ROOTUsers Guide A4

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User’s Guide
May 2014

2

Contents
Preface

21

1 Introduction

23

1.1

The ROOT Mailing Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

1.2

Contact Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23

1.3

Conventions Used in This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

1.4

The Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

1.4.1

What Is a Framework? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

24

1.4.2

Why Object-Oriented? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

1.5

Installing ROOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

25

1.6

The Organization of the ROOT Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

1.6.1

$ROOTSYS/bin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

1.6.2

$ROOTSYS/lib . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

1.6.3

$ROOTSYS/tutorials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30

1.6.4

$ROOTSYS/test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

1.6.5

$ROOTSYS/include . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

1.6.6

$ROOTSYS/ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

How to Find More Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31

1.7.1

31

1.7

Class Reference Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Getting Started

33

2.1

Setting the Environment Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33

2.2

Start and Quit a ROOT Session

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34

2.3

Using the GUI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

2.3.1

Main Menus and Toolbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

2.3.2

The Editor Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

2.3.3

Classes, Methods and Constructors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40

2.3.4

User Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42

2.3.5

Building a Multi-pad Canvas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

42

2.3.6

Saving the Canvas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

2.3.7

Printing the Canvas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

The ROOT Command Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

2.4.1

Multi-line Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

45

2.4.2

Cling Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

2.4.3

Helpful Hints for Command Line Typing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

2.4

3

4

CONTENTS
2.4.4
2.5

2.6

2.7

2.8

Regular Expression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

46

Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

2.5.1

Coding Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47

2.5.2

Machine Independent Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

2.5.3

TObject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

Global Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

48

2.6.1

gROOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

2.6.2

gFile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

2.6.3

gDirectory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

2.6.4

gPad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

2.6.5

gRandom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

49

2.6.6

gEnv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

Environment Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

2.7.1

Logon and Logoff Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

2.7.2

History File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

2.7.3

Tracking Memory Leaks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

2.7.4

Memory Checker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

51

Converting from PAW to ROOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52

2.8.1

52

Converting HBOOK/PAW Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Histograms

53

3.1

The Histogram Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

3.2

Creating Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53

3.2.1

Constant or Variable Bin Width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

54

Bin Numbering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

3.3.1

Convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

3.3.2

Re-binning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

Filling Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

55

3.4.1

Automatic Re-binning Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

3.5

Random Numbers and Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

3.6

Adding, Dividing, and Multiplying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

3.7

Projections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

3.8

Drawing Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

3.8.1

Setting the Style . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

3.8.2

Draw Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

3.8.3

Drawing a Sub-range of a 2-D Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

75

3.8.4

Superimposing Histograms with Different Scales . . . . . . . . . . . . . . . . . . . . . . . . . .

75

3.8.5

Statistics Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

3.8.6

Setting Line, Fill, Marker, and Text Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . .

77

3.8.7

Setting Tick Marks on the Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

3.8.8

Giving Titles to the X, Y and Z Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

Making a Copy of an Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

3.10 Normalizing Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

3.3

3.4

3.9

CONTENTS

5

3.11 Saving/Reading Histograms to/from a File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

3.12 Miscellaneous Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

79

3.13 Alphanumeric Bin Labels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

3.13.1 Option 1: SetBinLabel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

80

3.13.2 Option 2: Fill . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

3.13.3 Option 3: TTree::Draw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

3.13.4 Sort Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

81

3.14 Histogram Stacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

82

3.15 TH2Poly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

3.16 Profile Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

83

3.16.1 Build Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

84

3.16.2 Drawing a Profile without Error Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

3.16.3 Create a Profile from a 2D Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

3.16.4 Create a Histogram from a Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

3.16.5 Generating a Profile from a TTree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

86

3.16.6 2D Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

3.17 Iso Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

3.18 3D Implicit Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

3.19 TPie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

88

3.20 The User Interface for Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

3.20.1 TH1Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

3.20.2 TH2Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93

4 Graphs
4.1

97

TGraph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

4.1.1

Graph Draw Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

4.2

Superimposing Two Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

101

4.3

Graphs with Error Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

4.4

Graphs with Asymmetric Error Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

4.5

Graphs with Asymmetric Bent Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.6

TGraphPolar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

4.7

TGraph Exclusion Zone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.8

TGraphQQ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.9

104

107

4.8.1

Two Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.8.2

One Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

TMultiGraph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

4.10 TGraph2D

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

4.11 TGraph2DErrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.12 Fitting a Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.13 Setting the Graph’s Axis Title . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

114

4.14 Zooming a Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

114

4.15 The User Interface for Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

6

CONTENTS

5 Fitting Histograms
5.1

5.2

5.3

The Fit Method

117
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

117

5.1.1

The TH1::Fit Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

117

5.1.2

The TGraph::Fit Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

The TF1 function class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.2.1

Fit with a Predefined Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.2.2

Creating User-Defined Functions (TF1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

Configuring the Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

121

5.3.1

Fixing and Setting Parameters’ Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

121

5.3.2

Fitting Sub Ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

5.3.3

Fitting Multiple Sub Ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

5.3.4

Adding Functions to the List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

5.4

Example of fit: Combining Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

5.5

Result of the fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

124

5.5.1

Associated Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

124

5.5.2

Access to the Fit Parameters and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

5.5.3

Associated Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

5.5.4

Fit Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

5.6

5.7

The Fit Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.6.1

Function Choice and Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

5.6.2

Fitter Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

5.6.3

Draw Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.6.4

Advances Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.6.5

Print Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.6.6

Command Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.6.7

Minimization Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

New ROOT::Fit classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.7.1

Creating the input fit data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

5.7.2

Creating the Fit model

5.7.3

Fit Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

5.7.4

Minimizer Libraries and Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

5.7.5

Performing the Fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.7.6

Fit Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

5.7.7

TFitResult . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

131

134

5.8

The Minimization packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

5.9

MINUIT (Old TMInuit Version) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.9.1

Basic Concepts of Minuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

5.9.2

The Transformation of Limited Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

5.9.3

How to Get the Right Answer from Minuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.9.4

Reliability of Minuit Error Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

137

5.10 Minuit2 Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.11 FUMILI Minimization Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.12 Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

CONTENTS

7

5.12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.12.2 The MLP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.12.3 Learning Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.12.4 Using the Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
5.12.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6 A Little C++

147

6.1

Classes, Methods and Constructors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6.2

Inheritance and Data Encapsulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

6.3

147

6.2.1

Method Overriding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

6.2.2

Data Encapsulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

Creating Objects on the Stack and Heap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

7 The C++ Interpreter Cling

153

7.1

The ROOT Prompt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

7.2

Feeding Sources Files To ROOT: C++ Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
7.2.1

Executing a Script From a Script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

7.2.2

Executing a Script From the Invocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

7.3

C++ Extensions To Ease Scripting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

7.4

ACLiC: Compiling Scripts Into Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

157

7.4.1

Usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

157

7.4.2

Setting the Include Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

7.4.3

Dictionary Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

7.4.4

Intermediate Steps and Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

7.4.5

Moving between Interpreter and Compiler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

7.5

Classes Defined By Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7.6

Inspecting Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

8 Object Ownership

161

165

8.1

Ownership by Current Directory (gDirectory) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165

8.2

Ownership by the Master TROOT Object (gROOT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
8.2.1

The Collection of Specials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

8.2.2

Access to the Collection Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

8.3

Ownership by Other Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

167

8.4

Ownership by the User . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

167

8.4.1

The kCanDelete Bit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

167

8.4.2

The kMustCleanup Bit

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

9 Graphics and the Graphical User Interface

169

9.1

Drawing Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

9.2

Interacting with Graphical Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
9.2.1

Moving, Resizing and Modifying Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

9.2.2

Selecting Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

171

9.2.3

Context Menus: the Right Mouse Button . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

171

8

CONTENTS
9.2.4
9.3

9.4

9.5

9.6

9.7

9.8

Executing Events when a Cursor Passes on Top of an Object . . . . . . . . . . . . . . . . . . . 173

Graphical Containers: Canvas and Pad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

174

9.3.1

The Global Pad: gPad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

9.3.2

The Coordinate Systems of a Pad

9.3.3

Converting between Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

9.3.4

Dividing a Pad into Sub-pads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

9.3.5

Updating the Pad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

9.3.6

Making a Pad Transparent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

9.3.7

Setting the Log Scale

9.3.8

WaitPrimitive method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

181

9.3.9

Locking the Pad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

181

Graphical Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

181

9.4.1

Lines, Arrows and Polylines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

181

9.4.2

Circles and Ellipses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

9.4.3

Rectangles

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

184

9.4.4

Markers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

184

9.4.5

Curly and Wavy Lines for Feynman Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

9.4.6

Text and Latex Mathematical Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9.4.7

Greek Letters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

9.4.8

Mathematical Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

9.4.9

Text in a Pad . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

177

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

187

9.4.10 The TeX Processor TMathText . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

194

Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

194

9.5.1

Axis Title . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

9.5.2

Axis Options and Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

9.5.3

Setting the Number of Divisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

197

9.5.4

Zooming the Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

197

9.5.5

Drawing Axis Independently of Graphs or Histograms . . . . . . . . . . . . . . . . . . . . . . .

197

9.5.6

Orientation of Tick Marks on Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

9.5.7

Labels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

9.5.8

Axis with Time Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

9.5.9

Axis Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

204

Graphical Objects Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
9.6.1

Text Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

9.6.2

Line Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9.6.3

Fill Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

9.6.4

Color and Color Palettes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

211

The Graphics Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
9.7.1

TAxisEditor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215

9.7.2

TPadEditor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

Copy and Paste . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
9.8.1

Using the GUI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

9.8.2

Programmatically . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

CONTENTS
9.9

9

Legends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

9.10 The PostScript Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
9.10.1 Special Characters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
9.10.2 Writing Several Canvases to the Same PostScript File . . . . . . . . . . . . . . . . . . . . . . . 222
9.10.3 The Color Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

224

9.11 The PDF Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

224

9.12 Create or Modify a Style . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
9.13 3D Viewers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

227

9.13.1 Invoking a 3D viewer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

227

9.13.2 The GL Viewer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
9.13.3 The X3D Viewer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
9.13.4 Common 3D Viewer Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
10 Folders and Tasks

243

10.1 Folders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
10.2 Why Use Folders? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
10.3 How to Use Folders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
10.3.1 Creating a Folder Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
10.3.2 Posting Data to a Folder (Producer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
10.3.3 Reading Data from a Folder (Consumer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
10.4 Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

247

10.5 Execute and Debug Tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
11 Input/Output

251

11.1 The Physical Layout of ROOT Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

251

11.1.1 The File Header . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
11.1.2 The Top Directory Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
11.1.3 The Histogram Records . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
11.1.4 The Class Description List (StreamerInfo List) . . . . . . . . . . . . . . . . . . . . . . . . . . .

254

11.1.5 The List of Keys and the List of Free Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
11.1.6 File Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
11.2 The Logical ROOT File: TFile and TKey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
11.2.1 Viewing the Logical File Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
11.2.2 The Current Directory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
11.2.3 Objects in Memory and Objects on Disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259
11.2.4 Saving Histograms to Disk

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

261

11.2.5 Histograms and the Current Directory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
11.2.6 Saving Objects to Disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
11.2.7 Saving Collections to Disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
11.2.8 A TFile Object Going Out of Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

264

11.2.9 Retrieving Objects from Disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

264

11.2.10 Subdirectories and Navigation

264

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11.3 Streamers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

10

CONTENTS
11.3.1 Automatically Generated Streamers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

267

11.3.2 Transient Data Members (//!) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

267

11.3.3 The Pointer to Objects (//->) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
11.3.4 Variable Length Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
11.3.5 Double32_t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
11.3.6 Prevent Splitting (//|| ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
11.3.7 Streamers with Special Additions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
11.3.8 Writing Objects

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270

11.3.9 Ignore Object Streamers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

271

11.3.10 Streaming a TClonesArray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

271

11.4 Pointers and References in Persistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

271

11.4.1 Streaming C++ Pointers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
11.4.2 Motivation for the TRef Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
11.4.3 Using TRef . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
11.4.4 How Does It Work? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
11.4.5 Action on Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

274

11.4.6 Array of TRef . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275
11.5 Schema Evolution

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275

11.5.1 The TStreamerInfo Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 276
11.5.2 The TStreamerElement Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

277

11.5.3 Example: TH1 StreamerInfo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

277

11.5.4 Optimized StreamerInfo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
11.5.5 Automatic Schema Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
11.5.6 Manual Data Model Evolution Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
11.5.7 Manual Schema Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

281

11.5.8 Building Class Definitions with the StreamerInfo . . . . . . . . . . . . . . . . . . . . . . . . . .

281

11.5.9 Example: MakeProject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

281

11.6 Migrating to ROOT 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

284

11.7 Compression and Performance

284

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11.8 Remotely Access to ROOT Files via a rootd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
11.8.1 TNetFile URL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
11.8.2 Remote Authentication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
11.8.3 A Simple Session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
11.8.4 The rootd Daemon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
11.8.5 Starting rootd via inetd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
11.8.6 Command Line Arguments for rootd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
11.9 Reading ROOT Files via Apache Web Server . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

287

11.9.1 Using the General Open Function of TFile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

287

11.10XML Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288

CONTENTS

11

12 Trees

289

12.1 Why Should You Use a Tree? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
12.2 A Simple TTree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
12.3 Show an Entry with TTree::Show . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
12.4 Print the Tree Structure with TTree::Print

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

291

12.5 Scan a Variable the Tree with TTree::Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

291

12.6 The Tree Viewer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

291

12.7 Creating and Saving Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
12.7.1 Creating a Tree from a Folder Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
12.7.2 Tree and TRef Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
12.7.3 Autosave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
12.7.4 Trees with Circular Buffers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
12.7.5 Size of TTree in the File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
12.7.6 User Info Attached to a TTree Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
12.7.7 Indexing a Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
12.8 Branches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
12.9 Adding a Branch to Hold a List of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

297

12.10Adding a TBranch to Hold an Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
12.10.1 Setting the Split-level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
12.10.2 Exempt a Data Member from Splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
12.10.3 Adding a Branch to Hold a TClonesArray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
12.10.4 Identical Branch Names . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
12.11Adding a Branch with a Folder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300
12.12Adding a Branch with a Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

301

12.13Examples for Writing and Reading Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

301

12.14Example 1: A Tree with Simple Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

301

12.14.1 Writing the Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
12.14.2 Viewing the Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
12.14.3 Reading the Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

304

12.15Example 2: A Tree with a C Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
12.15.1 Writing the Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

307

12.15.2 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
12.16Example 3: Adding Friends to Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
12.16.1 Adding a Branch to an Existing Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
12.16.2 TTree::AddFriend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
12.17Example 4: A Tree with an Event Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
12.17.1 The Event Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
12.17.2 The EventHeader Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
12.17.3 The Track Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

314

12.17.4 Writing the Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

314

12.17.5 Reading the Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
12.18Example 5: Import an ASCII File into a TTree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

317

12.19Trees in Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

317

12

CONTENTS
12.20Simple Analysis Using TTree::Draw

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318

12.20.1 Using Selection with TTree:Draw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
12.20.2 Using TCut Objects in TTree::Draw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
12.20.3 Accessing the Histogram in Batch Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
12.20.4 Using Draw Options in TTree::Draw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
12.20.5 Superimposing Two Histograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

321

12.20.6 Setting the Range in TTree::Draw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

321

12.20.7 TTree::Draw Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

321

12.20.8 Multiple variables visualisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
12.20.9 Using TTree::Scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

337

12.20.10TEventList and TEntryList . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
12.20.11Filling a Histogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

341

12.21Using TTree::MakeClass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
12.21.1 Creating a Class with MakeClass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
12.21.2 MyClass.h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

344

12.21.3 MyClass.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
12.21.4 Modifying MyClass::Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345
12.21.5 Loading MyClass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
12.22Using TTree::MakeSelector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

347

12.22.1 Performance Benchmarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
12.23Impact of Compression on I/O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
12.24Chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
12.24.1 TChain::AddFriend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350
13 Math Libraries in ROOT
13.1 MathCore Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

351
351

13.2 MathMore Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
13.3 TMath . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
13.3.1 Numerical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
13.3.2 Elementary Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

354

13.3.3 Statistic Functions Operating on Arrays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

354

13.3.4 Special and Statistical Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

354

13.4 Random Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
13.4.1 TRandom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
13.4.2 TRandom1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
13.4.3 TRandom2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
13.4.4 TRandom3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
13.4.5 Seeding the Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
13.4.6 Examples of Using the Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
13.4.7 Random Number Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
13.4.8 UNURAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

357

13.4.9 Performances of Random Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
13.5 Mathematical Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358

CONTENTS

13

13.5.1 Special Functions in MathCore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 358
13.5.2 Special Functions in MathMore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
13.5.3 Probability Density Functions (PDF)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360

13.5.4 Cumulative Distribution Functions (CDF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

361

13.6 Numerical Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
13.7 ROOT::Math Function interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
13.7.1 One-dimensional Function Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362
13.7.2 Multi-dimensional Function Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
13.7.3 Parametric Function Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
13.7.4 Wrapper Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
13.8 Numerical Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
13.8.1 Integration of One-dimensional Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
13.8.2 One-dimensional Integration Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

371

13.8.3 Multi-dimensional Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
13.9 Function Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

374

13.10Numerical Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

374

13.10.1 One-Dimensional Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
13.10.2 Multi-Dimensional Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
13.11ROOT Finder Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
13.12Generic Vectors for 2, 3 and 4 Dimensions (GenVector) . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
13.12.1 Main Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
13.12.2 Example: 3D Vector Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
13.12.3 Example: 3D Point Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

381

13.12.4 Example: LorentzVector Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382
13.12.5 Example: Vector Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
13.12.6 Example with External Packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

387

13.13Linear Algebra: SMatrix Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
13.13.1 Example: Vector Class (SVector) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388
13.13.2 Example: Matrix Class (SMatrix) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
13.13.3 Example: Matrix and Vector Functions and Operators . . . . . . . . . . . . . . . . . . . . . . . 392
13.13.4 Matrix and Vector Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
13.14ROOT Statistics Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

394

13.14.1 Classes for Computing Limits and Confidence Levels . . . . . . . . . . . . . . . . . . . . . . . .

394

13.14.2 Specialized Classes for Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

394

13.14.3 Multi-variate Analysis Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

394

14 Linear Algebra in ROOT

395

14.1 Overview of Matrix Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
14.2 Matrix Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

397

14.2.1 Accessing Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

397

14.2.2 Setting Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

397

14.3 Creating and Filling a Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
14.4 Matrix Operators and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

14

CONTENTS
14.4.1 Arithmetic Operations between Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
14.4.2 Arithmetic Operations between Matrices and Real Numbers . . . . . . . . . . . . . . . . . . . . 400
14.4.3 Comparisons and Boolean Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
14.4.4 Matrix Norms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
14.4.5 Miscellaneous Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

401

14.5 Matrix Views . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

401

14.5.1 View Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
14.5.2 View Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
14.6 Matrix Decompositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
14.6.1 Tolerances and Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
14.6.2 Condition number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
14.6.3 LU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
14.6.4 Bunch-Kaufman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
14.6.5 Cholesky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

407

14.6.6 QRH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

407

14.6.7 SVD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

407

14.7 Matrix Eigen Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
14.8 Speed Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
15 Adding a Class

411

15.1 The Role of TObject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

411

15.1.1 Introspection, Reflection and Run Time Type Identification . . . . . . . . . . . . . . . . . . . .

411

15.1.2 Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

411

15.1.3 Input/Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
15.1.4 Paint/Draw . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
15.1.5 Clone/DrawClone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
15.1.6 Browse

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412

15.1.7 SavePrimitive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
15.1.8 GetObjectInfo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
15.1.9 IsFolder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
15.1.10 Bit Masks and Unique ID . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
15.2 Motivation

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413

15.2.1 Template Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

414

15.3 The Default Constructor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
15.4 rootcling: The Cling Dictionary Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
15.4.1 Dictionaries for STL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
15.5 Adding a Class with a Shared Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418
15.5.1 The LinkDef.h File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
15.6 genreflex: A Comfortable Interface to rootcling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
15.6.1 The ROOT::Meta::Selection namespace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425
15.7 Adding a Class with ACLiC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

CONTENTS
16 Collection Classes

15
427

16.1 Understanding Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

427

16.1.1 General Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

427

16.1.2 Determining the Class of Contained Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
16.1.3 Types of Collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
16.1.4 Ordered Collections (Sequences) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
16.2 Iterators: Processing a Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
16.3 Foundation Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
16.4 A Collectable Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430
16.5 The TIter Generic Iterator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

431

16.6 The TList Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
16.6.1 Iterating Over a TList . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
16.7 The TObjArray Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433
16.8 TClonesArray An Array of Identical Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

434

16.8.1 The Idea Behind TClonesArray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

434

16.9 Template Containers and STL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
17 Physics Vectors

437

17.1 The Physics Vector Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

437

17.2 TVector3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

437

17.2.1 Declaration / Access to the Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438
17.2.2 Other Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438
17.2.3 Arithmetic / Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
17.2.4 Related Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
17.2.5 Scalar and Vector Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
17.2.6 Angle between Two Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
17.2.7 Rotation around Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
17.2.8 Rotation around a Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
17.2.9 Rotation by TRotation Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
17.2.10 Transformation from Rotated Frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
17.3 TRotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
17.3.1 Declaration, Access, Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
17.3.2 Rotation around Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440
17.3.3 Rotation around Arbitrary Axis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

441

17.3.4 Rotation of Local Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

441

17.3.5 Inverse Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

441

17.3.6 Compound Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

441

17.3.7 Rotation of TVector3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

441

17.4 TLorentzVector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
17.4.1 Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
17.4.2 Access to Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
17.4.3 Vector Components in Non-Cartesian Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . 443
17.4.4 Arithmetic and Comparison Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443

16

CONTENTS
17.4.5 Magnitude/Invariant mass, beta, gamma, scalar product . . . . . . . . . . . . . . . . . . . . . . 443
17.4.6 Lorentz Boost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

444

17.4.7 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

444

17.4.8 Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

444

17.5 TLorentzRotation

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445

17.5.1 Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
17.5.2 Access to the Matrix Components/Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . 445
17.5.3 Transformations of a Lorentz Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
17.5.4 Transformation of a TLorentzVector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446
17.5.5 Physics Vector Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446
18 The Geometry Package

447

18.1 Quick Start: Creating the “world” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

447

18.1.1 Example 1: Creating the World . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

447

18.1.2 Example 2: A Geometrical Hierarchy Look and Feel . . . . . . . . . . . . . . . . . . . . . . . . 448
18.2 Materials and Tracking Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
18.2.1 Elements, Materials and Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
18.2.2 Radionuclides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452
18.2.3 Tracking Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
18.2.4 User Interface for Handling Materials and Media . . . . . . . . . . . . . . . . . . . . . . . . . . 455
18.3 Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
18.3.1 Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
18.3.2 Primitive Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456
18.3.3 Composite Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469
18.3.4 Navigation Methods Performed By Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473
18.3.5 Creating Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

474

18.3.6 Dividing Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
18.3.7 Parametric Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
18.4 Geometry Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
18.4.1 The Volume Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476
18.4.2 Creating and Positioning Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
18.4.3 Geometrical Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

484

18.4.4 Ownership of Geometry Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

487

18.5 Navigation and Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488
18.5.1 TGeoNavigator Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488
18.5.2 Initializing the Starting Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488
18.5.3 Initializing the Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
18.5.4 Initializing the State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
18.5.5 Checking the Current State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
18.5.6 Saving and Restoring the Current State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

491

18.5.7 Navigation Queries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

491

18.5.8 Creating and Visualizing Tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

494

18.6 Checking the Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495

CONTENTS

17

18.6.1 The Overlap Checker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496
18.6.2 Graphical Checking Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
18.7 The Drawing Package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

501

18.7.1 Drawing Volumes and Hierarchies of Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . .

501

18.7.2 Visualization Settings and Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502
18.7.3 Ray Tracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
18.8 Representing Misalignments of the Ideal Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

504

18.8.1 Physical Nodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

504

18.9 Geometry I/O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506
18.9.1 GDML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

507

18.10Navigation Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

507

18.10.1 Finding the State Corresponding to a Location (x,y,z) . . . . . . . . . . . . . . . . . . . . . . .

507

18.10.2 Finding the Distance to Next Crossed Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . 508
18.11Geometry Graphical User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512
18.11.1 Editing a Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512
18.11.2 The Geometry Manager Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
18.11.3 Editing Existing Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516
18.11.4 Creation of New Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
18.11.5 Editing Volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
18.11.6 How to Create a Valid Geometry with Geometry Editors . . . . . . . . . . . . . . . . . . . . . 523
19 Python and Ruby Interfaces

525

19.1 PyROOT Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525
19.1.1 Glue-ing Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525
19.1.2 Access to ROOT from Python . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
19.1.3 Access to Python from ROOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
19.1.4 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

527

19.1.5 Using PyROOT

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

527

19.1.6 Memory Handling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

531

19.1.7 Performance

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532

19.1.8 Use of Python Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532
19.1.9 Working with Trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

534

19.1.10 Using Your Own Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
19.2 How to Use ROOT with Ruby

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536

19.2.1 Building and Installing the Ruby Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20 The Tutorials and Tests

537
539

20.1 $ROOTSYS/tutorials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539
20.2 $ROOTSYS/test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539
20.2.1 Event - An Example of a ROOT Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . 540
20.2.2 stress - Test and Benchmark . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

544

20.2.3 guitest - A Graphical User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546

18

CONTENTS

21 Example Analysis

547

21.1 Explanation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

547

21.2 Script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550
22 Networking

555

22.1 Setting-up a Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555
22.2 Sending Objects over the Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555
22.3 Closing the Connection

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556

22.4 A Server with Multiple Sockets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556
23 Threads

559

23.1 Threads and Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559
23.1.1 Process Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559
23.1.2 Thread Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559
23.1.3 The Initial Thread . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560
23.2 Implementation of Threads in ROOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560
23.2.1 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560
23.2.2 Classes

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560

23.2.3 TThread for Pedestrians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560
23.2.4 TThread in More Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

561

23.3 Advanced TThread: Launching a Method in a Thread . . . . . . . . . . . . . . . . . . . . . . . . . . .

564

23.3.1 Known Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
23.4 The Signals of ROOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565
23.5 Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
24 PROOF: Parallel Processing

569

25 Writing a Graphical User Interface

571

25.1 The ROOT GUI Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

571

25.2 Widgets and Frames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

571

25.3 TVirtualX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572
25.4 A Simple Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572
25.4.1 A Standalone Version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576
25.5 Widgets Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
25.5.1 TGObject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
25.5.2 TGWidget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
25.5.3 TGWindow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579
25.5.4 Frames

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580

25.6 Layout Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582
25.7 Event Processing: Signals and Slots

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

584

25.8 Widgets in Detail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589
25.8.1 Buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 589
25.8.2 Text Entries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592
25.8.3 Number Entries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593

CONTENTS

19

25.8.4 Menus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595
25.8.5 Toolbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596
25.8.6 List Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598
25.8.7 Combo Boxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599
25.8.8 Sliders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 600
25.8.9 Triple Slider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

601

25.8.10 Progress Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

601

25.8.11 Static Widgets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
25.8.12 Status Bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
25.8.13 Splitters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603
25.8.14 TGCanvas, ViewPort and Container . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
25.8.15 Embedded Canvas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
25.9 The ROOT Graphics Editor (GED) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
25.9.1 Object Editors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
25.9.2 Editor Design Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

607

25.10Drag and Drop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608
25.10.1 Drag and Drop Data Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609
25.10.2 Handling Drag and Drop Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609
26 ROOT/Qt Integration Interfaces

611

26.1 Qt-ROOT Implementation of TVirtualX Interface (BNL) . . . . . . . . . . . . . . . . . . . . . . . . .

611

26.1.1 Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

611

26.1.2 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612
26.1.3 TQtWidget Class, Qt Signals / Slots and TCanvas Interface . . . . . . . . . . . . . . . . . . . . 619
26.2 GSI QtROOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

621

26.2.1 Create a New Project in the Designer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623
26.2.2 main() . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623
27 Automatic HTML Documentation

625

27.1 Reference Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625
27.1.1 Product and Module Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626
27.2 Converting Sources (and Other Files) to HTML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626
27.3 Special Documentation Elements: Directives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626
27.3.1 Latex Directive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

627

27.3.2 Macro Directive

627

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

27.4 Customizing HTML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628
27.4.1 Referencing Documentation for other Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . 628
27.4.2 Search Engine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628
27.4.3 ViewCVS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628
27.4.4 Wiki Pages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628
27.5 Tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628

20

CONTENTS

28 Appendix A: Install and Build ROOT

629

28.1 License . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629
28.2 Installing ROOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629
28.3 Choosing a Version . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629
28.4 Installing Precompiled Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629
28.5 Installing the Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630
28.5.1 Installing and Building the Source from a Compressed File . . . . . . . . . . . . . . . . . . . . 630
28.5.2 More Build Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630
28.6 File system.rootrc

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

631

28.6.1 TCanvas Specific Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633
28.6.2 THtml Specific Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

634

28.6.3 GUI Specific Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635
28.6.4 TBrowser Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636
28.6.5 TRint Specific Settings

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636

28.6.6 ACLiC Specific Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

637

28.6.7 PROOF Related Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

637

28.7 Documentation to Download . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

641

Preface
In late 1994, we decided to learn and investigate Object Oriented programming and C++ to better judge the suitability
of these relatively new techniques for scientific programming. We knew that there is no better way to learn a new
programming environment than to use it to write a program that can solve a real problem. After a few weeks, we
had our first histogramming package in C++. A few weeks later we had a rewrite of the same package using the,
at that time, very new template features of C++. Again, a few weeks later we had another rewrite of the package
without templates since we could only compile the version with templates on one single platform using a specific
compiler. Finally, after about four months we had a histogramming package that was faster and more efficient than the
well-known FORTRAN based HBOOK histogramming package. This gave us enough confidence in the new technologies
to decide to continue the development. Thus was born ROOT. Since its first public release at the end of 1995, ROOT
has enjoyed an ever-increasing popularity. Currently it is being used in all major High Energy and Nuclear Physics
laboratories around the world to monitor, to store and to analyse data. In the other sciences as well as the medical and
financial industries, many people are using ROOT. We estimate the current user base to be around several thousand
people. In 1997, Eric Raymond analysed in his paper “The Cathedral and the Bazaar” the development method that
makes Linux such a success. The essence of that method is: “release early, release often and listen to your customers”.
This is precisely how ROOT is being developed. Over the last five years, many of our “customers” became co-developers.
Here we would like to thank our main co-developers and contributors:
Masaharu Goto wrote the C++ interpreter CINT that was an essential part of ROOT before ROOT 6. Despite
being 8 time zones ahead of us, we have the feeling he has been sitting in the room next door since 1995.
Andrei and Mihaela Gheata (Alice collaboration) are co-authors of the ROOT geometry classes and Virtual
Monte-Carlo. They have been working with the ROOT team since 2000.
Olivier Couet, who after a successful development and maintenance of PAW, has joined the ROOT team in 2000 and
has been working on the graphics sub-system.
Ilka Antcheva has been working on the Graphical User Interface classes. She is also responsible for this latest edition
of the Users Guide with a better style, improved index and several new chapters (since 2002).
Bertrand Bellenot has been developing and maintaining the Win32GDK version of ROOT. Bertrand has also many
other contributions like the nice RootShower example (since 2001).
Valeriy Onoutchin has been working on several ROOT packages, in particular the graphics sub-system for Windows
and the GUI Builder (since 2000).
Gerri Ganis has been working on the authentication procedures to be used by the root daemons and the PROOF
system (since 2002).
Maarten Ballintijn (MIT) is one of the main developers of the PROOF sub-system (since 1995).
Valeri Fine (now at BNL) ported ROOT to Windows and contributed largely to the 3-D graphics. He is currently
working on the Qt layer of ROOT (since 1995).
Victor Perevoztchikov (BNL) worked on key elements of the I/O system, in particular the improved support for
STL collections (1997-2001).
Nenad Buncic developed the HTML documentation generation system and integrated the X3D viewer inside ROOT
(1995-1997).
Suzanne Panacek was the author of the first version of this User’s Guide and very active in preparing tutorials and
giving lectures about ROOT (1999-2002).
Axel Naumann has been developing further the HTML Reference Guide and helps in porting ROOT under Windows
(cygwin/gcc implementation) (since 2000).
Anna Kreshuk has developed the Linear Fitter and Robust Fitter classes as well as many functions in TMath, TF1,
TGraph (since 2005).
Richard Maunder has contributed to the GL viewer classes (since 2004).
21

22

CONTENTS

Timur Pocheptsov has contributed to the GL viewer classes and GL in pad classes (since 2004).
Sergei Linev has developed the XML driver and the TSQLFile classes (since 2003).
Stefan Roiser has been contributing to the reflex and cintex packages (since 2005).
Lorenzo Moneta has been contributing the MathCore, MathMore, Smatrix & Minuit2 packages (since 2005).
Wim Lavrijsen is the author of the PyRoot package (since 2004).
Further we would like to thank all the people mentioned in the $ROOTSYS/README/CREDITS file for their contributions,
and finally, everybody who gave comments, reported bugs and provided fixes.
Happy ROOTing!
Rene Brun & Fons Rademakers
Geneva, July 2007

Chapter 1

Introduction
In the mid 1990’s, René Brun and Fons Rademakers had many years of experience developing interactive tools and
simulation packages. They had lead successful projects such as PAW, PIAF, and GEANT, and they knew PAW the
twenty-year-old FORTRAN libraries had reached their limits. Although still very popular, these tools could not scale
up to the challenges offered by the Large Hadron Collider, where the data is a few orders of magnitude larger than
anything seen before.
At the same time, computer science had made leaps of progress especially in the area of Object Oriented Design, and
René and Fons were ready to take advantage of it.
ROOT was developed in the context of the NA49 experiment at CERN. NA49 has generated an impressive amount of
data, around 10 Terabytes per run. This rate provided the ideal environment to develop and test the next generation
data analysis.
ROOT was, and still is, developed in the “Bazaar style”, a term from the book “The Cathedral and the Bazaar” by
Eric S. Raymond. It means a liberal, informal development style that heavily relies on the diverse and deep talent of
the user community. The result is that physicists developed ROOT for themselves; this made it specific, appropriate,
useful, and over time refined and very powerful. The development of ROOT is a continuous conversation between users
and developers with the line between the two blurring at times and the users becoming co-developers.
When it comes to storing and mining large amount of data, physics plows the way with its Terabytes, but other fields
and industry follow close behind as they acquiring more and more data over time. They are ready to use the true and
tested technologies physics has invented. In this way, other fields and industries have found ROOT useful and they
have started to use it also.
In the bazaar view, software is released early and frequently to expose it to thousands of eager co-developers to pound
on, report bugs, and contribute possible fixes. More users find more bugs, because they stress the program in different
ways. By now, after ten years, the age of ROOT is quite mature. Most likely, you will find the features you are looking
for, and if you have found a hole, you are encouraged to participate in the dialog and post your suggestion or even
implementation on roottalk, the ROOT mailing list.

1.1

The ROOT Mailing Lists

The roottalk was the very first active ROOT mailing list. mailing list People can subscribe to it by registering at the
ROOT web site: http://root.cern.ch/root/Registration.phtml. The RootTalk Forum http://root.cern.ch/phpBB3/ has
been gradually replaced this mailing list since September 2003. The RootTalk Forum is a web-based news group with
about 10 discussion sub-units.
If you have a question, it is likely that it has been asked, answered, and stored in the roottalk or RootTalk Forum
archives. Please use the search engine to see if your question has already been answered before sending a mail to the
roottalk list or post a topic in the Forum.
You can browse the roottalk archives at: http://root.cern.ch/root/roottalk/AboutRootTalk.html. You can send your
question without subscribing to: roottalk@cern.ch

1.2

Contact Information

Several authors wrote this book and you may see a “change of voice” from one chapter to the next. We felt we could
accept this in order to have the expert explain what they know best. If you would like to contribute a chapter or
23

24

CHAPTER 1. INTRODUCTION

add to a section, please contact rootdoc@cern.ch. We count on you to send us suggestions on additional topics or on
the topics that need more documentation. Please send your comments, corrections, questions, and suggestions to the
rootdoc list: rootdoc@cern.ch
We attempt to give the user insight into the many capabilities of ROOT. The book begins with the elementary
functionality and progresses in complexity reaching the specialized topics at the end. The experienced user looking for
special topics may find these chapters useful: see “Networking”, “Writing a Graphical User Interface”, “Threads”, and
“PROOF: Parallel Processing”.

1.3

Conventions Used in This Book

We tried to follow a style convention for the sake of clarity. The styles in used are described below.
To show source code in scripts or source files:
{

}

cout << " Hello" << endl;
float x = 3.;
float y = 5.;
int
i = 101;
cout <<" x = "<

The directories we explored above are available when downloading the binaries. When downloading the source you also
get a directory for each library with the corresponding header and source files, located in the inc and src subdirectories.
To see what classes are in a library, you can check the /inc directory for the list of class definitions. For
example, the physics library libPhysics.so contains these class definitions:
> ls -m $ROOTSYS/math/physics/inc/
LinkDef.h, TFeldmanCousins.h, TGenPhaseSpace.h, TLorentzRotation.h,
TLorentzVector.h, TQuaternion.h, TRobustEstimator.h, TRolke.h,
TRotation.h, TVector2.h, TVector3.h

1.7

How to Find More Information

website The ROOT web site has up to date documentation. The ROOT source code automatically generates this
documentation, so each class is explicitly documented on its own web page, which is always up to date with the latest
official release of ROOT.
The ROOT Reference Guide web pages can be found at class index reference guide http://root.cern.ch/root/html/
ClassIndex.html. Each page contains a class description, and an explanation of each method. It shows the class
inheritance tree and lets you jump to the parent class page by clicking on the class name. If you want more details,
you can even see the source. There is a help page available in the little box on the upper right hand side of each class
documentation page. You can see on the next page what a typical class documentation web page looks like. The ROOT
web site also contains in addition to this Reference Guide, “How To’s”, a list of publications and example applications.

1.7.1

Class Reference Guide

The top of any class reference page lets you jump to different parts of the documentation. The first line links to the
class index and the index for the current module (a group of classes, often a library). The second line links to the
ROOT homepage and the class overviews. The third line links the source information - a HTML version of the source
and header file as well as the CVS (the source management system used for the ROOT development) information of
the files. The last line links the different parts of the current pages.

32

CHAPTER 1. INTRODUCTION

Figure 1.3: Example of function documentation, with automatically generated LaTeX-like graphics

Figure 1.4: Inheritance tree, showing what the current class derives from, and which classes inherit from it

Figure 1.5: HTML version of the source file linking all types and most functions

Chapter 2

Getting Started
We begin by showing you how to use ROOT interactively. There are two examples to click through and learn how to
use the GUI. We continue by using the command line, and explaining the coding conventions, global variables and the
environment setup. If you have not installed ROOT, you can do so by following the instructions in the appendix, or on
the ROOT web site: http://root.cern.ch/root/Availability.html

2.1

Setting the Environment Variables

Before you can run ROOT you need to set the environment variable ROOTSYS and change your path to include root/bin
and library path variables to include root/lib. Please note: the syntax is for bash, if you are running tcsh you will
have to use setenv instead of export.
1. Define the variable $ROOTSYS to the directory where you unpacked the ROOT:
$ export ROOTSYS=$HOME/root
2. Add ROOTSYS/bin to your PATH:
$ export PATH=$PATH:$ROOTSYS/bin
3. Setting the Library Path
On HP-UX, before executing the interactive module, you must set the library path:
$ export SHLIB_PATH=$SHLIB_PATH:$ROOTSYS/lib
On AIX, before executing the interactive module, you must set the library path:
$ [ -z "$LIBPATH" ] && export LIBPATH=/lib:/usr/lib
$ export LIBPATH=$LIBPATH:$ROOTSYS/lib
On Linux, Solaris, Alpha OSF and SGI, before executing the interactive module, you must set the library path:
$ export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$ROOTSYS/lib
On Solaris, in case your LD_LIBRARY_PATH is empty, you should set it:
$ export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:$ROOTSYS/lib:/usr/dt/lib
If you use the afs version you should set (vers = version number, arch = architecture):
$ export ROOTSYS=/afs/cern.ch/sw/lcg/external/root/vers/arch/root
If ROOT was installed in $HOME/myroot directory on a local machine, one can do:
cd $HOME/myroot
. bin/thisroot.sh

// or source bin/thisroot.sh

The new $ROOTSYS/bin/thisroot.[c]sh scripts will set correctly the ROOTSYS, LD_LIBRARY_PATH or other paths
depending on the platform and the MANPATH. To run the program just type: root.
33

34

CHAPTER 2. GETTING STARTED

2.2

Start and Quit a ROOT Session

$ root
-----------------------------------------------------------| Welcome to ROOT 6.00/00
http://root.cern.ch |
|
(c) 1995-2014, The ROOT Team |
| Built for linuxx8664gcc
|
| From tag v6-00-00, 30 May 2014
|
| Try '.help', '.demo', '.license', '.credits', '.quit'/'.q' |
-----------------------------------------------------------root [0]
To start ROOT you can type root at the system prompt. This starts up Cling, the ROOT command line C/C++
interpreter, and it gives you the ROOT prompt (root[0]).
It is possible to launch ROOT with some command line options, as shown below:
% root -?
Usage: root [-l] [-b] [-n] [-q] [dir] [[file:]data.root]
[file1.C ... fileN.C]
Options:
-b : run in batch mode without graphics
-n : do not execute logon and logoff macros as specified in .rootrc
-q : exit after processing command line macro files
-l : do not show splash screen
-x : exit on exception
dir : if dir is a valid directory cd to it before executing
-?
-h
--help
-config
-memstat

:
:
:
:
:

print usage
print usage
print usage
print ./configure options
run with memory usage monitoring

• -b ROOT session runs in batch mode, without graphics display. This mode is useful in case one does not want to
set the DISPLAY or cannot do it for some reason.
• -n usually, launching a ROOT session will execute a logon script and quitting will execute a logoff script. This
option prevents the execution of these two scripts.
• it is also possible to execute a script without entering a ROOT session. One simply adds the name of the script(s)
after the ROOT command. Be warned: after finishing the execution of the script, ROOT will normally enter a
new session.
• -q process command line script files and exit.
For example if you would like to run a script myMacro.C in the background, redirect the output into a file myMacro.log,
and exit after the script execution, use the following syntax:
root -b -q myMacro.C > myMacro.log
If you need to pass a parameter to the script use:
root -b -q 'myMacro.C(3)' > myMacro.log
Be mindful of the quotes, i.e. if you need to pass a string as a parameter, the syntax is:
root -b -q 'myMacro.C("text")' > myMacro.log
You can build a shared library with ACLiC and then use this shared library on the command line for a quicker execution
(i.e. the compiled speed rather than the interpreted speed). See also “Cling the C++ Interpreter”.

2.3. USING THE GUI

35

root -b -q myMacro.so > myMacro.log
ROOT has a powerful C/C++ interpreter giving you access to all available ROOT classes, global variables, and
functions via the command line. By typing C++ statements at the prompt, you can create objects, call functions,
execute scripts, etc. For example:
root[] 1+sqrt(9)
(const double)4.00000000000000000e+00
root[] for (int i = 0; i<4; i++) cout << "Hello" << i << endl
Hello 0
Hello 1
Hello 2
Hello 3
root[] .q
To exit the ROOT session, type .q.
root[] .q

2.3

Using the GUI

The basic whiteboard on which an object is drawn in ROOT is called a canvas (defined by the class TCanvas). Every
object in the canvas is a graphical object in the sense that you can grab it, resize it, and change some characteristics
using the mouse. The canvas area can be divided in several sub areas, so-called pads (the class TPad). A pad is a
canvas sub area that can contain other pads or graphical objects. At any one time, just one pad is the so-called active
pad. Any object at the moment of drawing will be drawn in the active pad. The obvious question is: what is the
relation between a canvas and a pad? In fact, a canvas is a pad that spans through an entire window. This is nothing
else than the notion of inheritance. The TPad class is the parent of the TCanvas class. In ROOT, most objects derive
from a base class TObject. This class has a virtual method Draw() such as all objects are supposed to be able to be
“drawn”. If several canvases are defined, there is only one active at a time. One draws an object in the active canvas by
using the statement:
object.Draw()
This instructs the object “object” to draw itself. If no canvas is opened, a default one (named “c1”) is created. In the
next example, the first statement defines a function and the second one draws it. A default canvas is created since
there was no opened one. You should see the picture as shown in the next figure.
root[] TF1 f1("func1","sin(x)/x",0,10)
root[] f1.Draw()
: created default TCanvas with name c1
The following components comprise the canvas window:
• Menu bar - contains main menus for global operations with files, print, clear canvas, inspect, etc.
• Tool bar - has buttons for global and drawing operations; such as arrow, ellipse, latex, pad, etc.
• Canvas - an area to draw objects.
• Status bar - displays descriptive messages about the selected object.
• Editor frame - responds dynamically and presents the user interface according to the selected object in the canvas.

2.3.1

Main Menus and Toolbar

At the top of the canvas window are File, Edit, View, Options, Inspect, Classes and Help menus.

36

CHAPTER 2. GETTING STARTED

Figure 2.1: A canvas with drawing
2.3.1.1

File Menu

• New Canvas: creates a new canvas window in the current ROOT session.
• Open. . . : popup a dialog to open a file.
• Close Canvas: close the canvas window.
• Save: save the drawing of the current canvas in a format selectable from the submenu. The current canvas name
is used as a file name for various formats such as PostScript, GIF, JPEG, C macro file, root file.
• Save As. . . : popup a dialog for saving the current canvas drawing in a new filename.
• Print: popup a dialog to print the current canvas drawing
• Quit ROOT : exit the ROOT session

2.3.1.2

Edit Menu

There is only one active menu entry in the Edit menu. The others menu entries will be implemented and will become
active in the near future.
• Clear: delete all objects in the canvas or in the selected pad according to the selected entry in the submenu.

2.3. USING THE GUI
2.3.1.3

37

View Menu

• Editor: toggles the view of the editor. If it is selected activates and shows up the editor on the left side of the
canvas window. According to the selected object, the editor loads the corresponding user interface for easy change
of the object’s attributes.
• Toolbar: toggles the view of the toolbar. If it is selected activates and shows up the toolbar. It contains buttons
for easy and fast access to most frequently used commands and for graphics primitive drawing. Tool tips are
provided for helping users.
• Status Bar: toggles the view of the status bar. If it is selected, the status bar below the canvas window shows
up. There the identification of the objects is displayed when moving the mouse (such as the object’s name, the
object’s type, its coordinates, etc.).
• Colors: creates a new canvas showing the color palette.
• Markers: creates a new canvas showing the various marker styles.
• Iconify: create the canvas window icon, does not close the canvas
• View With. . . : If the last selected pad contains a 3-d structure, a new canvas is created with a 3-D picture
according to the selection made from the cascaded menu: X3D or OpenGL. The 3-D image can be interactively
rotated, zoomed in wire-frame, solid, hidden line or stereo mode.

2.3.1.4

Options Menu

• Auto Resize Canvas: turns auto-resize of the canvas on/off :
– on - the canvas fits to the window when changing the window size;
– off - the canvas stays fixed when changing the window size.
• Resize Canvas: resizes and fits the canvas to the window size.
• Move Opaque: if selected, graphics objects are moved in opaque mode; otherwise, only the outline of objects
is drawn when moving them. The option opaque produces the best effect but it requires a reasonably fast
workstation or response time.
• Resize Opaque: if selected, graphics objects are resized in opaque mode; otherwise, only the outline of objects is
drawn when resizing them.
• Interrupt: interrupts the current drawing process.
• Refresh: redraws the canvas contents.
• Pad Auto Exec: executes the list of TExecs in the current pad.
• Statistics: toggles the display of the histogram statistics box.
• Histogram Title: toggles the display of the histogram title.
• Fit Parameters: toggles the display of the histogram or graph fit parameters.
• Can Edit Histogram: enables/disables the possibility to edit histogram bin contents.

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CHAPTER 2. GETTING STARTED

2.3.1.5

Inspect Menu

• ROOT : inspects the top-level gROOT object (in a new canvas).
• Start Browser: starts a new object browser (in a separate window).
• GUI Builder: starts the GUI builder application (in a separate window).

2.3.1.6

Help Menu

• Canvas: help on canvas as a whiteboard area for drawing.
• Menus: help on canvas menus.
• Graphics Editor: help on primitives’ drawing and objects’ editor.
• Browser: help on the ROOT objects’ and files’ browser.
• Objects: help on DrawClass, Inspect and Dump context menu items.
• PostScript: help on how to print a canvas to a PostScript file format.
• About ROOT : pops up the ROOT Logo with the version number.

2.3. USING THE GUI
2.3.1.7

39

Classes Menu

• Classes: starts the ClassTree viewer that draws inheritance tree for a list of classes.
2.3.1.8

Toolbar

The following menu shortcuts and utilities are available from the toolbar:
Create a new canvas window.
Popup the Open File dialog.
Popup the Save As. . . dialog.
Popup the Print dialog.
Interrupts the current drawing process.
Redraw the canvas.
Inspect the gROOT object.
Create a new objects’ browser.
You can create the following graphical objects using the toolbar buttons for primitive drawing. Tool tips are provided
for helping your choice.
An Arc or circle: Click on the center of the arc, and then move the mouse. A rubber band circle is shown. Click
again with the left button to freeze the arc.
A Line: Click with the left button at the point where you want to start the line, then move the mouse and click
again with the left button to freeze the line.
An Arrow:Click with the left button at the point where you want to start the arrow, then move the mouse and
click again with the left button to freeze the arrow.
A Diamond: Click with the left button and freeze again with the left button. The editor draws a rubber band
box to suggest the outline of the diamond.
An Ellipse: Proceed like for an arc. You can grow/shrink the ellipse by pointing to the sensitive points. They
are highlighted. You can move the ellipse by clicking on the ellipse, but not on the sensitive points. If, with the ellipse
context menu, you have selected a fill area color, you can move a filled-ellipse by pointing inside the ellipse and dragging
it to its new position.
A Pad: Click with the left button and freeze again with the left button. The editor draws a rubber band box to
suggest the outline of the pad.
A PaveLabel: Proceed like for a pad. Type the text of label and finish with a carriage return. The text will
appear in the box.
A Pave Text: Proceed like for a pad. You can then click on the TPaveText object with the right mouse button
and select the option InsertText.
Paves Text: Proceed like for a TPaveText.
A Poly Line: Click with the left button for the first point, move the moose, click again with the left button for a
new point. Close the poly-line with a double click. To edit one vertex point, pick it with the left button and drag to
the new point position.
A Curly Line: Proceed as for the arrow or line. Once done, click with the third button to change the characteristics
of the curly line, like transform it to wave, change the wavelength, etc.

40

CHAPTER 2. GETTING STARTED

A Curly Arc: Proceed like for an ellipse. The first click is located at the position of the center, the second click
at the position of the arc beginning. Once done, one obtains a curly ellipse, for which one can click with the third
button to change the characteristics, like transform it to wavy, change the wavelength, set the minimum and maximum
angle to make an arc that is not closed, etc.
A Text/Latex string: Click with the left button where you want to draw the text and then type in the text
terminated by carriage return. All TLatex expressions are valid. To move the text or formula, point on it keeping the
left mouse button pressed and drag the text to its new position. You can grow/shrink the text if you position the
mouse to the first top-third part of the string, then move the mouse up or down to grow or shrink the text respectively.
If you position the mouse near the bottom-end of the text, you can rotate it.
A Marker: Click with the left button where to place the marker. The marker can be modified by using the
method SetMarkerStyle() of TSystem.
A Graphical Cut: Click with the left button on each point of a polygon delimiting the selected area. Close the
cut by double clicking on the last point. A TCutG object is created. It can be used as a selection for a TTree::Draw.
You can get a pointer to this object with:
TCutG cut = (TCutG*)gPad->GetPrimitive("CUTG")
Once you are happy with your picture, you can select the Save as canvas.C item in the canvas File menu. This will
automatically generate a script with the C++ statements corresponding to the picture. This facility also works if you
have other objects not drawn with the graphics editor (histograms for example).

2.3.2

The Editor Frame

The ROOT graphics editor loads the corresponding object editor objEditor according to the selected object obj in
the canvas respecting the class inheritance. An object in the canvas is selected after the left mouse click on it. For
example, if the selected object is TAxis, the TAxisEditor will shows up in the editor frame giving the possibility for
changing different axis attributes. The graphics editor can be:
Embedded - connected only with the canvas in the application window that appears on the left of the canvas window
after been activated via View menu / Editor. It appears on the left side if the canvas window allowing users to edit the
attributes of the selected object via provided user interface. The name of the selected object is displayed on the top of
the editor frame in red color. If the user interface needs more space then the height of the canvas window, a vertical
scroll bar appears for easer navigation.
Global - has own application window and can be connected to any created canvas in a ROOT session. It can be
activated via the context menu entries for setting line, fill, text and marker attributes for backward compatibility, but
there will be a unique entry in the near future.
The user interface for the following classes is available since ROOT v.4.04: TAttLine, TAttFill, TAttMarker, TAttText,
TArrow, TAxis, TCurlyArc, TCurlyLine, TFrame, TH1, TH2, TGraph, TPad, TCanvas, TPaveStats. For more details,
see “The Graphics Editor”, “The User Interface for Histograms”, “The User Interface for Graphs”.

