Matlab/Octave function handlers and nargin

Question

I am writing program in Octave and I encountered a problem, I implemented Gauss-Legandre Quadrature and I pass to my Gauss-Legandre function few arguments, and I pass the function to be intergrated in a cell cube, so I can pass few function at a time. I have this piece of code:

    for weight=1:length(w)
        temp=1; 
        for fun=1:length(c)
            %liczenie iloczynu f(x_i)g(x_i), x_i - pieriwastki wielomianu Legandra
            f=c{fun};
            nargin(func2str(c{fun}))
            if (nargin (func2str(c{fun})) == 1)
                disp('a');
                temp*=c{fun}((b-a)/2 * x(weight) + (a+b)/2);
            else
                    (b-a)/2 * x(weight) + (a+b)/2;  
                temp*=f((b-a)/2 * x(weight) + (a+b)/2,I,points);
            end
        end
        %mnozenie wyniku przez odpowiedni wspolczynnik - wage
        temp*=w(weight);
        result+=temp;
    end

In cell array there are function handlers to functions which I want to integrate. Depending on number of arguments that function takes i want to use two different calls for function. If in cell array there is handler to a function that is written in .m file in the same directory as my Octave working directory everything works fine, but when i define function in Octave running time, for example:

    function result=a(x)
    result=x*x
    end

Type

    c{1}=@a

and pass this cell array to my function Kwadratury there is an error of nargin

    error: nargin: invalid function
    error: called from:

Why is that and how can I solve it, so I can define function not only in .m files but also in Octave.

Answer 1

I suspect I have a solution, but as this is Octave-specific and I'm mostly used to MATLAB, your mileage may vary.

You call the nargin function by supplying a string argument, this means that nargin will have to resolve that function and check the number of arguments. When you declare a function in-line, that function is defined within that scope (i.e. your base scope), so resolving the function name will not work from within any function (or it might resolve to a built-in function, which is even worse behavior).

The best solution is to use nargin(c{fun}) instead of nargin(func2str(c{fun})). That way you pass the actual function handle along, and there is no need to resolve the function name to the actual function, and hence no possible ambiguity.

In general I recommend against using strings to pass functions: that why function handles are included in MATLAB, so anyone reading your code (or a static code analysis tool) will be able to understand you are working with functions. When using strings, everything becomes ambiguous: does a string 'a' refer to the function a or to the first letter in the alphabet?

With regard to using inline functions, I don't know whether Octave supports this, but if you function is quite simple, it's easier to define an anonymous function, such as your example, by a = @(x)(x*x);. That is a construct that is supported by MATLAB, so that makes your code more portable to other environments (well, you'd still need to replace X *= A with X = X * A; to be MATLAB compatible).

edit: Another possibility could be to just try out whether a form with multiple parameters works and fall back to the one parameter form when necessary:

try
   (b-a)/2 * x(weight) + (a+b)/2;  
   temp*=f((b-a)/2 * x(weight) + (a+b)/2,I,points);
catch ME
   try
       disp('a');
       temp*=c{fun}((b-a)/2 * x(weight) + (a+b)/2);
   catch ME
   end
end

You might want to check whether the returned error ME really states that a wrong number of arguments is used to allow other errors through. I do admit this is an ugly work-around, but since Octave apparently doesn't support function handles for nargin, it might be the only way you'd get what you want for inline functions.