// @(#)root/spectrum:$Id$ // Author: Miroslav Morhac 25/09/2006 ///////////////////////////////////////////////////////////////////////////// // THIS CLASS CONTAINS ADVANCED TWO-DIMENSIONAL SPECTRA // // FITTING 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.: Efficient fitting algorithms applied to // // analysis of coincidence gamma-ray spectra. Computer Physics // // Communications, Vol 172/1 (2005) pp. 19-41. // // // // [2] M. Morhac et al.: Study of fitting algorithms applied to // // simultaneous analysis of large number of peaks in gamma-ray spectra. // // Applied Spectroscopy, Vol. 57, No. 7, pp. 753-760, 2003. // // // // // //____________________________________________________________________________ #include "TSpectrum2Fit.h" #include "TMath.h" ClassImp(TSpectrum2Fit) //______________________________________________________________________________ TSpectrum2Fit::TSpectrum2Fit() :TNamed("Spectrum2Fit", "Miroslav Morhac peak fitter") { //default constructor fNPeaks = 0; fNumberIterations = 1; fXmin = 0; fXmax = 100; fYmin = 0; fYmax = 100; fStatisticType = kFitOptimChiCounts; fAlphaOptim = kFitAlphaHalving; fPower = kFitPower2; fFitTaylor = kFitTaylorOrderFirst; fAlpha = 1; fChi = 0; fPositionInitX = 0; fPositionCalcX = 0; fPositionErrX = 0; fPositionInitY = 0; fPositionCalcY = 0; fPositionErrY = 0; fPositionInitX1 = 0; fPositionCalcX1 = 0; fPositionErrX1 = 0; fPositionInitY1 = 0; fPositionCalcY1 = 0; fPositionErrY1 = 0; fAmpInit = 0; fAmpCalc = 0; fAmpErr = 0; fAmpInitX1 = 0; fAmpCalcX1 = 0; fAmpErrX1 = 0; fAmpInitY1 = 0; fAmpCalcY1 = 0; fAmpErrY1 = 0; fVolume = 0; fVolumeErr = 0; fSigmaInitX = 2; fSigmaCalcX = 0; fSigmaErrX = 0; fSigmaInitY = 2; fSigmaCalcY = 0; fSigmaErrY = 0; fRoInit = 0; fRoCalc = 0; fRoErr = 0; fTxyInit = 0; fTxyCalc = 0; fTxyErr = 0; fTxInit = 0; fTxCalc = 0; fTxErr = 0; fTyInit = 0; fTyCalc = 0; fTyErr = 0; fBxInit = 1; fBxCalc = 0; fBxErr = 0; fByInit = 1; fByCalc = 0; fByErr = 0; fSxyInit = 0; fSxyCalc = 0; fSxyErr = 0; fSxInit = 0; fSxCalc = 0; fSxErr = 0; fSyInit = 0; fSyCalc = 0; fSyErr = 0; fA0Init = 0; fA0Calc = 0; fA0Err = 0; fAxInit = 0; fAxCalc = 0; fAxErr = 0; fAyInit = 0; fAyCalc = 0; fAyErr = 0; fFixPositionX = 0; fFixPositionY = 0; fFixPositionX1 = 0; fFixPositionY1 = 0; fFixAmp = 0; fFixAmpX1 = 0; fFixAmpY1 = 0; fFixSigmaX = false; fFixSigmaY = false; fFixRo = true; fFixTxy = true; fFixTx = true; fFixTy = true; fFixBx = true; fFixBy = true; fFixSxy = true; fFixSx = true; fFixSy = true; fFixA0 = true; fFixAx = true; fFixAy = true; } //______________________________________________________________________________ TSpectrum2Fit::TSpectrum2Fit(Int_t numberPeaks) :TNamed("Spectrum2Fit", "Miroslav Morhac peak fitter") { //numberPeaks: number of fitted peaks (must be greater than zero) //the constructor allocates arrays for all fitted parameters (peak positions, amplitudes etc) and sets the member //variables to their default values. One can change these variables by member functions (setters) of TSpectrumFit class. //Begin_Html

Shape function of the fitted peaks contains the two-dimensional symmetrical Gaussian two one-dimensional symmetrical Gaussian ridges as well as nonsymmetrical terms and background.

