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@ -34,56 +34,96 @@ |
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namespace storm { |
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namespace modelchecker { |
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namespace helper { |
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/**
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* Data structure holding result vectors (vLower, vUpper, wUpper) for Unif+. |
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*/ |
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template<typename ValueType> |
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struct UnifPlusVectors { |
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UnifPlusVectors() { |
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// Intentionally empty
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} |
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/**
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* Initialize results vectors. vLowerOld, vUpperOld and wUpper[k=N] are initialized with zeros. |
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*/ |
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UnifPlusVectors(uint64_t steps, uint64_t noStates) : numberOfStates(noStates), steps(steps), resLowerOld(numberOfStates, storm::utility::zero<ValueType>()), resLowerNew(numberOfStates, -1), resUpper(numberOfStates, storm::utility::zero<ValueType>()), wUpperOld(numberOfStates, storm::utility::zero<ValueType>()), wUpperNew(numberOfStates, -1) { |
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// Intentionally left empty
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} |
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/**
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* Prepare new iteration by setting the new result vectors as old result vectors, and initializing the new result vectors with -1 again. |
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*/ |
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void prepareNewIteration() { |
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resLowerOld.swap(resLowerNew); |
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std::fill(resLowerNew.begin(), resLowerNew.end(), -1); |
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wUpperOld.swap(wUpperNew); |
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std::fill(wUpperNew.begin(), wUpperNew.end(), -1); |
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} |
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uint64_t numberOfStates; |
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uint64_t steps; |
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std::vector<ValueType> resLowerOld; |
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std::vector<ValueType> resLowerNew; |
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std::vector<ValueType> resUpper; |
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std::vector<ValueType> wUpperOld; |
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std::vector<ValueType> wUpperNew; |
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}; |
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template<typename ValueType> |
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void calculateUnifPlusVector(Environment const& env, uint64_t k, uint64_t state, uint64_t const kind, ValueType lambda, uint64_t numberOfProbabilisticChoices, std::vector<std::vector<ValueType>> const & relativeReachability, OptimizationDirection dir, std::vector<std::vector<std::vector<ValueType>>>& unifVectors, storm::storage::SparseMatrix<ValueType> const& fullTransitionMatrix, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> const& solver, storm::utility::numerical::FoxGlynnResult<ValueType> const& poisson, bool cycleFree) { |
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if (unifVectors[kind][k][state] != -1) { |
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void calculateUnifPlusVector(Environment const& env, uint64_t k, uint64_t state, bool calcLower, ValueType lambda, uint64_t numberOfProbabilisticChoices, std::vector<std::vector<ValueType>> const & relativeReachability, OptimizationDirection dir, UnifPlusVectors<ValueType>& unifVectors, storm::storage::SparseMatrix<ValueType> const& fullTransitionMatrix, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> const& solver, storm::utility::numerical::FoxGlynnResult<ValueType> const& poisson, bool cycleFree) { |
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// Set reference to acutal vector
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std::vector<ValueType>& resVectorOld = calcLower ? unifVectors.resLowerOld : unifVectors.wUpperOld; |
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std::vector<ValueType>& resVectorNew = calcLower ? unifVectors.resLowerNew : unifVectors.wUpperNew; |
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if (resVectorNew[state] != -1) { |
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// Result already calculated.
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return; |
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} |
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auto numberOfStates = fullTransitionMatrix.getRowGroupCount(); |
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uint64_t N = unifVectors[kind].size() - 1; |
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uint64_t N = unifVectors.steps; |
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auto const& rowGroupIndices = fullTransitionMatrix.getRowGroupIndices(); |
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ValueType res; |
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// First case, k==N, independent from kind of state.
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if (k == N) { |
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unifVectors[kind][k][state] = storm::utility::zero<ValueType>(); |
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STORM_LOG_ASSERT(false, "Result for k=N was already calculated."); |
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resVectorNew[state] = storm::utility::zero<ValueType>(); |
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return; |
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} |
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// Goal state, independent from kind of state.
