IsEuclid: Is a Distance Matrix Euclidean?

In DescTools: Tools for Descriptive Statistics

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)

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.

Value

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

Author(s)

Daniel Chessel
Stephane Dray [e-mail]

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

DescTools documentation built on Sept. 26, 2024, 1:07 a.m.