateVu(uint64_t k, uint64_t node, ValueType lambda, std::vector<std::vector<ValueType>>& vu, std::vector<std::vector<ValueType>>& wu, storm::storage::SparseMatrix<ValueType> const& fullTransitionMatrix, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates){
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if (vu[k][node]!=-1){return;} //dynamic programming. avoiding multiple calculation.
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uint64_t N = vu.size()-1;
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auto rowGroupIndices = fullTransitionMatrix.getRowGroupIndices();
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ValueType res =0;
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for (uint_fast64_t i = k ; i < N ; i++ ){
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if (wu[N-1-(i-k)][node]==-1){
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calculateWu((N-1-(i-k)),node,lambda,wu,fullTransitionMatrix,markovianStates,psiStates);
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}
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res+=poisson(lambda, i)*wu[N-1-(i-k)][node];
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}
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vu[k][node]=res;
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}
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template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
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void SparseMarkovAutomatonCslHelper::calculateWu(uint64_t k, uint64_t node, ValueType lambda, std::vector<std::vector<ValueType>>& wu, storm::storage::SparseMatrix<ValueType> const& fullTransitionMatrix, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates){
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if (wu[k][node]!=-1){return;} //dynamic programming. avoiding multiple calculation.
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uint64_t N = wu.size()-1;
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auto const& rowGroupIndices = fullTransitionMatrix.getRowGroupIndices();
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ValueType res;
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if (k==N){
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wu[k][node]=0;
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return;
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}
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if (psiStates[node]){
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wu[k][node]=1;
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return;
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}
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if (markovianStates[node]){
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res = 0;
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auto line = fullTransitionMatrix.getRow(rowGroupIndices[node]);
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for (auto &element : line){
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uint64_t to = element.getColumn();
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if (wu[k+1][to]==-1){
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calculateWu(k+1,to,lambda,wu,fullTransitionMatrix,markovianStates,psiStates);
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}
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res+=element.getValue()*wu[k+1][to];
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}
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} else {
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res = 0;
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uint64_t rowStart = rowGroupIndices[node];
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uint64_t rowEnd = rowGroupIndices[node+1];
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for (uint64_t i = rowStart; i< rowEnd; i++){
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auto line = fullTransitionMatrix.getRow(i);
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ValueType between = 0;
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for (auto& element: line){
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uint64_t to = element.getColumn();
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if (to==node){
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continue;
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}
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if (wu[k][to]==-1){
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calculateWu(k,to,lambda,wu,fullTransitionMatrix,markovianStates,psiStates);
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}
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between+=element.getValue()*wu[k][to];
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}
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if (between > res){
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res = between;
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}
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}
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} // end no goal-prob state
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wu[k][node]=res;
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}
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template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
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void SparseMarkovAutomatonCslHelper::calculateVd(uint64_t k, uint64_t node, ValueType lambda, std::vector<std::vector<ValueType>>& vd, storm::storage::SparseMatrix<ValueType> const& fullTransitionMatrix, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates){
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std::ofstream logfile("U+logfile.txt", std::ios::app);
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if (vd[k][node]!=-1){return;} //dynamic programming. avoiding multiple calculation.
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logfile << "calculating vd for k = " << k << " node "<< node << " \t";
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uint64_t N = vd.size()-1;
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auto const& rowGroupIndices = fullTransitionMatrix.getRowGroupIndices();
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ValueType res;
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if (k==N){
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logfile << "k == N! res = 0\n";
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vd[k][node]=0;
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return;
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}
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//goal state
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if (psiStates[node]){
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res = 0;
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for (uint64_t i = k ; i<N ; i++){
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res+=poisson(lambda,i);
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}
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vd[k][node]=res;
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logfile << "goal state node " << node << " res = " << res << "\n";
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return;
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}
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// no-goal markovian state
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if (markovianStates[node]){
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logfile << "markovian state: ";
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res = 0;
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auto line = fullTransitionMatrix.getRow(rowGroupIndices[node]);
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for (auto &element : line){
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uint64_t to = element.getColumn();
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if (vd[k+1][to]==-1){
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calculateVd(k+1,to,lambda,vd, fullTransitionMatrix, markovianStates,psiStates);
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}
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res+=element.getValue()*vd[k+1][to];
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}
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} else { //no-goal prob state
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logfile << "prob state: ";
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res = 0;
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uint64_t rowStart = rowGroupIndices[node];
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uint64_t rowEnd = rowGroupIndices[node+1];
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for (uint64_t i = rowStart; i< rowEnd; i++){
