// @(#)root/spectrum:$Id: TSpectrum2.cxx 23423 2008-04-23 09:29:56Z brun $ // Author: Miroslav Morhac 17/01/2006 ///////////////////////////////////////////////////////////////////////////// // THIS CLASS CONTAINS ADVANCED SPECTRA PROCESSING FUNCTIONS. // // // // ONE-DIMENSIONAL BACKGROUND ESTIMATION FUNCTIONS // // TWO-DIMENSIONAL BACKGROUND ESTIMATION FUNCTIONS // // ONE-DIMENSIONAL SMOOTHING FUNCTIONS // // TWO-DIMENSIONAL SMOOTHING FUNCTIONS // // ONE-DIMENSIONAL DECONVOLUTION FUNCTIONS // // TWO-DIMENSIONAL DECONVOLUTION FUNCTIONS // // ONE-DIMENSIONAL PEAK SEARCH FUNCTIONS // // TWO-DIMENSIONAL PEAK SEARCH FUNCTIONS // // // // These functions were written by: // // Miroslav Morhac // // Institute of Physics // // Slovak Academy of Sciences // // Dubravska cesta 9, 842 28 BRATISLAVA // // SLOVAKIA // // // // email:fyzimiro@savba.sk, fax:+421 7 54772479 // // // // The original code in C has been repackaged as a C++ class by R.Brun // // // // The algorithms in this class have been published in the following // // references: // // [1] M.Morhac et al.: Background elimination methods for // // multidimensional coincidence gamma-ray spectra. Nuclear // // Instruments and Methods in Physics Research A 401 (1997) 113- // // 132. // // // // [2] M.Morhac et al.: Efficient one- and two-dimensional Gold // // deconvolution and its application to gamma-ray spectra // // decomposition. Nuclear Instruments and Methods in Physics // // Research A 401 (1997) 385-408. // // // // [3] M.Morhac et al.: Identification of peaks in multidimensional // // coincidence gamma-ray spectra. Nuclear Instruments and Methods in // // Research Physics A 443(2000), 108-125. // // // // These NIM papers are also available as Postscript files from: // // /* ftp://root.cern.ch/root/SpectrumDec.ps.gz ftp://root.cern.ch/root/SpectrumSrc.ps.gz ftp://root.cern.ch/root/SpectrumBck.ps.gz */ // ///////////////////////////////////////////////////////////////////////////// // /////////////////////NEW FUNCTIONS January 2006 //Begin_Html <!-- /* --> <div class=Section1> <p class=MsoNormal style='text-align:justify'><i><span lang=EN-US style='font-size:16.0pt'>All figures in this page were prepared using DaqProVis system, Data Acquisition, Processing and Visualization system, which is being developed at the Institute of Physics, Slovak Academy of Sciences, Bratislava, Slovakia: </span></i></p> <p class=MsoNormal style='text-align:justify'><i><span lang=EN-US style='font-size:16.0pt'><a href="http://www.fu.sav.sk/nph/projects/DaqProVis/">http://www.fu.sav.sk/nph/projects/DaqProVis/</a> under construction</span></i></p> <p class=MsoNormal style='text-align:justify'><i><span lang=EN-US style='font-size:16.0pt'><a href="http://www.fu.sav.sk/nph/projects/ProcFunc/">http://www.fu.sav.sk/nph/projects/ProcFunc/</a> .</span></i></p> </div> <!-- */ // --> End_Html //______________________________________________________________________________ #include "TSpectrum2.h" #include "TPolyMarker.h" #include "TList.h" #include "TH1.h" #include "TMath.h" #define PEAK_WINDOW 1024 Int_t TSpectrum2::fgIterations = 3; Int_t TSpectrum2::fgAverageWindow = 3; ClassImp(TSpectrum2) //______________________________________________________________________________ TSpectrum2::TSpectrum2() :TNamed("Spectrum", "Miroslav Morhac peak finder") { // Constructor. Int_t n = 100; fMaxPeaks = n; fPosition = new Float_t[n]; fPositionX = new Float_t[n]; fPositionY = new Float_t[n]; fResolution = 1; fHistogram = 0; fNPeaks = 0; } //______________________________________________________________________________ TSpectrum2::TSpectrum2(Int_t maxpositions, Float_t resolution) :TNamed("Spectrum", "Miroslav Morhac peak finder") { // maxpositions: maximum number of peaks // resolution: determines resolution of the neighboring peaks // default value is 1 correspond to 3 sigma distance // between peaks. Higher values allow higher resolution // (smaller distance between peaks. // May be set later through SetResolution. Int_t n = maxpositions; fMaxPeaks = n; fPosition = new Float_t[n]; fPositionX = new Float_t[n]; fPositionY = new Float_t[n]; fHistogram = 0; fNPeaks = 0; SetResolution(resolution); } //______________________________________________________________________________ TSpectrum2::~TSpectrum2() { // Destructor. delete [] fPosition; delete [] fPositionX; delete [] fPositionY; delete fHistogram; } //______________________________________________________________________________ void TSpectrum2::SetAverageWindow(Int_t w) { // static function: Set average window of searched peaks // see TSpectrum2::SearchHighRes fgAverageWindow = w; } //______________________________________________________________________________ void TSpectrum2::SetDeconIterations(Int_t n) { // static function: Set max number of decon iterations in deconvolution operation // see TSpectrum2::SearchHighRes fgIterations = n; } //______________________________________________________________________________ TH1 *TSpectrum2::Background(const TH1 * h, int number_of_iterations, Option_t * option) { ///////////////////////////////////////////////////////////////////////////// // TWO-DIMENSIONAL BACKGROUND ESTIMATION FUNCTION // // This function calculates the background spectrum in the input histogram h. // The background is returned as a histogram. // // Function parameters: // -h: input 2-d histogram // -numberIterations, (default value = 20) // Increasing numberIterations make the result smoother and lower. // -option: may contain one of the following options // - to set the direction parameter // "BackIncreasingWindow". By default the direction is BackDecreasingWindow // - filterOrder-order of clipping filter, (default "BackOrder2" // -possible values= "BackOrder4" // "BackOrder6" // "BackOrder8" // - "nosmoothing"- if selected, the background is not smoothed // By default the background is smoothed. // - smoothWindow-width of smoothing window, (default is "BackSmoothing3") // -possible values= "BackSmoothing5" // "BackSmoothing7" // "BackSmoothing9" // "BackSmoothing11" // "BackSmoothing13" // "BackSmoothing15" // - "Compton" if selected the estimation of Compton edge // will be included. // - "same" : if this option is specified, the resulting background // histogram is superimposed on the picture in the current pad. // // NOTE that the background is only evaluated in the current range of h. // ie, if h has a bin range (set via h->GetXaxis()->SetRange(binmin,binmax), // the returned histogram will be created with the same number of bins // as the input histogram h, but only bins from binmin to binmax will be filled // with the estimated background. // // ///////////////////////////////////////////////////////////////////////////// Error("Background","function not yet implemented: h=%s, iter=%d, option=%sn" , h->GetName(), number_of_iterations, option); return 0; } //______________________________________________________________________________ void TSpectrum2::Print(Option_t *) const { // Print the array of positions printf("\nNumber of positions = %d\n",fNPeaks); for (Int_t i=0;i<fNPeaks;i++) { printf(" x[%d] = %g, y[%d] = %g\n",i,fPositionX[i],i,fPositionY[i]); } } //______________________________________________________________________________ Int_t TSpectrum2::Search(const TH1 * hin, Double_t sigma, Option_t * option, Double_t threshold) { ///////////////////////////////////////////////////////////////////////////// // TWO-DIMENSIONAL PEAK SEARCH FUNCTION // // This function searches for peaks in source spectrum in hin // // The number of found peaks and their positions are written into // // the members fNpeaks and fPositionX. // // The search is performed in the current histogram range. // // // // Function parameters: // // hin: pointer to the histogram of source spectrum // // sigma: sigma of searched peaks, for details we refer to manual // // threshold: (default=0.05) peaks with amplitude less than // // threshold*highest_peak are discarded. 0<threshold<1 // // // // By default, the background is removed before deconvolution. // // Specify the option "nobackground" to not remove the background. // // // // // By default the "Markov" chain algorithm is used. // // Specify the option "noMarkov" to disable this algorithm // // Note that by default the source spectrum is replaced by a new spectrum// // // // // By default a polymarker object is created and added to the list of // // functions of the histogram. The histogram is drawn with the specified // // option and the polymarker object drawn on top of the histogram. // // The polymarker coordinates correspond to the npeaks peaks found in // // the histogram. // // A pointer to the polymarker object can be retrieved later via: // // TList *functions = hin->GetListOfFunctions(); // // TPolyMarker *pm = (TPolyMarker*)functions->FindObject("TPolyMarker") // // Specify the option "goff" to disable the storage and drawing of the // // polymarker. // // // ///////////////////////////////////////////////////////////////////////////// if (hin == 0) return 0; Int_t dimension = hin->GetDimension(); if (dimension != 2) { Error("Search", "Must be a 2-d histogram"); return 0; } TString opt = option; opt.ToLower(); Bool_t background = kTRUE; if (opt.Contains("nobackground")) { background = kFALSE; opt.ReplaceAll("nobackground",""); } Bool_t markov = kTRUE; if (opt.Contains("nomarkov")) { markov = kFALSE; opt.ReplaceAll("nomarkov",""); } Int_t sizex = hin->GetXaxis()->GetNbins(); Int_t sizey = hin->GetYaxis()->GetNbins(); Int_t i, j, binx,biny, npeaks; Float_t ** source = new float *[sizex]; Float_t ** dest = new float *[sizex]; for (i = 0; i < sizex; i++) { source[i] = new float[sizey]; dest[i] = new float[sizey]; for (j = 0; j < sizey; j++) { source[i][j] = (Float_t) hin->GetBinContent(i + 1, j + 1); } } //npeaks = SearchHighRes(source, dest, sizex, sizey, sigma, 100*threshold, kTRUE, 3, kTRUE, 10); //the smoothing option is used for 1-d but not for 2-d histograms npeaks = SearchHighRes(source, dest, sizex, sizey, sigma, 100*threshold, background, fgIterations, markov, fgAverageWindow); //The logic in the loop should be improved to use the fact //that fPositionX,Y give a precise position inside a bin. //The current algorithm takes the center of the bin only. for (i = 0; i < npeaks; i++) { binx = 1 + Int_t(fPositionX[i] + 0.5); biny = 1 + Int_t(fPositionY[i] + 0.5); fPositionX[i] = hin->GetXaxis()->GetBinCenter(binx); fPositionY[i] = hin->GetYaxis()->GetBinCenter(biny); } for (i = 0; i < sizex; i++) { delete [] source[i]; delete [] dest[i]; } delete [] source; delete [] dest; if (opt.Contains("goff")) return npeaks; if (!npeaks) return 0; TPolyMarker * pm = (TPolyMarker*)hin->GetListOfFunctions()->FindObject("TPolyMarker"); if (pm) { hin->GetListOfFunctions()->Remove(pm); delete pm; } pm = new TPolyMarker(npeaks, fPositionX, fPositionY); hin->GetListOfFunctions()->Add(pm); pm->SetMarkerStyle(23); pm->SetMarkerColor(kRed); pm->SetMarkerSize(1.3); ((TH1*)hin)->Draw(option); return npeaks; } //______________________________________________________________________________ void TSpectrum2::SetResolution(Float_t resolution) { // resolution: determines resolution of the neighboring peaks // default value is 1 correspond to 3 sigma distance // between peaks. Higher values allow higher resolution // (smaller distance between peaks. // May be set later through SetResolution. if (resolution > 1) fResolution = resolution; else fResolution = 1; } //_____________________________________________________________________________ //_____________________________________________________________________________ /////////////////////NEW FUNCTIONS JANUARY 2006 //______________________________________________________________________________ const char *TSpectrum2::Background(float **spectrum, Int_t ssizex, Int_t ssizey, Int_t numberIterationsX, Int_t numberIterationsY, Int_t direction, Int_t filterType) { ///////////////////////////////////////////////////////////////////////////// // 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 // // // // // ///////////////////////////////////////////////////////////////////////////// // //Begin_Html <!