# cailliez: Transformation to make Euclidean a distance matrix In ade4: Analysis of Ecological Data: Exploratory and Euclidean Methods in Environmental Sciences

## Description

This function computes the smallest positive constant that makes Euclidean a distance matrix and applies it.

## Usage

 `1` ```cailliez(distmat, print = FALSE, tol = 1e-07, cor.zero = TRUE) ```

## Arguments

 `distmat` an object of class `dist` `print` if TRUE, prints the eigenvalues of the matrix `tol` a tolerance threshold for zero `cor.zero` if TRUE, zero distances are not modified

## Value

an object of class `dist` containing a Euclidean distance matrix.

## Author(s)

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

## References

Cailliez, F. (1983) The analytical solution of the additive constant problem. Psychometrika, 48, 305–310.

Legendre, P. and Anderson, M.J. (1999) Distance-based redundancy analysis: testing multispecies responses in multifactorial ecological experiments. Ecological Monographs, 69, 1–24.

Legendre, P., and Legendre, L. (1998) Numerical ecology, 2nd English edition edition. Elsevier Science BV, Amsterdam.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```data(capitales) d0 <- capitales\$dist is.euclid(d0) # FALSE d1 <- cailliez(d0, TRUE) # Cailliez constant = 2429.87867 is.euclid(d1) # TRUE plot(d0, d1) abline(lm(unclass(d1)~unclass(d0))) print(coefficients(lm(unclass(d1)~unclass(d0))), dig = 8) # d1 = d + Cte is.euclid(d0 + 2428) # FALSE is.euclid(d0 + 2430) # TRUE the smallest constant ```

### Example output ``` FALSE
Cailliez constant = 2429.87867
 TRUE
(Intercept) unclass(d0)
2429.8787      1.0000
 FALSE
 TRUE
```

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