package scipy

Get an attribute of this module as a Py.Object.t. This is useful to pass a Python function to another function.

Compute distance between each pair of the two collections of inputs.

See Notes for common calling conventions.

Parameters ---------- XA : ndarray An :math:`m_A` by :math:`n` array of :math:`m_A` original observations in an :math:`n`-dimensional space. Inputs are converted to float type. XB : ndarray An :math:`m_B` by :math:`n` array of :math:`m_B` original observations in an :math:`n`-dimensional space. Inputs are converted to float type. metric : str or callable, optional The distance metric to use. If a string, the distance function can be 'braycurtis', 'canberra', 'chebyshev', 'cityblock', 'correlation', 'cosine', 'dice', 'euclidean', 'hamming', 'jaccard', 'jensenshannon', 'kulsinski', 'mahalanobis', 'matching', 'minkowski', 'rogerstanimoto', 'russellrao', 'seuclidean', 'sokalmichener', 'sokalsneath', 'sqeuclidean', 'wminkowski', 'yule'. *args : tuple. Deprecated. Additional arguments should be passed as keyword arguments **kwargs : dict, optional Extra arguments to `metric`: refer to each metric documentation for a list of all possible arguments.

Some possible arguments:

p : scalar The p-norm to apply for Minkowski, weighted and unweighted. Default: 2.

w : ndarray The weight vector for metrics that support weights (e.g., Minkowski).

V : ndarray The variance vector for standardized Euclidean. Default: var(vstack(XA, XB), axis=0, ddof=1)

VI : ndarray The inverse of the covariance matrix for Mahalanobis. Default: inv(cov(vstack(XA, XB.T))).T

out : ndarray The output array If not None, the distance matrix Y is stored in this array. Note: metric independent, it will become a regular keyword arg in a future scipy version

Returns ------- Y : ndarray A :math:`m_A` by :math:`m_B` distance matrix is returned. For each :math:`i` and :math:`j`, the metric ``dist(u=XAi, v=XBj)`` is computed and stored in the :math:`ij` th entry.

Raises ------ ValueError An exception is thrown if `XA` and `XB` do not have the same number of columns.

Notes ----- The following are common calling conventions:

1. ``Y = cdist(XA, XB, 'euclidean')``

Computes the distance between :math:`m` points using Euclidean distance (2-norm) as the distance metric between the points. The points are arranged as :math:`m` :math:`n`-dimensional row vectors in the matrix X.

2. ``Y = cdist(XA, XB, 'minkowski', p=2.)``

Computes the distances using the Minkowski distance :math:`||u-v||_p` (:math:`p`-norm) where :math:`p \geq 1`.

3. ``Y = cdist(XA, XB, 'cityblock')``

Computes the city block or Manhattan distance between the points.

4. ``Y = cdist(XA, XB, 'seuclidean', V=None)``

Computes the standardized Euclidean distance. The standardized Euclidean distance between two n-vectors ``u`` and ``v`` is

.. math::

\sqrt\sum {(u_i-v_i)^2 / V[x_i]

}

.

V is the variance vector; Vi is the variance computed over all the i'th components of the points. If not passed, it is automatically computed.

5. ``Y = cdist(XA, XB, 'sqeuclidean')``

Computes the squared Euclidean distance :math:`||u-v||_2^2` between the vectors.

6. ``Y = cdist(XA, XB, 'cosine')``

Computes the cosine distance between vectors u and v,

.. math::

1 - \fracu \cdot v { ||u|| _2 ||v|| _2

}

where :math:`||*||_2` is the 2-norm of its argument ``*``, and :math:`u \cdot v` is the dot product of :math:`u` and :math:`v`.

7. ``Y = cdist(XA, XB, 'correlation')``

Computes the correlation distance between vectors u and v. This is

.. math::

1 - \frac(u - \bar{u) \cdot (v - \bar

})}
               {{ ||(u - \bar{u})|| }_2 { ||(v - \bar{v})|| }_2}

   where :math:`\bar{v}` is the mean of the elements of vector v,
   and :math:`x \cdot y` is the dot product of :math:`x` and :math:`y`.


8. ``Y = cdist(XA, XB, 'hamming')``

   Computes the normalized Hamming distance, or the proportion of
   those vector elements between two n-vectors ``u`` and ``v``
   which disagree. To save memory, the matrix ``X`` can be of type
   boolean.

9. ``Y = cdist(XA, XB, 'jaccard')``

   Computes the Jaccard distance between the points. Given two
   vectors, ``u`` and ``v``, the Jaccard distance is the
   proportion of those elements ``u[i]`` and ``v[i]`` that
   disagree where at least one of them is non-zero.