2.3.3

Classes, Methods and Constructors

Object oriented programming introduces objects, which have data members and methods. The next line creates an
object named f1 of the class TF1 that is a one-dimensional function. The type of an object is called a class. The object
itself is called an instance of a class. When a method builds an object, it is called a constructor.
TF1 f1("func1","sin(x)/x",0,10)
In our constructor the function sin(x)/x is defined for use, and 0 and 10 are the limits. The first parameter, func1 is
the name of the object f1. Most objects in ROOT have a name. ROOT maintains a list of objects that can be searched
to find any object by its given name (in our example func1).
The syntax to call an object’s method, or if one prefers, to make an object to do something is:
object.method_name(parameters)

2.3. USING THE GUI

41

42

CHAPTER 2. GETTING STARTED

The dot can be replaced by “->” if object is a pointer. In compiled code, the dot MUST be replaced by a “->” if
object is a pointer.
object_ptr->method_name(parameters)
So now, we understand the two lines of code that allowed us to draw our function. f1.Draw() stands for “call the
method Draw() associated with the object f1 of the class TF1”. Other methods can be applied to the object f1 of the
class TF1. For example, the evaluating and calculating the derivative and the integral are what one would expect from
a function.
root[] f1.Eval(3)
(Double_t)4.70400026866224020e-02
root[] f1.Derivative(3)
(Double_t)(-3.45675056671992330e-01)
root[] f1.Integral(0,3)
(Double_t)1.84865252799946810e+00
root[] f1.Draw()
By default the method TF1::Paint(), that draws the function, computes 100 equidistant points to draw it. The
number of points can be set to a higher value with:
root[] f1.SetNpx(2000);
Note that while the ROOT framework is an object-oriented framework, this does not prevent the user from calling
plain functions.

2.3.4

User Interaction

Now we will look at some interactive capabilities. Try to draw the function sin(x)/x again. Every object in a window
(which is called a canvas) is, in fact, a graphical object in the sense that you can grab it, resize it, and change its
characteristics with a mouse click. For example, bring the cursor over the x-axis. The cursor changes to a hand with a
pointing finger when it is over the axis. Now, left click and drag the mouse along the axis to the right. You have a very
simple zoom.
When you move the mouse over any object, you can get access to selected methods by pressing the right mouse button
and obtaining a context menu. If you try this on the function TF1, you will get a menu showing available methods. The
other objects on this canvas are the title, a TPaveText object; the x and y-axis, TAxis objects, the frame, a TFrame
object, and the canvas a TCanvas object. Try clicking on these and observe the context menu with their methods.
For example try selecting the SetRange() method and putting -10, 10 in the dialog box fields. This is equivalent to
executing f1.SetRange(-10,10) from the command line, followed by f1.Draw(). Here are some other options you
can try.
Once the picture suits your wishes, you may want to see the code you should put in a script to obtain the same result.
To do that, choose Save / canvas.C entry of the File menu. This will generate a script showing the options set in
the current canvas. Notice that you can also save the picture into various file formats such as PostScript, GIF, etc.
Another interesting possibility is to save your canvas into the native ROOT format (.rootfile). This will enable you to
open it again and to change whatever you like. All objects associated to the canvas (histograms, graphs) are saved at
the same time.

2.3.5

Building a Multi-pad Canvas

Let us now try to build a canvas with several pads.
root[] TCanvas *MyC = new TCanvas("MyC","Test canvas",1)
root[] MyC->Divide(2,2)
Once again, we call the constructor of a class, this time the class TCanvas. The difference between this and the previous
constructor call (TF1) is that here we are creating a pointer to an object. Next, we call the method Divide() of the
TCanvas class (that is TCanvas::Divide()), which divides the canvas into four zones and sets up a pad in each of
them. We set the first pad as the active one and than draw the functionf1there.

2.3. USING THE GUI

43

Figure 2.2: A context menu

44

CHAPTER 2. GETTING STARTED

root[] MyC->cd(1)
root[] f1->Draw()
All objects will be drawn in that pad because it is the active one. The ways for changing the active pad are:
• Click the middle mouse button on a pad will set this pad as the active one.
• Use the method TCanvas::cd() with the pad number, as was done in the example above:
root[] MyC->cd(3)
Pads are numbered from left to right and from top to bottom. Each new pad created by TCanvas::Divide() has a
name, which is the name of the canvas followed by _1, _2, etc. To apply the method cd() to the third pad, you would
write:
root[] MyC_3->cd()
• Third pad will be selected since you called TPad::cd() for the object MyC_3. ROOT will find the pad that was
namedMyC_3when you typed it on the command line (see ROOT/Cling Extensions to C++).

2.3.6

Saving the Canvas

Figure 2.3: The SaveAs. . . dialog
Using the File menu / Save cascade menu users can save the canvas as one of the files from the list. Please note that
saving the canvas this way will overwrite the file with the same name without a warning.
All supported file types can be saved via File menu / SaveAs. . . This dialog gives a choice to show or suppress the
confirmation message for overwriting an existing file.
If the Ovewrite check box is not selected, a message dialog appears asking the user to overwrite the file (Yes/No). The
user choice is saved for the next time the Save As. . . dialog shows up.

2.3.7

Printing the Canvas

The Print command in the canvas File menu pops-up a print dialog where the user can specify a preferred print
command and the printer name.
Both print parameters can be set via the new Print.Command and Print.Printer rootrc resources as follows:

2.4. THE ROOT COMMAND LINE

# Printer settings.
WinNT.*.Print.Command:
Unix.*.Print.Command:
Print.Printer:
Print.Directory:

45

AcroRd32.exe
xprint -P%p %f
32-rb205-hp
.

If the %p and %f are specified as a part of the print command, they will be replaced by the specified printer name and
the file name. All other parameters will be kept as they are written. A print button is available in the canvas toolbar
(activated via View menu/Toolbar).

2.4

The ROOT Command Line

We have briefly touched on how to use the command line. There are different types of commands.
1. Cling commands start with “.”
root[] .? //this command will list all the Cling commands
root[] .L  //load [filename]
root[] .x  //load and execute [filename]
2. SHELL commands start with “.!” for example:
root[] .! ls
3. C++ commands follow C++ syntax (almost)
root[] TBrowser *b = new TBrowser()

2.4.1

Multi-line Commands

You can use the command line to execute multi-line commands. To begin a multi-line command you must type a single
left curly bracket {, and to end it you must type a single right curly bracket }. For example:
root[] {
end with
end with
end with
end with
end with
end with
end with
i = 0, j
i = 1, j
i = 2, j

'}'>
'}'>
'}'>
'}'>
'}'>
'}'>
'}'>
= 0
= 1
= 3

Int_t j = 0;
for (Int_t i = 0; i < 3; i++)
{
j= j + i;
cout << "i = " << i << ", j = " << j << endl;
}
}

It is more convenient to edit a script than the command line, and if your multi line commands are getting unmanageable,
you may want to start with a script instead.

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CHAPTER 2. GETTING STARTED

2.4.2

Cling Extensions

We should say that some things are not standard C++. The Cling interpreter has several extensions. See “ROOT/Cling
Extensions to C++”.

2.4.3

Helpful Hints for Command Line Typing

The interpreter knows all the classes, functions, variables, and user defined types. This enables ROOT to help users to
complete the command line. For example, if we do not know anything about the TLine class, the Tab feature helps us
to get a list of all classes starting with TL(where  means type the Tab key).
root[] l = new TLi
TList
TListIter
TLink
TLine
TLimitDataSource
TLimit
To list the different constructors and parameters for TLine use the  key as follows:
root[] l = new TLine(
TLine TLine()
TLine TLine(Double_t x1,Double_t y1,Double_t x2,Double_t y2)
TLine TLine(const TLine& line)

2.4.4

Regular Expression

The meta-characters below can be used in a regular expression:
• ‘ˆ’ start-of-line anchor
• ‘$’ end-of-line anchor
• ‘.’ matches any character
• ‘[’ start a character class
• ’]’end a character class
• ’ˆ’negates character class if first character
• ‘*’Kleene closure (matches 0 or more)
• ’+’Positive closure (1 or more)
• ‘?’ Optional closure (0 or 1)
When using wildcards the regular expression is assumed to be preceded by a ‘ˆ’ (BOL) and terminated by ‘$’ (EOL).
All ‘*’ (closures) are assumed to be preceded by a ‘.’, i.e. any character, except slash _/_. Its special treatment allows
the easy matching of pathnames. For example, _*.root_ will match _aap.root_, but not _pipo/aap.root_.
The escape characters are:
• \ backslash
• b backspace
• f form feed
• n new line
• r carriage return
• s space

2.5. CONVENTIONS

47

• t tab
• e ASCII ESC character (‘033’)
• DDD number formed of 1-3 octal digits
• xDD number formed of 1-2 hex digits
• ˆC C = any letter. Control code
The class TRegexp can be used to create a regular expression from an input string. If wildcard is true then the input
string contains a wildcard expression.
TRegexp(const char *re, Bool_t wildcard)
Regular expression and wildcards can be easily used in methods like:
Ssiz_t Index(const TString& string,Ssiz_t* len,Ssiz_t i) const
The method finds the first occurrence of the regular expression in the string and returns its position.

2.5

Conventions

In this paragraph, we will explain some of the conventions used in ROOT source and examples.

2.5.1

Coding Conventions

From the first days of ROOT development, it was decided to use a set of coding conventions. This allows a consistency
throughout the source code. Learning these will help you identify what type of information you are dealing with and
enable you to understand the code better and quicker. Of course, you can use whatever convention you want but if you
are going to submit some code for inclusion into the ROOT sources, you will need to use these.
These are the coding conventions:
• Classes begin with T: TLine, TTree
• Non-class types end with _t: Int_t
• Data members begin with f: fTree
• Member functions begin with a capital: Loop()
• Constants begin with k: kInitialSize, kRed
• Global variables begin with g: gEnv
• Static data members begin with fg: fgTokenClient
• Enumeration types begin with E: EColorLevel
• Locals and parameters begin with a lower case: nbytes
• Getters and setters begin with Get and Set: SetLast(), GetFirst()

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CHAPTER 2. GETTING STARTED

2.5.2

Machine Independent Types

Different machines may have different lengths for the same type. The most famous example is the int type. It may
be 16 bits on some old machines and 32 bits on some newer ones. To ensure the size of your variables, use these pre
defined types in ROOT:
• Char_t Signed Character 1 byte
• UChar_t Unsigned Character 1 byte
• Short_t Signed Short integer 2 bytes
• UShort_t Unsigned Short integer 2 bytes
• Int_t Signed integer 4 bytes
• UInt_tUnsigned integer 4 bytes
• Long64_t Portable signed long integer 8 bytes
• ULong64_t Portable unsigned long integer 8 bytes
• Float_t Float 4 bytes
• Double_t Float 8 bytes
• Double32_t Double 8 bytes in memory, written as a Float 4 bytes
• Bool_t Boolean (0=false, 1=true)
If you do not want to save a variable on disk, you can use int or Int_t, the result will be the same and the interpreter
or the compiler will treat them in exactly the same way.

2.5.3

TObject

In ROOT, almost all classes inherit from a common base class called TObject. This kind of architecture is also used in
the Java language. The TObject class provides default behavior and protocol for all objects in the ROOT system. The
main advantage of this approach is that it enforces the common behavior of the derived classes and consequently it
ensures the consistency of the whole system. See “The Role of TObject”.
TObject provides protocol, i.e. (abstract) member functions, for:
• Object I/O (Read(), Write())
• Error handling (Warning(), Error(), SysError(), Fatal())
• Sorting (IsSortable(), Compare(), IsEqual(), Hash())
• Inspection (Dump(), Inspect())
• Printing (Print())
• Drawing (Draw(), Paint(), ExecuteEvent())
• Bit handling (SetBit(), TestBit())
• Memory allocation (operatornew and delete, IsOnHeap())
• Access to meta information (IsA(), InheritsFrom())
• Object browsing (Browse(), IsFolder())

2.6

Global Variables

ROOT has a set of global variables that apply to the session. For example, gDirectory always holds the current
directory, and gStyle holds the current style.
All global variables begin with “g” followed by a capital letter.

2.6. GLOBAL VARIABLES

2.6.1

49

gROOT

The single instance of TROOT is accessible via the global gROOT and holds information relative to the current session.
By using the gROOT pointer, you get the access to every object created in a ROOT program. The TROOT object has
several lists pointing to the main ROOT objects. During a ROOT session, the gROOT keeps a series of collections to
manage objects. They can be accessed via gROOT ::GetListOf... methods.
gROOT->GetListOfClasses()
gROOT->GetListOfColors()
gROOT->GetListOfTypes()
gROOT->GetListOfGlobals()
gROOT->GetListOfGlobalFunctions()
gROOT->GetListOfFiles()
gROOT->GetListOfMappedFiles()
gROOT->GetListOfSockets()
gROOT->GetListOfCanvases()
gROOT->GetListOfStyles()
gROOT->GetListOfFunctions()
gROOT->GetListOfSpecials()
gROOT->GetListOfGeometries()
gROOT->GetListOfBrowsers()
gROOT->GetListOfMessageHandlers()
These methods return a TSeqCollection, meaning a collection of objects, and they can be used to do list operations
such as finding an object, or traversing the list and calling a method for each of the members. See the TCollection
class description for the full set of methods supported for a collection. For example, to find a canvas called c1you can
do:
root[] gROOT->GetListOfCanvases()->FindObject("c1")
This returns a pointer to a TObject, and before you can use it as a canvas you need to cast it to a TCanvas*.

2.6.2

gFile

gFile is the pointer to the current opened file in the ROOT session.

2.6.3

gDirectory

gDirectory is a pointer to the current directory. The concept and role of a directory is explained in the chapter
“Input/Output”.

2.6.4

gPad

A graphic object is always drawn on the active pad. It is convenient to access the active pad, no matter what it is. For
that, we have gPad that is always pointing to the active pad. For example, if you want to change the fill color of the
active pad to blue, but you do not know its name, you can use gPad .
root[] gPad->SetFillColor(38)
To get the list of colors, if you have an open canvas, click in the “View” menu, selecting the “Colors” entry.

2.6.5

gRandom

gRandom is a pointer to the current random number generator. By default, it points to a TRandom3 object,
based on the “Mersenne-Twister” generator. This generator is very fast and has very good random proprieties
(a very long period of 10600 ). Setting the seed to 0 implies that the seed will be uniquely generated using
the TUUID. Any other value will be used as a constant. The following basic random distributions are provided:
Rndm() or Uniform(min,max), Gaus(mean,sigma), Exp(tau), BreitWigner(mean,sigma), Landau(mean,sigma),
Poisson(mean), Binomial(ntot,prob). You can customize your ROOT session by replacing the random number
generator. You can delete gRandom and recreate it with your own. For example:

50

CHAPTER 2. GETTING STARTED

root[] delete gRandom;
root[] gRandom = new TRandom2(0); //seed=0
TRandom2 is another generator, which is also very fast and uses only three words for its state.

2.6.6

gEnv

gEnv is the global variable (of type TEnv) with all the environment settings for the current session. This variable is set
by reading the contents of a .rootrc file (or $ROOTSYS/etc/system.rootrc) at the beginning of the root session. See
Environment Setup below for more information.

2.7

Environment Setup

The behavior of a ROOT session can be tailored with the options in the .rootrc file. At start-up, ROOT looks for a
.rootrc file in the following order:
• ./.rootrc //local directory
• $HOME/.rootrc //user directory
• $ROOTSYS/etc/system.rootrc //global ROOT directory
If more than one .rootrc files are found in the search paths above, the options are merged, with precedence local,
user, global. While in a session, to see current settings, you can do:
root[] gEnv->Print()
The rootrc file typically looks like:
# Path used by dynamic loader to find shared libraries
Unix.*.Root.DynamicPath: .:~/rootlibs:$(ROOTSYS)/lib
Unix.*.Root.MacroPath:
.:~/rootmacros:$(ROOTSYS)/macros
# Path where to look for TrueType fonts
Unix.*.Root.UseTTFonts:
true
Unix.*.Root.TTFontPath:
...
# Activate memory statistics
Rint.Root.MemStat:
1
Rint.Load:
rootalias.C
Rint.Logon:
rootlogon.C
Rint.Logoff:
rootlogoff.C
...
Rint.Canvas.MoveOpaque: false
Rint.Canvas.HighLightColor: 5
The various options are explained in $ROOTSYS/etc/system.rootrc. The .rootrc file contents are combined. For
example, if the flag to use true type fonts is set to true in the system.rootrc file, you have to set explicitly it false in
your local .rootrc file if you do not want to use true type fonts. Removing the UseTTFontsstatement in the local
.rootrc file will not disable true fonts. The value of the environment variable ROOTDEBUG overrides the value in the
.rootrc file at startup. Its value is used to set gDebug and helps for quick turn on debug mode in TROOT startup.
ROOT looks for scripts in the path specified in the .rootrc file in the Root.Macro.Path variable. You can expand
this path to hold your own directories.

2.7. ENVIRONMENT SETUP

2.7.1

51

Logon and Logoff Scripts

The rootlogon.C and rootlogoff.C files are scripts loaded and executed at start-up and shutdown. The rootalias.C
file is loaded but not executed. It typically contains small utility functions. For example, the rootalias.C script
that comes with the ROOT distributions (located in $ROOTSYS/tutorials) defines the function edit(char *file).
This allows the user to call the editor from the command line. This particular function will start the VI editor if the
environment variable EDITOR is not set.
root[0] edit("c1.C")
For more details, see $ROOTSYS/tutorials/rootalias.C.

2.7.2

History File

You can use the up and down arrow at the command line, to access the previous and next command. The commands
are recorded in the history file $HOME/.root_hist. It is a text file, and you can edit, cut, and paste from it. You
can specify the history file in the system.rootrc file, by setting the Rint.Historyoption. You can also turn off the
command logging in the system.rootrc file with the option: Rint.History: The number of history lines to be kept can be set also in .rootrc by:
Rint.HistSize:
Rint.HistSave:

500
400

The first value defines the maximum of lines kept; once it is reached all, the last HistSave lines will be removed.
One can set HistSize to 0 to disable history line management. There is also implemented an environment variable
called ROOT_HIST. By setting ROOT_HIST=300:200 the above values can be overriden - the first value corresponds to
HistSize, the (optional) second one to HistSave. You can set ROOT_HIST=0 to disable the history.

2.7.3

Tracking Memory Leaks

You can track memory usage and detect leaks by monitoring the number of objects that are created and deleted (see
TObjectTable). To use this facility, edit the file $ROOTSYS/etc/system.rootrc or .rootrc if you have this file and
add the two following lines:
Root.MemStat:
Root.ObjectStat:

1
1

In your code or on the command line you can type the line:
gObjectTable->Print();
This line will print the list of all active classes and the number of instances for each class. By comparing consecutive
print outs, you can see objects that you forgot to delete. Note that this method cannot show leaks coming from the
allocation of non-objects or classes unknown to ROOT.

2.7.4

Memory Checker

A memory checking system was developed by D.Bertini and M.Ivanov and added in ROOT version 3.02.07. To activate
the memory checker you can set the resource Root.MemCheck to 1 (e.g.: Root.MemCheck: 1 in the .rootrc file). You
also have to link with libNew.so (e.g. use root-config --new --libs) or to use rootn.exe. When these settings
are in place, you will find a file “memcheck.out” in the directory where you started your ROOT program after the
completion of the program execution. You can also set the resource Root.MemCheckFile to the name of a file. The
memory information will be written to that file. The contents of this memcheck.out can be analyzed and transformed
into printable text via the memprobe program (in $ROOTSYS/bin).

52

2.8

CHAPTER 2. GETTING STARTED

Converting from PAW to ROOT

The web page at: http://root.cern.ch/root/HowtoConvertFromPAW.html#TABLE gives the “translation” table
of some commonly used PAW commands into ROOT. If you move the mouse cursor over the picture at: http:
//root.cern.ch/root/HowtoConvertFromPAW.html#SET, you will get the corresponding ROOT commands as tooltips.

2.8.1

Converting HBOOK/PAW Files

ROOT has a utility called h2root that you can use to convert your HBOOK/PAW histograms or ntuple files into
ROOT files. To use this program, you type the shell script command:
h2root





If you do not specify the second parameter, a file name is automatically generated for you. If hbookfile is of the
form file.hbook, then the ROOT file will be called file.root. This utility converts HBOOK histograms into ROOT
histograms of the class TH1F. HBOOK profile histograms are converted into ROOT profile histograms (see class
TProfile). HBOOK row-wise and column-wise ntuples are automatically converted to ROOT Trees. See “Trees”.
Some HBOOK column-wise ntuples may not be fully converted if the columns are an array of fixed dimension (e.g.
var[6]) or if they are a multi-dimensional array.
HBOOK integer identifiers are converted into ROOT named objects by prefixing the integer identifier with the letter “h”
if the identifier is a positive integer and by "h_" if it is a negative integer identifier. In case of row-wise or column-wise
ntuples, each column is converted to a branch of a tree. Note that h2root is able to convert HBOOK files containing
several levels of sub-directories. Once you have converted your file, you can look at it and draw histograms or process
ntuples using the ROOT command line. An example of session is shown below:
// this connects the file hbookconverted.root
root[] TFile f("hbookconverted.root");
// display histogram named h10 (was HBBOK id 10)
root[] h10.Draw();
// display column "var" from ntuple h30
root[] h30.Draw("var");
You can also use the ROOT browser (see TBrowser) to inspect this file.
The chapter on trees explains how to read a tree. ROOT includes a function TTree::MakeClass to generate
automatically the code for a skeleton analysis function. See “Example Analysis”.
In case one of the ntuple columns has a variable length (e.g. px(ntrack)), h.Draw("px") will histogram the px column
for all tracks in the same histogram. Use the script quoted above to generate the skeleton function and create/fill the
relevant histogram yourself.

Chapter 3

Histograms
This chapter covers the functionality of the histogram classes. We begin with an overview of the histogram classes,
after which we provide instructions and examples on the histogram features.
We have put this chapter ahead of the graphics chapter so that you can begin working with histograms as soon as
possible. Some of the examples have graphics commands that may look unfamiliar to you. These are covered in the
chapter “Input/Output”.

3.1

The Histogram Classes

ROOT supports histograms up to three dimensions. Separate concrete classes are provided for one-dimensional,
two-dimensional and three-dimensional classes. The histogram classes are split into further categories, depending on
the set of possible bin values:
• TH1C, TH2C and TH3C contain one byte per bin (maximum bin content = 255)
• TH1S, TH2S and TH3S contain one short per bin (maximum bin content = 65 535).
• TH1I, TH2I and TH3I contain one integer per bin (maximum bin content = 2 147 483 647).
• TH1F, TH2F and TH3F contain one float per bin (maximum precision = 7 digits).
• TH1D, TH2D and TH3D contain one double per bin (maximum precision = 14 digits).
ROOT also supports profile histograms, which constitute an elegant replacement of two-dimensional histograms in
many cases. The inter-relation of two measured quantities X and Y can always be visualized with a two-dimensional
histogram or scatter-plot. Profile histograms, on the other hand, are used to display the mean value of Y and its RMS
for each bin in X. If Y is an unknown but single-valued approximate function of X, it will have greater precision in a
profile histogram than in a scatter plot.
• TProfile : one dimensional profiles
• TProfile2D : two dimensional profiles
All ROOT histogram classes are derived from the base class TH1 (see figure above). This means that two-dimensional
and three-dimensional histograms are seen as a type of a one-dimensional histogram, in the same way in which
multidimensional C arrays are just an abstraction of a one-dimensional contiguous block of memory.

3.2

Creating Histograms

There are several ways in which you can create a histogram object in ROOT. The straightforward method is to use
one of the several constructors provided for each concrete class in the histogram hierarchy. For more details on the
constructor parameters, see the subsection “Constant or Variable Bin Width” below. Histograms may also be created
by:
• Calling the Clone() method of an existing histogram
53

54

CHAPTER 3. HISTOGRAMS

Figure 3.1: The class hierarchy of histogram classes
• Making a projection from a 2-D or 3-D histogram
• Reading a histogram from a file (see Input/Output chapter)
// using various constructors
TH1* h1 = new TH1I("h1", "h1 title", 100, 0.0, 4.0);
TH2* h2 = new TH2F("h2", "h2 title", 40, 0.0, 2.0, 30, -1.5, 3.5);
TH3* h3 = new TH3D("h3", "h3 title", 80, 0.0, 1.0, 100, -2.0, 2.0,
50, 0.0, 3.0);
// cloning a histogram
TH1* hc = (TH1*)h1->Clone();
// projecting histograms
// the projections always contain double values !
TH1* hx = h2->ProjectionX(); // ! TH1D, not TH1F
TH1* hy = h2->ProjectionY(); // ! TH1D, not TH1F

3.2.1

Constant or Variable Bin Width

The histogram classes provide a variety of ways to construct a histogram, but the most common way is to provide the
name and title of histogram and for each dimension: the number of bins, the minimum x (lower edge of the first bin)
and the maximum x (upper edge of the last bin).
TH2* h = new TH2D(
/* name */ "h2",
/* title */ "Hist with constant bin width",
/* X-dimension */ 100, 0.0, 4.0,
/* Y-dimension */ 200, -3.0, 1.5);
When employing this constructor, you will create a histogram with constant (fixed) bin width on each axis. For the
example above, the interval [0.0, 4.0] is divided into 100 bins of the same width w X = 4.0 - 0.0 100 = 0.04 for
the X axis (dimension). Likewise, for the Y axis (dimension), we have bins of equal width w Y = 1.5 - (-3.0) 200 =
0.0225.
If you want to create histograms with variable bin widths, ROOT provides another constructor suited for this purpose.
Instead of passing the data interval and the number of bins, you have to pass an array (single or double precision) of
bin edges. When the histogram has n bins, then there are n+1 distinct edges, so the array you pass must be of size n+1.
const Int_t NBINS = 5;
Double_t edges[NBINS + 1] = {0.0, 0.2, 0.3, 0.6, 0.8, 1.0};
// Bin 1 corresponds to range [0.0, 0.2]
// Bin 2 corresponds to range [0.2, 0.3] etc...
TH1* h = new TH1D(
/* name */ "h1",

3.3. BIN NUMBERING

);

55

/* title */ "Hist with variable bin width",
/* number of bins */ NBINS,
/* edge array */ edges

Each histogram object contains three TAxis objects: fXaxis , fYaxis, and fZaxis, but for one-dimensional histograms
only the X-axis is relevant, while for two-dimensional histograms the X-axis and Y-axis are relevant. See the class
TAxis for a description of all the access methods. The bin edges are always stored internally in double precision.
You can examine the actual edges / limits of the histogram bins by accessing the axis parameters, like in the example
below:
const Int_t XBINS = 5; const Int_t YBINS = 5;
Double_t xEdges[XBINS + 1] = {0.0, 0.2, 0.3, 0.6, 0.8, 1.0};
Double_t yEdges[YBINS + 1] = {-1.0, -0.4, -0.2, 0.5, 0.7, 1.0};
TH2* h = new TH2D("h2", "h2", XBINS, xEdges, YBINS, yEdges);
TAxis* xAxis = h->GetXaxis(); TAxis* yAxis = h->GetYaxis();
cout << "Third bin on Y-dimension: " << endl; // corresponds to
// [-0.2, 0.5]
cout << "\tLower edge: " << yAxis->GetBinLowEdge(3) << endl;
cout << "\tCenter: " << yAxis->GetBinCenter(3) << endl;
cout << "\tUpper edge: " << yAxis->GetBinUpEdge(3) << endl;

3.3

Bin Numbering

All histogram types support fixed or variable bin sizes. 2-D histograms may have fixed size bins along X and variable
size bins along Y or vice-versa. The functions to fill, manipulate, draw, or access histograms are identical in both cases.

3.3.1

Convention

For all histogram types: nbins , xlow , xup
Bin# 0 contains the underflow.
Bin# 1 contains the first bin with low-edge ( xlow INCLUDED).
The second to last bin (bin# nbins) contains the upper-edge (xup EXCLUDED).
The Last bin (bin# nbins+1) contains the overflow.
In case of 2-D or 3-D histograms, a “global bin” number is defined. For example, assuming a 3-D histogram h with
binx, biny, binz, the function returns a global/linear bin number.
Int_t bin = h->GetBin(binx, biny, binz);
This global bin is useful to access the bin information independently of the dimension.

3.3.2

Re-binning

At any time, a histogram can be re-binned via the TH1::Rebin() method. It returns a new histogram with the
re-binned contents. If bin errors were stored, they are recomputed during the re-binning.

3.4

Filling Histograms

A histogram is typically filled with statements like:

56

CHAPTER 3. HISTOGRAMS
h1->Fill(x);
h1->Fill(x,w); // with weight
h2->Fill(x,y);
h2->Fill(x,y,w);
h3->Fill(x,y,z);
h3->Fill(x,y,z,w);

The Fill method computes the bin number corresponding to the given x, y or z argument and increments this bin by
the given weight. The Fill() method returns the bin number for 1-D histograms or global bin number for 2-D and
3-D histograms. If TH1::Sumw2() has been called before filling, the sum of squares is also stored. One can increment a
bin number directly by calling TH1::AddBinContent(), replace the existing content via TH1::SetBinContent() , and
access the bin content of a given bin via TH1::GetBinContent() .
Double_t binContent = h->GetBinContent(bin);

3.4.1

Automatic Re-binning Option

By default, the number of bins is computed using the range of the axis. You can change this to re-bin automatically by
setting the automatic re-binning option:
h->SetBit(TH1::kCanRebin);
Once this is set, the Fill() method will automatically extend the axis range to accommodate the new value specified
in the Fill() argument. The used method is to double the bin size until the new value fits in the range, merging bins
two by two. The TTree::Draw() method extensively uses this automatic binning option when drawing histograms of
variables in TTree with an unknown range. The automatic binning option is supported for 1-D, 2-D and 3-D histograms.
During filling, some statistics parameters are incremented to compute the mean value and root mean square with the
maximum precision. In case of histograms of type TH1C, TH1S, TH2C, TH2S, TH3C, TH3S a check is made that the bin
contents do not exceed the maximum positive capacity (127 or 65 535). Histograms of all types may have positive
or/and negative bin contents.

3.5

Random Numbers and Histograms

TH1::FillRandom() can be used to randomly fill a histogram using the contents of an existing TF1 function or another
TH1 histogram (for all dimensions). For example, the following two statements create and fill a histogram 10 000 times
with a default Gaussian distribution of mean 0 and sigma 1 :
root[] TH1F h1("h1","Histo from a Gaussian",100,-3,3);
root[] h1.FillRandom("gaus",10000);
TH1::GetRandom() can be used to get a random number distributed according the contents of a histogram. To fill a
histogram following the distribution in an existing histogram you can use the second signature of TH1::FillRandom().
Next code snipped assumes that h is an existing histogram (TH1 ).
root[] TH1F h2("h2","Histo from existing histo",100,-3,3);
root[] h2.FillRandom(&h1, 1000);
The distribution contained in the histogram h1 ( TH1 ) is integrated over the channel contents. It is normalized to one.
The second parameter (1000) indicates how many random numbers are generated.
Getting 1 random number implies:
• Generating a random number between 0 and 1 (say r1 )
• Find the bin in the normalized integral for r1
• Fill histogram channel
You can see below an example of the TH1::GetRandom() method which can be used to get a random number distributed
according the contents of a histogram.

3.6. ADDING, DIVIDING, AND MULTIPLYING

57

void getrandomh() {
TH1F *source = new TH1F("source","source hist",100,-3,3);
source->FillRandom("gaus",1000);
TH1F *final = new TH1F("final","final hist",100,-3,3);
// continued...

}

for (Int_t i=0;i<10000;i++) {
final->Fill(source->GetRandom());
}
TCanvas *c1 = new TCanvas("c1","c1",800,1000);
c1->Divide(1,2);
c1->cd(1);
source->Draw();
c1->cd(2);
final->Draw();
c1->cd();

3.6

Adding, Dividing, and Multiplying

Many types of operations are supported on histograms or between histograms:
• Addition of a histogram to the current histogram
• Additions of two histograms with coefficients and storage into the current histogram
• Multiplications and divisions are supported in the same way as additions.
• The Add , Divide and Multiply methods also exist to add, divide or multiply a histogram by a function.
Histograms objects (not pointers) TH1F h1 can be multiplied by a constant using:
h1.Scale(const)
A new histogram can be created without changing the original one by doing:
TH1F h3 = 8*h1;
To multiply two histogram objects and put the result in a 3rd one do:
TH1F h3 = h1*h2;
The same operations can be done with histogram pointers TH1F *h1, *h2 following way:
h1->Scale(const) TH1F h3 = 8*(*h1); TH1F h3 = (*h1)*(*h2);
Of course, the TH1 methods Add , Multiply and Divide can be used instead of these operators.
If a histogram has associated error bars ( TH1::Sumw2() has been called), the resulting error bars are also computed
assuming independent histograms. In case of divisions, binomial errors are also supported.

3.7

Projections

One can make:
• a 1-D projection of a 2-D histogram or profile. See TH2::ProfileX, TH2::ProfileY,TProfile::ProjectionX,
TProfile2D::ProjectionXY, TH2::ProjectionX, TH2::ProjectionY .
• a 1-D, 2-D or profile out of a 3-D histogram see TH3::ProjectionZ, TH3::Project3D.
These projections can be fit via: TH2::FitSlicesX, TH2::FitSlicesY, TH3::FitSlicesZ.

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CHAPTER 3. HISTOGRAMS

3.8

Drawing Histograms

When you call the Draw method of a histogram ( TH1::Draw ) for the first time, it creates a THistPainter object and
saves a pointer to painter as a data member of the histogram. The THistPainter class specializes in the drawing of
histograms. It allows logarithmic axes (x, y, z) when the CONT drawing option is using. The THistPainter class is
separated from the histogram so that one can have histograms without the graphics overhead, for example in a batch
program. The choice to give each histogram has its own painter rather than a central singleton painter, allows two
histograms to be drawn in two threads without overwriting the painter’s values. When a displayed histogram is filled
again, you do not have to call the Draw method again. The image is refreshed the next time the pad is updated. A pad
is updated after one of these three actions:
• A carriage control on the ROOT command line
• A click inside the pad
• A call to TPad::Update()
By default, the TH1::Draw clears the pad before drawing the new image of the histogram. You can use the "SAME"
option to leave thevprevious display in tact and superimpose the new histogram. The same histogram can be drawn
with different graphics options in different pads. When a displayed histogram is deleted, its image is automatically
removed from the pad. To create a copy of the histogram when drawing it, you can use TH1::DrawClone(). This will
clone the histogram and allow you to change and delete the original one without affecting the clone. You can use
TH1::DrawNormalized() to draw a normalized copy of a histogram.
TH1 *TH1::DrawNormalized(Option_t *option,Double_t norm) const
A clone of this histogram is normalized to norm and drawn with option. A pointer to the normalized histogram is
returned. The contents of the histogram copy are scaled such that the new sum of weights (excluding under and
overflow) is equal to norm .
Note that the returned normalized histogram is not added to the list of histograms in the current directory in memory.
It is the user’s responsibility to delete this histogram. The kCanDelete bit is set for the returned object. If a pad
containing this copy is cleared, the histogram will be automatically deleted. See “Draw Options” for the list of options.

3.8.1

Setting the Style

Histograms use the current style gStyle , which is the global object of class TStyle. To change the current style for
histograms, the TStyle class provides a multitude of methods ranging from setting the fill color to the axis tick marks.
Here are a few examples:
void
void
void
void
void

SetHistFillColor(Color_t
SetHistFillStyle(Style_t
SetHistLineColor(Color_t
SetHistLineStyle(Style_t
SetHistLineWidth(Width_t

color = 1)
styl = 0)
color = 1)
styl = 0)
width = 1)

When you change the current style and would like to propagate the change to a previously created histogram you can
call TH1::UseCurrentStyle(). You will need to call UseCurrentStyle() on each histogram. When reading many
histograms from a file and you wish to update them to the current style, you can use gROOT ::ForceStyle and all
histograms read after this call will be updated to use the current style. See “Graphics and the Graphical User Interface”.
When a histogram is automatically created as a result of a TTree::Draw , the style of the histogram is inherited from
the tree attributes and the current style is ignored. The tree attributes are the ones set in the current TStyle at the time
the tree was created. You can change the existing tree to use the current style, by calling TTree::UseCurrentStyle()
.

3.8.2

Draw Options

The following draw options are supported on all histogram classes:
• “AXIS”: Draw only the axis.

3.8. DRAWING HISTOGRAMS

59

• “HIST”: When a histogram has errors, it is visualized by default with error bars. To visualize it without errors
use HIST together with the required option (e.g. “HIST SAME C”).
• “SAME”: Superimpose on previous picture in the same pad.
• “CYL”: Use cylindrical coordinates.
• “POL”: Use polar coordinates.
• “SPH”: Use spherical coordinates.
• “PSR”: Use pseudo-rapidity/phi coordinates.
• “LEGO”: Draw a lego plot with hidden line removal.
• “LEGO1”: Draw a lego plot with hidden surface removal.
• “LEGO2”: Draw a lego plot using colors to show the cell contents.
• “SURF”: Draw a surface plot with hidden line removal.
• “SURF1”: Draw a surface plot with hidden surface removal.
• “SURF2”: Draw a surface plot using colors to show the cell contents.
• “SURF3”: Same as SURF with a contour view on the top.
• “SURF4”: Draw a surface plot using Gouraud shading.
• “SURF5”: Same as SURF3 but only the colored contour is drawn. Used with option CYL , SPH or PSR it allows to
draw colored contours on a sphere, a cylinder or in a pseudo rapidly space. In Cartesian or polar coordinates,
option SURF3 is used.
The following options are supported for 1-D histogram classes:
• “AH”: Draw the histogram, but not the axis labels and tick marks
• “B”: Draw a bar chart
• “C”: Draw a smooth curve through the histogram bins
• “E”: Draw the error bars
• “E0”: Draw the error bars including bins with 0 contents
• “E1”: Draw the error bars with perpendicular lines at the edges
• “E2”: Draw the error bars with rectangles
• “E3”: Draw a fill area through the end points of the vertical error bars
• “E4”: Draw a smoothed filled area through the end points of the error bars
• “L”: Draw a line through the bin contents
• “P”: Draw a (poly)marker at each bin using the histogram’s current marker style
• “P0”: Draw current marker at each bin including empty bins
• “PIE”: Draw a Pie Chart
• “*H”: Draw histogram with a * at each bin
• “LF2”: Draw histogram as with option “L” but with a fill area. Note that “L” also draws a fill area if the histogram
fill color is set but the fill area corresponds to the histogram contour.
• “9”: Force histogram to be drawn in high resolution mode. By default, the histogram is drawn in low resolution
in case the number of bins is greater than the number of pixels in the current pad
• “][”: Draw histogram without the vertical lines for the first and the last bin. Use it when superposing many
histograms on the same picture.
The following options are supported for 2-D histogram classes:

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CHAPTER 3. HISTOGRAMS
• “ARR”: Arrow mode. Shows gradient between adjacent cells
• “BOX”: Draw a box for each cell with surface proportional to contents
• “BOX1”: A sunken button is drawn for negative values, a raised one for positive values
• “COL”: Draw a box for each cell with a color scale varying with contents
• “COLZ”: Same as “COL” with a drawn color palette
• “CONT”: Draw a contour plot (same as CONT0 )
• “CONTZ”: Same as “CONT” with a drawn color palette
• “CONT0”: Draw a contour plot using surface colors to distinguish contours
• “CONT1”: Draw a contour plot using line styles to distinguish contours
• “CONT2”: Draw a contour plot using the same line style for all contours
• “CONT3”: Draw a contour plot using fill area colors
• “CONT4”: Draw a contour plot using surface colors (SURF2 option at theta = 0)
• "CONT5": Use Delaunay triangles to compute the contours
• “LIST”: Generate a list of TGraph objects for each contour
• “FB”: To be used with LEGO or SURFACE , suppress the Front-Box
• “BB”: To be used with LEGO or SURFACE , suppress the Back-Box
• “A”: To be used with LEGO or SURFACE , suppress the axis
• “SCAT”: Draw a scatter-plot (default)
• “SPEC”: Use TSpectrum2Painter tool for drawing
• “TEXT”: Draw bin contents as text (format set via gStyle->SetPaintTextFormat) .
• “TEXTnn”: Draw bin contents as text at angle nn ( 0Draw("E1SAME");
h->Draw("e1same");
The options are not case sensitive. The options BOX , COL and COLZ use the color palette defined in the current style
(see TStyle::SetPalette). The options CONT , SURF , and LEGO have by default 20 equidistant contour levels, you can
change the number of levels with TH1::SetContour. You can also set the default drawing option with TH1::SetOption
. To see the current option use TH1::GetOption . For example:
h->SetOption("lego");
h->Draw(); // will use the lego option
h->Draw("scat") // will use the scatter plot option

3.8. DRAWING HISTOGRAMS
3.8.2.1

61

The SCATter Plot Option

By default, 2D histograms are drawn as scatter plots. For each cell (i,j) a number of points proportional to the cell
content are drawn. A maximum of 500 points per cell are drawn. If the maximum is above 500 contents are normalized
to 500.

3.8.2.2

The ARRow Option

The ARR option shows the gradient between adjacent cells. For each cell (i,j) an arrow is drawn. The orientation of
the arrow follows the cell gradient.

3.8.2.3

The BOX Option

For each cell (i,j) a box is drawn with surface proportional to contents. The size of the box is proportional to the
absolute value of the cell contents. The cells with negative contents are drawn with an X on top of the boxes. With
option BOX1 a button is drawn for each cell with surface proportional to contents’ absolute value. A sunken button is
drawn for negative values, a raised one for positive values.

3.8.2.4

The ERRor Bars Options

• "E" Default. Draw only error bars, without markers
• "E0" Draw also bins with 0 contents (turn off the symbols clipping).
• "E1" Draw small lines at the end of error bars
• "E2" Draw error rectangles
• "E3" Draw a fill area through the end points of vertical error bars
• "E4" Draw a smoothed filled area through the end points of error bars
Note that for all options, the line and fill attributes of the histogram are used for the errors or errors contours. Use
gStyle->SetErrorX(dx) to control the size of the error along x. The parameter dx is a percentage of bin width for
errors along X. Set dx=0 to suppress the error along X. Use gStyle->SetEndErrorSize(np) to control the size of the
lines at the end of the error bars (when option 1 is used). By default np=1 (np represents the number of pixels).

3.8.2.5

The Color Option

For each cell (i,j) a box is drawn with a color proportional to the cell content. The color table used is defined in the
current style (gStyle ). The color palette in TStyle can be modified with TStyle::SetPalette .

3.8.2.6

The TEXT Option

For each cell (i,j) the cell content is printed. The text attributes are:
• Text font = current font set by TStyle
• Text size= 0.02 * pad-height * marker-size
• Text color= marker color

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CHAPTER 3. HISTOGRAMS

Figure 3.2: The “E1” bars’ option
3.8.2.7

The CONTour Options

The following contour options are supported:
• "CONT": Draw a contour plot (same as CONT0)
• "CONT0": Draw a contour plot using surface colors to distinguish contours
• "CONT1": Draw a contour plot using line styles to distinguish contours
• "CONT2": Draw a contour plot using the same line style for all contours
• "CONT3": Draw a contour plot using fill area colors
• "CONT4":Draw a contour plot using surface colors (SURF2 option at theta = 0); see also options “AITOFF”,
“MERCATOR”, etc. below
• "CONT5": Use Delaunay triangles to compute the contours
The default number of contour levels is 20 equidistant levels. It can be changed with TH1::SetContour. When option
“LIST” is specified together with option “CONT”, all points used for contour drawing, are saved in the TGraph object
and are accessible in the following way:
TObjArray *contours =
gROOT->GetListOfSpecials()->FindObject("contours");
Int_t ncontours = contours->GetSize(); TList *list =
(TList*)contours->At(i);
Where “i” is a contour number and list contains a list of TGraph objects. For one given contour, more than one disjoint
poly-line may be generated. The TGraph numbers per contour are given by list->GetSize(). Here we show how to
access the first graph in the list.

3.8. DRAWING HISTOGRAMS

63

Figure 3.3: Different draw options

64

CHAPTER 3. HISTOGRAMS

Figure 3.4: The TEXT option

3.8. DRAWING HISTOGRAMS

65

Figure 3.5: Different contour options

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CHAPTER 3. HISTOGRAMS
TGraph *gr1 = (TGraph*)list->First();
• “AITOFF”: Draw a contour via an AITOFF projection
• “MERCATOR”: Draw a contour via a Mercator projection
• “SINUSOIDAL”: Draw a contour via a Sinusoidal projection
• “PARABOLIC”: Draw a contour via a Parabolic projection

The tutorial macro earth.C uses these four options and produces the following picture:

Figure 3.6: The earth.C macro output

3.8.2.8

The LEGO Options

In a lego plot, the cell contents are drawn as 3D boxes, with the height of the box proportional to the cell content.
• “LEGO”: Draw a lego plot with hidden line removal
• “LEGO1”: Draw a lego plot with hidden surface removal
• “LEGO2”: Draw a lego plot using colors to show the cell contents
A lego plot can be represented in several coordinate systems; the default system is Cartesian coordinates. Other
possible coordinate systems are CYL , POL , SPH , and PSR .

3.8. DRAWING HISTOGRAMS

67

Figure 3.7: “LEGO” and “SURF” options

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CHAPTER 3. HISTOGRAMS
• “CYL”: Cylindrical coordinates: x-coordinate is mapped on the angle; y-coordinate - on the cylinder length.
• “POL”: Polar coordinates: x-coordinate is mapped on the angle; y-coordinate - on the radius.
• “SPH”: Spherical coordinates: x-coordinate is mapped on the latitude; y-coordinate - on the longitude.
• “PSR”: PseudoRapidity/Phi coordinates: x-coordinate is mapped on Phi.

With TStyle::SetPalette the color palette can be changed. We suggest you use palette 1 with the call:
gStyle->SetPalette(1);
3.8.2.9

The SURFace Options

In a surface plot, cell contents are represented as a mesh. The height of the mesh is proportional to the cell content. A
surface plot can be represented in several coordinate systems. The default is Cartesian coordinates, and the other
possible systems are CYL, POL, SPH, and PSR . The following picture uses SURF1 . With TStyle::SetPalette the color
palette can be changed. We suggest you use palette 1 with the call:
gStyle->SetPalette(1);

Figure 3.8: Different surface options

• “SURF”: Draw a surface plot with hidden line removal
• “SURF1”: Draw a surface plot with hidden surface removal
• “SURF2”: Draw a surface plot using colors to show the cell contents
• “SURF3”: Same as SURF with a contour view on the top

3.8. DRAWING HISTOGRAMS

69

• “SURF4”: Draw a surface plot using Gouraud shading
• “SURF5”: Same as SURF3 but only the colored contour is drawn. Used with options CYL , SPH or PSR it allows to
draw colored contours on a sphere, a cylinder or in a pseudo rapidly space. In Cartesian or polar coordinates,
option SURF3 is used.
3.8.2.10

The BAR Options

When the option “bar” or “hbar” is specified, a bar chart is drawn.
The options for vertical bar chart are “bar”, “bar0”, “bar1”, “bar2”, “bar3”, “bar4”.

Figure 3.9: Vertical bar charts
•
•
•
•

The
The
The
The
–
–
–
–
–

bar is filled with the histogram fill color.
left side of the bar is drawn with a light fill color.
right side of the bar is drawn with a dark fill color.
percentage of the bar drawn with either the light or dark color is:
0 per cent for option "bar" or "bar0"
10 per cent for option "bar1"
20 per cent for option "bar2"
30 per cent for option "bar3"
40 per cent for option "bar4"

Use TH1::SetBarWidth() to control the bar width (default is the bin width). Use TH1::SetBarOffset to control the
bar offset (default is 0). See the example $ROOTSYS/tutorials/hist/hbars.C
The options for the horizontal bar chart are “hbar”, “hbar0”, “hbar1”, “hbar2”, “hbar3”, and “hbar4”.
•
•
•
•
•

A horizontal bar is drawn for each bin.
The bar is filled with the histogram fill color.
The bottom side of the bar is drawn with a light fill color.
The top side of the bar is drawn with a dark fill color.
The percentage of the bar drawn with either the light or dark color is:
– 0 per cent for option “hbar” or “hbar0”

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CHAPTER 3. HISTOGRAMS
–
–
–
–

10
20
30
40

per
per
per
per

cent
cent
cent
cent

for
for
for
for

option
option
option
option

“hbar1”
“hbar2”
“hbar3”
“hbar4”

Use TH1::SetBarWidth to control the bar width (default is the bin width). Use TH1::SetBarOffset to control the
bar offset (default is 0). See the example $ROOTSYS/tutorials/hist/hbars.C

Figure 3.10: Horizontal bar charts

3.8.2.11

The Z Option: Display the Color Palette on the Pad

The “Z” option can be specified with the options: COL, CONT, SURF, and LEGO to display the color palette with an axis
indicating the value of the corresponding color on the right side of the picture. If there is not enough space on the right
side, you can increase the size of the right margin by calling TPad::SetRightMargin(). The attributes used to display
the palette axis values are taken from the Z axis of the object. For example, you can set the labels size on the palette
axis with:
hist->GetZaxis()->SetLabelSize();
3.8.2.12

Setting the Color Palette

You can set the color palette with TStyle::SetPalette , e.g.
gStyle->SetPalette(ncolors,colors);
For example, the option COL draws a 2-D histogram with cells represented by a box filled with a color index, which is a
function of the cell content. If the cell content is N, the color index used will be the color number in colors[N] . If
the maximum cell content is greater than ncolors , all cell contents are scaled to ncolors. If ncolors<=0, a default
palette of 50 colors is defined. This palette is recommended for pads, labels. It defines:
•
•
•
•

Index
Index
Index
Index

0 to 9: shades of gray
10 to 19:shades of brown
20 to 29:shades of blue
30 to 39: shades of red

3.8. DRAWING HISTOGRAMS

71

• Index 40 to 49:basic colors
The color numbers specified in this palette can be viewed by selecting the menu entry Colors in the View menu of the
canvas menu bar. The color’s red, green, and blue values can be changed via TColor::SetRGB.
If ncolors == 1 && colors == 0, then a Pretty Palette with a spectrum violet to red is created with 50 colors.
That’s the default rain bow palette.
Other prefined palettes with 255 colors are available when colors == 0. The following value of ncolors (with colors
= 0) give access to:
•
•
•
•
•
•

ncolors
ncolors
ncolors
ncolors
ncolors
ncolors

=
=
=
=
=
=

51
52
53
54
55
56

:
:
:
:
:
:

Deep Sea palette.
Grey Scale palette.
Dark Body Radiator palette.
Two-color hue palette palette. (dark blue through neutral gray to bright yellow)
Rain Bow palette.
Inverted Dark Body Radiator palette.

The color numbers specified in the palette can be viewed by selecting the item “colors” in the “VIEW” menu of the
canvas toolbar. The color parameters can be changed via TColor::SetRGB.
Note that when drawing a 2D histogram h2 with the option “COL” or “COLZ” or with any “CONT” options using the
color map, the number of colors used is defined by the number of contours n specified with: h2->SetContour(n)
3.8.2.13

TPaletteAxis

A TPaletteAxisobject is used to display the color palette when drawing 2D histograms. The object is automatically
created when drawing a 2D histogram when the option “z” is specified. It is added to the histogram list of functions.
It can be retrieved and its attributes can be changed with:
TPaletteAxis *palette=(TPaletteAxis*)h->FindObject("palette");
The palette can be interactively moved and resized. The context menu can be used to set the axis attributes. It is
possible to select a range on the axis, to set the min/max in z.
3.8.2.14

The SPEC Option

The “SPEC” option offers a large set of options/attributes to visualize 2D histograms thanks to “operators” following
the “SPEC” keyword. For example, to draw the 2-D histogram h2 using all default attributes except the viewing angles,
one can do:
h2->Draw("SPEC a(30,30,0)");
The operators’ names are case unsensitive (i.e. one can use “a” or “A”) and their parameters are seperated by coma “,”.
Operators can be put in any order in the option and must be separated by a space " “. No space characters should be
put in an operator. All the available operators are described below.
The way how a 2D histogram will be painted is controled by two parameters: the “Display modes groups” and the
“Display Modes”. “Display modes groups” can take the following values:
•
•
•
•

0 = Simple - simple display modes using one color only
1 = Light - the shading is carried out according to the position of the fictive light source
2 = Height - the shading is carried out according to the channel contents
3 = LightHeight - combination of two previous shading algorithms (one can control the weight between both
algorithms).