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if (psiStates[state]) { |
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if (kind == 0) { |
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// Vd
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if (calcLower) { |
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// v lower
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res = storm::utility::zero<ValueType>(); |
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for (uint64_t i = k; i < N; ++i){ |
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if (i >= poisson.left && i <= poisson.right) { |
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ValueType between = poisson.weights[i - poisson.left]; |
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res += between; |
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res += poisson.weights[i - poisson.left]; |
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} |
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} |
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unifVectors[kind][k][state] = res; |
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resVectorNew[state] = res; |
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} else { |
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// WU
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unifVectors[kind][k][state] = storm::utility::one<ValueType>(); |
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// w upper
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resVectorNew[state] = storm::utility::one<ValueType>(); |
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} |
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return; |
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} |
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// Markovian non-goal state.
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if (markovianStates[state]) { |
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res = storm::utility::zero<ValueType>(); |
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for (auto const& element : fullTransitionMatrix.getRow(rowGroupIndices[state])) { |
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uint64_t to = element.getColumn(); |
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if (unifVectors[kind][k+1][to] == -1) { |
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calculateUnifPlusVector(env, k+1, to, kind, lambda, numberOfProbabilisticChoices, relativeReachability, dir, unifVectors, fullTransitionMatrix, markovianStates, psiStates, solver, poisson, cycleFree); |
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uint64_t successor = element.getColumn(); |
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if (resVectorOld[successor] == -1) { |
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STORM_LOG_ASSERT(false, "Need to calculate previous result."); |
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calculateUnifPlusVector(env, k+1, successor, calcLower, lambda, numberOfProbabilisticChoices, relativeReachability, dir, unifVectors, fullTransitionMatrix, markovianStates, psiStates, solver, poisson, cycleFree); |
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} |
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res += element.getValue()*unifVectors[kind][k+1][to]; |
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res += element.getValue() * resVectorOld[successor]; |
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} |
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unifVectors[kind][k][state]=res; |
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resVectorNew[state]=res; |
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return; |
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} |
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@ -93,7 +133,7 @@ namespace storm { |
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res = -1; |
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for (uint64_t i = rowGroupIndices[state]; i < rowGroupIndices[state + 1]; ++i) { |
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auto row = fullTransitionMatrix.getRow(i); |
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ValueType between = 0; |
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ValueType between = storm::utility::zero<ValueType>(); |
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for (auto const& element : row) { |
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uint64_t successor = element.getColumn(); |
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@ -102,10 +142,10 @@ namespace storm { |
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continue; |
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} |
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if (unifVectors[kind][k][successor] == -1) { |
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calculateUnifPlusVector(env, k, successor, kind, lambda, numberOfProbabilisticChoices, relativeReachability, dir, unifVectors, fullTransitionMatrix, markovianStates, psiStates, solver, poisson, cycleFree); |
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if (resVectorNew[successor] == -1) { |
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calculateUnifPlusVector(env, k, successor, calcLower, lambda, numberOfProbabilisticChoices, relativeReachability, dir, unifVectors, fullTransitionMatrix, markovianStates, psiStates, solver, poisson, cycleFree); |
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} |
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between += element.getValue() * unifVectors[kind][k][successor]; |
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between += element.getValue() * resVectorNew[successor]; |
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} |
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if (maximize(dir)) { |
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res = storm::utility::max(res, between); |
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@ -117,11 +157,11 @@ namespace storm { |
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} |
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} |
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} |
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unifVectors[kind][k][state] = res; |
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resVectorNew[state] = res; |
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return; |
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} |
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// If we arrived at this point, the model is not cycle free. Use the solver to solve the unterlying equation system.
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// If we arrived at this point, the model is not cycle free. Use the solver to solve the underlying equation system.
