TF1Convolution.cxx

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// @(#)root/hist:$Id$
// Authors: Lorenzo Moneta, Aurélie Flandi  27/08/14
//
/**********************************************************************
 *                                                                    *
 * Copyright (c) 2015  ROOT  Team, CERN/PH-SFT                        *
 *                                                                    *
 *                                                                    *
 **********************************************************************/
 
#include <memory>
 
#include "TF1Convolution.h"
#include "TROOT.h"
#include "TObject.h"
#include "TObjString.h"
#include "TObjArray.h"
#include "TMath.h"
#include "Math/Integrator.h"
#include "Math/IntegratorMultiDim.h"
#include "Math/IntegratorOptions.h"
#include "Math/GaussIntegrator.h"
#include "Math/GaussLegendreIntegrator.h"
#include "Math/AdaptiveIntegratorMultiDim.h"
#include "Math/Functor.h"
#include "TVirtualFFT.h"
 
/** \class TF1Convolution
    \ingroup Functions
    \brief Class wrapping convolution of two functions
 
Class wrapping convolution of two functions: evaluation of \f$\int f(x)g(x-t)dx\f$
 
The convolution is performed by default using FFTW if it is available .
One can pass optionally the range of the convolution (by default the first function range is used).
Note that when using Discrete Fourier Transform (as FFTW), it is a circular transform, so the functions should be
approximately zero at the end of the range. If they are significantly different than zero on one side (e.g. the left side)
a spill over will occur on the other side (e.g right side).
If no function range is given by default the function1 range + 10% is used
One should use also a not too small number of points for the DFT (a minimum of 1000).  By default 10000 points are used.
*/
 
 
Double_t TF1Convolution::fgExtraRangeFraction = 0.1;
 
class TF1Convolution_EvalWrapper
{
   TF1 *  fFunc1;
   TF1 *  fFunc2;
   Double_t fT0;
 
public:
   TF1Convolution_EvalWrapper(TF1 &f1, TF1 &f2, Double_t t) :
      fFunc1(&f1),
      fFunc2(&f2),
      fT0(t)
   {}
   Double_t operator()(Double_t x) const
   {
      // use EvalPar that is faster
      Double_t xx[2];
      xx[0] = x;
      xx[1] = fT0-x;
      return fFunc1->EvalPar(xx,nullptr) * fFunc2->EvalPar(xx+1,nullptr);
   }
};
 
////////////////////////////////////////////////////////////////////////////////
/// Internal function to initialize data members.
/// Use TF1::Copy instead of Clone.
 
void TF1Convolution::InitializeDataMembers(TF1* function1, TF1* function2, Bool_t useFFT)
{
   if (function1) {
      // functions must be 1d- if not flag an error
      if (function1->GetNdim() != 1)
         Error("InitializeDataMembers","function1 %s is not of dimension 1 ",function1->GetName());
      //TF1 * fnew1 = (TF1*) function1->IsA()->New();
      // since function1 is a TF1 (cannot be a derived class) we can instantiate it directly
      fFunction1 = std::make_unique<TF1> ();
      function1->Copy(*fFunction1);
   }
   if (function2) {
       if (function2->GetNdim() != 1)
         Error("InitializeDataMembers","function2 %s is not of dimension 1 ",function2->GetName());
      //TF1 * fnew2 = (TF1*) function2->IsA()->New();
      fFunction2 = std::make_unique<TF1>();
      function2->Copy(*fFunction2);
   }
   if (fFunction1 == nullptr|| fFunction2 == nullptr)
      Fatal("InitializeDataMembers","Invalid functions - Abort");
 
   // Set kNotGlobal bit
   fFunction1->SetBit(TF1::kNotGlobal, kTRUE);
   fFunction2->SetBit(TF1::kNotGlobal, kTRUE);
 