“Display modes” can take the following values:
• 1 = Points
• 2 = Grid

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CHAPTER 3. HISTOGRAMS
•
•
•
•
•
•
•
•
•

3 = Contours
4 = Bars
5 = LinesX
6 = LinesY
7 = BarsX
8 = BarsY
9 = Needles
10 = Surface
11 = Triangles

These parameters can be set by using the “dm” operator in the option.
h2->Draw("SPEC dm(1,2)");
The above example draws the histogram using the “Light Display mode group” and the “Grid Display mode”. The
following tables summarize all the possible combinations of both groups:

Simple
Light
Height
LightHeight

Points
x
x
x
x

Simple
Light
Height
LightHeight

BarsX
x
•
x
•

Grid
x
x
x
x

Contours
x
•
x
•

BarsY
x
•
x
•

Needles
x
•
•
•

Bars
x
•
x
•

LinesX
x
x
x
x

Surface
•
x
x
x

LinesY
x
x
x
x

Triangles
x
x
x
x

The “Pen Attributes” can be changed using pa(color,style,width). Next example sets line color to 2, line type to 1
and line width to 2. Note that if pa() is not specified, the histogram line attributes are used:
h2->Draw("SPEC dm(1,2) pa(2,1,2)");
The number of “Nodes” can be changed with n(nodesx,nodesy). Example:
h2->Draw("SPEC n(40,40)");
Sometimes the displayed region is rather large. When displaying all channels the pictures become very dense and
complicated. It is very difficult to understand the overall shape of data. “n(nx,ny)” allows to change the density of
displayed channels. Only the channels coinciding with given nodes are displayed.
The visualization “Angles” can be changed with “a(alpha,beta,view)”: “alpha” is the angle between the bottom
horizontal screen line and the displayed space on the right side of the picture and “beta” on the left side, respectively.
One can rotate the 3-d space around the vertical axis using the “view” parameter. Allowed values are 0, 90, 180 and
270 degrees.
h2->Draw("SPEC n(40,40) dm(0,1) a(30,30,0)");
The operator “zs(scale)” changes the scale of the Z-axis. The possible values are:
• 0 = Linear (default),
• 1 = Log,
• 2 = Sqrt.
If gPad->SetLogz() has been set, the log scale on Z-axis is set automatically, i.e. there is no need for using the zs()
operator. Note that the X and Y axis are always linear.

3.8. DRAWING HISTOGRAMS

73

The operator “ci(r,g,b)” defines the colors increments (r, g and b are floats). For sophisticated shading (Light, Height
and LightHeight Display Modes Groups) the color palette starts from the basic pen color (see pa() function). There is
a predefined number of color levels (256). Color in every level is calculated by adding the increments of the r , g , b
components to the previous level. Using this function one can change the color increments between two neighboring
color levels. The function does not apply on the Simple Display Modes Group. The default values are: (1,1,1).
The operator “ca(color_algorithm)” allows to choose the Color Algorithm. To define the colors one can use one of
the following color algorithms (RGB, CMY, CIE, YIQ, HVS models). When the level of a component reaches the limit
value one can choose either smooth transition (by decreasing the limit value) or a sharp modulo transition (continuing
with 0 value). This allows various visual effects. One can choose from the following set of the algorithms:
•
•
•
•
•
•
•
•
•
•

0
1
2
3
4
5
6
7
8
9

=
=
=
=
=
=
=
=
=
=

RGB Smooth,
RGB Modulo,
CMY Smooth,
CMY Modulo,
CIE Smooth
CIE Modulo,
YIQ Smooth,
YIQ Modulo,
HVS Smooth,
HVS Modulo

This function does not apply on Simple display modes group. Default value is 0. Example choosing CMY Modulo to
paint the 2D histogram:
h2->Draw("SPEC c1(3) dm(0,1) a(30,30,0)");
The operator “lp(x,y,z)” sets the light position. In Light and LightHeight display modes groups the color palette is
calculated according to the fictive light source position in 3-d space. Using this function one can change the source’s
position and thus achieve various graphical effects. This function does not apply for Simple and Height display modes
groups. Default is: lp(1000,1000,100) .
The operator “s(shading,shadow)” allows to set the shading. The surface picture is composed of triangles. The edges
of the neighboring triangles can be smoothed (shaded). The shadow can be painted as well. The function does not
apply on Simple display modes group. The possible values for shading are:
• 0 = Not Shaded,
• 1 = Shaded.
The possible values for shadow are:
• 0 = Shadows are not painted,
• 1 = Shadows are painted.
Default values: s(1,0) .
The operator “b(bezier)” sets the Bezier smoothing. For Simple display modes group and for Grid, LinesX and
LinesY display modes one can smooth data using Bezier smoothing algorithm. The function does not apply on other
display modes groups and display modes. Possible values are: 0 = No bezier smoothing, 1 = Bezier smoothing. Default
value is: b(0).
The operator “cw(width)” sets the contour width. This function applies only on for the Contours display mode. One
can change the width between horizontal slices and thus their density. Default value: cw(50) .
The operator “lhw(weight)” sets the light height weight. For LightHeight display modes group one can change the
weight between both shading algorithms. The function does not apply on other display modes groups. Default value is
lhw(0.5) .
The operator “cm(enable,color,width,height,style)” allows to draw a marker on each node. In addition to the
surface drawn using any above given algorithm one can display channel marks. One can control the color as well as the
width, height (in pixels) and the style of the marks. The parameter enable can be set to 0 = Channel marks are not
drawn or 1 = Channel marks drawn. The possible styles are:

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CHAPTER 3. HISTOGRAMS
•
•
•
•
•
•
•

1
2
3
4
5
6
7

=
=
=
=
=
=
=

Dot,
Cross,
Star,
Rectangle,
X,
Diamond,
Triangle.

The operator “cg(enable,color)” channel grid. In addition to the surface drawn using any above given algorithm
one can display grid using the color parameter. The parameter enable can be set to:
• 0 = Grid not drawn,
• 1 = Grid drawn.
See the example in $ROOTSYS/tutorials/spectrum/spectrumpainter.C .

Figure 3.11: The picture produced by spectrumpainter.C macro

3.8.2.15

3-D Histograms

By default a 3D scatter plot is drawn. If the “BOX” option is specified, a 3D box with a volume proportional to the
cell content is drawn.

3.8. DRAWING HISTOGRAMS

75

Figure 3.12: The picture produced by fit2a.C macro

3.8.3

Drawing a Sub-range of a 2-D Histogram

Using a TCutG object, it is possible to draw a 2D histogram sub-range. One must create a graphical cut (mouse or
C++) and specify the name of the cut between “[” and “]” in the Draw option.
For example, with a TCutGnamed “cutg”, one can call:
myhist->Draw("surf1 [cutg]");
Or, assuming two graphical cuts with name “cut1” and “cut2”, one can do:
h1.Draw("lego");
h2.Draw("[cut1,-cut2],surf,same");
The second Draw will superimpose on top of the first lego plot a subset of h2using the “surf” option with:
• all the bins inside cut1
• all the bins outside cut2
Up to 16 cuts may be specified in the cut string delimited by "[..]". Currently only the following drawing options are
sensitive to the cuts option: col , box , scat , hist , lego , surf and cartesian coordinates only. See a complete
example in the tutorial $ROOTSYS/tutorials/fit/fit2a.C .

3.8.4

Superimposing Histograms with Different Scales

The following script creates two histograms; the second histogram is the bins integral of the first one. It shows a
procedure to draw the two histograms in the same pad and it draws the scale of the second histogram using a new
vertical axis on the right side.

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CHAPTER 3. HISTOGRAMS

Figure 3.13: Superimposed histograms with different scales

void twoscales() {
TCanvas *c1 = new TCanvas("c1","different scales hists",600,400);
//create, fill and draw h1
gStyle->SetOptStat(kFALSE);
TH1F *h1 = new TH1F("h1","my histogram",100,-3,3);
for (Int_t i=0;i<10000;i++) h1->Fill(gRandom->Gaus(0,1));
h1->Draw();
c1->Update();
//create hint1 filled with the bins integral of h1
TH1F *hint1 = new TH1F("hint1","h1 bins integral",100,-3,3);
Float_t sum = 0;
for (Int_t i=1;i<=100;i++) {
sum += h1->GetBinContent(i);
hint1->SetBinContent(i,sum);
}
//scale hint1 to the pad coordinates
Float_t rightmax = 1.1*hint1->GetMaximum();
Float_t scale
= gPad->GetUymax()/rightmax;
hint1->SetLineColor(kRed);
hint1->Scale(scale);
hint1->Draw("same");
//draw an axis on the right side
TGaxis*axis = new TGaxis(gPad->GetUxmax(),gPad->GetUymin(),
gPad->GetUxmax(),gPad->GetUymax(),
0,rightmax,510,"+L");
axis->SetLineColor(kRed);
axis->SetLabelColor(kRed);
axis->Draw();
}

3.8. DRAWING HISTOGRAMS

3.8.5

77

Statistics Display

By default, a histogram drawing includes the statistics box. Use TH1::SetStats(kFALSE) to eliminate the statistics
box. If the statistics box is drawn, gStyle->SetOptStat(mode) allow you to select the type of displayed information .
The parameter mode has up to nine digits that can be set OFF (0) or ON as follows:
mode = ksiourmen (default =000001111)
•
•
•
•
•
•
•
•
•
•
•
•
•

n
e
m
m
r
r
u
o
i
s
s
k
k

=
=
=
=
=
=
=
=
=
=
=
=
=

1
1
1
2
1
2
1
1
1
1
2
1
2

the
the
the
the
the
the
the
the
the
the
the
the
the

name of histogram is printed
number of entries
mean value
mean and mean error values
root mean square (RMS)
RMS and RMS error
number of underflows
number of overflows
integral of bins
skewness
skewness and the skewness error
kurtosis
kurtosis and the kurtosis error

Never call SetOptStat(0001111) , but SetOptStat(1111) , because 0001111 will be taken as an octal number.
The method TStyle::SetOptStat(Option_t*option) can also be called with a character string as a parameter. The
parameter option can contain:
•
•
•
•
•
•
•
•
•
•
•
•
•

n
e
m
M
r
R
u
o
i
s
S
k
K

for printing the name of histogram
the number of entries
the mean value
the mean and mean error values
the root mean square (RMS)
the RMS and RMS error
the number of underflows
the number of overflows
the integral of bins
the skewness
the skewness and the skewness error
the kurtosis
the kurtosis and the kurtosis error

gStyle->SetOptStat("ne");

//
//
gStyle->SetOptStat("n");
//
gStyle->SetOptStat("nemr"); //

prints the histogram name and number
of entries
prints the histogram name
the default value

With the option "same", the statistic box is not redrawn. With the option "sames", it is re-drawn. If it hides the
previous statistics box, you can change its position with the next lines (where h is the histogram pointer):
root[] TPaveStats *s =
(TPaveStats*)h->GetListOfFunctions()->FindObject("stats");
root[] s->SetX1NDC (newx1); // new x start position
root[] s->SetX2NDC (newx2); // new x end position

3.8.6

Setting Line, Fill, Marker, and Text Attributes

The histogram classes inherit from the attribute classes: TAttLine, TAttFill, TAttMarker and TAttText. See the
description of these classes for the list of options.

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CHAPTER 3. HISTOGRAMS

3.8.7

Setting Tick Marks on the Axis

The TPad::SetTicks() method specifies the type of tick marks on the axis.
ty=gPad->GetTicky().
•
•
•
•
•

Let tx=gPad->GetTickx() and

tx = 1; tick marks on top side are drawn (inside)
tx = 2; tick marks and labels on top side are drawn
ty = 1; tick marks on right side are drawn (inside)
ty = 2; tick marks and labels on right side are drawn
tx=ty=0 by default only the left Y axis and X bottom axis are drawn

Use TPad::SetTicks(tx,ty) to set these options. See also the methods of TAxis that set specific axis attributes. If
multiple color-filled histograms are drawn on the same pad, the fill area may hide the axis tick marks. One can force
the axis redrawing over all the histograms by calling:
gPad->RedrawAxis();

3.8.8

Giving Titles to the X, Y and Z Axis

Because the axis title is an attribute of the axis, you have to get the axis first and then call TAxis::SetTitle.
h->GetXaxis()->SetTitle("X axis title");
h->GetYaxis()->SetTitle("Y axis title");
h->GetZaxis()->SetTitle("Z axis title");
The histogram title and the axis titles can be any TLatex string. The titles are part of the persistent histogram. For
example if you wanted to write E with a subscript (T) you could use this:
h->GetXaxis()->SetTitle("E_{T}");
For a complete explanation of the Latex mathematical expressions, see “Graphics and the Graphical User Interface”. It
is also possible to specify the histogram title and the axis titles at creation time. These titles can be given in the “title”
parameter. They must be separated by “;”:
TH1F* h=new TH1F("h","Histogram title;X Axis;Y Axis;Z Axis",
100,0,1);
Any title can be omitted:
TH1F* h=new TH1F("h","Histogram title;;Y Axis",100,0,1);
TH1F* h=new TH1F("h",";;Y Axis",100,0,1);
The method SetTitle has the same syntax:
h->SetTitle("Histogram title;An other X title Axis");

3.9

Making a Copy of an Histogram

Like for any other ROOT object derived from TObject , the Clone method can be used. This makes an identical copy
of the original histogram including all associated errors and functions:
TH1F *hnew = (TH1F*)h->Clone(); // renaming is recommended,
hnew->SetName("hnew");
// because otherwise you will have
// two histograms with the same
// name

3.10. NORMALIZING HISTOGRAMS

3.10

79

Normalizing Histograms

You can scale a histogram ( TH1 *h ) such that the bins integral is equal to the normalization parameter norm:
Double_t scale = norm/h->Integral();
h->Scale(scale);

3.11

Saving/Reading Histograms to/from a File

The following statements create a ROOT file and store a histogram on the file. Because TH1 derives from TNamed , the
key identifier on the file is the histogram name:
TFile f("histos.root","new");
TH1F h1("hgaus","histo from a gaussian",100,-3,3);
h1.FillRandom("gaus",10000);
h1->Write();
To read this histogram in another ROOT session, do:
TFile f("histos.root");
TH1F *h = (TH1F*)f.Get("hgaus");
One can save all histograms in memory to the file by:
file->Write();
For a more detailed explanation, see “Input/Output”.

3.12

Miscellaneous Operations

• TH1::KolmogorovTest( TH1* h2,Option_t *option) is statistical test of compatibility in shape between two
histograms. The parameter option is a character string that specifies:
• “U” include Underflows in test (also for 2-dim)
• “O” include Overflows (also valid for 2-dim)
• “N” include comparison of normalizations
• “D” put out a line of “Debug” printout
• “M” return the maximum Kolmogorov distance instead of prob
• “X” run the pseudo experiments post-processor with the following procedure: it makes pseudo experiments based
on random values from the parent distribution and compare the KS distance of the pseudo experiment to the
parent distribution. Bin the KS distances in a histogram, and then take the integral of all the KS values above the
value obtained from the original data to Monte Carlo distribution. The number of pseudo-experiments NEXPT
is currently fixed at 1000. The function returns the integral. Note that this option “X” is much slower.
• TH1::Smooth - smoothes the bin contents of a 1D histogram.
• TH1::Integral(Option_t *opt)-returns the integral of bin contents in a given bin range. If the option “width”
is specified, the integral is the sum of the bin contents multiplied by the bin width in x .
• TH1::GetMean(int axis) - returns the mean value along axis.
• TH1::GetRMS(int axis) - returns the Root Mean Square along axis.
• TH1::GetEntries() - returns the number of entries.
• TH1::GetAsymmetry(TH1 *h2,Double_t c2,Double_tdc2)

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CHAPTER 3. HISTOGRAMS
– returns an histogram containing the asymmetry of this histogram with h2, where the asymmetry is defined
as:
Asymmetry = (h1 - h2)/(h1 + h2); //where h1 = this
• It works for 1D , 2D , etc. histograms. The parameter c2 is an optional argument that gives a relative weight
between the two histograms, and dc 2 is the error on this weight. This is useful, for example, when forming an
asymmetry between two histograms from two different data sets that need to be normalized to each other in
some way. The function calculates the errors assuming Poisson statistics on h1 and h2 (that is, dh=sqrt(h)). In
the next example we assume that h1 and h2 are already filled:
h3 = h1->GetAsymmetry(h2);
• Then h3 is created and filled with the asymmetry between h1 and h2 ; h1 and h2 are left intact.
• Note that the user’s responsibility is to manage the created histograms.
• TH1::Reset() - resets the bin contents and errors of a histogram

3.13

Alphanumeric Bin Labels

By default, a histogram axis is drawn with its numeric bin labels. One can specify alphanumeric labels instead.

3.13.1

Option 1: SetBinLabel

To set an alphanumeric bin label call:
TAxis::SetBinLabel(bin,label);
This can always be done before or after filling. Bin labels will be automatically drawn with the histogram.

Figure 3.14: Histograms with alphanumeric bin labels
See example in $ROOTSYS/tutorials/hist/hlabels1.C , hlabels2.C

3.13. ALPHANUMERIC BIN LABELS

3.13.2

81

Option 2: Fill

You can also call a Fill() function with one of the arguments being a string:
hist1->Fill(somename,weigth);
hist2->Fill(x,somename,weight);
hist2->Fill(somename,y,weight);
hist2->Fill(somenamex,somenamey,weight);

3.13.3

Option 3: TTree::Draw

You can use a char* variable type to histogram strings with TTree::Draw().
// here "Nation" and "Division" are two char* branches of a Tree
tree.Draw("Nation::Division", "", "text");

Figure 3.15: Using a *char variable type in TTree::Draw
There is an example in $ROOTSYS/tutorials/tree/cernstaff.C.
If a variable is defined as char* it is drawn as a string by default. You change that and draw the value of char[0] as
an integer by adding an arithmetic operation to the expression as shown below.
// draw the integer value of MyChar[0] where "MyChar" is char[5]
tree.Draw("MyChar + 0");

3.13.4

Sort Options

When using the options 2 or 3 above, the labels are automatically added to the list (THashList) of labels for a given
axis. By default, an axis is drawn with the order of bins corresponding to the filling sequence. It is possible to reorder
the axis alphabetically or by increasing or decreasing values. The reordering can be triggered via the TAxis context
menu by selecting the menu item “LabelsOption” or by calling directly.

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CHAPTER 3. HISTOGRAMS
TH1::LabelsOption(option,axis);

Here axis may be X, Y, or Z. The parameter option may be:
•
•
•
•
•
•
•

“a”
“>”
“<”
“h”
“v”
“u”
“d”

sort by alphabetic order
sort by decreasing values
sort by increasing values
draw labels horizontal
draw labels vertical
draw labels up (end of label right adjusted)
draw labels down (start of label left adjusted)

When using the option second above, new labels are added by doubling the current number of bins in case one label
does not exist yet. When the filling is terminated, it is possible to trim the number of bins to match the number of
active labels by calling:
TH1::LabelsDeflate(axis);
Here axis may be X, Y, or Z. This operation is automatic when using TTree::Draw . Once bin labels have been created,
they become persistent if the histogram is written to a file or when generating the C++ code via SavePrimitive .

3.14

Histogram Stacks

A THStack is a collection of TH1 (or derived) objects. Use THStack::Add( TH1 *h) to add a histogram to the stack.
The THStack does not own the objects in the list.

Figure 3.16: Stacked histograms
By default, THStack::Draw draws the histograms stacked as shown in the left pad in the picture above. If the option
"nostack" is used, the histograms are superimposed as if they were drawn one at a time using the "same" draw option
. The right pad in this picture illustrates the THStack drawn with the "nostack" option.
hs->Draw("nostack");
Next is a simple example, for a more complex one see $ROOTSYS/tutorials/hist/hstack.C.

3.15. TH2POLY
{

}

83

THStack hs("hs","test stacked histograms");
TH1F *h1 = new TH1F("h1","test hstack",100,-4,4);
h1->FillRandom("gaus",20000);
h1->SetFillColor(kRed);
hs.Add(h1);
TH1F *h2 = new TH1F("h2","test hstack",100,-4,4);
h2->FillRandom("gaus",15000);
h2->SetFillColor(kBlue);
hs.Add(h2);
TH1F *h3 = new TH1F("h3","test hstack",100,-4,4);
h3->FillRandom("gaus",10000);
h3->SetFillColor(kGreen);
hs.Add(h3);
TCanvas c1("c1","stacked hists",10,10,700,900);
c1.Divide (1,2);
c1.cd(1);
hs.Draw();
c1.cd(2);
hs->Draw("nostack");

3.15

TH2Poly

TH2Poly is a 2D Histogram class allowing to define polygonal bins of arbitary shape.
Each bin in the TH2Poly histogram is a TH2PolyBin object. TH2PolyBin is a very simple class containing the vertices
and contents of the polygonal bin as well as several related functions.
Bins are defined using one of the AddBin() methods. The bin definition should be done before filling.
The following very simple macro shows how to build and fill a TH2Poly:
{

}

TH2Poly *h2p = new TH2Poly();
Double_t x1[] = {0, 5, 5};
Double_t y1[] = {0, 0, 5};
Double_t x2[] = {0, -1, -1, 0};
Double_t y2[] = {0, 0, -1, -1};
Double_t x3[] = {4, 3, 0, 1, 2.4};
Double_t y3[] = {4, 3.7, 1, 4.7, 3.5};
h2p->AddBin(3, x1, y1);
h2p->AddBin(3, x2, y2);
h2p->AddBin(3, x3, y3);
h2p->Fill( 3, 1, 3);
// fill bin 1
h2p->Fill(-0.5, -0.5, 7); // fill bin 2
h2p->Fill(-0.7, -0.5, 1); // fill bin 2
h2p->Fill( 1, 3, 5);
// fill bin 3

More examples can bin found in $ROOTSYS/tutorials/hist/th2poly*.C

3.16

Profile Histograms

Profile histograms are in many cases an elegant replacement of two-dimensional histograms. The relationship of
two quantities X and Y can be visualized by a two-dimensional histogram or a scatter-plot; its representation is not
particularly satisfactory, except for sparse data. If Y is an unknown [but single-valued] function of X, it can be displayed
by a profile histogram with much better precision than by a scatter-plot. Profile histograms display the mean value
of Y and its RMS for each bin in X. The following shows the contents [capital letters] and the values shown in the
graphics [small letters] of the elements for bin j. When you fill a profile histogram with TProfile.Fill(x,y) :

84

CHAPTER 3. HISTOGRAMS

Figure 3.17: A TH2Poly histogram example
• H[j] will contain for each bin j the sum of the y values for this bin
• L[j] contains the number of entries in the bin j
• e[j] or s[j] will be the resulting error depending on the selected option. See “Build Options”.
E[j]
L[j]
H[j]
h[j]
s[j]
e[j]

=
=
=
=
=
=

sum Y**2
number of entries in bin J
sum Y
H[j] / L[j]
sqrt[E[j] / L[j] - h[j]**2]
s[j] / sqrt[L[j]]

In the special case where s[j] is zero, when there is only one entry per bin, e[j] is computed from the average of the
s[j] for all bins. This approximation is used to keep the bin during a fit operation. The TProfile constructor takes
up to eight arguments. The first five parameters are similar to TH1D constructor.
TProfile(const char *name,const char *title,Int_t nbinsx,
Double_t xlow, Double_t xup, Double_t ylow, Double_t yup,
Option_t *option)
All values of y are accepted at filling time. To fill a profile histogram, you must use TProfile::Fill function. Note
that when filling the profile histogram the method TProfile::Fill checks if the variable y is between fYmin and
fYmax. If a minimum or maximum value is set for the Y scale before filling, then all values below ylow or above yup
will be discarded. Setting the minimum or maximum value for the Y scale before filling has the same effect as calling
the special TProfile constructor above where ylow and yup are specified.

3.16.1

Build Options

The last parameter is the build option. If a bin has N data points all with the same value Y, which is the case when
dealing with integers, the spread in Y for that bin is zero, and the uncertainty assigned is also zero, and the bin is
ignored in making subsequent fits. If SQRT(Y) was the correct error in the case above, then SQRT(Y)/SQRT(N) would
be the correct error here. In fact, any bin with non-zero number of entries N but with zero spread (spread = s[j])

3.16. PROFILE HISTOGRAMS

85

should have an uncertainty SQRT(Y)/SQRT(N). Now, is SQRT(Y)/SQRT(N) really the correct uncertainty ? That it is
only in the case where the Y variable is some sort of counting statistics, following a Poisson distribution. This is
the default case. However, Y can be any variable from an original NTUPLE, and does not necessarily follow a Poisson
distribution. The computation of errors is based on Y = values of data points; N = number of data points.
• ’ ’ - the default is blank, the errors are:
• spread/SQRT(N) for a non-zero spread
• SQRT(Y)/SQRT(N) for a spread of zero and some data points
• 0 for no data points
• ‘s’ - errors are:
• spread for a non-zero spread
• SQRT(Y) for a Spread of zero and some data points
• 0 for no data points
• ‘i’ - errors are:
• spread/SQRT(N) for a non-zero spread
• 1/SQRT(12*N) for a Spread of zero and some data points
• 0 for no data points
• ‘G’ - errors are:
• spread/SQRT(N) for a non-zero spread
• sigma/SQRT(N) for a spread of zero and some data points
• 0 for no data points
The option ‘i’ is used for integer Y values with the uncertainty of ±0.5, assuming the probability that Y takes any
value between Y-0.5 and Y+0.5 is uniform (the same argument for Y uniformly distributed between Y and Y+1).
An example is an ADC measurement. The ‘G’ option is useful, if all Y variables are distributed according to some
known Gaussian of standard deviation Sigma. For example when all Y’s are experimental quantities measured with the
same instrument with precision Sigma. The next figure shows the graphic output of this simple example of a profile
histogram.
{

// Create a canvas giving the coordinates and the size
TCanvas *c1 = new TCanvas("c1", "Profile example",200,10,700,500);
// Create a profile with the name, title, the number of bins,
// the low and high limit of the x-axis and the low and high
// limit of the y-axis.
// No option is given so the default is used.
hprof = new TProfile("hprof",
"Profile of pz versus px",100,-4,4,0,20);

}

// Fill the profile 25000 times with random numbers
Float_t px, py, pz;
for ( Int_t i=0; i<25000; i++) {
// Use the random number generator to get two numbers following
// a gaussian distribution with mean=0 and sigma=1
gRandom->Rannor(px,py);
pz = px*px + py*py;
hprof->Fill(px,pz,1);
}
hprof->Draw();

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CHAPTER 3. HISTOGRAMS

Figure 3.18: A profile histogram example

3.16.2

Drawing a Profile without Error Bars

To draw a profile histogram and not show the error bars use the “HIST” option in the TProfile::Draw method. This
will draw the outline of the TProfile.

3.16.3

Create a Profile from a 2D Histogram

You can make a profile from a histogram using the methods TH2::ProfileX and TH2::ProfileY.

3.16.4

Create a Histogram from a Profile

To create a regular histogram from a profile histogram, use the method TProfile::ProjectionX .This example
instantiates a TH1D object by copying the TH1D piece of TProfile.
TH1D *sum = myProfile.ProjectionX();
You can do the same with a 2D profile using the method TProfile2D::ProjectionXY .

3.16.5

Generating a Profile from a TTree

The ’prof’ and ’profs’ options in the TTree::Draw method generate a profile histogram ( TProfile ), given a two
dimensional expression in the tree, or a TProfile2D given a three dimensional expression. See “Trees”. Note that you
can specify ’prof’ or ’profs’ : ’prof’ generates a TProfile with error on the mean, ’profs’ generates a TProfile
with error on the spread.

3.16. PROFILE HISTOGRAMS

3.16.6

87

2D Profiles

The class for a 2D Profile is called TProfile2D . It is in many cases an elegant replacement of a three-dimensional
histogram. The relationship of three measured quantities X, Y and Z can be visualized by a three-dimensional histogram
or scatter-plot; its representation is not particularly satisfactory, except for sparse data. If Z is an unknown (but
single-valued) function of (X,Y), it can be displayed with a TProfile2D with better precision than by a scatter-plot.
A TProfile2D displays the mean value of Z and its RMS for each cell in X, Y. The following shows the cumulated
contents (capital letters) and the values displayed (small letters) of the elements for cell i,j.
When you fill a profile histogram with TProfile2D.Fill(x,y,z):
• E[i,j] contains for each bin i,j the sum of the z values for this bin
• L[i,j] contains the number of entries in the bin j
• e[j] or s[j] will be the resulting error depending on the selected option. See “Build Options”.
E[i,j]
L[i,j]
h[i,j]
s[i,j]
e[i,j]

=
=
=
=
=

sum z
sum l
H[i,j ] / L[i,j]
sqrt[E[i,j] / L[i,j]- h[i,j]**2]
s[i,j] / sqrt[L[i,j]]

In the special case where s[i,j] is zero, when there is only one entry per cell, e[i,j] is computed from the average of
the s[i,j] for all cells. This approximation is used to keep the cell during a fit operation.

Figure 3.19: A TProfile2D histogram example
{

// Creating a Canvas and a TProfile2D
TCanvas *c1 = new TCanvas("c1",
"Profile histogram example",
200, 10,700,500);

88

CHAPTER 3. HISTOGRAMS
hprof2d = new TProfile2D("hprof2d",
"Profile of pz versus px and py",
40,-4,4,40,-4,4,0,20);

}

// Filling the TProfile2D with 25000 points
Float_t px, py, pz;
for (Int_t i=0; i<25000; i++) {
gRandom->Rannor(px,py);
pz = px*px + py*py;
hprof2d->Fill(px,py,pz,1);
}
hprof2d->Draw();

3.17

Iso Surfaces

Paint one Gouraud shaded 3d iso surface though a 3d histogram at the value computed as follow: SumOfWeights/(NbinsX*NbinsY*N
void hist3d() {
TH3D *h3 = new TH3D("h3", "h3", 20, -2, 2, 20, -2, 2, 20, 0, 4);
Double_t x,y,z;
for (Int_t i=0; i<10000; i++) {
gRandom->
Rannor(x,y);
z=x*x+y*y;
h3->Fill(x,y,z);
}
h3->Draw("iso");
}

3.18

3D Implicit Functions

TF3 *fun3 = new TF3("fun3","sin(x*x+y*y+z*z-36)",-2,2,-2,2,-2,2);
fun3->Draw();

3.19

TPie

The TPie class allows to create a Pie Chart representation of a one dimensional data set. The data can come from an
array of Double_t (or Float_t ) or from a 1D-histogram. The possible options to draw a TPie are:
• “R” Paint the labels along the central “R”adius of slices.
• “T” Paint the labels in a direction “T”angent to circle that describes the TPie.
• “3D” Draw the pie-chart with a pseudo 3D effect.
• “NOL” No OutLine: do not draw the slices’ outlines; any property over the slices’ line is ignored.
The method SetLabelFormat() is used to customize the label format. The format string must contain one of these
modifiers:
•

– %txt : to print the text label associated with the slice

•

– %val : to print the numeric value of the slice

•

– %frac : to print the relative fraction of this slice

•

– %perc : to print the % of this slice

mypie->SetLabelFormat("%txt (%frac)");
See the macro $ROOTSYS/tutorials/graphics/piechart.C .

3.19. TPIE

89

Figure 3.20: Iso surfaces

Figure 3.21: 3D implicit function

90

CHAPTER 3. HISTOGRAMS

Figure 3.22: The picture generated by tutorial macro piechart.C

3.20. THE USER INTERFACE FOR HISTOGRAMS

3.20

91

The User Interface for Histograms

The classes T H1 Editor and T H2 Editor provides the user interface for setting histogram’s attributes and rebinning
interactively.

3.20.1

TH1Editor

3.20.1.1

The Style Tab

3.20.1.1.1

Title sets the title of the histogram.

3.20.1.1.2

Plot draw a 2D or 3D plot; according to the dimension, different drawing possibilities can be set.

3.20.1.1.3

Error add different error bars to the histogram (no errors, simple, etc.).

3.20.1.1.4

Add further things which can be added to the histogram (None, simple/smooth line, fill area, etc.)

3.20.1.2

2-D Plot

3.20.1.2.1 Simple Drawing draw a simple histogram without errors (= “HIST” draw option). In combination
with some other draw options an outer line is drawn on top of the histogram

3.20.1.2.2

Show markers

3.20.1.2.3

Draw bar chart draw a bar chart (=“B” draw option).

draw a marker on to of each bin (=“P” draw option).

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CHAPTER 3. HISTOGRAMS

3.20.1.2.4 Bar option draw a bar chart (=“BAR” draw option); if selected, it will show an additional interface
elements for bars: width, offset, percentage and the possibility to draw horizontal bars.

3.20.1.3

3-D Plot

3.20.1.3.1

Add set histogram type Lego-Plot or Surface draw (Lego, Lego1.2, Surf, Surf1. . . 5).

3.20.1.3.2

Coords set the coordinate system (Cartesian, Spheric, etc.).

3.20.1.3.3

Error same as for 2D plot.

3.20.1.3.4

Bar set the bar attributes: width and offset.

3.20.1.3.5

Horizontal Bar

3.20.1.4

draw a horizontal bar chart.

The Binning tab

The binning tab has two different layouts. One is for a histogram, which is not drawn from an ntuple. The other one
is available for a histogram, which is drawn from an ntuple. In this case, the rebin algorithm can create a rebinned
histogram from the original data i.e. the ntuple.

To see the differences do:
TFile f("hsimple.root");
hpx->Draw("BAR1"); // non ntuple histogram
ntuple->Draw("px");// ntuple histogram

3.20. THE USER INTERFACE FOR HISTOGRAMS
3.20.1.5

93

Non ntuple histogram

Rebin with a slider and the number of bins (shown in the field below the slider). The number of bins can be changed
to any number, which divides the number of bins of the original histogram. A click on the Apply button will delete the
origin histogram and will replace it by the rebinned one on the screen. A click on the Ignore button will restore the
origin histogram.
3.20.1.6

Histogram drawn from an ntuple

3.20.1.6.1 Rebin with the slider, the number of bins can be enlarged by a factor of 2, 3, 4, 5 (moving to the right)
or reduced by a factor of 12 , 13 , 41 , 15 .
3.20.1.6.2 BinOffset with a BinOffset slider the origin of the histogram can be changed within one binwidth.
Using this slider the effect of binning the data into bins can be made visible (statistical fluctuations).
3.20.1.6.3 Axis Range with a double slider it is possible to zoom into the specified axis range. It is also possible
to set the upper and lower limit in fields below the slider.
3.20.1.6.4 Delayed drawing all the Binning sliders can set to delay draw mode. Then the changes on the
histogram are only updated, when the Slider is released. This should be activated if the redrawing of the histogram is
time consuming.

3.20.2

TH2Editor

3.20.2.1

Style Tab:

3.20.2.1.1

Title set the title of the histogram

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CHAPTER 3. HISTOGRAMS

3.20.2.1.2

Histogram change the draw options of the histogram.

3.20.2.1.3
different.

Plot draw a 2D or 3D plot of the histogram; according to the dimension, the drawing possibilities are

3.20.2.2

2-D Plot

3.20.2.2.1

Contour draw a contour plot (None, Cont0. . . 5)

3.20.2.2.2

Cont #

3.20.2.2.3

Arrow set the arrow mode and shows the gradient between adjacent cells;

3.20.2.2.4

Col a box is drawn for each cell with a color scale varying with contents;

3.20.2.2.5

Text draw bin contents as text;

3.20.2.2.6

Box a box is drawn for each cell with surface proportional to contents;

3.20.2.2.7

Scat draw a scatter-plot (default);

3.20.2.2.8

Palette the color palette is drawn.

3.20.2.3

set the number of Contours;

3-D Plot

3.20.2.3.1

Type set histogram type to Lego or surface plot; draw (Lego, Lego1.2, Surf, Surf1. . . 5)

3.20.2.3.2

Coords set the coordinate system (Cartesian, Spheric, etc.);

3.20.2.3.3

Cont #

3.20.2.3.4

Errors draw errors in a Cartesian lego plot;

3.20.2.3.5

Palette draw the color palette;

3.20.2.3.6

Front

3.20.2.3.7

Back draw the back box of a Cartesian lego plot;

3.20.2.3.8

Bar change the bar attributes: the width and offset.

3.20.2.4

set the number of Contours (for e.g. Lego2 draw option);

draw the front box of a Cartesian lego plot;

Rebinning Tab

The Rebinning tab has two different layouts. One is for a histogram that is not drawn from an ntuple; the other one
is available for a histogram, which is drawn from an ntuple. In this case, the rebin algorithm can create a rebinned
histogram from the original data i.e. the ntuple. To see the differences do for example:
TFile f ("hsimple.root");
hpxpy->Draw("Lego2"); // non ntuple histogram
ntuple->Draw("px:py","","Lego2"); // ntuple histogram

3.20. THE USER INTERFACE FOR HISTOGRAMS
3.20.2.5

95

Non-ntuple histogram:

Rebin with sliders (one for the x, one for the y-axis) and the number of bins (shown in the field below them can
be changed to any number, which divides the number of bins of the original histogram. Selecting the Apply button
will delete the origin histogram and will replace it by the rebinned one on the screen. Selecting the Ignore the origin
histogram will be restored.

3.20.2.6

Histogram drawn from an ntuple

3.20.2.6.1 Rebin with the sliders the number of bins can be enlarged by a factor of 2,3,4,5 (moving to the right)
or reduced by a factor of 12 , 13 , 41 , 15 .
3.20.2.6.2 BinOffset with the BinOffset slider the origin of the histogram can be changed within one binwidth.
Using this slider the effect of binning the data into bins can be made visible (=> statistical fluctuations).
3.20.2.6.3 Axis Range with a double slider that gives the possibility for zooming. It is also possible to set the
upper and lower limit in fields below the slider.
3.20.2.6.4 Delayed drawing all the binning sliders can be set to delay draw mode. Then the changes on the
histogram are only updated, when the Slider is released. This should be activated if the redrawing of the histogram is
too time consuming.

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CHAPTER 3. HISTOGRAMS

Chapter 4

Graphs
A graph is a graphics object made of two arrays X and Y, holding the x,y coordinates of n points. There are several
graph classes; they are TGraph, TGraphErrors, TGraphAsymmErrors, and TMultiGraph.

4.1

TGraph

The TGraph class supports the general case with non-equidistant points, and the special case with equidistant points.
Graphs are created with the TGraph constructor. First, we define the arrays of coordinates and then create the graph.
The coordinates can be arrays of doubles or floats.
Int_t n = 20;
Double_t x[n], y[n];
for (Int_t i=0; iDraw("AC*");

4.1.1.2

Bar Graphs (AB)

root[] TGraph *gr1 = new TGraph(n,x,y);
root[] gr1->SetFillColor(40);
root[] gr1->Draw("AB");

4.1. TGRAPH

99

Figure 4.2: A graph drawn with axis and bar (option AB)
This code will only work if n, x, and y is defined. The previous example defines these. You need to set the fill color,
because by default the fill color is white and will not be visible on a white canvas. You also need to give it an axis, or
the bar chart will not be displayed properly.
4.1.1.3

Filled Graphs (AF)

root[] TGraph *gr3 = new TGraph(n,x,y);
root[] gr3->SetFillColor(45);
root[] gr3->Draw("AF")
This code will only work if n, x, yare defined. The first example defines them. You need to set the fill color, because by
default the fill color is white and will not be visible on a white canvas. You also need to give it an axis, or the filled
polygon will not be displayed properly.
4.1.1.4
{

Marker Options

Int_t n = 20;
Double_t x[n], y[n];
// build the arrays with the coordinate of points
for (Int_t i=0; iSetMarkerStyle(21);
c1->cd(4);
gr3->Draw("APL");
// get the points in the graph and put them into an array
Double_t *nx = gr3->GetX();
Double_t *ny = gr3->GetY();

}

// create markers of different colors
for (Int_t j=2; jSetMarkerSize(2);
m->SetMarkerColor(31+j);
m->Draw();
}

4.2

Superimposing Two Graphs

To super impose two graphs you need to draw the axis only once, and leave out the “A” in the draw options for the
second graph. Next is an example:

Figure 4.5: Superimposing two graphs
{

Int_t n = 20;
Double_t x[n], y[n], x1[n], y1[n];
// create a blue graph with a cos function

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CHAPTER 4. GRAPHS
gr1->SetLineColor(4);
gr1->Draw("AC*");

}

// superimpose the second graph by leaving out the axis option "A"
gr2->SetLineWidth(3);
gr2->SetMarkerStyle(21);
gr2->SetLineColor(2);
gr2->Draw("CP");

4.3

Graphs with Error Bars

A TGraphErrors is a TGraph with error bars. The various draw format options of TGraphErrors::Paint() are derived
from TGraph.
void TGraphErrors::Paint(Option_t *option)

Figure 4.6: Graphs with different draw options of error bars
In addition, it can be drawn with the “Z” option to leave off the small lines at the end of the error bars. If option
contains “>”, an arrow is drawn at the end of the error bars. If option contains “|>”, a full arrow is drawn at the end
of the error bars. The size of the arrow is set to 2/3 of the marker size.
The option “[]” is interesting to superimpose systematic errors on top of the graph with the statistical errors. When it
is specified, only the end vertical/horizontal lines of the error bars are drawn.
To control the size of the lines at the end of the error bars (when option 1 is chosen) use SetEndErrorSize(np). By
default np=1; np represents the number of pixels.
gStyle->SetEndErrorSize(np);

4.4. GRAPHS WITH ASYMMETRIC ERROR BARS

103

The four parameters of TGraphErrors are: X, Y (as in TGraph), X-errors, and Y-errors - the size of the errors in the x
and y direction. Next example is $ROOTSYS/tutorials/graphs/gerrors.C.
{

c1 = new TCanvas("c1","A Simple Graph with error bars",200,10,700,500);
c1->SetGrid();
// create the coordinate arrays
Int_t n = 10;
Float_t x[n] = {-.22,.05,.25,.35,.5,.61,.7,.85,.89,.95};
Float_t y[n] = {1,2.9,5.6,7.4,9,9.6,8.7,6.3,4.5,1};
// create the error arrays
Float_t ex[n] = {.05,.1,.07,.07,.04,.05,.06,.07,.08,.05};
Float_t ey[n] = {.8,.7,.6,.5,.4,.4,.5,.6,.7,.8};

}

// create the TGraphErrors and draw it
gr = new TGraphErrors(n,x,y,ex,ey);
gr->SetTitle("TGraphErrors Example");
gr->SetMarkerColor(4);
gr->SetMarkerStyle(21);
gr->Draw("ALP");
c1->Update();

4.4

Graphs with Asymmetric Error Bars

Figure 4.7: A graph with asymmetric error bars
A TGraphAsymmErrors is a TGraph with asymmetric error bars. It inherits the various draw format options from
TGraph. Its method Paint(Option_t *option) paints the TGraphAsymmErrors with the current attributes. You can
set the following additional options for drawing:

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CHAPTER 4. GRAPHS

• “z” or “Z”the horizontal and vertical small lines are not drawn at the end of error bars
• “>”an arrow is drawn at the end of the error bars
• “|>”a full arrow is drawn at the end of the error bar; its size is

2
3

of the marker size

• “[]”only the end vertical/horizontal lines of the error bars are drawn; this option is interesting to superimpose
systematic errors on top of a graph with statistical errors.
The constructor has six arrays as parameters: X and Y as TGraph and low X-errors and high X-errors, low Y-errors
and high Y-errors. The low value is the length of the error bar to the left and down, the high value is the length of the
error bar to the right and up.
{

c1 = new TCanvas("c1","A Simple Graph with error bars",
200,10,700,500);
c1->SetGrid();
// create the arrays for the points
Int_t n = 10;
Double_t x[n] = {-.22,.05,.25,.35,.5, .61,.7,.85,.89,.95};
Double_t y[n] = {1,2.9,5.6,7.4,9,9.6,8.7,6.3,4.5,1};
// create the arrays with high and low errors
Double_t exl[n] = {.05,.1,.07,.07,.04,.05,.06,.07,.08,.05};
Double_t eyl[n] = {.8,.7,.6,.5,.4,.4,.5,.6,.7,.8};
Double_t exh[n] = {.02,.08,.05,.05,.03,.03,.04,.05,.06,.03};
Double_t eyh[n] = {.6,.5,.4,.3,.2,.2,.3,.4,.5,.6};

}

// create TGraphAsymmErrors with the arrays
gr = new TGraphAsymmErrors(n,x,y,exl,exh,eyl,eyh);
gr->SetTitle("TGraphAsymmErrors Example");
gr->SetMarkerColor(4);
gr->SetMarkerStyle(21);
gr->Draw("ALP");

4.5

Graphs with Asymmetric Bent Errors

A TGraphBentErrors is a TGraph with bent, asymmetric error bars. The various format options to draw a
TGraphBentErrors are explained in TGraphBentErrors::Paint method. The TGraphBentErrors is drawn by
default with error bars and small horizontal and vertical lines at the end of the error bars. If option “z” or “Z” is
specified, these small lines are not drawn. If the option “X” is specified, the errors are not drawn (the TGraph::Paint
method equivalent).
• if option contains “>”, an arrow is drawn at the end of the error bars
• if option contains “|>”, a full arrow is drawn at the end of the error bars
• the size of the arrow is set to 2/3 of the marker size
• if option “[]” is specified, only the end vertical/horizontal lines of the error bars are drawn. This option is
interesting to superimpose systematic errors on top of a graph with statistical errors.
This figure has been generated by the following macro:
{

Int_t n = 10;
Double_t x[n] =
Double_t y[n] =
Double_t exl[n]
Double_t eyl[n]

{-0.22,0.05,0.25,0.35,0.5,0.61,0.7,0.85,0.89,0.95};
{1,2.9,5.6,7.4,9,9.6,8.7,6.3,4.5,1};
= {.05,.1,.07,.07,.04,.05,.06,.07,.08,.05};
= {.8,.7,.6,.5,.4,.4,.5,.6,.7,.8};

4.6. TGRAPHPOLAR

105

Figure 4.8: A graph with asymmetric bent error bars
Double_t
Double_t
Double_t
Double_t
Double_t
Double_t
gr = new

}

exh[n] = {.02,.08,.05,.05,.03,.03,.04,.05,.06,.03};
eyh[n] = {.6,.5,.4,.3,.2,.2,.3,.4,.5,.6};
exld[n] = {.0,.0,.0,.0,.0,.0,.0,.0,.0,.0};
eyld[n] = {.0,.0,.0,.0,.0,.0,.0,.0,.0,.0};
exhd[n] = {.0,.0,.0,.0,.0,.0,.0,.0,.0,.0};
eyhd[n] = {.0,.0,.0,.0,.0,.0,.0,.0,.05,.0};
TGraphBentErrors(n,x,y,
exl,exh,eyl,eyh,exld,exhd,eyld,eyhd);
gr->SetTitle("TGraphBentErrors Example");
gr->SetMarkerColor(4);
gr->SetMarkerStyle(21);
gr->Draw("ALP");

4.6

TGraphPolar

The TGraphPolar class creates a polar graph (including error bars). A TGraphPolar is a TGraphErrors represented in
polar coordinates. It uses the class TGraphPolargram to draw the polar axis.
{

TCanvas *CPol = new TCanvas("CPol","TGraphPolar Examples",700,700);
Double_t rmin=0;
Double_t rmax=TMath::Pi()*2;
Double_t r[1000];
Double_t theta[1000];
TF1 * fp1 = new TF1("fplot","cos(x)",rmin,rmax);
for (Int_t ipt = 0; ipt < 1000; ipt++) {
r[ipt] = ipt*(rmax-rmin)/1000+rmin;
theta[ipt] = fp1->Eval(r[ipt]);

106

}

CHAPTER 4. GRAPHS
}
TGraphPolar * grP1 = new TGraphPolar(1000,r,theta);
grP1->SetLineColor(2);
grP1->Draw("AOL");

The TGraphPolar drawing options are:
“O” Polar labels are paint orthogonally to the polargram radius.
“P” Polymarker are paint at each point position.
“E” Paint error bars.
“F” Paint fill area (closed polygon).
“A”Force axis redrawing even if a polagram already exists.

Figure 4.9: A polar graph

4.7. TGRAPH EXCLUSION ZONE

4.7

107

TGraph Exclusion Zone

When a graph is painted with the option “C” or “L”, it is possible to draw a filled area on one side of the line. This is
useful to show exclusion zones. This drawing mode is activated when the absolute value of the graph line width (set
thanks to SetLineWidth) is greater than 99. In that case the line width number is interpreted as 100*ff+ll = ffll.
The two-digit numbers “ll” represent the normal line width whereas “ff” is the filled area width. The sign of “ffll”
allows flipping the filled area from one side of the line to the other. The current fill area attributes are used to draw
the hatched zone.

Figure 4.10: Graphs with exclusion zones

{

c1 = new TCanvas("c1","Exclusion graphs examples",200,10,700,500);
c1->SetGrid();
// create the multigraph
TMultiGraph *mg = new TMultiGraph();
mg->SetTitle("Exclusion graphs");
// create the graphs points
const Int_t n = 35;
Double_t x1[n], x2[n], x3[n], y1[n], y2[n], y3[n];
for (Int_t i=0;iSetLineColor(2);
gr1->SetLineWidth(1504);
gr1->SetFillStyle(3005);
// create the 2nd TGraph

108

CHAPTER 4. GRAPHS
gr2 = new TGraph(n,x2,y2);
gr2->SetLineColor(4);
gr2->SetLineWidth(-2002);
gr2->SetFillStyle(3004);
gr2->SetFillColor(9);
// create the 3rd TGraph
gr3 = new TGraph(n,x3,y3);
gr3->SetLineColor(5);
gr3->SetLineWidth(-802);
gr3->SetFillStyle(3002);
gr3->SetFillColor(2);
// put the graphs in the multigraph
mg->Add(gr1);
mg->Add(gr2);
mg->Add(gr3);

}

// draw the multigraph
mg->Draw("AC");

4.8

TGraphQQ

A TGraphQQ allows drawing quantile-quantile plots. Such plots can be drawn for two datasets, or for one dataset and a
theoretical distribution function.

4.8.1

Two Datasets

Figure 4.11: Examples of qq-plots of 2 datasets
Quantile-quantile plots are used to determine whether two samples come from the same distribution. A qq-plot draws
the quantiles of one dataset against the quantile of the other. The quantiles of the dataset with fewer entries are on
Y-axis, with more entries - on X-axis. A straight line, going through 0.25 and 0.75 quantiles is also plotted for reference.
It represents a robust linear fit, not sensitive to the extremes of the datasets. If the datasets come from the same
distribution, points of the plot should fall approximately on the 45 degrees line. If they have the same distribution
function, but different parameters of location or scale, they should still fall on the straight line, but not the 45 degrees
one.

4.9. TMULTIGRAPH

109

The greater their departure from the straight line, the more evidence there is that the datasets come from different
distributions. The advantage of qq-plot is that it not only shows that the underlying distributions are different,
but, unlike the analytical methods, it also gives information on the nature of this difference: heavier tails, different
location/scale, different shape, etc.

4.8.2

One Dataset

Figure 4.12: Examples of qq-plots of 1 dataset
Quantile-quantile plots are used to determine if the dataset comes from the specified theoretical distribution, such as
normal. A qq-plot draws quantiles of the dataset against quantiles of the specified theoretical distribution. Note, that
density, not CDF should be specified a straight line, going through 0.25 and 0.75 quantiles could also be plotted for
reference. It represents a robust linear fit, not sensitive to the extremes of the dataset. As in the two datasets case,
departures from straight line indicate departures from the specified distribution. Next picture shows an example of a
qq-plot of a dataset from N(3, 2) distribution and TMath::Gaus(0, 1) theoretical function. Fitting parameters are
estimates of the distribution mean and sigma.

4.9

TMultiGraph

A TMultiGraph is a collection of TGraph (or derived) objects. Use TMultiGraph::Addto add a new graph to the list.
The TMultiGraph owns the objects in the list. The drawing and fitting options are the same as for TGraph.
{

// create the points
Int_t n = 10;
Double_t x[n] = {-.22,.05,.25,.35,.5,.61,.7,.85,.89,.95};
Double_t y[n] = {1,2.9,5.6,7.4,9,9.6,8.7,6.3,4.5,1};
Double_t x2[n] = {-.12,.15,.35,.45,.6,.71,.8,.95,.99,1.05};

110

CHAPTER 4. GRAPHS

Figure 4.13: A multigraph example
Double_t y2[n]

= {1,2.9,5.6,7.4,9,9.6,8.7,6.3,4.5,1};

// create the width of errors in x and y direction
Double_t ex[n] = {.05,.1,.07,.07,.04,.05,.06,.07,.08,.05};
Double_t ey[n] = {.8,.7,.6,.5,.4,.4,.5,.6,.7,.8};
// create two graphs
TGraph *gr1 = new TGraph(n,x2,y2);
TGraphErrors *gr2 = new TGraphErrors(n,x,y,ex,ey);

}

// create a multigraph and draw it
TMultiGraph *mg = new TMultiGraph();
mg->Add(gr1);
mg->Add(gr2);
mg->Draw("ALP");

4.10

TGraph2D

This class is a set of N points x[i], y[i], z[i] in a non-uniform grid. Several visualization techniques are implemented,
including Delaunay triangulation. Delaunay triangulation is defined as follow: ‘for a set S of points in the Euclidean
plane, the unique triangulation DT(S) of S such that no point in S is inside the circum-circle of any triangle in DT(S).
DT(S) is the dual of the Voronoi diagram of S. If n is the number of points in S, the Voronoi diagram of S is the
partitioning of the plane containing S points into n convex polygons such that each polygon contains exactly one point
and every point in a given polygon is closer to its central point than to any other. A Voronoi diagram is sometimes
also known as a Dirichlet tessellation.
The TGraph2D class has the following constructors:
• With an arrays’ dimension n and three arrays x, y, and z (can be arrays of doubles, floats, or integers):

4.10. TGRAPH2D

111

Figure 4.14: Delaunay triangles and Voronoi diagram
TGraph2D *g = new TGraph2D(n,x,y,z);
• With an array dimension only:
TGraph2D *g = new TGraph2D(n);
• Internal arrays are filled with the method SetPoint at the position “i” with the values x, y, z:
g->SetPoint(i,x,y,z);
• Without parameters; the method SetPoint must be used to fill the internal arrays.
TGraph2D *g = new TGraph2D();
• From a file:
TGraph2D *g = new TGraph2D("graph.dat");
The arrays are read from the ASCII file “graph.dat” according to a specified format. The format’s default value is
“%lg %lg %lg”. Note that in any of last three cases, the SetPoint method can be used to change a data point or to add
a new one. If the data point index (i) is greater than the size of the internal arrays, they are automatically extended.
Specific drawing options can be used to paint a TGraph2D:
• “TRI” the Delaunay triangles are drawn using filled area. A hidden surface drawing technique is used. The surface
is painted with the current fill area color. The edges of the 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 the triangles are painted with the
current line color;
• “TRI2” the Delaunay triangles are painted with color levels;
• “P”draws a marker at each vertex;
• “P0” draws a circle at each vertex. Each circle background is white.
A TGraph2D can be also drawn with ANY options valid for 2D histogram drawing. In this case, an intermediate 2D
histogram is filled using the Delaunay triangles technique to interpolate the data set. TGraph2D linearly interpolate a Z
value for any (X,Y) point given some existing (X,Y,Z) points. The existing (X,Y,Z) points can be randomly scattered.
The algorithm works by joining the existing points to make Delaunay triangles in (X,Y). These are then used to define
flat planes in (X,Y,Z) over which to interpolate. The interpolated surface thus takes the form of tessellating triangles
at various angles. Output can take the form of a 2D histogram or a vector. The triangles found can be drawn in 3D.
This software cannot be guaranteed to work under all circumstances. It was originally written to work with a few
hundred points in anXY space with similar X and Y ranges.

