#include "storm/solver/NativeLinearEquationSolver.h"
#include "storm/environment/solver/NativeSolverEnvironment.h"
#include "storm/utility/ConstantsComparator.h"
#include "storm/utility/KwekMehlhorn.h"
#include "storm/utility/NumberTraits.h"
#include "storm/utility/constants.h"
#include "storm/utility/vector.h"
#include "storm/exceptions/InvalidStateException.h"
#include "storm/exceptions/InvalidEnvironmentException.h"
#include "storm/exceptions/UnmetRequirementException.h"
#include "storm/exceptions/PrecisionExceededException.h"
namespace storm {
namespace solver {
template<typename ValueType>
NativeLinearEquationSolver<ValueType>::NativeLinearEquationSolver() : localA(nullptr), A(nullptr) {
// Intentionally left empty.
}
template<typename ValueType>
NativeLinearEquationSolver<ValueType>::NativeLinearEquationSolver(storm::storage::SparseMatrix<ValueType> const& A) : localA(nullptr), A(nullptr) {
this->setMatrix(A);
}
template<typename ValueType>
NativeLinearEquationSolver<ValueType>::NativeLinearEquationSolver(storm::storage::SparseMatrix<ValueType>&& A) : localA(nullptr), A(nullptr) {
this->setMatrix(std::move(A));
}
template<typename ValueType>
void NativeLinearEquationSolver<ValueType>::setMatrix(storm::storage::SparseMatrix<ValueType> const& A) {
localA.reset();
this->A = &A;
clearCache();
}
template<typename ValueType>
void NativeLinearEquationSolver<ValueType>::setMatrix(storm::storage::SparseMatrix<ValueType>&& A) {
localA = std::make_unique<storm::storage::SparseMatrix<ValueType>>(std::move(A));
this->A = localA.get();
clearCache();
}
template<typename ValueType>
bool NativeLinearEquationSolver<ValueType>::solveEquationsSOR(Environment const& env, std::vector<ValueType>& x, std::vector<ValueType> const& b, ValueType const& omega) const {
STORM_LOG_INFO("Solving linear equation system (" << x.size() << " rows) with NativeLinearEquationSolver (Gauss-Seidel, SOR omega = " << omega << ")");
if (!this->cachedRowVector) {
this->cachedRowVector = std::make_unique<std::vector<ValueType>>(getMatrixRowCount());
}
ValueType precision = storm::utility::convertNumber<ValueType>(env.solver().native().getPrecision());
uint64_t maxIter = env.solver().native().getMaximalNumberOfIterations();
bool relative = env.solver().native().getRelativeTerminationCriterion();
// Set up additional environment variables.
uint_fast64_t iterations = 0;
bool converged = false;
bool terminate = false;
this->startMeasureProgress();
while (!converged && !terminate && iterations < maxIter) {
A->performSuccessiveOverRelaxationStep(omega, x, b);
// Now check if the process already converged within our precision.
converged = storm::utility::vector::equalModuloPrecision<ValueType>(*this->cachedRowVector, x, precision, relative);
terminate = this->terminateNow(x, SolverGuarantee::None);
// If we did not yet converge, we need to backup the contents of x.
if (!converged) {
*this->cachedRowVector = x;
}
// Potentially show progress.
this->showProgressIterative(iterations);
// Increase iteration count so we can abort if convergence is too slow.
++iterations;
}
if (!this->isCachingEnabled()) {
clearCache();
}
this->logIterations(converged, terminate, iterations);
return converged;
}
template<typename ValueType>
bool NativeLinearEquationSolver<ValueType>::solveEquationsJacobi(Environment const& env, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
STORM_LOG_INFO("Solving linear equation system (" << x.size() << " rows) with NativeLinearEquationSolver (Jacobi)");
if (!this->cachedRowVector) {
this->cachedRowVector = std::make_unique<std::vector<ValueType>>(getMatrixRowCount());
}
// Get a Jacobi decomposition of the matrix A.
if (!jacobiDecomposition) {
jacobiDecomposition = std::make_unique<std::pair<storm::storage::SparseMatrix<ValueType>, std::vector<ValueType>>>(A->getJacobiDecomposition());
}
ValueType precision = storm::utility::convertNumber<ValueType>(env.solver().native().getPrecision());
uint64_t maxIter = env.solver().native().getMaximalNumberOfIterations();
bool relative = env.solver().native().getRelativeTerminationCriterion();
storm::storage::SparseMatrix<ValueType> const& jacobiLU = jacobiDecomposition->first;
std::vector<ValueType> const& jacobiD = jacobiDecomposition->second;
std::vector<ValueType>* currentX = &x;
std::vector<ValueType>* nextX = this->cachedRowVector.get();
// Set up additional environment variables.
