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.


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 and diag(X) is close to zero. These values are ignored any way so they do not disrupt the squareform transformation.


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.


  1. v = squareform(X)

    Given a square d-by-d symmetric distance matrix X, v = squareform(X) returns a d * (d-1) / 2 (or \({n \choose 2}\)) sized vector v.

\(v[{n \choose 2}-{n-i \choose 2} + (j-i-1)]\) is the distance between points i and j. If X is non-square or asymmetric, an error is returned.

  1. X = squareform(v)

Given a d*(d-1)/2 sized v for some integer d >= 2 encoding distances as described, X = squareform(v) returns a d by d distance matrix X. The X[i, j] and X[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.

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