(lambda-expressions)=
# Lambda expressions in C++

I'd love to finish the topic of writing functions for `RDataFrame` in
C++ at this point, and move on to torturing the Python programmers
with what they have to put up with.

Unfortunately, I can't. The [RDataFrame
tutorials](https://root.cern.ch/doc/master/group__tutorial__dataframe.html)
make heavy use of C++ lambda expressions. In order for you to be able
to understand the code in those examples, I feel I have to review
this somewhat-esoteric coding practice.

:::{admonition} Not so fast, Python programmers!
:class: warning
I know you want to leap ahead to the next section. I don't blame you. Before
you do, there's a couple of things you should know that may influence your
choice:

- Even though there is usually an equivalent Python example for every C++
  example in the [ROOT tutorials](https://root.cern.ch/doc/master/group__Tutorials.html),
  sometimes there's only a `.C` file, probably because the Python equivalent is
  not yet possible. You'll want to be able to interpret the C++ code so you
  can figure out what it's supposed to do.[^comments]

<p />

- If you're a skilled Python programmer, you know that there are lambda expressions
  in Python. Unfortunately, Python-based lambda expressions can't be used as
  arguments to `Define` and `Filter`.[^work]

Now that you're informed, I leave it up to you to decide what to read.[^always]
:::

[^comments]: "Can't I tell what the C++ code is supposed to do from the comments?"
    Oh, how I {ref}`wish <clear-code>` that were true!

[^work]: At least, not in the current version as of the time of this writing
    (ROOT 6.26), or not without a whole lot of extra code wrappers and decorators.
    Frankly, it's not worth the effort.

[^always]: Of course, since I have no way to make you do anything, the
    decision is always up to you!

A [lambda
expression](https://stackoverflow.com/questions/7627098/what-is-a-lambda-expression-in-c11)[^better]
is a way of defining a function without giving it a name. It's normally used for short functions to
make the code more convenient.[^long]

[^better]: I think that [this web page](https://www.programiz.com/cpp-programming/lambda-expression)
    offers a better explanation of lambda expressions. However, it also includes an annoying
    pop-up ad.

[^long]: I'll confess that I often write multi-statement lambda functions. I
    do this because when I use the function in `RDataFrame` or an
    iterative function like
    [for_each](https://www.geeksforgeeks.org/for_each-loop-c/),
    I feel it's helpful for the function to be defined right above the
    C++ statement that's going to use it. 

Here's an example of a lambda expression that defines how to calculate our old friend
**`pt`**:

:::{code-block} c++
auto pt_func = [](float x, float y) { return std::sqrt(x*x + y*y); };
:::

Compare this with {numref}`Listing %s <c-pt-func>`:

:::{code-block} c++
float pt_func( float x, float y ) {
    return std::sqrt( x*x + y*y );
}
:::

Your first reaction may be that we're using a fancy syntax to do
exactly the same thing. But lambda expressions offer more than that:
They allow you to define a function within the body of the code, instead
of in a separate declaration before the current routine.

Let's break this down:

- `[]` means "this is a lambda expression."[^brackets]

<p />

- `(float x, float y)` - As with any function, we have to declare its
  arguments.

<p />

- `{ return std::sqrt(x*x + y*y); }` - this is the body of the function, the
  same as any other function.

<p />

- `;` - Don't forget the semi-colon at the end! To C++, this line is a statement,
  not a function definition. It has to end with a `;` so the compiler will
  recognize it.

<p />

- `auto` - You've seen me use the `auto` before, to let the compiler
  do the work of specifying a complicated type.

<p />

- `pt_func` - The name I assign to this lambda expression.[^anon]

<p />

- If you're sharp of eye and mind, you may have noticed that we didn't have to
  declare the return type of the function, the way we had to in {numref}`Listing %s <c-pt-func>`.
  That's because the C++ compiler can automatically deduce the return type from
  the type of the value in the `return` statement.[^not-always]

[^brackets]: It means something to put variable names within those
    brackets, but this page is long enough, and I need room for the
    xkcd cartoon. I'll let you learn this topic from doing a web
    search on "c++ lambda capture".

