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back copz fox glznn 

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Timo Philipp Gros 8 years ago
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2 changed files with 331 additions and 14 deletions
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  1. 26
      src/storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.cpp
  2. 319
      src/storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.h

26
src/storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.cpp
View File

@ -211,7 +211,7 @@ namespace storm {
template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type> template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type>
void SparseMarkovAutomatonCslHelper::calculateVu(std::vector<std::vector<ValueType>> const& relativeReachability, OptimizationDirection dir, uint64_t k, uint64_t node, uint64_t const kind, ValueType lambda, uint64_t probSize, 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, std::ofstream& logfile){
void SparseMarkovAutomatonCslHelper::calculateVu(std::vector<std::vector<ValueType>> const& relativeReachability, OptimizationDirection dir, uint64_t k, uint64_t node, uint64_t const kind, ValueType lambda, uint64_t probSize, 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, std::ofstream& logfile, std::vector<double> poisson){
if (unifVectors[1][k][node]!=-1){return;} //dynamic programming. avoiding multiple calculation. if (unifVectors[1][k][node]!=-1){return;} //dynamic programming. avoiding multiple calculation.
uint64_t N = unifVectors[1].size()-1; uint64_t N = unifVectors[1].size()-1;
auto rowGroupIndices = fullTransitionMatrix.getRowGroupIndices(); auto rowGroupIndices = fullTransitionMatrix.getRowGroupIndices();
@ -219,10 +219,10 @@ namespace storm {
ValueType res =0; ValueType res =0;
for (uint64_t i = k ; i < N ; i++ ){ for (uint64_t i = k ; i < N ; i++ ){
if (unifVectors[2][N-1-(i-k)][node]==-1){ if (unifVectors[2][N-1-(i-k)][node]==-1){
calculateUnifPlusVector(N-1-(i-k),node,2,lambda,probSize,relativeReachability,dir,unifVectors,fullTransitionMatrix, markovianStates,psiStates,solver, logfile);
calculateUnifPlusVector(N-1-(i-k),node,2,lambda,probSize,relativeReachability,dir,unifVectors,fullTransitionMatrix, markovianStates,psiStates,solver, logfile, poisson);
//old: relativeReachability, dir, (N-1-(i-k)),node,lambda,wu,fullTransitionMatrix,markovianStates,psiStates, solver); //old: relativeReachability, dir, (N-1-(i-k)),node,lambda,wu,fullTransitionMatrix,markovianStates,psiStates, solver);
} }
res+=poisson(lambda, i)*unifVectors[2][N-1-(i-k)][node];
res+=poisson[i]*unifVectors[2][N-1-(i-k)][node];
} }
unifVectors[1][k][node]=res; unifVectors[1][k][node]=res;
} }
@ -238,7 +238,7 @@ namespace storm {
storm::storage::SparseMatrix<ValueType> const &fullTransitionMatrix, storm::storage::SparseMatrix<ValueType> const &fullTransitionMatrix,
storm::storage::BitVector const &markovianStates, storm::storage::BitVector const &markovianStates,
storm::storage::BitVector const &psiStates, storm::storage::BitVector const &psiStates,
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> const &solver, std::ofstream& logfile) {
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> const &solver, std::ofstream& logfile, std::vector<double> poisson) {
if (unifVectors[kind][k][node]!=-1){ if (unifVectors[kind][k][node]!=-1){
@ -267,7 +267,7 @@ namespace storm {
// Vd // Vd
res = storm::utility::zero<ValueType>(); res = storm::utility::zero<ValueType>();
for (uint64_t i = k ; i<N ; i++){ for (uint64_t i = k ; i<N ; i++){
ValueType between = poisson(lambda,i);
ValueType between = poisson[i];
res+=between; res+=between;
} }
unifVectors[kind][k][node]=res; unifVectors[kind][k][node]=res;
@ -287,7 +287,7 @@ namespace storm {
for (auto &element : line){ for (auto &element : line){
uint64_t to = element.getColumn(); uint64_t to = element.getColumn();
if (unifVectors[kind][k+1][to]==-1){ if (unifVectors[kind][k+1][to]==-1){
calculateUnifPlusVector(k+1,to,kind,lambda,probSize,relativeReachability,dir,unifVectors,fullTransitionMatrix,markovianStates,psiStates,solver, logfile);
calculateUnifPlusVector(k+1,to,kind,lambda,probSize,relativeReachability,dir,unifVectors,fullTransitionMatrix,markovianStates,psiStates,solver, logfile, poisson);
} }
