#include "src/modelchecker/prctl/helper/SparseMdpPrctlHelper.h"
#include "src/models/sparse/StandardRewardModel.h"
#include "src/storage/MaximalEndComponentDecomposition.h"
#include "src/utility/macros.h"
#include "src/utility/vector.h"
#include "src/utility/graph.h"
#include "src/storage/expressions/Variable.h"
#include "src/storage/expressions/Expression.h"
#include "src/solver/MinMaxLinearEquationSolver.h"
#include "src/solver/LpSolver.h"
#include "src/exceptions/InvalidStateException.h"
#include "src/exceptions/InvalidPropertyException.h"
namespace storm {
namespace modelchecker {
namespace helper {
template<typename ValueType>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::computeBoundedUntilProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, uint_fast64_t stepBound, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
std::vector<ValueType> result(transitionMatrix.getRowCount(), storm::utility::zero<ValueType>());
// Determine the states that have 0 probability of reaching the target states.
storm::storage::BitVector maybeStates;
if (dir == OptimizationDirection::Minimize) {
maybeStates = storm::utility::graph::performProbGreater0A(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, phiStates, psiStates, true, stepBound);
} else {
maybeStates = storm::utility::graph::performProbGreater0E(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, phiStates, psiStates, true, stepBound);
}
maybeStates &= ~psiStates;
STORM_LOG_INFO("Found " << maybeStates.getNumberOfSetBits() << " 'maybe' states.");
if (!maybeStates.empty()) {
// We can eliminate the rows and columns from the original transition probability matrix that have probability 0.
storm::storage::SparseMatrix<ValueType> submatrix = transitionMatrix.getSubmatrix(true, maybeStates, maybeStates, false);
std::vector<ValueType> b = transitionMatrix.getConstrainedRowGroupSumVector(maybeStates, psiStates);
// Create the vector with which to multiply.
std::vector<ValueType> subresult(maybeStates.getNumberOfSetBits());
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = minMaxLinearEquationSolverFactory.create(submatrix);
solver->performMatrixVectorMultiplication(dir, subresult, &b, stepBound);
// Set the values of the resulting vector accordingly.
storm::utility::vector::setVectorValues(result, maybeStates, subresult);
}
storm::utility::vector::setVectorValues(result, psiStates, storm::utility::one<ValueType>());
return result;
}
template<typename ValueType>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::computeNextProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& nextStates, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
// Create the vector with which to multiply and initialize it correctly.
std::vector<ValueType> result(transitionMatrix.getRowCount());
storm::utility::vector::setVectorValues(result, nextStates, storm::utility::one<ValueType>());
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = minMaxLinearEquationSolverFactory.create(transitionMatrix);
solver->performMatrixVectorMultiplication(dir, result);
return result;
}
template<typename ValueType>
MDPSparseModelCheckingHelperReturnType<ValueType> SparseMdpPrctlHelper<ValueType>::computeUntilProbabilities(storm::solver::SolveGoal const& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, bool qualitative, bool getPolicy, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
uint_fast64_t numberOfStates = transitionMatrix.getRowCount();
// We need to identify the states which have to be taken out of the matrix, i.e.
// all states that have probability 0 and 1 of satisfying the until-formula.
std::pair<storm::storage::BitVector, storm::storage::BitVector> statesWithProbability01;
if (goal.minimize()) {
statesWithProbability01 = storm::utility::graph::performProb01Min(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, phiStates, psiStates);
} else {
statesWithProbability01 = storm::utility::graph::performProb01Max(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, phiStates, psiStates);
}
storm::storage::BitVector statesWithProbability0 = std::move(statesWithProbability01.first);
storm::storage::BitVector statesWithProbability1 = std::move(statesWithProbability01.second);
storm::storage::BitVector maybeStates = ~(statesWithProbability0 | statesWithProbability1);
LOG4CPLUS_INFO(logger, "Found " << statesWithProbability0.getNumberOfSetBits() << " 'no' states.");
LOG4CPLUS_INFO(logger, "Found " << statesWithProbability1.getNumberOfSetBits() << " 'yes' states.");
LOG4CPLUS_INFO(logger, "Found " << maybeStates.getNumberOfSetBits() << " 'maybe' states.");
// Create resulting vector.
