How to dynamically change a function to solve a list of problems?

Hello everybody. I have a list of problems that need to be solve by a list of algorithm. In fact, I have 28 problems where each of them needs to be solved by each of 10 algorithms. So I need create a routine that change automatically the name of problem and algorithm. How can I do it?

Let suppose, prob1, prob2, prob3, etc the problems who needs to be solved by the algorithms alg1, alg2, alg3, etc. Where alg1, alg2, alg3, etc are functions.

The problemas are given test problems. To solve, for example, the prob1 using the alg1, I need to do

[M, jM] = alg1(@prob1)

My question is, how can I dinamically change the names of algorithms and problems such that all the problems are solved by all the algorithms?

I try put all algorithms in a 'cell array' like

alg = {'alg1','alg2','alg3'} 

and all the problems in another 'cell array' like

prob ={@prob1,@prob2,@prob3}

and then do

for i = 1:numel(alg)
    for j = 1: numel(prob)
        [M,jM]=(alg{i})(prob{j}) % I think here is the problem.
    end
end

but it didn't work.

Can anyone help me?

Thank you.

Answer 1

[Guillaume]

In some ways your question is strange because the solution is to use an array of functions handles instead of an array of function names. You're already using function handles for your problems (whatever these are) which is a bit unexpected. I would have thought that problems would be variables not functions.

alg = {@alg1, @alg2, @alg3};  %array of function handles
for i = 1:numel(alg)
    for i = 1:numel(prob)
        [M, jM] = alg{i}(prob{j});  %obviously you'd want to store the results in arrays/or cell arrays instead of overwriting them at each step of the loop
    end
end

[ELCIO S]

Thank you. Is exactly this what I need. Truely I have looked for what the '@' means, but didn't found anything. Now you told me, it is a 'function handle' so now I can researsh and understand how it works. I knew that the '@' needs to be used in 'prob' because there is it in the code of the problem, but at that time I didn't understand what its means. Now it is okay. Thank you a lot.

[Stephen23]

When I used [a major internet search engine] to search for "MATLAB at symbol" these were the very first two results returned:

https://www.mathworks.com/help/matlab/matlab_prog/matlab-operators-and-special-characters.html

https://www.mathworks.com/matlabcentral/answers/320129-what-does-do

Both of those pages explain that the "at" symbol defines function handles, and they have links to the appropriate documentation.

[Guillaume]

"I knew that the '@' needs to be used in 'prob' because there is it in the code of the problem, but at that time I didn't understand what its means"

It means that your problems are actually functions and what you are passing to the algorithms are the problem functions themselves. At some point the algorithm must call the function.