res+=element.getValue()*unifVectors[kind][k+1][to]; res+=element.getValue()*unifVectors[kind][k+1][to];
} }
@ -317,7 +317,7 @@ namespace storm {
if (unifVectors[kind][k][to] == -1) { if (unifVectors[kind][k][to] == -1) {
calculateUnifPlusVector(k, to, kind, lambda, probSize, relativeReachability, dir, calculateUnifPlusVector(k, to, kind, lambda, probSize, relativeReachability, dir,
unifVectors, fullTransitionMatrix, markovianStates, unifVectors, fullTransitionMatrix, markovianStates,
psiStates, solver, logfile);
psiStates, solver, logfile, poisson);
} }
res = res + relativeReachability[j][to] * unifVectors[kind][k][to]; res = res + relativeReachability[j][to] * unifVectors[kind][k][to];
} }
@ -465,8 +465,6 @@ namespace storm {
std::vector<ValueType> SparseMarkovAutomatonCslHelper::unifPlus(OptimizationDirection dir, std::pair<double, double> const& boundsPair, std::vector<ValueType> const& exitRateVector, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& markovStates, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory){ std::vector<ValueType> SparseMarkovAutomatonCslHelper::unifPlus(OptimizationDirection dir, std::pair<double, double> const& boundsPair, std::vector<ValueType> const& exitRateVector, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& markovStates, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory){
STORM_LOG_TRACE("Using UnifPlus to compute bounded until probabilities."); STORM_LOG_TRACE("Using UnifPlus to compute bounded until probabilities.");
std::ofstream logfile("U+logfile.txt", std::ios::app); std::ofstream logfile("U+logfile.txt", std::ios::app);
ValueType maxNorm = storm::utility::zero<ValueType>(); ValueType maxNorm = storm::utility::zero<ValueType>();
ValueType oldDiff = -storm::utility::zero<ValueType>(); ValueType oldDiff = -storm::utility::zero<ValueType>();
@ -589,6 +587,9 @@ namespace storm {
exitRate[i] = exitNew; exitRate[i] = exitNew;
} }
// calculate poisson distribution
std::vector<double> poisson = foxGlynnProb(lambda*T, N, epsilon*kappa);
// (4) define vectors/matrices // (4) define vectors/matrices
std::vector<ValueType> init(numberOfStates, -1); std::vector<ValueType> init(numberOfStates, -1);
vd = std::vector<std::vector<ValueType>> (N + 1, init); vd = std::vector<std::vector<ValueType>> (N + 1, init);
@ -604,9 +605,9 @@ namespace storm {
// (5) calculate vectors and maxNorm // (5) calculate vectors and maxNorm
for (uint64_t i = 0; i < numberOfStates; i++) { for (uint64_t i = 0; i < numberOfStates; i++) {
for (uint64_t k = N; k <= N; k--) { for (uint64_t k = N; k <= N; k--) {
calculateUnifPlusVector(k,i,0,lambda,probSize,relReachability,dir,unifVectors,fullTransitionMatrix,markovianStates,psiStates,solver, logfile);
calculateUnifPlusVector(k,i,2,lambda,probSize,relReachability,dir,unifVectors,fullTransitionMatrix,markovianStates,psiStates,solver, logfile);
calculateVu(relReachability,dir,k,i,1,lambda,probSize,unifVectors,fullTransitionMatrix,markovianStates,psiStates,solver, logfile);
calculateUnifPlusVector(k,i,0,lambda,probSize,relReachability,dir,unifVectors,fullTransitionMatrix,markovianStates,psiStates,solver, logfile, poisson);
calculateUnifPlusVector(k,i,2,lambda,probSize,relReachability,dir,unifVectors,fullTransitionMatrix,markovianStates,psiStates,solver, logfile, poisson);
calculateVu(relReachability,dir,k,i,1,lambda,probSize,unifVectors,fullTransitionMatrix,markovianStates,psiStates,solver, logfile, poisson);
//also use iteration to keep maxNorm of vd and vup to date, so the loop-condition is easy to prove //also use iteration to keep maxNorm of vd and vup to date, so the loop-condition is easy to prove
ValueType diff = std::abs(unifVectors[0][k][i]-unifVectors[1][k][i]); ValueType diff = std::abs(unifVectors[0][k][i]-unifVectors[1][k][i]);
maxNorm = std::max(maxNorm, diff); maxNorm = std::max(maxNorm, diff);
@ -615,6 +616,7 @@ namespace storm {
printTransitions(N, maxNorm, fullTransitionMatrix,exitRate,markovianStates,psiStates,relReachability,psiStates, psiStates,unifVectors, logfile); //TODO remove printTransitions(N, maxNorm, fullTransitionMatrix,exitRate,markovianStates,psiStates,relReachability,psiStates, psiStates,unifVectors, logfile); //TODO remove
// (6) double lambda // (6) double lambda
lambda=2*lambda; lambda=2*lambda;
// (7) escape if not coming closer to solution // (7) escape if not coming closer to solution