uint_fast64_t iterations = 0;
bool converged = false;
bool terminate = false;
this->startMeasureProgress();
while (!converged && !terminate && iterations < maxIter) {
// Compute D^-1 * (b - LU * x) and store result in nextX.
multiplier.multAdd(jacobiLU, *currentX, nullptr, *nextX);
storm::utility::vector::subtractVectors(b, *nextX, *nextX);
storm::utility::vector::multiplyVectorsPointwise(jacobiD, *nextX, *nextX);
// Now check if the process already converged within our precision.
converged = storm::utility::vector::equalModuloPrecision<ValueType>(*currentX, *nextX, precision, relative);
terminate = this->terminateNow(*currentX, SolverGuarantee::None);
// Swap the two pointers as a preparation for the next iteration.
std::swap(nextX, currentX);
// Potentially show progress.
this->showProgressIterative(iterations);
// Increase iteration count so we can abort if convergence is too slow.
++iterations;
}
// If the last iteration did not write to the original x we have to swap the contents, because the
// output has to be written to the input parameter x.
if (currentX == this->cachedRowVector.get()) {
std::swap(x, *currentX);
}
if (!this->isCachingEnabled()) {
clearCache();
}
this->logIterations(converged, terminate, iterations);
return converged;
}
template<typename ValueType>
NativeLinearEquationSolver<ValueType>::WalkerChaeData::WalkerChaeData(storm::storage::SparseMatrix<ValueType> const& originalMatrix, std::vector<ValueType> const& originalB) : t(storm::utility::convertNumber<ValueType>(1000.0)) {
computeWalkerChaeMatrix(originalMatrix);
computeNewB(originalB);
precomputeAuxiliaryData();
}
template<typename ValueType>
void NativeLinearEquationSolver<ValueType>::WalkerChaeData::computeWalkerChaeMatrix(storm::storage::SparseMatrix<ValueType> const& originalMatrix) {
storm::storage::BitVector columnsWithNegativeEntries(originalMatrix.getColumnCount());
ValueType zero = storm::utility::zero<ValueType>();
for (auto const& e : originalMatrix) {
if (e.getValue() < zero) {
columnsWithNegativeEntries.set(e.getColumn());
}
}
std::vector<uint64_t> columnsWithNegativeEntriesBefore = columnsWithNegativeEntries.getNumberOfSetBitsBeforeIndices();
// We now build an extended equation system matrix that only has non-negative coefficients.
storm::storage::SparseMatrixBuilder<ValueType> builder;
uint64_t row = 0;
for (; row < originalMatrix.getRowCount(); ++row) {
for (auto const& entry : originalMatrix.getRow(row)) {
if (entry.getValue() < zero) {
builder.addNextValue(row, originalMatrix.getRowCount() + columnsWithNegativeEntriesBefore[entry.getColumn()], -entry.getValue());
} else {
builder.addNextValue(row, entry.getColumn(), entry.getValue());
}
}
}
ValueType one = storm::utility::one<ValueType>();
for (auto column : columnsWithNegativeEntries) {
builder.addNextValue(row, column, one);
builder.addNextValue(row, originalMatrix.getRowCount() + columnsWithNegativeEntriesBefore[column], one);
++row;
}
matrix = builder.build();
}
template<typename ValueType>
void NativeLinearEquationSolver<ValueType>::WalkerChaeData::computeNewB(std::vector<ValueType> const& originalB) {
b = std::vector<ValueType>(originalB);
b.resize(matrix.getRowCount());
}
template<typename ValueType>
void NativeLinearEquationSolver<ValueType>::WalkerChaeData::precomputeAuxiliaryData() {
columnSums = std::vector<ValueType>(matrix.getColumnCount());
for (auto const& e : matrix) {
columnSums[e.getColumn()] += e.getValue();
}
newX.resize(matrix.getRowCount());
}
template<typename ValueType>
bool NativeLinearEquationSolver<ValueType>::solveEquationsWalkerChae(Environment const& env, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
STORM_LOG_INFO("Solving linear equation system (" << x.size() << " rows) with NativeLinearEquationSolver (WalkerChae)");
// (1) Compute an equivalent equation system that has only non-negative coefficients.
if (!walkerChaeData) {
walkerChaeData = std::make_unique<WalkerChaeData>(*this->A, b);
}
// (2) Enlarge the vectors x and b to account for additional variables.
x.resize(walkerChaeData->matrix.getRowCount());
// Square the error bound, so we can use it to check for convergence. We take the squared error, because we
// do not want to compute the root in the 2-norm computation.
