added override to LESolver

src/storm/solver/IterativeMinMaxLinearEquationSolver.cpp

@@ -5,6 +5,7 @@
 
 #include "storm/environment/solver/MinMaxSolverEnvironment.h"
 #include "storm/environment/solver/OviSolverEnvironment.h"
+#include "storm/environment/solver/MultiplierEnvironment.h"
 
 #include "storm/utility/ConstantsComparator.h"
 #include "storm/utility/KwekMehlhorn.h"
@@ -19,27 +20,27 @@
 
 namespace storm {
     namespace solver {
-        
+
         template<typename ValueType>
         IterativeMinMaxLinearEquationSolver<ValueType>::IterativeMinMaxLinearEquationSolver(std::unique_ptr<LinearEquationSolverFactory<ValueType>>&& linearEquationSolverFactory) : linearEquationSolverFactory(std::move(linearEquationSolverFactory)) {
             // Intentionally left empty
         }
-        
+
         template<typename ValueType>
         IterativeMinMaxLinearEquationSolver<ValueType>::IterativeMinMaxLinearEquationSolver(storm::storage::SparseMatrix<ValueType> const& A, std::unique_ptr<LinearEquationSolverFactory<ValueType>>&& linearEquationSolverFactory) : StandardMinMaxLinearEquationSolver<ValueType>(A), linearEquationSolverFactory(std::move(linearEquationSolverFactory)) {
             // Intentionally left empty.
         }
-        
+
         template<typename ValueType>
         IterativeMinMaxLinearEquationSolver<ValueType>::IterativeMinMaxLinearEquationSolver(storm::storage::SparseMatrix<ValueType>&& A, std::unique_ptr<LinearEquationSolverFactory<ValueType>>&& linearEquationSolverFactory) : StandardMinMaxLinearEquationSolver<ValueType>(std::move(A)), linearEquationSolverFactory(std::move(linearEquationSolverFactory)) {
             // Intentionally left empty.
         }
-        
+
         template<typename ValueType>
         MinMaxMethod IterativeMinMaxLinearEquationSolver<ValueType>::getMethod(Environment const& env, bool isExactMode) const {
             // Adjust the method if none was specified and we want exact or sound computations.
             auto method = env.solver().minMax().getMethod();
-            
+
             if (isExactMode && method != MinMaxMethod::PolicyIteration && method != MinMaxMethod::RationalSearch && method != MinMaxMethod::ViToPi) {
                 if (env.solver().minMax().isMethodSetFromDefault()) {
                     STORM_LOG_INFO("Selecting 'Policy iteration' as the solution technique to guarantee exact results. If you want to override this, please explicitly specify a different method.");
@@ -58,7 +59,7 @@ namespace storm {
             STORM_LOG_THROW(method == MinMaxMethod::ValueIteration || method == MinMaxMethod::PolicyIteration || method == MinMaxMethod::RationalSearch || method == MinMaxMethod::SoundValueIteration || method == MinMaxMethod::IntervalIteration || method == MinMaxMethod::OptimisticValueIteration || method == MinMaxMethod::ViToPi, storm::exceptions::InvalidEnvironmentException, "This solver does not support the selected method.");
             return method;
         }
-        
+
         template<typename ValueType>
         bool IterativeMinMaxLinearEquationSolver<ValueType>::internalSolveEquations(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
             bool result = false;
@@ -87,14 +88,14 @@ namespace storm {
                 default:
                     STORM_LOG_THROW(false, storm::exceptions::InvalidEnvironmentException, "This solver does not implement the selected solution method");
             }
-            
+
             return result;
         }
 