10. ``Y = cdist(XA, XB, 'chebyshev')``

   Computes the Chebyshev distance between the points. The
   Chebyshev distance between two n-vectors ``u`` and ``v`` is the
   maximum norm-1 distance between their respective elements. More
   precisely, the distance is given by

   .. math::

      d(u,v) = \max_i { |u_i-v_i| }.

11. ``Y = cdist(XA, XB, 'canberra')``

   Computes the Canberra distance between the points. The
   Canberra distance between two points ``u`` and ``v`` is

   .. math::

     d(u,v) = \sum_i \frac{ |u_i-v_i| }
                          { |u_i|+|v_i| }.

12. ``Y = cdist(XA, XB, 'braycurtis')``

   Computes the Bray-Curtis distance between the points. The
   Bray-Curtis distance between two points ``u`` and ``v`` is


   .. math::

        d(u,v) = \frac{\sum_i (|u_i-v_i|)}
                      {\sum_i (|u_i+v_i|)}

13. ``Y = cdist(XA, XB, 'mahalanobis', VI=None)``

   Computes the Mahalanobis distance between the points. The
   Mahalanobis distance between two points ``u`` and ``v`` is
   :math:`\sqrt{(u-v)(1/V)(u-v)^T}` where :math:`(1/V)` (the ``VI``
   variable) is the inverse covariance. If ``VI`` is not None,
   ``VI`` will be used as the inverse covariance matrix.

14. ``Y = cdist(XA, XB, 'yule')``

   Computes the Yule distance between the boolean
   vectors. (see `yule` function documentation)

15. ``Y = cdist(XA, XB, 'matching')``

   Synonym for 'hamming'.

16. ``Y = cdist(XA, XB, 'dice')``

   Computes the Dice distance between the boolean vectors. (see
   `dice` function documentation)

17. ``Y = cdist(XA, XB, 'kulsinski')``

   Computes the Kulsinski distance between the boolean
   vectors. (see `kulsinski` function documentation)

18. ``Y = cdist(XA, XB, 'rogerstanimoto')``

   Computes the Rogers-Tanimoto distance between the boolean
   vectors. (see `rogerstanimoto` function documentation)

19. ``Y = cdist(XA, XB, 'russellrao')``

   Computes the Russell-Rao distance between the boolean
   vectors. (see `russellrao` function documentation)

20. ``Y = cdist(XA, XB, 'sokalmichener')``

   Computes the Sokal-Michener distance between the boolean
   vectors. (see `sokalmichener` function documentation)

21. ``Y = cdist(XA, XB, 'sokalsneath')``

   Computes the Sokal-Sneath distance between the vectors. (see
   `sokalsneath` function documentation)


22. ``Y = cdist(XA, XB, 'wminkowski', p=2., w=w)``

   Computes the weighted Minkowski distance between the
   vectors. (see `wminkowski` function documentation)

23. ``Y = cdist(XA, XB, f)``

   Computes the distance between all pairs of vectors in X
   using the user supplied 2-arity function f. For example,
   Euclidean distance between the vectors could be computed
   as follows::

     dm = cdist(XA, XB, lambda u, v: np.sqrt(((u-v)**2).sum()))

   Note that you should avoid passing a reference to one of
   the distance functions defined in this library. For example,::

     dm = cdist(XA, XB, sokalsneath)

   would calculate the pair-wise distances between the vectors in
   X using the Python function `sokalsneath`. This would result in
   sokalsneath being called :math:`{n \choose 2}` times, which
   is inefficient. Instead, the optimized C version is more
   efficient, and we call it using the following syntax::

     dm = cdist(XA, XB, 'sokalsneath')

Examples
--------
Find the Euclidean distances between four 2-D coordinates:

>>> from scipy.spatial import distance
>>> coords = [(35.0456, -85.2672),
...           (35.1174, -89.9711),
...           (35.9728, -83.9422),
...           (36.1667, -86.7833)]
>>> distance.cdist(coords, coords, 'euclidean')
array([[ 0.    ,  4.7044,  1.6172,  1.8856],
       [ 4.7044,  0.    ,  6.0893,  3.3561],
       [ 1.6172,  6.0893,  0.    ,  2.8477],
       [ 1.8856,  3.3561,  2.8477,  0.    ]])


Find the Manhattan distance from a 3-D point to the corners of the unit
cube:

>>> a = np.array([[0, 0, 0],
...               [0, 0, 1],
...               [0, 1, 0],
...               [0, 1, 1],
...               [1, 0, 0],
...               [1, 0, 1],
...               [1, 1, 0],
...               [1, 1, 1]])
>>> b = np.array([[ 0.1,  0.2,  0.4]])
>>> distance.cdist(a, b, 'cityblock')
array([[ 0.7],
       [ 0.9],
       [ 1.3],
       [ 1.5],
       [ 1.5],
       [ 1.7],
       [ 2.1],
       [ 2.3]])

Pairwise distances between observations in n-dimensional space.

