class TSpectrum2: public TNamed

TWO-DIMENSIONAL BACKGROUND ESTIMATION FUNCTION - RECTANGULAR RIDGES
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
numberIterationsX-maximal x width of clipping window
numberIterationsY-maximal y 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

New value in the estimated channel is calculated as

 

 

 

.

 

where p = 1, 2, …, number_of_iterations.

 

Function:

const char* TSpectrum2::Background (float **spectrum, int ssizex, int ssizey, int numberIterationsX, int numberIterationsY, int direction, int filterType) 

 

This function calculates background spectrum from the source spectrum.  The result is placed in the matrix pointed by spectrum 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:

        spectrum-pointer to the matrix of source spectrum                 

        ssizex, ssizey-lengths of the spectrum matrix                                

        numberIterationsX, numberIterationsYmaximal widths of clipping

        window,                                

        direction- direction of change of clipping window                 

               - possible values=kBackIncreasingWindow                     

                                            kBackDecreasingWindow                     

        filterType-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 Back_gamma64.c :

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

Fig. 2 Background estimated from data from Fig. 1 using decreasing clipping window with widths 4, 4 and algorithm based on successive comparisons. The estimate includes not only continuously changing background but also one-dimensional ridges.

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

 

 

Script:

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

// To execute this example, do

// root > .x Back_gamma64.C

 

#include <TSpectrum>

 

void Back_gamma64() {

   Int_t i, j;

   Double_t nbinsx = 64;

   Double_t nbinsy = 64;  

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbinsx;

   Double_t ymin  = 0;

   Double_t ymax  = (Double_t)nbinsy;  

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

   for (i=0;i<nbinsx;i++)

      source[i]=new float[nbinsy];    

   TH2F *back = new TH2F("back","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   TFile *f = new TFile("spectra2\\TSpectrum2.root");

   back=(TH2F*) f->Get("back1;1");

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

   TSpectrum *s = new TSpectrum();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }     

 s->Background(source,nbinsx,nbinsy,4,4,kBackDecreasingWindow,kBackSuccessiveFiltering);

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++)

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

   }

   back->Draw("SURF"); 

   }

 

Example 2– script Back_gamma256.c :

Fig. 4 Original two-dimensional gamma-gamma-ray spectrum 256x256 channels

Fig. 5 Peaks after subtraction of the estimated background (increasing clipping window with widths 8, 8 and algorithm based on successive comparisons) from original two-dimensional gamma-gamma-ray spectrum (Fig. 4).

 

Script:

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

// To execute this example, do

// root > .x Back_gamma256.C

 

#include <TSpectrum>

 

void Back_gamma256() {

   Int_t i, j;

   Double_t nbinsx = 64;

   Double_t nbinsy = 64;  

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbinsx;

   Double_t ymin  = 0;

   Double_t ymax  = (Double_t)nbinsy;  

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

   for (i=0;i<nbinsx;i++)

      source[i]=new float[nbinsy];    

   TH2F *back = new TH2F("back","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   TFile *f = new TFile("spectra2\\TSpectrum2.root");

   back=(TH2F*) f->Get("back2;1");

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

   TSpectrum *s = new TSpectrum();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }     

 s->Background(source,nbinsx,nbinsy,8,8,kBackIncreasingWindow,kBackSuccessiveFiltering);

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++)

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

   }

   back->Draw("SURF"); 

   }

Example 3– script Back_synt256.c :

Fig. 6 Original two-dimensional synthetic spectrum 256x256 channels

Fig. 7 Peaks after subtraction of the estimated background (increasing clipping window with widths 8, 8 and algorithm based on successive comparisons) from original two-dimensional gamma-gamma-ray spectrum (Fig. 6). One can observe artifacts (ridges) around the peaks due to the employed algorithm.

Fig. 8 Peaks after subtraction of the estimated background (increasing clipping window with widths 8, 8 and algorithm based on one step filtering) from original two-dimensional gamma-gamma-ray spectrum (Fig. 6).  The artifacts from the above given Fig. 7 disappeared.