         template<typename ValueType>
         bool IterativeMinMaxLinearEquationSolver<ValueType>::solveInducedEquationSystem(Environment const& env, std::unique_ptr<LinearEquationSolver<ValueType>>& linearEquationSolver, std::vector<uint64_t> const& scheduler, std::vector<ValueType>& x, std::vector<ValueType>& subB, std::vector<ValueType> const& originalB) const {
             assert(subB.size() == x.size());
-            
+
             // Resolve the nondeterminism according to the given scheduler.
             bool convertToEquationSystem = this->linearEquationSolverFactory->getEquationProblemFormat(env) == LinearEquationSolverProblemFormat::EquationSystem;
             storm::storage::SparseMatrix<ValueType> submatrix = this->A->selectRowsFromRowGroups(scheduler, convertToEquationSystem);
@@ -102,7 +103,7 @@ namespace storm {
                 submatrix.convertToEquationSystem();
             }
             storm::utility::vector::selectVectorValues<ValueType>(subB, scheduler, this->A->getRowGroupIndices(), originalB);
-            
+
             // Check whether the linear equation solver is already initialized
             if (!linearEquationSolver) {
                 // Initialize the equation solver
@@ -116,14 +117,14 @@ namespace storm {
             // Solve the equation system for the 'DTMC' and return true upon success
             return linearEquationSolver->solveEquations(env, x, subB);
         }
-        
+
         template<typename ValueType>
         bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsPolicyIteration(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
             // Create the initial scheduler.
             std::vector<storm::storage::sparse::state_type> scheduler = this->hasInitialScheduler() ? this->getInitialScheduler() : std::vector<storm::storage::sparse::state_type>(this->A->getRowGroupCount());
             return performPolicyIteration(env, dir, x, b, std::move(scheduler));
         }
-        
+
         template<typename ValueType>
         bool IterativeMinMaxLinearEquationSolver<ValueType>::performPolicyIteration(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b, std::vector<storm::storage::sparse::state_type>&& initialPolicy) const {
             std::vector<storm::storage::sparse::state_type> scheduler = std::move(initialPolicy);
@@ -162,7 +163,7 @@ namespace storm {
             do {
                 // Solve the equation system for the 'DTMC'.
                 solveInducedEquationSystem(environmentOfSolver, solver, scheduler, x, subB, b);
-                
+
                 // Go through the multiplication result and see whether we can improve any of the choices.
                 bool schedulerImproved = false;
                 for (uint_fast64_t group = 0; group < this->A->getRowGroupCount(); ++group) {
@@ -172,14 +173,14 @@ namespace storm {
                         if (choice - this->A->getRowGroupIndices()[group] == currentChoice) {
                             continue;
                         }
-                        
+
                         // Create the value of the choice.
                         ValueType choiceValue = storm::utility::zero<ValueType>();
                         for (auto const& entry : this->A->getRow(choice)) {
                             choiceValue += entry.getValue() * x[entry.getColumn()];
                         }
                         choiceValue += b[choice];
-                        
+
                         // If the value is strictly better than the solution of the inner system, we need to improve the scheduler.
                         // TODO: If the underlying solver is not precise, this might run forever (i.e. when a state has two choices where the (exact) values are equal).
                         // only changing the scheduler if the values are not equal (modulo precision) would make this unsound.
@@ -190,12 +191,12 @@ namespace storm {
                         }
                     }
                 }
-                
+
                 // If the scheduler did not improve, we are done.
                 if (!schedulerImproved) {
                     status = SolverStatus::Converged;
                 }
-                
+
                 // Update environment variables.
                 ++iterations;
                 status = this->updateStatus(status, x, dir == storm::OptimizationDirection::Minimize ? SolverGuarantee::GreaterOrEqual : SolverGuarantee::LessOrEqual, iterations, env.solver().minMax().getMaximalNumberOfIterations());
@@ -203,21 +204,21 @@ namespace storm {
                 // Potentially show progress.
                 this->showProgressIterative(iterations);
             } while (status == SolverStatus::InProgress);
-            
+
             this->reportStatus(status, iterations);
-            
+
             // If requested, we store the scheduler for retrieval.
             if (this->isTrackSchedulerSet()) {
                 this->schedulerChoices = std::move(scheduler);
             }
-            
+
             if (!this->isCachingEnabled()) {
                 clearCache();
             }
 
             return status == SolverStatus::Converged || status == SolverStatus::TerminatedEarly;
         }
-        
+
         template<typename ValueType>
         bool IterativeMinMaxLinearEquationSolver<ValueType>::valueImproved(OptimizationDirection dir, ValueType const& value1, ValueType const& value2) const {
             if (dir == OptimizationDirection::Minimize) {
@@ -230,7 +231,7 @@ namespace storm {
         template<typename ValueType>
         MinMaxLinearEquationSolverRequirements IterativeMinMaxLinearEquationSolver<ValueType>::getRequirements(Environment const& env, boost::optional<storm::solver::OptimizationDirection> const& direction, bool const& hasInitialScheduler) const {
             auto method = getMethod(env, storm::NumberTraits<ValueType>::IsExact || env.solver().isForceExact());
-            
+
             // Check whether a linear equation solver is needed and potentially start with its requirements
             bool needsLinEqSolver = false;
             needsLinEqSolver |= method == MinMaxMethod::PolicyIteration;
@@ -259,7 +260,7 @@ namespace storm {
                     requirements.requireUniqueSolution();
                 }
                 requirements.requireLowerBounds();
-                
+
             } else if (method == MinMaxMethod::IntervalIteration) {
                 // Interval iteration requires a unique solution and lower+upper bounds
                 if (!this->hasUniqueSolution()) {
@@ -296,18 +297,18 @@ namespace storm {
 