   // use by default range of first function
   fFunction1->GetRange(fXmin, fXmax);
   // when using FFT add by default an extra 10% on  each side
   if (useFFT) {
      SetExtraRange(fgExtraRangeFraction);
   }
   fNofParams1 = fFunction1->GetNpar();
   fNofParams2 = fFunction2->GetNpar();
   fParams1    = std::vector<Double_t>(fNofParams1);
   fParams2    = std::vector<Double_t>(fNofParams2);
   fCstIndex = (fFunction1->GetParNumber("Constant") == -1)
                  ? -1
                  : fFunction2->GetParNumber("Constant"); // TODO: add dropConstantParam flag?
   fFlagFFT    = useFFT;
   fFlagGraph  = false;
   fNofPoints  = 10000;
 
   fParNames.reserve( fNofParams1 + fNofParams2);
   for (int i=0; i<fNofParams1; i++)
   {
      fParams1[i] = fFunction1 -> GetParameter(i);
      fParNames.push_back(fFunction1 -> GetParName(i) );
   }
   for (int i=0; i<fNofParams2; i++)
   {
      fParams2[i] = fFunction2 -> GetParameter(i);
      if (i != fCstIndex) fParNames.push_back(fFunction2 -> GetParName(i) );
   }
   if (fCstIndex!=-1)
   {
      fFunction2  -> FixParameter(fCstIndex,1.);
      fNofParams2 =  fNofParams2-1;
      fParams2.erase(fParams2.begin()+fCstIndex);
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// constructor without arguments.
 
TF1Convolution::TF1Convolution()
{
   // Nothing to do
}
 
////////////////////////////////////////////////////////////////////////////////
/// constructor from the two function pointer and a flag is using FFT.
 
TF1Convolution::TF1Convolution(TF1* function1, TF1* function2, Bool_t useFFT)
{
   InitializeDataMembers(function1,function2, useFFT);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Constructor from the two function pointer and the convolution range.
 
TF1Convolution::TF1Convolution(TF1* function1, TF1* function2, Double_t xmin, Double_t xmax, Bool_t useFFT)
{
   InitializeDataMembers(function1, function2,useFFT);
   if (xmin < xmax) {
      fXmin      = xmin;
      fXmax      = xmax;
      if (useFFT) SetExtraRange(fgExtraRangeFraction);
   } else {
      Info("TF1Convolution", "Using default range [-inf, inf] for TF1Convolution");
      SetRange(-TMath::Infinity(), TMath::Infinity());
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Constructor from a formula expression as f1 * f2 where f1 and f2 are two functions known to ROOT.
 
TF1Convolution::TF1Convolution(TString formula,  Double_t xmin, Double_t xmax, Bool_t useFFT)
{
   TF1::InitStandardFunctions();
 
   TObjArray *objarray   = formula.Tokenize("*");
   std::vector < TString > stringarray(2);
   std::vector < TF1*    > funcarray(2);
   for (int i=0; i<2; i++)
   {
      stringarray[i] = ((TObjString*)((*objarray)[i])) -> GetString();
      stringarray[i].ReplaceAll(" ","");
      funcarray[i]   = (TF1*)(gROOT -> GetListOfFunctions() -> FindObject(stringarray[i]));
      // case function is not found try to use as a TFormula
      if (funcarray[i] == nullptr) {
         TF1 * f = new TF1(TString::Format("f_conv_%d",i+1),stringarray[i]);
         if (!f->GetFormula()->IsValid() )
            Error("TF1Convolution","Invalid formula : %s",stringarray[i].Data() );
         if (i == 0)
            fFunction1 = std::unique_ptr<TF1>(f);
         else
            fFunction2 = std::unique_ptr<TF1>(f);
      }
   }
   InitializeDataMembers(funcarray[0], funcarray[1],useFFT);
   if (xmin < xmax) {
      fXmin      = xmin;
      fXmax      = xmax;
      if (useFFT) SetExtraRange(fgExtraRangeFraction);
   } else {
      Info("TF1Convolution", "Using default range [-inf, inf] for TF1Convolution");
      SetRange(-TMath::Infinity(), TMath::Infinity());
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Constructor from 2 function names where f1 and f2 are two functions known to
/// ROOT.
///
/// If the function names are not known to ROOT, tries to interpret them as
/// TFormula.
TF1Convolution::TF1Convolution(TString formula1, TString formula2,  Double_t xmin, Double_t xmax, Bool_t useFFT)
{
   TF1::InitStandardFunctions();
   (TString)formula1.ReplaceAll(" ","");
   (TString)formula2.ReplaceAll(" ","");
   TF1* f1 = (TF1*)(gROOT -> GetListOfFunctions() -> FindObject(formula1));
   TF1* f2 = (TF1*)(gROOT -> GetListOfFunctions() -> FindObject(formula2));
   // if function do not exists try using TFormula
   if (!f1) {
      fFunction1 = std::make_unique<TF1>("f_conv_1", formula1);
      if (!fFunction1->GetFormula()->IsValid() )
         Error("TF1Convolution","Invalid formula for : %s",formula1.Data() );
   }
   if (!f2) {
      fFunction2 = std::make_unique<TF1>("f_conv_1", formula2);
      if (!fFunction2->GetFormula()->IsValid() )
         Error("TF1Convolution","Invalid formula for : %s",formula2.Data() );
   }
   // if f1 or f2 are null ptr are not used in InitializeDataMembers
   InitializeDataMembers(f1, f2,useFFT);
   if (xmin < xmax) {
      fXmin      = xmin;
      fXmax      = xmax;
   } else {
      Info("TF1Convolution", "Using default range [-inf, inf] for TF1Convolution");
      SetRange(-TMath::Infinity(), TMath::Infinity());
   }
}
 
