How to get indexes of logical matrix without using find in matlab?

Question

Let's assume my matrix A is the output of comparison function i.e. logical matrix having values 0 and 1's only. For a small matrix of size 3*4, we might have something like:

A =

     1     1     0     0
     0     0     1     0
     0     0     1     1

Now, I am generating another matrix B which is of the same size as A, but its rows are filled with indexes of A and any leftover values in each row are set to zero.

B =

     1     2     0     0
     3     0     0     0
     3     4     0     0

Currently, I am using find function on each row of A to get matrix B. Complete code can be written as:

A=[1,1,0,0;0,0,1,0;0,0,1,1];
[rows,columns]=size(A);
B=zeros(rows,columns);

for i=1:rows
    currRow=find(A(i,:));
    B(i,1:length(currRow))=currRow;
end

For large martixes, "find" function is taking time in the calculation as per Matlab Profiler. Is there any way to generate matrix B faster?

Note: Matrix A is having more than 1000 columns in each row but non-zero elements are never more than 50. Here, I am taking Matrix B as the same size as A but Matrix B can be of much smaller size column-wise.

You can replace find with an indexing operation, but I’d be surprised if that’s faster. I = 1:columns; currRow = I(A(i,:)); — Cris Luengo
I was thinking along the lines that "for" loop can be removed altogether for faster operation. Is that possible? — lonstud
Have you considered storing your matrix as a sparse matrix? I would also store the transpose of the matrix so as to make the searches along the columns, the way they're stored in MATLAB. — beaker
for loops in Matlab are not necessarily slow. Historically they were but that's not so true nowadays. With the suggestions from Cris and beaker I wouldn't expect a vectorised version to be faster. — David

Burak Burak · Accepted Answer · 2020-01-01T17:00:07

I would suggest using parfor, but the overhead is too much here, and there are more issues with it, so it is not a good solution.

rows = 5e5;
cols = 1000;
A = rand(rows, cols) < 0.050;
I = uint16(1:cols);
B = zeros(size(A), 'uint16');
% [r,c] = find(A);
tic
for i=1:rows
%     currRow = find(A(i,:));
    currRow = I(A(i,:));
    B(i,1:length(currRow)) = currRow;
end
toc

@Cris suggests replacing find with an indexing operation. It increases the performance by about 10%.

Apparently, there is not a better optimization unless B is required to be in that specific form you tell. I suggest using [r,c] = find(A); if the indexes are not required in a matrix form.

How to get indexes of logical matrix without using find in matlab?

1 Answers