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Module « scipy.spatial.distance »

Fonction squareform - module scipy.spatial.distance

Signature de la fonction squareform

def squareform(X, force='no', checks=True) 

Description

help(scipy.spatial.distance.squareform)

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

Parameters
----------
X : array_like
    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 ``X[i, j]`` and ``X[j, 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.

Examples
--------
>>> import numpy as np
>>> from scipy.spatial.distance import pdist, squareform

``x`` is an array of five points in three-dimensional space.

>>> x = np.array([[2, 0, 2], [2, 2, 3], [-2, 4, 5], [0, 1, 9], [2, 2, 4]])

``pdist(x)`` computes the Euclidean distances between each pair of
points in ``x``.  The distances are returned in a one-dimensional
array with length ``5*(5 - 1)/2 = 10``.

>>> distvec = pdist(x)
>>> distvec
array([2.23606798, 6.40312424, 7.34846923, 2.82842712, 4.89897949,
       6.40312424, 1.        , 5.38516481, 4.58257569, 5.47722558])

``squareform(distvec)`` returns the 5x5 distance matrix.

>>> m = squareform(distvec)
>>> m
array([[0.        , 2.23606798, 6.40312424, 7.34846923, 2.82842712],
       [2.23606798, 0.        , 4.89897949, 6.40312424, 1.        ],
       [6.40312424, 4.89897949, 0.        , 5.38516481, 4.58257569],
       [7.34846923, 6.40312424, 5.38516481, 0.        , 5.47722558],
       [2.82842712, 1.        , 4.58257569, 5.47722558, 0.        ]])

When given a square distance matrix ``m``, ``squareform(m)`` returns
the one-dimensional condensed distance vector associated with the
matrix.  In this case, we recover ``distvec``.

>>> squareform(m)
array([2.23606798, 6.40312424, 7.34846923, 2.82842712, 4.89897949,
       6.40312424, 1.        , 5.38516481, 4.58257569, 5.47722558])

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