         template<typename ValueType>
         typename IterativeMinMaxLinearEquationSolver<ValueType>::ValueIterationResult IterativeMinMaxLinearEquationSolver<ValueType>::performValueIteration(Environment const& env, OptimizationDirection dir, std::vector<ValueType>*& currentX, std::vector<ValueType>*& newX, std::vector<ValueType> const& b, ValueType const& precision, bool relative, SolverGuarantee const& guarantee, uint64_t currentIterations, uint64_t maximalNumberOfIterations, storm::solver::MultiplicationStyle const& multiplicationStyle) const {
-            
+
             STORM_LOG_ASSERT(currentX != newX, "Vectors must not be aliased.");
-            
+
             // Get handle to multiplier.
             storm::solver::Multiplier<ValueType> const& multiplier = *this->multiplierA;
-            
+
             // Allow aliased multiplications.
             bool useGaussSeidelMultiplication = multiplicationStyle == storm::solver::MultiplicationStyle::GaussSeidel;
-            
+
             // Proceed with the iterations as long as the method did not converge or reach the maximum number of iterations.
             uint64_t iterations = currentIterations;
-            
+
             SolverStatus status = SolverStatus::InProgress;
             while (status == SolverStatus::InProgress) {
                 // Compute x' = min/max(A*x + b).
@@ -318,12 +319,12 @@ namespace storm {
                 } else {
                     multiplier.multiplyAndReduce(env, dir, *currentX, &b, *newX);
                 }
-                
+
                 // Determine whether the method converged.
                 if (storm::utility::vector::equalModuloPrecision<ValueType>(*currentX, *newX, precision, relative)) {
                     status = SolverStatus::Converged;
                 }
-                
+
                 // Update environment variables.
                 std::swap(currentX, newX);
                 ++iterations;
@@ -332,7 +333,7 @@ namespace storm {
                 // Potentially show progress.
                 this->showProgressIterative(iterations);
             }
-            
+
             return ValueIterationResult(iterations - currentIterations, status);
         }
 
@@ -367,7 +368,7 @@ namespace storm {
                 }
                 return true;
             }
-            
+
             if (!auxiliaryRowGroupVector) {
                 auxiliaryRowGroupVector = std::make_unique<std::vector<ValueType>>(this->A->getRowGroupCount());
             }
@@ -376,14 +377,14 @@ namespace storm {
             }
 
             storm::solver::helper::OptimisticValueIterationHelper<ValueType> helper(*this->A);
-            
+
             // x has to start with a lower bound.
             this->createLowerBoundsVector(x);
 
             std::vector<ValueType>* lowerX = &x;
             std::vector<ValueType>* upperX = auxiliaryRowGroupVector.get();
 
-            
+
             auto statusIters = helper.solveEquations(env, lowerX, upperX, b,
                                                      env.solver().minMax().getRelativeTerminationCriterion(),
                                                      storm::utility::convertNumber<ValueType>(env.solver().minMax().getPrecision()),
@@ -413,14 +414,19 @@ namespace storm {
             if (!this->multiplierA) {
                 this->multiplierA = storm::solver::MultiplierFactory<ValueType>().create(env, *this->A);
             }
-            
+
+            // TODO cleanup
+            if(env.solver().multiplier().getOptimizationDirectionOverride().is_initialized()) {
+                multiplierA->setOptimizationDirectionOverride(env.solver().multiplier().getOptimizationDirectionOverride().get());
+            }
+
             if (!auxiliaryRowGroupVector) {
                 auxiliaryRowGroupVector = std::make_unique<std::vector<ValueType>>(this->A->getRowGroupCount());
             }
-            
+
             // By default, we can not provide any guarantee
             SolverGuarantee guarantee = SolverGuarantee::None;
-            
+
             if (this->hasInitialScheduler()) {
                 // Solve the equation system induced by the initial scheduler.
                 std::unique_ptr<storm::solver::LinearEquationSolver<ValueType>> linEqSolver;
@@ -469,7 +475,7 @@ namespace storm {
 
             std::vector<ValueType>* newX = auxiliaryRowGroupVector.get();
             std::vector<ValueType>* currentX = &x;
-            
+
             this->startMeasureProgress();
             ValueIterationResult result = performValueIteration(env, dir, currentX, newX, b, storm::utility::convertNumber<ValueType>(env.solver().minMax().getPrecision()), env.solver().minMax().getRelativeTerminationCriterion(), guarantee, 0, env.solver().minMax().getMaximalNumberOfIterations(), env.solver().minMax().getMultiplicationStyle());
 
