#include "storm/solver/IterativeMinMaxLinearEquationSolver.h"
#include "storm/settings/SettingsManager.h"
#include "storm/settings/modules/MinMaxEquationSolverSettings.h"
#include "storm/utility/vector.h"
#include "storm/utility/macros.h"
#include "storm/exceptions/InvalidSettingsException.h"
#include "storm/exceptions/InvalidStateException.h"
namespace storm {
namespace solver {
template<typename ValueType>
IterativeMinMaxLinearEquationSolverSettings<ValueType>::IterativeMinMaxLinearEquationSolverSettings() {
// Get the settings object to customize linear solving.
storm::settings::modules::MinMaxEquationSolverSettings const& settings = storm::settings::getModule<storm::settings::modules::MinMaxEquationSolverSettings>();
maximalNumberOfIterations = settings.getMaximalIterationCount();
precision = storm::utility::convertNumber<ValueType>(settings.getPrecision());
relative = settings.getConvergenceCriterion() == storm::settings::modules::MinMaxEquationSolverSettings::ConvergenceCriterion::Relative;
setSolutionMethod(settings.getMinMaxEquationSolvingMethod());
}
template<typename ValueType>
void IterativeMinMaxLinearEquationSolverSettings<ValueType>::setSolutionMethod(SolutionMethod const& solutionMethod) {
this->solutionMethod = solutionMethod;
}
template<typename ValueType>
void IterativeMinMaxLinearEquationSolverSettings<ValueType>::setSolutionMethod(MinMaxMethod const& solutionMethod) {
switch (solutionMethod) {
case MinMaxMethod::ValueIteration: this->solutionMethod = SolutionMethod::ValueIteration; break;
case MinMaxMethod::PolicyIteration: this->solutionMethod = SolutionMethod::PolicyIteration; break;
case MinMaxMethod::Acyclic: this->solutionMethod = SolutionMethod::Acyclic; break;
default:
STORM_LOG_THROW(false, storm::exceptions::InvalidSettingsException, "Unsupported technique for iterative MinMax linear equation solver.");
}
}
template<typename ValueType>
void IterativeMinMaxLinearEquationSolverSettings<ValueType>::setMaximalNumberOfIterations(uint64_t maximalNumberOfIterations) {
this->maximalNumberOfIterations = maximalNumberOfIterations;
}
template<typename ValueType>
void IterativeMinMaxLinearEquationSolverSettings<ValueType>::setRelativeTerminationCriterion(bool value) {
this->relative = value;
}
template<typename ValueType>
void IterativeMinMaxLinearEquationSolverSettings<ValueType>::setPrecision(ValueType precision) {
this->precision = precision;
}
template<typename ValueType>
typename IterativeMinMaxLinearEquationSolverSettings<ValueType>::SolutionMethod const& IterativeMinMaxLinearEquationSolverSettings<ValueType>::getSolutionMethod() const {
return solutionMethod;
}
template<typename ValueType>
uint64_t IterativeMinMaxLinearEquationSolverSettings<ValueType>::getMaximalNumberOfIterations() const {
return maximalNumberOfIterations;
}
template<typename ValueType>
ValueType IterativeMinMaxLinearEquationSolverSettings<ValueType>::getPrecision() const {
return precision;
}
template<typename ValueType>
bool IterativeMinMaxLinearEquationSolverSettings<ValueType>::getRelativeTerminationCriterion() const {
return relative;
}
template<typename ValueType>
IterativeMinMaxLinearEquationSolver<ValueType>::IterativeMinMaxLinearEquationSolver(std::unique_ptr<LinearEquationSolverFactory<ValueType>>&& linearEquationSolverFactory, IterativeMinMaxLinearEquationSolverSettings<ValueType> const& settings) : StandardMinMaxLinearEquationSolver<ValueType>(std::move(linearEquationSolverFactory)), settings(settings) {
// Intentionally left empty
}
template<typename ValueType>
IterativeMinMaxLinearEquationSolver<ValueType>::IterativeMinMaxLinearEquationSolver(storm::storage::SparseMatrix<ValueType> const& A, std::unique_ptr<LinearEquationSolverFactory<ValueType>>&& linearEquationSolverFactory, IterativeMinMaxLinearEquationSolverSettings<ValueType> const& settings) : StandardMinMaxLinearEquationSolver<ValueType>(A, std::move(linearEquationSolverFactory)), settings(settings) {
// Intentionally left empty.