 

Script:

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

// To execute this example, do

// root > .x Back_synt256.C

 

#include <TSpectrum>

 

void Back_synt256() {

   Int_t i, j;

   Double_t nbinsx = 64;

   Double_t nbinsy = 64;  

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbinsx;

   Double_t ymin  = 0;

   Double_t ymax  = (Double_t)nbinsy;  

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

   for (i=0;i<nbinsx;i++)

      source[i]=new float[nbinsy];    

   TH2F *back = new TH2F("back","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   TFile *f = new TFile("spectra2\\TSpectrum2.root");

   back=(TH2F*) f->Get("back3;1");

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

   TSpectrum *s = new TSpectrum();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }     

 s->Background(source,nbinsx,nbinsy,8,8,kBackIncreasingWindow,kBackSuccessiveFiltering);//kBackOneStepFiltering

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++)

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

   }

   back->Draw("SURF"); 

   }

   TWO-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 source pointer.

   Function parameters:
   source-pointer to the array of source spectrum
   ssizex-x length of source
   ssizey-y length of source
   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 algortihm to two dimensions.

 

Function:

const char* TSpectrum2::SmoothMarkov(float **fSpectrum, int ssizex, int ssizey,  int averWindow) 

 

This function calculates smoothed spectrum from the source spectrum based on Markov chain method. The result is placed in the vector 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                 

        ssizex, ssizey -lengths of the spectrum matrix                                

        averWindow-width of averaging smoothing window

 

Reference:

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

Example 4 – script Smooth.c :

Fig. 9 Original noisy spectrum.    Fig. 10 Smoothed spectrum m=3

Peaks can hardly be observed.     Peaks become apparent.

Fig. 11 Smoothed spectrum m=5 Fig.12 Smoothed spectrum m=7

 

Script:

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

// To execute this example, do

// root > .x Smooth.C

#include <TSpectrum>

void Smooth() {

   Int_t i, j;

   Double_t nbinsx = 256;

   Double_t nbinsy = 256;  

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbinsx;

   Double_t ymin  = 0;

   Double_t ymax  = (Double_t)nbinsy;  

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

   for (i=0;i<nbinsx;i++)

                                    source[i]=new float[nbinsy];    

   TH2F *smooth = new TH2F("smooth","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   TFile *f = new TFile("spectra2\\TSpectrum2.root");

   smooth=(TH2F*) f->Get("smooth1;1");

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

   TSpectrum *s = new TSpectrum();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }

   s->SmoothMarkov(source,nbinsx,nbinsx,3);//5,7

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++)

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

   }

   smooth->Draw("SURF"); 

   }

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

   Function parameters:
   source-pointer to the matrix of source spectrum
   resp-pointer to the matrix of response spectrum
   ssizex-x 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 2-dimensional convolution system is

 

 

 

 

 

 

 

 

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

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

•         the deconvolution represents solution of the overdetermined system of linear equations, i.e.,  the calculation of the matrix 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], [2].

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

 

Function:

const char* TSpectrum2::Deconvolution(float **source, const float **resp, int ssizex, int ssizey, int numberIterations, int numberRepetitions, double boost)

 

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

 

Parameters:

        source-pointer to the matrix of source spectrum                 

        resp-pointer to the matrix of response spectrum                 

        ssizex, ssizey-lengths of the spectrum matrix                                

        numberIterations-number of iterations

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

        greater or equal to one.

        boost-boosting coefficient, applies only if numberRepetitions 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 5 – script Decon.c :

•         response function (usually peak) should be shifted to the beginning of the coordinate system (see Fig. 13)

 

Fig. 13 2-dimensional response spectrum

Fig. 14 2-dimensional gamma-gamma-ray input spectrum (before deconvolution)

Fig. 15 Spectrum from Fig. 14 after deconvolution (1000 iterations)

 

Script:

// Example to illustrate the Gold deconvolution (class TSpectrum2).