std::vector<ValueType> result(numberOfStates);
// Set values of resulting vector that are known exactly.
storm::utility::vector::setVectorValues<ValueType>(result, statesWithProbability0, storm::utility::zero<ValueType>());
storm::utility::vector::setVectorValues<ValueType>(result, statesWithProbability1, storm::utility::one<ValueType>());
// Check whether we need to compute exact probabilities for some states.
if (qualitative) {
// Set the values for all maybe-states to 0.5 to indicate that their probability values are neither 0 nor 1.
storm::utility::vector::setVectorValues<ValueType>(result, maybeStates, ValueType(0.5));
} else {
if (!maybeStates.empty()) {
// In this case we have have to compute the probabilities.
// First, we can eliminate the rows and columns from the original transition probability matrix for states
// whose probabilities are already known.
storm::storage::SparseMatrix<ValueType> submatrix = transitionMatrix.getSubmatrix(true, maybeStates, maybeStates, false);
// Prepare the right-hand side of the equation system. For entry i this corresponds to
// the accumulated probability of going from state i to some 'yes' state.
std::vector<ValueType> b = transitionMatrix.getConstrainedRowGroupSumVector(maybeStates, statesWithProbability1);
// Create vector for results for maybe states.
std::vector<ValueType> x(maybeStates.getNumberOfSetBits());
// Solve the corresponding system of equations.
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = storm::solver::configureMinMaxLinearEquationSolver(goal, minMaxLinearEquationSolverFactory, submatrix);
solver->solveEquationSystem(x, b);
// Set values of resulting vector according to result.
storm::utility::vector::setVectorValues<ValueType>(result, maybeStates, x);
}
}
return MDPSparseModelCheckingHelperReturnType<ValueType>(std::move(result));
}
template<typename ValueType>
MDPSparseModelCheckingHelperReturnType<ValueType> SparseMdpPrctlHelper<ValueType>::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, bool getPolicy, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
storm::solver::SolveGoal goal(dir);
return std::move(computeUntilProbabilities(goal, transitionMatrix, backwardTransitions, phiStates, psiStates, qualitative, getPolicy, minMaxLinearEquationSolverFactory));
}
template<typename ValueType>
template<typename RewardModelType>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::computeInstantaneousRewards(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, RewardModelType const& rewardModel, uint_fast64_t stepCount, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
// Only compute the result if the model has a state-based reward this->getModel().
STORM_LOG_THROW(rewardModel.hasStateRewards(), storm::exceptions::InvalidPropertyException, "Missing reward model for formula. Skipping formula.");
// Initialize result to state rewards of the this->getModel().
std::vector<ValueType> result(rewardModel.getStateRewardVector());
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = minMaxLinearEquationSolverFactory.create(transitionMatrix);
solver->performMatrixVectorMultiplication(dir, result, nullptr, stepCount);
return result;
}
template<typename ValueType>
template<typename RewardModelType>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::computeCumulativeRewards(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, RewardModelType const& rewardModel, uint_fast64_t stepBound, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
// Only compute the result if the model has at least one reward this->getModel().
STORM_LOG_THROW(!rewardModel.empty(), storm::exceptions::InvalidPropertyException, "Missing reward model for formula. Skipping formula.");
// Compute the reward vector to add in each step based on the available reward models.
std::vector<ValueType> totalRewardVector = rewardModel.getTotalRewardVector(transitionMatrix);
// Initialize result to either the state rewards of the model or the null vector.
std::vector<ValueType> result;
if (rewardModel.hasStateRewards()) {
result = rewardModel.getStateRewardVector();
} else {
result.resize(transitionMatrix.getRowCount());
}
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = minMaxLinearEquationSolverFactory.create(transitionMatrix);
solver->performMatrixVectorMultiplication(dir, result, &totalRewardVector, stepBound);
return result;
}
template<typename ValueType>
template<typename RewardModelType>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::computeReachabilityRewards(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, RewardModelType const& rewardModel, storm::storage::BitVector const& targetStates, bool qualitative, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
// Only compute the result if the model has at least one reward this->getModel().
