void WeightedAverage::operator()(Data * dt, int ** classification, Classifier ** classifiers, int numClassifiers)
{
int i, j, k;
int chosen;
std::vector<float> averages(dt->getNLabels(), 0.0f);
for (i = 0; i < dt->getNSamples(); i++)
{
for (float & av : averages)
av = 0.0f;
for (j = 0; j < numClassifiers; j++)
{
for (k = 0; k < dt->getNLabels(); k++)
{
if(classifiers[j]->hasScore())
{
averages[k] += classifiers[j]->getScore(i, k) * weight[j];
}
}
}
chosen = 0;
for (j = 0; j < dt->getNLabels(); j++)
{
if (averages[j] > averages[chosen])
chosen = j;
}
dt->setClassificationLabel(i, chosen + 1);
}
}
QVi RegionService::calcAverage(const MatSet& matSet, QLP region) {
QVi averages(9,0);
if(!region.size()) {
qDebug() << "region.count()=0";
return averages;
}
QVi sumOfValue = countSum(matSet, region);
for(int i=0; i<9; i++) {
averages[i] = sumOfValue[i] / region.count();
}
return averages;
}
void RegionService::calcMedianAndTolerance(const MatSet& matSet, QLPs regions, vint& medians, vint& upperTolerances, vint& underTolerances) {
int pixelSum=0;
vint averages(9,0);
int greenFrequency[256] = {0};
int yFrequency[256] = {0};
int crFrequency[256] = {0};
int cbFrequency[256] = {0};
for(QLP region : regions) {
for(Point point : region) {
greenFrequency[G(matSet.bgr(), point.x, point.y)]++;
yFrequency[B(matSet.ycrcb(), point.x, point.y)]++;
crFrequency[G(matSet.ycrcb(), point.x, point.y)]++;
cbFrequency[R(matSet.ycrcb(), point.x, point.y)]++;
pixelSum++;
}
}
int harfOfPixelSum = (int)((double)pixelSum/2.0);
int underOfPixelSum = (int)((double)pixelSum*0.05);
int upperOfPixelSum = (int)((double)pixelSum*0.95);
int greenPixelCount = 0;
int greenMedian = 0;
int greenUpperTolerance = 0;
int greenUnderTolerance = 0;
for(int bin =0; bin<256; bin++ ) {
greenPixelCount = greenPixelCount + greenFrequency[bin];
if(greenPixelCount <= underOfPixelSum) {
greenUnderTolerance = bin;
continue;
}
if(greenPixelCount <= harfOfPixelSum) {
greenMedian = bin;
continue;
}
if(greenPixelCount >= upperOfPixelSum) {
greenUpperTolerance = bin;
break;
}
}
int yPixelCount = 0;
int yMedian = 0;
int yUpperTolerance = 0;
int yUnderTolerance = 0;
for(int bin =0; bin<256; bin++ ) {
yPixelCount = yPixelCount + yFrequency[bin];
if(yPixelCount <= underOfPixelSum) {
yUnderTolerance = bin;
continue;
}
if(yPixelCount <= harfOfPixelSum) {
yMedian = bin;
continue;
}
if(yPixelCount >= upperOfPixelSum) {
yUpperTolerance = bin;
break;
}
}
int crPixelCount = 0;
int crMedian = 0;
int crUpperTolerance = 0;
int crUnderTolerance = 0;
for(int bin =0; bin<256; bin++ ) {
crPixelCount = crPixelCount + crFrequency[bin];
if(crPixelCount <= underOfPixelSum) {
crUnderTolerance = bin;
continue;
}
if(crPixelCount <= harfOfPixelSum) {
crMedian = bin;
continue;
}
if(crPixelCount >= upperOfPixelSum) {
crUpperTolerance = bin;
break;
}
}
int cbPixelCount = 0;
int cbMedian = 0;
int cbUpperTolerance = 0;
int cbUnderTolerance = 0;
for(int bin =0; bin<256; bin++ ) {
cbPixelCount = cbPixelCount + cbFrequency[bin];
if(cbPixelCount <= underOfPixelSum) {
cbUnderTolerance = bin;
continue;
}
if(cbPixelCount <= harfOfPixelSum) {
cbMedian = bin;
continue;
}
if(cbPixelCount >= upperOfPixelSum) {
cbUpperTolerance = bin;
break;
}
}
medians[1] = greenMedian;
medians[6] = yMedian;
medians[7] = crMedian;
medians[8] = cbMedian;
upperTolerances[1] = greenUpperTolerance;
upperTolerances[6] = yUpperTolerance;
upperTolerances[7] = crUpperTolerance;
upperTolerances[8] = cbUpperTolerance;
underTolerances[1] = greenUnderTolerance;
underTolerances[6] = yUnderTolerance;
underTolerances[7] = crUnderTolerance;
underTolerances[8] = cbUnderTolerance;
}
void CF<FactorizerType>::GetRecommendations(const size_t numRecs,
arma::Mat<size_t>& recommendations,
arma::Col<size_t>& users)
{
// Generate new table by multiplying approximate values.
