What is it better?

From the computational point of view, is it better one cycle for with following if statements, or several cycles for for each if statement? I think it's better this:

for i = 1:length(GR)
  if tool == 1
      Bmud(i,1) = B_3_c(1,1) .* (rho(i,1) .* 8.345) + B_3_c(2,1);
  elseif tool == 2
      Bmud(i,1) = B_3_e(1,1) .* (rho(i,1) .* 8.345) + B_3_e(2,1); 
  end
end

than

if tool == 1
   for i = 1:length(GR)
      Bmud(i,1) = B_3_c(1,1) .* (rho(i,1) .* 8.345) + B_3_c(2,1);
   end
elseif tool == 2
   for i = 1:length(GR)
      Bmud(i,1) = B_3_e(1,1) .* (rho(i,1) .* 8.345) + B_3_e(2,1); 
   end
end

Answer 1

[Sean de Wolski]

The second one. Every computation you can pull outside fo a for-loop is a good thing!

Also note this can be easily vectorized, for example with tool==2

Bmud(1:length(GR),1) = B_3_e(1,1) .* (rho(1:length(GR),1) .* 8.345) + B_3_e(2,1);

[Daniel Shub]

Is MATLAB smart about the multiplication ordering (i.e., scalar, matrix, scalar)?

[Jan]

No, Matlab is not smart for the ordering: it multiplies from left to right. Therefore:

A = rand(2000); b = rand; c = rand;

tic; for i=1:100; B = A * b * c; clear('B'); end; toc

tic; for i=1:100; B = A * (b * c); clear('B'); end; toc

tic; for i=1:100; B = (A * b) * c; clear('B'); end; toc

Sorry, I cannot measure it currently, because the virus-scanner has hijacked my machine.

[Daniel Shub]

@Jan, I did a similar test. It appears to go left to right.

Answer 2

[Daniel Shub]

I hope this is not homework ...

With only a single for loop you make the tool==1 comparison length(GR) times, while in the dual loop case you only make it once. So there is a slight computational edge. As there are only two multiplications and an addition within the loop (assuming B_3_* are matrices and not functions) that comparison may be a non-trival portion of your compute time ...

Ideally you want to get as much work outside the loop as possible, so a better approach would be:

if tool == 1
  m = B_3_c(1, 1).*8.345;
  b = B_3_c(2, 1);
  N = length(GR);
elseif tool == 2
  m = B_3_e(1, 1).*8.345;
  b = B_3_e(2, 1);
  N = length(GR);
else
  N = 0;
end
Bmud = nan(length(GR), 1); % You may have already done the intialization ...
for i = 1:N
  Bmud(i, 1) = m*rho(i, 1)+b;
end

So the loop only has 1 multiplication and 1 addition instead of 2 multiplications.

The MATLAB answer of course is to get rid of the loop completely.

if tool == 1
   Bmud = (8.345.*B_3_c(1,1).*rho(1:length(GR),1))+B_3_c(2,1);
elseif tool == 2
   Bmud = (8.345.*B_3_e(1,1).*rho(1:length(GR),1))+B_3_e(2,1);
end