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1318 lines
78 KiB
1318 lines
78 KiB
#include <functional>
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#include <limits>
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#include "storm/solver/IterativeMinMaxLinearEquationSolver.h"
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#include "storm/utility/ConstantsComparator.h"
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#include "storm/environment/solver/MinMaxSolverEnvironment.h"
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#include "storm/environment/solver/OviSolverEnvironment.h"
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#include "storm/utility/KwekMehlhorn.h"
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#include "storm/utility/NumberTraits.h"
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#include "storm/utility/Stopwatch.h"
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#include "storm/utility/vector.h"
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#include "storm/utility/macros.h"
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#include "storm/exceptions/InvalidEnvironmentException.h"
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#include "storm/exceptions/InvalidStateException.h"
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#include "storm/exceptions/UnmetRequirementException.h"
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#include "storm/exceptions/NotSupportedException.h"
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#include "storm/exceptions/PrecisionExceededException.h"
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namespace storm {
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namespace solver {
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template<typename ValueType>
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IterativeMinMaxLinearEquationSolver<ValueType>::IterativeMinMaxLinearEquationSolver(std::unique_ptr<LinearEquationSolverFactory<ValueType>>&& linearEquationSolverFactory) : linearEquationSolverFactory(std::move(linearEquationSolverFactory)) {
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// Intentionally left empty
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}
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template<typename ValueType>
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IterativeMinMaxLinearEquationSolver<ValueType>::IterativeMinMaxLinearEquationSolver(storm::storage::SparseMatrix<ValueType> const& A, std::unique_ptr<LinearEquationSolverFactory<ValueType>>&& linearEquationSolverFactory) : StandardMinMaxLinearEquationSolver<ValueType>(A), linearEquationSolverFactory(std::move(linearEquationSolverFactory)) {
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// Intentionally left empty.
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}
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template<typename ValueType>
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IterativeMinMaxLinearEquationSolver<ValueType>::IterativeMinMaxLinearEquationSolver(storm::storage::SparseMatrix<ValueType>&& A, std::unique_ptr<LinearEquationSolverFactory<ValueType>>&& linearEquationSolverFactory) : StandardMinMaxLinearEquationSolver<ValueType>(std::move(A)), linearEquationSolverFactory(std::move(linearEquationSolverFactory)) {
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// Intentionally left empty.
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}
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template<typename ValueType>
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MinMaxMethod IterativeMinMaxLinearEquationSolver<ValueType>::getMethod(Environment const& env, bool isExactMode) const {
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// Adjust the method if none was specified and we want exact or sound computations.
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auto method = env.solver().minMax().getMethod();
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if (isExactMode && method != MinMaxMethod::PolicyIteration && method != MinMaxMethod::RationalSearch && method != MinMaxMethod::ViToPi) {
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if (env.solver().minMax().isMethodSetFromDefault()) {
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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.");
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method = MinMaxMethod::PolicyIteration;
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} else {
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STORM_LOG_WARN("The selected solution method " << toString(method) << " does not guarantee exact results.");
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}
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} else if (env.solver().isForceSoundness() && method != MinMaxMethod::SoundValueIteration && method != MinMaxMethod::IntervalIteration && method != MinMaxMethod::PolicyIteration && method != MinMaxMethod::RationalSearch && method != MinMaxMethod::OptimisticValueIteration) {
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if (env.solver().minMax().isMethodSetFromDefault()) {
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STORM_LOG_INFO("Selecting 'sound value iteration' as the solution technique to guarantee sound results. If you want to override this, please explicitly specify a different method.");
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method = MinMaxMethod::SoundValueIteration;
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} else {
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STORM_LOG_WARN("The selected solution method does not guarantee sound results.");
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}
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}
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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.");
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return method;
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}
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template<typename ValueType>
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bool IterativeMinMaxLinearEquationSolver<ValueType>::internalSolveEquations(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
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bool result = false;
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switch (getMethod(env, storm::NumberTraits<ValueType>::IsExact || env.solver().isForceExact())) {
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case MinMaxMethod::ValueIteration:
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result = solveEquationsValueIteration(env, dir, x, b);
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break;
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case MinMaxMethod::OptimisticValueIteration:
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result = solveEquationsOptimisticValueIteration(env, dir, x, b);
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break;
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case MinMaxMethod::PolicyIteration:
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result = solveEquationsPolicyIteration(env, dir, x, b);
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break;
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case MinMaxMethod::RationalSearch:
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result = solveEquationsRationalSearch(env, dir, x, b);
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break;
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case MinMaxMethod::IntervalIteration:
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result = solveEquationsIntervalIteration(env, dir, x, b);
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break;
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case MinMaxMethod::SoundValueIteration:
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result = solveEquationsSoundValueIteration(env, dir, x, b);
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break;
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case MinMaxMethod::ViToPi:
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result = solveEquationsViToPi(env, dir, x, b);
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break;
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default:
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STORM_LOG_THROW(false, storm::exceptions::InvalidEnvironmentException, "This solver does not implement the selected solution method");
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}
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return result;
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}
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template<typename ValueType>
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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 {
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assert(subB.size() == x.size());
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// Resolve the nondeterminism according to the given scheduler.
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bool convertToEquationSystem = this->linearEquationSolverFactory->getEquationProblemFormat(env) == LinearEquationSolverProblemFormat::EquationSystem;
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storm::storage::SparseMatrix<ValueType> submatrix = this->A->selectRowsFromRowGroups(scheduler, convertToEquationSystem);
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if (convertToEquationSystem) {
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submatrix.convertToEquationSystem();
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}
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storm::utility::vector::selectVectorValues<ValueType>(subB, scheduler, this->A->getRowGroupIndices(), originalB);
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// Check whether the linear equation solver is already initialized
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if (!linearEquationSolver) {
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// Initialize the equation solver
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linearEquationSolver = this->linearEquationSolverFactory->create(env, std::move(submatrix));
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linearEquationSolver->setBoundsFromOtherSolver(*this);
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linearEquationSolver->setCachingEnabled(true);
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} else {
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// If the equation solver is already initialized, it suffices to update the matrix
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linearEquationSolver->setMatrix(std::move(submatrix));
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}
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// Solve the equation system for the 'DTMC' and return true upon success
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return linearEquationSolver->solveEquations(env, x, subB);
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}
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template<typename ValueType>
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bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsPolicyIteration(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
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// Create the initial scheduler.
