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memory overflow with double factorial function

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I am trying to create a recursive formula to calculate the double factorial of a number, n. The code I have come up with currently is as follows:
function [DFact] = DFactorialRec(n)
DFact = n*DFactorialRec(n-2)
end
This clearly does not work as it will recursively continue for negative values of n. Please could someone suggest an alteration to stop the memory overflow error?
================================================================
Out of memory. The likely cause is an infinite recursion within the program.
Error in DFactorialRec (line 2)
DFact = n*DFactorialRec(n-2)
================================================================
Thanks!

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Walter Roberson
Walter Roberson on 9 Oct 2020
function [DFact] = DFactorialRec(n)
if n==0
disp("n is equal to 1")
DFact = 1;
else if n==1
disp("n is equal to 1")
DFact = 1;
else
DFact = n*DFactorialRec(n-2);
end
end
end
However I would recommend you rewrite using elseif instead of else if
Harry Rogers
Harry Rogers on 9 Oct 2020
thank you for the correction however this does not solve the error.. do you have any advice regarding how to make this work?
Walter Roberson
Walter Roberson on 9 Oct 2020
The code I posted worked for me provided that n is a scalar. If it is a non-scalar then you have the problem that your if is comparing a non-scalar to a scalar, and that comparison might be true for some elements but false for others...

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Accepted Answer

John D'Errico
John D'Errico on 9 Oct 2020
Edited: John D'Errico on 9 Oct 2020
Recursive formulas like this always seem useful, but they are terrible in terms of coding, in terms of efficiency. You don't want to write it that way! Yes, the code you wrote looks pretty. That it will not work as you wrote it is a problem of course.
Think about it. For every recursive call, you need to allocate a new workspace, you incur function call overhead. This is a bad thing, and done for absolutely no good reason. Instead, a simple loop is all you need. Start at the bottom.
But better even yet is to not bother with an explicit loop. You can write this function in not much more than one line of code. Just use prod. The rest of what I did was mostly to make it friendly.
function DFact = DFactorial(n)
% Double factorial function, n!!
% https://en.wikipedia.org/wiki/Double_factorial
%
% n!! = 1 for both n == 1 and n == 0.
if isempty(n) || (numel(n) > 1) || (n < 0) || (mod(n,1) ~= 0)
error('The sky is falling. n must be scalar, non-negative, integer.')
end
DFact = 1;
if n > 1
start = 1 + mod(n + 1,2); % caters for either parity of n
DFact = prod(start:2:n);
end
end
Will this code fail for large values of n? Of course. It is easy to overwhelm the dynamic range of a double. But that will happen for any code that uses double precision. An exact integer will not be produced for n > 29 when done in double precision, and inf will result above 300. But again, that will happen in any case.
It is also easy to write a version that handles vector or array arguments for n.

  1 Comment

Harry Rogers
Harry Rogers on 10 Oct 2020
Thats brilliant thank you. You've given me a deeper understanding about different operators that can be used within matlab. I'm faily new to using it so thanks for the advice.

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