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making game solver respect equation solver format

main
dehnert 7 years ago
parent
10da10a7d1
commit
a08cb4ac18
10 changed files with 245 additions and 96 deletions
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  1. 182
      src/storm-pars-cli/storm-pars.cpp
  2. 27
      src/storm-pars/modelchecker/instantiation/SparseCtmcInstantiationModelChecker.cpp
  3. 28
      src/storm-pars/modelchecker/instantiation/SparseCtmcInstantiationModelChecker.h
  4. 2
      src/storm-pars/modelchecker/instantiation/SparseDtmcInstantiationModelChecker.cpp
  5. 4
      src/storm-pars/modelchecker/instantiation/SparseInstantiationModelChecker.cpp
  6. 2
      src/storm-pars/modelchecker/instantiation/SparseMdpInstantiationModelChecker.cpp
  7. 6
      src/storm-pars/settings/modules/ParametricSettings.cpp
  8. 6
      src/storm-pars/settings/modules/ParametricSettings.h
  9. 2
      src/storm/solver/StandardGameSolver.cpp

182
src/storm-pars-cli/storm-pars.cpp
View File

@ -15,6 +15,8 @@
#include "storm/utility/Stopwatch.h"
#include "storm/utility/macros.h"
#include "storm-pars/modelchecker/instantiation/SparseCtmcInstantiationModelChecker.h"
#include "storm/settings/modules/GeneralSettings.h"
#include "storm/settings/modules/CoreSettings.h"
#include "storm/settings/modules/IOSettings.h"
@ -29,7 +31,19 @@ namespace storm {
typedef typename storm::cli::SymbolicInput SymbolicInput;
template <typename ValueType>
struct SampleInformation {
SampleInformation(bool graphPreserving = false) : graphPreserving(graphPreserving) {
// Intentionally left empty.
}
bool empty() const {
return cartesianProducts.empty();
}
std::vector<std::map<typename utility::parametric::VariableType<ValueType>::type, std::vector<typename utility::parametric::CoefficientType<ValueType>::type>>> cartesianProducts;
bool graphPreserving;
};
template <typename ValueType>
std::vector<storm::storage::ParameterRegion<ValueType>> parseRegions(std::shared_ptr<storm::models::ModelBase> const& model) {
@ -42,12 +56,12 @@ namespace storm {
}
template <typename ValueType>
std::map<typename utility::parametric::VariableType<ValueType>::type, std::vector<typename utility::parametric::CoefficientType<ValueType>::type>> parseSamples(std::shared_ptr<storm::models::ModelBase> const& model, std::string const& sampleString) {
SampleInformation<ValueType> parseSamples(std::shared_ptr<storm::models::ModelBase> const& model, std::string const& sampleString, bool graphPreserving) {
STORM_LOG_THROW(model->isSparseModel(), storm::exceptions::NotSupportedException, "Sampling is only supported for sparse models.");
std::map<typename utility::parametric::VariableType<ValueType>::type, std::vector<typename utility::parametric::CoefficientType<ValueType>::type>> samplesForVariables;
SampleInformation<ValueType> sampleInfo(graphPreserving);
if (sampleString.empty()) {
return samplesForVariables;
return sampleInfo;
}
// Get all parameters from the model.
@ -57,14 +71,21 @@ namespace storm {
auto rewParameters = storm::models::sparse::getRewardParameters(sparseModel);
modelParameters.insert(rewParameters.begin(), rewParameters.end());
std::vector<std::string> cartesianProducts;
boost::split(cartesianProducts, sampleString, boost::is_any_of(";"));
for (auto& product : cartesianProducts) {
boost::trim(product);
// Get the values string for each variable.
std::vector<std::string> valuesForVariables;
boost::split(valuesForVariables, sampleString, boost::is_any_of(","));
boost::split(valuesForVariables, product, boost::is_any_of(","));
for (auto& values : valuesForVariables) {
boost::trim(values);
}
std::set<typename utility::parametric::VariableType<ValueType>::type> encounteredParameters;
sampleInfo.cartesianProducts.emplace_back();
auto& newCartesianProduct = sampleInfo.cartesianProducts.back();
for (auto const& varValues : valuesForVariables) {
auto equalsPosition = varValues.find("=");
STORM_LOG_THROW(equalsPosition != varValues.npos, storm::exceptions::WrongFormatException, "Incorrect format of samples.");
@ -78,7 +99,6 @@ namespace storm {
for (auto const& parameter : modelParameters) {
std::stringstream parameterStream;
parameterStream << parameter;
std::cout << parameterStream.str() << " vs " << variableName << std::endl;
if (parameterStream.str() == variableName) {
foundParameter = true;
theParameter = parameter;
@ -91,17 +111,18 @@ namespace storm {
boost::split(splitValues, values, boost::is_any_of(":"));
STORM_LOG_THROW(!splitValues.empty(), storm::exceptions::WrongFormatException, "Expecting at least one value per parameter.");
auto& list = samplesForVariables[theParameter];
auto& list = newCartesianProduct[theParameter];
for (auto& value : splitValues) {
boost::trim(value);
list.push_back(storm::utility::convertNumber<typename utility::parametric::CoefficientType<ValueType>::type>(value));
