MATLAB: How to evaluate a function with multiple inputs on all possible combinations of input vectors

Question

Say I have a simple function with three inputs

f = @(a,b,c) a+b+c

I would like to evaluate this function on combinations of inputs

A = 1:10
B = 2:2:10
C = 0.1:0.1:1

and store the output in a matrix F.

Right now I am doing this as follows:

F = NaN(length(A),length(B),length(C));

for ia = 1:length(A)
   for ib = 1:length(B)
     for ic = 1:length(C)
        F(ia,ib,ic) = f(A(ia),B(ib),C(ic))
     end
   end
end

I am wondering if there is an efficient way to do this without the use of sloppy for loops, *and without having to vectorize the function f.

Getting rid of the loops and vectorizing `f` are eseentiallythe same thing, as I see it. You could use `bsxfun` with a custom non-vectorized function, but I doubt it will be faster than loops — Luis Mendo, May 08 '15 at 18:34
You can use `meshgrid` for `A,B,C` then use just one loop. It is not efficient but might look smarter! — Rashid, May 08 '15 at 18:36
@LuisMendo How? Speed isn't an issue this time, I just wanted cleaner syntax :-) — Berk U., May 08 '15 at 18:39
@knedlsepp Whoops! Thanks for pointing this out. I just fixed it. — Berk U., May 08 '15 at 18:42
@BerkU. I mean something like `f = @(a,b) a+b; A = 1:10; B = 2:2:10; resultAB = bsxfun(f, A(:), B(:).');`. But it only works for two variables ` — Luis Mendo, May 08 '15 at 18:45

score 4 · Accepted Answer · edited May 23 '17 at 11:43

If you want neat syntax and don't care much about memory or speed, you can use:

ndgrid to generate all combinations; and then
arrayfun to call f on each combination:

The second step exploits the fact that arrayfun can be called with several arrays as input, and in that case it takes corresponding elements from each array:

[aa, bb, cc] = ndgrid(A,B,C);        %// step 1
result = arrayfun(f, aa, bb, cc);    %// step 2

As for the memory and speed concerns I mentioned above:

Step 1 requires quite a lot of memory if the input vectors are large, because all combinations are generated at once.
Step 2 may result in code slower than using for loops; see for example here.

MATLAB: How to evaluate a function with multiple inputs on all possible combinations of input vectors

1 Answers1