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auto line = fullTransitionMatrix.getRow(i);
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ValueType between = 0;
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for (auto& element: line){
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uint64_t to = element.getColumn();
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if (to==node){
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logfile << "ignoring self loops for now";
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continue;
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}
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if (vd[k][to]==-1){
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calculateVd(k,to,lambda,vd, fullTransitionMatrix, markovianStates,psiStates);
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}
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between+=element.getValue()*vd[k][to];
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}
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if (between > res){
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res = between;
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}
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}
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}
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vd[k][node]=res;
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logfile << " res = " << res << "\n";
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}
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template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
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std::vector<ValueType> SparseMarkovAutomatonCslHelper::unifPlus( std::pair<double, double> const& boundsPair, std::vector<ValueType> const& exitRateVector, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates){
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STORM_LOG_TRACE("Using UnifPlus to compute bounded until probabilities.");
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std::ofstream logfile("U+logfile.txt", std::ios::app);
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ValueType maxNorm = 0;
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//bitvectors to identify different kind of states
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// storm::storage::BitVector const &markovianNonGoalStates = markovianStates & ~psiStates;
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// storm::storage::BitVector const &probabilisticNonGoalStates = ~markovianStates & ~psiStates;
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storm::storage::BitVector allStates(markovianStates.size(), true);
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//vectors to save calculation
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std::vector<std::vector<ValueType>> vd,vu,wu;
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//transition matrix with diagonal entries. The values can be changed during uniformisation
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typename storm::storage::SparseMatrix<ValueType> fullTransitionMatrix = transitionMatrix.getSubmatrix(true, allStates , allStates , true);
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auto rowGroupIndices = fullTransitionMatrix.getRowGroupIndices();
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std::vector<ValueType> exitRate{exitRateVector};
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//(1) define horizon, epsilon, kappa , N, lambda,
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double T = boundsPair.second;
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ValueType kappa = storm::utility::one<ValueType>() /10; // would be better as option-parameter
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uint64_t numberOfStates = fullTransitionMatrix.getRowGroupCount();
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ValueType epsilon = storm::settings::getModule<storm::settings::modules::GeneralSettings>().getPrecision();
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ValueType lambda = exitRateVector[0];
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for (ValueType act: exitRateVector) {
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lambda = std::max(act, lambda);
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}
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uint64_t N;
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// while not close enough to precision:
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do {
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// (2) update parameter
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N = ceil(lambda*T*exp(2)-log(kappa*epsilon));
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// (3) uniform - just applied to markovian states
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for (uint_fast64_t i = 0; i < fullTransitionMatrix.getRowGroupCount(); i++) {
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if (!markovianStates[i]) {
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continue;
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}
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uint64_t from = rowGroupIndices[i]; //markovian state -> no Nondeterminism -> only one row
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if (exitRate[i] == lambda) {
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continue; //already unified
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}
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auto line = fullTransitionMatrix.getRow(from);
|
|
ValueType exitOld = exitRate[i];
|
|
ValueType exitNew = lambda;
|
|
for (auto &v : line) {
|
|
if (v.getColumn() == i) { //diagonal element
|
|
ValueType newSelfLoop = exitNew - exitOld + v.getValue();
|
|
ValueType newRate = newSelfLoop / exitNew;
|
|
v.setValue(newRate);
|
|
} else { //modify probability
|
|
ValueType propOld = v.getValue();
|
|
ValueType propNew = propOld * exitOld / exitNew;
|
|
v.setValue(propNew);
|
|
}
|
|
}
|
|
exitRate[i] = exitNew;
|
|
}
|
|
|
|
// (4) define vectors/matrices
|
|
std::vector<ValueType> init(numberOfStates, -1);
|
|
vd = std::vector<std::vector<ValueType>> (N + 1, init);
|
|
vu = std::vector<std::vector<ValueType>> (N + 1, init);
|
|
wu = std::vector<std::vector<ValueType>> (N + 1, init);
|
|
|
|
printTransitions(exitRate, fullTransitionMatrix, markovianStates,vd,vu,wu); // TODO: delete when develepmont is finished
|
|
|
|
// (5) calculate vectors and maxNorm
|
|
for (uint64_t i = 0; i < numberOfStates; i++) {
|
|
for (uint64_t k = N; k <= N; k--) {
|
|
calculateVd(k, i, T*lambda, vd, fullTransitionMatrix, markovianStates, psiStates);
|
|
calculateWu(k, i, T*lambda, wu, fullTransitionMatrix, markovianStates, psiStates);
|
|
calculateVu(k, i, T*lambda, vu, wu, fullTransitionMatrix, markovianStates, psiStates);
|
|
//also use iteration to keep maxNorm of vd and vu up to date, so the loop-condition is easy to prove
|
|
ValueType diff = std::abs(vd[k][i]-vu[k][i]);
|
|
maxNorm = std::max(maxNorm, diff);
|
|
}
|
|
}
|
|
printTransitions(exitRate, fullTransitionMatrix, markovianStates,vd,vu,wu); // TODO: delete when development is finished
|
|
|
|
|
|
// (6) double lambda
|
|
lambda=2*lambda;
|
|
|
|
} while (maxNorm>epsilon*(1-kappa));
|
|
return vd[0];
|
|
}
|
|
|
|
template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
|
|
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeBoundedUntilProbabilitiesImca(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, std::pair<double, double> const& boundsPair, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
|
|
STORM_LOG_TRACE("Using IMCA's technique to compute bounded until probabilities.");
|
|
|
|
uint64_t numberOfStates = transitionMatrix.getRowGroupCount();
|
|
|
|
// 'Unpack' the bounds to make them more easily accessible.
|
|
double lowerBound = boundsPair.first;
|
|
double upperBound = boundsPair.second;
|
|
|
|
// (1) Compute the accuracy we need to achieve the required error bound.
|
|
ValueType maxExitRate = 0;
|
|
for (auto value : exitRateVector) {
|
|
maxExitRate = std::max(maxExitRate, value);
|
|
}
|
|
ValueType delta = (2 * storm::settings::getModule<storm::settings::modules::GeneralSettings>().getPrecision()) / (upperBound * maxExitRate * maxExitRate);
|
|
|
|
// (2) Compute the number of steps we need to make for the interval.
|
|
uint64_t numberOfSteps = static_cast<uint64_t>(std::ceil((upperBound - lowerBound) / delta));
|
|
STORM_LOG_INFO("Performing " << numberOfSteps << " iterations (delta=" << delta << ") for interval [" << lowerBound << ", " << upperBound << "]." << std::endl);
|
|
|
|
// (3) Compute the non-goal states and initialize two vectors
|
|
// * vProbabilistic holds the probability values of probabilistic non-goal states.
|
|
// * vMarkovian holds the probability values of Markovian non-goal states.