319
src/storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.h
View File

@ -57,7 +57,7 @@ namespace storm {
private: private:
template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type=0> template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type=0>
static void calculateUnifPlusVector(uint64_t k, uint64_t node, uint64_t const kind, ValueType lambda, uint64_t probSize, 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, std::ofstream& logfile);
static void calculateUnifPlusVector(uint64_t k, uint64_t node, uint64_t const kind, ValueType lambda, uint64_t probSize, 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, std::ofstream& logfile, std::vector<double> poisson);
template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type=0> template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type=0>
static void deleteProbDiagonals(storm::storage::SparseMatrix<ValueType>& transitionMatrix, storm::storage::BitVector const& markovianStates); static void deleteProbDiagonals(storm::storage::SparseMatrix<ValueType>& transitionMatrix, storm::storage::BitVector const& markovianStates);
@ -80,6 +80,321 @@ namespace storm {
template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type=0> template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type=0>
static storm::storage::BitVector identifyProbCycles(storm::storage::SparseMatrix<ValueType> const& TransitionMatrix, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates); static storm::storage::BitVector identifyProbCycles(storm::storage::SparseMatrix<ValueType> const& TransitionMatrix, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& psiStates);
//TODO: move this
typedef struct FoxGlynn
{
int left;
int right;
double total_weight;
double *weights;
} FoxGlynn;
static std::vector<double> foxGlynnProb(double lambdaT, int N, double precision){
FoxGlynn* fg = NULL;
if(!fox_glynn(lambdaT, DBL_MIN, DBL_MAX, precision, &fg)) {
printf("ERROR: fox-glynn failed\n");
return std::vector<double>{};
}
long double sumOfPoissonProbs = 0.0;
std::vector<double> poisson_p(N,0.0);
unsigned long iter_num;
//for(int i=fg->left; i<=fg->right; i++) {
for (int i = 0; i<N ; i++){
poisson_p[i] = fg->weights[i-fg->left]/fg->total_weight;
sumOfPoissonProbs+=poisson_p[i];
}
/*for(int i=fg->left-1; i>=0; i--) {
poisson_p[i] = poisson_p[i+1]*((i+1)/(lambdaT));
sumOfPoissonProbs+=poisson_p[i];
}*/
iter_num = fg->right;
freeFG(fg);
return poisson_p;
}
static bool finder(const int m, const double lambda, const double tau, const double omega,
const double epsilon, double * pw_m, FoxGlynn *pFG)
{
/*The pi constant*/
static const double pi = 3.14159265358979323846264;
static const double lambda_25 = 25.0;
static const double lambda_400 = 40;
const double sqrt_2_pi = sqrt( 2.0 * pi );
const double sqrt_2 = sqrt(2.0);
const double sqrt_lambda = sqrt(lambda);
double lambda_max, k, k_rtp = HUGE_VAL, k_prime, c_m_inf, result, al, dkl, bl;
/*Simple bad cases, when we quit*/
if( lambda == 0.0 )
{
printf("ERROR: Fox-Glynn: lambda = 0, terminating the algorithm\n");
return false;
}
/* The requested error level must not be smaller than the minimum machine precision
(needed to guarantee the convergence of the error conditions) */
if( epsilon < tau)
{
printf("ERROR: Fox-Glynn: epsilon < tau, invalid error level, terminating the algorithm\n");
printf("epsilon %f, tau %f\n",epsilon,tau);
return false;
}
/* zero is used as left truncation point for lambda <= 25 */
pFG->left = 0;
lambda_max = lambda;
/* for lambda below 25 the exponential can be smaller than tau */
/* if that is the case we expect underflows and warn the user */
if( 0.0 < lambda && lambda <= lambda_25 )
{
if( exp( -lambda ) <= tau )
{
printf("ERROR: Fox-Glynn: 0 < lambda < 25, underflow. The results are UNRELIABLE.\n");
}
}
bl = (1.0 + 1.0/lambda) * exp(1.0 / (8.0 * lambda));
/****Compute pFG->right truncation point****/
/*According to Fox-Glynn, if lambda < 400 we should take lambda = 400,
otherwise use the original value. This is for computing the right truncation point*/
if(lambda < lambda_400)
lambda_max = lambda_400;
k = 4;
al = (1.0+1.0/lambda_max) * exp(1.0/16.0) * sqrt_2;
dkl = exp(-2.0/9.0 * (k * sqrt(2.0 * lambda_max) + 1.5 ));
dkl = 1.0 / (1.0 - dkl);
/* find right truncation point */
/* This loop is a modification to the original Fox-Glynn paper.
