#include <functional>
#include <limits>
#include "storm/solver/IterativeMinMaxLinearEquationSolver.h"
#include "storm/utility/ConstantsComparator.h"
#include "storm/environment/solver/MinMaxSolverEnvironment.h"
#include "storm/environment/solver/OviSolverEnvironment.h"
#include "storm/utility/KwekMehlhorn.h"
#include "storm/utility/NumberTraits.h"
#include "storm/utility/Stopwatch.h"
#include "storm/utility/vector.h"
#include "storm/utility/macros.h"
#include "storm/exceptions/InvalidEnvironmentException.h"
#include "storm/exceptions/InvalidStateException.h"
#include "storm/exceptions/UnmetRequirementException.h"
#include "storm/exceptions/NotSupportedException.h"
#include "storm/exceptions/PrecisionExceededException.h"
namespace storm {
namespace solver {
template<typename ValueType>
IterativeMinMaxLinearEquationSolver<ValueType>::IterativeMinMaxLinearEquationSolver(std::unique_ptr<LinearEquationSolverFactory<ValueType>>&& linearEquationSolverFactory) : linearEquationSolverFactory(std::move(linearEquationSolverFactory)) {
// Intentionally left empty
}
template<typename ValueType>
IterativeMinMaxLinearEquationSolver<ValueType>::IterativeMinMaxLinearEquationSolver(storm::storage::SparseMatrix<ValueType> const& A, std::unique_ptr<LinearEquationSolverFactory<ValueType>>&& linearEquationSolverFactory) : StandardMinMaxLinearEquationSolver<ValueType>(A), linearEquationSolverFactory(std::move(linearEquationSolverFactory)) {
// Intentionally left empty.
}
template<typename ValueType>
IterativeMinMaxLinearEquationSolver<ValueType>::IterativeMinMaxLinearEquationSolver(storm::storage::SparseMatrix<ValueType>&& A, std::unique_ptr<LinearEquationSolverFactory<ValueType>>&& linearEquationSolverFactory) : StandardMinMaxLinearEquationSolver<ValueType>(std::move(A)), linearEquationSolverFactory(std::move(linearEquationSolverFactory)) {
// Intentionally left empty.
}
template<typename ValueType>
MinMaxMethod IterativeMinMaxLinearEquationSolver<ValueType>::getMethod(Environment const& env, bool isExactMode) const {
// Adjust the method if none was specified and we want exact or sound computations.
auto method = env.solver().minMax().getMethod();
if (isExactMode && method != MinMaxMethod::PolicyIteration && method != MinMaxMethod::RationalSearch && method != MinMaxMethod::ViToPi) {
if (env.solver().minMax().isMethodSetFromDefault()) {
STORM_LOG_INFO("Selecting 'Policy iteration' as the solution technique to guarantee exact results. If you want to override this, please explicitly specify a different method.");
method = MinMaxMethod::PolicyIteration;
} else {
STORM_LOG_WARN("The selected solution method " << toString(method) << " does not guarantee exact results.");
}
} else if (env.solver().isForceSoundness() && method != MinMaxMethod::SoundValueIteration && method != MinMaxMethod::IntervalIteration && method != MinMaxMethod::PolicyIteration && method != MinMaxMethod::RationalSearch && method != MinMaxMethod::OptimisticValueIteration) {
if (env.solver().minMax().isMethodSetFromDefault()) {
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.");
method = MinMaxMethod::SoundValueIteration;
} else {
STORM_LOG_WARN("The selected solution method does not guarantee sound results.");
}
}
STORM_LOG_THROW(method == MinMaxMethod::ValueIteration || method == MinMaxMethod::PolicyIteration || method == MinMaxMethod::RationalSearch || method == MinMaxMethod::SoundValueIteration || method == MinMaxMethod::IntervalIteration || method == MinMaxMethod::OptimisticValueIteration || method == MinMaxMethod::ViToPi, storm::exceptions::InvalidEnvironmentException, "This solver does not support the selected method.");
return method;
}
template<typename ValueType>
bool IterativeMinMaxLinearEquationSolver<ValueType>::internalSolveEquations(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
bool result = false;
switch (getMethod(env, storm::NumberTraits<ValueType>::IsExact || env.solver().isForceExact())) {