|
|
storm::storage::BitVector const& markovianNonGoalStates = markovianStates & ~psiStates;
|
|
storm::storage::BitVector const& probabilisticNonGoalStates = ~markovianStates & ~psiStates;
|
|
std::vector<ValueType> vProbabilistic(probabilisticNonGoalStates.getNumberOfSetBits());
|
|
std::vector<ValueType> vMarkovian(markovianNonGoalStates.getNumberOfSetBits());
|
|
|
|
computeBoundedReachabilityProbabilities(dir, transitionMatrix, exitRateVector, psiStates, markovianNonGoalStates, probabilisticNonGoalStates, vMarkovian, vProbabilistic, delta, numberOfSteps, minMaxLinearEquationSolverFactory);
|
|
|
|
// (4) If the lower bound of interval was non-zero, we need to take the current values as the starting values for a subsequent value iteration.
|
|
if (lowerBound != storm::utility::zero<ValueType>()) {
|
|
std::vector<ValueType> vAllProbabilistic((~markovianStates).getNumberOfSetBits());
|
|
std::vector<ValueType> vAllMarkovian(markovianStates.getNumberOfSetBits());
|
|
|
|
// Create the starting value vectors for the next value iteration based on the results of the previous one.
|
|
storm::utility::vector::setVectorValues<ValueType>(vAllProbabilistic, psiStates % ~markovianStates, storm::utility::one<ValueType>());
|
|
storm::utility::vector::setVectorValues<ValueType>(vAllProbabilistic, ~psiStates % ~markovianStates, vProbabilistic);
|
|
storm::utility::vector::setVectorValues<ValueType>(vAllMarkovian, psiStates % markovianStates, storm::utility::one<ValueType>());
|
|
storm::utility::vector::setVectorValues<ValueType>(vAllMarkovian, ~psiStates % markovianStates, vMarkovian);
|
|
|
|
// Compute the number of steps to reach the target interval.
|
|
numberOfSteps = static_cast<uint64_t>(std::ceil(lowerBound / delta));
|
|
STORM_LOG_INFO("Performing " << numberOfSteps << " iterations (delta=" << delta << ") for interval [0, " << lowerBound << "]." << std::endl);
|
|
|
|
// Compute the bounded reachability for interval [0, b-a].
|
|
computeBoundedReachabilityProbabilities(dir, transitionMatrix, exitRateVector, storm::storage::BitVector(numberOfStates), markovianStates, ~markovianStates, vAllMarkovian, vAllProbabilistic, delta, numberOfSteps, minMaxLinearEquationSolverFactory);
|
|
|
|
// Create the result vector out of vAllProbabilistic and vAllMarkovian and return it.
|
|
std::vector<ValueType> result(numberOfStates, storm::utility::zero<ValueType>());
|
|
storm::utility::vector::setVectorValues(result, ~markovianStates, vAllProbabilistic);
|
|
storm::utility::vector::setVectorValues(result, markovianStates, vAllMarkovian);
|
|
|
|
return result;
|
|
} else {
|
|
// Create the result vector out of 1_G, vProbabilistic and vMarkovian and return it.
|
|
std::vector<ValueType> result(numberOfStates);
|
|
storm::utility::vector::setVectorValues<ValueType>(result, psiStates, storm::utility::one<ValueType>());
|
|
storm::utility::vector::setVectorValues(result, probabilisticNonGoalStates, vProbabilistic);
|
|
storm::utility::vector::setVectorValues(result, markovianNonGoalStates, vMarkovian);
|
|
return result;
|
|
}
|
|
}
|
|
|
|
template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
|
|
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeBoundedUntilProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, std::pair<double, double> const& boundsPair, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
|
|
|
|
auto const& markovAutomatonSettings = storm::settings::getModule<storm::settings::modules::MarkovAutomatonSettings>();
|
|
if (markovAutomatonSettings.getTechnique() == storm::settings::modules::MarkovAutomatonSettings::BoundedReachabilityTechnique::Imca) {
|
|
return computeBoundedUntilProbabilitiesImca(dir, transitionMatrix, exitRateVector, markovianStates, psiStates, boundsPair, minMaxLinearEquationSolverFactory);
|
|
} else {
|
|
STORM_LOG_ASSERT(markovAutomatonSettings.getTechnique() == storm::settings::modules::MarkovAutomatonSettings::BoundedReachabilityTechnique::UnifPlus, "Unknown solution technique.");
|
|
|
|
// Why is optimization direction not passed?
|
|
return unifPlus(boundsPair, exitRateVector, transitionMatrix, markovianStates, psiStates);
|
|
}
|
|
}
|
|
|
|
template <typename ValueType, typename std::enable_if<!storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
|
|
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeBoundedUntilProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, std::pair<double, double> const& boundsPair, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
|
|
STORM_LOG_THROW(false, storm::exceptions::InvalidOperationException, "Computing bounded until probabilities is unsupported for this value type.");
|
|
}
|
|
|
|
|
|
template<typename ValueType>
|
|
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeUntilProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool qualitative, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
|
|
return std::move(storm::modelchecker::helper::SparseMdpPrctlHelper<ValueType>::computeUntilProbabilities(dir, transitionMatrix, backwardTransitions, phiStates, psiStates, qualitative, false, minMaxLinearEquationSolverFactory).values);
|
|
}
|
|
|
|
template <typename ValueType, typename RewardModelType>
|
|
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeReachabilityRewards(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, RewardModelType const& rewardModel, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
|
|
|
|
// Get a reward model where the state rewards are scaled accordingly
|
|
std::vector<ValueType> stateRewardWeights(transitionMatrix.getRowGroupCount(), storm::utility::zero<ValueType>());
|
|
for (auto const markovianState : markovianStates) {
|
|
stateRewardWeights[markovianState] = storm::utility::one<ValueType>() / exitRateVector[markovianState];
|
|
}
|
|
std::vector<ValueType> totalRewardVector = rewardModel.getTotalActionRewardVector(transitionMatrix, stateRewardWeights);
|
|
RewardModelType scaledRewardModel(boost::none, std::move(totalRewardVector));
|
|
|
|
return SparseMdpPrctlHelper<ValueType>::computeReachabilityRewards(dir, transitionMatrix, backwardTransitions, scaledRewardModel, psiStates, false, false, minMaxLinearEquationSolverFactory).values;
|
|
}
|
|
|
|
template<typename ValueType>
|
|
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeLongRunAverageProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
|
|
|
|
uint64_t numberOfStates = transitionMatrix.getRowGroupCount();
|
|
|
|
// If there are no goal states, we avoid the computation and directly return zero.