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std::vector<storm::storage::sparse::state_type> scheduler = this->hasInitialScheduler() ? this->getInitialScheduler() : std::vector<storm::storage::sparse::state_type>(this->A->getRowGroupCount());
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return performPolicyIteration(env, dir, x, b, std::move(scheduler));
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}
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template<typename ValueType>
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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 {
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std::vector<storm::storage::sparse::state_type> scheduler = std::move(initialPolicy);
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// Get a vector for storing the right-hand side of the inner equation system.
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if (!auxiliaryRowGroupVector) {
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auxiliaryRowGroupVector = std::make_unique<std::vector<ValueType>>(this->A->getRowGroupCount());
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}
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std::vector<ValueType>& subB = *auxiliaryRowGroupVector;
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// The solver that we will use throughout the procedure.
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std::unique_ptr<storm::solver::LinearEquationSolver<ValueType>> solver;
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// The linear equation solver should be at least as precise as this solver
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std::unique_ptr<storm::Environment> environmentOfSolverStorage;
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auto precOfSolver = env.solver().getPrecisionOfLinearEquationSolver(env.solver().getLinearEquationSolverType());
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if (!storm::NumberTraits<ValueType>::IsExact) {
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bool changePrecision = precOfSolver.first && precOfSolver.first.get() > env.solver().minMax().getPrecision();
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bool changeRelative = precOfSolver.second && !precOfSolver.second.get() && env.solver().minMax().getRelativeTerminationCriterion();
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if (changePrecision || changeRelative) {
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environmentOfSolverStorage = std::make_unique<storm::Environment>(env);
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boost::optional<storm::RationalNumber> newPrecision;
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boost::optional<bool> newRelative;
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if (changePrecision) {
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newPrecision = env.solver().minMax().getPrecision();
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}
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if (changeRelative) {
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newRelative = true;
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}
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environmentOfSolverStorage->solver().setLinearEquationSolverPrecision(newPrecision, newRelative);
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}
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}
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storm::Environment const& environmentOfSolver = environmentOfSolverStorage ? *environmentOfSolverStorage : env;
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SolverStatus status = SolverStatus::InProgress;
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uint64_t iterations = 0;
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this->startMeasureProgress();
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do {
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// Solve the equation system for the 'DTMC'.
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solveInducedEquationSystem(environmentOfSolver, solver, scheduler, x, subB, b);
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// Go through the multiplication result and see whether we can improve any of the choices.
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bool schedulerImproved = false;
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for (uint_fast64_t group = 0; group < this->A->getRowGroupCount(); ++group) {
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uint_fast64_t currentChoice = scheduler[group];
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for (uint_fast64_t choice = this->A->getRowGroupIndices()[group]; choice < this->A->getRowGroupIndices()[group + 1]; ++choice) {
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// If the choice is the currently selected one, we can skip it.
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if (choice - this->A->getRowGroupIndices()[group] == currentChoice) {
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continue;
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}
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// Create the value of the choice.
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ValueType choiceValue = storm::utility::zero<ValueType>();
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for (auto const& entry : this->A->getRow(choice)) {
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choiceValue += entry.getValue() * x[entry.getColumn()];
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}
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choiceValue += b[choice];
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// If the value is strictly better than the solution of the inner system, we need to improve the scheduler.
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// 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).
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// only changing the scheduler if the values are not equal (modulo precision) would make this unsound.
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if (valueImproved(dir, x[group], choiceValue)) {
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schedulerImproved = true;
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scheduler[group] = choice - this->A->getRowGroupIndices()[group];
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x[group] = std::move(choiceValue);
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}
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}
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}
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// If the scheduler did not improve, we are done.
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if (!schedulerImproved) {
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status = SolverStatus::Converged;
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}
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// Update environment variables.
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++iterations;
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status = updateStatusIfNotConverged(status, x, iterations, env.solver().minMax().getMaximalNumberOfIterations(), dir == storm::OptimizationDirection::Minimize ? SolverGuarantee::GreaterOrEqual : SolverGuarantee::LessOrEqual);
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// Potentially show progress.
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this->showProgressIterative(iterations);
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} while (status == SolverStatus::InProgress);
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reportStatus(status, iterations);
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// If requested, we store the scheduler for retrieval.
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if (this->isTrackSchedulerSet()) {
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this->schedulerChoices = std::move(scheduler);
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}
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if (!this->isCachingEnabled()) {
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clearCache();
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}
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return status == SolverStatus::Converged || status == SolverStatus::TerminatedEarly;
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}
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template<typename ValueType>
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bool IterativeMinMaxLinearEquationSolver<ValueType>::valueImproved(OptimizationDirection dir, ValueType const& value1, ValueType const& value2) const {
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if (dir == OptimizationDirection::Minimize) {
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return value2 < value1;
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} else {
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return value2 > value1;
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}
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}
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template<typename ValueType>
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MinMaxLinearEquationSolverRequirements IterativeMinMaxLinearEquationSolver<ValueType>::getRequirements(Environment const& env, boost::optional<storm::solver::OptimizationDirection> const& direction, bool const& hasInitialScheduler) const {
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auto method = getMethod(env, storm::NumberTraits<ValueType>::IsExact || env.solver().isForceExact());
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// Check whether a linear equation solver is needed and potentially start with its requirements
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bool needsLinEqSolver = false;
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needsLinEqSolver |= method == MinMaxMethod::PolicyIteration;
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needsLinEqSolver |= method == MinMaxMethod::ValueIteration && (this->hasInitialScheduler() || hasInitialScheduler);
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needsLinEqSolver |= method == MinMaxMethod::ViToPi;
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MinMaxLinearEquationSolverRequirements requirements = needsLinEqSolver ? MinMaxLinearEquationSolverRequirements(this->linearEquationSolverFactory->getRequirements(env)) : MinMaxLinearEquationSolverRequirements();
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if (method == MinMaxMethod::ValueIteration) {
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if (!this->hasUniqueSolution()) { // Traditional value iteration has no requirements if the solution is unique.
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// Computing a scheduler is only possible if the solution is unique
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if (this->isTrackSchedulerSet()) {
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requirements.requireUniqueSolution();
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} else {
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// As we want the smallest (largest) solution for maximizing (minimizing) equation systems, we have to approach the solution from below (above).
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if (!direction || direction.get() == OptimizationDirection::Maximize) {
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requirements.requireLowerBounds();
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}
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if (!direction || direction.get() == OptimizationDirection::Minimize) {
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requirements.requireUpperBounds();
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}
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}
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}
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} else if (method == MinMaxMethod::OptimisticValueIteration) {
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// OptimisticValueIteration always requires lower bounds and a unique solution.