ValueType squaredErrorBound = storm::utility::pow(storm::utility::convertNumber<ValueType>(env.solver().native().getPrecision()), 2);
uint64_t maxIter = env.solver().native().getMaximalNumberOfIterations();
// Set up references to the x-vectors used in the iteration loop.
std::vector<ValueType>* currentX = &x;
std::vector<ValueType>* nextX = &walkerChaeData->newX;
std::vector<ValueType> tmp = walkerChaeData->matrix.getRowSumVector();
storm::utility::vector::applyPointwise(tmp, walkerChaeData->b, walkerChaeData->b, [this] (ValueType const& first, ValueType const& second) { return walkerChaeData->t * first + second; } );
// Add t to all entries of x.
storm::utility::vector::applyPointwise(x, x, [this] (ValueType const& value) { return value + walkerChaeData->t; });
// Create a vector that always holds Ax.
std::vector<ValueType> currentAx(x.size());
multiplier.multAdd(walkerChaeData->matrix, *currentX, nullptr, currentAx);
// (3) Perform iterations until convergence.
bool converged = false;
uint64_t iterations = 0;
this->startMeasureProgress();
while (!converged && iterations < maxIter) {
// Perform one Walker-Chae step.
walkerChaeData->matrix.performWalkerChaeStep(*currentX, walkerChaeData->columnSums, walkerChaeData->b, currentAx, *nextX);
// Compute new Ax.
multiplier.multAdd(walkerChaeData->matrix, *nextX, nullptr, currentAx);
// Check for convergence.
converged = storm::utility::vector::computeSquaredNorm2Difference(currentAx, walkerChaeData->b) <= squaredErrorBound;
// Swap the x vectors for the next iteration.
std::swap(currentX, nextX);
// Potentially show progress.
this->showProgressIterative(iterations);
// Increase iteration count so we can abort if convergence is too slow.
++iterations;
}
// If the last iteration did not write to the original x we have to swap the contents, because the
// output has to be written to the input parameter x.
if (currentX == &walkerChaeData->newX) {
std::swap(x, *currentX);
}
// Resize the solution to the right size.
x.resize(this->A->getRowCount());
// Finalize solution vector.
storm::utility::vector::applyPointwise(x, x, [this] (ValueType const& value) { return value - walkerChaeData->t; } );
if (!this->isCachingEnabled()) {
clearCache();
}
if (converged) {
STORM_LOG_INFO("Iterative solver converged in " << iterations << " iterations.");
} else {
STORM_LOG_WARN("Iterative solver did not converge in " << iterations << " iterations.");
}
return converged;
}
template<typename ValueType>
typename NativeLinearEquationSolver<ValueType>::PowerIterationResult NativeLinearEquationSolver<ValueType>::performPowerIteration(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 maxIterations, storm::solver::MultiplicationStyle const& multiplicationStyle) const {
bool useGaussSeidelMultiplication = multiplicationStyle == storm::solver::MultiplicationStyle::GaussSeidel;
std::vector<ValueType>* originalX = currentX;
bool converged = false;
bool terminate = this->terminateNow(*currentX, guarantee);
uint64_t iterations = currentIterations;
while (!converged && !terminate && iterations < maxIterations) {
if (useGaussSeidelMultiplication) {
*newX = *currentX;
this->multiplier.multAddGaussSeidelBackward(*this->A, *newX, &b);
} else {
this->multiplier.multAdd(*this->A, *currentX, &b, *newX);
}
// Now check for termination.
converged = storm::utility::vector::equalModuloPrecision<ValueType>(*currentX, *newX, precision, relative);
terminate = this->terminateNow(*currentX, guarantee);
// Potentially show progress.
this->showProgressIterative(iterations);
// Set up next iteration.
std::swap(currentX, newX);
++iterations;
}
// Swap the pointers so that the output is always in currentX.
if (originalX == newX) {
std::swap(currentX, newX);
}
return PowerIterationResult(iterations - currentIterations, converged ? SolverStatus::Converged : (terminate ? SolverStatus::TerminatedEarly : SolverStatus::MaximalIterationsExceeded));
}
template<typename ValueType>
bool NativeLinearEquationSolver<ValueType>::solveEquationsPower(Environment const& env, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
STORM_LOG_INFO("Solving linear equation system (" << x.size() << " rows) with NativeLinearEquationSolver (Power)");
// Prepare the solution vectors.
if (!this->cachedRowVector) {
this->cachedRowVector = std::make_unique<std::vector<ValueType>>(getMatrixRowCount());
}
std::vector<ValueType>* currentX = &x;
SolverGuarantee guarantee = SolverGuarantee::None;
if (this->hasCustomTerminationCondition()) {
if (this->getTerminationCondition().requiresGuarantee(SolverGuarantee::LessOrEqual) && this->hasLowerBound()) {
this->createLowerBoundsVector(*currentX);
guarantee = SolverGuarantee::LessOrEqual;
} else if (this->getTerminationCondition().requiresGuarantee(SolverGuarantee::GreaterOrEqual) && this->hasUpperBound()) {
this->createUpperBoundsVector(*currentX);
guarantee = SolverGuarantee::GreaterOrEqual;
}
}
std::vector<ValueType>* newX = this->cachedRowVector.get();
// Forward call to power iteration implementation.