|
|
if (psiStates.empty()) {
|
|
return std::vector<ValueType>(numberOfStates, storm::utility::zero<ValueType>());
|
|
}
|
|
|
|
// Likewise, if all bits are set, we can avoid the computation and set.
|
|
if (psiStates.full()) {
|
|
return std::vector<ValueType>(numberOfStates, storm::utility::one<ValueType>());
|
|
}
|
|
|
|
// Otherwise, reduce the long run average probabilities to long run average rewards.
|
|
// Every Markovian goal state gets reward one.
|
|
std::vector<ValueType> stateRewards(transitionMatrix.getRowGroupCount(), storm::utility::zero<ValueType>());
|
|
storm::utility::vector::setVectorValues(stateRewards, markovianStates & psiStates, storm::utility::one<ValueType>());
|
|
storm::models::sparse::StandardRewardModel<ValueType> rewardModel(std::move(stateRewards));
|
|
|
|
return computeLongRunAverageRewards(dir, transitionMatrix, backwardTransitions, exitRateVector, markovianStates, rewardModel, minMaxLinearEquationSolverFactory);
|
|
|
|
}
|
|
|
|
template<typename ValueType, typename RewardModelType>
|
|
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeLongRunAverageRewards(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, RewardModelType const& rewardModel, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
|
|
|
|
uint64_t numberOfStates = transitionMatrix.getRowGroupCount();
|
|
|
|
// Start by decomposing the Markov automaton into its MECs.
|
|
storm::storage::MaximalEndComponentDecomposition<ValueType> mecDecomposition(transitionMatrix, backwardTransitions);
|
|
|
|
// Get some data members for convenience.
|
|
std::vector<uint64_t> const& nondeterministicChoiceIndices = transitionMatrix.getRowGroupIndices();
|
|
|
|
// Now start with compute the long-run average for all end components in isolation.
|
|
std::vector<ValueType> lraValuesForEndComponents;
|
|
|
|
// While doing so, we already gather some information for the following steps.
|
|
std::vector<uint64_t> stateToMecIndexMap(numberOfStates);
|
|
storm::storage::BitVector statesInMecs(numberOfStates);
|
|
|
|
for (uint64_t currentMecIndex = 0; currentMecIndex < mecDecomposition.size(); ++currentMecIndex) {
|
|
storm::storage::MaximalEndComponent const& mec = mecDecomposition[currentMecIndex];
|
|
|
|
// Gather information for later use.
|
|
for (auto const& stateChoicesPair : mec) {
|
|
uint64_t state = stateChoicesPair.first;
|
|
|
|
statesInMecs.set(state);
|
|
stateToMecIndexMap[state] = currentMecIndex;
|
|
}
|
|
|
|
// Compute the LRA value for the current MEC.
|
|
lraValuesForEndComponents.push_back(computeLraForMaximalEndComponent(dir, transitionMatrix, exitRateVector, markovianStates, rewardModel, mec, minMaxLinearEquationSolverFactory));
|
|
}
|
|
|
|
// For fast transition rewriting, we build some auxiliary data structures.
|
|
storm::storage::BitVector statesNotContainedInAnyMec = ~statesInMecs;
|
|
uint64_t firstAuxiliaryStateIndex = statesNotContainedInAnyMec.getNumberOfSetBits();
|
|
uint64_t lastStateNotInMecs = 0;
|
|
uint64_t numberOfStatesNotInMecs = 0;
|
|
std::vector<uint64_t> statesNotInMecsBeforeIndex;
|
|
statesNotInMecsBeforeIndex.reserve(numberOfStates);
|
|
for (auto state : statesNotContainedInAnyMec) {
|
|
while (lastStateNotInMecs <= state) {
|
|
statesNotInMecsBeforeIndex.push_back(numberOfStatesNotInMecs);
|
|
++lastStateNotInMecs;
|
|
}
|
|
++numberOfStatesNotInMecs;
|
|
}
|
|
uint64_t numberOfSspStates = numberOfStatesNotInMecs + mecDecomposition.size();
|
|
|
|
// Finally, we are ready to create the SSP matrix and right-hand side of the SSP.
|
|
std::vector<ValueType> b;
|
|
typename storm::storage::SparseMatrixBuilder<ValueType> sspMatrixBuilder(0, numberOfSspStates , 0, false, true, numberOfSspStates);
|
|
|
|
// If the source state is not contained in any MEC, we copy its choices (and perform the necessary modifications).
|
|
uint64_t currentChoice = 0;
|
|
for (auto state : statesNotContainedInAnyMec) {
|
|
sspMatrixBuilder.newRowGroup(currentChoice);
|
|
|
|
for (uint64_t choice = nondeterministicChoiceIndices[state]; choice < nondeterministicChoiceIndices[state + 1]; ++choice, ++currentChoice) {
|
|
std::vector<ValueType> auxiliaryStateToProbabilityMap(mecDecomposition.size());
|
|
b.push_back(storm::utility::zero<ValueType>());
|
|
|
|
for (auto element : transitionMatrix.getRow(choice)) {
|
|
if (statesNotContainedInAnyMec.get(element.getColumn())) {
|
|
// If the target state is not contained in an MEC, we can copy over the entry.
|
|
sspMatrixBuilder.addNextValue(currentChoice, statesNotInMecsBeforeIndex[element.getColumn()], element.getValue());
|
|
} else {
|
|
// If the target state is contained in MEC i, we need to add the probability to the corresponding field in the vector
|
|
// so that we are able to write the cumulative probability to the MEC into the matrix.