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if (!this->hasUniqueSolution()) {
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requirements.requireUniqueSolution();
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}
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requirements.requireLowerBounds();
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} else if (method == MinMaxMethod::IntervalIteration) {
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// Interval iteration requires a unique solution and lower+upper bounds
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if (!this->hasUniqueSolution()) {
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requirements.requireUniqueSolution();
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}
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requirements.requireBounds();
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} else if (method == MinMaxMethod::RationalSearch) {
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// Rational search needs to approach the solution from below.
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requirements.requireLowerBounds();
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// The solution needs to be unique in case of minimizing or in cases where we want a scheduler.
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if (!this->hasUniqueSolution() && (!direction || direction.get() == OptimizationDirection::Minimize || this->isTrackSchedulerSet())) {
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requirements.requireUniqueSolution();
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}
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} else if (method == MinMaxMethod::PolicyIteration) {
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// The initial scheduler shall not select an end component
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if (!this->hasNoEndComponents()) {
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requirements.requireValidInitialScheduler();
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}
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} else if (method == MinMaxMethod::SoundValueIteration) {
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if (!this->hasUniqueSolution()) {
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requirements.requireUniqueSolution();
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}
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requirements.requireBounds(false);
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} else if (method == MinMaxMethod::ViToPi) {
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// Since we want to use value iteration to extract an initial scheduler, the solution has to be unique.
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if (!this->hasUniqueSolution()) {
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requirements.requireUniqueSolution();
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}
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} else {
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STORM_LOG_THROW(false, storm::exceptions::InvalidEnvironmentException, "Unsupported technique for iterative MinMax linear equation solver.");
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}
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return requirements;
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}
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template<typename ValueType>
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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 {
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STORM_LOG_ASSERT(currentX != newX, "Vectors must not be aliased.");
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// Get handle to multiplier.
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storm::solver::Multiplier<ValueType> const& multiplier = *this->multiplierA;
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// Allow aliased multiplications.
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bool useGaussSeidelMultiplication = multiplicationStyle == storm::solver::MultiplicationStyle::GaussSeidel;
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// Proceed with the iterations as long as the method did not converge or reach the maximum number of iterations.
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uint64_t iterations = currentIterations;
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SolverStatus status = SolverStatus::InProgress;
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while (status == SolverStatus::InProgress) {
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// Compute x' = min/max(A*x + b).
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if (useGaussSeidelMultiplication) {
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// Copy over the current vector so we can modify it in-place.
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*newX = *currentX;
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multiplier.multiplyAndReduceGaussSeidel(env, dir, *newX, &b);
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} else {
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multiplier.multiplyAndReduce(env, dir, *currentX, &b, *newX);
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}
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// Determine whether the method converged.
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if (storm::utility::vector::equalModuloPrecision<ValueType>(*currentX, *newX, precision, relative)) {
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status = SolverStatus::Converged;
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}
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// Update environment variables.
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std::swap(currentX, newX);
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++iterations;
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status = updateStatusIfNotConverged(status, *currentX, iterations, maximalNumberOfIterations, guarantee);
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// Potentially show progress.
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this->showProgressIterative(iterations);
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}
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return ValueIterationResult(iterations - currentIterations, status);
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}
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template<typename ValueType>
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ValueType computeMaxAbsDiff(std::vector<ValueType> const& allValues, storm::storage::BitVector const& relevantValues, std::vector<ValueType> const& oldValues) {
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ValueType result = storm::utility::zero<ValueType>();
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auto oldValueIt = oldValues.begin();
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for (auto value : relevantValues) {
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result = storm::utility::max<ValueType>(result, storm::utility::abs<ValueType>(allValues[value] - *oldValueIt));
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++oldValueIt;
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}
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return result;
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}
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template<typename ValueType>
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ValueType computeMaxAbsDiff(std::vector<ValueType> const& allOldValues, std::vector<ValueType> const& allNewValues, storm::storage::BitVector const& relevantValues) {
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ValueType result = storm::utility::zero<ValueType>();
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for (auto value : relevantValues) {
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result = storm::utility::max<ValueType>(result, storm::utility::abs<ValueType>(allNewValues[value] - allOldValues[value]));
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}
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return result;
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}
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template<typename ValueType>
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ValueType computeMaxAbsDiff(std::vector<ValueType> const& allOldValues, std::vector<ValueType> const& allNewValues) {