The search for the right truncation point is only terminated by
the error condition and not by the stop index from the FG paper.
This can yield more accurate results if neccesary.*/
while((epsilon/2.0) < ((al * dkl * exp(-(k*k)/2.0))/(k*sqrt_2_pi)))
{
k++;
dkl = exp(-2.0/9.0 * (k * sqrt_2 * sqrt(lambda_max) + 1.5 ));
dkl = 1.0 / (1.0 - dkl);
}
k_rtp = k;
pFG->right = (int)ceil(m + k_rtp * sqrt_2 * sqrt(lambda_max) + 1.5 );
/****Compute pFG->left truncation point****/
/* compute the left truncation point for lambda > 25 */
/* for lambda <= 25 we use zero as left truncation point */
if(lambda > lambda_25)
{
/*Start looking for the left truncation point*/
/* start search at k=4 (taken from original Fox-Glynn paper */
k = 4;
/* increase the left truncation point as long as we fulfill the error condition */
/* This loop is a modification to the original Fox-Glynn paper.
The search for the left truncation point is only terminated by
the error condition and not by the stop index from the FG paper.
This can yield more accurate results if neccesary.*/
while((epsilon/2.0) < ((bl * exp(-(k*k)/2.0))/(k * sqrt_2_pi)))
k++;
/*Finally the left truncation point is found*/
pFG->left = (int)floor(m - k*sqrt(lambda)- 1.5 );
/* for small lambda the above calculation can yield negative truncation points, crop them here */
if(pFG->left < 0)
pFG->left = 0;
/* perform underflow check */
k_prime = k + 3.0 / (2.0 * sqrt_lambda);
/*We take the c_m_inf = 0.02935 / sqrt( m ), as for lambda >= 25
c_m = 1 / ( sqrt( 2.0 * pi * m ) ) * exp( m - lambda - 1 / ( 12.0 * m ) ) => c_m_inf*/
c_m_inf = 0.02935 / sqrt((double) m);
result = 0.0;
if( 0.0 < k_prime && k_prime <= sqrt_lambda / 2.0 )
{
result = c_m_inf * exp( - pow(k_prime,2.0) / 2.0 - pow(k_prime, 3.0) / (3.0 * sqrt_lambda) );
}
else
{
if( k_prime <= sqrt( m + 1.0 ) / m )
{
double result_1 = c_m_inf * pow(
1.0 - k_prime / sqrt((double) (m + 1)),
k_prime * sqrt((double) (m + 1)));
double result_2 = exp( - lambda );
/*Take the maximum*/
result = ( result_1 > result_2 ? result_1 : result_2);
}
else
{
/*NOTE: It will be an underflow error*/;
printf("ERROR: Fox-Glynn: lambda >= 25, underflow. The results are UNRELIABLE.\n");
}
}
if ( result * omega / ( 1.0e+10 * ( pFG->right - pFG->left ) ) <= tau )
{
printf("ERROR: Fox-Glynn: lambda >= 25, underflow. The results are UNRELIABLE.\n");
}
}
/*We still have to perform an underflow check for the right truncation point when lambda >= 400*/
if( lambda >= lambda_400 )
{
k_prime = k_rtp * sqrt_2 + 3.0 / (2.0 * sqrt_lambda);
/*We take the c_m_inf = 0.02935 / sqrt( m ), as for lambda >= 25
c_m = 1 / ( sqrt( 2.0 * pi * m ) ) * exp( m - lambda - 1 / ( 12.0 * m ) ) => c_m_inf*/
c_m_inf = 0.02935 / sqrt((double) m);
result = c_m_inf * exp( - pow( k_prime + 1.0 , 2.0 ) / 2.0 );
if( result * omega / ( 1.0e+10 * ( pFG->right - pFG->left ) ) <= tau)
{
printf("ERROR: Fox-Glynn: lambda >= 400, underflow. The results are UNRELIABLE.\n");
}
}
/*Time to set the initial value for weights*/
*pw_m = omega / ( 1.0e+10 * ( pFG->right - pFG->left ) );
return true;
}
/*****************************************************************************
Name : weighter
Role : The WEIGHTER function from the Fox-Glynn algorithm
@param : double lambda: (rate of uniformization)*(mission time)
@param : double tau: underflow
@param : double omega: overflow
@param : double epsilon: error bound
@param : FoxGlynn *: return by reference
@return : TRUE if everything is fine, otherwise FALSE.