[^anon]: Wait a second. I just said that lambda expressions are used to define
    functions without giving them a name ({dfn}`anonymous functions`), and yet
    here I am giving it a name.

    I'm giving this lambda expression a name, `pt_func`, for the sake of
    convenience. Read on; I'll show you a completely anonymous lambda
    expression in a few paragraphs. 

[^not-always]: This is not always true. If you looked at the web pages I linked
    to above, or you do your own web search on "C++ lambda expressions", you'll
    see examples in which you do have to declare a lambda expression's return type.
    However, this is not likely to matter for functions that you'd write
    for `RDataFrame`. 

You can use this definition of `pt_func` in exactly the same way as in
{numref}`Listing %s <define-func-c>`:

:::{code-block}	c++
auto pt_func = [](float x, float y) { return std::sqrt(x*x + y*y); };
auto pt_dataframe = dataframe.Define("pt",pt_func,{"px","py"});
:::

Consider those two lines of code. I define `pt_func`, use it as an argument to
`Define`, then never use `pt_func` again. As an alternative, we can use
the lambda expression as an argument to `Define` to define an anonymous function:

:::{code-block}	c++
:name: c-anon-define
:caption: An example of a completely anonymous lambda expression
auto pt_dataframe = dataframe
    .Define("pt",
            [](float x, float y) { return std::sqrt(x*x + y*y); },
	    {"px","py"} );
:::

I've inserted some line breaks to separate the arguments to `Define`.

This may seem like a bit much. But it's the sort of expression that
you'll see in the [RDataFrame
tutorials](https://root.cern.ch/doc/master/group__tutorial__dataframe.html)
(though without the convenient line breaks).

Using lambda expressions in this way makes more sense with `Filter`:

:::{code-block}	c++
:name: c-anon-filter
:caption: Using a lambda expression with `Filter`
auto ptcut_dataframe = pt_dataframe
    .Filter( [](float e){ return e < 145; }, {"pt"} );
:::

It's not all that different from what we used before:

:::{code-block}	c++
auto ptcut_dataframe = pt_dataframe.Filter("pt < 145");
:::

:::::{admonition} I feel a need. The need for speed!
:class: note

There is a reason why the ROOT tutorials use lambda expressions so
often: speed.[^slick] As I noted before, compiled code is faster
than "jit"ed code. If you're working with a C++ notebook, you can
easily see this for yourself: Create two new notebooks and put in the
following:

[^slick]: It has nothing to do with the ROOT developers' need to
    demonstrate how cool they are. Of course not.

    Now, if you'll excuse me, I've got to go write another
    smart-aleck footnote or stick another xkcd cartoon somewhere.

:::{code-block}	c++
:name: c-notebook-jit
:caption: The C++ notebook for testing the speed of jit-ed code
// In the first cell, copy-and-paste:
ROOT::RDataFrame dataframe("tree1","experiment.root");
TCanvas canvas;
auto pt_hist = dataframe.Define("pt","sqrt(px*px + py*py)").Histo1D("pt");

// In the second cell, copy-and-paste:
%%time
pt_hist->Draw();
:::

:::{code-block}	c++
:name: c-notebook-lambda
:caption: The C++ notebook for testing the speed of compiled code
// In the first cell, copy-and-paste:
ROOT::RDataFrame dataframe("tree1","experiment.root");
TCanvas canvas;
auto pt_calc = [](float x,float y) { return std::sqrt(x*x+y*y); };
auto pt_hist = dataframe.Define("pt",pt_calc,{"px","py"}).Histo1D("pt");

// In the second cell, copy-and-paste:
%%time
pt_hist->Draw();
:::

Run both notebooks. Bear in mind that this speed difference would be
even greater if {file}`experiment.root` were larger in both number of
rows and number of columns.

:::::

:::{figure-md} excel_lambda-fig
:class: align-center

<img src="https://imgs.xkcd.com/comics/excel_lambda.png" alt="xkcd excel_lambda" width="75%">

<https://xkcd.com/2453/> by Randall Munroe
:::