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ValueType result = storm::utility::zero<ValueType>();
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for (uint64_t i = 0; i < allOldValues.size(); ++i) {
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result = storm::utility::max<ValueType>(result, storm::utility::abs<ValueType>(allNewValues[i] - allOldValues[i]));
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}
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return result;
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}
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template<typename ValueType>
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ValueType computeMaxRelDiff(std::vector<ValueType> const& allOldValues, std::vector<ValueType> const& allNewValues, storm::storage::BitVector const& relevantValues) {
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ValueType result = storm::utility::zero<ValueType>();
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for (auto const& i : relevantValues) {
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STORM_LOG_ASSERT(!storm::utility::isZero(allNewValues[i]) || storm::utility::isZero(allOldValues[i]), "Unexpected entry in iteration vector.");
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if (!storm::utility::isZero(allNewValues[i])) {
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result = storm::utility::max<ValueType>(result, storm::utility::abs<ValueType>(allNewValues[i] - allOldValues[i]) / allNewValues[i]);
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}
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}
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return result;
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}
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template<typename ValueType>
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ValueType computeMaxRelDiff(std::vector<ValueType> const& allOldValues, std::vector<ValueType> const& allNewValues) {
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ValueType result = storm::utility::zero<ValueType>();
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for (uint64_t i = 0; i < allOldValues.size(); ++i) {
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STORM_LOG_ASSERT(!storm::utility::isZero(allNewValues[i]) || storm::utility::isZero(allOldValues[i]), "Unexpected entry in iteration vector.");
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if (!storm::utility::isZero(allNewValues[i])) {
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result = storm::utility::max<ValueType>(result, storm::utility::abs<ValueType>(allNewValues[i] - allOldValues[i]) / allNewValues[i]);
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}
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}
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return result;
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}
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template<typename ValueType>
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ValueType updateIterationPrecision(storm::Environment const& env, std::vector<ValueType> const& currentX, std::vector<ValueType> const& newX, bool const& relative, boost::optional<storm::storage::BitVector> const& relevantValues) {
|
|
auto factor = storm::utility::convertNumber<ValueType>(env.solver().ovi().getPrecisionUpdateFactor());
|
|
bool useRelevant = relevantValues.is_initialized() && env.solver().ovi().useRelevantValuesForPrecisionUpdate();
|
|
if (relative) {
|
|
return (useRelevant ? computeMaxRelDiff(newX, currentX, relevantValues.get()) : computeMaxRelDiff(newX, currentX)) * factor;
|
|
} else {
|
|
return (useRelevant ? computeMaxAbsDiff(newX, currentX, relevantValues.get()) : computeMaxAbsDiff(newX, currentX)) * factor;
|
|
}
|
|
}
|
|
|
|
template<typename ValueType>
|
|
void guessUpperBoundRelative(std::vector<ValueType> const& x, std::vector<ValueType> &target, ValueType const& relativeBoundGuessingScaler) {
|
|
storm::utility::vector::applyPointwise<ValueType, ValueType>(x, target, [&relativeBoundGuessingScaler] (ValueType const& argument) -> ValueType { return argument * relativeBoundGuessingScaler; });
|
|
}
|
|
|
|
template<typename ValueType>
|
|
void guessUpperBoundAbsolute(std::vector<ValueType> const& x, std::vector<ValueType> &target, ValueType const& precision) {
|
|
storm::utility::vector::applyPointwise<ValueType, ValueType>(x, target, [&precision] (ValueType const& argument) -> ValueType { return argument + precision; });
|
|
}
|
|
|
|
template<typename ValueType>
|
|
bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsOptimisticValueIteration(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
|
|
|
|
uint64_t overallIterations = 0;
|
|
uint64_t maxOverallIterations = env.solver().minMax().getMaximalNumberOfIterations();
|
|
uint64_t lastValueIterationIterations = 0;
|
|
uint64_t currentVerificationIterations = 0;
|
|
uint64_t valueIterationInvocations = 0;
|
|
|
|
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());
|
|
}
|
|
|
|
// By default, we can not provide any guarantee
|
|
SolverGuarantee guarantee = SolverGuarantee::None;
|
|
// Get handle to multiplier.
|
|
storm::solver::Multiplier<ValueType> const &multiplier = *this->multiplierA;
|
|
// Allow aliased multiplications.
|
|
storm::solver::MultiplicationStyle multiplicationStyle = env.solver().minMax().getMultiplicationStyle();
|
|
bool useGaussSeidelMultiplication = multiplicationStyle == storm::solver::MultiplicationStyle::GaussSeidel;
|
|
// Relative errors
|
|
bool relative = env.solver().minMax().getRelativeTerminationCriterion();
|
|
// Upper bound only iterations
|
|
uint64_t upperBoundOnlyIterations = env.solver().ovi().getUpperBoundOnlyIterations();
|
|
|
|
boost::optional<storm::storage::BitVector> relevantValues;
|
|
if (this->hasRelevantValues()) {
|
|
relevantValues = this->getRelevantValues();
|
|
}
|
|
|
|
// x has to start with a lower bound.
|
|
this->createLowerBoundsVector(x);
|
|
|
|
std::vector<ValueType> *currentX = &x;
|
|
std::vector<ValueType> *newX = auxiliaryRowGroupVector.get();
|
|
std::vector<ValueType> currentUpperBound(currentX->size());
|
|
std::vector<ValueType> newUpperBound(x.size());
|
|
|
|
ValueType two = storm::utility::convertNumber<ValueType>(2.0);
|
|
ValueType precision = storm::utility::convertNumber<ValueType>(env.solver().minMax().getPrecision());
|
|
ValueType relativeBoundGuessingScaler = (storm::utility::one<ValueType>() + storm::utility::convertNumber<ValueType>(env.solver().ovi().getUpperBoundGuessingFactor()) * precision);
|
|
ValueType doublePrecision = precision * two;
|
|
ValueType iterationPrecision = precision;
|
|
|
|
SolverStatus status = SolverStatus::InProgress;
|
|
this->startMeasureProgress();
|
|
|
|
while (status == SolverStatus::InProgress && overallIterations < maxOverallIterations) {
|
|
|
|
// Perform value iteration until convergence
|
|
++valueIterationInvocations;
|
|
ValueIterationResult result = performValueIteration(env, dir, currentX, newX, b, iterationPrecision, relative, guarantee, overallIterations, env.solver().minMax().getMaximalNumberOfIterations(), multiplicationStyle);
|
|
lastValueIterationIterations = result.iterations;
|
|
overallIterations += result.iterations;
|
|
|
|
if (result.status != SolverStatus::Converged) {
|
|
status = result.status;
|
|
} else {
|
|
bool intervalIterationNeeded = false;
|
|
currentVerificationIterations = 0;
|
|
|
|
if (relative) {
|
|
guessUpperBoundRelative(*currentX, currentUpperBound, relativeBoundGuessingScaler);
|
|
} else {
|
|
guessUpperBoundAbsolute(*currentX, currentUpperBound, precision);
|
|
}
|
|
|
|
bool cancelGuess = false;
|
|
while (status == SolverStatus::InProgress && overallIterations < maxOverallIterations && !cancelGuess) {
|
|
// Perform value iteration stepwise for lower bound and guessed upper bound
|
|
|
|
// Lower and upper bound iteration
|
|
// Compute x' = min/max(A*x + b).
|
|
if (useGaussSeidelMultiplication) {
|
|
// Copy over the current vectors so we can modify them in-place.
|
|
// This is necessary as we want to compare the new values with the current ones.
|
|
newUpperBound = currentUpperBound;
|
|
// Do the calculation.
|
|
multiplier.multiplyAndReduceGaussSeidel(env, dir, newUpperBound, &b);
|
|
if (intervalIterationNeeded || currentVerificationIterations > upperBoundOnlyIterations) {
|
|
// Now do interval iteration.
|
|
*newX = *currentX;
|
|
multiplier.multiplyAndReduceGaussSeidel(env, dir, *newX, &b);
|
|
}
|
|
} else {
|
|
multiplier.multiplyAndReduce(env, dir, currentUpperBound, &b, newUpperBound);
|
|
if (intervalIterationNeeded || currentVerificationIterations > upperBoundOnlyIterations) {
|
|
// Now do interval iteration.