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CHAPTER 4. GRAPHS

Figure 4.15: Graph2D drawn with option “surf1” and “tri1 p0”
{

}

TCanvas *c = new TCanvas("c","Graph2D example",0,0,700,600);
Double_t x, y, z, P = 6.;
Int_t np = 200;
TGraph2D *dt = new TGraph2D();
TRandom *r = new TRandom();
for (Int_t N=0; NRndm(N))-P;
y = 2*P*(r->Rndm(N))-P;
z = (sin(x)/x)*(sin(y)/y)+0.2;
dt->SetPoint(N,x,y,z);
}
gStyle->SetPalette(55);
dt->Draw("surf1");
// use "surf1" to generate the left picture
// use "tri1 p0" to generate the right one

A more complete example is $ROOTSYS/tutorials/fit/graph2dfit.C that produces the next figure.

4.11

TGraph2DErrors

A TGraph2DErrors is a TGraph2D with errors. It is useful to perform fits with errors on a 2D graph. An example is
the macro $ROOTSYS/tutorials/graphs/graph2derrorsfit.C.

4.12

Fitting a Graph

The graph Fit method in general works the same way as the TH1::Fit. See “Fitting Histograms”.

4.12. FITTING A GRAPH

113

Figure 4.16: Output of macro graph2dfit.C

114

CHAPTER 4. GRAPHS

4.13

Setting the Graph’s Axis Title

To give the axis of a graph a title you need to draw the graph first, only then does it actually have an axis object.
Once drawn, you set the title by getting the axis and calling the TAxis::SetTitle method, and if you want to center
it, you can call the TAxis::CenterTitle method.
Assuming that n, x, and y are defined. Next code sets the titles of the x and y axes.
root[] gr5 = new TGraph(n,x,y)
root[] gr5->Draw()
: created default TCanvas with name c1
root[] gr5->Draw("ALP")
root[] gr5->GetXaxis()->SetTitle("X-Axis")
root[] gr5->GetYaxis()->SetTitle("Y-Axis")
root[] gr5->GetXaxis()->CenterTitle()
root[] gr5->GetYaxis()->CenterTitle()
root[] gr5->Draw("ALP")
For more graph examples see the scripts: $ROOTSYS/tutorials directory graph.C, gerrors.C, zdemo.C, and
gerrors2.C.

Figure 4.17: A graph with axis titles

4.14

Zooming a Graph

To zoom a graph you can create a histogram with the desired axis range first. Draw the empty histogram and then
draw the graph using the existing axis from the histogram.
{

c1 = new TCanvas("c1","A Zoomed Graph",200,10,700,500);
hpx = new TH2F("hpx","Zoomed Graph Example",10,0,0.5,10,1.0,8.0);

4.15. THE USER INTERFACE FOR GRAPHS

}

hpx->SetStats(kFALSE);
// no statistics
hpx->Draw();
Int_t n = 10;
Double_t x[n] = {-.22,.05,.25,.35,.5,.61,.7,.85,.89,.95};
Double_t y[n] = {1,2.9,5.6,7.4,9,9.6,8.7,6.3,4.5,1};
gr = new TGraph(n,x,y);
gr->SetMarkerColor(4);
gr->SetMarkerStyle(20);
gr->Draw("LP");// and draw it without an axis

The next example is the same graph as above with a zoom in the x and y directions.

Figure 4.18: A zoomed graph

4.15

The User Interface for Graphs

The class TGraphEditor provides the user interface for setting the following graph attributes interactively:
• Title text entry field . . . sets the title of the graph.
• Shape radio button group - sets the graph shapes:
–
–
–
–
–

No Line: draw unconnected points;
Smooth Line: a smooth curve;
Simple Line: a simple poly-line;
Bart Chart: a bar chart at each point.
Fill Area: a fill area is drawn.

• Show Marker - sets markers as visible or invisible.
• Exclusion Zone - specifies the exclusion zone parameters :

115

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CHAPTER 4. GRAPHS
– ’+-‘ check button: sets on which side of the line the exclusion zone will be drawn;
– Width combo box: defines the width of the zone.

Chapter 5

Fitting Histograms
To fit a histogram you can use the Fit Panel on a visible histogram via the context menu, or you can use the TH1::Fit
method. The Fit Panel, which is limited, is best for prototyping. The histogram needs to be drawn in a pad before the
Fit Panel is invoked. The method TH1::Fit is more powerful and is used in scripts and programs.

5.1

The Fit Method

The Fit method is implemented in ROOT for the histogram classes TH1, the sparce histogram classes, THnSparse, the
graph classes, TGraph, TGraph2D and TMultiGraph for fitting a collection of Graphs with the same function.

5.1.1

The TH1::Fit Method

To fit a histogram programmatically, you can use the TH1::Fit method. Here is the signatures of TH1::Fit and an
explanation of the parameters:
TFitResultPtr Fit(TF1 *function, Option_t *option, Option_t *goption,
Axis_t xxmin, Axis_t xxmax)
• function a pointer to the fitted function (the fit model) object. One can also use the function name. This name
may be one of ROOT pre-defined function names or a user-defined function. See the next paragraph for the list
of pre-defined functions.
• *option: The second parameter is the fitting option. Here is the list of fitting options:
– “W” Set all weights to 1 for non empty bins; ignore error bars
– “WW” Set all weights to 1 including empty bins; ignore error bars
– “I” Use integral of function in bin instead of value at bin center
– “L” Use log likelihood method (default is chi-square method). To be used when the histogram represents
counts
– “WL” Weighted log likelihood method. To be used when the histogram has been filled with weights different
than 1.
– “P” Use Pearson chi-square method, using expected errors instead of the observed one given by
TH1::GetBinError (default case). The expected error is instead estimated from the the square-root of the
bin function value.
– “Q” Quiet mode (minimum printing)
– “V” Verbose mode (default is between Q and V)
– “S” The result of the fit is returned in the TFitResultPtr.
– “E” Perform better errors estimation using the Minos technique
– “M” Improve fit results, by using the IMPROVE algorithm of TMinuit.
– “R” Use the range specified in the function range
– “N” Do not store the graphics function, do not draw
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CHAPTER 5. FITTING HISTOGRAMS
– “0” Do not plot the result of the fit. By default the fitted function is drawn unless the option “N” above is
specified.
– “+” Add this new fitted function to the list of fitted functions (by default, the previous function is deleted
and only the last one is kept)
– “B”Use this option when you want to fix one or more parameters and the fitting function is a predefined one,
like polN, expo, landau, gaus. Note that in case of pre-defined functions some default initial values and
limits are set.
– “C”In case of linear fitting, don’t calculate the chisquare (saves time).
– “F”If fitting a linear function (e.g. polN), switch to use the default minimizer (e.g. Minuit). By default,
polN functions are fitted by the linear fitter.

• *goption:The third parameter is the graphics option that is the same as in the TH1::Draw (see the chapter
Draw Options).
• xxmin, xxmax:Thee fourth and fifth parameters specify the range over which to apply the fit.
By default, the fitted function object is added to the histogram and is drawn in the current pad.

5.1.2

The TGraph::Fit Method

The signature for fitting a TGraph is exactly the same as for the TH1. Only some options apply only for fitting
histograms, these are the options “L”, “WL” and “I”. These options apply instead only for TGraph::Fit, the rest of
options (appart from “L”, “WL” and “I” are the same)
• TGraph specific options
– “EX0” When fitting a TGraphErrors or a TgraphAsymErrors the errors on the coordinates are not used in
the fit
– “ROB” in case of linear fitting use the Robust fitting. Compute the LTS regression coefficients (robust
(resistant) regression), using the default fraction of good points.
– “ROB=0.x” as above, but compute the LTS regression coefficients, using 0.x as a fraction of good points.

5.2

The TF1 function class

Here we will show how to create the TF1 class that is used for fitting histograms and graphs.

5.2.1

Fit with a Predefined Function

To fit a histogram with a predefined function, simply pass the name of the function in the first parameter of TH1::Fit.
For example, this line fits histogram object hist with a Gaussian.
root[] hist.Fit("gaus");
The initial parameter values (and eventual limits) for pre-defined functions are set automatically. For overriding the
default limits values use the fit option B.
The list of pre-defined functions that can be used with the Fit method is the following:
• “gaus” Gaussian function with 3 parameters: f(x) = p0*exp(-0.5*((x-p1)/p2)ˆ2)
• “expo”An Exponential with 2 parameters: f(x) = exp(p0+p1*x)
• “polN ” A polynomial of degree N, where N is a number between 0 and 9: f(x) = p0 + p1*x + p2*x2 +...
• “chebyshevN ” A Chebyshev polynomial of degree N, where N is a number between 0 and 9: f(x) = p0 + p1*x
+ p2*(2*x2-1) +...
• “landau” Landau function with mean and sigma. This function has been adapted from the CERNLIB routine
G110 denlan (see TMath::Landau).
• “gausn Normalized form of the gaussian function with 3 parameters f(x) = p0*exp(-0.5*((x-p1)/p2)ˆ2)/(p2
*sqrt(2PI))

5.2. THE TF1 FUNCTION CLASS

5.2.2

119

Creating User-Defined Functions (TF1)

You can create a TF1 object and use it in the call the TH1::Fit. The parameter in to the Fit method is the NAME of
the TF1 object. There are three ways to create a TF1.
• Using C++ expression using x with a fixed set of operators and functions defined in TFormula.
• Same as first one, with parameters
• Using a function that you have defined. This can be a free function or a functor object or a particular member
function of a class.
5.2.2.1

Creating a TF1 with a Formula

Let’s look at the first case. Here we call the TF1 constructor by giving it the formula: sin(x)/x.
root[] TF1

*f1 = new TF1("f1","sin(x)/x",0,10)

You can also use a TF1 object in the constructor of another TF1.
root[] TF1
5.2.2.2

*f2 = new TF1("f2","f1*2",0,10)

Creating a TF1 with Parameters

The second way to construct a TF1 is to add parameters to the expression. Here we use two parameters:
root[] TF1 *f1 = new TF1("f1","[0]*x*sin([1]*x)",-3,3);

Figure 5.1: The function x*sin(x)
The parameter index is enclosed in square brackets. To set the initial parameters explicitly you can use:

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CHAPTER 5. FITTING HISTOGRAMS

root[] f1->SetParameter(0,10);
This sets parameter 0 to 10. You can also use SetParameters to set multiple parameters at once.
root[] f1->SetParameters(10,5);
This sets parameter 0 to 10 and parameter 1 to 5. We can now draw the TF1:
root[] f1->Draw()
5.2.2.3

Creating a TF1 with a User Function

The third way to build a TF1 is to define a function yourself and then pass the function pointer to the constructor. A
function for a TF1 constructor needs to have this exact signature:
Double_t fitf(Double_t *x,Double_t *par)
The two parameters are:
• x a pointer to the dimension array. Each element contains a dimension. For a 1D histogram only x[0] is used, for
a 2D histogram x[0] and x[1] is used, and for a 3D histogram x[0], x[1], and x[2] are used. For histograms,
only 3 dimensions apply, but this method is also used to fit other objects, for example an ntuple could have 10
dimensions.
• par a pointer to the parameters array. This array contains the current values of parameters when it is called by
the fitting function.
The following script $ROOTSYS/tutorials/fit/myfit.C illustrates how to fit a 1D histogram with a user-defined
function. First we declare the function.
// define a function with 3 parameters
Double_t fitf(Double_t *x,Double_t *par) {
Double_t arg = 0;
if (par[2]!=0) arg = (x[0] - par[1])/par[2];
Double_t fitval = par[0]*TMath::Exp(-0.5*arg*arg);
return fitval;
}
Now we use the function:
// this function used fitf to fit a histogram
void fitexample() {
// open a file and get a histogram
TFile *f = new TFile("hsimple.root");
TH1F *hpx = (TH1F*)f->Get("hpx");
// Create a TF1 object using the function defined above.
// The last three parameters specify the number of parameters
// for the function.
TF1 *func = new TF1("fit",fitf,-3,3,3);
// set the parameters to the mean and RMS of the histogram
func->SetParameters(500,hpx->GetMean(),hpx->GetRMS());
// give the parameters meaningful names
func->SetParNames ("Constant","Mean_value","Sigma");

}

// call TH1::Fit with the name of the TF1 object
hpx->Fit("fit");

5.3. CONFIGURING THE FIT

121

You can create a TF1 also from a C++ function object (functor) with parameters A TF1 can be created from any
C++ class implementing this member function:
double operator()(double *x, double *p)
The advantage of the function object is that it can have a state and reference therefore what-ever other object the user
needs, without using globals. This is an example to define first the function object
class MyFunctionObject {
public:
// use constructor to customize your function object
MyFunctionObject(......) { ......}

};

double operator() (double *x, double *p) {
// function implementation using class data members
}

and then use it to create the TF1:

MyFunctionObject fobj(....);
// create the function object
TF1 * f = new TF1("f",fobj,xmin,xmax,npar);
// create TF1 class with n-parameters and range [xmin,xm
If using C++11, one can create a TF1 also from a C++ lambda function:
// create TF1 class with 2 parameters and range [xmin,xmax] using a lambda
TF1 * f = new TF1("f",[](double*x,double*p){return p[0] + p[1]*x[0];},xmin,xmax,2);

5.3

Configuring the Fit

We will show here some configuration actions that can or must be done when fitting histogram or graph using the Fit
method.

5.3.1

Fixing and Setting Parameters’ Bounds

Parameters must be initialized before invoking the Fit method. The setting of the parameter initial values is automatic
for the predefined functions: poln, exp, gaus, and landau. You can fix one or more parameters by specifying the “B”
option when calling the Fit method. When a function is not predefined, the fit parameters must be initialized to some
value as close as possible to the expected values before calling the fit function.
To set bounds for one parameter, use TF1::SetParLimits:
func->SetParLimits(0,-1,1);
When the lower and upper limits are equal, the parameter is fixed. Next two statements fix parameter 4 at 10.
func->SetParameter(4,10);
func->SetParLimits(4,10,10);
However, to fix a parameter to 0, one must call the FixParameter function:
func->SetParameter(4,0);
func->FixParameter(4,0);
Note that you are not forced to set the limits for all parameters. For example, if you fit a function with 6 parameters,
you can:
func->SetParameters(0,3.1,1.e-6,-1.5,0,100);
func->SetParLimits(3,-10,4);
func->FixParameter(4,0);
With this setup, parameters 0->2 can vary freely, parameter 3 has boundaries [-10, 4] with initial value -1.5, and
parameter 4 is fixed to 0.

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CHAPTER 5. FITTING HISTOGRAMS

5.3.2

Fitting Sub Ranges

By default, TH1::Fit will fit the function on the defined histogram range. You can specify the option “R” in the second
parameter of TH1::Fit to restrict the fit to the range specified in the TF1 constructor. In this example, the fit will be
limited to -3 to 3, the range specified in the TF1 constructor.
root[] TF1 *f1 = new TF1("f1","[0]*x*sin([1]*x)",-3,3);
root[] hist->Fit("f1","R");
You can also specify a range in the call to TH1::Fit:
root[] hist->Fit("f1","","",-2,2)
See macros $ROOTSYS/tutorials/fit/myfit.C and multifit.C as more completed examples.

5.3.3

Fitting Multiple Sub Ranges

The script for this example is $ROOTSYS/tutorials/fit/multifit.C. It shows how to use several Gaussian functions
with different parameters on separate sub ranges of the same histogram. To use a Gaussian, or any other ROOT built
in function, on a sub range you need to define a new TF1. Each is ‘derived’ from the canned function gaus.

Figure 5.2: Fitting a histogram with several Gaussian functions
First, four TF1 objects are created - one for each sub-range:
g1 = new TF1("m1","gaus",85,95);
g2 = new TF1("m2","gaus",98,108);
g3 = new TF1("m3","gaus",110,121);
// The total is the sum of the three, each has 3 parameters
total = new TF1("mstotal","gaus(0)+gaus(3)+gaus(6)",85,125);

5.4. EXAMPLE OF FIT: COMBINING FUNCTIONS

123

Next, we fill a histogram with bins defined in the array x.
// Create a histogram and set it's contents
h = new TH1F("g1","Example of several fits in subranges",
np,85,134);
h->SetMaximum(7);
for (int i=0; iSetBinContent(i+1,x[i]);
}
// Define the parameter array for the total function
Double_t par[9];
When fitting simple functions, such as a Gaussian, the initial values of the parameters are automatically computed by
ROOT. In the more complicated case of the sum of 3 Gaussian functions, the initial values of parameters must be set.
In this particular case, the initial values are taken from the result of the individual fits. The use of the “+” sign is
explained below:
// Fit each function and add it to the list of functions
h->Fit(g1,"R");
h->Fit(g2,"R+");
h->Fit(g3,"R+");
// Get the parameters from the fit
g1->GetParameters(&par[0]);
g2->GetParameters(&par[3]);
g3->GetParameters(&par[6]);
// Use the parameters on the sum
total->SetParameters(par);
h->Fit(total,"R+");

5.3.4

Adding Functions to the List

The example $ROOTSYS/tutorials/fit/multifit.C also illustrates how to fit several functions on the same histogram.
By default a Fit command deletes the previously fitted function in the histogram object. You can specify the option
“+” in the second parameter to add the newly fitted function to the existing list of functions for the histogram.
root[] hist->Fit("f1","+","",-2,2)
Note that the fitted function(s) are saved with the histogram when it is written to a ROOT file.

5.4

Example of fit: Combining Functions

You can combine functions to fit a histogram with their sum as it is illustrated in the macro FitDemo.C
($ROOTSYS/tutorials/fit/FittingDemo.C). We have a function that is the combination of a background and
Lorentzian peak. Each function contributes 3 parameters:

y(E) = a1 + a2 E + a3 E 2 +

G
Ap ( 2p
)
2
(E − m)2 + ( G
2)

BackgroundLorentzian Peak
par[0] = a1 par[0] = Ap
par[1] = a2 par[1] = G
par[2] = a3 par[2] = m
The combination function (fitFunction) has six parameters:
fitFunction = background(x,par) + LorentzianPeak(x,&par[3])

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CHAPTER 5. FITTING HISTOGRAMS

par[0]=a1 par[1]=a2 par[2]=a3 par[3]=Ap par[4]=G par[5]=m
This script creates a histogram and fits it with the combination of two functions. First we define the two functions and
the combination function:
// Quadratic background function
Double_t background(Double_t *x, Double_t *par) {
return par[0] + par[1]*x[0] + par[2]*x[0]*x[0];
}
// Lorentzian Peak function
Double_t lorentzianPeak(Double_t *x, Double_t *par) {
return (0.5*par[0]*par[1]/TMath::Pi()) / TMath::Max(1.e-10,
(x[0]-par[2])*(x[0]-par[2])+ .25*par[1]*par[1]);
}
// Sum of background and peak function
Double_t fitFunction(Double_t *x, Double_t *par) {
return background(x,par) + lorentzianPeak(x,&par[3]);
}
void FittingDemo() {
// bevington exercise by P. Malzacher, modified by R. Brun
const int nBins = 60;
Stat_t data[nBins] = { 6, 1,10,12, 6,13,23,22,15,21,
23,26,36,25,27,35,40,44,66,81,
75,57,48,45,46,41,35,36,53,32,
40,37,38,31,36,44,42,37,32,32,
43,44,35,33,33,39,29,41,32,44,
26,39,29,35,32,21,21,15,25,15};
TH1F *histo = new TH1F("example_9_1",
"Lorentzian Peak on Quadratic Background",60,0,3);
for(int i=0; i < nBins; i++) {
// we use these methods to explicitly set the content
// and error instead of using the fill method.
histo->SetBinContent(i+1,data[i]);
histo->SetBinError(i+1,TMath::Sqrt(data[i]));
}
// create a TF1 with the range from 0 to 3 and 6 parameters
TF1 *fitFcn = new TF1("fitFcn",fitFunction,0,3,6);
// first try without starting values for the parameters
// this defaults to 1 for each param.
histo->Fit("fitFcn");
// this results in an ok fit for the polynomial function however
// the non-linear part (Lorentzian

5.5

Result of the fit

Here we will show how to obtain the result of the fit (fitted function, parameter values, errors and eventually the
covariance and correlation matrix).

5.5.1

Associated Function

One or more objects (typically a TF1*) can be added to the list of functions (fFunctions) associated to each histogram.
A call to TH1::Fit adds the fitted function to this list. Given a histogram h, one can retrieve the associated function
with:
TF1 *myfunc = h->GetFunction("myfunc");

5.5. RESULT OF THE FIT

125

Figure 5.3: The output of the FittingDemo() example

5.5.2

Access to the Fit Parameters and Results

If the histogram (or graph) is made persistent, the list of associated functions is also persistent. Retrieve a pointer to the
function with the TH1::GetFunction()method. Then you can retrieve the fit parameters from the function
(**TF1‘**) with calls such as:
root[] TF1 *fit
root[] Double_t
// value of the
root[] Double_t
// error of the
root[] Double_t

= hist->GetFunction(function_name);
chi2 = fit->GetChisquare();
first parameter
p1 = fit->GetParameter(0);
first parameter
e1 = fit->GetParError(0);

Using the fit option S one can access the full result of the fit including the covariance and correlation matrix. See later
the paragraph TFitResult.

5.5.3

Associated Errors

By default, for each bin, the sum of weights is computed at fill time. One can also call TH1::Sumw2 to force the storage
and computation of the sum of the square of weights per bin. If Sumw2 has been called, the error per bin is computed
as the sqrt(sum of squares of weights); otherwise, the error is set equal to the sqrt(bin content). To return
the error for a given bin number, do:
Double_t error = h->GetBinError(bin);
Empty bins are excluded in the fit when using the Chi-square fit method. When fitting an histogram representing
counts (i.e with Poisson statistics) it is recommended to use the Log-Likelihood method (option ‘L’ or “WL”), particularly
in case of low statistics. When the histogram has been filled with weights different than one, a weighted likelihood
method can be used and the errors retrieved from the fit are corrected following a procedure described in paragraph
8.5.2 of the book, F. James, Statistical Methods in Experimental Physics, 2nd Edition.

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CHAPTER 5. FITTING HISTOGRAMS

5.5.4

Fit Statistics

You can change the statistics box to display the fit parameters with the TStyle::SetOptFit(mode) method. This
parameter has four digits: mode = pcev (default = 0111)
•
•
•
•

p
c
e
v

=
=
=
=

1
1
1
1

print
print
print
print

probability
Chi-square/number of degrees of freedom
errors (if e=1, v must be 1)
name/values of parameters

For example, to print the fit probability, parameter names/values, and errors, use:
gStyle->SetOptFit(1011);

5.6

The Fit Panel

To display the Fit Panel right click on a histogram to pop up the context menu, and then select the menu entry Fit
Panel.
The new Fit Panel GUI is available in ROOT v5.14. Its goal is to replace the old Fit Panel and to provide more user
friendly way for performing, exploring and comparing fits.
By design, this user interface is planned to contain two tabs: “General” and “Minimization”. Currently, the “General”
tab provides user interface elements for setting the fit function, fit method and different fit, draw, print options. The
“Minimization tab” provides the option to set the Minimizer to use in the fit and its specific options.
The new fit panel is a modeless dialog, i.e. when opened, it does not prevent users from interacting with other windows.
Its first prototype is a singleton application. When the Fit Panel is activated, users can select an object for fitting in
the usual way, i.e. by left-mouse click on it. If the selected object is suitable for fitting, the fit panel is connected with
this object and users can perform fits by setting different parameters and options.

5.6.1

Function Choice and Settings

‘Predefined’ combo box - contains a list of predefined functions in ROOT. You have a choice of several polynomials, a
Gaussian, a Landau, and an Exponential function. The default one is Gaussian.
‘Operation’ radio button group defines the selected operational mode between functions:
Nop - no operation (default);
Add - addition;
Conv - convolution (will be implemented in the future).
Users can enter the function expression into the text entry field below the ‘Predefined’ combo box. The entered string
is checked after the Enter key was pressed and an error message shows up, if the function string is not accepted.
‘Set Parameters’ button opens a dialog for parameters settings, which will be explaned later.

5.6.2

Fitter Settings

‘Method’ combo box currently provides only two fit model choices: Chi-square and Binned Likelihood. The default one
is Chi-square. The Binned Likelihood is recomended for bins with low statistics.
‘Linear Fit’ check button sets the use of Linear fitter when is selected. Otherwise the minimization is done by Minuit,
i.e. fit option “F” is applied. The Linear fitter can be selected only for functions linears in parameters (for example polN).
‘Robust’ number entry sets the robust value when fitting graphs.
‘No Chi-square’ check button switch On/Off the fit option “C” - do not calculate Chi-square (for Linear fitter).
‘Integral’ check button switch On/Off the option “I” - use integral of function instead of value in bin center.
‘Best Errors’ sets On/Off the option “E” - better errors estimation by using Minos technique.

5.6. THE FIT PANEL

127

Figure 5.4: The Fit Panel

128

CHAPTER 5. FITTING HISTOGRAMS

‘All weights = 1’ sets On/Off the option “W”- all weights set to 1 excluding empty bins; error bars ignored.
‘Empty bins, weights=1’ sets On/Off the option “WW” - all weights equal to 1 including empty bins; error bars ignored.
‘Use range’ sets On/Off the option “R” - fit only data within the specified function range. Sliders settings are used if
this option is set to On. Users can change the function range values by pressing the left mouse button near to the
left/right slider edges. It is possible to change both values simultaneously by pressing the left mouse button near to the
slider center and moving it to a new position.
‘Improve fit results’ sets On/Off the option “M”- after minimum is found, search for a new one.
‘Add to list’ sets On/Off the option “+”- add function to the list without deleting the previous one. When fitting a
histogram, the function is attached to the histogram’s list of functions. By default, the previously fitted function is
deleted and replaced with the most recent one, so the list only contains one function. Setting this option to On will
add the newly fitted function to the existing list of functions for the histogram. Note that the fitted functions are
saved with the histogram when it is written to a ROOT file. By default, the function is drawn on the pad displaying
the histogram.

5.6.3

Draw Options

‘SAME’ sets On/Off function drawing on the same pad. When a fit is executed, the image of the function is drawn on
the current pad.
‘No drawing’ sets On/Off the option “0”- do not draw the fit results.
‘Do not store/draw’ sets On/Off option “N”- do not store the function and do not draw it.

5.6.4

Advances Options

The advance option button is enabled only after having performed the fit and provides additional drawing options that
can be used after having done the fit. These new drawing tools, which can be selected by the “Advanced Drawing Tool”
panel that pops up when clicking the “Advanced” button, are:
• Contour: to plot the confidence contour of two chosen parameters. One can select the number of points to draw
the contour (more points might require more time to compute it), the parameters and the desired confidence
level .
• Scan : to plot a scan of the minimization function (likelihood or chi-squared) around the minimum as function of
the chosen parameter.
• Conf Interval : to plot the confidence interval of the fitted function as a filled coloured band around its central
value. One can select the desired confidence level for the band to be plotted.

5.6.5

Print Options

This set of options specifies the amount of feedback printed on the root command line after performed fits.
‘Verbose’ - prints fit results after each iteration.
‘Quiet’ - no fit information is printed.
‘Default’ - between Verbose and Quiet.

5.6.6

Command Buttons

Fit button - performs a fit taking different option settings via the Fit Panel interface.
Reset - sets the GUI elements and related fit settings to the default ones.
Close - closes the Fit panel window.

5.7. NEW ROOT::FIT CLASSES

5.6.7

129

Minimization Options

With this tab one can select specific options for minimization. These include
• The minimizer library ( Minuit, Minuit2, Fumili, GSL, Genetics )
• The method (algorithm) for minimization. For example for Minuit one can choose between (Migrad, Simplex or
Scan)
• Error definition
• Minimization tolerance
• Number of iterations/function calls
• Print Level: (Default, Verbose or Quiet).

5.7

New ROOT::Fit classes

The fitting of the data objects in ROOT, histograms, graphs and tree is performed via some common classes, which are
defined in the ROOT::Fit namespace. These classes can be classified in the following groups:
• User classes driving the fit: ROOT::Fit::Fitter for executing the fit, ROOT::Fit::FitConfig for configuring
the fit, ROOT::Fit::ParameterSettings to define the properties of the fit parameters (initial values, bounds,
etc..), ROOT::Fit::FitResult for storing the result of the fit.
• Data classes containing the data sets used in the fitting. These classes are theROOT::Fit::BinDatafor describing
bin data sets, thus data points containing both coordinates and a corresponding value/weight with optionally
an error on the value or the coordinate and the ROOT::Fit::UnBinData for un-binned data sets, which consisst
only of a vector of coordinate values. The coordinate values can be one-dimensional (i.e. one entry per event) or
multi-dimensional (N entries per event).
• Function classes defining the type of fit (the objective function used for fitting):
– ROOT::Fit::Chi2FCN for chi2 (least-square fits),
– ROOT::Fit::PoissonLikelihoodFCN for binned likelihood fits of histograms,
– ROOT::Fit::LogLikelihoodFCN for generic un-binned likelihood fits. These classes are templated
on the type of function interface they implement (see later). User convenient typedefs are also
provided. They derive from the common generic interface multi-dimensional for function evaluation,
ROOT::Math::IBaseFunctionMultiDim.

In addition the fitter classes make uses of the generic interfaces for parametric function evaluations, ROOT::Math::IParametricFunc
to define the fit model function and use the ROOT::Math::Minimizer interface to perform the minimization of the
objective function.
More information about the function interface and the multi-dimensional minimization in ROOT is given in the
Mathematical Library chapter.
Here we present a detailed description of the ROOT::Fit classes and how to use them. Using these classes instead of
the interface provided directly in the ROOT data objects, like TH1::Fit allow are more fine control to configure and
customise the fits. For example, using these classes a combined fit of several histograms can be performed.
To understand how these class work, let’s go through a simple example, such as fitting an histogram.
When fitting an histogram, instead of using TH1::Fit we will show in the following hot wo use the ROOT::Fit classes.
We will show how to perform the following different type of fits with the histogram data: * a least square fit using
the observed errors (Neyman chi-squared); * a least square fit using the expected errors from the function (Pearson
chi-squared); * a binned likelihood fit; * an extended unbinned likelihood fits, if the histogram has been set to store in
the buffer the original data used to fill it.
Let’s go through all the steps required for performing these fits using the ROOT::Fit::Fitter class. These steps are:
1. Create the input fit data object. 2. Create the input model function. 3. Configure the fit. 4. Perform the data
fitting. 5. Examine the result.

5.7.1

Creating the input fit data

We have two types of input data, binned data (class ROOT::Fit::BinData) used for least square (chi-square) fits of
histograms or TGraph objects or un-binned data (class ROOT::Fit::UnBinData) used for fitting vectors of data points
(e.g. from a TTree).

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5.7.1.1

Using Binned data

Let’s suppose we have an histogram, represented as a TH1 type object (it can be one or multi-dimensional). The
following shows how to create and fill a ROOT:Fit::BinData object.
ROOT::Fit::DataOptions opt;
opt.fIntegral = true;
ROOT::Fit::BinData data(opt);
// fill the bin data using the histogram
// we can do this using the following helper function from the Hist library
TH1 * h1 = (TH1*) gDirectory->Get("myHistogram");
ROOT::Fit::FillData(data, h1);
In this code example, we have used the utility function of the Hist library, ROOT::Fit::FillData to fill the BinData
object. The ROOT::Fit::FillData is defined in the headerfile HFitInterface.h and it has a signature for all different
ROOT objects, like TH1, THnBase, TGraph, TGraph2D and TMultiGraph It is possible to specify, when creating the
BinData object, the data range we want to use and some fitting options we want to apply to fill in the object and
later when fitting. The fit data options are controlled by the ROOT::Fit::DataOptions class, the range by the
ROOT::Fit::DataRange class.
Here is an example how to specify the input option to use the integral of the function value in the bin instead of using
the function value evaluated at the bin center, when doing the fit and to use a range beween the ‘xmin’ and ‘xmax’
values.
ROOT::Fit::DataOptions opt;
opt.fIntegral = true;
ROOT::Fit::DataRange range(xmin,xmax);
ROOT::Fit::BinData data(opt,range);
// fill the bin data using the histogram
// we can do this using the following helper function from the Hist library
TH1 * h1 = (TH1*) gDirectory->Get("myHistogram");
ROOT::Fit::FillData(data, h1);
The list of possible fit options available is the following:

ROOT::Fit::DataOptions opt;
opt.fIntegral = true;
// use integral of bin content instead of bin center (default is false).
opt.fBinVolume = true;
// normalize data by the bin volume (default is false).
// This is for fitting density functions in histograms with variable bin si
opt.fUseRange =true;
// use the function range when creating the fit data (default is false).
opt.fExpErrors = true;
// use the expected errors estimated from the function values
// assuming Poisson statistics and not the observed errors (default is fals
opt.fUseEmpty = true;
// use empty bins when fitting (default is false). If fExpErrors
// is not set an arbitrary error = 1 is assigned to those bins.
opt.fErrors1 = true;
// Set all measured errors to 1 (default is false).
opt.fCoordErrors = false; // When available coordinate errors are not used in the fit
// (default is true: the errors are used when they are available,
// e.g. fitting a TGraphErrors).
opt.fAsymErrors = false;
// When available asymmetric errors are considered in the fit
// (default is true, the asymmetric errors are used when they are available
// e.g. fitting a TGraphAsymmErrors).
The ROOT::Fit::DataRange class supports defining multiple rectangular ranges in each dimension, and supports
n-dimension. The function DataRange::AddRange(icoord,xmin,xmax) adds a range in the coordinate icoord with
lower value xmin and upper value xmax:
ROOT::Fit::DataRange range;
range.AddRange(icoordinate, xmin, xmax);

5.7. NEW ROOT::FIT CLASSES
5.7.1.2

131

Using Un-Binned data

The unbinned data sets are represented with the ROOT::Fit::UnBinData class. For creating un-binned data sets, a
ROOT::Fit::UnBinData object, one has two possibilities: 1. Copy the data inside ROOT::Fit::UnBinData. One can
create an empty UnBinData object, iterate on the data and add the data point one by one, or directly create the
UnBinData object from a data iterator. In this case an input ROOT::Fit::DataRange object is passed in order to copy
the data according to the given range. 2. Use ROOT::Fit::UnBinData as a wrapper to an external data storage. In
this case the UnBinData object is created from an iterator or pointers to the data and the data are not copied inside.
In this case the data cannot be selected according to a specified range. All the data points will be included in the fit.
The ROOT::Fit::UnBinData class supports also weighted data. In addition to the data points (coordinates), which
can be of arbitrary k dimensions, the class can be constructed from a vector of weights. This is an example of taking
data from an histogram buffer of a TH1 object:
double * buffer = histogram->GetBuffer();
// number of entry is first entry in the buffer
int n = buffer[0];
// when creating the data object it is important to create with the size of the data
ROOT::Fit::UnBinData data(n);
for (int i = 0; i < n; ++i)
data.add(buffer[2*i+1]); // the buffer of 1D histogram contains nevt,x1,w1,x2,w2,......
Instead in this example we will create a 2-dim UnBinData object with the contents from a ROOT TTree
TFile * file = TFile::Open("hsimple.root");
TTree *ntuple = 0; file->GetObject("ntuple",ntuple);
// select from the tree the data we want to use for fitting
// we use TTree::Draw for this
int nevt = ntuple->Draw("px:py","","goff");
double * x = ntuple->GetV1();
double * y = ntuple->GetV2();
ROOT::Fit::UnBinData data(nevt, x, y );

5.7.2

Creating the Fit model

In order to fit a data sets we need a model to describe our data, e.g. a probability density function describing our
observed data or an hypothetical function describing the relation between the independent variables X and the single
dependent variable Y. We can have an arbitrary number k of independent variables. For example, when fitting a
k-dimensional histogram, the independent variables X are the bin center coordinates and Y is the bin weight.
The model function needs to be expressed as function of some unknown parameters. The fitting will find the best
parameter value to describe the observed data.
We can use the ROOT TF1 class, the parametric function class, to describe the model function. However
the ROOT::Fit::Fitter class, to be independent of the ROOT Hist library, takes as input a more general
parametric function object, the interface (abstract) class ROOT::Math::IParametricFunctionMultiDim, which
describe a generic one or multi-dimensional function with parameters. This interface extends the abstract class
ROOT::Math::IBaseFunctionMultiDim, with methods to set/retrieve parameter values and to evaluate the function
given the independent vector of values X and vector of parameters P. More information about the different ROOT::Math
function interfaces is available in the Mathematical Library chapter.
An end-user can convert a TF1 object in a ROOT::Math::IParametricFunctionMultiDim, using the wrapper class
ROOT::Math::WrapperMultiTF1:
TF1 * f1 = new TF1("f1","gaus");
ROOT::Math::WrappedMultiTF1 fitFunction(f1, f1->GetNdim() );
ROOT::Fit::Fitter fitter;
fitter.SetFunction( fitFunction, false);
When creating the wrapper, the parameter values stored in TF1 will be copied in the ROOT::Math::WrappedMultiTF1
object. The function object representing the model function is given to the ROOT::Fitter class using the
Fitter::SetFunction method.

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The user has also the possibility to provide a function object, which implements the derivatives of the function
with respect to the parameters. This information might be useful for some types of fits. In this case he needs to
provide the function object as a class deriving from the ROOT::Math::IParametricGradFunctionMultiDim interface.
Note that the wrapper class ROOT::Math::WrappedMultiTF1 implements also the gradient interface, using internally
TF1::GradientPar, which is based on numerical differentiation, apart for the case of linear functions (i.e. when
TF1::IsLinear() is true). The parameter derivatives of the model function can be useful to some minimization
algorithms, such as Fumili. However, in general is better to leave the minimization algorithm (e.g. Minuit) to compute
the needed derivatives using its own customised numerical differentiation algorithm. In order to not provide to the
fitter the parameter derivatives, we explicitly passed in Fitter::SetFunction a false value.

5.7.3

Fit Configuration

The configuration of the fit is done via the ROOT::Fit::FitConfig class and its contained ROOT::Fit::ParameterSettings
class. These are the possible allowed fit configurations:
•
•
•
•
•
•

setting the initial values of the parameters;
setting the parameter step sizes;
setting eventual parameter bounds;
setting the minimizer library and the particular algorithm to use;
setting different minimization options (print level, tolerance, max iterations, etc. . . )
setting the type of parameter errors to compute (parabolic error, Minos errors, re-normalize errors using fitted
chi2 values)

The initial parameter values can be set directly in the input model function object. However, for setting parameter bounds and step sizes to values different than the automatically computed ones, one needs to use the
ROOT::Fit::ParameterSetting class. This example code will set the lower/upper bounds for the first parameter and
a lower bound for the second parameter
fitter.SetFunction( fitFunction, false);
fitter.Config().ParSettings(0).SetLimits(0,1.E6);
fitter.Config().ParSettings(2).SetLowerLimit(0);
Note that a ROOT::Fit::ParameterSettings objects exists for each fit parameter and it created by the
ROOT::Fit::FitConfig class, after the model function has been set in the Fitter. Only when the function is set, the
number of parameter is known and automatically the FitConfig creates the corresponding ParameterSetting objects.
When fitting, different minimizer can be used. The can be implemented in different libraries and loaded ar run time
by the plug-in manager system of ROOT. Each different minimizer (e.g. Minuit, Minuit2, Fumili, etc.) consists of a
different implementation of the ROOT::Math::Minimizer interface. Within the same minimizer, thus within the same
class implementing the Minimizer interface, different algorithms can exist. For example in the case of Minuit, we have
Migrad, Simplex or Minimize. The minimizer and its corresponding algorithm, when available, can be set by using
the function FitConfig::SetMinimizer("minimizerName") or by using directly the ROOT:Math::MinimizerOptions
class.
If the requested minimizer is not available in ROOT, the default one is used. The default minimizer type and algorithm
can be specified by using the static function ROOT::Math::MinimizerOptions::SetDefaultMinimizer("minimizerName")

5.7.4

Minimizer Libraries and Algorithms

The list of available minimizer libraries currently available in ROOT, with their corresponding available algorithms is
the following one. Some minimizers (e.g. Minuit) contain several algorithms that the user can choose. Others are
based on a single algorithm (e.g. Fumili)
• Minuit (library libMinuit). Old version of Minuit, based on the TMinuit class. The list of possible algorithms
are:
–
–
–
–
–

Migrad (default one)
Simplex
Minimize (it is a combination of Migrad and Simplex)
MigradImproved
Scan

5.7. NEW ROOT::FIT CLASSES

133

– Seek
• Minuit2 (library libMinuit2 ). New C++ version of Minuit. The list of possible algorithm is :
–
–
–
–
–

Migrad (default)
Simplex
Minimize
Scan
Fumili . This is the same algorithm of TFumili, but implemented in the Minuit2 library.

• Fumili. Implement a dedicated minimization algorithm for least-square and likelihood fits. It has requirements
on the type of method function to be used. No specific algorithm exists
• GSLMultiMin (library libMathMore). Minimizer based on the Multidimensional Minimization routines of the Gnu
Scientific Library (GSL). The list of available algorithms is
–
–
–
–
–

BFGS2 (default) : second version of the vector Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm;
BFGS : old version of the vector Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm;
ConjugateFR : Fletcher-Reeves conjugate gradient algorithm;
ConjugatePR : Polak-Ribiere conjugate gradient algorithm;
SteepestDescent : steepest descent algorithm;

• GSLMultiFit (library libMathMore). Minimizer based on the Non-Linear Least-Square routines of GSL. This
minimizer can be used only for least-square fits.
• GSLSimAn (library libMathMore). Minimizer based on simulated annealing.
• Genetic (library libGenetic). Genetic minimizer based on an algorithm implemented in the TMVA package.
Each minimizer can be configured using the ROOT::Math::MinimizerOptions class. The list of possible option that
can be set are:
• Minimizer type (MinimizerOptions::SetMinimizerType(const char *)) .
• Minimizer algorithm (MinimizerOptions::SetMinimizerAlgorithm(const char *)).
• Print Level (MinimizerOptions::SetPrintLevel(int )) to set the verbose printing level (default is 0).
• Tolerance (MinimizerOptions::SetTolerance(double )) tolerance used to control the iterations.
• Maximum number of function calls (MinimizerOptions::SetMaxFunctionCalls(int )).
• Maximum number of iterations (MinimizerOptions::SetMaxIterations(int )). Note that this is not used by
Minuit
• FCN Upper value for Error Definition (MinimizerOptions::SetMaxIterations(int )). Value in the minimization function used to compute the parameter errors. The default is to get the uncertainties at the 68% CL is a
value of 1 for a chi-squared function minimization and 0.5 for a log-likelihood function.
• Strategy (MinimizerOptions::SetStrategy(int )), minimization strategy used. For each minimization strategy
Minuit uses different configuration parameters (e.g. different requirements in computing derivatives, computing
full Hessian (strategy = 2) or an approximate version. The default is a value of 1. In this case the full Hessian
matrix is computed only after the minimization.
• Precision (MinimizerOptions::SetTolerance(double )). Precision value in the evaluation of the minimization
function. Default is numerical double precision.
Note that not all the options are implemented by all the minimizers. For example in Minuit is possible to set the
maximum number of function calls, but not the maximum number of iterations. The Strategy and the Precision options
apply instead only for Minuit (and Minuit2 ).
The class supports also setting different default values for the options, by using the static functions
MinimizerOptions::SetDefault... (for example MinimizerOptions::SetDefaultPrintLevel(int )). The
list of the current option values can be inspected by using MinimizerOptions::Print.
ROOT::Math::MinimizerOptions() opt;
// print the default minimizer option values
opt.Print();

In addition it is possible to provide extra options which might apply for a particular minimizer MinimizerOptions::SetExtraOptio
IOptions & ). See the documentation of the particular minimizer to use for the list of possible additional options
available.

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CHAPTER 5. FITTING HISTOGRAMS

5.7.5

Performing the Fit

Here we have now all the required input ingredients for the fit, the data and the function to fit. Depending on these we
have now several different way to perform the fit, using the corresponding methods of the ROOT::Fit::Fitter class
and depending on the type of input data.
5.7.5.1

Available fit methods

• Least-square fit: Fitter::LeastSquare(const BinData & ) or Fitter::Fit(const Bindata &). It requires the user to pass a BinData object. It should be used when the data values follow a Gaussian distribution.
This fit method is implemented using the class ROOT::Fit::Chi2FCN.
• Binned Likelihood fit : Fitter::LikelihoodFit(const Bindata & ). The user needs to pass a BinData
object. It should be used when the data values follow a Poisson or a multinomial distribution. The Poisson case
(extended fit) is the default and in this case the function normalization is also fit to the data. The Multi-nominal
case can be selected by passing the optional extended boolean flag as false. This method is implemented by the
class ROOT::Fit:::PoissonLikelihoodFCN.
• Un-Binned likelihood fit: Fitter::LikelihoodFit(const UnBindata &). The user needs to pass an
UnBinData object. By default the fit is not extended (i.e. the normalization is not fitted to the data). As
above the user can select an extended likelihood fit by passing the optional extended boolean flag as true. This
methos is implemented using the class LogLikelihoodFCN
• Linear Fit: A linear fit can be selected (no iterative minimization is needed in this case, but using linear algebra
algorithms from the Matrix library), if the model function is linear in the parameters.
5.7.5.2

Customised Fit methods

Above we described the pre-defined methods used for fitting. A user can also implement its own fitting methods, thus
its version of the chi-square or likelihood function he wants to minimize. In this cas, the user does not really need to
build as input a ROOT::Fit data set and model function as we described before. He can implements its own version of
the method function using on its own data set objects and functions.
In this case ROOT::Fit::Fitter::SetFCN is used to set the method function and ROOT::Fit::FitFCN is used for
fitting. The method function can be passed also in ROOT::Fit::FitFCN, but in this case a previously defined fitting
configuration is used.
The possible type of method functions that can be bassed in ROOT::Fit::Fitter::SetFCN are:
• A generic functor object implementing operator()(const double * p) where p is the parameter vectors. In
this case one needs to pass the number of parameters, the function object and optionally a vector of initial
parameter values. Other optional parameter include the size of the data sets and a flag specifying if it is a chi2
(least-square fit). In the last two parameters are given, the chi2/ndf can be computed after fitting the data.
template 
bool Fitter::SetFCN(unsigned int npar, Function & f,
const double * initialParameters = 0,
unsigned int dataSize=0, bool isChi2Fit = false)
• A function object implementing the ROOT::Math::IBaseFunctionMultiDim interface:
bool Fitter::SetFCN(const ROOT::Math::IBaseFunctionMultiDim & f,
const double * initialParameters = 0,
unsigned int dataSize=0, bool isChi2Fit = false)
• A function object implementing the ROOT::Math::FitMethodFunction interface. This is an interface class
extending the ROOT::Math::IBaseFunctionMultiDim with some extra functionality which can be used when
fitting. This extra functionality is required by dedicated fitting algorithms like Fumili or GSLMultiFit.
bool Fitter::SetFCN(const ROOT::Math::FitMethodFunction & f,
const double * initialParameters = 0, unsigned int dataSize=0)
• A old-Minuit like FCN interface (i.e. a free function with the signature fcn(int &npar, double *gin, double
&f, double *u, int flag).
typedef void(* MinuitFCN)(int &npar, double *gin, double &f, double *u, int flag)
bool Fitter::SetFCN(MinuitFCN fcn, int npar,
const double * initialParameters = 0,
unsigned int dataSize=0, bool isChi2Fit = false)

5.8. THE MINIMIZATION PACKAGES

5.7.6

135

Fit Result

The result of the fit is contained in the ROOT::Fit::Result object. A reference to the result object is obtained with
the function Fitter::Result(). The ROOT::Fit::FitResult class provides an API for retrieving parameter values,
errors, covariance and correlation matrix from the fit, minimum chi2/likelihood values, etc. . .
A FitResult::Print method is also available to print the result of the fit.
The class has a self-explanatory API so, see its reference documentation for the possible information available after the
fit.
One extra functionality offered by ROOT::Fit::FitResult is the possibility to compute the confidence intervals of
the function after the fit. The function ROOT::Fit::FitResult::GetConfidenceInterval given an input data sets
(e.g. a BinData object) and a confidence level value (e.g. 68%) computes the lower/upper band values of the model
function at the given data points.

5.7.7

TFitResult

TFitResult is a class deriving from ROOT::Fit::Result and providing in addition some convenient methods to return
a covariance or correlation matrix as a TMatrixDSym object. In addition TFitResult derives from TNamed and can be
conveniently stored in a file.
When fitting an histogram ( a TH1 object) or a graph (a TGraph object) it is possible to return a TFitResult via the
TFitResultPtr object, which behaves as a smart pointer to a TFitResult. TFitResultPtr is the return object by
TH1::Fit or TGraph::Fit. By default the TFitResultPtr contains only the status of the fit and can be obtained by an
automatic conversion of the TFitResultPtr to an integer.
If the fit option S is instead used, TFitResultPtr contains the TFitResult and behaves as a smart pointer to it. This
is an example:
int fitStatus =
TFitResultPtr r
TMatrixDSym cov
Double_t chi2
Double_t par0
Double_t err0
r->Print("V");
r->Write();

5.8

hist->Fit(myFunction);
=
=
=
=
=

// TFitResultPtr contains only the fit status

hist->Fit(myFunction,"S");
r->GetCovarianceMatrix();
r->Chi2();
r->Parameter(0);
r->ParError(0);

//
//
//
//
//
//
//

TFitResultPtr contains the TFitResult
to access the covariance matrix
to retrieve the fit chi2
retrieve the value for the parameter 0
retrieve the error for the parameter 0
print full information of fit including covariance matrix
store the result in a file

The Minimization packages

As explained before various minimization packages can be used when fitting in ROOT. We have seen before how
to configure the Fitter class to use different minimization packages and different minimization options. When
using the Fit method the minimization package (and its options) can be selected using the static methods of the
ROOT::Math::MinimizerOptions class. For example to select Minuit2 instead of Minuit for fitting an histogram do:
ROOT::Math::MinimizerOptions::SetDefaultMinimizer("Minuit2");
// fit the histogram histo with the gaussian pre-defined function
histo->Fit("gaus");
In the following we will give some brief description of the minimization packages. The packages all implement the
ROOT::Math::Minimizer interface which can be use for finding the minimum of a multi-dimensional function. The
interface is documented in the Mathematical Library Chapter.
In addition packages like Minuit or Minuit2 provide their own interfaces.