}
}
STORM_LOG_THROW(encounteredParameters == modelParameters, storm::exceptions::WrongFormatException, "Variables for all parameters are required when providing samples.")
STORM_LOG_THROW(encounteredParameters == modelParameters, storm::exceptions::WrongFormatException, "Variables for all parameters are required when providing samples.");
}
return samplesForVariables;
return sampleInfo;
}
template <typename ValueType>
@ -169,9 +190,24 @@ namespace storm {
}
template<typename ValueType>
void printInitialStatesResult(std::unique_ptr<storm::modelchecker::CheckResult> const& result, storm::jani::Property const& property, storm::utility::Stopwatch* watch = nullptr) {
void printInitialStatesResult(std::unique_ptr<storm::modelchecker::CheckResult> const& result, storm::jani::Property const& property, storm::utility::Stopwatch* watch = nullptr, storm::utility::parametric::Valuation<ValueType> const* valuation = nullptr) {
if (result) {
STORM_PRINT_AND_LOG("Result (initial states): " << std::endl);
STORM_PRINT_AND_LOG("Result (initial states)");
if (valuation) {
bool first = true;
std::stringstream ss;
for (auto const& entry : *valuation) {
if (!first) {
ss << ", ";
} else {
first = false;
}
ss << entry.first << "=" << entry.second;
}
STORM_PRINT_AND_LOG(" for instance [" << ss.str() << "]");
}
STORM_PRINT_AND_LOG(": ")
auto const* regionCheckResult = dynamic_cast<storm::modelchecker::RegionCheckResult<ValueType> const*>(result.get());
if (regionCheckResult != nullptr) {
@ -195,7 +231,7 @@ namespace storm {
STORM_PRINT_AND_LOG(*result << std::endl);
}
if (watch) {
STORM_PRINT_AND_LOG("Time for model checking: " << *watch << "." << std::endl);
STORM_PRINT_AND_LOG("Time for model checking: " << *watch << "." << std::endl << std::endl);
}
} else {
STORM_PRINT_AND_LOG(" failed, property is unsupported by selected engine/settings." << std::endl);
@ -214,8 +250,78 @@ namespace storm {
}
}
template<template<typename, typename> class ModelCheckerType, typename ModelType, typename ValueType, typename SolveValueType = double>
void verifyPropertiesAtSamplePoints(ModelType const& model, SymbolicInput const& input, SampleInformation<ValueType> const& samples) {
// When samples are provided, we create an instantiation model checker.
ModelCheckerType<ModelType, SolveValueType> modelchecker(model);
for (auto const& property : input.properties) {
storm::cli::printModelCheckingProperty(property);
modelchecker.specifyFormula(storm::api::createTask<ValueType>(property.getRawFormula(), true));
modelchecker.setInstantiationsAreGraphPreserving(samples.graphPreserving);
storm::utility::parametric::Valuation<ValueType> valuation;
std::vector<typename utility::parametric::VariableType<ValueType>::type> parameters;
std::vector<typename std::vector<typename utility::parametric::CoefficientType<ValueType>::type>::const_iterator> iterators;
std::vector<typename std::vector<typename utility::parametric::CoefficientType<ValueType>::type>::const_iterator> iteratorEnds;
storm::utility::Stopwatch watch(true);
for (auto const& product : samples.cartesianProducts) {
parameters.clear();
iterators.clear();
iteratorEnds.clear();
for (auto const& entry : product) {
parameters.push_back(entry.first);
iterators.push_back(entry.second.cbegin());
iteratorEnds.push_back(entry.second.cend());
}
bool done = false;
while (!done) {
// Read off valuation.
for (uint64_t i = 0; i < parameters.size(); ++i) {
valuation[parameters[i]] = *iterators[i];
}
storm::utility::Stopwatch valuationWatch(true);
std::unique_ptr<storm::modelchecker::CheckResult> result = modelchecker.check(Environment(), valuation);
valuationWatch.stop();
if (result) {
result->filter(storm::modelchecker::ExplicitQualitativeCheckResult(model.getInitialStates()));
}
printInitialStatesResult<ValueType>(result, property, &valuationWatch, &valuation);
for (uint64_t i = 0; i < parameters.size(); ++i) {
++iterators[i];
if (iterators[i] == iteratorEnds[i]) {
// Reset iterator and proceed to move next iterator.
iterators[i] = product.at(parameters[i]).cbegin();
// If the last iterator was removed, we are done.
if (i == parameters.size() - 1) {
done = true;
}
} else {
// If an iterator was moved but not reset, we have another valuation to check.
break;
}
}
}
}
watch.stop();
STORM_PRINT_AND_LOG("Overall time for sampling all instances: " << watch << std::endl << std::endl);
}
}
template <typename ValueType>
void verifyPropertiesWithSparseEngine(std::shared_ptr<storm::models::sparse::Model<ValueType>> const& model, SymbolicInput const& input, std::map<typename utility::parametric::VariableType<ValueType>::type, std::vector<typename utility::parametric::CoefficientType<ValueType>::type>> const& samples) {