this->startMeasureProgress();
ValueType precision = storm::utility::convertNumber<ValueType>(env.solver().native().getPrecision());
PowerIterationResult result = this->performPowerIteration(currentX, newX, b, precision, env.solver().native().getRelativeTerminationCriterion(), guarantee, 0, env.solver().native().getMaximalNumberOfIterations(), env.solver().native().getPowerMethodMultiplicationStyle());
// Swap the result in place.
if (currentX == this->cachedRowVector.get()) {
std::swap(x, *newX);
}
if (!this->isCachingEnabled()) {
clearCache();
}
this->logIterations(result.status == SolverStatus::Converged, result.status == SolverStatus::TerminatedEarly, result.iterations);
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;
}
template<typename ValueType>
bool NativeLinearEquationSolver<ValueType>::solveEquationsSoundPower(Environment const& env, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
STORM_LOG_THROW(this->hasLowerBound(), storm::exceptions::UnmetRequirementException, "Solver requires lower bound, but none was given.");
STORM_LOG_THROW(this->hasUpperBound(), storm::exceptions::UnmetRequirementException, "Solver requires upper bound, but none was given.");
STORM_LOG_INFO("Solving linear equation system (" << x.size() << " rows) with NativeLinearEquationSolver (SoundPower)");
std::vector<ValueType>* lowerX = &x;
this->createLowerBoundsVector(*lowerX);
this->createUpperBoundsVector(this->cachedRowVector, this->getMatrixRowCount());
std::vector<ValueType>* upperX = this->cachedRowVector.get();
bool useGaussSeidelMultiplication = env.solver().native().getPowerMethodMultiplicationStyle() == storm::solver::MultiplicationStyle::GaussSeidel;
std::vector<ValueType>* tmp;
if (!useGaussSeidelMultiplication) {
cachedRowVector2 = std::make_unique<std::vector<ValueType>>(x.size());
tmp = cachedRowVector2.get();
}
bool converged = false;
bool terminate = false;
uint64_t iterations = 0;
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>();
ValueType precision = storm::utility::convertNumber<ValueType>(env.solver().native().getPrecision());
bool relative = env.solver().native().getRelativeTerminationCriterion();
if (!relative) {
precision *= storm::utility::convertNumber<ValueType>(2.0);
}
uint64_t maxIter = env.solver().native().getMaximalNumberOfIterations();
this->startMeasureProgress();
while (!converged && !terminate && iterations < maxIter) {
// Remember in which directions we took steps in this iteration.
bool lowerStep = false;
bool upperStep = false;
// In every thousandth iteration or if the differences are the same, we improve both bounds.
if (iterations % 1000 == 0 || maxLowerDiff == maxUpperDiff) {
lowerStep = true;
upperStep = true;
if (useGaussSeidelMultiplication) {
if (useDiffs) {
preserveOldRelevantValues(*lowerX, this->getRelevantValues(), oldValues);
}
this->multiplier.multAddGaussSeidelBackward(*this->A, *lowerX, &b);
if (useDiffs) {
maxLowerDiff = computeMaxAbsDiff(*lowerX, this->getRelevantValues(), oldValues);
preserveOldRelevantValues(*upperX, this->getRelevantValues(), oldValues);
}
this->multiplier.multAddGaussSeidelBackward(*this->A, *upperX, &b);
if (useDiffs) {
maxUpperDiff = computeMaxAbsDiff(*upperX, this->getRelevantValues(), oldValues);
}
} else {
this->multiplier.multAdd(*this->A, *lowerX, &b, *tmp);
if (useDiffs) {
maxLowerDiff = computeMaxAbsDiff(*lowerX, *tmp, this->getRelevantValues());
}
std::swap(tmp, lowerX);
this->multiplier.multAdd(*this->A, *upperX, &b, *tmp);
if (useDiffs) {
maxUpperDiff = computeMaxAbsDiff(*upperX, *tmp, this->getRelevantValues());
}
std::swap(tmp, upperX);
}
} 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->multiplier.multAddGaussSeidelBackward(*this->A, *lowerX, &b);
if (useDiffs) {
maxLowerDiff = computeMaxAbsDiff(*lowerX, this->getRelevantValues(), oldValues);
}
lowerStep = true;
} else {
if (useDiffs) {
preserveOldRelevantValues(*upperX, this->getRelevantValues(), oldValues);
}
this->multiplier.multAddGaussSeidelBackward(*this->A, *upperX, &b);
if (useDiffs) {
maxUpperDiff = computeMaxAbsDiff(*upperX, this->getRelevantValues(), oldValues);
}
upperStep = true;
}
} else {
if (maxLowerDiff >= maxUpperDiff) {
this->multiplier.multAdd(*this->A, *lowerX, &b, *tmp);
if (useDiffs) {
maxLowerDiff = computeMaxAbsDiff(*lowerX, *tmp, this->getRelevantValues());
}
std::swap(tmp, lowerX);
lowerStep = true;
} else {
this->multiplier.multAdd(*this->A, *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) {
// Now check if the process already converged within our precision. Note that we double the target
// precision here. Doing so, we need to take the means of the lower and upper values later to guarantee
// the original precision.
