2.2.1 图表

图表的概念

最基本的数据可视化方法是使用由两个（TGraph）或三个（TGraph2D）数组组成的坐标表示数据的大小或位置，称作 Graph 。这与直方图（Histogram）不同。

ROOT 提供了许多图形类，如TGraph图表，TGraphErrors具有对称误差线的图表，TGraph2D由三个数组 X、Y 和 Z 组成的图表等。

图表的使用

TGraph支持批量创建和运算，TGraph的创建方法是：

// 创建了一个名字是name，标题是title，有n个坐标为x,y的点：
TGraph *gr = new TGraph("name", "title", number, x, y)
TGraph* gr = new TGraph("name", "title", number, x, y)
TGraph *gr = new TGraph(number, x, y)
auto gr = new TGraph(number, x, y)
auto gr = new TGraph()    // 使用AddPoint()函数添加坐标点
auto dt = new TGraph2D()    // 二维图表，其他形式同理

绘制图表前需要先定义坐标数组，然后使用TGraph构造图形。E.g. 

   int n = 20;
   double x[n], y[n];
   for (int i=0; i<n; i++) {
      x[i] = i*0.1;
      y[i] = 10*sin(x[i]+0.2);
   }
   auto gr = new TGraph (n, x, y);

也支持使用AddPoint()函数添加点：

auto gr = new TGraph();
for (int i=0; i<20; i++) gr->AddPoint(i*0.1, 10*sin(i*0.1+0.2));

使用TGraph::Draw()绘制图形，且有多种绘图选项可选：

   auto gr = new TGraph();
   for (int i=0; i<20; i++) gr->AddPoint(i*0.1, 10*sin(i*0.1+0.2));
   gr->Draw();

从文件中读取数据

数据的保存格式有很多，常见的是文本格式和 root 格式：

  • 文本格式数据绘制 Graph

这里要求文件中的坐标中间是空格或者制表符，不可以是逗号。E.g.

int directdata(){
    TGraph *gr = new TGraph("mydata.txt");
    gr->Draw("AC*");    // 绘出 axis，坐标点以 curve 链接，坐标点形状为 * 型
}

从图表中读取数据

  • 数组模式

double *px = gr->GetX(); 将gr1图像中点数据以数组形式输出。

  • 指针模式

ToggleEventStatus()是 canvas 的成员函数。用于展示指针处的数据状态，打开后，指针所在位置的数据信息会被呈现在面板下方。

  • 高亮模式

高亮模式适用于TGraph（和TH1）类。 当高亮模式打开时，鼠标在点上的移动将以图形表示。 点将突出显示为“点圆”（由标记对象表示）。 此外，任何高亮显示（点变化）都会发出信号TCanvas::Highlighted()，允许用户做出反应并调用自己的函数。 为了更好地理解，请参阅教程$ROOTSYS/tutorials/graphs/hlGraph*.C 文件。

属性设置

图表的轴、标题、颜色均可以进行设置，参考章节：

2.3 属性设置

绘图选项

使用以下选项绘制图表，在Draw()命令中它们不区分大小写，可不间隔的使用多个参数如Draw("APL")和Draw("A p l")，均表示绘制包涵坐标轴和坐标点的图，并用直线相连：

Option
Description

"A"

绘制出坐标轴

"I"

Combine with option 'A' it draws invisible axis

"L"

在点之间使用直线相连，最终呈现的效果是折线

"F"

绘制填充区域（“CF”绘制平滑填充区域）

"C"

绘制平滑曲线

"*"

每数据点以星号显示

"P"

绘制出每个 marker

"B"

绘制柱状图/条形图/直方图

"1"

当使用柱状图B时，使柱状图从底部开始，否则从0开始

"X+"

X轴在上

"Y+"

Y轴在右

"PFC"

调色板填充颜色：图表的填充颜色取自当前调色板中

"PLC"

调色板线条颜色：图形的线条颜色取自当前调色板中

"PMC"

调色板标记颜色：图表的标记颜色取自当前调色板中

"RX"

X轴刻度反转

"RY"

Y轴刻度反转

"HIST"