void verifyPropertiesWithSparseEngine(std::shared_ptr<storm::models::sparse::Model<ValueType>> const& model, SymbolicInput const& input, SampleInformation<ValueType> const& samples) {
if (samples.empty()) {
verifyProperties<ValueType>(input.properties,
@ -235,43 +341,15 @@ namespace storm {
}
});
} else {
STORM_LOG_THROW(model->isOfType(storm::models::ModelType::Dtmc), storm::exceptions::NotSupportedException, "Sampling is currently only supported for DTMCs.");
// When samples are provided, we create an instantiation model checker.
std::unique_ptr<storm::modelchecker::SparseDtmcInstantiationModelChecker<storm::models::sparse::Dtmc<ValueType>, double>> modelchecker(*model->template as<storm::models::sparse::Dtmc<ValueType>>());
for (auto const& property : input.properties) {
storm::cli::printModelCheckingProperty(property);
modelchecker->specifyFormula(property.getRawFormula(storm::api::createTask<ValueType>(property.getRawFormula(), true)));
// TODO: check.
modelchecker->setInstantiationsAreGraphPreserving(true);
storm::utility::parametric::Valuation<ValueType> valuation;
// Enumerate all sample points.
for () {
bool first = true;
std::stringstream ss;
ss << "Treating instance [";
for (auto const& entry : valuation) {
if (!first) {
ss << ", ";
STORM_LOG_TRACE("Sampling the model at given points.");
if (model->isOfType(storm::models::ModelType::Dtmc)) {
verifyPropertiesAtSamplePoints<storm::modelchecker::SparseDtmcInstantiationModelChecker, storm::models::sparse::Dtmc<ValueType>, ValueType, double>(*model->template as<storm::models::sparse::Dtmc<ValueType>>(), input, samples);
} else if (model->isOfType(storm::models::ModelType::Ctmc)) {
verifyPropertiesAtSamplePoints<storm::modelchecker::SparseCtmcInstantiationModelChecker, storm::models::sparse::Ctmc<ValueType>, ValueType, double>(*model->template as<storm::models::sparse::Ctmc<ValueType>>(), input, samples);
} else if (model->isOfType(storm::models::ModelType::Ctmc)) {
verifyPropertiesAtSamplePoints<storm::modelchecker::SparseMdpInstantiationModelChecker, storm::models::sparse::Mdp<ValueType>, ValueType, double>(*model->template as<storm::models::sparse::Mdp<ValueType>>(), input, samples);
} else {
first = false;
}
ss << entry.first << ": " << entry.second;
}
ss << "]...";
STORM_PRINT_AND_LOG(ss.str());
storm::utility::Stopwatch watch(true);
std::unique_ptr<storm::modelchecker::CheckResult> result = modelchecker->check(Environment(), valuation);
watch.stop();
printInitialStatesResult<ValueType>(result, property, &watch);
}
STORM_LOG_THROW(false, storm::exceptions::NotSupportedException, "Sampling is currently only supported for DTMCs, CTMCs and MDPs.");
}
}
}
@ -331,7 +409,7 @@ namespace storm {
}
template <typename ValueType>
void verifyWithSparseEngine(std::shared_ptr<storm::models::sparse::Model<ValueType>> const& model, SymbolicInput const& input, std::vector<storm::storage::ParameterRegion<ValueType>> const& regions, std::map<typename utility::parametric::VariableType<ValueType>::type, std::vector<typename utility::parametric::CoefficientType<ValueType>::type>> const& samples) {
void verifyWithSparseEngine(std::shared_ptr<storm::models::sparse::Model<ValueType>> const& model, SymbolicInput const& input, std::vector<storm::storage::ParameterRegion<ValueType>> const& regions, SampleInformation<ValueType> const& samples) {
if (regions.empty()) {
storm::pars::verifyPropertiesWithSparseEngine(model, input, samples);
} else {
@ -340,7 +418,7 @@ namespace storm {
}
template <storm::dd::DdType DdType, typename ValueType>
void verifyParametricModel(std::shared_ptr<storm::models::ModelBase> const& model, SymbolicInput const& input, std::vector<storm::storage::ParameterRegion<ValueType>> const& regions, std::map<typename utility::parametric::VariableType<ValueType>::type, std::vector<typename utility::parametric::CoefficientType<ValueType>::type>> const& samples) {
void verifyParametricModel(std::shared_ptr<storm::models::ModelBase> const& model, SymbolicInput const& input, std::vector<storm::storage::ParameterRegion<ValueType>> const& regions, SampleInformation<ValueType> const& samples) {
STORM_LOG_ASSERT(model->isSparseModel(), "Unexpected model type.");
storm::pars::verifyWithSparseEngine<ValueType>(model->as<storm::models::sparse::Model<ValueType>>(), input, regions, samples);
}
@ -376,7 +454,7 @@ namespace storm {
}
std::vector<storm::storage::ParameterRegion<ValueType>> regions = parseRegions<ValueType>(model);
std::map<typename utility::parametric::VariableType<ValueType>::type, std::vector<typename utility::parametric::CoefficientType<ValueType>::type>> samples = parseSamples<ValueType>(model, parSettings.getSamples());
SampleInformation<ValueType> samples = parseSamples<ValueType>(model, parSettings.getSamples(), parSettings.isSamplesAreGraphPreservingSet());
if (model) {
storm::cli::exportModel<DdType, ValueType>(model, input);