-- /* --> <div class=Section1> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:20.0pt'>Background estimation</span></b></p> <p class=MsoNormal style='text-align:justify'><i><span style='font-size:18.0pt'> </span></i></p> <p class=MsoNormal style='text-align:justify'><i><span style='font-size:18.0pt'>Goal: Separation of useful information (peaks) from useless information (background)</span></i><span style='font-size:18.0pt'> </span></p> <p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent: -18.0pt'><span style='font-size:16.0pt'>•<span style='font:7.0pt "Times New Roman"'> </span></span><span style='font-size:16.0pt'>method is based on Sensitive Nonlinear Iterative Peak (SNIP) clipping algorithm [1]</span></p> <p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent: -18.0pt'><span style='font-size:16.0pt'>•<span style='font:7.0pt "Times New Roman"'> </span></span><span style='font-size:16.0pt'>there exist two algorithms for the estimation of new value in the channel “<sub><img width=28 height=24 src="gif/TSpectrum2_Background1.gif"></sub>”</span></p> <p class=MsoNormal style='margin-left:18.0pt;text-align:justify'><span style='font-size:16.0pt'> </span></p> <p class=MsoNormal style='text-align:justify'><i><span style='font-size:16.0pt'>Algorithm based on Successive Comparisons</span></i></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'>It is an extension of one-dimensional SNIP algorithm to another dimension. For details we refer to [2].</span></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'> </span></p> <p class=MsoNormal style='text-align:justify'><i><span style='font-size:16.0pt'>Algorithm based on One Step Filtering</span></i></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'>New value in the estimated channel is calculated as</span></p> <p class=MsoNormal style='text-align:justify'><sub><img width=133 height=39 src="gif/TSpectrum2_Background2.gif"></sub></p> <p class=MsoNormal style='text-align:justify'> </p> <p class=MsoNormal style='text-align:justify'> </p> <p class=MsoNormal style='text-align:justify'><sub><img width=600 height=128 src="gif/TSpectrum2_Background3.gif"></sub></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'> </span></p> <p class=MsoNormal><sub><img width=190 height=38 src="gif/TSpectrum2_Background4.gif"></sub>.</p> <p class=MsoNormal> </p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'>where p = 1, 2, …, number_of_iterations. </span></p> <p class=MsoNormal><i><span style='font-size:18.0pt'> </span></i></p> <p class=MsoNormal><i><span style='font-size:18.0pt'>Function:</span></i></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:18.0pt'>const <a href="http://root.cern.ch/root/html/ListOfTypes.html#char" target="_parent">char</a>* </span></b><span style='font-size:18.0pt'><a href="http://root.cern.ch/root/html/TSpectrum.html#TSpectrum:Fit1Awmi"><b>TSpectrum2::Background</b></a><b> (<a href="http://root.cern.ch/root/html/ListOfTypes.html#float" target="_parent">float</a> **spectrum, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int" target="_parent">int</a> ssizex, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int" target="_parent">int</a> ssizey, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int" target="_parent">int</a> numberIterationsX, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int" target="_parent">int</a> numberIterationsY, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int" target="_parent">int</a> direction, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int" target="_parent">int</a> filterType) </b></span></p> <p class=MsoNormal> </p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'>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.</span><span style='font-size:18.0pt'> </span><span style='font-size:16.0pt'>On successful completion it returns 0. On error it returns pointer to the string describing error.</span></p> <p class=MsoNormal> </p> <p class=MsoNormal><i><span style='font-size:16.0pt;color:red'>Parameters:</span></i></p> <p class=MsoNormal> <b><span style='font-size:14.0pt'>spectrum</span></b>-pointer to the matrix of source spectrum </p> <p class=MsoNormal> <b><span style='font-size:14.0pt'>ssizex, ssizey</span></b>-lengths of the spectrum matrix </p> <p class=MsoNormal style='text-align:justify'> <b><span style='font-size:14.0pt'>numberIterationsX, numberIterationsY</span></b>maximal widths of clipping</p> <p class=MsoNormal style='text-align:justify'> window, </p> <p class=MsoNormal> <b><span style='font-size:14.0pt'>direction</span></b>- direction of change of clipping window </p> <p class=MsoNormal> - possible values=kBackIncreasingWindow </p> <p class=MsoNormal> kBackDecreasingWindow </p> <p class=MsoNormal> <b><span style='font-size:14.0pt'>filterType</span></b>-type of the clipping algorithm, </p> <p class=MsoNormal> -possible values=kBack SuccessiveFiltering</p> <p class=MsoNormal> kBackOneStepFiltering </p> <p class=MsoNormal> </p> <p class=MsoNormal><b><i><span style='font-size:18.0pt'>References:</span></i></b></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'>[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.</span></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'>[2] </span><span lang=SK style='font-size:16.0pt'> M. Morháč, J. Kliman, V. Matoušek, M. Veselský, I. Turzo</span><span style='font-size:16.0pt'>.: Background elimination methods for multidimensional gamma-ray spectra. NIM, A401 (1997) 113-132.</span></p> </div> <!-- */ // --> End_Html //Begin_Html <!-- /* --> <div class=Section1> <p class=MsoNormal><i><span style='font-size:18.0pt'>Example 1– script Back_gamma64.c :</span></i></p> <p class=MsoNormal><img width=602 height=418 src="gif/TSpectrum2_Background1.jpg"></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 1 Original two-dimensional gamma-gamma-ray spectrum</span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'><img width=602 height=418 src="gif/TSpectrum2_Background2.jpg"></span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>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.</span></b></p> <p class=MsoNormal><b><span style='font-size:14.0pt;color:green'><img width=602 height=418 src="gif/TSpectrum2_Background3.jpg"></span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 3 Resulting peaks after subtraction of the estimated background (Fig. 2) from original two-dimensional gamma-gamma-ray spectrum (Fig. 1).</span></b></p> <p class=MsoNormal><b><span style='font-size:14.0pt;color:green'> </span></b></p> <p class=MsoNormal><b><span style='font-size:14.0pt;color:green'> </span></b></p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:green'>Script:</span></b></p> <p class=MsoNormal>// Example to illustrate the background estimator (class TSpectrum).</p> <p class=MsoNormal>// To execute this example, do</p> <p class=MsoNormal>// root > .x Back_gamma64.C</p> <p class=MsoNormal> </p> <p class=MsoNormal>#include <TSpectrum> </p> <p class=MsoNormal> </p> <p class=MsoNormal>void Back_gamma64() {</p> <p class=MsoNormal> Int_t i, j;</p> <p class=MsoNormal> Double_t nbinsx = 64;</p> <p class=MsoNormal> Double_t nbinsy = 64; </p> <p class=MsoNormal> Double_t xmin = 0;</p> <p class=MsoNormal> Double_t xmax = (Double_t)nbinsx;</p> <p class=MsoNormal> Double_t ymin = 0;</p> <p class=MsoNormal> Double_t ymax = (Double_t)nbinsy; </p> <p class=MsoNormal> Float_t ** source = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> source[i]=new float[nbinsy]; </p> <p class=MsoNormal> TH2F *back = new TH2F("back","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> TFile *f = new TFile("spectra2\\TSpectrum2.root");</p> <p class=MsoNormal> back=(TH2F*) f->Get("back1;1");</p> <p class=MsoNormal> TCanvas *Background = new TCanvas("Background","Estimation of background with increasing window",10,10,1000,700);</p> <p class=MsoNormal> TSpectrum *s = new TSpectrum();</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> source[i][j] = back->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> } </p> <p class=MsoNormal> s->Background(source,nbinsx,nbinsy,4,4,kBackDecreasingWindow,kBackSuccessiveFiltering);</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++)</p> <p class=MsoNormal> back->SetBinContent(i + 1,j + 1, source[i][j]); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> back->Draw("SURF"); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> </p> <p class=MsoNormal><i><span style='font-size:18.0pt'>Example 2– script Back_gamma256.c :</span></i></p> <p class=MsoNormal><img width=602 height=418 src="gif/TSpectrum2_Background4.jpg"></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 4 Original two-dimensional gamma-gamma-ray spectrum 256x256 channels</span></b></p> <p class=MsoNormal><img width=602 height=418 src="gif/TSpectrum2_Background5.jpg"></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>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).</span></b></p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:green'> </span></b></p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:green'>Script:</span></b></p> <p class=MsoNormal>// Example to illustrate the background estimator (class TSpectrum).</p> <p class=MsoNormal>// To execute this example, do</p> <p class=MsoNormal>// root > .x Back_gamma256.C</p> <p class=MsoNormal> </p> <p class=MsoNormal>#include <TSpectrum> </p> <p class=MsoNormal> </p> <p class=MsoNormal>void Back_gamma256() {</p> <p class=MsoNormal> Int_t i, j;</p> <p class=MsoNormal> Double_t nbinsx = 64;</p> <p class=MsoNormal> Double_t nbinsy = 64; </p> <p class=MsoNormal> Double_t xmin = 0;</p> <p class=MsoNormal> Double_t xmax = (Double_t)nbinsx;</p> <p class=MsoNormal> Double_t ymin = 0;</p> <p class=MsoNormal> Double_t ymax = (Double_t)nbinsy; </p> <p class=MsoNormal> Float_t ** source = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> source[i]=new float[nbinsy]; </p> <p class=MsoNormal> TH2F *back = new TH2F("back","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> TFile *f = new TFile("spectra2\\TSpectrum2.root");</p> <p class=MsoNormal> back=(TH2F*) f->Get("back2;1");</p> <p class=MsoNormal> TCanvas *Background = new TCanvas("Background","Estimation of background with increasing window",10,10,1000,700);</p> <p class=MsoNormal> TSpectrum *s = new TSpectrum();</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> source[i][j] = back->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> } </p> <p class=MsoNormal> s->Background(source,nbinsx,nbinsy,8,8,kBackIncreasingWindow,kBackSuccessiveFiltering);</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++)</p> <p class=MsoNormal> back->SetBinContent(i + 1,j + 1, source[i][j]); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> back->Draw("SURF"); </p> <p class=MsoNormal> }</p> <p class=MsoNormal><i><span style='font-size:18.0pt'>Example 3– script Back_synt256.c :</span></i></p> <p class=MsoNormal><img width=602 height=418 src="gif/TSpectrum2_Background6.jpg"></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 6 Original two-dimensional synthetic spectrum 256x256 channels</span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'><img width=602 height=418 src="gif/TSpectrum2_Background7.jpg"></span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>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.</span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'><img width=602 height=418 src="gif/TSpectrum2_Background8.jpg"></span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>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.</span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'> </span></b></p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:green'>Script:</span></b></p> <p class=MsoNormal>// Example to illustrate the background estimator (class TSpectrum).