rating = w * h;
// Now, we will use the decomposed w and h matrices to estimate what the user
// would have rated items as, and then pick the best items.
// Temporarily store feature vector of queried users.
arma::mat query(rating.n_rows, users.n_elem);
// Select feature vectors of queried users.
for (size_t i = 0; i < users.n_elem; i++)
query.col(i) = rating.col(users(i));
// Temporary storage for neighborhood of the queried users.
arma::Mat<size_t> neighborhood;
// Calculate the neighborhood of the queried users.
// This should be a templatized option.
neighbor::AllkNN a(rating);
arma::mat resultingDistances; // Temporary storage.
a.Search(query, numUsersForSimilarity, neighborhood, resultingDistances);
// Temporary storage for storing the average rating for each user in their
// neighborhood.
arma::mat averages = arma::zeros<arma::mat>(rating.n_rows, query.n_cols);
// Iterate over each query user.
for (size_t i = 0; i < neighborhood.n_cols; ++i)
{
// Iterate over each neighbor of the query user.
for (size_t j = 0; j < neighborhood.n_rows; ++j)
averages.col(i) += rating.col(neighborhood(j, i));
// Normalize average.
averages.col(i) /= neighborhood.n_rows;
}
// Generate recommendations for each query user by finding the maximum numRecs
// elements in the averages matrix.
recommendations.set_size(numRecs, users.n_elem);
recommendations.fill(cleanedData.n_rows); // Invalid item number.
arma::mat values(numRecs, users.n_elem);
values.fill(-DBL_MAX); // The smallest possible value.
for (size_t i = 0; i < users.n_elem; i++)
{
// Look through the averages column corresponding to the current user.
for (size_t j = 0; j < averages.n_rows; ++j)
{
// Ensure that the user hasn't already rated the item.
if (cleanedData(j, users(i)) != 0.0)
continue; // The user already rated the item.
// Is the estimated value better than the worst candidate?
const double value = averages(j, i);
if (value > values(values.n_rows - 1, i))
{
// It should be inserted. Which position?
size_t insertPosition = values.n_rows - 1;
while (insertPosition > 0)
{
if (value <= values(insertPosition - 1, i))
break; // The current value is the right one.
insertPosition--;
}
// Now insert it into the list.
InsertNeighbor(i, insertPosition, j, value, recommendations,
values);
}
}
// If we were not able to come up with enough recommendations, issue a
// warning.
if (recommendations(values.n_rows - 1, i) == cleanedData.n_rows + 1)
Log::Warn << "Could not provide " << values.n_rows << " recommendations "
<< "for user " << users(i) << " (not enough un-rated items)!"
<< std::endl;
}
}
int main(int argn, char* args[])
{
static char *desc[] = {
"This script will read the xtc trajectory from an MD simulation",
"performed by GROMACS and output all data related to the analysis",
"of preferential interactions.",
"[PAR]",
"Generated: Thu Aug 20 16:49:21 EDT 2015.[BR]",
"Last updated: Thu Aug 27 17:26:01 EDT 2015.",
"[PAR]",
"Future Developments:[BR]",
"[BB]1.[bb] Partition calculation into groups (constituent amino acids).[BR]",
"[BB]2.[bb] Calculate residence times.[BR]",
"[BB]3.[bb] Include a measure for geometric orientation.[BR]",
"[BB]4.[bb] Calculate molecular distributions.[BR]",
"[BB]5.[bb] Parallelize it.",
"[PAR]",
"Remember to check the dependencie of the results on the number of block",
" used by using [TT]-block[tt].",
"Also, check that your simulation has been properly equilibrated by using [TT]-f0[tt].",
"In terms of reducing the computational cost of the analysis, use the option",
"[TT]-skip[tt] to only use every nr[TT]-th[tt] frame from the trajectory."
