compare anonymous function handles

The following comparison of two function handles should return true in my opinion

f1=@(x,y)(x*y)
f2=@(x,y)(x*y)
isequal(f1,f2)

However, R2016a returns false on this comparison, which is a bug in my opinion. According to the documentation:

Unlike handles to named functions, function handles that represent the same anonymous function are not equal. They are considered unequal because MATLAB cannot guarantee that the frozen values of nonargument variables are the same

In my example, both x and y ARE argument variables. The result is always the same for given arguments. What do you think?

Answer 1

[Matt J]

The documentation that you quoted is referring to situations like this:

    >> a=1; f1=@(x,y)(x*y+a);
    >> a=2; f2=@(x,y)(x*y+a);

These display the same,

    >> f1,f2  

    f1 = 

        @(x,y)(x*y+a)

    f2 = 

        @(x,y)(x*y+a)

but give different output for the same input arguments:

    >> f1(0,0), f2(0,0)

    ans =

         1

    ans =

         2

If you consider 2 anonymous functions to be equal if they display the same, you could compare them this way,

>> strcmp(func2str(f1),func2str(f2))

ans =

       1

[Markus Leuthold]

Yes, you're right, the documentation covers the case where you have nonargument values like variable a in your example. Matlab cannot guarantee that a is frozen, as they call it.

However, in my example, Matlab can guarantee the same result for both f1 and f2 with the same input, since I don't have something like variable a from your example. Therefore they should be considererd "equal" in my opinion.

As for func2str(), I cannot use that in my particular use case. I have two huge hierarchical structs to compare. One of the fields contains f1 in the first struct, and f2 in the second struct. I'd like to use

    A.x.r.fcn=@(x,y)(x+y);
    A.x.s=1;

    B.x.r.fcn=@(x,y)(x+y);
    B.x.s=1;

    isequal(A,B)

If I'd use instead

    isequal_based_on_func2str(A,B)

where I iterate over all the fields and hierarchy of A and B, then yes, I could use func2str if the datatype of the current field is a function handle and the built-in isequal for all the other datatypes. That's what I am using right now. Unfortunately, this is slower by a factor of 100 compared to the Matlab built-in isequal in my particular use case.

Answer 2

[Walter Roberson]

funinfo(1) = functions(f1);
funinfo(2) = functions(f2);
strcmp(funinfo(1).function, funinfo(2).function) && isequal(funinfo(1).workspace{1}, funinfo(2).workspace{1})

[Matt J]

Just as a heads up, TMW says that the behavior of funinfo.workspace is undocumented and subject to change, so there are hazards to designing tools around it.

[Markus Leuthold]

Interesting solution, I wasn't aware of

   funinfo=functions(fcn)

However, since I don't have nonargument variables, my local workspace

    funinfo(1).workspace{1}

is always empty. But interesting anyways!

And it still doesn't solve my problem where I have a fcnhandles in deeply nested structs to compare

[Walter Roberson]

I doubt Mathworks will change this behaviour any time soon. The alternative would require that Mathworks search all existing function handles, in all scopes, to see if it could find a match.

I suggest you grab a File Exchange Contribution such as http://www.mathworks.com/matlabcentral/fileexchange/34565-micro-cache--memoize-cache-function-results and create a routine that takes in strings and return function handles -- we know that you can convert to string since you do not use any variables from your workspace. The routine would keep a copy of each function handle it generates and upon being presented with the same string would return the same function handle, which would then permit isequal() to operate.