STORM_LOG_THROW(!rewardModel.empty(), storm::exceptions::InvalidPropertyException, "Missing reward model for formula. Skipping formula.");
return computeReachabilityRewardsHelper(dir, transitionMatrix, backwardTransitions,
[&rewardModel] (uint_fast64_t rowCount, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& maybeStates) {
return rewardModel.getTotalRewardVector(rowCount, transitionMatrix, maybeStates);
},
targetStates, qualitative, minMaxLinearEquationSolverFactory);
}
#ifdef STORM_HAVE_CARL
template<typename ValueType>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::computeReachabilityRewards(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::models::sparse::StandardRewardModel<storm::Interval> const& intervalRewardModel, storm::storage::BitVector const& targetStates, bool qualitative, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
// Only compute the result if the reward model is not empty.
STORM_LOG_THROW(!intervalRewardModel.empty(), storm::exceptions::InvalidPropertyException, "Missing reward model for formula. Skipping formula.");
return computeReachabilityRewardsHelper(dir, transitionMatrix, backwardTransitions, \
[&] (uint_fast64_t rowCount, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& maybeStates) {
std::vector<ValueType> result;
result.reserve(rowCount);
std::vector<storm::Interval> subIntervalVector = intervalRewardModel.getTotalRewardVector(rowCount, transitionMatrix, maybeStates);
for (auto const& interval : subIntervalVector) {
result.push_back(dir == OptimizationDirection::Minimize ? interval.lower() : interval.upper());
}
return result;
}, \
targetStates, qualitative, minMaxLinearEquationSolverFactory);
}
#endif
template<typename ValueType>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::computeReachabilityRewardsHelper(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::function<std::vector<ValueType>(uint_fast64_t, storm::storage::SparseMatrix<ValueType> const&, storm::storage::BitVector const&)> const& totalStateRewardVectorGetter, storm::storage::BitVector const& targetStates, bool qualitative, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
// Determine which states have a reward of infinity by definition.
storm::storage::BitVector infinityStates;
storm::storage::BitVector trueStates(transitionMatrix.getRowCount(), true);
if (dir == OptimizationDirection::Minimize) {
infinityStates = storm::utility::graph::performProb1E(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, trueStates, targetStates);
} else {
infinityStates = storm::utility::graph::performProb1A(transitionMatrix, transitionMatrix.getRowGroupIndices(), backwardTransitions, trueStates, targetStates);
}
infinityStates.complement();
storm::storage::BitVector maybeStates = ~targetStates & ~infinityStates;
LOG4CPLUS_INFO(logger, "Found " << infinityStates.getNumberOfSetBits() << " 'infinity' states.");
LOG4CPLUS_INFO(logger, "Found " << targetStates.getNumberOfSetBits() << " 'target' states.");
LOG4CPLUS_INFO(logger, "Found " << maybeStates.getNumberOfSetBits() << " 'maybe' states.");
// Create resulting vector.
std::vector<ValueType> result(transitionMatrix.getRowCount(), storm::utility::zero<ValueType>());
// Check whether we need to compute exact rewards for some states.
if (qualitative) {
LOG4CPLUS_INFO(logger, "The rewards for the initial states were determined in a preprocessing step. No exact rewards were computed.");
// Set the values for all maybe-states to 1 to indicate that their reward values
// are neither 0 nor infinity.
storm::utility::vector::setVectorValues<ValueType>(result, maybeStates, storm::utility::one<ValueType>());
} else {
if (!maybeStates.empty()) {
// In this case we have to compute the reward values for the remaining states.
