# Distance computations (scipy.spatial.distance)¶

## Function Reference¶

Distance matrix computation from a collection of raw observation vectors stored in a rectangular array.

 pdist(X[, metric]) Pairwise distances between observations in n-dimensional space. cdist(XA, XB[, metric]) Compute distance between each pair of the two collections of inputs. squareform(X[, force, checks]) Convert a vector-form distance vector to a square-form distance matrix, and vice-versa. directed_hausdorff(u, v[, seed]) Compute the directed Hausdorff distance between two N-D arrays.

Predicates for checking the validity of distance matrices, both condensed and redundant. Also contained in this module are functions for computing the number of observations in a distance matrix.

 is_valid_dm(D[, tol, throw, name, warning]) Return True if input array is a valid distance matrix. is_valid_y(y[, warning, throw, name]) Return True if the input array is a valid condensed distance matrix. num_obs_dm(d) Return the number of original observations that correspond to a square, redundant distance matrix. num_obs_y(Y) Return the number of original observations that correspond to a condensed distance matrix.

Distance functions between two numeric vectors u and v. Computing distances over a large collection of vectors is inefficient for these functions. Use pdist for this purpose.

 braycurtis(u, v[, w]) Compute the Bray-Curtis distance between two 1-D arrays. canberra(u, v[, w]) Compute the Canberra distance between two 1-D arrays. chebyshev(u, v[, w]) Compute the Chebyshev distance. cityblock(u, v[, w]) Compute the City Block (Manhattan) distance. correlation(u, v[, w, centered]) Compute the correlation distance between two 1-D arrays. cosine(u, v[, w]) Compute the Cosine distance between 1-D arrays. euclidean(u, v[, w]) Computes the Euclidean distance between two 1-D arrays. jensenshannon(p, q[, base]) Compute the Jensen-Shannon distance (metric) between two 1-D probability arrays. mahalanobis(u, v, VI) Compute the Mahalanobis distance between two 1-D arrays. minkowski(u, v[, p, w]) Compute the Minkowski distance between two 1-D arrays. seuclidean(u, v, V) Return the standardized Euclidean distance between two 1-D arrays. sqeuclidean(u, v[, w]) Compute the squared Euclidean distance between two 1-D arrays. wminkowski(u, v, p, w) Compute the weighted Minkowski distance between two 1-D arrays.

Distance functions between two boolean vectors (representing sets) u and v. As in the case of numerical vectors, pdist is more efficient for computing the distances between all pairs.

 dice(u, v[, w]) Compute the Dice dissimilarity between two boolean 1-D arrays. hamming(u, v[, w]) Compute the Hamming distance between two 1-D arrays. jaccard(u, v[, w]) Compute the Jaccard-Needham dissimilarity between two boolean 1-D arrays. kulsinski(u, v[, w]) Compute the Kulsinski dissimilarity between two boolean 1-D arrays. rogerstanimoto(u, v[, w]) Compute the Rogers-Tanimoto dissimilarity between two boolean 1-D arrays. russellrao(u, v[, w]) Compute the Russell-Rao dissimilarity between two boolean 1-D arrays. sokalmichener(u, v[, w]) Compute the Sokal-Michener dissimilarity between two boolean 1-D arrays. sokalsneath(u, v[, w]) Compute the Sokal-Sneath dissimilarity between two boolean 1-D arrays. yule(u, v[, w]) Compute the Yule dissimilarity between two boolean 1-D arrays.

hamming also operates over discrete numerical vectors.