|
|
multiplier.multiplyAndReduce(env, dir, *currentX, &b, *newX);
|
|
}
|
|
}
|
|
|
|
bool newUpperBoundAlwaysHigherEqual = true;
|
|
bool newUpperBoundAlwaysLowerEqual = true;
|
|
bool valuesCrossed = false;
|
|
for (uint64_t i = 0; i < x.size(); ++i) {
|
|
if (newUpperBound[i] < currentUpperBound[i]) {
|
|
newUpperBoundAlwaysHigherEqual = false;
|
|
} else if (newUpperBound[i] != currentUpperBound[i]) {
|
|
newUpperBoundAlwaysLowerEqual = false;
|
|
}
|
|
}
|
|
|
|
if (intervalIterationNeeded || currentVerificationIterations > upperBoundOnlyIterations) {
|
|
for (uint64_t i = 0; i < x.size(); ++i) {
|
|
if (newUpperBound[i] < (*newX)[i]) {
|
|
valuesCrossed = true;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Update bounds
|
|
std::swap(currentX, newX);
|
|
std::swap(currentUpperBound, newUpperBound);
|
|
|
|
if (newUpperBoundAlwaysHigherEqual & ! newUpperBoundAlwaysLowerEqual) {
|
|
iterationPrecision = updateIterationPrecision(env, *currentX, *newX, relative, relevantValues);
|
|
// Not all values moved up or stayed the same
|
|
// If we have a single fixed point, we can safely set the new lower bound, to the wrongly guessed upper bound
|
|
if (this->hasUniqueSolution()) {
|
|
*currentX = currentUpperBound;
|
|
}
|
|
break;
|
|
} else if (valuesCrossed) {
|
|
STORM_LOG_ASSERT(false, "Cross case occurred.");
|
|
iterationPrecision = updateIterationPrecision(env, *currentX, *newX, relative, relevantValues);
|
|
break;
|
|
} else if (newUpperBoundAlwaysLowerEqual) {
|
|
// All values moved down or stayed the same and we have a maximum difference of twice the requested precision
|
|
// We can safely use twice the requested precision, as we calculate the center of both vectors
|
|
// We can use max_if instead of computeMaxAbsDiff, as x is definitely a lower bound and ub is larger in all elements
|
|
// Recalculate terminationPrecision if relative error requested
|
|
bool reachedPrecision = true;
|
|
for (auto const& valueIndex : relevantValues ? relevantValues.get() : storm::storage::BitVector(x.size(), true)) {
|
|
ValueType absDiff = currentUpperBound[valueIndex] - (*currentX)[valueIndex];
|
|
if (relative) {
|
|
if (absDiff > doublePrecision * (*currentX)[valueIndex]) {
|
|
reachedPrecision = false;
|
|
break;
|
|
}
|
|
} else {
|
|
if (absDiff > doublePrecision) {
|
|
reachedPrecision = false;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
if (reachedPrecision) {
|
|
// Calculate the center of both vectors and store it in currentX
|
|
storm::utility::vector::applyPointwise<ValueType, ValueType, ValueType>(*currentX, currentUpperBound, *currentX, [&two] (ValueType const& a, ValueType const& b) -> ValueType { return (a + b) / two; });
|
|
status = SolverStatus::Converged;
|
|
}
|
|
else {
|
|
intervalIterationNeeded = true;
|
|
}
|
|
}
|
|
|
|
ValueType scaledIterationCount = storm::utility::convertNumber<ValueType>(currentVerificationIterations) * storm::utility::convertNumber<ValueType>(env.solver().ovi().getMaxVerificationIterationFactor());
|
|
if (scaledIterationCount >= storm::utility::convertNumber<ValueType>(lastValueIterationIterations)) {
|
|
cancelGuess = true;
|
|
iterationPrecision = updateIterationPrecision(env, *currentX, *newX, relative, relevantValues);
|
|
}
|
|
|
|
++overallIterations;
|
|
++currentVerificationIterations;
|
|
}
|
|
}
|
|
}
|
|
|
|
if (overallIterations > maxOverallIterations) {
|
|
status = SolverStatus::MaximalIterationsExceeded;
|
|
}
|
|
|
|
// Swap the result into the output x.
|
|
if (currentX == auxiliaryRowGroupVector.get()) {
|
|
std::swap(x, *currentX);
|
|
}
|
|
|
|
reportStatus(status, overallIterations);
|
|
|
|
// 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());
|
|
this->multiplierA->multiplyAndReduce(env, dir, x, &b, *auxiliaryRowGroupVector.get(), &this->schedulerChoices.get());
|
|
}
|
|
|
|
if (!this->isCachingEnabled()) {
|
|
clearCache();
|
|
}
|
|
|
|
return status == SolverStatus::Converged || status == SolverStatus::TerminatedEarly;
|
|
}
|
|
|
|
template<typename ValueType>
|
|
bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsValueIteration(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
|
|
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());
|
|
}
|
|
|
|
// 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;
|
|
// The linear equation solver should be at least as precise as this solver
|
|
std::unique_ptr<storm::Environment> environmentOfSolverStorage;
|
|
auto precOfSolver = env.solver().getPrecisionOfLinearEquationSolver(env.solver().getLinearEquationSolverType());
|
|
if (!storm::NumberTraits<ValueType>::IsExact) {
|
|
bool changePrecision = precOfSolver.first && precOfSolver.first.get() > env.solver().minMax().getPrecision();
|
|
bool changeRelative = precOfSolver.second && !precOfSolver.second.get() && env.solver().minMax().getRelativeTerminationCriterion();
|
|
if (changePrecision || changeRelative) {
|
|
environmentOfSolverStorage = std::make_unique<storm::Environment>(env);
|
|
boost::optional<storm::RationalNumber> newPrecision;
|
|
boost::optional<bool> newRelative;
|
|
if (changePrecision) {
|
|
newPrecision = env.solver().minMax().getPrecision();
|
|
}
|
|
if (changeRelative) {
|
|
newRelative = true;
|
|
}
|
|
environmentOfSolverStorage->solver().setLinearEquationSolverPrecision(newPrecision, newRelative);
|
|
}
|
|
}
|
|
storm::Environment const& environmentOfSolver = environmentOfSolverStorage ? *environmentOfSolverStorage : env;
|
|
|
|
solveInducedEquationSystem(environmentOfSolver, linEqSolver, this->getInitialScheduler(), x, *auxiliaryRowGroupVector, b);
|
|
// If we were given an initial scheduler and are maximizing (minimizing), our current solution becomes
|
|
// always less-or-equal (greater-or-equal) than the actual solution.