End_Html if (numberPeaks <= 0){ Error ("TSpectrum2Fit","Invalid number of peaks, must be > than 0"); return; } fNPeaks = numberPeaks; fNumberIterations = 1; fXmin = 0; fXmax = 100; fYmin = 0; fYmax = 100; fStatisticType = kFitOptimChiCounts; fAlphaOptim = kFitAlphaHalving; fPower = kFitPower2; fFitTaylor = kFitTaylorOrderFirst; fAlpha = 1; fChi = 0; fPositionInitX = new Double_t[numberPeaks]; fPositionCalcX = new Double_t[numberPeaks]; fPositionErrX = new Double_t[numberPeaks]; fPositionInitY = new Double_t[numberPeaks]; fPositionCalcY = new Double_t[numberPeaks]; fPositionErrY = new Double_t[numberPeaks]; fPositionInitX1 = new Double_t[numberPeaks]; fPositionCalcX1 = new Double_t[numberPeaks]; fPositionErrX1 = new Double_t[numberPeaks]; fPositionInitY1 = new Double_t[numberPeaks]; fPositionCalcY1 = new Double_t[numberPeaks]; fPositionErrY1 = new Double_t[numberPeaks]; fAmpInit = new Double_t[numberPeaks]; fAmpCalc = new Double_t[numberPeaks]; fAmpErr = new Double_t[numberPeaks]; fAmpInitX1 = new Double_t[numberPeaks]; fAmpCalcX1 = new Double_t[numberPeaks]; fAmpErrX1 = new Double_t[numberPeaks]; fAmpInitY1 = new Double_t[numberPeaks]; fAmpCalcY1 = new Double_t[numberPeaks]; fAmpErrY1 = new Double_t[numberPeaks]; fVolume = new Double_t[numberPeaks]; fVolumeErr = new Double_t[numberPeaks]; fSigmaInitX = 2; fSigmaCalcX = 0; fSigmaErrX = 0; fSigmaInitY = 2; fSigmaCalcY = 0; fSigmaErrY = 0; fRoInit = 0; fRoCalc = 0; fRoErr = 0; fTxyInit = 0; fTxyCalc = 0; fTxyErr = 0; fTxInit = 0; fTxCalc = 0; fTxErr = 0; fTyInit = 0; fTyCalc = 0; fTyErr = 0; fBxInit = 1; fBxCalc = 0; fBxErr = 0; fByInit = 1; fByCalc = 0; fByErr = 0; fSxyInit = 0; fSxyCalc = 0; fSxyErr = 0; fSxInit = 0; fSxCalc = 0; fSxErr = 0; fSyInit = 0; fSyCalc = 0; fSyErr = 0; fA0Init = 0; fA0Calc = 0; fA0Err = 0; fAxInit = 0; fAxCalc = 0; fAxErr = 0; fAyInit = 0; fAyCalc = 0; fAyErr = 0; fFixPositionX = new Bool_t[numberPeaks]; fFixPositionY = new Bool_t[numberPeaks]; fFixPositionX1 = new Bool_t[numberPeaks]; fFixPositionY1 = new Bool_t[numberPeaks]; fFixAmp = new Bool_t[numberPeaks]; fFixAmpX1 = new Bool_t[numberPeaks]; fFixAmpY1 = new Bool_t[numberPeaks]; fFixSigmaX = false; fFixSigmaY = false; fFixRo = true; fFixTxy = true; fFixTx = true; fFixTy = true; fFixBx = true; fFixBy = true; fFixSxy = true; fFixSx = true; fFixSy = true; fFixA0 = true; fFixAx = true; fFixAy = true; } //______________________________________________________________________________ TSpectrum2Fit::~TSpectrum2Fit() { // destructor delete [] fPositionInitX; delete [] fPositionCalcX; delete [] fPositionErrX; delete [] fFixPositionX; delete [] fPositionInitY; delete [] fPositionCalcY; delete [] fPositionErrY; delete [] fFixPositionY; delete [] fPositionInitX1; delete [] fPositionCalcX1; delete [] fPositionErrX1; delete [] fFixPositionX1; delete [] fPositionInitY1; delete [] fPositionCalcY1; delete [] fPositionErrY1; delete [] fFixPositionY1; delete [] fAmpInit; delete [] fAmpCalc; delete [] fAmpErr; delete [] fFixAmp; delete [] fAmpInitX1; delete [] fAmpCalcX1; delete [] fAmpErrX1; delete [] fFixAmpX1; delete [] fAmpInitY1; delete [] fAmpCalcY1; delete [] fAmpErrY1; delete [] fFixAmpY1; delete [] fVolume; delete [] fVolumeErr; } /////////////////BEGINNING OF AUXILIARY FUNCTIONS USED BY FITTING FUNCTIONS////////////////////////// //______________________________________________________________________________ Double_t TSpectrum2Fit::Erfc(Double_t x) { ////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates error function of x. // // // ////////////////////////////////////////////////////////////////////////////// Double_t da1 = 0.1740121, da2 = -0.0479399, da3 = 0.3739278, dap = 0.47047; Double_t a, t, c, w; a = TMath::Abs(x); w = 1. + dap * a; t = 1. / w; w = a * a; if (w < 700) c = exp(-w); else { c = 0; } c = c * t * (da1 + t * (da2 + t * da3)); if (x < 0) c = 1. - c; return (c); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derfc(Double_t x) { ////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of error function of x. // // // ////////////////////////////////////////////////////////////////////////////// Double_t a, t, c, w; Double_t da1 = 0.1740121, da2 = -0.0479399, da3 = 0.3739278, dap = 0.47047; a = TMath::Abs(x); w = 1. + dap * a; t = 1. / w; w = a * a; if (w < 700) c = exp(-w); else { c = 0; } c = (-1.) * dap * c * t * t * (da1 + t * (2. * da2 + t * 3. * da3)) - 2. * a * Erfc(a); return (c); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Ourpowl(Double_t a, Int_t pw) { //power function Double_t c; Double_t a2 = a*a; c = 1; if (pw > 0) c *= a2; if (pw > 2) c *= a2; if (pw > 4) c *= a2; if (pw > 6) c *= a2; if (pw > 8) c *= a2; if (pw > 10) c *= a2; if (pw > 12) c *= a2; return (c); } void TSpectrum2Fit::StiefelInversion(Double_t **a, Int_t size) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates solution of the system of linear equations. // // The matrix a should have a dimension size*(size+4) // // The calling function should fill in the matrix, the column size should // // contain vector y (right side of the system of equations). The result is // // placed into size+1 column of the matrix. // // according to sigma of peaks. // // Function parameters: // // -a-matrix with dimension size*(size+4) // // // -size-number of rows of the matrix // // // ////////////////////////////////////////////////////////////////////////////////// Int_t i, j, k = 0; Double_t sk = 0, b, lambdak, normk, normk_old = 0; do { normk = 0; //calculation of rk and norm for (i = 0; i < size; i++) { a[i][size + 2] = -a[i][size]; //rk=-C for (j = 0; j < size; j++) { a[i][size + 2] += a[i][j] * a[j][size + 1]; //A*xk-C } normk += a[i][size + 2] * a[i][size + 2]; //calculation normk } //calculation of sk if (k != 0) { sk = normk / normk_old; } //calculation of uk for (i = 0; i < size; i++) { a[i][size + 3] = -a[i][size + 2] + sk * a[i][size + 3]; //uk=-rk+sk*uk-1 } //calculation of lambdak lambdak = 0; for (i = 0; i < size; i++) { for (j = 0, b = 0; j < size; j++) { b += a[i][j] * a[j][size + 3]; //A*uk } lambdak += b * a[i][size + 3]; } if (TMath::Abs(lambdak) > 1e-50) //computer zero lambdak = normk / lambdak; else lambdak = 0; for (i = 0; i < size; i++) a[i][size + 1] += lambdak * a[i][size + 3]; //xk+1=xk+lambdak*uk normk_old = normk; k += 1; } while (k < size && TMath::Abs(normk) > 1e-50); //computer zero return; } //______________________________________________________________________________ Double_t TSpectrum2Fit::Shape2(Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t ro, Double_t a0, Double_t ax, Double_t ay, Double_t txy, Double_t sxy, Double_t tx, Double_t ty, Double_t sx, Double_t sy, Double_t bx, Double_t by) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates 2D peaks shape function (see manual) // // Function parameters: // // -numOfFittedPeaks-number of fitted peaks // // -x-channel in x-dimension // // -y-channel in y-dimension // // -parameter-array of peaks parameters (amplitudes and positions) // // -sigmax-sigmax of peaks // // -sigmay-sigmay of peaks // // -ro-correlation coefficient // // -a0,ax,ay-bac kground coefficients // // -txy,tx,ty, sxy,sy,sx-relative amplitudes // // -bx, by-slopes // // // ////////////////////////////////////////////////////////////////////////////////// Int_t j; Double_t r, p, r1, e, ex, ey, vx, s2, px, py, rx, ry, erx, ery; vx = 0; s2 = TMath::Sqrt(2.0); for (j = 0; j < numOfFittedPeaks; j++) { p = (x - parameter[7 * j + 1]) / sigmax; r = (y - parameter[7 * j + 2]) / sigmay; if (TMath::Abs(p) < 3 && TMath::Abs(r) < 3) { e = (p * p - 2 * ro * p * r + r * r) / (2 * (1 - ro * ro)); if (e < 700) r1 = exp(-e); else { r1 = 0; } if (txy != 0) { px = 0, py = 0; erx = Erfc(p / s2 + 1 / (2 * bx)), ery = Erfc(r / s2 + 1 / (2 * by)); ex = p / (s2 * bx), ey = r / (s2 * by); if (TMath::Abs(ex) < 9 && TMath::Abs(ey) < 9) { px = exp(ex) * erx, py = exp(ey) * ery; } r1 += 0.5 * txy * px * py; } if (sxy != 0) { rx = Erfc(p / s2), ry = Erfc(r / s2); r1 += 0.5 * sxy * rx * ry; } vx = vx + parameter[7 * j] * r1; } p = (x - parameter[7 * j + 5]) / sigmax; if (TMath::Abs(p) < 3) { e = p * p / 2; if (e < 700) r1 = exp(-e); else { r1 = 0; } if (tx != 0) { px = 0; erx = Erfc(p / s2 + 1 / (2 * bx)); ex = p / (s2 * bx); if (TMath::Abs(ex) < 9) { px = exp(ex) * erx; } r1 += 0.5 * tx * px; } if (sx != 0) { rx = Erfc(p / s2); r1 += 0.5 * sx * rx; } vx = vx + parameter[7 * j + 3] * r1; } r = (y - parameter[7 * j + 6]) / sigmay; if (TMath::Abs(r) < 3) { e = r * r / 2; if (e < 700) r1 = exp(-e); else { r1 = 0; } if (ty != 0) { py = 0; ery = Erfc(r / s2 + 1 / (2 * by)); ey = r / (s2 * by); if (TMath::Abs(ey) < 9) { py = exp(ey) * ery; } r1 += 0.5 * ty * py; } if (sy != 0) { ry = Erfc(r / s2); r1 += 0.5 * sy * ry; } vx = vx + parameter[7 * j + 4] * r1; } } vx = vx + a0 + ax * x + ay * y; return (vx); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Deramp2(Double_t x, Double_t y, Double_t x0, Double_t y0, Double_t sigmax, Double_t sigmay, Double_t ro, Double_t txy, Double_t sxy, Double_t bx, Double_t by) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of 2D peaks shape function (see manual) // // according to amplitude of 2D peak // // Function parameters: // // -x-channel in x-dimension // // -y-channel in y-dimension // // -x0-position of peak in x-dimension // // -y0-position of peak in y-dimension // // -sigmax-sigmax of peaks // // -sigmay-sigmay of peaks // // -ro-correlation coefficient // // -txy, sxy-relative amplitudes // // -bx, by-slopes // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r, r1 = 0, e, ex, ey, px, py, rx, ry, erx, ery, s2; p = (x - x0) / sigmax; r = (y - y0) / sigmay; if (TMath::Abs(p) < 3 && TMath::Abs(r) < 3) { s2 = TMath::Sqrt(2.0); e = (p * p - 2 * ro * p * r + r * r) / (2 * (1 - ro * ro)); if (e < 700) r1 = exp(-e); else { r1 = 0; } if (txy != 0) { px = 0, py = 0; erx = Erfc(p / s2 + 1 / (2 * bx)), ery = Erfc(r / s2 + 1 / (2 * by)); ex = p / (s2 * bx), ey = r / (s2 * by); if (TMath::Abs(ex) < 9 && TMath::Abs(ey) < 9) { px = exp(ex) * erx, py = exp(ey) * ery; } r1 += 0.5 * txy * px * py; } if (sxy != 0) { rx = Erfc(p / s2), ry = Erfc(r / s2); r1 += 0.5 * sxy * rx * ry; } } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derampx(Double_t x, Double_t x0, Double_t sigmax, Double_t tx, Double_t sx, Double_t bx) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of 2D peaks shape function (see manual) // // according to amplitude of the ridge // // Function parameters: // // -x-channel in x-dimension // // -x0-position of peak in x-dimension // // -y0-position of peak in y-dimension // // -sigmax-sigmax of peaks // // -ro-correlation coefficient // // -tx, sx-relative amplitudes // // -bx-slope // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r1 = 0, px, erx, rx, ex, s2; p = (x - x0) / sigmax; if (TMath::Abs(p) < 3) { s2 = TMath::Sqrt(2.0); p = p * p / 2; if (p < 700) r1 = exp(-p); else { r1 = 0; } if (tx != 0) { px = 0; erx = Erfc(p / s2 + 1 / (2 * bx)); ex = p / (s2 * bx); if (TMath::Abs(ex) < 9) { px = exp(ex) * erx; } r1 += 0.5 * tx * px; } if (sx != 0) { rx = Erfc(p / s2); r1 += 0.5 * sx * rx; } } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Deri02(Double_t x, Double_t y, Double_t a, Double_t x0, Double_t y0, Double_t sigmax, Double_t sigmay, Double_t ro, Double_t txy, Double_t sxy, Double_t bx, Double_t by) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of 2D peaks shape function (see manual) // // according to x position of 2D peak // // Function parameters: // // -x-channel in x-dimension // // -y-channel in y-dimension // // -a-amplitude // // -x0-position of peak in x-dimension // // -y0-position of peak in y-dimension // // -sigmax-sigmax of peaks // // -sigmay-sigmay of peaks // // -ro-correlation coefficient // // -txy, sxy-relative amplitudes // // -bx, by-slopes // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r, r1 = 0, e, ex, ey, px, py, rx, ry, erx, ery, s2; p = (x - x0) / sigmax; r = (y - y0) / sigmay; if (TMath::Abs(p) < 3 && TMath::Abs(r) < 3) { s2 = TMath::Sqrt(2.0); e = (p * p - 2 * ro * p * r + r * r) / (2 * (1 - ro * ro)); if (e < 700) r1 = exp(-e); else { r1 = 0; } e = -(ro * r - p) / sigmax; e = e / (1 - ro * ro); r1 = r1 * e; if (txy != 0) { px = 0, py = 0; erx = (-Erfc(p / s2 + 1 / (2 * bx)) / (s2 * bx * sigmax) - Derfc(p / s2 + 1 / (2 * bx)) / (s2 * sigmax)), ery = Erfc(r / s2 + 1 / (2 * by)); ex = p / (s2 * bx), ey = r / (s2 * by); if (TMath::Abs(ex) < 9 && TMath::Abs(ey) < 9) { px = exp(ex) * erx, py = exp(ey) * ery; } r1 += 0.5 * txy * px * py; } if (sxy != 0) { rx = -Derfc(p / s2) / (s2 * sigmax), ry = Erfc(r / s2); r1 += 0.5 * sxy * rx * ry; } r1 = a * r1; } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derderi02(Double_t x, Double_t y, Double_t a, Double_t x0, Double_t y0, Double_t sigmax, Double_t sigmay, Double_t ro) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates second derivative of 2D peaks shape function // // (see manual) according to x position of 2D peak // // Function parameters: // // -x-channel in x-dimension // // -y-channel in y-dimension // // -a-amplitude // // -x0-position of peak in x-dimension // // -y0-position of peak in y-dimension // // -sigmax-sigmax of peaks // // -sigmay-sigmay of peaks // // -ro-correlation coefficient // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r, r1 = 0, e; p = (x - x0) / sigmax; r = (y - y0) / sigmay; if (TMath::Abs(p) < 3 && TMath::Abs(r) < 3) { e = (p * p - 2 * ro * p * r + r * r) / (2 * (1 - ro * ro)); if (e < 700) r1 = exp(-e); else { r1 = 0; } e = -(ro * r - p) / sigmax; e = e / (1 - ro * ro); r1 = r1 * (e * e - 1 / ((1 - ro * ro) * sigmax * sigmax)); r1 = a * r1; } return (r1); } Double_t TSpectrum2Fit::Derj02(Double_t x, Double_t y, Double_t a, Double_t x0, Double_t y0, Double_t sigmax, Double_t sigmay, Double_t ro, Double_t txy, Double_t sxy, Double_t bx, Double_t by) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of 2D peaks shape function (see manual) // // according to y position of 2D peak // // Function parameters: // // -x-channel in x-dimension // // -y-channel in y-dimension // // -a-amplitude // // -x0-position of peak in x-dimension // // -y0-position of peak in y-dimension // // -sigmax-sigmax of peaks // // -sigmay-sigmay of peaks // // -ro-correlation coefficient // // -txy, sxy-relative amplitudes // // -bx, by-slopes // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r, r1 = 0, e, ex, ey, px, py, rx, ry, erx, ery, s2; p = (x - x0) / sigmax; r = (y - y0) / sigmay; if (TMath::Abs(p) < 3 && TMath::Abs(r) < 3) { s2 = TMath::Sqrt(2.0); e = (p * p - 2 * ro * p * r + r * r) / (2 * (1 - ro * ro)); if (e < 700) r1 = exp(-e); else { r1 = 0; } e = -(ro * p - r) / sigmay; e = e / (1 - ro * ro); r1 = r1 * e; if (txy != 0) { px = 0, py = 0; ery = (-Erfc(r / s2 + 1 / (2 * by)) / (s2 * by * sigmay) - Derfc(r / s2 + 1 / (2 * by)) / (s2 * sigmay)), erx = Erfc(p / s2 + 1 / (2 * bx)); ex = p / (s2 * bx), ey = r / (s2 * by); if (TMath::Abs(ex) < 9 && TMath::Abs(ey) < 9) { px = exp(ex) * erx, py = exp(ey) * ery; } r1 += 0.5 * txy * px * py; } if (sxy != 0) { ry = -Derfc(r / s2) / (s2 * sigmay), rx = Erfc(p / s2); r1 += 0.5 * sxy * rx * ry; } r1 = a * r1; } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derderj02(Double_t x, Double_t y, Double_t a, Double_t x0, Double_t y0, Double_t sigmax, Double_t sigmay, Double_t ro) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates second derivative of 2D peaks shape function // // (see manual) according to y position of 2D peak // // Function parameters: // // -x-channel in x-dimension // // -y-channel in y-dimension // // -a-amplitude // // -x0-position of peak in x-dimension // // -y0-position of peak in y-dimension // // -sigmax-sigmax of peaks // // -sigmay-sigmay of peaks // // -ro-correlation coefficient // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r, r1 = 0, e; p = (x - x0) / sigmax; r = (y - y0) / sigmay; if (TMath::Abs(p) < 3 && TMath::Abs(r) < 3) { e = (p * p - 2 * ro * p * r + r * r) / (2 * (1 - ro * ro)); if (e < 700) r1 = exp(-e); else { r1 = 0; } e = -(ro * p - r) / sigmay; e = e / (1 - ro * ro); r1 = r1 * (e * e - 1 / ((1 - ro * ro) * sigmay * sigmay)); r1 = a * r1; } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Deri01(Double_t x, Double_t ax, Double_t x0, Double_t sigmax, Double_t tx, Double_t sx, Double_t bx) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of 2D peaks shape function (see manual) // // according to x position of 1D ridge // // Function parameters: // // -x-channel in x-dimension // // -ax-amplitude of ridge // // -x0-position of peak in x-dimension // // -sigmax-sigmax of peaks // // -ro-correlation coefficient // // -tx, sx-relative amplitudes // // -bx-slope // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, e, r1 = 0, px, rx, erx, ex, s2; p = (x - x0) / sigmax; if (TMath::Abs(p) < 3) { s2 = TMath::Sqrt(2.0); e = p * p / 2; if (e < 700) r1 = exp(-e); else { r1 = 0; } r1 = r1 * p / sigmax; if (tx != 0) { px = 0; erx = (-Erfc(p / s2 + 1 / (2 * bx)) / (s2 * bx * sigmax) - Derfc(p / s2 + 1 / (2 * bx)) / (s2 * sigmax)); ex = p / (s2 * bx); if (TMath::Abs(ex) < 9) px = exp(ex) * erx; r1 += 0.5 * tx * px; } if (sx != 0) { rx = -Derfc(p / s2) / (s2 * sigmax); r1 += 0.5 * sx * rx; } r1 = ax * r1; } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derderi01(Double_t x, Double_t ax, Double_t x0, Double_t sigmax) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates second derivative of 2D peaks shape function // // (see manual) according to x position of 1D ridge // // Function parameters: // // -x-channel in x-dimension // // -ax-amplitude of ridge // // -x0-position of peak in x-dimension // // -sigmax-sigmax of peaks // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, e, r1 = 0; p = (x - x0) / sigmax; if (TMath::Abs(p) < 3) { e = p * p / 2; if (e < 700) r1 = exp(-e); else { r1 = 0; } r1 = r1 * (p * p / (sigmax * sigmax) - 1 / (sigmax * sigmax)); r1 = ax * r1; } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Dersigmax(Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t ro, Double_t txy, Double_t sxy, Double_t tx, Double_t sx, Double_t bx, Double_t by) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of peaks shape function (see manual) // // according to sigmax of peaks. // // Function parameters: // // -numOfFittedPeaks-number of fitted peaks // // -x,y-position of channel // // -parameter-array of peaks parameters (amplitudes and positions) // // -sigmax-sigmax of peaks // // -sigmay-sigmay of peaks // // -ro-correlation coefficient // // -txy, sxy, tx, sx-relative amplitudes // // -bx, by-slopes // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r, r1 = 0, e, a, b, x0, y0, s2, px, py, rx, ry, erx, ery, ex, ey; Int_t j; s2 = TMath::Sqrt(2.0); for (j = 0; j < numOfFittedPeaks; j++) { a = parameter[7 * j]; x0 = parameter[7 * j + 1]; y0 = parameter[7 * j + 2]; p = (x - x0) / sigmax; r = (y - y0) / sigmay; if (TMath::Abs(p) < 3 && TMath::Abs(r) < 3) { e = (p * p - 2 * ro * p * r + r * r) / (2 * (1 - ro * ro)); if (e < 700) e = exp(-e); else { e = 0; } b = -(ro * p * r - p * p) / sigmax; e = e * b / (1 - ro * ro); if (txy != 0) { px = 0, py = 0; erx = -Erfc(p / s2 + 1 / (2 * bx)) * p / (s2 * bx * sigmax) - Derfc(p / s2 + 1 / (2 * bx)) * p / (s2 * sigmax), ery = Erfc(r / s2 + 1 / (2 * by)); ex = p / (s2 * bx), ey = r / (s2 * by); if (TMath::Abs(ex) < 9 && TMath::Abs(ey) < 9) { px = exp(ex) * erx, py = exp(ey) * ery; } e += 0.5 * txy * px * py; } if (sxy != 0) { rx = -Derfc(p / s2) * p / (s2 * sigmax), ry = Erfc(r / s2); e += 0.5 * sxy * rx * ry; } r1 = r1 + a * e; } if (TMath::Abs(p) < 3) { x0 = parameter[7 * j + 5]; p = (x - x0) / sigmax; b = p * p / 2; if (b < 700) e = exp(-b); else { e = 0; } e = 2 * b * e / sigmax; if (tx != 0) { px = 0; erx = (-Erfc(p / s2 + 1 / (2 * bx)) * p / (s2 * bx * sigmax) - Derfc(p / s2 + 1 / (2 * bx)) * p / (s2 * sigmax)); ex = p / (s2 * bx); if (TMath::Abs(ex) < 9) px = exp(ex) * erx; e += 0.5 * tx * px; } if (sx != 0) { rx = -Derfc(p / s2) * p / (s2 * sigmax); e += 0.5 * sx * rx; } r1 += parameter[7 * j + 3] * e; } } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derdersigmax(Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t ro) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates second derivative of peaks shape function // // (see manual) according to sigmax of peaks. // // Function parameters: // // -numOfFittedPeaks-number of fitted peaks // // -x,y-position of channel // // -parameter-array of peaks parameters (amplitudes and positions) // // -sigmax-sigmax of peaks // // -sigmay-sigmay of peaks // // -ro-correlation coefficient // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r, r1 = 0, e, a, b, x0, y0; Int_t j; for (j = 0; j < numOfFittedPeaks; j++) { a = parameter[7 * j]; x0 = parameter[7 * j + 1]; y0 = parameter[7 * j + 2]; p = (x - x0) / sigmax; r = (y - y0) / sigmay; if (TMath::Abs(p) < 3 && TMath::Abs(r) < 3) { e = (p * p - 2 * ro * p * r + r * r) / (2 * (1 - ro * ro)); if (e < 700) e = exp(-e); else { e = 0; } b = -(ro * p * r - p * p) / sigmax; e = e * (b * b / (1 - ro * ro) - (3 * p * p - 2 * ro * p * r) / (sigmax * sigmax)) / (1 - ro * ro); r1 = r1 + a * e; } if (TMath::Abs(p) < 3) { x0 = parameter[7 * j + 5]; p = (x - x0) / sigmax; b = p * p / 2; if (b < 700) e = exp(-b); else { e = 0; } e = e * (4 * b * b - 6 * b) / (sigmax * sigmax); r1 += parameter[7 * j + 3] * e; } } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Dersigmay(Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t ro, Double_t txy, Double_t sxy, Double_t ty, Double_t sy, Double_t bx, Double_t by) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of peaks shape function (see manual) // // according to sigmax of peaks. // // Function parameters: // // -numOfFittedPeaks-number of fitted peaks // // -x,y-position of channel // // -parameter-array of peaks parameters (amplitudes and positions) // // -sigmax-sigmax of peaks // // -sigmay-sigmay of peaks // // -ro-correlation coefficient // // -txy, sxy, ty, sy-relative amplitudes // // -bx, by-slopes // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r, r1 = 0, e, a, b, x0, y0, s2, px, py, rx, ry, erx, ery, ex, ey; Int_t j; s2 = TMath::Sqrt(2.0); for (j = 0; j < numOfFittedPeaks; j++) { a = parameter[7 * j]; x0 = parameter[7 * j + 1]; y0 = parameter[7 * j + 2]; p = (x - x0) / sigmax; r = (y - y0) / sigmay; if (TMath::Abs(p) < 3 && TMath::Abs(r) < 3) { e = (p * p - 2 * ro * p * r + r * r) / (2 * (1 - ro * ro)); if (e < 700) e = exp(-e); else { e = 0; } b = -(ro * p * r - r * r) / sigmay; e = e * b / (1 - ro * ro); if (txy != 0) { px = 0, py = 0; ery = -Erfc(r / s2 + 1 / (2 * by)) * r / (s2 * by * sigmay) - Derfc(r / s2 + 1 / (2 * by)) * r / (s2 * sigmay), erx = Erfc(p / s2 + 1 / (2 * bx)); ex = p / (s2 * bx), ey = r / (s2 * by); if (TMath::Abs(ex) < 9 && TMath::Abs(ey) < 9) { px = exp(ex) * erx, py = exp(ey) * ery; } e += 0.5 * txy * px * py; } if (sxy != 0) { ry = -Derfc(r / s2) * r / (s2 * sigmay), rx = Erfc(p / s2); e += 0.5 * sxy * rx * ry; } r1 = r1 + a * e; } if (TMath::Abs(r) < 3) { y0 = parameter[7 * j + 6]; r = (y - y0) / sigmay; b = r * r / 2; if (b < 700) e = exp(-b); else { e = 0; } e = 2 * b * e / sigmay; if (ty != 0) { py = 0; ery = (-Erfc(r / s2 + 1 / (2 * by)) * r / (s2 * by * sigmay) - Derfc(r / s2 + 1 / (2 * by)) * r / (s2 * sigmay)); ey = r / (s2 * by); if (TMath::Abs(ey) < 9) py = exp(ey) * ery; e += 0.5 * ty * py; } if (sy != 0) { ry = -Derfc(r / s2) * r / (s2 * sigmay); e += 0.5 * sy * ry; } r1 += parameter[7 * j + 4] * e; } } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derdersigmay(Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t ro) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates second derivative of peaks shape function // // (see manual) according to sigmay of peaks. // // Function parameters: // // -numOfFittedPeaks-number of fitted peaks // // -x,y-position of channel // // -parameter-array of peaks parameters (amplitudes and positions) // // -sigmax-sigmax of peaks // // -sigmay-sigmay of peaks // // -ro-correlation coefficient // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r, r1 = 0, e, a, b, x0, y0; Int_t j; for (j = 0; j < numOfFittedPeaks; j++) { a = parameter[7 * j]; x0 = parameter[7 * j + 1]; y0 = parameter[7 * j + 2]; p = (x - x0) / sigmax; r = (y - y0) / sigmay; if (TMath::Abs(p) < 3 && TMath::Abs(r) < 3) { e = (p * p - 2 * ro * p * r + r * r) / (2 * (1 - ro * ro)); if (e < 700) e = exp(-e); else { e = 0; } b = -(ro * p * r - r * r) / sigmay; e = e * (b * b / (1 - ro * ro) - (3 * r * r - 2 * ro * r * p) / (sigmay * sigmay)) / (1 - ro * ro); r1 = r1 + a * e; } if (TMath::Abs(r) < 3) { y0 = parameter[7 * j + 6]; r = (y - y0) / sigmay; b = r * r / 2; if (b < 700) e = exp(-b); else { e = 0; } e = e * (4 * b * b - 6 * b) / (sigmay * sigmay); r1 += parameter[7 * j + 4] * e; } } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derro(Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sx, Double_t sy, Double_t r) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of peaks shape function (see manual) // // according to correlation coefficient ro. // // Function parameters: // // -numOfFittedPeaks-number of fitted peaks // // -x,y-position of channel // // -parameter-array of peaks parameters (amplitudes and positions) // // -sx-sigmax of peaks // // -sy-sigmay of peaks // // -r-correlation coefficient ro // // // ////////////////////////////////////////////////////////////////////////////////// Double_t px, qx, rx, vx, x0, y0, a, ex, tx; Int_t j; vx = 0; for (j = 0; j < numOfFittedPeaks; j++) { a = parameter[7 * j]; x0 = parameter[7 * j + 1]; y0 = parameter[7 * j + 2]; px = (x - x0) / sx; qx = (y - y0) / sy; if (TMath::Abs(px) < 3 && TMath::Abs(qx) < 3) { rx = (px * px - 2 * r * px * qx + qx * qx); ex = rx / (2 * (1 - r * r)); if ((ex) < 700) ex = exp(-ex); else { ex = 0; } tx = px * qx / (1 - r * r); tx = tx - r * rx / ((1 - r * r) * (1 - r * r)); vx = vx + a * ex * tx; } } return (vx); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Dertxy(Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t bx, Double_t by) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of peaks shape function (see manual) // // according to relative amplitude txy. // // Function parameters: // // -numOfFittedPeaks-number of fitted peaks // // -x,y-position of channel // // -parameter-array of peaks parameters (amplitudes and positions) // // -sigmax-sigmax of peaks // // -sigmay-sigmay of peaks // // -bx, by-slopes // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r, r1 = 0, ex, ey, px, py, erx, ery, s2, x0, y0, a; Int_t j; s2 = TMath::Sqrt(2.0); for (j = 0; j < numOfFittedPeaks; j++) { a = parameter[7 * j]; x0 = parameter[7 * j + 1]; y0 = parameter[7 * j + 2]; p = (x - x0) / sigmax; r = (y - y0) / sigmay; px = 0, py = 0; erx = Erfc(p / s2 + 1 / (2 * bx)), ery = Erfc(r / s2 + 1 / (2 * by)); ex = p / (s2 * bx), ey = r / (s2 * by); if (TMath::Abs(ex) < 9 && TMath::Abs(ey) < 9) { px = exp(ex) * erx, py = exp(ey) * ery; } r1 += 0.5 * a * px * py; } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Dersxy(Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of peaks shape function (see manual) // // according to relative amplitude sxy. // // Function parameters: // // -numOfFittedPeaks-number of fitted peaks // // -x,y-position of channel // // -parameter-array of peaks parameters (amplitudes and positions) // // -sigmax-sigmax of peaks // // -sigmay-sigmay of peaks // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r, r1 = 0, rx, ry, x0, y0, a, s2; Int_t j; s2 = TMath::Sqrt(2.0); for (j = 0; j < numOfFittedPeaks; j++) { a = parameter[7 * j]; x0 = parameter[7 * j + 1]; y0 = parameter[7 * j + 2]; p = (x - x0) / sigmax; r = (y - y0) / sigmay; rx = Erfc(p / s2), ry = Erfc(r / s2); r1 += 0.5 * a * rx * ry; } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Dertx(Int_t numOfFittedPeaks, Double_t x, const Double_t *parameter, Double_t sigmax, Double_t bx) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of peaks shape function (see manual) // // according to relative amplitude tx. // // Function parameters: // // -numOfFittedPeaks-number of fitted peaks // // -x-position of channel // // -parameter-array of peaks parameters (amplitudes and positions) // // -sigmax-sigma of 1D ridge // // -bx-slope // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r1 = 0, ex, px, erx, s2, ax, x0; Int_t j; s2 = TMath::Sqrt(2.0); for (j = 0; j < numOfFittedPeaks; j++) { ax = parameter[7 * j + 3]; x0 = parameter[7 * j + 5]; p = (x - x0) / sigmax; px = 0; erx = Erfc(p / s2 + 1 / (2 * bx)); ex = p / (s2 * bx); if (TMath::Abs(ex) < 9) { px = exp(ex) * erx; } r1 += 0.5 * ax * px; } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derty(Int_t numOfFittedPeaks, Double_t x, const Double_t *parameter, Double_t sigmax, Double_t bx) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of peaks shape function (see manual) // // according to relative amplitude ty. // // Function parameters: // // -numOfFittedPeaks-number of fitted peaks // // -x-position of channel // // -parameter-array of peaks parameters (amplitudes and positions) // // -sigmax-sigma of 1D ridge // // -bx-slope // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r1 = 0, ex, px, erx, s2, ax, x0; Int_t j; s2 = TMath::Sqrt(2.0); for (j = 0; j < numOfFittedPeaks; j++) { ax = parameter[7 * j + 4]; x0 = parameter[7 * j + 6]; p = (x - x0) / sigmax; px = 0; erx = Erfc(p / s2 + 1 / (2 * bx)); ex = p / (s2 * bx); if (TMath::Abs(ex) < 9) { px = exp(ex) * erx; } r1 += 0.5 * ax * px; } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Dersx(Int_t numOfFittedPeaks, Double_t x, const Double_t *parameter, Double_t sigmax) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of peaks shape function (see manual) // // according to relative amplitude sx. // // Function parameters: // // -numOfFittedPeaks-number of fitted peaks // // -x-position of channel // // -parameter-array of peaks parameters (amplitudes and positions) // // -sigmax-sigma of 1D ridge // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r1 = 0, rx, ax, x0, s2; Int_t j; s2 = TMath::Sqrt(2.0); for (j = 0; j < numOfFittedPeaks; j++) { ax = parameter[7 * j + 3]; x0 = parameter[7 * j + 5]; p = (x - x0) / sigmax; s2 = TMath::Sqrt(2.0); rx = Erfc(p / s2); r1 += 0.5 * ax * rx; } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Dersy(Int_t numOfFittedPeaks, Double_t x, const Double_t *parameter, Double_t sigmax) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of peaks shape function (see manual) // // according to relative amplitude sy. // // Function parameters: // // -numOfFittedPeaks-number of fitted peaks // // -x-position of channel // // -parameter-array of peaks parameters (amplitudes and positions) // // -sigmax-sigma of 1D ridge // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r1 = 0, rx, ax, x0, s2; Int_t j; s2 = TMath::Sqrt(2.0); for (j = 0; j < numOfFittedPeaks; j++) { ax = parameter[7 * j + 4]; x0 = parameter[7 * j + 6]; p = (x - x0) / sigmax; s2 = TMath::Sqrt(2.0); rx = Erfc(p / s2); r1 += 0.5 * ax * rx; } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derbx(Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t txy, Double_t tx, Double_t bx, Double_t by) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of peaks shape function (see manual) // // according to slope bx. // // Function parameters: // // -numOfFittedPeaks-number of fitted peaks // // -x,y-position of channel // // -parameter-array of peaks parameters (amplitudes and positions) // // -sigmax-sigmax of peaks // // -sigmay-sigmay of peaks // // -txy, tx-relative amplitudes // // -bx, by-slopes // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r, r1 = 0, a, x0, y0, s2, px, py, erx, ery, ex, ey; Int_t j; s2 = TMath::Sqrt(2.0); for (j = 0; j < numOfFittedPeaks; j++) { a = parameter[7 * j]; x0 = parameter[7 * j + 1]; y0 = parameter[7 * j + 2]; p = (x - x0) / sigmax; r = (y - y0) / sigmay; if (txy != 0) { px = 0, py = 0; erx = -Erfc(p / s2 + 1 / (2 * bx)) * p / (s2 * bx * bx) - Derfc(p / s2 + 1 / (2 * bx)) / (s2 * bx * bx), ery = Erfc(r / s2 + 1 / (2 * by)); ex = p / (s2 * bx), ey = r / (s2 * by); if (TMath::Abs(ex) < 9 && TMath::Abs(ey) < 9) { px = exp(ex) * erx, py = exp(ey) * ery; } r1 += 0.5 * a * txy * px * py; } a = parameter[7 * j + 3]; x0 = parameter[7 * j + 5]; p = (x - x0) / sigmax; if (tx != 0) { px = 0; erx = (-Erfc(p / s2 + 1 / (2 * bx)) * p / (s2 * bx * bx) - Derfc(p / s2 + 1 / (2 * bx)) / (s2 * bx * bx)); ex = p / (s2 * bx); if (TMath::Abs(ex) < 9) px = exp(ex) * erx; r1 += 0.5 * a * tx * px; } } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derby(Int_t numOfFittedPeaks, Double_t x, Double_t y, const Double_t *parameter, Double_t sigmax, Double_t sigmay, Double_t txy, Double_t ty, Double_t bx, Double_t by) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of peaks shape function (see manual) // // according to slope by. // // Function parameters: // // -numOfFittedPeaks-number of fitted peaks // // -x,y-position of channel // // -parameter-array of peaks parameters (amplitudes and positions) // // -sigmax-sigmax of peaks // // -sigmay-sigmay of peaks // // -txy, ty-relative amplitudes // // -bx, by-slopes // // // ////////////////////////////////////////////////////////////////////////////////// Double_t p, r, r1 = 0, a, x0, y0, s2, px, py, erx, ery, ex, ey; Int_t j; s2 = TMath::Sqrt(2.0); for (j = 0; j < numOfFittedPeaks; j++) { a = parameter[7 * j]; x0 = parameter[7 * j + 1]; y0 = parameter[7 * j + 2]; p = (x - x0) / sigmax; r = (y - y0) / sigmay; if (txy != 0) { px = 0, py = 0; ery = -Erfc(r / s2 + 1 / (2 * by)) * r / (s2 * by * by) - Derfc(r / s2 + 1 / (2 * by)) / (s2 * by * by), erx = Erfc(p / s2 + 1 / (2 * bx)); ex = p / (s2 * bx), ey = r / (s2 * by); if (TMath::Abs(ex) < 9 && TMath::Abs(ey) < 9) { px = exp(ex) * erx, py = exp(ey) * ery; } r1 += 0.5 * a * txy * px * py; } a = parameter[7 * j + 4]; y0 = parameter[7 * j + 6]; r = (y - y0) / sigmay; if (ty != 0) { py = 0; ery = (-Erfc(r / s2 + 1 / (2 * by)) * r / (s2 * by * by) - Derfc(r / s2 + 1 / (2 * by)) / (s2 * by * by)); ey = r / (s2 * by); if (TMath::Abs(ey) < 9) py = exp(ey) * ery; r1 += 0.5 * a * ty * py; } } return (r1); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Volume(Double_t a, Double_t sx, Double_t sy, Double_t ro) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates volume of a peak // // Function parameters: // // -a-amplitude of the peak // // -sx,sy-sigmas of peak // // -ro-correlation coefficient // // // ////////////////////////////////////////////////////////////////////////////////// Double_t pi = 3.1415926535, r; r = 1 - ro * ro; if (r > 0) r = TMath::Sqrt(r); else { return (0); } r = 2 * a * pi * sx * sy * r; return (r); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derpa2(Double_t sx, Double_t sy, Double_t ro) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of the volume of a peak // // according to amplitute // // Function parameters: // // -sx,sy-sigmas of peak // // -ro-correlation coefficient // // // ////////////////////////////////////////////////////////////////////////////////// Double_t pi = 3.1415926535, r; r = 1 - ro * ro; if (r > 0) r = TMath::Sqrt(r); else { return (0); } r = 2 * pi * sx * sy * r; return (r); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derpsigmax(Double_t a, Double_t sy, Double_t ro) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of the volume of a peak // // according to sigmax // // Function parameters: // // -a-amplitude of peak // // -sy-sigma of peak // // -ro-correlation coefficient // // // ////////////////////////////////////////////////////////////////////////////////// Double_t pi = 3.1415926535, r; r = 1 - ro * ro; if (r > 0) r = TMath::Sqrt(r); else { return (0); } r = a * 2 * pi * sy * r; return (r); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derpsigmay(Double_t a, Double_t sx, Double_t ro) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of the volume of a peak // // according to sigmay // // Function parameters: // // -a-amplitude of peak // // -sx-sigma of peak // // -ro-correlation coefficient // // // ////////////////////////////////////////////////////////////////////////////////// Double_t pi = 3.1415926535, r; r = 1 - ro * ro; if (r > 0) r = TMath::Sqrt(r); else { return (0); } r = a * 2 * pi * sx * r; return (r); } //______________________________________________________________________________ Double_t TSpectrum2Fit::Derpro(Double_t a, Double_t sx, Double_t sy, Double_t ro) { ////////////////////////////////////////////////////////////////////////////////// // AUXILIARY FUNCTION // // // // This function calculates derivative of the volume of a peak // // according to ro // // Function parameters: // // -a-amplitude of peak // // -sx,sy-sigmas of peak // // -ro-correlation coefficient // // // ////////////////////////////////////////////////////////////////////////////////// Double_t pi = 3.1415926535, r; r = 1 - ro * ro; if (r > 0) r = TMath::Sqrt(r); else { return (0); } r = -a * 2 * pi * sx * sy * ro / r; return (r); } /////////////////END OF AUXILIARY FUNCTIONS USED BY FITTING FUNCTION fit2////////////////////////// /////////////////FITTING FUNCTION WITHOUT MATRIX INVERSION/////////////////////////////////////// //______________________________________________________________________________ void TSpectrum2Fit::FitAwmi(Float_t **source) { ///////////////////////////////////////////////////////////////////////////// // TWO-DIMENSIONAL FIT FUNCTION // ALGORITHM WITHOUT MATRIX INVERSION // This function fits the source spectrum. The calling program should // fill in input parameters of the TSpectrum2Fit class. // The fitted parameters are written into // TSpectrum2Fit class output parameters and fitted data are written into // source spectrum. // // Function parameters: // source-pointer to the matrix of source spectrum // ///////////////////////////////////////////////////////////////////////////// // //Begin_Html