// To execute this example, do

// root > .x Decon.C

 

#include <TSpectrum2>

 

void Decon() {

   Int_t i, j;

   Double_t nbinsx = 256;

   Double_t nbinsy = 256;  

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbinsx;

   Double_t ymin  = 0;

   Double_t ymax  = (Double_t)nbinsy;  

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

   for (i=0;i<nbinsx;i++)

                                    source[i]=new float[nbinsy];    

   TH2F *decon = new TH2F("decon","Gold deconvolution",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   TFile *f = new TFile("spectra2\\TSpectrum2.root");

   decon=(TH2F*) f->Get("decon1;1");

   Float_t ** response = new float *[nbinsx];  

   for (i=0;i<nbinsx;i++)

                                    response[i]=new float[nbinsy];    

   TH2F *resp = new TH2F("resp","Response matrix",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   resp=(TH2F*) f->Get("resp1;1");  

   TCanvas *Deconvol = new TCanvas("Deconvolution","Gold deconvolution",10,10,1000,700);

   TSpectrum *s = new TSpectrum();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }  

   s->Deconvolution(source,response,nbinsx,nbinsy,1000,1,1);  

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++)

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

   }

  

   decon->Draw("SURF"); 

   }

Example 6 – script Decon2.c :

Fig. 16 Response spectrum

Fig. 17 Original synthetic input spectrum (before deconvolution). It is composed of 17 peaks. 5 peaks are overlapping in the outlined multiplet and two peaks in doublet.

Fig. 18 Spectrum from Fig. 17 after deconvolution (1000 iterations). Resolution is improved but the peaks in multiplet remained unresolved.

Script:

// Example to illustrate the Gold deconvolution (class TSpectrum2).

// To execute this example, do

// root > .x Decon2.C

 

#include <TSpectrum2>

 

void Decon2() {

   Int_t i, j;

   Double_t nbinsx = 64;

   Double_t nbinsy = 64;  

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbinsx;

   Double_t ymin  = 0;

   Double_t ymax  = (Double_t)nbinsy;  

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

   for (i=0;i<nbinsx;i++)

                                    source[i]=new float[nbinsy];    

   TH2F *decon = new TH2F("decon","Gold deconvolution",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   TFile *f = new TFile("spectra2\\TSpectrum2.root");

   decon=(TH2F*) f->Get("decon2;1");

   Float_t ** response = new float *[nbinsx];  

   for (i=0;i<nbinsx;i++)

                                    response[i]=new float[nbinsy];    

   TH2F *resp = new TH2F("resp","Response matrix",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   resp=(TH2F*) f->Get("resp2;1");  

   TCanvas *Deconvol = new TCanvas("Deconvolution","Gold deconvolution",10,10,1000,700);

   TSpectrum *s = new TSpectrum();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }  

   s->Deconvolution(source,response,nbinsx,nbinsy,1000,1,1);  

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++)

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

   }

   decon->Draw("SURF"); 

   }

Example 7 – script Decon2HR.c :

Fig. 19 Spectrum from Fig. 17 after boosted deconvolution (50 iterations repeated 20 times, boosting coefficient was 1.2). All the peaks in multiplet as well as in doublet are completely decomposed.

Script:

// Example to illustrate boosted Gold deconvolution (class TSpectrum2).

// To execute this example, do

// root > .x Decon2HR.C

 

//#include <TSpectrum2>

 

void Decon2HR() {

   Int_t i, j;

   Double_t nbinsx = 64;

   Double_t nbinsy = 64;  

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbinsx;

   Double_t ymin  = 0;

   Double_t ymax  = (Double_t)nbinsy;  

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

   for (i=0;i<nbinsx;i++)

                                    source[i]=new float[nbinsy];    

   TH2F *decon = new TH2F("decon","Boosted Gold deconvolution",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   TFile *f = new TFile("spectra2\\TSpectrum2.root");

   decon=(TH2F*) f->Get("decon2;1");

   Float_t ** response = new float *[nbinsx];  

   for (i=0;i<nbinsx;i++)

                                    response[i]=new float[nbinsy];    

   TH2F *resp = new TH2F("resp","Response matrix",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   resp=(TH2F*) f->Get("resp2;1");  

   TCanvas *Deconvol = new TCanvas("Deconvolution","Gold deconvolution",10,10,1000,700);

   TSpectrum *s = new TSpectrum();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }  

   s->Deconvolution(source,response,nbinsx,nbinsy,1000,1,1);  

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++)

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

   }

   decon->Draw("SURF"); 

   }

 

TWO-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.

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
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-fold coincidences (ridges) and statistical fluctuations - noise.