|
|
guarantee = maximize(dir) ? SolverGuarantee::LessOrEqual : SolverGuarantee::GreaterOrEqual;
|
|
} else if (!this->hasUniqueSolution()) {
|
|
if (maximize(dir)) {
|
|
this->createLowerBoundsVector(x);
|
|
guarantee = SolverGuarantee::LessOrEqual;
|
|
} else {
|
|
this->createUpperBoundsVector(x);
|
|
guarantee = SolverGuarantee::GreaterOrEqual;
|
|
}
|
|
} else if (this->hasCustomTerminationCondition()) {
|
|
if (this->getTerminationCondition().requiresGuarantee(SolverGuarantee::LessOrEqual) && this->hasLowerBound()) {
|
|
this->createLowerBoundsVector(x);
|
|
guarantee = SolverGuarantee::LessOrEqual;
|
|
} else if (this->getTerminationCondition().requiresGuarantee(SolverGuarantee::GreaterOrEqual) && this->hasUpperBound()) {
|
|
this->createUpperBoundsVector(x);
|
|
guarantee = SolverGuarantee::GreaterOrEqual;
|
|
}
|
|
}
|
|
|
|
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());
|
|
|
|
// Swap the result into the output x.
|
|
if (currentX == auxiliaryRowGroupVector.get()) {
|
|
std::swap(x, *currentX);
|
|
}
|
|
|
|
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
|
|
* extended to rewards by Baier, Klein, Leuschner, Parker and Wunderlich (Ensuring the Reliability of Your
|
|
* Model Checker: Interval Iteration for Markov Decision Processes, CAV 2017).
|
|
*/
|
|
template<typename ValueType>
|
|
bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsIntervalIteration(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
|
|
STORM_LOG_THROW(this->hasUpperBound(), storm::exceptions::UnmetRequirementException, "Solver requires upper bound, but none was given.");
|
|
|
|
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();
|
|
std::vector<ValueType> oldValues;
|
|
if (useGaussSeidelMultiplication && useDiffs) {
|
|
oldValues.resize(this->getRelevantValues().getNumberOfSetBits());
|
|
}
|
|
ValueType maxLowerDiff = storm::utility::zero<ValueType>();
|
|
ValueType maxUpperDiff = storm::utility::zero<ValueType>();
|
|
bool relative = env.solver().minMax().getRelativeTerminationCriterion();
|
|
ValueType precision = storm::utility::convertNumber<ValueType>(env.solver().minMax().getPrecision());
|
|
if (!relative) {
|
|
precision *= storm::utility::convertNumber<ValueType>(2.0);
|
|
}
|
|
this->startMeasureProgress();
|
|
while (status == SolverStatus::InProgress && iterations < env.solver().minMax().getMaximalNumberOfIterations()) {
|
|
// Remember in which directions we took steps in this iteration.
|
|
bool lowerStep = false;
|
|
bool upperStep = false;
|
|
|
|
// In every thousandth iteration, we improve both bounds.
|
|
if (iterations % 1000 == 0 || maxLowerDiff == maxUpperDiff) {
|
|
lowerStep = true;
|
|
upperStep = true;
|
|
if (useGaussSeidelMultiplication) {
|
|
if (useDiffs) {
|
|
preserveOldRelevantValues(*lowerX, this->getRelevantValues(), oldValues);
|
|
}
|
|
this->multiplierA->multiplyAndReduceGaussSeidel(env, dir, *lowerX, &b);
|
|
if (useDiffs) {
|
|
maxLowerDiff = computeMaxAbsDiff(*lowerX, this->getRelevantValues(), oldValues);
|
|
preserveOldRelevantValues(*upperX, this->getRelevantValues(), oldValues);
|
|
}
|
|
this->multiplierA->multiplyAndReduceGaussSeidel(env, dir, *upperX, &b);
|
|
if (useDiffs) {
|
|
maxUpperDiff = computeMaxAbsDiff(*upperX, this->getRelevantValues(), oldValues);
|
|
}
|
|
} else {
|
|
this->multiplierA->multiplyAndReduce(env, dir, *lowerX, &b, *tmp);
|
|
if (useDiffs) {
|
|
maxLowerDiff = computeMaxAbsDiff(*lowerX, *tmp, this->getRelevantValues());
|
|
}
|
|
std::swap(lowerX, tmp);
|
|
this->multiplierA->multiplyAndReduce(env, dir, *upperX, &b, *tmp);
|
|
if (useDiffs) {
|
|
maxUpperDiff = computeMaxAbsDiff(*upperX, *tmp, this->getRelevantValues());
|
|
}
|
|
std::swap(upperX, tmp);
|
|
}
|
|
} else {
|
|
// In the following iterations, we improve the bound with the greatest difference.
|
|
if (useGaussSeidelMultiplication) {
|
|
if (maxLowerDiff >= maxUpperDiff) {
|
|
if (useDiffs) {
|
|
preserveOldRelevantValues(*lowerX, this->getRelevantValues(), oldValues);
|
|
}
|
|
this->multiplierA->multiplyAndReduceGaussSeidel(env, dir, *lowerX, &b);
|
|
if (useDiffs) {
|
|
maxLowerDiff = computeMaxAbsDiff(*lowerX, this->getRelevantValues(), oldValues);
|
|
}
|
|
lowerStep = true;
|
|
} else {
|
|
if (useDiffs) {
|
|
preserveOldRelevantValues(*upperX, this->getRelevantValues(), oldValues);
|
|
}
|
|
this->multiplierA->multiplyAndReduceGaussSeidel(env, dir, *upperX, &b);
|
|
if (useDiffs) {
|
|
maxUpperDiff = computeMaxAbsDiff(*upperX, this->getRelevantValues(), oldValues);
|
|
}
|
|
upperStep = true;
|
|
}
|
|
} else {
|
|
if (maxLowerDiff >= maxUpperDiff) {
|
|
this->multiplierA->multiplyAndReduce(env, dir, *lowerX, &b, *tmp);
|
|
if (useDiffs) {
|
|
maxLowerDiff = computeMaxAbsDiff(*lowerX, *tmp, this->getRelevantValues());
|
|
}
|
|
std::swap(tmp, lowerX);
|
|
lowerStep = true;
|
|
} else {
|
|
this->multiplierA->multiplyAndReduce(env, dir, *upperX, &b, *tmp);
|
|
if (useDiffs) {
|
|
maxUpperDiff = computeMaxAbsDiff(*upperX, *tmp, this->getRelevantValues());
|
|
}
|
|
std::swap(tmp, upperX);
|
|
upperStep = true;
|
|
}
|
|
}
|
|
}
|
|
STORM_LOG_ASSERT(maxLowerDiff >= storm::utility::zero<ValueType>(), "Expected non-negative lower diff.");
|
|
STORM_LOG_ASSERT(maxUpperDiff >= storm::utility::zero<ValueType>(), "Expected non-negative upper diff.");
|
|
if (iterations % 1000 == 0) {
|
|
STORM_LOG_TRACE("Iteration " << iterations << ": lower difference: " << maxLowerDiff << ", upper difference: " << maxUpperDiff << ".");
|
|
}
|
|
|
|
if (doConvergenceCheck) {
|
|
// Determine whether the method converged.