Fitting

 

Goal: to estimate simultaneously peak shape parameters in spectra with large number of peaks

 

•         peaks can be fitted separately, each peak (or multiplets) in a region or together all peaks in a spectrum. To fit separately each peak one needs to determine the fitted region. However it can happen that the regions of neighboring peaks are overlapping. Then the results of fitting are very poor. On the other hand, when fitting together all peaks found in a  spectrum, one needs to have a method that is  stable (converges) and fast enough to carry out fitting in reasonable time

•         we have implemented the nonsymmetrical semiempirical peak shape function

•         it contains the two-dimensional symmetrical Gaussian two one-dimensional symmetrical Gaussian ridges as well as nonsymmetrical terms and background.

where Txy, Tx, Ty, Sxy, Sx, Sy are relative amplitudes and Bx, By are slopes.

 

•         algorithm without matrix inversion (AWMI) allows fitting tens, hundreds of peaks simultaneously that represent sometimes thousands of parameters [2], [5].

 

 

Function:

void TSpectrumFit2::FitAwmi(float **fSource)

 

This function fits the source spectrum using AWMI algorithm. The calling program should fill in input parameters of the TSpectrumFit2 class using a set of TSpectrumFit2 setters. The fitted parameters are written into the class and fitted data are written into source spectrum.

 

 

Parameter:

        fSource-pointer to the matrix of source spectrum                 

 

 

Member variables of  TSpectrumFit2 class:

   Int_t     fNPeaks;                        //number of peaks present in fit, input parameter, it should be > 0

   Int_t     fNumberIterations;              //number of iterations in fitting procedure, input parameter, it should be > 0

   Int_t     fXmin;                          //first fitted channel in x direction

   Int_t     fXmax;                          //last fitted channel in x direction

   Int_t     fYmin;                          //first fitted channel in y direction

   Int_t     fYmax;                          //last fitted channel in y direction

   Int_t     fStatisticType;                 //type of statistics, possible values kFitOptimChiCounts (chi square statistics with counts as weighting coefficients), kFitOptimChiFuncValues (chi square statistics with function values as weighting coefficients),kFitOptimMaxLikelihood

   Int_t     fAlphaOptim;                    //optimization of convergence algorithm, possible values kFitAlphaHalving, kFitAlphaOptimal

   Int_t     fPower;                         //possible values kFitPower2,4,6,8,10,12, for details see references. It applies only for Awmi fitting function.

   Int_t     fFitTaylor;                     //order of Taylor expansion, possible values kFitTaylorOrderFirst, kFitTaylorOrderSecond. It applies only for Awmi fitting function.

   Double_t  fAlpha;                         //convergence coefficient, input parameter, it should be positive number and <=1, for details see references

   Double_t  fChi;                           //here the fitting functions return resulting chi square  

   Double_t *fPositionInitX;                 //[fNPeaks] array of initial values of x positions of 2D peaks, input parameters

   Double_t *fPositionCalcX;                 //[fNPeaks] array of calculated values of x positions of 2D peaks, output parameters

   Double_t *fPositionErrX;                  //[fNPeaks] array of error values of x positions of 2D peaks, output parameters

   Double_t *fPositionInitY;                 //[fNPeaks] array of initial values of y positions of 2D peaks, input parameters

   Double_t *fPositionCalcY;                 //[fNPeaks] array of calculated values of y positions of 2D peaks, output parameters

   Double_t *fPositionErrY;                  //[fNPeaks] array of error values of y positions of 2D peaks, output parameters

   Double_t *fPositionInitX1;                //[fNPeaks] array of initial x positions of 1D ridges, input parameters

   Double_t *fPositionCalcX1;                //[fNPeaks] array of calculated x positions of 1D ridges, output parameters

   Double_t *fPositionErrX1;                 //[fNPeaks] array of x positions errors of 1D ridges, output parameters

   Double_t *fPositionInitY1;                //[fNPeaks] array of initial y positions of 1D ridges, input parameters

   Double_t *fPositionCalcY1;                //[fNPeaks] array of calculated y positions of 1D ridges, output parameters

   Double_t *fPositionErrY1;                 //[fNPeaks] array of y positions errors of 1D ridges, output parameters

   Double_t *fAmpInit;                       //[fNPeaks] array of initial values of amplitudes of 2D peaks, input parameters

   Double_t *fAmpCalc;                       //[fNPeaks] array of calculated values of amplitudes of 2D peaks, output parameters

   Double_t *fAmpErr;                        //[fNPeaks] array of amplitudes errors of 2D peaks, output parameters

   Double_t *fAmpInitX1;                     //[fNPeaks] array of initial values of amplitudes of 1D ridges in x direction, input parameters

   Double_t *fAmpCalcX1;                     //[fNPeaks] array of calculated values of amplitudes of 1D ridges in x direction, output parameters

   Double_t *fAmpErrX1;                      //[fNPeaks] array of amplitudes errors of 1D ridges in x direction, output parameters

   Double_t *fAmpInitY1;                     //[fNPeaks] array of initial values of amplitudes of 1D ridges in y direction, input parameters

   Double_t *fAmpCalcY1;                     //[fNPeaks] array of calculated values of amplitudes of 1D ridges in y direction, output parameters

   Double_t *fAmpErrY1;                      //[fNPeaks] array of amplitudes errors of 1D ridges in y direction, output parameters

   Double_t *fVolume;                        //[fNPeaks] array of calculated volumes of 2D peaks, output parameters

   Double_t *fVolumeErr;                     //[fNPeaks] array of volumes errors of 2D peaks, output parameters

   Double_t  fSigmaInitX;                    //initial value of sigma x parameter

   Double_t  fSigmaCalcX;                    //calculated value of sigma x parameter

   Double_t  fSigmaErrX;                     //error value of sigma x parameter

   Double_t  fSigmaInitY;                    //initial value of sigma y parameter

   Double_t  fSigmaCalcY;                    //calculated value of sigma y parameter

   Double_t  fSigmaErrY;                     //error value of sigma y parameter

   Double_t  fRoInit;                        //initial value of correlation coefficient

   Double_t  fRoCalc;                        //calculated value of correlation coefficient

   Double_t  fRoErr;                         //error value of correlation coefficient

   Double_t  fTxyInit;                       //initial value of t parameter for 2D peaks (relative amplitude of tail), for details see html manual and references

   Double_t  fTxyCalc;                       //calculated value of t parameter for 2D peaks

   Double_t  fTxyErr;                        //error value of t parameter for 2D peaks

   Double_t  fSxyInit;                       //initial value of s parameter for 2D peaks (relative amplitude of step), for details see html manual and references

   Double_t  fSxyCalc;                       //calculated value of s parameter for 2D peaks

   Double_t  fSxyErr;                        //error value of s parameter for 2D peaks

   Double_t  fTxInit;                        //initial value of t parameter for 1D ridges in x direction (relative amplitude of tail), for details see html manual and references

   Double_t  fTxCalc;                        //calculated value of t parameter for 1D ridges in x direction

   Double_t  fTxErr;                         //error value of t parameter for 1D ridges in x direction

   Double_t  fTyInit;                        //initial value of t parameter for 1D ridges in y direction (relative amplitude of tail), for details see html manual and references

   Double_t  fTyCalc;                        //calculated value of t parameter for 1D ridges in y direction

   Double_t  fTyErr;                         //error value of t parameter for 1D ridges in y direction

   Double_t  fSxInit;                        //initial value of s parameter for 1D ridges in x direction (relative amplitude of step), for details see html manual and references

   Double_t  fSxCalc;                        //calculated value of s parameter for 1D ridges in x direction

   Double_t  fSxErr;                         //error value of s parameter for 1D ridges in x direction

   Double_t  fSyInit;                        //initial value of s parameter for 1D ridges in y direction (relative amplitude of step), for details see html manual and references

   Double_t  fSyCalc;                        //calculated value of s parameter for 1D ridges in y direction

   Double_t  fSyErr;                         //error value of s parameter for 1D ridges in y direction

   Double_t  fBxInit;                        //initial value of b parameter for 1D ridges in x direction (slope), for details see html manual and references

   Double_t  fBxCalc;                        //calculated value of b parameter for 1D ridges in x direction

   Double_t  fBxErr;                         //error value of b parameter for 1D ridges in x direction

   Double_t  fByInit;                        //initial value of b parameter for 1D ridges in y direction (slope), for details see html manual and references

   Double_t  fByCalc;                        //calculated value of b parameter for 1D ridges in y direction

   Double_t  fByErr;                         //error value of b parameter for 1D ridges in y direction

   Double_t  fA0Init;                        //initial value of background a0 parameter(backgroud is estimated as a0+ax*x+ay*y)

   Double_t  fA0Calc;                        //calculated value of background a0 parameter

   Double_t  fA0Err;                         //error value of background a0 parameter

   Double_t  fAxInit;                        //initial value of background ax parameter(backgroud is estimated as a0+ax*x+ay*y)

   Double_t  fAxCalc;                        //calculated value of background ax parameter

   Double_t  fAxErr;                         //error value of background ax parameter

   Double_t  fAyInit;                        //initial value of background ay parameter(backgroud is estimated as a0+ax*x+ay*y)

   Double_t  fAyCalc;                        //calculated value of background ay parameter

   Double_t  fAyErr;                         //error value of background ay parameter  

   Bool_t   *fFixPositionX;                  //[fNPeaks] array of logical values which allow to fix appropriate x positions of 2D peaks (not fit). However they are present in the estimated functional

   Bool_t   *fFixPositionY;                  //[fNPeaks] array of logical values which allow to fix appropriate y positions of 2D peaks (not fit). However they are present in the estimated functional

   Bool_t   *fFixPositionX1;                 //[fNPeaks] array of logical values which allow to fix appropriate x positions of 1D ridges (not fit). However they are present in the estimated functional

   Bool_t   *fFixPositionY1;                 //[fNPeaks] array of logical values which allow to fix appropriate y positions of 1D ridges (not fit). However they are present in the estimated functional

   Bool_t   *fFixAmp;                        //[fNPeaks] array of logical values which allow to fix appropriate amplitudes of 2D peaks (not fit). However they are present in the estimated functional

   Bool_t   *fFixAmpX1;                      //[fNPeaks] array of logical values which allow to fix appropriate amplitudes of 1D ridges in x direction (not fit). However they are present in the estimated functional

   Bool_t   *fFixAmpY1;                      //[fNPeaks] array of logical values which allow to fix appropriate amplitudes of 1D ridges in y direction (not fit). However they are present in the estimated functional

   Bool_t    fFixSigmaX;                     //logical value of sigma x parameter, which allows to fix the parameter (not to fit).

   Bool_t    fFixSigmaY;                     //logical value of sigma y parameter, which allows to fix the parameter (not to fit).

   Bool_t    fFixRo;                         //logical value of correlation coefficient, which allows to fix the parameter (not to fit).

   Bool_t    fFixTxy;                        //logical value of t parameter for 2D peaks, which allows to fix the parameter (not to fit).

   Bool_t    fFixSxy;                        //logical value of s parameter for 2D peaks, which allows to fix the parameter (not to fit).

   Bool_t    fFixTx;                         //logical value of t parameter for 1D ridges in x direction, which allows to fix the parameter (not to fit).

   Bool_t    fFixTy;                         //logical value of t parameter for 1D ridges in y direction, which allows to fix the parameter (not to fit).

   Bool_t    fFixSx;                         //logical value of s parameter for 1D ridges in x direction, which allows to fix the parameter (not to fit).

   Bool_t    fFixSy;                         //logical value of s parameter for 1D ridges in y direction, which allows to fix the parameter (not to fit).

   Bool_t    fFixBx;                         //logical value of b parameter for 1D ridges in x direction, which allows to fix the parameter (not to fit).

   Bool_t    fFixBy;                         //logical value of b parameter for 1D ridges in y direction, which allows to fix the parameter (not to fit).

   Bool_t    fFixA0;                         //logical value of a0 parameter, which allows to fix the parameter (not to fit).

   Bool_t    fFixAx;                         //logical value of ax parameter, which allows to fix the parameter (not to fit).

   Bool_t    fFixAy;                         //logical value of ay parameter, which allows to fix the parameter (not to fit).

 

References:

[1] Phillps G.W., Marlow K.W., NIM 137 (1976) 525.

[2] I. A. Slavic: Nonlinear least-squares fitting without matrix inversion applied to complex Gaussian spectra analysis. NIM 134 (1976) 285-289.

[3] T. Awaya: A new method for curve fitting to the data with low statistics not using chi-square method. NIM 165 (1979) 317-323.

[4] T. Hauschild, M. Jentschel: Comparison of maximum likelihood estimation and chi-square statistics applied to counting experiments. NIM A 457 (2001) 384-401.

 [5]  M. Morháč,  J. Kliman,  M. Jandel,  Ľ. Krupa, V. Matoušek: Study of fitting algorithms applied to simultaneous analysis of large number of peaks in -ray spectra. Applied Spectroscopy, Vol. 57, No. 7, pp. 753-760, 2003

 

Example  – script FitAwmi2.c:

Fig. 1 Original two-dimensional spectrum with found peaks (using TSpectrum2 peak searching function). The positions of peaks were used as initial estimates in fitting procedure.

Fig. 2 Fitted (generated from fitted parameters) spectrum of the data from Fig. 1 using Algorithm Without Matrix Inversion. Each peak was represented by 7 parameters, which together with Sigmax, Sigmay and a0 resulted in 38 fitted parameters. The chi-square after 1000 iterations was 0.642342.

 

Script:

 

// Example to illustrate fitting function, algorithm without matrix inversion (AWMI) (class TSpectrumFit2).