case MinMaxMethod::ValueIteration:
result = solveEquationsValueIteration(env, dir, x, b);
break;
case MinMaxMethod::OptimisticValueIteration:
result = solveEquationsOptimisticValueIteration(env, dir, x, b);
break;
case MinMaxMethod::PolicyIteration:
result = solveEquationsPolicyIteration(env, dir, x, b);
break;
case MinMaxMethod::RationalSearch:
result = solveEquationsRationalSearch(env, dir, x, b);
break;
case MinMaxMethod::IntervalIteration:
result = solveEquationsIntervalIteration(env, dir, x, b);
break;
case MinMaxMethod::SoundValueIteration:
result = solveEquationsSoundValueIteration(env, dir, x, b);
break;
case MinMaxMethod::ViToPi:
result = solveEquationsViToPi(env, dir, x, b);
break;
default:
STORM_LOG_THROW(false, storm::exceptions::InvalidEnvironmentException, "This solver does not implement the selected solution method");
}
return result;
}
template<typename ValueType>
bool IterativeMinMaxLinearEquationSolver<ValueType>::solveInducedEquationSystem(Environment const& env, std::unique_ptr<LinearEquationSolver<ValueType>>& linearEquationSolver, std::vector<uint64_t> const& scheduler, std::vector<ValueType>& x, std::vector<ValueType>& subB, std::vector<ValueType> const& originalB) const {
assert(subB.size() == x.size());
// Resolve the nondeterminism according to the given scheduler.
bool convertToEquationSystem = this->linearEquationSolverFactory->getEquationProblemFormat(env) == LinearEquationSolverProblemFormat::EquationSystem;
storm::storage::SparseMatrix<ValueType> submatrix = this->A->selectRowsFromRowGroups(scheduler, convertToEquationSystem);
if (convertToEquationSystem) {
submatrix.convertToEquationSystem();
}
storm::utility::vector::selectVectorValues<ValueType>(subB, scheduler, this->A->getRowGroupIndices(), originalB);
// Check whether the linear equation solver is already initialized
if (!linearEquationSolver) {
// Initialize the equation solver
linearEquationSolver = this->linearEquationSolverFactory->create(env, std::move(submatrix));
linearEquationSolver->setBoundsFromOtherSolver(*this);
linearEquationSolver->setCachingEnabled(true);
} else {
// If the equation solver is already initialized, it suffices to update the matrix
linearEquationSolver->setMatrix(std::move(submatrix));
}
// Solve the equation system for the 'DTMC' and return true upon success
return linearEquationSolver->solveEquations(env, x, subB);
}
template<typename ValueType>
bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsPolicyIteration(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
// Create the initial scheduler.
std::vector<storm::storage::sparse::state_type> scheduler = this->hasInitialScheduler() ? this->getInitialScheduler() : std::vector<storm::storage::sparse::state_type>(this->A->getRowGroupCount());
return performPolicyIteration(env, dir, x, b, std::move(scheduler));
}
template<typename ValueType>
bool IterativeMinMaxLinearEquationSolver<ValueType>::performPolicyIteration(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b, std::vector<storm::storage::sparse::state_type>&& initialPolicy) const {
std::vector<storm::storage::sparse::state_type> scheduler = std::move(initialPolicy);
// 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;
// The solver that we will use throughout the procedure.
std::unique_ptr<storm::solver::LinearEquationSolver<ValueType>> solver;
// 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;
SolverStatus status = SolverStatus::InProgress;
uint64_t iterations = 0;
this->startMeasureProgress();
do {
// Solve the equation system for the 'DTMC'.
solveInducedEquationSystem(environmentOfSolver, solver, scheduler, x, subB, b);
// Go through the multiplication result and see whether we can improve any of the choices.
bool schedulerImproved = false;
for (uint_fast64_t group = 0; group < this->A->getRowGroupCount(); ++group) {
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 = SolverStatus::Converged;
}
// Update environment variables.