@@ -477,27 +483,27 @@ namespace storm {
             if (currentX == auxiliaryRowGroupVector.get()) {
                 std::swap(x, *currentX);
             }
-            
+
             this->reportStatus(result.status, result.iterations);
-            
+
             // If requested, we store the scheduler for retrieval.
             if (this->isTrackSchedulerSet()) {
                 this->schedulerChoices = std::vector<uint_fast64_t>(this->A->getRowGroupCount());
                 this->multiplierA->multiplyAndReduce(env, dir, x, &b, *auxiliaryRowGroupVector.get(), &this->schedulerChoices.get());
             }
-            
+
             if (!this->isCachingEnabled()) {
                 clearCache();
             }
-            
+
             return result.status == SolverStatus::Converged || result.status == SolverStatus::TerminatedEarly;
         }
-        
+
         template<typename ValueType>
         void preserveOldRelevantValues(std::vector<ValueType> const& allValues, storm::storage::BitVector const& relevantValues, std::vector<ValueType>& oldValues) {
             storm::utility::vector::selectVectorValues(oldValues, relevantValues, allValues);
         }
-        
+
         /*!
          * This version of value iteration is sound, because it approaches the solution from below and above. This
          * technique is due to Haddad and Monmege (Interval iteration algorithm for MDPs and IMDPs, TCS 2017) and was
@@ -511,28 +517,28 @@ namespace storm {
             if (!this->multiplierA) {
                 this->multiplierA = storm::solver::MultiplierFactory<ValueType>().create(env, *this->A);
             }
-            
+
             if (!auxiliaryRowGroupVector) {
                 auxiliaryRowGroupVector = std::make_unique<std::vector<ValueType>>(this->A->getRowGroupCount());
             }
-            
+
             // Allow aliased multiplications.
             bool useGaussSeidelMultiplication = env.solver().minMax().getMultiplicationStyle() == storm::solver::MultiplicationStyle::GaussSeidel;
-            
+
             std::vector<ValueType>* lowerX = &x;
             this->createLowerBoundsVector(*lowerX);
             this->createUpperBoundsVector(this->auxiliaryRowGroupVector, this->A->getRowGroupCount());
             std::vector<ValueType>* upperX = this->auxiliaryRowGroupVector.get();
-            
+
             std::vector<ValueType>* tmp = nullptr;
             if (!useGaussSeidelMultiplication) {
                 auxiliaryRowGroupVector2 = std::make_unique<std::vector<ValueType>>(lowerX->size());
                 tmp = auxiliaryRowGroupVector2.get();
             }
-            
+
             // Proceed with the iterations as long as the method did not converge or reach the maximum number of iterations.
             uint64_t iterations = 0;
-            
+
             SolverStatus status = SolverStatus::InProgress;
             bool doConvergenceCheck = true;
             bool useDiffs = this->hasRelevantValues() && !env.solver().minMax().isSymmetricUpdatesSet();
@@ -636,7 +642,7 @@ namespace storm {
                         status = storm::utility::vector::equalModuloPrecision<ValueType>(*lowerX, *upperX, precision, relative) ? SolverStatus::Converged : status;
                     }
                 }
-                
+
                 // Update environment variables.
                 ++iterations;
                 doConvergenceCheck = !doConvergenceCheck;
@@ -650,33 +656,33 @@ namespace storm {
                 // Potentially show progress.
                 this->showProgressIterative(iterations);
             }
-            
+
             this->reportStatus(status, iterations);
 
