Difference between a function handle and function

Question

What is the difference between a function handle and a function itself in MATLAB? Is it like the difference between a function pointer and function in C/C++?

Answer 1

I have no idea about C/C++ but in MATLAB a function is a non-anonymous program which (possibly) takes input and (possibly) gives output, and is defined using the function keyword, e.g.

function a = MySum(b)
    a = sum(b);
end

whereas a function handle is a sort of short-cut to a function which is anonymous, i.e. can't be called from outside that script. It is created using the @ syntax:

f=@(b)sum(b);

The function is saved as a .m file, with the function name as file name, so, using the above example, MySum.m. Having saved this on your path, and defined the anonymous function as per the above this is how you call them:

b = [1 2];
f=@(b)sum(b);
aFunction = MySum(b); % = 3
aAnon = f(b); % =3

If we now have a new script on the same path, we can't use the anonymous function if we don't define it, try:

b = [1 2];
aFunction = MySum(b); % = 3
aAnon = f(b); % gives error that f is undefined

If you create a script outside your path, also the function itself will fail:

b = [1 2];
aFunction = MySum(b); % gives error that MySum is undefined
aAnon = f(b); % gives error that f is undefined

Function handles are used for several reasons, of which the two most prominent in my opinion: inside "disguised loop functions" such as arrayfun or bsxfun which require a syntax like arrayfun(@function,array), or when using e.g. a certain combination of functions very often in a script, e.g. nnz(rand(size(N)>M), to shorten the sequence: f = @(M,N)nnz(rand(size(N)>M) and now one can call f(N,M) instead of nnz(rand(size(N)>M).

Following Wolfie's comment there is indeed a dual nature of a function handle: it can act as a pointer, i.e. how f in the above example is a pointer to the function sum, but can also be a function in it's own right, like the combination of functions nnz(rand(size(N)>M) or things like a polynomial: f=@(b) b.^2 + 5*b + 1.

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Note on the "possibly" takes in-/output:

You could define a function as

function MySine()
    x = 1:10;
    y = sin(x);
    plot(x,y)
end

which is a perfectly valid function which takes no in- or output arguments.