|
|
auxiliaryStateToProbabilityMap[stateToMecIndexMap[element.getColumn()]] += element.getValue();
|
|
}
|
|
}
|
|
|
|
// Now insert all (cumulative) probability values that target an MEC.
|
|
for (uint64_t mecIndex = 0; mecIndex < auxiliaryStateToProbabilityMap.size(); ++mecIndex) {
|
|
if (auxiliaryStateToProbabilityMap[mecIndex] != 0) {
|
|
sspMatrixBuilder.addNextValue(currentChoice, firstAuxiliaryStateIndex + mecIndex, auxiliaryStateToProbabilityMap[mecIndex]);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Now we are ready to construct the choices for the auxiliary states.
|
|
for (uint64_t mecIndex = 0; mecIndex < mecDecomposition.size(); ++mecIndex) {
|
|
storm::storage::MaximalEndComponent const& mec = mecDecomposition[mecIndex];
|
|
sspMatrixBuilder.newRowGroup(currentChoice);
|
|
|
|
for (auto const& stateChoicesPair : mec) {
|
|
uint64_t state = stateChoicesPair.first;
|
|
boost::container::flat_set<uint64_t> const& choicesInMec = stateChoicesPair.second;
|
|
|
|
for (uint64_t choice = nondeterministicChoiceIndices[state]; choice < nondeterministicChoiceIndices[state + 1]; ++choice) {
|
|
|
|
// If the choice is not contained in the MEC itself, we have to add a similar distribution to the auxiliary state.
|
|
if (choicesInMec.find(choice) == choicesInMec.end()) {
|
|
std::vector<ValueType> auxiliaryStateToProbabilityMap(mecDecomposition.size());
|
|
b.push_back(storm::utility::zero<ValueType>());
|
|
|
|
for (auto element : transitionMatrix.getRow(choice)) {
|
|
if (statesNotContainedInAnyMec.get(element.getColumn())) {
|
|
// If the target state is not contained in an MEC, we can copy over the entry.
|
|
sspMatrixBuilder.addNextValue(currentChoice, statesNotInMecsBeforeIndex[element.getColumn()], element.getValue());
|
|
} else {
|
|
// If the target state is contained in MEC i, we need to add the probability to the corresponding field in the vector
|
|
// so that we are able to write the cumulative probability to the MEC into the matrix.
|
|
auxiliaryStateToProbabilityMap[stateToMecIndexMap[element.getColumn()]] += element.getValue();
|
|
}
|
|
}
|
|
|
|
// Now insert all (cumulative) probability values that target an MEC.
|
|
for (uint64_t targetMecIndex = 0; targetMecIndex < auxiliaryStateToProbabilityMap.size(); ++targetMecIndex) {
|
|
if (auxiliaryStateToProbabilityMap[targetMecIndex] != 0) {
|
|
sspMatrixBuilder.addNextValue(currentChoice, firstAuxiliaryStateIndex + targetMecIndex, auxiliaryStateToProbabilityMap[targetMecIndex]);
|
|
}
|
|
}
|
|
|
|
++currentChoice;
|
|
}
|
|
}
|
|
}
|
|
|
|
// For each auxiliary state, there is the option to achieve the reward value of the LRA associated with the MEC.
|
|
++currentChoice;
|
|
b.push_back(lraValuesForEndComponents[mecIndex]);
|
|
}
|
|
|
|
// Finalize the matrix and solve the corresponding system of equations.
|
|
storm::storage::SparseMatrix<ValueType> sspMatrix = sspMatrixBuilder.build(currentChoice, numberOfSspStates, numberOfSspStates);
|
|
|
|
std::vector<ValueType> x(numberOfSspStates);
|
|
|
|
// Check for requirements of the solver.
|
|
storm::solver::MinMaxLinearEquationSolverRequirements requirements = minMaxLinearEquationSolverFactory.getRequirements(true, dir);
|
|
requirements.clearBounds();
|
|
STORM_LOG_THROW(requirements.empty(), storm::exceptions::UncheckedRequirementException, "Cannot establish requirements for solver.");
|
|
|
|
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = minMaxLinearEquationSolverFactory.create(sspMatrix);
|
|
solver->setHasUniqueSolution();
|
|
solver->setLowerBound(storm::utility::zero<ValueType>());
|
|
solver->setUpperBound(*std::max_element(lraValuesForEndComponents.begin(), lraValuesForEndComponents.end()));
|
|
solver->setRequirementsChecked();
|
|
solver->solveEquations(dir, x, b);
|
|
|
|
// Prepare result vector.
|
|
std::vector<ValueType> result(numberOfStates);
|
|
|
|
// Set the values for states not contained in MECs.
|
|
storm::utility::vector::setVectorValues(result, statesNotContainedInAnyMec, x);
|
|
|
|
// Set the values for all states in MECs.