////////////////////////////////////////////////////////////////////////////////
/// Copy constructor (necessary to hold unique_ptr as member variable).
 
TF1Convolution::TF1Convolution(const TF1Convolution &conv)
{
   conv.TF1Convolution::Copy(*this);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Operator =
 
TF1Convolution &TF1Convolution::operator=(const TF1Convolution &rhs)
{
   if (this != &rhs)
      rhs.TF1Convolution::Copy(*this);
   return *this;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Perform the FFT of the two functions.
 
void TF1Convolution::MakeFFTConv()
{
   if (gDebug)
      Info("MakeFFTConv","Making FFT convolution using %d points in range [%g,%g]",fNofPoints,fXmin,fXmax);
 
   std::vector < Double_t > x  (fNofPoints);
   std::vector < Double_t > in1(fNofPoints);
   std::vector < Double_t > in2(fNofPoints);
 
   TVirtualFFT *fft1 = TVirtualFFT::FFT(1, &fNofPoints, "R2C K");
   TVirtualFFT *fft2 = TVirtualFFT::FFT(1, &fNofPoints, "R2C K");
   if (fft1 == nullptr || fft2 == nullptr) {
      Warning("MakeFFTConv","Cannot use FFT, probably FFTW package is not available. Switch to numerical convolution");
      fFlagFFT = false;
      return;
   }
 
   // apply a shift in order to have the second function centered around middle of the range of the convolution
   Double_t shift2 = 0.5*(fXmin+fXmax);
   Double_t x2;
   for (int i=0; i<fNofPoints; i++)
   {
      x[i]   = fXmin + (fXmax-fXmin)/(fNofPoints-1)*i;
      x2     = x[i] - shift2;
      in1[i] = fFunction1 -> EvalPar( &x[i], nullptr);
      in2[i] = fFunction2 -> EvalPar( &x2, nullptr);
      fft1  -> SetPoint(i, in1[i]);
      fft2  -> SetPoint(i, in2[i]);
   }
   fft1 -> Transform();
   fft2 -> Transform();
 
   //inverse transformation of the product
 
   TVirtualFFT *fftinverse = TVirtualFFT::FFT(1, &fNofPoints, "C2R K");
   Double_t re1, re2, im1, im2, out_re, out_im;
 
   for (int i=0;i<=fNofPoints/2.;i++)
   {
      fft1 -> GetPointComplex(i,re1,im1);
      fft2 -> GetPointComplex(i,re2,im2);
      out_re = re1*re2 - im1*im2;
      out_im = re1*im2 + re2*im1;
      fftinverse -> SetPoint(i, out_re, out_im);
   }
   fftinverse -> Transform();
 