5.9

MINUIT (Old TMInuit Version)

This package was originally written in FORTRAN by Fred James and part of PACKLIB (patch D506). It has been
converted to a C++ class by René Brun. The current implementation in C++ is a straightforward conversion of the
original FORTRAN version. The main changes are:

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CHAPTER 5. FITTING HISTOGRAMS

• The variables in the various Minuit labeled common blocks have been changed to the TMinuit class data members
• The internal arrays with a maximum dimension depending on the maximum number of parameters are now data
members’ arrays with a dynamic dimension such that one can fit very large problems by simply initializing the
TMinuit constructor with the maximum number of parameters
• The include file Minuit.h has been commented as much as possible using existing comments in the code or the
printed documentation
• The original Minuit subroutines are now member functions
• Constructors and destructor have been added
• Instead of passing the FCN function in the argument list, the addresses of this function is stored as pointer in the
data members of the class. This is by far more elegant and flexible in an interactive environment. The member
function SetFCN can be used to define this pointer
• The ROOT static function Printf is provided to replace all format statements and to print on currently defined
output file
• The functions SetObjectFit/GetObjectFit can be used inside the FCN function to set/get a referenced object
instead of using global variables
• By default fGraphicsMode is true. When calling the Minuit functions such as mncont, mnscan, or any Minuit
command invoking mnplot, TMinuit::mnplot() produces a TGraph object pointed by fPlot. One can retrieve
this object with TMinuit::GetPlot(). For example:
h->Fit("gaus");
gMinuit->Command("SCAn 1");
TGraph *gr = (TGraph*)gMinuit->GetPlot();
gr->SetMarkerStyle(21);
gr->Draw("alp");
• To set Minuit in no graphics mode, call
gMinuit->SetGraphicsMode(kFALSE);

5.9.1

Basic Concepts of Minuit

The Minuit package acts on a multi parameter FORTRAN function to which one must give the generic name FCN. In
the ROOT implementation, the function FCN is defined via the Minuit SetFCN member function when a HistogramFit
command is invoked. The value of FCN will in general depend on one or more variable parameters.
To take a simple example, in case of ROOT histograms (classes TH1C, TH1S, TH1F, TH1D) the Fit function defines the Minuit fitting function as being H1FitChisquare or H1FitLikelihood depending on the options selected.
H1FitChisquare calculates the chi-square between the user fitting function (Gaussian, polynomial, user defined, etc)
and the data for given values of the parameters. It is the task of Minuit to find those values of the parameters which
give the lowest value of chi-square.

5.9.2

The Transformation of Limited Parameters

For variable parameters with limits, Minuit uses the following transformation:
Pint = arcsin(2((Pext-a)/(b-a))-1)
Pext = a+((b-a)/(2))(sinPint+1)
so that the internal value Pint can take on any value, while the external value Pext can take on values only between
the lower limit a and the ext upper limit b. Since the transformation is necessarily non-linear, it would transform
a nice linear problem into a nasty non-linear one, which is the reason why limits should be avoided if not necessary.
In addition, the transformation does require some computer time, so it slows down the computation a little bit, and
more importantly, it introduces additional numerical inaccuracy into the problem in addition to what is introduced in
the numerical calculation of the FCN value. The effects of non-linearity and numerical round off both become more
important as the external value gets closer to one of the limits (expressed as the distance to nearest limit divided by
distance between limits). The user must therefore be aware of the fact that, for example, if they put limits of (0, 1010)
on a parameter, then the values 0.0 and 1. 0 will be indistinguishable to the accuracy of most machines.

5.9. MINUIT (OLD TMINUIT VERSION)

137

The transformation also affects the parameter error matrix, of course, so Minuit does a transformation of the error
matrix (and the ‘’parabolic” parameter errors) when there are parameter limits. Users should however realize that the
transformation is only a linear approximation, and that it cannot give a meaningful result if one or more parameters is
ext
very close to a limit, where ∂P
∂P int 6= 0. Therefore, it is recommended that:
• Limits on variable parameters should be used only when needed in order to prevent the parameter from taking
on unphysical values
• When a satisfactory minimum has been found using limits, the limits should then be removed if possible, in order
to perform or re-perform the error analysis without limits

5.9.3

How to Get the Right Answer from Minuit

Minuit offers the user a choice of several minimization algorithms. The MIGRAD algorithm is in general the best
minimized for nearly all functions. It is a variable-metric method with inexact line search, a stable metric updating
scheme, and checks for positive-definiteness. Its main weakness is that it depends heavily on knowledge of the first
derivatives, and fails miserably if they are very inaccurate.
If parameter limits are needed, in spite of the side effects, then the user should be aware of the following techniques to
alleviate problems caused by limits:

5.9.3.1

Getting the Right Minimum with Limits

If MIGRAD converges normally to a point where no parameter is near one of its limits, then the existence of limits has
probably not prevented Minuit from finding the right minimum. On the other hand, if one or more parameters is
near its limit at the minimum, this may be because the true minimum is indeed at a limit, or it may be because the
minimized has become ‘’blocked” at a limit. This may normally happen only if the parameter is so close to a limit
(internal value at an odd multiple of ± π2 that Minuit prints a warning to this effect when it prints the parameter
values. The minimized can become blocked at a limit, because at a limit the derivative seen by the minimized ∂P∂Fint is
zero no matter what the real derivative ∂P∂Fext is.


5.9.3.2

∂F
∂P int




=

∂F
∂P ext



∂P ext
∂P int




=

∂F
∂P ext


=0

Getting the Right Parameter Errors with Limits

In the best case, where the minimum is far from any limits, Minuit will correctly transform the error matrix, and the
parameter errors it reports should be accurate and very close to those you would have got without limits. In other
cases (which should be more common, since otherwise you would not need limits), the very meaning of parameter
errors becomes problematic. Mathematically, since the limit is an absolute constraint on the parameter, a parameter
at its limit has no error, at least in one direction. The error matrix, which can assign only symmetric errors, then
becomes essentially meaningless.

5.9.3.3

Interpretation of Parameter Errors

There are two kinds of problems that can arise: the reliability of Minuit’s error estimates, and their statistical
interpretation, assuming they are accurate.

5.9.3.4

Statistical Interpretation

For discussion of basic concepts, such as the meaning of the elements of the error matrix, or setting of exact confidence
levels see the articles:
• F.James. Determining the statistical Significance of experimental Results. Technical Report DD/81/02 and
CERN Report 81-03, CERN, 1981
• W.T.Eadie, D.Drijard, F.James, M.Roos, and B.Sadoulet. Statistical Methods in Experimental Physics. NorthHolland, 1971

138

5.9.4

CHAPTER 5. FITTING HISTOGRAMS

Reliability of Minuit Error Estimates

Minuit always carries around its own current estimates of the parameter errors, which it will print out on request, no
matter how accurate they are at any given point in the execution. For example, at initialization, these estimates are just
the starting step sizes as specified by the user. After a HESSE step, the errors are usually quite accurate, unless there
has been a problem. Minuit, when it prints out error values, also gives some indication of how reliable it thinks they
are. For example, those marked CURRENT GUESS ERROR are only working values not to be believed, and APPROXIMATE
ERROR means that they have been calculated but there is reason to believe that they may not be accurate.
If no mitigating adjective is given, then at least Minuit believes the errors are accurate, although there is always a
small chance that Minuit has been fooled. Some visible signs that Minuit may have been fooled:
• Warning messages produced during the minimization or error analysis
• Failure to find new minimum
• Value of EDM too big (estimated Distance to Minimum)
• Correlation coefficients exactly equal to zero, unless some parameters are known to be uncorrelated with the
others
• Correlation coefficients very close to one (greater than 0.99). This indicates both an exceptionally difficult
problem, and one which has been badly parameterized so that individual errors are not very meaningful because
they are so highly correlated
• Parameter at limit. This condition, signaled by a Minuit warning message, may make both the function minimum
and parameter errors unreliable. See the discussion above ‘Getting the right parameter errors with limits’
The best way to be absolutely sure of the errors is to use ‘’independent’‘calculations and compare them, or compare
the calculated errors with a picture of the function. Theoretically, the covariance matrix for a’‘physical” function must
be positive-definite at the minimum, although it may not be so for all points far away from the minimum, even for a
well-determined physical problem. Therefore, if MIGRAD reports that it has found a non-positive-definite covariance
matrix, this may be a sign of one or more of the following:
5.9.4.1

A Non-physical Region

On its way to the minimum, MIGRAD may have traversed a region that has unphysical behavior, which is of course not
a serious problem as long as it recovers and leaves such a region.
5.9.4.2

An Underdetermined Problem

If the matrix is not positive-definite even at the minimum, this may mean that the solution is not well defined, for
example that there are more unknowns than there are data points, or that the parameterization of the fit contains a
linear dependence. If this is the case, then Minuit (or any other program) cannot solve your problem uniquely. The
error matrix will necessarily be largely meaningless, so the user must remove the under determinedness by reformulating
the parameterization. Minuit cannot do this itself.
5.9.4.3

Numerical Inaccuracies

It is possible that the apparent lack of positive-definiteness is due to excessive round off errors in numerical calculations
(in the user function), or not enough precision. This is unlikely in general, but becomes more likely if the number
of free parameters is very large, or if the parameters are badly scaled (not all of the same order of magnitude), and
correlations are large. In any case, whether the non-positive-definiteness is real or only numerical is largely irrelevant,
since in both cases the error matrix will be unreliable and the minimum suspicious.
5.9.4.4

An Ill-posed Problem

For questions of parameter dependence, see the discussion above on positive-definiteness. Possible other mathematical
problems are the following:
• Excessive numerical round off - be especially careful of exponential and factorial functions which get big very
quickly and lose accuracy.
• Starting too far from the solution - the function may have unphysical local minima, especially at infinity in some
variables.

5.10. MINUIT2 PACKAGE

5.10

139

Minuit2 Package

Minuit2 is a new object-oriented implementation, written in C++, of the popular MINUIT minimization package.
Compared with the TMinuit class, which is a direct conversion from FORTRAN to C++, Minuit2 is a complete
redesign and re-implementation of the package. This new version provides all the functionality present in the old
FORTRAN version, with almost equivalent numerical accuracy and computational performances. Furthermore, it
contains some fixes and small improvements and this new functionality: * The possibility to set single side parameter
limits * the FUMILI algorithm (see the next paragraph “FUMILI Minimization Package”), which is an optimized
method for least square and log likelihood minimizations.
Minuit2 has been originally developed by M. Winkler and F. James in the SEAL project. More information can be
found on the MINUIT Web Site and in particular at the following documentation page at http://www.cern.ch/minuit/
doc/doc.html.
A detailed User Guide for Minuit2 exists, describing the API of the internal classes. ROOT uses Minuit2 for fitting
via the Minuit2Minimizer class which implements the ROOT::Math::Minimizer interface.
Minuit2 is also distributed as an independent package of ROOT and can be built without any other dependency on
the ROOT libraries.
Examples on how to use the Minuit2 and Fumili2 plug-ins are provided in the tutorials’ directory $ROOTSYS/tutorials/fit:
minuit2FitBench.C, minuit2FitBench2D.C and minuit2GausFit.C. More information on the classes and functions
present in Minuit2 is available at online reference documentation.
Useful information on MINUIT and minimization in general is provided in the following documents:
F. James, Minuit Tutorial on Function Minimization ( http://seal.cern.ch/documents/minuit/mntutorial.pdf); F.
James, The Interpretation of Errors in Minuit ( http://seal.cern.ch/documents/minuit/mnerror.pdf);

5.11

FUMILI Minimization Package

FUMILI is used to minimize Chi-square function or to search maximum of likelihood function. Experimentally measured
~ where x~i are coordinates, and θ~ - vector of parameters. For
values Fi are fitted with theoretical functions fi (x~i , θ),
better convergence Chi-square function has to be the following form
n

χ2
1X
=
2
2 i=1

~ − Fi
fi (x~i , θ)
σi

!2

where σi are errors of the measured function. The minimum condition is:
n
i
X
∂χ2
1 ∂fi h
~ − Fj = 0, i = 1...m
.
=
(x~j , θ)
2
∂θi
σ ∂θi
j=1 j

where m is the quantity of parameters. Expanding left part of this equation over parameter increments and retaining
only linear terms one gets


∂χ2
θi


+
~0
θ=θ

X  ∂ 2 χ2 
.(θk − θk0 ) = 0
∂θi ∂θk θ=θ~0
k

here θ~0 is some initial value of parameters. In general case:
n

n

X 1 ∂fj ∂fj X (fj − Fj ) ∂ 2 fj
∂ 2 χ2
=
+
·
∂θi ∂θk
σ 2 θi θk
σj2
∂θi ∂θk
j=1 j
j=1
In FUMILI algorithm for second derivatives of Chi-square approximate expression is used when last term in previous
equation is discarded. It is often done, not always wittingly, and sometimes causes troubles, for example, if user wants
to limit parameters with positive values by writing down θi2 instead of θi . FUMILI will fail if one tries minimize
~ where g is arbitrary function.
χ2 = g 2 (θ)
Approximate value is:

140

CHAPTER 5. FITTING HISTOGRAMS

n

X 1 ∂fj ∂fj
∂ 2 χ2
≈ Zik =
∂θi ∂θk
σ 2 θi θk
j=1 j
Then the equations for parameter increments are:


∂χ2
∂θi


+
~ θ
~0
θ=

X

Zik · (θk − θk0 ) = 0,

i = 1...m

k

Remarkable feature of algorithm is the technique for step restriction. For an initial value of parameter θ~0 a parallelepiped
P0 is built with the center at θ~0 and axes parallel to coordinate axes θi . The lengths of parallelepiped sides along i-th
~ are quasi-linear all over the parallelepiped.
axis is 2bi , where bi is such a value that the functions fj (θ)
FUMILI takes into account simple linear inequalities in the form:
θimin ≤ θi ≤ θimax
They form parallelepiped P (P0 may be deformed by P ). Very similar step formulae are used in FUMILI for negative
logarithm of the likelihood function with the same idea - linearization of function argument.

5.12

Neural Networks

5.12.1

Introduction

Neural Networks are used in various fields for data analysis and classification, both for research and commercial
institutions. Some randomly chosen examples are image analysis, financial movements’ predictions and analysis, or
sales forecast and product shipping optimization. In particles physics neural networks are mainly used for classification
tasks (signal over background discrimination). A vast majority of commonly used neural networks are multilayer
perceptrons. This implementation of multilayer perceptrons is inspired from the MLPfit package, which remains one of
the fastest tools for neural networks studies.

5.12.2

The MLP

The multilayer perceptron is a simple feed-forward network with the following structure showed on the left.
It is made of neurons characterized by a bias and weighted links in between - let’s call those links synapses. The
input neurons receive the inputs, normalize them and forward them to the first hidden layer. Each neuron in any
subsequent layer first computes a linear combination of the outputs of the previous layer. The output of the neuron is
then function of that combination with f being linear for output neurons or a sigmoid for hidden layers.
Such a structure is very useful because of two theorems:
1- A linear combination of sigmoids can approximate any continuous function.
2- Trained with output=1 for the signal and 0 for the background, the approximated function of inputs X is the
probability of signal, knowing X.

5.12.3

Learning Methods

The aim of all learning methods is to minimize the total error on a set of weighted examples. The error is defined
as the sum in quadrate, divided by two, of the error on each individual output neuron. In all methods implemented
in this library, one needs to compute the first derivative of that error with respect to the weights. Exploiting the
well-known properties of the derivative, one can express this derivative as the product of the local partial derivative by
the weighted sum of the outputs derivatives (for a neuron) or as the product of the input value with the local partial
derivative of the output neuron (for a synapse). This computation is called “back-propagation of the errors”. Six
learning methods are implemented.

5.12. NEURAL NETWORKS

5.12.3.1

141

Stochastic Minimization

This is the most trivial learning method. The Robbins-Monro stochastic approximation is applied to multilayer
perceptrons. The weights are updated after each example according to the formula:
wij (t + 1) = wij (t) + ∆wij (t)
with:

∆wij (t) = −η


∂ep
+ δ + ∆wij (t − 1)
∂wij

The parameters for this method are Eta, EtaDecay, Delta and Epsilon.
5.12.3.2

Steepest Descent With Fixed Step Size (Batch Learning)

It is the same as the stochastic minimization, but the weights are updated after considering all the examples, with the
total derivative dEdw. The parameters for this method are Eta, EtaDecay, Delta and Epsilon.
5.12.3.3

Steepest Descent Algorithm

Weights are set to the minimum along the line defined by the gradient. The only parameter for this method is Tau.
Lower Tau = higher precision = slower search. A value Tau=3 seems reasonable.
5.12.3.4

Conjugate Gradients With the Polak-Ribiere Updating Formula

Weights are set to the minimum along the line defined by the conjugate gradient. Parameters are Tau and Reset, which
defines the epochs where the direction is reset to the steepest descent (estimated by using the Polak-Ribiere formula).

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CHAPTER 5. FITTING HISTOGRAMS

5.12.3.5

Conjugate Gradients With the Fletcher-Reeves Updating Formula

Weights are set to the minimum along the line defined by the conjugate gradient. Parameters are Tau and Reset, which
defines the epochs where the direction is reset to the steepest descent (estimated by using the Fletcher-Reeves formula).
5.12.3.6

The Broyden, Fletcher, Goldfarb, Shanno (BFGS) Method

It implies the computation of a NxN matrix, but seems more powerful at least for less than 300 weights. Parameters are
Tau and Reset, which defines the epochs where the direction is reset to the steepest descent.

5.12.4

Using the Network

Neural network are build from a set of “samples”. A sample is a set of values defining the inputs and the corresponding
output that the network should ideally provide. In ROOT this is a TTree entry. The first thing to be decided is the
network layout. This layout is described in a string where the layers are separated by semicolons. The input/output
layers are defined by giving the expression for each neuron, separated by comas. Hidden layers are just described by
the number of neurons.
In addition, input and output layer formulas can be preceded by ‘@’ (e.g. “@out”) if one wants to normalize the
corresponding value. Also, if the string ends with ‘!’, output neurons are set up for classification, i.e. with a sigmoid (1
neuron) or softmax (more neurons) activation function.
Many questions on the good usage of neural network, including rules of dumb to determine the best network topology
are addressed at ftp://ftp.sas.com/pub/neural/FAQ.html
// a simple network: 2 inputs, 10 hidden and 1 normalized
// output neuron
TMultiLayerPerceptron network("r,z:10:@Br",tree);
Expressions are evaluated as for TTree::Draw().
Input and outputs are taken from the TTree associated with the network. This TTree can be given as argument of the constructor or defined later with
TMultiLayerPerceptron::SetData(). Events can also be weighted. The weight expression can be given in
the constructor or set later with the method SetWeight() of the class TMultiLayerPerceptron. Two datasets must
be defined before learning the network: a training dataset that is used when minimizing the error, and a test dataset
that will avoid bias. Those two datasets can be build aside and then given to the network, or can be build from a
standard expression. By default, half of the events are put in both datasets.
// a more complex 4:8:1 network
// the ptsumf branch is used as weigh;
// default event lists are explicit
TMultiLayerPerceptron network("m,pt,acol,acopl:8:type","pt",tree,
"Entry$%2","Entry$/2");
The method TMultiLayerPerceptron::SetLearningMethod() defines the learning method. Learning methods are:
TMultiLayerPerceptron::kStochastic,
TMultiLayerPerceptron::kBatch,
TMultiLayerPerceptron::kSteepestDescent,
TMultiLayerPerceptron::kRibierePolak,
TMultiLayerPerceptron::kFletcherReeves,
TMultiLayerPerceptron::kBFGS
// default
The training can start with TMultiLayerPerceptron::Train(Int_t nepoch,Option_t* options). The first argument is the number of epochs while option is a string that can contain “text” (simple text output), “graph” (evaluating
graphical training curves), “update = X” (step for the text/graph output update) or “+” (will skip the randomization
and start from the previous values). All combinations are available.
network.Train(1000,"text,graph,update=10"); // full output every
// 10 epochs
network.Train(100,"text,+");
// 100 more epochs
//starts with existing weights

5.12. NEURAL NETWORKS

143

The weights can be saved to a file (DumpWeights) and then reloaded (LoadWeights) to a new compatible network. The
output can also be evaluated (Evaluate) for a given output neuron and an array of double input parameters or the
network can be exported (Export) as a standalone code. Up to now, this is only as a C++ or PYTHON class, but
other languages could be implemented.

5.12.5

Examples

An example of how to use TMultiLayerPerceptron is the macro mlpHiggs.C in $ROOTSYS/tutorials. Using some
standard simulated information that could have been obtained at LEP, a neural network is build, which can make the
difference between WW events and events containing a Higgs boson. Starting with a TFile containing two TTrees: one
for the signal, the other for the background, a simple script is used:
void mlpHiggs(Int_t ntrain=100) {
if (!gROOT->GetClass("TMultiLayerPerceptron"))
gSystem->Load("libMLP");
// prepare inputs - the 2 trees are merged into one, and a
// "type" branch, equal to 1 for the signal and 0 for the
// background is added
TFile input("mlpHiggs.root");
TTree *signal = (TTree *)input.Get("sig_filtered");
TTree *background = (TTree *)input.Get("bg_filtered");
TTree *simu = new TTree("MonteCarlo",
"Filtered Monte Carlo Events");
...
Since the input is a TTree and we are starting from two different TTrees (with different names), they are first merged
into one, and a “type” branch is added, that says whether there is a signal or a background event. Those irrelevant
details are skipped here.
...
TMultiLayerPerceptron *mlp = new TMultiLayerPerceptron(
"msumf,ptsumf, acolin, acopl:8:type","ptsumf",simu,
"Entry$%2","Entry$/2");
mlp->Train(ntrain, "text,graph,update=10");
The neural network is instantiated and trained. “ptsumf” is used as a weight, and the standard event lists are explicit.
The network that is then build has four input neurons, eight additional ones in the only hidden layer and one single
output neuron.
// Use the NN to plot the results for each sample
TH1F *bg = new TH1F("bgh","NN output",50,-.5,1.5);
TH1F *sig = new TH1F("sigh","NN output",50,-.5,1.5);
bg->SetDirectory(0);
sig->SetDirectory(0);
Double_t params[4];
for (i = 0; i < background->GetEntries(); i++) {
background->GetEntry(i);
params[0] = msumf;
params[1] = ptsumf;
params[2] = acolin;
params[3] = acopl;
bg->Fill(mlp->Evaluate(0,params));
}
for (i = 0; i < signal->GetEntries(); i++) {
signal->GetEntry(i);
params[0] = msumf;
params[1] = ptsumf;
params[2] = acolin;
params[3] = acopl;
sig->Fill(mlp->Evaluate(0,params));
}
TCanvas *cv = new TCanvas("NNout_cv","Neural net output");
bg->SetFillStyle(3008);

144

CHAPTER 5. FITTING HISTOGRAMS
bg->SetFillColor(kBlue);
sig->SetFillStyle(3003);
sig->SetFillColor(kRed);
bg->SetStats(0);
sig->SetStats(0);
bg->Draw();
sig->Draw("same");
TLegend *legend = new TLegend(.75,.80,.95,.95);
legend->AddEntry(bg,"Background(WW)");
legend->AddEntry(sig,"Signal(Higgs)");
legend->Draw();

The neural net output is then used to display the final difference between background and signal events. The figure
“The neural net output” shows this plot.

Figure 5.5: The neural net output
As it can be seen, this is a quite efficient technique. As mentioned earlier, neural networks are also used for fitting
function. For some application with a cylindrical symmetry, a magnetic field simulation gives as output the angular
component of the potential vector A, as well as the radial and z components of the B field.
One wants to fit those distributions with a function in order to plug them into the Geant simulation code. Polynomial
fits could be tried, but it seems difficult to reach the desired precision over the full range. One could also use a spline
interpolation between known points. In all cases, the resulting field would not be C-infinite.
An example of output (for Br) is shown. First the initial function can be seen as the target. Then, the resulting
(normalized) neural net output. In order to ease the learning, the “normalize output” was used here. The initial
amplitude can be recovered by multiplying by the original RMS and then shifting by the original mean.

5.12. NEURAL NETWORKS

145

Figure 5.6: The original and the neural net for Br

146

CHAPTER 5. FITTING HISTOGRAMS

Chapter 6

A Little C++
This chapter introduces you to some useful insights into C++, to allow you to use of the most advanced features in
ROOT. It is in no case a full course in C++.

6.1

Classes, Methods and Constructors

C++ extends C with the notion of class. If you’re used to structures in C, a class is a struct that is a group of
related variables, which is extended with functions and routines specific to this structure (class). What is the interest?
Consider a struct that is defined this way:
struct Line {
float x1;
float y1;
float x2;
float y2;
}
This structure represents a line to be drawn in a graphical window. (x1,y1) are the coordinates of the first point,
(x2,y2) the coordinates of the second point. In the standard C, if you want to draw effectively such a line, you first
have to define a structure and initialize the points (you can try this):
Line firstline;
firstline.x1 = 0.2;
firstline.y1 = 0.2;
firstline.x2 = 0.8;
firstline.y2 = 0.9;
This defines a line going from the point (0.2,0.2) to the point (0.8,0.9). To draw this line, you will have to write a
function, say LineDraw(Line l) and call it with your object as argument:
LineDraw(firstline);
In C++, we would not do that. We would instead define a class like this:
class TLine {
Double_t x1;
Double_t y1;
Double_t x2;
Double_t y2;
TLine(int x1, int y1, int x2, int y2);
void Draw();
}
Here we added two functions, that we will call methods or member functions, to the TLine class. The first method is
used for initializing the line objects we would build. It is called a constructor. The second one is the Draw method
itself. Therefore, to build and draw a line, we have to do:
147

148

CHAPTER 6. A LITTLE C++
TLine l(0.2,0.2,0.8,0.9);
l.Draw();

The first line builds the object lby calling its constructor. The second line calls the TLine::Draw() method of this
object. You don’t need to pass any parameters to this method since it applies to the object l, which knows the
coordinates of the line. These are internal variables x1, y1, x2, y2 that were initialized by the constructor.

6.2

Inheritance and Data Encapsulation

We have defined a TLine class that contains everything necessary to draw a line. If we want to draw an arrow, is it so
different from drawing a line? We just have to draw a triangle at one end. It would be very inefficient to define the
class TArrow from scratch. Fortunately, inheritance allows a class to be defined from an existing class. We would write
something like:
class TArrow : public TLine {
int ArrowHeadSize;
void Draw();
void SetArrowSize(int arrowsize);
}
The keyword “public” will be explained later. The class TArrow now contains everything that the class TLine does,
and a couple of things more, the size of the arrowhead and a function that can change it. The Draw method of TArrow
will draw the head and call the draw method of TLine. We just have to write the code for drawing the head!

6.2.1

Method Overriding

Giving the same name to a method (remember: method = member function of a class) in the child class (TArrow)
as in the parent (TLine) does not give any problem. This is called overriding a method. Draw in TArrow overrides
Draw in TLine. There is no possible ambiguity since, when one calls the Draw() method; this applies to an object
which type is known. Suppose we have an object l of type TLine and an object a of type TArrow. When you want to
draw the line, you do:
l.Draw();
Draw() from TLine is called. If you do:
a.Draw();
Draw() from TArrow is called and the arrow a is drawn.

6.2.2

Data Encapsulation

We have seen previously the keyword “public”. This keyword means that every name declared public is seen by the
outside world. This is opposed to “private” that means only the class where the name was declared private could see
this name. For example, suppose we declare in TArrow the variable ArrowHeadSize private.
private:
int ArrowHeadSize;
Then, only the methods (i.e. member functions) of TArrow will be able to access this variable. Nobody else will see it.
Even the classes that we could derive from TArrow will not see it. On the other hand, if we declare the method Draw()
as public, everybody will be able to see it and use it. You see that the character public or private does not depend
of the type of argument. It can be a data member, a member function, or even a class. For example, in the case of
TArrow, the base class TLine is declared as public:
class TArrow : public TLine { ...

6.3. CREATING OBJECTS ON THE STACK AND HEAP

149

This means that all methods of TArrow will be able to access all methods of TLine, but this will be also true for
anybody in the outside world. Of course, this is true if TLine accepts the outside world to see its methods/data
members. If something is declared private in TLine, nobody will see it, not even TArrow members, even if TLine is
declared as a public base class.
What if TLine is declared “private” instead of “public” ? Well, it will behave as any other name declared private in
TArrow: only the data members and methods of TArrow will be able to access TLine, its methods and data members,
nobody else. This may seem a little bit confusing and readers should read a good C++ book if they want more details.
Especially since, besides public and private, a member can be protected. Usually, one puts private the methods that the
class uses internally, like some utilities classes, and that the programmer does not want to be seen in the outside world.
With “good” C++ practice (which we have tried to use in ROOT), all data members of a class are private. This is
called data encapsulation and is one of the strongest advantages of Object Oriented Programming (OOP). Private data
members of a class are not visible, except to the class itself. So, from the outside world, if one wants to access those
data members, one should use so called “getters” and “setters” methods, which are special methods used only to get or
set the data members. The advantage is that if the programmers want to modify the inner workings of their classes,
they can do so without changing what the user sees. The user does not even have to know that something has changed
(for the better, hopefully). For example, in our TArrow class, we would have set the data member ArrowHeadSize
private. The setter method is SetArrowSize(), we do not need a getter method:
class TArrow : public TLine {
private:
int ArrowHeadSize;
public:
void Draw();
void SetArrowSize(int arrowsize);
}
To define an arrow object you call the constructor. This will also call the constructor of TLine, which is the parent
class of TArrow, automatically. Then we can call any of the line or arrow public methods:
root[] TArrow *myarrow = new TArrow(1,5,89,124);
root[] myarrow->SetArrowSize(10);
root[] myarrow->Draw();

6.3

Creating Objects on the Stack and Heap

To explain how objects are created on the stack and on the heap we will use the Quad class. You can find the
definition in $ROOTSYS/tutorials/quadp/Quad.h and Quad.cxx. The Quad class has four methods. The constructor
and destructor, Evaluate that evaluates ax**2 + bx +c, and Solve which solves the quadratic equation ax**2 + bx
+c = 0.
Quad.h :
class Quad {
public:
Quad(Float_t a, Float_t b, Float_t c);
~Quad();
Float_t Evaluate(Float_t x) const;
void Solve() const;
private:
Float_t fA;
Float_t fB;
Float_t fC;
};
Quad.cxx:
#include 
#include 
#include "Quad.h"

150

CHAPTER 6. A LITTLE C++

Quad::Quad(Float_t a, Float_t b, Float_t c) {
fA = a;
fB = b;
fC = c;
}
Quad::~Quad() {
Cout <<"deleting object with coeffts: "<< fA << "," << fB << ","
<< fC << endl;
}
Float_t Quad::Evaluate(Float_t x) const {
return fA*x*x + fB*x + fC;
}
void Quad::Solve() const {
Float_t temp = fB*fB - 4.*fA*fC;
if ( temp > 0. ) {
temp = sqrt( temp );
cout << "There are two roots: " << ( -fB - temp ) / (2.*fA)
<< " and " << ( -fB + temp ) / (2.*fA) << endl;
} else {
if ( temp == 0. ) {
cout << "There are two equal roots: " << -fB / (2.*fA)
<< endl;
} else {
cout << "There are no roots" << endl;
}
}
}
Let us first look how we create an object. When we create an object by:
root[] Quad my_object(1.,2.,-3.);
We are creating an object on the stack. A FORTRAN programmer may be familiar with the idea; it is not unlike a
local variable in a function or subroutine. Although there are still a few old timers who do not know it, FORTRAN
is under no obligation to save local variables once the function or subroutine returns unless the SAVE statement is
used. If not then it is likely that FORTRAN will place them on the stack and they will “pop off” when the RETURN
statement is reached. To give an object more permanence it has to be placed on the heap.
root[] .L Quad.cxx
root[] Quad *my_objptr = new Quad(1.,2.,-3.);
The second line declares a pointer to Quad called my_objptr. From the syntax point of view, this is just like all the
other declarations we have seen so far, i.e. this is a stack variable. The value of the pointer is set equal to
new Quad(1.,2.,-3.);
new, despite its looks, is an operator and creates an object or variable of the type that comes next, Quad in this case,
on the heap. Just as with stack objects it has to be initialized by calling its constructor. The syntax requires that the
argument list follow the type. This one statement has brought two items into existence, one on the heap and one on
the stack. The heap object will live until the delete operator is applied to it.
There is no FORTRAN parallel to a heap object; variables either come or go as control passes in and out of a function
or subroutine, or, like a COMMON block variables, live for the lifetime of the program. However, most people in HEP
who use FORTRAN will have experience of a memory manager and the act of creating a bank is a good equivalent of
a heap object. For those who know systems like ZEBRA, it will come as a relief to learn that objects do not move,
C++ does not garbage collect, so there is never a danger that a pointer to an object becomes invalid for that reason.
However, having created an object, it is the user’s responsibility to ensure that it is deleted when no longer needed, or
to pass that responsibility onto to some other object. Failing to do that will result in a memory leak, one of the most
common and most hard-to-find C++ bugs.
To send a message to an object via a pointer to it, you need to use the “->” operator e.g.:

6.3. CREATING OBJECTS ON THE STACK AND HEAP

151

root[] my_objptr->Solve();
Although we chose to call our pointer my_objptr, to emphasize that it is a pointer, heap objects are so common in an
object-oriented program that pointer names rarely reflect the fact - you have to be careful that you know if you are
dealing with an object or its pointer! Fortunately, the compiler won’t tolerate an attempt to do something like:
root[] my_objptr.Solve();
Although this is a permitted by the Cling shortcuts, it is one that you are strongly advised not to follow! As we have
seen, heap objects have to be accessed via pointers, whereas stack objects can be accessed directly. They can also be
accessed via pointers:
root[] Quad stack_quad(1.,2.,-3.);
root[] Quad *stack_ptr = &stack_quad;
root[] stack_ptr->Solve();
Here we have a Quad pointer that has been initialized with the address of a stack object. Be very careful if you take
the address of stack objects. As we shall see soon, they are deleted automatically, which could leave you with an illegal
pointer. Using it will corrupt and may well crash the program!
It is time to look at the destruction of objects. A destructor is a special C++ function that releases resources for
(or destroy) an object of a class. It is opposite of a constructor that create the object of a class when is called. The
compiler will provide a destructor that does nothing if none is provided. We will add one to our Quad class so that we
can see when it is called. The class names the destructor but with a prefix ~ which is the C++ one’s complement
i.e. bit wise complement, and hence has destruction overtones! We declare it in the .h file and define it in the .cxx file.
It does not do much except print out that it has been called (still a useful debug technique despite today’s powerful
debuggers!).
Now run root, load the Quad class and create a heap object:
root[] .L Quad.cxx
root[] Quad *my_objptr = new Quad(1.,2.,-3.);
To delete the object:
root[] delete my_objptr;
root[] my_objptr = 0;
You should see the print out from its destructor. Setting the pointer to zero afterwards is not strictly necessary (and
Cling does it automatically), but the object is no more accessible, and any attempt to use the pointer again will, as has
already been stated, cause grief. So much for heap objects, but how are stack objects deleted? In C++, a stack object
is deleted as soon as control leaves the innermost compound statement that encloses it. Therefore, it is singularly futile
to do something like:
root[] {

Quad my_object(1.,2.,-3.); }

Cling does not follow this rule; if you type in the above line, you will not see the destructor message. As explained in
the Script lesson, you can load in compound statements, which would be a bit pointless if everything disappeared as
soon as it was loaded! Instead, to reset the stack you have to type:
root[] gROOT->Reset();
This sends the Reset message via the global pointer to the ROOT object, which, amongst its many roles, acts as a
resource manager. Start ROOT again and type in the following:
root[]
root[]
root[]
root[]

.L Quad.cxx
Quad my_object(1.,2.,-3.);
Quad *my_objptr = new Quad(4.,5.,-6.);
gROOT->Reset();

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CHAPTER 6. A LITTLE C++

You will see that this deletes the first object but not the second. We have also painted ourselves into a corner, as
my_objptr was also on the stack. This command will fail.
root[] my_objptr->Solve();
Cling no longer knows what my_objptr is. This is a great example of a memory leak; the heap object exists but we
have lost our way to access it. In general, this is not a problem. If any object will outlive the compound statement in
which it was created then a more permanent pointer will point to it, which frequently is part of another heap object.
See Resetting the Interpreter Environment in the chapter “Cling the C++ Interpreter”.

Chapter 7

The C++ Interpreter Cling
ROOT has a C++ interpreter called cling built in. It is used for the prompt, both C++ and Python. It also serves as a
source of information to store C++ objects, and provides the back-end for ROOT’s signal/slot and plug-in mechanisms.
This chapter focuses on the parts of cling that you will encounter while interacting with ROOT.

7.1

The ROOT Prompt

Start up a ROOT session by typing root at the system prompt.
$ root
-----------------------------------------------------------| Welcome to ROOT 6.00/00
http://root.cern.ch |
|
(c) 1995-2014, The ROOT Team |
| Built for linuxx8664gcc
|
| From tag v6-00-00, 30 May 2014
|
| Try '.help', '.demo', '.license', '.credits', '.quit'/'.q' |
-----------------------------------------------------------root [0]
Now we create a TLine object:
root [1] TLine l;
root [2] l.Print()
TLine X1=0.000000 Y1=0.000000 X2=0.000000 Y2=0.000000
root [3] l.SetX1(10)
root [4] l.SetY1(11)
root [5] l.Print()
TLine X1=10.000000 Y1=11.000000 X2=0.000000 Y2=0.000000
root [6] .g l
.g l
ROOT_prompt_0
1 (address: NA) class TLine l, size = 72
root [7] l.GetX1();
root [8] l.GetX1()
(Double_t) 1.000000e+01
Note some of the features of the ROOT prompt: - Terminating with ‘;‘ is not required, see “C++ Extensions To Ease
Scripting” below. - Emacs style command line editing. - Raw interpreter commands start with a dot; .g l for instance
shows the interpreter information on the global called l. - To show the result of an expression just do not type the
trailing ;.
For the further examples we will “abbreviate” root [0] etc by root [].
root [] .class TLine
===========================================================================
153

154

CHAPTER 7. THE C++ INTERPRETER CLING

class TLine
SIZE: 72 FILE: TLine.h LINE: 39
Base classes: -------------------------------------------------------0x20
public TAttBBox2D
List of member variables -------------------------------------------------TLine.h
42 0x28
protected: Double_t fX1
TLine.h
43 0x30
protected: Double_t fY1
TLine.h
44 0x38
protected: Double_t fX2
TLine.h
45 0x40
protected: Double_t fY2
TLine.h
50 0x0
public: enum TLine:: test.log
root [] l.Dump();
root [] .>
root [] ?
Here we see:
•
•
•
•

Use .class as quick help and reference
Unix like I/O redirection using .> out.txt and unredirection with .>
Use ? to get help on all “raw” interpreter commands
Use @ to abort a multi-line command

Now let us execute a multi-line command:
root [] {
root [] ? TLine l;
root [] ? for (int i = 0; i < 5; i++) {
root [] ?
l.SetX1(i);
root [] ?
l.SetY1(i+1);
root [] ?
l.Print();
root [] ? }
root [] ? }
TLine X1=0.000000 Y1=1.000000 X2=0.000000
TLine X1=1.000000 Y1=2.000000 X2=0.000000
TLine X1=2.000000 Y1=3.000000 X2=0.000000
TLine X1=3.000000 Y1=4.000000 X2=0.000000
TLine X1=4.000000 Y1=5.000000 X2=0.000000
root [] .q

Y2=0.000000
Y2=0.000000
Y2=0.000000
Y2=0.000000
Y2=0.000000

Here we note:
•
•
•
•
•

7.2

A multi-line command starts with a { and ends with a }.
Inside continuation, every line has to be correctly terminated with a ; (like in “real” C++).
All objects are created in global scope.
There is no way to back up; you are better off writing a script.
Use .q to exit root.

Feeding Sources Files To ROOT: C++ Scripts

ROOT script files (often called “Macros”) contain pure C++ code. They can contain a simple sequence of statements
like in the multi command line example given above, but also arbitrarily complex class and function definitions.
The most frequent interaction with the ROOT prompt uses .x to “run” a file:
root [] .x myScript.C
This loads myScript.C into the interpreter and calls the function myScript(). You can pass arguments using .x
myScript.C(12, "A String").
Alternatively you can load the script and then run a function explicitly:
root [] .L myScript.C
root [] myScript()
The above is equivalent to .x myScript.C.
In a named script, the objects created on the stack are deleted when the function exits. In a common scenario you
create a histogram in a named script on the stack. You draw the histogram, but when the function exits the canvas is
empty and the histogram has disappeared. To avoid the histogram from disappearing you can create it on the heap (by
using new). This will leave the histogram object intact, but the pointer in the named script scope will be “gone”. Since
histograms (and trees) are added to the list of objects in the current directory, you can always retrieve them to delete
them if needed.

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CHAPTER 7. THE C++ INTERPRETER CLING

root[] TH1F *h = (TH1F*)gDirectory->Get("myHist");
// or
root[] TH1F *h = (TH1F*)gDirectory->GetList()->FindObject("myHist");
In addition, histograms and trees are automatically deleted when the current directory is closed. This will automatically
take care of the clean up. See “Input/Output”.

7.2.1

Executing a Script From a Script

You may want to execute a script conditionally inside another script. To do it you need to call the interpreter and
you can do that with TROOT::ProcessLine(). The example $ROOTSYS/tutorials/tree/cernstaff.C calls a script
to build the root file if it does not exist:
void cernstaff() {
if (gSystem->AccessPathName("cernstaff.root")) {
gROOT->ProcessLine(".x cernbuild.C");
}
ProcessLine takes a parameter, which is a pointer to an int or to a TInterpreter::EErrorCode to let you
access the interpreter error code after an attempt to interpret. This will contain the error as defined in enum
TInterpreter::EErrorCode with TInterpreter::kSuccess being the value for a successful execution.

7.2.2

Executing a Script From the Invocation

Instead if starting ROOT and running a script on the prompt you can also pass it to ROOT in its invocation:
$ root -l -b 'myCode.C("some String", 12)'
The exact kind of quoting depends on your shell; the one shown here works for bash-like shells.
ROOT can evaluate any expression as part of the invocation; another version of the previous example can be spelled
like this:
$ root -l -b -e 'gROOT->ProcessLine(".x myCode.C(\"some String\", 12)");'

7.3

C++ Extensions To Ease Scripting

In the next example, we demonstrate three of the most important extensions ROOT and Cling make to C++. Start
ROOT in the directory $ROOTSYS/tutorials (make sure to have first run .x hsimple.C):
root [0] f = new TFile("hsimple.root")
(class TFile *) 0x4045e690
root [1] f->ls()
TFile**
hsimple.root
TFile*
hsimple.root
KEY: TH1F
hpx;1
This is the px distribution
KEY: TH2F
hpxpy;1 py ps px
KEY: THProfile
hprof;1 Profile of pz versus px
KEY: TNtuple ntuple;1
Demo ntuple
root [2] hpx->Draw()
Warning in : creating a default canvas with name c1
root [3] .q
The root [0] command shows the first extension; the declaration of f may be omitted as a shortcut for auto.
Cling will correctly create f as pointer to object of class TFile. Nonetheless we recommend to use auto f = new
TFile("hsimple.root").
The second extension is more important. In case Cling cannot find an object being referenced, it will ask ROOT
to search for an object with an identical name in the search path defined by TROOT::FindObject(). If ROOT finds
the object, it returns a pointer to this object to Cling and a pointer to its class definition and Cling will execute the

7.4. ACLIC: COMPILING SCRIPTS INTO LIBRARIES

157

requested member function. This shortcut is quite natural for an interactive system and saves much typing. In this
example, ROOT searches for hpx and finds it in hsimple.root.
The next, fundamental extension is shown below. There is no need to put a semicolon at the end of a line. When you
leave it off the value of the expression will be printed on the next line. For example:
root[] 23+5
(int)28
root[] 23+5;
root[] TMath::Sin
(Double_t (*)(Double_t)) Function @0x7ffff7ebb090
at include/TMath.h:418:
inline Double_t TMath::Sin(Double_t x)
{ return sin(x); }
Be aware that these extensions do not work when a compiler replaces the interpreter. Your code will not compile,
hence when writing large scripts, it is best to stay away from these shortcuts. It will save you from having problems
compiling your scripts using a real C++ compiler.

7.4

ACLiC: Compiling Scripts Into Libraries

Instead of having Cling interpret your script there is a way to have your scripts compiled, linked and dynamically
loaded using the C++ compiler and linker. The advantage of this is that your scripts will run with the speed of
compiled C++ and that you can use language constructs that are not fully supported by Cling. On the other hand, you
cannot use any Cling shortcuts (see “C++ Extensions To Ease Scripting” above) and for small scripts, the overhead of
the compile/link cycle might be larger than just executing the script in the interpreter.
ACLiC will build a dictionary and a shared library from your C++ script, using the compiler and the compiler options
that were used to compile the ROOT executable. You do not have to write a Makefile remembering the correct compiler
options, and you do not have to exit ROOT.

7.4.1

Usage

Before you can compile your interpreted script you need to add include statements for the classes used in the script.
Once you did that, you can build and load a shared library containing your script. To load it use the command .L and
append the file name with a +.
root[] .L MyScript.C+
The + option generates the shared library and names it by taking the name of the file “filename” but replacing the
dot before the extension by an underscore and by adding the shared library extension for the current platform. For
example on most platforms, hsimple.cxx will generate hsimple_cxx.so.
The + command rebuild the library only if the script or any of the files it includes are newer than the library. When
checking the timestamp, ACLiC generates a dependency file which name is the same as the library name, just replacing
the ‘so’ extension by the extension ‘d’. For example on most platforms, hsimple.cxx will generate hsimple_cxx.d.
To ensure that the shared library is rebuilt you can use the ++ syntax:
root[] .L MyScript.C++
To build, load, and execute the function with the same name as the file you can use the .x command. This is the same
as executing a named script; you can also provide parameters. The only difference is you need to append a + or a ++.
root[] .x MyScript.C+(4000)
Creating shared library /home/./MyScript_C.so
You can select whether the script in compiled with debug symbol or with optimization by appending the letter ‘g’ or
‘O’ after the ‘+’ or ‘++’. Without the specification, the script is compiled with the same level of debugging symbol and
optimization as the currently running ROOT executable. For example:

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CHAPTER 7. THE C++ INTERPRETER CLING

root[] .L MyScript.C++g
will compile MyScript.C with debug symbols; usually this means giving the -g option to compiler.
root[] .L MyScript.C++O
will compile MyScript.C with optimizations; usually this means giving the -O option to compiler. The syntax:
root[] .L MyScript.C++
is using the default optimization level. The initial default is to compile with the same level of optimization as the root
executable itself. The default can be changed by:
root[] gSystem->SetAclicMode(TSystem::kDebug);
root[] gSystem->SetAclicMode(TSystem::kOpt);
Note that the commands:
root[] .L MyScript.C+g
root[] .L MyScript.C+O
respectively compile MyScript.C with debug and optimization if the library does not exist yet; they will not change
the debug and the optimization level if the library already exist and it is up to date. To use ACLiC from compiled
code or from inside another macro, we recommend using gROOT->ProcessLine(). For example, in one script you can
use ACLiC to compile and load another script.
gROOT->ProcessLine(".L MyScript.C+")
gROOT->ProcessLine(".L MyScript.C++")

7.4.2

Setting the Include Path

You can get the include path by typing:
root[] .include
You can append to the include path by typing:
root[] .include $HOME/mypackage/include
In a script you can append to the include path:
gSystem->AddIncludePath(" -I$HOME/mypackage/include ")
You can also overwrite the existing include path:
gSystem->SetIncludePath(" -I$HOME/mypackage/include ")
The $ROOTSYS/include directory is automatically appended to the include path, so you do not have to worry about
including it. To add library that should be used during linking of the shared library use something like:
gSystem->AddLinkedLibs("-L/my/path -lanylib");
This is especially useful for static libraries. For shared ones you can also simply load them before trying to compile the
script:
gSystem->Load("mydir/mylib");

7.4. ACLIC: COMPILING SCRIPTS INTO LIBRARIES

159

ACLiC uses the directive fMakeSharedLibs to create the shared library. If loading the shared library fails, it tries to
output a list of missing symbols by creating an executable (on some platforms like OSF, this does not HAVE to be an
executable) containing the script. It uses the directive fMakeExe to do so. For both directives, before passing them
to TSystem::Exec(), it expands the variables $SourceFiles, $SharedLib, $LibName, $IncludePath, $LinkedLibs,
$ExeNameand$ObjectFiles. See SetMakeSharedLib() for more information on those variables. When the file being
passed to ACLiC is on a read only file system, ACLiC warns the user and creates the library in a temporary directory:
root[] .L readonly/t.C++
Warning in : /scratch/aclic/subs/./readonly is not writable!
Warning in : Output will be written to /tmp
Info in : creating shared library
/tmp//scratch/aclic/subs/./readonly/t_C.so
To select the temporary directory ACLiC looks at $TEMP, $TEMP_DIR, $TEMPDIR, $TMP, $TMPDIR, $TMP_DIRor uses
/tmp (or C:/). Also, a new interface TSystem::Get/SetBuildDir is introduced to let users select an alternative ‘root’ for building of the ACLiC libraries. For filename/full/path/name/macro.C, the library is created as
fBuildDir/full/path/name/macro_C.so.

7.4.3

Dictionary Generation

You can direct what is added to the dictionary generated by ACLiC in two ways. The simplest way is to add at the
end of script (i.e. after the symbols have been defined) something like:
#if defined(__ROOTCLING__)
#pragma link C++ class MyOtherClass;
#endif
You can also write this portion of code in a file name MyScript_linkdef.h where the suffix ’_linkdef’is the prefix defined by the key ‘ACLiC.Linkdef‘ in the currently used resource file (usually .rootrcor$ROOTSYS/etc/system.rootrc)
and the prefix is the name of your script.
The default behavior of rootcling is to not link in (i.e. generate the dictionary for) any of the symbols. In particular,
this means that the following lines are, in the general case, unnecessary.
#pragma link off all globals;
#pragma link off all classes;
#pragma link off all functions;
This also means that linking the instantiation of a class template:
#pragma link C++ class mytemplate;
ONLY links this specific class. You need to request the generation of the iterators explicitly.
See the documentation of rootcling for details how pragma can be used.
NOTE: You should not call ACLiC with a script that has a function called main().

7.4.4

Intermediate Steps and Files

ACLiC executes two steps and a third one if needed. These are:
• Calling rootcling to create a dictionary using rootcling.
• Calling the compiler to build the shared library from the script.
• If there are errors, it calls the compiler to build a dummy executable to clearly report unresolved symbols.
ACLiC makes a shared library with a dictionary containing the classes and functions declared in the script. It also
adds the classes and functions declared in included files with the same name as the script file and any of the following
extensions: .h, .hh, .hpp, .hxx, .hPP, .hXX. This means that, by default, you cannot combine scripts from different
files into one library by using #include statements; you will need to compile each script separately. In a future release,
we plan to add the global variables declared in the script to the dictionary also. If you are curious about the specific
calls, you can raise the ROOT debug level: gDebug=3 and ACLiC will print these steps. If you need to keep the
intermediate files around, for example when debugging the script using gdb, use gDebug=7.

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7.4.5

CHAPTER 7. THE C++ INTERPRETER CLING

Moving between Interpreter and Compiler

The best way to develop portable scripts is to make sure you can always run them with both, the interpreter and with
ACLiC. To do so, do not use the Cling extensions and program around the Cling limitations. When it is not possible
or desirable to program around the Cling limitations, you can use the C preprocessor symbols defined for Cling and
rootcling.
The preprocessor symbol __CLING__ is defined for both ROOT and rootcling. The symbol __ROOTCLING__ (and
__ROOTCLING__ for backward compatibility) is only defined in rootcling.
Use !defined(__CLING__) || defined(__ROOTCLING__) to bracket code that needs to be seen by the compiler and
rootcling, but will be invisible to the interpreter.
Use !defined(__CLING__)to bracket code that should be seen only by the compiler and not by Cling nor rootcling.For
example, the following will hide the declaration and initialization of the array gArray from both Cling and rootcling.
#if !defined(__CLING__)
int gArray[] = { 2, 3, 4};
#endif
Because ACLiC calls rootcling to build a dictionary, the declaration of gArray will not be included in the dictionary,
and consequently, gArray will not be available at the command line even if ACLiC is used. Cling and rootcling
will ignore all statements between the "#if !defined (__CLING__)" and “#endif". If you want to use gArray in
the same script as its declaration, you can do so. However, if you want use the script in the interpreter you have to
bracket the usage of gArray between #if’s, since the definition is not visible. If you add the following preprocessor
statements:
#if !defined(__CLING__)
int gArray[] = { 2, 3, 4};
#elif defined(__ROOTCLING__)
int gArray[];
#endif
gArray will be visible to rootcling but still not visible to Cling. If you use ACLiC, gArray will be available at the
command line and be initialized properly by the compiled code.
We recommend you always write scripts with the needed include statements. In most cases, the script will still run
with the interpreter. However, a few header files are not handled very well by Cling.
These types of headers can be included in interpreted and compiled mode:
• The subset of standard C/C++ headers defined in $ROOTSYS/Cling/include.
• Headers of classes defined in a previously loaded library (including ROOT own). The defined class must have a
name known to ROOT (i.e. a class with a ClassDef).
Hiding header files from rootcling that are necessary for the compiler but optional for the interpreter can lead to a
subtle but fatal error. For example:
#ifndef __CLING__
#include "TTree.h"
#else
class TTree;
#endif
class subTree : public TTree {
};
In this case, rootcling does not have enough information about the TTree class to produce the correct dictionary file.
If you try this, rootcling and compiling will be error free, however, instantiating a subTree object from the Cling
command line will cause a fatal error. In general, it is recommended to let rootcling see as many header files as
possible.

