Question

Suppose, in MATLAB, that I have a matrix, A, whose elements are either 0 or 1.

How do I get a vector of the index of the last non-zero element of each column in a faster, vectorized way?

I could do

[B, I] = max(cumsum(A));

and use I, but is there a faster way? (I’m assuming cumsum would cost a bit of time even suming 0’s and 1’s).

Edit: I guess that I vectorized even more than I need fast – Mr. Fooz’ loop is great but each loop in MATLAB seems to cost me a lot in debugging time even if it is fast.

Answer 1

As shown by Mr Fooz, for loops can be pretty fast now with newer versions of MATLAB. However, if you really want to have compact vectorized code, I would suggest trying this:

[B,I] = max(flipud(A));
I = size(A,1)-I+1;

This is faster than your CUMSUM-based answer, but still not quite as fast as Mr Fooz’s looping options.

Two additional things to consider:

• What results do you want to get for a column that has no ones in it at all? With the above option I gave you, I believe you will get an index of size(A,1) (i.e. the number of rows in A) in such a case. For your option, I believe you will get a 1 in such a case, while the nested-for-loops option from Mr Fooz will give you a 0.

• The relative speed of these different options will likely vary based on the size of A and the number of non-zeroes you expect it to have.