How to Use arrayfun with a Multivariate Function of n Variables?

Suppose f(X) is a function of a vector X = [x1, x2, ..., xn]. How to evaluate the function at a certain range of values, say y1, y2, ..., ym, for the variable xi while keeping all other variables fixed?

To make it simple: Say x1, ..., x59, x61, ..., x100 = 10, and we want to evaluate the function for three different values for x60, say at 1.5, -3, and 12. Can we do this without for loops?

Answer 1

[Arthur Roué]

arrayfun is generally not faste than a for loop, becaut it has an internal for loop. read this for more details : https://fr.mathworks.com/matlabcentral/answers/324130-is-arrayfun-faster-much-more-than-for-loop

So I reccomend something like

X = [x1 .. xn];
x60 = [1.5, -3, 12];
Y = NaN(1, numel(x60)); % Pre-allocation (not required for small vectors)
for idx = 1:numel(x60)
    X(60) = x60(idx)
    Y(idx) = yourFun(X)
end

[Souradeep Mukhopadhyay]

Here also for loop is used. Is this possible without a single for loop?

[Arthur Roué]

Anotherway is to vectorize the operation in the function. The idea is to create a matrix 3xN where each line is a different version of X and calculate all results in one time.

[Kareem Elgindy]

OK. But how to calculate the 3xN matrix quickly then. Can we do it without for loops?

[Arthur Roué]

Can you share the code of your function ?

Answer 2

[Souradeep Mukhopadhyay]

You should make 3 different X arrays here X1, X2, X3 and then pass the 3 arrays in function 3 times to compute y 3 times.