# Graphs # In this Chapter we will learn how to exploit some of the functionalities that ROOT provides to display data exploiting the class `TGraphErrors`, which you already got to know previously. ## Read Graph Points from File ## The fastest way in which you can fill a graph with experimental data is to use the constructor which reads data points and their errors from a file in ASCII (i.e. standard text) format: ``` {.cpp} TGraphErrors(const char *filename, const char *format="%lg %lg %lg %lg", Option_t *option=""); ``` The format string can be: - `"\%lg \%lg"` read only 2 first columns into X,Y - `"\%lg \%lg \%lg"` read only 3 first columns into X,Y and EY - `"\%lg \%lg \%lg \%lg"` read only 4 first columns into X,Y,EX,EY This approach has the nice feature of allowing the user to reuse the macro for many different data sets. Here is an example of an input file. The nice graphic result shown is produced by the macro below, which reads two such input files and uses different options to display the data points. ``` # Measurement of Friday 26 March # Experiment 2 Physics Lab 1 6 5 2 12 5 3 14 4.7 4 20 4.5 5 22 4.2 6 24 5.1 7 35 2.9 8 45 4.1 9 44 4.8 10 53 5.43 ``` ![](figures/graph_with_expectation.png) ``` {.cpp} // Reads the points from a file and produces a simple graph. int macro2(){ TCanvas* c=new TCanvas(); c->SetGrid(); TGraphErrors graph_expected("./macro2_input_expected.txt", "%lg %lg %lg"); graph_expected.SetTitle( "Measurement XYZ and Expectation; lenght [cm]; Arb.Units"); graph_expected.SetFillColor(kYellow); graph_expected.DrawClone("E3AL"); // E3 draws the band TGraphErrors graph("./macro2_input.txt","%lg %lg %lg"); graph.SetMarkerStyle(kCircle); graph.SetFillColor(0); graph.DrawClone("PESame"); // Draw the Legend TLegend leg(.1,.7,.3,.9,"Lab. Lesson 2"); leg.SetFillColor(0); leg.AddEntry(&graph_expected,"Expected Points"); leg.AddEntry(&graph,"Measured Points"); leg.DrawClone("Same"); graph.Print(); } ``` In addition to the inspection of the plot, you can check the actual contents of the graph with the `TGraph::Print()` method at any time, obtaining a printout of the coordinates of data points on screen. The macro also shows us how to print a coloured band around a graph instead of error bars, quite useful for example to represent the errors of a theoretical prediction. ## Polar Graphs ## With ROOT you can profit from rather advanced plotting routines, like the ones implemented in the `TPolarGraph`, a class to draw graphs in polar coordinates. It is very easy to use, as you see in the example macro and the resulting Figure [4.1](#f41): ``` {.cpp .numberLines} // Builds a polar graph in a square Canvas. void macro3(){ TCanvas* c = new TCanvas("myCanvas","myCanvas",600,600); double rmin=0; double rmax=TMath::Pi()*6; const int npoints=1000; Double_t r[npoints]; Double_t theta[npoints]; for (Int_t ipt = 0; ipt < npoints; ipt++) { r[ipt] = ipt*(rmax-rmin)/npoints+rmin; theta[ipt] = TMath::Sin(r[ipt]); } TGraphPolar grP1 (npoints,r,theta); grP1.SetTitle("A Fan"); grP1.SetLineWidth(3); grP1.SetLineColor(2); grP1.DrawClone("AOL"); } ``` A new element was added on line 4, the size of the canvas: it is sometimes optically better to show plots in specific canvas sizes. [f41]: figures/polar_graph.png "f41" ![The graph of a fan obtained with ROOT.\label{f41}][f41] ## 2D Graphs ## Under specific circumstances, it might be useful to plot some quantities versus two variables, therefore creating a bi-dimensional graph. Of course ROOT can help you in this task, with the `TGraph2DErrors` class. The following macro produces a bi-dimensional graph representing a hypothetical measurement, fits a bi-dimensional function to it and draws it together with its x and y projections. Some points of the code will be explained in detail. This time, the graph is populated with data points using random numbers, introducing a new and very important ingredient, the ROOT `TRandom3` random number generator using the Mersenne Twister algorithm [@MersenneTwister]. ``` {.cpp .numberLines} // Create, Draw and fit a TGraph2DErrors void macro4(){ gStyle->SetPalette(1); const double e = 0.3; const int nd = 500; TRandom3 my_random_generator; TF2 *f2 = new TF2("f2", "1000*(([0]*sin(x)/x)*([1]*sin(y)/y))+200", -6,6,-6,6); f2->SetParameters(1,1); TGraph2DErrors *dte = new TGraph2DErrors(nd); // Fill the 2D graph double rnd, x, y, z, ex, ey, ez; for (Int_t i=0; iGetRandom2(x,y); // A random number in [-e,e] rnd = my_random_generator.Uniform(-e,e); z = f2->Eval(x,y)*(1+rnd); dte->SetPoint(i,x,y,z); ex = 0.05*my_random_generator.Uniform(); ey = 0.05*my_random_generator.Uniform(); ez = TMath::Abs(z*rnd); dte->SetPointError(i,ex,ey,ez); } // Fit function to generated data f2->SetParameters(0.7,1.5); // set initial values for fit f2->SetTitle("Fitted 2D function"); dte->Fit(f2); // Plot the result TCanvas *c1 = new TCanvas(); f2->Draw("Surf1"); dte->Draw("P0 Same"); // Make the x and y projections TCanvas* c_p= new TCanvas("ProjCan", "The Projections",1000,400); c_p->Divide(2,1); c_p->cd(1); dte->Project("x")->Draw(); c_p->cd(2); dte->Project("y")->Draw(); } ``` Let's go through the code, step by step to understand what is going on: - Line *3*: This sets the palette colour code to a much nicer one than the default. Comment this line to give it a try. - Line *7*: The instance of the random generator. You can then draw out of this instance random numbers distributed according to different probability density functions, like the Uniform one at lines *27-29*. See the on-line documentation to appreciate the full power of this ROOT feature. - Line *12*: You are already familiar with the `TF1` class. This is its two-dimensional correspondent. At line *24* two random numbers distributed according to the `TF2` formula are drawn with the method `TF2::GetRandom2(double& a, double&b)`. - Line *27-29*: Fitting a 2-dimensional function just works like in the one-dimensional case, i.e. initialisation of parameters and calling of the `Fit()` method. - Line *32*: The *Surf1* option draws the `TF2` objects (but also bi-dimensional histograms) as coloured surfaces with a wire-frame on three-dimensional canvases. See Figure [4.2](#f42). - Line *37-41*: Here you learn how to create a canvas, partition it in two sub-pads and access them. It is very handy to show multiple plots in the same window or image. [f42]: figures/fitted2dFunction.png "f42" ![A dataset fitted with a bidimensional function visualised as a colored surface.\label{f42}][f42]