if (this->hasRelevantValues()) {
converged = storm::utility::vector::equalModuloPrecision<ValueType>(*lowerX, *upperX, this->getRelevantValues(), precision, relative);
} else {
converged = storm::utility::vector::equalModuloPrecision<ValueType>(*lowerX, *upperX, precision, relative);
}
if (lowerStep) {
terminate |= this->terminateNow(*lowerX, SolverGuarantee::LessOrEqual);
}
if (upperStep) {
terminate |= this->terminateNow(*upperX, SolverGuarantee::GreaterOrEqual);
}
}
// Potentially show progress.
this->showProgressIterative(iterations);
// Set up next iteration.
++iterations;
doConvergenceCheck = !doConvergenceCheck;
}
// We take the means of the lower and upper bound so we guarantee the desired precision.
storm::utility::vector::applyPointwise(*lowerX, *upperX, *lowerX, [] (ValueType const& a, ValueType const& b) { return (a + b) / storm::utility::convertNumber<ValueType>(2.0); });
// 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->cachedRowVector.get()) {
std::swap(x, *this->cachedRowVector);
}
if (!this->isCachingEnabled()) {
clearCache();
}
this->logIterations(converged, terminate, iterations);
return converged;
}
template<typename ValueType>
bool NativeLinearEquationSolver<ValueType>::solveEquationsQuickSoundPower(Environment const& env, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
STORM_LOG_INFO("Solving linear equation system (" << x.size() << " rows) with NativeLinearEquationSolver (QuickPower)");
// Prepare the solution vectors.
if (!this->cachedRowVector) {
this->cachedRowVector = std::make_unique<std::vector<ValueType>>(getMatrixRowCount(), storm::utility::zero<ValueType>());
} else {
this->cachedRowVector->assign(getMatrixRowCount(), storm::utility::zero<ValueType>());
}
if (!this->cachedRowVector2) {
this->cachedRowVector2 = std::make_unique<std::vector<ValueType>>(getMatrixRowCount(), storm::utility::one<ValueType>());
} else {
this->cachedRowVector2->assign(getMatrixRowCount(), storm::utility::one<ValueType>());
}
std::vector<ValueType>* stepBoundedValues = this->cachedRowVector.get();
std::vector<ValueType>* stepBoundedStayProbabilities = this->cachedRowVector2.get();
std::vector<ValueType>* tmp = &x;
bool converged = false;
bool terminate = false;
uint64_t iterations = 0;
ValueType precision = storm::utility::convertNumber<ValueType>(env.solver().native().getPrecision());
ValueType lowerValueBound, upperValueBound;
bool relative = env.solver().native().getRelativeTerminationCriterion();
if (!relative) {
precision *= storm::utility::convertNumber<ValueType>(2.0);
}
uint64_t maxIter = env.solver().native().getMaximalNumberOfIterations();
this->startMeasureProgress();
uint64_t firstProb1Entry = 0;
while (!converged && !terminate && iterations < maxIter) {
this->multiplier.multAdd(*this->A, *stepBoundedValues, &b, *tmp);
std::swap(tmp, stepBoundedValues);
this->multiplier.multAdd(*this->A, *stepBoundedStayProbabilities, nullptr, *tmp);
std::swap(tmp, stepBoundedStayProbabilities);
for (; firstProb1Entry != stepBoundedStayProbabilities->size(); ++firstProb1Entry) {
static_assert(NumberTraits<ValueType>::IsExact || std::is_same<ValueType, double>::value, "Considered ValueType not handled.");
if (NumberTraits<ValueType>::IsExact) {
if (storm::utility::isOne(stepBoundedStayProbabilities->at(firstProb1Entry))) {
break;
}
} else {
if (storm::utility::isAlmostOne(storm::utility::convertNumber<double>(stepBoundedStayProbabilities->at(firstProb1Entry)))) {
break;
}
}
}
if (firstProb1Entry == stepBoundedStayProbabilities->size()) {
auto valIt = stepBoundedValues->begin();
auto valIte = stepBoundedValues->end();
auto probIt = stepBoundedStayProbabilities->begin();
STORM_LOG_ASSERT(!storm::utility::isOne(*probIt), "Did not expect staying-probability 1 at this point.");
lowerValueBound = *valIt / (storm::utility::one<ValueType>() - *probIt);
upperValueBound = lowerValueBound;
ValueType largestStayProb = *probIt;
for (; valIt != valIte; ++valIt, ++probIt) {
STORM_LOG_ASSERT(!storm::utility::isOne(*probIt), "Did not expect staying-probability 1 at this point.");
ValueType currentBound = *valIt / (storm::utility::one<ValueType>() - *probIt);
lowerValueBound = std::min(lowerValueBound, currentBound);
upperValueBound = std::max(upperValueBound, currentBound);
largestStayProb = std::max(largestStayProb, *probIt);
}
STORM_LOG_ASSERT(!relative, "Relative termination criterion not implemented currently.");
converged = largestStayProb * (upperValueBound - lowerValueBound) < precision;
STORM_LOG_INFO_COND(!converged, "Lower value bound: " << lowerValueBound << " Upper value bound: " << upperValueBound << " Largest stay prob.: " << largestStayProb);
}
// Potentially show progress.