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uint64_t numberOfProbabilisticStates = numberOfStates - markovianStates.getNumberOfSetBits(); |
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std::vector<ValueType> b(numberOfProbabilisticChoices, storm::utility::zero<ValueType>()); |
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std::vector<ValueType> x(numberOfProbabilisticStates, storm::utility::zero<ValueType>()); |
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@ -142,10 +182,10 @@ namespace storm { |
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continue; |
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} |
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if (unifVectors[kind][k][successor] == -1) { |
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calculateUnifPlusVector(env, k, successor, kind, lambda, numberOfProbabilisticStates, relativeReachability, dir, unifVectors, fullTransitionMatrix, markovianStates, psiStates, solver, poisson, cycleFree); |
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if (resVectorNew[successor] == -1) { |
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calculateUnifPlusVector(env, k, successor, calcLower, lambda, numberOfProbabilisticStates, relativeReachability, dir, unifVectors, fullTransitionMatrix, markovianStates, psiStates, solver, poisson, cycleFree); |
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} |
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res = res + relativeReachability[j][stateCount] * unifVectors[kind][k][successor]; |
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res += relativeReachability[j][stateCount] * resVectorNew[successor]; |
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++stateCount; |
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} |
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@ -158,28 +198,7 @@ namespace storm { |
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solver->solveEquations(env, dir, x, b); |
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// Expand the solution for the probabilistic states to all states.
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storm::utility::vector::setVectorValues(unifVectors[kind][k], ~markovianStates, x); |
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} |
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template <typename ValueType> |
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void calculateVu(Environment const& env, std::vector<std::vector<ValueType>> const& relativeReachability, OptimizationDirection dir, uint64_t k, uint64_t state, uint64_t const kind, ValueType lambda, uint64_t numberOfProbabilisticStates, std::vector<std::vector<std::vector<ValueType>>>& unifVectors, storm::storage::SparseMatrix<ValueType> const& fullTransitionMatrix, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates, std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> const& solver, storm::utility::numerical::FoxGlynnResult<ValueType> const & poisson, bool cycleFree) { |
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// Avoiding multiple computation of the same value.
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if (unifVectors[1][k][state] != -1) { |
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return; |
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} |
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uint64_t N = unifVectors[1].size() - 1; |
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ValueType res = storm::utility::zero<ValueType>(); |
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for (uint64_t i = k; i < N; ++i) { |
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if (unifVectors[2][N-1-(i-k)][state] == -1) { |
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calculateUnifPlusVector(env, N-1-(i-k), state, 2, lambda, numberOfProbabilisticStates, relativeReachability, dir, unifVectors, fullTransitionMatrix, markovianStates, psiStates, solver, poisson, cycleFree); |
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} |
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if (i >= poisson.left && i <= poisson.right) { |
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res += poisson.weights[i - poisson.left] * unifVectors[2][N-1-(i-k)][state]; |
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} |
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} |
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unifVectors[1][k][state] = res; |
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storm::utility::vector::setVectorValues(resVectorNew, ~markovianStates, x); |
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} |
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template <typename ValueType> |
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@ -227,9 +246,9 @@ namespace storm { |
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// Searching for SCCs in probabilistic fragment to decide which algorithm is applied.
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storm::storage::StronglyConnectedComponentDecomposition<ValueType> sccDecomposition(transitionMatrix, probabilisticStates, true, false); |
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bool cycleFree = sccDecomposition.empty(); |
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// Vectors to store computed vectors.
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std::vector<std::vector<std::vector<ValueType>>> unifVectors(3); |
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UnifPlusVectors<ValueType> unifVectors; |
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// Transitions from goal states will be ignored. However, we mark them as non-probabilistic to make sure
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// we do not apply the MDP algorithm to them.
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@ -255,17 +274,22 @@ namespace storm { |
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// (1) define/declare horizon, epsilon, kappa, N, lambda, maxNorm
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uint64_t numberOfStates = fullTransitionMatrix.getRowGroupCount(); |
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double T = boundsPair.second; |
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// 'Unpack' the bounds to make them more easily accessible.
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double lowerBound = boundsPair.first; |
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double upperBound = boundsPair.second; |
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// Lower bound > 0 is not implemented!