|
|
if (this->hasRelevantValues()) {
|
|
status = storm::utility::vector::equalModuloPrecision<ValueType>(*lowerX, *upperX, this->getRelevantValues(), precision, relative) ? SolverStatus::Converged : status;
|
|
} else {
|
|
status = storm::utility::vector::equalModuloPrecision<ValueType>(*lowerX, *upperX, precision, relative) ? SolverStatus::Converged : status;
|
|
}
|
|
}
|
|
|
|
// Update environment variables.
|
|
++iterations;
|
|
doConvergenceCheck = !doConvergenceCheck;
|
|
if (lowerStep) {
|
|
status = updateStatusIfNotConverged(status, *lowerX, iterations, env.solver().minMax().getMaximalNumberOfIterations(), SolverGuarantee::LessOrEqual);
|
|
}
|
|
if (upperStep) {
|
|
status = updateStatusIfNotConverged(status, *upperX, iterations, env.solver().minMax().getMaximalNumberOfIterations(), SolverGuarantee::GreaterOrEqual);
|
|
}
|
|
|
|
// Potentially show progress.
|
|
this->showProgressIterative(iterations);
|
|
}
|
|
|
|
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 {
|
|
|
|
// Prepare the solution vectors and the helper.
|
|
assert(x.size() == this->A->getRowGroupCount());
|
|
if (!this->auxiliaryRowGroupVector) {
|
|
this->auxiliaryRowGroupVector = std::make_unique<std::vector<ValueType>>();
|
|
}
|
|
if (!this->soundValueIterationHelper) {
|
|
this->soundValueIterationHelper = std::make_unique<storm::solver::helper::SoundValueIterationHelper<ValueType>>(*this->A, x, *this->auxiliaryRowGroupVector, env.solver().minMax().getRelativeTerminationCriterion(), storm::utility::convertNumber<ValueType>(env.solver().minMax().getPrecision()));
|
|
} 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));
|
|
}
|
|
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);
|
|
if (this->soundValueIterationHelper->checkConvergenceUpdateBounds(dir, relevantValuesPtr)) {
|
|
status = SolverStatus::Converged;
|
|
} else {
|
|
// Update the status accordingly
|
|
if (this->hasCustomTerminationCondition() && this->soundValueIterationHelper->checkCustomTerminationCondition(this->getTerminationCondition())) {
|
|
status = SolverStatus::TerminatedEarly;
|
|
} else if (iterations >= env.solver().minMax().getMaximalNumberOfIterations()) {
|
|
status = SolverStatus::MaximalIterationsExceeded;
|
|
}
|
|
}
|
|
|
|
// 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());
|
|
this->A->multiplyAndReduce(dir, this->A->getRowGroupIndices(), x, &b, *this->auxiliaryRowGroupVector, &this->schedulerChoices.get());
|
|
}
|
|
|
|
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.
|
|
std::vector<storm::storage::sparse::state_type> initialSched;
|
|
{
|
|
Environment viEnv = env;
|
|
viEnv.solver().minMax().setMethod(MinMaxMethod::ValueIteration);
|
|
auto impreciseSolver = GeneralMinMaxLinearEquationSolverFactory<double>().create(viEnv, this->A->template toValueType<double>());
|
|
impreciseSolver->setHasUniqueSolution(this->hasUniqueSolution());
|
|
impreciseSolver->setTrackScheduler(true);
|
|
if (this->hasInitialScheduler()) {
|
|
auto initSched = this->getInitialScheduler();
|
|
impreciseSolver->setInitialScheduler(std::move(initSched));
|
|
}
|
|
STORM_LOG_THROW(!impreciseSolver->getRequirements(viEnv, dir).hasEnabledCriticalRequirement(), storm::exceptions::UnmetRequirementException, "The value-iteration based solver has an unmet requirement.");
|
|
auto xVi = storm::utility::vector::convertNumericVector<double>(x);
|
|
auto bVi = storm::utility::vector::convertNumericVector<double>(b);
|
|
impreciseSolver->solveEquations(viEnv, dir, xVi, bVi);
|
|
initialSched = impreciseSolver->getSchedulerChoices();
|
|
}
|
|
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) {
|
|
ValueType groupValue = *bIt;
|
|
uint64_t row = matrix.getRowGroupIndices()[group];
|
|
groupValue += matrix.multiplyRowWithVector(row, values);
|
|
|
|
++row;
|
|
++bIt;
|
|
|
|
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;
|
|
}
|
|
|
|
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);
|
|
|
|
if (IterativeMinMaxLinearEquationSolver<RationalType>::isSolution(dir, A, tmp, b)) {
|
|
return true;
|
|
}
|
|
}
|
|
return false;
|
|
}
|
|
|
|
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 imprecise.
|
|
|
|
// Create a rational representation of the input so we can check for a proper solution later.
|
|
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) {
|
|
*targetIt = storm::utility::convertNumber<ValueType>(*it);
|
|
}
|
|
|
|
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;
|
|
}
|
|
|
|
template<typename ValueType>
|
|
template<typename ImpreciseType>
|
|
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());
|
|
{
|
|
std::vector<ValueType> tmp(x.size());
|
|
this->createLowerBoundsVector(tmp);
|
|
auto targetIt = impreciseX.begin();
|
|
for (auto sourceIt = tmp.begin(); targetIt != impreciseX.end(); ++targetIt, ++sourceIt) {
|
|
*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.
|
|
converged = solveEquationsRationalSearchHelper<ValueType, ImpreciseType>(env, dir, impreciseSolver, *this->A, x, b, impreciseA, impreciseX, impreciseB, impreciseTmpX);
|
|
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());
|
|
}
|
|
|
|
// Translate the imprecise value iteration result to the one we are going to use from now on.