27
src/storm-pars/modelchecker/instantiation/SparseCtmcInstantiationModelChecker.cpp
View File

@ -0,0 +1,27 @@
#include "storm-pars/modelchecker/instantiation/SparseCtmcInstantiationModelChecker.h"
#include "storm/modelchecker/csl/SparseCtmcCslModelChecker.h"
#include "storm/exceptions/InvalidStateException.h"
namespace storm {
namespace modelchecker {
template <typename SparseModelType, typename ConstantType>
SparseCtmcInstantiationModelChecker<SparseModelType, ConstantType>::SparseCtmcInstantiationModelChecker(SparseModelType const& parametricModel) : SparseInstantiationModelChecker<SparseModelType, ConstantType>(parametricModel), modelInstantiator(parametricModel) {
//Intentionally left empty
}
template <typename SparseModelType, typename ConstantType>
std::unique_ptr<CheckResult> SparseCtmcInstantiationModelChecker<SparseModelType, ConstantType>::check(Environment const& env, storm::utility::parametric::Valuation<typename SparseModelType::ValueType> const& valuation) {
STORM_LOG_THROW(this->currentCheckTask, storm::exceptions::InvalidStateException, "Checking has been invoked but no property has been specified before.");
auto const& instantiatedModel = modelInstantiator.instantiate(valuation);
storm::modelchecker::SparseCtmcCslModelChecker<storm::models::sparse::Ctmc<ConstantType>> modelChecker(instantiatedModel);
return modelChecker.check(env, *this->currentCheckTask);
}
template class SparseCtmcInstantiationModelChecker<storm::models::sparse::Ctmc<storm::RationalFunction>, double>;
template class SparseCtmcInstantiationModelChecker<storm::models::sparse::Ctmc<storm::RationalFunction>, storm::RationalNumber>;
}
}