}
template<typename ValueType>
IterativeMinMaxLinearEquationSolver<ValueType>::IterativeMinMaxLinearEquationSolver(storm::storage::SparseMatrix<ValueType>&& A, std::unique_ptr<LinearEquationSolverFactory<ValueType>>&& linearEquationSolverFactory, IterativeMinMaxLinearEquationSolverSettings<ValueType> const& settings) : StandardMinMaxLinearEquationSolver<ValueType>(std::move(A), std::move(linearEquationSolverFactory)), settings(settings) {
// Intentionally left empty.
}
template<typename ValueType>
bool IterativeMinMaxLinearEquationSolver<ValueType>::internalSolveEquations(OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
switch (this->getSettings().getSolutionMethod()) {
case IterativeMinMaxLinearEquationSolverSettings<ValueType>::SolutionMethod::ValueIteration:
return solveEquationsValueIteration(dir, x, b);
case IterativeMinMaxLinearEquationSolverSettings<ValueType>::SolutionMethod::PolicyIteration:
return solveEquationsPolicyIteration(dir, x, b);
case IterativeMinMaxLinearEquationSolverSettings<ValueType>::SolutionMethod::Acyclic:
return solveEquationsAcyclic(dir, x, b);
default:
STORM_LOG_THROW(false, storm::exceptions::InvalidSettingsException, "This solver does not implement the selected solution method");
}
return false;
}
template<typename ValueType>
bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsPolicyIteration(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());
// Get a vector for storing the right-hand side of the inner equation system.
if(!auxiliaryRowGroupVector) {
auxiliaryRowGroupVector = std::make_unique<std::vector<ValueType>>(this->A->getRowGroupCount());
}
std::vector<ValueType>& subB = *auxiliaryRowGroupVector;
// Resolve the nondeterminism according to the current scheduler.
storm::storage::SparseMatrix<ValueType> submatrix = this->A->selectRowsFromRowGroups(scheduler, true);
submatrix.convertToEquationSystem();
storm::utility::vector::selectVectorValues<ValueType>(subB, scheduler, this->A->getRowGroupIndices(), b);
// Create a solver that we will use throughout the procedure. We will modify the matrix in each iteration.
auto solver = this->linearEquationSolverFactory->create(std::move(submatrix));
if (this->lowerBound) {
solver->setLowerBound(this->lowerBound.get());
}
if (this->upperBound) {
solver->setUpperBound(this->upperBound.get());
}
solver->setCachingEnabled(true);
Status status = Status::InProgress;
uint64_t iterations = 0;
do {
// Solve the equation system for the 'DTMC'.
solver->solveEquations(x, subB);
// 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) {
uint_fast64_t currentChoice = scheduler[group];
for (uint_fast64_t choice = this->A->getRowGroupIndices()[group]; choice < this->A->getRowGroupIndices()[group + 1]; ++choice) {
// If the choice is the currently selected one, we can skip it.
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.
if (valueImproved(dir, x[group], choiceValue)) {
schedulerImproved = true;
scheduler[group] = choice - this->A->getRowGroupIndices()[group];
x[group] = std::move(choiceValue);
}
}
}
// If the scheduler did not improve, we are done.
if (!schedulerImproved) {
status = Status::Converged;
} else {
// Update the scheduler and the solver.
submatrix = this->A->selectRowsFromRowGroups(scheduler, true);
submatrix.convertToEquationSystem();
storm::utility::vector::selectVectorValues<ValueType>(subB, scheduler, this->A->getRowGroupIndices(), b);
solver->setMatrix(std::move(submatrix));
}
// Update environment variables.
