class TSpectrum3: public TNamed

THREE-DIMENSIONAL BACKGROUND ESTIMATION FUNCTIONS
This function calculates background spectrum from source spectrum.
The result is placed to the array pointed by spectrum pointer.

Function parameters:
spectrum-pointer to the array of source spectrum
ssizex-x length of spectrum
ssizey-y length of spectrum
ssizez-z length of spectrum
numberIterationsX-maximal x width of clipping window
numberIterationsY-maximal y width of clipping window
numberIterationsZ-maximal z width of clipping window
for details we refer to manual
direction- direction of change of clipping window
- possible values=kBackIncreasingWindow
kBackDecreasingWindow
filterType-determines the algorithm of the filtering
-possible values=kBackSuccessiveFiltering
kBackOneStepFiltering

Background estimation

 

Goal: Separation of useful information (peaks) from useless information (background)

•         method is based on Sensitive Nonlinear Iterative Peak (SNIP) clipping algorithm [1]

•         there exist two algorithms for the estimation of new value in the channel “”

 

Algorithm based on Successive Comparisons

It is an extension of one-dimensional SNIP algorithm to another dimension. For details we refer to [2].

 

Algorithm based on One Step Filtering

The algorithm is analogous to that for 2-dimensional data. For details we refer to TSpectrum2. New value in the estimated channel is calculated as

 

 

where p = 1, 2, …, number_of_iterations.

 

Function:

const char* TSpectrum3::Background (float ***fSpectrum, int fSizex, int fSizey, int fSizez, int fNumberIterationsX, int fNumberIterationsY, int fNumberIterationsZ,  int fDirection, int fFilterType) 

 

This function calculates background spectrum from the source spectrum.  The result is placed in the matrix pointed by fSpectrum pointer.  One can also switch the direction of the change of the clipping window and to select one of the two above given algorithms. On successful completion it returns 0. On error it returns pointer to the string describing error.

 

Parameters:

        fSpectrum-pointer to the matrix of source spectrum                 

        fSizex, fSizey, fSizez -lengths of the spectrum matrix                                

        fNumberIterationsX, fNumberIterationsY, fNumberIterationsZ maximal

        widths of clipping window,                                

        fDirection- direction of change of clipping window                 

               - possible values=kBackIncreasingWindow                     

                                            kBackDecreasingWindow                     

        fFilterType-type of the clipping algorithm,                              

                  -possible values=kBack SuccessiveFiltering

                                              kBackOneStepFiltering                             

 

References:

[1]  C. G Ryan et al.: SNIP, a statistics-sensitive background treatment for the quantitative analysis of PIXE spectra in geoscience applications. NIM, B34 (1988), 396-402.

[2]  M. Morháč, J. Kliman, V. Matoušek, M. Veselský, I. Turzo.: Background elimination methods for multidimensional gamma-ray spectra. NIM, A401 (1997) 113-132.

 

Example 1– script Back3.c :

 

Fig. 1 Original three-dimensional gamma-gamma-gamma-ray spectrum

Fig. 2 Background estimated from data from Fig. 1 using decreasing clipping window with widths 5, 5, 5 and algorithm based on successive comparisons. The estimate includes not only continuously changing background but also one- and two-dimensional ridges.

 

Fig. 3 Resulting peaks after subtraction of the estimated background (Fig. 2) from original three-dimensional gamma-gamma-gamma-ray spectrum (Fig. 1).

 

 

Script:

// Example to illustrate the background estimator (class TSpectrum3).

// To execute this example, do

// root > .x Back3.C

 

void Back3() {

   Int_t i, j, k;

   Int_t nbinsx = 64;

   Int_t nbinsy = 64;

   Int_t nbinsz = 64;  

   Int_t xmin  = 0;

   Int_t xmax  = nbinsx;

   Int_t ymin  = 0;

   Int_t ymax  = nbinsy;  

   Int_t zmin  = 0;

   Int_t zmax  = nbinsz;     

   float *** source = new float **[nbinsx];

   float *** dest = new float **[nbinsx];     

   for(i=0;i<nbinsx;i++){

      source[i]=new float* [nbinsy];

      for(j=0;j<nbinsy;j++)

         source[i][j]=new float [nbinsz];