             // We take the means of the lower and upper bound so we guarantee the desired precision.
             ValueType two = storm::utility::convertNumber<ValueType>(2.0);
             storm::utility::vector::applyPointwise<ValueType, ValueType, ValueType>(*lowerX, *upperX, *lowerX, [&two] (ValueType const& a, ValueType const& b) -> ValueType { return (a + b) / two; });
-            
+
             // Since we shuffled the pointer around, we need to write the actual results to the input/output vector x.
             if (&x == tmp) {
                 std::swap(x, *tmp);
             } else if (&x == this->auxiliaryRowGroupVector.get()) {
                 std::swap(x, *this->auxiliaryRowGroupVector);
             }
-            
+
             // If requested, we store the scheduler for retrieval.
             if (this->isTrackSchedulerSet()) {
                 this->schedulerChoices = std::vector<uint_fast64_t>(this->A->getRowGroupCount());
                 this->multiplierA->multiplyAndReduce(env, dir, x, &b, *this->auxiliaryRowGroupVector, &this->schedulerChoices.get());
             }
-            
+
             if (!this->isCachingEnabled()) {
                 clearCache();
             }
-            
+
             return status == SolverStatus::Converged;
         }
-        
+
         template<typename ValueType>
         bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsSoundValueIteration(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
 
@@ -690,7 +696,7 @@ namespace storm {
             } else {
                 this->soundValueIterationHelper = std::make_unique<storm::solver::helper::SoundValueIterationHelper<ValueType>>(std::move(*this->soundValueIterationHelper), x, *this->auxiliaryRowGroupVector, env.solver().minMax().getRelativeTerminationCriterion(), storm::utility::convertNumber<ValueType>(env.solver().minMax().getPrecision()));
             }
-            
+
             // Prepare initial bounds for the solution (if given)
             if (this->hasLowerBound()) {
                 this->soundValueIterationHelper->setLowerBound(this->getLowerBound(true));
@@ -698,16 +704,16 @@ namespace storm {
             if (this->hasUpperBound()) {
                 this->soundValueIterationHelper->setUpperBound(this->getUpperBound(true));
             }
-            
+
             storm::storage::BitVector const* relevantValuesPtr = nullptr;
             if (this->hasRelevantValues()) {
                 relevantValuesPtr = &this->getRelevantValues();
             }
-            
+
             SolverStatus status = SolverStatus::InProgress;
             this->startMeasureProgress();
             uint64_t iterations = 0;
-            
+
             while (status == SolverStatus::InProgress && iterations < env.solver().minMax().getMaximalNumberOfIterations()) {
                 ++iterations;
                 this->soundValueIterationHelper->performIterationStep(dir, b);
@@ -716,12 +722,12 @@ namespace storm {
                 } else {
                     status = this->updateStatus(status, this->hasCustomTerminationCondition() && this->soundValueIterationHelper->checkCustomTerminationCondition(this->getTerminationCondition()), iterations, env.solver().minMax().getMaximalNumberOfIterations());
                 }
-                
+
                 // Potentially show progress.
                 this->showProgressIterative(iterations);
             }
             this->soundValueIterationHelper->setSolutionVector();
-            
+
             // If requested, we store the scheduler for retrieval.
             if (this->isTrackSchedulerSet()) {
                 this->schedulerChoices = std::vector<uint_fast64_t>(this->A->getRowGroupCount());
@@ -729,14 +735,14 @@ namespace storm {
             }
 
             this->reportStatus(status, iterations);
-            
+
             if (!this->isCachingEnabled()) {
                 clearCache();
             }
-            
+
             return status == SolverStatus::Converged;
         }
-        
+
         template<typename ValueType>
         bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsViToPi(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
             // First create an (inprecise) vi solver to get a good initial strategy for the (potentially precise) policy iteration solver.
@@ -760,11 +766,11 @@ namespace storm {
             STORM_LOG_INFO("Found initial policy using Value Iteration. Starting Policy iteration now.");
             return performPolicyIteration(env, dir, x, b, std::move(initialSched));
         }
-        
+
         template<typename ValueType>
         bool IterativeMinMaxLinearEquationSolver<ValueType>::isSolution(storm::OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& matrix, std::vector<ValueType> const& values, std::vector<ValueType> const& b) {
             storm::utility::ConstantsComparator<ValueType> comparator;
-            
+
             auto valueIt = values.begin();
             auto bIt = b.begin();
             for (uint64_t group = 0; group < matrix.getRowGroupCount(); ++group, ++valueIt) {
@@ -778,18 +784,18 @@ namespace storm {
                 for (auto endRow = matrix.getRowGroupIndices()[group + 1]; row < endRow; ++row, ++bIt) {
                     ValueType newValue = *bIt;
                     newValue += matrix.multiplyRowWithVector(row, values);
-                    
+
                     if ((dir == storm::OptimizationDirection::Minimize && newValue < groupValue) || (dir == storm::OptimizationDirection::Maximize && newValue > groupValue)) {
                         groupValue = newValue;
                     }
                 }
-                
+
                 // If the value does not match the one in the values vector, the given vector is not a solution.
                 if (!comparator.isEqual(groupValue, *valueIt)) {
                     return false;
                 }
             }
-            
+
             // Checked all values at this point.
             return true;
         }
@@ -797,7 +803,7 @@ namespace storm {
         template<typename ValueType>
         template<typename RationalType, typename ImpreciseType>
         bool IterativeMinMaxLinearEquationSolver<ValueType>::sharpen(storm::OptimizationDirection dir, uint64_t precision, storm::storage::SparseMatrix<RationalType> const& A, std::vector<ImpreciseType> const& x, std::vector<RationalType> const& b, std::vector<RationalType>& tmp) {
-            
+
             for (uint64_t p = 0; p <= precision; ++p) {
                 storm::utility::kwek_mehlhorn::sharpen(p, x, tmp);
 