7.5. CLASSES DEFINED BY SCRIPTS

7.5

161

Classes Defined By Scripts

Lets create a small class TMyClass and a derived class TChild. The virtual method TMyClass::Print()is overridden
in TChild. Save this in file called script4.C.
#include 
class TMyClass {
private:
float
fX;
//x position in centimeters
float
fY;
//y position in centimeters
public:
TMyClass() { fX = fY = -1; }
virtual void Print() const;
void SetX(float x) { fX = x; }
void SetY(float y) { fY = y; }
};
void TMyClass::Print() const // parent print method
{
cout << "fX = " << fX << ", fY = " << fY << endl;
}
class TChild : public TMyClass {
public:
void Print() const;
};
void TChild::Print() const // child print metod
{
cout << "This is TChild::Print()" << endl;
TMyClass::Print();
}
To execute script4.C do:
root[] .L script4.C
root[] TMyClass *a = new TChild
root[] a->Print()
This is TChild::Print()
fX = -1, fY = -1
root[] a->SetX(10)
root[] a->SetY(12)
root[] a->Print()
This is TChild::Print()
fX = 10, fY = 12
root[] .class TMyClass
=====================================================
class TMyClass
size=0x8 FILE:script4.C LINE:3
List of base class----------------------------------List of member variable-----------------------------Defined in TMyClass
0x0
private: float fX
0x4
private: float fY
List of member function-----------------------------Defined in TMyClass
filename
line:size busy function type and name
script4.C
16:5
0 public: class TMyClass TMyClass(void);
script4.C
22:4
0 public: void Print(void);
script4.C
12:1
0 public: void SetX(float x);
script4.C
13:1
0 public: void SetY(float y);
root[] .q
As you can see, an interpreted class behaves just like a compiled class. See “Adding a Class” for ways how to add a
class with a shared library and with ACLiC.

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7.6

CHAPTER 7. THE C++ INTERPRETER CLING

Inspecting Objects

An object of a class inheriting from TObject can be inspected, with the Inspect() method. The TObject::Inspect
method creates a window listing the current values of the objects members. For example, the next picture is of TFile.
root[] TFile f("staff.root")
root[] f.Inspect()
You can see the pointers are in red and can be clicked on to follow the pointer to the object. If you clicked on fList, the
list of objects in memory and there were none, no new canvas would be shown. On top of the page are the navigation
buttons to see the previous and next screen.

Figure 7.1: ROOT object inspector of TFile

7.6. INSPECTING OBJECTS

Figure 7.2: The object inspector of fKeys, the list of keys in the memory

163

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CHAPTER 7. THE C++ INTERPRETER CLING

Chapter 8

Object Ownership
An object has ownership of another object if it has permission to delete it. Usually a collection or a parent object
such as a pad holds ownership. To prevent memory leaks and multiple attempts to delete an object, you need to know
which objects ROOT owns and which are owned by you.
The following rules apply to the ROOT classes.
• Histograms, trees, and event lists created by the user are owned by current directory (gDirectory ). When the
current directory is closed or deleted the objects it owns are deleted.
• The TROOT master object (gROOT ) has several collections of objects. Objects that are members of these collections
are owned by gROOT see “Ownership by the Master TROOT Object (gROOT).
• Objects created by another object, for example the function object (e.g.TF1) created by the TH1::Fitmethod is
owned by the histogram.
• An object created by DrawCopy methods, is owned by the pad it is drawn in.
If an object fits none of these cases, the user has ownership. The next paragraphs describe each rule and user ownership
in more detail.

8.1

Ownership by Current Directory (gDirectory)

When a histogram, tree, or event list (TEventList) is created, it is added to the list of objects in the current directory
by default. You can get the list of objects in a directory and retrieve a pointer to a specific object with the GetList
method. This example retrieves a histogram.
TH1F *h = (TH1F*)gDirectory->GetList()->FindObject("myHist");
The method TDirectory::GetList() returns a TList of objects in the directory. It looks in memory, and is
implemented in all ROOT collections. You can change the directory of a histogram, tree, or event list with the
SetDirectory method. Here we use a histogram for an example, but the same applies to trees and event lists.
h->SetDirectory(newDir);
You can also remove a histogram from a directory by using SetDirectory(0). Once a histogram is removed from the
directory, it will not be deleted when the directory is closed. It is now your responsibility to delete this histogram once
you have finished with it. To change the default that automatically adds the histogram to the current directory, you
can call the static function:
TH1::AddDirectory(kFALSE);
Not all histograms created here after will be added to the current directory. In this case, you own all histogram objects
and you will need to delete them and clean up the references. You can still set the directory of a histogram by calling
SetDirectory once it has been created as described above.
Note that, when a file goes out of scope or is closed all objects on its object list are deleted.
165

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8.2

CHAPTER 8. OBJECT OWNERSHIP

Ownership by the Master TROOT Object (gROOT)

The master object gROOT , maintains several collections of objects. For example, a canvas is added to the collection of
canvases and it is owned by the canvas collection.
TSeqCollection*
TSeqCollection*
TSeqCollection*
TSeqCollection*
TSeqCollection*
TSeqCollection*
TSeqCollection*
TSeqCollection*
TSeqCollection*
TSeqCollection*
TSeqCollection*
TSeqCollection*

fFiles
fMappedFiles
fSockets
fCanvases
fStyles
fFunctions
fTasks
fColors
fGeometries
fBrowsers
fSpecials
fCleanups

List
List
List
List
List
List
List
List
List
List
List
List

of
of
of
of
of
of
of
of
of
of
of
of

TFile
TMappedFile
TSocket and TServerSocket
TCanvas
TStyle
TF1, TF2, TF3
TTask
TColor
geometries
TBrowser
special objects
recursiveRemove collections

These collections are also displayed in the root folder of the Object Browser. Most of these collections are self
explanatory. The special cases are the collections of specials and cleanups.

8.2.1

The Collection of Specials

This collection contains objects of the following classes: TCutG, TMultiDimFit, TPrincipal, TChains. In addition it
contains the gHtml object, gMinuit objects, and the array of contours graphs (TGraph) created when calling the Draw
method of a histogram with the "CONT, LIST" option.

8.2.2

Access to the Collection Contents

The current content for a collection listed above can be accessed with the corresponding gROOT->GetListOf method
(for example gROOT->GetListOfCanvases). In addition, gROOT->GetListOfBrowsables returns a collection of all
objects visible on the left side panel in the browser. See the image of the Object Browser in the next figure.

Figure 8.1: The ROOT Object Browser

8.3. OWNERSHIP BY OTHER OBJECTS

8.3

167

Ownership by Other Objects

When an object creates another, the creating object is the owner of the created one. For example:
myHisto->Fit("gaus")
The call to Fit copies the global TF1 Gaussian function and attaches the copy to the histogram. When the histogram is
deleted, the copy is deleted also.
When a pad is deleted or cleared, all objects in the pad with the kCanDelete bit set are deleted automatically. Currently
the objects created by the DrawCopy methods, have the kCanDelete bit set and are therefore owned by the pad.

8.4

Ownership by the User

The user owns all objects not described in one of the above cases. TObject has two bits, kCanDelete and kMustCleanup,
that influence how an object is managed (in TObject::fBits). These are in an enumeration in TObject.h. To set
these bits do:
MyObject->SetBit(kCanDelete)
MyObject->SetBit(kMustCleanup)
The bits can be reset and tested with the TObject::ResetBit and TObject::TestBit methods.

8.4.1

The kCanDelete Bit

The gROOT collections (see above) own their members and will delete them regardless of the kCanDelete bit. In all
other collections, when the collection Clear method is called (i.e. TList::Clear()), members with the kCanDelete
bit set, are deleted and removed from the collection. If the kCanDelete bit is not set, the object is only removed from
the collection but not deleted.
If a collection Delete (TList::Delete()) method is called, all objects in the collection are deleted without considering
the kCanDelete bit. It is important to realize that deleting the collection (i.e. delete MyCollection), DOES NOT
delete the members of the collection.
If the user specified MyCollection->SetOwner() the collection owns the objects and delete MyCollection will delete
all its members. Otherwise, you need to:
// delete all member objects in the collection
MyCollection->Delete();
// and delete the collection object
delete MyCollection;
Note that kCanDelete is automatically set by the DrawCopy method and the user can set it for any object. For example,
the user must manage all graphics primitives. If you want TCanvas to delete the primitive you created you have to set
the kCanDelete bit.
The kCanDelete bit setting is displayed with TObject::ls(). The last number is either 1 or 0 and is the kCanDelete
bit.
root[] TCanvas MyCanvas("MyCanvas")
root[] MyCanvas.Divide(2,1)
root[] MyCanvas->cd(MyCanvas_1)
root[] hstat.Draw()
// hstat is an existing TH1F
root[] MyCanvas->cd(MyCanvas_2)
root[] hstat.DrawCopy()
// DrawCopy sets the kCanDelete bit
(class TH1*)0x88e73f8
root[] MyCanvas.ls()
Canvas Name=MyCanvas ...
TCanvas ... Name= MyCanvas ...
TPad
... Name= MyCanvas_1 ...

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CHAPTER 8. OBJECT OWNERSHIP

TFrame ...
OBJ: TH1F
hstat
Event Histogram : 0
TPaveText
... title
TPaveStats ... stats
TPad ... Name= MyCanvas_2 ...
TFrame ...
OBJ: TH1F
hstat
Event Histogram : 1
TPaveText
... title
TPaveStats ... stats

8.4.2

The kMustCleanup Bit

When the kMustCleanup bit is set, the object destructor will remove the object and its references from all collections
in the clean up collection (gROOT ::fCleanups). An object can be in several collections, for example if an object is in a
browser and on two canvases. If the kMustCleanup bit is set, it will be removed automatically from the browser and
both canvases when the destructor of the object is called.
The kMustCleanup bit is set:
• When an object is added to a pad (or canvas) in TObject::AppendPad.
• When an object is added to a TBrowser with TBrowser::Add.
• When an object is added to a TFolder withTFolder::Add.
• When creating an inspector canvas with TInspectCanvas::Inspector.
• When creating a TCanvas.
• When painting a frame for a pad, the frame’s kMustCleanup is set in TPad::PaintPadFrame
The user can add their own collection to the collection of clean ups, to take advantage of the automatic garbage
collection. For example:
// create two list
TList *myList1, *myList2;
// add both to of clean ups
gROOT->GetListOfCleanUps()->Add(myList1);
gROOT->GetListOfCleanUps()->Add(myList2);
// assuming myObject is in myList1 and myList2, when calling:
delete myObject;
// the object is deleted from both lists

Chapter 9

Graphics and the Graphical User
Interface
Graphical capabilities of ROOT range from 2D objects (lines, polygons, arrows) to various plots, histograms, and 3D
graphical objects. In this chapter, we are going to focus on principals of graphics and 2D objects. Plots and histograms
are discussed in a chapter of their own.

9.1

Drawing Objects

In ROOT, most objects derive from a base class TObject. This class has a virtual method Draw() so all objects are
supposed to be able to be “drawn”. The basic whiteboard on which an object is drawn is called a canvas (defined by
the class TCanvas). If several canvases are defined, there is only one active at a time. One draws an object in the active
canvas by using the statement:
object.Draw()
This instructs the object “object” to draw itself. If no canvas is opened, a default one (named “c1”) is instantiated
and is drawn.
root[] TLine a(0.1,0.1,0.6,0.6)
root[] a.Draw()
: created default TCanvas with name c1
The first statement defines a line and the second one draws it. A default canvas is drawn since there was no opened one.

9.2

Interacting with Graphical Objects

When an object is drawn, one can interact with it. For example, the line drawn in the previous paragraph may be
moved or transformed. One very important characteristic of ROOT is that transforming an object on the screen will
also transform it in memory. One actually interacts with the real object, not with a copy of it on the screen. You can
try for instance to look at the starting X coordinate of the line:
root[] a.GetX1()
(double)1.000000000e-1
X1 is the x value of the starting coordinate given in the definition above. Now move it interactively by clicking with the
left mouse button in the line’s middle and try to do again:
root[] a.GetX1()
(Double_t)1.31175468483816005e-01
You do not obtain the same result as before, the coordinates of ‘a’ have changed. As said, interacting with an object
on the screen changes the object in memory.
169

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9.2.1

CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE

Moving, Resizing and Modifying Objects

Changing the graphic objects attributes can be done with the GUI or programmatically. First, let’s see how it is done
in the GUI.
9.2.1.1

The Left Mouse Button

As was just seen moving or resizing an object is done with the left mouse button. The cursor changes its shape to
indicate what may be done:
Point the object or one part of it:

Rotate:

Resize (exists also for the other directions):
Enlarge (used for text):
Move:
Here are some examples of:

Moving:

Resizing:

Rotating:
9.2.1.2

With C++ Statements (Programmatically)

How would one move an object in a script? Since there is a tight correspondence between what is seen on the screen
and the object in memory, changing the object changes it on the screen. For example, try to do:
root[] a.SetX1(0.9)

9.2. INTERACTING WITH GRAPHICAL OBJECTS

171

This should change one of the coordinates of our line, but nothing happens on the screen. Why is that? In short, the
canvas is not updated with each change for performance reasons. See “Updating the Pad”.

9.2.2

Selecting Objects

9.2.2.1

The Middle Mouse Button

Objects in a canvas, as well as in a pad, are stacked on top of each other in the order they were drawn. Some objects
may become “active” objects, which mean they are reordered to be on top of the others. To interactively make an
object “active”, you can use the middle mouse button. In case of canvases or pads, the border becomes highlighted
when it is active.
9.2.2.2

With C++ Statements (Programmatically)

Frequently we want to draw in different canvases or pads. By default, the objects are drawn in the active canvas. To
activate a canvas you can use the TPad::cd() method.
root[] c1->cd()

9.2.3

Context Menus: the Right Mouse Button

The context menus are a way to interactively call certain methods of an object. When designing a class, the programmer
can add methods to the context menu of the object by making minor changes to the header file.
9.2.3.1

Using Context Menus

On a ROOT canvas, you can right-click on any object and see the context menu for it. The script hsimple.C draws
a histogram. The image below shows the context menus for some of the objects on the canvas. Next picture shows
that drawing a simple histogram involves as many as seven objects. When selecting a method from the context menu
and that method has options, the user will be asked for numerical values or strings to fill in the option. For example,
TAxis::SetTitle will prompt you for a string to use for the axis title.
9.2.3.2

Structure of the Context Menus

The curious reader will have noticed that each entry in the context menu corresponds to a method of the class. Look
for example to the menu named TAxis::xaxis. xaxis is the name of the object and TAxis the name of its class. If we
look at the list of TAxis methods, for example in http://root.cern.ch/root/htmldoc/TAxis.html, we see the methods
SetTimeDisplay() andUnZoom(), which appear also in the context menu.
There are several divisions in the context menu, separated by lines. The top division is a list of the class methods; the
second division is a list of the parent class methods. The subsequent divisions are the methods other parent classes
in case of multiple inheritance. For example, see the TPaveText::title context menu. A TPaveText inherits from
TAttLine, which has the method SetLineAttributes().
9.2.3.3

Adding Context Menus for a Class

For a method to appear in the context menu of the object it has to be marked by // *MENU* in the header file. Below
is the line from TAttLine.h that adds the SetLineAttribute method to the context menu.
virtual void

SetLineAttributes(); // *MENU*

Nothing else is needed, since Cling knows the classes and their methods. It takes advantage of that to create the
context menu on the fly when the object is clicking on. If you click on an axis, ROOT will ask the interpreter what are
the methods of the TAxis and which ones are set for being displayed in a context menu.
Now, how does the interpreter know this? Remember, when you build a class that you want to use in the ROOT
environment, you use rootcling that builds the so-called stub functions and the dictionary. These functions and
the dictionary contain the knowledge of the used classes. To do this, rootcling parses all the header files. ROOT

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CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE

Figure 9.1: Context menus of different objects in a canvas

9.2. INTERACTING WITH GRAPHICAL OBJECTS

173

has defined some special syntax to inform Cling of certain things, this is done in the comments so that the code still
compiles with a C++ compiler.
For example, you have a class with a Draw() method, which will display itself. You would like a context menu to
appear when on clicks on the image of an object of this class. The recipe is the following:
• The class has to contain the ClassDef/ClassImp macros
• For each method you want to appear in the context menu, put a comment after the declaration containing *MENU*
or *TOGGLE* depending on the behavior you expect. One usually uses Set methods (setters). The *TOGGLE*
comment is used to toggle a boolean data field. In that case, it is safe to call the data field fMyBool where
MyBool is the name of the setter SetMyBool. Replace MyBool with your own boolean variable.
• You can specify arguments and the data members in which to store the arguments.
For example:
class MyClass : public TObject {
private:
int
fV1;
// first variable
double
fV2;
// second variable
public:
int
GetV1() {return fV1;}
double GetV2() {return fV2;}
void
SetV1(int x1) { fV1 = x1;}
// *MENU*
void
SetV2(double d2) { fV2 = d2;} // *MENU*
void
SetBoth(int x1, double d2) {fV1 = x1; fV2 = d2;}
}

ClassDef (MyClass,1)

To specify arguments:
void SetXXX(Int_t x1, Float_t y2); //*MENU* *ARGS={x1=>fV1}
This statement is in the comment field, after the *MENU*. If there is more than one argument, these arguments are
separated by commas, where fX1 and fY2 are data fields in the same class.
void SetXXX(Int_t x1, Float_t y2); //*MENU* *ARGS={x1=>fX1,y2=>fY2}
If the arguments statement is present, the option dialog displayed when selecting SetXXX field will show the values of
variables. We indicate to the system which argument corresponds to which data member of the class.

9.2.4

Executing Events when a Cursor Passes on Top of an Object

This paragraph is for class designers. When a class is designed, it is often desirable to include drawing methods for it.
We will have a more extensive discussion about this, but drawing an object in a canvas or a pad consists in “attaching”
the object to that pad. When one uses object.Draw(), the object is NOT painted at this moment. It is only attached
to the active pad or canvas.
Another method should be provided for the object to be painted, the Paint() method. This is all explained in the next
paragraph. As well as Draw() and Paint(), other methods may be provided by the designer of the class. When the
mouse is moved or a button pressed/released, the TCanvas function named HandleInput() scans the list of objects in
all it’s pads and for each object calls some standard methods to make the object react to the event (mouse movement,
click or whatever).
The second one is DistanceToPrimitive(px,py). This function computes a “distance” to an object from the mouse
position at the pixel position (px, py, see definition at the end of this paragraph) and returns this distance in pixel
units. The selected object will be the one with the shortest computed distance. To see how this works, select the
“Event Status” item in the canvas “Options” menu. ROOT will display one status line showing the picked object. If
the picked object is, for example, a histogram, the status line indicates the name of the histogram, the position x,y in
histogram coordinates, the channel number and the channel content.

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CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE

It is nice for the canvas to know what the closest object from the mouse is, but it’s even nicer to be able to make this
object react. The third standard method to be provided is ExecuteEvent(). This method actually does the event
reaction. Its prototype is where px and py are the coordinates at which the event occurred, except if the event is a key
press, in which case px contains the key code.
void ExecuteEvent(Int_t event, Int_t px, Int_t py);
Where event is the event that occurs and is one of the following (defined in Buttons.h):
kNoEvent,
kButton3Down,
kButton2Up,
kButton2Motion,
kButton1Locate,
kKeyUp,
kButton3Double,
kMouseLeave

kButton1Down,
kKeyDown,
kButton3Up,
kButton3Motion,
kButton2Locate,
kButton1Double,
kMouseMotion,

kButton2Down,
kButton1Up,
kButton1Motion,
kKeyPress,
kButton3Locate,
kButton2Double,
kMouseEnter,

We hope the names are self-explanatory.
Designing an ExecuteEvent method is not very easy, except if one wants very basic treatment. We will not go into
that and let the reader refer to the sources of classes like TLine or TBox. Go and look at their ExecuteEvent method!
We can nevertheless give some reference to the various actions that may be performed. For example, one often wants
to change the shape of the cursor when passing on top of an object. This is done with the SetCursor method:
gPad->SetCursor(cursor)
The argument cursor is the type of cursor. It may be:
kBottomLeft,
kTopRight,
kTopSide,
kCross,
kHand,
kArrowRight,

kBottomRight,
kBottomSide,
kRightSide,
kArrowHor,
kRotate,
kCaret,

kTopLeft,
kLeftSide,
kMove,
kArrowVer,
kPointer,
kWatch

They are defined in TVirtualX.h and again we hope the names are self-explanatory. If not, try them by designing a
small class. It may derive from something already known like TLine.
Note that the ExecuteEvent() functions may in turn; invoke such functions for other objects, in case an object is
drawn using other objects. You can also exploit at best the virtues of inheritance. See for example how the class
TArrow (derived from TLine) use or redefine the picking functions in its base class.
The last comment is that mouse position is always given in pixel units in all these standard functions. px=0 and py=0
corresponds to the top-left corner of the canvas. Here, we have followed the standard convention in windowing systems.
Note that user coordinates in a canvas (pad) have the origin at the bottom-left corner of the canvas (pad). This is all
explained in the paragraph “The Coordinate Systems of a Pad”.

9.3

Graphical Containers: Canvas and Pad

We have talked a lot about canvases, which may be seen as windows. More generally, a graphical entity that contains
graphical objects is called a Pad. A Canvas is a special kind of Pad. From now on, when we say something about pads,
this also applies to canvases. A pad (class TPad) is a graphical container in the sense it contains other graphical objects
like histograms and arrows. It may contain other pads (sub-pads) as well. A Pad is a linked list of primitives of any
type (graphs, histograms, shapes, tracks, etc.). It is a kind of display list.
Drawing an object is nothing more than adding its pointer to this list. Look for example at the code of TH1::Draw().
It is merely ten lines of code. The last statement is AppendPad(). This statement calls method of TObject that just
adds the pointer of the object, here a histogram, to the list of objects attached to the current pad. Since this is a
TObject’s method, every object may be “drawn”, which means attached to a pad.
When is the painting done then ? The answer is: when needed. Every object that derives from TObject has a Paint()
method. It may be empty, but for graphical objects, this routine contains all the instructions to paint effectively it in

9.3. GRAPHICAL CONTAINERS: CANVAS AND PAD

Figure 9.2: The pad display list

Figure 9.3: Pad painting

175

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CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE

the active pad. Since a Pad has the list of objects it owns, it will call successively the Paint() method of each object,
thus re-painting the whole pad on the screen. If the object is a sub-pad, its Paint() method will call the Paint()
method of the objects attached, recursively calling Paint() for all the objects.
In some cases a pad need to be painted during a macro execution. To force the pad painting gPad->Update() (see
next section) should be performed.
The list of primitives stored in the pad is also used to pick objects and to interact with them.

9.3.1

The Global Pad: gPad

When an object is drawn, it is always in the so-called active pad. For every day use, it is comfortable to be able to
access the active pad, whatever it is. For that purpose, there is a global pointer, called gPad . It is always pointing to
the active pad. If you want to change the fill color of the active pad to blue but you do not know its name, do this.
root[] gPad->SetFillColor(38)
To get the list of colors, go to the paragraph “Color and color palettes” or if you have an opened canvas, click on the
View menu, selecting the Colors item.
9.3.1.1

Finding an Object in a Pad

Now that we have a pointer to the active pad, gPad and that we know this pad contains some objects, it is sometimes
interesting to access one of those objects. The method GetPrimitive() of TPad, i.e. TPad::GetPrimitive(const
char* name) does exactly this. Since most of the objects that a pad contains derive from TObject, they have a name.
The following statement will return a pointer to the object myobjectname and put that pointer into the variable obj.
As you can see, the type of returned pointer is TObject*.
root[] obj = gPad->GetPrimitive("myobjectname")
(class TObject*)0x1063cba8
Even if your object is something more complicated, like a histogram TH1F, this is normal. A function cannot return
more than one type. So the one chosen was the lowest common denominator to all possible classes, the class from
which everything derives, TObject. How do we get the right pointer then? Simply do a cast of the function output
that will transform the output (pointer) into the right type. For example if the object is a TPaveLabel:
root[] obj = (TPaveLabel*)(gPad->GetPrimitive("myobjectname"))
(class TPaveLabel*)0x1063cba8
This works for all objects deriving from TObject. However, a question remains. An object has a name if it derives
from TNamed, not from TObject. For example, an arrow (TArrow) doesn’t have a name. In that case, the “name” is
the name of the class. To know the name of an object, just click with the right button on it. The name appears at
the top of the context menu. In case of multiple unnamed objects, a call to GetPrimitive("className") returns the
instance of the class that was first created. To retrieve a later instance you can use GetListOfPrimitives(), which
returns a list of all the objects on the pad. From the list you can select the object you need.
9.3.1.2

Hiding an Object

Hiding an object in a pad can be made by removing it from the list of objects owned by that pad. This list is accessible
by the GetListOfPrimitives() method of TPad. This method returns a pointer to a TList. Suppose we get the
pointer to the object, we want to hide, call it obj (see paragraph above). We get the pointer to the list:
root[] li = gPad->GetListOfPrimitives()
Then remove the object from this list:
root[] li->Remove(obj)
The object will disappear from the pad as soon as the pad is updated (try to resize it for example). If one wants to
make the object reappear:
root[] obj->Draw()
Caution, this will not work with composed objects, for example many histograms drawn on the same plot (with the
option “same”). There are other ways! Try to use the method described here for simple objects.

9.3. GRAPHICAL CONTAINERS: CANVAS AND PAD

9.3.2

177

The Coordinate Systems of a Pad

There are coordinate systems in a TPad: user coordinates, normalized coordinates (NDC), and pixel coordinates.

Figure 9.4: Pad coordinate systems

9.3.2.1

The User Coordinate System

The most common is the user coordinate system. Most methods of TPad use the user coordinates, and all graphic
primitives have their parameters defined in terms of user coordinates. By default, when an empty pad is drawn, the
user coordinates are set to a range from 0 to 1 starting at the lower left corner. At this point they are equivalent of the
NDC coordinates (see below). If you draw a high level graphical object, such as a histogram or a function, the user
coordinates are set to the coordinates of the histogram. Therefore, when you set a point it will be in the histogram
coordinates.
For a newly created blank pad, one may use TPad::Range to set the user coordinate system. This function is defined
as:
void Range(float x1,float y1,float x2,float y2)
The arguments x1, x2 defines the new range in the x direction, and the y1, y2 define the new range in the y-direction.
root[] TCanvas MyCanvas ("MyCanvas")
root[] gPad->Range(-100,-100,100,100)
This will set the active pad to have both coordinates to go from -100 to 100, with the center of the pad at (0,0). You
can visually check the coordinates by viewing the status bar in the canvas. To display the status bar select Event
Status entry in the View canvas menu.

Figure 9.5: The status bar

9.3.2.2

The Normalized Coordinate System (NDC)

Normalized coordinates are independent of the window size and of the user system. The coordinates range from 0 to 1
and (0, 0) corresponds to the bottom-left corner of the pad. Several internal ROOT functions use the NDC system (3D
primitives, PostScript, log scale mapping to linear scale). You may want to use this system if the user coordinates are
not known ahead of time.

9.3.2.3

The Pixel Coordinate System

The least common is the pixel coordinate system, used by functions such as DistanceToPrimitive() and
ExecuteEvent(). Its primary use is for cursor position, which is always given in pixel coordinates. If (px,py) is the
cursor position, px=0 and py=0 corresponds to the top-left corner of the pad, which is the standard convention in
windowing systems.

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CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE
Using NDC for a particular Object

Most of the time, you will be using the user coordinate system. But sometimes, you will want to use NDC. For example,
if you want to draw text always at the same place over a histogram, no matter what the histogram coordinates are.
There are two ways to do this. You can set the NDC for one object or may convert NDC to user coordinates. Most
graphical objects offer an option to be drawn in NDC. For instance, a line (TLine) may be drawn in NDC by using
DrawLineNDC(). A latex formula or a text may use TText::SetNDC() to be drawn in NDC coordinates.

9.3.3

Converting between Coordinate Systems

There are a few utility functions in TPad to convert from one system of coordinates to another. In the following table, a
point is defined by (px,py) in pixel coordinates, (ux,uy) in user coordinates, (ndcx,ndcy) in normalized coordinates,
(apx, apy) are in absolute pixel coordinates.
Conversion
NDC to Pixel
Pixel to User

User to Pixel

User to absolute pixel

Absolute pixel to user

TPad’s Methods
UtoPixel(ndcx)
VtoPixel(ndcy)
PixeltoX(px)
PixeltoY(py)
PixeltoXY(px,py,&ux,&uy)
XtoPixel(ux)
YtoPixel(uy)
XYtoPixel(ux,uy,&px,&py)
XtoAbsPixel(ux)
YtoAbsPixel(uy)
XYtoAbsPixel(ux,uy,&apx,&apy)
AbsPixeltoX(apx)
AbsPixeltoY(apy)
AbsPixeltoXY(apx,apy,&ux,&uy)

Returns
Int_t
Int_t
Double_t
Double_t
Double_t ux,uy
Int_t
Int_t
Int_t px,py
Int_t
Int_t
Int_t apx,apy
Double_t
Double_t
Double_t ux,uy

Note: all the pixel conversion functions along the Y axis consider that py=0 is at the top of the pad except PixeltoY()
which assume that the position py=0 is at the bottom of the pad. To make PixeltoY() converting the same way as
the other conversion functions, it should be used the following way (p is a pointer to a TPad):
p->PixeltoY(py - p->GetWh());

9.3.4

Dividing a Pad into Sub-pads

Dividing a pad into sub pads in order for instance to draw a few histograms, may be done in two ways. The first is to
build pad objects and to draw them into a parent pad, which may be a canvas. The second is to automatically divide a
pad into horizontal and vertical sub pads.

9.3.4.1

Creating a Single Sub-pad

The simplest way to divide a pad is to build sub-pads in it. However, this forces the user to explicitly indicate the size
and position of those sub-pads. Suppose we want to build a sub-pad in the active pad (pointed by gPad ). First, we
build it, using a TPad constructor:
root[] spad1 = new TPad("spad1","The first subpad",.1,.1,.5,.5)
One gives the coordinates of the lower left point (0.1, 0.1) and of the upper right one (0.5, 0.5). These coordinates are
in NDC. This means that they are independent of the user coordinates system, in particular if you have already drawn
for example a histogram in the mother pad. The only thing left is to draw the pad:
root[] spad1->Draw()
If you want more sub-pads, you have to repeat this procedure as many times as necessary.

9.3. GRAPHICAL CONTAINERS: CANVAS AND PAD
9.3.4.2

179

Dividing a Canvas into Sub-Pads

The manual way of dividing a pad into sub-pads is sometimes very tedious. There is a way to automatically generate
horizontal and vertical sub-pads inside a given pad.
root[] pad1->Divide(3,2)

Figure 9.6: Dividing a pad into 6 sub-pads

Figure 9.7: Dividing a pad into 6 sub-pads
If pad1 is a pad then, it will divide the pad into 3 columns of 2 sub-pads. The generated sub-pads get names pad1_i
where the index i=1 to nxm (in our case pad1_1, pad1_2. . . pad1_6). The names pad1_1etc. . . correspond to new
variables in Cling, so you may use them as soon as the executed method was pad->Divide(). However, in a compiled
program, one has to access these objects. Remember that a pad contains other objects and that these objects may
themselves be pads. So we can use the GetPrimitive() method:
TPad* pad1_1 = (TPad*)(pad1->GetPrimitive("pad1_1"))
One question remains. In case one does an automatic divide, how one can set the default margins between pads? This
is done by adding two parameters to Divide(), which are the margins in x and y:
root[] pad1->Divide(3,2,0.1,0.1)
The margins are here set to 10% of the parent pad width.

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9.3.5

Updating the Pad

For performance reasons, a pad is not updated with every change. For example, changing the coordinates of the pad
does not automatically redraw it. Instead, the pad has a “bit-modified” that triggers a redraw. This bit is automatically
set by:
• Touching the pad with the mouse - for example resizing it with the mouse.
• Finishing the execution of a script.
• Adding a new primitive or modifying some primitives for example the name and title of an object.
• You can also set the “bit-modified” explicitly with the Modified method:
// the pad has changed
root[] pad1->Modified()
// recursively update all modified pads:
root[] c1->Update()
A subsequent call to TCanvas::Update() scans the list of sub-pads and repaints the pads declared modified.
In compiled code or in a long macro, you may want to access an object created during the paint process. To do so, you
can force the painting with a TCanvas::Update(). For example, a TGraph creates a histogram (TH1) to paint itself. In
this case the internal histogram obtained with TGraph::GetHistogram() is created only after the pad is painted. The
pad is painted automatically after the script is finished executing or if you force the painting with TPad::Modified()
followed by a TCanvas::Update(). Note that it is not necessary to call TPad::Modified() after a call to Draw(). The
“bit-modified” is set automatically by Draw(). A note about the “bit-modified” in sub pads: when you want to update
a sub pad in your canvas, you need to call pad->Modified() rather than canvas->Modified(), and follow it with a
canvas->Update(). If you use canvas->Modified(), followed by a call to canvas->Update(), the sub pad has not
been declared modified and it will not be updated. Also note that a call to pad->Update() where pad is a sub pad of
canvas, calls canvas->Update() and recursively updates all the pads on the canvas.

9.3.6

Making a Pad Transparent

As we will see in the paragraph “Fill Attributes”, a fill style (type of hatching) may be set for a pad.
root[] pad1->SetFillStyle(istyle)
This is done with the SetFillStyle method where istyle is a style number, defined in “Fill Attributes”. A special
set of styles allows handling of various levels of transparency. These are styles number 4000 to 4100, 4000 being fully
transparent and 4100 fully opaque. So, suppose you have an existing canvas with several pads. You create a new pad
(transparent) covering for example the entire canvas. Then you draw your primitives in this pad. The same can be
achieved with the graphics editor. For example:
root[]
root[]
root[]
root[]
root[]
root[]

9.3.7

.x tutorials/hist/h1draw.C
TPad *newpad=new TPad("newpad","Transparent pad",0,0,1,1);
newpad->SetFillStyle(4000);
newpad->Draw();
newpad->cd();
// create some primitives, etc

Setting the Log Scale

Setting the scale to logarithmic or linear is an attribute of the pad, not the axis or the histogram. The scale is an
attribute of the pad because you may want to draw the same histogram in linear scale in one pad and in log scale in
another pad. Frequently, we see several histograms on top of each other in the same pad. It would be very inconvenient
to set the scale attribute for each histogram in a pad.
Furthermore, if the logic was set in the histogram class (or each object) the scale setting in each Paint method of all
objects should be tested.
If you have a pad with a histogram, a right-click on the pad, outside of the histograms frame will convince you. The
SetLogx(), SetLogy() and SetLogz() methods are there. As you see, TPad defines log scale for the two directions x
and y plus z if you want to draw a 3D representation of some function or histogram.
The way to set log scale in the x direction for the active pad is:

9.4. GRAPHICAL OBJECTS

181

root[] gPad->SetLogx(1)
To reset log in the z direction:
root[] gPad->SetLogz(0)
If you have a divided pad, you need to set the scale on each of the sub-pads. Setting it on the containing pad does not
automatically propagate to the sub-pads. Here is an example of how to set the log scale for the x-axis on a canvas with
four sub-pads:
root[]
root[]
root[]
root[]
root[]
root[]
root[]
root[]

9.3.8

TCanvas MyCanvas("MyCanvas","My Canvas")
MyCanvas->Divide(2,2)
MyCanvas->cd(1)
gPad->SetLogx()
MyCanvas->cd(2)
gPad->SetLogx()
MyCanvas->cd(3)
gPad->SetLogx()

WaitPrimitive method

When the TPad::WaitPrimitive() method is called with no arguments, it will wait until a double click or any key
pressed is executed in the canvas. A call to gSystem->Sleep(10) has been added in the loop to avoid consuming at all
the CPU. This new option is convenient when executing a macro. By adding statements like:
canvas->WaitPrimitive();
You can monitor the progress of a running macro, stop it at convenient places with the possibility to interact with the
canvas and resume the execution with a double click or a key press.

9.3.9

Locking the Pad

You can make the TPad non-editable. Then no new objects can be added, and the existing objects and the pad can not
be changed with the mouse or programmatically. By default the TPad is editable.
TPad::SetEditable(kFALSE)

9.4

Graphical Objects

In this paragraph, we describe the various simple 2D graphical objects defined in ROOT. Usually, one defines these
objects with their constructor and draws them with their Draw() method. Therefore, the examples will be very brief.
Most graphical objects have line and fill attributes (color, width) that will be described in “Graphical objects attributes”.
If the user wants more information, the class names are given and they may refer to the online developer documentation.
This is especially true for functions and methods that set and get internal values of the objects described here. By
default 2D graphical objects are created in User Coordinates with (0, 0) in the lower left corner.

9.4.1

Lines, Arrows and Polylines

The simplest graphical object is a line. It is implemented in the TLine class. The line constructor is:
TLine(Double_t x1,Double_t y1,Double_t x2,Double_t y2)
The arguments x1, y1, x2, y2 are the coordinates of the first and second point. It can be used:
root[] l = new TLine(0.2,0.2,0.8,0.3)
root[] l->Draw()

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The arrow constructor is:
TArrow(Double_t x1, Double_t y1,
Double_t x2, Double_t y2,
Float_t arrowsize, Option_t *option)
It defines an arrow between points x1,y1 and x2,y2. The arrow size is in percentage of the pad height. The option
parameter has the following meanings:
“>”

“<|”

“<”

“|>”

“<>”
“<|>”
Once an arrow is drawn on the screen, one can:
• click on one of the edges and move this edge.
• click on any other arrow part to move the entire arrow.

Figure 9.8: Different arrow formats

9.4. GRAPHICAL OBJECTS

183

If FillColor is 0, an open triangle is drawn; else a full triangle is filled with the set fill color. If ar is an arrow object,
fill color is set with:
ar.SetFillColor(icolor);
Where icolor is the color defined in “Color and Color Palettes”.
The default-opening angle between the two sides of the arrow is 60 degrees. It can be changed with the method
ar->SetAngle(angle), where angle is expressed in degrees.
A poly-line is a set of joint segments. It is defined by a set of N points in a 2D space. Its constructor is:
TPolyLine(Int_t n,Double_t* x,Double_t* y,Option_t* option)
Where n is the number of points, and x and y are arrays of n elements with the coordinates of the points. TPolyLine
can be used by it self, but is also a base class for other objects, such as curly arcs.

9.4.2

Circles and Ellipses

An ellipse can be truncated and rotated. It is defined by its center (x1,y1) and two radii r1 and r2. A minimum and
maximum angle may be specified (phimin,phimax). The ellipse may be rotated with an angle theta. All these angles
are in degrees. The attributes of the outline line are set via TAttLine, of the fill area - via TAttFill class. They are
described in “Graphical Objects Attributes”.

Figure 9.9: Different types of ellipses
When an ellipse sector is drawn only, the lines between the center and the end points of the sector are drawn by default.
By specifying the drawn option “only”, these lines can be avoided. Alternatively, the method SetNoEdges() can be
called. To remove completely the ellipse outline, specify zero (0) as a line style.
The TEllipse constructor is:
TEllipse(Double_t x1, Double_t y1, Double_t r1, Double_t r2,
Double_t phimin, Double_t phimax, Double_t theta)
An ellipse may be created with:
root[] e = new TEllipse(0.2,0.2,0.8,0.3)
root[] e->Draw()

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CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE

Rectangles

The class TBox defines a rectangle. It is a base class for many different higher-level graphical primitives. Its bottom left
coordinates x1, y1 and its top right coordinates x2, y2, defines a box. The constructor is:
TBox(Double_t x1,Double_t y1,Double_t x2,Double_t y2)
It may be used as in:
root[] b = new TBox(0.2,0.2,0.8,0.3)
root[] b->SetFillColor(5)
root[] b->Draw()

Figure 9.10: A rectangle with a border
A TWbox is a rectangle (TBox) with a border size and a border mode. The attributes of the outline line and of the fill
area are described in “Graphical Objects Attributes”

9.4.4

Markers

A marker is a point with a fancy shape! The possible markers are shown in the next figure.

Figure 9.11: Markers
The marker constructor is:
TMarker(Double_t x,Double_t y,Int_t marker)
The parameters x and y are the marker coordinates and marker is the marker type, shown in the previous figure.
Suppose the pointer ma is a valid marker. The marker size is set via ma->SetMarkerSize(size), where size is the
desired size. Note, that the marker types 1, 6 and 7 (the dots) cannot be scaled. They are always drawn with the same
number of pixels. SetMarkerSize does not apply on them. To have a “scalable dot” a circle shape should be used
instead, for example, the marker type 20. The default marker type is 1, if SetMarkerStyle is not specified. It is the
most common one to draw scatter plots.
The user interface for changing the marker color, style and size looks like shown in this picture. It takes place in the
editor frame anytime the selected object inherits the class TAttMarker.

9.4. GRAPHICAL OBJECTS

185

Figure 9.12: Different marker sizes

Figure 9.13: Different marker sizes

Figure 9.14: The use of non-symmetric markers

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Non-symmetric symbols should be used carefully in plotting. The next two graphs show how the misleading a careless
use of symbols can be. The two plots represent the same data sets but because of a bad symbol choice, the two on the
top appear further apart from the next example.
A TPolyMaker is defined by an array on N points in a 2D space. At each point x[i], y[i] a marker is drawn. The list
of marker types is shown in the previous paragraph. The marker attributes are managed by the class TAttMarker and
are described in “Graphical Objects Attributes”. The TPolyMarker constructor is:
TPolyMarker(Int_t n,Double_t *x,Double_t *y,Option_t *option)
Where x and y are arrays of coordinates for the n points that form the poly-marker.

9.4.5

Curly and Wavy Lines for Feynman Diagrams

This is a peculiarity of particle physics, but we do need sometimes to draw Feynman diagrams. Our friends working
in banking can skip this part. A set of classes implements curly or wavy poly-lines typically used to draw Feynman
diagrams. Amplitudes and wavelengths may be specified in the constructors, via commands or interactively from
context menus. These classes are TCurlyLine and TCurlyArc. These classes make use of TPolyLine by inheritance;
ExecuteEvent methods are highly inspired from the methods used in TPolyLine and TArc.

Figure 9.15: The picture generated by the tutorial macro feynman.C
The TCurlyLine constructor is:
TCurlyLine(Double_t x1, Double_t y1, Double_t x2, Double_t y2,
Double_t wavelength, Double_t amplitude)
The coordinates (x1, y1) define the starting point, (x2, y2) - the end-point. The wavelength and the amplitude are
given in percent of the pad height.
The TCurlyArc constructor is:
TCurlyArc(Double_t x1, Double_t y1, Double_t rad,
Double_t phimin, Double_t phimax,
Double_t wavelength, Double_t amplitude)
The curly arc center is (x1, y1) and the radius is rad. The wavelength and the amplitude are given in percent of the
line length. The parameters phimin and phimax are the starting and ending angle of the arc (given in degrees). Refer
to $ROOTSYS/tutorials/graphics/feynman.C for the script that built the figure above.

9.4. GRAPHICAL OBJECTS

9.4.6

187

Text and Latex Mathematical Expressions

Text displayed in a pad may be embedded into boxes, called paves (TPaveLabel), or titles of graphs or many other
objects but it can live a life of its own. All text displayed in ROOT graphics is an object of class TText. For a physicist,
it will be most of the time a TLatex expression (which derives from TText). TLatex has been conceived to draw
mathematical formulas or equations. Its syntax is very similar to the Latex in mathematical mode.
9.4.6.1

Subscripts and Superscripts

Subscripts and superscripts are made with the _ and ˆ commands. These commands can be combined to make complex
subscript and superscript expressions. You may choose how to display subscripts and superscripts using the 2 functions
SetIndiceSize(Double_t) and SetLimitIndiceSize(Int_t). Examples of what can be obtained using subscripts
and superscripts:
The expression
xˆ{2y}
x_{2y}

9.4.6.2

Gives
x2y
x2y

The expression
xˆ{yˆ{2}}
xˆ{y_{1}}

Gives
2
xy
xy1

The expression
x_{1}ˆ{y_{1}}
x_{1}ˆ{y}

Gives
xy11
xy1

Fractions

Fractions denoted by the / symbol are made in the obvious way. The #frac command is used for large fractions in
displayed formula; it has two arguments: the numerator and the denominator. For example, the equation x = y + z 2
y 2 + 1 is obtained by following expression x=#frac{y+z/2}{yˆ{2}+1}.

9.4.6.3

Roots

The #sqrt command produces the square ROOT of its argument; it has an optional first argument for other roots.

Example: #sqrt{10} #sqrt[3]{10}

9.4.6.4

Delimiters

You can produce three kinds of proportional delimiters.
#[]{....} or “à la” Latex
#left[.....#right]big square brackets
#{}{....} or #left{.....#right}big curly brackets
#||{....} or #left|.....#right|big absolute value symbol
#(){....} or #left(.....#right)big parenthesis

9.4.6.5

Changing Style in Math Mode

You can change the font and the text color at any moment using:
#font[font-number]{...} and #color[color-number]{...}

9.4.6.6

Line Splitting

A TLatex string may be split in two with the following command: #splitline{top}{bottom}. TAxis and TGaxis
objects can take advantage of this feature. For example, the date and time could be shown in the time axis over two
lines with: #splitline{21 April 2003}{14:23:56}

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9.4.7

CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE

Greek Letters

The command to produce a lowercase Greek letter is obtained by adding # to the name of the letter. For an uppercase
Greek letter, just capitalize the first letter of the command name.
#alpha
#gamma
#mu
#sigma
#psi
#Epsilon
#vartheta
#Theta
#varsigma

9.4.8

#beta
#eta
#nu
#tau
#zeta
#Phi
#Lambda
#Rho
#Xi

#chi
#iota
#omicron
#upsilon
#Alpha
#Gamma
#Mu
#Sigma
#Psi

#delta
#varphi
#pi
#varomega
#Beta
#Eta
#Nu
#Tau
#epsilon

#varepsilon
#kappa
#theta
#omega
#Chi
#Iota
#Omicron
#Upsilon
#varUpsilon

#phi
#lambda
#rho
#xi
#Delta
#Kappa
#Pi
#Omega
#Zeta

Mathematical Symbols

TLatex can make mathematical and other symbols. A few of them, such as + and >, are produced by typing the
corresponding keyboard character. Others are obtained with the commands as shown in the table above.
9.4.8.1

Accents, Arrows and Bars

Symbols in a formula are sometimes placed one above another. TLatex provides special commands for that.
#hat{a} =hat
#check =inverted hat
#acute =acute
#grave =accent grave
#dot =derivative
#ddot =double derivative
#tilde =tilde
#slash =special sign. Draw a slash on top of the text between brackets for example
#slash{E}_{T}generates “Missing ET”
a _ is obtained with #bar{a}
a -> is obtained with #vec{a}
9.4.8.2

Example 1

The script $ROOTSYS/tutorials/graphics/latex.C:
{

}

TCanvas c1("c1","Latex",600,700);
TLatex l;
l.SetTextAlign(12);
l.SetTextSize(0.04);
l.DrawLatex(0.1,0.8,"1) C(x) = d #sqrt{#frac{2}{#lambdaD}}
#int^{x}_{0}cos(#frac{#pi}{2}t^{2})dt");
l.DrawLatex(0.1,0.6,"2) C(x) = d #sqrt{#frac{2}{#lambdaD}}
#int^{x}cos(#frac{#pi}{2}t^{2})dt");
l.DrawLatex(0.1,0.4,"3) R = |A|^{2} =
#frac{1}{2}(#[]{#frac{1}{2}+C(V)}^{2}+
#[]{#frac{1}{2}+S(V)}^{2})");
l.DrawLatex(0.1,0.2,"4) F(t) = #sum_{i=
-#infty}^{#infty}A(i)cos#[]{#frac{i}{t+i}}");

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189

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9.4. GRAPHICAL OBJECTS

Figure 9.16: The picture generated by the tutorial macro latex.C

191

192
9.4.8.3

CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE
Example 2

The script $ROOTSYS/tutorials/graphics/latex2.C:
{

}

TCanvas c1("c1","Latex",600,700);
TLatex l;
l.SetTextAlign(23);
l.SetTextSize(0.1);
l.DrawLatex(0.5,0.95,"e^{+}e^{-}#rightarrowZ^{0}
#rightarrowI#bar{I}, q#bar{q}");
l.DrawLatex(0.5,0.75,"|#vec{a}#bullet#vec{b}|=
#Sigmaa^{i}_{jk}+b^{bj}_{i}");
l.DrawLatex(0.5,0.5,"i(#partial_{#mu}#bar{#psi}#gamma^{#mu}
+m#bar{#psi}=0
#Leftrightarrow(#Box+m^{2})#psi=0");
l.DrawLatex(0.5,0.3,"L_{em}=eJ^{#mu}_{em}A_{#mu} ,
J^{#mu}_{em}=#bar{I}#gamma_{#mu}I
M^{j}_{i}=#SigmaA_{#alpha}#tau^{#alphaj}_{i}");

Figure 9.17: The picture generated by the tutorial macro latex2.C

9.4.8.4

Example 3

The script $ROOTSYS/tutorials/graphics/latex3.C:
{

TCanvas c1("c1");
TPaveText pt(.1,.5,.9,.9);
pt.AddText("#frac{2s}{#pi#alpha^{2}}
#frac{d#sigma}{dcos#theta} (e^{+}e^{-}
#rightarrow f#bar{f} ) = ");

9.4. GRAPHICAL OBJECTS

}

193

pt.AddText("#left| #frac{1}{1 - #Delta#alpha} #right|^{2}
(1+cos^{2}#theta");
pt.AddText("+ 4 Re #left{ #frac{2}{1 - #Delta#alpha} #chi(s)
#[]{#hat{g}_{#nu}^{e}#hat{g}_{#nu}^{f}
(1 + cos^{2}#theta) + 2 #hat{g}_{a}^{e}
#hat{g}_{a}^{f} cos#theta) } #right}");
pt.SetLabel("Born equation");
pt.Draw();

Figure 9.18: The picture generated by the tutorial macro latex3.C

9.4.9

Text in a Pad

Text displayed in a pad may be embedded into boxes, called paves, or may be drawn alone. In any case, it is
recommended to use a Latex expression, which is covered in the previous paragraph. Using TLatex is valid whether
the text is embedded or not. In fact, you will use Latex expressions without knowing it since it is the standard for all
the embedded text. A pave is just a box with a border size and a shadow option. The options common to all types of
paves and used when building those objects are the following:
option = "T" top frame
option = "B" bottom frame
option = "R" right frame
option = "L" left frame
option = "NDC" x1,y1,x2,y2 are given in NDC
option = "ARC" corners are rounded
We will see the practical use of these options in the description of the more functional objects like TPaveLabels. There
are several categories of paves containing text: TPaveLabel, TPaveText and TPavesText. TPaveLabels are panels
containing one line of text. They are used for labeling.
TPaveLabel(Double_t x1, Double_t y1, Double_t x2, Double_t y2,
const char *label, Option_t *option)
Where (x1, y1) are the coordinates of the bottom left corner, (x2,y2) - coordinates of the upper right corner. “label”
is the text to be displayed and “option” is the drawing option, described above. By default, the border size is 5 and the
option is “br”. If one wants to set the border size to some other value, one may use the method SetBorderSize(). For

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example, suppose we have a histogram, which limits are (-100,100) in the x direction and (0, 1000) in the y direction.
The following lines will draw a label in the center of the histogram, with no border. If one wants the label position to
be independent of the histogram coordinates, or user coordinates, one can use the option “NDC”. See “The Coordinate
Systems of a Pad”.
root[] pl = new TPaveLabel(-50,0,50,200,"Some text")
root[] pl->SetBorderSize(0)
root[] pl->Draw()

Figure 9.19: PaveLabels drawn with different options
A TPaveLabel can contain only one line of text. A TPaveText may contain several lines. This is the only difference.
This picture illustrates and explains some of the points of TPaveText. Once a TPaveText is drawn, a line can be added
or removed by brining up the context menu with the mouse.
A TPavesText is a stack of text panels (see TPaveText). One can set the number of stacked panels at building time. It
has the following constructor: By default, the number of stacked panels is 5, option=“br”.
TPavesText(Double_t x1, Double_t y1, Double_t x2, Double_t y2,
Int_t npaves, Option_t* option)

9.4.10

The TeX Processor TMathText

TMathText’s purpose is to write mathematical equations, exactly as TeX would do it. The syntax is the same as the
TeX’s one.
The script $ROOTSYS/tutorials/graphics/tmathtex.C:
gives the following output:
TMathText uses plain TeX syntax and uses “\” as control instead of “#”. If a piece of text containing “\” is given to
TLatex then TMathText is automatically invoked. Therefore, as histograms’ titles, axis titles, labels etc . . . are drawn
using TLatex, the TMathText syntax can be used for them also.

9.5

Axis

The axis objects are automatically built by various high level objects such as histograms or graphs. Once build, one
may access them and change their characteristics. It is also possible, for some particular purposes to build axis on their
own. This may be useful for example in the case one wants to draw two axis for the same plot, one on the left and one
on the right.
For historical reasons, there are two classes representing axis. TAxis * axis is the axis object, which will be returned
when calling the TH1::GetAxis() method.
TAxis *axis = histo->GetXaxis()
Of course, you may do the same for Y and Z-axis. The graphical representation of an axis is done with the TGaxis
class. The histogram classes and TGraph generate instances of this class. This is internal and the user should not have
to see it.

