Functional Programming in Matlab - Declaring variables in anonymous functions

declaring_variables_in_anonymity.m

% Consider the scenario where you want to declare 
%  an anonymous function to do some task, but it 
%  requires multiple uses of a result that is 
%  expensive to compute. 
% For example, consider the following series of statements:

a = rand(1000); 
b = rand(1000);
c = a * b;
[a./c b./c]

% Let's say you want to encapsulate this procedure as an 
%  anonymous function of 'a' and 'b':
fun = @(a,b) [a./(a*b) b./(a*b)]

% This can be done by replacing 'c' with its definition. 
%  But if this definition is expensive to compute, you'd 
%  rather compute it once and reuse the results. 
% Enter the 'apply' function:

apply = @(varargin) varargin{end}(varargin{1:end-1});

% Apply takes a series of arguments and passes them to 
%  the final argument. For example:

apply(1, 2, @(x, y) x + y)

% Returns 1 + 2 = 3
% This is useful in a functional programming context because 
%  it lets us declare secondary variables in an anonymous 
%  function:

fun = @(a,b) apply( a * b, @(c) [a./c b./c] )

% Now we have an anonymous function of two variables that 
%  performs a computation, captures the output, and uses 
%  the output in additional computations. 
% Go team!