// We can eliminate the rows and columns from the original transition probability matrix for states
// whose reward values are already known.
storm::storage::SparseMatrix<ValueType> submatrix = transitionMatrix.getSubmatrix(true, maybeStates, maybeStates, false);
// Prepare the right-hand side of the equation system.
std::vector<ValueType> b = totalStateRewardVectorGetter(submatrix.getRowCount(), transitionMatrix, maybeStates);
// Create vector for results for maybe states.
std::vector<ValueType> x(maybeStates.getNumberOfSetBits());
// Solve the corresponding system of equations.
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = minMaxLinearEquationSolverFactory.create(submatrix);
solver->solveEquationSystem(dir, x, b);
// Set values of resulting vector according to result.
storm::utility::vector::setVectorValues<ValueType>(result, maybeStates, x);
}
}
// Set values of resulting vector that are known exactly.
storm::utility::vector::setVectorValues(result, infinityStates, storm::utility::infinity<ValueType>());
return result;
}
template<typename ValueType>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::computeLongRunAverage(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& psiStates, bool qualitative, storm::utility::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
// If there are no goal states, we avoid the computation and directly return zero.
uint_fast64_t numberOfStates = transitionMatrix.getRowGroupCount();
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).empty()) {
return std::vector<ValueType>(numberOfStates, storm::utility::one<ValueType>());
}
// Start by decomposing the MDP into its MECs.
storm::storage::MaximalEndComponentDecomposition<double> mecDecomposition(transitionMatrix, backwardTransitions);
// Get some data members for convenience.
std::vector<uint_fast64_t> const& nondeterministicChoiceIndices = transitionMatrix.getRowGroupIndices();
ValueType zero = storm::utility::zero<ValueType>();
//first calculate LRA for the Maximal End Components.
storm::storage::BitVector statesInMecs(numberOfStates);
std::vector<uint_fast64_t> stateToMecIndexMap(transitionMatrix.getColumnCount());
std::vector<ValueType> lraValuesForEndComponents(mecDecomposition.size(), zero);
for (uint_fast64_t currentMecIndex = 0; currentMecIndex < mecDecomposition.size(); ++currentMecIndex) {
storm::storage::MaximalEndComponent const& mec = mecDecomposition[currentMecIndex];
lraValuesForEndComponents[currentMecIndex] = computeLraForMaximalEndComponent(dir, transitionMatrix, psiStates, mec);
// Gather information for later use.
for (auto const& stateChoicesPair : mec) {
statesInMecs.set(stateChoicesPair.first);
stateToMecIndexMap[stateChoicesPair.first] = currentMecIndex;
}
}
// For fast transition rewriting, we build some auxiliary data structures.
storm::storage::BitVector statesNotContainedInAnyMec = ~statesInMecs;
uint_fast64_t firstAuxiliaryStateIndex = statesNotContainedInAnyMec.getNumberOfSetBits();
uint_fast64_t lastStateNotInMecs = 0;
uint_fast64_t numberOfStatesNotInMecs = 0;
std::vector<uint_fast64_t> statesNotInMecsBeforeIndex;
statesNotInMecsBeforeIndex.reserve(numberOfStates);
for (auto state : statesNotContainedInAnyMec) {
while (lastStateNotInMecs <= state) {
statesNotInMecsBeforeIndex.push_back(numberOfStatesNotInMecs);
++lastStateNotInMecs;
}
++numberOfStatesNotInMecs;
}
// 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, 0, 0, false, true, numberOfStatesNotInMecs + mecDecomposition.size());
// If the source state is not contained in any MEC, we copy its choices (and perform the necessary modifications).