</p> <p class=MsoNormal>// To execute this example, do</p> <p class=MsoNormal>// root > .x Back_synt256.C</p> <p class=MsoNormal> </p> <p class=MsoNormal>#include <TSpectrum> </p> <p class=MsoNormal> </p> <p class=MsoNormal>void Back_synt256() {</p> <p class=MsoNormal> Int_t i, j;</p> <p class=MsoNormal> Double_t nbinsx = 64;</p> <p class=MsoNormal> Double_t nbinsy = 64; </p> <p class=MsoNormal> Double_t xmin = 0;</p> <p class=MsoNormal> Double_t xmax = (Double_t)nbinsx;</p> <p class=MsoNormal> Double_t ymin = 0;</p> <p class=MsoNormal> Double_t ymax = (Double_t)nbinsy; </p> <p class=MsoNormal> Float_t ** source = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> source[i]=new float[nbinsy]; </p> <p class=MsoNormal> TH2F *back = new TH2F("back","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> TFile *f = new TFile("spectra2\\TSpectrum2.root");</p> <p class=MsoNormal> back=(TH2F*) f->Get("back3;1");</p> <p class=MsoNormal> TCanvas *Background = new TCanvas("Background","Estimation of background with increasing window",10,10,1000,700);</p> <p class=MsoNormal> TSpectrum *s = new TSpectrum();</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> source[i][j] = back->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> } </p> <p class=MsoNormal> s->Background(source,nbinsx,nbinsy,8,8,kBackIncreasingWindow,kBackSuccessiveFiltering);//kBackOneStepFiltering</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++)</p> <p class=MsoNormal> back->SetBinContent(i + 1,j + 1, source[i][j]); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> back->Draw("SURF"); </p> <p class=MsoNormal> }</p> </div> <!-- */ // --> End_Html int i, x, y, sampling, r1, r2; float a, b, p1, p2, p3, p4, s1, s2, s3, s4; if (ssizex <= 0 || ssizey <= 0) return "Wrong parameters"; if (numberIterationsX < 1 || numberIterationsY < 1) return "Width of Clipping Window Must Be Positive"; if (ssizex < 2 * numberIterationsX + 1 || ssizey < 2 * numberIterationsY + 1) return ("Too Large Clipping Window"); float **working_space = new float *[ssizex]; for (i = 0; i < ssizex; i++) working_space[i] = new float[ssizey]; sampling = (int) TMath::Max(numberIterationsX, numberIterationsY); if (direction == kBackIncreasingWindow) { if (filterType == kBackSuccessiveFiltering) { for (i = 1; i <= sampling; i++) { r1 = (int) TMath::Min(i, numberIterationsX), r2 = (int) TMath::Min(i, numberIterationsY); for (y = r2; y < ssizey - r2; y++) { for (x = r1; x < ssizex - r1; x++) { a = spectrum[x][y]; p1 = spectrum[x - r1][y - r2]; p2 = spectrum[x - r1][y + r2]; p3 = spectrum[x + r1][y - r2]; p4 = spectrum[x + r1][y + r2]; s1 = spectrum[x][y - r2]; s2 = spectrum[x - r1][y]; s3 = spectrum[x + r1][y]; s4 = spectrum[x][y + r2]; b = (p1 + p2) / 2.0; if (b > s2) s2 = b; b = (p1 + p3) / 2.0; if (b > s1) s1 = b; b = (p2 + p4) / 2.0; if (b > s4) s4 = b; b = (p3 + p4) / 2.0; if (b > s3) s3 = b; s1 = s1 - (p1 + p3) / 2.0; s2 = s2 - (p1 + p2) / 2.0; s3 = s3 - (p3 + p4) / 2.0; s4 = s4 - (p2 + p4) / 2.0; b = (s1 + s4) / 2.0 + (s2 + s3) / 2.0 + (p1 + p2 + p3 + p4) / 4.0; if (b < a && b > 0) a = b; working_space[x][y] = a; } } for (y = r2; y < ssizey - r2; y++) { for (x = r1; x < ssizex - r1; x++) { spectrum[x][y] = working_space[x][y]; } } } } else if (filterType == kBackOneStepFiltering) { for (i = 1; i <= sampling; i++) { r1 = (int) TMath::Min(i, numberIterationsX), r2 = (int) TMath::Min(i, numberIterationsY); for (y = r2; y < ssizey - r2; y++) { for (x = r1; x < ssizex - r1; x++) { a = spectrum[x][y]; b = -(spectrum[x - r1][y - r2] + spectrum[x - r1][y + r2] + spectrum[x + r1][y - r2] + spectrum[x + r1][y + r2]) / 4 + (spectrum[x][y - r2] + spectrum[x - r1][y] + spectrum[x + r1][y] + spectrum[x][y + r2]) / 2; if (b < a && b > 0) a = b; working_space[x][y] = a; } } for (y = i; y < ssizey - i; y++) { for (x = i; x < ssizex - i; x++) { spectrum[x][y] = working_space[x][y]; } } } } } else if (direction == kBackDecreasingWindow) { if (filterType == kBackSuccessiveFiltering) { for (i = sampling; i >= 1; i--) { r1 = (int) TMath::Min(i, numberIterationsX), r2 = (int) TMath::Min(i, numberIterationsY); for (y = r2; y < ssizey - r2; y++) { for (x = r1; x < ssizex - r1; x++) { a = spectrum[x][y]; p1 = spectrum[x - r1][y - r2]; p2 = spectrum[x - r1][y + r2]; p3 = spectrum[x + r1][y - r2]; p4 = spectrum[x + r1][y + r2]; s1 = spectrum[x][y - r2]; s2 = spectrum[x - r1][y]; s3 = spectrum[x + r1][y]; s4 = spectrum[x][y + r2]; b = (p1 + p2) / 2.0; if (b > s2) s2 = b; b = (p1 + p3) / 2.0; if (b > s1) s1 = b; b = (p2 + p4) / 2.0; if (b > s4) s4 = b; b = (p3 + p4) / 2.0; if (b > s3) s3 = b; s1 = s1 - (p1 + p3) / 2.0; s2 = s2 - (p1 + p2) / 2.0; s3 = s3 - (p3 + p4) / 2.0; s4 = s4 - (p2 + p4) / 2.0; b = (s1 + s4) / 2.0 + (s2 + s3) / 2.0 + (p1 + p2 + p3 + p4) / 4.0; if (b < a && b > 0) a = b; working_space[x][y] = a; } } for (y = r2; y < ssizey - r2; y++) { for (x = r1; x < ssizex - r1; x++) { spectrum[x][y] = working_space[x][y]; } } } } else if (filterType == kBackOneStepFiltering) { for (i = sampling; i >= 1; i--) { r1 = (int) TMath::Min(i, numberIterationsX), r2 = (int) TMath::Min(i, numberIterationsY); for (y = r2; y < ssizey - r2; y++) { for (x = r1; x < ssizex - r1; x++) { a = spectrum[x][y]; b = -(spectrum[x - r1][y - r2] + spectrum[x - r1][y + r2] + spectrum[x + r1][y - r2] + spectrum[x + r1][y + r2]) / 4 + (spectrum[x][y - r2] + spectrum[x - r1][y] + spectrum[x + r1][y] + spectrum[x][y + r2]) / 2; if (b < a && b > 0) a = b; working_space[x][y] = a; } } for (y = i; y < ssizey - i; y++) { for (x = i; x < ssizex - i; x++) { spectrum[x][y] = working_space[x][y]; } } } } } for (i = 0; i < ssizex; i++) delete[]working_space[i]; delete[]working_space; return 0; } //_____________________________________________________________________________ const char* TSpectrum2::SmoothMarkov(float **source, Int_t ssizex, Int_t ssizey, Int_t averWindow) { ///////////////////////////////////////////////////////////////////////////// // 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 // ///////////////////////////////////////////////////////////////////////////// //Begin_Html <!-- /* --> <div class=Section1> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:20.0pt'>Smoothing</span></b></p> <p class=MsoNormal style='text-align:justify'><i><span style='font-size:18.0pt'> </span></i></p> <p class=MsoNormal><i><span style='font-size:18.0pt'>Goal: Suppression of statistical fluctuations</span></i></p> <p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent: -18.0pt'><span style='font-size:16.0pt'>•<span style='font:7.0pt "Times New Roman"'> </span></span><span style='font-size:16.0pt'>the algorithm is based on discrete Markov chain, which has very simple invariant distribution</span></p> <p class=MsoNormal> </p> <p class=MsoNormal> <sub><img width=551 height=63 src="gif/TSpectrum2_Smoothing1.gif"></sub><span style='font-size:16.0pt; font-family:Arial'> </span></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt; font-family:Arial'> </span><sub><img width=28 height=36 src="gif/TSpectrum2_Smoothing2.gif"></sub><span style='font-size:16.0pt; font-family:Arial'> being defined from the normalization condition </span><sub><img width=70 height=52 src="gif/TSpectrum2_Smoothing3.gif"></sub></p> <p class=MsoNormal> </p> <p class=MsoNormal><span style='font-size:16.0pt;font-family:Arial'> n is the length of the smoothed spectrum and </span></p> <p class=MsoNormal> <table cellpadding=0 cellspacing=0 align=left> <tr> <td width=57 height=15></td> </tr> <tr> <td></td> <td><img width=258 height=60 src="gif/TSpectrum2_Smoothing4.gif"></td> </tr> </table> <span style='font-size:16.0pt;font-family:Arial'> </span></p> <p class=MsoNormal><span style='font-size:18.0pt'> </span></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'> </span></p> <br clear=ALL> <p class=MsoNormal style='margin-left:34.2pt;text-align:justify'><span style='font-size:16.0pt;font-family:Arial'>is the probability of the change of the peak position from channel i to the channel i+1. </span> <sub><img width=28 height=36 src="gif/TSpectrum2_Smoothing5.gif"></sub><span style='font-size:16.0pt;font-family:Arial'>is the normalization constant so that </span><span style='font-family:Arial'><sub><img width=133 height=34 src="gif/TSpectrum2_Smoothing6.gif"></sub> </span><span style='font-size:16.0pt; font-family:Arial'>and m is a width of smoothing window. We have extended this algortihm to two dimensions. </span></p> <p class=MsoNormal><i><span style='font-size:18.0pt'> </span></i></p> <p class=MsoNormal><i><span style='font-size:18.0pt'>Function:</span></i></p> <p class=MsoNormal><b><span style='font-size:18.0pt'>const <a href="http://root.cern.ch/root/html/ListOfTypes.html#char" target="_parent">char</a>* </span></b><span style='font-size:18.0pt'><a href="http://root.cern.ch/root/html/TSpectrum.html#TSpectrum:Fit1Awmi"><b>TSpectrum2::SmoothMarkov</b></a><b>(<a href="http://root.cern.ch/root/html/ListOfTypes.html#float" target="_parent">float</a> **fSpectrum, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int" target="_parent">int</a> ssizex, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int" target="_parent">int</a> ssizey, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int" target="_parent">int</a> averWindow) </b></span></p> <p class=MsoNormal> </p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'>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.</span></p> <p class=MsoNormal> </p> <p class=MsoNormal><i><span style='font-size:16.0pt;color:red'>Parameters:</span></i></p> <p class=MsoNormal> <b><span style='font-size:14.0pt'>fSpectrum</span></b>-pointer to the matrix of source spectrum </p> <p class=MsoNormal> <b><span style='font-size:14.0pt'>ssizex, ssizey</span></b> -lengths of the spectrum matrix </p> <p class=MsoNormal> <b><span style='font-size:14.0pt'>averWindow</span></b>-width of averaging smoothing window </p> <p class=MsoNormal> </p> <p class=MsoNormal><b><i><span style='font-size:18.0pt'>Reference:</span></i></b></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'>[1] Z.K. Silagadze, A new algorithm for automatic photopeak searches. NIM A 376 (1996), 451<b>.</b> </span></p> </div> <!-- */ // --> End_Html //Begin_Html <!-- /* --> <div class=Section1> <p class=MsoNormal><i><span style='font-size:16.0pt'>Example 4 – script Smooth.c :</span></i></p> <p class=MsoNormal><span style='font-size:16.0pt'><img width=300 height=209 src="gif/TSpectrum2_Smoothing1.jpg"><img width=297 height=207 src="gif/TSpectrum2_Smoothing2.jpg"></span></p> <p class=MsoNormal><b><span style='font-size:16.0pt'>Fig. 9 Original noisy spectrum.</span></b><b><span style='font-size:14.0pt'> </span></b><b><span style='font-size:16.0pt'>Fig. 10 Smoothed spectrum m=3</span></b></p> <p class=MsoNormal><b><span style='font-size:16.0pt'>Peaks can hardly be observed. Peaks become apparent.</span></b></p> <p class=MsoNormal><b><span style='font-size:14.0pt'><img width=293 height=203 src="gif/TSpectrum2_Smoothing3.jpg"><img width=297 height=205 src="gif/TSpectrum2_Smoothing4.jpg"></span></b></p> <p class=MsoNormal><b><span style='font-size:16.0pt'>Fig. 11 Smoothed spectrum m=5 Fig.12 Smoothed spectrum m=7</span></b></p> <p class=MsoNormal> </p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:#339966'>Script:</span></b></p> <p class=MsoNormal>// Example to illustrate the Markov smoothing (class TSpectrum).