   }          

   for(i=0;i<nbinsx;i++){

      dest[i]=new float* [nbinsy];

      for(j=0;j<nbinsy;j++)

         dest[i][j]=new float [nbinsz];

   }              

   TH3F *back = new TH3F("back","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax,nbinsz,zmin,zmax);

   TFile *f = new TFile("TSpectrum3.root");

   back=(TH3F*) f->Get("back;1");

   TCanvas *Background = new TCanvas("Background","Estimation of background with decreasing window",10,10,1000,700);

   TSpectrum3 *s = new TSpectrum3();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

                  for (k = 0; k < nbinsz; k++){

                       source[i][j][k] = back->GetBinContent(i + 1,j + 1,k + 1);

                       dest[i][j][k] = back->GetBinContent(i + 1,j + 1,k + 1);                     

                    }

                 }

   }

   s->Background(dest,nbinsx,nbinsy,nbinsz,5,5,5,s->kBackDecreasingWindow,s->kBackSuccessiveFiltering);

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

        for (k = 0; k < nbinsz; k++){

           back->SetBinContent(i + 1,j + 1,k + 1, dest[i][j][k]);

        }   

     }

   }

 

   FILE *out;

   char PATH[80];  

   strcpy(PATH,"spectra3\\back_output_5ds.spe");  

   out=fopen(PATH,"wb");

   for(i=0;i<nbinsx;i++){

      for(j=0;j<nbinsy;j++){                  

         fwrite(dest[i][j], sizeof(dest[0][0][0]),nbinsz,out);

      }

   }  

   fclose(out);  

  

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

        for (k = 0; k < nbinsz; k++){

           source[i][j][k] = source[i][j][k] - dest[i][j][k];

        }   

     }

   }

  

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

        for (k = 0; k < nbinsz; k++){

           back->SetBinContent(i + 1,j + 1,k + 1, source[i][j][k]);

        }   

     }

   }  

  

   strcpy(PATH,"spectra3\\back_peaks_5ds.spe");  

   out=fopen(PATH,"wb");

   for(i=0;i<nbinsx;i++){

      for(j=0;j<nbinsy;j++){                  

         fwrite(source[i][j], sizeof(source[0][0][0]),nbinsz,out);

      }

   }  

   fclose(out);     

  

   back->Draw(""); 

}

 

 

THREE-DIMENSIONAL MARKOV SPECTRUM SMOOTHING FUNCTION

This function calculates smoothed spectrum from source spectrum
based on Markov chain method.
The result is placed in the array pointed by spectrum pointer.

Function parameters:
source-pointer to the array of source spectrum
working_space-pointer to the working array
ssizex-x length of spectrum and working space arrays
ssizey-y length of spectrum and working space arrays
ssizey-z length of spectrum and working space arrays
averWindow-width of averaging smoothing window

Smoothing

 

Goal: Suppression of statistical fluctuations

•         the algorithm is based on discrete Markov chain, which has very simple invariant distribution

 

                 

          being defined from the normalization condition

         n is the length of the smoothed spectrum and

 

 

 

is the probability of the change of the peak position from channel i to the channel i+1.  is the normalization constant so that  and m is a width of smoothing window. We have extended this algorithm to three dimensions.

 

Function:

const char* TSpectrum3::SmoothMarkov(float ***fSpectrum, int fSizex, int fSizey, int fSizey,  int fAverWindow) 

 

This function calculates smoothed spectrum from the source spectrum based on Markov chain method. The result is placed in the field pointed by source pointer. On successful completion it returns 0. On error it returns pointer to the string describing error.

 

Parameters:

        fSpectrum-pointer to the matrix of source spectrum                 

        fSizex, fSizey, fSizez -lengths of the spectrum matrix                                 

        fAverWindow-width of averaging smoothing window

 

Reference:

[1] Z.K. Silagadze, A new algorithm for automatic photopeak searches. NIM A 376 (1996), 451. 

 

Example 1 – script SmootMarkov3.c :

Fig. 1 Original noisy spectrum.   

Fig. 2 Smoothed spectrum with averaging window m=3.