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195

Figure 9.20: PaveText examples

Figure 9.21: A PaveText example

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Figure 9.22: A TMathText example

9.5.1

Axis Title

The axis title is set, as with all named objects, by
axis->SetTitle("Whatever title you want");
When the axis is embedded into a histogram or a graph, one has to first extract the axis object:
h->GetXaxis()->SetTitle("Whatever title you want")

9.5.2

Axis Options and Characteristics

The axis options are most simply set with the styles. The available style options controlling specific axis options are
the following:
TAxis *axis = histo->GetXaxis();
axis->SetAxisColor(Color_t color = 1);
axis->SetLabelColor(Color_t color = 1);
axis->SetLabelFont(Style_t font = 62);
axis->SetLabelOffset(Float_t offset = 0.005);
axis->SetLabelSize(Float_t size = 0.04);
axis->SetNdivisions(Int_t n = 510, Bool_t optim = kTRUE);
axis->SetNoExponent(Bool_t noExponent = kTRUE);
axis->SetTickLength(Float_t length = 0.03);
axis->SetTitleOffset(Float_t offset = 1);
axis->SetTitleSize(Float_t size = 0.02);
The getters corresponding to the described setters are also available. The general options, not specific to axis, as for
instance SetTitleTextColor() are valid and do have an effect on axis characteristics.

9.5. AXIS

9.5.3

197

Setting the Number of Divisions

Use TAxis::SetNdivisions(ndiv,optim) to set the number of divisions for an axis. The ndiv and optim are as
follows:
• ndiv = N1 + 100*N2 + 10000*N3
• N1 = number of first divisions.
• N2 = number of secondary divisions.
• N3 = number of tertiary divisions.
• optim = kTRUE (default), the divisions’ number will be optimized around the specified value.
• optim = kFALSE, or n < 0, the axis will be forced to use exactly n divisions.
For example:
ndiv = 0: no tick marks.
ndiv = 2: 2 divisions, one tick mark in the middle of the axis.
ndiv = 510: 10 primary divisions, 5 secondary divisions
ndiv = -10: exactly 10 primary divisions

9.5.4

Zooming the Axis

You can use TAxis::SetRange or TAxis::SetRangeUser to zoom the axis.
TAxis::SetRange(Int_t binfirst,Int_t binlast)
The SetRange method parameters are bin numbers. They are not axis. For example if a histogram plots the values
from 0 to 500 and has 100 bins, SetRange(0,10) will cover the values 0 to 50. The parameters for SetRangeUser are
user coordinates. If the start or end is in the middle of a bin the resulting range is approximation. It finds the low edge
bin for the start and the high edge bin for the high.
TAxis::SetRangeUser(Axis_t ufirst,Axis_t ulast)
Both methods, SetRange and SetRangeUser, are in the context menu of any axis and can be used interactively. In
addition, you can zoom an axis interactively: click on the axis on the start, drag the cursor to the end, and release the
mouse button.

9.5.5

Drawing Axis Independently of Graphs or Histograms

An axis may be drawn independently of a histogram or a graph. This may be useful to draw for example a supplementary
axis for a graph. In this case, one has to use the TGaxis class, the graphical representation of an axis. One may use
the standard constructor for this kind of objects:
TGaxis(Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax,
Double_t wmin, Double_t wmax, Int_t ndiv = 510,
Option_t* chopt,Double_t gridlength = 0)
The arguments xmin, ymin are the coordinates of the axis’ start in the user coordinates system, and xmax, ymax
are the end coordinates. The arguments wmin and wmax are the minimum (at the start) and maximum (at the end)
values to be represented on the axis; ndiv is the number of divisions. The options, given by the “chopt” string are the
following:
• chopt = ’G’: logarithmic scale, default is linear.
• chopt = ’B’: Blank axis (it is useful to superpose the axis).

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Instead of the wmin,wmax arguments of the normal constructor, i.e. the limits of the axis, the name of a TF1 function
can be specified. This function will be used to map the user coordinates to the axis values and ticks.
The constructor is the following:
TGaxis(Double_t xmin, Double_t ymin, Double_t xmax, Double_t ymax,
const char* funcname, Int_t ndiv=510,
Option_t* chopt, Double_t gridlength=0)
In such a way, it is possible to obtain exponential evolution of the tick marks position, or even decreasing. In fact,
anything you like.

9.5.6

Orientation of Tick Marks on Axis

Tick marks are normally drawn on the positive side of the axis, however, if xmin = xmax, then negative.
• chopt = ’+’: tick marks are drawn on Positive side. (Default)
• chopt = ’-’: tick marks are drawn on the negative side.
• chopt = ’+-’: tick marks are drawn on both sides of the axis.
• chopt = ‘U’: unlabeled axis, default is labeled.

9.5.7

Labels

9.5.7.1

Position

Labels are normally drawn on side opposite to tick marks. However, chopt = ’=’: on Equal side. The function
TAxis::CenterLabels() sets the bit kCenterLabels and it is visible from TAxis context menu. It centers the bin
labels and it makes sense only when the number of bins is equal to the number of tick marks. The class responsible for
drawing the axis TGaxis inherits this property.
9.5.7.2

Orientation

Labels are normally drawn parallel to the axis. However, if xmin = xmax, then they are drawn orthogonal, and if
ymin=ymax they are drawn parallel.
9.5.7.3

Labels for Exponents

By default, an exponent of the form 10ˆN is used when the label values are either all very small or very large. One can
disable the exponent by calling:
TAxis::SetNoExponent(kTRUE)
Note that this option is implicitly selected if the number of digits to draw a label is less than the fgMaxDigits global
member. If the property SetNoExponent was set in TAxis (via TAxis::SetNoExponent), the TGaxis will inherit this
property. TGaxis is the class responsible for drawing the axis. The method SetNoExponent is also available from the
axis context menu.
9.5.7.4

Number of Digits in Labels

TGaxis::fgMaxDigits is the maximum number of digits permitted for the axis labels above which the notation with
10ˆN is used. It must be greater than 0. By default fgMaxDigits is 5 and to change it use the TGaxis::SetMaxDigits
method. For example to set fgMaxDigits to accept 6 digits and accept numbers like 900000 on an axis call:
TGaxis::SetMaxDigits(6)

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199

Figure 9.23: Y-axis with and without exponent labels
9.5.7.5

Tick Mark Positions

Labels are centered on tick marks. However, if xmin = xmax, then they are right adjusted.
• chopt = ’R’: labels are right adjusted on tick mark (default is centered)
• chopt = ’L’: labels are left adjusted on tick mark.
• chopt = ’C’: labels are centered on tick mark.
• chopt = ’M’: In the Middle of the divisions.
9.5.7.6

Label Formatting

Blank characters are stripped, and then the label is correctly aligned. The dot, if last character of the string, is also
stripped. In the following, we have some parameters, like tick marks length and characters height (in percentage of the
length of the axis, in user coordinates). The default values are as follows:
• Primary tick marks: 3.0 %
• Secondary tick marks: 1.5 %
• Third order tick marks: .75 %
• Characters height for labels: 4%
• Labels offset: 1.0 %
9.5.7.7

Stripping Decimals

Use the TStyle::SetStripDecimals to strip decimals when drawing axis labels. By default, the option is set to true,
and TGaxis::PaintAxis removes trailing zeros after the dot in the axis labels, e.g. {0, 0.5, 1, 1.5, 2, 2.5, etc.}
TStyle::SetStripDecimals (Bool_t strip=kTRUE)
If this function is called with strip=kFALSE, TGaxis::PaintAxis() will draw labels with the same number of digits
after the dot, e.g. {0.0, 0.5, 1.0, 1.5, 2.0, 2.5, etc.}

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CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE
Optional Grid

chopt = ’W’: cross-Wire
9.5.7.9

Axis Binning Optimization

By default, the axis binning is optimized.
• chopt = ’N’: No binning optimization
• chopt = ’I’: Integer labeling

9.5.8

Axis with Time Units

Histograms’ axis can be defined as “time axis”. To do that it is enough to activate the SetTimeDisplay attribute on a
given axis. If h is a histogram, it is done the following way:
h->GetXaxis()->SetTimeDisplay(1);

// X axis is a time axis

Two parameters can be adjusted in order to define time axis: the time format and the time offset.
9.5.8.1

Time Format

It defines the format of the labels along the time axis. It can be changed using the TAxis method SetTimeFormat. The
time format is the one used by the C function strftime(). It is a string containing the following formatting characters:
For the date:

For the time:

%a abbreviated weekday name
%b abbreviated month name
%d day of the month (01-31)
%m month (01-12)
%y year without century
%Y year with century
%H hour (24-hour clock)
%I hour (12-hour clock)
%p local equivalent of AM or PM
%M minute (00-59)
%S seconds (00-61)
%% %

The other characters are output as is. For example to have a format like dd/mm/yyyy one should do:
h->GetXaxis()->SetTimeFormat("%d/%m/%Y");
If the time format is not defined, a default one will be computed automatically.
9.5.8.2

Time Offset

This is a time in seconds in the UNIX standard UTC format (the universal time, not the local one), defining the
starting date of a histogram axis. This date should be greater than 01/01/95 and is given in seconds. There are three
ways to define the time offset:
1- By setting the global default time offset:
TDatime da(2003,02,28,12,00,00);
gStyle->SetTimeOffset(da.Convert());
If no time offset is defined for a particular axis, the default time offset will be used. In the example above, notice the
usage of TDatime to translate an explicit date into the time in seconds required by SetTimeFormat.
2- By setting a time offset to a particular axis:

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201

TDatime dh(2001,09,23,15,00,00);
h->GetXaxis()->SetTimeOffset(dh.Convert());
3- Together with the time format using SetTimeFormat. The time offset can be specified using the control character
%F after the normal time format. %F is followed by the date in the format: yyyy-mm-dd hh:mm:ss.
h->GetXaxis()->SetTimeFormat("%d/%m/%y%F2000-02-28 13:00:01");
Notice that this date format is the same used by the TDatime function AsSQLString. If needed, this function can be
used to translate a time in seconds into a character string which can be appended after %F. If the time format is not
specified (before %F) the automatic one will be used. The following example illustrates the various possibilities.
{

}

gStyle->SetTitleH(0.08);
TDatime da(2003,02,28,12,00,00);
gStyle->SetTimeOffset(da.Convert());
ct = new TCanvas("ct","Time on axis",0,0,600,600);
ct->Divide(1,3);
ht1 = new TH1F("ht1","ht1",30000,0.,200000.);
ht2 = new TH1F("ht2","ht2",30000,0.,200000.);
ht3 = new TH1F("ht3","ht3",30000,0.,200000.);
for (Int_t i=1;i<30000;i++) {
Float_t noise = gRandom->Gaus(0,120);
ht1->SetBinContent(i,noise);
ht2->SetBinContent(i,noise*noise);
ht3->SetBinContent(i,noise*noise*noise);
}
ct->cd(1);
ht1->GetXaxis()->SetLabelSize(0.06);
ht1->GetXaxis()->SetTimeDisplay(1);
ht1->GetXaxis()->SetTimeFormat("%d/%m/%y%F2000-02-2813:00:01");
ht1->Draw();
ct->cd(2);
ht2->GetXaxis()->SetLabelSize(0.06);
ht2->GetXaxis()->SetTimeDisplay(1);
ht2->GetXaxis()->SetTimeFormat("%d/%m/%y");
ht2->Draw();
ct->cd(3);
ht3->GetXaxis()->SetLabelSize(0.06);
TDatime dh(2001,09,23,15,00,00);
ht3->GetXaxis()->SetTimeDisplay(1);
ht3->GetXaxis()->SetTimeOffset(dh.Convert());
ht3->Draw();

The output is shown in the figure below. If a time axis has no specified time offset, the global time offset will be stored
in the axis data structure. The histogram limits are in seconds. If wmin and wmax are the histogram limits, the time
axis will spread around the time offset value from TimeOffset+wmin to TimeOffset+wmax. Until now all examples had
a lowest value equal to 0. The following example demonstrates how to define the histogram limits relatively to the time
offset value.
{

// Define the time offset as 2003, January 1st
TDatime T0(2003,01,01,00,00,00);
int X0 = T0.Convert();
gStyle->SetTimeOffset(X0);
// Define the lowest histogram limit as 2002,September 23rd
TDatime T1(2002,09,23,00,00,00);
int X1 = T1.Convert()-X0;
// Define the highest histogram limit as 2003, March 7th

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Figure 9.24: Time axis examples

9.5. AXIS

203

TDatime T2(2003,03,07,00,00,00);
int X2 = T2.Convert(1)-X0;
TH1F * h1 = new TH1F("h1","test",100,X1,X2);
TRandom r;
for (Int_t i=0;i<30000;i++) {
Double_t noise = r.Gaus(0.5*(X1+X2),0.1*(X2-X1));
h1->Fill(noise);
}

}

h1->GetXaxis()->SetTimeDisplay(1);
h1->GetXaxis()->SetLabelSize(0.03);
h1->GetXaxis()->SetTimeFormat("%Y/%m/%d");
h1->Draw();

The output is shown in the next figure. Usually time axes are created automatically via histograms, but one may also
want to draw a time axis outside a “histogram context”. Therefore, it is useful to understand how TGaxis works for
such axis. The time offset can be defined using one of the three methods described before. The time axis will spread
around the time offset value. Actually, it will go from TimeOffset+wmin to TimeOffset+wmax where wmin and wmax
are the minimum and maximum values (in seconds) of the axis. Let us take again an example. Having defined “2003,
February 28 at 12h”, we would like to see the axis a day before and a day after.

Figure 9.25: A histogram with time axis X
A TGaxis can be created the following way (a day has 86400 seconds):
TGaxis *axis = new TGaxis(x1,y1,x2,y2,-100000,150000,2405,"t");
the “t” option (in lower case) means it is a “time axis”. The axis goes form 100000 seconds before TimeOffset and
150000 seconds after. So the complete macro is:

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{

}

CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE

c1 = new TCanvas("c1","Examples of TGaxis",10,10,700,500);
c1->Range(-10,-1,10,1);
TGaxis *axis = new TGaxis(-8,-0.6,8,-0.6,-100000,150000,2405,"t");
axis->SetLabelSize(0.03);
TDatime da(2003,02,28,12,00,00);
axis->SetTimeOffset(da.Convert());
axis->SetTimeFormat("%d/%m/%Y");
axis->Draw();

The time format is specified with:
axis->SetTimeFormat("%d/%m/%Y");
The macro gives the following output:

Thanks to the TLatex directive #splitline it is possible to write the time labels on two lines. In the previous example
changing the SetTimeFormat line by:
axis->SetLabelOffset(0.02);
axis->SetTimeFormat("#splitline{%Y}{%d/%m}");
will produce the following axis:

9.5.9

Axis Examples

To illustrate what was said, we provide two scripts. The first one creates the picture shown in the next figure.
The first script is:
{

c1 = new TCanvas("c1","Examples of Gaxis",10,10,700,500);
c1->Range(-10,-1,10,1);
TGaxis *axis1 = new TGaxis(-4.5,-0.2,5.5,-0.2,-6,8,510,"");
axis1->SetName("axis1");
axis1->Draw();
TGaxis *axis2 = new TGaxis(4.5,0.2,5.5,0.2,0.001,10000,510,"G");
axis2->SetName("axis2");
axis2->Draw();
TGaxis *axis3 = new TGaxis(-9,-0.8,-9,0.8,-8,8,50510,"");
axis3->SetName("axis3");
axis3->Draw();
TGaxis *axis4 = new TGaxis(-7,-0.8,7,0.8,1,10000,50510,"G");
axis4->SetName("axis4");
axis4->Draw();

9.5. AXIS

205

Figure 9.26: The first axis example
TGaxis *axis5 = new TGaxis(-4.5,-6,5.5,-6,1.2,1.32,80506,"-+");
axis5->SetName("axis5");
axis5->SetLabelSize(0.03);
axis5->SetTextFont(72);
axis5->SetLabelOffset(0.025);
axis5->Draw();
TGaxis *axis6 = new TGaxis(-4.5,0.6,5.5,0.6,100,900,50510,"-");
axis6->SetName("axis6");
axis6->Draw();
TGaxis *axis7 = new TGaxis(8,-0.8,8,0.8,0,9000,50510,"+L");
axis7->SetName("axis7");
axis7->SetLabelOffset(0.01);
axis7->Draw();

}

// one can make axis top->bottom. However because of a problem,
// the two x values should not be equal
TGaxis *axis8 = new TGaxis(6.5,0.8,6.499,-0.8,0,90,50510,"-");
axis8->SetName("axis8");
axis8->Draw();

The second example shows the use of the second form of the constructor, with axis ticks position determined by a
function TF1:
void gaxis3a()
{
gStyle->SetOptStat(0);
TH2F *h2 = new TH2F("h","Axes",2,0,10,2,-2,2);

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Figure 9.27: The second axis example
h2->Draw();
TF1 *f1=new TF1("f1","-x",-10,10);
TGaxis *A1 = new TGaxis(0,2,10,2,"f1",510,"-");
A1->SetTitle("axis with decreasing values");
A1->Draw();
TF1 *f2=new TF1("f2","exp(x)",0,2);
TGaxis *A2 = new TGaxis(1,1,9,1,"f2");
A2->SetTitle("exponential axis");
A2->SetLabelSize(0.03);
A2->SetTitleSize(0.03);
A2->SetTitleOffset(1.2);
A2->Draw();

}

TF1 *f3=new TF1("f3","log10(x)",0,800);
TGaxis *A3 = new TGaxis(2,-2,2,0,"f3",505);
A3->SetTitle("logarithmic axis");
A3->SetLabelSize(0.03);
A3->SetTitleSize(0.03);
A3->SetTitleOffset(1.2);
A3->Draw();

// strip chart example
void seism() {
TStopwatch sw; sw.Start();
//set time offset
TDatime dtime;
gStyle->SetTimeOffset(dtime.Convert());

9.5. AXIS

207

Figure 9.28: An axis example with time display

TCanvas *c1 = new TCanvas("c1","Time on axis",10,10,1000,500);
c1->SetFillColor(42);
c1->SetFrameFillColor(33);
c1->SetGrid();
Float_t bintime = 1;
// one bin = 1 second. change it to set the time scale
TH1F *ht = new TH1F("ht","The ROOT seism",10,0,10*bintime);
Float_t signal = 1000;
ht->SetMaximum(signal);
ht->SetMinimum(-signal);
ht->SetStats(0);
ht->SetLineColor(2);
ht->GetXaxis()->SetTimeDisplay(1);
ht->GetYaxis()->SetNdivisions(520);
ht->Draw();

}

for (Int_t i=1;i<2300;i++) {
// Build a signal : noisy damped sine
Float_t noise = gRandom->Gaus(0,120);
if (i > 700)
noise += signal*sin((i-700.)*6.28/30)*exp((700.-i)/300.);
ht->SetBinContent(i,noise);
c1->Modified();
c1->Update();
gSystem->ProcessEvents();
//canvas can be edited during the loop
}
printf("Real Time = %8.3fs,Cpu Time = %8.3fsn",sw.RealTime(),
sw.CpuTime());

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9.6
9.6.1

CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE

Graphical Objects Attributes
Text Attributes

When a class contains text or derives from a text class, it needs to be able to set text attributes like font type, size,
and color. To do so, the class inherits from the TAttText class (a secondary inheritance), which defines text attributes.
TLatex and TText inherit from TAttText.

9.6.1.1

Setting Text Alignment

Text alignment may be set by a method call. What is said here applies to all objects deriving from TAttText, and
there are many. We will take an example that may be transposed to other types. Suppose “la” is a TLatex object.
The alignment is set with:
root[] la->SetTextAlign(align)
The parameter align is a short describing the alignment:
align = 10*HorizontalAlign + VerticalAlign
For horizontal alignment, the following convention applies:

• 1 = left
• 2 = centered
• 3 = right

For vertical alignment, the following convention applies:

• 1 = bottom
• 2 = centered
• 3 = top

For example, align: 11 = left adjusted and bottom adjusted; 32 = right adjusted and vertically centered.

9.6.1.2

Setting Text Angle

Use TAttText::SetTextAngle to set the text angle. The angle is the degrees of the horizontal.
root[] la->SetTextAngle(angle)

9.6.1.3

Setting Text Color

Use TAttText::SetTextColor to set the text color. The color is the color index. The colors are described in “Color
and Color Palettes”.
root[] la->SetTextColor(color)

9.6. GRAPHICAL OBJECTS ATTRIBUTES
9.6.1.4

209

Setting Text Font

Use TAttText::SetTextFont to set the font. The parameter font is the font code, combining the font and precision:
font = 10 * fontID + precision
root[] la->SetTextFont(font)
The table below lists the available fonts. The font IDs must be between 1 and 14. The precision can be:
• Precision = 0 fast hardware fonts (steps in the size)
• Precision = 1 scalable and rotate-able hardware fonts (see below)
• Precision = 2 scalable and rotate-able hardware fonts
When precision 0 is used, only the original non-scaled system fonts are used. The fonts have a minimum (4) and
maximum (37) size in pixels. These fonts are fast and are of good quality. Their size varies with large steps and they
cannot be rotated. Precision 1 and 2 fonts have a different behavior depending if True Type Fonts (TTF) are used
or not. If TTF are used, you always get very good quality scalable and rotate-able fonts. However, TTF are slow.
Precision 1 and 2 fonts have a different behavior for PostScript in case of TLatex objects:
• With precision 1, the PostScript text uses the old convention (see TPostScript) for some special characters to
draw sub and superscripts or Greek text.
• With precision 2, the “PostScript” special characters are drawn as such. To draw sub and superscripts it is highly
recommended to use TLatex objects instead.
For example: font = 62 is the font with ID 6 and precision 2.
The available fonts are:
Font ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14

X11
times-medium-i-normal
times-bold-r-normal
times-bold-i-normal
helvetica-medium-r-norma l
helvetica-medium-o-norma l
helvetica-bold-r-normal
helvetica-bold-o-normal
courier-medium-r-normal
courier-medium-o-normal
courier-bold-r-normal
courier-bold-o-normal
symbol-medium-r-normal
times-medium-r-normal

True Type name
“Times New Roman”
“Times New Roman”
“Times New Roman”
“Arial”
“Arial”
“Arial”
“Arial”
“Courier New”
“Courier New”
“Courier New”
“Courier New”
“Symbol”
“Times New Roman”
“Wingdings”

This script makes the image of the different fonts:
{

textc = new TCanvas("textc","Example of text",1);
for (int i=1;i<15;i++) {
cid = new char[8];
sprintf(cid,"ID %d :",i);
cid[7] = 0;
lid = new TLatex(0.1,1-(double)i/15,cid);
lid->SetTextFont(62);
lid->Draw();
l = new TLatex(.2,1-(double)i/15,
"The quick brown fox is not here anymore")
l->SetTextFont(i*10+2);
l->Draw();

Is italic
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
No
No
No

“boldness”
4
7
7
4
4
7
7
4
4
7
7
6
4
4

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CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE

Figure 9.29: Font’s examples

9.6. GRAPHICAL OBJECTS ATTRIBUTES

}

211

}

9.6.1.5

How to use True Type Fonts

You can activate the True Type Fonts by adding the following line in your .rootrc file.
Unix.*.Root.UseTTFonts:

true

You can check that you indeed use the TTF in your Root session. When the TTF is active, you get the following
message at the start of a session: “Free Type Engine v1.x used to render TrueType fonts.” You can also check with the
command:
gEnv->Print()
9.6.1.6

Setting Text Size

Use TAttText::SetTextSize to set the text size.
root[] la->SetTextSize(size)
The size is the text size expressed in percentage of the current pad size.
The text size in pixels will be:
• If current pad is horizontal, the size in pixels = textsize * canvas_height
• If current pad is vertical, the size in pixels = textsize * canvas_width

The user interface for changing the text color, size, font and allignment looks like
shown in this picture. It takes place in the editor frame anytime the selected object inherits the class TAttText.

9.6.2

Line Attributes

All classes manipulating lines have to deal with line attributes: color, style and width. This is done by using secondary
inheritance of the class TAttLine. The line color may be set by a method call. What is said here applies to all objects
deriving from TAttLine, and there are many (histograms, plots). We will take an example that may be transposed to
other types. Suppose “li” is a TLine object. The line color is set with:
root[] li->SetLineColor(color)
The argument color is a color number. The colors are described in “Color and Color Palettes”
The line style may be set by a method call. What is said here applies to all objects deriving from TAttLine, and there
are many (histograms, plots). We will take an example that may be transposed to other types. Suppose “li” is a
TLine object. The line style is set with:
root[] li->SetLineStyle(style)
The argument style is one of: 1=solid, 2=dash, 3=dot, 4=dash-dot.
The line width may be set by a method call. What is said here applies to all objects deriving from TAttLine, and
there are many (histograms, plots). We will take an example that may be transposed to other types. Suppose “li” is a
TLine object. The line width is set with:

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root[] li->SetLineWidth(width)
The width is the width expressed in pixel units.

The user interface for changing the line color, line width and style looks like shown in this
picture. It takes place in the editor frame anytime the selected object inherits the class TAttLine.

9.6.3

Fill Attributes

Almost all graphics classes have a fill area somewhere. These classes have to deal with fill attributes. This is done by
using secondary inheritance of the class TAttFill. Fill color may be set by a method call. What is said here applies to
all objects deriving from TAttFill, and there are many (histograms, plots). We will take an example that may be
transposed to other types. Suppose “h” is a TH1F (1 dim histogram) object. The histogram fill color is set with:
root[] h->SetFillColor(color)
The color is a color number. The colors are described in “Color and color palettes”
Fill style may be set by a method call. What is said here applies to all objects deriving from TAttFill, and there are
many (histograms, plots). We will take an example that may be transposed to other types. Suppose “h” is a TH1F (1
dim histogram) object. The histogram fill style is set with:
root[] h->SetFillStyle(style)
The convention for style is: 0:hollow, 1001:solid, 2001:hatch style, 3000+pattern number:patterns, 4000 to 4100:transparency, 4000:fully transparent, 4100: fully opaque.
Fill styles >3100 and <3999 are hatches. They are defined according to the FillStyle=3ijk value as follows:
• i(1-9) specifies the space between each hatch (1=minimum space, 9=maximum). The final spacing is set by
SetHatchesSpacing() method and it is*GetHatchesSpacing().
• j(0-9) specifies the angle between 0 and 90 degres as follows: 0=0, 1=10, 2=20, 3=30, 4=45, 5=not drawn, 6=60,
7=70, 8=80 and 9=90.
• k(0-9) specifies the angle between 0 and 90 degres as follows: 0=180, 1=170, 2=160, 3=150, 4=135, 5=not drawn,
6=120, 7=110, 8=100 and 9=90.

9.6.4

Color and Color Palettes

At initialization time, a table of basic colors is generated when the first Canvas constructor is called. This table is a
linked list, which can be accessed from the gROOT object (see TROOT::GetListOfColors()). Each color has an index
and when a basic color is defined, two “companion” colors are defined:
• the dark version (color index + 100)
• the bright version (color index + 150)
The dark and bright colors are used to give 3-D effects when drawing various boxes (see TWbox, TPave, TPaveText,
TPaveLabel, etc). If you have a black and white copy of the manual, here are the basic colors and their indices.
The list of currently supported basic colors (here dark and bright colors are not shown) are shown. The color numbers
specified in the basic palette, and the picture above, can be viewed by selecting the menu entry Colors in the View
canvas menu. The user may define other colors. To do this, one has to build a new TColor:
TColor(Int_t color,Float_t r,Float_t g,Float_t b,const char* name)

9.6. GRAPHICAL OBJECTS ATTRIBUTES

Figure 9.30: The various patterns

Figure 9.31: The basic ROOT colors

213

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One has to give the color number and the three Red, Green, Blue values, each being defined from 0 (min) to 1(max).
An optional name may be given. When built, this color is automatically added to the existing list of colors. If the color
number already exists, one has to extract it from the list and redefine the RGB values. This may be done for example
with:
root[] color=(TColor*)(gROOT->GetListOfColors()->At(index_color))
root[] color->SetRGB(r,g,b)
Where r, g and b go from 0 to 1 and index_color is the color number you wish to change.

The user interface for changing the fill color and style looks like shown in this picture. It
takes place in the editor frame anytime the selected object inherits the class TAttFill.
9.6.4.1

Color Palette (for Histograms)

Defining one color at a time may be tedious. The histogram classes (see Draw Options) use the color palette. For
example, TH1::Draw("col") draws a 2-D histogram with cells represented by a box filled with a color CI function of
the cell content. If the cell content is N, the color CI used will be the color number in colors[N]. If the maximum cell
content is >ncolors, all cell contents are scaled to ncolors. The current color palette does not have a class or global
object of its own. It is defined in the current style as an array of color numbers. The current palette can be changed
with:
TStyle::SetPalette(Int_t ncolors,Int_t*color_indexes).
By default, or if ncolors <= 0, a default palette (see above) of 50 colors is defined. The colors defined in this palette
are good for coloring pads, labels, and other graphic objects. If ncolors > 0 and colors = 0, the default palette
is used with a maximum of ncolors. If ncolors == 1 && colors == 0, then a pretty palette with a spectrum
Violet->Red is created. It is recommended to use this pretty palette when drawing lego(s), surfaces or contours. For
example, to set the current palette to the “pretty” one, do:
root[] gStyle->SetPalette(1)
A more complete example is shown below. It illustrates the definition of a custom palette. You can adapt it to suit
your needs. In case you use it for contour coloring, with the current color/contour algorithm, always define two more
colors than the number of contours.
void palette() {
// Example of creating new colors (purples)
const Int_t colNum = 10;
// and defining of a new palette
Int_t palette[colNum];
for (Int_t i=0; iGetColor(230+i) ){
TColor *color =

9.7. THE GRAPHICS EDITOR

215

new TColor(230+i,1-(i/((colNum)*1.0)),0.3,0.5,"");
} else {
TColor *color = gROOT->GetColor(230+i);
color->SetRGB(1-(i/((colNum)*1.0)),0.3,0.5);
}
palette[i] = 230+i;

}

}
gStyle->SetPalette(colNum,palette);
TF2 *f2 = new TF2("f2","exp(-(x^2)-(y^2))",-3,3,-3,3);
// two contours less than the number of colors in palette
f2->SetContour(colNum-2);
f2->Draw("cont");

9.7

The Graphics Editor

A new graphics editor took place in ROOT v4.0. The editor can be activated by selecting the Editor menu entry in the
canvas View menu or one of the context menu entries for setting line, fill, marker or text attributes. The following
object editors are available for the current ROOT version.

9.7.1

TAxisEditor

This user interface gives the possibility for changing the following axis attributes:

• color of the selected axis, the axis’ title and labels;
• the length of thick parameters and the possibility to set them on both axis sides (if +- is selected);
• to set logarithmic or linear scale along the selected axis with a choice for optimized or more logarithmic labels;
• primary, secondary and tertiary axis divisions can be set via the three number fields;
• the axis title can be added or edited and the title’s color, position, offset, size and font can be set interactively;
• the color, size, and offset of axis labels can be set similarly. In addition, there is a check box for no exponent
choice, and another one for setting the same decimal part for all labels.

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CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE

TPadEditor

• It provides the following user interface:
• Fixed aspect ratio - can be set for pad resizing.
• Edit - sets pad or canvas as editable.
• Cross-hair - sets a cross hair on the pad.
• TickX - set ticks along the X axis.
• TickY - set ticks along the Y axis.
• GridX - set a grid along the X axis.
• GridY - set a grid along the Y axis.
• The pad or canvas border size can be set if a sunken or a raised border mode is
• selected; no border mode can be set too.

9.8

Copy and Paste

You can make a copy of a canvas using TCanvas::DrawClonePad. This method is unique to TCanvas. It clones the
entire canvas to the active pad. There is a more general method TObject::DrawClone, which all objects descendent of
TObject, specifically all graphic objects inherit. Below are two examples, one to show the use of DrawClonePad and
the other to show the use of DrawClone.

9.8.1

Using the GUI

In this example we will copy an entire canvas to a new one with DrawClonePad. Run the script draw2dopt.C.
root[] .x tutorials/hist/draw2dopt.C
This creates a canvas with 2D histograms. To make a copy of the canvas follow the steps:
• Right-click on it to bring up the context menu
• Select DrawClonePad
This copies the entire canvas and all its sub-pads to a new canvas. The copied canvas is a deep clone, and all the
objects on it are copies and independent of the original objects. For instance, change the fill on one of the original
histograms, and the cloned histogram retains its attributes. DrawClonePad will copy the canvas to the active pad; the
target does not have to be a canvas. It can also be a pad on a canvas.
If you want to copy and paste a graphic object from one canvas or pad to another canvas or pad, you can do so with
DrawClone method inherited from TObject. All graphics objects inherit the TObject::DrawClone method. In this
example, we create a new canvas with one histogram from each of the canvases from the script draw2dopt.C.

9.8. COPY AND PASTE

217

Figure 9.32: Different draw options

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CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE

• Start a new ROOT session and execute the script draw2dopt.C
• Select a canvas displayed by the script, and create a new canvas c1 from the File menu.
• Make sure that the target canvas (c1) is the active one by middle clicking on it. If you do this step right after
step 2, c1 will be active.
• Select the pad with the first histogram you want to copy and paste.
• Right click on it to show the context menu, and select DrawClone.
• Leave the option blank and hit OK.
Repeat these steps for one histogram on each of the canvases created by the script, until you have one pad from each
type. If you wanted to put the same annotation on each of the sub pads in the new canvas, you could use DrawClone
to do so. Here we added the date to each pad. The steps to this are:
• Create the label in on of the pads with the graphics editor.
• Middle-click on the target pad to make it the active pad
• Use DrawClone method of the label to draw it in each of the other panels.
The option in the DrawClone method argument is the Draw option for a histogram or graph. A call to TH1::DrawClone
can clone the histogram with a different draw option.

9.8.2

Programmatically

To copy and paste the four pads from the command line or in a script you would execute the following statements:
root[]
root[]
root[]
root[]
root[]
root[]
root[]
root[]
root[]
root[]
root[]
root[]
root[]
root[]
root[]
root[]

.x tutorials/hist/draw2dopt.C
TCanvas c1("c1","Copy Paste",200,200,800,600);
surfaces->cd(1); // get the first pad
TPad *p1 = gPad;
lego->cd(2);// get the next pad
TPad *p2 = gPad;
cont->cd(3);// get the next pad
TPad *p3 = gPad;
c2h->cd(4);// get the next pad
TPad *p4 = gPad;
// to draw the four clones
c1->cd();
p1->DrawClone();
p2->DrawClone();
p3->DrawClone();
p4->DrawClone();

Note that the pad is copied to the new canvas in the same location as in the old canvas. For example if you were to
copy the third pad of surf to the top left corner of the target canvas you would have to reset the coordinates of the
cloned pad.

9.9

Legends

Legends for a graph are obtained with a TLegend object. This object points to markers, lines, boxes, histograms,
graphs and represent their marker, line, fill attributes. Any object that has a marker or line or fill attribute may have
an associated legend. A TLegend is a panel with several entries (class TLegendEntry) and is created by the constructor
TLegend(Double_t x1, Double_t y1, Double_t x2, Double_t y2,
const char *header, Option_t *option)
The legend is defined with default coordinates, border size and option. The legend coordinates (NDC) in the current
pad are x1, y1, x2, y2. The default text attributes for the legend are:

9.10. THE POSTSCRIPT INTERFACE

219

• Alignment = 12 left adjusted and vertically centered
• Angle = 0 (degrees)
• Color = 1 (black)
• Size = calculate when number of entries is known
• Font = helvetica-medium-r-normal scalable font = 42, and bold = 62 for title
The title is a regular entry and supports TLatex. The default is no title (header = 0). The options are the same as
for TPave; by default, they are “brand”. Once the legend box is created, one has to add the text with the AddEntry()
method:
TLegendEntry* TLegend::AddEntry(TObject *obj,
const char *label,
Option_t *option)
The parameters are:
• *objis a pointer to an object having marker, line, or fill attributes (a histogram, or a graph)
• label is the label to be associated to the object
• option:
• “L” draw line associated with line attributes of obj, if obj inherits from TAttLine.
• “P” draw poly-marker associated with marker attributes of obj, if obj inherits TAttMarker.
• “F” draw a box with fill associated with fill attributes of obj, if obj inherits TAttFill.
One may also use the other form of the method AddEntry:
TLegendEntry* TLegend::AddEntry(const char *name,
const char *label,
Option_t *option)
Here name is the name of the object in the pad. Other parameters are as in the previous case. Next example shows
how to create a legend:
leg = new TLegend(0.4,0.6,0.89,0.89);
leg->AddEntry(fun1,"One Theory","l");
leg->AddEntry(fun3,"Another Theory","f");
leg->AddEntry(gr,"The Data","p");
leg->Draw();
// oops we forgot the blue line... add it after
leg->AddEntry(fun2,
"#sqrt{2#pi} P_{T} (#gamma) latex
// and add a header (or "title") for the legend
leg->SetHeader("The Legend Title");
leg->Draw();

formula","f");

Here fun1, fun2, fun3 and gr are pre-existing functions and graphs. You can edit the TLegend by right clicking on it.

9.10

The PostScript Interface

To generate a PostScript (or encapsulated PostScript) file for a single image in a canvas, you can:
• Select to print the canvas in the PostScript file format from the File menu / Save or Save As menu entries. By
default, a PostScript file is generated, if you do not specify the file format.

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Figure 9.33: A legend example

9.10. THE POSTSCRIPT INTERFACE

221

• Click in the canvas area, near the edges, with the right mouse button and select the Print context menu entry.
This will generate a file of canvas pointed to by c1. You can select the name of the PostScript file. If the file
name is xxx.ps, you will generate a PostScript file named xxx.ps. If the file name is xxx.eps, you generate an
encapsulated Postscript file instead. In your program (or script), you can type:
c1->Print("xxx.ps") // or
c1->Print("xxx.eps")
Next example prints the picture in the pad pointed by pad1.
pad1->Print("xxx.ps")
The TPad::Print method has a second parameter called option. Its value can be:
• 0 which is the default and is the same as “ps”
• “ps” a Postscript file is produced
• “Portrait” a Postscript file is produced with Portrait orientation
• “Landscape” a Postscript file is produced with Landscape orientation
• “eps”an Encapsulated Postscript file
• “Preview”an Encapsulated Postscript file with preview is produced
• “gif” a Graphics Interchange Format file
• “cxx” a C++ macro file is generated
• “pdf”a Portable Document Format file
• “xml” a eXtensible Mark-up Language file
• “jpg”a Joint Photographic Experts Group file
• “png” a Portable Network Graphics Format (PNG file)
• “xpm” a X11 Pixel Map Format
• “svg” a Scalable Vector Graphics file
• “tiff” a Tagged-Image File Format
• “root”a ROOT binary file is produced
You do not need to specify this second parameter; you can indicate by the filename extension what format you want to
save a canvas in (i.e. canvas.ps, canvas.gif, canvas.C, etc).
The size of the PostScript picture, by default, is computed to keep the aspect ratio of the picture on the screen, where
the size along x is always 20 cm. You can set the size of the PostScript picture before generating the picture with a
command such as:
TPostScript myps("myfile.ps",111)
myps.Range(xsize,ysize);
object->Draw();
myps.Close();
The first parameter in the TPostScript constructor is the name of the file; the second one is the format option:
• 111 - ps portrait
• 112 - ps landscape
• 113 - eps
You can set the default paper size with:
gStyle->SetPaperSize(xsize,ysize);
You can resume writing again in this file with myps.Open(). Note that you may have several Post Script files opened
simultaneously. Use TPostScript::Text(x,y,"string") to add text to a postscript file. This method writes the
string in quotes into a PostScript file at position x, y in world coordinates.

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9.10.1

Special Characters

The following characters have a special action on the PostScript file:
• ‘ - go to Greek
• ’ - go to special
• ~ - go to Zapf Dingbats
• ? - go to subscript
• ˆ - go to superscript
• ! - go to normal level of script
• & - backspace one character
• # - end of Greek or end of ZapfDingbats
These special characters are printed as such on the screen. To generate one of these characters on the PostScript file,
you must escape it with the escape character “@”. The use of these special characters is illustrated in several scripts
referenced by the TPostScript constructor.

9.10.2

Writing Several Canvases to the Same PostScript File

The following sequence writes the canvas to “c1.ps” and closes the postscript file:
TCanvas c1("c1");
h1.Draw();
c1.Print("c1.ps");
If the Postscript file name finishes with “(”, the file remains opened (it is not closed). If the Postscript file name
finishes with “)” and the file has been opened with “(”, the file is closed.
{

}

TCanvas c1("c1");
h1.Draw();
c1.Print("c1.ps("); // write canvas and keep the ps file open
h2.Draw();
c1.Print("c1.ps"); // canvas is added to "c1.ps"
h3.Draw();
c1.Print("c1.ps)"); // canvas is added to "c1.ps"
// and ps file is closed

The TCanvas::Print("file.ps(") mechanism is very useful, but it can be a little inconvenient to have the action of
opening/closing a file being atomic with printing a page. Particularly if pages are being generated in some loop, one
needs to detect the special cases of first and last page. The “[” and “]” can be used instead of “(” and “)” as shown in
the next example.
c1.Print("file.ps[");
// no actual print; just open file.ps
for (i=0; i<10; ++i) {
// fill canvas for context i
...
c1.Print("file.ps");
// actually print canvas to file.ps
} // end loop
c1.Print("file.ps]");
// no actual print; just close file.ps
The following script illustrates how to open a postscript file and draw several pictures. The generation of a new
postscript page is automatic when TCanvas::Clear is called by object->Draw().

9.10. THE POSTSCRIPT INTERFACE
{

223

TFile f("hsimple.root");
TCanvas c1("c1","canvas",800,600);
//select PostScript output type
Int_t type = 111;
//portrait ps
// Int_t type = 112;
//landscape ps
// Int_t type = 113;
//eps
//create a PostScript file and set the paper size
TPostScript ps("test.ps",type);
ps.Range(16,24);
//set x,y of printed page

}

//draw 3 histograms from file hsimple.root on separate pages
hpx->Draw();
c1.Update();
//force drawing in a script
hprof->Draw();
c1.Update();
hpx->Draw("lego1");
c1.Update();
ps.Close();

The next example does the same:
{

TFile f("hsimple.root");
TCanvas c1("c1","canvas",800,600);
//set x,y of printed page
gStyle->SetPaperSize(16,24);

}

//draw 3 histograms from file hsimple.root on separate pages
hpx->Draw();
c1->Print("test1.ps(", "Portrait");
hprof->Draw();
c1->Print("test1.ps");
hpx->Draw("lego1");
c1->Print("test1.ps)");

This following example shows two pages. The canvas is divided. TPostScript::NewPage must be called before starting
a new picture. object->Draw does not clear the canvas in this case because we clear only the pads and not the main
canvas. Note that c1->Update must be called at the end of the first picture.
{

TFile *f1 = new TFile("hsimple.root");
TCanvas *c1 = new TCanvas("c1");
TPostScript *ps = new TPostScript("file.ps",112);
// picture 1
c1->Divide(2,1);
ps->NewPage();
c1->cd(1);
hpx->Draw();
c1->cd(2);
hprof->Draw();
// picture 2
c1->Update();
ps->NewPage();
c1->cd(1);

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CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE
hpxpy->Draw();
c1->cd(2);
ntuple->Draw("px");
c1->Update();
ps->Close();

}

// invoke PostScript viewer
gSystem->Exec("gs file.ps");

The next one does the same:
{

TFile *f1 = new TFile("hsimple.root");
TCanvas *c1 = new TCanvas("c1");
c1->Divide(2,1);
// picture 1
c1->cd(1);
hpx->Draw();
c1->cd(2);
hprof->Draw();
c1->Print("test2.ps(", "Landscape");

}

// picture 2
c1->cd(1);
hpxpy->Draw();
c1->cd(2);
ntuple->Draw("px");
c1->Print("test2.ps)");
gSystem->Exec("gs file.ps");

9.10.3

// invoke PostScript

viewer

The Color Models

TPostScript (and TPDF) support two color models: RGB and CMYK. CMY and CMYK models are subtractive color
models unlike RGB which is an additive. They are mainly used for printing purposes. CMY means Cyan Magenta
Yellow to convert RGB to CMY it is enough to do: C=1-R, M=1-G and Y=1-B. CMYK has one more component K
(black). The conversion from RGB to CMYK is:
Double_t
Double_t
Double_t
Double_t

Black
Cyan
Magenta
Yellow

=
=
=
=

TMath::Min(TMath::Min(1-Red,1-Green),1-Blue);
(1-Red-Black)/(1-Black);
(1-Green-Black)/(1-Black);
(1-Blue-Black)/(1-Black);

CMYK add the black component which allows to have a better quality for black printing. TPostScript (and TPDF)
support the CMYK model. To change the color model use:
gStyle->SetColorModelPS(c);
• c = 0 means TPostScript will use RGB color model (default)
• c = 1 means TPostScript will use CMYK color model

9.11

The PDF Interface

Like PostScript, PDF is a vector graphics output format allowing a very high graphics output quality. The functionnalities
provided by this class are very similar to those provided by TPostScript‘.
Compare to PostScript output, the PDF files are usually smaller because some parts of them can be compressed.
PDF also allows to define table of contents. This facility can be used in ROOT. The following example shows how to
proceed:

9.12. CREATE OR MODIFY A STYLE
{

}

225

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");

Each character string following the keyword “Title:” makes a new entry in the table of contents.

9.12

Create or Modify a Style

All objects that can be drawn in a pad inherit from one or more attribute classes like TAttLine, TAttFill, TAttText,
TAttMarker. When objects are created, their default attributes are taken from the current style. The current style
is an object of the class TStyle and can be referenced via the global variable gStyle (in TStyle.h). See the class
TStyle for a complete list of the attributes that can be set in one style.
ROOT provides several styles called:
• “Default” - the default style
• “Plain” - the simple style (black and white)
• “Bold” - bolder lines
• “Video” - suitable for html output or screen viewing
The “Default” style is created by:
TStyle *default = new TStyle("Default","Default Style");
The “Plain” style can be used if you want to get a “conventional” PostScript output or if you are working on a
monochrome display. The following example shows how to create it.
TStyle *plain

= new TStyle("Plain",
"Plain Style(no colors/fill areas)");
plain->SetCanvasBorderMode(0);
plain->SetPadBorderMode(0);
plain->SetPadColor(0);
plain->SetCanvasColor(0);
plain->SetTitleColor(0);
plain->SetStatColor(0);
You can set the current style by:
gROOT->SetStyle(style_name);
You can get a pointer to an existing style by:

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CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE

TStyle *style = gROOT->GetStyle(style_name);
You can create additional styles by:
TStyle *st1 = new TStyle("st1","my style");
st1->Set...
st1->cd(); // this becomes now the current style gStyle
In your rootlogon.C file, you can redefine the default parameters via statements like:
gStyle->SetStatX(0.7);
gStyle->SetStatW(0.2);
gStyle->SetLabelOffset(1.2);
gStyle->SetLabelFont(72);
Note that when an object is created, its attributes are taken from the current style. For example, you may have created
a histogram in a previous session and saved it in a file. Meanwhile, if you have changed the style, the histogram will be
drawn with the old attributes. You can force the current style attributes to be set when you read an object from a file
by calling ForceStyle before reading the objects from the file.
gROOT->ForceStyle();
When you call gROOT->ForceStyle() and read an object from a ROOT file, the object’s method UseCurrentStyle
is called. The attributes saved with the object are replaced by the current style attributes. You call also call
myObject->UseCurrentStyle() directly. For example if you have a canvas or pad with your histogram or any other
object, you can force these objects to get the attributes of the current style by:
canvas->UseCurrentStyle();
The description of the style functions should be clear from the name of the TStyle setters or getters. Some functions
have an extended description, in particular:
• TStyle::SetLabelFont
• TStyle::SetLineStyleString: set the format of dashed lines.
• TStyle::SetOptStat
• TStyle::SetPalette to change the colors palette
• TStyle::SetTitleOffset
• TStyle::SetOptDate(Int_t optdate) to support several date formats. If optdate is non-null, the current
date/time will be printed in the canvas. The position of the date string can be controlled by: optdate =
10*format+mode
• mode = 1 the date is printed in the bottom/left corner
• mode = 2 date is printed in the bottom/right corner
• mode = 3 date is printed in the top/right corner
• format = 0 (default) date format is like: “Wed Sep 25 17:10:35 2002”
• format = 1 date format is: “2002-09-25”
• format = 2 date format is: “2002-09-25 17:10:35”

9.13. 3D VIEWERS

9.13

227

3D Viewers

ROOT provides several viewers capable of displaying 3D content:
• the Pad - simple line drawing using TPad and associated projection class TView;
• GL Viewer - high quality and performance viewer(See “The GL Viewer”);
• X3D viewer - simple legacy viewer (See “The X3D Viewer”);
• GL-in-pad - combination of basic GL viewer in TPad, with no hardware acceleration.
The X3D and GL viewers are created as external windows, associated with a pad, and displaying the same content
as it. Only these external viewers are detailed here - for Pad (TPad, TView classes) you should refer to “Graphical
Containers: Canvas and Pad” and the class definitions.
All viewers use a common architecture to publish 3D objects to the viewer - described in “Common 3D Viewer
Architecture” below. In most cases, you will not need to use this, working instead with a package, such as the “The
Geometry Package”, which provides comprehensive, high level functionality to create and place objects into complex
3D scenes, and uses the viewer architecture internally to show the result in your chosen viewer.

9.13.1

Invoking a 3D viewer

A 3D viewer can be created in a script by passing the appropriate option to Draw()when attaching the drawn object(s)
to a pad. For a fuller explanation of pads, attaching objects with Draw() etc. refer to “Graphical Containers: Canvas
and Pad”.
root[] myShapes->Draw("ogl");
Valid option strings are:
• “ogl” : external GL viewer
• “x3d”: external X3D viewer
• “pad”: pad viewer
If no option is passed to Draw() then the “pad” is used by default. If you already have content in a pad, which you
would like to display in one of the external viewers you can select from the canvas View menu / View With, and pick
the viewer type.

Figure 9.34: Invoking external 3D viewers from canvas menus
Note: A current limitation means that when an external viewer is created the pad is no longer redrawn. When the
external viewer is closed, clicking in the pad will refresh.

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CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE

The GL Viewer

The GL Viewer uses (or compliant libraries such as ) to generate high quality, high-performance 3D renderings, with
sophisticated lighting, materials and rendering styles for 3D scenes. Many users will be able to take advantage of
hardware acceleration of the underlying OpenGL commands by their computer’s video card, resulting is considerable
performance gains - up to interactive manipulation of 1000’s of complex shapes in real-time.
The GL Viewer is supported on all official ROOT platforms (assuming you have suitable libraries), and is the main 3D
viewer, which development effort is concentrated upon. As OpenGL® is a trademark we refer to our viewer built on
this technology as the ‘GL Viewer’. The code for it can be found under $ROOTSYS/gl.

Figure 9.35: The GL 3D Viewer
You can manipulate the viewer via the GUI or via the base TGLViewer object behind the interface. These are detailed
below - see also $ROOTSYS/tutorials/gl/glViewerExercise.C.
9.13.2.1

Projections Modes (Cameras)

The GL Viewer supports two basic types of camera, which affect how the 3D world is projected onto the 2D render
area:
• Perspective: Objects are drawn with characteristic ‘foreshortening’ effect, where distant objects appear smaller
than near ones. This is useful for obtaining a ‘real world’ views. The degree of foreshortening is affected by the
current camera field of view (focal length of its ‘lens’) - see “Adjusting Cameras”.
• Orthographic: Distance from camera does not affect object size. These projections are useful for measurement or
checking alignments, as the sizes and angles between objects are preserved.
You can select the active camera from the viewer’s Camera menu on the top menu bar. There are three perspective
camera choices:
• Perspective (Floor XOZ) Default
• Perspective (Floor YOZ)

9.13. 3D VIEWERS

229

• Perspective (Floor XOY)
In each case the perspective camera is constrained to keep the chosen floor plane, defined by a pair of world axes,
appearing level at all times - i.e. there is no banking of the ‘horizon’ that you experience when a plane rolls. There are
also three orthographic camera choices:
• Orthographic (XOY)
• Orthographic (XOZ)
• Orthographic (ZOY)
Orthographic projections are generally constrained to look down one of the global axes of the world, with the other two
axes lying horizontal/vertical on the viewer window. Therefore, XOY has the X-axis horizontal, the Y-axis vertical.
You can always confirm the orientation and constraints of the camera in the world by enabling axis drawing in the
“Guides” tab - see sections “Guides” and “Clipping” below. For orthographic camera a ruler-depicting current scene
units is also available.
You can also pick the current camera by obtaining a handle to the GL Viewer object behind the interface:
TGLViewer * v = (TGLViewer *)gPad->GetViewer3D();
calling the method TGLViewer::SetCurrentCamera with one of the TGLViewer::ECameraType types:
v->SetCurrentCamera(TGLViewer::kCameraPerspXOZ);
See also $ROOTSYS/tutorials/gl/glViewerExercise.C.
9.13.2.2

Adjusting Cameras

The interactions with the camera are summarized above. In each case the interaction is listed, along with description
and user actions required to achieve it. For all cameras you can reset the original default view, framing the entire
scene, by double clicking any mouse button.