// To execute this example, do

// root > .x FitAwmi2.C

 

void FitAwmi2() {

   Int_t i, j, nfound;

   Int_t nbinsx = 64;

   Int_t nbinsy = 64;  

   Int_t xmin  = 0;

   Int_t xmax  = nbinsx;

   Int_t ymin  = 0;

   Int_t ymax  = nbinsy;

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

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

   for (i=0;i<nbinsx;i++)

                                                source[i]=new float[nbinsy];

   for (i=0;i<nbinsx;i++)

                                                dest[i]=new float[nbinsy];

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

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

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

   TCanvas *Searching = new TCanvas("Searching","Two-dimensional fitting using Algorithm Without Matrix Inversion",10,10,1000,700);

   TSpectrum2 *s = new TSpectrum2();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

                 }

   }

   //searching for candidate peaks positions    

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

   Bool_t *FixPosX = new Bool_t[nfound];

   Bool_t *FixPosY = new Bool_t[nfound];  

   Bool_t *FixAmp = new Bool_t[nfound];     

   Float_t *PosX = new Float_t[nfound];        

   Float_t *PosY = new Float_t[nfound];

   Float_t *Amp = new Float_t[nfound];     

   Float_t *AmpXY = new Float_t[nfound];        

   PosX = s->GetPositionX();

   PosY = s->GetPositionY();      

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

   for(i = 0; i< nfound ; i++){

      FixPosX[i] = kFALSE;

      FixPosY[i] = kFALSE;     

      FixAmp[i] = kFALSE;   

      Amp[i] = source[(int)(PosX[i]+0.5)][(int)(PosY[i]+0.5)];      //initial values of peaks amplitudes, input parameters         

      AmpXY[i] = 0;

   }

   //filling in the initial estimates of the input parameters

   TSpectrumFit2 *pfit=new TSpectrumFit2(nfound);

   pfit->SetFitParameters(xmin, xmax-1, ymin, ymax-1, 1000, 0.1, pfit->kFitOptimChiCounts, pfit->kFitAlphaHalving, pfit->kFitPower2, pfit->kFitTaylorOrderFirst);  

   pfit->SetPeakParameters(2, kFALSE, 2, kFALSE, 0, kTRUE, PosX, (Bool_t *) FixPosX, PosY, (Bool_t *) FixPosY, PosX, (Bool_t *) FixPosX, PosY, (Bool_t *) FixPosY, Amp, (Bool_t *) FixAmp, AmpXY, (Bool_t *) FixAmp, AmpXY, (Bool_t *) FixAmp);     

   pfit->SetBackgroundParameters(0, kFALSE, 0, kTRUE, 0, kTRUE);  

   pfit->FitAwmi(source);

    for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

                 }

   }  

   search->Draw("SURF");

}

 

Example 2 – script FitA2.c:

Fig. 3 Original two-dimensional gamma-gamma-ray spectrum with found peaks (using TSpectrum2 peak searching function).

Fig. 4 Fitted (generated from fitted parameters) spectrum of the data from Fig. 3 using Algorithm Without Matrix Inversion. 152 peaks were identified. Each peak was represented by 7 parameters, which together with Sigmax, Sigmay and a0 resulted in 1067 fitted parameters. The chi-square after 1000 iterations was 0.728675. One can observe good correspondence with the original data.

 

Script:

// Example to illustrate fitting function, algorithm without matrix inversion (AWMI) (class TSpectrumFit2).

// To execute this example, do

// root > .x FitA2.C

void FitA2() {

   Int_t i, j, nfound;

   Int_t nbinsx = 256;

   Int_t nbinsy = 256;  

   Int_t xmin  = 0;

   Int_t xmax  = nbinsx;

   Int_t ymin  = 0;

   Int_t ymax  = nbinsy;

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

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

   for (i=0;i<nbinsx;i++)

                                                source[i]=new float[nbinsy];

   for (i=0;i<nbinsx;i++)

                                                dest[i]=new float[nbinsy];  

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

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

   search=(TH2F*) f->Get("fit1;1");

   TCanvas *Searching = new TCanvas("Searching","Two-dimensional fitting using Algorithm Without Matrix Inversion",10,10,1000,700);

   TSpectrum2 *s = new TSpectrum2(1000,1);

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

                 }

   }  

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

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

   Bool_t *FixPosX = new Bool_t[nfound];

   Bool_t *FixPosY = new Bool_t[nfound];  

   Bool_t *FixAmp = new Bool_t[nfound];     

   Float_t *PosX = new Float_t[nfound];        

   Float_t *PosY = new Float_t[nfound];

   Float_t *Amp = new Float_t[nfound];     

   Float_t *AmpXY = new Float_t[nfound];        

   PosX = s->GetPositionX();

   PosY = s->GetPositionY();     

   for(i = 0; i< nfound ; i++){

      FixPosX[i] = kFALSE;

      FixPosY[i] = kFALSE;     

      FixAmp[i] = kFALSE;   

      Amp[i] = source[(int)(PosX[i]+0.5)][(int)(PosY[i]+0.5)];      //initial values of peaks amplitudes, input parameters         

      AmpXY[i] = 0;

   }

   //filling in the initial estimates of the input parameters

   TSpectrumFit2 *pfit=new TSpectrumFit2(nfound);

   pfit->SetFitParameters(xmin, xmax-1, ymin, ymax-1, 1000, 0.1, pfit->kFitOptimChiCounts, pfit->kFitAlphaHalving, pfit->kFitPower2, pfit->kFitTaylorOrderFirst);  

   pfit->SetPeakParameters(2, kFALSE, 2, kFALSE, 0, kTRUE, PosX, (Bool_t *) FixPosX, PosY, (Bool_t *) FixPosY, PosX, (Bool_t *) FixPosX, PosY, (Bool_t *) FixPosY, Amp, (Bool_t *) FixAmp, AmpXY, (Bool_t *) FixAmp, AmpXY, (Bool_t *) FixAmp);     

   pfit->SetBackgroundParameters(0, kFALSE, 0, kTRUE, 0, kTRUE);  

   pfit->FitAwmi(source);

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

                 }

   }  

   search->Draw("SURF");  

}

 