++iterations;
status = updateStatusIfNotConverged(status, x, iterations);
} while (status == Status::InProgress);
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 == Status::Converged || status == Status::TerminatedEarly;
}
template<typename ValueType>
bool IterativeMinMaxLinearEquationSolver<ValueType>::valueImproved(OptimizationDirection dir, ValueType const& value1, ValueType const& value2) const {
if (dir == OptimizationDirection::Minimize) {
return value2 < value1;
} else {
return value2 > value1;
}
}
template<typename ValueType>
ValueType IterativeMinMaxLinearEquationSolver<ValueType>::getPrecision() const {
return this->getSettings().getPrecision();
}
template<typename ValueType>
bool IterativeMinMaxLinearEquationSolver<ValueType>::getRelative() const {
return this->getSettings().getRelativeTerminationCriterion();
}
template<typename ValueType>
MinMaxLinearEquationSolverRequirements IterativeMinMaxLinearEquationSolver<ValueType>::getRequirements(EquationSystemType const& equationSystemType, boost::optional<storm::solver::OptimizationDirection> const& direction) const {
MinMaxLinearEquationSolverRequirements requirements;
if (equationSystemType == EquationSystemType::UntilProbabilities) {
if (this->getSettings().getSolutionMethod() == IterativeMinMaxLinearEquationSolverSettings<ValueType>::SolutionMethod::PolicyIteration) {
if (!direction || direction.get() == OptimizationDirection::Maximize) {
requirements.set(MinMaxLinearEquationSolverRequirements::Element::ValidInitialScheduler);
}
}
} else if (equationSystemType == EquationSystemType::ReachabilityRewards) {
if (!direction || direction.get() == OptimizationDirection::Minimize) {
requirements.set(MinMaxLinearEquationSolverRequirements::Element::ValidInitialScheduler);
}
}
return requirements;
}
template<typename ValueType>
bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsValueIteration(OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
if (!this->linEqSolverA) {
this->linEqSolverA = this->linearEquationSolverFactory->create(*this->A);
this->linEqSolverA->setCachingEnabled(true);
}
if (!auxiliaryRowGroupVector) {
auxiliaryRowGroupVector = std::make_unique<std::vector<ValueType>>(this->A->getRowGroupCount());
}
if (this->hasInitialScheduler()) {
// Resolve the nondeterminism according to the initial scheduler.
storm::storage::SparseMatrix<ValueType> submatrix = this->A->selectRowsFromRowGroups(this->getInitialScheduler(), true);
submatrix.convertToEquationSystem();
storm::utility::vector::selectVectorValues<ValueType>(*auxiliaryRowGroupVector, this->getInitialScheduler(), this->A->getRowGroupIndices(), b);
// Solve the resulting equation system.
auto submatrixSolver = this->linearEquationSolverFactory->create(std::move(submatrix));
submatrixSolver->setCachingEnabled(true);
if (this->lowerBound) {
submatrixSolver->setLowerBound(this->lowerBound.get());
}
if (this->upperBound) {
submatrixSolver->setUpperBound(this->upperBound.get());
}
submatrixSolver->solveEquations(x, *auxiliaryRowGroupVector);
}
std::vector<ValueType>* newX = auxiliaryRowGroupVector.get();
std::vector<ValueType>* currentX = &x;
// Proceed with the iterations as long as the method did not converge or reach the maximum number of iterations.
uint64_t iterations = 0;
Status status = Status::InProgress;
while (status == Status::InProgress) {
// Compute x' = min/max(A*x + b).
this->linEqSolverA->multiplyAndReduce(dir, this->A->getRowGroupIndices(), *currentX, &b, *newX);
// Determine whether the method converged.
if (storm::utility::vector::equalModuloPrecision<ValueType>(*currentX, *newX, this->getSettings().getPrecision(), this->getSettings().getRelativeTerminationCriterion())) {
status = Status::Converged;
}
// Update environment variables.
std::swap(currentX, newX);
++iterations;
status = updateStatusIfNotConverged(status, *currentX, iterations);
}
reportStatus(status, iterations);
// If we performed an odd number of iterations, we need to swap the x and currentX, because the newest result
// is currently stored in currentX, but x is the output vector.
if (currentX == auxiliaryRowGroupVector.get()) {
std::swap(x, *currentX);
}
// If requested, we store the scheduler for retrieval.
if (this->isTrackSchedulerSet()) {
this->linEqSolverA->multiplyAndReduce(dir, this->A->getRowGroupIndices(), x, &b, *currentX, &this->schedulerChoices.get());
}
if (!this->isCachingEnabled()) {
clearCache();
}
return status == Status::Converged || status == Status::TerminatedEarly;
}
template<typename ValueType>
bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsAcyclic(OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
uint64_t numGroups = this->A->getRowGroupCount();
// Allocate memory for the scheduler (if required)
if (this->isTrackSchedulerSet()) {
if (this->schedulerChoices) {
this->schedulerChoices->resize(numGroups);
} else {
this->schedulerChoices = std::vector<uint_fast64_t>(numGroups);
}
}
// We now compute a topological sort of the row groups.