</p> <p class=MsoNormal>// To execute this example, do</p> <p class=MsoNormal>// root > .x Smooth.C</p> <p class=MsoNormal>#include <TSpectrum> </p> <p class=MsoNormal>void Smooth() {</p> <p class=MsoNormal> Int_t i, j;</p> <p class=MsoNormal> Double_t nbinsx = 256;</p> <p class=MsoNormal> Double_t nbinsy = 256; </p> <p class=MsoNormal> Double_t xmin = 0;</p> <p class=MsoNormal> Double_t xmax = (Double_t)nbinsx;</p> <p class=MsoNormal> Double_t ymin = 0;</p> <p class=MsoNormal> Double_t ymax = (Double_t)nbinsy; </p> <p class=MsoNormal> Float_t ** source = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> source[i]=new float[nbinsy]; </p> <p class=MsoNormal> TH2F *smooth = new TH2F("smooth","Background estimation",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> TFile *f = new TFile("spectra2\\TSpectrum2.root");</p> <p class=MsoNormal> smooth=(TH2F*) f->Get("smooth1;1");</p> <p class=MsoNormal> TCanvas *Smoothing = new TCanvas("Smoothing","Markov smoothing",10,10,1000,700);</p> <p class=MsoNormal> TSpectrum *s = new TSpectrum();</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> source[i][j] = smooth->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> }</p> <p class=MsoNormal> s->SmoothMarkov(source,nbinsx,nbinsx,3);//5,7</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++)</p> <p class=MsoNormal> smooth->SetBinContent(i + 1,j + 1, source[i][j]); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> smooth->Draw("SURF"); </p> <p class=MsoNormal> }</p> </div> <!-- */ // --> End_Html int xmin, xmax, ymin, ymax, i, j, l; double a, b, maxch; double nom, nip, nim, sp, sm, spx, spy, smx, smy, plocha = 0; if(averWindow <= 0) return "Averaging Window must be positive"; float **working_space = new float* [ssizex]; for(i = 0; i < ssizex; i++) working_space[i] = new float[ssizey]; xmin = 0; xmax = ssizex - 1; ymin = 0; ymax = ssizey - 1; for(i = 0, maxch = 0; i < ssizex; i++){ for(j = 0; j < ssizey; j++){ working_space[i][j] = 0; if(maxch < source[i][j]) maxch = source[i][j]; plocha += source[i][j]; } } if(maxch == 0) return 0; nom = 0; working_space[xmin][ymin] = 1; for(i = xmin; i < xmax; i++){ nip = source[i][ymin] / maxch; nim = source[i + 1][ymin] / maxch; sp = 0,sm = 0; for(l = 1; l <= averWindow; l++){ if((i + l) > xmax) a = source[xmax][ymin] / maxch; else a = source[i + l][ymin] / maxch; b = a - nip; if(a + nip <= 0) a = 1; else a = TMath::Sqrt(a + nip); b = b / a; b = TMath::Exp(b); sp = sp + b; if(i - l + 1 < xmin) a = source[xmin][ymin] / maxch; else a = source[i - l + 1][ymin] / maxch; b = a - nim; if(a + nim <= 0) a = 1; else a = TMath::Sqrt(a + nim); b = b / a; b = TMath::Exp(b); sm = sm + b; } a = sp / sm; a = working_space[i + 1][ymin] = a * working_space[i][ymin]; nom = nom + a; } for(i = ymin; i < ymax; i++){ nip = source[xmin][i] / maxch; nim = source[xmin][i + 1] / maxch; sp = 0,sm = 0; for(l = 1; l <= averWindow; l++){ if((i + l) > ymax) a = source[xmin][ymax] / maxch; else a = source[xmin][i + l] / maxch; b = a - nip; if(a + nip <= 0) a = 1; else a = TMath::Sqrt(a + nip); b = b / a; b = TMath::Exp(b); sp = sp + b; if(i - l + 1 < ymin) a = source[xmin][ymin] / maxch; else a = source[xmin][i - l + 1] / maxch; b = a - nim; if(a + nim <= 0) a = 1; else a = TMath::Sqrt(a + nim); b = b / a; b = TMath::Exp(b); sm = sm + b; } a = sp / sm; a = working_space[xmin][i + 1] = a * working_space[xmin][i]; nom = nom + a; } for(i = xmin; i < xmax; i++){ for(j = ymin; j < ymax; j++){ nip = source[i][j + 1] / maxch; nim = source[i + 1][j + 1] / maxch; spx = 0,smx = 0; for(l = 1; l <= averWindow; l++){ if(i + l > xmax) a = source[xmax][j] / maxch; else a = source[i + l][j] / maxch; b = a - nip; if(a + nip <= 0) a = 1; else a = TMath::Sqrt(a + nip); b = b / a; b = TMath::Exp(b); spx = spx + b; if(i - l + 1 < xmin) a = source[xmin][j] / maxch; else a = source[i - l + 1][j] / maxch; b = a - nim; if(a + nim <= 0) a = 1; else a = TMath::Sqrt(a + nim); b = b / a; b = TMath::Exp(b); smx = smx + b; } spy = 0,smy = 0; nip = source[i + 1][j] / maxch; nim = source[i + 1][j + 1] / maxch; for (l = 1; l <= averWindow; l++) { if (j + l > ymax) a = source[i][ymax]/maxch; else a = source[i][j + l] / maxch; b = a - nip; if (a + nip <= 0) a = 1; else a = TMath::Sqrt(a + nip); b = b / a; b = TMath::Exp(b); spy = spy + b; if (j - l + 1 < ymin) a = source[i][ymin] / maxch; else a = source[i][j - l + 1] / maxch; b = a - nim; if (a + nim <= 0) a = 1; else a = TMath::Sqrt(a + nim); b = b / a; b = TMath::Exp(b); smy = smy + b; } a = (spx * working_space[i][j + 1] + spy * working_space[i + 1][j]) / (smx +smy); working_space[i + 1][j + 1] = a; nom = nom + a; } } for(i = xmin; i <= xmax; i++){ for(j = ymin; j <= ymax; j++){ working_space[i][j] = working_space[i][j] / nom; } } for(i = 0;i < ssizex; i++){ for(j = 0; j < ssizey; j++){ source[i][j] = plocha * working_space[i][j]; } } for (i = 0; i < ssizex; i++) delete[]working_space[i]; delete[]working_space; return 0; } //______________________________________________________________________________________________________________________________ const char *TSpectrum2::Deconvolution(float **source, float **resp, Int_t ssizex, Int_t ssizey, Int_t numberIterations, Int_t numberRepetitions, Double_t boost) { ///////////////////////////////////////////////////////////////////////////// // 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 // ///////////////////////////////////////////////////////////////////////////// //Begin_Html <!-- /* --> <div class=Section1> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:20.0pt'>Deconvolution</span></b></p> <p class=MsoNormal style='text-align:justify'><i><span style='font-size:18.0pt'> </span></i></p> <p class=MsoNormal style='text-align:justify'><i><span style='font-size:18.0pt'>Goal: Improvement of the resolution in spectra, decomposition of multiplets</span></i></p> <p class=MsoNormal><span style='font-size:16.0pt'> </span></p> <p class=MsoNormal><span style='font-size:16.0pt'>Mathematical formulation of the 2-dimensional convolution system is</span></p> <p class=MsoNormal style='margin-left:18.0pt'> <table cellpadding=0 cellspacing=0 align=left> <tr> <td width=0 height=18></td> </tr> <tr> <td></td> <td><img width=577 height=138 src="gif/TSpectrum2_Deconvolution1.gif"></td> </tr> </table> <span style='font-size:16.0pt'> </span></p> <p class=MsoNormal><span style='font-size:16.0pt'> </span></p> <p class=MsoNormal> </p> <p class=MsoNormal> </p> <p class=MsoNormal> </p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'> </span></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'> </span></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'> </span></p> <br clear=ALL> <p class=MsoNormal><span style='font-size:16.0pt'>where h(i,j) is the impulse response function, x, y are input and output matrices, respectively, <sub><img width=45 height=24 src="gif/TSpectrum2_Deconvolution2.gif"></sub> are the lengths of x and h matrices</span><i><span style='font-size:18.0pt'> </span></i></p> <p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent: -18.0pt'><span style='font-size:16.0pt'>•<span style='font:7.0pt "Times New Roman"'> </span></span><span style='font-size:16.0pt'>let us assume that we know the response and the output matrices (spectra) of the above given system. </span></p> <p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent: -18.0pt'><span style='font-size:16.0pt'>•<span style='font:7.0pt "Times New Roman"'> </span></span><span style='font-size:16.0pt'>the deconvolution represents solution of the overdetermined system of linear equations, i.e., the calculation of the matrix <b>x.</b></span></p> <p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent: -18.0pt'><span style='font-size:16.0pt'>•<span style='font:7.0pt "Times New Roman"'> </span></span><span style='font-size:16.0pt'>from numerical stability point of view the operation of deconvolution is extremely critical (ill-posed problem) as well as time consuming operation. </span></p> <p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent: -18.0pt'><span style='font-size:16.0pt'>•<span style='font:7.0pt "Times New Roman"'> </span></span><span style='font-size:16.0pt'>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].</span></p> <p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent: -18.0pt'><span style='font-size:16.0pt'>•<span style='font:7.0pt "Times New Roman"'> </span></span><span style='font-size:16.0pt'>for Gold deconvolution algorithm as well as for boosted deconvolution algorithm we refer also to TSpectrum </span></p> <p class=MsoNormal><i><span style='font-size:18.0pt'> </span></i></p> <p class=MsoNormal><i><span style='font-size:18.0pt'>Function:</span></i></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:18.0pt'>const <a href="http://root.cern.ch/root/html/ListOfTypes.html#char">char</a>* </span></b><a name="TSpectrum:Deconvolution1"></a><a href="http://root.cern.ch/root/html/TSpectrum.html#TSpectrum:Fit1Awmi"><b><span style='font-size:18.0pt'>TSpectrum2::Deconvolution</span></b></a><b><span style='font-size:18.0pt'>(<a href="http://root.cern.ch/root/html/ListOfTypes.html#float">float</a> **source, const <a href="http://root.cern.ch/root/html/ListOfTypes.html#float">float</a> **resp, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int">int</a> ssizex, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int">int</a> ssizey, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int">int</a> numberIterations, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int">int</a> numberRepetitions, <a href="http://root.cern.ch/root/html/ListOfTypes.html#double">double</a></span></b><b><span style='font-size:16.0pt'> </span></b><b><span style='font-size:18.0pt'>boost)</span></b></p> <p class=MsoNormal> </p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'>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.</span></p> <p class=MsoNormal> </p> <p class=MsoNormal><i><span style='font-size:16.0pt;color:red'>Parameters:</span></i></p> <p class=MsoNormal> <b><span style='font-size:14.0pt'>source</span></b>-pointer to the matrix of source spectrum </p> <p class=MsoNormal> <b><span style='font-size:14.0pt'>resp</span></b>-pointer to the matrix of response spectrum </p> <p class=MsoNormal> <b><span style='font-size:14.0pt'>ssizex, ssizey</span></b>-lengths of the spectrum matrix </p> <p class=MsoNormal style='text-align:justify'> <b><span style='font-size:14.0pt'>numberIterations</span></b>-number of iterations </p> <p class=MsoNormal style='text-align:justify'> <b><span style='font-size:14.0pt'>numberRepetitions</span></b>-number of repetitions for boosted deconvolution. It must be </p> <p class=MsoNormal style='text-align:justify'> greater or equal to one.</p> <p class=MsoNormal style='text-align:justify'> <b><span style='font-size:14.0pt'>boost</span></b>-boosting coefficient, applies only if numberRepetitions is greater than one. </p> <p class=MsoNormal style='text-align:justify'> <span style='font-size: 14.0pt;color:fuchsia'>Recommended range <1,2>.</span></p> <p class=MsoNormal> </p> <p class=MsoNormal><b><i><span style='font-size:18.0pt'>References:</span></i></b></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'> [1] </span><span lang=SK style='font-size:16.0pt'>M. Morháč, J. Kliman, V. Matoušek, M. Veselský, I. Turzo</span><span style='font-size:16.0pt'>.: Efficient one- and two-dimensional Gold deconvolution and its application to gamma-ray spectra decomposition. NIM, A401 (1997) 385-408.</span></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'>[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. </span></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'> </span></p> </div> <!-- */ // --> End_Html //Begin_Html <!-- /* --> <div class=Section1> <p class=MsoNormal><i><span style='font-size:16.0pt'>Example 5 – script Decon.c :</span></i></p> <p class=MsoNormal style='margin-left:36.0pt;text-align:justify;text-indent: -18.0pt'><span style='font-size:16.0pt'>•<span style='font:7.0pt "Times New Roman"'> </span></span><span style='font-size:16.0pt'>response function (usually peak) should be shifted to the beginning of the coordinate system (see Fig. 13)</span></p> <p class=MsoNormal> </p> <p class=MsoNormal><img width=602 height=418 src="gif/TSpectrum2_Deconvolution1.jpg"></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 13 2-dimensional response spectrum</span></b></p> <p class=MsoNormal><img width=602 height=418 src="gif/TSpectrum2_Deconvolution2.jpg"></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 14 2-dimensional gamma-gamma-ray input spectrum (before deconvolution)</span></b></p> <p class=MsoNormal><img width=602 height=418 src="gif/TSpectrum2_Deconvolution3.jpg"></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 15 Spectrum from Fig. 14 after deconvolution (1000 iterations)</span></b></p> <p class=MsoNormal> </p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:#339966'>Script:</span></b></p> <p class=MsoNormal>// Example to illustrate the Gold deconvolution (class TSpectrum2).