This is the F parameter of Fox-Glynn finder function.
remark :
******************************************************************************/
static bool weighter(const double lambda, const double tau, const double omega, const double epsilon, FoxGlynn *pFG)
{
static const double pi = 3.14159265358979323846264;
static const double lambda_25 = 25.0;
static const double lambda_400 = 40;
/*The magic m point*/
const int m = (int)floor(lambda);
double w_m = 0;
int j, s, t;
if( ! finder( m, lambda, tau, omega, epsilon, &w_m, pFG ) )
return false;
/*Allocate space for weights*/
pFG->weights = (double *) calloc((size_t) (pFG->right - pFG->left + 1),
sizeof(double));
/*Set an initial weight*/
pFG->weights[ m - pFG->left ] = w_m;
/*Fill the left side of the array*/
for( j = m; j > pFG->left; j-- )
pFG->weights[ ( j - pFG->left ) - 1 ] = ( j / lambda ) * pFG->weights[ j - pFG->left ];
/*Fill the right side of the array, have two cases lambda < 400 & lambda >= 400*/
if( lambda < lambda_400 )
{
/*Perform the underflow check, according to Fox-Glynn*/
if( pFG->right > 600 )
{
printf("ERROR: Fox-Glynn: pFG->right > 600, underflow is possible\n");
return false;
}
/*Compute weights*/
for( j = m; j < pFG->right; j++ )
{
double q = lambda / ( j + 1 );
if( pFG->weights[ j - pFG->left ] > tau / q )
{
pFG->weights[ ( j - pFG->left ) + 1 ] = q * pFG->weights[ j - pFG->left ];
}else{
pFG->right = j;
break; /*It's time to compute W*/
}
}
}else{
/*Compute weights*/
for( j = m; j < pFG->right; j++ )
pFG->weights[ ( j - pFG->left ) + 1 ] = ( lambda / ( j + 1 ) ) * pFG->weights[ j - pFG->left ];
}
/*It is time to compute the normalization weight W*/
pFG->total_weight = 0.0;
s = pFG->left;
t = pFG->right;
while( s < t )
{
if( pFG->weights[ s - pFG->left ] <= pFG->weights[ t - pFG->left ] )
{
pFG->total_weight += pFG->weights[ s - pFG->left ];
s++;
}else{
pFG->total_weight += pFG->weights[ t - pFG->left ];
t--;
}
}
pFG->total_weight += pFG->weights[ s - pFG->left ];
/* printf("Fox-Glynn: ltp = %d, rtp = %d, w = %10.15le \n", pFG->left, pFG->right, pFG->total_weight); */
return true;
}
/*****************************************************************************
Name : fox_glynn
Role : get poisson probabilities.
@param : double lambda: (rate of uniformization)*(mission time)
@param : double tau: underflow
@param : double omega: overflow
@param : double epsilon: error bound
@param : FoxGlynn **: return a new FoxGlynn structure by reference
@return : TRUE if it worked fine, otherwise false
remark :
******************************************************************************/
static bool fox_glynn(const double lambda, const double tau, const double omega, const double epsilon, FoxGlynn **ppFG)
{
/* printf("Fox-Glynn: lambda = %3.3le, epsilon = %1.8le\n",lambda, epsilon); */
*ppFG = (FoxGlynn *) calloc((size_t) 1, sizeof(FoxGlynn));
(*ppFG)->weights = NULL;
return weighter(lambda, tau, omega, epsilon, *ppFG);
}
/**
* Fries the memory allocated for the FoxGlynn structure
* @param fg the structure to free
*/
static void freeFG(FoxGlynn * fg)
{
if( fg ){
if( fg->weights )
free(fg->weights);
free(fg);
}
}
/*!
* Computes the poission-distribution
*
*
* @param parameter lambda to use
* @param point i
* TODO: replace with Fox-Lynn
* @return the probability
*/
/*! /*!
* Computes the poission-distribution * Computes the poission-distribution
* *
@ -100,7 +415,7 @@ namespace storm {
* *
*/ */
template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type=0> template <typename ValueType, typename std::enable_if<storm::NumberTraits<ValueType>::SupportsExponential, int>::type=0>
static void calculateVu(std::vector<std::vector<ValueType>> const& relativeReachability, OptimizationDirection dir, uint64_t k, uint64_t node, uint64_t const kind, ValueType lambda, uint64_t probSize, 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, std::ofstream& logfile);
static void calculateVu(std::vector<std::vector<ValueType>> const& relativeReachability, OptimizationDirection dir, uint64_t k, uint64_t node, uint64_t const kind, ValueType lambda, uint64_t probSize, 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, std::ofstream& logfile, std::vector<double> poisson);

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