// If caching is enabled, it might be possible to obtain this sort from the cache.
if (this->isCachingEnabled()) {
if (rowGroupOrdering) {
for (auto const& group : *rowGroupOrdering) {
computeOptimalValueForRowGroup(group, dir, x, b, this->isTrackSchedulerSet() ? &this->schedulerChoices.get()[group] : nullptr);
}
return true;
} else {
rowGroupOrdering = std::make_unique<std::vector<uint64_t>>();
rowGroupOrdering->reserve(numGroups);
}
}
auto transposedMatrix = this->A->transpose(true);
// We store the groups that have already been processed, i.e., the groups for which x[group] was already set to the correct value.
storm::storage::BitVector processedGroups(numGroups, false);
// Furthermore, we keep track of all candidate groups for which we still need to check whether this group can be processed now.
// A group can be processed if all successors have already been processed.
// Notice that the BitVector candidates is considered in a reversed way, i.e., group i is a candidate iff candidates.get(numGroups - i - 1) is true.
// This is due to the observation that groups with higher indices usually need to be processed earlier.
storm::storage::BitVector candidates(numGroups, true);
uint64_t candidate = numGroups - 1;
for (uint64_t numCandidates = candidates.size(); numCandidates > 0; --numCandidates) {
candidates.set(numGroups - candidate - 1, false);
// Check if the candidate row group has an unprocessed successor
bool hasUnprocessedSuccessor = false;
for (auto const& entry : this->A->getRowGroup(candidate)) {
if (!processedGroups.get(entry.getColumn())) {
hasUnprocessedSuccessor = true;
break;
}
}
uint64_t nextCandidate = numGroups - candidates.getNextSetIndex(numGroups - candidate - 1 + 1) - 1;
if (!hasUnprocessedSuccessor) {
// This candidate can be processed.
processedGroups.set(candidate);
computeOptimalValueForRowGroup(candidate, dir, x, b, this->isTrackSchedulerSet() ? &this->schedulerChoices.get()[candidate] : nullptr);
if (this->isCachingEnabled()) {
rowGroupOrdering->push_back(candidate);
}
// Add new candidates
for (auto const& predecessorEntry : transposedMatrix.getRow(candidate)) {
uint64_t predecessor = predecessorEntry.getColumn();
if (!candidates.get(numGroups - predecessor - 1)) {
candidates.set(numGroups - predecessor - 1, true);
nextCandidate = std::max(nextCandidate, predecessor);
++numCandidates;
}
}
}
candidate = nextCandidate;
}
assert(candidates.empty());
STORM_LOG_THROW(processedGroups.full(), storm::exceptions::InvalidOperationException, "The MinMax equation system is not acyclic.");
return true;
}
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)) {
if (choiceVal < xi) {
xi = choiceVal;
optimalRow = row;
}
} else {
if (choiceVal > xi) {
xi = choiceVal;
optimalRow = row;
}
}
}
if (choice != nullptr) {
*choice = optimalRow - this->A->getRowGroupIndices()[group];
}
}
template<typename ValueType>
typename IterativeMinMaxLinearEquationSolver<ValueType>::Status IterativeMinMaxLinearEquationSolver<ValueType>::updateStatusIfNotConverged(Status status, std::vector<ValueType> const& x, uint64_t iterations) const {
if (status != Status::Converged) {
if (this->hasCustomTerminationCondition() && this->getTerminationCondition().terminateNow(x)) {
status = Status::TerminatedEarly;
} else if (iterations >= this->getSettings().getMaximalNumberOfIterations()) {
status = Status::MaximalIterationsExceeded;
}
}
return status;
}
template<typename ValueType>
void IterativeMinMaxLinearEquationSolver<ValueType>::reportStatus(Status status, uint64_t iterations) const {
switch (status) {
case Status::Converged: STORM_LOG_INFO("Iterative solver converged after " << iterations << " iterations."); break;
case Status::TerminatedEarly: STORM_LOG_INFO("Iterative solver terminated early after " << iterations << " iterations."); break;