 

Script:

// Example to illustrate the Markov smoothing (class TSpectrum3).

// To execute this example, do

// root > .x SmoothMarkov3.C

 

void SmoothMarkov3() {

   Int_t i, j, k;

   Int_t nbinsx = 64;

   Int_t nbinsy = 64;

   Int_t nbinsz = 64;  

   Int_t xmin  = 0;

   Int_t xmax  = nbinsx;

   Int_t ymin  = 0;

   Int_t ymax  = nbinsy;  

   Int_t zmin  = 0;

   Int_t zmax  = nbinsz;     

   float *** source = new float **[nbinsx];

   for(i=0;i<nbinsx;i++){

      source[i]=new float* [nbinsy];

      for(j=0;j<nbinsy;j++)

         source[i][j]=new float [nbinsz];

   }          

   TH3F *sm = new TH3F("Smoothing","Markov smoothing",nbinsx,xmin,xmax,nbinsy,ymin,ymax,nbinsz,zmin,zmax);

   TFile *f = new TFile("TSpectrum3.root");

   sm=(TH3F*) f->Get("back;1");

   TCanvas *Background = new TCanvas("Smoothing","Markov smoothing",10,10,1000,700);

   TSpectrum3 *s = new TSpectrum3();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

                  for (k = 0; k < nbinsz; k++){

                       source[i][j][k] = sm->GetBinContent(i + 1,j + 1,k + 1);

                    }

                 }

   }

   s->SmoothMarkov(source,nbinsx,nbinsy,nbinsz,3);

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

        for (k = 0; k < nbinsz; k++){

           sm->SetBinContent(i + 1,j + 1,k + 1, source[i][j][k]);

        }   

     }

   }

   sm->Draw(""); 

}

THREE-DIMENSIONAL DECONVOLUTION FUNCTION
This function calculates deconvolution from source spectrum
according to response spectrum
The result is placed in the cube pointed by source pointer.

Function parameters:
source-pointer to the cube of source spectrum
resp-pointer to the cube of response spectrum
ssizex-x length of source and response spectra
ssizey-y length of source and response spectra
ssizey-y length of source and response spectra
numberIterations, for details we refer to manual
numberRepetitions, for details we refer to manual
boost, boosting factor, for details we refer to manual

Deconvolution

 

Goal: Improvement of the resolution in spectra, decomposition of multiplets

 

Mathematical formulation of the 3-dimensional convolution system is

 

 

 

 

where h(i,j,k) is the impulse response function, x, y are input and output fields, respectively, , are the lengths of x and h fields

•         let us assume that we know the response and the output fields (spectra) of the above given system.

•         the deconvolution represents solution of the overdetermined system of linear equations, i.e.,  the calculation of the field x.

•         from numerical stability point of view the operation of deconvolution is extremely critical (ill-posed  problem) as well as time consuming operation.

•         the Gold deconvolution algorithm proves to work very well even for 2-dimensional systems. Generalization of the algorithm for 2-dimensional systems was presented in [1], and for multidimensional systems in [2].

•         for Gold deconvolution algorithm as well as for boosted deconvolution algorithm we refer also to TSpectrum and TSpectrum2

 

Function:

const char* TSpectrum3::Deconvolution(float ***fSource, const float ***fResp, int fSizex, int fSizey, int fSizez, int fNumberIterations, int fNumberRepetitions, double fBoost)

 

This function calculates deconvolution from source spectrum according to response spectrum using Gold deconvolution algorithm. The result is placed in the field pointed by source pointer. On successful completion it returns 0. On error it returns pointer to the string describing error. If desired after every fNumberIterations one can apply boosting operation (exponential function with exponent given by fBoost coefficient) and repeat it fNumberRepetitions times.

 

Parameters:

        fSource-pointer to the matrix of source spectrum                 

        fResp-pointer to the matrix of response spectrum                 

        fSizex, fSizey, fSizez -lengths of the spectrum matrix                                

        fNumberIterations-number of iterations

        fNumberRepetitions-number of repetitions for boosted deconvolution. It must be

        greater or equal to one.

        fBoost-boosting coefficient, applies only if fNumberRepetitions is greater than one. 

