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Project: ROOT
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Kernel: ROOT (

ROOT in CoCalc

This uses the "ROOT" kernel, and shows some randomly picked examples from

TCanvas *c1 = new TCanvas("c1","test",600,700);
TLatex l; l.SetTextAlign(12); l.SetTextSize(0.04); l.DrawLatex(0.1,0.9,"1) C(x) = d #sqrt{#frac{2}{#lambdaD}}\ #int^{x}_{0}cos(#frac{#pi}{2}t^{2})dt"); l.DrawLatex(0.1,0.7,"2) C(x) = d #sqrt{#frac{2}{#lambdaD}}\ #int^{x}cos(#frac{#pi}{2}t^{2})dt"); l.DrawLatex(0.1,0.5,"3) R = |A|^{2} = #frac{1}{2}#left(#[]{#frac{1}{2}+\ C(V)}^{2}+#[]{#frac{1}{2}+S(V)}^{2}#right)"); l.DrawLatex(0.1,0.3, "4) F(t) = #sum_{i=-#infty}^{#infty}A(i)cos#[]{#frac{i}{t+i}}"); l.DrawLatex(0.1,0.1,"5) {}_{3}^{7}Li"); c1->Print("");
Info in <TCanvas::Print>: ps file has been created
Image in a Jupyter notebook
TCanvas * CPol = new TCanvas("CPol","TGraphPolar Examples",1200,600); CPol->Divide(2,1); CPol->cd(1); Double_t xmin=0; Double_t xmax=TMath::Pi()*2; Double_t x[1000]; Double_t y[1000]; Double_t xval1[20]; Double_t yval1[20]; TF1 * fplot = new TF1("fplot","cos(2*x)*cos(20*x)",xmin,xmax); for (Int_t ipt = 0; ipt < 1000; ipt++){ x[ipt] = ipt*(xmax-xmin)/1000+xmin; y[ipt] = fplot->Eval(x[ipt]); } TGraphPolar * grP = new TGraphPolar(1000,x,y); grP->SetLineColor(2); grP->SetLineWidth(2); grP->SetFillStyle(3012); grP->SetFillColor(2); grP->Draw("AFL"); for (Int_t ipt = 0; ipt < 20; ipt++){ xval1[ipt] = x[1000/20*ipt]; yval1[ipt] = y[1000/20*ipt]; } TGraphPolar * grP1 = new TGraphPolar(20,xval1,yval1); grP1->SetMarkerStyle(29); grP1->SetMarkerSize(2); grP1->SetMarkerColor(4); grP1->SetLineColor(4); grP1->Draw("CP");
CPol->Update(); grP1->GetPolargram()->SetTextColor(8); grP1->GetPolargram()->SetRangePolar(-TMath::Pi(),TMath::Pi()); grP1->GetPolargram()->SetNdivPolar(703); grP1->GetPolargram()->SetToRadian(); CPol->cd(2); Double_t x2[30]; Double_t y2[30]; Double_t ex[30]; Double_t ey[30]; for (Int_t ipt = 0; ipt < 30; ipt++){ x2[ipt] = x[1000/30*ipt]; y2[ipt] = 1.2 + 0.4*sin(TMath::Pi()*2*ipt/30); ex[ipt] = 0.2+0.1*cos(2*TMath::Pi()/30*ipt); ey[ipt] = 0.2; } TGraphPolar * grPE = new TGraphPolar(30,x2,y2,ex,ey); grPE->SetMarkerStyle(22); grPE->SetMarkerSize(1.5); grPE->SetMarkerColor(5); grPE->SetLineColor(6); grPE->SetLineWidth(2); grPE->Draw("EP"); CPol->Update(); grPE->GetPolargram()->SetTextSize(0.03); grPE->GetPolargram()->SetTwoPi(); grPE->GetPolargram()->SetToRadian();
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#include "TH1D.h" #include "TVirtualFFT.h" #include "TF1.h" #include "TCanvas.h" #include "TMath.h"
void FFT() { // 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",0.01,0.67,0.49,0.99); TPad *c1_2 = new TPad("c1_2", "c1_2",0.51,0.67,0.99,0.99); TPad *c1_3 = new TPad("c1_3", "c1_3",0.01,0.34,0.49,0.65); TPad *c1_4 = new TPad("c1_4", "c1_4",0.51,0.34,0.99,0.65); TPad *c1_5 = new TPad("c1_5", "c1_5",0.01,0.01,0.49,0.32); TPad *c1_6 = new