以histogram格式绘制/亦或称作阶梯图

E.g. X轴在上Y轴反转和自动取色
void graphpalettecolor () {
 
   gStyle->SetOptTitle(kFALSE);
   gStyle->SetPalette(kSolar);
 
   double x[5]  = {1,2,3,4,5};
   double y1[5] = {1.0,2.0,1.0,2.5,3.0};
   double y2[5] = {1.1,2.1,1.1,2.6,3.1};
   double y3[5] = {1.2,2.2,1.2,2.7,3.2};
   double y4[5] = {1.3,2.3,1.3,2.8,3.3};
   double y5[5] = {1.4,2.4,1.4,2.9,3.4};
 
   TGraph *g1 = new TGraph(5,x,y1); g1->SetTitle("Graph with a red star");
   TGraph *g2 = new TGraph(5,x,y2); g2->SetTitle("Graph with a circular marker");
   TGraph *g3 = new TGraph(5,x,y3); g3->SetTitle("Graph with an open square marker");
   TGraph *g4 = new TGraph(5,x,y4); g4->SetTitle("Graph with a blue star");
   TGraph *g5 = new TGraph(5,x,y5); g5->SetTitle("Graph with a full square marker");
 
   g1->SetLineWidth(3); g1->SetMarkerColor(kRed);
   g2->SetLineWidth(3); g2->SetMarkerStyle(kCircle);
   g3->SetLineWidth(3); g3->SetMarkerStyle(kOpenSquare);
   g4->SetLineWidth(3); g4->SetMarkerColor(kBlue);
   g5->SetLineWidth(3); g5->SetMarkerStyle(kFullSquare);
 
   g1->Draw("CA*x+ry PLC PFC");
   g2->Draw("PCx+ry  PLC PFC");
   g3->Draw("PC  PLC PFC");
   g4->Draw("*C  PLC PFC");
   g5->Draw("PC  PLC PFC");
 
   gPad->BuildLegend();
}
X轴在上Y轴反转和自动取色

成果保存

将分析成果保存并反复展示。root 格式支持保存数据，也支持保存分析图片，而且图片保存为 root 格式后还可以反复打开并进行进一步的美化工作，十分便捷。

Save()

SaveAs()函数，支持

Write()函数

Print()

E.g. 将多个画布与图片连续保存到一个 PDF 文件中
{
   TCanvas* canvas = new TCanvas("canvas");
   TH1F* histo = new TH1F("histo","test 1",10,0.,10.);
   histo->SetFillColor(2);
   histo->Fill(2.);
   histo->Draw();
   canvas->Print("plots.pdf(","Title:One bin filled");
   histo->Fill(4.);
   histo->Draw();
   canvas->Print("plots.pdf","Title:Two bins filled");
   histo->Fill(6.);
   histo->Draw();
   canvas->Print("plots.pdf","Title:Three bins filled");
   histo->Fill(8.);
   histo->Draw();
   canvas->Print("plots.pdf","Title:Four bins filled");
   histo->Fill(8.);
   histo->Draw();
   canvas->Print("plots.pdf)","Title:The fourth bin content is 2");
}

误差与拟合

2.2.5 误差与拟合

二维图表

使用符合标准的数据可以绘制二维图表。E.g.

{
   auto c = new TCanvas("c","Graph2D example",0,0,700,600);   // 画布距离左上角的距离(0,0)
   double x, y, z, P = 6.;
   int np = 200;
   auto dt = new TGraph2D();
   auto r  = new TRandom();
   for (int N=0; N<np; N++) {
      x = 2*P*(r->Rndm(N))-P;
      y = 2*P*(r->Rndm(N))-P;
      z = (sin(x)/x)*(sin(y)/y)+0.2;
      dt->SetPoint(N,x,y,z);
   }
   dt->Draw("tri1 p0");
}
二维图表

绘图选项

Option
Description

"TRI"

The Delaunay triangles are drawn using filled area. An hidden surface drawing technique is used. The surface is painted with the current fill area color. The edges of each triangles are painted with the current line color.

"TRIW"

The Delaunay triangles are drawn as wire frame.

"TRI1"

The Delaunay triangles are painted with color levels. The edges of each triangles are painted with the current line color.

