calculate the (geometrical) distance between points of a matrix

Lets say I have a large matrix full of zeros, with a few numbers (1,2,3,4,5) located at various positions. Now I want to calculate the distances from point 1 to 2, 1 to 3, 1 to 4 and 1 to 5. Assuming that e.g. the width of the columns in this matrix is 0.4mm and the width of the rows is 0.25mm. Maybe there is already a code/toolbox out there to do such things?

Answer 1

[Andrei Bobrov]

eg:

data =[0     0     0     0     0     0     0     0     0     0
     0     0     0     0     3     0     0     0     0     0
     0     1     0     0     0     0     0     0     0     0
     0     0     0     2     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     0     0     0
     0     0     0     0     0     4     0     0     0     0
     0     0     0     0     0     0     0     0     0     0
     0     0     0     0     0     0     0     5     0     0
     0     0     0     0     0     0     0     0     0     0]

[i1,j1,c] = find(data)
ijc = sortrows([i1,j1,c],3)
d = bsxfun(@minus,ijc(2:end,1:2),ijc(1,1:2))
out = hypot(d(:,1)*.25,d(:,2)*.4)

OR

use function dist from Neural Network Toolbox

c = dist(bsxfun(@times,ijc(:,1:2),[.25 .4]).');
out = c(:,1);

[Felix]

Thanks, this works great for me, even though I don't understand it.

(I assume here the cells are considered to be infinitesimal points connected with lines of defined lengths?)

I have to check out the documentation of this toolbox, one thing I might want to do is calculate the distance of the path from 1 to 2 to 3, 1 to 2 to 3 to 4 and 1 to 2 to 3 to 4 to 5.

[Andrei Bobrov]

out = diag(dist(bsxfun(@times,ij,[.25; .4])),1)

this is 1 to 2 to 3 to 4 to 5.