++iterations;
status = updateStatusIfNotConverged(status, x, iterations, env.solver().minMax().getMaximalNumberOfIterations(), dir == storm::OptimizationDirection::Minimize ? SolverGuarantee::GreaterOrEqual : SolverGuarantee::LessOrEqual);
// Potentially show progress.
this->showProgressIterative(iterations);
} while (status == SolverStatus::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 == SolverStatus::Converged || status == SolverStatus::TerminatedEarly;
}
template<typename ValueType>
bool IterativeMinMaxLinearEquationSolver<ValueType>::valueImproved(OptimizationDirection dir, ValueType const& value1, ValueType const& value2) const {
if (dir == OptimizationDirection::Minimize) {
return value2 < value1;
} else {
return value2 > value1;
}
}
template<typename ValueType>
MinMaxLinearEquationSolverRequirements IterativeMinMaxLinearEquationSolver<ValueType>::getRequirements(Environment const& env, boost::optional<storm::solver::OptimizationDirection> const& direction, bool const& hasInitialScheduler) const {
auto method = getMethod(env, storm::NumberTraits<ValueType>::IsExact || env.solver().isForceExact());
// Check whether a linear equation solver is needed and potentially start with its requirements
bool needsLinEqSolver = false;
needsLinEqSolver |= method == MinMaxMethod::PolicyIteration;
needsLinEqSolver |= method == MinMaxMethod::ValueIteration && (this->hasInitialScheduler() || hasInitialScheduler);
needsLinEqSolver |= method == MinMaxMethod::ViToPi;
MinMaxLinearEquationSolverRequirements requirements = needsLinEqSolver ? MinMaxLinearEquationSolverRequirements(this->linearEquationSolverFactory->getRequirements(env)) : MinMaxLinearEquationSolverRequirements();
if (method == MinMaxMethod::ValueIteration) {
if (!this->hasUniqueSolution()) { // Traditional value iteration has no requirements if the solution is unique.
// Computing a scheduler is only possible if the solution is unique
if (this->isTrackSchedulerSet()) {
requirements.requireUniqueSolution();
} else {
// As we want the smallest (largest) solution for maximizing (minimizing) equation systems, we have to approach the solution from below (above).
if (!direction || direction.get() == OptimizationDirection::Maximize) {
requirements.requireLowerBounds();
}
if (!direction || direction.get() == OptimizationDirection::Minimize) {
requirements.requireUpperBounds();
}
}
}
} else if (method == MinMaxMethod::OptimisticValueIteration) {
// OptimisticValueIteration always requires lower bounds and a unique solution.
if (!this->hasUniqueSolution()) {
requirements.requireUniqueSolution();
}
requirements.requireLowerBounds();
} else if (method == MinMaxMethod::IntervalIteration) {
// Interval iteration requires a unique solution and lower+upper bounds
if (!this->hasUniqueSolution()) {
requirements.requireUniqueSolution();
}
requirements.requireBounds();
} else if (method == MinMaxMethod::RationalSearch) {
// Rational search needs to approach the solution from below.
requirements.requireLowerBounds();
// The solution needs to be unique in case of minimizing or in cases where we want a scheduler.
if (!this->hasUniqueSolution() && (!direction || direction.get() == OptimizationDirection::Minimize || this->isTrackSchedulerSet())) {
requirements.requireUniqueSolution();
}
} else if (method == MinMaxMethod::PolicyIteration) {
// The initial scheduler shall not select an end component
if (!this->hasNoEndComponents()) {
requirements.requireValidInitialScheduler();
}
} else if (method == MinMaxMethod::SoundValueIteration) {
if (!this->hasUniqueSolution()) {
requirements.requireUniqueSolution();
}
requirements.requireBounds(false);
} else if (method == MinMaxMethod::ViToPi) {
// Since we want to use value iteration to extract an initial scheduler, the solution has to be unique.