@@ -817,18 +823,18 @@ namespace storm {
             storm::storage::SparseMatrix<storm::RationalNumber> rationalA = this->A->template toValueType<storm::RationalNumber>();
             std::vector<storm::RationalNumber> rationalX(x.size());
             std::vector<storm::RationalNumber> rationalB = storm::utility::vector::convertNumericVector<storm::RationalNumber>(b);
-            
+
             if (!this->multiplierA) {
                 this->multiplierA = storm::solver::MultiplierFactory<ValueType>().create(env, *this->A);
             }
-            
+
             if (!auxiliaryRowGroupVector) {
                 auxiliaryRowGroupVector = std::make_unique<std::vector<ValueType>>(this->A->getRowGroupCount());
             }
-            
+
             // Forward the call to the core rational search routine.
             bool converged = solveEquationsRationalSearchHelper<storm::RationalNumber, ImpreciseType>(env, dir, *this, rationalA, rationalX, rationalB, *this->A, x, b, *auxiliaryRowGroupVector);
-            
+
             // Translate back rational result to imprecise result.
             auto targetIt = x.begin();
             for (auto it = rationalX.begin(), ite = rationalX.end(); it != ite; ++it, ++targetIt) {
@@ -838,30 +844,30 @@ namespace storm {
             if (!this->isCachingEnabled()) {
                 this->clearCache();
             }
-            
+
             return converged;
         }
-        
+
         template<typename ValueType>
         template<typename ImpreciseType>
         typename std::enable_if<std::is_same<ValueType, ImpreciseType>::value && NumberTraits<ValueType>::IsExact, bool>::type IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsRationalSearchHelper(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
             // Version for when the overall value type is exact and the same type is to be used for the imprecise part.
-            
+
             if (!this->multiplierA) {
                 this->multiplierA = storm::solver::MultiplierFactory<ValueType>().create(env, *this->A);
             }
-            
+
             if (!auxiliaryRowGroupVector) {
                 auxiliaryRowGroupVector = std::make_unique<std::vector<ValueType>>(this->A->getRowGroupCount());
             }
-            
+
             // Forward the call to the core rational search routine.
             bool converged = solveEquationsRationalSearchHelper<ValueType, ImpreciseType>(env, dir, *this, *this->A, x, b, *this->A, *auxiliaryRowGroupVector, b, x);
 
             if (!this->isCachingEnabled()) {
                 this->clearCache();
             }
-            
+
             return converged;
         }
 
