How to Calculate Moving Product?

Is there any vectorized way of calculating moving products. If A is a vector, how can I calculate its moving product with a specified window size.

For example, for a window size of 3, the moving product should be equal to:

[A(3)*A(2)*A(1), A(4)*A(3)*A(2), A(5)*A(4)*A(3), ..., A(N)*A(N-1)*A(N-2)]

How do I calculate it without using a for loop. I know that the 'filter' function can be used for calculating moving means in a vectorized manner; but I have not seen any function that can calculate a moving product.

Can someone please help. Thanks.

[Guido Marco]

try somthing like this... function Y=divf(X) % divisive differential

X0=X(1:end-1); X1=X(2:end); Y=X1./X0;

Answer 1

[Jonathan Agg]

The function movprod was added in 17a. There's also a list of similar functions here which are included in MATLAB, like movsum and movmax.

[Gaurav Soni]

This is so great.

Answer 2

[Guillaume]

One way to achieve what you want:

function mp = movingproduct(v, windowsize)
   %add input validation code
   vv = repmat([v(:); nan], 1, windowsize);
   vv = reshape(vv(1:end-windowsize), [], windowsize);
   mp = prod(vv(windowsize:end, :), 2);
   if isrow(v), mp = mp.'; end
end

[Gaurav Soni]

Thank you. This is a nice method to avoid a For loop. I was also able to find a way. Here it is:

function mp = movingproduct(v, windowsize)
logv = log(v);
b = (1/windowsize)*ones(1,windowsize);
mp = exp(windowsize*filter(b,1,logv));
mp = mp(windowsize:end);
end

This method is a bit faster than what you devised above, but it suffers from numerical errors that accumulate due to log and exp operations.

[Guillaume]

Another possible implementation, which has no numerical errors. It does have a loop (through arrayfun) but only over the window size.

function mp = movingproduct(v, windowsize)
  %add input validation code
  vv = repmat({v(:)}, 1, windowsize);
  vv = arrayfun(@(row) circshift(vv{row}, row-1), 1:windowsize, 'UniformOutput', false);
  vv = [vv{:}];
  mp = prod(vv(windowsize:end, :), 2);
  if isrow(v), mp = mp.'; end
end

Answer 3

[Image Analyst]

One possibility is to use nlfilter() where you can define the filter to be used on the window to do absolutely anything you want it to do, such as prod().

output = nlfilter(yourMatrix, [1, 3], @prod);

I attach a full blown demo where I use nlfilter to compute the Otsu threshold on a sliding 3x3 window basis.

[Gaurav Soni]

Thanks. I think this would be pretty useful for people who have access to Image Processing toolbox. It looks like nlfilter is only available in the Image Processing Toolbox.

Answer 4

[Mark Britten-Jones]

The problem with the loop approach is that it repeats calculations. For example A(3)*A(2) is calculated twice in a moving product of window size 3. The vectorised versions also suffer from this repetition. It can be avoided using a recursive approach which recognises that e.g. for k even a k moving product can be calculates as a k/2 moving product times the k/2 lag of the k/2 moving product. For large k the increases in speed are dramatic. Here is the code, which relies on a lag function (few lines to code up):

function y = cumprodk(x,k)
y = x;
if k==1; return; end;
y = cumprodk(y, floor(k/2));
y = lag(y, floor(k/2)).*y;
if rem(k,2) == 1 % if k odd need to multiply by lag k-1      
y = lag(x,k-1).*y;
end
end

Thats it. No loops and faster for large k