Vectorization

Hi all,

Answer please in terms of 'Vectorization For Dummies'.

If I have a nested for loop of the form:

for i = 1:10

   for j = 1:10

      for k = 1:10

         array(i,j,k) = function(input1(i), input2(j), input3(k))

      end
   end
end

What is the shortened codeneed to use to vectorize this?

Thanks

Alan

[Daniel Shub]

Why do you want to vectorize it? Loops are no longer slow in MATLAB.

[Oleg Komarov]

The answer would be to vectorize the function such that it accepts arrays instead of scalars.

[Daniel Shub]

I believe the speed up to loops has been around since the introduction of the JIT (maybe MATLAB 6.5). TMW tends not to give details of the JIT because it is a moving target. The profiler also does not use the JIT so timing becomes problematic. One advantage of loops is you can use parfor loops and take advantage of all you CPUs/cores.

Answer 1

[Jan]

No new answer, but more explicit:

Very slow:

for i = 1:100
  for j = 1:100
    for k = 1:100
       array(i,j,k) = sin(i+j+k);
    end
  end
end

Faster with pre-allocation:

array = zeros(100,100,100);
for i = 1:100
  for j = 1:100
    for k = 1:100
       array(i,j,k) = sin(i+j+k);
    end
  end
end

Fast partial vectorization:

array = zeros(100,100,100);
for i = 1:100
  for j = 1:100
    array(i,j,1:100) = sin(i+j+(1:100));
  end
end

Full vectorization:

value = bsxfun(@plus, bsxfun(@plus, 1:100, transpose(1:100)), reshape(1:100, 1, 1, 100));
array = sin(value);

For large problems the creation of the large temporary arrays needs more time that the vectorized operation can save. Therefore the full vectorization is optimal for expensive functions, which have a lot of overhead for checking of inputs etc.

[Alan Shillitoe]

Thanks Jan.

That is the sort of thing I was after. I'll have a closer look at bsxfun to understand it better.

A.

[Daniel Shub]

+1, but why not make the outer loop a parfor?

Answer 2

[Alan Shillitoe]

Aren't they? This is the first I have read about this. Have you got a link to this in the documentation?

A.

[Oleg Komarov]

Please use comments.

Answer 3

[Alan Shillitoe]

Oleg,

How do I do that? I'm pretty new to this, so need it in really basic terms.

A.

[Oleg Komarov]

Edit your original question and post the relevant code of the function.

Answer 4

[Walter Roberson]

Loops are no longer as slow in MATLAB, but function calls are. You want to reduce the number of function calls, which you do by rewriting the function itself to be vectorized. If you cannot do that, then there is effectively no available speed-up for your current code (assuming you have pre-allocated the output array)