# lingoes: Transformation of a Distance Matrix for becoming Euclidean In ade4: Analysis of Ecological Data: Exploratory and Euclidean Methods in Environmental Sciences

 lingoes R Documentation

## Transformation of a Distance Matrix for becoming Euclidean

### Description

transforms a distance matrix in a Euclidean one.

### Usage

```lingoes(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

### Details

The function uses the smaller positive constant k which transforms the matrix of sqrt(dij² + 2*k) in an Euclidean one

### Value

returns an object of class `dist` with a Euclidean distance

### Author(s)

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

### References

Lingoes, J.C. (1971) Some boundary conditions for a monotone analysis of symmetric matrices. Psychometrika, 36, 195–203.

### Examples

```data(capitales)
d0 <- capitales\$dist
is.euclid(d0) # FALSE
d1 <- lingoes(d0, TRUE)
# Lingoes constant = 2120982
is.euclid(d1) # TRUE
plot(d0, d1)
x0 <- sort(unclass(d0))
lines(x0, sqrt(x0^2 + 2 * 2120982), lwd = 3)

is.euclid(sqrt(d0^2 + 2 * 2120981), tol = 1e-10) # FALSE
is.euclid(sqrt(d0^2 + 2 * 2120982), tol = 1e-10) # FALSE
is.euclid(sqrt(d0^2 + 2 * 2120983), tol = 1e-10)
# TRUE the smaller constant
```

ade4 documentation built on Nov. 2, 2022, 1:07 a.m.