28
src/storm-pars/modelchecker/instantiation/SparseCtmcInstantiationModelChecker.h
View File

@ -0,0 +1,28 @@
#pragma once
#include <memory>
#include <boost/optional.hpp>
#include "storm-pars/modelchecker/instantiation/SparseInstantiationModelChecker.h"
#include "storm-pars/utility/ModelInstantiator.h"
#include "storm/models/sparse/Dtmc.h"
#include "storm/models/sparse/StandardRewardModel.h"
#include "storm/modelchecker/prctl/SparseDtmcPrctlModelChecker.h"
namespace storm {
namespace modelchecker {
/*!
* Class to efficiently check a formula on a parametric model with different parameter instantiations.
*/
template <typename SparseModelType, typename ConstantType>
class SparseCtmcInstantiationModelChecker : public SparseInstantiationModelChecker<SparseModelType, ConstantType> {
public:
SparseCtmcInstantiationModelChecker(SparseModelType const& parametricModel);
virtual std::unique_ptr<CheckResult> check(Environment const& env, storm::utility::parametric::Valuation<typename SparseModelType::ValueType> const& valuation) override;
storm::utility::ModelInstantiator<SparseModelType, storm::models::sparse::Ctmc<ConstantType>> modelInstantiator;
};
}
}

2
src/storm-pars/modelchecker/instantiation/SparseDtmcInstantiationModelChecker.cpp
View File

@ -20,7 +20,7 @@ namespace storm {
std::unique_ptr<CheckResult> SparseDtmcInstantiationModelChecker<SparseModelType, ConstantType>::check(Environment const& env, storm::utility::parametric::Valuation<typename SparseModelType::ValueType> const& valuation) {
STORM_LOG_THROW(this->currentCheckTask, storm::exceptions::InvalidStateException, "Checking has been invoked but no property has been specified before.");
auto const& instantiatedModel = modelInstantiator.instantiate(valuation);
STORM_LOG_ASSERT(instantiatedModel.getTransitionMatrix().isProbabilistic(), "Instantiated matrix is not probabilistic!");
STORM_LOG_THROW(instantiatedModel.getTransitionMatrix().isProbabilistic(), storm::exceptions::InvalidArgumentException, "Instantiation point is invalid as the transition matrix becomes non-stochastic.");
storm::modelchecker::SparseDtmcPrctlModelChecker<storm::models::sparse::Dtmc<ConstantType>> modelChecker(instantiatedModel);
// Check if there are some optimizations implemented for the specified property

4
src/storm-pars/modelchecker/instantiation/SparseInstantiationModelChecker.cpp
View File

@ -2,6 +2,7 @@
#include "storm/adapters/RationalFunctionAdapter.h"
#include "storm/models/sparse/Dtmc.h"
#include "storm/models/sparse/Ctmc.h"
#include "storm/models/sparse/Mdp.h"
#include "storm/models/sparse/StandardRewardModel.h"
@ -15,7 +16,6 @@ namespace storm {
// Intentionally left empty
}
template <typename SparseModelType, typename ConstantType>
void SparseInstantiationModelChecker<SparseModelType, ConstantType>::specifyFormula(storm::modelchecker::CheckTask<storm::logic::Formula, typename SparseModelType::ValueType> const& checkTask) {
currentFormula = checkTask.getFormula().asSharedPointer();
@ -33,9 +33,11 @@ namespace storm {
}
template class SparseInstantiationModelChecker<storm::models::sparse::Dtmc<storm::RationalFunction>, double>;
template class SparseInstantiationModelChecker<storm::models::sparse::Ctmc<storm::RationalFunction>, double>;
template class SparseInstantiationModelChecker<storm::models::sparse::Mdp<storm::RationalFunction>, double>;
template class SparseInstantiationModelChecker<storm::models::sparse::Dtmc<storm::RationalFunction>, storm::RationalNumber>;
template class SparseInstantiationModelChecker<storm::models::sparse::Ctmc<storm::RationalFunction>, storm::RationalNumber>;
template class SparseInstantiationModelChecker<storm::models::sparse::Mdp<storm::RationalFunction>, storm::RationalNumber>;
}

