diff --git a/examples/Test_Dpipi.cc b/examples/Test_Dpipi.cc index 0e76fa0..cf7c363 100644 --- a/examples/Test_Dpipi.cc +++ b/examples/Test_Dpipi.cc @@ -1,444 +1,444 @@ #include #include #include #include #include "TFile.h" #include "TH2.h" #include "TRandom.h" #include "TString.h" #include "TSystem.h" #include "TF1.h" #include "TCanvas.h" #include "Lau1DHistPdf.hh" #include "Lau1DCubicSpline.hh" #include "LauBinnedDecayTimeEfficiency.hh" #include "LauBkgndDPModel.hh" #include "LauDaughters.hh" #include "LauDecayTime.hh" #include "LauDecayTimePdf.hh" #include "LauDecayTimePhysicsModel.hh" #include "LauDecayTimeResolution.hh" #include "LauEffModel.hh" #include "LauFlavTag.hh" #include "LauIsobarDynamics.hh" #include "LauMagPhaseCoeffSet.hh" #include "LauRandom.hh" #include "LauRealImagCoeffSet.hh" #include "LauSplineDecayTimeEfficiency.hh" #include "LauTimeDepFitModel.hh" #include "LauVetoes.hh" #include "Test_Dpipi_ProgOpts.hh" int main(const int argc, const char ** argv) { const TestDpipi_ProgramSettings settings{argc,argv}; if ( settings.helpRequested ) { return EXIT_SUCCESS; } if ( ! settings.parsedOK ) { return EXIT_FAILURE; } LauRandom::setSeed(settings.RNGseed); LauDaughters* daughtersB0bar = new LauDaughters("B0_bar", "pi+", "pi-", "D0"); LauDaughters* daughtersB0 = new LauDaughters("B0", "pi+", "pi-", "D0_bar"); // efficiency LauVetoes* vetoes = new LauVetoes(); LauEffModel* effModelB0bar = new LauEffModel(daughtersB0bar, vetoes); LauEffModel* effModelB0 = new LauEffModel(daughtersB0, vetoes); // background types /* std::map bkgndInfo { {"Bkgnd1",LauFlavTag::BkgndType::Combinatorial}, {"Bkgnd2",LauFlavTag::BkgndType::SignalLike} }; */ // setup flavour tagging const Bool_t useAveDeltaCalibVals { settings.useAveDeltaCalibVals }; const Bool_t useEtaPrime { kFALSE }; LauFlavTag* flavTag = new LauFlavTag(useAveDeltaCalibVals,useEtaPrime); //LauFlavTag* flavTag = new LauFlavTag(useAveDeltaCalibVals,useEtaPrime,BkgndTypes); if (settings.dType == LauTimeDepFitModel::CPEigenvalue::QFS) { flavTag->setDecayFlvVarName("decayFlv"); } flavTag->setTrueTagVarName("trueTag"); TFile* etaFile = TFile::Open("ft-eta-hist.root"); TH1* etaHist = dynamic_cast(etaFile->Get("ft_eta_hist")); // Crude check as to whether we're doing perfect vs realistic mis-tag // - in the former case all entries should be in the first bin // If the tagging is perfect then don't interpolate the eta histogram // and also make it perfectly efficient, otherwise do interpolate and // make it 50% efficient const Double_t meanEta { etaHist->GetMean() }; const Bool_t interpolateEtaHist { meanEta > etaHist->GetBinWidth(1) }; Lau1DHistPdf* etaHistPDF = new Lau1DHistPdf( "eta", etaHist, 0.0, 0.5, interpolateEtaHist, kFALSE ); const Double_t tagEffVal { (interpolateEtaHist) ? 0.5 : 1.0 }; std::pair tagEff {tagEffVal, useAveDeltaCalibVals ? 0.0 : tagEffVal}; // use a null calibration for the time being, so p0 = and p1 = 1 std::pair calib0 {meanEta, useAveDeltaCalibVals ? 0.0 : meanEta}; std::pair calib1 {1.0, useAveDeltaCalibVals ? 0.0 : 1.0}; flavTag->addTagger("OSTagger", "tagVal_OS", "mistagVal_OS", etaHistPDF, tagEff, calib0, calib1); flavTag->floatAllCalibPars(); // flavour tagging setup for backgrounds /* std::map BkgndEtas; TFile* bkgndEtaFile = TFile::Open("ft-bkgnd-eta-hists.root"); for(auto& [name, _] : BkgndTypes) { TH1* bkgndEtaHist = dynamic_cast(bkgndEtaFile->Get( name+"_eta_hist" )); Lau1DHistPdf* bkgndEtaHistPDF = new Lau1DHistPdf("eta",bkgndEtaHist,0.0,0.5,kTRUE,kFALSE); BkgndEtas.emplace( std::make_pair(name, bkgndEtaHistPDF) ); } for(auto& [name,hist] : BkgndEtas) {flavTag->setBkgndParams(name, "IFT", hist, tagEff );} */ // signal dynamics LauIsobarDynamics* sigModelB0bar = new LauIsobarDynamics(daughtersB0bar, effModelB0bar); sigModelB0bar->setIntFileName("integ_B0bar.dat"); sigModelB0bar->addResonance("D*+_2", 2, LauAbsResonance::RelBW); sigModelB0bar->addResonance("D*+_0", 2, LauAbsResonance::RelBW); sigModelB0bar->addResonance("rho0(770)", 3, LauAbsResonance::RelBW); sigModelB0bar->addResonance("f_0(980)", 3, LauAbsResonance::RelBW); sigModelB0bar->addResonance("f_2(1270)", 3, LauAbsResonance::RelBW); LauIsobarDynamics* sigModelB0 = new LauIsobarDynamics(daughtersB0, effModelB0); sigModelB0->setIntFileName("integ_B0.dat"); sigModelB0->addResonance("D*-_2", 1, LauAbsResonance::RelBW); sigModelB0->addResonance("D*-_0", 1, LauAbsResonance::RelBW); sigModelB0->addResonance("rho0(770)", 3, LauAbsResonance::RelBW); sigModelB0->addResonance("f_0(980)", 3, LauAbsResonance::RelBW); sigModelB0->addResonance("f_2(1270)", 3, LauAbsResonance::RelBW); // fit model LauTimeDepFitModel* fitModel = new LauTimeDepFitModel(sigModelB0bar,sigModelB0,flavTag); std::vector coeffset; coeffset.push_back( new LauRealImagCoeffSet("D*+_2", 1.00, 0.00, kTRUE, kTRUE) ); coeffset.push_back( new LauRealImagCoeffSet("D*+_0", 0.53*TMath::Cos( 3.00), 0.53*TMath::Sin( 3.00), kFALSE, kFALSE) ); coeffset.push_back( new LauRealImagCoeffSet("rho0(770)", 1.22*TMath::Cos( 2.25), 1.22*TMath::Sin( 2.25), kFALSE, kFALSE) ); coeffset.push_back( new LauRealImagCoeffSet("f_0(980)", 0.19*TMath::Cos(-2.48), 0.19*TMath::Sin(-2.48), kFALSE, kFALSE) ); coeffset.push_back( new LauRealImagCoeffSet("f_2(1270)", 0.75*TMath::Cos( 2.97), 0.75*TMath::Sin( 2.97), kFALSE, kFALSE) ); for (std::vector::iterator iter=coeffset.begin(); iter!