 

The common problems connected with correct peak identification in two-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 – background in both dimensions) and their crossings
• ability to identify peaks close to the edges of the spectrum region. Usually peak finders fail to detect them
• resolution, decomposition of doublets and multiplets. The algorithm should be able to recognize close positioned peaks.
• ability to identify peaks with different sigma

 

Function:

Int_t TSpectrum2::SearchHighRes (float **source,float **dest, int ssizex, int ssizey, float sigma, double threshold, bool backgroundRemove,int deconIterations, bool markov, int averWindow)   

 

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. The order of peaks is arranged according to their heights in the spectrum after background elimination. The highest peak is the first in the list. On success it returns number of found peaks.

 

Parameters:

        source-pointer to the matrix of source spectrum                 

        dest-resulting spectrum after deconvolution

        ssizex, ssizey-lengths of the source and destination spectra               

        sigma-sigma of searched peaks

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

backgroundRemove- background_remove-logical variable, true 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-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.

Examples 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 8 – script Src.c:

Fig. 20 Two-dimensional spectrum with found peaks denoted by markers (, threshold=5%, 3 iterations steps in the deconvolution)

Fig. 21 Spectrum from Fig. 20 after background elimination and deconvolution

Script:

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

// To execute this example, do

// root > .x Src.C

 

#include <TSpectrum2>

 

void Src() {

   Int_t i, j, nfound;

   Double_t nbinsx = 64;

   Double_t nbinsy = 64;  

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbinsx;

   Double_t ymin  = 0;

   Double_t ymax  = (Double_t)nbinsy;  

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

   for (i=0;i<nbinsx;i++)

                                    source[i]=new float[nbinsy];

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

   for (i=0;i<nbinsx;i++)

                                    dest[i]=new float[nbinsy];

   TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   TFile *f = new TFile("spectra2\\TSpectrum2.root");

   search=(TH2F*) f->Get("search4;1");

   TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);

   TSpectrum2 *s = new TSpectrum2();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }  

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

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

   for(i=0;i<nfound;i++)

             printf("posx= %d, posy= %d, value= %d\n",(int)(fPositionX[i]+0.5), (int)(fPositionY[i]+0.5), (int)source[(int)(fPositionX[i]+0.5)][(int)(fPositionY[i]+0.5)]);       

}

Example 9 – script Src2.c:

Fig. 22 Two-dimensional noisy spectrum with found peaks denoted by markers (, threshold=10%, 10 iterations steps in the deconvolution). One can observe that the algorithm is insensitive to the crossings of one-dimensional ridges. It identifies only two-cooincidence peaks.

Fig. 23 Spectrum from Fig. 22 after background elimination and deconvolution

 

Script:

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

// To execute this example, do

// root > .x Src2.C

 

#include <TSpectrum2>

 

void Src2() {

   Int_t i, j, nfound;

   Double_t nbinsx = 256;

   Double_t nbinsy = 256;  

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbinsx;

   Double_t ymin  = 0;

   Double_t ymax  = (Double_t)nbinsy;  

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

   for (i=0;i<nbinsx;i++)

                                    source[i]=new float[nbinsy];

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

   for (i=0;i<nbinsx;i++)

                                    dest[i]=new float[nbinsy];

   TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   TFile *f = new TFile("spectra2\\TSpectrum2.root");

   search=(TH2F*) f->Get("back3;1");

   TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);

   TSpectrum2 *s = new TSpectrum2();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }  

   nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 2, 10, kTRUE, 10, kFALSE, 3);  

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

   for(i=0;i<nfound;i++)

             printf("posx= %d, posy= %d, value= %d\n",(int)(fPositionX[i]+0.5), (int)(fPositionY[i]+0.5), (int)source[(int)(fPositionX[i]+0.5)][(int)(fPositionY[i]+0.5)]);       

}

Example 10 – script Src3.c:

Fig. 24 Two-dimensional spectrum with 15 found peaks denoted by markers. Some peaks are positioned close to each other. It is necessary to increase number of iterations in the deconvolution. In next 3 Figs. we shall study the influence of this parameter.

Fig. 25 Spectrum from Fig. 24 after deconvolution (# of iterations = 3). Number of identified peaks = 13.

Fig. 26 Spectrum from Fig. 24 after deconvolution (# of iterations = 10). Number of identified peaks = 13.