        Recommended range <1,2>.

 

References:

 [1] M. Morháč, J. Kliman, V. Matoušek, M. Veselský, I. Turzo.: Efficient one- and two-dimensional Gold deconvolution and its application to gamma-ray spectra decomposition. NIM, A401 (1997) 385-408.

[2] Morháč M., Matoušek V., Kliman J., Efficient algorithm of multidimensional deconvolution and its application to nuclear data processing, Digital Signal Processing 13 (2003) 144.

 

Example 1 – script Decon.c :

•         response function (usually peak) should be shifted to the beginning of the coordinate system (see Fig. 1)

Fig. 1 Three-dimensional response spectrum

 

 

Fig. 2 Three-dimensional input spectrum (before deconvolution)

 

Fig. 3 Spectrum from Fig. 2 after deconvolution (100 iterations)

 

Script:

// Example to illustrate the Gold deconvolution (class TSpectrum3).

// To execute this example, do

// root > .x Decon3.C

 

#include <TSpectrum3>

 

void Decon3() {

   Int_t i, j, k;

   Int_t nbinsx = 32;

   Int_t nbinsy = 32;

   Int_t nbinsz = 32;  

   Int_t xmin  = 0;

   Int_t xmax  = nbinsx;

   Int_t ymin  = 0;

   Int_t ymax  = nbinsy;  

   Int_t zmin  = 0;

   Int_t zmax  = nbinsz;     

   float *** source = new float **[nbinsx];

   float *** resp = new float **[nbinsx];     

   for(i=0;i<nbinsx;i++){

      source[i]=new float* [nbinsy];

      for(j=0;j<nbinsy;j++)

         source[i][j]=new float [nbinsz];

   }          

   for(i=0;i<nbinsx;i++){

      resp[i]=new float* [nbinsy];

      for(j=0;j<nbinsy;j++)

         resp[i][j]=new float [nbinsz];

   }              

   TH3F *decon_in = new TH3F("decon_in","Deconvolution",nbinsx,xmin,xmax,nbinsy,ymin,ymax,nbinsz,zmin,zmax);

   TH3F *decon_resp = new TH3F("decon_resp","Deconvolution",nbinsx,xmin,xmax,nbinsy,ymin,ymax,nbinsz,zmin,zmax);  

   TFile *f = new TFile("TSpectrum3.root");

   decon_in=(TH3F*) f->Get("decon_in;1");

   decon_resp=(TH3F*) f->Get("decon_resp;1");  

   TCanvas *Deconvolution = new TCanvas("Deconvolution","Deconvolution of 3-dimensional spectra",10,10,1000,700);

   TSpectrum3 *s = new TSpectrum3();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

                  for (k = 0; k < nbinsz; k++){

                       source[i][j][k] = decon_in->GetBinContent(i + 1,j + 1,k + 1);

                       resp[i][j][k] = decon_resp->GetBinContent(i + 1,j + 1,k + 1);                        

                    }

                 }

   }

   s->Deconvolution(source,resp,nbinsx,nbinsy,nbinsz,100,1,1);

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

        for (k = 0; k < nbinsz; k++){

           decon_in->SetBinContent(i + 1,j + 1,k + 1, source[i][j][k]);

        }   

     }

   }

   decon_in->Draw(""); 

}

 

Example 2 – script Decon_hr.c :

This example illustrates repeated Gold deconvolution with boosting. After every 10 iterations we apply power function with exponent = 2 to the spectrum given in Fig. 2.

 

Fig. 4 Spectrum from Fig. 2 after boosted deconvolution (10 iterations repeated 10 times). It decomposes completely cluster of peaks from Fig 2.

 

Script:

// Example to illustrate the Gold deconvolution (class TSpectrum3).

