scipy.spatial.distance.squareform#
- scipy.spatial.distance.squareform(X, force='no', checks=True)[source]#
Convert a vector-form distance vector to a square-form distance matrix, and vice-versa.
- Parameters:
- Xarray_like
Either a condensed or redundant distance matrix.
- forcestr, 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.- checksbool, 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 anddiag(X)
is close to zero. These values are ignored any way so they do not disrupt the squareform transformation.
- Returns:
- Yndarray
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
v = squareform(X)
Given a square n-by-n symmetric distance matrix
X
,v = squareform(X)
returns an * (n-1) / 2
(i.e. binomial coefficient n choose 2) sized vector v where \(v[{n \choose 2} - {n-i \choose 2} + (j-i-1)]\) is the distance between distinct pointsi
andj
. IfX
is non-square or asymmetric, an error is raised.X = squareform(v)
Given a
n * (n-1) / 2
sized vectorv
for some integern >= 1
encoding distances as described,X = squareform(v)
returns a n-by-n distance matrixX
. TheX[i, j]
andX[j, i]
values are set to \(v[{n \choose 2} - {n-i \choose 2} + (j-i-1)]\) 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 inx
. The distances are returned in a one-dimensional array with length5*(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 recoverdistvec
.>>> squareform(m) array([2.23606798, 6.40312424, 7.34846923, 2.82842712, 4.89897949, 6.40312424, 1. , 5.38516481, 4.58257569, 5.47722558])