How can I determine the distance of two points, if the point's coord are in other vectors?

Dear All,

Please help me!

I have got 5 random points (just for example). Each of them has an X coordinate and a Y coordinate. These coords are in two vectors:

example (becasue every element of the vectors are randomly generated) X=[1,5,8,8,2]; Y=[5,6,8,4,2]; P1(1,5); P2(5,6) and so on P5(2,2);

so I would like to determine each of the distances between each points. I mean d_1_2=sqrt((x1-x2)^2+(y1-y2)^2) . . .

d_1_5=sqrt((x1-x5)^2+(y1-y5)^2)

I would like to use the distances in the future, so I need all of them.

Thank you!

Szabi

Answer 1

[Sean de Wolski]

If you have the Statistics Toolbox

doc pdist

Else:

doc hypot

[szasza654 szasza654]

sorry for the late

so, i am very glad for your answer, but it is the hard way, and i now these commands. i would like to solve the problem with some kind of loop or don' t know.. in my case there are a lot of points (many many), and i would like to know each distance point pairs..(putting a new point if the new point's distance is bigger than 8 mm from every other (previously packed point-- i tried to make for loops, but didn' t work all right). if you have another tip, please wright it! thx :)

[Jan]

Accepting an answer means, that it solves the problem.

"Many many" could mean 64 or 64'000'000'000. Such details matter, so please be as explicit as possible.

If you have some code, post it here and explain "didn't work all right" with more details. Then it is easy to suggest an improvement.

Answer 2

[Jan]

X = [1,5,8,8,2];
Y = [5,6,8,4,2]; 
Dist = sqrt(bsxfun(@plus, X.^2, Y(:).^2);

This does not have a loop and does not consider, that the resulting matrix is symmetric, such that a loop could have the double speed in theory:

X = [1,5,8,8,2];
Y = [5,6,8,4,2]; 
Dist = zeros(length(X), length(Y));
for iY = 1:length(Y)
  YY           = Y(iY)^2;             % Avoid repeated calculation
  Dist(iY, iY) = sqrt(X(iY)^2 + YY);  % Diagonal element
  for iX = iY + 1:length(X)
    d            = sqrt(X(iX)^2 + YY);
    Dist(iX, iY) = d;
    Dist(iY, iX) = d;                 % Mirroring
  end
end

But if you are not talking about billions of points, squaring the values once is more efficient:

XX = X .* X;
YY = Y .* Y;
Dist = zeros(length(X), length(Y));
for iY = 1:length(Y)
  Dist(iY, iY) = sqrt(X(iY)^2 + YY(iY));  % Diagonal element
  for iX = iY + 1:length(X)
    d            = sqrt(XX(iX) + YY(iY));
    Dist(iX, iY) = d;
    Dist(iY, iX) = d;                 % Mirroring
  end
end