How can I calculate results from a function with two inputs using two arrays?

I have written a two-argument ackerman function as below. The code works and returns correct values if I specify the values or a variable (with a set value for the command line).

I need to test the function for all combinations of the arrays m=0:1:4 and n=0:1:3 (24 combinations). I can input an array using a for loop for m whilst setting n to 0 and this works fine and returns 6 answers for the cases (0,0) (1,0) (2,0) (3,0) (4,0) (5,0) (6,0). When I add the second array I only get 17 values rather than the 24 combinations.

How can I write this code so that it returns a list of all combinations (24)?

My command line input was below:

n=0:1:3;m=0:1:4;
for a=m
  for b=n
    res=ack(a,b)
  end
end

function res=ack(m,n)
  if m==0
    res = n+1;
  elseif m>0 && n==0
    res = ack(m-1,1);
  elseif m>0 && n>0
    res = ack(m-1,ack(m,n-1));
  end

Answer 1

[Mark McBroom]

code looks correct. Does your code actually complete? Or is it simply taking a very long time to complete the 18th combination? Your function has very deep recursion and could therefore take a long time to compute whenever n > 0.

[FortuitousMonkey]

Edit: The correct values I were required to use were m=0:1:3 and n=0:1:4.It now computes all of the values required. This is was computable. When m goes above 4 it appears not computable with my current code.

Thanks for the feedback.

I just checked after I left the computer for a while and a noticed appeared, so your guy sounds right.

Out of memory. The likely cause is an infinite recursion within the program.

Is there a way to compute these larger numbers in Matlab?

Answer 2

[Jan]

Something goes wrong.

 I need to test the function for all combinations of the arrays m=0:1:4 and n=0:1:3
 (24 combinations).

m has 5 elements, n has 4 elements, such that you get 20 combinations, not 24.

 6 answers for the cases (0,0) (1,0) (2,0) (3,0) (4,0) (5,0) (6,0).

No, there is no 6. m goes from 0 to 4.

 When I add the second array I only get 17 values rather than the 24 combinations.

Do you mean inputs or outputs?

As Mark M has said already: The function takes a long time for the input [4,1]. Currently it is still running on my computer...

[EDITED] ... still running - the values grow and grow

[EDITED 2] ... still running. I give up. Do you have an evidence, that the computations ends?

[FortuitousMonkey]

Yep my mistake on the number of elements, just mixed up to different arrays.

My code failed eventually, I included the error message above.

Edit: Ackerman function always terminates. The recursion is bounded because in each recursive application either m decreases, or m remains the same and n decreases. (Wikipedia)