# is.euclid: Is a Distance Matrix Euclidean? In ade4: Analysis of Ecological Data: Exploratory and Euclidean Methods in Environmental Sciences

## Description

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

## Usage

 ```1 2 3``` ```is.euclid(distmat, plot = FALSE, print = FALSE, tol = 1e-07) ## S3 method for class 'dist' summary(object, ...) ```

## Arguments

 `distmat` an object of class 'dist' `plot` a logical value indicating whether the eigenvalues bar plot of the matrix of the term -1/2 dij² centred by rows and columns should be diplayed `print` a logical value indicating whether the eigenvalues of the matrix of the term -1/2 dij² 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. `object` an object of class 'dist' `...` further arguments passed to or from other methods

## Value

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

## Author(s)

Daniel Chessel
Stéphane Dray stephane.dray@univ-lyon1.fr

## References

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

## Examples

 ```1 2 3 4 5 6 7 8``` ```w <- matrix(runif(10000), 100, 100) w <- dist(w) summary(w) is.euclid (w) # TRUE w <- quasieuclid(w) # no correction need in: quasieuclid(w) w <- lingoes(w) # no correction need in: lingoes(w) w <- cailliez(w) # no correction need in: cailliez(w) rm(w) ```

### Example output

```Class: dist
Distance matrix by lower triangle : d21, d22, ..., d2n, d32, ...
Size: 100
Labels:
call: dist(x = w)
method: euclidean
Euclidean matrix (Gower 1966): TRUE
 TRUE
Warning message:
In quasieuclid(w) : Euclidean distance found : no correction need
Warning message:
In lingoes(w) : Euclidean distance found : no correction need
Warning message:
In cailliez(w) : Euclidean distance found : no correction need
```

ade4 documentation built on June 17, 2021, 5:14 p.m.