   // fill a graph with the result of the convolution
   if (!fGraphConv)
      fGraphConv = std::make_unique<TGraph>(fNofPoints);
 
   for (int i=0;i<fNofPoints;i++)
   {
      // we need this since we have applied a shift in the middle of f2
      int j = i + fNofPoints/2;
      if (j >= fNofPoints) j -= fNofPoints;
      // need to normalize by dividing by the number of points and multiply by the bin width = Range/Number of points
      fGraphConv->SetPoint(i, x[i], fftinverse->GetPointReal(j)*(fXmax-fXmin)/(fNofPoints*fNofPoints) );
   }
   fGraphConv->SetBit(TGraph::kIsSortedX); // indicate that points are sorted in X to speed up TGraph::Eval
   fFlagGraph = true; // we can use the graph
 
   // delete the fft objects
   delete fft1;
   delete fft2;
   delete fftinverse;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Perform FFT convolution.
 
Double_t TF1Convolution::EvalFFTConv(Double_t t)
{
   if (!fFlagGraph) {
      MakeFFTConv();
   }
   // if cannot make FFT use numconv
   if (fGraphConv)
      return  fGraphConv -> Eval(t);
   else
 
      return EvalNumConv(t);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Perform numerical convolution.
///
 
Double_t TF1Convolution::EvalNumConv(Double_t t)
{
   /// Could in principle cache the integral  in a Graph as it is done for the FFTW
   TF1Convolution_EvalWrapper fconv( *fFunction1, *fFunction2, t);
   Double_t result = 0;
 
   ROOT::Math::IntegratorOneDim integrator(fconv, ROOT::Math::IntegratorOneDimOptions::DefaultIntegratorType(), 1e-9, 1e-9);
   if      (fXmin != - TMath::Infinity() && fXmax != TMath::Infinity() )
      result =  integrator.Integral(fXmin, fXmax);
   else if (fXmin == - TMath::Infinity() && fXmax != TMath::Infinity() )
      result = integrator.IntegralLow(fXmax);
   else if (fXmin != - TMath::Infinity() && fXmax == TMath::Infinity() )
      result = integrator.IntegralUp(fXmin);
   else if (fXmin == - TMath::Infinity() && fXmax == TMath::Infinity() )
      result = integrator.Integral();
 
   return result;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Used in TF1 when doing the fit, will be evaluated at each point.
 
Double_t TF1Convolution::operator()(const Double_t *x, const Double_t *p)
{
   if (p!=nullptr)   TF1Convolution::SetParameters(p);                           // first refresh the parameters
 
   Double_t result = 0.;
   if (fFlagFFT)
      result = EvalFFTConv(x[0]);
   else
      result = EvalNumConv(x[0]);
   return result;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set the number of points used for the FFT convolution.
 
void TF1Convolution::SetNofPointsFFT(Int_t n)
{
   if (n<0) return;
   fNofPoints = n;
   if (fGraphConv) fGraphConv -> Set(fNofPoints);
   fFlagGraph = false; // to indicate we need to re-do the graph
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set the vector of parameters p for the convolution function g(x,p) = f1 * f2.
 
void TF1Convolution::SetParameters(const Double_t *params)
{
   bool equalParams = true;
   for (int i=0; i<fNofParams1; i++) {
      fFunction1->SetParameter(i, params[i]);
      equalParams &= (fParams1[i] == params[i]);
      fParams1[i] = params[i];
   }
   Int_t k       = 0;
   Int_t offset  = 0;
   Int_t offset2 = 0;
   if (fCstIndex!=-1)   offset = 1;
   Int_t totalnofparams = fNofParams1+fNofParams2+offset;
   for (int i=fNofParams1; i<totalnofparams; i++)   {
      if (k==fCstIndex)
      {
         k++;
         offset2=1;
         continue;
      }
      fFunction2->SetParameter(k, params[i - offset2]);
      equalParams &= (fParams2[k - offset2] == params[i - offset2]);
      fParams2[k - offset2] = params[i - offset2];
      k++;
   }
 
   if (!equalParams) fFlagGraph = false; // to indicate we need to re-do the convolution
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set the parameter values for the convolution function.
 