See Notes for common calling conventions.

Parameters ---------- X : ndarray An m by n array of m original observations in an n-dimensional space. metric : str or function, optional The distance metric to use. The distance function can be 'braycurtis', 'canberra', 'chebyshev', 'cityblock', 'correlation', 'cosine', 'dice', 'euclidean', 'hamming', 'jaccard', 'jensenshannon', 'kulsinski', 'mahalanobis', 'matching', 'minkowski', 'rogerstanimoto', 'russellrao', 'seuclidean', 'sokalmichener', 'sokalsneath', 'sqeuclidean', 'yule'. *args : tuple. Deprecated. Additional arguments should be passed as keyword arguments **kwargs : dict, optional Extra arguments to `metric`: refer to each metric documentation for a list of all possible arguments.

Some possible arguments:

p : scalar The p-norm to apply for Minkowski, weighted and unweighted. Default: 2.

w : ndarray The weight vector for metrics that support weights (e.g., Minkowski).

V : ndarray The variance vector for standardized Euclidean. Default: var(X, axis=0, ddof=1)

VI : ndarray The inverse of the covariance matrix for Mahalanobis. Default: inv(cov(X.T)).T

out : ndarray. The output array If not None, condensed distance matrix Y is stored in this array. Note: metric independent, it will become a regular keyword arg in a future scipy version

Returns ------- Y : ndarray Returns a condensed distance matrix Y. For each :math:`i` and :math:`j` (where :math:`i<j<m`),where m is the number of original observations. The metric ``dist(u=Xi, v=Xj)`` is computed and stored in entry ``ij``.

See Also -------- squareform : converts between condensed distance matrices and square distance matrices.

Notes ----- See ``squareform`` for information on how to calculate the index of this entry or to convert the condensed distance matrix to a redundant square matrix.

The following are common calling conventions.

1. ``Y = pdist(X, 'euclidean')``

Computes the distance between m points using Euclidean distance (2-norm) as the distance metric between the points. The points are arranged as m n-dimensional row vectors in the matrix X.

2. ``Y = pdist(X, 'minkowski', p=2.)``

Computes the distances using the Minkowski distance :math:`||u-v||_p` (p-norm) where :math:`p \geq 1`.

3. ``Y = pdist(X, 'cityblock')``

Computes the city block or Manhattan distance between the points.

4. ``Y = pdist(X, 'seuclidean', V=None)``

Computes the standardized Euclidean distance. The standardized Euclidean distance between two n-vectors ``u`` and ``v`` is

.. math::

\sqrt\sum {(u_i-v_i)^2 / V[x_i]

}

V is the variance vector; Vi is the variance computed over all the i'th components of the points. If not passed, it is automatically computed.

5. ``Y = pdist(X, 'sqeuclidean')``

Computes the squared Euclidean distance :math:`||u-v||_2^2` between the vectors.

6. ``Y = pdist(X, 'cosine')``

Computes the cosine distance between vectors u and v,

.. math::

1 - \fracu \cdot v { ||u|| _2 ||v|| _2

}

where :math:`||*||_2` is the 2-norm of its argument ``*``, and :math:`u \cdot v` is the dot product of ``u`` and ``v``.

7. ``Y = pdist(X, 'correlation')``

Computes the correlation distance between vectors u and v. This is

.. math::

1 - \frac(u - \bar{u) \cdot (v - \bar

})}
               {{ ||(u - \bar{u})|| }_2 { ||(v - \bar{v})|| }_2}

   where :math:`\bar{v}` is the mean of the elements of vector v,
   and :math:`x \cdot y` is the dot product of :math:`x` and :math:`y`.

8. ``Y = pdist(X, 'hamming')``

   Computes the normalized Hamming distance, or the proportion of
   those vector elements between two n-vectors ``u`` and ``v``
   which disagree. To save memory, the matrix ``X`` can be of type
   boolean.

9. ``Y = pdist(X, 'jaccard')``

   Computes the Jaccard distance between the points. Given two
   vectors, ``u`` and ``v``, the Jaccard distance is the
   proportion of those elements ``u[i]`` and ``v[i]`` that
   disagree.

