What I want to do is the following:
Given a matrix A of size [M,N] (rows are vectors) and another matrix B of size [Q,N] (rows are vectors) I want to construct a matrix with the squared distance between each vector of A with all the vectors of B and put it in matrix D. So D(i,j) = sum(((A(i,:)-B(j,:)).^2)
I want to avoid using a double for loop over i and j for creating this because I want to speed up the process. If matrix A would be of size [1,N] I'd think I could transform it into a matrix C of size [Q,N] with on every row the same vector and just go D = sum((C-A).^2) . I'm not sure if this would be a good idea and then I'd still need a for loop to go over the other vectors if A wasn't a [1,N] matrix.
Is there any logical solution or should I just stick to for loops?
If you have the Statistics Toolbox, you can use the PDIST2 function. It is very fast.
A = rand(200,100); B = rand(300,100); pdist2(A,B).^2
sum(bsxfun(@minus,permute(A,[1 3 2]),permute(B,[3 1 2])).^2,3)
There are also some generalizations of this capability on the FEX, e.g.,
If you organize your vectors column-wise instead of row-wise, you can do this without PERMUTE operations, using the utility below. Permute operations are slow.
function Graph=interdists(A,B) %Finds the graph of distances between point coordinates % % (1) Graph=interdists(A,B) % % in: % % A: matrix whose columns are coordinates of points, for example % [[x1;y1;z1], [x2;y2;z2] ,..., [xM;yM;zM]] % but the columns may be points in a space of any dimension, not just 3D. % % B: A second matrix whose columns are coordinates of points in the same % Euclidean space. Default B=A. % % % out: % % Graph: The MxN matrix of separation distances in l2 norm between the coordinates. % Namely, Graph(i,j) will be the distance between A(:,i) and B(:,j). % % % (2) interdists(A,'noself') is the same as interdists(A), except the output % diagonals will be NaN instead of zero. Hence, for example, operations % like min(interdists(A,'noself')) will ignore self-distances. % % See also getgraph
noself=false; if nargin<2 B=A; elseif ischar(B)&&strcmpi(B,'noself') noself=true; B=A; end
Graph=l2norm(bsxfun(@minus, A, B),1);
if noself n=length(Graph); Graph(linspace(1,n^2,n))=nan; end