};
unsigned int protein_sequence=20; /* parse tpr.itp for info */
unsigned int N_co=4; /* look at topology for number of co-solvents */
unsigned int num_sol=7906; /* look at topology as well */
unsigned int skip_nr=1;
unsigned int granularity=2*100;
unsigned int f0=0;
bool bIndex=false;
t_pargs pa[] = {
{"-start", FALSE, etINT, {&f0}, "Start after n-th frame."},
{"-skip", FALSE, etINT, {&skip_nr}, "Only write every nr-th frame."},
{"-grid", FALSE, etINT, {&granularity}, "Number points to calculate."},
{"-seq", FALSE, etINT,{&protein_sequence}, "Number of amino acids in protein sequence."},
{"-Nco", FALSE, etINT,{&N_co}, "Number of cosolvent molecules."},
{"-Sol", FALSE, etINT,{&num_sol}, "Number of water molecules."}
};
char title[STRLEN];
t_topology top;
int ePBC;
rvec *xtop;
matrix box;
t_filenm fnm[] = { /* See filenm.h */
{ efTOP, NULL, NULL, ffREAD },
{ efTPS, NULL, NULL, ffREAD }, /* topology */
{ efTRX, "-f", NULL, ffREAD }, /* trajcetory */
{ efNDX, "-n", NULL, ffOPTRD } /* index file */
};
#define NFILE asize(fnm)
/* Interface. Adds default options. */
CopyRight(stderr,args[0]);
parse_common_args(&argn,args,PCA_CAN_TIME | PCA_CAN_VIEW, NFILE,fnm,asize(pa),pa,asize(desc),desc,0,NULL);
read_tps_conf( ftp2fn(efTPS, NFILE, fnm), title, &top, &ePBC, &xtop, NULL, box, TRUE);
sfree(xtop);
/*******************************************************************************************************************/
/*
int iter;
for (iter=0;iter<top.atoms.nr/100;++iter)
{
printf("Atom name: %s\tAtom charge: %f\n", *(top.atoms.atomname[iter]), top.atoms.atom[iter].q );
printf("Atom type: %d\tAtomic Residue NUmber: %d\n", top.atoms.atom[iter].type, top.atoms.atom[iter].resnr );
printf("Chain Identifier: %u\tNr of residues names: %d\n", top.atoms.atom[iter].ptype, top.atoms.nres );
printf("Residue name: %s\n\n", *(top.atoms.resname[iter]) );
}
*/
/*******************************************************************************************************************/
int status;
t_trxframe fr;
int flags = TRX_READ_X;
/* Count Number of Frames */
unsigned int bframes=0, frames=0;
int bwrite;
read_first_frame(&status, ftp2fn(efTRX,NFILE,fnm), &fr, flags);
do {
bwrite = bframes % skip_nr;
++bframes;
if ((bframes>f0) && (bwrite==0)){ ++frames; }
} while ( read_next_frame(status,&fr) );
/* Preparing Block Analysis */
bIndex = ftp2bSet(efNDX,NFILE,fnm);
std::vector<int> blocks_list;
if (bIndex)
{
FILE *fp = ffopen(opt2fn("-n",NFILE,fnm),"r");
int numblock;
while(fscanf(fp,"%d",&numblock)!=EOF)
{
blocks_list.push_back(numblock);
}
fclose(fp);
} else {
blocks_list.push_back(1);
}
/* Actual Calculation */
std::vector<Info> protein;
std::vector<Info> cosolvent;
std::vector<Info> solvent;
std::vector<double> cutoff, coefficients;
double molals=0, molars=0;
/* BLOCK AVERAGE */
typedef std::vector<double> Row;
typedef std::vector<Row> Matrix;
unsigned int num_blocks;
/////////////
//////////// std::ofstream test_partition("partition.txt");
for (unsigned int iter=0; iter<blocks_list.size(); ++iter)
{
num_blocks = blocks_list[iter];
unsigned int partition = (frames)/num_blocks;
unsigned int frame_counter=0;
std::vector<double> positions(granularity), averages(granularity), averages_sqr(granularity), sigma(granularity);
Matrix values(num_blocks,Row(granularity)), values_sqr(num_blocks,Row(granularity));
unsigned int frame=0, twrite=0;
read_first_frame(&status, ftp2fn(efTRX,NFILE,fnm), &fr, flags);
do
{
twrite = frame % skip_nr; /* if twrite==0 then read frame. */
++frame;
if ((frame > f0) && (twrite==0))
{
/* READING */
unsigned int protein_co=protein_sequence+N_co;
unsigned int solvated=protein_co+num_sol;
for (unsigned int n=0; n<top.atoms.nr; ++n)
{
/* Parsing */
Info atomo;