Fig. 27 Spectrum from Fig. 24 after deconvolution (# of iterations = 100). Number of identified peaks = 15. Now the algorithm is able to decompose two doublets in the spectrum.

 

Script:

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

// To execute this example, do

// root > .x Src3.C

 

#include <TSpectrum2>

 

void Src3() {

   Int_t i, j, nfound;

   Double_t nbinsx = 64;

   Double_t nbinsy = 64;  

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbinsx;

   Double_t ymin  = 0;

   Double_t ymax  = (Double_t)nbinsy;  

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

   for (i=0;i<nbinsx;i++)

                                    source[i]=new float[nbinsy];

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

   for (i=0;i<nbinsx;i++)

                                    dest[i]=new float[nbinsy];

   TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   TFile *f = new TFile("spectra2\\TSpectrum2.root");

   search=(TH2F*) f->Get("search1;1");

   TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);

   TSpectrum2 *s = new TSpectrum2();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }  

   nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 2, 2, kFALSE, 3, kFALSE, 1);//3, 10, 100  

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

 

   for(i=0;i<nfound;i++)

             printf("posx= %d, posy= %d, value= %d\n",(int)(fPositionX[i]+0.5), (int)(fPositionY[i]+0.5), (int)source[(int)(fPositionX[i]+0.5)][(int)(fPositionY[i]+0.5)]);       

}

Example 11 – script Src4.c:

Fig. 28 Two-dimensional spectrum with peaks with different sigma denoted by markers (, threshold=5%, 10 iterations steps in the deconvolution, Markov smoothing with window=3)

Fig. 29 Spectrum from Fig. 28 after smoothing and deconvolution.

 

Script:

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

// To execute this example, do

// root > .x Src4.C

 

#include <TSpectrum2>

 

void Src4() {

   Int_t i, j, nfound;

   Double_t nbinsx = 64;

   Double_t nbinsy = 64;  

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbinsx;

   Double_t ymin  = 0;

   Double_t ymax  = (Double_t)nbinsy;  

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

   for (i=0;i<nbinsx;i++)

                                    source[i]=new float[nbinsy];

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

   for (i=0;i<nbinsx;i++)

                                    dest[i]=new float[nbinsy];

   TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   TFile *f = new TFile("spectra2\\TSpectrum2.root");

   search=(TH2F*) f->Get("search2;1");

   TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);

   TSpectrum2 *s = new TSpectrum2();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }  

   nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 3, 5, kFALSE, 10, kTRUE, 3);  

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

   for(i=0;i<nfound;i++)

             printf("posx= %d, posy= %d, value= %d\n",(int)(fPositionX[i]+0.5), (int)(fPositionY[i]+0.5), (int)source[(int)(fPositionX[i]+0.5)][(int)(fPositionY[i]+0.5)]);       

}

Example 12 – script Src5.c:

Fig. 30 Two-dimensional spectrum with peaks positioned close to the edges denoted by markers (, threshold=5%, 10 iterations steps in the deconvolution)

Fig. 31 Spectrum from Fig. 30 after deconvolution.

 

Script:

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

// To execute this example, do

// root > .x Src5.C

 

#include <TSpectrum2>

 

void Src5() {

   Int_t i, j, nfound;

   Double_t nbinsx = 64;

   Double_t nbinsy = 64;  

   Double_t xmin  = 0;

   Double_t xmax  = (Double_t)nbinsx;

   Double_t ymin  = 0;

   Double_t ymax  = (Double_t)nbinsy;  

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

   for (i=0;i<nbinsx;i++)

                                    source[i]=new float[nbinsy];

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

   for (i=0;i<nbinsx;i++)

                                    dest[i]=new float[nbinsy];

   TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);

   TFile *f = new TFile("spectra2\\TSpectrum2.root");

   search=(TH2F*) f->Get("search3;1");

   TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);

   TSpectrum2 *s = new TSpectrum2();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

             }

   }  

   nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 2, 5, kFALSE, 10, kFALSE, 1);  

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

   for(i=0;i<nfound;i++)

             printf("posx= %d, posy= %d, value= %d\n",(int)(fPositionX[i]+0.5), (int)(fPositionY[i]+0.5), (int)source[(int)(fPositionX[i]+0.5)][(int)(fPositionY[i]+0.5)]);       

}