"TRI2"

The Delaunay triangles are painted with color levels.

"P"

Draw a marker at each vertex.

"P0"

Draw a circle at each vertex. Each circle background is white.

"PCOL"

Draw a marker at each vertex. The color of each marker is defined according to its Z position.

"LINE"

Draw a 3D polyline.

"CONT5"

Draw a contour plot using Delaunay triangles.

极坐标 TGraphPolar

极坐标TGraphPolar()的绘图选项有：

Option
Description

"O"

极坐标标签与极坐标图半径正交绘制。

"P"

在每个点位置绘制多标记。

"E"

绘出误差棒

"F"

绘制填充区域（闭合多边形）

"A"

即使极坐标图已经存在，也强制重绘轴

"N"

禁止显示极坐标标签

E.g. 极坐标例子
{
   auto c46 = new TCanvas("c46","c46",500,500);
   auto grP1 = new TGraphPolar();
   grP1->SetTitle("TGraphPolar example");
 
   grP1->SetPoint(0, (1*TMath::Pi())/4., 0.05);
   grP1->SetPoint(1, (2*TMath::Pi())/4., 0.10);
   grP1->SetPoint(2, (3*TMath::Pi())/4., 0.15);
   grP1->SetPoint(3, (4*TMath::Pi())/4., 0.20);
   grP1->SetPoint(4, (5*TMath::Pi())/4., 0.25);
   grP1->SetPoint(5, (6*TMath::Pi())/4., 0.30);
   grP1->SetPoint(6, (7*TMath::Pi())/4., 0.35);
   grP1->SetPoint(7, (8*TMath::Pi())/4., 0.40);
 
   grP1->SetMarkerStyle(20);
   grP1->SetMarkerSize(1.);
   grP1->SetMarkerColor(4);
   grP1->SetLineColor(4);
   grP1->Draw("ALP");
 
   // Update, otherwise GetPolargram returns 0
   c46->Update();
   grP1->GetPolargram()->SetToRadian();
}
极坐标例子

饼状图 TPie

多图绘法

root 支持在一张 canvas 上绘制多幅图表或者直方图。

独立绘制

使用TCanvas::Divide()函数将 Canvas 分割为不同的 Pad，例如将名为 c1 的 canvas 分为 2 列 3 行写作：c1->Divide(2,3)，然后使用c1->cd()分别控制不同的 pad，pad 的名称从左向右，从上至下分别是1，2，……，例如可以在 pad1 上绘制 histogram，在 pad2 上绘制 graph。

共轴绘制

最简单的共轴画法是在TCanvas::Divide()函数中添加参数，例如c1->Divide(2,3,0)，但当要进行一些美化工作的时候，就会发现它们的标题大小，marker 大小不再能通过统一的数值控制，这非常影响美观。

所以这里有一个稍微复杂的解决方法，能够使它们的大小保持一致，仅供参考：

CanvasPartition https://root.cern.ch/doc/master/canvas2_8C.html
 
void CanvasPartition(TCanvas *C,const Int_t Nx = 2,const Int_t Ny = 2,
                     Float_t lMargin = 0.15, Float_t rMargin = 0.05,
                     Float_t bMargin = 0.15, Float_t tMargin = 0.05);
double XtoPad(double x);
double YtoPad(double x);
 
void canvas2()
{
   gStyle->SetOptStat(0);
 
   auto C = (TCanvas*) gROOT->FindObject("C");
   if (C) delete C;
   C = new TCanvas("C","canvas",1024,640);
   C->SetFillStyle(4000);
 
   // Number of PADS
   const Int_t Nx = 5;
   const Int_t Ny = 5;
 
   // Margins
   Float_t lMargin = 0.12;
   Float_t rMargin = 0.05;
   Float_t bMargin = 0.15;
   Float_t tMargin = 0.05;
 
   // Canvas setup
   CanvasPartition(C,Nx,Ny,lMargin,rMargin,bMargin,tMargin);
 
   // Dummy histogram.
   auto h = (TH1F*) gROOT->FindObject("histo");
   if (h) delete h;
   h = new TH1F("histo","",100,-5.0,5.0);
   h->FillRandom("gaus",10000);
   h->GetXaxis()->SetTitle("x axis");
   h->GetYaxis()->SetTitle("y axis");
 
