Optimising code to get matrix indices based on point coordinates

I have the code

 xnum = 600;    xstp = 1/(xnum-1);    xgrid = 0:xstp:1;
 ynum = 600;    ystp = 1/(ynum-1);    ygrid = 0:xstp:1;

 xystp = xstp;
 nums  = 100000;

 O=rand(ynum,xnum);

 for i=1:1000
 x=rand(nums,1);
 y=rand(nums,1);

 elposx = x./xystp;
 elposy = y./xystp;

 elposx = round(elposx);
 elposy = round(elposy);

 pos_ind  = round(elposx.*ynum+elposy+1); % indices for element positions

 Onew = O(pos_ind)

 end

So, the idea is to use the coordinates (x,y), which represent the positions of points within the a matrix of size (xnum,ynum), to get the indices of the nearest element in the matrix. Then, using those indices, sample any matrix of this size (e.g. "O").

The above is the fastest I have been able to get it. This computation represents about 85% of the work of my total code, so it is a significant bottleneck. Is there a way to do these computations faster? Different functions? Parfors? GPU?

Any help is appreciated.

Answer 1

[Matt J]

No need to loop, as far as I can see. Also, no need to round() the calculation of pos_ind. It's all integer arithmetic,

    numO=1000;

     x=rand(nums,numO);
     y=rand(nums,numO);

     elposx = round( x*(xnum-1)+1 );
     elposy = round( y*(ynum-1)+1 );

     pos_ind  = sub2ind([ynum,xnum],elposy,elposx); % indices for element positions

     Onew = reshape(O(pos_ind),xnum,ynum,numO);

[Christopher]

Thanks for your thoughts!

For the example you are right, but my real code is more complicated so I don't think I can adopt your vectorized non-looping version, but thanks.

Removing round(), and your different function to find elposx and elposy helped.

However the use of sub2ind is about 5 or 6 times more expensive than:

 pos_ind  = (elposx-1).*ynum+elposy; % also corrected from the OP

Also, I have found that using

 pos_ind = uint32((elposx-1).*ynum+elposy);

results in doubling the performance for all calls using this vector such as in:

 O(pos_ind)

These changes have significantly improved performance. If you or anyone else have any more ideas please let me know. Although I improved it above, I wish the call O(pos_ind) could be significantly improved. Unfortunately, the discussion here seems to indicate that this indexing is just naturally slow in matlab (at least in 2012), but I am still researching this.

 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%Current optimized code:

 xnum = 600;  xnum1=xnum-1;  
 ynum = 600;  ynum1=ynum-1;
 nums = 100000;
 O    = rand(ynum,xnum);

 for i=1:1000
 x = rand(nums,1);
 y = rand(nums,1);

 elposx  = round(x*xnum1+1);
 elposy  = round(y*ynum1+1);

 pos_ind  = uint32((elposx-1).*ynum+elposy); % indices
 Onew     = O(pos_ind);
 end

Answer 2

[Matt J]

Using griddedInterpolant might be better. Should rely on more optimized builtin code, at least to do the rounding of the coordinates,

[m,n]=size(O);

F=griddedInterpolant(O,'nearest');

   for i=1:1000

       x = rand(nums,1)*(m-1)+1;
       y = rand(nums,1)*(n-1)+1;

      Onew=F(x,y);

    end

Further acceleration is possible for this example using PARFOR, but since your true code isn't available, hard to say if it's parfor-compatible.