How to reduce execution time without using FOR loops?

while(error>0.01)
  iter = iter+1;
  %      for i = 2:1:xdim-1 % 57 secs
  %           for j = 2:1:ydim-1
  %              v_now(i,j) = (v_now(i-1,j)+v_now(i,j-1)+v_now(i+1,j)+v_now(i,j+1))/4;
  %           end
  %      end
  j = 2:xdim-1;
  i = 2:xdim-1;
  v_now(i,j) = (v_now(i-1,j)+v_now(i,j-1)+v_now(i+1,j)+v_now(i,j+1))/4;
  error = max(max(abs(v_now-v_prev)));
  v_prev = v_now;
end;

Answer 1

[dpb]

Can replace the computation of v_now with conv2

>> a=rand(5);
>> for i=2:4,for j=2:4,b(i,j)=(a(i-1,j)+a(i,j-1)+a(i+1,j)+a(i,j+1))/4;end,end
>> f=[0 1 0;1 0 1;0 1 0]/4
f =
       0    0.2500         0
  0.2500         0    0.2500
       0    0.2500         0
>> conv2(a,f,'valid')
ans =
  0.6302    0.4538    0.5160
  0.5800    0.7296    0.7551
  0.7276    0.8768    0.8236
>> b
b =
       0         0         0         0
       0    0.6302    0.4538    0.5160
       0    0.5800    0.7296    0.7551
       0    0.7276    0.8768    0.8236

Also, when compute error, can avoid the nested max call by using

max(abs(v_now(:)-v_prev(:))

Whether it'll make any appreciable difference, don't know otomh...