How to evaluate a multivariable function at different value of the variable effectively ?

I am having a function f() this function is complicated function and its varialbles are epxi, beta, a1_t2, a2_t3, and xai. All of these variable are from 0 to 1. However, because some NaN problem, I decided to change it a little bit that is all the variable are from 0.1 to 0.9.

epxi = [0.1:0.1:0.9];
beta = [0.1:0.1:0.9];
a1_t2 = [0.1:0.1:0.9];
a2_t3 = [0.1:0.1:0.9];
xai = [0.1:0.1:0.9];

I want to evaluate my function f at all posible combination of epxi, beta, a1_t2, a2_t3, and xai to find out the max value effectively ( I have a multi-cores computer) but dont know how to do this.

Currently, my implemenation is quite naive and bad:

for c1 = 1:length(epxi)
    for c2 = 1:length(beta)
        for c3 = 1:length(a1_t2)
            for c4 = 1:length(a2_t3)
                for c5 = 1:length(xai)
                    temp = f(epxi(c1),beta(c2),a1_t2(c3),a2_t3(c4),xai(c5);
                    result = [result temp];
                end
            end
        end
    end
end

Particularly, f() here is the function of interest. I store the evaluation to an array that keep expanding. The expanding array is the variable result.

Note that this function f is not a symbolic function.

I intended to use the built-in matlab function max on the result vector but I understand that this implementation is not efficient. I guess that some pre-allocation of the variable result would be more efficient but fail to do so.

Please help me with this !

Thank you for your enthusiasm !

Answer 1

[Tuong Nguyen Minh]

I have finally found a way to do it by using the built-in combvec function

all_combination= combvec(epxi,beta,a1_t2,a2_t3,xai)';
function_value_array = zeros(1,length(epxi)*length(beta)*length(a1_t2)*length(a2_t3)*length(xai));
parfor jj = 1:length(function_value_array)
    function_value_array(jj) = TotalSTP_Exhaustive(all_combination(jj,1),all_combination(jj,2),all_combination(jj,3),all_combination(jj,4),all_combination(jj,5));
end
    y = max(function_value_array);