# ROOT Basics #

Now that you have installed ROOT, what's this interactive shell thing
you're running ? It's like this: ROOT leads a double life. It has an
interpreter for macros (Cling [@Cling]) that you can run from the command
line or run like applications. But it is also an interactive shell that
can evaluate arbitrary statements and expressions. This is extremely
useful for debugging, quick hacking and testing. Let us first have a
look at some very simple examples.

## ROOT as calculator ##

You can even use the ROOT interactive shell in lieu of a calculator!
Launch the ROOT interactive shell with the command

``` {.cpp}
 > root
```

on your Linux box. The prompt should appear shortly:

``` {.cpp}
 root [0]
```

and let's dive in with the steps shown here:

``` {.cpp}
root [0] 1+1
(int) 2
root [1] 2*(4+2)/12.
(double) 1.000000
root [2] sqrt(3.)
(double) 1.732051
root [3] 1 > 2
(bool) false
root [4] TMath::Pi()
(double) 3.141593
root [5] TMath::Erf(.2)
(double) 0.222703
```

Not bad. You can see that ROOT offers you the possibility not only to
type in `C++` statements, but also advanced mathematical functions,
which live in the `TMath` namespace.

Now let's do something more elaborated. A numerical example with the
well known geometrical series:

``` {.cpp}
root [6] double x=.5
(double) 0.500000
root [7] int N=30
(int) 30
root [8] double geom_series=0
(double) 0.000000
root [9] for (int i=0;i<N;++i)geom_series+=TMath::Power(x,i)
root [10]  cout << TMath::Abs(geom_series - (1-TMath::Power(x,N-1))/(1-x)) <<endl;
1.86265e-09
```

Here we made a step forward. We even declared variables and used a *for*
control structure. Note that there are some subtle differences between
Cling and the standard `C++` language. You do not need the ";" at the end
of line in interactive mode -- try the difference e.g. using the command
at line `root [6]`.

## Learn C++ at the ROOT prompt ##
Behind the ROOT prompt there is an interpreter based on a real compiler toolkit:
LLVM. It is therefore possible to exercise many features of `C++` and the
standard library. For example in the following snippet we define a lambda
function, a vector and we sort it in different ways:
``` {.cpp}
root [0] using doubles = std::vector<double>;
root [1] auto pVec = [](const doubles& v){for (auto&& x:v) cout << x << endl;};
root [2] doubles v{0,3,5,4,1,2};
root [3] pVec(v);
0
3
5
4
1
2
root [4] std::sort(v.begin(),v.end());
root [5] pVec(v);
0
1
2
3
4
5
root [6] std::sort(v.begin(),v.end(),[](double a, double b){return a>b;});
root [7] pVec(v);
5
4
3
2
1
0
```
Or, if you prefer random number generation:
``` {.cpp}
root [0] std::default_random_engine generator;
root [1] std::normal_distribution<double> distribution(0.,1.);
root [2] distribution(generator)
(std::normal_distribution<double>::result_type) -1.219658e-01
root [3] distribution(generator)
(std::normal_distribution<double>::result_type) -1.086818e+00
root [4] distribution(generator)
(std::normal_distribution<double>::result_type) 6.842899e-01
```
Impressive isn't it?

## ROOT as function plotter ##
Using one of ROOT's powerful classes, here `TF1` [^2], will allow us to
display a function of one variable, *x*. Try the following:

``` {.cpp}
root [11] TF1 f1("f1","sin(x)/x",0.,10.);
root [12] f1.Draw();
```

`f1` is an instance of a TF1 class, the arguments are used
in the constructor; the first one of type string is a name to be entered
in the internal ROOT memory management system, the second string type
parameter defines the function, here `sin(x)/x`, and the two parameters
of type double define the range of the variable *x*. The `Draw()`
method, here without any parameters, displays the function in a window
which should pop up after you typed the above two lines.

A slightly extended version of this example is the definition of a
function with parameters, called `[0]`, `[1]` and so on in the ROOT
formula syntax. We now need a way to assign values to these parameters;
this is achieved with the method
`SetParameter(<parameter_number>,<parameter_value>)` of class `TF1`.
Here is an example:

``` {.cpp}
root [13] TF1 f2("f2","[0]*sin([1]*x)/x",0.,10.);
root [14] f2.SetParameter(0,1);
root [15] f2.SetParameter(1,1);
root [16] f2.Draw();
```

Of course, this version shows the same results as the initial one. Try
playing with the parameters and plot the function again. The class `TF1`
has a large number of very useful methods, including integration and
differentiation. To make full use of this and other ROOT classes, visit
the documentation on the Internet under
<http://root.cern.ch/drupal/content/reference-guide>. Formulae in ROOT
are evaluated using the class `TFormula`, so also look up the relevant
class documentation for examples, implemented functions and syntax.