atomo.setAtom( (std::string) *(top.atoms.atomname[n]) );
atomo.setResnum( (unsigned int) top.atoms.atom[n].resnr );
atomo.setResname( (std::string) *(top.atoms.resname[atomo.getResnum()]) );
atomo.setCoords( (double) fr.x[n][XX], (double) fr.x[n][YY], (double) fr.x[n][ZZ] );
/* Testing for partition of groups */
/////// atomo.print(test_partition);
/* Appending */
// if
if ( atomo.getAtom()[0]!='H') // atomo.atom[0]!='H')
{
if ( atomo.getResnum() < protein_sequence ){
protein.push_back(atomo);
} else if ( (atomo.getResnum() >= protein_sequence) && (atomo.getResnum() < protein_co) ){
cosolvent.push_back(atomo);
} else if ( (atomo.getResnum() >= protein_co) && (atomo.getResnum() < solvated) ){
// if (atomo.getResname().compare("SOL")!=0)
// we want to avoid inputing number of waters for analysis
solvent.push_back(atomo);
}
}
}
/* MAIN */
double box_size = fr.box[0][0];
/* Local calculation for cosolvents */
std::vector<double> close_co; /* Stores Distances of closest */
for (unsigned int i=0; i<N_co; ++i)
{
std::vector<double> local_co;
double minimum_calculated = box_size*box_size;
unsigned int Nco_size=cosolvent.size()/N_co;
for (unsigned int n=(i*Nco_size); n<((i+1)*Nco_size); ++n)
{
for (unsigned int j=0; j<protein.size(); ++j)
{
double dist = cosolvent[n].distance(protein[j],box_size);
if (dist < minimum_calculated ){ minimum_calculated = dist; }
}
local_co.push_back(minimum_calculated);
}
close_co.push_back( *min_element(local_co.begin(), local_co.end()) );
}
/* Local calculation for water */
std::vector<double> local_wat;
for (unsigned int i=0; i<solvent.size(); ++i)
{
double minimum_calculated = box_size*box_size;
for (unsigned int j=0; j<protein.size(); ++j)
{
double dist = solvent[i].distance(protein[j],box_size);
if (dist < minimum_calculated){ minimum_calculated = dist; }
}
local_wat.push_back(minimum_calculated);
}
/* Preferential Interaction Coefficient */
double N_wat = solvent.size();
linspace(0,box_size,granularity,cutoff);
for (unsigned int x=0; x<granularity; ++x)
{
unsigned int n3=0, n1=0;
for (unsigned int i=0; i<close_co.size(); ++i){ if (close_co[i] < (cutoff[x]*cutoff[x])) ++n3; }
for (unsigned int i=0; i<local_wat.size(); ++i){ if (local_wat[i] < (cutoff[x]*cutoff[x])) ++n1; }
coefficients.push_back(pref_coef(N_co, N_wat, n3, n1));
}
molals+= molality(N_co, (int) N_wat);
molars+= molarity(N_co, box_size);
/* Storage */
for (unsigned int i=0; i<granularity; ++i){ positions[i] += cutoff[i]; }
for (unsigned int j=0; j<granularity; ++j)
{
values[(int) (frame_counter/(partition+1))][j] += coefficients[j];
values_sqr[(int) (frame_counter/(partition+1))][j] += coefficients[j]*coefficients[j];
}
cutoff.clear();
coefficients.clear();
protein.clear();
cosolvent.clear();
solvent.clear();
++frame_counter;
}
} while ( read_next_frame(status,&fr) );
//thanx(stderr);
/* FINAL REUSLTS */
double normalization = partition;
molals /= (num_blocks*normalization);
molars /= (num_blocks*normalization);
for (unsigned int i=0; i<granularity; ++i){ positions[i] /= (num_blocks*normalization); }
for (unsigned int i=0; i<num_blocks; ++i)
{
for (unsigned int j=0; j<granularity; ++j)
{
values[i][j] /= normalization;
values_sqr[i][j] /= normalization;
}
}
/* AVERAGES */
for (unsigned int i=0; i<granularity; ++i)
{
for (unsigned int j=0; j<num_blocks; ++j)
{
averages[i] += values[j][i];
averages_sqr[i] += values_sqr[j][i];
}
averages[i] /= (double) num_blocks;
averages_sqr[i] /= (double) num_blocks;
}
/* STANDARD DEVIATIONS */
for (unsigned int i=0; i<granularity; ++i)
{
sigma[i] += sqrt( averages_sqr[i] - averages[i]*averages[i] );
}
/* OUTPUT */
std::ofstream distances("dimensions.dat");
for (unsigned int i=0; i<granularity/2; ++i){ distances << std::setw(1) << positions[i] <<'\n'; }
