Matlab element within ranges and distance between two points

Question

I have a $53534\times 3$ matrix with $x$, $y$, and $z$ coordinates. I want to find the element of matrix within ranges as follows:

% coordinate range;
x1(x<-25|x>0);
x2(x<0|x>25);
y1(y<-40|y>0);
y2(y<0|y>40);
z1(z<45|z>0);
z2(z<0|z>82);

and insert them into a new matrix, so that it becomes

point1=[x1, y1, z1];
point2=[x2, y2, z2];

I need to find the distance between the two points.

% define points;
xd=x2-x1;
yd=y2-y1;
zd=z2-z1;
Distance=sqrt(xd*xd+yd*yd+zd*zd);

Is loop preferably efficient?

Answer 1

I'm suspecting a typo in at least some of the conditionals. For instance, z<45|z>0 is trivially true. But I'm going to pretend its not and write the code out anyway, so that if you correct it (perhaps z<-45|z>0) you'll still have the right structure.

x  = A(:,1); y = A(:,2); z = A(:,3); 
i1 = find((x<-25|x>0)&(y<-40|y>0)&(z<45|z>0),1,'first'); 
i2 = find((x<0|x>25)&(y<0|y>40)&(z<0|z>82),1,'first'); 
point1 = A(i1,:); 
point2 = A(i2,:); 
Distance = norm(point1-point2);

Like Dr. Sam showed, using tight for loops in MATLAB is truly disastrous for performance. Obviously, as Wolfgang pointed out, MATLAB is using optimized for loops internally to iterate through the elements of the vectors, but that's compiled code. If you were doing this with compiled C, you'd use for loops too, and avoid a lot of the temporary generation that MATLAB is doing here.

Answer 2

I made some tests on a slightly different example (you can easily adapt to your need): I generate a 53534x3 random matrix in Matlab (7.9.0)

R = rand(53534,3);

and I try to extract those row indices where all the three coordinates are greater than 0.5. I made a first version with a loop:

I1=[];
for i=1:53534
    if ( R(i,1)>0.5 && R(i,2)>0.5 && R(i,3)>0.5 )
       I1 = [I1; i];
    end
end

and a second version without loop but with the find function

I2 = find( (R(:,1) > 0.5) .* (R(:,2)> 0.5) .* (R(:,3)>0.5) )

(The element-wise product replaces the AND here). Both codes give exactly the same results.

Now the interesting part is the time required for both codes to run:

• The version with loop takes around 0.05 secondes
• The version without loop takes around 0.004 secondes

So, there is one order of magnitude between them! So, at least in my example, the loop was not the most efficient implementation.

One could argue that you have more flexibility with the loop. For example, if you know that there will be only one index, you can run the loop only until you find it (not until the end). However, this makes you win (in average) only a factor 2, and the find function has also something similar (check the help).