=coeffset.end(); ++iter) { fitModel->setAmpCoeffSet(*iter); } // background DP models /* LauBkgndDPModel* Bkgnd1Model = new LauBkgndDPModel(daughtersB0, vetoes); LauBkgndDPModel* Bkgnd1Modelbar = new LauBkgndDPModel(daughtersB0bar, vetoes); LauBkgndDPModel* Bkgnd2Model = new LauBkgndDPModel(daughtersB0, vetoes); LauBkgndDPModel* Bkgnd2Modelbar = new LauBkgndDPModel(daughtersB0bar, vetoes); fitModel->setBkgndDPModels( "Bkgnd1", Bkgnd1Model, Bkgnd1Modelbar ); fitModel->setBkgndDPModels( "Bkgnd2", Bkgnd2Model, Bkgnd2Modelbar ); */ // decay type and mixing parameter const Bool_t fixPhiMix{ settings.fixPhiMix || settings.dType == LauTimeDepFitModel::CPEigenvalue::QFS }; const Bool_t useSinCos{ settings.useSinCos }; fitModel->setCPEigenvalue( settings.dType ); fitModel->setPhiMix( 2.0*LauConstants::beta, fixPhiMix, useSinCos ); // production asymmetries fitModel->setAsymmetries( 0.0, kTRUE ); /* for(auto& [name, _] : BkgndTypes) { fitModel->setBkgndAsymmetries( name, 0.0, kTRUE ); } */ // decay time PDFs const Double_t minDt(0.0); const Double_t maxDt(15.0); const Double_t minDtErr(0.0); const Double_t maxDtErr(0.15); LauParameter * tau = new LauParameter("dt_tau", 1.519, 0.5, 5.0, settings.fixLifetime); LauParameter * freq = new LauParameter("dt_deltaM", 0.5064, 0.0, 1.0, settings.fixDeltaM); std::vector dtPhysPars { tau, freq }; auto dtPhysModel = std::make_unique( LauDecayTime::FuncType::ExpTrig, dtPhysPars ); const std::vector scale { settings.perEventTimeErr && true, settings.perEventTimeErr && true, }; const std::size_t nGauss{scale.size()}; LauParameter * mean0 = new LauParameter("dt_mean_0", scale[0] ? -2.01290e-03 : -2.25084e-03, -0.01, 0.01, kTRUE ); LauParameter * mean1 = new LauParameter("dt_mean_1", scale[1] ? -2.01290e-03 : -5.04275e-03, -0.01, 0.01, kTRUE ); LauParameter * sigma0 = new LauParameter("dt_sigma_0", scale[0] ? 9.95145e-01 : 3.03923e-02, 0.0, 2.0, kTRUE ); LauParameter * sigma1 = new LauParameter("dt_sigma_1", scale[1] ? 1.81715e+00 : 6.22376e-02, 0.0, 2.5, kTRUE ); LauParameter * frac1 = new LauParameter("dt_frac_1", scale[0] && scale[1] ? 1.-9.35940e-01 : 1.-7.69603e-01, 0.0, 1.0, kTRUE); std::vector dtResoPars { mean0, mean1, sigma0, sigma1, frac1 }; auto dtResoModel = std::make_unique( nGauss, dtResoPars, scale ); // Decay time error histogram // (always set this so that it gets generated properly, whether we're using it in the PDF or not) TFile* dtErrFile = TFile::Open("dte-hist.root"); TH1* dtErrHist = dynamic_cast(dtErrFile->Get("dte_hist")); LauDecayTimePdf * dtPdf{nullptr}; if ( settings.timeResolution ) { if ( settings.perEventTimeErr ) { dtPdf = new LauDecayTimePdf( "decayTime", minDt, maxDt, "decayTimeErr", minDtErr, maxDtErr, std::move(dtPhysModel), std::move(dtResoModel), dtErrHist ); } else { dtPdf = new LauDecayTimePdf( "decayTime", minDt, maxDt, std::move(dtPhysModel), std::move(dtResoModel) ); } } else { dtPdf = new LauDecayTimePdf( "decayTime", minDt, maxDt, std::move(dtPhysModel) ); } // Decay time acceptance histogram TFile* dtaFile = TFile::Open("dta-hist.root"); TH1* dtaHist = dynamic_cast(dtaFile->Get("dta_hist")); // Create the spline knot positions and // starting Y values, to be fit to dtaHist const std::vector dtvals { 0.0, 0.5, 1.0, 2.0, 3.0, 4.0, 7.0, 10.0, 15.0}; const std::vector effvals {0.000, 0.010, 0.022, 0.035, 0.042, 0.050, 0.051, 0.052, 0.055}; const std::vector corvals { 1.10, 1.08, 1.06, 1.04, 1.02, 1.00, 0.98, 0.96, 0.94}; switch(settings.timeEffModel) { case LauDecayTime::EfficiencyMethod::Spline: { fitModel->setASqMaxValue(0.06); auto dtEffSpline = std::make_unique(dtvals,effvals,Lau1DCubicSpline::AkimaSpline,Lau1DCubicSpline::Natural,Lau1DCubicSpline::Natural); - dtEffSpline->fitToTH1(dtaHist); auto dtaModel = std::make_unique>( "dteff_QFS", std::move(dtEffSpline) ); + dtaModel->fitToTH1(dtaHist); // Set which knots to float and which to fix (at least 1 knot must be fixed, not the first one) // Knots should only be floating if requested AND the B lifetime is fixed! if ( settings.fixSplineKnots or not settings.fixLifetime ) { dtaModel->fixKnots(); } else { dtaModel->floatKnots(); dtaModel->fixKnot( 0, true ); dtaModel->fixKnot( 3, true ); } if ( settings.dType == LauTimeDepFitModel::CPEigenvalue::QFS ) { // For the QFS mode we just use the cubic model as it is dtPdf->setSplineEfficiency( std::move(dtaModel) ); } else { // For the CP modes we modify it using a corrective spline auto dtCorrSpline = std::make_unique(dtvals,corvals,Lau1DCubicSpline::AkimaSpline,Lau1DCubicSpline::Natural,Lau1DCubicSpline::Natural); auto dtaCPModel = std::make_unique>( "dteff_CP", *dtaModel, std::move( dtCorrSpline ) ); dtPdf->setSplineEfficiency( std::move(dtaCPModel) ); } break; } case LauDecayTime::EfficiencyMethod::Binned: { fitModel->setASqMaxValue(0.06); auto dtaBinnedModel = std::make_unique( *dtaHist ); dtPdf->setBinnedEfficiency( std::move(dtaBinnedModel) ); break; } case LauDecayTime::EfficiencyMethod::Uniform: { fitModel->setASqMaxValue(4.45); break; } } fitModel->setSignalDtPdf( dtPdf ); //Background dt part /* TFile* background_dt = TFile::Open("Lifetimes_PV_WL.root"); TH1* bkgnd1DtHist = dynamic_cast( background_dt->Get("Bkgnd1") ); TH1* bkgnd2DtHist = dynamic_cast( background_dt->Get("Bkgnd2") ); TH1* bkgnd1DtErrHist = dynamic_cast( background_dt->Get("Bkgnd1_Err") ); TH1* bkgnd2DtErrHist = dynamic_cast( background_dt->Get("Bkgnd2_Err") ); LauDecayTimePdf* bkgnd1DtPdf{nullptr}; LauDecayTimePdf* bkgnd2DtPdf{nullptr}; if ( settings.timeResolution and settings.perEventTimeErr ) { bkgnd1DtPdf= new LauDecayTimePdf( "decayTime", minDt, maxDt, bkgnd1DtHist, bkgnd1DtErrHist ); bkgnd2DtPdf= new LauDecayTimePdf( "decayTime", minDt, maxDt, bkgnd2DtHist, bkgnd2DtErrHist ); } else { bkgnd1DtPdf= new LauDecayTimePdf( "decayTime", minDt, maxDt, bkgnd1DtHist ); bkgnd2DtPdf= new LauDecayTimePdf( "decayTime", minDt, maxDt, bkgnd2DtHist ); } fitModel->setBkgndDtPdf("Bkgnd1",bkgnd1DtPdf); fitModel->setBkgndDtPdf("Bkgnd2",bkgnd2DtPdf); */ // set the signal yield Double_t nSigEvents{0}; switch (settings.dType) { case LauTimeDepFitModel::CPEigenvalue::CPEven : nSigEvents = 15000; break; case LauTimeDepFitModel::CPEigenvalue::CPOdd : nSigEvents = 5000; break; case LauTimeDepFitModel::CPEigenvalue::QFS : nSigEvents = 50000; break; } // set the background yields /* const Double_t nBkgnd1(100), nBkgnd2(200); LauParameter* Bkgnd1Yield = new LauParameter("Bkgnd1",nBkgnd1,-1.0*nBkgnd1,2.0*nBkgnd1,kFALSE); LauParameter* Bkgnd2Yield = new LauParameter("Bkgnd2",nBkgnd2,-1.0*nBkgnd2,2.0*nBkgnd2,kFALSE); fitModel->setNBkgndEvents(Bkgnd1Yield); fitModel->setNBkgndEvents(Bkgnd2Yield); */ std::cout<<"nSigEvents = "<setNSigEvents(nSigPar); // set the number of experiments if (settings.command == Command::Generate) { fitModel->setNExpts(settings.nExptGen, settings.firstExptGen); } else { fitModel->setNExpts(settings.nExptFit, settings.firstExptFit); } fitModel->useAsymmFitErrors(kFALSE); fitModel->useRandomInitFitPars(kFALSE); fitModel->writeLatexTable(kFALSE); const Bool_t haveBkgnds = ( fitModel->nBkgndClasses() > 0 ); fitModel->doPoissonSmearing(haveBkgnds); fitModel->doEMLFit(haveBkgnds); TString dTypeStr; switch (settings.dType) { case LauTimeDepFitModel::CPEigenvalue::CPEven : dTypeStr = "CPEven"; break; case LauTimeDepFitModel::CPEigenvalue::CPOdd : dTypeStr = "CPOdd"; break; case LauTimeDepFitModel::CPEigenvalue::QFS : dTypeStr = "QFS"; break; } TString dataFile(""); TString treeName("fitTree"); TString rootFileName(""); TString tableFileName(""); TString fitToyFileName(""); TString splotFileName(""); dataFile = "TEST-Dpipi"; dataFile += "_"+dTypeStr; switch(settings.timeEffModel) { case LauDecayTime::EfficiencyMethod::Spline: dataFile += "_Spline"; break; case LauDecayTime::EfficiencyMethod::Binned: dataFile += "_Binned"; break; case LauDecayTime::EfficiencyMethod::Uniform: dataFile += "_Uniform"; break; } if (settings.timeResolution) { if (settings.perEventTimeErr) { dataFile += "_DTRperevt"; } else { dataFile += "_DTRavg"; } } else { dataFile += "_DTRoff"; } dataFile += "_expts"; dataFile += settings.firstExptGen; dataFile += "-"; dataFile += settings.firstExptGen+settings.nExptGen-1; dataFile += ".root"; if (settings.command == Command::Generate) { rootFileName = "dummy.root"; tableFileName = "genResults"; } else { rootFileName = "fit"; rootFileName += settings.iFit; rootFileName += "_Results_"; rootFileName += dTypeStr; rootFileName += "_expts"; rootFileName += settings.firstExptFit; rootFileName += "-"; rootFileName += settings.firstExptFit+settings.nExptFit-1; rootFileName += ".root"; tableFileName = "fit"; tableFileName += settings.iFit; tableFileName += "_Results_"; tableFileName += dTypeStr; tableFileName += "_expts"; tableFileName += settings.firstExptFit; tableFileName += "-"; tableFileName += settings.firstExptFit+settings.nExptFit-1; fitToyFileName = "fit"; fitToyFileName += settings.iFit; fitToyFileName += "_ToyMC_"; fitToyFileName += dTypeStr; fitToyFileName += "_expts"; fitToyFileName += settings.firstExptFit; fitToyFileName += "-"; fitToyFileName += settings.firstExptFit+settings.nExptFit-1; fitToyFileName += ".root"; splotFileName = "fit"; splotFileName += settings.iFit; splotFileName += "_sPlot_"; splotFileName += dTypeStr; splotFileName += "_expts"; splotFileName += settings.firstExptFit; splotFileName += "-"; splotFileName += settings.firstExptFit+settings.nExptFit-1; splotFileName += ".root"; } // Generate toy from the fitted parameters //fitModel->compareFitData(1, fitToyFileName); // Write out per-event likelihoods and sWeights //fitModel->writeSPlotData(splotFileName, "splot", kFALSE); // Execute the generation/fit switch (settings.command) { case Command::Generate : fitModel->run( "gen", dataFile, treeName, rootFileName, tableFileName ); break; case Command::Fit : fitModel->run( "fit", dataFile, treeName, rootFileName, tableFileName ); break; case Command::SimFit : fitModel->runTask( dataFile, treeName, rootFileName, tableFileName, "localhost", settings.port ); break; } return EXIT_SUCCESS; } diff --git a/inc/Lau1DCubicSpline.hh b/inc/Lau1DCubicSpline.hh index 633715f..7302474 100644 --- a/inc/Lau1DCubicSpline.hh +++ b/inc/Lau1DCubicSpline.hh @@ -1,251 +1,256 @@ /* Copyright 2015 University of Warwick Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. */ /* Laura++ package authors: John Back Paul Harrison Thomas Latham */ /*! \file Lau1DCubicSpline.hh \brief File containing declaration of Lau1DCubicSpline class. */ /*! \class Lau1DCubicSpline \brief Class for defining a 1D cubic spline based on a set of knots. Class for defining a 1D cubic spline based on a set of knots. Interpolation between the knots is performed either by one of two types of cubic spline (standard or Akima) or by linear interpolation. The splines are defined by a piecewise cubic function which, between knots i and i+1, has the form f_i(x) = (1 - t)*y_i + t*y_i+1 + t*(1 - t)(a*(1 - t) + b*t) where t = (x - x_i)/(x_i+1 - x_i), a = k_i *(x_i+1 - x_i) - (y_i+1 - y_i), b = -k_i+1*(x_i+1 - x_i) + (y_i+1 - y_i) and k_i is (by construction) the first derivative at knot i. f(x) and f'(x) are continuous at the internal knots by construction. For the standard splines, f''(x) is required to be continuous at all internal knots placing n-2 constraints on the n parameters, k_i. The final two constraints are set by the boundary conditions. At each boundary, the function may be: (i) Clamped : f'(x) = C at the last knot (ii) Natural : f''(x) = 0 at the last knot (iii) Not a knot : f'''(x) continuous at the second last knot The algorithms used in these splines can be found on: http://en.wikipedia.org/wiki/Spline_interpolation#Algorithm_to_find_the_interpolating_cubic_spline http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm For the Akima splines, the values of k_i are determined from the slopes of the four nearest segments (a_i-1, a_i, a_i+1 and a_i+2) as k_i = ( | a_i+2 - a_i+1 | a_i + | a_i - a_i-1 | a_i+1 ) / ( | a_i+2 - a_i+1 | + | a_i - a_i-1 | ) and as k_i = ( a_i + a_i+1 ) / 2 in the special case a_i-1 == a_i != a_i+1 == a_i+2. Boundary conditions are specified by the relations a_2 - a_1 = a_1 - a_0 = a_0 - a_-1 and a_n-1 - a_n-2 = a_n - a_n-1 = a_n+1 - a_n The algorithms used in these splines can be found in: J.ACM vol. 17 no. 4 pp 589-602 */ #ifndef LAU_1DCUBICSPLINE #define LAU_1DCUBICSPLINE #include #include -#include "LauParameter.hh" + #include "Rtypes.h" #include "TF1.h" +#include "TFitResultPtr.h" + +class TH1; +class LauAbsRValue; +class LauParameter; class Lau1DCubicSpline final { public: //! Define the allowed interpolation types enum LauSplineType { StandardSpline, /*!< standard cubic splines with f''(x) continuous at all internal knots */ AkimaSpline, /*!