Vectorized code not faster

Hello, i had the following code:

for i=1:length(rho);
  for j=i:length(theta);
      PolarImage(j,i)=diag(CartImage(Y(i,j),X(i,j)));
  end
end

Elapsed time is 0.019816 seconds

I changed it to:

   for i=1:length(rho);
        PolarImage(:,i)=diag(CartImage(Y(i,:),X(i,:)));
   end

Elapsed time is 0.093083 seconds

I do not understand, why the vectorized code is a lot slower than the previous one. does anyone know an efficient way, for faster calculation? thanks ahead, Bart

[Walter Roberson]

Is CartImage a matrix or a function? If it is a matrix then CartImage(Y(i,j),X(i,j)) would be a single value and diag() of a single value is just going to be the value, so it is not clear why you would bother. If CartImage is a function then we need more information about what it computes.

[Bart van Essen]

CartImage is a binary Image file, so it is a binary matrix

[Walter Roberson]

What value are you expecting diag(CartImage(Y(i,j),X(i,j))) to be that is different from CartImage(Y(i,j),X(i,j)) ?

Answer 1

[Walter Roberson]

for i = 1:length(rho)
  idx = sub2ind(size(CartImage), Y(i,:), X(i,:));
  PolarImage(:,i) = CartImage(idx);
end

Or to be more efficient:

nrow = size(CartImage,1);
for i = 1:length(rho)
  PolarImage(:,i) = CartImage( (X(i,:) - 1) * nrow + Y(i,:) );
end

[Bart van Essen]

i had made a mistake copying my code, it was meant to be:

   for i=1:length(rho);
     for j=i:length(theta);
       PolarImage(j,i)=CartImage(Y(i,j),X(i,j));
     end
   end

so what i basically wanted to know, if you had ideas how i can vectorize the code of the double loop to make it faster, my vectorization using the diag command is 10 times slower than the double loop :/

[Walter Roberson]

nrow = size(CartImage,1);
PolarImage = CartImage( (X - 1) * nrow + Y ) .';