# 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, out]) | Pairwise distances between observations in n-dimensional space.
`cdist`(XA, XB[, metric, out]) | 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 2-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, axis, keepdims]) | Compute the Jensen-Shannon distance (metric) between two 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.

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.
`kulczynski1`(u, v, *[, w]) | Compute the Kulczynski 1 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.