this->showProgressIterative(iterations);
// Set up next iteration.
++iterations;
}
// Finally set up the solution vector
ValueType meanBound = (upperValueBound - lowerValueBound) / storm::utility::convertNumber<ValueType>(2.0);
storm::utility::vector::applyPointwise(*stepBoundedValues, *stepBoundedStayProbabilities, x, [&meanBound] (ValueType const& v, ValueType const& p) { return v + p * meanBound; });
if (!this->isCachingEnabled()) {
clearCache();
}
this->logIterations(converged, terminate, iterations);
return converged;
}
template<typename ValueType>
bool NativeLinearEquationSolver<ValueType>::solveEquationsRationalSearch(Environment const& env, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
return solveEquationsRationalSearchHelper<double>(env, x, b);
}
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 NativeLinearEquationSolver<ValueType>::solveEquationsRationalSearchHelper(Environment const& env, NativeLinearEquationSolver<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 {
ValueType precision = storm::utility::convertNumber<ValueType>(env.solver().native().getPrecision());
uint64_t maxIter = env.solver().native().getMaximalNumberOfIterations();
bool relative = env.solver().native().getRelativeTerminationCriterion();
auto multiplicationStyle = env.solver().native().getPowerMethodMultiplicationStyle();
std::vector<ImpreciseType>* currentX = &x;
std::vector<ImpreciseType>* newX = &tmpX;
SolverStatus status = SolverStatus::InProgress;
uint64_t overallIterations = 0;
uint64_t valueIterationInvocations = 0;
impreciseSolver.startMeasureProgress();
while (status == SolverStatus::InProgress && overallIterations < maxIter) {
// Perform value iteration with the current precision.
typename NativeLinearEquationSolver<ImpreciseType>::PowerIterationResult result = impreciseSolver.performPowerIteration(currentX, newX, b, storm::utility::convertNumber<ImpreciseType, ValueType>(precision), relative, SolverGuarantee::LessOrEqual, overallIterations, maxIter, multiplicationStyle);
// At this point, the result of the imprecise value iteration is stored in the (imprecise) current x.
++valueIterationInvocations;
STORM_LOG_TRACE("Completed " << valueIterationInvocations << " power 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(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 = precision / 10;
}
}
if (status == SolverStatus::InProgress && overallIterations == maxIter) {
status = SolverStatus::MaximalIterationsExceeded;
}
this->logIterations(status == SolverStatus::Converged, status == SolverStatus::TerminatedEarly, overallIterations);
return status == SolverStatus::Converged || status == SolverStatus::TerminatedEarly;
}
template<typename ValueType>
template<typename ImpreciseType>
typename std::enable_if<std::is_same<ValueType, ImpreciseType>::value && !NumberTraits<ValueType>::IsExact, bool>::type NativeLinearEquationSolver<ValueType>::solveEquationsRationalSearchHelper(Environment const& env, 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->cachedRowVector) {
this->cachedRowVector = std::make_unique<std::vector<ValueType>>(this->A->getRowCount());
}
// Forward the call to the core rational search routine.
bool converged = solveEquationsRationalSearchHelper<storm::RationalNumber, ImpreciseType>(env, *this, rationalA, rationalX, rationalB, *this->A, x, b, *this->cachedRowVector);
// 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 NativeLinearEquationSolver<ValueType>::solveEquationsRationalSearchHelper(Environment const& env, 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 (!this->cachedRowVector) {
this->cachedRowVector = std::make_unique<std::vector<ValueType>>(this->A->getRowCount());
}
// Forward the call to the core rational search routine.
bool converged = solveEquationsRationalSearchHelper<ValueType, ImpreciseType>(env, *this, *this->A, x, b, *this->A, *this->cachedRowVector, 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 NativeLinearEquationSolver<ValueType>::solveEquationsRationalSearchHelper(Environment const& env, 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.