< Akima cubic splines with f'(x) at each knot defined locally by the positions of only five knots */ LinearInterpolation /*! Linear interpolation between each pair of knots */ }; //! Define the allowed boundary condition types /*! These are only supported by standard splines */ enum LauSplineBoundaryType { Clamped, /*!< clamped boundary - f'(x) = C */ Natural, /*!< natural boundary - f''(x) = 0 */ NotAKnot /*!< 'not a knot' boundary - f'''(x) continuous at second last knot */ }; //! Constructor /*! /param [in] xs the x-values of the knots /param [in] ys the y-values of the knots /param [in] leftBound the left-hand boundary condition /param [in] rightBound the right-hand boundary condition /param [in] dydx0 the gradient at the left-hand boundary of a clamped spline /param [in] dydxn the gradient at the right-hand boundary of a clamped spline */ Lau1DCubicSpline(const std::vector& xs, const std::vector& ys, LauSplineType type = Lau1DCubicSpline::StandardSpline, LauSplineBoundaryType leftBound = Lau1DCubicSpline::NotAKnot, LauSplineBoundaryType rightBound = Lau1DCubicSpline::NotAKnot, Double_t dydx0 = 0.0, Double_t dydxn = 0.0); //! Evaluate the function at given point /*! \param [in] x the x-coordinate \return the value of the spline at x */ Double_t evaluate(Double_t x) const; //! Update the y-values of the knots /*! \param [in] ys the y-values of the knots */ void updateYValues(const std::vector& ys); //! Update the y-values of the knots /*! \param [in] ys the y-values of the knots */ void updateYValues(const std::vector& ys); //! Update the y-values of the knots /*! \param [in] ys the y-values of the knots */ void updateYValues(const std::vector& ys); //! Update the type of interpolation to perform /*! \param [in] type the type of interpolation */ void updateType(LauSplineType type); //! Update the boundary conditions for the spline /*! /param [in] leftBound the left-hand boundary condition /param [in] rightBound the right-hand boundary condition /param [in] dydx0 the gradient at the left-hand boundary of a clamped spline /param [in] dydxn the gradient at the right-hand boundary of a clamped spline */ void updateBoundaryConditions(LauSplineBoundaryType leftBound, LauSplineBoundaryType rightBound, Double_t dydx0 = 0.0, Double_t dydxn = 0.0); //! Return the number of knots - UInt_t getnKnots() const {return nKnots_;} + std::size_t getnKnots() const {return nKnots_;} //! Get y values const std::vector& getYValues() const {return y_;} //! Get x values const std::vector& getXValues() const {return x_;} //! Get the coefficients of spline section i in the form a + bx + cx^2 + dx^3 /*! \params [in] i refers to the left-hand index of the knot (i = 0 gets the params between x_0 and x_1) \return coefficients {a, b, c, d} */ - std::array getCoefficients(const UInt_t i, const bool normalise = false) const; + std::array getCoefficients(const std::size_t i, const bool normalise = false) const; //! Get the integral over all the spline segments Double_t integral() const; //! Make a TF1 showing the spline with its current knot values /*! \params [in] normalise whether or not you want the spline normalised \return 1D function object */ TF1* makeTF1(const bool normalise = false) const; //! Fit the the normalisation of the spline to a TH1 //! So they look as good as possible when plotted on top of one another //! Useful when a sample has been generated with a hist and fitted with a spline to compare them /*! \params [in] The histogram to be fit to \return a TF1 fit to `hist` */ TF1* normaliseToTH1(TH1* hist) const; //! Fit the spline to a TH1 //! Useful as a starting-point for fitting a spline to data (maybe the hist is taken from MC) /*! \params [in] The histogram to be fit to */ - void fitToTH1(TH1* hist); + TFitResultPtr fitToTH1(TH1* hist); private: //! Initialise the class void init(); //! Calculate the first derivative at each knot void calcDerivatives(); //! Calculate the first derivatives according to the standard method void calcDerivativesStandard(); //! Calculate the first derivatives according to the Akima method void calcDerivativesAkima(); //! The number of knots in the spline - const UInt_t nKnots_; + const std::size_t nKnots_; //! The x-value at each knot std::vector x_; //! The y-value at each knot std::vector y_; //! The first derivative at each knot std::vector dydx_; //! The 'a' coefficients used to determine the derivatives std::vector a_; //! The 'b' coefficients used to determine the derivatives std::vector b_; //! The 'c' coefficients used to determine the derivatives std::vector c_; //! The 'd' coefficients used to determine the derivatives std::vector d_; //! The type of interpolation to be performed LauSplineType type_; //! The left-hand boundary condition on the spline LauSplineBoundaryType leftBound_; //! The right-hand boundary condition on the spline LauSplineBoundaryType rightBound_; //! The gradient at the left boundary for a clamped spline Double_t dydx0_; //! The gradient at the right boundary for a clamped spline Double_t dydxn_; ClassDef(Lau1DCubicSpline, 0); // Class for defining a 1D cubic spline }; #endif diff --git a/inc/LauSplineDecayTimeEfficiency.hh b/inc/LauSplineDecayTimeEfficiency.hh index ba7cb46..bcb8625 100644 --- a/inc/LauSplineDecayTimeEfficiency.hh +++ b/inc/LauSplineDecayTimeEfficiency.hh @@ -1,375 +1,406 @@ /* Copyright 2021 University of Warwick Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. */ /* Laura++ package authors: John Back Paul Harrison Thomas Latham */ /*! \file LauSplineDecayTimeEfficiency.hh \brief File containing declaration of LauSplineDecayTimeEfficiency class. */ /*! \class LauSplineDecayTimeEfficiency \brief Class for defining a spline-interpolated model for decay time efficiency */ #ifndef LAU_SPLINE_DECAYTIME_EFFICIENCY #define LAU_SPLINE_DECAYTIME_EFFICIENCY #include #include #include #include "Rtypes.h" +#include "TFitResult.h" #include "TSystem.h" #include "Lau1DCubicSpline.hh" #include "LauAbsDecayTimeEfficiency.hh" #include "LauParameter.hh" +class TH1; + //! Defines the allowed orders of spline polynomials enum class LauSplineOrder : std::size_t { Cubic = 3, //!< 3rd order Sixth = 6 //!