</p> <p class=MsoNormal>// To execute this example, do</p> <p class=MsoNormal>// root > .x Decon.C</p> <p class=MsoNormal> </p> <p class=MsoNormal>#include <TSpectrum2> </p> <p class=MsoNormal> </p> <p class=MsoNormal>void Decon() {</p> <p class=MsoNormal> Int_t i, j;</p> <p class=MsoNormal> Double_t nbinsx = 256;</p> <p class=MsoNormal> Double_t nbinsy = 256; </p> <p class=MsoNormal> Double_t xmin = 0;</p> <p class=MsoNormal> Double_t xmax = (Double_t)nbinsx;</p> <p class=MsoNormal> Double_t ymin = 0;</p> <p class=MsoNormal> Double_t ymax = (Double_t)nbinsy; </p> <p class=MsoNormal> Float_t ** source = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> source[i]=new float[nbinsy]; </p> <p class=MsoNormal> TH2F *decon = new TH2F("decon","Gold deconvolution",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> TFile *f = new TFile("spectra2\\TSpectrum2.root");</p> <p class=MsoNormal> decon=(TH2F*) f->Get("decon1;1");</p> <p class=MsoNormal> Float_t ** response = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> response[i]=new float[nbinsy]; </p> <p class=MsoNormal> TH2F *resp = new TH2F("resp","Response matrix",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> resp=(TH2F*) f->Get("resp1;1"); </p> <p class=MsoNormal> TCanvas *Deconvol = new TCanvas("Deconvolution","Gold deconvolution",10,10,1000,700);</p> <p class=MsoNormal> TSpectrum *s = new TSpectrum();</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> source[i][j] = decon->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> }</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> response[i][j] = resp->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> } </p> <p class=MsoNormal> s->Deconvolution(source,response,nbinsx,nbinsy,1000,1,1); </p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++)</p> <p class=MsoNormal> decon->SetBinContent(i + 1,j + 1, source[i][j]); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> </p> <p class=MsoNormal> decon->Draw("SURF"); </p> <p class=MsoNormal> }</p> <p class=MsoNormal><i><span style='font-size:16.0pt'>Example 6 – script Decon2.c :</span></i></p> <p class=MsoNormal><img width=602 height=418 src="gif/TSpectrum2_Deconvolution4.jpg"></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 16 Response spectrum</span></b></p> <p class=MsoNormal><img width=602 height=418 src="gif/TSpectrum2_Deconvolution5.jpg"></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>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.</span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'><img width=602 height=418 src="gif/TSpectrum2_Deconvolution6.jpg"></span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 18 Spectrum from Fig. 17 after deconvolution (1000 iterations). Resolution is improved but the peaks in multiplet remained unresolved.</span></b></p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:#339966'>Script:</span></b></p> <p class=MsoNormal>// Example to illustrate the Gold deconvolution (class TSpectrum2).</p> <p class=MsoNormal>// To execute this example, do</p> <p class=MsoNormal>// root > .x Decon2.C</p> <p class=MsoNormal> </p> <p class=MsoNormal>#include <TSpectrum2> </p> <p class=MsoNormal> </p> <p class=MsoNormal>void Decon2() {</p> <p class=MsoNormal> Int_t i, j;</p> <p class=MsoNormal> Double_t nbinsx = 64;</p> <p class=MsoNormal> Double_t nbinsy = 64; </p> <p class=MsoNormal> Double_t xmin = 0;</p> <p class=MsoNormal> Double_t xmax = (Double_t)nbinsx;</p> <p class=MsoNormal> Double_t ymin = 0;</p> <p class=MsoNormal> Double_t ymax = (Double_t)nbinsy; </p> <p class=MsoNormal> Float_t ** source = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> source[i]=new float[nbinsy]; </p> <p class=MsoNormal> TH2F *decon = new TH2F("decon","Gold deconvolution",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> TFile *f = new TFile("spectra2\\TSpectrum2.root");</p> <p class=MsoNormal> decon=(TH2F*) f->Get("decon2;1");</p> <p class=MsoNormal> Float_t ** response = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> response[i]=new float[nbinsy]; </p> <p class=MsoNormal> TH2F *resp = new TH2F("resp","Response matrix",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> resp=(TH2F*) f->Get("resp2;1"); </p> <p class=MsoNormal> TCanvas *Deconvol = new TCanvas("Deconvolution","Gold deconvolution",10,10,1000,700);</p> <p class=MsoNormal> TSpectrum *s = new TSpectrum();</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> source[i][j] = decon->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> }</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> response[i][j] = resp->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> } </p> <p class=MsoNormal> s->Deconvolution(source,response,nbinsx,nbinsy,1000,1,1); </p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++)</p> <p class=MsoNormal> decon->SetBinContent(i + 1,j + 1, source[i][j]); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> decon->Draw("SURF"); </p> <p class=MsoNormal> }</p> <p class=MsoNormal><i><span style='font-size:16.0pt'>Example 7 – script Decon2HR.c :</span></i></p> <p class=MsoNormal><img width=602 height=418 src="gif/TSpectrum2_Deconvolution7.jpg"></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>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.</span></b></p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:#339966'>Script:</span></b></p> <p class=MsoNormal>// Example to illustrate boosted Gold deconvolution (class TSpectrum2).</p> <p class=MsoNormal>// To execute this example, do</p> <p class=MsoNormal>// root > .x Decon2HR.C</p> <p class=MsoNormal> </p> <p class=MsoNormal>//#include <TSpectrum2> </p> <p class=MsoNormal> </p> <p class=MsoNormal>void Decon2HR() {</p> <p class=MsoNormal> Int_t i, j;</p> <p class=MsoNormal> Double_t nbinsx = 64;</p> <p class=MsoNormal> Double_t nbinsy = 64; </p> <p class=MsoNormal> Double_t xmin = 0;</p> <p class=MsoNormal> Double_t xmax = (Double_t)nbinsx;</p> <p class=MsoNormal> Double_t ymin = 0;</p> <p class=MsoNormal> Double_t ymax = (Double_t)nbinsy; </p> <p class=MsoNormal> Float_t ** source = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> source[i]=new float[nbinsy]; </p> <p class=MsoNormal> TH2F *decon = new TH2F("decon","Boosted Gold deconvolution",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> TFile *f = new TFile("spectra2\\TSpectrum2.root");</p> <p class=MsoNormal> decon=(TH2F*) f->Get("decon2;1");</p> <p class=MsoNormal> Float_t ** response = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> response[i]=new float[nbinsy]; </p> <p class=MsoNormal> TH2F *resp = new TH2F("resp","Response matrix",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> resp=(TH2F*) f->Get("resp2;1"); </p> <p class=MsoNormal> TCanvas *Deconvol = new TCanvas("Deconvolution","Gold deconvolution",10,10,1000,700);</p> <p class=MsoNormal> TSpectrum *s = new TSpectrum();</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> source[i][j] = decon->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> }</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> response[i][j] = resp->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> } </p> <p class=MsoNormal> s->Deconvolution(source,response,nbinsx,nbinsy,1000,1,1); </p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++)</p> <p class=MsoNormal> decon->SetBinContent(i + 1,j + 1, source[i][j]); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> decon->Draw("SURF"); </p> <p class=MsoNormal> }</p> <p class=MsoNormal style='text-align:justify'> </p> </div> <!-- */ // --> End_Html int i, j, lhx, lhy, i1, i2, j1, j2, k1, k2, lindex, i1min, i1max, i2min, i2max, j1min, j1max, j2min, j2max, positx = 0, posity = 0, repet; double lda, ldb, ldc, area, maximum = 0; if (ssizex <= 0 || ssizey <= 0) return "Wrong parameters"; if (numberIterations <= 0) return "Number of iterations must be positive"; if (numberRepetitions <= 0) return "Number of repetitions must be positive"; double **working_space = new double *[ssizex]; for (i = 0; i < ssizex; i++) working_space[i] = new double[5 * ssizey]; area = 0; lhx = -1, lhy = -1; for (i = 0; i < ssizex; i++) { for (j = 0; j < ssizey; j++) { lda = resp[i][j]; if (lda != 0) { if ((i + 1) > lhx) lhx = i + 1; if ((j + 1) > lhy) lhy = j + 1; } working_space[i][j] = lda; area = area + lda; if (lda > maximum) { maximum = lda; positx = i, posity = j; } } } if (lhx == -1 || lhy == -1) return ("Zero response data"); //calculate ht*y and write into p for (i2 = 0; i2 < ssizey; i2++) { for (i1 = 0; i1 < ssizex; i1++) { ldc = 0; for (j2 = 0; j2 <= (lhy - 1); j2++) { for (j1 = 0; j1 <= (lhx - 1); j1++) { k2 = i2 + j2, k1 = i1 + j1; if (k2 >= 0 && k2 < ssizey && k1 >= 0 && k1 < ssizex) { lda = working_space[j1][j2]; ldb = source[k1][k2]; ldc = ldc + lda * ldb; } } } working_space[i1][i2 + ssizey] = ldc; } } //calculate matrix b=ht*h i1min = -(lhx - 1), i1max = lhx - 1; i2min = -(lhy - 1), i2max = lhy - 1; for (i2 = i2min; i2 <= i2max; i2++) { for (i1 = i1min; i1 <= i1max; i1++) { ldc = 0; j2min = -i2; if (j2min < 0) j2min = 0; j2max = lhy - 1 - i2; if (j2max > lhy - 1) j2max = lhy - 1; for (j2 = j2min; j2 <= j2max; j2++) { j1min = -i1; if (j1min < 0) j1min = 0; j1max = lhx - 1 - i1; if (j1max > lhx - 1) j1max = lhx - 1; for (j1 = j1min; j1 <= j1max; j1++) { lda = working_space[j1][j2]; if (i1 + j1 < ssizex && i2 + j2 < ssizey) ldb = working_space[i1 + j1][i2 + j2]; else ldb = 0; ldc = ldc + lda * ldb; } } working_space[i1 - i1min][i2 - i2min + 2 * ssizey ] = ldc; } } //initialization in x1 matrix for (i2 = 0; i2 < ssizey; i2++) { for (i1 = 0; i1 < ssizex; i1++) { working_space[i1][i2 + 3 * ssizey] = 1; working_space[i1][i2 + 4 * ssizey] = 0; } } //START OF ITERATIONS for (repet = 0; repet < numberRepetitions; repet++) { if (repet != 0) { for (i = 0; i < ssizex; i++) { for (j = 0; j < ssizey; j++) { working_space[i][j + 3 * ssizey] = TMath::Power(working_space[i][j + 3 * ssizey], boost); } } } for (lindex = 0; lindex < numberIterations; lindex++) { for (i2 = 0; i2 < ssizey; i2++) { for (i1 = 0; i1 < ssizex; i1++) { ldb = 0; j2min = i2; if (j2min > lhy - 1) j2min = lhy - 1; j2min = -j2min; j2max = ssizey - i2 - 1; if (j2max > lhy - 1) j2max = lhy - 1; j1min = i1; if (j1min > lhx - 1) j1min = lhx - 1; j1min = -j1min; j1max = ssizex - i1 - 1; if (j1max > lhx - 1) j1max = lhx - 1; for (j2 = j2min; j2 <= j2max; j2++) { for (j1 = j1min; j1 <= j1max; j1++) { ldc = working_space[j1 - i1min][j2 - i2min + 2 * ssizey]; lda = working_space[i1 + j1][i2 + j2 + 3 * ssizey]; ldb = ldb + lda * ldc; } } lda = working_space[i1][i2 + 3 * ssizey]; ldc = working_space[i1][i2 + 1 * ssizey]; if (ldc * lda != 0 && ldb != 0) { lda = lda * ldc / ldb; } else lda = 0; working_space[i1][i2 + 4 * ssizey] = lda; } } for (i2 = 0; i2 < ssizey; i2++) { for (i1 = 0; i1 < ssizex; i1++) working_space[i1][i2 + 3 * ssizey] = working_space[i1][i2 + 4 * ssizey]; } } } for (i = 0; i < ssizex; i++) { for (j = 0; j < ssizey; j++) source[(i + positx) % ssizex][(j + posity) % ssizey] = area * working_space[i][j + 3 * ssizey]; } for (i = 0; i < ssizex; i++) delete[]working_space[i]; delete[]working_space; return 0; } //____________________________________________________________________________ Int_t TSpectrum2::SearchHighRes(float **source,float **dest, Int_t ssizex, Int_t ssizey, Double_t sigma, Double_t threshold, Bool_t backgroundRemove,Int_t deconIterations, Bool_t markov, Int_t averWindow) { ///////////////////////////////////////////////////////////////////////////// // 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) // // // ///////////////////////////////////////////////////////////////////////////// //Begin_Html <!