End_Html Int_t i, i1, i2, j, k, shift = 7 * fNPeaks + 14, peak_vel, size, iter, pw, regul_cycle, flag; Double_t a, b, c, d = 0, alpha, chi_opt, yw, ywm, f, chi2, chi_min, chi = 0, pi, pmin = 0, chi_cel = 0, chi_er; Double_t *working_space = new Double_t[5 * (7 * fNPeaks + 14)]; for (i = 0, j = 0; i < fNPeaks; i++) { working_space[7 * i] = fAmpInit[i]; //vector parameter if (fFixAmp[i] == false) { working_space[shift + j] = fAmpInit[i]; //vector xk j += 1; } working_space[7 * i + 1] = fPositionInitX[i]; //vector parameter if (fFixPositionX[i] == false) { working_space[shift + j] = fPositionInitX[i]; //vector xk j += 1; } working_space[7 * i + 2] = fPositionInitY[i]; //vector parameter if (fFixPositionY[i] == false) { working_space[shift + j] = fPositionInitY[i]; //vector xk j += 1; } working_space[7 * i + 3] = fAmpInitX1[i]; //vector parameter if (fFixAmpX1[i] == false) { working_space[shift + j] = fAmpInitX1[i]; //vector xk j += 1; } working_space[7 * i + 4] = fAmpInitY1[i]; //vector parameter if (fFixAmpY1[i] == false) { working_space[shift + j] = fAmpInitY1[i]; //vector xk j += 1; } working_space[7 * i + 5] = fPositionInitX1[i]; //vector parameter if (fFixPositionX1[i] == false) { working_space[shift + j] = fPositionInitX1[i]; //vector xk j += 1; } working_space[7 * i + 6] = fPositionInitY1[i]; //vector parameter if (fFixPositionY1[i] == false) { working_space[shift + j] = fPositionInitY1[i]; //vector xk j += 1; } } peak_vel = 7 * i; working_space[7 * i] = fSigmaInitX; //vector parameter if (fFixSigmaX == false) { working_space[shift + j] = fSigmaInitX; //vector xk j += 1; } working_space[7 * i + 1] = fSigmaInitY; //vector parameter if (fFixSigmaY == false) { working_space[shift + j] = fSigmaInitY; //vector xk j += 1; } working_space[7 * i + 2] = fRoInit; //vector parameter if (fFixRo == false) { working_space[shift + j] = fRoInit; //vector xk j += 1; } working_space[7 * i + 3] = fA0Init; //vector parameter if (fFixA0 == false) { working_space[shift + j] = fA0Init; //vector xk j += 1; } working_space[7 * i + 4] = fAxInit; //vector parameter if (fFixAx == false) { working_space[shift + j] = fAxInit; //vector xk j += 1; } working_space[7 * i + 5] = fAyInit; //vector parameter if (fFixAy == false) { working_space[shift + j] = fAyInit; //vector xk j += 1; } working_space[7 * i + 6] = fTxyInit; //vector parameter if (fFixTxy == false) { working_space[shift + j] = fTxyInit; //vector xk j += 1; } working_space[7 * i + 7] = fSxyInit; //vector parameter if (fFixSxy == false) { working_space[shift + j] = fSxyInit; //vector xk j += 1; } working_space[7 * i + 8] = fTxInit; //vector parameter if (fFixTx == false) { working_space[shift + j] = fTxInit; //vector xk j += 1; } working_space[7 * i + 9] = fTyInit; //vector parameter if (fFixTy == false) { working_space[shift + j] = fTyInit; //vector xk j += 1; } working_space[7 * i + 10] = fSxyInit; //vector parameter if (fFixSx == false) { working_space[shift + j] = fSxInit; //vector xk j += 1; } working_space[7 * i + 11] = fSyInit; //vector parameter if (fFixSy == false) { working_space[shift + j] = fSyInit; //vector xk j += 1; } working_space[7 * i + 12] = fBxInit; //vector parameter if (fFixBx == false) { working_space[shift + j] = fBxInit; //vector xk j += 1; } working_space[7 * i + 13] = fByInit; //vector parameter if (fFixBy == false) { working_space[shift + j] = fByInit; //vector xk j += 1; } size = j; for (iter = 0; iter < fNumberIterations; iter++) { for (j = 0; j < size; j++) { working_space[2 * shift + j] = 0, working_space[3 * shift + j] = 0; //der,temp } //filling vectors alpha = fAlpha; chi_opt = 0, pw = fPower - 2; for (i1 = fXmin; i1 <= fXmax; i1++) { for (i2 = fYmin; i2 <= fYmax; i2++) { yw = source[i1][i2]; ywm = yw; f = Shape2(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 3], working_space[peak_vel + 4], working_space[peak_vel + 5], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 8], working_space[peak_vel + 9], working_space[peak_vel + 10], working_space[peak_vel + 11], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (fStatisticType == kFitOptimMaxLikelihood) { if (f > 0.00001) chi_opt += yw * TMath::Log(f) - f; } else { if (ywm != 0) chi_opt += (yw - f) * (yw - f) / ywm; } if (fStatisticType == kFitOptimChiFuncValues) { ywm = f; if (f < 0.00001) ywm = 0.00001; } else if (fStatisticType == kFitOptimMaxLikelihood) { ywm = f; if (f < 0.00001) ywm = 0.00001; } else { if (ywm == 0) ywm = 1; } //calculation of gradient vector for (j = 0, k = 0; j < fNPeaks; j++) { if (fFixAmp[j] == false) { a = Deramp2((Double_t) i1, (Double_t) i2, working_space[7 * j + 1], working_space[7 * j + 2], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (ywm != 0) { c = Ourpowl(a, pw); if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixPositionX[j] == false) { a = Deri02((Double_t) i1, (Double_t) i2, working_space[7 * j], working_space[7 * j + 1], working_space[7 * j + 2], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (fFitTaylor == kFitTaylorOrderSecond) d = Derderi02((Double_t) i1, (Double_t) i2, working_space[7 * j], working_space[7 * j + 1], working_space[7 * j + 2], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2]); if (ywm != 0) { c = Ourpowl(a, pw); if (TMath::Abs(a) > 0.00000001 && fFitTaylor == kFitTaylorOrderSecond) { d = d * TMath::Abs(yw - f) / (2 * a * ywm); if (((a + d) <= 0 && a >= 0) || ((a + d) >= 0 && a <= 0)) d = 0; } else d = 0; a = a + d; if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixPositionY[j] == false) { a = Derj02((Double_t) i1, (Double_t) i2, working_space[7 * j], working_space[7 * j + 1], working_space[7 * j + 2], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (fFitTaylor == kFitTaylorOrderSecond) d = Derderj02((Double_t) i1, (Double_t) i2, working_space[7 * j], working_space[7 * j + 1], working_space[7 * j + 2], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2]); if (ywm != 0) { c = Ourpowl(a, pw); if (TMath::Abs(a) > 0.00000001 && fFitTaylor == kFitTaylorOrderSecond) { d = d * TMath::Abs(yw - f) / (2 * a * ywm); if (((a + d) <= 0 && a >= 0) || ((a + d) >= 0 && a <= 0)) d = 0; } else d = 0; a = a + d; if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixAmpX1[j] == false) { a = Derampx((Double_t) i1, working_space[7 * j + 5], working_space[peak_vel], working_space[peak_vel + 8], working_space[peak_vel + 10], working_space[peak_vel + 12]); if (ywm != 0) { c = Ourpowl(a, pw); if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixAmpY1[j] == false) { a = Derampx((Double_t) i2, working_space[7 * j + 6], working_space[peak_vel + 1], working_space[peak_vel + 9], working_space[peak_vel + 11], working_space[peak_vel + 13]); if (ywm != 0) { c = Ourpowl(a, pw); if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixPositionX1[j] == false) { a = Deri01((Double_t) i1, working_space[7 * j + 3], working_space[7 * j + 5], working_space[peak_vel], working_space[peak_vel + 8], working_space[peak_vel + 10], working_space[peak_vel + 12]); if (fFitTaylor == kFitTaylorOrderSecond) d = Derderi01((Double_t) i1, working_space[7 * j + 3], working_space[7 * j + 5], working_space[peak_vel]); if (ywm != 0) { c = Ourpowl(a, pw); if (TMath::Abs(a) > 0.00000001 && fFitTaylor == kFitTaylorOrderSecond) { d = d * TMath::Abs(yw - f) / (2 * a * ywm); if (((a + d) <= 0 && a >= 0) || ((a + d) >= 0 && a <= 0)) d = 0; } else d = 0; a = a + d; if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //Der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //Der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixPositionY1[j] == false) { a = Deri01((Double_t) i2, working_space[7 * j + 4], working_space[7 * j + 6], working_space[peak_vel + 1], working_space[peak_vel + 9], working_space[peak_vel + 11], working_space[peak_vel + 13]); if (fFitTaylor == kFitTaylorOrderSecond) d = Derderi01((Double_t) i2, working_space[7 * j + 4], working_space[7 * j + 6], working_space[peak_vel + 1]); if (ywm != 0) { c = Ourpowl(a, pw); if (TMath::Abs(a) > 0.00000001 && fFitTaylor == kFitTaylorOrderSecond) { d = d * TMath::Abs(yw - f) / (2 * a * ywm); if (((a + d) <= 0 && a >= 0) || ((a + d) >= 0 && a <= 0)) d = 0; } else d = 0; a = a + d; if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } } if (fFixSigmaX == false) { a = Dersigmax(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 8], working_space[peak_vel + 10], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (fFitTaylor == kFitTaylorOrderSecond) d = Derdersigmax(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2]); if (ywm != 0) { c = Ourpowl(a, pw); if (TMath::Abs(a) > 0.00000001 && fFitTaylor == kFitTaylorOrderSecond) { d = d * TMath::Abs(yw - f) / (2 * a * ywm); if (((a + d) <= 0 && a >= 0) || ((a + d) >= 0 && a <= 0)) d = 0; } else d = 0; a = a + d; if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixSigmaY == false) { a = Dersigmay(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 9], working_space[peak_vel + 11], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (fFitTaylor == kFitTaylorOrderSecond) d = Derdersigmay(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2]); if (ywm != 0) { c = Ourpowl(a, pw); if (TMath::Abs(a) > 0.00000001 && fFitTaylor == kFitTaylorOrderSecond) { d = d * TMath::Abs(yw - f) / (2 * a * ywm); if (((a + d) <= 0 && a >= 0) || ((a + d) >= 0 && a <= 0)) d = 0; } else d = 0; a = a + d; if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixRo == false) { a = Derro(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2]); if (ywm != 0) { c = Ourpowl(a, pw); if (TMath::Abs(a) > 0.00000001 && fFitTaylor == kFitTaylorOrderSecond) { d = d * TMath::Abs(yw - f) / (2 * a * ywm); if (((a + d) <= 0 && a >= 0) || ((a + d) >= 0 && a <= 0)) d = 0; } else d = 0; a = a + d; if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixA0 == false) { a = 1.; if (ywm != 0) { c = Ourpowl(a, pw); if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixAx == false) { a = i1; if (ywm != 0) { c = Ourpowl(a, pw); if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixAy == false) { a = i2; if (ywm != 0) { c = Ourpowl(a, pw); if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixTxy == false) { a = Dertxy(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (ywm != 0) { c = Ourpowl(a, pw); if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixSxy == false) { a = Dersxy(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1]); if (ywm != 0) { c = Ourpowl(a, pw); if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixTx == false) { a = Dertx(fNPeaks, (Double_t) i1, working_space, working_space[peak_vel], working_space[peak_vel + 12]); if (ywm != 0) { c = Ourpowl(a, pw); if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixTy == false) { a = Derty(fNPeaks, (Double_t) i2, working_space, working_space[peak_vel + 1], working_space[peak_vel + 13]); if (ywm != 0) { c = Ourpowl(a, pw); if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixSx == false) { a = Dersx(fNPeaks, (Double_t) i1, working_space, working_space[peak_vel]); if (ywm != 0) { c = Ourpowl(a, pw); if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixSy == false) { a = Dersy(fNPeaks, (Double_t) i2, working_space, working_space[peak_vel + 1]); if (ywm != 0) { c = Ourpowl(a, pw); if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixBx == false) { a = Derbx(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 6], working_space[peak_vel + 8], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (ywm != 0) { c = Ourpowl(a, pw); if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } if (fFixBy == false) { a = Derby(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 6], working_space[peak_vel + 8], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (ywm != 0) { c = Ourpowl(a, pw); if (fStatisticType == kFitOptimChiFuncValues) { b = a * (yw * yw - f * f) / (ywm * ywm); working_space[2 * shift + k] += b * c; //der b = a * a * (4 * yw - 2 * f) / (ywm * ywm); working_space[3 * shift + k] += b * c; //temp } else { b = a * (yw - f) / ywm; working_space[2 * shift + k] += b * c; //der b = a * a / ywm; working_space[3 * shift + k] += b * c; //temp } } k += 1; } } } for (j = 0; j < size; j++) { if (TMath::Abs(working_space[3 * shift + j]) > 0.000001) working_space[2 * shift + j] = working_space[2 * shift + j] / TMath::Abs(working_space[3 * shift + j]); //der[j]=der[j]/temp[j] else working_space[2 * shift + j] = 0; //der[j] } //calculate chi_opt chi2 = chi_opt; chi_opt = TMath::Sqrt(TMath::Abs(chi_opt)); //calculate new parameters regul_cycle = 0; for (j = 0; j < size; j++) { working_space[4 * shift + j] = working_space[shift + j]; //temp_xk[j]=xk[j] } do { if (fAlphaOptim == kFitAlphaOptimal) { if (fStatisticType != kFitOptimMaxLikelihood) chi_min = 10000 * chi2; else chi_min = 0.1 * chi2; flag = 0; for (pi = 0.1; flag == 0 && pi <= 100; pi += 0.1) { for (j = 0; j < size; j++) { working_space[shift + j] = working_space[4 * shift + j] + pi * alpha * working_space[2 * shift + j]; //xk[j]=temp_xk[j]+pi*alpha*der[j] } for (i = 0, j = 0; i < fNPeaks; i++) { if (fFixAmp[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i] = working_space[shift + j]; //parameter[7*i]=xk[j] j += 1; } if (fFixPositionX[i] == false) { if (working_space[shift + j] < fXmin) //xk[j] working_space[shift + j] = fXmin; //xk[j] if (working_space[shift + j] > fXmax) //xk[j] working_space[shift + j] = fXmax; //xk[j] working_space[7 * i + 1] = working_space[shift + j]; //parameter[7*i+1]=xk[j] j += 1; } if (fFixPositionY[i] == false) { if (working_space[shift + j] < fYmin) //xk[j] working_space[shift + j] = fYmin; //xk[j] if (working_space[shift + j] > fYmax) //xk[j] working_space[shift + j] = fYmax; //xk[j] working_space[7 * i + 2] = working_space[shift + j]; //parameter[7*i+2]=xk[j] j += 1; } if (fFixAmpX1[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i + 3] = working_space[shift + j]; //parameter[7*i+3]=xk[j] j += 1; } if (fFixAmpY1[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i + 4] = working_space[shift + j]; //parameter[7*i+4]=xk[j] j += 1; } if (fFixPositionX1[i] == false) { if (working_space[shift + j] < fXmin) //xk[j] working_space[shift + j] = fXmin; //xk[j] if (working_space[shift + j] > fXmax) //xk[j] working_space[shift + j] = fXmax; //xk[j] working_space[7 * i + 5] = working_space[shift + j]; //parameter[7*i+5]=xk[j] j += 1; } if (fFixPositionY1[i] == false) { if (working_space[shift + j] < fYmin) //xk[j] working_space[shift + j] = fYmin; //xk[j] if (working_space[shift + j] > fYmax) //xk[j] working_space[shift + j] = fYmax; //xk[j] working_space[7 * i + 6] = working_space[shift + j]; //parameter[7*i+6]=xk[j] j += 1; } } if (fFixSigmaX == false) { if (working_space[shift + j] < 0.001) { //xk[j] working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel] = working_space[shift + j]; //parameter[peak_vel]=xk[j] j += 1; } if (fFixSigmaY == false) { if (working_space[shift + j] < 0.001) { //xk[j] working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 1] = working_space[shift + j]; //parameter[peak_vel+1]=xk[j] j += 1; } if (fFixRo == false) { if (working_space[shift + j] < -1) { //xk[j] working_space[shift + j] = -1; //xk[j] } if (working_space[shift + j] > 1) { //xk[j] working_space[shift + j] = 1; //xk[j] } working_space[peak_vel + 2] = working_space[shift + j]; //parameter[peak_vel+2]=xk[j] j += 1; } if (fFixA0 == false) { working_space[peak_vel + 3] = working_space[shift + j]; //parameter[peak_vel+3]=xk[j] j += 1; } if (fFixAx == false) { working_space[peak_vel + 4] = working_space[shift + j]; //parameter[peak_vel+4]=xk[j] j += 1; } if (fFixAy == false) { working_space[peak_vel + 5] = working_space[shift + j]; //parameter[peak_vel+5]=xk[j] j += 1; } if (fFixTxy == false) { working_space[peak_vel + 6] = working_space[shift + j]; //parameter[peak_vel+6]=xk[j] j += 1; } if (fFixSxy == false) { working_space[peak_vel + 7] = working_space[shift + j]; //parameter[peak_vel+7]=xk[j] j += 1; } if (fFixTx == false) { working_space[peak_vel + 8] = working_space[shift + j]; //parameter[peak_vel+8]=xk[j] j += 1; } if (fFixTy == false) { working_space[peak_vel + 9] = working_space[shift + j]; //parameter[peak_vel+9]=xk[j] j += 1; } if (fFixSx == false) { working_space[peak_vel + 10] = working_space[shift + j]; //parameter[peak_vel+10]=xk[j] j += 1; } if (fFixSy == false) { working_space[peak_vel + 11] = working_space[shift + j]; //parameter[peak_vel+11]=xk[j] j += 1; } if (fFixBx == false) { if (TMath::Abs(working_space[shift + j]) < 0.001) { //xk[j] if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = -0.001; //xk[j] else working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 12] = working_space[shift + j]; //parameter[peak_vel+12]=xk[j] j += 1; } if (fFixBy == false) { if (TMath::Abs(working_space[shift + j]) < 0.001) { //xk[j] if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = -0.001; //xk[j] else working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 13] = working_space[shift + j]; //parameter[peak_vel+13]=xk[j] j += 1; } chi2 = 0; for (i1 = fXmin; i1 <= fXmax; i1++) { for (i2 = fYmin; i2 <= fYmax; i2++) { yw = source[i1][i2]; ywm = yw; f = Shape2(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 3], working_space[peak_vel + 4], working_space[peak_vel + 5], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 8], working_space[peak_vel + 9], working_space[peak_vel + 10], working_space[peak_vel + 11], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (fStatisticType == kFitOptimChiFuncValues) { ywm = f; if (f < 0.00001) ywm = 0.00001; } if (fStatisticType == kFitOptimMaxLikelihood) { if (f > 0.00001) chi2 += yw * TMath::Log(f) - f; } else { if (ywm != 0) chi2 += (yw - f) * (yw - f) / ywm; } } } if ((chi2 < chi_min && fStatisticType != kFitOptimMaxLikelihood) || (chi2 > chi_min && fStatisticType == kFitOptimMaxLikelihood)) { pmin = pi, chi_min = chi2; } else flag = 1; if (pi == 0.1) chi_min = chi2; chi = chi_min; } if (pmin != 0.1) { for (j = 0; j < size; j++) { working_space[shift + j] = working_space[4 * shift + j] + pmin * alpha * working_space[2 * shift + j]; //xk[j]=temp_xk[j]+pmin*alpha*der[j] } for (i = 0, j = 0; i < fNPeaks; i++) { if (fFixAmp[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i] = working_space[shift + j]; //parameter[7*i]=xk[j] j += 1; } if (fFixPositionX[i] == false) { if (working_space[shift + j] < fXmin) //xk[j] working_space[shift + j] = fXmin; //xk[j] if (working_space[shift + j] > fXmax) //xk[j] working_space[shift + j] = fXmax; //xk[j] working_space[7 * i + 1] = working_space[shift + j]; //parameter[7*i+1]=xk[j] j += 1; } if (fFixPositionY[i] == false) { if (working_space[shift + j] < fYmin) //xk[j] working_space[shift + j] = fYmin; //xk[j] if (working_space[shift + j] > fYmax) //xk[j] working_space[shift + j] = fYmax; //xk[j] working_space[7 * i + 2] = working_space[shift + j]; //parameter[7*i+2]=xk[j] j += 1; } if (fFixAmpX1[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i + 3] = working_space[shift + j]; //parameter[7*i+3]=xk[j] j += 1; } if (fFixAmpY1[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i + 4] = working_space[shift + j]; //parameter[7*i+4]=xk[j] j += 1; } if (fFixPositionX1[i] == false) { if (working_space[shift + j] < fXmin) //xk[j] working_space[shift + j] = fXmin; //xk[j] if (working_space[shift + j] > fXmax) //xk[j] working_space[shift + j] = fXmax; //xk[j] working_space[7 * i + 5] = working_space[shift + j]; //parameter[7*i+5]=xk[j] j += 1; } if (fFixPositionY1[i] == false) { if (working_space[shift + j] < fYmin) //xk[j] working_space[shift + j] = fYmin; //xk[j] if (working_space[shift + j] > fYmax) //xk[j] working_space[shift + j] = fYmax; //xk[j] working_space[7 * i + 6] = working_space[shift + j]; //parameter[7*i+6]=xk[j] j += 1; } } if (fFixSigmaX == false) { if (working_space[shift + j] < 0.001) { //xk[j] working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel] = working_space[shift + j]; //parameter[peak_vel]=xk[j] j += 1; } if (fFixSigmaY == false) { if (working_space[shift + j] < 0.001) { //xk[j] working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 1] = working_space[shift + j]; //parameter[peak_vel+1]=xk[j] j += 1; } if (fFixRo == false) { if (working_space[shift + j] < -1) { //xk[j] working_space[shift + j] = -1; //xk[j] } if (working_space[shift + j] > 1) { //xk[j] working_space[shift + j] = 1; //xk[j] } working_space[peak_vel + 2] = working_space[shift + j]; //parameter[peak_vel+2]=xk[j] j += 1; } if (fFixA0 == false) { working_space[peak_vel + 3] = working_space[shift + j]; //parameter[peak_vel+3]=xk[j] j += 1; } if (fFixAx == false) { working_space[peak_vel + 4] = working_space[shift + j]; //parameter[peak_vel+4]=xk[j] j += 1; } if (fFixAy == false) { working_space[peak_vel + 5] = working_space[shift + j]; //parameter[peak_vel+5]=xk[j] j += 1; } if (fFixTxy == false) { working_space[peak_vel + 6] = working_space[shift + j]; //parameter[peak_vel+6]=xk[j] j += 1; } if (fFixSxy == false) { working_space[peak_vel + 7] = working_space[shift + j]; //parameter[peak_vel+7]=xk[j] j += 1; } if (fFixTx == false) { working_space[peak_vel + 8] = working_space[shift + j]; //parameter[peak_vel+8]=xk[j] j += 1; } if (fFixTy == false) { working_space[peak_vel + 9] = working_space[shift + j]; //parameter[peak_vel+9]=xk[j] j += 1; } if (fFixSx == false) { working_space[peak_vel + 10] = working_space[shift + j]; //parameter[peak_vel+10]=xk[j] j += 1; } if (fFixSy == false) { working_space[peak_vel + 11] = working_space[shift + j]; //parameter[peak_vel+11]=xk[j] j += 1; } if (fFixBx == false) { if (TMath::Abs(working_space[shift + j]) < 0.001) { //xk[j] if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = -0.001; //xk[j] else working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 12] = working_space[shift + j]; //parameter[peak_vel+12]=xk[j] j += 1; } if (fFixBy == false) { if (TMath::Abs(working_space[shift + j]) < 0.001) { //xk[j] if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = -0.001; //xk[j] else working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 13] = working_space[shift + j]; //parameter[peak_vel+13]=xk[j] j += 1; } chi = chi_min; } } else { for (j = 0; j < size; j++) { working_space[shift + j] = working_space[4 * shift + j] + alpha * working_space[2 * shift + j]; //xk[j]=temp_xk[j]+pi*alpha*der[j] } for (i = 0, j = 0; i < fNPeaks; i++) { if (fFixAmp[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i] = working_space[shift + j]; //parameter[7*i]=xk[j] j += 1; } if (fFixPositionX[i] == false) { if (working_space[shift + j] < fXmin) //xk[j] working_space[shift + j] = fXmin; //xk[j] if (working_space[shift + j] > fXmax) //xk[j] working_space[shift + j] = fXmax; //xk[j] working_space[7 * i + 1] = working_space[shift + j]; //parameter[7*i+1]=xk[j] j += 1; } if (fFixPositionY[i] == false) { if (working_space[shift + j] < fYmin) //xk[j] working_space[shift + j] = fYmin; //xk[j] if (working_space[shift + j] > fYmax) //xk[j] working_space[shift + j] = fYmax; //xk[j] working_space[7 * i + 2] = working_space[shift + j]; //parameter[7*i+2]=xk[j] j += 1; } if (fFixAmpX1[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i + 3] = working_space[shift + j]; //parameter[7*i+3]=xk[j] j += 1; } if (fFixAmpY1[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i + 4] = working_space[shift + j]; //parameter[7*i+4]=xk[j] j += 1; } if (fFixPositionX1[i] == false) { if (working_space[shift + j] < fXmin) //xk[j] working_space[shift + j] = fXmin; //xk[j] if (working_space[shift + j] > fXmax) //xk[j] working_space[shift + j] = fXmax; //xk[j] working_space[7 * i + 5] = working_space[shift + j]; //parameter[7*i+5]=xk[j] j += 1; } if (fFixPositionY1[i] == false) { if (working_space[shift + j] < fYmin) //xk[j] working_space[shift + j] = fYmin; //xk[j] if (working_space[shift + j] > fYmax) //xk[j] working_space[shift + j] = fYmax; //xk[j] working_space[7 * i + 6] = working_space[shift + j]; //parameter[7*i+6]=xk[j] j += 1; } } if (fFixSigmaX == false) { if (working_space[shift + j] < 0.001) { //xk[j] working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel] = working_space[shift + j]; //parameter[peak_vel]=xk[j] j += 1; } if (fFixSigmaY == false) { if (working_space[shift + j] < 0.001) { //xk[j] working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 1] = working_space[shift + j]; //parameter[peak_vel+1]=xk[j] j += 1; } if (fFixRo == false) { if (working_space[shift + j] < -1) { //xk[j] working_space[shift + j] = -1; //xk[j] } if (working_space[shift + j] > 1) { //xk[j] working_space[shift + j] = 1; //xk[j] } working_space[peak_vel + 2] = working_space[shift + j]; //parameter[peak_vel+2]=xk[j] j += 1; } if (fFixA0 == false) { working_space[peak_vel + 3] = working_space[shift + j]; //parameter[peak_vel+3]=xk[j] j += 1; } if (fFixAx == false) { working_space[peak_vel + 4] = working_space[shift + j]; //parameter[peak_vel+4]=xk[j] j += 1; } if (fFixAy == false) { working_space[peak_vel + 5] = working_space[shift + j]; //parameter[peak_vel+5]=xk[j] j += 1; } if (fFixTxy == false) { working_space[peak_vel + 6] = working_space[shift + j]; //parameter[peak_vel+6]=xk[j] j += 1; } if (fFixSxy == false) { working_space[peak_vel + 7] = working_space[shift + j]; //parameter[peak_vel+7]=xk[j] j += 1; } if (fFixTx == false) { working_space[peak_vel + 8] = working_space[shift + j]; //parameter[peak_vel+8]=xk[j] j += 1; } if (fFixTy == false) { working_space[peak_vel + 9] = working_space[shift + j]; //parameter[peak_vel+9]=xk[j] j += 1; } if (fFixSx == false) { working_space[peak_vel + 10] = working_space[shift + j]; //parameter[peak_vel+10]=xk[j] j += 1; } if (fFixSy == false) { working_space[peak_vel + 11] = working_space[shift + j]; //parameter[peak_vel+11]=xk[j] j += 1; } if (fFixBx == false) { if (TMath::Abs(working_space[shift + j]) < 0.001) { //xk[j] if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = -0.001; //xk[j] else working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 12] = working_space[shift + j]; //parameter[peak_vel+12]=xk[j] j += 1; } if (fFixBy == false) { if (TMath::Abs(working_space[shift + j]) < 0.001) { //xk[j] if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = -0.001; //xk[j] else working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 13] = working_space[shift + j]; //parameter[peak_vel+13]=xk[j] j += 1; } chi = 0; for (i1 = fXmin; i1 <= fXmax; i1++) { for (i2 = fYmin; i2 <= fYmax; i2++) { yw = source[i1][i2]; ywm = yw; f = Shape2(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 3], working_space[peak_vel + 4], working_space[peak_vel + 5], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 8], working_space[peak_vel + 9], working_space[peak_vel + 10], working_space[peak_vel + 11], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (fStatisticType == kFitOptimChiFuncValues) { ywm = f; if (f < 0.00001) ywm = 0.00001; } if (fStatisticType == kFitOptimMaxLikelihood) { if (f > 0.00001) chi += yw * TMath::Log(f) - f; } else { if (ywm != 0) chi += (yw - f) * (yw - f) / ywm; } } } } chi2 = chi; chi = TMath::Sqrt(TMath::Abs(chi)); if (fAlphaOptim == kFitAlphaHalving && chi > 1E-6) alpha = alpha * chi_opt / (2 * chi); else if (fAlphaOptim == kFitAlphaOptimal) alpha = alpha / 10.0; iter += 1; regul_cycle += 1; } while (((chi > chi_opt && fStatisticType != kFitOptimMaxLikelihood) || (chi < chi_opt && fStatisticType == kFitOptimMaxLikelihood)) && regul_cycle < kFitNumRegulCycles); for (j = 0; j < size; j++) { working_space[4 * shift + j] = 0; //temp_xk[j] working_space[2 * shift + j] = 0; //der[j] } for (i1 = fXmin, chi_cel = 0; i1 <= fXmax; i1++) { for (i2 = fYmin; i2 <= fYmax; i2++) { yw = source[i1][i2]; if (yw == 0) yw = 1; f = Shape2(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 3], working_space[peak_vel + 4], working_space[peak_vel + 5], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 8], working_space[peak_vel + 9], working_space[peak_vel + 10], working_space[peak_vel + 11], working_space[peak_vel + 12], working_space[peak_vel + 13]); chi_opt = (yw - f) * (yw - f) / yw; chi_cel += (yw - f) * (yw - f) / yw; //calculate gradient vector for (j = 0, k = 0; j < fNPeaks; j++) { if (fFixAmp[j] == false) { a = Deramp2((Double_t) i1, (Double_t) i2, working_space[7 * j + 1], working_space[7 * j + 2], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixPositionX[j] == false) { a = Deri02((Double_t) i1, (Double_t) i2, working_space[7 * j], working_space[7 * j + 1], working_space[7 * j + 2], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixPositionY[j] == false) { a = Derj02((Double_t) i1, (Double_t) i2, working_space[7 * j], working_space[7 * j + 1], working_space[7 * j + 2], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixAmpX1[j] == false) { a = Derampx((Double_t) i1, working_space[7 * j + 5], working_space[peak_vel], working_space[peak_vel + 8], working_space[peak_vel + 10], working_space[peak_vel + 12]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixAmpY1[j] == false) { a = Derampx((Double_t) i2, working_space[7 * j + 6], working_space[peak_vel + 1], working_space[peak_vel + 9], working_space[peak_vel + 11], working_space[peak_vel + 13]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixPositionX1[j] == false) { a = Deri01((Double_t) i1, working_space[7 * j + 3], working_space[7 * j + 5], working_space[peak_vel], working_space[peak_vel + 8], working_space[peak_vel + 10], working_space[peak_vel + 12]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixPositionY1[j] == false) { a = Deri01((Double_t) i2, working_space[7 * j + 4], working_space[7 * j + 6], working_space[peak_vel + 1], working_space[peak_vel + 9], working_space[peak_vel + 11], working_space[peak_vel + 13]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } } if (fFixSigmaX == false) { a = Dersigmax(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 8], working_space[peak_vel + 10], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixSigmaY == false) { a = Dersigmay(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 9], working_space[peak_vel + 11], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixRo == false) { a = Derro(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixA0 == false) { a = 1.; if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixAx == false) { a = i1; if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixAy == false) { a = i2; if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixTxy == false) { a = Dertxy(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixSxy == false) { a = Dersxy(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixTx == false) { a = Dertx(fNPeaks, (Double_t) i1, working_space, working_space[peak_vel], working_space[peak_vel + 12]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixTy == false) { a = Derty(fNPeaks, (Double_t) i2, working_space, working_space[peak_vel + 1], working_space[peak_vel + 13]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixSx == false) { a = Dersx(fNPeaks, (Double_t) i1, working_space, working_space[peak_vel]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixSy == false) { a = Dersy(fNPeaks, (Double_t) i2, working_space, working_space[peak_vel + 1]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixBx == false) { a = Derbx(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 6], working_space[peak_vel + 8], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } if (fFixBy == false) { a = Derby(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 6], working_space[peak_vel + 8], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { c = Ourpowl(a, pw); working_space[2 * shift + k] += chi_opt * c; //der[k] b = a * a / yw; working_space[4 * shift + k] += b * c; //temp_xk[k] } k += 1; } } } } b = (fXmax - fXmin + 1) * (fYmax - fYmin + 1) - size; chi_er = chi_cel / b; for (i = 0, j = 0; i < fNPeaks; i++) { fVolume[i] = Volume(working_space[7 * i], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2]); if (fVolume[i] > 0) { c = 0; if (fFixAmp[i] == false) { a = Derpa2(working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2]); b = working_space[4 * shift + j]; //temp_xk[j] if (b == 0) b = 1; else b = 1 / b; c = c + a * a * b; } if (fFixSigmaX == false) { a = Derpsigmax(working_space[shift + j], working_space[peak_vel + 1], working_space[peak_vel + 2]); b = working_space[4 * shift + peak_vel]; //temp_xk[j] if (b == 0) b = 1; else b = 1 / b; c = c + a * a * b; } if (fFixSigmaY == false) { a = Derpsigmay(working_space[shift + j], working_space[peak_vel], working_space[peak_vel + 2]); b = working_space[4 * shift + peak_vel + 1]; //temp_xk[j] if (b == 0) b = 1; else b = 1 / b; c = c + a * a * b; } if (fFixRo == false) { a = Derpro(working_space[shift + j], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2]); b = working_space[4 * shift + peak_vel + 2]; //temp_xk[j] if (b == 0) b = 1; else b = 1 / b; c = c + a * a * b; } fVolumeErr[i] = TMath::Sqrt(TMath::Abs(chi_er * c)); } else { fVolumeErr[i] = 0; } if (fFixAmp[i] == false) { fAmpCalc[i] = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) fAmpErr[i] = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fAmpCalc[i] = fAmpInit[i]; fAmpErr[i] = 0; } if (fFixPositionX[i] == false) { fPositionCalcX[i] = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) fPositionErrX[i] = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fPositionCalcX[i] = fPositionInitX[i]; fPositionErrX[i] = 0; } if (fFixPositionY[i] == false) { fPositionCalcY[i] = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) fPositionErrY[i] = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fPositionCalcY[i] = fPositionInitY[i]; fPositionErrY[i] = 0; } if (fFixAmpX1[i] == false) { fAmpCalcX1[i] = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) fAmpErrX1[i] = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fAmpCalcX1[i] = fAmpInitX1[i]; fAmpErrX1[i] = 0; } if (fFixAmpY1[i] == false) { fAmpCalcY1[i] = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) fAmpErrY1[i] = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fAmpCalcY1[i] = fAmpInitY1[i]; fAmpErrY1[i] = 0; } if (fFixPositionX1[i] == false) { fPositionCalcX1[i] = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) fPositionErrX1[i] = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fPositionCalcX1[i] = fPositionInitX1[i]; fPositionErrX1[i] = 0; } if (fFixPositionY1[i] == false) { fPositionCalcY1[i] = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) fPositionErrY1[i] = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fPositionCalcY1[i] = fPositionInitY1[i]; fPositionErrY1[i] = 0; } } if (fFixSigmaX == false) { fSigmaCalcX = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fSigmaErrX = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fSigmaCalcX = fSigmaInitX; fSigmaErrX = 0; } if (fFixSigmaY == false) { fSigmaCalcY = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fSigmaErrY = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fSigmaCalcY = fSigmaInitY; fSigmaErrY = 0; } if (fFixRo == false) { fRoCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fRoErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fRoCalc = fRoInit; fRoErr = 0; } if (fFixA0 == false) { fA0Calc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fA0Err = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fA0Calc = fA0Init; fA0Err = 0; } if (fFixAx == false) { fAxCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fAxErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fAxCalc = fAxInit; fAxErr = 0; } if (fFixAy == false) { fAyCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fAyErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fAyCalc = fAyInit; fAyErr = 0; } if (fFixTxy == false) { fTxyCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fTxyErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fTxyCalc = fTxyInit; fTxyErr = 0; } if (fFixSxy == false) { fSxyCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fSxyErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fSxyCalc = fSxyInit; fSxyErr = 0; } if (fFixTx == false) { fTxCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fTxErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fTxCalc = fTxInit; fTxErr = 0; } if (fFixTy == false) { fTyCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fTyErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fTyCalc = fTyInit; fTyErr = 0; } if (fFixSx == false) { fSxCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fSxErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fSxCalc = fSxInit; fSxErr = 0; } if (fFixSy == false) { fSyCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fSyErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fSyCalc = fSyInit; fSyErr = 0; } if (fFixBx == false) { fBxCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fBxErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fBxCalc = fBxInit; fBxErr = 0; } if (fFixBy == false) { fByCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fByErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fByCalc = fByInit; fByErr = 0; } b = (fXmax - fXmin + 1) * (fYmax - fYmin + 1) - size; fChi = chi_cel / b; for (i1 = fXmin; i1 <= fXmax; i1++) { for (i2 = fYmin; i2 <= fYmax; i2++) { f = Shape2(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 3], working_space[peak_vel + 4], working_space[peak_vel + 5], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 8], working_space[peak_vel + 9], working_space[peak_vel + 10], working_space[peak_vel + 11], working_space[peak_vel + 12], working_space[peak_vel + 13]); source[i1][i2] = f; } } delete [] working_space; return; } // ____________________________________________________________________________________________________________________________ void TSpectrum2Fit::FitStiefel(Float_t **source) { ///////////////////////////////////////////////////////////////////////////// // TWO-DIMENSIONAL FIT FUNCTION USING STIEFEL-HESTENS // ALGORITHM. // This function fits the source spectrum. The calling program should // fill in input parameters of the TSpectrum2Fit class. // The fitted parameters are written into // TSpectrum2Fit class output parameters and fitted data are written into // source spectrum. // // Function parameters: // source-pointer to the matrix of source spectrum // ///////////////////////////////////////////////////////////////////////////// // //Begin_Html

