| % EUCL: Calculates the euclidean distances among a set of points, or between a | |
| % reference point and a set of points, or among all possible pairs of two | |
| % sets of points, in P dimensions. Returns a single distance for two points. | |
| % | |
| % Syntax: dists = eucl(crds1,crds2) | |
| % | |
| % crds1 = [N1 x P] matrix of point coordinates. If N=1, it is taken to | |
| % be the reference point. | |
| % crds2 = [N2 x P] matrix of point coordinates. If N=1, it is taken to | |
| % be the reference point. | |
| % ----------------------------------------------------------------------- | |
| % dists = [N1 x N1] symmetric matrix of pairwise distances (if only crds1 | |
| % is specified); | |
| % [N1 x 1] col vector of euclidean distances (if crds1 & ref | |
| % are specified); | |
| % [1 x N2] row vector of euclidean distances (if ref & crds2 | |
| % are specified); | |
| % [N1 x N2] rectangular matrix of pairwise distances (if crds1 | |
| % & crds2 are specified); | |
| % [1 x 1] scalar (if crds1 is a [2 x P] matrix or ref1 & ref2 | |
| % are specified); | |
| % | |
| % RE Strauss, 5/4/94 | |
| % 10/28/95 - output row (rather than column) vector for the (reference | |
| % point)-(set of points) case; still outputs column vector for the | |
| % (set of points)-(reference point) case. | |
| % 10/30/95 - for double for-loops, put one matrix-col access in outer loop | |
| % to increase speed. | |
| % 10/12/96 - vectorize inner loop to increase speed. | |
| % 6/12/98 - allow for P=1. | |
| % 11/11/03 - initialize dists to NaN for error return. | |
| function dists = eucl(crds1,crds2) | |
| if nargin == 0, help eucl; return; end; | |
| dists = NaN; | |
| if (nargin < 2) % If only crds1 provided, | |
| [N,P] = size(crds1); | |
| if (N<2) | |
| error(' EUCL: need at least two points'); | |
| end; | |
| crds1 = crds1'; % Transpose crds | |
| dists = zeros(N,N); % Calculate pairwise distances | |
| for i = 1:N-1 | |
| c1 = crds1(:,i) * ones(1,N-i); | |
| if (P>1) | |
| d = sqrt(sum((c1-crds1(:,(i+1:N))).^2)); | |
| else | |
| d = abs(c1-crds1(:,(i+1:N))); | |
| end; | |
| dists(i,(i+1:N)) = d; | |
| dists((i+1:N),i) = d'; | |
| end; | |
| if (N==2) % Single distance for two points | |
| dists = dists(1,2); | |
| end; | |
| else % If crds1 & crds2 provided, | |
| [N1,P1] = size(crds1); | |
| [N2,P2] = size(crds2); | |
| if (P1~=P2) | |
| error(' EUCL: sets of coordinates must be of same dimension'); | |
| else | |
| P = P1; | |
| end; | |
| crds1 = crds1'; % Transpose crds | |
| crds2 = crds2'; | |
| if (N1>1 & N2>1) % If two matrices provided, | |
| dists = zeros(N1,N2); % Calc all pairwise distances between them | |
| for i = 1:N1 | |
| c1 = crds1(:,i) * ones(1,N2); | |
| if (P>1) | |
| d = sqrt(sum((c1-crds2).^2)); | |
| else | |
| d = abs(c1-crds2); | |
| end; | |
| dists(i,:) = d; | |
| end; | |
| end; | |
| if (N1==1 & N2==1) % If two vectors provided, | |
| dists = sqrt(sum((crds1-crds2).^2)); % Calc scalar | |
| end; | |
| if (N1>1 & N2==1) % If matrix & reference point provided, | |
| crds1 = crds1 - (ones(N1,1)*crds2')'; % Center points on reference point | |
| if (P>1) % Calc euclidean distances in P-space | |
| dists = sqrt(sum(crds1.^2))'; | |
| else | |
| dists = abs(crds1)'; | |
| end; | |
| end; % Return column vector | |
| if (N1==1 & N2>1) % If reference point & matrix provided, | |
| crds2 = crds2 - (ones(N2,1)*crds1')'; % Center points on reference point | |
| if (P>1) % Calc euclidean distances in P-space | |
| dists = sqrt(sum(crds2.^2)); | |
| else | |
| dists = abs(crds2); | |
| end; | |
| end; % Return row vector | |
| end; | |
| return; | |