-- /* --> <div class=Section1> <p class=MsoNormal><b><span style='font-size:20.0pt'>Peaks searching</span></b></p> <p class=MsoNormal style='text-align:justify'><i><span style='font-size:18.0pt'> </span></i></p> <p class=MsoNormal style='text-align:justify'><i><span style='font-size:18.0pt'>Goal: to identify automatically the peaks in spectrum with the presence of the continuous background, one-fold coincidences (ridges) and statistical fluctuations - noise.</span></i><span style='font-size:18.0pt'> </span></p> <p class=MsoNormal><span style='font-size:16.0pt;font-family:Arial'> </span></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt; font-family:Arial'>The common problems connected with correct peak identification in two-dimensional coincidence spectra are</span></p> <ul style='margin-top:0mm' type=disc> <li class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt; font-family:Arial'>non-sensitivity to noise, i.e., only statistically relevant peaks should be identified</span></li> <li class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt; font-family:Arial'>non-sensitivity of the algorithm to continuous background</span></li> <li class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt; font-family:Arial'>non-sensitivity to one-fold coincidences (coincidences peak – background in both dimensions) and their crossings</span></li> <li class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt; font-family:Arial'>ability to identify peaks close to the edges of the spectrum region. Usually peak finders fail to detect them</span></li> <li class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt; font-family:Arial'>resolution, decomposition of doublets and multiplets. The algorithm should be able to recognize close positioned peaks.</span><span style='font-size:18.0pt'> </span></li> <li class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt; font-family:Arial'>ability to identify peaks with different sigma</span></li> </ul> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'> </span></p> <p class=MsoNormal><i><span style='font-size:18.0pt'>Function:</span></i></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:18.0pt'><a href="http://root.cern.ch/root/html/ListOfTypes.html#Int_t">Int_t</a> </span></b><a name="TSpectrum:Search1HighRes"></a><a href="http://root.cern.ch/root/html/TSpectrum.html#TSpectrum:Fit1Awmi"><b><span style='font-size:18.0pt'>TSpectrum2::SearchHighRes</span></b></a><b><span style='font-size:18.0pt'> (<a href="http://root.cern.ch/root/html/ListOfTypes.html#float">float</a> **source,<a href="http://root.cern.ch/root/html/ListOfTypes.html#float">float</a> **dest, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int">int</a> ssizex, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int">int</a> ssizey, <a href="http://root.cern.ch/root/html/ListOfTypes.html#float">float</a> sigma, <a href="http://root.cern.ch/root/html/ListOfTypes.html#double">double</a> threshold, <a href="http://root.cern.ch/root/html/ListOfTypes.html#bool">bool</a> backgroundRemove,<a href="http://root.cern.ch/root/html/ListOfTypes.html#int">int</a> deconIterations, <a href="http://root.cern.ch/root/html/ListOfTypes.html#bool">bool</a> markov, <a href="http://root.cern.ch/root/html/ListOfTypes.html#int">int</a> averWindow) </span></b></p> <p class=MsoNormal> </p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'>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.</span></p> <p class=MsoNormal> </p> <p class=MsoNormal><i><span style='font-size:16.0pt;color:red'>Parameters:</span></i></p> <p class=MsoNormal style='text-align:justify'> <b><span style='font-size:14.0pt'>source</span></b>-pointer to the matrix of source spectrum </p> <p class=MsoNormal style='text-align:justify'> <b><span style='font-size:14.0pt'>dest</span></b>-resulting spectrum after deconvolution</p> <p class=MsoNormal style='text-align:justify'> <b><span style='font-size:14.0pt'>ssizex, ssizey</span></b>-lengths of the source and destination spectra </p> <p class=MsoNormal style='text-align:justify'> <b><span style='font-size:14.0pt'>sigma</span></b>-sigma of searched peaks</p> <p class=MsoNormal style='margin-left:22.8pt;text-align:justify'><b><span style='font-size:14.0pt'>threshold</span></b>-<span style='font-size:16.0pt'> </span>threshold value in % for selected peaks, peaks with amplitude less than threshold*highest_peak/100 are ignored</p> <p class=MsoNormal style='margin-left:22.8pt;text-align:justify'><b><span style='font-size:14.0pt'>backgroundRemove</span></b>-<span style='font-size: 16.0pt'> </span>background_remove-logical variable, true if the removal of background before deconvolution is desired </p> <p class=MsoNormal style='margin-left:22.8pt;text-align:justify'><b><span style='font-size:14.0pt'>deconIterations</span></b>-number of iterations in deconvolution operation</p> <p class=MsoNormal style='margin-left:22.8pt;text-align:justify'><b><span style='font-size:14.0pt'>markov</span></b>-logical variable, if it is true, first the source spectrum is replaced by new spectrum calculated using Markov chains method </p> <p class=MsoNormal style='margin-left:19.95pt;text-align:justify;text-indent: 2.85pt'><b><span style='font-size:14.0pt'>averWindow</span></b>-width of averaging smoothing window </p> <p class=MsoNormal> </p> <p class=MsoNormal><b><i><span style='font-size:18.0pt'>References:</span></i></b></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'>[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.</span></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'>[2] </span><span lang=SK style='font-size:16.0pt'> M. Morháč, J. Kliman, V. Matoušek, M. Veselský, I. Turzo</span><span style='font-size:16.0pt'>.:Identification of peaks in multidimensional coincidence gamma-ray spectra. NIM, A443 (2000) 108-125.</span></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'>[3] Z.K. Silagadze, A new algorithm for automatic photopeak searches. NIM A 376 (1996), 451.</span></p> </div> <!-- */ // --> End_Html //Begin_Html <!-- /* --> <div class=Section1> <p class=MsoNormal><b><span style='font-size:18.0pt'>Examples of peak searching method</span></b></p> <p class=MsoNormal><span style='font-size:16.0pt'> </span></p> <p class=MsoNormal style='text-align:justify'><span style='font-size:16.0pt'><a href="http://root.cern.ch/root/html/src/TSpectrum.cxx.html#TSpectrum:Search1HighRes" target="_parent">SearchHighRes</a> 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. </span></p> <p class=MsoNormal><i><span style='font-size:16.0pt'>Example 8 – script Src.c:</span></i></p> <p class=MsoNormal><span style='font-size:16.0pt'><img border=0 width=602 height=455 src="gif/TSpectrum2_Searching1.jpg"></span></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 20 Two-dimensional spectrum with found peaks denoted by markers (<sub><img border=0 width=40 height=19 src="gif/TSpectrum2_Searching2.gif"></sub>, threshold=5%, 3 iterations steps in the deconvolution)</span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'><img border=0 width=602 height=455 src="gif/TSpectrum2_Searching3.jpg"></span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 21 Spectrum from Fig. 20 after background elimination and deconvolution</span></b></p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:#339966'>Script:</span></b></p> <p class=MsoNormal>// Example to illustrate high resolution peak searching function (class TSpectrum).</p> <p class=MsoNormal>// To execute this example, do</p> <p class=MsoNormal>// root > .x Src.C</p> <p class=MsoNormal> </p> <p class=MsoNormal>#include <TSpectrum2></p> <p class=MsoNormal> </p> <p class=MsoNormal>void Src() {</p> <p class=MsoNormal> Int_t i, j, nfound;</p> <p class=MsoNormal> Double_t nbinsx = 64;</p> <p class=MsoNormal> Double_t nbinsy = 64; </p> <p class=MsoNormal> Double_t xmin = 0;</p> <p class=MsoNormal> Double_t xmax = (Double_t)nbinsx;</p> <p class=MsoNormal> Double_t ymin = 0;</p> <p class=MsoNormal> Double_t ymax = (Double_t)nbinsy; </p> <p class=MsoNormal> Float_t ** source = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> source[i]=new float[nbinsy];</p> <p class=MsoNormal> Float_t ** dest = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> dest[i]=new float[nbinsy];</p> <p class=MsoNormal> TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> TFile *f = new TFile("spectra2\\TSpectrum2.root");</p> <p class=MsoNormal> search=(TH2F*) f->Get("search4;1");</p> <p class=MsoNormal> TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);</p> <p class=MsoNormal> TSpectrum2 *s = new TSpectrum2();</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> source[i][j] = search->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> } </p> <p class=MsoNormal> nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 2, 5, kTRUE, 3, kFALSE, 3); </p> <p class=MsoNormal> printf("Found %d candidate peaks\n",nfound);</p> <p class=MsoNormal> for(i=0;i<nfound;i++)</p> <p class=MsoNormal> 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)]); </p> <p class=MsoNormal>}</p> <p class=MsoNormal><i><span style='font-size:16.0pt'>Example 9 – script Src2.c:</span></i></p> <p class=MsoNormal><img border=0 width=602 height=455 src="gif/TSpectrum2_Searching4.jpg"></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 22 Two-dimensional noisy spectrum with found peaks denoted by markers (<sub><img border=0 width=40 height=19 src="gif/TSpectrum2_Searching2.gif"></sub>, 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.</span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'><img border=0 width=602 height=455 src="gif/TSpectrum2_Searching5.jpg"></span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 23 Spectrum from Fig. 22 after background elimination and deconvolution</span></b></p> <p class=MsoNormal> </p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:#339966'>Script:</span></b></p> <p class=MsoNormal>// Example to illustrate high resolution peak searching function (class TSpectrum).</p> <p class=MsoNormal>// To execute this example, do</p> <p class=MsoNormal>// root > .x Src2.C</p> <p class=MsoNormal> </p> <p class=MsoNormal>#include <TSpectrum2></p> <p class=MsoNormal> </p> <p class=MsoNormal>void Src2() {</p> <p class=MsoNormal> Int_t i, j, nfound;</p> <p class=MsoNormal> Double_t nbinsx = 256;</p> <p class=MsoNormal> Double_t nbinsy = 256; </p> <p class=MsoNormal> Double_t xmin = 0;</p> <p class=MsoNormal> Double_t xmax = (Double_t)nbinsx;</p> <p class=MsoNormal> Double_t ymin = 0;</p> <p class=MsoNormal> Double_t ymax = (Double_t)nbinsy; </p> <p class=MsoNormal> Float_t ** source = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> source[i]=new float[nbinsy];</p> <p class=MsoNormal> Float_t ** dest = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> dest[i]=new float[nbinsy];</p> <p class=MsoNormal> TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> TFile *f = new TFile("spectra2\\TSpectrum2.root");</p> <p class=MsoNormal> search=(TH2F*) f->Get("back3;1");</p> <p class=MsoNormal> TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);</p> <p class=MsoNormal> TSpectrum2 *s = new TSpectrum2();</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> source[i][j] = search->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> } </p> <p class=MsoNormal> nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 2, 10, kTRUE, 10, kFALSE, 3); </p> <p class=MsoNormal> printf("Found %d candidate peaks\n",nfound);</p> <p class=MsoNormal> for(i=0;i<nfound;i++)</p> <p class=MsoNormal> 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)]); </p> <p class=MsoNormal>}</p> <p class=MsoNormal><i><span style='font-size:16.0pt'>Example 10 – script Src3.c:</span></i></p> <p class=MsoNormal><img border=0 width=602 height=455 src="gif/TSpectrum2_Searching6.jpg"></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>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.