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STORM_LOG_THROW(lowerBound == 0, storm::exceptions::NotImplementedException, "Support for lower bound > 0 not implemented in Unif+."); |
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// Truncation error
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// TODO: make kappa a parameter.
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ValueType kappa = storm::utility::one<ValueType>() / 10; |
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// Approximation error
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ValueType epsilon = storm::settings::getModule<storm::settings::modules::GeneralSettings>().getPrecision(); |
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// Lambda is largest exit rate
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ValueType lambda = exitRateVector[0]; |
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for (ValueType const& rate : exitRateVector) { |
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lambda = std::max(rate, lambda); |
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} |
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STORM_LOG_TRACE("Initial lambda is " << lambda << "."); |
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uint64_t N; |
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ValueType maxNorm = storm::utility::zero<ValueType>(); |
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STORM_LOG_DEBUG("Initial lambda is " << lambda << "."); |
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// Compute the relative reachability vectors and create solver for models with SCCs.
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std::vector<std::vector<ValueType>> relativeReachabilities(transitionMatrix.getRowCount()); |
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@ -300,16 +324,19 @@ namespace storm { |
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} |
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} |
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ValueType maxNorm = storm::utility::zero<ValueType>(); |
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// Maximal step size
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uint64_t N; |
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storm::utility::ProgressMeasurement progressIterations("iterations"); |
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size_t iteration = 0; |
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progressIterations.startNewMeasurement(iteration); |
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// Loop until result is within precision bound.
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std::vector<ValueType> init(numberOfStates, -1); |
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do { |
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maxNorm = storm::utility::zero<ValueType>(); |
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// (2) update parameter
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N = storm::utility::ceil(lambda * T * std::exp(2) - storm::utility::log(kappa * epsilon)); |
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N = storm::utility::ceil(lambda * upperBound * std::exp(2) - storm::utility::log(kappa * epsilon)); |
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// (3) uniform - just applied to Markovian states.
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for (uint64_t i = 0; i < fullTransitionMatrix.getRowGroupCount(); i++) { |
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for (uint64_t i = 0; i < numberOfStates; i++) { |
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if (!markovianAndGoalStates[i] || psiStates[i]) { |
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continue; |
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} |
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@ -340,7 +367,7 @@ namespace storm { |
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} |
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// Compute poisson distribution.
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storm::utility::numerical::FoxGlynnResult<ValueType> foxGlynnResult = storm::utility::numerical::foxGlynn(lambda * T, epsilon * kappa / 100); |
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storm::utility::numerical::FoxGlynnResult<ValueType> foxGlynnResult = storm::utility::numerical::foxGlynn(lambda * upperBound, epsilon * kappa / 100); |
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// Scale the weights so they sum to one.
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for (auto& element : foxGlynnResult.weights) { |
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@ -348,35 +375,48 @@ namespace storm { |
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} |
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// (4) Define vectors/matrices.
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std::vector<std::vector<ValueType>> v = std::vector<std::vector<ValueType>>(N + 1, init); |
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unifVectors[0] = v; |
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unifVectors[1] = v; |
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unifVectors[2] = v; |
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// Initialize result vectors and already insert zeros for iteration N
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unifVectors = UnifPlusVectors<ValueType>(N, numberOfStates); |
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// Define 0=vd, 1=vu, 2=wu.
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// (5) Compute vectors and maxNorm.
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for (uint64_t i = 0; i < numberOfStates; ++i) { |
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for (uint64_t k = N; k <= N; --k) { |
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calculateUnifPlusVector(env, k, i, 0, lambda, numberOfProbabilisticChoices, relativeReachabilities, dir, unifVectors, fullTransitionMatrix, markovianAndGoalStates, psiStates, solver, foxGlynnResult, cycleFree); |
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calculateUnifPlusVector(env, k, i, 2, lambda, numberOfProbabilisticChoices, relativeReachabilities, dir, unifVectors, fullTransitionMatrix, markovianAndGoalStates, psiStates, solver, foxGlynnResult, cycleFree); |
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calculateVu(env, relativeReachabilities, dir, k, i, 1, lambda, numberOfProbabilisticChoices, unifVectors, fullTransitionMatrix, markovianAndGoalStates, psiStates, solver, foxGlynnResult, cycleFree); |
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// Iteration k = N was already performed by initializing with zeros.