Figure 9.36: GL Viewer camera interactions
For the Zoom interaction you can use the following modifiers combinations to adjust the sensitivity:

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• Shiftx 10
• Ctrlx 0.1
• Shift + Ctrlx 0.01
The modifiers must be applied after the zoom action has started (right mouse button is down).
Note for orthographic cameras:
• There is no field of view of view/focal length - dollying and zooming producing an identical scaling action.
• There is a fixed eye direction - so the ‘Orbit’ action is disabled.
Note for perspective cameras:
• Dollying (moving the camera backwards/forwards) and zooming are often confused, and may appear very similar.
• When you dolly the camera the lens focal length does not change, hence the distortions associated with the
projections are unaffected. However the movement can result in objects coming ‘through the front’ of the camera
and disappearing.
• When you zoom, the camera does not move - hence clipping of near objects is unaffected. However with extremely
small zooms (FOV large/focal length short) noticeable distortions, causing straight lines to become curved, can
be seen with objects near the camera - the ‘fisheye’ lens effect.
• Generally dollying is more ‘natural’, but you may need to use both to achieve the desired perspective and eye
position - particularly when you are working inside or very close to 3D objects.
Configure the camera by calling the methods SetPerspectiveCamera() or SetOrthographicCamera() of TGLViewer:
TGLViewer * v = (TGLViewer *)gPad->GetViewer3D();
v->SetOrthoCamera(TGLViewer::kCameraOrthoXOY,
left,right,top,bottom);
...
v->SetPerspectiveCamera (camera,fov,dolly,center,hRotate,vRotate);
Note - you can configure any of the six cameras in the viewer at any time, but you will not see the result until the
camera is made current.
9.13.2.3

Draw Styles

The GL Viewer supports three different rendering modes, which are applied to all the objects in your scene, but not
Clip Shapes and Guides (See “Clipping” and “Manipulators”). These are shown below, along with the key used to
activate the style.

Figure 9.37: GL Viewer draw styles
Filled Polygons Wireframe Outline Enable with ‘r’ key Enable with ‘w’ key Enable with ‘t’ key Solid polygons,
with hidden surface Object edges in color, with Combination of Filled Polygons removal, color surface materials, no
surface filling/hiding. and Outline styles. Solid opacity, specular reflection etc. shapes with edges. Black background.
Black background. White background.
Call method TGLViewer::SetStyle with one of TGLRnrCtx::EDrawStyleflags kFill, kOutline, kWireFrame:
v->SetStyle(TGLRnrCtx::kFill);

9.13. 3D VIEWERS
9.13.2.4

231

Lighting / Style

The GL viewer creates five diffuse lights (left, right, top, bottom, and front) arranged around the 3D scene. These
lights are carried with the camera - that is they are always in same position relative to your eye - the left light always
shines from the left.
Light controls are located: Viewer Controls Pane ‘Style’.
Each light has a checkbox to enable/disable it. Set lights on/off with TGLLightSet::SetLight e.g.
v->GetLightSet()->SetLight(TGLLightSet::kLightBottom, kFALSE);
9.13.2.5

Clipping

The GL viewer supports interactive clipping, enabling you to remove sections of your 3D scene and the shapes, revealing
internal details.

Figure 9.38: GL Viewer interactive box clipping
The controls for clipping can be found under: Viewer Controls Pane ‘Clipping’ tab.
Two clipping ‘shapes’ are currently supported:
• Single plane
• Box
Pick the type from the radio buttons - only one (or none) may be active at one time.
The clip object can be adjusted by:
• Adjusting the values in the properties panel GUI
• Directly manipulating the clip object in the viewer

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To show and/or directly manipulate the object check the ‘Show / Edit in Viewer’ checkbox. The clip object is drawn in
semi-transparent light brown. The current manipulator is attached to it, allowing you direct control over its position,
scale and rotation. See “Manipulators” section below for details on using viewer manipulators.
The clip plane is described by the standard plane equation: ax+by+cz+d=0, where the factors a, b, c, d are entered
into the edit boxes, and applied using the ‘Apply’ button.
The clip box is described by its center position, entered in the ‘Center X’, ‘Center Y’ and ‘Center Z’ edit boxes, and its
lengths (extents) entered in the ‘Length X’, ‘Length Y’ and ‘Length Z’ edit boxes.
This clipping is achieved using OpenGL clip plane support; as such, there are certain limitations:
• Solid shapes are not capped - they appear hollow.
• Only shapes, which can be described with combination of planes, can be rendered in this fashion - e.g. a clipping
tube is not possible.
• Each additional clipping plane requires an additional render pass - so the more active planes the more time the
render will take.
Set the current clip object with TGLClipSet::SetClipType
v->GetClipSet()->SetClipType(TGLClipSet::kClipPlane);
Configure the clip object with TGLClipSet::SetClipState
Double_t planeEq[4] = {0.5,1.0,-1.0, 2.0};
v->GetClipSet()->SetClipState(TGLClipSet::kClipPlane, planeEq);
As with cameras, any clip can be configured at any time, but you must set the clip current to see the effect.
9.13.2.6

Manipulators

Manipulators are GUI ‘widgets’ or controls attached to a 3D object in the viewer, allowing a direct manipulation of
the object’s geometry. There are three manipulators for the three basic geometries transformations. In each case, the
manipulator consists of three components, one for each local axis of the object, shown in standard colors: red (X),
green (Y) and blue (Z).
Activate the manipulator by moving the mouse over one of these components (which turns yellow to indicate active
state). Click with left mouse and drag this active component to perform the manipulation. Toggle between the
manipulator types using the ‘x’, ‘c’, ‘v’ keys while the mouse cursoris above the manipulator. Note: Manipulators
cannot be controlled via the API at present.
9.13.2.7

Guides

Guides are visual aids drawn into the viewer world. Controls for these are under the “Guides” tab:
Viewer Controls Pane Guides Tab
Axes show the world (global) frame coordinatedirections: X (red), Y (green) and Z (blue). The negative portion of the
axis line is shown in dark color, the positive in bright. The axis name and minimum / maximum values are labeled in
the same color. There are three options for axes drawing - selected by radio buttons:
• None - not drawn (default).
• Edge - draw axes on the (minimum) edge of the scene extents box.
• Origin - drawn axes through the origin.
For edge axes, the zero value for each axis is marked on the axis line with a colored sphere. For origin axes, a single
white sphere is shown at the origin.
Edge axes are depth clipped - i.e. are obscured by 3D objects in front of them. Origin axes (which generally pass
through the middle of the 3D scene) are not depth clipped - so always visible.

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233

Figure 9.39: GL Viewer object manipulators

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A single orange sphere of fixed view port (window) size can be shown at any arbitrary position. Enable / disable the
drawing with ‘Show’ checkbox. Enter X/Y/Z position in the edit boxes to set position. Initial position is at the center
of the scene.
Set the guides using TGLViewer::SetGuideState e.g. to enable edge axes, and enable a reference marker at world
position 50, 60, 100:
Double_t refPos[3] = {50.0,60.0,100.0};
v->SetGuideState(TGLUtil::kAxesEdge, kTRUE, refPos);
9.13.2.8

Selecting Scene Shapes

You can select a single shape from your scene by pressing ‘Shift’ key, pointing and left clicking anywhere on the shape
in the viewer. Selection is currently shown by drawing the shape-bounding box (not depth clipped) in white (polygon
or wire frame render styles) or red (outline render style). Manipulators supported by the shape are drawn in red, green
and blue while the non-supported ones are drawn in grey. To deselect a shape, either select another, or shift/click
anywhere on the background (empty space) in the viewer. You cannot select Manipulators or Guides (Axes / Reference
Marker).
9.13.2.9

Editing Shapes

When a shape is selected, the viewer’s control pane shows the user interface that allows you to review and adjust the
color and geometry properties of the shape.
Note: At present modifications to the shapes are local to the viewer - they are not propagated back to external
objects/client that published to the viewer. The changes are preserved only until the viewer is closed. In some cases,
this will never be feasible as there is not a one-to-one correspondence between a shape in the viewer and a single
external object in which the modification could be stored.
9.13.2.10

Colors / Style

Viewer Controls Pane ‘Style’ tab.
A full description of OpenGL materials, colors and lighting is beyond the scope of this document. You should refer to
the OpenGL programming manual (Red Book) for a full discussion. In most cases adjustment of the Diffuse color
material + Opacity/Shine properties is sufficient to achieve desired results.
A shape has four-color materials (components):
• Diffuse
• Ambient
• Specular
• Emissive
For each of these you can select the component via the radio buttons. Each component can have the red, green and
blue values for the component adjusted via the sliders. You can apply this adjustment to the shape itself, or to all
shapes sharing a common ‘family’. Shapes of the same family have external objects with the same TObject name string.
You can also adjust the ‘Opacity’ and ‘Shine’ for the shapes materials via the sliders.
9.13.2.11

Geometry

Viewer Controls Pane ‘Geometry’ tab.
Review and modify the shapes X/Y/Z center and scaling factors via the edit boxes. Selection and editing of shapes is
not available via the API at present.
9.13.2.12

Outputting Viewer Contents

The current viewer rendering can be output to an external EPS or PDF, using the options under the ‘File’ menu on the
top menu bar. The file is named ‘viewer.eps’ or ‘viewer.pdf’ and written to the current ROOT directory.

9.13. 3D VIEWERS

9.13.3

235

The X3D Viewer

The X3D viewer is a fairly simple and limited viewer, capable of showing basic lines and polygons. It lacks the quality,
performance and more advanced features of the GL Viewer, and additionally is not supported on Windows. It is not
actively developed and you are encouraged to use the GL Viewer out of preference. The below table presents the main
interactions - these are repeated in the Help dialog of the viewer.
Action KeyActionKey
Wireframe Mode wRotate about xx a
Hidden Line Mode eRotate about yy b
Hidden Surface Mode rRotate about zz c
Move object down uAuto-rotate about x1 2 3
Move object up iAuto-rotate about y4 5 6
Move object left lAuto-rotate about z7 8 9
Move object right hToggle controls styleo
Move object forward jToggle stereo displays
Move object backward kToggle blue stereo viewd
Adjust focus (stereo mode) [ ] { }Toggle double bufferf
Rotate object Left mouse button down + move.

9.13.4

Common 3D Viewer Architecture

The 3D Viewer Architecture provides a common mechanism for viewer clients to publish 3D objects to it. It enables:
• Decoupling of producers (geometry packages etc) who model collection of 3D objects from consumers (viewers)
which display them.
• Producer code free of explicit drawing commands & viewer specific branching.
• Support differing viewers and clients capabilities, e.g.
• Mix of native (in viewer) shapes and generic client side tessellation.
• Local/global frame object description
• Bounding boxes
• Placing copies sharing common geometry (logical/physical shapes).
The architecture consists of:
• TVirtualViewer3D interface: An abstract handle to the viewer, allowing client to add objects, test preferences
etc.
• TBuffer3D class hierarchy: Used to describe 3D objects (“shapes”) - filled /added by negotiation with viewer via
TVirtualViewer3D.
A typical interaction between viewer and client using these, taken from TGeoPainter is:
TVirtualViewer3D * viewer = gPad->GetViewer3D();
// Does viewer prefer local frame positions?
Bool_t localFrame = viewer->PreferLocalFrame();
// Perform first fetch of buffer from the shape and try adding it to the viewer
const TBuffer3D &buffer = shape.GetBuffer3D(TBuffer3D::kCore |
TBuffer3D::kBoundingBox |
TBuffer3D::kShapeSpecific,
localFrame);
Int_t reqSections = viewer->AddObject(buffer, &addDaughters);

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// If the viewer requires additional sections fetch from the shape
// (if possible) and add again
if (reqSections != TBuffer3D::kNone)
shape.GetBuffer3D(reqSections, localFrame);
Together these allow clients to publish objects to any one of the 3D viewers free of viewer specific drawing code. They
allow our simple x3d viewer, and considerably more sophisticated OpenGL one to both work with both geometry
libraries (g3d and geom) efficiently.
In addition to external viewers, created in separate windows, this architecture is also used by internal TPad drawing
when it requires 3D projections. Publishing to a viewer consists of the following steps:
1- Create / obtain viewer handle.
2- Begin scene on viewer.
3- Fill mandatory parts of TBuffer3D describing object.
4- Add to viewer.
5- Fill optional parts of TBuffer3D as requested by viewer.
[ . . . . repeat 3/4/5 as required for other/child objects]
6- End scene on viewer.
You should attach the top-level node of your external geometry (or the manager) to a TPad object using
TObject::Draw(), and perform the publishing to the viewer in your object’s TObject::Paint() overloaded method. See “Scene Rebuilds”, and example scripts, for more details.
9.13.4.1

Creating / Obtaining Viewer Handle

External viewers are bound to a TPad object (this may be removed as a requirement in the future). You can create or
obtain the current viewer handle via the method:
TVirtualViewer3D * v = gPad->GetViewer3D("type");
Here the “type” string defines the viewer type - currently one of:
• “ogl” : External GL viewer
• “x3d”: External X3D viewer
• “pad”: Pad viewer
If no type is passed (null string), and there is no current viewer, then the type is defaulted to “pad”. If no type is passed
and there is a current viewer, then this is returned - hence once a viewer is created it can be obtained elsewhere by:
TVirtualViewer3D * v = gPad->GetViewer3D();
9.13.4.2

Opening / Closing Scenes

Objects must be added to viewer between BeginScene() and EndScene() calls e.g.
viewer->BeginScene();
// Add objects
viewer ->EndScene();
These calls enable the viewer to suspend redraws, and perform internal caching/setup. If the object you attach to the
pad derives from TAtt3D, then the pad will take responsibility for calling BeginScene() and EndScene() for you. You
can always test if the scene is already open for object addition with:
viewer->BuildingScene();
Note: the x3d viewer does not support rebuilding of scenes - objects added after the first Open/Close Scene pair will
be ignored.

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237

Figure 9.40: Overview of 3D viewer architecture
9.13.4.3

Describing Objects - Filling TBuffer3D

The viewers behind the TVirtualViewer3D interface differ greatly in their capabilities e.g.
• Some support native shape (e.g. spheres/tubes in OpenGL) and can draw these based on an abstract description.
Others always require a tessellation description based on TBuffer3D’s kRaw / kRawSizes points/lines/segments
sections.
• Some need the 3D object positions in the master (world) frame, others can cope with local frames and a translation
matrix to place the object.
• Some require bounding boxes for objects - others do not.
Similarly some viewer clients are only capable of providing positions in master frame, cannot provide bounding boxes
etc. Additionally we do not want to incur the cost of expensive tessellation operations if the viewer does not require
them. To cope with these variations the TBuffer3D objects are filled by negotiation with the viewer.
TBuffer3D classes are conceptually divided into enumerated sections: kCore, kBoundingBox, kRaw - see the class
diagram and the file TBuffer3D.h for more details. The TBuffer3D methods SectionsValid(), SetSectionsValid(),
ClearSectionsValid() are used to test, set, clear these section validity flags e.g.
buffer.SetSectionsValid(TBuffer3D::kShapeSpecific);
...
if (buffer.SectionsValid(TBuffer3D:: kShapeSpecific)) {
...
}
The sections found in the base TBuffer3D (kCore/kBoundingBox/kRawSizes/kRaw) are sufficient to describe any
tessellated shape in a generic fashion. An additional kShapeSpecific section is added in TBuffer3D derived classes,
allowing a more abstract shape description (“a sphere of inner radius x, outer radius y”). This enables a viewer, which
knows how to draw (tessellate) the shape itself to do so, while providing a generic fallback suitable for all viewers. The
rules for client negotiation with the viewer are:

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Figure 9.41: TBuffer3D class hierarchy

9.13. 3D VIEWERS

239

• If suitable specialized TBuffer3D class exists, use it, otherwise use TBuffer3D.
• Complete the mandatory kCore section.
• Complete the kShapeSpecific section if applicable.
• Complete the kBoundingBox if you can.
• Pass this buffer to the viewer using one of the TBuffer3D::AddObject() methods.
If the viewer requires more sections to be completed (kRaw/kRawSizes) TBuffer3D::AddObject() will return flags
indicating which ones, otherwise it returns kNone. If requested, you must fill the buffer, mark these sections valid, and
call TBuffer3D::AddObject again, to complete adding the object. For example, in out TGeo geometry package, in
TGeoPainter::PaintShape, we perform the negotiation with viewer:
TVirtualViewer3D * viewer = gPad->GetViewer3D();
if (shape.IsA() != TGeoCompositeShape::Class()) {
// Does viewer prefer local frame positions?
Bool_t localFrame = viewer->PreferLocalFrame();
// Perform first fetch of buffer from the shape and adding
// it to the viewer
const TBuffer3D &buffer = shape.GetBuffer3D(TBuffer3D::kCore |
TBuffer3D::kBoundingBox |
TBuffer3D::kShapeSpecific, localFrame);
Int_t reqSections = viewer->AddObject(buffer, &addDaughters);
// If the viewer requires additional sections fetch from the
// shape (if possible) and add again
if (reqSections != TBuffer3D::kNone) {
shape.GetBuffer3D(reqSections, localFrame);
viewer->AddObject(buffer, &addDaughters);
}
}
The buffer is supplied/filled by the appropriate TShape::GetBuffer3D() and TShape::FillBuffer3D overloads
e.g. for a sphere in TGeoSphere.
const TBuffer3D &TGeoSphere::GetBuffer3D(Int_t reqSections,
Bool_t localFrame) const {
// Fills a static 3D buffer and returns a reference.
static TBuffer3DSphere buffer;
// Filling of kBoundingBox is defered to TGeoBBox, and
// kCore on up to TGeoShape
TGeoBBox::FillBuffer3D(buffer, reqSections, localFrame);
// Complete kShapeSpecific section for sphere
if (reqSections & TBuffer3D::kShapeSpecific) {
buffer.fRadiusInner = fRmin;
buffer.fRadiusOuter = fRmax;
...
buffer.SetSectionsValid(TBuffer3D::kShapeSpecific);
}
// Complete kRawSizes section
if (reqSections & TBuffer3D::kRawSizes) {
...
buffer.SetSectionsValid(TBuffer3D::kRawSizes);
}
}
// Complete kRaw tesselation section
if ((reqSections & TBuffer3D::kRaw) &&
buffer.SectionsValid(TBuffer3D::kRawSizes)) {
SetPoints(buffer.fPnts);
// Transform points to master frame if viewer requires it
// The fLocalFrame flag and translation matrix will have
// already been set in TGeoShape::FillBuffer3D() as required

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if (!buffer.fLocalFrame)
TransformPoints(buffer.fPnts, buffer.NbPnts());
SetSegsAndPols(buffer);
buffer.SetSectionsValid(TBuffer3D::kRaw);

}

}
return buffer;

Note:
• we use a static TBuffer3D derived object for efficiency - once the object is added the buffer can be reused.
• kRawSize (the calculation of tessellation sizing required in buffer) and kRaw (the actual filling of tessellation) is
split, as the X3D viewer requires two publication passes - one to establish the full tessellation capacity for all
shapes, and another to actually add them. Splitting avoids having to do the expensive tessellation on the first
pass.
9.13.4.4

Shape Specific TBuffer3D Derived Classes

Currently we provide the following shape specific classes, which the GL Viewer can take advantage of (see TBuffer3D.h
and TBuffer3DTypes.h)
• TBuffer3DSphere - solid, hollow and cut spheres (GL Viewer only supports solid spheres at present - cut / hollow
ones will be requested as tessellated objects by client.)
• TBuffer3DTube - basic tube with inner/outer radius and length.
• TBuffer3DTubeSeg - angle tube segment.
• TBuffer3DCutTube - angle tube segment with plane cut ends.
See the above example from TGeoSphere::GetBuffer3D and also equivalent functions in TGeoTube, TGeoTubeSeg and
TGeoCtub. Anyone is free to add new TBuffer3D classes, but it should be clear that one or more viewers will require
updating to be able to take advantage of them. Hence we only provide classes which existing viewers can benefit from.
The number of native shapes in GL Viewer will be expanded in the future.
9.13.4.5

Master / Local Reference Frames

The Core section of TBuffer3D contains two members relating to reference frames:
• fLocalFrame: indicates if any positions in the buffer (bounding box and tessellation vertexes) are in local or
master (world frame).
• fLocalMaster: is a standard 4x4 translation matrix (OpenGL column major ordering) for placing the object
into the 3D master frame.
If fLocalFrame is false, fLocalMaster should contain an identity matrix. This is set by default, and can be reset
using the TBuffer3D::SetLocalMasterIdentity() method.
9.13.4.6

Bounding Boxes

You are not obliged to complete the kBoundingBox section, as any viewer requiring one internally (GL Viewer) will
build it if you do not provide. However to do this the viewer will force you to provide the (expensive) raw tessellation,
and the resulting box will be axis aligned with the overall scene, which is non-ideal for rotated shapes. As we need
to support orientated (rotated) bounding boxes, TBuffer3D requires the 6 vertices of the box. We also provide a
convenience function, TBuffer::SetAABoundingBox(), for simpler case of setting an axis aligned bounding box. The
bounding box should be filled in same frame (local / master) as the rest of the TBuffer3D, and inaccordance with
fLocalFrame flag.
A typical example from TGeoBBox::FillBuffer3D:

9.13. 3D VIEWERS

241

if (reqSections & TBuffer3D::kBoundingBox) {
Double_t halfLengths[3] = { fDX, fDY, fDZ };
buffer.SetAABoundingBox(fOrigin, halfLengths);
if (!buffer.fLocalFrame) {
TransformPoints(buffer.fBBVertex[0], 8);
}
buffer.SetSectionsValid(TBuffer3D::kBoundingBox);
}
9.13.4.7

Logical and Physical Objects

Some viewers can support two types of object placement:
• Add object as a single independent entity in the world reference frame - e.g. a sphere, radius r, at x, y, z.
• Repeated placement (copying) in world frame of this locally unique piece of geometry (described in local reference
frame) e.g. define a sphere S (radius r), place copy at x1, y1, z1, another copy at x2, y2, z2 etc.
The second case is very typical in geometry packages, e.g. ROOT’s TGeo package, GEANT4 etc, where we have very
large number repeated placements of relatively few unique “shapes”.
Some viewers (GL Viewer only at present) are able to take advantage of this by identifying unique logical shapes from
the fID logical ID member of TBuffer3D. If repeated addition of the same fID is found, the shape is cached already and the costly tessellation does not need to be sent again. The viewer can also perform internal GL specific caching
(display lists) with considerable performance gains in these cases. For this to work correctly the logical object in must
be described in TBuffer3D in the local reference frame, complete with the local/master translation. In some cases you
will not have a real object you can reasonably set TBuffer3D::fID to, or the object is recycled or temporary.
To suppress internal caching in the GL Viewer in these cases, set TBuffer3D::fID to 0 (null).
The viewer indicates it can support local frame objects through the TVirtualViewer3D interface method:
PreferLocalFrame(). If this returns kTRUE you can make repeated calls to AddObject(), with TBuffer3D containing
the same fID, and different fLocalMaster placements.
For viewers supporting logical/physical objects, the TBuffer3D content refers to the properties of the logical object,
with the exception of:
• fLocalMaster transform
• fColor
• fTransparency
attributes, which can be varied for each physical object.
As a minimum requirement all clients must be capable of filling the raw tessellation of the object buffer, in the
master reference frame. Conversely viewers must always be capable of displaying the object described by this buffer. If
either does not meet this requirement the object may not be displayed.
9.13.4.8

Scene Rebuilds

TBuffer3D::AddObject is not an explicit command to the viewer - it may for various reasons decide to ignore it:
• It already has the object internally cached.
• The object falls outside some ‘interest’ limits of the viewer camera.
• The object is too small to be worth drawing.
In all these cases TBuffer3D::AddObject() returns kNone, as it does for successful addition, indicating it does not
require further information about this object. Hence you should not try to make any assumptions about what the
viewer did with the object. The viewer may decide to force the client to rebuild (republish) the scene, obtaining a
different collection of objects, if the internal viewer state changes .e.g. significant camera move. It does this presently
by forcing a repaint on the attached TPad object - hence you should attach you master geometry object to the pad (via
TObject::Draw()), and perform the publishing to the viewer in response to TObject::Paint().

242
9.13.4.9

CHAPTER 9. GRAPHICS AND THE GRAPHICAL USER INTERFACE
Physical IDs

TVirtualViewer3D provides for two methods of object addition:
virtual Int_t AddObject(const TBuffer3D &buffer,
Bool_t * addChildren = 0)
virtual Int_t AddObject(UInt_t physicalID,
const TBuffer3D & buffer,
Bool_t *addChildren = 0)
If you use the first (simple) case a viewer using logical/physical pairs will generate sequential IDs for each physical
object internally. Scene rebuilds will require destruction and recreation of all physical objects. For the second you
can specify an identifier from the client side, which must be unique and stable - i.e. the IDs of a published object is
consistent, regardless of changes in termination of contained child geometry branches. In this case the viewer can safely
cache the physical objects across scene rebuilds, discarding those no longer of interest.
9.13.4.10

Child Objects

In many geometries there is a rigid containment hierarchy, and so if the viewer is not interested in a certain object due
to limits/size then it will also not be interest in any of the contained branch of siblings. Both TBuffer3D::AddObject()
methods have an addChildren return parameter. The viewer will complete this (if passed) indicating if children of the
object just sent are worth sending.
9.13.4.11

Recycling TBuffer3D

Once add TBuffer3D::AddObject() has been called, the contents are copied to the viewer’s internal data structures.
You are free to destroy this TBuffer3D, or recycle it for the next object if suitable.
9.13.4.12

Examples

For an example of a simple geometry, working in master reference frame examine the code under $ROOTSYS/g3d. For
a more complex example, which works in both master and local frames, and uses logical/physical division of shape
geometry and placement, examine the code under $ROOTSYS/geom - in particular TGeoShape hierarchy, and the painter
object TGeoPainter (under geopainter) where the negotiation with the viewer is performed.

Chapter 10

Folders and Tasks
10.1

Folders

A TFolder is a collection of objects visible and expandable in the ROOT object browser. Folders have a name and a
title and are identified in the folder hierarchy by an “UNIX-like” naming convention. The base of all folders is //root.
It is visible at the top of the left panel in the browser. The browser shows several folders under //root.
New folders can be added and removed to/from a folder.

10.2

Why Use Folders?

One reason to use folders is to reduce class dependencies and improve modularity. Each set of data has a producer
class and one or many consumer classes. When using folders, the producer class places a pointer to the data into a
folder, and the consumer class retrieves a reference to the folder.
The consumer can access the objects in a folder by specifying the path name of the folder.
Here is an example of a folder’s path name:
//root/Event/Hits/TCP
One does not have to specify the full path name. If the partial path name is unique, it will find it; otherwise it will
return the first occurrence of the path.
The first diagram shows a system without folders. The objects have pointers to each other to access each other’s data.
Pointers are an efficient way to share data between classes. However, a direct pointer creates a direct coupling between
classes. This design can become a very tangled web of dependencies in a system with a large number of classes.
In the second diagram, a reference to the data is in the folder and the consumers refer to the folder rather than
each other to access the data. The naming and search service provided by the ROOT folders hierarchy provides an
alternative. It loosely couples the classes and greatly enhances I/O operations. In this way, folders separate the data
from the algorithms and greatly improve the modularity of an application by minimizing the class dependencies.
In addition, the folder hierarchy creates a picture of the data organization. This is useful when discussing data design
issues or when learning the data organization. The example below illustrates this point.

10.3

How to Use Folders

Using folders means to build a hierarchy of folders, posting the reference to the data in the folder by the producer, and
creating a reference to the folder by the user.

10.3.1

Creating a Folder Hierarchy

To create a folder hierarchy you add the top folder of your hierarchy to //root. Then you add a folder to an existing
folder with the TFolder::AddFolder method. This method takes two parameters: the name and title of the folder to
be added. It returns a pointer of the newly created folder.
The code below creates the folder hierarchy shown in the browser. In this macro, the folder is also added to the list of
browsable. This way, it is visible in the browser on the top level.
243

244

CHAPTER 10. FOLDERS AND TASKS

10.3. HOW TO USE FOLDERS

{

245

// Add the top folder of my hierary to //root
TFolder *aliroot=gROOT->GetRootFolder()->AddFolder("aliroot",
"aliroot top level folders");
// Add the hierarchy to the list of browsables
gROOT->GetListOfBrowsables()->Add(aliroot,"aliroot");
// Create and add the constants folder
TFolder *constants=aliroot->AddFolder("Constants",
"Detector constants");
// Create and add the pdg folder to pdg
TFolder *pdg = constants->AddFolder("DatabasePDG","PDG database");
// Create and add the run folder
TFolder *run = aliroot->AddFolder("Run","Run dependent folders");
// Create and add the configuration folder to run
TFolder *configuration = run->AddFolder("Configuration",
"Run configuration");
// Create and add the run_mc folder
TFolder *run_mc = aliroot->AddFolder("RunMC",
"MonteCarlo run dependent folders");

}

// Create and add the configuration_mc folder to run_mc
TFolder *configuration_mc = run_mc->AddFolder("Configuration",
"MonteCarlo run configuration");

10.3.2

Posting Data to a Folder (Producer)

A TFolder can contain other folders as shown above or any TObject descendents. In general, users will not post a
single object to a folder; they will store a collection or multiple collections in a folder. For example, to add an array to
a folder:
TObjArray *array;
run_mc->Add(array);

10.3.3

Reading Data from a Folder (Consumer)

One can search for a folder or an object in a folder using the TROOT::FindObjectAny method. It analyzes the string
passed as its argument and searches in the hierarchy until it finds an object or folder matching the name. With
FindObjectAny, you can give the full path name, or the name of the folder. If only the name of the folder is given, it

246

CHAPTER 10. FOLDERS AND TASKS

10.4. TASKS

247

will return the first instance of that name. A string-based search is time consuming. If the retrieved object is used
frequently or inside a loop, you should save a pointer to the object as a class data member. Use the naming service
only in the initialization of the consumer class. When a folder is deleted, any reference to it in the parent or other
folder is deleted also.
conf=(TFolder*)gROOT->FindObjectAny("/aliroot/Run/Configuration");
// or ...
conf=(TFolder*)gROOT->FindObjectAny("Configuration");
By default, a folder does not own the object it contains. You can overwrite that with TFolder::SetOwner. Once
the folder is the owner of its contents, the contents are deleted when the folder is deleted. Some ROOT objects are
automatically added to the folder hierarchy. For example, the following folders exist on start up:
//root/ROOT Files with the list of open Root files
//root/Classes with the list of active classes
//root/Geometries with active geometries
//root/Canvases with the list of active canvases
//root/Styles with the list of graphics styles
//root/Colors with the list of active colors
For example, if a file myFile.root is added to the list of files, one can retrieve a pointer to the corresponding TFile
object with a statement like:
TFile *myFile = (TFile*)gROOT->FindObjectAny(
"/ROOTFiles/myFile.root");
//or...
TFile *myFile = (TFile*)gROOT->FindObjectAny("myFile.root");

10.4

Tasks

Tasks can be organized into a hierarchy and displayed in the browser. The TTask class is the base class from which
the tasks are derived. To give task functionality, you need to subclass the TTask class and override the Exec method.
An example of TTask subclassesis $ROOTSYS/tutorials/MyTasks.cxx. The script that creates a task hierarchy and
adds it to the browser is $ROOTSYS/tutorials/tasks.C. Here is a part of MyTasks.cxx that shows how to subclass
from TTask.
// A set of classes deriving from TTask see macro tasks.C. The Exec
// function of each class prints one line when it is called.
#include "TTask.h"
class MyRun : public TTask {
public:
MyRun() { ; }
MyRun(const char *name,const char *title);
virtual ~MyRun() { ; }
void Exec(Option_t *option="");
ClassDef(MyRun,1)
// Run Reconstruction task
};
class MyEvent : public TTask {
public:
MyEvent() { ; }
MyEvent(const char *name,const char *title);
virtual ~MyEvent() { ; }
void Exec(Option_t *option="");
ClassDef(MyEvent,1)
// Event Reconstruction task
};
Later in MyTasks.cxx, we can see examples of the constructor and overridden Exec() method:

248

CHAPTER 10. FOLDERS AND TASKS

ClassImp(MyRun)
MyRun::MyRun(const char *name,const char *title):TTask(name,title)
{
...
}
void MyRun::Exec(Option_t *option)
{
printf("MyRun executingn");
}
Each TTask derived class may contain other TTasks that can be executed recursively. In this way, a complex program
can be dynamically built and executed by invoking the services of the top level task or one of its subtasks. The
constructor of TTask has two arguments: the name and the title. This script creates the task defined above, and
creates a hierarchy of tasks.
// Show the tasks in a browser. To execute a Task, select
// "ExecuteTask" in the context menu see also other functions in the
// TTask context menu, such as:
//
-setting a breakpoint in one or more tasks
//
-enabling/disabling one task, etc
void tasks() {
gROOT->ProcessLine(".L MyTasks.cxx+");
TTask *run = new MyRun("run","Process one run");
TTask *event = new MyEvent("event","Process one event");
TTask *geomInit = new MyGeomInit("geomInit",
"Geometry Initialisation");
TTask *matInit
= new MyMaterialInit("matInit",
"MaterialsInitialisation");
TTask *tracker = new MyTracker("tracker","Tracker manager");
TTask *tpc
= new MyRecTPC("tpc","TPC Reconstruction");
TTask *its
= new MyRecITS("its","ITS Reconstruction");
TTask *muon
= new MyRecMUON("muon","MUON Reconstruction");
TTask *phos
= new MyRecPHOS("phos","PHOS Reconstruction");
TTask *rich
= new MyRecRICH("rich","RICH Reconstruction");
TTask *trd
= new MyRecTRD("trd","TRD Reconstruction");
TTask *global = new MyRecGlobal("global","Global Reconstruction");
// Create a hierarchy by adding sub tasks
run->Add(geomInit);
run->Add(matInit);
run->Add(event);
event->Add(tracker);
event->Add(global);
tracker->Add(tpc);
tracker->Add(its);
tracker->Add(muon);
tracker->Add(phos);
tracker->Add(rich);
tracker->Add(trd);
// Add the top level task
gROOT->GetListOfTasks()->Add(run);

}

// Add the task to the browser
gROOT->GetListOfBrowsables()->Add(run);
new TBrowser;

Note that the first line loads the class definitions in MyTasks.cxx with ACLiC. ACLiC builds a shared library and
adds the classes to the Cling dictionary. See “Adding a Class with ACLiC”.
To execute a TTask, you call the ExecuteTask method. ExecuteTask will recursively call:

10.4. TASKS

249

Figure 10.1: Tasks in the ROOT browser

250

CHAPTER 10. FOLDERS AND TASKS

• the TTask::Execmethod of the derived class;
• the TTask::ExecuteTasks to execute for each task the list of its subtasks;
If the top level task is added to the list of ROOT browseable objects, the tree of tasks can be seen in the ROOT
browser. To add it to the browser, get the list of browseable objects first and add it to the collection.
gROOT->GetListOfBrowsables()->Add(run);
The first parameter of the Add method is a pointer to a TTask, the second parameter is the string to show in the
browser. If the string is left out, the name of the task is used.
After executing, the script above the browser will look like in this figure.

10.5

Execute and Debug Tasks

The browser can be used to start a task, set break points at the beginning of a task or when the task has completed.
At a breakpoint, data structures generated by the execution up this point may be inspected asynchronously and then
the execution can be resumed by selecting the “Continue” function of a task.
A task may be active or inactive (controlled by TTask::SetActive). When a task is inactive, its sub tasks are not
executed. A task tree may be made persistent, saving the status of all the tasks.

Chapter 11

Input/Output
This chapter covers the saving and reading of objects to and from ROOT files. It begins with an explanation of the
physical layout of a ROOT file. It includes a discussion on compression, and file recovery. Then we explain the logical
file, the class TFile and its methods. We show how to navigate in a file, how to save objects and read them back. We
also include a discussion on Streamers. Streamers are the methods responsible to capture an objects current state to
save it to disk or send it over the network. At the end of the chapter is a discussion on the two specialized ROOT files:
TNetFile and TWebFile.

11.1

The Physical Layout of ROOT Files

A ROOT file is like a UNIX file directory. It can contain directories and objects organized in unlimited number of
levels. It also is stored in machine independent format (ASCII, IEEE floating point, Big Endian byte ordering). To
look at the physical layout of a ROOT file, we first create one. This example creates a ROOT file and 15 histograms,
fills each histogram with 1000 entries from a Gaussian distribution, and writes them to the file.
{

}

char name[10], title[20];
TObjArray Hlist(0);
// create an array of Histograms
TH1F* h;
// create a pointer to a histogram
// make and fill 15 histograms and add them to the object array
for (Int_t i = 0; i < 15; i++) {
sprintf(name,"h%d",i);
sprintf(title,"histo nr:%d",i);
h = new TH1F(name,title,100,-4,4);
Hlist.Add(h);
h->FillRandom("gaus",1000);
}
// open a file and write the array to the file
TFile f("demo.root","recreate");
Hlist.Write();
f.Close();

The example begins with a call to the TFile constructor. This class is describing the ROOT file (that has the extension
“.root”). In the next section, we will cover TFile in details. The last line of the example closes the file. To view its
contents we need to open it again, and to create a TBrowser object by:
root[] TFile f("demo.root")
root[] TBrowser browser;
You can check if the file is correctly opened by:
TFile f("demo.root");
if (f.IsZombie()) {
cout << "Error opening file" << endl;
251

252

CHAPTER 11. INPUT/OUTPUT

Figure 11.1: The browser with 15 created histograms
exit(-1);
} else {
...
}
Once we have the TFile object, we can call the TFile::Map() method to view the physical layout. The output prints
the date/time, the start record address, the number of bytes in the record, the class name of the record and the
compression factor.
root[] f.Map()
20051208/124502
20051208/124502
20051208/124502
20051208/124502
20051208/124502
20051208/124502
20051208/124502
20051208/124502
20051208/124502
20051208/124502
20051208/124502
20051208/124502
20051208/124502
20051208/124502
20051208/124502
20051208/124502
20051208/124503
20051208/124503
20051208/124503
20051208/124503

At:100
At:214
At:627
At:1037
At:1433
At:1833
At:2235
At:2651
At:3057
At:3460
At:3871
At:4271
At:4680
At:5089
At:5509
At:5915
At:6320
At:9372
At:10104
At:10157

N=114
N=413
N=410
N=396
N=400
N=402
N=416
N=406
N=403
N=411
N=400
N=409
N=409
N=420
N=406
N=405
N=3052
N=732
N=53
N=1

TFile
TH1F
TH1F
TH1F
TH1F
TH1F
TH1F
TH1F
TH1F
TH1F
TH1F
TH1F
TH1F
TH1F
TH1F
TH1F
StreamerInfo
KeysList
FreeSegments
END

CX
CX
CX
CX
CX
CX
CX
CX
CX
CX
CX
CX
CX
CX
CX
CX

=
=
=
=
=
=
=
=
=
=
=
=
=
=
=
=

2.35
2.36
2.45
2.42
2.41
2.33
2.39
2.40
2.36
2.42
2.38
2.38
2.32
2.40
2.40
3.16

Here we see the fifteen histograms (TH1F’s) with the first one starting at byte 148. We also see an entry TFile. You
may notice that the first entry starts at byte 100. The first 100 bytes are taken by the file header.

11.1.1

The File Header

This table shows the file header information. When fVersion is greater than 1000000, the file is a large file (> 2 GB)
and the offsets will be 8 bytes long. The location in brackets are the location in the case of a large file.

11.1. THE PHYSICAL LAYOUT OF ROOT FILES
Byte
1 -> 4
5 -> 8
9 -> 12
13 -> 16
17 -> 20
21 -> 24
25 -> 28
29 -> 32
33 -> 33
34 -> 37
34 -> 37
34 -> 37
34 -> 37

Value Name
“root”
fVersion
fBEGIN
fEND
fSeekFree
fNbytesFree
nfree
fNbytesName
fUnits
fCompress
fSeekInfo
fNBytesInfo
fCompress

[13->20]
[21->28]
[29->32]
[33->36]
[37->40]
[41->41]
[42->45]
[46->53]
[54->57]
[58->75]

253
Description
Root file identifier
File format version
Pointer to first data record
Pointer to first free word at the EOF
Pointer to FREE data record
Number of bytes in FREE data record
Number of free data records
Number of bytes in TNamed at creation time
Number of bytes for file pointers
Zip compression level
Pointer to TStreamerInfo record
Number of bytes in TStreamerInfo record
Universal Unique ID

The first four bytes of the file header contain the string “root” which identifies a file as a ROOT file. Because of this
identifier, ROOT is not dependent on the “.root” extension. It is still a good idea to use the extension, just for us
to recognize them easier. The nfree and value is the number of free records. This variable along with FNBytesFree
keeps track of the free space in terms of records and bytes. This count also includes the deleted records, which are
available again.

11.1.2

The Top Directory Description

The 84 bytes after the file header contain the top directory description, including the name, the date and time it was
created, and the date and time of the last modification.
20010404/092347

11.1.3

At:64

N=84

TFile

The Histogram Records

What follows are the 15 histograms, in records of variable length.
20010404/092347
20010404/092347

At:148
At:528

N=380
N=377

TH1F
TH1F

CX =
CX =

2.49
2.51

The first 4 bytes of each record is an integer holding the number of bytes in this record. A negative number flags the
record as deleted, and makes the space available for recycling in the next writing. The rest of bytes in the header
contain all the information to identify uniquely a data block on the file. It is followed by the object data.
The next table explains the values in each individual record. If the key is located past the 32 bit file limit (> 2 GB)
then some fields will be 8 bytes instead of 4 bytes (values between the brackets):
Byte
1 -> 4
5 -> 6
7 -> 10
11 -> 14
15 -> 16
17 -> 18
19 -> 22 [19->26]
23 -> 26 [27->34]
27 -> 27 [35->35]
28 -> . . . [36->..
. . . -> . . .
. . . -> . . .
. . . -> . . .
. . . -> . . .
. . . -> . . .

Value Name
Nbytes
Version
ObjLen
Datime
KeyLen
Cycle
SeekKey
SeekPdir
lname
.] | ClassName
| lname
| Name
| lTitle
| Title
| DATA

Description
Length of compressed object (in bytes)
TKey version identifier
Length of uncompressed object
Date and time when object was written to file
Length of the key structure (in bytes)
Cycle of key
Pointer to record itself (consistency check)
Pointer to directory header
Number of bytes in the class name
| Object Class Name
| Number of bytes in the object name
| lName bytes with the name of the object
| Number of bytes in the object title
| Title of the object
| Data bytes associated to the object

You see a reference to TKey. It is explained in detail in the next section.

254

11.1.4

CHAPTER 11. INPUT/OUTPUT

The Class Description List (StreamerInfo List)

The histogram records are followed by the StreamerInfo list of class descriptions. The list contains the description of
each class that has been written to file.
20010404/092347

At:5854

N=2390

StreamerInfo

CX =

3.41

The class description is recursive, because to fully describe a class, its ancestors and object data members have to be
described also. In demo.root, the class description list contains the description for:
• TH1F
• all classes in the TH1F inheritance tree
• all classes of the object data members
• all classes in the object data members’ inheritance tree.
This description is implemented by the TStreamerInfo class, and is often referred to as simply StreamerInfo. You
can print a file’s StreamerInfolist with the TFile::ShowStreamerInfo method. Below is an example of the output.
Only the first line of each class description is shown. The demo.root example contains only TH1F objects. Here we see
the recursive nature of the class description; it contains the StreamerInfoof all the classes needed to describe TH1F.
root[] f.ShowStreamerInfo()
StreamerInfo for class: TH1F, version=1
BASE
TH1
offset=0 type= 0 1-Dim histogram base class
BASE
TArrayF
offset=0 type= 0 Array of floats
StreamerInfo for class: TH1, version=3
BASE
TNamed
offset=0 type=67
BASE
TAttLine
offset=0 type=0
BASE
TAttFill
offset=0 type=0
BASE
TAttMarker offset=0 type=0
Int_t
fNcells
offset=0 type=3
TAxis
fXaxis
offset=0 type=61
TAxis
fYaxis
offset=0 type=61
TAxis
fZaxis
offset=0 type=61
Short_t fBarOffset offset=0 type=2
Short_t fBarWidth
offset=0 type=2
Stat_t
fEntries
offset=0 type=8
Stat_t
fTsumw
offset=0 type=8
Stat_t
fTsumw2
offset=0 type=8
Stat_t
fTsumwx
offset=0 type=8
Stat_t
fTsumwx2
offset=0 type=8
Double_t fMaximum
offset=0 type=8
Double_t fMinimum
offset=0 type=8
Double_t fNormFactor offset=0 type=8
TArrayD fContour
offset=0 type=62
TArrayD fSumw2
offset=0 type=62
TString fOption
offset=0 type=65
TList*
fFunctions offset=0 type=63
StreamerInfo
...
StreamerInfo
...
StreamerInfo
...
StreamerInfo
...
StreamerInfo
...
StreamerInfo

The basis for named object(name,title)
Line attributes
Fill area attributes
Marker attributes
number bins(1D),cells(2D)+U/Overflows
X axis descriptor
Y axis descriptor
Z axis descriptor
(1000*offset) for barcharts or legos
(1000*width) for bar charts or legos
Number of entries//continued...
Total Sum of weights
Total Sum of squares of weights
Total Sum of weight*X
Total Sum of weight*X*X
Maximum value for plotting
Minimum value for plotting
Normalization factor
Array to display contour levels
Array of sum of squares of weights
histogram options
->Pointer to list of functions(fits,user)

for class: TNamed, version=1
for class: TAttLine, version=1
for class: TAttFill, version=1
for class: TAttMarker, version=1
for class: TArrayF, version=1
for class: TArray, version=1

11.2. THE LOGICAL ROOT FILE: TFILE AND TKEY

255

...
StreamerInfo for class: TAxis, version=6
...
StreamerInfo for class: TAttAxis, version=4
...
ROOT allows a class to have multiple versions, and each version has its own description in form of a StreamerInfo.
Above you see the class name and version number. The StreamerInfolist has only one description for each class/version
combination it encountered. The file can have multiple versions of the same class, for example objects of old and new
versions of a class can be in the same file. The StreamerInfois described in detail in the section on Streamers.

11.1.5

The List of Keys and the List of Free Blocks

The last three entries on the output of TFile::Map() are the list of keys, the list of free segments, and the address
where the data ends.. When a file is closed, it writes a linked list of keys at the end of the file. This is what we see in
the third to the last entry. In our example, the list of keys is stored in 732 bytes beginning at byte# 8244.
20010404/092347
20010404/092347
20010404/092347

At:8244
At:8976
At:9029

N=732
N=53
N=1

KeysList
FreeSegments
END

The second to last entry is a list of free segments. In our case, this starts 8976 and is not very long, only 53 bytes,
since we have not deleted any objects. The last entry is the address of the last byte in the file.

11.1.6

File Recovery

A file may become corrupted or it may be impossible to write it to disk and close it properly. For example if the file
is too large and exceeds the disk quota, or the job crashes or a batch job reaches its time limit before the file can
be closed. In these cases, it is imperative to recover and retain as much information as possible. ROOT provides an
intelligent and elegant file recovery mechanism using the redundant directory information in the record header.
If a file that has been not properly closed is opened again, it is scanned and rebuilt according to the information in
the record header. The recovery algorithm reads the file and creates the saved objects in memory according to the
header information. It then rebuilds the directory and file structure. If the file is opened in write mode, the recovery
makes the correction on disk when the file is closed; however if the file is opened in read mode, the correction can not
be written to disk. You can also explicitly invoke the recovery procedure by calling the TFile::Recover() method.
You can recover the directory structure, but you cannot save what you recovered to the file on disk. In the following
example, we interrupted and aborted the previous ROOT session, causing the file not to be closed. When we start a
new session and attempt to open the file, it gives us an explanation and status on the recovery attempt.

root[] TFile f("demo.root")
Warning in : file demo.root probably not closed, trying to recover successfully recovered 15

11.2

The Logical ROOT File: TFile and TKey

We saw that the TFile::Map() method reads the file sequentially and prints information about each record while
scanning the file. It is not feasible to support only sequential access and hence ROOT provides random or direct access,
i.e. reading a specified object at a time. To do so, TFile keeps a list of TKeys, which is essentially an index to the
objects in the file. The TKey class describes the record headers of objects in the file. For example, we can get the list of
keys and print them. To find a specific object on the file we can use the TFile::Get() method.
root[] TFile f("demo.root")
root[] f.GetListOfKeys()->Print()
TKey Name = h0, Title = histo nr:0,
TKey Name = h1, Title = histo nr:1,
TKey Name = h2, Title = histo nr:2,
TKey Name = h3, Title = histo nr:3,
TKey Name = h4, Title = histo nr:4,
TKey Name = h5, Title = histo nr:5,

Cycle
Cycle
Cycle
Cycle
Cycle
Cycle

=
=
=
=
=
=

1
1
1
1
1
1

256

CHAPTER 11. INPUT/OUTPUT

TKey Name =
TKey Name =
TKey Name =
TKey Name =
TKey Name =
TKey Name =
TKey Name =
TKey Name =
TKey Name =
root[] TH1F

h6, Title = histo nr:6, Cycle =
h7, Title = histo nr:7, Cycle =
h8, Title = histo nr:8, Cycle =
h9, Title = histo nr:9, Cycle =
h10, Title = histo nr:10, Cycle
h11, Title = histo nr:11, Cycle
h12, Title = histo nr:12, Cycle
h13, Title = histo nr:13, Cycle
h14, Title = histo nr:14, Cycle
*h9 = (TH1F*)f.Get("h9");

1
1
1
1
=
=
=
=
=

1
1
1
1
1

The TFile::Get() finds the TKey object with name “h9”. Using the TKey info it will import in memory the object in
the file at the file address #3352 (see the output from the TFile::Map above). This is done by the Streamer method
that is covered in detail in a later section. Since the keys are available in a TList of TKeys we can iterate over the
list of keys:
{

}

TFile f("demo.root");
TIter next(f.GetListOfKeys());
TKey *key;
while ((key=(TKey*)next())) {
printf("key: %s points to an object of class: %s at %dn",
key->GetName(),
key->GetClassName(),key->GetSeekKey());
}

The output of this script is:
root[] .x iterate.C
key: h0 points to an object of class: TH1F at 150
key: h1 points to an object of class: TH1F at 503
key: h2 points to an object of class: TH1F at 854
key: h3 points to an object of class: TH1F at 1194
key: h4 points to an object of class: TH1F at 1539
key: h5 points to an object of class: TH1F at 1882
key: h6 points to an object of class: TH1F at 2240
key: h7 points to an object of class: TH1F at 2582
key: h8 points to an object of class: TH1F at 2937
key: h9 points to an object of class: TH1F at 3293
key: h10 points to an object of class: TH1F at 3639
key: h11 points to an object of class: TH1F at 3986
key: h12 points to an object of class: TH1F at 4339
key: h13 points to an object of class: TH1F at 4694
key: h14 points to an object of class: TH1F at 5038
In addition to the list of keys, TFile also keeps two other lists: TFile::fFree is a TList of free blocks used to recycle
freed up space in the file. ROOT tries to find the best free block. If a free block matches the size of the new object to
be stored, the object is written in the free block and this free block is deleted from the list. If not, the first free block
bigger than the object is used. TFile::fListHead contains a sorted list (TSortedList) of objects in memory. The
diagram below illustrates the logical view of the TFile and TKey.

11.2.1

Viewing the Logical File Contents

TFile is a descendent of TDirectory, which means it behaves like a TDirectory. We can list the contents, print the
name, and create subdirectories. In a ROOT session, you are always in a directory and the directory you are in is
called the current directory and is stored in the global variable gDirectory . Let us look at a more detailed example of
a ROOT file and its role as the current directory. First, we create a ROOT file by executing a sample script.
root[] .x $ROOTSYS/tutorials/hsimple.C

11.2. THE LOGICAL ROOT FILE: TFILE AND TKEY

Figure 11.2: ROOT File/Directory/Key description

257

258

CHAPTER 11. INPUT/OUTPUT

Now you should have hsimple.root in your directory. The file was closed by the script so we have to open it again to
work with it. We open the file with the intent to update it, and list its contents.
root[] TFile f ("hsimple.root","UPDATE")
root[] f.ls()
TFile** hsimple.root
TFile* hsimple.root
KEY: TH1F hpx;1 This is the px distribution
KEY: TH2F hpxpy;1 py vs px
KEY: TProfile hprof;1 Profile of pz versus px
KEY: TNtuple ntuple;1 Demo ntuple
It shows the two lines starting with TFile followed by four lines starting with the word “KEY”. The four keys tell us
that there are four objects on disk in this file. The syntax of the listing is:
KEY:  ;