finding the distance between two points

PDIST2 Pairwise distance between two sets of observations. D = PDIST2(X,Y) returns a matrix D containing the Euclidean distances between each pair of observations in the MX-by-N data matrix X and MY-by-N data matrix Y. Rows of X and Y correspond to observations, and columns correspond to variables. D is an MX-by-MY matrix, with the (I,J) entry equal to distance between observation I in X and observation J in Y. D = PDIST2(X,Y,DISTANCE) computes D using DISTANCE. Choices are: 'euclidean' - Euclidean distance (default) 'squaredeuclidean' - Squared Euclidean distance 'seuclidean' - Standardized Euclidean distance. Each coordinate difference between rows in X and Y is scaled by dividing by the corresponding element of the standard deviation computed from X, S=NANSTD(X). To specify another value for S, use D = PDIST2(X,Y,'seuclidean',S). 'cityblock' - City Block distance 'minkowski' - Minkowski distance. The default exponent is 2. To specify a different exponent, use D = PDIST2(X,Y,'minkowski',P), where the exponent P is a scalar positive value. 'chebychev' - Chebychev distance (maximum coordinate difference) 'mahalanobis' - Mahalanobis distance, using the sample covariance of X as computed by NANCOV. To compute the distance with a different covariance, use D = PDIST2(X,Y,'mahalanobis',C), where the matrix C is symmetric and positive definite. 'cosine' - One minus the cosine of the included angle between observations (treated as vectors) 'correlation' - One minus the sample linear correlation between observations (treated as sequences of values). 'spearman' - One minus the sample Spearman's rank correlation between observations (treated as sequences of values) 'hamming' - Hamming distance, percentage of coordinates that differ 'jaccard' - One minus the Jaccard coefficient, the percentage of nonzero coordinates that differ function - A distance function specified using @, for example @DISTFUN A distance function must be of the form function D2 = DISTFUN(ZI,ZJ), taking as arguments a 1-by-N vector ZI containing a single observation from X or Y, an M2-by-N matrix ZJ containing multiple observations from X or Y, and returning an M2-by-1 vector of distances D2, whose Jth element is the distance between the observations ZI and ZJ(J,:). For built-in distance metrics, the distance between observation I in X and observation J in Y will be NaN if observation I in X or observation J in Y contains NaNs. D = PDIST2(X,Y,DISTANCE,'Smallest',K) returns a K-by-MY matrix D containing the K smallest pairwise distances to observations in X for each observation in Y. PDIST2 sorts the distances in each column of D in ascending order. D = PDIST2(X,Y,DISTANCE, 'Largest',K) returns the K largest pairwise distances sorted in descending order. If K is greater than MX, PDIST2 returns an MX-by-MY distance matrix. For each observation in Y, PDIST2 finds the K smallest or largest distances by computing and comparing the distance values to all the observations in X. [D,I] = PDIST2(X,Y,DISTANCE,'Smallest',K) returns a K-by-MY matrix I containing indices of the observations in X corresponding to the K smallest pairwise distances in D. [D,I] = PDIST2(X,Y,DISTANCE, 'Largest',K) returns indices corresponding to the K largest pairwise distances. Example: % Compute the ordinary Euclidean distance X = randn(100, 5); Y = randn(25, 5); D = pdist2(X,Y,'euclidean'); % euclidean distance % Compute the Euclidean distance with each coordinate difference % scaled by the standard deviation Dstd = pdist2(X,Y,'seuclidean'); % Use a function handle to compute a distance that weights each % coordinate contribution differently. Wgts = [.1 .3 .3 .2 .1]; % coordinate weights weuc = @(XI,XJ,W)(sqrt((XI - XJ).^2 * W')); Dwgt = pdist2(X,Y, @(Xi,Xj) weuc(Xi,Xj,Wgts)); See also PDIST, KNNSEARCH, CREATENS, KDTreeSearcher, ExhaustiveSearcher. Documentation for pdist2 doc pdist2 Other uses of pdist2 gpuArray/pdist2 tall/pdist2