if (!this->hasUniqueSolution()) {
requirements.requireUniqueSolution();
}
} else {
STORM_LOG_THROW(false, storm::exceptions::InvalidEnvironmentException, "Unsupported technique for iterative MinMax linear equation solver.");
}
return requirements;
}
template<typename ValueType>
typename IterativeMinMaxLinearEquationSolver<ValueType>::ValueIterationResult IterativeMinMaxLinearEquationSolver<ValueType>::performValueIteration(Environment const& env, OptimizationDirection dir, std::vector<ValueType>*& currentX, std::vector<ValueType>*& newX, std::vector<ValueType> const& b, ValueType const& precision, bool relative, SolverGuarantee const& guarantee, uint64_t currentIterations, uint64_t maximalNumberOfIterations, storm::solver::MultiplicationStyle const& multiplicationStyle) const {
STORM_LOG_ASSERT(currentX != newX, "Vectors must not be aliased.");
// Get handle to multiplier.
storm::solver::Multiplier<ValueType> const& multiplier = *this->multiplierA;
// Allow aliased multiplications.
bool useGaussSeidelMultiplication = multiplicationStyle == storm::solver::MultiplicationStyle::GaussSeidel;
// Proceed with the iterations as long as the method did not converge or reach the maximum number of iterations.
uint64_t iterations = currentIterations;
SolverStatus status = SolverStatus::InProgress;
while (status == SolverStatus::InProgress) {
// Compute x' = min/max(A*x + b).
if (useGaussSeidelMultiplication) {
// Copy over the current vector so we can modify it in-place.
*newX = *currentX;
multiplier.multiplyAndReduceGaussSeidel(env, dir, *newX, &b);
} else {
multiplier.multiplyAndReduce(env, dir, *currentX, &b, *newX);
}
// Determine whether the method converged.
if (storm::utility::vector::equalModuloPrecision<ValueType>(*currentX, *newX, precision, relative)) {
status = SolverStatus::Converged;
}
// Update environment variables.
std::swap(currentX, newX);
++iterations;
status = updateStatusIfNotConverged(status, *currentX, iterations, maximalNumberOfIterations, guarantee);
// Potentially show progress.
this->showProgressIterative(iterations);
}
return ValueIterationResult(iterations - currentIterations, status);
}
template<typename ValueType>
ValueType computeMaxAbsDiff(std::vector<ValueType> const& allValues, storm::storage::BitVector const& relevantValues, std::vector<ValueType> const& oldValues) {
ValueType result = storm::utility::zero<ValueType>();
auto oldValueIt = oldValues.begin();
for (auto value : relevantValues) {
result = storm::utility::max<ValueType>(result, storm::utility::abs<ValueType>(allValues[value] - *oldValueIt));
++oldValueIt;
}
return result;
}
template<typename ValueType>
ValueType computeMaxAbsDiff(std::vector<ValueType> const& allOldValues, std::vector<ValueType> const& allNewValues, storm::storage::BitVector const& relevantValues) {
ValueType result = storm::utility::zero<ValueType>();
for (auto value : relevantValues) {
result = storm::utility::max<ValueType>(result, storm::utility::abs<ValueType>(allNewValues[value] - allOldValues[value]));
}
return result;
}
template<typename ValueType>
ValueType computeMaxAbsDiff(std::vector<ValueType> const& allOldValues, std::vector<ValueType> const& allNewValues) {
ValueType result = storm::utility::zero<ValueType>();
for (uint64_t i = 0; i < allOldValues.size(); ++i) {
result = storm::utility::max<ValueType>(result, storm::utility::abs<ValueType>(allNewValues[i] - allOldValues[i]));
}
return result;
}
template<typename ValueType>
ValueType computeMaxRelDiff(std::vector<ValueType> const& allOldValues, std::vector<ValueType> const& allNewValues, storm::storage::BitVector const& relevantValues) {
ValueType result = storm::utility::zero<ValueType>();
for (auto const& i : relevantValues) {
STORM_LOG_ASSERT(!storm::utility::isZero(allNewValues[i]) || storm::utility::isZero(allOldValues[i]), "Unexpected entry in iteration vector.");
if (!storm::utility::isZero(allNewValues[i])) {
result = storm::utility::max<ValueType>(result, storm::utility::abs<ValueType>(allNewValues[i] - allOldValues[i]) / allNewValues[i]);
}
}
return result;
}
template<typename ValueType>
ValueType computeMaxRelDiff(std::vector<ValueType> const& allOldValues, std::vector<ValueType> const& allNewValues) {
ValueType result = storm::utility::zero<ValueType>();
for (uint64_t i = 0; i < allOldValues.size(); ++i) {
STORM_LOG_ASSERT(!storm::utility::isZero(allNewValues[i]) || storm::utility::isZero(allOldValues[i]), "Unexpected entry in iteration vector.");
if (!storm::utility::isZero(allNewValues[i])) {
result = storm::utility::max<ValueType>(result, storm::utility::abs<ValueType>(allNewValues[i] - allOldValues[i]) / allNewValues[i]);
}
}
return result;
}
template<typename ValueType>
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());
// At this point, the result of the imprecise value iteration is stored in the (imprecise) current x.