distances.close();
std::string output1="preferential_val.dat";
std::string output2="preferential_sig.dat";
std::string result;
std::ostringstream convert;
convert << num_blocks; //skip;
result = convert.str();
output1.insert(16,result);
output2.insert(16,result);
std::ofstream pic1(output1.c_str());
std::ofstream pic2(output2.c_str());
for (unsigned int i=0; i<granularity/2; ++i)
{
pic1 << std::setw(10)<< averages[i] <<'\n';
pic2 << std::setw(10)<< sigma[i] <<'\n';
}
pic1.close();
pic2.close();
std::ofstream concentrations("concentrations.dat");
concentrations<< std::setw(10) << "Molality" <<'\t'<< std::setw(10) << "Molarity" <<'\n';
concentrations<< std::setw(10) << molals <<'\t'<< std::setw(10) << molars << '\n';
concentrations.close();
std::cout << "ANALYSIS COMPLETED!" <<'\n';
std::cout<<"Total number of frames: "<<frame_counter<<'\n';
}
//////////////// test_partition.close();
thanx(stderr);
return 0;
}
void CViGrA_Watershed::Segmentation(TImage_In &Input, TImage_Out &Output, double Scale, bool bEdges)
{
typedef typename vigra::NumericTraits<typename TImage_In::value_type>::RealPromote TmpType;
vigra::BasicImage<TmpType> gradientx (Get_NX(), Get_NY());
vigra::BasicImage<TmpType> gradienty (Get_NX(), Get_NY());
vigra::FImage gradientmag (Get_NX(), Get_NY());
vigra::IImage labels (Get_NX(), Get_NY());
//-----------------------------------------------------
// calculate the x- and y-components of the image gradient at given scale
Process_Set_Text(_TL("calculate gradients"));
recursiveFirstDerivativeX (srcImageRange(Input) , destImage(gradientx), Scale);
recursiveSmoothY (srcImageRange(gradientx) , destImage(gradientx), Scale);
recursiveFirstDerivativeY (srcImageRange(Input) , destImage(gradienty), Scale);
recursiveSmoothX (srcImageRange(gradienty) , destImage(gradienty), Scale);
//-----------------------------------------------------
// transform components into gradient magnitude
Process_Set_Text(_TL("calculate gradient magnitude"));
combineTwoImages(
srcImageRange(gradientx),
srcImage(gradienty),
destImage(gradientmag),
GradientSquaredMagnitudeFunctor()
);
//-----------------------------------------------------
// find the local minima of the gradient magnitude (might be larger than one pixel)
Process_Set_Text(_TL("find local minima"));
labels = 0;
extendedLocalMinima(srcImageRange(gradientmag), destImage(labels), 1);
//-----------------------------------------------------
// label the minima just found
Process_Set_Text(_TL("label minima"));
int max_region_label = labelImageWithBackground(srcImageRange(labels), destImage(labels), false, 0);
//-----------------------------------------------------
// create a statistics functor for region growing
vigra::ArrayOfRegionStatistics<vigra::SeedRgDirectValueFunctor<float> >gradstat(max_region_label);
//-----------------------------------------------------
// perform region growing, starting from the minima of the gradient magnitude;
// as the feature (first input) image contains the gradient magnitude,
// this calculates the catchment basin of each minimum
Process_Set_Text(_TL("perform region growing"));
seededRegionGrowing(srcImageRange(gradientmag), srcImage(labels), destImage(labels), gradstat);
//-----------------------------------------------------
// initialize a functor to determine the average gray-value or color for each region (catchment basin) just found
vigra::ArrayOfRegionStatistics<vigra::FindAverage<TmpType> >averages(max_region_label);
//-----------------------------------------------------
// calculate the averages
Process_Set_Text(_TL("calculate averages"));
inspectTwoImages(srcImageRange(Input), srcImage(labels), averages);
//-----------------------------------------------------