|
|
auto targetIt = auxiliaryRowGroupVector->begin();
|
|
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>();
|
|
impreciseB = std::vector<ImpreciseType>();
|
|
impreciseA = storm::storage::SparseMatrix<ImpreciseType>();
|
|
|
|
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;
|
|
}
|
|
|
|
template<typename RationalType, typename ImpreciseType>
|
|
struct TemporaryHelper {
|
|
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) {
|
|
return newX;
|
|
}
|
|
|
|
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);
|
|
} else {
|
|
// Still, we may assume that the rational solution is not current x and is therefore new x.
|
|
std::swap(rationalX, *rationalSolution);
|
|
std::swap(x, *currentX);
|
|
}
|
|
}
|
|
};
|
|
|
|
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 {
|
|
|
|
std::vector<ImpreciseType> const* originalX = &x;
|
|
|
|
std::vector<ImpreciseType>* currentX = &x;
|
|
std::vector<ImpreciseType>* newX = &tmpX;
|
|
|
|
SolverStatus status = SolverStatus::InProgress;
|
|
uint64_t overallIterations = 0;
|
|
uint64_t valueIterationInvocations = 0;
|
|
ValueType precision = storm::utility::convertNumber<ValueType>(env.solver().minMax().getPrecision());
|
|
impreciseSolver.startMeasureProgress();
|
|
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());
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// At this point, the result of the imprecise value iteration is stored in the (imprecise) current x.
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++valueIterationInvocations;
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STORM_LOG_TRACE("Completed " << valueIterationInvocations << " value iteration invocations, the last one with precision " << precision << " completed in " << result.iterations << " iterations.");
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// Count the iterations.
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overallIterations += result.iterations;
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// Compute maximal precision until which to sharpen.
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uint64_t p = storm::utility::convertNumber<uint64_t>(storm::utility::ceil(storm::utility::log10<ValueType>(storm::utility::one<ValueType>() / precision)));
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// Make sure that currentX and rationalX are not aliased.
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std::vector<RationalType>* temporaryRational = TemporaryHelper<RationalType, ImpreciseType>::getTemporary(rationalX, currentX, newX);
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// Sharpen solution and place it in the temporary rational.
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bool foundSolution = sharpen(dir, p, rationalA, *currentX, rationalB, *temporaryRational);
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// After sharpen, if a solution was found, it is contained in the free rational.
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if (foundSolution) {
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status = SolverStatus::Converged;
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TemporaryHelper<RationalType, ImpreciseType>::swapSolutions(rationalX, temporaryRational, x, currentX, newX);
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} else {
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// Increase the precision.
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precision /= storm::utility::convertNumber<ValueType>(static_cast<uint64_t>(10));
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}
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}
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// Swap the two vectors if the current result is not in the original x.
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if (currentX != originalX) {
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std::swap(x, tmpX);
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}
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if (status == SolverStatus::InProgress && overallIterations == env.solver().minMax().getMaximalNumberOfIterations()) {
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status = SolverStatus::MaximalIterationsExceeded;
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}
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reportStatus(status, overallIterations);
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return status == SolverStatus::Converged || status == SolverStatus::TerminatedEarly;
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}
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template<typename ValueType>
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bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsRationalSearch(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
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return solveEquationsRationalSearchHelper<double>(env, dir, x, b);
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}
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template<typename ValueType>
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void IterativeMinMaxLinearEquationSolver<ValueType>::computeOptimalValueForRowGroup(uint_fast64_t group, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b, uint_fast64_t* choice) const {
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uint64_t row = this->A->getRowGroupIndices()[group];
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uint64_t groupEnd = this->A->getRowGroupIndices()[group + 1];
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assert(row != groupEnd);
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auto bIt = b.begin() + row;
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ValueType& xi = x[group];
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xi = this->A->multiplyRowWithVector(row, x) + *bIt;
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uint64_t optimalRow = row;
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|
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for (++row, ++bIt; row < groupEnd; ++row, ++bIt) {
|
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ValueType choiceVal = this->A->multiplyRowWithVector(row, x) + *bIt;
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if (minimize(dir)) {
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if (choiceVal < xi) {
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xi = choiceVal;
|
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optimalRow = row;
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}
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} else {
|
|
if (choiceVal > xi) {
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|
xi = choiceVal;
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|
optimalRow = row;
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}
|
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}
|
|
}
|
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if (choice != nullptr) {
|
|
*choice = optimalRow - this->A->getRowGroupIndices()[group];
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}
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|
}
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template<typename ValueType>
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SolverStatus IterativeMinMaxLinearEquationSolver<ValueType>::updateStatusIfNotConverged(SolverStatus status, std::vector<ValueType> const& x, uint64_t iterations, uint64_t maximalNumberOfIterations, SolverGuarantee const& guarantee) const {
|
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if (status != SolverStatus::Converged) {
|
|
if (this->hasCustomTerminationCondition() && this->getTerminationCondition().terminateNow(x, guarantee)) {
|
|
status = SolverStatus::TerminatedEarly;
|
|
} else if (iterations >= maximalNumberOfIterations) {
|
|
status = SolverStatus::MaximalIterationsExceeded;
|
|
}
|
|
}
|
|
return status;
|
|
}
|
|
|
|
template<typename ValueType>
|
|
void IterativeMinMaxLinearEquationSolver<ValueType>::reportStatus(SolverStatus status, uint64_t iterations) {
|
|
switch (status) {
|
|
case SolverStatus::Converged: STORM_LOG_TRACE("Iterative solver converged after " << iterations << " iterations."); break;
|
|
case SolverStatus::TerminatedEarly: STORM_LOG_TRACE("Iterative solver terminated early after " << iterations << " iterations."); break;
|
|
case SolverStatus::MaximalIterationsExceeded: STORM_LOG_WARN("Iterative solver did not converge after " << iterations << " iterations."); break;
|
|
default:
|
|
STORM_LOG_THROW(false, storm::exceptions::InvalidStateException, "Iterative solver terminated unexpectedly.");
|
|
}
|
|
}
|
|
|
|
template<typename ValueType>
|
|
void IterativeMinMaxLinearEquationSolver<ValueType>::clearCache() const {
|
|
multiplierA.reset();
|
|
auxiliaryRowGroupVector.reset();
|
|
auxiliaryRowGroupVector2.reset();
|
|
soundValueIterationHelper.reset();
|
|
StandardMinMaxLinearEquationSolver<ValueType>::clearCache();
|
|
}
|
|
|
|
template class IterativeMinMaxLinearEquationSolver<double>;
|
|
|
|
#ifdef STORM_HAVE_CARL
|
|
template class IterativeMinMaxLinearEquationSolver<storm::RationalNumber>;
|
|
#endif
|
|
}
|
|
}
|