NativeLinearEquationSolver<ImpreciseType> impreciseSolver;
impreciseSolver.setMatrix(impreciseA);
impreciseSolver.setCachingEnabled(true);
bool converged = false;
try {
// Forward the call to the core rational search routine.
converged = solveEquationsRationalSearchHelper<ValueType, ImpreciseType>(env, 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 (!this->cachedRowVector) {
this->cachedRowVector = 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 = this->cachedRowVector->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>();
// 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, *this, *this->A, x, b, *this->A, *this->cachedRowVector, b, x);
}
if (!this->isCachingEnabled()) {
this->clearCache();
}
return converged;
}
template<typename ValueType>
template<typename RationalType, typename ImpreciseType>
bool NativeLinearEquationSolver<ValueType>::sharpen(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 (NativeLinearEquationSolver<RationalType>::isSolution(A, tmp, b)) {
return true;
}
}
return false;
}
template<typename ValueType>
bool NativeLinearEquationSolver<ValueType>::isSolution(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 row = 0; row < matrix.getRowCount(); ++row, ++valueIt, ++bIt) {
ValueType rowValue = *bIt + matrix.multiplyRowWithVector(row, values);
// If the value does not match the one in the values vector, the given vector is not a solution.
if (!comparator.isEqual(rowValue, *valueIt)) {
return false;
}
}
// Checked all values at this point.
return true;
}
template<typename ValueType>
void NativeLinearEquationSolver<ValueType>::logIterations(bool converged, bool terminate, uint64_t iterations) const {
if (converged) {
STORM_LOG_INFO("Iterative solver converged in " << iterations << " iterations.");
} else if (terminate) {
STORM_LOG_INFO("Iterative solver terminated after " << iterations << " iterations.");
} else {
STORM_LOG_WARN("Iterative solver did not converge in " << iterations << " iterations.");
}
}
template<typename ValueType>
NativeLinearEquationSolverMethod NativeLinearEquationSolver<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().native().getMethod();
if (isExactMode && method != NativeLinearEquationSolverMethod::RationalSearch) {
if (env.solver().native().isMethodSetFromDefault()) {
method = NativeLinearEquationSolverMethod::RationalSearch;
STORM_LOG_INFO("Selecting '" + toString(method) + "' as the solution technique to guarantee exact results. If you want to override this, please explicitly specify a different method.");
} else {
STORM_LOG_WARN("The selected solution method does not guarantee exact results.");
}
} else if (env.solver().isForceSoundness() && method != NativeLinearEquationSolverMethod::Power && method != NativeLinearEquationSolverMethod::RationalSearch && method != NativeLinearEquationSolverMethod::QuickPower) {
if (env.solver().native().isMethodSetFromDefault()) {
method = NativeLinearEquationSolverMethod::Power;
STORM_LOG_INFO("Selecting '" + toString(method) + "' as the solution technique to guarantee sound results. If you want to override this, please explicitly specify a different method.");
} else {
STORM_LOG_WARN("The selected solution method does not guarantee sound results.");
}
}
return method;
}
template<typename ValueType>
bool NativeLinearEquationSolver<ValueType>::internalSolveEquations(Environment const& env, std::vector<ValueType>& x, std::vector<ValueType> const& b) const {
switch(getMethod(env, storm::NumberTraits<ValueType>::IsExact)) {
case NativeLinearEquationSolverMethod::SOR:
return this->solveEquationsSOR(env, x, b, storm::utility::convertNumber<ValueType>(env.solver().native().getSorOmega()));
case NativeLinearEquationSolverMethod::GaussSeidel:
return this->solveEquationsSOR(env, x, b, storm::utility::one<ValueType>());
case NativeLinearEquationSolverMethod::Jacobi:
return this->solveEquationsJacobi(env, x, b);
case NativeLinearEquationSolverMethod::WalkerChae:
return this->solveEquationsWalkerChae(env, x, b);
case NativeLinearEquationSolverMethod::Power:
if (env.solver().isForceSoundness()) {
return this->solveEquationsSoundPower(env, x, b);
} else {
return this->solveEquationsPower(env, x, b);
}
case NativeLinearEquationSolverMethod::QuickPower:
return this->solveEquationsQuickSoundPower(env, x, b);
case NativeLinearEquationSolverMethod::RationalSearch:
return this->solveEquationsRationalSearch(env, x, b);
}
STORM_LOG_THROW(false, storm::exceptions::InvalidEnvironmentException, "Unknown solving technique.");
return false;
}
template<typename ValueType>
void NativeLinearEquationSolver<ValueType>::multiply(std::vector<ValueType>& x, std::vector<ValueType> const* b, std::vector<ValueType>& result) const {
if (&x != &result) {
multiplier.multAdd(*A, x, b, result);
} else {
// If the two vectors are aliases, we need to create a temporary.