</span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'><img border=0 width=602 height=455 src="gif/TSpectrum2_Searching7.jpg"></span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 25 Spectrum from Fig. 24 after deconvolution (# of iterations = 3). Number of identified peaks = 13.</span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'><img border=0 width=602 height=455 src="gif/TSpectrum2_Searching8.jpg"></span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 26 Spectrum from Fig. 24 after deconvolution (# of iterations = 10). Number of identified peaks = 13.</span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'><img border=0 width=602 height=455 src="gif/TSpectrum2_Searching9.jpg"></span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>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.</span></b></p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:#339966'> </span></b></p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:#339966'>Script:</span></b></p> <p class=MsoNormal>// Example to illustrate high resolution peak searching function (class TSpectrum).</p> <p class=MsoNormal>// To execute this example, do</p> <p class=MsoNormal>// root > .x Src3.C</p> <p class=MsoNormal> </p> <p class=MsoNormal>#include <TSpectrum2></p> <p class=MsoNormal> </p> <p class=MsoNormal>void Src3() {</p> <p class=MsoNormal> Int_t i, j, nfound;</p> <p class=MsoNormal> Double_t nbinsx = 64;</p> <p class=MsoNormal> Double_t nbinsy = 64; </p> <p class=MsoNormal> Double_t xmin = 0;</p> <p class=MsoNormal> Double_t xmax = (Double_t)nbinsx;</p> <p class=MsoNormal> Double_t ymin = 0;</p> <p class=MsoNormal> Double_t ymax = (Double_t)nbinsy; </p> <p class=MsoNormal> Float_t ** source = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> source[i]=new float[nbinsy];</p> <p class=MsoNormal> Float_t ** dest = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> dest[i]=new float[nbinsy];</p> <p class=MsoNormal> TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> TFile *f = new TFile("spectra2\\TSpectrum2.root");</p> <p class=MsoNormal> search=(TH2F*) f->Get("search1;1");</p> <p class=MsoNormal> TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);</p> <p class=MsoNormal> TSpectrum2 *s = new TSpectrum2();</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> source[i][j] = search->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> } </p> <p class=MsoNormal> nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 2, 2, kFALSE, 3, kFALSE, 1);//3, 10, 100 </p> <p class=MsoNormal> printf("Found %d candidate peaks\n",nfound);</p> <p class=MsoNormal> </p> <p class=MsoNormal> for(i=0;i<nfound;i++)</p> <p class=MsoNormal> 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)]); </p> <p class=MsoNormal>}</p> <p class=MsoNormal><i><span style='font-size:16.0pt'>Example 11 – script Src4.c:</span></i></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'><img border=0 width=602 height=455 src="gif/TSpectrum2_Searching10.jpg"></span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 28 Two-dimensional spectrum with peaks with different sigma denoted by markers (<sub><img border=0 width=39 height=19 src="gif/TSpectrum2_Searching11.gif"></sub>, threshold=5%, 10 iterations steps in the deconvolution, Markov smoothing with window=3)</span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'><img border=0 width=602 height=455 src="gif/TSpectrum2_Searching12.jpg"></span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 29 Spectrum from Fig. 28 after smoothing and deconvolution.</span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'> </span></b></p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:#339966'>Script:</span></b></p> <p class=MsoNormal>// Example to illustrate high resolution peak searching function (class TSpectrum).</p> <p class=MsoNormal>// To execute this example, do</p> <p class=MsoNormal>// root > .x Src4.C</p> <p class=MsoNormal> </p> <p class=MsoNormal>#include <TSpectrum2></p> <p class=MsoNormal> </p> <p class=MsoNormal>void Src4() {</p> <p class=MsoNormal> Int_t i, j, nfound;</p> <p class=MsoNormal> Double_t nbinsx = 64;</p> <p class=MsoNormal> Double_t nbinsy = 64; </p> <p class=MsoNormal> Double_t xmin = 0;</p> <p class=MsoNormal> Double_t xmax = (Double_t)nbinsx;</p> <p class=MsoNormal> Double_t ymin = 0;</p> <p class=MsoNormal> Double_t ymax = (Double_t)nbinsy; </p> <p class=MsoNormal> Float_t ** source = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> source[i]=new float[nbinsy];</p> <p class=MsoNormal> Float_t ** dest = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> dest[i]=new float[nbinsy];</p> <p class=MsoNormal> TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> TFile *f = new TFile("spectra2\\TSpectrum2.root");</p> <p class=MsoNormal> search=(TH2F*) f->Get("search2;1");</p> <p class=MsoNormal> TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);</p> <p class=MsoNormal> TSpectrum2 *s = new TSpectrum2();</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> source[i][j] = search->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> } </p> <p class=MsoNormal> nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 3, 5, kFALSE, 10, kTRUE, 3); </p> <p class=MsoNormal> printf("Found %d candidate peaks\n",nfound);</p> <p class=MsoNormal> for(i=0;i<nfound;i++)</p> <p class=MsoNormal> 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)]); </p> <p class=MsoNormal>}</p> <p class=MsoNormal><i><span style='font-size:16.0pt'>Example 12 – script Src5.c:</span></i></p> <p class=MsoNormal><img border=0 width=602 height=455 src="gif/TSpectrum2_Searching13.jpg"></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 30 Two-dimensional spectrum with peaks positioned close to the edges denoted by markers (<sub><img border=0 width=40 height=19 src="gif/TSpectrum2_Searching2.gif"></sub>, threshold=5%, 10 iterations steps in the deconvolution)</span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'><img border=0 width=602 height=455 src="gif/TSpectrum2_Searching14.jpg"></span></b></p> <p class=MsoNormal style='text-align:justify'><b><span style='font-size:16.0pt'>Fig. 31 Spectrum from Fig. 30 after deconvolution.</span></b></p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:#339966'> </span></b></p> <p class=MsoNormal><b><span style='font-size:16.0pt;color:#339966'>Script:</span></b></p> <p class=MsoNormal>// Example to illustrate high resolution peak searching function (class TSpectrum).</p> <p class=MsoNormal>// To execute this example, do</p> <p class=MsoNormal>// root > .x Src5.C</p> <p class=MsoNormal> </p> <p class=MsoNormal>#include <TSpectrum2></p> <p class=MsoNormal> </p> <p class=MsoNormal>void Src5() {</p> <p class=MsoNormal> Int_t i, j, nfound;</p> <p class=MsoNormal> Double_t nbinsx = 64;</p> <p class=MsoNormal> Double_t nbinsy = 64; </p> <p class=MsoNormal> Double_t xmin = 0;</p> <p class=MsoNormal> Double_t xmax = (Double_t)nbinsx;</p> <p class=MsoNormal> Double_t ymin = 0;</p> <p class=MsoNormal> Double_t ymax = (Double_t)nbinsy; </p> <p class=MsoNormal> Float_t ** source = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> source[i]=new float[nbinsy];</p> <p class=MsoNormal> Float_t ** dest = new float *[nbinsx]; </p> <p class=MsoNormal> for (i=0;i<nbinsx;i++)</p> <p class=MsoNormal> dest[i]=new float[nbinsy];</p> <p class=MsoNormal> TH2F *search = new TH2F("search","High resolution peak searching",nbinsx,xmin,xmax,nbinsy,ymin,ymax);</p> <p class=MsoNormal> TFile *f = new TFile("spectra2\\TSpectrum2.root");</p> <p class=MsoNormal> search=(TH2F*) f->Get("search3;1");</p> <p class=MsoNormal> TCanvas *Searching = new TCanvas("Searching","High resolution peak searching",10,10,1000,700);</p> <p class=MsoNormal> TSpectrum2 *s = new TSpectrum2();</p> <p class=MsoNormal> for (i = 0; i < nbinsx; i++){</p> <p class=MsoNormal> for (j = 0; j < nbinsy; j++){</p> <p class=MsoNormal> source[i][j] = search->GetBinContent(i + 1,j + 1); </p> <p class=MsoNormal> }</p> <p class=MsoNormal> } </p> <p class=MsoNormal> nfound = s->SearchHighRes(source, dest, nbinsx, nbinsy, 2, 5, kFALSE, 10, kFALSE, 1); </p> <p class=MsoNormal> printf("Found %d candidate peaks\n",nfound);</p> <p class=MsoNormal> for(i=0;i<nfound;i++)</p> <p class=MsoNormal> 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)]); </p> <p class=MsoNormal>}</p> </div> <!-- */ // --> End_Html int number_of_iterations = (int)(4 * sigma + 0.5); int k, lindex, priz; double lda, ldb, ldc, area, maximum; int xmin, xmax, l, peak_index = 0, ssizex_ext = ssizex + 4 * number_of_iterations, ssizey_ext = ssizey + 4 * number_of_iterations, shift = 2 * number_of_iterations; int ymin, ymax, i, j; double a, b, ax, ay, maxch, plocha = 0; double nom, nip, nim, sp, sm, spx, spy, smx, smy; double p1, p2, p3, p4, s1, s2, s3, s4; int x, y; int lhx, lhy, i1, i2, j1, j2, k1, k2, i1min, i1max, i2min, i2max, j1min, j1max, j2min, j2max, positx, posity; if (sigma < 1) { Error("SearchHighRes", "Invalid sigma, must be greater than or equal to 1"); return 0; } if(threshold<=0||threshold>=100){ Error("SearchHighRes", "Invalid threshold, must be positive and less than 100"); return 0; } j = (int) (5.0 * sigma + 0.5); if (j >= PEAK_WINDOW / 2) { Error("SearchHighRes", "Too large sigma"); return 0; } if (markov == true) { if (averWindow <= 0) { Error("SearchHighRes", "Averanging window must be positive"); return 0; } } if(backgroundRemove == true){ if(ssizex_ext < 2 * number_of_iterations + 1 || ssizey_ext < 2 * number_of_iterations + 1){ Error("SearchHighRes", "Too large clipping window"); return 0; } } i = (int)(4 * sigma + 0.5); i = 4 * i; double **working_space = new double *[ssizex + i]; for (j = 0; j < ssizex + i; j++) { Double_t *wsk = working_space[j] = new double[16 * (ssizey + i)]; for (k=0;k<16 * (ssizey + i);k++) wsk[k] = 0; } for(j = 0; j < ssizey_ext; j++){ for(i = 0; i < ssizex_ext; i++){ if(i < shift){ if(j < shift) working_space[i][j + ssizey_ext] = source[0][0]; else if(j >= ssizey + shift) working_space[i][j + ssizey_ext] = source[0][ssizey - 1]; else working_space[i][j + ssizey_ext] = source[0][j - shift]; } else if(i >= ssizex + shift){ if(j < shift) working_space[i][j + ssizey_ext] = source[ssizex - 1][0]; else if(j >= ssizey + shift) working_space[i][j + ssizey_ext] = source[ssizex - 1][ssizey - 1]; else working_space[i][j + ssizey_ext] = source[ssizex - 1][j - shift]; } else{ if(j < shift) working_space[i][j + ssizey_ext] = source[i - shift][0]; else if(j >= ssizey + shift) working_space[i][j + ssizey_ext] = source[i - shift][ssizey - 1]; else working_space[i][j + ssizey_ext] = source[i - shift][j - shift]; } } } if(backgroundRemove == true){ for(i = 1; i <= number_of_iterations; i++){ for(y = i; y < ssizey_ext - i; y++){ for(x = i; x < ssizex_ext - i; x++){ a = working_space[x][y + ssizey_ext]; p1 = working_space[x - i][y + ssizey_ext - i]; p2 = working_space[x - i][y + ssizey_ext + i]; p3 = working_space[x + i][y + ssizey_ext - i]; p4 = working_space[x + i][y + ssizey_ext + i]; s1 = working_space[x][y + ssizey_ext - i]; s2 = working_space[x - i][y + ssizey_ext]; s3 = working_space[x + i][y + ssizey_ext]; s4 = working_space[x][y + ssizey_ext + i]; b = (p1 + p2) / 2.0; if(b > s2) s2 = b; b = (p1 + p3) / 2.0; if(b > s1) s1 = b; b = (p2 + p4) / 2.0; if(b > s4) s4 = b; b = (p3 + p4) / 2.0; if(b > s3) s3 = b; s1 = s1 - (p1 + p3) / 2.0; s2 = s2 - (p1 + p2) / 2.0; s3 = s3 - (p3 + p4) / 2.0; s4 = s4 - (p2 + p4) / 2.0; b = (s1 + s4) / 2.0 + (s2 + s3) / 2.0 + (p1 + p2 + p3 + p4) / 4.0; if(b < a) a = b; working_space[x][y] = a; } } for(y = i;y < ssizey_ext - i; y++){ for(x = i; x < ssizex_ext - i; x++){ working_space[x][y + ssizey_ext] = working_space[x][y]; } } } for(j = 0;j < ssizey_ext; j++){ for(i = 0; i < ssizex_ext; i++){ if(i < shift){ if(j < shift) working_space[i][j + ssizey_ext] = source[0][0] - working_space[i][j + ssizey_ext]; else if(j >= ssizey + shift) working_space[i][j + ssizey_ext] = source[0][ssizey - 1] - working_space[i][j + ssizey_ext]; else working_space[i][j + ssizey_ext] = source[0][j - shift] - working_space[i][j + ssizey_ext]; } else if(i >= ssizex + shift){ if(j < shift) working_space[i][j + ssizey_ext] = source[ssizex - 1][0] - working_space[i][j + ssizey_ext]; else if(j >= ssizey + shift) working_space[i][j + ssizey_ext] = source[ssizex - 1][ssizey - 1] - working_space[i][j + ssizey_ext]; else working_space[i][j + ssizey_ext] = source[ssizex - 1][j - shift] - working_space[i][j + ssizey_ext]; } else{ if(j < shift) working_space[i][j + ssizey_ext] = source[i - shift][0] - working_space[i][j + ssizey_ext]; else if(j >= ssizey + shift) working_space[i][j + ssizey_ext] = source[i - shift][ssizey - 1] - working_space[i][j + ssizey_ext]; else working_space[i][j + ssizey_ext] = source[i - shift][j - shift] - working_space[i][j + ssizey_ext]; } } } } for(j = 0; j < ssizey_ext; j++){ for(i = 0; i < ssizex_ext; i++){ working_space[i][j + 15*ssizey_ext] = working_space[i][j + ssizey_ext]; } } if(markov == true){ for(i = 0;i < ssizex_ext; i++){ for(j = 0; j < ssizey_ext; j++) working_space[i][j + 2 * ssizex_ext] = working_space[i][ssizey_ext + j]; } xmin = 0; xmax = ssizex_ext - 1; ymin = 0; ymax = ssizey_ext - 1; for(i = 0, maxch = 0; i < ssizex_ext; i++){ for(j = 0; j < ssizey_ext; j++){ working_space[i][j] = 0; if(maxch < working_space[i][j + 2 * ssizey_ext]) maxch = working_space[i][j + 2 * ssizey_ext]; plocha += working_space[i][j + 2 * ssizey_ext]; } } if(maxch == 0) return 0; nom=0; working_space[xmin][ymin] = 1; for(i = xmin; i < xmax; i++){ nip = working_space[i][ymin + 2 * ssizey_ext] / maxch; nim = working_space[i + 1][ymin + 2 * ssizey_ext] / maxch; sp = 0,sm = 0; for(l = 1;l <= averWindow; l++){ if((i + l) > xmax) a = working_space[xmax][ymin + 2 * ssizey_ext] / maxch; else a = working_space[i + l][ymin + 2 * ssizey_ext] / maxch; b = a - nip; if(a + nip <= 0) a = 1; else a=TMath::Sqrt(a + nip); b = b / a; b = TMath::Exp(b); sp = sp + b; if(i - l + 1 < xmin) a = working_space[xmin][ymin + 2 * ssizey_ext] / maxch; else a = working_space[i - l + 1][ymin + 2 * ssizey_ext] / maxch; b = a - nim; if(a + nim <= 0) a = 1; else a=TMath::Sqrt(a + nim); b = b / a; b = TMath::Exp(b); sm = sm + b; } a = sp / sm; a = working_space[i + 1][ymin] = a * working_space[i][ymin]; nom = nom + a; } for(i = ymin; i < ymax; i++){ nip = working_space[xmin][i + 2 * ssizey_ext] / maxch; nim = working_space[xmin][i + 1 + 2 * ssizey_ext] / maxch; sp = 0,sm = 0; for(l = 1; l <= averWindow; l++){ if((i + l) > ymax) a = working_space[xmin][ymax + 2 * ssizey_ext] / maxch; else a = working_space[xmin][i + l + 2 * ssizey_ext] / maxch; b = a - nip; if(a + nip <= 0) a=1; else a=TMath::Sqrt(a + nip); b = b / a; b = TMath::Exp(b); sp = sp + b; if(i - l + 1 < ymin) a = working_space[xmin][ymin + 2 * ssizey_ext] / maxch; else a = working_space[xmin][i - l + 1 + 2 * ssizey_ext] / maxch; b = a - nim; if(a + nim <= 0) a = 1; else a=TMath::Sqrt(a + nim); b = b / a; b = TMath::Exp(b); sm = sm + b; } a = sp / sm; a = working_space[xmin][i + 1] = a * working_space[xmin][i]; nom = nom + a; } for(i = xmin; i < xmax; i++){ for(j = ymin; j < ymax; j++){ nip = working_space[i][j + 1 + 2 * ssizey_ext] / maxch; nim = working_space[i + 1][j + 1 + 2 * ssizey_ext] / maxch; spx = 0,smx = 0; for(l = 1; l <= averWindow; l++){ if(i + l > xmax) a = working_space[xmax][j + 2 * ssizey_ext] / maxch; else a = working_space[i + l][j + 2 * ssizey_ext] / maxch; b = a - nip; if(a + nip <= 0) a = 1; else a=TMath::Sqrt(a + nip); b = b / a; b = TMath::Exp(b); spx = spx + b; if(i - l + 1 < xmin) a = working_space[xmin][j + 2 * ssizey_ext] / maxch; else a = working_space[i - l + 1][j + 2 * ssizey_ext] / maxch; b = a - nim; if(a + nim <= 0) a=1; else a=TMath::Sqrt(a + nim); b = b / a; b = TMath::Exp(b); smx = smx + b; } spy = 0,smy = 0; nip = working_space[i + 1][j + 2 * ssizey_ext] / maxch; nim = working_space[i + 1][j + 1 + 2 * ssizey_ext] / maxch; for(l = 1; l <= averWindow; l++){ if(j + l > ymax) a = working_space[i][ymax + 2 * ssizey_ext] / maxch; else a = working_space[i][j + l + 2 * ssizey_ext] / maxch; b = a - nip; if(a + nip <= 0) a = 1; else a=TMath::Sqrt(a + nip); b = b / a; b = TMath::Exp(b); spy = spy + b; if(j - l + 1 < ymin) a = working_space[i][ymin + 2 * ssizey_ext] / maxch; else a = working_space[i][j - l + 1 + 2 * ssizey_ext] / maxch; b=a-nim; if(a + nim <= 0) a = 1; else a=TMath::Sqrt(a + nim); b = b / a; b = TMath::Exp(b); smy = smy + b; } a = (spx * working_space[i][j + 1] + spy * working_space[i + 1][j]) / (smx + smy); working_space[i + 1][j + 1] = a; nom = nom + a; } } for(i = xmin; i <= xmax; i++){ for(j = ymin; j <= ymax; j++){ working_space[i][j] = working_space[i][j] / nom; } } for(i = 0; i < ssizex_ext; i++){ for(j = 0; j < ssizey_ext; j++){ working_space[i][j + ssizey_ext] = working_space[i][j] * plocha; working_space[i][2 * ssizey_ext + j] = working_space[i][ssizey_ext + j]; } } } //deconvolution starts area = 0; lhx = -1,lhy = -1; positx = 0,posity = 0; maximum = 0; //generate response matrix for(i = 0; i < ssizex_ext; i++){ for(j = 0; j < ssizey_ext; j++){ lda = (double)i - 3 * sigma; ldb = (double)j - 3 * sigma; lda = (lda * lda + ldb * ldb) / (2 * sigma * sigma); k=(int)(1000 * TMath::Exp(-lda)); lda = k; if(lda != 0){ if((i + 1) > lhx) lhx = i + 1; if((j + 1) > lhy) lhy = j + 1; } working_space[i][j] = lda; area = area + lda; if(lda > maximum){ maximum = lda; positx = i,posity = j; } } } //read source matrix for(i = 0;i < ssizex_ext; i++){ for(j = 0;j < ssizey_ext; j++){ working_space[i][j + 14 * ssizey_ext] = TMath::Abs(working_space[i][j + ssizey_ext]); } } //calculate matrix b=ht*h i = lhx - 1; if(i > ssizex_ext) i = ssizex_ext; j = lhy - 1; if(j>ssizey_ext) j = ssizey_ext; i1min = -i,i1max = i; i2min = -j,i2max = j; for(i2 = i2min; i2 <= i2max; i2++){ for(i1 = i1min; i1 <= i1max; i1++){ ldc = 0; j2min = -i2; if(j2min < 0) j2min = 0; j2max = lhy - 1 - i2; if(j2max > lhy - 1) j2max = lhy - 1; for(j2 = j2min; j2 <= j2max; j2++){ j1min = -i1; if(j1min < 0) j1min = 0; j1max = lhx - 1 - i1; if(j1max > lhx - 1) j1max = lhx - 1; for(j1 = j1min; j1 <= j1max; j1++){ lda = working_space[j1][j2]; ldb = working_space[i1 + j1][i2 + j2]; ldc = ldc + lda * ldb; } } k = (i1 + ssizex_ext) / ssizex_ext; working_space[(i1 + ssizex_ext) % ssizex_ext][i2 + ssizey_ext + 10 * ssizey_ext + k * 2 * ssizey_ext] = ldc; } } //calculate at*y and write into p i = lhx - 1; if(i > ssizex_ext) i = ssizex_ext; j = lhy - 1; if(j > ssizey_ext) j = ssizey_ext; i2min = -j,i2max = ssizey_ext + j - 1; i1min = -i,i1max = ssizex_ext + i - 1; for(i2 = i2min; i2 <= i2max; i2++){ for(i1=i1min;i1<=i1max;i1++){ ldc=0; for(j2 = 0; j2 <= (lhy - 1); j2++){ for(j1 = 0; j1 <= (lhx - 1); j1++){ k2 = i2 + j2,k1 = i1 + j1; if(k2 >= 0 && k2 < ssizey_ext && k1 >= 0 && k1 < ssizex_ext){ lda = working_space[j1][j2]; ldb = working_space[k1][k2 + 14 * ssizey_ext]; ldc = ldc + lda * ldb; } } } k = (i1 + ssizex_ext) / ssizex_ext; working_space[(i1 + ssizex_ext) % ssizex_ext][i2 + ssizey_ext + ssizey_ext + k * 3 * ssizey_ext] = ldc; } } //move matrix p for(i2 = 0; i2 < ssizey_ext; i2++){ for(i1 = 0; i1 < ssizex_ext; i1++){ k = (i1 + ssizex_ext) / ssizex_ext; ldb = working_space[(i1 + ssizex_ext) % ssizex_ext][i2 + ssizey_ext + ssizey_ext + k * 3 * ssizey_ext]; working_space[i1][i2 + 14 * ssizey_ext] = ldb; } } //initialization in x1 matrix for(i2 = 0; i2 < ssizey_ext; i2++){ for(i1 = 0; i1 < ssizex_ext; i1++){ working_space[i1][i2 + ssizey_ext] = 1; working_space[i1][i2 + 2 * ssizey_ext] = 0; } } //START OF ITERATIONS for(lindex = 0; lindex < deconIterations; lindex++){ for(i2 = 0; i2 < ssizey_ext; i2++){ for(i1 = 0; i1 < ssizex_ext; i1++){ lda = working_space[i1][i2 + ssizey_ext]; ldc = working_space[i1][i2 + 14 * ssizey_ext]; if(lda > 0.000001 && ldc > 0.000001){ ldb=0; j2min=i2; if(j2min > lhy - 1) j2min = lhy - 1; j2min = -j2min; j2max = ssizey_ext - i2 - 1; if(j2max > lhy - 1) j2max = lhy - 1; j1min = i1; if(j1min > lhx - 1) j1min = lhx - 1; j1min = -j1min; j1max = ssizex_ext - i1 - 1; if(j1max > lhx - 1) j1max = lhx - 1; for(j2 = j2min; j2 <= j2max; j2++){ for(j1 = j1min; j1 <= j1max; j1++){ k = (j1 + ssizex_ext) / ssizex_ext; ldc = working_space[(j1 + ssizex_ext) % ssizex_ext][j2 + ssizey_ext + 10 * ssizey_ext + k * 2 * ssizey_ext]; lda = working_space[i1 + j1][i2 + j2 + ssizey_ext]; ldb = ldb + lda * ldc; } } lda = working_space[i1][i2 + ssizey_ext]; ldc = working_space[i1][i2 + 14 * ssizey_ext]; if(ldc * lda != 0 && ldb != 0){ lda =lda * ldc / ldb; } else lda=0; working_space[i1][i2 + 2 * ssizey_ext] = lda; } } } for(i2 = 0; i2 < ssizey_ext; i2++){ for(i1 = 0; i1 < ssizex_ext; i1++) working_space[i1][i2 + ssizey_ext] = working_space[i1][i2 + 2 * ssizey_ext]; } } //looking for maximum maximum=0; for(i = 0; i < ssizex_ext; i++){ for(j = 0; j < ssizey_ext; j++){ working_space[(i + positx) % ssizex_ext][(j + posity) % ssizey_ext] = area * working_space[i][j + ssizey_ext]; if(maximum < working_space[(i + positx) % ssizex_ext][(j + posity) % ssizey_ext]) maximum = working_space[(i + positx) % ssizex_ext][(j + posity) % ssizey_ext]; } } //searching for peaks in deconvolved spectrum for(i = 1; i < ssizex_ext - 1; i++){ for(j = 1; j < ssizey_ext - 1; j++){ if(working_space[i][j] > working_space[i - 1][j] && working_space[i][j] > working_space[i - 1][j - 1] && working_space[i][j] > working_space[i][j - 1] && working_space[i][j] > working_space[i + 1][j - 1] && working_space[i][j] > working_space[i + 1][j] && working_space[i][j] > working_space[i + 1][j + 1] && working_space[i][j] > working_space[i][j + 1] && working_space[i][j] > working_space[i - 1][j + 1]){ if(i >= shift && i < ssizex + shift && j >= shift && j < ssizey + shift){ if(working_space[i][j] > threshold * maximum / 100.0){ if(peak_index < fMaxPeaks){ for(k = i - 1,a = 0,b = 0; k <= i + 1; k++){ a += (double)(k - shift) * working_space[k][j]; b += working_space[k][j]; } ax=a/b; if(ax < 0) ax = 0; if(ax >= ssizex) ax = ssizex - 1; for(k = j - 1,a = 0,b = 0; k <= j + 1; k++){ a += (double)(k - shift) * working_space[i][k]; b += working_space[i][k]; } ay=a/b; if(ay < 0) ay = 0; if(ay >= ssizey) ay = ssizey - 1; if(peak_index == 0){ fPositionX[0] = ax; fPositionY[0] = ay; peak_index = 1; } else{ for(k = 0, priz = 0; k < peak_index && priz == 0; k++){ if(working_space[shift+(int)(ax+0.5)][15 * ssizey_ext + shift + (int)(ay+0.5)] > working_space[shift+(int)(fPositionX[k]+0.5)][15 * ssizey_ext + shift + (int)(fPositionY[k]+0.5)]) priz = 1; } if(priz == 0){ if(k < fMaxPeaks){ fPositionX[k] = ax; fPositionY[k] = ay; } } else{ for(l = peak_index; l >= k; l--){ if(l < fMaxPeaks){ fPositionX[l] = fPositionX[l - 1]; fPositionY[l] = fPositionY[l - 1]; } } fPositionX[k - 1] = ax; fPositionY[k - 1] = ay; } if(peak_index < fMaxPeaks) peak_index += 1; } } } } } } } //writing back deconvolved spectrum for(i = 0; i < ssizex; i++){ for(j = 0; j < ssizey; j++){ dest[i][j] = working_space[i + shift][j + shift]; } } i = (int)(4 * sigma + 0.5); i = 4 * i; for (j = 0; j < ssizex + i; j++) delete[]working_space[j]; delete[]working_space; fNPeaks = peak_index; return fNPeaks; } // STATIC functions (called by TH1) //_______________________________________________________________________________ Int_t TSpectrum2::StaticSearch(const TH1 *hist, Double_t sigma, Option_t *option, Double_t threshold) { //static function, interface to TSpectrum2::Search TSpectrum2 s; return s.Search(hist,sigma,option,threshold); } //_______________________________________________________________________________ TH1 *TSpectrum2::StaticBackground(const TH1 *hist,Int_t niter, Option_t *option) { //static function, interface to TSpectrum2::Background TSpectrum2 s; return s.Background(hist,niter,option); }
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