2
src/storm-pars/modelchecker/instantiation/SparseMdpInstantiationModelChecker.cpp
View File

@ -23,7 +23,7 @@ namespace storm {
std::unique_ptr<CheckResult> SparseMdpInstantiationModelChecker<SparseModelType, ConstantType>::check(Environment const& env, storm::utility::parametric::Valuation<typename SparseModelType::ValueType> const& valuation) {
STORM_LOG_THROW(this->currentCheckTask, storm::exceptions::InvalidStateException, "Checking has been invoked but no property has been specified before.");
auto const& instantiatedModel = modelInstantiator.instantiate(valuation);
STORM_LOG_ASSERT(instantiatedModel.getTransitionMatrix().isProbabilistic(), "Instantiated matrix is not probabilistic!");
STORM_LOG_THROW(instantiatedModel.getTransitionMatrix().isProbabilistic(), storm::exceptions::InvalidArgumentException, "Instantiation point is invalid as the transition matrix becomes non-stochastic.");
storm::modelchecker::SparseMdpPrctlModelChecker<storm::models::sparse::Mdp<ConstantType>> modelChecker(instantiatedModel);
// Check if there are some optimizations implemented for the specified property

6
src/storm-pars/settings/modules/ParametricSettings.cpp
View File

@ -19,6 +19,7 @@ namespace storm {
const std::string ParametricSettings::transformContinuousShortOptionName = "tc";
const std::string ParametricSettings::onlyWellformednessConstraintsOptionName = "onlyconstraints";
const std::string ParametricSettings::samplesOptionName = "samples";
const std::string ParametricSettings::samplesGraphPreservingOptionName = "samples-graph-preserving";
ParametricSettings::ParametricSettings() : ModuleSettings(moduleName) {
this->addOption(storm::settings::OptionBuilder(moduleName, exportResultOptionName, false, "A path to a file where the parametric result should be saved.")
@ -28,6 +29,7 @@ namespace storm {
this->addOption(storm::settings::OptionBuilder(moduleName, onlyWellformednessConstraintsOptionName, false, "Sets whether you only want to obtain the wellformedness constraints").build());
this->addOption(storm::settings::OptionBuilder(moduleName, samplesOptionName, false, "The points at which to sample the model.")
.addArgument(storm::settings::ArgumentBuilder::createStringArgument("samples", "The samples given in the form 'Var1=Val1:Val2:...:Valk,Var2=...").setDefaultValueString("").build()).build());
this->addOption(storm::settings::OptionBuilder(moduleName, samplesGraphPreservingOptionName, false, "Sets whether it can be assumed that the samples are graph-preserving.").build());
}
bool ParametricSettings::exportResultToFile() const {
@ -54,6 +56,10 @@ namespace storm {
return this->getOption(samplesOptionName).getArgumentByName("samples").getValueAsString();
}
bool ParametricSettings::isSamplesAreGraphPreservingSet() const {
return this->getOption(samplesGraphPreservingOptionName).getHasOptionBeenSet();
}
} // namespace modules
} // namespace settings
} // namespace storm

6
src/storm-pars/settings/modules/ParametricSettings.h
View File

@ -54,6 +54,11 @@ namespace storm {
*/
std::string getSamples() const;
/*!
* Retrieves whether the samples are graph preserving.
*/
bool isSamplesAreGraphPreservingSet() const;
const static std::string moduleName;
private:
@ -63,6 +68,7 @@ namespace storm {
const static std::string transformContinuousShortOptionName;
const static std::string onlyWellformednessConstraintsOptionName;
const static std::string samplesOptionName;
const static std::string samplesGraphPreservingOptionName;
};
} // namespace modules

2
src/storm/solver/StandardGameSolver.cpp
View File

@ -123,7 +123,9 @@ namespace storm {
} else {
// Update the solver.
getInducedMatrixVector(x, b, player1Choices, player2Choices, submatrix, subB);
if (this->linearEquationSolverFactory->getEquationProblemFormat(environmentOfSolver) == LinearEquationSolverProblemFormat::EquationSystem) {
submatrix.convertToEquationSystem();
}
submatrixSolver->setMatrix(std::move(submatrix));
}

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