# `sklearn.metrics.pairwise`.euclidean_distances¶

`sklearn.metrics.pairwise.``euclidean_distances`(X, Y=None, Y_norm_squared=None, squared=False, X_norm_squared=None)[source]

Considering the rows of X (and Y=X) as vectors, compute the distance matrix between each pair of vectors.

For efficiency reasons, the euclidean distance between a pair of row vector x and y is computed as:

```dist(x, y) = sqrt(dot(x, x) - 2 * dot(x, y) + dot(y, y))
```

This formulation has two advantages over other ways of computing distances. First, it is computationally efficient when dealing with sparse data. Second, if one argument varies but the other remains unchanged, then dot(x, x) and/or dot(y, y) can be pre-computed.

However, this is not the most precise way of doing this computation, and the distance matrix returned by this function may not be exactly symmetric as required by, e.g., `scipy.spatial.distance` functions.

Read more in the User Guide.

Parameters: X : {array-like, sparse matrix}, shape (n_samples_1, n_features) Y : {array-like, sparse matrix}, shape (n_samples_2, n_features) Y_norm_squared : array-like, shape (n_samples_2, ), optional Pre-computed dot-products of vectors in Y (e.g., `(Y**2).sum(axis=1)`) squared : boolean, optional Return squared Euclidean distances. X_norm_squared : array-like, shape = [n_samples_1], optional Pre-computed dot-products of vectors in X (e.g., `(X**2).sum(axis=1)`) distances : {array, sparse matrix}, shape (n_samples_1, n_samples_2)

`paired_distances`
distances betweens pairs of elements of X and Y.

Examples

```>>> from sklearn.metrics.pairwise import euclidean_distances
>>> X = [[0, 1], [1, 1]]
>>> # distance between rows of X
>>> euclidean_distances(X, X)
array([[ 0.,  1.],
[ 1.,  0.]])
>>> # get distance to origin
>>> euclidean_distances(X, [[0, 0]])
array([[ 1.        ],
[ 1.41421356]])
```