< 6th order }; template class LauSplineDecayTimeEfficiency : public LauAbsDecayTimeEfficiency { public: //! Constructor for a Cubic spline /*! \param [in] prefix the prefix to use when forming the names of the knot parameters \param [in] effSpline the cubic spline to be used to represent the efficiency variation */ template = true> LauSplineDecayTimeEfficiency( const TString& prefix, std::unique_ptr effSpline ) : prefix_{prefix}, effSpline_{std::move(effSpline)} { this->initialSetup(); } //! Constructor for a Sixth order spline /*! \param [in] prefix the prefix to use when forming the names of the knot parameters \param [in] effSpline the cubic spline being used to represent the efficiency variation in another channel \param [in] correctionSpline the cubic spline to be used to represent the correction to effSpline to obtain the efficiency variation for this channel */ template = true> LauSplineDecayTimeEfficiency( const TString& prefix, const LauSplineDecayTimeEfficiency& effSpline, std::unique_ptr correctionSpline ) : prefix_{prefix}, effSpline_{std::move(correctionSpline)}, otherSpline_{std::make_unique>(effSpline)} { this->initialSetup(); } //! Destructor ~LauSplineDecayTimeEfficiency() = default; //! Move constructor (default) LauSplineDecayTimeEfficiency(LauSplineDecayTimeEfficiency&& other) = default; //! Move assignment operator (default) LauSplineDecayTimeEfficiency& operator=(LauSplineDecayTimeEfficiency&& other) = default; //! Copy constructor (custom) LauSplineDecayTimeEfficiency(const LauSplineDecayTimeEfficiency& other); //! Copy assignment operator (deleted) LauSplineDecayTimeEfficiency& operator=(const LauSplineDecayTimeEfficiency& other) = delete; //! The number of coefficients of each spline segment static constexpr std::size_t nCoeffs { static_cast>(Order) + 1 }; //! Retrieve the efficiency for a given value of the decay time /*! \param abscissa the value of the decay time \return the efficiency */ Double_t getEfficiency( const Double_t abscissa ) const override; //! Retrieve the parameters of the efficiency model so that they can be loaded into a fit /*! \return the parameters of the efficiency model */ std::vector getParameters() override { return params_; } //! Initialise the parameter cache /*! Must be called prior to starting fitting or generation */ void initialise() override; //! Propagate any updates to parameters and recalculate information as neeeded /*! Should be called at each fit iteration */ void propagateParUpdates() override; //! Retrieve the number of segments in the spline std::size_t nSegments() const { return effSpline_->getnKnots() - 1; } //! Retrieve the positions of the spline knots const std::vector& knotPositions() const { return effSpline_->getXValues(); } //! Fix all knots void fixKnots(); //! Float all knots void floatKnots(); //! Fix or float a specific knot /*! \param knotIndex the index of the knot to fix/float \param fixed true if knot to be fixed, false if knot to be floated */ void fixKnot( const std::size_t knotIndex, const bool fixed ); //! Retrieve the polynomial coefficients for the given spline segment /*! \param segmentIndex the index of the spline segment \return the polynomial coefficients */ std::array getCoefficients( const std::size_t segmentIndex ) const; //! Retrieve whether any of the parameters are floating in the fit bool anythingFloating() const { return anyKnotFloating_; } //! Retrieve whether any of the parameters have changed in the latest fit iteration const bool& anythingChanged() const override { return anyKnotChanged_; } + //! Fit our spline to a TH1 + /*! + Useful to obtain reasonable starting values and uncertainties for the knot parameters + + \params [in] The histogram to be fit to + */ + void fitToTH1( TH1* hist ); + private: //! Perform the initial setup - shared by the various constructors void initialSetup( const LauSplineDecayTimeEfficiency* other = nullptr ); //! Update the cached parameter values void updateParameterCache(); //! The prefix for the parameter names const TString prefix_; //! The spline std::unique_ptr effSpline_; //! The other spline std::unique_ptr> otherSpline_; //! The spline parameters std::vector> ownedParams_; //! The spline parameters (for giving access) std::vector params_; //! The spline values std::vector values_; //! Are any of our knot parameters floating in the fit? bool ourKnotsFloating_{false}; //! Are any of the other spline's knot parameters floating in the fit? bool otherKnotsFloating_{false}; //! Are any of the knot parameters floating in the fit? bool anyKnotFloating_{false}; //! Have any of our knot parameters changed in the latest fit iteration? bool ourKnotsChanged_{false}; //! Have any of the other spline's knot parameters changed in the latest fit iteration? bool otherKnotsChanged_{false}; //! Have any of the knot parameters changed in the lastest fit iteration? bool anyKnotChanged_{false}; ClassDefOverride(LauSplineDecayTimeEfficiency, 0) }; templateClassImp(LauSplineDecayTimeEfficiency); template void LauSplineDecayTimeEfficiency::initialSetup( const LauSplineDecayTimeEfficiency* other ) { if ( not effSpline_ ) { std::cerr<<"ERROR in LauSplineDecayTimeEfficiency::initialSetup : supplied efficiency spline pointer is null"<Exit(EXIT_FAILURE); } if constexpr ( Order == LauSplineOrder::Sixth ) { std::vector ourKnots { effSpline_->getXValues() }; std::vector otherKnots { otherSpline_->knotPositions() }; if ( ourKnots != otherKnots ) { std::cerr<<"ERROR in LauSplineDecayTimeEfficiency::initialSetup : mismatch in knot positions"<Exit(EXIT_FAILURE); } // TODO - any other checks we need to do? } values_ = effSpline_->getYValues(); const std::size_t nPars { values_.size() }; ownedParams_.reserve( nPars ); if ( other ) { for ( auto& ptr : other->ownedParams_ ) { // TODO - maybe need a way to give these a unique prefix? ownedParams_.emplace_back( ptr->createClone() ); } } else { for( std::size_t index{0}; index < nPars; ++index ) { - ownedParams_.emplace_back( std::make_unique( Form( "%s_knot_%lu", prefix_.Data(), index ), values_[index], 0.0, 2.0, kTRUE ) ); + constexpr Double_t maxVal { (Order == LauSplineOrder::Cubic) ? 