if (!this->cachedRowVector) {
this->cachedRowVector = std::make_unique<std::vector<ValueType>>(getMatrixRowCount());
}
multiplier.multAdd(*A, x, b, *this->cachedRowVector);
result.swap(*this->cachedRowVector);
if (!this->isCachingEnabled()) {
clearCache();
}
}
}
template<typename ValueType>
void NativeLinearEquationSolver<ValueType>::multiplyAndReduce(OptimizationDirection const& dir, std::vector<uint64_t> const& rowGroupIndices, std::vector<ValueType>& x, std::vector<ValueType> const* b, std::vector<ValueType>& result, std::vector<uint_fast64_t>* choices) const {
if (&x != &result) {
multiplier.multAddReduce(dir, rowGroupIndices, *A, x, b, result, choices);
} else {
// If the two vectors are aliases, we need to create a temporary.
if (!this->cachedRowVector) {
this->cachedRowVector = std::make_unique<std::vector<ValueType>>(getMatrixRowCount());
}
multiplier.multAddReduce(dir, rowGroupIndices, *A, x, b, *this->cachedRowVector, choices);
result.swap(*this->cachedRowVector);
if (!this->isCachingEnabled()) {
clearCache();
}
}
}
template<typename ValueType>
bool NativeLinearEquationSolver<ValueType>::supportsGaussSeidelMultiplication() const {
return true;
}
template<typename ValueType>
void NativeLinearEquationSolver<ValueType>::multiplyGaussSeidel(std::vector<ValueType>& x, std::vector<ValueType> const* b) const {
STORM_LOG_ASSERT(this->A->getRowCount() == this->A->getColumnCount(), "This function is only applicable for square matrices.");
multiplier.multAddGaussSeidelBackward(*A, x, b);
}
template<typename ValueType>
void NativeLinearEquationSolver<ValueType>::multiplyAndReduceGaussSeidel(OptimizationDirection const& dir, std::vector<uint64_t> const& rowGroupIndices, std::vector<ValueType>& x, std::vector<ValueType> const* b, std::vector<uint_fast64_t>* choices) const {
multiplier.multAddReduceGaussSeidelBackward(dir, rowGroupIndices, *A, x, b, choices);
}
template<typename ValueType>
LinearEquationSolverProblemFormat NativeLinearEquationSolver<ValueType>::getEquationProblemFormat(Environment const& env) const {
auto method = getMethod(env, storm::NumberTraits<ValueType>::IsExact);
if (method == NativeLinearEquationSolverMethod::Power || method == NativeLinearEquationSolverMethod::RationalSearch || method == NativeLinearEquationSolverMethod::QuickPower) {
return LinearEquationSolverProblemFormat::FixedPointSystem;
} else {
return LinearEquationSolverProblemFormat::EquationSystem;
}
}
template<typename ValueType>
LinearEquationSolverRequirements NativeLinearEquationSolver<ValueType>::getRequirements(Environment const& env, LinearEquationSolverTask const& task) const {
LinearEquationSolverRequirements requirements;
if (task != LinearEquationSolverTask::Multiply) {
auto method = getMethod(env, storm::NumberTraits<ValueType>::IsExact);
if (method == NativeLinearEquationSolverMethod::Power && env.solver().isForceSoundness()) {
requirements.requireBounds();
} else if (method == NativeLinearEquationSolverMethod::RationalSearch) {
requirements.requireLowerBounds();
}
}
return requirements;
}
template<typename ValueType>
void NativeLinearEquationSolver<ValueType>::clearCache() const {
jacobiDecomposition.reset();
cachedRowVector2.reset();
walkerChaeData.reset();
LinearEquationSolver<ValueType>::clearCache();
}
template<typename ValueType>
uint64_t NativeLinearEquationSolver<ValueType>::getMatrixRowCount() const {
return this->A->getRowCount();
}
template<typename ValueType>
uint64_t NativeLinearEquationSolver<ValueType>::getMatrixColumnCount() const {
return this->A->getColumnCount();
}
template<typename ValueType>
std::unique_ptr<storm::solver::LinearEquationSolver<ValueType>> NativeLinearEquationSolverFactory<ValueType>::create(Environment const& env, LinearEquationSolverTask const& task) const {
return std::make_unique<storm::solver::NativeLinearEquationSolver<ValueType>>();
}
template<typename ValueType>
std::unique_ptr<LinearEquationSolverFactory<ValueType>> NativeLinearEquationSolverFactory<ValueType>::clone() const {
return std::make_unique<NativeLinearEquationSolverFactory<ValueType>>(*this);
}
// Explicitly instantiate the linear equation solver.
template class NativeLinearEquationSolver<double>;
template class NativeLinearEquationSolverFactory<double>;
#ifdef STORM_HAVE_CARL
template class NativeLinearEquationSolver<storm::RationalNumber>;
template class NativeLinearEquationSolverFactory<storm::RationalNumber>;
#endif
}
}