#include "storm/solver/IterativeMinMaxLinearEquationSolver.h"
#include "storm/utility/ConstantsComparator.h"
#include "storm/environment/solver/MinMaxSolverEnvironment.h"
#include "storm/utility/KwekMehlhorn.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) : StandardMinMaxLinearEquationSolver<ValueType>(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, 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), 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 are using rational numbers.
auto method = env.solver().minMax().getMethod();
if (isExactMode && method != MinMaxMethod::PolicyIteration && method != MinMaxMethod::RationalSearch) {
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 does not guarantee exact results.");
}
}
STORM_LOG_THROW(method == MinMaxMethod::ValueIteration || method == MinMaxMethod::PolicyIteration || method == MinMaxMethod::RationalSearch, 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, std::is_same<ValueType, storm::RationalNumber>::value)) {
case MinMaxMethod::ValueIteration:
if (env.solver().isForceSoundness()) {
result = solveEquationsSoundValueIteration(env, dir, x, b);
} else {
result = solveEquationsValueIteration(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;
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() == 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(std::move(submatrix));
if (this->lowerBound) { // TODO
linearEquationSolver->setLowerBound(this->lowerBound.get());
}
if (this->upperBound) {
linearEquationSolver->setUpperBound(this->upperBound.get());
}
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(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());
// 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;
SolverStatus status = SolverStatus::InProgress;
uint64_t iterations = 0;
this->startMeasureProgress();
do {
// Solve the equation system for the 'DTMC'.
solveInducedEquationSystem(env, 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) const {
// Start by copying the requirements of the linear equation solver.
MinMaxLinearEquationSolverRequirements requirements(this->linearEquationSolverFactory->getRequirements());
auto method = getMethod(env, std::is_same<ValueType, storm::RationalNumber>::value);
if (method == MinMaxMethod::ValueIteration) {
if (env.solver().isForceSoundness()) {
// Interval iteration requires a unique solution and lower+upper bounds
if (!this->hasUniqueSolution()) {
requirements.requireNoEndComponents();
}
requirements.requireBounds();
} else 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.requireNoEndComponents();
} 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::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.requireNoEndComponents();
}
} else if (method == MinMaxMethod::PolicyIteration) {
if (!this->hasUniqueSolution()) {
requirements.requireValidInitialScheduler();
}
} 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(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 linear equation solver.
storm::solver::LinearEquationSolver<ValueType> const& linearEquationSolver = *this->linEqSolverA;
// Allow aliased multiplications.
bool useGaussSeidelMultiplication = linearEquationSolver.supportsGaussSeidelMultiplication() && 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;
std::vector<ValueType>* originalX = currentX;
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;
linearEquationSolver.multiplyAndReduceGaussSeidel(dir, this->A->getRowGroupIndices(), *newX, &b);
} else {
linearEquationSolver.multiplyAndReduce(dir, this->A->getRowGroupIndices(), *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);
}
// Swap the pointers so that the output is always in currentX.
if (originalX == newX) {
std::swap(currentX, newX);
}
return ValueIterationResult(iterations - currentIterations, status);
}
template<typename ValueType>
bool IterativeMinMaxLinearEquationSolver<ValueType>::solveEquationsValueIteration(Environment const& env, 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());
}
// 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;
solveInducedEquationSystem(env, 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->createLowerBoundsVector(x);
guarantee = SolverGuarantee::LessOrEqual;
} else if (this->getTerminationCondition().requiresGuarantee(SolverGuarantee::GreaterOrEqual)) {
this->createUpperBoundsVector(x);
guarantee = SolverGuarantee::GreaterOrEqual;
}
}
std::vector<ValueType>* newX = auxiliaryRowGroupVector.get();
std::vector<ValueType>* currentX = &x;
this->startMeasureProgress();
ValueIterationResult result = performValueIteration(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->linEqSolverA->multiplyAndReduce(dir, this->A->getRowGroupIndices(), 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);
}
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));
}
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;
}
/*!
* 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>::solveEquationsSoundValueIteration(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->linEqSolverA) {
this->linEqSolverA = this->linearEquationSolverFactory->create(*this->A);
this->linEqSolverA->setCachingEnabled(true);
}
if (!auxiliaryRowGroupVector) {
auxiliaryRowGroupVector = std::make_unique<std::vector<ValueType>>(this->A->getRowGroupCount());
}
// Allow aliased multiplications.