uint_fast64_t currentChoice = 0;
for (auto state : statesNotContainedInAnyMec) {
sspMatrixBuilder.newRowGroup(currentChoice);
for (uint_fast64_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 (uint_fast64_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 (uint_fast64_t mecIndex = 0; mecIndex < mecDecomposition.size(); ++mecIndex) {
storm::storage::MaximalEndComponent const& mec = mecDecomposition[mecIndex];
sspMatrixBuilder.newRowGroup(currentChoice);
for (auto const& stateChoicesPair : mec) {
uint_fast64_t state = stateChoicesPair.first;
boost::container::flat_set<uint_fast64_t> const& choicesInMec = stateChoicesPair.second;
for (uint_fast64_t choice = nondeterministicChoiceIndices[state]; choice < nondeterministicChoiceIndices[state + 1]; ++choice) {
std::vector<ValueType> auxiliaryStateToProbabilityMap(mecDecomposition.size());
// 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()) {
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 (uint_fast64_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);
std::vector<ValueType> sspResult(numberOfStatesNotInMecs + mecDecomposition.size());
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = minMaxLinearEquationSolverFactory.create(sspMatrix);
solver->solveEquationSystem(dir, sspResult, b);
// Prepare result vector.
std::vector<ValueType> result(numberOfStates, zero);
// Set the values for states not contained in MECs.
storm::utility::vector::setVectorValues(result, statesNotContainedInAnyMec, sspResult);
// Set the values for all states in MECs.
for (auto state : statesInMecs) {
result[state] = sspResult[firstAuxiliaryStateIndex + stateToMecIndexMap[state]];
}
return result;
}
template<typename ValueType>
ValueType SparseMdpPrctlHelper<ValueType>::computeLraForMaximalEndComponent(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& psiStates, storm::storage::MaximalEndComponent const& mec) {
std::shared_ptr<storm::solver::LpSolver> solver = storm::utility::solver::getLpSolver("LRA for MEC");
solver->setOptimizationDirection(invert(dir));
// First, we need to create the variables for the problem.
std::map<uint_fast64_t, storm::expressions::Variable> stateToVariableMap;
for (auto const& stateChoicesPair : mec) {
std::string variableName = "h" + std::to_string(stateChoicesPair.first);
stateToVariableMap[stateChoicesPair.first] = solver->addUnboundedContinuousVariable(variableName);
}
storm::expressions::Variable lambda = solver->addUnboundedContinuousVariable("L", 1);
solver->update();
// Now we encode the problem as constraints.
for (auto const& stateChoicesPair : mec) {
uint_fast64_t state = stateChoicesPair.first;
// Now, based on the type of the state, create a suitable constraint.
for (auto choice : stateChoicesPair.second) {
storm::expressions::Expression constraint = -lambda;
ValueType r = 0;
for (auto element : transitionMatrix.getRow(choice)) {
constraint = constraint + stateToVariableMap.at(element.getColumn()) * solver->getConstant(element.getValue());
if (psiStates.get(element.getColumn())) {
r += element.getValue();
}
}
constraint = solver->getConstant(r) + constraint;
if (dir == OptimizationDirection::Minimize) {
constraint = stateToVariableMap.at(state) <= constraint;
} else {
constraint = stateToVariableMap.at(state) >= constraint;
}
solver->addConstraint("state" + std::to_string(state) + "," + std::to_string(choice), constraint);
}
}
solver->optimize();
return solver->getContinuousValue(lambda);
}
template class SparseMdpPrctlHelper<double>;
template std::vector<double> SparseMdpPrctlHelper<double>::computeInstantaneousRewards(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::models::sparse::StandardRewardModel<double> const& rewardModel, uint_fast64_t stepCount, storm::utility::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
template std::vector<double> SparseMdpPrctlHelper<double>::computeCumulativeRewards(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::models::sparse::StandardRewardModel<double> const& rewardModel, uint_fast64_t stepBound, storm::utility::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
template std::vector<double> SparseMdpPrctlHelper<double>::computeReachabilityRewards(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::BitVector const& targetStates, bool qualitative, storm::utility::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
}
}
}