Stiefel fitting algorithm

 

Function:

void TSpectrumFit2::FitStiefel(float **fSource)

This function fits the source spectrum using Stiefel-Hestens method [1].  The calling program should fill in input fitting parameters of the TSpectrumFit2 class using a set of TSpectrumFit2 setters. The fitted parameters are written into the class and the fitted data are written into source spectrum. It converges faster than Awmi method.

 

Parameter:

        fSource-pointer to the matrix of source spectrum                 

       

Reference:

[1] B. Mihaila: Analysis of complex gamma spectra, Rom. Jorn. Phys., Vol. 39, No. 2, (1994), 139-148.

 

Example 1 – script FitS.c:

Fig. 1 Original two-dimensional spectrum with found peaks (using TSpectrum2 peak searching function). The positions of peaks were used as initial estimates in fitting procedure.

Fig. 2 Fitted (generated from fitted parameters) spectrum of the data from Fig. 1 using Stiefel-Hestens method. Each peak was represented by 7 parameters, which together with Sigmax, Sigmay and a0 resulted in 38 fitted parameters. The chi-square after 1000 iterations was 0.642157.

 

Script:

// Example to illustrate fitting function, algorithm without matrix inversion (AWMI) (class TSpectrumFit2).

// To execute this example, do

// root > .x FitStiefel2.C

 

void FitStiefel2() {

   Int_t i, j, nfound;

   Int_t nbinsx = 64;

   Int_t nbinsy = 64;  

   Int_t xmin  = 0;

   Int_t xmax  = nbinsx;

   Int_t ymin  = 0;

   Int_t ymax  = nbinsy;

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

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

   for (i=0;i<nbinsx;i++)

                                                source[i]=new float[nbinsy];

   for (i=0;i<nbinsx;i++)

                                                dest[i]=new float[nbinsy];

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

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

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

   TCanvas *Searching = new TCanvas("Searching","Two-dimensional fitting using Stiefel-Hestens method",10,10,1000,700);

   TSpectrum2 *s = new TSpectrum2();

   for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

                 }

   }  

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

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

   Bool_t *FixPosX = new Bool_t[nfound];

   Bool_t *FixPosY = new Bool_t[nfound];   

   Bool_t *FixAmp = new Bool_t[nfound];     

   Float_t *PosX = new Float_t[nfound];        

   Float_t *PosY = new Float_t[nfound];

   Float_t *Amp = new Float_t[nfound];     

   Float_t *AmpXY = new Float_t[nfound];        

   PosX = s->GetPositionX();

   PosY = s->GetPositionY();     

   for(i = 0; i< nfound ; i++){

      FixPosX[i] = kFALSE;

      FixPosY[i] = kFALSE;     

      FixAmp[i] = kFALSE;   

      Amp[i] = source[(int)(PosX[i]+0.5)][(int)(PosY[i]+0.5)];      //initial values of peaks amplitudes, input parameters         

      AmpXY[i] = 0;

   }

   //filling in the initial estimates of the input parameters

   TSpectrumFit2 *pfit=new TSpectrumFit2(nfound);

   pfit->SetFitParameters(xmin, xmax-1, ymin, ymax-1, 1000, 0.1, pfit->kFitOptimChiCounts, pfit->kFitAlphaHalving, pfit->kFitPower2, pfit->kFitTaylorOrderFirst);  

   pfit->SetPeakParameters(2, kFALSE, 2, kFALSE, 0, kTRUE, PosX, (Bool_t *) FixPosX, PosY, (Bool_t *) FixPosY, PosX, (Bool_t *) FixPosX, PosY, (Bool_t *) FixPosY, Amp, (Bool_t *) FixAmp, AmpXY, (Bool_t *) FixAmp, AmpXY, (Bool_t *) FixAmp);     

   pfit->SetBackgroundParameters(0, kFALSE, 0, kTRUE, 0, kTRUE);  

   pfit->FitStiefel(source);

    for (i = 0; i < nbinsx; i++){

     for (j = 0; j < nbinsy; j++){

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

                 }

   }  

   search->Draw("SURF");

