How to Calculate Moving Product?
3 views (last 30 days)
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.
More Answers (3)
Guillaume on 18 Dec 2015
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
Image Analyst on 19 Dec 2015
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.
Mark Britten-Jones on 21 May 2016
Edited: Guillaume on 21 May 2016
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;
Thats it. No loops and faster for large k