++valueIterationInvocations;
STORM_LOG_TRACE("Completed " << valueIterationInvocations << " value iteration invocations, the last one with precision " << precision << " completed in " << result.iterations << " iterations.");
// Count the iterations.
overallIterations += result.iterations;
// Compute maximal precision until which to sharpen.
uint64_t p = storm::utility::convertNumber<uint64_t>(storm::utility::ceil(storm::utility::log10<ValueType>(storm::utility::one<ValueType>() / precision)));
// Make sure that currentX and rationalX are not aliased.
std::vector<RationalType>* temporaryRational = TemporaryHelper<RationalType, ImpreciseType>::getTemporary(rationalX, currentX, newX);
// Sharpen solution and place it in the temporary rational.
bool foundSolution = sharpen(dir, p, rationalA, *currentX, rationalB, *temporaryRational);
// After sharpen, if a solution was found, it is contained in the free rational.
if (foundSolution) {
status = SolverStatus::Converged;
TemporaryHelper<RationalType, ImpreciseType>::swapSolutions(rationalX, temporaryRational, x, currentX, newX);
} else {
// Increase the precision.
precision /= storm::utility::convertNumber<ValueType>(static_cast<uint64_t>(10));
}
}
// Swap the two vectors if the current result is not in the original x.
if (currentX != originalX) {
std::swap(x, tmpX);
}
if (status == SolverStatus::InProgress && overallIterations == env.solver().minMax().getMaximalNumberOfIterations()) {
status = SolverStatus::MaximalIterationsExceeded;
}
reportStatus(status, overallIterations);
return status == SolverStatus::Converged || status == SolverStatus::TerminatedEarly;
}
template<typename ValueType>
bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsRationalSearch(Environment const& env, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
return solveEquationsRationalSearchHelper<double>(env, dir, x, b);
}
template<typename ValueType>
void IterativeMinMaxLinearEquationSolver<ValueType>::computeOptimalValueForRowGroup(uint_fast64_t group, OptimizationDirection dir, std::vector<ValueType>& x, std::vector<ValueType> const& b, uint_fast64_t* choice) const {
uint64_t row = this->A->getRowGroupIndices()[group];
uint64_t groupEnd = this->A->getRowGroupIndices()[group + 1];
assert(row != groupEnd);
auto bIt = b.begin() + row;
ValueType& xi = x[group];
xi = this->A->multiplyRowWithVector(row, x) + *bIt;
uint64_t optimalRow = row;
for (++row, ++bIt; row < groupEnd; ++row, ++bIt) {
ValueType choiceVal = this->A->multiplyRowWithVector(row, x) + *bIt;
if (minimize(dir)) {
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>
SolverStatus IterativeMinMaxLinearEquationSolver<ValueType>::updateStatusIfNotConverged(SolverStatus status, std::vector<ValueType> const& x, uint64_t iterations, uint64_t maximalNumberOfIterations, SolverGuarantee const& guarantee) const {
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
}
}