bool useGaussSeidelMultiplication = this->linEqSolverA->supportsGaussSeidelMultiplication() && 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();
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->linEqSolverA->multiplyAndReduceGaussSeidel(dir, this->A->getRowGroupIndices(), *lowerX, &b);
if (useDiffs) {
maxLowerDiff = computeMaxAbsDiff(*lowerX, this->getRelevantValues(), oldValues);
preserveOldRelevantValues(*upperX, this->getRelevantValues(), oldValues);
}
this->linEqSolverA->multiplyAndReduceGaussSeidel(dir, this->A->getRowGroupIndices(), *upperX, &b);
if (useDiffs) {
maxUpperDiff = computeMaxAbsDiff(*upperX, this->getRelevantValues(), oldValues);
}
} else {
this->linEqSolverA->multiplyAndReduce(dir, this->A->getRowGroupIndices(), *lowerX, &b, *tmp);
if (useDiffs) {
maxLowerDiff = computeMaxAbsDiff(*lowerX, *tmp, this->getRelevantValues());
}
std::swap(lowerX, tmp);
this->linEqSolverA->multiplyAndReduce(dir, this->A->getRowGroupIndices(), *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->linEqSolverA->multiplyAndReduceGaussSeidel(dir, this->A->getRowGroupIndices(), *lowerX, &b);
if (useDiffs) {
maxLowerDiff = computeMaxAbsDiff(*lowerX, this->getRelevantValues(), oldValues);
}
lowerStep = true;
} else {
if (useDiffs) {
preserveOldRelevantValues(*upperX, this->getRelevantValues(), oldValues);
}
this->linEqSolverA->multiplyAndReduceGaussSeidel(dir, this->A->getRowGroupIndices(), *upperX, &b);
if (useDiffs) {
maxUpperDiff = computeMaxAbsDiff(*upperX, this->getRelevantValues(), oldValues);
}
upperStep = true;
}
} else {
if (maxLowerDiff >= maxUpperDiff) {
this->linEqSolverA->multiplyAndReduce(dir, this->A->getRowGroupIndices(), *lowerX, &b, *tmp);
if (useDiffs) {
maxLowerDiff = computeMaxAbsDiff(*lowerX, *tmp, this->getRelevantValues());
}
std::swap(tmp, lowerX);
lowerStep = true;
} else {
this->linEqSolverA->multiplyAndReduce(dir, this->A->getRowGroupIndices(), *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->linEqSolverA->multiplyAndReduce(dir, this->A->getRowGroupIndices(), x, &b, *this->auxiliaryRowGroupVector, &this->schedulerChoices.get());
}
if (!this->isCachingEnabled()) {
clearCache();
}
return status == SolverStatus::Converged;
}
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>
void IterativeMinMaxLinearEquationSolver<ValueType>::createLinearEquationSolver() const {
this->linEqSolverA = this->linearEquationSolverFactory->create(*this->A);
}
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->linEqSolverA) {
this->linEqSolverA = this->linearEquationSolverFactory->create(*this->A);
this->linEqSolverA->setCachingEnabled(true);
}
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->linEqSolverA) {
this->linEqSolverA = this->linearEquationSolverFactory->create(*this->A);
this->linEqSolverA->setCachingEnabled(true);
}
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.createLinearEquationSolver();
impreciseSolver.setCachingEnabled(true);
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);
} 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->linEqSolverA) {
this->linEqSolverA = this->linearEquationSolverFactory->create(*this->A);
this->linEqSolverA->setCachingEnabled(true);
}
// 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>* 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(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 /= 10;
}
}
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_INFO("Iterative solver converged after " << iterations << " iterations."); break;
case SolverStatus::TerminatedEarly: STORM_LOG_INFO("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 {
auxiliaryRowGroupVector.reset();
auxiliaryRowGroupVector2.reset();
rowGroupOrdering.reset();
StandardMinMaxLinearEquationSolver<ValueType>::clearCache();
}
template<typename ValueType>
IterativeMinMaxLinearEquationSolverFactory<ValueType>::IterativeMinMaxLinearEquationSolverFactory() : StandardMinMaxLinearEquationSolverFactory<ValueType>() {
// Intentionally left empty
}
template<typename ValueType>
IterativeMinMaxLinearEquationSolverFactory<ValueType>::IterativeMinMaxLinearEquationSolverFactory(std::unique_ptr<LinearEquationSolverFactory<ValueType>>&& linearEquationSolverFactory) : StandardMinMaxLinearEquationSolverFactory<ValueType>(std::move(linearEquationSolverFactory)) {
// Intentionally left empty
}
template<typename ValueType>
IterativeMinMaxLinearEquationSolverFactory<ValueType>::IterativeMinMaxLinearEquationSolverFactory(EquationSolverType const& solverType) : StandardMinMaxLinearEquationSolverFactory<ValueType>(solverType) {
// Intentionally left empty
}
template<typename ValueType>
std::unique_ptr<MinMaxLinearEquationSolver<ValueType>> IterativeMinMaxLinearEquationSolverFactory<ValueType>::create(Environment const& env) const {
STORM_LOG_ASSERT(this->linearEquationSolverFactory, "Linear equation solver factory not initialized.");
auto method = env.solver().minMax().getMethod();
STORM_LOG_THROW(method == MinMaxMethod::ValueIteration || method == MinMaxMethod::PolicyIteration || method == MinMaxMethod::RationalSearch, storm::exceptions::InvalidEnvironmentException, "This solver does not support the selected method.");
std::unique_ptr<MinMaxLinearEquationSolver<ValueType>> result = std::make_unique<IterativeMinMaxLinearEquationSolver<ValueType>>(this->linearEquationSolverFactory->clone());
result->setRequirementsChecked(this->isRequirementsCheckedSet());
return result;
}
template class IterativeMinMaxLinearEquationSolver<double>;
template class IterativeMinMaxLinearEquationSolverFactory<double>;
#ifdef STORM_HAVE_CARL
template class IterativeMinMaxLinearEquationSolver<storm::RationalNumber>;
template class IterativeMinMaxLinearEquationSolverFactory<storm::RationalNumber>;
#endif
}
}