|
|
for (auto state : statesInMecs) {
|
|
result[state] = x[firstAuxiliaryStateIndex + stateToMecIndexMap[state]];
|
|
}
|
|
|
|
return result;
|
|
}
|
|
|
|
template <typename ValueType>
|
|
std::vector<ValueType> SparseMarkovAutomatonCslHelper::computeReachabilityTimes(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
|
|
|
|
// Get a reward model representing expected sojourn times
|
|
std::vector<ValueType> rewardValues(transitionMatrix.getRowCount(), storm::utility::zero<ValueType>());
|
|
for (auto const markovianState : markovianStates) {
|
|
rewardValues[transitionMatrix.getRowGroupIndices()[markovianState]] = storm::utility::one<ValueType>() / exitRateVector[markovianState];
|
|
}
|
|
storm::models::sparse::StandardRewardModel<ValueType> rewardModel(boost::none, std::move(rewardValues));
|
|
|
|
return SparseMdpPrctlHelper<ValueType>::computeReachabilityRewards(dir, transitionMatrix, backwardTransitions, rewardModel, psiStates, false, false, minMaxLinearEquationSolverFactory).values;
|
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}
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|
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template<typename ValueType, typename RewardModelType>
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ValueType SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponent(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, RewardModelType const& rewardModel, storm::storage::MaximalEndComponent const& mec, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
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// If the mec only consists of a single state, we compute the LRA value directly
|
|
if (++mec.begin() == mec.end()) {
|
|
uint64_t state = mec.begin()->first;
|
|
STORM_LOG_THROW(markovianStates.get(state), storm::exceptions::InvalidOperationException, "Markov Automaton has Zeno behavior. Computation of Long Run Average values not supported.");
|
|
ValueType result = rewardModel.hasStateRewards() ? rewardModel.getStateReward(state) : storm::utility::zero<ValueType>();
|
|
if (rewardModel.hasStateActionRewards() || rewardModel.hasTransitionRewards()) {
|
|
STORM_LOG_ASSERT(mec.begin()->second.size() == 1, "Markovian state has nondeterministic behavior.");
|
|
uint64_t choice = *mec.begin()->second.begin();
|
|
result += exitRateVector[state] * rewardModel.getTotalStateActionReward(state, choice, transitionMatrix, storm::utility::zero<ValueType>());
|
|
}
|
|
return result;
|
|
}
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// Solve MEC with the method specified in the settings
|
|
storm::solver::LraMethod method = storm::settings::getModule<storm::settings::modules::MinMaxEquationSolverSettings>().getLraMethod();
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|
if (method == storm::solver::LraMethod::LinearProgramming) {
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|
return computeLraForMaximalEndComponentLP(dir, transitionMatrix, exitRateVector, markovianStates, rewardModel, mec);
|
|
} else if (method == storm::solver::LraMethod::ValueIteration) {
|
|
return computeLraForMaximalEndComponentVI(dir, transitionMatrix, exitRateVector, markovianStates, rewardModel, mec, minMaxLinearEquationSolverFactory);
|
|
} else {
|
|
STORM_LOG_THROW(false, storm::exceptions::InvalidSettingsException, "Unsupported technique.");
|
|
}
|
|
}
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|
template<typename ValueType, typename RewardModelType>
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ValueType SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponentLP(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, RewardModelType const& rewardModel, storm::storage::MaximalEndComponent const& mec) {
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std::unique_ptr<storm::utility::solver::LpSolverFactory<ValueType>> lpSolverFactory(new storm::utility::solver::LpSolverFactory<ValueType>());
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|
std::unique_ptr<storm::solver::LpSolver<ValueType>> solver = lpSolverFactory->create("LRA for MEC");
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|
solver->setOptimizationDirection(invert(dir));
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|
|
|
// First, we need to create the variables for the problem.
|
|
std::map<uint64_t, storm::expressions::Variable> stateToVariableMap;
|
|
for (auto const& stateChoicesPair : mec) {
|
|
std::string variableName = "x" + std::to_string(stateChoicesPair.first);
|
|
stateToVariableMap[stateChoicesPair.first] = solver->addUnboundedContinuousVariable(variableName);
|
|
}
|
|
storm::expressions::Variable k = solver->addUnboundedContinuousVariable("k", storm::utility::one<ValueType>());
|
|
solver->update();
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|
|
|
// Now we encode the problem as constraints.
|
|
std::vector<uint64_t> const& nondeterministicChoiceIndices = transitionMatrix.getRowGroupIndices();
|
|
for (auto const& stateChoicesPair : mec) {
|
|
uint64_t state = stateChoicesPair.first;
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|
|
|
// Now, based on the type of the state, create a suitable constraint.
|
|
if (markovianStates.get(state)) {
|
|
STORM_LOG_ASSERT(stateChoicesPair.second.size() == 1, "Markovian state " << state << " is not deterministic: It has " << stateChoicesPair.second.size() << " choices.");
|
|
uint64_t choice = *stateChoicesPair.second.begin();
|
|
|
|
storm::expressions::Expression constraint = stateToVariableMap.at(state);
|
|
|
|
for (auto element : transitionMatrix.getRow(nondeterministicChoiceIndices[state])) {
|
|
constraint = constraint - stateToVariableMap.at(element.getColumn()) * solver->getManager().rational((element.getValue()));
|
|
}
|
|
|
|
constraint = constraint + solver->getManager().rational(storm::utility::one<ValueType>() / exitRateVector[state]) * k;
|
|
|
|
storm::expressions::Expression rightHandSide = solver->getManager().rational(rewardModel.getTotalStateActionReward(state, choice, transitionMatrix, (ValueType) (storm::utility::one<ValueType>() / exitRateVector[state])));
|
|
if (dir == OptimizationDirection::Minimize) {
|
|
constraint = constraint <= rightHandSide;
|
|
} else {
|
|
constraint = constraint >= rightHandSide;
|
|
}
|
|
solver->addConstraint("state" + std::to_string(state), constraint);
|
|
} else {
|
|
// For probabilistic states, we want to add the constraint x_s <= sum P(s, a, s') * x_s' where a is the current action
|
|
// and the sum ranges over all states s'.