// To execute this example, do

// root > .x Decon3_hr.C

void Decon3_hr() {

   Int_t i, j, k;

   Int_t nbinsx = 32;

   Int_t nbinsy = 32;

   Int_t nbinsz = 32;  

   Int_t xmin  = 0;

   Int_t xmax  = nbinsx;

   Int_t ymin  = 0;

   Int_t ymax  = nbinsy;  

   Int_t zmin  = 0;

   Int_t zmax  = nbinsz;     

   float *** source = new float **[nbinsx];

   float *** resp = new float **[nbinsx];     

   for(i=0;i<nbinsx;i++){

      source[i]=new float* [nbinsy];

      for(j=0;j<nbinsy;j++)

         source[i][j]=new float [nbinsz];

   }          

   for(i=0;i<nbinsx;i++){

      resp[i]=new float* [nbinsy];

      for(j=0;j<nbinsy;j++)

         resp[i][j]=new float [nbinsz];

   }              

   TH3F *decon_in = new TH3F("decon_in","Deconvolution",nbinsx,xmin,xmax,nbinsy,ymin,ymax,nbinsz,zmin,zmax);

   TH3F *decon_resp = new TH3F("decon_resp","Deconvolution",nbinsx,xmin,xmax,nbinsy,ymin,ymax,nbinsz,zmin,zmax);  

   TFile *f = new TFile("TSpectrum3.root");

   decon_in=(TH3F*) f->Get("decon_in;1");

   decon_resp=(TH3F*) f->Get("decon_resp;1");  

   TCanvas *Deconvolution = new TCanvas("Deconvolution","High resolution deconvolution of 3-dimensional spectra",10,10,1000,700);

   TSpectrum3 *s = new TSpectrum3();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

                  for (k = 0; k < nbinsz; k++){

                       source[i][j][k] = decon_in->GetBinContent(i + 1,j + 1,k + 1);

                       resp[i][j][k] = decon_resp->GetBinContent(i + 1,j + 1,k + 1);                        

                    }

                 }

   }

   s->Deconvolution(source,resp,nbinsx,nbinsy,nbinsz,10,10,2);

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

        for (k = 0; k < nbinsz; k++){

           decon_in->SetBinContent(i + 1,j + 1,k + 1, source[i][j][k]);

        }   

     }

   }

   decon_in->Draw(""); 

}

 

 

THREE-DIMENSIONAL HIGH-RESOLUTION PEAK SEARCH FUNCTION
This function searches for peaks in source spectrum
It is based on deconvolution method. First the background is
removed (if desired), then Markov spectrum is calculated
(if desired), then the response function is generated
according to given sigma and deconvolution is carried out.
It returns number of found peaks.

Function parameters:
source-pointer to the matrix of source spectrum
dest-pointer to the matrix of resulting deconvolved spectrum
ssizex-x length of source spectrum
ssizey-y length of source spectrum
ssizez-z length of source spectrum
sigma-sigma of searched peaks, for details we refer to manual
threshold-threshold value in % for selected peaks, peaks with
amplitude less than threshold*highest_peak/100
are ignored, see manual
backgroundRemove-logical variable, set if the removal of
background before deconvolution is desired
deconIterations-number of iterations in deconvolution operation
markov-logical variable, if it is true, first the source spectrum
is replaced by new spectrum calculated using Markov
chains method.
averWindow-averanging window of searched peaks, for details
we refer to manual (applies only for Markov method)

Peaks searching

 

Goal: to identify automatically the peaks in spectrum with the presence of the continuous background, one- and two-fold coincidences (ridges) and statistical fluctuations - noise.

 

The common problems connected with correct peak identification in three-dimensional coincidence spectra are

• non-sensitivity to noise, i.e., only statistically relevant peaks should be identified
• non-sensitivity of the algorithm to continuous background
• non-sensitivity to one-fold coincidences (coincidences peak – peak – background in all dimensions) and their crossings
• non-sensitivity to two-fold coincidences (coincidences peak – background – background in all dimensions) and their crossings
• ability to identify peaks close to the edges of the spectrum region
• resolution, decomposition of doublets and multiplets. The algorithm should be able to recognize close positioned peaks.

 

Function:

Int_t TSpectrum3::SearchHighRes (const float ***fSource,float ***fDest, int fSizex, int fSizey, int fSizez, float fSigma, double fThreshold, bool fBackgroundRemove,int fDeconIterations, bool fMarkov, int fAverWindow)   

 

This function searches for peaks in source spectrum. It is based on deconvolution method. First the background is removed (if desired), then Markov smoothed spectrum is calculated (if desired), then the response function is generated according to given sigma and deconvolution is carried out. On success it returns number of found peaks.

