how to vectorise an xor operation in matlab

Question

I have run the following code in Profiler in Matlab and it is quite essential for me to vectorise this code as I feel that this is an unnecessary for loop.

I have 2 matrices G and source_data. every column in G will determine the rows which I need to pick up from source_data and xor them together.

I am creating G and source_data using the following piece of code

for i=1:10
 source_data(i,:)=rand(1,20)<.8;
end 

for i=1:15
 G(:,i)=rand(10,1)<.9;
end

I am performing an xor operation using the for loop below:

z=1;
while(i<=15) 
for j=1:10
    if(G(j,i)==1)
       intersum(z+1,:)=xor(intersum(z,:), source_data(j,:));
        z=z+1;
    end
end
C(i,:)=intersum(z,:);
i=i+1;
end

Is there a way to vectorise this code ? The time lag is acceptable for a small matrix but for large matrices this code is quite in efficient.

Thanks,

Bhavya

Answer 1

Assuming that:

• i starts at 1
• intersum starts at zeros

Here's a vectorized form of you code that produces the exact same result as your original:

function C = version_a()
  source_data = rand(10,20)<.8;
  G = rand(10,15)<.9;

  intersum = zeros(1, size(source_data,2));
  z = 1;
  i = 1;
  while i <= 15
    for j=1:10
        if(G(j,i)==1)
           intersum(z+1,:)=xor(intersum(z,:), source_data(j,:));
            z=z+1;
        end
    end

    C(i,:)=intersum(z,:);
    i=i+1;
  end
  ret = C;
end

function C = version_b()
  source_data = rand(10,20)<.8; % Can initialize in a single call
  G = rand(10,15)<.9;           % Same here
  C = zeros(size(G,2),size(source_data,2));

  C(1,:) = mod(sum(source_data(G(:,1),:)),2);
  for i = 2:15
    C(i,:) = mod(C(i-1,:) + sum(source_data(G(:,i),:)),2);
  end
end

To check the timing of both versions I used this test function:

function ret = xor_test()
  ret = 0;

  seed = 123456789;
  laps = 10000;

  tic
  for i = 1:laps
    RandStream.getDefaultStream.reset(seed);
    a = version_a();
  end
  toc

  tic
  for i = 1:laps
    RandStream.getDefaultStream.reset(seed);
    b = version_b();
  end
  toc

  ret = ret + sum(sum(b ~= a));
end

And I got the following timings on my machine:

Elapsed time is 13.537738 seconds.
Elapsed time is 2.302747 seconds.
ans =
     0

Now to why I changed it that way...

A xor operation over an array of logical s is pretty much checking the parity of the sum (treating true values as 1). Furhtermore, intersum is being used as an accumulator, so there's who's values eventually ends up in C so we skip it altogether. Taking the rows for which G(j,i) is 1 can be done by logical indexing .

And finally, even if you don't like this proposed version, I'd recommend preallocating your your C and intersum vectors (in case you're not doing so already). That has made a lot of difference for me in the past.