|
|
for (auto choice : stateChoicesPair.second) {
|
|
storm::expressions::Expression constraint = stateToVariableMap.at(state);
|
|
|
|
for (auto element : transitionMatrix.getRow(choice)) {
|
|
constraint = constraint - stateToVariableMap.at(element.getColumn()) * solver->getManager().rational(element.getValue());
|
|
}
|
|
|
|
storm::expressions::Expression rightHandSide = solver->getManager().rational(rewardModel.getTotalStateActionReward(state, choice, transitionMatrix, storm::utility::zero<ValueType>()));
|
|
if (dir == OptimizationDirection::Minimize) {
|
|
constraint = constraint <= rightHandSide;
|
|
} else {
|
|
constraint = constraint >= rightHandSide;
|
|
}
|
|
solver->addConstraint("state" + std::to_string(state), constraint);
|
|
}
|
|
}
|
|
}
|
|
|
|
solver->optimize();
|
|
return solver->getContinuousValue(k);
|
|
}
|
|
|
|
template<typename ValueType, typename RewardModelType>
|
|
ValueType SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponentVI(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, std::vector<ValueType> const& exitRateVector, storm::storage::BitVector const& markovianStates, RewardModelType const& rewardModel, storm::storage::MaximalEndComponent const& mec, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
|
|
|
|
// Initialize data about the mec
|
|
|
|
storm::storage::BitVector mecStates(transitionMatrix.getRowGroupCount(), false);
|
|
storm::storage::BitVector mecChoices(transitionMatrix.getRowCount(), false);
|
|
for (auto const& stateChoicesPair : mec) {
|
|
mecStates.set(stateChoicesPair.first);
|
|
for (auto const& choice : stateChoicesPair.second) {
|
|
mecChoices.set(choice);
|
|
}
|
|
}
|
|
storm::storage::BitVector markovianMecStates = mecStates & markovianStates;
|
|
storm::storage::BitVector probabilisticMecStates = mecStates & ~markovianStates;
|
|
storm::storage::BitVector probabilisticMecChoices = transitionMatrix.getRowFilter(probabilisticMecStates) & mecChoices;
|
|
STORM_LOG_THROW(!markovianMecStates.empty(), storm::exceptions::InvalidOperationException, "Markov Automaton has Zeno behavior. Computation of Long Run Average values not supported.");
|
|
|
|
// Get the uniformization rate
|
|
|
|
ValueType uniformizationRate = storm::utility::vector::max_if(exitRateVector, markovianMecStates);
|
|
// To ensure that the model is aperiodic, we need to make sure that every Markovian state gets a self loop.
|
|
// Hence, we increase the uniformization rate a little.
|
|
uniformizationRate += storm::utility::one<ValueType>(); // Todo: try other values such as *=1.01
|
|
|
|
// Get the transitions of the submodel, that is
|
|
// * a matrix aMarkovian with all (uniformized) transitions from Markovian mec states to all Markovian mec states.
|
|
// * a matrix aMarkovianToProbabilistic with all (uniformized) transitions from Markovian mec states to all probabilistic mec states.
|
|
// * a matrix aProbabilistic with all transitions from probabilistic mec states to other probabilistic mec states.
|
|
// * a matrix aProbabilisticToMarkovian with all transitions from probabilistic mec states to all Markovian mec states.
|
|
typename storm::storage::SparseMatrix<ValueType> aMarkovian = transitionMatrix.getSubmatrix(true, markovianMecStates, markovianMecStates, true);
|
|
typename storm::storage::SparseMatrix<ValueType> aMarkovianToProbabilistic = transitionMatrix.getSubmatrix(true, markovianMecStates, probabilisticMecStates);
|
|
typename storm::storage::SparseMatrix<ValueType> aProbabilistic = transitionMatrix.getSubmatrix(false, probabilisticMecChoices, probabilisticMecStates);
|
|
typename storm::storage::SparseMatrix<ValueType> aProbabilisticToMarkovian = transitionMatrix.getSubmatrix(false, probabilisticMecChoices, markovianMecStates);
|
|
// The matrices with transitions from Markovian states need to be uniformized.
|
|
uint64_t subState = 0;
|
|
for (auto state : markovianMecStates) {
|
|
ValueType uniformizationFactor = exitRateVector[state] / uniformizationRate;
|
|
for (auto& entry : aMarkovianToProbabilistic.getRow(subState)) {
|
|
entry.setValue(entry.getValue() * uniformizationFactor);
|
|
}
|
|
for (auto& entry : aMarkovian.getRow(subState)) {
|
|
if (entry.getColumn() == subState) {
|
|
entry.setValue(storm::utility::one<ValueType>() - uniformizationFactor * (storm::utility::one<ValueType>() - entry.getValue()));
|
|
} else {
|
|
entry.setValue(entry.getValue() * uniformizationFactor);
|
|
}
|
|
}
|
|
++subState;
|
|
}
|
|
|
|
// Compute the rewards obtained in a single uniformization step
|
|
|
|
std::vector<ValueType> markovianChoiceRewards;
|
|
markovianChoiceRewards.reserve(aMarkovian.getRowCount());
|
|
for (auto const& state : markovianMecStates) {
|
|
ValueType stateRewardScalingFactor = storm::utility::one<ValueType>() / uniformizationRate;
|
|
ValueType actionRewardScalingFactor = exitRateVector[state] / uniformizationRate;
|
|
assert(transitionMatrix.getRowGroupSize(state) == 1);
|
|
uint64_t choice = transitionMatrix.getRowGroupIndices()[state];
|
|
markovianChoiceRewards.push_back(rewardModel.getTotalStateActionReward(state, choice, transitionMatrix, stateRewardScalingFactor, actionRewardScalingFactor));
|
|
}
|
|
|
|
std::vector<ValueType> probabilisticChoiceRewards;
|
|
probabilisticChoiceRewards.reserve(aProbabilistic.getRowCount());
|
|
for (auto const& state : probabilisticMecStates) {
|
|
uint64_t groupStart = transitionMatrix.getRowGroupIndices()[state];
|
|
uint64_t groupEnd = transitionMatrix.getRowGroupIndices()[state + 1];
|
|
for (uint64_t choice = probabilisticMecChoices.getNextSetIndex(groupStart); choice < groupEnd; choice = probabilisticMecChoices.getNextSetIndex(choice + 1)) {
|
|
probabilisticChoiceRewards.push_back(rewardModel.getTotalStateActionReward(state, choice, transitionMatrix, storm::utility::zero<ValueType>()));
|
|
}
|
|
}
|
|
|
|
// start the iterations
|
|
|
|
ValueType precision = storm::utility::convertNumber<ValueType>(storm::settings::getModule<storm::settings::modules::MinMaxEquationSolverSettings>().getPrecision()) / uniformizationRate;
|
|
std::vector<ValueType> v(aMarkovian.getRowCount(), storm::utility::zero<ValueType>());
|
|
std::vector<ValueType> w = v;
|
|
std::vector<ValueType> x(aProbabilistic.getRowGroupCount(), storm::utility::zero<ValueType>());
|
|
std::vector<ValueType> b = probabilisticChoiceRewards;
|
|
|
|
// Check for requirements of the solver.