You should definitely download this guide to your own system to have it
at you disposal whenever you need it.

To extend a little bit on the above example, consider a more complex
function you would like to define. You can also do this using standard
`C` or `C++` code.

Consider the example below, which calculates and displays the
interference pattern produced by light falling on a multiple slit.
Please do not type in the example below at the ROOT command line, there
is a much simpler way: Make sure you have the file `slits.C` on disk,
and type `root slits.C` in the shell. This will start root and make it
read the "macro" `slits.C`, i.e. all the lines in the file will be
executed one after the other.

``` {.cpp .numberLines}
@ROOT_INCLUDE_FILE macros/slits.C
```
[f21]: figures/TF1_DoubleSlit.png "f21"
<a name="f21"></a>

![Output of slits.C with parameters 0.2 and 2.\label{f21}][f21]

The example first asks for user input, namely the ratio of slit width
over slit distance, and the number of slits. After entering this
information, you should see the graphical output as is shown in Figure [2.1](#f21).

This is a more complicated example than the ones we have seen before, so
spend some time analysing it carefully, you should have understood it
before continuing. Let us go through it in detail:

Lines *7-18* define the necessary functions in `C++` code, split into
three separate functions, as suggested by the problem considered. The
full interference pattern is given by the product of a function
depending on the ratio of the width and distance of the slits, and a
second one depending on the number of slits. More important for us here
is the definition of the interface of these functions to make them
usable for the ROOT class `TF1`: the first argument is the pointer to
*x*, the second one points to the array of parameters.

The main program starts at line 21 with the definition of a function
`slits()` of type `void`. After asking for user input, a ROOT function
is defined using the C-type function given in the beginning. We can now
use all methods of the `TF1` class to control the behaviour of our
function -- nice, isn't it ?

If you like, you can easily extend the example to also plot the
interference pattern of a single slit, using function `double single`,
or of a grid with narrow slits, function `double nslit0`, in `TF1`
instances.

Here, we used a macro, some sort of lightweight program, that the
interpreter distributed with ROOT, Cling, is able to execute. This is a
rather extraordinary situation, since `C++` is not natively an interpreted
language! There is much more to say: chapter is indeed dedicated to
macros.

## Controlling ROOT ##

One more remark at this point: as every command you type into ROOT is
usually interpreted by Cling, an "escape character" is needed to pass
commands to ROOT directly. This character is the dot at the beginning of
a line:

``` {.cpp}
root [1] .<command>
```

This is a selection of the most common commands.

-   **quit root**, simply type `.q`

-   obtain a **list of commands**, use `.?`

-   **access the shell** of the operating system, type `.!<OS_command>`;
    try, e.g. `.!ls` or `.!pwd`

-   **execute a macro**, enter `.x <file_name>`; in the above example,
    you might have used `.x slits.C` at the ROOT prompt

-   **load a macro**, type `.L <file_name>`; in the above example, you
    might instead have used the command `.L slits.C` followed by the
    function call `slits();`. Note that after loading a macro all
    functions and procedures defined therein are available at the ROOT
    prompt.

-   **compile a macro**, type `.L <file_name>+`; ROOT is able to manage
    for you the `C++` compiler behind the scenes and to produce machine
    code starting from your macro. One could decide to compile a macro
    in order to obtain better performance or to get nearer to the
    production environment.

Use `.help` at the prompt to inspect the full list.

## Plotting Measurements ##

To display measurements in ROOT, including errors, there exists a
powerful class `TGraphErrors` with different types of constructors. In
the example here, we use data from the file `ExampleData.txt` in text
format:

``` {.cpp}
root [0] TGraphErrors gr("ExampleData.txt");
root [1] gr.Draw("AP");
```

You should see the output shown in Figure [2.2](#f22).

[f22]: figures/TGraphErrors_Example.png "f22"
<a name="f22"></a>

![Visualisation of data points with errors using the class TGraphErrors. \label{f22}][f22]

Make sure the file `ExampleData.txt` is available in the directory from
which you started ROOT. Inspect this file now with your favourite
editor, or use the command `less ExampleData.txt` to inspect the file,
you will see that the format is very simple and easy to understand.
Lines beginning with `#` are ignored. It is very convenient to add some
comments about the type of data. The data itself consist of lines with
four real numbers each, representing the x- and y- coordinates and their
errors of each data point.

The argument of the method `Draw("AP")` is important here. Behind the scenes,
it tells the `TGraphPainter` class to show the axes and to plot markers at the
*x* and *y* positions of the specified data points. Note that this simple
example relies on the default settings of ROOT, concerning the size of
the canvas holding the plot, the marker type and the line colours and
thickness used and so on. In a well-written, complete example, all this
would need to be specified explicitly in order to obtain nice and well
readable results. A full chapter on graphs will explain many
more of the features of the class `TGraphErrors` and its relation to
other ROOT classes in much more detail.

