Vectorize this for loop

Hey everyone,

I have identified the following for-loop to be a time-eater in my program and I'm looking to find a more efficient solution, possibly vectorizing the whole thing.

What I have is a tool path that consists of - x,y,z coordinates - o1,o2,o3 which are the orientation vector components - t as the time vector

Now I want to calculate the coodinates of an eccentric movement orthogonal to the orientation with frequency fecc and radius recc to that toolpath. For that I have come up with the following code:

for i=1:length(t)
   v=null([o1(:,i) o2(:,i) o3(:,i)]); %Create orthogonal vectors in circle plane
   xecc=recc*(sin(fecc*t)*v(1,1)+cos(fecc*t)*v(1,2)); %x of circle in 3D
   yecc=recc*(sin(fecc*t)*v(2,1)+cos(fecc*t)*v(2,2)); %y of circle in 3D
   zecc=recc*(sin(fecc*t)*v(3,1)+cos(fecc*t)*v(3,2)); %z of circle in 3D
end

This works fine but takes a lot of time (some paths include up to 100k points). Is there any way to vectorize this or increase efficiency by other means?

Thanks in advance!

Michael

I attached an example so you see what this is about. Cyan is x,y,z and Red is x+xecc, y+yecc, z+zecc: http://img836.imageshack.us/img836/750/examplekp.jpg

[Jan]

I assume there is a missing ( in the "xecc=recc*sin(" line.

[Michael Fink]

yeah thanks, I corrected it now

Answer 1

[Robert Cumming]

did you use

    profile on
    profile viewer

to ID where the time is lost?

You could pull the

    sin(fecc*t) 
    cos(fecc*t)

outside the loop since you are doing the calculation everytime when the result is always the same (no dependence on t(i).

[Michael Fink]

no just used tic toc to measure the time spent in the loop

Answer 2

[Jan]

At first start with the standard method to accelerate loops: Move all repeated calculations outside!

s = sin(fecc * t);
c = cos(fecc * t);
for i=1:length(t)
  v = null([o1(:,i), o2(:,i), o3(:,i)]);    
  xecc = recc * (s * v(1,1) + c * v(1,2));
  yecc = recc * (s * v(2,1) + c * v(2,2));
  zecc = recc * (s * v(3,1) + c * v(3,2));
end

But now I'm confused: the values for xecc, yecc and zecc are overwritten in each iteration. Then the loop is not necessary at all. This makes a further vectorization hard...

[Michael Fink]

i think that was part of the problem because every iteration the whole vector is recalculated

Answer 3

[Michael Fink]

thanks to both of you for the fast replies. I changed the code to

xecc=zeros(1,length(t));
yecc=zeros(1,length(t));
zecc=zeros(1,length(t));
c_sin=recc*sin(fecc*t);
c_cos=recc*cos(fecc*t);
for i=1:length(t)
 v=null([o1(:,i) o2(:,i) o3(:,i)]);
 xecc(i)=c_sin(i)*v(1,1)+c_cos(i)*v(1,2);
 yecc(i)=c_sin(i)*v(2,1)+c_cos(i)*v(2,2);
 zecc(i)=c_sin(i)*v(3,1)+c_cos(i)*v(3,2);
end

that took me from Elapsed time is 9.421981 seconds. to Elapsed time is 0.1321981 seconds.

Thanks!!