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

 cailliez R Documentation

## Transformation to make Euclidean a distance matrix

### Description

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

### Usage

```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

```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
```

ade4 documentation built on Feb. 16, 2023, 7:58 p.m.