void TF1Convolution::SetParameters(Double_t p0, Double_t p1, Double_t p2, Double_t p3,
                                   Double_t p4, Double_t p5, Double_t p6, Double_t p7)
{
   Double_t params[]={p0,p1,p2,p3,p4,p5,p6,p7};
   TF1Convolution::SetParameters(params);
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set the fraction of extra range used when doing an convolution.
/// The extra range is often needed to avoid mirroring effect of the resulting convolution
/// function at the borders.
/// By default an extra range of 0.1 is used when doing FFT and it is not use for numerical convolution
 
void TF1Convolution::SetExtraRange(Double_t percentage)
{
   if (percentage<0) return;
   double range = fXmax - fXmin;
   fXmin -= percentage * range;
   fXmax += percentage * range;
   fFlagGraph = false;  // to indicate we need to re-do the convolution
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set the actual range used for the convolution.
/// In case  a or b are -inf or +inf and FFT convolution is used, then the
/// range of the first function will be used and extended by the default extra range fraction.
 
void TF1Convolution::SetRange(Double_t a, Double_t b)
{
   if (a >= b) {
      Warning("SetRange", "Invalid range: %f >= %f", a, b);
      return;
   }
 
   fXmin = a;
   fXmax = b;
   if (fFlagFFT && ( a==-TMath::Infinity() || b==TMath::Infinity() ) )
   {
      Warning("TF1Convolution::SetRange()","In FFT mode, range can not be infinite. Infinity has been replaced by range of first function plus a bufferzone to avoid spillover.");
      if (a ==-TMath::Infinity()) fXmin = fFunction1 -> GetXmin();
      if ( b== TMath::Infinity()) fXmax = fFunction1 -> GetXmax();
      // add a spill over of 10% in this case
      SetExtraRange(fgExtraRangeFraction);
   }
   fFlagGraph = false;  // to indicate we need to re-do the convolution
}
 
////////////////////////////////////////////////////////////////////////////////
/// Set the default extra range fraction used when doing a FFT convolution.
/// By default the value is 0.1 (10%).
/// The function return the previous default defined value.
 
Double_t TF1Convolution::SetDefaultExtraRange(Double_t fraction)
{
   Double_t prevValue = fgExtraRangeFraction;
   fgExtraRangeFraction = fraction;
   return prevValue;
}
 
////////////////////////////////////////////////////////////////////////////////
/// Get the range used for the convolution.
 
void TF1Convolution::GetRange(Double_t &a, Double_t &b) const
{
   a = fXmin;
   b = fXmax;
}
 
////////////////////////////////////////////////////////////////////////////////
///   Update the two component functions of the convolution.
 
void TF1Convolution::Update()
{
   fFunction1->Update();
   fFunction2->Update();
}
 
////////////////////////////////////////////////////////////////////////////////
 
void TF1Convolution::Copy(TObject &obj) const
{
   // copy numbers
   ((TF1Convolution &)obj).fXmin = fXmin;
   ((TF1Convolution &)obj).fXmax = fXmax;
   ((TF1Convolution &)obj).fNofParams1 = fNofParams1;
   ((TF1Convolution &)obj).fNofParams2 = fNofParams2;
   ((TF1Convolution &)obj).fCstIndex = fCstIndex;
   ((TF1Convolution &)obj).fNofPoints = fNofPoints;
   ((TF1Convolution &)obj).fFlagFFT = fFlagFFT;
   ((TF1Convolution &)obj).fFlagGraph = false; // since we're not copying the graph
 
   // copy vectors
   ((TF1Convolution &)obj).fParams1 = fParams1;
   ((TF1Convolution &)obj).fParams2 = fParams2;
   ((TF1Convolution &)obj).fParNames = fParNames;
 
   // we need to copy the content of the  unique_ptr's
   ((TF1Convolution &)obj).fFunction1 = std::make_unique<TF1>();
   ((TF1Convolution &)obj).fFunction2 = std::make_unique<TF1>();
   fFunction1->Copy(*(((TF1Convolution &)obj).fFunction1));
   fFunction2->Copy(*(((TF1Convolution &)obj).fFunction2));
   // fGraphConv is transient anyway, so we don't bother to copy it
}