Given two vectors A,B - how can I create a vector v where v(n) = A(n):B(n)

Hello, and lots of thanks in advance to anyone that can help me out here! Now some more details about this question:

• A and B are of equal size.
• It doesn't matter (to me) whether v is a vector, cell array, or any other data type; whatever works will do.

Here an example:

A = [ 1 , 2 , 3 , 4 ]; B = [ 5 , 5 , 6 , 7] ==> C = [ (1,2,3,4,5), (2,3,4,5), (3,4,5,6), (4,5,6,7) ]

Why I'm asking: I tried implementing morphological operations myself, which all in all works, but performs very poorly, as the current version contains a double-for-loop. One instance of my functions would be the following:

function dilatedImage = ownDilate(binaryImage)
  dilatedImage = binaryImage;
  dilatedImage = dilatePoint(binaryImage,1:size(binaryArea,1)-1,1:size(binaryArea,2)-1);
end
function result = dilatePoint(binaryImage,py,px)
  result = binaryImage;
  x0 = max(1,px - 3);
  y0 = max(1,py - 3);
  x1 = min(size(binaryArea,2),px + 3);
  y1 = min(size(binaryArea,1),py + 3);
  %
  dx0 = max(1,5-px);
  dy0 = max(1,5-py);
  dx1 = min(7,size(binaryArea,2) - px + 4);
  dy1 = min(7,size(binaryArea,1) - py + 4);
  %
  for j = px
      for i = py
          se = structureElement(dy0(i):dy1(i),dx0(j):dx1(j));
          if binaryArea(i,j)
              result(y0(i):y1(i),x0(j):x1(j)) = or(se,result(y0(i):y1(i),x0(j):x1(j)));
          end
      end
  end
end

Rather than using i,j in a for loop I would have liked to use py,px and without a for loop. Replacing the if statement would be easy I figure, I only need to create a vector of indices for which the if statement would apply and then use that for the assignment below. But what gives me headaches is the statement above that, since i cannot use the colon operator to create something as stated in the question. I know avoiding for statements isn't ALWAYS possible in Matlab, but I can't get rid of the feeling that it can in my case.

Anyways, thanks for your time, I hope I put everything detailed enough, but if I forgot something, please tell me!

Answer 1

[Brendan Hamm]

The function you are looking for is called arrayfun. This takes a function handle and n arrays and calls the function n-times, once for each element. Of course there is the potential in your example to have different sizes of data passed back so we set the UniformOutput flag to false.

A = [1,2,3,4];
B = [5,5,6,7];
f = @(a,b) a:b;
myData = arrayfun(f,A,B,'UniformOutput',false);

We can see the result is what you were looking for.

myData{1}
ans =
     1     2     3     4     5
myData{2}
ans =
     2     3     4     5
myData{3}
ans =
     3     4     5     6
myData{4}
ans =
     4     5     6     7

[Christoph Michael Essler]

Thank you very much, that was precisely the kind of function i was looking for! Additionally it seems to perform rather well, possibly better than for loops would. Thanks again and have a nice day!