reducing time in using for-loop

Below is the code I wrote to calculate the minimum distance of some points (shown by "A") from some lines made by pairs of points (Shown by "B1" and "B2"). I used arrayfun to compute the distance of each A point to all lines. Unfortunately using for loops to apply the arrayfun to all the A points makes the code too sluggish. I was wondering if there is anyway that I can make the code run faster (I am aware of parfor and spmd).

A=importdata('1.txt'); %This file contains two rows of the x and y of each point

B=importdata('2.txt'); %This file contains four rows of the x and y of the two points which make the line

B1=[B(:,1) B(:,2) zeros(size(B,1),1)]; %This line is not important/relevant to my question

B2=[B(:,3) B(:,4) zeros(size(B,1),1)]; %This line is not important/relevant to my question

Distance=zeros(size(A,1),1);

Bcounter=1:size(B,1);

for i=1:size(A,1)
  x=A(i,1);
  y=A(i,2);
  p=[x y zeros(size(A,1),1)]; %This line is not important/relevant to my question

   Distance(i,1)=min(cell2mat(arrayfun(@(Bcounter) Distance(p(i,:), B1(GBcounter,:), B2(GBcounter,:)), Bcounter, 'UniformOutput', false))); % Calculate nearest distance of p to line made by B1 and B2 points 

end

Answer 1

[Roger Stafford]

Why not try a direct computation with the data rather than using 'arrayfun'.? It just might be faster.

 X = A(:,1);
 Y = A(:,2);
 X1 = B(:,1); % I assume that B(:,1) & B(:,2) are x and y coordinates of one end of lines
 Y1 = B(:,2);
 X2 = B(:,3); % and that B(:,3) & B(:,4) are x and y coordinates of the opposite ends
 Y2 = B(:,4);
 L = sqrt((X2-X1),^2+(Y2-Y1).^2);
 P = (X2-X1)./L;
 Q = (Y2-Y1)./L;
 R = (X1.*Y2-Y1.*X2)./L;
 D = zeros(size(A,1),1);
 for k = 1:size(A,1)
   D(k) = min(abs(P*Y(k)-Q*X(k)+R));
 end

Also I assume that distance here is measured to the closest point on an extended line, not just to the line segment.