## Histograms in ROOT ##

Frequency distributions in ROOT are handled by a set of classes derived
from the histogram class `TH1`, in our case `TH1F`. The letter `F`
stands for "float", meaning that the data type `float` is used to store
the entries in one histogram bin.

``` {.cpp}
root [0] TF1 efunc("efunc","exp([0]+[1]*x)",0.,5.);
root [1] efunc.SetParameter(0,1);
root [2] efunc.SetParameter(1,-1);
root [3] TH1F h("h","example histogram",100,0.,5.);
root [4] for (int i=0;i<1000;i++) {h.Fill(efunc.GetRandom());}
root [5] h.Draw();
```

The first three lines of this example define a function, an exponential
in this case, and set its parameters. In line *3* a histogram is
instantiated, with a name, a title, a certain number of bins (100 of
them, equidistant, equally sized) in the range from 0 to 5.

[f23]: figures/TH1F_Example.png "f23"
<a name="f23"></a>

![Visualisation of a histogram filled with exponentially distributed,
random numbers. \label{f23}][f23]

We use yet another new feature of ROOT to fill this histogram with data,
namely pseudo-random numbers generated with the method `TF1::GetRandom`,
which in turn uses an instance of the ROOT class `TRandom` created when
ROOT is started. Data is entered in the histogram at line *4* using the
method `TH1F::Fill` in a loop construct. As a result, the histogram is
filled with 1000 random numbers distributed according to the defined
function. The histogram is displayed using the method `TH1F::Draw()`.
You may think of this example as repeated measurements of the life time
of a quantum mechanical state, which are entered into the histogram,
thus giving a visual impression of the probability density distribution.
The plot is shown in Figure [2.3](#f23).

Note that you will not obtain an identical plot when executing the lines
above, depending on how the random number generator is initialised.

The class `TH1F` does not contain a convenient input format from plain
text files. The following lines of `C++` code do the job. One number per
line stored in the text file "expo.dat" is read in via an input stream
and filled in the histogram until end of file is reached.

``` {.cpp}
root [1] TH1F h("h","example histogram",100,0.,5.);
root [2] ifstream inp; double x;
root [3] inp.open("expo.dat");
root [4] while (inp >> x) { h.Fill(x); }
root [5] h.Draw();
root [6] inp.close();
```

Histograms and random numbers are very important tools in statistical
data analysis, a whole chapter will be dedicated to this topic.

## Interactive ROOT ##

Look at one of your plots again and move the mouse across. You will
notice that this is much more than a static picture, as the mouse
pointer changes its shape when touching objects on the plot. When the
mouse is over an object, a right-click opens a pull-down menu displaying
in the top line the name of the ROOT class you are dealing with, e.g.
`TCanvas` for the display window itself, `TFrame` for the frame of the
plot, `TAxis` for the axes, `TPaveText` for the plot name. Depending on
which plot you are investigating, menus for the ROOT classes `TF1`,
`TGraphErrors` or `TH1F` will show up when a right-click is performed on
the respective graphical representations. The menu items allow direct
access to the members of the various classes, and you can even modify
them, e.g. change colour and size of the axis ticks or labels, the
function lines, marker types and so on. Try it!

[f24]: figures/ROOTPanel_SetParameters.png "f24"
<a name="f24"></a>

![Interactive ROOT panel for setting function parameters.\label{f24}][f24]

You will probably like the following: in the output produced by the
example `slits.C`, right-click on the function line and select
"SetLineAttributes", then left-click on "Set Parameters". This gives
access to a panel allowing you to interactively change the parameters of
the function, as shown in Figure [2.4](#f24). Change the slit width, or go from one to
two and then three or more slits, just as you like. When clicking on
"Apply", the function plot is updated to reflect the actual value of the
parameters you have set.

[f25]: figures/ROOTPanel_FitPanel.png "f25"
<a name="f25"></a>

![Fit Panel. \label{f25}][f25]

Another very useful interactive tool is the `FitPanel`, available for the
classes `TGraphErrors` and `TH1F`. Predefined fit functions can be selected
from a pull-down menu, including "`gaus`", "`expo`" and "`pol0`" - "`pol9`"
for Gaussian and exponential functions or polynomials of degree 0 to 9,
respectively. In addition, user-defined functions using the same syntax as
for functions with parameters are possible.

After setting the initial parameters, a fit of the selected function to the
data of a graph or histogram can be performed and the result displayed on the plot.
The fit panel is shown in Figure [2.5](#f25). The fit panel has a number of control options to
select the fit method, fix or release individual parameters in the fit, to steer
the level of output printed on the console, or to extract and display additional
information like contour lines showing parameter correlations. As function fitting
is of prime importance in any kind of data analysis, this topic will again show up
later.