// write the averages into the destination image (the functor 'averages' acts as a look-up table)
transformImage(srcImageRange(labels), destImage(Output), averages);
//-----------------------------------------------------
// mark the watersheds (region boundaries) black
if( bEdges )
{
regionImageToEdgeImage(srcImageRange(labels), destImage(Output), vigra::NumericTraits<typename TImage_Out::value_type>::zero());
}
}
void NETWORK::get_coordinates( double _z, double _dx, double _dy, std::vector<double>& _lrc, std::vector<double>& _x, std::vector<double>& _y ) const
{
/// create reachable set sizes
std::vector<double> rss( Order, 0.0 );
for(int i=0; i<Order; i++)
rss[i] = (double)Order * _lrc[i];
/// make levels
// sort local reaching centralities
std::vector<int> ids( Order, 0 );
for(int i=0; i<Order; i++)
ids[i] = i;
int len = Order;
double rss_elem;
int id;
bool swapped = false;
do
{
swapped = false;
for(int i=1; i<len; i++)
{
if( rss[i-1] > rss[i] )
{
rss_elem = rss[i-1];
rss[i-1] = rss[i];
rss[i] = rss_elem;
id = ids[i-1];
ids[i-1] = ids[i];
ids[i] = id;
swapped = true;
}
}
len--;
} while( swapped );
// network reaching centrality mean and variance
double global_av = 0.0;
double global_sd = 0.0;
double threshold = 0.0;
for(int i=0; i<Order; i++)
{
global_av += rss[i];
global_sd += rss[i]*rss[i];
}
global_av /= (double)Order;
global_sd = sqrt( fabs(global_sd/(double)Order - global_av*global_av) );
threshold = _z * global_sd + 0.00001; // in case of GRC = 0
// sort nodes in levels
int number_of_levels = 0;
int level_first_node = 0;
int current_node = 1;
std::vector<int> levels( Order, -1 );
levels[0] = 0;
// start putting nodes in level until we reach last node
while( current_node < Order )
{
// pick the next node and calculate level average and standard deviation
double level_av = 0.0;
double level_sd = 0.0;
for(int i=level_first_node; i<=current_node; i++)
{
level_av += rss[i];
level_sd += rss[i]*rss[i];
}
level_av /= 1 + current_node - level_first_node;
level_sd = sqrt( fabs(level_sd/double(1+current_node-level_first_node) - level_av*level_av) );
// if level deviation is lower than the threshold, keep node, otherwise start new level and put node there
if( level_sd < threshold )
{
levels[current_node] = number_of_levels;
current_node++;
}
else
{
levels[current_node] = number_of_levels + 1;
number_of_levels++;
level_first_node = current_node;
current_node++;
}
}
number_of_levels++;
/// set y coordinates
std::vector<int> nodes_per_level( number_of_levels, 0 );
// calculate level averages
std::vector<double> averages( number_of_levels, 0.0 );
for(int i=0; i<Order; i++)
{
averages[levels[i]] += rss[i];
nodes_per_level[levels[i]]++;
}
for(int i=0; i<number_of_levels; i++)
averages[i] /= nodes_per_level[i];
std::vector<double> y_differences( number_of_levels, 0.0 );
std::vector<double> y_coordinates( number_of_levels, 0.0 );
y_differences[0] = 0.0;
y_coordinates[0] = 0.0;
double minimum_difference = _dy * (double)Order;
for(int i=1; i<number_of_levels; i++)
{
y_differences[i] = log( averages[i]-averages[i-1] + 1.0 );
if( y_differences[i] < minimum_difference )
minimum_difference = y_differences[i];
}
for(int i=1; i<number_of_levels; i++)
y_coordinates[i] = y_coordinates[i-1] + _dy*y_differences[i]/minimum_difference;
_y.assign( Order, 0.0 );
for(int i=0; i<Order; i++)
_y[ids[i]] = y_coordinates[levels[i]];
/// set x coordinates
std::vector<double> x_coordinate_starts( number_of_levels, 0.0 );
for(int i=0; i<number_of_levels; i++)
{
x_coordinate_starts[i] = -0.5 * _dx * (nodes_per_level[i] - 1);
nodes_per_level[i] = 0;
}
_x.assign( Order, 0.0 );
for(int i=0; i<Order; i++)
{
_x[ids[i]] = x_coordinate_starts[levels[i]] + _dx * nodes_per_level[levels[i]];
nodes_per_level[levels[i]]++;
}
}