@@ -870,10 +876,10 @@ namespace storm {
         typename std::enable_if<!std::is_same<ValueType, ImpreciseType>::value, bool>::type IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsRationalSearchHelper(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
             // Version for when the overall value type is exact and the imprecise one is not. We first try to solve the
             // problem using the imprecise data type and fall back to the exact type as needed.
-            
+
             // Translate A to its imprecise version.
             storm::storage::SparseMatrix<ImpreciseType> impreciseA = this->A->template toValueType<ImpreciseType>();
-            
+
             // Translate x to its imprecise version.
             std::vector<ImpreciseType> impreciseX(x.size());
             {
@@ -884,23 +890,23 @@ namespace storm {
                     *targetIt = storm::utility::convertNumber<ImpreciseType, ValueType>(*sourceIt);
                 }
             }
-            
+
             // Create temporary storage for an imprecise x.
             std::vector<ImpreciseType> impreciseTmpX(x.size());
-            
+
             // Translate b to its imprecise version.
             std::vector<ImpreciseType> impreciseB(b.size());
             auto targetIt = impreciseB.begin();
             for (auto sourceIt = b.begin(); targetIt != impreciseB.end(); ++targetIt, ++sourceIt) {
                 *targetIt = storm::utility::convertNumber<ImpreciseType, ValueType>(*sourceIt);
             }
-            
+
             // Create imprecise solver from the imprecise data.
             IterativeMinMaxLinearEquationSolver<ImpreciseType> impreciseSolver(std::make_unique<storm::solver::GeneralLinearEquationSolverFactory<ImpreciseType>>());
             impreciseSolver.setMatrix(impreciseA);
             impreciseSolver.setCachingEnabled(true);
             impreciseSolver.multiplierA = storm::solver::MultiplierFactory<ImpreciseType>().create(env, impreciseA);
-            
+
             bool converged = false;
             try {
                 // Forward the call to the core rational search routine.
@@ -908,7 +914,7 @@ namespace storm {
                 impreciseSolver.clearCache();
             } catch (storm::exceptions::PrecisionExceededException const& e) {
                 STORM_LOG_WARN("Precision of value type was exceeded, trying to recover by switching to rational arithmetic.");
-                
+
                 if (!auxiliaryRowGroupVector) {
                     auxiliaryRowGroupVector = std::make_unique<std::vector<ValueType>>(this->A->getRowGroupCount());
                 }
@@ -918,7 +924,7 @@ namespace storm {
                 for (auto it = impreciseX.begin(), ite = impreciseX.end(); it != ite; ++it, ++targetIt) {
                     *targetIt = storm::utility::convertNumber<ValueType>(*it);
                 }
-                
+
                 // Get rid of the superfluous data structures.
                 impreciseX = std::vector<ImpreciseType>();
                 impreciseTmpX = std::vector<ImpreciseType>();
@@ -928,15 +934,15 @@ namespace storm {
                 if (!this->multiplierA) {
                     this->multiplierA = storm::solver::MultiplierFactory<ValueType>().create(env, *this->A);
                 }
-                
+
                 // Forward the call to the core rational search routine, but now with our value type as the imprecise value type.
                 converged = solveEquationsRationalSearchHelper<ValueType, ValueType>(env, dir, *this, *this->A, x, b, *this->A, *auxiliaryRowGroupVector, b, x);
             }
-            
+
             if (!this->isCachingEnabled()) {
                 this->clearCache();
             }
-            
+
             return converged;
         }
 
