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bundles / scipy 1.17.1 / scipy / spatial / distance / squareform

function

scipy.spatial.distance:squareform

source: /scipy/spatial/distance.py :2154

Signature

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

Summary

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

  • v = squareform(X)

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

  • X = squareform(v)

    Given an n * (n-1) / 2 sized vector v for some integer n >= 1 encoding distances as described, X = squareform(v) returns an n-by-n distance matrix X. The X[i, j] and X[j, i] values are set to 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
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``squareform(distvec)`` returns the 5x5 distance matrix. 
m = squareform(distvec)
✓
m
✗
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)
✗

Aliases

  • scipy.cluster._optimal_leaf_ordering.squareform

Referenced by

This package