case Status::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>
IterativeMinMaxLinearEquationSolverSettings<ValueType> const& IterativeMinMaxLinearEquationSolver<ValueType>::getSettings() const {
return settings;
}
template<typename ValueType>
void IterativeMinMaxLinearEquationSolver<ValueType>::setSettings(IterativeMinMaxLinearEquationSolverSettings<ValueType> const& newSettings) {
settings = newSettings;
}
template<typename ValueType>
void IterativeMinMaxLinearEquationSolver<ValueType>::clearCache() const {
auxiliaryRowGroupVector.reset();
rowGroupOrdering.reset();
StandardMinMaxLinearEquationSolver<ValueType>::clearCache();
}
template<typename ValueType>
IterativeMinMaxLinearEquationSolverFactory<ValueType>::IterativeMinMaxLinearEquationSolverFactory(MinMaxMethodSelection const& method, bool trackScheduler) : StandardMinMaxLinearEquationSolverFactory<ValueType>(method, trackScheduler) {
settings.setSolutionMethod(this->getMinMaxMethod());
}
template<typename ValueType>
IterativeMinMaxLinearEquationSolverFactory<ValueType>::IterativeMinMaxLinearEquationSolverFactory(std::unique_ptr<LinearEquationSolverFactory<ValueType>>&& linearEquationSolverFactory, MinMaxMethodSelection const& method, bool trackScheduler) : StandardMinMaxLinearEquationSolverFactory<ValueType>(std::move(linearEquationSolverFactory), method, trackScheduler) {
settings.setSolutionMethod(this->getMinMaxMethod());
}
template<typename ValueType>
IterativeMinMaxLinearEquationSolverFactory<ValueType>::IterativeMinMaxLinearEquationSolverFactory(EquationSolverType const& solverType, MinMaxMethodSelection const& method, bool trackScheduler) : StandardMinMaxLinearEquationSolverFactory<ValueType>(solverType, method, trackScheduler) {
settings.setSolutionMethod(this->getMinMaxMethod());
}
template<typename ValueType>
std::unique_ptr<MinMaxLinearEquationSolver<ValueType>> IterativeMinMaxLinearEquationSolverFactory<ValueType>::create() const {
STORM_LOG_ASSERT(this->linearEquationSolverFactory, "Linear equation solver factory not initialized.");
std::unique_ptr<MinMaxLinearEquationSolver<ValueType>> result = std::make_unique<IterativeMinMaxLinearEquationSolver<ValueType>>(this->linearEquationSolverFactory->clone(), settings);
result->setTrackScheduler(this->isTrackSchedulerSet());
result->setRequirementsChecked(this->isRequirementsCheckedSet());
return result;
}
template<typename ValueType>
IterativeMinMaxLinearEquationSolverSettings<ValueType>& IterativeMinMaxLinearEquationSolverFactory<ValueType>::getSettings() {
return settings;
}
template<typename ValueType>
IterativeMinMaxLinearEquationSolverSettings<ValueType> const& IterativeMinMaxLinearEquationSolverFactory<ValueType>::getSettings() const {
return settings;
}
template<typename ValueType>
void IterativeMinMaxLinearEquationSolverFactory<ValueType>::setMinMaxMethod(MinMaxMethodSelection const& newMethod) {
MinMaxLinearEquationSolverFactory<ValueType>::setMinMaxMethod(newMethod);
settings.setSolutionMethod(this->getMinMaxMethod());
}
template<typename ValueType>
void IterativeMinMaxLinearEquationSolverFactory<ValueType>::setMinMaxMethod(MinMaxMethod const& newMethod) {
MinMaxLinearEquationSolverFactory<ValueType>::setMinMaxMethod(newMethod);
settings.setSolutionMethod(this->getMinMaxMethod());
}
template class IterativeMinMaxLinearEquationSolverSettings<double>;
template class IterativeMinMaxLinearEquationSolver<double>;
template class IterativeMinMaxLinearEquationSolverFactory<double>;
#ifdef STORM_HAVE_CARL
template class IterativeMinMaxLinearEquationSolverSettings<storm::RationalNumber>;
template class IterativeMinMaxLinearEquationSolver<storm::RationalNumber>;
template class IterativeMinMaxLinearEquationSolverFactory<storm::RationalNumber>;
#endif
}
}