#include "TH1D.h"
#include "TVirtualFFT.h"
#include "TF1.h"
#include "TCanvas.h"

void FFT()
{
//This tutorial illustrates the Fast Fourier Transforms interface in ROOT.
//FFT transform types provided in ROOT:
// - "C2CFORWARD" - a complex input/output discrete Fourier transform (DFT) 
//                  in one or more dimensions, -1 in the exponent
// - "C2CBACKWARD"- a complex input/output discrete Fourier transform (DFT) 
//                  in one or more dimensions, +1 in the exponent
// - "R2C"        - a real-input/complex-output discrete Fourier transform (DFT)
//                  in one or more dimensions,
// - "C2R"        - inverse transforms to "R2C", taking complex input 
//                  (storing the non-redundant half of a logically Hermitian array) 
//                  to real output
// - "R2HC"       - a real-input DFT with output in ¡Èhalfcomplex¡É format, 
//                  i.e. real and imaginary parts for a transform of size n stored as
//                  r0, r1, r2, ..., rn/2, i(n+1)/2-1, ..., i2, i1
// - "HC2R"       - computes the reverse of FFTW_R2HC, above
// - "DHT"        - computes a discrete Hartley transform
// Sine/cosine transforms:
//  DCT-I  (REDFT00 in FFTW3 notation)
//  DCT-II (REDFT10 in FFTW3 notation)
//  DCT-III(REDFT01 in FFTW3 notation)
//  DCT-IV (REDFT11 in FFTW3 notation)
//  DST-I  (RODFT00 in FFTW3 notation)
//  DST-II (RODFT10 in FFTW3 notation)
//  DST-III(RODFT01 in FFTW3 notation)
//  DST-IV (RODFT11 in FFTW3 notation)
//First part of the tutorial shows how to transform the histograms
//Second part shows how to transform the data arrays directly


//********* Histograms ********//

   //prepare the canvas for drawing
   TCanvas *myc = new TCanvas("myc", "Fast Fourier Transform", 800, 600);
   myc->SetFillColor(45);
   TPad *c1_1 = new TPad("c1_1", "c1_1",0.01,0.51,0.49,0.99);
   TPad *c1_2 = new TPad("c1_2", "c1_2",0.51,0.51,0.99,0.99);
   TPad *c1_3 = new TPad("c1_3", "c1_3",0.01,0.01,0.49,0.49);
   TPad *c1_4 = new TPad("c1_4", "c1_4",0.51,0.01,0.99,0.49);
   c1_1->Draw();
   c1_2->Draw();
   c1_3->Draw();
   c1_4->Draw();
   c1_1->SetFillColor(30);
   c1_1->SetFrameFillColor(42);
   c1_2->SetFillColor(30);
   c1_2->SetFrameFillColor(42);
   c1_3->SetFillColor(30);
   c1_3->SetFrameFillColor(42);
   c1_4->SetFillColor(30);
   c1_4->SetFrameFillColor(42);
   c1_1->cd();

   //A function to sample
   TF1 *fsin = new TF1("fsin", "sin(x)+sin(2*x)+sin(0.5*x)+1", 0, 4*TMath::Pi());
   fsin->Draw();
   Int_t n=25;
   TH1D *hsin = new TH1D("hsin", "hsin", n+1, 0, 4*TMath::Pi());
   Double_t x;
   //Fill the histogram with function values
   for (Int_t i=0; i<=n; i++){
      x = (Double_t(i)/n)*(4*TMath::Pi());
      hsin->SetBinContent(i+1, fsin->Eval(x));
   }
   hsin->Draw("same");
   fsin->GetXaxis()->SetLabelSize(0.05);
   fsin->GetYaxis()->SetLabelSize(0.05);
   c1_2->cd();
   //Compute the transform and look at the magnitude of the output
   TH1 *hm =0;
   hm = hsin->FFT(hm, "MAG");
   hm->Draw();
   hm->SetStats(kFALSE);
   hm->GetXaxis()->SetLabelSize(0.05);
   hm->GetYaxis()->SetLabelSize(0.05);
   c1_3->cd();
   //Look at the phase of the output
   TH1 *hp = 0;
   hp = hsin->FFT(hp, "PH");
   hp->Draw();
   hp->SetStats(kFALSE);
   hp->GetXaxis()->SetLabelSize(0.05);
   hp->GetYaxis()->SetLabelSize(0.05);
   //Look at the DC component and the Nyquist harmonic:
   TVirtualFFT *fft = TVirtualFFT::GetCurrentTransform();
   Double_t re, im;
   fft->GetPointComplex(0, re, im);
   printf("1st transform: DC component: %f\n", re);
   fft->GetPointComplex(n/2+1, re, im);
   printf("1st transform: Nyquist harmonic: %f\n", re);

//********* Data array - same transform ********//

   //Allocate an array big enough to hold the transform output
   //Transform output in 1d contains, for a transform of size N, 
   //N/2+1 complex numbers, i.e. 2*(N/2+1) real numbers
   //our transform is of size n+1, because the histogram has n+1 bins

   Double_t *in = new Double_t[2*((n+1)/2+1)];
   for (Int_t i=0; i<=n; i++){
      x = (Double_t(i)/n)*(4*TMath::Pi());
      in[i] =  fsin->Eval(x);
   }

   //Make our own TVirtualFFT object (using option "K")
   //Third parameter (option) consists of 3 parts:
   //-transform type:
   // real input/complex output in our case
   //-transform flag: 
   // the amount of time spent in planning
   // the transform (see TVirtualFFT class description)
   //-to create a new TVirtualFFT object (option "K") or use the global (default)
   Int_t n_size = n+1;
   TVirtualFFT *fft_own = TVirtualFFT::FFT(1, &n_size, "R2C ES K");
   fft_own->SetPoints(in);
   fft_own->Transform();

   //Copy all the output points:
   fft_own->GetPoints(in);
   //Draw the real part of the output
   c1_4->cd();
   TH1 *hr = 0;
   hr = TH1::TransformHisto(fft_own, hr, "RE");
   hr->Draw();
   hr->SetStats(kFALSE);
   hr->GetXaxis()->SetLabelSize(0.05);
   hr->GetYaxis()->SetLabelSize(0.05);
   myc->cd();
   //Now let's make another transform of the same size
   //The same transform object can be used, as the size and the type of the transform
   //haven't changed
   TF1 *fcos = new TF1("fcos", "cos(x)+cos(0.5*x)+cos(2*x)+1", 0, 4*TMath::Pi());
   for (Int_t i=0; i<=n; i++){
      x = (Double_t(i)/n)*(4*TMath::Pi());
      in[i] =  fcos->Eval(x);
   }
   fft_own->SetPoints(in);
   fft_own->Transform();
   fft_own->GetPointComplex(0, re, im);
   printf("2nd transform: DC component: %f\n", re);
   fft_own->GetPointComplex(n/2+1, re, im);
   printf("2nd transform: Nyquist harmonic: %f\n", re);
   delete fft_own;



}