@@ -945,12 +951,12 @@ namespace storm {
             static std::vector<RationalType>* getTemporary(std::vector<RationalType>& rationalX, std::vector<ImpreciseType>*& currentX, std::vector<ImpreciseType>*& newX) {
                 return &rationalX;
             }
-            
+
             static void swapSolutions(std::vector<RationalType>& rationalX, std::vector<RationalType>*& rationalSolution, std::vector<ImpreciseType>& x, std::vector<ImpreciseType>*& currentX, std::vector<ImpreciseType>*& newX) {
                 // Nothing to do.
             }
         };
-        
+
         template<typename RationalType>
         struct TemporaryHelper<RationalType, RationalType> {
             static std::vector<RationalType>* getTemporary(std::vector<RationalType>& rationalX, std::vector<RationalType>*& currentX, std::vector<RationalType>*& newX) {
@@ -960,7 +966,7 @@ namespace storm {
             static void swapSolutions(std::vector<RationalType>& rationalX, std::vector<RationalType>*& rationalSolution, std::vector<RationalType>& x, std::vector<RationalType>*& currentX, std::vector<RationalType>*& newX) {
                 if (&rationalX == rationalSolution) {
                     // In this case, the rational solution is in place.
-                    
+
                     // However, since the rational solution is no alias to current x, the imprecise solution is stored
                     // in current x and and rational x is not an alias to x, we can swap the contents of currentX to x.
                     std::swap(x, *currentX);
@@ -971,7 +977,7 @@ namespace storm {
                 }
             }
         };
-        
+
         template<typename ValueType>
         template<typename RationalType, typename ImpreciseType>
         bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsRationalSearchHelper(Environment const& env, OptimizationDirection dir, IterativeMinMaxLinearEquationSolver<ImpreciseType> const& impreciseSolver, storm::storage::SparseMatrix<RationalType> const& rationalA, std::vector<RationalType>& rationalX, std::vector<RationalType> const& rationalB, storm::storage::SparseMatrix<ImpreciseType> const& A, std::vector<ImpreciseType>& x, std::vector<ImpreciseType> const& b, std::vector<ImpreciseType>& tmpX) const {
@@ -989,29 +995,29 @@ namespace storm {
             while (status == SolverStatus::InProgress && overallIterations < env.solver().minMax().getMaximalNumberOfIterations()) {
                 // Perform value iteration with the current precision.
                 typename IterativeMinMaxLinearEquationSolver<ImpreciseType>::ValueIterationResult result = impreciseSolver.performValueIteration(env, dir, currentX, newX, b, storm::utility::convertNumber<ImpreciseType, ValueType>(precision), env.solver().minMax().getRelativeTerminationCriterion(), SolverGuarantee::LessOrEqual, overallIterations, env.solver().minMax().getMaximalNumberOfIterations(), env.solver().minMax().getMultiplicationStyle());
-                
+
                 // At this point, the result of the imprecise value iteration is stored in the (imprecise) current x.
-                
+
                 ++valueIterationInvocations;
                 STORM_LOG_TRACE("Completed " << valueIterationInvocations << " value iteration invocations, the last one with precision " << precision << " completed in " << result.iterations << " iterations.");
-                
+
                 // Count the iterations.
                 overallIterations += result.iterations;
-                
+
                 // Compute maximal precision until which to sharpen.
                 uint64_t p = storm::utility::convertNumber<uint64_t>(storm::utility::ceil(storm::utility::log10<ValueType>(storm::utility::one<ValueType>() / precision)));
-                
+
                 // Make sure that currentX and rationalX are not aliased.
                 std::vector<RationalType>* temporaryRational = TemporaryHelper<RationalType, ImpreciseType>::getTemporary(rationalX, currentX, newX);
-                
+
                 // Sharpen solution and place it in the temporary rational.
                 bool foundSolution = sharpen(dir, p, rationalA, *currentX, rationalB, *temporaryRational);
-                
+
                 // After sharpen, if a solution was found, it is contained in the free rational.
-                
+
                 if (foundSolution) {
                     status = SolverStatus::Converged;
-                    
+
                     TemporaryHelper<RationalType, ImpreciseType>::swapSolutions(rationalX, temporaryRational, x, currentX, newX);
                 } else {
                     // Increase the precision.
@@ -1020,14 +1026,14 @@ namespace storm {
 
                 status = this->updateStatus(status, false, overallIterations, env.solver().minMax().getMaximalNumberOfIterations());
             }
-            
+
             // Swap the two vectors if the current result is not in the original x.
             if (currentX != originalX) {
                 std::swap(x, tmpX);
             }
-            
+
             this->reportStatus(status, overallIterations);
-            
+
             return status == SolverStatus::Converged || status == SolverStatus::TerminatedEarly;
         }
 
@@ -1035,18 +1041,18 @@ namespace storm {
         bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsRationalSearch(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
             return solveEquationsRationalSearchHelper<double>(env, dir, x, b);
         }
-        
+
         template<typename ValueType>
         void IterativeMinMaxLinearEquationSolver<ValueType>::computeOptimalValueForRowGroup(uint_fast64_t group, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b, uint_fast64_t* choice) const {
             uint64_t row = this->A->getRowGroupIndices()[group];
             uint64_t groupEnd = this->A->getRowGroupIndices()[group + 1];
             assert(row != groupEnd);
-            
+
             auto bIt = b.begin() + row;
             ValueType& xi = x[group];
             xi = this->A->multiplyRowWithVector(row, x) + *bIt;
             uint64_t optimalRow = row;
-            
+
             for (++row, ++bIt; row < groupEnd; ++row, ++bIt) {
                 ValueType choiceVal = this->A->multiplyRowWithVector(row, x) + *bIt;
                 if (minimize(dir)) {
@@ -1065,7 +1071,7 @@ namespace storm {
                 *choice = optimalRow - this->A->getRowGroupIndices()[group];
             }
         }
-        
+
         template<typename ValueType>
         void IterativeMinMaxLinearEquationSolver<ValueType>::clearCache() const {
             multiplierA.reset();
@@ -1075,9 +1081,9 @@ namespace storm {
             optimisticValueIterationHelper.reset();
             StandardMinMaxLinearEquationSolver<ValueType>::clearCache();
         }
-        
+
         template class IterativeMinMaxLinearEquationSolver<double>;
-        
+
 #ifdef STORM_HAVE_CARL
         template class IterativeMinMaxLinearEquationSolver<storm::RationalNumber>;
 #endif