If you are satisfied with your plot, you probably want to save it. Just
close all selector boxes you opened previously and select the menu item
`Save as...` from the menu line of the window. It will pop up a file
selector box to allow you to choose the format, file name and target
directory to store the image. There is one very noticeable feature here:
you can store a plot as a root macro! In this macro, you find the C++
representation of all methods and classes involved in generating the
plot. This is a valuable source of information for your own macros,
which you will hopefully write after having worked through this
tutorial.

Using ROOT's interactive capabilities is useful for a first exploration
of possibilities. Other ROOT classes you will encounter in this tutorial
have such graphical interfaces. We will not comment further on this,
just be aware of the existence of ROOT's interactive features and use
them if you find them convenient. Some trial-and-error is certainly necessary
to find your way through the huge number of menus and parameter
settings.

## ROOT Beginners' FAQ ##

At this point of the guide, some basic questions could have already come
to your mind. We will try to clarify some of them with further
explanations in the following.

### ROOT type declarations for basic data types ###

In the official ROOT documentation, you find special data types
replacing the normal ones, e.g. `Double_t`, `Float_t` or `Int_t`
replacing the standard `double`, `float` or `int` types. Using the ROOT
types makes it easier to port code between platforms (64/32 bit) or
operating systems (windows/Linux), as these types are mapped to suitable
ones in the ROOT header files. If you want adaptive code of this type,
use the ROOT type declarations. However, usually you do not need such
adaptive code, and you can safely use the standard C type declarations
for your private code, as we did and will do throughout this guide. If
you intend to become a ROOT developer, however, you better stick to the
official coding rules!

### Configure ROOT at start-up ###

The behaviour of a ROOT session can be tailored with the options in the
`.rootrc` file. Examples of the tunable parameters are the ones related
to the operating and window system, to the fonts to be used, to the
location of start-up files. 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. The parsing
and interpretation of this file is handled by the ROOT class `TEnv`.
Have a look to its documentation if you need such rather advanced
features. The file `.rootrc` defines the location of two rather
important files inspected at start-up: `rootalias.C` and `rootlogon.C`.
They can contain code that needs to be loaded and executed at ROOT
startup. `rootalias.C` is only loaded and best used to define some often
used functions. `rootlogon.C` contains code that will be executed at
startup: this file is extremely useful for example to pre-load a custom
style for the plots created with ROOT. This is done most easily by
creating a new `TStyle` object with your preferred settings, as
described in the class reference guide, and then use the command
`gROOT->SetStyle("MyStyleName");` to make this new style definition the
default one. As an example, have a look in the file `rootlogon.C` coming
with this tutorial. Another relevant file is `rootlogoff.C` that it
called when the session is finished.

### ROOT command history ###

Every command typed at the ROOT prompt is stored in a file `.root_hist`
in your home directory. ROOT uses this file to allow for navigation in
the command history with the up-arrow and down-arrow keys. It is also
convenient to extract successful ROOT commands with the help of a text
editor for use in your own macros.

### ROOT Global Pointers ###

All global pointers in ROOT begin with a small "g". Some of them were
already implicitly introduced (for example in the section
[Configure ROOT at start-up](#configure-root-at-start-up)).
The most important among them are presented in the following:

-   **[gROOT](http://root.cern.ch/root/htmldoc/TROOT.html)**: the `gROOT`
    variable is the entry point to the ROOT system. Technically it is an
    instance of the `TROOT` class. Using the `gROOT` pointer one has
    access to basically every object created in a ROOT based program.
    The `TROOT` object is essentially a container of several lists
    pointing to the main `ROOT` objects.

-   **[gStyle](http://root.cern.ch/root/htmldoc/TStyle.html)**: By default
    ROOT creates a default style that can be accessed via the `gStyle`
    pointer. This class includes functions to set some of the following
    object attributes.

    -   Canvas
    -   Pad
    -   Histogram axis
    -   Lines
    -   Fill areas
    -   Text
    -   Markers
    -   Functions
    -   Histogram Statistics and Titles
    -   etc ...

-   **[gSystem](http://root.cern.ch/root/htmldoc/TSystem.html)**: An
    instance of a base class defining a generic interface to the
    underlying Operating System, in our case `TUnixSystem`.

-   **[gInterpreter](http://root.cern.ch/htmldoc/html/TInterpreter.html)**: The
    entry point for the ROOT interpreter. Technically an abstraction level
    over a singleton instance of `TCling`.

At this point you have already learnt quite a bit about some basic
features of ROOT.

***Please move on to become an expert!***

[^2]: All ROOT classes' names start with the letter T. A notable exception is
RooFit. In this context all classes' names are of the form Roo*.
