In MATLAB, can I have a script and a function definition in the same file?

Suppose I have a function f() and I want to use it in my_file.m, which is a script.

1. Is it possible to have the function defined in my_file.m?
2. If not, suppose I have it defined in f.m. How do I call it in my_file.m?

I read the online documentation, but it wasn't clear what is the best way to do this.

As of release R2016b, you can have local functions in scripts, like so:

data = 1:10;            % A vector of data
squaredData = f(data);  % Invoke the local function

function y = f(x)
  y = x.^2;
end

Prior to release R2016b, the only type of function that could be defined inside a MATLAB script was an anonymous function. For example:

data = 1:10;            % A vector of data
f = @(x) x.^2;          % An anonymous function
squaredData = f(data);  % Invoke the anonymous function

Note that anonymous functions are better suited to simple operations, since they have to be defined in a single expression. For more complicated functions, you will have to define them in their own files, place them somewhere on the MATLAB path to make them accessible to your script, and then call them from your script as you would any other function.

The way I get around this limitation, is to turn my scripts into functions that take no arguments (if I need variables from the global namespace, I either explicitly pass them in the function, or use "evalin" to grab them.)

Then you can define all the additional functions you need in the "script." It's a hack, but I have found it to be quite powerful in those cases where I need several non-trivial functions.

EDIT: Here's a simplistic example. All this can reside in a single file.

function [] = myScriptAsAFunction()
   img = randn(200);
   img = smooth(img);
   figure(1);
   imagesc(img);
   axis image;
   colorbar;
end

function simg = smooth(img)
    simg = img / 5;
end

You can do something like this (assuming your file is named my_file.m):

function my_file
   %script here
end

function out = f(in)
   %function here
end

If you click the run button the function my_file will be executed as default.

1) You cannot nest a function inside a script.

2) Make sure f.m is on your path or in current directory, and you can call it like any other function.

As of R2016b, you can define local functions within a script.

x = 1;
y = add1(x);

function z = add1(x)
    z = x + 1;
end