}

End_Html Int_t i, i1, i2, j, k, shift = 7 * fNPeaks + 14, peak_vel, size, iter, regul_cycle, flag; Double_t a, b, c, alpha, chi_opt, yw, ywm, f, chi2, chi_min, chi = 0 , pi, pmin = 0, chi_cel = 0, chi_er; Double_t *working_space = new Double_t[5 * (7 * fNPeaks + 14)]; for (i = 0, j = 0; i < fNPeaks; i++) { working_space[7 * i] = fAmpInit[i]; //vector parameter if (fFixAmp[i] == false) { working_space[shift + j] = fAmpInit[i]; //vector xk j += 1; } working_space[7 * i + 1] = fPositionInitX[i]; //vector parameter if (fFixPositionX[i] == false) { working_space[shift + j] = fPositionInitX[i]; //vector xk j += 1; } working_space[7 * i + 2] = fPositionInitY[i]; //vector parameter if (fFixPositionY[i] == false) { working_space[shift + j] = fPositionInitY[i]; //vector xk j += 1; } working_space[7 * i + 3] = fAmpInitX1[i]; //vector parameter if (fFixAmpX1[i] == false) { working_space[shift + j] = fAmpInitX1[i]; //vector xk j += 1; } working_space[7 * i + 4] = fAmpInitY1[i]; //vector parameter if (fFixAmpY1[i] == false) { working_space[shift + j] = fAmpInitY1[i]; //vector xk j += 1; } working_space[7 * i + 5] = fPositionInitX1[i]; //vector parameter if (fFixPositionX1[i] == false) { working_space[shift + j] = fPositionInitX1[i]; //vector xk j += 1; } working_space[7 * i + 6] = fPositionInitY1[i]; //vector parameter if (fFixPositionY1[i] == false) { working_space[shift + j] = fPositionInitY1[i]; //vector xk j += 1; } } peak_vel = 7 * i; working_space[7 * i] = fSigmaInitX; //vector parameter if (fFixSigmaX == false) { working_space[shift + j] = fSigmaInitX; //vector xk j += 1; } working_space[7 * i + 1] = fSigmaInitY; //vector parameter if (fFixSigmaY == false) { working_space[shift + j] = fSigmaInitY; //vector xk j += 1; } working_space[7 * i + 2] = fRoInit; //vector parameter if (fFixRo == false) { working_space[shift + j] = fRoInit; //vector xk j += 1; } working_space[7 * i + 3] = fA0Init; //vector parameter if (fFixA0 == false) { working_space[shift + j] = fA0Init; //vector xk j += 1; } working_space[7 * i + 4] = fAxInit; //vector parameter if (fFixAx == false) { working_space[shift + j] = fAxInit; //vector xk j += 1; } working_space[7 * i + 5] = fAyInit; //vector parameter if (fFixAy == false) { working_space[shift + j] = fAyInit; //vector xk j += 1; } working_space[7 * i + 6] = fTxyInit; //vector parameter if (fFixTxy == false) { working_space[shift + j] = fTxyInit; //vector xk j += 1; } working_space[7 * i + 7] = fSxyInit; //vector parameter if (fFixSxy == false) { working_space[shift + j] = fSxyInit; //vector xk j += 1; } working_space[7 * i + 8] = fTxInit; //vector parameter if (fFixTx == false) { working_space[shift + j] = fTxInit; //vector xk j += 1; } working_space[7 * i + 9] = fTyInit; //vector parameter if (fFixTy == false) { working_space[shift + j] = fTyInit; //vector xk j += 1; } working_space[7 * i + 10] = fSxyInit; //vector parameter if (fFixSx == false) { working_space[shift + j] = fSxInit; //vector xk j += 1; } working_space[7 * i + 11] = fSyInit; //vector parameter if (fFixSy == false) { working_space[shift + j] = fSyInit; //vector xk j += 1; } working_space[7 * i + 12] = fBxInit; //vector parameter if (fFixBx == false) { working_space[shift + j] = fBxInit; //vector xk j += 1; } working_space[7 * i + 13] = fByInit; //vector parameter if (fFixBy == false) { working_space[shift + j] = fByInit; //vector xk j += 1; } size = j; Double_t **working_matrix = new Double_t *[size]; for (i = 0; i < size; i++) working_matrix[i] = new Double_t[size + 4]; for (iter = 0; iter < fNumberIterations; iter++) { for (j = 0; j < size; j++) { working_space[3 * shift + j] = 0; //temp for (k = 0; k <= size; k++) { working_matrix[j][k] = 0; } } //filling working matrix alpha = fAlpha; chi_opt = 0; for (i1 = fXmin; i1 <= fXmax; i1++) { for (i2 = fYmin; i2 <= fYmax; i2++) { //calculation of gradient vector for (j = 0, k = 0; j < fNPeaks; j++) { if (fFixAmp[j] == false) { working_space[2 * shift + k] = Deramp2((Double_t) i1, (Double_t) i2, working_space[7 * j + 1], working_space[7 * j + 2], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 12], working_space[peak_vel + 13]); k += 1; } if (fFixPositionX[j] == false) { working_space[2 * shift + k] = Deri02((Double_t) i1, (Double_t) i2, working_space[7 * j], working_space[7 * j + 1], working_space[7 * j + 2], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 12], working_space[peak_vel + 13]); k += 1; } if (fFixPositionY[j] == false) { working_space[2 * shift + k] = Derj02((Double_t) i1, (Double_t) i2, working_space[7 * j], working_space[7 * j + 1], working_space[7 * j + 2], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 12], working_space[peak_vel + 13]); k += 1; } if (fFixAmpX1[j] == false) { working_space[2 * shift + k] = Derampx((Double_t) i1, working_space[7 * j + 5], working_space[peak_vel], working_space[peak_vel + 8], working_space[peak_vel + 10], working_space[peak_vel + 12]); k += 1; } if (fFixAmpY1[j] == false) { working_space[2 * shift + k] = Derampx((Double_t) i2, working_space[7 * j + 6], working_space[peak_vel + 1], working_space[peak_vel + 9], working_space[peak_vel + 11], working_space[peak_vel + 13]); k += 1; } if (fFixPositionX1[j] == false) { working_space[2 * shift + k] = Deri01((Double_t) i1, working_space[7 * j + 3], working_space[7 * j + 5], working_space[peak_vel], working_space[peak_vel + 8], working_space[peak_vel + 10], working_space[peak_vel + 12]); k += 1; } if (fFixPositionY1[j] == false) { working_space[2 * shift + k] = Deri01((Double_t) i2, working_space[7 * j + 4], working_space[7 * j + 6], working_space[peak_vel + 1], working_space[peak_vel + 9], working_space[peak_vel + 11], working_space[peak_vel + 13]); k += 1; } } if (fFixSigmaX == false) { working_space[2 * shift + k] = Dersigmax(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 8], working_space[peak_vel + 10], working_space[peak_vel + 12], working_space[peak_vel + 13]); k += 1; } if (fFixSigmaY == false) { working_space[2 * shift + k] = Dersigmay(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 9], working_space[peak_vel + 11], working_space[peak_vel + 12], working_space[peak_vel + 13]); k += 1; } if (fFixRo == false) { working_space[2 * shift + k] = Derro(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2]); k += 1; } if (fFixA0 == false) { working_space[2 * shift + k] = 1.; k += 1; } if (fFixAx == false) { working_space[2 * shift + k] = i1; k += 1; } if (fFixAy == false) { working_space[2 * shift + k] = i2; k += 1; } if (fFixTxy == false) { working_space[2 * shift + k] = Dertxy(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 12], working_space[peak_vel + 13]); k += 1; } if (fFixSxy == false) { working_space[2 * shift + k] = Dersxy(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1]); k += 1; } if (fFixTx == false) { working_space[2 * shift + k] = Dertx(fNPeaks, (Double_t) i1, working_space, working_space[peak_vel], working_space[peak_vel + 12]); k += 1; } if (fFixTy == false) { working_space[2 * shift + k] = Derty(fNPeaks, (Double_t) i2, working_space, working_space[peak_vel + 1], working_space[peak_vel + 13]); k += 1; } if (fFixSx == false) { working_space[2 * shift + k] = Dersx(fNPeaks, (Double_t) i1, working_space, working_space[peak_vel]); k += 1; } if (fFixSy == false) { working_space[2 * shift + k] = Dersy(fNPeaks, (Double_t) i2, working_space, working_space[peak_vel + 1]); k += 1; } if (fFixBx == false) { working_space[2 * shift + k] = Derbx(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 6], working_space[peak_vel + 8], working_space[peak_vel + 12], working_space[peak_vel + 13]); k += 1; } if (fFixBy == false) { working_space[2 * shift + k] = Derby(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 6], working_space[peak_vel + 8], working_space[peak_vel + 12], working_space[peak_vel + 13]); k += 1; } yw = source[i1][i2]; ywm = yw; f = Shape2(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 3], working_space[peak_vel + 4], working_space[peak_vel + 5], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 8], working_space[peak_vel + 9], working_space[peak_vel + 10], working_space[peak_vel + 11], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (fStatisticType == kFitOptimMaxLikelihood) { if (f > 0.00001) chi_opt += yw * TMath::Log(f) - f; } else { if (ywm != 0) chi_opt += (yw - f) * (yw - f) / ywm; } if (fStatisticType == kFitOptimChiFuncValues) { ywm = f; if (f < 0.00001) ywm = 0.00001; } else if (fStatisticType == kFitOptimMaxLikelihood) { ywm = f; if (f < 0.00001) ywm = 0.00001; } else { if (ywm == 0) ywm = 1; } for (j = 0; j < size; j++) { for (k = 0; k < size; k++) { b = working_space[2 * shift + j] * working_space[2 * shift + k] / ywm; if (fStatisticType == kFitOptimChiFuncValues) b = b * (4 * yw - 2 * f) / ywm; working_matrix[j][k] += b; if (j == k) working_space[3 * shift + j] += b; } } if (fStatisticType == kFitOptimChiFuncValues) b = (f * f - yw * yw) / (ywm * ywm); else b = (f - yw) / ywm; for (j = 0; j < size; j++) { working_matrix[j][size] -= b * working_space[2 * shift + j]; } } } for (i = 0; i < size; i++) { working_matrix[i][size + 1] = 0; //xk } StiefelInversion(working_matrix, size); for (i = 0; i < size; i++) { working_space[2 * shift + i] = working_matrix[i][size + 1]; //der } //calculate chi_opt chi2 = chi_opt; chi_opt = TMath::Sqrt(TMath::Abs(chi_opt)); //calculate new parameters regul_cycle = 0; for (j = 0; j < size; j++) { working_space[4 * shift + j] = working_space[shift + j]; //temp_xk[j]=xk[j] } do { if (fAlphaOptim == kFitAlphaOptimal) { if (fStatisticType != kFitOptimMaxLikelihood) chi_min = 10000 * chi2; else chi_min = 0.1 * chi2; flag = 0; for (pi = 0.1; flag == 0 && pi <= 100; pi += 0.1) { for (j = 0; j < size; j++) { working_space[shift + j] = working_space[4 * shift + j] + pi * alpha * working_space[2 * shift + j]; //xk[j]=temp_xk[j]+pi*alpha*der[j] } for (i = 0, j = 0; i < fNPeaks; i++) { if (fFixAmp[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i] = working_space[shift + j]; //parameter[7*i]=xk[j] j += 1; } if (fFixPositionX[i] == false) { if (working_space[shift + j] < fXmin) //xk[j] working_space[shift + j] = fXmin; //xk[j] if (working_space[shift + j] > fXmax) //xk[j] working_space[shift + j] = fXmax; //xk[j] working_space[7 * i + 1] = working_space[shift + j]; //parameter[7*i+1]=xk[j] j += 1; } if (fFixPositionY[i] == false) { if (working_space[shift + j] < fYmin) //xk[j] working_space[shift + j] = fYmin; //xk[j] if (working_space[shift + j] > fYmax) //xk[j] working_space[shift + j] = fYmax; //xk[j] working_space[7 * i + 2] = working_space[shift + j]; //parameter[7*i+2]=xk[j] j += 1; } if (fFixAmpX1[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i + 3] = working_space[shift + j]; //parameter[7*i+3]=xk[j] j += 1; } if (fFixAmpY1[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i + 4] = working_space[shift + j]; //parameter[7*i+4]=xk[j] j += 1; } if (fFixPositionX1[i] == false) { if (working_space[shift + j] < fXmin) //xk[j] working_space[shift + j] = fXmin; //xk[j] if (working_space[shift + j] > fXmax) //xk[j] working_space[shift + j] = fXmax; //xk[j] working_space[7 * i + 5] = working_space[shift + j]; //parameter[7*i+5]=xk[j] j += 1; } if (fFixPositionY1[i] == false) { if (working_space[shift + j] < fYmin) //xk[j] working_space[shift + j] = fYmin; //xk[j] if (working_space[shift + j] > fYmax) //xk[j] working_space[shift + j] = fYmax; //xk[j] working_space[7 * i + 6] = working_space[shift + j]; //parameter[7*i+6]=xk[j] j += 1; } } if (fFixSigmaX == false) { if (working_space[shift + j] < 0.001) { //xk[j] working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel] = working_space[shift + j]; //parameter[peak_vel]=xk[j] j += 1; } if (fFixSigmaY == false) { if (working_space[shift + j] < 0.001) { //xk[j] working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 1] = working_space[shift + j]; //parameter[peak_vel+1]=xk[j] j += 1; } if (fFixRo == false) { if (working_space[shift + j] < -1) { //xk[j] working_space[shift + j] = -1; //xk[j] } if (working_space[shift + j] > 1) { //xk[j] working_space[shift + j] = 1; //xk[j] } working_space[peak_vel + 2] = working_space[shift + j]; //parameter[peak_vel+2]=xk[j] j += 1; } if (fFixA0 == false) { working_space[peak_vel + 3] = working_space[shift + j]; //parameter[peak_vel+3]=xk[j] j += 1; } if (fFixAx == false) { working_space[peak_vel + 4] = working_space[shift + j]; //parameter[peak_vel+4]=xk[j] j += 1; } if (fFixAy == false) { working_space[peak_vel + 5] = working_space[shift + j]; //parameter[peak_vel+5]=xk[j] j += 1; } if (fFixTxy == false) { working_space[peak_vel + 6] = working_space[shift + j]; //parameter[peak_vel+6]=xk[j] j += 1; } if (fFixSxy == false) { working_space[peak_vel + 7] = working_space[shift + j]; //parameter[peak_vel+7]=xk[j] j += 1; } if (fFixTx == false) { working_space[peak_vel + 8] = working_space[shift + j]; //parameter[peak_vel+8]=xk[j] j += 1; } if (fFixTy == false) { working_space[peak_vel + 9] = working_space[shift + j]; //parameter[peak_vel+9]=xk[j] j += 1; } if (fFixSx == false) { working_space[peak_vel + 10] = working_space[shift + j]; //parameter[peak_vel+10]=xk[j] j += 1; } if (fFixSy == false) { working_space[peak_vel + 11] = working_space[shift + j]; //parameter[peak_vel+11]=xk[j] j += 1; } if (fFixBx == false) { if (TMath::Abs(working_space[shift + j]) < 0.001) { //xk[j] if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = -0.001; //xk[j] else working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 12] = working_space[shift + j]; //parameter[peak_vel+12]=xk[j] j += 1; } if (fFixBy == false) { if (TMath::Abs(working_space[shift + j]) < 0.001) { //xk[j] if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = -0.001; //xk[j] else working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 13] = working_space[shift + j]; //parameter[peak_vel+13]=xk[j] j += 1; } chi2 = 0; for (i1 = fXmin; i1 <= fXmax; i1++) { for (i2 = fYmin; i2 <= fYmax; i2++) { yw = source[i1][i2]; ywm = yw; f = Shape2(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 3], working_space[peak_vel + 4], working_space[peak_vel + 5], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 8], working_space[peak_vel + 9], working_space[peak_vel + 10], working_space[peak_vel + 11], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (fStatisticType == kFitOptimChiFuncValues) { ywm = f; if (f < 0.00001) ywm = 0.00001; } if (fStatisticType == kFitOptimMaxLikelihood) { if (f > 0.00001) chi2 += yw * TMath::Log(f) - f; } else { if (ywm != 0) chi2 += (yw - f) * (yw - f) / ywm; } } } if ((chi2 < chi_min && fStatisticType != kFitOptimMaxLikelihood) || (chi2 > chi_min && fStatisticType == kFitOptimMaxLikelihood)) { pmin = pi, chi_min = chi2; } else flag = 1; if (pi == 0.1) chi_min = chi2; chi = chi_min; } if (pmin != 0.1) { for (j = 0; j < size; j++) { working_space[shift + j] = working_space[4 * shift + j] + pmin * alpha * working_space[2 * shift + j]; //xk[j]=temp_xk[j]+pmin*alpha*der[j] } for (i = 0, j = 0; i < fNPeaks; i++) { if (fFixAmp[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i] = working_space[shift + j]; //parameter[7*i]=xk[j] j += 1; } if (fFixPositionX[i] == false) { if (working_space[shift + j] < fXmin) //xk[j] working_space[shift + j] = fXmin; //xk[j] if (working_space[shift + j] > fXmax) //xk[j] working_space[shift + j] = fXmax; //xk[j] working_space[7 * i + 1] = working_space[shift + j]; //parameter[7*i+1]=xk[j] j += 1; } if (fFixPositionY[i] == false) { if (working_space[shift + j] < fYmin) //xk[j] working_space[shift + j] = fYmin; //xk[j] if (working_space[shift + j] > fYmax) //xk[j] working_space[shift + j] = fYmax; //xk[j] working_space[7 * i + 2] = working_space[shift + j]; //parameter[7*i+2]=xk[j] j += 1; } if (fFixAmpX1[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i + 3] = working_space[shift + j]; //parameter[7*i+3]=xk[j] j += 1; } if (fFixAmpY1[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i + 4] = working_space[shift + j]; //parameter[7*i+4]=xk[j] j += 1; } if (fFixPositionX1[i] == false) { if (working_space[shift + j] < fXmin) //xk[j] working_space[shift + j] = fXmin; //xk[j] if (working_space[shift + j] > fXmax) //xk[j] working_space[shift + j] = fXmax; //xk[j] working_space[7 * i + 5] = working_space[shift + j]; //parameter[7*i+5]=xk[j] j += 1; } if (fFixPositionY1[i] == false) { if (working_space[shift + j] < fYmin) //xk[j] working_space[shift + j] = fYmin; //xk[j] if (working_space[shift + j] > fYmax) //xk[j] working_space[shift + j] = fYmax; //xk[j] working_space[7 * i + 6] = working_space[shift + j]; //parameter[7*i+6]=xk[j] j += 1; } } if (fFixSigmaX == false) { if (working_space[shift + j] < 0.001) { //xk[j] working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel] = working_space[shift + j]; //parameter[peak_vel]=xk[j] j += 1; } if (fFixSigmaY == false) { if (working_space[shift + j] < 0.001) { //xk[j] working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 1] = working_space[shift + j]; //parameter[peak_vel+1]=xk[j] j += 1; } if (fFixRo == false) { if (working_space[shift + j] < -1) { //xk[j] working_space[shift + j] = -1; //xk[j] } if (working_space[shift + j] > 1) { //xk[j] working_space[shift + j] = 1; //xk[j] } working_space[peak_vel + 2] = working_space[shift + j]; //parameter[peak_vel+2]=xk[j] j += 1; } if (fFixA0 == false) { working_space[peak_vel + 3] = working_space[shift + j]; //parameter[peak_vel+3]=xk[j] j += 1; } if (fFixAx == false) { working_space[peak_vel + 4] = working_space[shift + j]; //parameter[peak_vel+4]=xk[j] j += 1; } if (fFixAy == false) { working_space[peak_vel + 5] = working_space[shift + j]; //parameter[peak_vel+5]=xk[j] j += 1; } if (fFixTxy == false) { working_space[peak_vel + 6] = working_space[shift + j]; //parameter[peak_vel+6]=xk[j] j += 1; } if (fFixSxy == false) { working_space[peak_vel + 7] = working_space[shift + j]; //parameter[peak_vel+7]=xk[j] j += 1; } if (fFixTx == false) { working_space[peak_vel + 8] = working_space[shift + j]; //parameter[peak_vel+8]=xk[j] j += 1; } if (fFixTy == false) { working_space[peak_vel + 9] = working_space[shift + j]; //parameter[peak_vel+9]=xk[j] j += 1; } if (fFixSx == false) { working_space[peak_vel + 10] = working_space[shift + j]; //parameter[peak_vel+10]=xk[j] j += 1; } if (fFixSy == false) { working_space[peak_vel + 11] = working_space[shift + j]; //parameter[peak_vel+11]=xk[j] j += 1; } if (fFixBx == false) { if (TMath::Abs(working_space[shift + j]) < 0.001) { //xk[j] if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = -0.001; //xk[j] else working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 12] = working_space[shift + j]; //parameter[peak_vel+12]=xk[j] j += 1; } if (fFixBy == false) { if (TMath::Abs(working_space[shift + j]) < 0.001) { //xk[j] if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = -0.001; //xk[j] else working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 13] = working_space[shift + j]; //parameter[peak_vel+13]=xk[j] j += 1; } chi = chi_min; } } else { for (j = 0; j < size; j++) { working_space[shift + j] = working_space[4 * shift + j] + alpha * working_space[2 * shift + j]; //xk[j]=temp_xk[j]+pi*alpha*der[j] } for (i = 0, j = 0; i < fNPeaks; i++) { if (fFixAmp[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i] = working_space[shift + j]; //parameter[7*i]=xk[j] j += 1; } if (fFixPositionX[i] == false) { if (working_space[shift + j] < fXmin) //xk[j] working_space[shift + j] = fXmin; //xk[j] if (working_space[shift + j] > fXmax) //xk[j] working_space[shift + j] = fXmax; //xk[j] working_space[7 * i + 1] = working_space[shift + j]; //parameter[7*i+1]=xk[j] j += 1; } if (fFixPositionY[i] == false) { if (working_space[shift + j] < fYmin) //xk[j] working_space[shift + j] = fYmin; //xk[j] if (working_space[shift + j] > fYmax) //xk[j] working_space[shift + j] = fYmax; //xk[j] working_space[7 * i + 2] = working_space[shift + j]; //parameter[7*i+2]=xk[j] j += 1; } if (fFixAmpX1[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i + 3] = working_space[shift + j]; //parameter[7*i+3]=xk[j] j += 1; } if (fFixAmpY1[i] == false) { if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = 0; //xk[j] working_space[7 * i + 4] = working_space[shift + j]; //parameter[7*i+4]=xk[j] j += 1; } if (fFixPositionX1[i] == false) { if (working_space[shift + j] < fXmin) //xk[j] working_space[shift + j] = fXmin; //xk[j] if (working_space[shift + j] > fXmax) //xk[j] working_space[shift + j] = fXmax; //xk[j] working_space[7 * i + 5] = working_space[shift + j]; //parameter[7*i+5]=xk[j] j += 1; } if (fFixPositionY1[i] == false) { if (working_space[shift + j] < fYmin) //xk[j] working_space[shift + j] = fYmin; //xk[j] if (working_space[shift + j] > fYmax) //xk[j] working_space[shift + j] = fYmax; //xk[j] working_space[7 * i + 6] = working_space[shift + j]; //parameter[7*i+6]=xk[j] j += 1; } } if (fFixSigmaX == false) { if (working_space[shift + j] < 0.001) { //xk[j] working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel] = working_space[shift + j]; //parameter[peak_vel]=xk[j] j += 1; } if (fFixSigmaY == false) { if (working_space[shift + j] < 0.001) { //xk[j] working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 1] = working_space[shift + j]; //parameter[peak_vel+1]=xk[j] j += 1; } if (fFixRo == false) { if (working_space[shift + j] < -1) { //xk[j] working_space[shift + j] = -1; //xk[j] } if (working_space[shift + j] > 1) { //xk[j] working_space[shift + j] = 1; //xk[j] } working_space[peak_vel + 2] = working_space[shift + j]; //parameter[peak_vel+2]=xk[j] j += 1; } if (fFixA0 == false) { working_space[peak_vel + 3] = working_space[shift + j]; //parameter[peak_vel+3]=xk[j] j += 1; } if (fFixAx == false) { working_space[peak_vel + 4] = working_space[shift + j]; //parameter[peak_vel+4]=xk[j] j += 1; } if (fFixAy == false) { working_space[peak_vel + 5] = working_space[shift + j]; //parameter[peak_vel+5]=xk[j] j += 1; } if (fFixTxy == false) { working_space[peak_vel + 6] = working_space[shift + j]; //parameter[peak_vel+6]=xk[j] j += 1; } if (fFixSxy == false) { working_space[peak_vel + 7] = working_space[shift + j]; //parameter[peak_vel+7]=xk[j] j += 1; } if (fFixTx == false) { working_space[peak_vel + 8] = working_space[shift + j]; //parameter[peak_vel+8]=xk[j] j += 1; } if (fFixTy == false) { working_space[peak_vel + 9] = working_space[shift + j]; //parameter[peak_vel+9]=xk[j] j += 1; } if (fFixSx == false) { working_space[peak_vel + 10] = working_space[shift + j]; //parameter[peak_vel+10]=xk[j] j += 1; } if (fFixSy == false) { working_space[peak_vel + 11] = working_space[shift + j]; //parameter[peak_vel+11]=xk[j] j += 1; } if (fFixBx == false) { if (TMath::Abs(working_space[shift + j]) < 0.001) { //xk[j] if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = -0.001; //xk[j] else working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 12] = working_space[shift + j]; //parameter[peak_vel+12]=xk[j] j += 1; } if (fFixBy == false) { if (TMath::Abs(working_space[shift + j]) < 0.001) { //xk[j] if (working_space[shift + j] < 0) //xk[j] working_space[shift + j] = -0.001; //xk[j] else working_space[shift + j] = 0.001; //xk[j] } working_space[peak_vel + 13] = working_space[shift + j]; //parameter[peak_vel+13]=xk[j] j += 1; } chi = 0; for (i1 = fXmin; i1 <= fXmax; i1++) { for (i2 = fYmin; i2 <= fYmax; i2++) { yw = source[i1][i2]; ywm = yw; f = Shape2(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 3], working_space[peak_vel + 4], working_space[peak_vel + 5], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 8], working_space[peak_vel + 9], working_space[peak_vel + 10], working_space[peak_vel + 11], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (fStatisticType == kFitOptimChiFuncValues) { ywm = f; if (f < 0.00001) ywm = 0.00001; } if (fStatisticType == kFitOptimMaxLikelihood) { if (f > 0.00001) chi += yw * TMath::Log(f) - f; } else { if (ywm != 0) chi += (yw - f) * (yw - f) / ywm; } } } } chi2 = chi; chi = TMath::Sqrt(TMath::Abs(chi)); if (fAlphaOptim == kFitAlphaHalving && chi > 1E-6) alpha = alpha * chi_opt / (2 * chi); else if (fAlphaOptim == kFitAlphaOptimal) alpha = alpha / 10.0; iter += 1; regul_cycle += 1; } while (((chi > chi_opt && fStatisticType != kFitOptimMaxLikelihood) || (chi < chi_opt && fStatisticType == kFitOptimMaxLikelihood)) && regul_cycle < kFitNumRegulCycles); for (j = 0; j < size; j++) { working_space[4 * shift + j] = 0; //temp_xk[j] working_space[2 * shift + j] = 0; //der[j] } for (i1 = fXmin, chi_cel = 0; i1 <= fXmax; i1++) { for (i2 = fYmin; i2 <= fYmax; i2++) { yw = source[i1][i2]; if (yw == 0) yw = 1; f = Shape2(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 3], working_space[peak_vel + 4], working_space[peak_vel + 5], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 8], working_space[peak_vel + 9], working_space[peak_vel + 10], working_space[peak_vel + 11], working_space[peak_vel + 12], working_space[peak_vel + 13]); chi_opt = (yw - f) * (yw - f) / yw; chi_cel += (yw - f) * (yw - f) / yw; //calculate gradient vector for (j = 0, k = 0; j < fNPeaks; j++) { if (fFixAmp[j] == false) { a = Deramp2((Double_t) i1, (Double_t) i2, working_space[7 * j + 1], working_space[7 * j + 2], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixPositionX[j] == false) { a = Deri02((Double_t) i1, (Double_t) i2, working_space[7 * j], working_space[7 * j + 1], working_space[7 * j + 2], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixPositionY[j] == false) { a = Derj02((Double_t) i1, (Double_t) i2, working_space[7 * j], working_space[7 * j + 1], working_space[7 * j + 2], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixAmpX1[j] == false) { a = Derampx((Double_t) i1, working_space[7 * j + 5], working_space[peak_vel], working_space[peak_vel + 8], working_space[peak_vel + 10], working_space[peak_vel + 12]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixAmpY1[j] == false) { a = Derampx((Double_t) i2, working_space[7 * j + 6], working_space[peak_vel + 1], working_space[peak_vel + 9], working_space[peak_vel + 11], working_space[peak_vel + 13]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixPositionX1[j] == false) { a = Deri01((Double_t) i1, working_space[7 * j + 3], working_space[7 * j + 5], working_space[peak_vel], working_space[peak_vel + 8], working_space[peak_vel + 10], working_space[peak_vel + 12]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixPositionY1[j] == false) { a = Deri01((Double_t) i2, working_space[7 * j + 4], working_space[7 * j + 6], working_space[peak_vel + 1], working_space[peak_vel + 9], working_space[peak_vel + 11], working_space[peak_vel + 13]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } } if (fFixSigmaX == false) { a = Dersigmax(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 8], working_space[peak_vel + 10], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixSigmaY == false) { a = Dersigmay(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 9], working_space[peak_vel + 11], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixRo == false) { a = Derro(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixA0 == false) { a = 1.; if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixAx == false) { a = i1; if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixAy == false) { a = i2; if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixTxy == false) { a = Dertxy(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixSxy == false) { a = Dersxy(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixTx == false) { a = Dertx(fNPeaks, (Double_t) i1, working_space, working_space[peak_vel], working_space[peak_vel + 12]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixTy == false) { a = Derty(fNPeaks, (Double_t) i2, working_space, working_space[peak_vel + 1], working_space[peak_vel + 13]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixSx == false) { a = Dersx(fNPeaks, (Double_t) i1, working_space, working_space[peak_vel]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixSy == false) { a = Dersy(fNPeaks, (Double_t) i2, working_space, working_space[peak_vel + 1]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixBx == false) { a = Derbx(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 6], working_space[peak_vel + 8], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } if (fFixBy == false) { a = Derby(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 6], working_space[peak_vel + 8], working_space[peak_vel + 12], working_space[peak_vel + 13]); if (yw != 0) { working_space[2 * shift + k] += chi_opt; //der[k] b = a * a / yw; working_space[4 * shift + k] += b; //temp_xk[k] } k += 1; } } } } b = (fXmax - fXmin + 1) * (fYmax - fYmin + 1) - size; chi_er = chi_cel / b; for (i = 0, j = 0; i < fNPeaks; i++) { fVolume[i] = Volume(working_space[7 * i], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2]); if (fVolume[i] > 0) { c = 0; if (fFixAmp[i] == false) { a = Derpa2(working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2]); b = working_space[4 * shift + j]; //temp_xk[j] if (b == 0) b = 1; else b = 1 / b; c = c + a * a * b; } if (fFixSigmaX == false) { a = Derpsigmax(working_space[shift + j], working_space[peak_vel + 1], working_space[peak_vel + 2]); b = working_space[4 * shift + peak_vel]; //temp_xk[j] if (b == 0) b = 1; else b = 1 / b; c = c + a * a * b; } if (fFixSigmaY == false) { a = Derpsigmay(working_space[shift + j], working_space[peak_vel], working_space[peak_vel + 2]); b = working_space[4 * shift + peak_vel + 1]; //temp_xk[j] if (b == 0) b = 1; else b = 1 / b; c = c + a * a * b; } if (fFixRo == false) { a = Derpro(working_space[shift + j], working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2]); b = working_space[4 * shift + peak_vel + 2]; //temp_xk[j] if (b == 0) b = 1; else b = 1 / b; c = c + a * a * b; } fVolumeErr[i] = TMath::Sqrt(TMath::Abs(chi_er * c)); } else { fVolumeErr[i] = 0; } if (fFixAmp[i] == false) { fAmpCalc[i] = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) fAmpErr[i] = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fAmpCalc[i] = fAmpInit[i]; fAmpErr[i] = 0; } if (fFixPositionX[i] == false) { fPositionCalcX[i] = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) fPositionErrX[i] = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fPositionCalcX[i] = fPositionInitX[i]; fPositionErrX[i] = 0; } if (fFixPositionY[i] == false) { fPositionCalcY[i] = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) fPositionErrY[i] = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fPositionCalcY[i] = fPositionInitY[i]; fPositionErrY[i] = 0; } if (fFixAmpX1[i] == false) { fAmpCalcX1[i] = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) fAmpErrX1[i] = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fAmpCalcX1[i] = fAmpInitX1[i]; fAmpErrX1[i] = 0; } if (fFixAmpY1[i] == false) { fAmpCalcY1[i] = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) fAmpErrY1[i] = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fAmpCalcY1[i] = fAmpInitY1[i]; fAmpErrY1[i] = 0; } if (fFixPositionX1[i] == false) { fPositionCalcX1[i] = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) fPositionErrX1[i] = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fPositionCalcX1[i] = fPositionInitX1[i]; fPositionErrX1[i] = 0; } if (fFixPositionY1[i] == false) { fPositionCalcY1[i] = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) fPositionErrY1[i] = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fPositionCalcY1[i] = fPositionInitY1[i]; fPositionErrY1[i] = 0; } } if (fFixSigmaX == false) { fSigmaCalcX = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fSigmaErrX = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fSigmaCalcX = fSigmaInitX; fSigmaErrX = 0; } if (fFixSigmaY == false) { fSigmaCalcY = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fSigmaErrY = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fSigmaCalcY = fSigmaInitY; fSigmaErrY = 0; } if (fFixRo == false) { fRoCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fRoErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fRoCalc = fRoInit; fRoErr = 0; } if (fFixA0 == false) { fA0Calc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fA0Err = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fA0Calc = fA0Init; fA0Err = 0; } if (fFixAx == false) { fAxCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fAxErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fAxCalc = fAxInit; fAxErr = 0; } if (fFixAy == false) { fAyCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fAyErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fAyCalc = fAyInit; fAyErr = 0; } if (fFixTxy == false) { fTxyCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fTxyErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fTxyCalc = fTxyInit; fTxyErr = 0; } if (fFixSxy == false) { fSxyCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fSxyErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fSxyCalc = fSxyInit; fSxyErr = 0; } if (fFixTx == false) { fTxCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fTxErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fTxCalc = fTxInit; fTxErr = 0; } if (fFixTy == false) { fTyCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fTyErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fTyCalc = fTyInit; fTyErr = 0; } if (fFixSx == false) { fSxCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fSxErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fSxCalc = fSxInit; fSxErr = 0; } if (fFixSy == false) { fSyCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fSyErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fSyCalc = fSyInit; fSyErr = 0; } if (fFixBx == false) { fBxCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fBxErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fBxCalc = fBxInit; fBxErr = 0; } if (fFixBy == false) { fByCalc = working_space[shift + j]; //xk[j] if (working_space[3 * shift + j] != 0) //temp[j] fByErr = TMath::Sqrt(TMath::Abs(working_space[2 * shift + j])) / TMath::Sqrt(TMath::Abs(working_space[3 * shift + j])); //der[j]/temp[j] j += 1; } else { fByCalc = fByInit; fByErr = 0; } b = (fXmax - fXmin + 1) * (fYmax - fYmin + 1) - size; fChi = chi_cel / b; for (i1 = fXmin; i1 <= fXmax; i1++) { for (i2 = fYmin; i2 <= fYmax; i2++) { f = Shape2(fNPeaks, (Double_t) i1, (Double_t) i2, working_space, working_space[peak_vel], working_space[peak_vel + 1], working_space[peak_vel + 2], working_space[peak_vel + 3], working_space[peak_vel + 4], working_space[peak_vel + 5], working_space[peak_vel + 6], working_space[peak_vel + 7], working_space[peak_vel + 8], working_space[peak_vel + 9], working_space[peak_vel + 10], working_space[peak_vel + 11], working_space[peak_vel + 12], working_space[peak_vel + 13]); source[i1][i2] = f; } } for (i = 0; i < size; i++) delete [] working_matrix[i]; delete [] working_matrix; delete [] working_space; return; } void TSpectrum2Fit::SetFitParameters(Int_t xmin,Int_t xmax,Int_t ymin,Int_t ymax, Int_t numberIterations, Double_t alpha, Int_t statisticType, Int_t alphaOptim, Int_t power, Int_t fitTaylor) { ////////////////////////////////////////////////////////////////////////////// // SETTER FUNCTION // // This function sets the following fitting parameters: // -xmin, xmax, ymin, ymax - fitting region // -numberIterations - # of desired iterations in the fit // -alpha - convergence coefficient, it should be positive number and <=1, for details see references // -statisticType - type of statistics, possible values kFitOptimChiCounts (chi square statistics with counts as weighting coefficients), kFitOptimChiFuncValues (chi square statistics with function values as weighting coefficients),kFitOptimMaxLikelihood // -alphaOptim - optimization of convergence algorithm, possible values kFitAlphaHalving, kFitAlphaOptimal // -power - possible values kFitPower2,4,6,8,10,12, for details see references. It applies only for Awmi fitting function. // -fitTaylor - order of Taylor expansion, possible values kFitTaylorOrderFirst, kFitTaylorOrderSecond. It applies only for Awmi fitting function. ////////////////////////////////////////////////////////////////////////////// if(xmin<0 || xmax <= xmin || ymin<0 || ymax <= ymin){ Error("SetFitParameters", "Wrong range"); return; } if (numberIterations <= 0){ Error("SetFitParameters","Invalid number of iterations, must be positive"); return; } if (alpha <= 0 || alpha > 1){ Error ("SetFitParameters","Invalid step coefficient alpha, must be > than 0 and <=1"); return; } if (statisticType != kFitOptimChiCounts && statisticType != kFitOptimChiFuncValues && statisticType != kFitOptimMaxLikelihood){ Error("SetFitParameters","Wrong type of statistic"); return; } if (alphaOptim != kFitAlphaHalving && alphaOptim != kFitAlphaOptimal){ Error("SetFitParameters","Wrong optimization algorithm"); return; } if (power != kFitPower2 && power != kFitPower4 && power != kFitPower6 && power != kFitPower8 && power != kFitPower10 && power != kFitPower12){ Error("SetFitParameters","Wrong power"); return; } if (fitTaylor != kFitTaylorOrderFirst && fitTaylor != kFitTaylorOrderSecond){ Error("SetFitParameters","Wrong order of Taylor development"); return; } fXmin=xmin,fXmax=xmax,fYmin=ymin,fYmax=ymax,fNumberIterations=numberIterations,fAlpha=alpha,fStatisticType=statisticType,fAlphaOptim=alphaOptim,fPower=power,fFitTaylor=fitTaylor; } //______________________________________________________________________________ void TSpectrum2Fit::SetPeakParameters(Double_t sigmaX, Bool_t fixSigmaX, Double_t sigmaY, Bool_t fixSigmaY, Double_t ro, Bool_t fixRo, const Float_t *positionInitX, const Bool_t *fixPositionX, const Float_t *positionInitY, const Bool_t *fixPositionY, const Float_t *positionInitX1, const Bool_t *fixPositionX1, const Float_t *positionInitY1, const Bool_t *fixPositionY1, const Float_t *ampInit, const Bool_t *fixAmp, const Float_t *ampInitX1, const Bool_t *fixAmpX1, const Float_t *ampInitY1, const Bool_t *fixAmpY1) { ////////////////////////////////////////////////////////////////////////////// // SETTER FUNCTION // // This function sets the following fitting parameters of peaks: // -sigmaX - initial value of sigma x parameter // -fixSigmaX - logical value of sigma x parameter, which allows to fix the parameter (not to fit) // -sigmaY - initial value of sigma y parameter // -fixSigmaY - logical value of sigma y parameter, which allows to fix the parameter (not to fit) // -ro - initial value of ro parameter (correlation coefficient) // -fixRo - logical value of ro parameter, which allows to fix the parameter (not to fit) // -positionInitX - aray of initial values of peaks x positions // -fixPositionX - array of logical values which allow to fix appropriate x positions (not fit). However they are present in the estimated functional. // -positionInitY - aray of initial values of peaks y positions // -fixPositionY - array of logical values which allow to fix appropriate y positions (not fit). However they are present in the estimated functional. // -ampInit - aray of initial values of 2D peaks amplitudes // -fixAmp - aray of logical values which allow to fix appropriate amplitudes of 2D peaks (not fit). However they are present in the estimated functional // -ampInitX1 - aray of initial values of amplitudes of 1D ridges in x direction // -fixAmpX1 - aray of logical values which allow to fix appropriate amplitudes of 1D ridges in x direction (not fit). However they are present in the estimated functional // -ampInitY1 - aray of initial values of amplitudes of 1D ridges in y direction // -fixAmpY1 - aray of logical values which allow to fix appropriate amplitudes of 1D ridges in y direction (not fit). However they are present in the estimated functional ////////////////////////////////////////////////////////////////////////////// if (sigmaX <= 0 || sigmaY <= 0){ Error ("SetPeakParameters","Invalid sigma, must be > than 0"); return; } if (ro < -1 || ro > 1){ Error ("SetPeakParameters","Invalid ro, must be from region <-1,1>"); return; } Int_t i; for(i=0; i < fNPeaks; i++){ if(positionInitX[i] < fXmin || positionInitX[i] > fXmax){ Error ("SetPeakParameters","Invalid peak position, must be in the range fXmin, fXmax"); return; } if(positionInitY[i] < fYmin || positionInitY[i] > fYmax){ Error ("SetPeakParameters","Invalid peak position, must be in the range fYmin, fYmax"); return; } if(positionInitX1[i] < fXmin || positionInitX1[i] > fXmax){ Error ("SetPeakParameters","Invalid ridge position, must be in the range fXmin, fXmax"); return; } if(positionInitY1[i] < fYmin || positionInitY1[i] > fYmax){ Error ("SetPeakParameters","Invalid ridge position, must be in the range fYmin, fYmax"); return; } if(ampInit[i] < 0){ Error ("SetPeakParameters","Invalid peak amplitude, must be > than 0"); return; } if(ampInitX1[i] < 0){ Error ("SetPeakParameters","Invalid x ridge amplitude, must be > than 0"); return; } if(ampInitY1[i] < 0){ Error ("SetPeakParameters","Invalid y ridge amplitude, must be > than 0"); return; } } fSigmaInitX = sigmaX, fFixSigmaX = fixSigmaX, fSigmaInitY = sigmaY, fFixSigmaY = fixSigmaY, fRoInit = ro, fFixRo = fixRo; for(i=0; i < fNPeaks; i++){ fPositionInitX[i] = (Double_t) positionInitX[i]; fFixPositionX[i] = fixPositionX[i]; fPositionInitY[i] = (Double_t) positionInitY[i]; fFixPositionY[i] = fixPositionY[i]; fPositionInitX1[i] = (Double_t) positionInitX1[i]; fFixPositionX1[i] = fixPositionX1[i]; fPositionInitY1[i] = (Double_t) positionInitY1[i]; fFixPositionY1[i] = fixPositionY1[i]; fAmpInit[i] = (Double_t) ampInit[i]; fFixAmp[i] = fixAmp[i]; fAmpInitX1[i] = (Double_t) ampInitX1[i]; fFixAmpX1[i] = fixAmpX1[i]; fAmpInitY1[i] = (Double_t) ampInitY1[i]; fFixAmpY1[i] = fixAmpY1[i]; } } //______________________________________________________________________________ void TSpectrum2Fit::SetBackgroundParameters(Double_t a0Init, Bool_t fixA0, Double_t axInit, Bool_t fixAx, Double_t ayInit, Bool_t fixAy) { ////////////////////////////////////////////////////////////////////////////// // SETTER FUNCTION // // This function sets the following fitting parameters of background: // -a0Init - initial value of a0 parameter (backgroud is estimated as a0+ax*x+ay*y) // -fixA0 - logical value of a0 parameter, which allows to fix the parameter (not to fit) // -axInit - initial value of ax parameter // -fixAx - logical value of ax parameter, which allows to fix the parameter (not to fit) // -ayInit - initial value of ay parameter // -fixAy - logical value of ay parameter, which allows to fix the parameter (not to fit) ////////////////////////////////////////////////////////////////////////////// fA0Init = a0Init; fFixA0 = fixA0; fAxInit = axInit; fFixAx = fixAx; fAyInit = ayInit; fFixAy = fixAy; } //______________________________________________________________________________ void TSpectrum2Fit::SetTailParameters(Double_t tInitXY, Bool_t fixTxy, Double_t tInitX, Bool_t fixTx, Double_t tInitY, Bool_t fixTy, Double_t bInitX, Bool_t fixBx, Double_t bInitY, Bool_t fixBy, Double_t sInitXY, Bool_t fixSxy, Double_t sInitX, Bool_t fixSx, Double_t sInitY, Bool_t fixSy) { ////////////////////////////////////////////////////////////////////////////// // SETTER FUNCTION // // This function sets the following fitting parameters of tails of peaks // -tInitXY - initial value of txy parameter // -fixTxy - logical value of txy parameter, which allows to fix the parameter (not to fit) // -tInitX - initial value of tx parameter // -fixTx - logical value of tx parameter, which allows to fix the parameter (not to fit) // -tInitY - initial value of ty parameter // -fixTy - logical value of ty parameter, which allows to fix the parameter (not to fit) // -bInitX - initial value of bx parameter // -fixBx - logical value of bx parameter, which allows to fix the parameter (not to fit) // -bInitY - initial value of by parameter // -fixBy - logical value of by parameter, which allows to fix the parameter (not to fit) // -sInitXY - initial value of sxy parameter // -fixSxy - logical value of sxy parameter, which allows to fix the parameter (not to fit) // -sInitX - initial value of sx parameter // -fixSx - logical value of sx parameter, which allows to fix the parameter (not to fit) // -sInitY - initial value of sy parameter // -fixSy - logical value of sy parameter, which allows to fix the parameter (not to fit) ////////////////////////////////////////////////////////////////////////////// fTxyInit = tInitXY; fFixTxy = fixTxy; fTxInit = tInitX; fFixTx = fixTx; fTyInit = tInitY; fFixTy = fixTy; fBxInit = bInitX; fFixBx = fixBx; fByInit = bInitY; fFixBy = fixBy; fSxyInit = sInitXY; fFixSxy = fixSxy; fSxInit = sInitX; fFixSx = fixSx; fSyInit = sInitY; fFixSy = fixSy; } //______________________________________________________________________________ void TSpectrum2Fit::GetPositions(Float_t *positionsX, Float_t *positionsY, Float_t *positionsX1, Float_t *positionsY1) { ////////////////////////////////////////////////////////////////////////////// // GETTER FUNCTION // // This function gets the positions of fitted 2D peaks and 1D ridges // -positionX - gets vector of x positions of 2D peaks // -positionY - gets vector of y positions of 2D peaks // -positionX1 - gets vector of x positions of 1D ridges // -positionY1 - gets vector of y positions of 1D ridges ////////////////////////////////////////////////////////////////////////////// for( Int_t i=0; i < fNPeaks; i++){ positionsX[i] = (Float_t) fPositionCalcX[i]; positionsY[i] = (Float_t) fPositionCalcY[i]; positionsX1[i] = (Float_t) fPositionCalcX1[i]; positionsY1[i] = (Float_t) fPositionCalcY1[i]; } } //______________________________________________________________________________ void TSpectrum2Fit::GetPositionErrors(Float_t *positionErrorsX, Float_t *positionErrorsY, Float_t *positionErrorsX1, Float_t *positionErrorsY1) { ////////////////////////////////////////////////////////////////////////////// // GETTER FUNCTION // // This function gets the errors of positions of fitted 2D peaks and 1D ridges // -positionErrorsX - gets vector of errors of x positions of 2D peaks // -positionErrorsY - gets vector of errors of y positions of 2D peaks // -positionErrorsX1 - gets vector of errors of x positions of 1D ridges // -positionErrorsY1 - gets vector of errors of y positions of 1D ridges ////////////////////////////////////////////////////////////////////////////// for( Int_t i=0; i < fNPeaks; i++){ positionErrorsX[i] = (Float_t) fPositionErrX[i]; positionErrorsY[i] = (Float_t) fPositionErrY[i]; positionErrorsX1[i] = (Float_t) fPositionErrX1[i]; positionErrorsY1[i] = (Float_t) fPositionErrY1[i]; } } //______________________________________________________________________________ void TSpectrum2Fit::GetAmplitudes(Float_t *amplitudes, Float_t *amplitudesX1, Float_t *amplitudesY1) { ////////////////////////////////////////////////////////////////////////////// // GETTER FUNCTION // // This function gets the amplitudes of fitted 2D peaks and 1D ridges // -amplitudes - gets vector of amplitudes of 2D peaks // -amplitudesX1 - gets vector of amplitudes of 1D ridges in x direction // -amplitudesY1 - gets vector of amplitudes of 1D ridges in y direction ////////////////////////////////////////////////////////////////////////////// for( Int_t i=0; i < fNPeaks; i++){ amplitudes[i] = (Float_t) fAmpCalc[i]; amplitudesX1[i] = (Float_t) fAmpCalcX1[i]; amplitudesY1[i] = (Float_t) fAmpCalcY1[i]; } } //______________________________________________________________________________ void TSpectrum2Fit::GetAmplitudeErrors(Float_t *amplitudeErrors, Float_t *amplitudeErrorsX1, Float_t *amplitudeErrorsY1) { ////////////////////////////////////////////////////////////////////////////// // GETTER FUNCTION // // This function gets the amplitudes of fitted 2D peaks and 1D ridges // -amplitudeErrors - gets vector of amplitudes errors of 2D peaks // -amplitudeErrorsX1 - gets vector of amplitudes errors of 1D ridges in x direction // -amplitudesErrorY1 - gets vector of amplitudes errors of 1D ridges in y direction ////////////////////////////////////////////////////////////////////////////// for( Int_t i=0; i < fNPeaks; i++){ amplitudeErrors[i] = (Float_t) fAmpErr[i]; amplitudeErrorsX1[i] = (Float_t) fAmpErrX1[i]; amplitudeErrorsY1[i] = (Float_t) fAmpErrY1[i]; } } //______________________________________________________________________________ void TSpectrum2Fit::GetVolumes(Float_t *volumes) { ////////////////////////////////////////////////////////////////////////////// // GETTER FUNCTION // // This function gets the volumes of fitted 2D peaks // -volumes - gets vector of volumes of 2D peaks ////////////////////////////////////////////////////////////////////////////// for( Int_t i=0; i < fNPeaks; i++){ volumes[i] = (Float_t) fVolume[i]; } } //______________________________________________________________________________ void TSpectrum2Fit::GetVolumeErrors(Float_t *volumeErrors) { ////////////////////////////////////////////////////////////////////////////// // GETTER FUNCTION // // This function gets errors of the volumes of fitted 2D peaks // -volumeErrors - gets vector of volumes errors of 2D peaks ////////////////////////////////////////////////////////////////////////////// for( Int_t i=0; i < fNPeaks; i++){ volumeErrors[i] = (Float_t) fVolumeErr[i]; } } //______________________________________________________________________________ void TSpectrum2Fit::GetSigmaX(Double_t &sigmaX, Double_t &sigmaErrX) { ////////////////////////////////////////////////////////////////////////////// // GETTER FUNCTION // // This function gets the sigma x parameter and its error // -sigmaX - gets the fitted value of sigma x parameter // -sigmaErrX - gets error value of sigma x parameter ////////////////////////////////////////////////////////////////////////////// sigmaX=fSigmaCalcX; sigmaErrX=fSigmaErrX; } //______________________________________________________________________________ void TSpectrum2Fit::GetSigmaY(Double_t &sigmaY, Double_t &sigmaErrY) { ////////////////////////////////////////////////////////////////////////////// // GETTER FUNCTION // // This function gets the sigma y parameter and its error // -sigmaY - gets the fitted value of sigma y parameter // -sigmaErrY - gets error value of sigma y parameter ////////////////////////////////////////////////////////////////////////////// sigmaY=fSigmaCalcY; sigmaErrY=fSigmaErrY; } //______________________________________________________________________________ void TSpectrum2Fit::GetRo(Double_t &ro, Double_t &roErr) { ////////////////////////////////////////////////////////////////////////////// // GETTER FUNCTION // // This function gets the ro parameter and its error // -ro - gets the fitted value of ro parameter // -roErr - gets error value of ro parameter ////////////////////////////////////////////////////////////////////////////// ro=fRoCalc; roErr=fRoErr; } //______________________________________________________________________________ void TSpectrum2Fit::GetBackgroundParameters(Double_t &a0, Double_t &a0Err, Double_t &ax, Double_t &axErr, Double_t &ay, Double_t &ayErr) { ////////////////////////////////////////////////////////////////////////////// // GETTER FUNCTION // // This function gets the background parameters and their errors // -a0 - gets the fitted value of a0 parameter // -a0Err - gets error value of a0 parameter // -ax - gets the fitted value of ax parameter // -axErr - gets error value of ax parameter // -ay - gets the fitted value of ay parameter // -ayErr - gets error value of ay parameter ////////////////////////////////////////////////////////////////////////////// a0 = fA0Calc; a0Err = fA0Err; ax = fAxCalc; axErr = fAxErr; ay = fAyCalc; ayErr = fAyErr; } //______________________________________________________________________________ void TSpectrum2Fit::GetTailParameters(Double_t &txy, Double_t &txyErr, Double_t &tx, Double_t &txErr, Double_t &ty, Double_t &tyErr, Double_t &bx, Double_t &bxErr, Double_t &by, Double_t &byErr, Double_t &sxy, Double_t &sxyErr, Double_t &sx, Double_t &sxErr, Double_t &sy, Double_t &syErr) { ////////////////////////////////////////////////////////////////////////////// // GETTER FUNCTION // // This function gets the tail parameters and their errors // -txy - gets the fitted value of txy parameter // -txyErr - gets error value of txy parameter // -tx - gets the fitted value of tx parameter // -txErr - gets error value of tx parameter // -ty - gets the fitted value of ty parameter // -tyErr - gets error value of ty parameter // -bx - gets the fitted value of bx parameter // -bxErr - gets error value of bx parameter // -by - gets the fitted value of by parameter // -byErr - gets error value of by parameter // -sxy - gets the fitted value of sxy parameter // -sxyErr - gets error value of sxy parameter // -sx - gets the fitted value of sx parameter // -sxErr - gets error value of sx parameter // -sy - gets the fitted value of sy parameter // -syErr - gets error value of sy parameter ////////////////////////////////////////////////////////////////////////////// txy = fTxyCalc; txyErr = fTxyErr; tx = fTxCalc; txErr = fTxErr; ty = fTyCalc; tyErr = fTyErr; bx = fBxCalc; bxErr = fBxErr; by = fByCalc; byErr = fByErr; sxy = fSxyCalc; sxyErr = fSxyErr; sx = fSxCalc; sxErr = fSxErr; sy = fSyCalc; syErr = fSyErr; }