TPad("c1_6", "c1_6",0.51,0.01,0.99,0.32); c1_1->Draw(); c1_2->Draw(); c1_3->Draw(); c1_4->Draw(); c1_5->Draw(); c1_6->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_5->SetFillColor(30); c1_5->SetFrameFillColor(42); c1_6->SetFillColor(30); c1_6->SetFrameFillColor(42); c1_1->cd(); TH1::AddDirectory(kFALSE); //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; TVirtualFFT::SetTransform(0); hm = hsin->FFT(hm, "MAG"); hm->SetTitle("Magnitude of the 1st transform"); hm->Draw(); //NOTE: for "real" frequencies you have to divide the x-axes range with the range of your function //(in this case 4*Pi); y-axes has to be rescaled by a factor of 1/SQRT(n) to be right: this is not done automatically! 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->SetTitle("Phase of the 1st transform"); hp->Draw(); hp->SetStats(kFALSE); hp->GetXaxis()->SetLabelSize(0.05); hp->GetYaxis()->SetLabelSize(0.05); //Look at the DC component and the Nyquist harmonic: Double_t re, im; //That's the way to get the current transform object: TVirtualFFT *fft = TVirtualFFT::GetCurrentTransform(); c1_4->cd(); //Use the following method to get just one point of the output 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); //Use the following method to get the full output: Double_t *re_full = new Double_t[n]; Double_t *im_full = new Double_t[n]; fft->GetPointsComplex(re_full,im_full); //Now let's make a backward transform: TVirtualFFT *fft_back = TVirtualFFT::FFT(1, &n, "C2R M K"); fft_back->SetPointsComplex(re_full,im_full); fft_back->Transform(); TH1 *hb = 0; //Let's look at the output hb = TH1::TransformHisto(fft_back,hb,"Re"); hb->SetTitle("The backward transform result"); hb->Draw(); //NOTE: here you get at the x-axes number of bins and not real values //(in this case 25 bins has to be rescaled to a range between 0 and 4*Pi; //also here the y-axes has to be rescaled (factor 1/bins) hb->SetStats(kFALSE); hb->GetXaxis()->SetLabelSize(0.05); hb->GetYaxis()->SetLabelSize(0.05); delete fft_back; fft_back=0; // 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)]; Double_t re_2,im_2; 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"); if (!fft_own) return; fft_own->SetPoints(in); fft_own->Transform(); //Copy all the output points: fft_own->GetPoints(in); //Draw the real part of the output c1_5->cd(); TH1 *hr = 0; hr = TH1::TransformHisto(fft_own, hr, "RE"); hr->SetTitle("Real part of the 3rd (array) tranfsorm"); hr->Draw(); hr->SetStats(kFALSE); hr->GetXaxis()->SetLabelSize(0.05); hr->GetYaxis()->SetLabelSize(0.05); c1_6->cd(); TH1 *him = 0; him = TH1::TransformHisto(fft_own, him, "IM"); him->SetTitle("Im. part of the 3rd (array) transform"); him->Draw(); him->SetStats(kFALSE); him->GetXaxis()->SetLabelSize(0.05); him->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_2, im_2); printf("2nd transform: DC component: %f\n", re_2); fft_own->GetPointComplex(n/2+1, re_2, im_2); printf("2nd transform: Nyquist harmonic: %f\n", re_2); delete fft_own; delete [] in; delete [] re_full; delete [] im_full; }
1st transform: DC component: 26.000000 1st transform: Nyquist harmonic: -0.932840 2nd transform: DC component: 29.000000 2nd transform: Nyquist harmonic: -0.000000
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