Building matrix of differences

Say I have a vector v=[v1,...,vn].'. How can I generate the matrix D with components D(i,j) = vi - vj ? The dimension of the vector n is very large, so efficiency matters. Ideally I would like to generate the following matrix E(i,j) = 1/(vi-vj) for vi ~= vj (which we may assume corresponds to i~=j) and E(i,i) = 0.

Is there a fast way to do it? Doing it with loops is very slow.

Thanks a lot,

L

Answer 1

[Star Strider]

See if this does what you want:

v = randi(9, 1, 5);                                         % Create Data
D = bsxfun(@minus, v, v');                                  % Subtract To Create Matrix
Dnz = D~=0;                                                 % Logical Matrix (Becomes Numeric)
Dinv = Dnz./D;                                              % Element-Wise ‘Inverse’

Note that ‘0/0’ become NaN values.

[Lorenzo]

Thanks this is pretty good! I was using a combination of meshgrid, cat and reshape but this is more slick. Do you know a way to convert the Nan into zeroes? Unfortunately it still seems to be slower than half of the double loop. I will wait a little bit to see if there are more answer and then accept this one. Thanks again!

[Star Strider]

My pleasure!

To convert the NaN values to 0, add this assignment to my previous code:

Dinv(~Dnz) = 0;                                             % Convert ‘NaN’ To ‘0’