|
|
// The solution is unique as we assume non-zeno MAs.
|
|
storm::solver::MinMaxLinearEquationSolverRequirements requirements = minMaxLinearEquationSolverFactory.getRequirements(true, dir);
|
|
requirements.clearLowerBounds();
|
|
STORM_LOG_THROW(requirements.empty(), storm::exceptions::UncheckedRequirementException, "Cannot establish requirements for solver.");
|
|
|
|
auto solver = minMaxLinearEquationSolverFactory.create(std::move(aProbabilistic));
|
|
solver->setLowerBound(storm::utility::zero<ValueType>());
|
|
solver->setHasUniqueSolution(true);
|
|
solver->setRequirementsChecked(true);
|
|
solver->setCachingEnabled(true);
|
|
|
|
while (true) {
|
|
// Compute the expected total rewards for the probabilistic states
|
|
solver->solveEquations(dir, x, b);
|
|
|
|
// now compute the values for the markovian states. We also keep track of the maximal and minimal difference between two values (for convergence checking)
|
|
auto vIt = v.begin();
|
|
uint64_t row = 0;
|
|
ValueType newValue = markovianChoiceRewards[row] + aMarkovianToProbabilistic.multiplyRowWithVector(row, x) + aMarkovian.multiplyRowWithVector(row, w);
|
|
ValueType maxDiff = newValue - *vIt;
|
|
ValueType minDiff = maxDiff;
|
|
*vIt = newValue;
|
|
for (++vIt, ++row; row < aMarkovian.getRowCount(); ++vIt, ++row) {
|
|
newValue = markovianChoiceRewards[row] + aMarkovianToProbabilistic.multiplyRowWithVector(row, x) + aMarkovian.multiplyRowWithVector(row, w);
|
|
ValueType diff = newValue - *vIt;
|
|
maxDiff = std::max(maxDiff, diff);
|
|
minDiff = std::min(minDiff, diff);
|
|
*vIt = newValue;
|
|
}
|
|
|
|
// Check for convergence
|
|
if (maxDiff - minDiff < precision) {
|
|
break;
|
|
}
|
|
|
|
// update the rhs of the MinMax equation system
|
|
ValueType referenceValue = v.front();
|
|
storm::utility::vector::applyPointwise<ValueType, ValueType>(v, w, [&referenceValue] (ValueType const& v_i) -> ValueType { return v_i - referenceValue; });
|
|
aProbabilisticToMarkovian.multiplyWithVector(w, b);
|
|
storm::utility::vector::addVectors(b, probabilisticChoiceRewards, b);
|
|
|
|
}
|
|
return v.front() * uniformizationRate;
|
|
|
|
}
|
|
|
|
template std::vector<double> SparseMarkovAutomatonCslHelper::computeBoundedUntilProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, std::pair<double, double> const& boundsPair, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template std::vector<double> SparseMarkovAutomatonCslHelper::computeUntilProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool qualitative, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template std::vector<double> SparseMarkovAutomatonCslHelper::computeReachabilityRewards(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template std::vector<double> SparseMarkovAutomatonCslHelper::computeLongRunAverageProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template std::vector<double> SparseMarkovAutomatonCslHelper::computeLongRunAverageRewards(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template std::vector<double> SparseMarkovAutomatonCslHelper::computeReachabilityTimes(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template void SparseMarkovAutomatonCslHelper::computeBoundedReachabilityProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<double> const& exitRates, storm::storage::BitVector const& goalStates, storm::storage::BitVector const& markovianNonGoalStates, storm::storage::BitVector const& probabilisticNonGoalStates, std::vector<double>& markovianNonGoalValues, std::vector<double>& probabilisticNonGoalValues, double delta, uint64_t numberOfSteps, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template double SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponent(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::MaximalEndComponent const& mec, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template double SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponentLP(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::MaximalEndComponent const& mec);
|
|
|
|
template double SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponentVI(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, std::vector<double> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::MaximalEndComponent const& mec, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeBoundedUntilProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, std::pair<double, double> const& boundsPair, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeUntilProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool qualitative, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeReachabilityRewards(OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeLongRunAverageProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeLongRunAverageRewards(OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template std::vector<storm::RationalNumber> SparseMarkovAutomatonCslHelper::computeReachabilityTimes(OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template void SparseMarkovAutomatonCslHelper::computeBoundedReachabilityProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<storm::RationalNumber> const& exitRates, storm::storage::BitVector const& goalStates, storm::storage::BitVector const& markovianNonGoalStates, storm::storage::BitVector const& probabilisticNonGoalStates, std::vector<storm::RationalNumber>& markovianNonGoalValues, std::vector<storm::RationalNumber>& probabilisticNonGoalValues, storm::RationalNumber delta, uint64_t numberOfSteps, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template storm::RationalNumber SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponent(OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::MaximalEndComponent const& mec, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
|
|
|
|
template storm::RationalNumber SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponentLP(OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::MaximalEndComponent const& mec);
|
|
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template storm::RationalNumber SparseMarkovAutomatonCslHelper::computeLraForMaximalEndComponentVI(OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, std::vector<storm::RationalNumber> const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::MaximalEndComponent const& mec, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
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}
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}
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}
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