DescTools (version 0.99.53)

IsEuclid: Is a Distance Matrix Euclidean?

Description

Confirmation of the Euclidean nature of a distance matrix by the Gower's theorem.
IsEuclid is used in summary.dist.

Usage

IsEuclid(distmat, plot = FALSE, print = FALSE, tol = 1e-07)

Value

returns a logical value indicating if all the eigenvalues are positive or equal to zero

Arguments

distmat

an object of class 'dist'

plot

a logical value indicating whether the eigenvalues bar plot of the matrix of the term \(-\frac{1}{2} {d_{ij}^2}\) centred by rows and columns should be diplayed

print

a logical value indicating whether the eigenvalues of the matrix of the term \(-\frac{1}{2} {d_{ij}^2}\) centred by rows and columns should be printed

tol

a tolerance threshold : an eigenvalue is considered positive if it is larger than -tol*lambda1 where lambda1 is the largest eigenvalue.

Author

Daniel Chessel
Stephane Dray

References

Gower, J.C. and Legendre, P. (1986) Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification, 3, 5--48.

Examples

w <- matrix(runif(10000), 100, 100)
w <- dist(w)
summary(w)
IsEuclid (w) # TRUE