1.0 : 2.0 }; + ownedParams_.emplace_back( std::make_unique( Form( "%s_knot_%lu", prefix_.Data(), index ), values_[index], 0.0, maxVal, kTRUE ) ); } } if constexpr ( Order == LauSplineOrder::Sixth ) { params_ = otherSpline_->getParameters(); params_.reserve( 2*nPars ); } else { params_.reserve( nPars ); } for ( auto& ptr : ownedParams_ ) { params_.push_back( ptr.get() ); } } template LauSplineDecayTimeEfficiency::LauSplineDecayTimeEfficiency(const LauSplineDecayTimeEfficiency& other) : prefix_{ other.prefix_ }, effSpline_{ std::make_unique( * other.effSpline_ ) }, otherSpline_{ other.otherSpline_ ? std::make_unique>( *other.otherSpline_ ) : nullptr } { this->initialSetup( &other ); } template void LauSplineDecayTimeEfficiency::fixKnots() { for ( auto& ptr : ownedParams_ ) { ptr->fixed(true); } } template void LauSplineDecayTimeEfficiency::floatKnots() { for ( auto& ptr : ownedParams_ ) { ptr->fixed(false); } } template void LauSplineDecayTimeEfficiency::fixKnot( const std::size_t knotIndex, const bool fixed ) { if ( knotIndex >= ownedParams_.size() ) { std::cerr<<"ERROR in LauSplineDecayTimeEfficiency::fixKnot : supplied knot index is out of range"<fixed(fixed); } template Double_t LauSplineDecayTimeEfficiency::getEfficiency( const Double_t abscissa ) const { Double_t eff { effSpline_->evaluate( abscissa ) }; if constexpr ( Order == LauSplineOrder::Sixth ) { eff *= otherSpline_->getEfficiency( abscissa ); } return eff; } template std::array::nCoeffs> LauSplineDecayTimeEfficiency::getCoefficients( const std::size_t segmentIndex ) const { if constexpr ( Order == LauSplineOrder::Cubic ) { return effSpline_->getCoefficients(segmentIndex); } else { std::array ourCoeffs { effSpline_->getCoefficients(segmentIndex) }; std::array otherCoeffs { otherSpline_->getCoefficients(segmentIndex) }; std::array coeffs; coeffs[0] = ourCoeffs[0] * otherCoeffs[0]; coeffs[1] = ourCoeffs[0] * otherCoeffs[1] + ourCoeffs[1] * otherCoeffs[0]; coeffs[2] = ourCoeffs[0] * otherCoeffs[2] + ourCoeffs[1] * otherCoeffs[1] + ourCoeffs[2] * otherCoeffs[0]; coeffs[3] = ourCoeffs[0] * otherCoeffs[3] + ourCoeffs[1] * otherCoeffs[2] + ourCoeffs[2] * otherCoeffs[1] + ourCoeffs[3] * otherCoeffs[0]; coeffs[4] = ourCoeffs[1] * otherCoeffs[3] + ourCoeffs[2] * otherCoeffs[2] + ourCoeffs[3] * otherCoeffs[1]; coeffs[5] = ourCoeffs[2] * otherCoeffs[3] + ourCoeffs[3] * otherCoeffs[2]; coeffs[6] = ourCoeffs[3] * otherCoeffs[3]; return coeffs; } } template void LauSplineDecayTimeEfficiency::initialise() { static auto isFixed = []( const std::unique_ptr& par ){ return par->fixed(); }; anyKnotFloating_ = ourKnotsFloating_ = not std::all_of( ownedParams_.begin(), ownedParams_.end(), isFixed ); if constexpr ( Order == LauSplineOrder::Sixth ) { otherSpline_->initialise(); otherKnotsFloating_ = otherSpline_->anythingFloating(); anyKnotFloating_ |= otherKnotsFloating_; } this->updateParameterCache(); } template void LauSplineDecayTimeEfficiency::updateParameterCache() { static auto assignValue = []( const std::unique_ptr& par ){ return par->unblindValue(); }; // Update our local cache std::transform( ownedParams_.begin(), ownedParams_.end(), values_.begin(), assignValue ); // Update the spline itself effSpline_->updateYValues( values_ ); } template void LauSplineDecayTimeEfficiency::propagateParUpdates() { // If none of the parameters are floating there's nothing to do if ( not anyKnotFloating_ ) { return; } // Otherwise, determine which of the floating parameters have changed (if any) and act accordingly if ( ourKnotsFloating_ ) { static auto checkEquality = []( const std::unique_ptr& par, const Double_t cacheVal ){ return par->unblindValue() == cacheVal; }; anyKnotChanged_ = ourKnotsChanged_ = not std::equal( ownedParams_.begin(), ownedParams_.end(), values_.begin(), checkEquality); // Update the acceptance spline if any of the knot values have changed if ( ourKnotsChanged_ ) { this->updateParameterCache(); } } if constexpr ( Order == LauSplineOrder::Sixth ) { if ( otherKnotsFloating_ ) { otherSpline_->propagateParUpdates(); otherKnotsChanged_ = otherSpline_->anythingChanged(); anyKnotChanged_ |= otherKnotsChanged_; } } } +template +void LauSplineDecayTimeEfficiency::fitToTH1( TH1* hist ) +{ + TFitResultPtr fitResult { effSpline_->fitToTH1( hist ) }; + + const std::size_t nKnots { ownedParams_.size() }; + for ( std::size_t knot{0}; knot < nKnots; ++knot ) { + const Double_t knotVal { fitResult->Value(knot) }; + const Double_t knotErr { fitResult->Error(knot) }; + + ownedParams_[knot]->value( knotVal ); + ownedParams_[knot]->genValue( knotVal ); + ownedParams_[knot]->initValue( knotVal ); + ownedParams_[knot]->error( knotErr ); + } + + this->updateParameterCache(); +} + #endif diff --git a/src/Lau1DCubicSpline.cc b/src/Lau1DCubicSpline.cc index 272ef7c..251d057 100644 --- a/src/Lau1DCubicSpline.cc +++ b/src/Lau1DCubicSpline.cc @@ -1,532 +1,532 @@ /* Copyright 2015 University of Warwick Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License. */ /* Laura++ package authors: John Back Paul Harrison Thomas Latham */ /*! \file Lau1DCubicSpline.cc \brief File containing implementation of Lau1DCubicSpline class. */ #include #include #include #include #include #include "Lau1DCubicSpline.hh" +#include "LauAbsRValue.hh" +#include "LauParameter.hh" ClassImp(Lau1DCubicSpline) Lau1DCubicSpline::Lau1DCubicSpline(const std::vector& xs, const std::vector& ys, LauSplineType type, LauSplineBoundaryType leftBound, LauSplineBoundaryType rightBound, Double_t dydx0, Double_t dydxn) : nKnots_(xs.size()), x_(xs), y_(ys), type_(type), leftBound_(leftBound), rightBound_(rightBound), dydx0_(dydx0), dydxn_(dydxn) { init(); } Double_t Lau1DCubicSpline::evaluate(Double_t x) const { // do not attempt to extrapolate the spline if( xx_[nKnots_-1] ) { std::cerr << "WARNING in Lau1DCubicSpline::evaluate : function is only defined between " << x_[0] << " and " << x_[nKnots_-1] << std::endl; std::cerr << " value at " << x << " returned as 0" << std::endl; return 0.; } // first determine which 'cell' of the spline x is in // cell i runs from knot i to knot i+1 Int_t cell(0); while( x > x_[cell+1] ) { ++cell; } // obtain x- and y-values of the neighbouring knots Double_t xLow = x_[cell]; Double_t xHigh = x_[cell+1]; Double_t yLow = y_[cell]; Double_t yHigh = y_[cell+1]; if(type_ == Lau1DCubicSpline::LinearInterpolation) { return yHigh*(x-xLow)/(xHigh-xLow) + yLow*(xHigh-x)/(xHigh-xLow); } // obtain t, the normalised x-coordinate within the cell, // and the coefficients a and b, which are defined in cell i as: // // a_i = k_i *(x_i+1 - x_i) - (y_i+1 - y_i), // b_i = -k_i+1*(x_i+1 - x_i) + (y_i+1 - y_i) // // where k_i is (by construction) the first derivative at knot i Double_t t = (x - xLow) / (xHigh - xLow); Double_t a = dydx_[cell] * (xHigh - xLow) - (yHigh - yLow); Double_t b = -1.