10. ``Y = pdist(X, 'chebyshev')``

   Computes the Chebyshev distance between the points. The
   Chebyshev distance between two n-vectors ``u`` and ``v`` is the
   maximum norm-1 distance between their respective elements. More
   precisely, the distance is given by

   .. math::

      d(u,v) = \max_i { |u_i-v_i| }

11. ``Y = pdist(X, 'canberra')``

   Computes the Canberra distance between the points. The
   Canberra distance between two points ``u`` and ``v`` is

   .. math::

     d(u,v) = \sum_i \frac{ |u_i-v_i| }
                          { |u_i|+|v_i| }


12. ``Y = pdist(X, 'braycurtis')``

   Computes the Bray-Curtis distance between the points. The
   Bray-Curtis distance between two points ``u`` and ``v`` is


   .. math::

        d(u,v) = \frac{\sum_i { |u_i-v_i| }}
                       {\sum_i { |u_i+v_i| }}

13. ``Y = pdist(X, 'mahalanobis', VI=None)``

   Computes the Mahalanobis distance between the points. The
   Mahalanobis distance between two points ``u`` and ``v`` is
   :math:`\sqrt{(u-v)(1/V)(u-v)^T}` where :math:`(1/V)` (the ``VI``
   variable) is the inverse covariance. If ``VI`` is not None,
   ``VI`` will be used as the inverse covariance matrix.

14. ``Y = pdist(X, 'yule')``

   Computes the Yule distance between each pair of boolean
   vectors. (see yule function documentation)

15. ``Y = pdist(X, 'matching')``

   Synonym for 'hamming'.

16. ``Y = pdist(X, 'dice')``

   Computes the Dice distance between each pair of boolean
   vectors. (see dice function documentation)

17. ``Y = pdist(X, 'kulsinski')``

   Computes the Kulsinski distance between each pair of
   boolean vectors. (see kulsinski function documentation)

18. ``Y = pdist(X, 'rogerstanimoto')``

   Computes the Rogers-Tanimoto distance between each pair of
   boolean vectors. (see rogerstanimoto function documentation)

19. ``Y = pdist(X, 'russellrao')``

   Computes the Russell-Rao distance between each pair of
   boolean vectors. (see russellrao function documentation)

20. ``Y = pdist(X, 'sokalmichener')``

   Computes the Sokal-Michener distance between each pair of
   boolean vectors. (see sokalmichener function documentation)

21. ``Y = pdist(X, 'sokalsneath')``

   Computes the Sokal-Sneath distance between each pair of
   boolean vectors. (see sokalsneath function documentation)

22. ``Y = pdist(X, 'wminkowski', p=2, w=w)``

   Computes the weighted Minkowski distance between each pair of
   vectors. (see wminkowski function documentation)

23. ``Y = pdist(X, f)``

   Computes the distance between all pairs of vectors in X
   using the user supplied 2-arity function f. For example,
   Euclidean distance between the vectors could be computed
   as follows::

     dm = pdist(X, lambda u, v: np.sqrt(((u-v)**2).sum()))

   Note that you should avoid passing a reference to one of
   the distance functions defined in this library. For example,::

     dm = pdist(X, sokalsneath)

   would calculate the pair-wise distances between the vectors in
   X using the Python function sokalsneath. This would result in
   sokalsneath being called :math:`{n \choose 2}` times, which
   is inefficient. Instead, the optimized C version is more
   efficient, and we call it using the following syntax.::

     dm = pdist(X, 'sokalsneath')

Convert a vector-form distance vector to a square-form distance matrix, and vice-versa.

Parameters ---------- X : ndarray Either a condensed or redundant distance matrix. force : str, optional As with MATLAB(TM), if force is equal to ``'tovector'`` or ``'tomatrix'``, the input will be treated as a distance matrix or distance vector respectively. checks : bool, optional If set to False, no checks will be made for matrix symmetry nor zero diagonals. This is useful if it is known that ``X - X.T1`` is small and ``diag(X)`` is close to zero. These values are ignored any way so they do not disrupt the squareform transformation.

Returns ------- Y : ndarray If a condensed distance matrix is passed, a redundant one is returned, or if a redundant one is passed, a condensed distance matrix is returned.

Notes ----- 1. ``v = squareform(X)``

Given a square n-by-n symmetric distance matrix ``X``, ``v = squareform(X)`` returns a ``n * (n-1) / 2`` (i.e. binomial coefficient n choose 2) sized vector `v` where :math:`v{n \choose 2} - {n-i \choose 2} + (j-i-1)` is the distance between distinct points ``i`` and ``j``. If ``X`` is non-square or asymmetric, an error is raised.

2. ``X = squareform(v)``

Given a ``n * (n-1) / 2`` sized vector ``v`` for some integer ``n >= 1`` encoding distances as described, ``X = squareform(v)`` returns a n-by-n distance matrix ``X``. The ``Xi, j`` and ``Xj, i`` values are set to :math:`v{n \choose 2} - {n-i \choose 2} + (j-i-1)` and all diagonal elements are zero.

In SciPy 0.19.0, ``squareform`` stopped casting all input types to float64, and started returning arrays of the same dtype as the input.

xlogy(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True, signature, extobj)

xlogy(x, y)

Compute ``x*log(y)`` so that the result is 0 if ``x = 0``.

Parameters ---------- x : array_like Multiplier y : array_like Argument

Returns ------- z : array_like Computed x*log(y)

Notes -----

.. versionadded:: 0.13.0