   TPad *pad[Nx][Ny];
 
   for (Int_t i = 0; i < Nx; i++) {
      for (Int_t j = 0; j < Ny; j++) {
         C->cd(0);
 
         // Get the pads previously created.
         pad[i][j] = (TPad*) C->FindObject(TString::Format("pad_%d_%d",i,j).Data());
         pad[i][j]->Draw();
         pad[i][j]->SetFillStyle(4000);
         pad[i][j]->SetFrameFillStyle(4000);
         pad[i][j]->cd();
 
         // Size factors
         Float_t xFactor = pad[0][0]->GetAbsWNDC()/pad[i][j]->GetAbsWNDC();
         Float_t yFactor = pad[0][0]->GetAbsHNDC()/pad[i][j]->GetAbsHNDC();
 
         TH1F *hFrame = (TH1F*) h->Clone(TString::Format("h_%d_%d",i,j).Data());
 
         // y axis range
         hFrame->SetMinimum(0.0001); // do not show 0
         hFrame->SetMaximum(1.2*h->GetMaximum());
 
         // Format for y axis
         hFrame->GetYaxis()->SetLabelFont(43);
         hFrame->GetYaxis()->SetLabelSize(16);
         hFrame->GetYaxis()->SetLabelOffset(0.02);
         hFrame->GetYaxis()->SetTitleFont(43);
         hFrame->GetYaxis()->SetTitleSize(16);
         hFrame->GetYaxis()->SetTitleOffset(2);
 
         hFrame->GetYaxis()->CenterTitle();
         hFrame->GetYaxis()->SetNdivisions(505);
 
         // TICKS Y Axis
         hFrame->GetYaxis()->SetTickLength(xFactor*0.04/yFactor);
 
         // Format for x axis
         hFrame->GetXaxis()->SetLabelFont(43);
         hFrame->GetXaxis()->SetLabelSize(16);
         hFrame->GetXaxis()->SetLabelOffset(0.02);
         hFrame->GetXaxis()->SetTitleFont(43);
         hFrame->GetXaxis()->SetTitleSize(16);
         hFrame->GetXaxis()->SetTitleOffset(1);
         hFrame->GetXaxis()->CenterTitle();
         hFrame->GetXaxis()->SetNdivisions(505);
 
         // TICKS X Axis
         hFrame->GetXaxis()->SetTickLength(yFactor*0.06/xFactor);
 
         // Draw cloned histogram with individual settings
         hFrame->Draw();
 
         TText text;
         text.SetTextAlign(31);
         text.SetTextFont(43);
         text.SetTextSize(10);
         text.DrawTextNDC(XtoPad(0.9), YtoPad(0.8), gPad->GetName());
      }
   }
   C->cd();
}
 
 
 
void CanvasPartition(TCanvas *C,const Int_t Nx,const Int_t Ny,
                     Float_t lMargin, Float_t rMargin,
                     Float_t bMargin, Float_t tMargin)
{
   if (!C) return;
 
   // Setup Pad layout:
   Float_t vSpacing = 0.0;
   Float_t vStep  = (1.- bMargin - tMargin - (Ny-1) * vSpacing) / Ny;
 
   Float_t hSpacing = 0.0;
   Float_t hStep  = (1.- lMargin - rMargin - (Nx-1) * hSpacing) / Nx;
 
   Float_t vposd,vposu,vmard,vmaru,vfactor;
   Float_t hposl,hposr,hmarl,hmarr,hfactor;
 
   for (Int_t i=0;i<Nx;i++) {
 
      if (i==0) {
         hposl = 0.0;
         hposr = lMargin + hStep;
         hfactor = hposr-hposl;
         hmarl = lMargin / hfactor;
         hmarr = 0.0;
      } else if (i == Nx-1) {
         hposl = hposr + hSpacing;
         hposr = hposl + hStep + rMargin;
         hfactor = hposr-hposl;
         hmarl = 0.0;
         hmarr = rMargin / (hposr-hposl);
      } else {
         hposl = hposr + hSpacing;
         hposr = hposl + hStep;
         hfactor = hposr-hposl;
         hmarl = 0.0;
         hmarr = 0.0;
      }
 