*dydx_[cell+1] * (xHigh - xLow) + (yHigh - yLow); Double_t retVal = (1 - t) * yLow + t * yHigh + t * (1 - t) * ( a * (1 - t) + b * t ); return retVal; } void Lau1DCubicSpline::updateYValues(const std::vector& ys) { y_ = ys; this->calcDerivatives(); } void Lau1DCubicSpline::updateYValues(const std::vector& ys) { - for (UInt_t i=0; iunblindValue(); } this->calcDerivatives(); } void Lau1DCubicSpline::updateYValues(const std::vector& ys) { - for (UInt_t i=0; iunblindValue(); } this->calcDerivatives(); } void Lau1DCubicSpline::updateType(LauSplineType type) { if(type_ != type) { type_ = type; this->calcDerivatives(); } } void Lau1DCubicSpline::updateBoundaryConditions(LauSplineBoundaryType leftBound, LauSplineBoundaryType rightBound, Double_t dydx0, Double_t dydxn) { - Bool_t updateDerivatives(kFALSE); + bool updateDerivatives{false}; if(leftBound_ != leftBound || rightBound_ != rightBound) { leftBound_ = leftBound; rightBound_ = rightBound; - updateDerivatives = kTRUE; + updateDerivatives = true; } if(dydx0_ != dydx0) { dydx0_ = dydx0; - if(leftBound_ == Lau1DCubicSpline::Clamped) updateDerivatives = kTRUE; + if(leftBound_ == Lau1DCubicSpline::Clamped) updateDerivatives = true; } if(dydxn_ != dydxn) { dydxn_ = dydxn; - if(rightBound_ == Lau1DCubicSpline::Clamped) updateDerivatives = kTRUE; + if(rightBound_ == Lau1DCubicSpline::Clamped) updateDerivatives = true; } if(updateDerivatives) { this->calcDerivatives(); } } -std::array Lau1DCubicSpline::getCoefficients(const UInt_t i, const bool normalise) const +std::array Lau1DCubicSpline::getCoefficients(const std::size_t i, const bool normalise) const { std::array result = {0.,0.,0.,0.}; if(i >= nKnots_-1) { std::cerr << "ERROR in Lau1DCubicSpline::getCoefficients requested for too high a knot value" << std::endl; return result; } Double_t xL = x_[i] , xH = x_[i+1]; Double_t yL = y_[i] , yH = y_[i+1]; Double_t h = xH-xL; //This number comes up a lot switch(type_) { case Lau1DCubicSpline::StandardSpline: case Lau1DCubicSpline::AkimaSpline: { Double_t kL = dydx_[i], kH = dydx_[i+1]; //a and b based on definitions from https://en.wikipedia.org/wiki/Spline_interpolation#Algorithm_to_find_the_interpolating_cubic_spline Double_t a = kL*h-(yH-yL); Double_t b =-kH*h+(yH-yL); Double_t denom = -h*h*h;//The terms have a common demoninator result[0] = -b*xL*xL*xH + a*xL*xH*xH + h*h*(xL*yH - xH*yL); result[1] = -a*xH*(2*xL+xH) + b*xL*(xL+2*xH) + h*h*(yL-yH); result[2] = -b*(2*xL+xH) + a*(xL+2*xH); result[3] = -a+b; for(auto& res : result){res /= denom;} break; } /* case Lau1DCubicSpline::AkimaSpline: // Double check the Akima description of splines (in evaluate) right now they're the same except for the first derivatives { //using fomulae from https://asmquantmacro.com/2015/09/01/akima-spline-interpolation-in-excel/ std::function m = [&](Int_t j) //formula to get the straight line gradient { if(j < 0){return 2*m(j+1)-m(j+2);} if(j >= nKnots_){return 2*m(j-1)-m(j-2);} return (y_[j+1]-y_[j]) / (x_[j+1]-x_[j]); }; auto t = [&](Int_t j) { Double_t res = 0.; //originally res was called 't' but that produced a shadow warning Double_t denom = TMath::Abs(m(j+1)-m(j)) + TMath::Abs(m(j-1)-m(j-2)); if(denom == 0){res = (m(j)-m(j-1))/2;} //Special case for when denom = 0 else { res = TMath::Abs(m(j+1)-m(j))*m(j-1) + TMath::Abs(m(j-1)-m(j-2))*m(j); res /= denom; } return res; }; //These are the p's to get the spline in the form p_k(x-xL)^k Double_t pDenom = x_[i+1]/x_[i]; //a denominator used for p[2] and p[3] std::array p = {y_[i],t(i),0.,0.}; //we'll do the last 2 below p[2] = 3*m(i)-2*t(i)-t(i+1); p[2]/= pDenom; p[3] = t(i)+t(i+1)-2*m(i); p[3]/= pDenom*pDenom; //Now finally rearranging the p's into the desired results result[0] = p[0]-p[1]*xL+p[2]*xL*xL-p[3]*xL*xL*xL; result[1] = p[1]-2*p[2]*xL+3*p[3]*xL*xL; result[2] = p[2]-3*p[3]*xL; result[3] = p[3]; break; }*/ case Lau1DCubicSpline::LinearInterpolation: { result[0] = xH*yL-xL*yH; result[1] = yH-yL; for(auto& res : result){res /= h;} break; } } if(normalise) { Double_t integral = this->integral(); for(auto& res : result){res /= integral;} } return result; } Double_t Lau1DCubicSpline::integral() const { - Double_t integral = 0.; - for(UInt_t iKnot = 0; iKnot < nKnots_ -1; ++iKnot) + Double_t integral{0.0}; + for(std::size_t iKnot{0}; iKnot < nKnots_ -1; ++iKnot) { - Double_t minAbs = x_[iKnot]; - Double_t maxAbs = x_[iKnot+1]; + const Double_t minAbs { x_[iKnot] }; + const Double_t maxAbs { x_[iKnot+1] }; - std::array coeffs = this -> getCoefficients(iKnot, false); + const std::array coeffs { this->getCoefficients(iKnot, false) }; - auto integralFunc = [&coeffs](Double_t x){return coeffs[0]*x + coeffs[1]*x*x/2 + coeffs[2]*x*x*x/3 + coeffs[3]*x*x*x*x/4;}; + auto integralFunc = [&coeffs](Double_t x){return coeffs[0]*x + coeffs[1]*x*x/2.0 + coeffs[2]*x*x*x/3.0 + coeffs[3]*x*x*x*x/4.0;}; integral += integralFunc(maxAbs); integral -= integralFunc(minAbs); } return integral; } TF1* Lau1DCubicSpline::makeTF1(const bool normalise) const { - TString functionString = ""; //make a long piecewise construction of all the spline pieces - for(UInt_t i = 0; i < nKnots_-1; ++i) + TString functionString{""}; //make a long piecewise construction of all the spline pieces + for(std::size_t i{0}; i < nKnots_-1; ++i) { + const std::array coeffs { this->getCoefficients(i,normalise) }; functionString += Form("(x>%f && x<= %f)*",x_[i],x_[i+1]);//get the bounds of this piece - std::array coeffs = this->getCoefficients(i,normalise); functionString += Form("(%f + %f*x + %f*x^2 + %f*x^3)",coeffs[0],coeffs[1],coeffs[2],coeffs[3]); if(i < nKnots_ -2){functionString += " + \n";}//add to all lines except the last } TF1* func = new TF1("SplineFunction", functionString, x_.front(), x_.back()); return func; } TF1* Lau1DCubicSpline::normaliseToTH1(TH1* hist) const { //first define the fit function auto fitf = [this](Double_t* x, Double_t* par) {//there is only 1 x (the abscissa) and 1 par (a scaling of the entire thing) return this->evaluate( x[0] ) * par[0]; }; //Make the function TF1* FittedFunc = new TF1("FittedFunc",fitf,x_.front(),x_.back(),1); //Set the parameter name FittedFunc -> SetParNames("Constant"); //Set the parameter limits and default value FittedFunc -> SetParLimits(0,0.,10.); FittedFunc -> SetParameter(0,1.); hist->Fit("FittedFunc","N O V"); return FittedFunc; } -void Lau1DCubicSpline::fitToTH1(TH1* hist) +TFitResultPtr Lau1DCubicSpline::fitToTH1(TH1* hist) { auto fitf = [this](Double_t* x, Double_t* par) { this -> updateYValues( std::vector(par, par + nKnots_) ); return this -> evaluate( x[0] ); }; - //Make the function + TF1 FittedFunc("FittedFunc",fitf,x_.front(),x_.back(),nKnots_); - const Double_t knotMax = hist->GetMaximum() * 1.5; + const Double_t knotMax { hist->GetMaximum() * 1.5 }; - for(UInt_t knot = 0; knot <= nKnots_ ; ++knot) + for(std::size_t knot{0}; knot <= nKnots_ ; ++knot) { - FittedFunc.SetParName(knot, Form("Knot%u",knot)); + FittedFunc.SetParName(knot, Form("Knot%lu",knot)); FittedFunc.SetParLimits(knot, 0., knotMax); FittedFunc.SetParameter(knot, y_[knot]); } - hist->Fit("FittedFunc","N O V"); - - return; + return hist->Fit("FittedFunc","N O V S"); } void Lau1DCubicSpline::init() { if( y_.size() != x_.size()) { std::cerr << "ERROR in Lau1DCubicSpline::init : The number of y-values given does not match the number of x-values" << std::endl; std::cerr << " Found " << y_.size() << ", expected " << x_.size() << std::endl; gSystem->Exit(EXIT_FAILURE); } if( nKnots_ < 3 ) { std::cerr << "ERROR in Lau1DCubicSpline::init : The number of knots is too small" << std::endl; std::cerr << " Found " << nKnots_ << ", expected at least 3 (to have at least 1 internal knot)" << std::endl; gSystem->Exit(EXIT_FAILURE); } dydx_.assign(nKnots_,0.0); a_.assign(nKnots_,0.0); b_.assign(nKnots_,0.0); c_.assign(nKnots_,0.0); d_.assign(nKnots_,0.0); this->calcDerivatives(); } void Lau1DCubicSpline::calcDerivatives() { switch ( type_ ) { case Lau1DCubicSpline::StandardSpline : this->calcDerivativesStandard(); break; case Lau1DCubicSpline::AkimaSpline : this->calcDerivativesAkima(); break; case Lau1DCubicSpline::LinearInterpolation : //derivatives not needed for linear interpolation break; } } void Lau1DCubicSpline::calcDerivativesStandard() { // derivatives are determined such that the second derivative is continuous at internal knots // derivatives, k_i, are the solutions to a set of linear equations of the form: // a_i * k_i-1 + b_i * k+i + c_i * k_i+1 = d_i with a_0 = 0, c_n-1 = 0 // this is solved using the tridiagonal matrix algorithm as on en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm // first and last equations give boundary conditions // - for natural boundary, require f''(x) = 0 at end knot // - for 'not a knot' boundary, require f'''(x) continuous at second knot // - for clamped boundary, require predefined value of f'(x) at end knot // non-zero values of a_0 and c_n-1 would give cyclic boundary conditions a_[0] = 0.; c_[nKnots_-1] = 0.; // set left boundary condition if(leftBound_ == Lau1DCubicSpline::Natural) { b_[0] = 2./(x_[1]-x_[0]); c_[0] = 1./(x_[1]-x_[0]); d_[0] = 3.*(y_[1]-y_[0])/((x_[1]-x_[0])*(x_[1]-x_[0])); } else if(leftBound_ == Lau1DCubicSpline::NotAKnot) { // define the width, h, and the 'slope', delta, of the first cell Double_t h1(x_[1]-x_[0]), h2(x_[2]-x_[0]); Double_t delta1((y_[1]-y_[0])/h1), delta2((y_[2]-y_[1])/h2); // these coefficients can be determined by requiring f'''_0(x_1) = f'''_1(x_1) // the requirement f''_0(x_1) = f''_1(x_1) has been used to remove the dependence on k_2 b_[0] = h2; c_[0] = h1+h2; d_[0] = delta1*(2.*h2*h2 + 3.*h1*h2)/(h1+h2) + delta2*5.*h1*h1/(h1+h2); } else { //Clamped b_[0] = 1.; c_[0] = 0.; d_[0] = dydx0_; } // set right boundary condition if(rightBound_ == Lau1DCubicSpline::Natural) { a_[nKnots_-1] = 1./(x_[nKnots_-1]-x_[nKnots_-2]); b_[nKnots_-1] = 2./(x_[nKnots_-1]-x_[nKnots_-2]); d_[nKnots_-1] = 3.*(y_[nKnots_-1]-y_[nKnots_-2])/((x_[nKnots_-1]-x_[nKnots_-2])*(x_[nKnots_-1]-x_[nKnots_-2])); } else if(rightBound_ == Lau1DCubicSpline::NotAKnot) { // define the width, h, and the 'slope', delta, of the last cell Double_t hnm1(x_[nKnots_-1]-x_[nKnots_-2]), hnm2(x_[nKnots_-2]-x_[nKnots_-3]); Double_t deltanm1((y_[nKnots_-1]-y_[nKnots_-2])/hnm1), deltanm2((y_[nKnots_-2]-y_[nKnots_-3])/hnm2); // these coefficients can be determined by requiring f'''_n-3(x_n-2) = f'''_n-2(x_n-2) // the requirement f''_n-3(x_n-2) = f''_n-2(x_n-2) has been used to remove // the dependence on k_n-3 a_[nKnots_-1] = hnm2 + hnm1; b_[nKnots_-1] = hnm1; d_[nKnots_-1] = deltanm2*hnm1*hnm1/(hnm2+hnm1) + deltanm1*(2.*hnm2*hnm2 + 3.*hnm2*hnm1)/(hnm2+hnm1); } else { //Clamped a_[nKnots_-1] = 0.; b_[nKnots_-1] = 1.; d_[nKnots_-1] = dydxn_; } // the remaining equations ensure that f_i-1''(x_i) = f''_i(x_i) for all internal knots - for(UInt_t i=1; i=0; --i) { + for(int i {static_cast(nKnots_-2)}; i>=0; --i) { dydx_[i] = d_[i] - c_[i]*dydx_[i+1]; } } void Lau1DCubicSpline::calcDerivativesAkima() { //derivatives are calculated according to the Akima method // J.ACM vol. 17 no. 4 pp 589-602 Double_t am1(0.), an(0.), anp1(0.); // a[i] is the slope of the segment from point i-1 to point i // // n.b. segment 0 is before point 0 and segment n is after point n-1 // internal segments are numbered 1 - n-1 - for(UInt_t i=1; i