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// Iterations k < N
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storm::utility::ProgressMeasurement progressSteps("steps in iteration " + std::to_string(iteration)); |
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progressSteps.setMaxCount(N); |
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progressSteps.startNewMeasurement(0); |
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for (int64_t k = N-1; k >= 0; --k) { |
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if (k < (int64_t)(N-1)) { |
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unifVectors.prepareNewIteration(); |
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} |
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for (uint64_t state = 0; state < numberOfStates; ++state) { |
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// Calculate results for lower bound and wUpper
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calculateUnifPlusVector(env, k, state, true, lambda, numberOfProbabilisticChoices, relativeReachabilities, dir, unifVectors, fullTransitionMatrix, markovianAndGoalStates, psiStates, solver, foxGlynnResult, cycleFree); |
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calculateUnifPlusVector(env, k, state, false, lambda, numberOfProbabilisticChoices, relativeReachabilities, dir, unifVectors, fullTransitionMatrix, markovianAndGoalStates, psiStates, solver, foxGlynnResult, cycleFree); |
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// Calculate result for upper bound
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uint64_t index = N-1-k; |
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if (index >= foxGlynnResult.left && index <= foxGlynnResult.right) { |
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STORM_LOG_ASSERT(unifVectors.wUpperNew[state] != -1, "wUpper was not computed before."); |
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unifVectors.resUpper[state] += foxGlynnResult.weights[index - foxGlynnResult.left] * unifVectors.wUpperNew[state]; |
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} |
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} |
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progressSteps.updateProgress(N-k); |
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} |
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// Only iterate over result vector, as the results can only get more precise.
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maxNorm = storm::utility::zero<ValueType>(); |
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for (uint64_t i = 0; i < numberOfStates; i++){ |
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ValueType diff = storm::utility::abs(unifVectors[0][0][i] - unifVectors[1][0][i]); |
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ValueType diff = storm::utility::abs(unifVectors.resUpper[i] - unifVectors.resLowerNew[i]); |
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maxNorm = std::max(maxNorm, diff); |
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} |
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// (6) Double lambda.
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lambda *= 2; |
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STORM_LOG_TRACE("Increased lambda to " << lambda << ", max diff is " << maxNorm << "."); |
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STORM_LOG_DEBUG("Increased lambda to " << lambda << ", max diff is " << maxNorm << "."); |
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progressIterations.updateProgress(++iteration); |
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} while (maxNorm > epsilon * (1 - kappa)); |
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return unifVectors[0][0]; |
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return unifVectors.resLowerNew; |
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} |
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template <typename ValueType> |
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@ -569,7 +609,12 @@ namespace storm { |
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return computeBoundedUntilProbabilitiesImca(env, dir, transitionMatrix, exitRateVector, markovianStates, psiStates, boundsPair); |
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} else { |
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STORM_LOG_ASSERT(settings.getMarkovAutomatonBoundedReachabilityMethod() == storm::settings::modules::MinMaxEquationSolverSettings::MarkovAutomatonBoundedReachabilityMethod::UnifPlus, "Unknown solution method."); |
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return computeBoundedUntilProbabilitiesUnifPlus(env, dir, transitionMatrix, exitRateVector, markovianStates, psiStates, boundsPair); |
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if (!storm::utility::isZero(boundsPair.first)) { |
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STORM_LOG_WARN("Using IMCA method because Unif+ does not support a lower bound > 0."); |
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return computeBoundedUntilProbabilitiesImca(env, dir, transitionMatrix, exitRateVector, markovianStates, psiStates, boundsPair); |
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} else { |
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return computeBoundedUntilProbabilitiesUnifPlus(env, dir, transitionMatrix, exitRateVector, markovianStates, psiStates, boundsPair); |
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} |
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} |
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} |
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