      for (Int_t j=0;j<Ny;j++) {
 
         if (j==0) {
            vposd = 0.0;
            vposu = bMargin + vStep;
            vfactor = vposu-vposd;
            vmard = bMargin / vfactor;
            vmaru = 0.0;
         } else if (j == Ny-1) {
            vposd = vposu + vSpacing;
            vposu = vposd + vStep + tMargin;
            vfactor = vposu-vposd;
            vmard = 0.0;
            vmaru = tMargin / (vposu-vposd);
         } else {
            vposd = vposu + vSpacing;
            vposu = vposd + vStep;
            vfactor = vposu-vposd;
            vmard = 0.0;
            vmaru = 0.0;
         }
 
         C->cd(0);
 
         auto name = TString::Format("pad_%d_%d",i,j);
         auto pad = (TPad*) C->FindObject(name.Data());
         if (pad) delete pad;
         pad = new TPad(name.Data(),"",hposl,vposd,hposr,vposu);
         pad->SetLeftMargin(hmarl);
         pad->SetRightMargin(hmarr);
         pad->SetBottomMargin(vmard);
         pad->SetTopMargin(vmaru);
 
         pad->SetFrameBorderMode(0);
         pad->SetBorderMode(0);
         pad->SetBorderSize(0);
 
         pad->Draw();
      }
   }
}
 
double XtoPad(double x)
{
   double xl,yl,xu,yu;
   gPad->GetPadPar(xl,yl,xu,yu);
   double pw = xu-xl;
   double lm = gPad->GetLeftMargin();
   double rm = gPad->GetRightMargin();
   double fw = pw-pw*lm-pw*rm;
   return (x*fw+pw*lm)/pw;
}
 
double YtoPad(double y)
{
   double xl,yl,xu,yu;
   gPad->GetPadPar(xl,yl,xu,yu);
   double ph = yu-yl;
   double tm = gPad->GetTopMargin();
   double bm = gPad->GetBottomMargin();
   double fh = ph-ph*bm-ph*tm;
   return (y*fh+bm*ph)/ph;
}
CanvasPartition

重叠绘制

将多个 graph 绘制在一张 pad 上，只需要在TGraph::Draw()函数中使用same参数即可。

合并绘制

TMultiGraph::TMultiGraph()，函数支持将一组图作为单个实体进行操作。且绘制时 X 轴和 Y 轴范围会自动计算，因此所有图形都将可见。TMultiGraph::Add()用于将新图表添加到列表中。E.g.

TGraph *gr1 = new TGraph(...
TGraphErrors *gr2 = new TGraphErrors(...
TMultiGraph *mg = new TMultiGraph();
mg->Add(gr1,"lp");
mg->Add(gr2,"cp");
mg->Draw("a");

标题、颜色、统计信息均可使用TMultiGraph类中的成员函数，用法与 graph 一致。

单个 graph 通过mg->GetListOfGraphs()->GetEntries();方式检索。

多页绘制

将graph保存到多页PDF中。

{
    TCanvas* canvas = new TCanvas ("canvas") ;
    TH1F* histo = new THIF("histo"c, "test 1", 10, 0., 10.) ;
    histo->SetFillColor (2); histo->Fil1(2.); histo->Draw();
    canvas->Print("plots.pdf(","Title:One bin filled"); histo->Fi11(4.); histo->Draw();
    canvas->Print "plots.pdf", "Title:Two bins filled"); histo->Fi11(6.);
    histo->Draw();
    canvas->Print ("plots.pdf", "Title: Three bins filled");
    histo->Fill (8.);
    histo->Draw();
    canvas->Print("plots.pdf", "Title:Four bins filled");
    histo->Fi11(8.);
    histo->Draw():
    canvas->Print ("plots.pdf)", "Title:The fourth bin content is 2");
}

图例

TLegend

参考

https://root.cern/doc/master/classTGaxis.html

https://root.cern/doc/master/classTGraphPainter.html

https://root.cern.ch/doc/master/classTHistPainter.html

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