How might i optimize / vectorize this function?

I have been using the function:

http://www.mathworks.com/matlabcentral/fileexchange/29130-shortest-distance-between-two-lines-in-n-dimensions/content/distBW2lines.m

to find the distance between two lines.

However, i would like to find the distance between 1 line and say, 100,000 different lines. I will be performing this computation over many iterations and i am finding looping 1 by 1 100,000 times each iteration is significantly increasing the time of what i am trying to do.

I had thought maybe to create a matrix of the one i am trying to check (so 100,000 copies of hte same line) to compare with the corrseponding 100,000 other lines and found that this code doesnt lend itself to matrix inputs - there is a line in the code (40 i believe which has a ^2 term which produces a NxN matrix of NaN)

Anyone have any idea how to use the basic checking in this code (i.e. distance between two lines) but check 1 line vs 100,000 lines in an efficient manner?

Any help would be greatly appreciated!

[Matt J]

In what dimension will the lines be? R^3?

[Tyler]

yes, 3D

Answer 1

[Matt J]

Assuming the lines are all non-parallel, the following should do it

    %Test data
    N=1e5;
    r0=[0;0;0]; d0=[1;1;1]; %fixed line, parametric equations:  r0+t*d0
    R=rand(3,N); D=ones(3,N); %other lines, equations: R(:,i)+t*D(:,i)

    %Distance computations

    tic;
    d=l2unitize(d0);
    D=l2unitize(D);

    distances=abs(sum(cross(repmat(d,1,N),D).*bsxfun(@minus,r0,R)));
    toc;
    %Elapsed time is 0.010295 seconds.

    function n=l2norm(A,varargin)

      n=sqrt(sum(A.^2,varargin{:}));

    function A=l2unitize(A,varargin)

      n=l2norm(A,varargin{:});
      A=bsxfun(@rdivide,A,n);