 

Parameters:

        fSource-pointer to the matrix of source spectrum                 

        fDest-resulting spectrum after deconvolution

        fSizex, fSizey, fSizez -lengths of the source and destination spectra               

        fSigma-sigma of searched peaks

fThreshold- threshold value in % for selected peaks, peaks with amplitude less than threshold*highest_peak/100 are ignored

fBackgroundRemove- background_remove-logical variable, true if the removal of background before deconvolution is desired 

fDeconIterations-number of iterations in deconvolution operation

fMarkov-logical variable, if it is true, first the source spectrum is replaced by new spectrum calculated using Markov chains method

fAverWindow-width of averaging smoothing window

 

References:

[1] M.A. Mariscotti: A method for identification of peaks in the presence of background and its application to spectrum analysis. NIM 50 (1967), 309-320.

[2]  M. Morháč, J. Kliman, V. Matoušek, M. Veselský, I. Turzo.:Identification of peaks in multidimensional coincidence gamma-ray spectra. NIM, A443 (2000) 108-125.

[3] Z.K. Silagadze, A new algorithm for automatic photopeak searches. NIM A 376 (1996), 451.

 

Example of peak searching method

 

SearchHighRes function provides users with the possibility to vary the input parameters and with the access to the output deconvolved data in the destination spectrum. Based on the output data one can tune the parameters.

Example 1 – script Search3.c:

 

Fig. 1 Three-dimensional spectrum with 5 peaks (, threshold=5%, 3 iterations steps in the deconvolution)

 

Fig. 2 Spectrum from Fig. 1 after background elimination and deconvolution

 

Script:

// Example to illustrate high resolution peak searching function (class TSpectrum3).

// To execute this example, do

// root > .x Search3.C

void Search3() {

   Int_t i, j, k, nfound;

   Int_t nbinsx = 32;

   Int_t nbinsy = 32;

   Int_t nbinsz = 32;  

   Int_t xmin  = 0;

   Int_t xmax  = nbinsx;

   Int_t ymin  = 0;

   Int_t ymax  = nbinsy;  

   Int_t zmin  = 0;

   Int_t zmax  = nbinsz;     

   float *** source = new float **[nbinsx];

   float *** dest = new float **[nbinsx];     

   for(i=0;i<nbinsx;i++){

      source[i]=new float* [nbinsy];

      for(j=0;j<nbinsy;j++)

         source[i][j]=new float [nbinsz];

   }          

   for(i=0;i<nbinsx;i++){

      dest[i]=new float* [nbinsy];

      for(j=0;j<nbinsy;j++)

         dest[i][j]=new float [nbinsz];

   }              

   TH3F *search = new TH3F("Search","Peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax,nbinsz,zmin,zmax);

   TFile *f = new TFile("TSpectrum3.root");

   search=(TH3F*) f->Get("search2;1");  

   TCanvas *Search = new TCanvas("Search","Peak searching",10,10,1000,700);

   TSpectrum3 *s = new TSpectrum3();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

                  for (k = 0; k < nbinsz; k++){

                       source[i][j][k] = search->GetBinContent(i + 1,j + 1,k + 1);

                    }

                 }

   }

   nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, nbinsz, 2, 5, kTRUE, 3, kFALSE, 3);  

   printf("Found %d candidate peaks\n",nfound);  

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

        for (k = 0; k < nbinsz; k++){

           search->SetBinContent(i + 1,j + 1,k + 1, dest[i][j][k]);

        }   

     }

   }

   Float_t *PosX = new Float_t[nfound];        

   Float_t *PosY = new Float_t[nfound];

   Float_t *PosZ = new Float_t[nfound];     

   PosX = s->GetPositionX();

   PosY = s->GetPositionY();        

   PosZ = s->GetPositionZ();           

   for(i=0;i<nfound;i++)

                    printf("posx= %d, posy= %d, posz= %d\n",(int)(PosX[i]+0.5), (int)(PosY[i]+0.5), (int)(PosZ[i]+0.5));          

   search->Draw(""); 

}