# Euclid: Calculation of the Euclidean Distance In guenardg/codep: Multiscale Codependence Analysis

 Euclid R Documentation

## Calculation of the Euclidean Distance

### Description

Function `Euclid` carries out the calculation of pairwise Euclidean distances within a set of coordinates or between two sets thereof, with optional weights.

### Usage

``````Euclid(x, y, squared = FALSE)
``````

### Arguments

 `x` A set of coordinates in the form of a `matrix` or `data.frame`. `y` An optional second set of coordinates in the same dimensions as argument `x`. `squared` Should the squared Euclidean distances be returned (default: FALSE).

### Details

When only one set of coordinates is given to the function (i.e., when argument `y` is omitted), the function returns the pairwise distances in the form of a 'dist-class' object representing a lower-triangle matrix. If weights are omitted, the result is identical to that produced by function dist with argument `method = "euclidean"` (the function's default).

The standard 'R' function used to calculate the Euclidean distance (`dist`), only allows one to calculate pairwise distances between the rows of a single matrix of Cartesian coordinates and return a 'dist-class' object, which is a one-dimensional array meant to be interpreted as a lower-triangular matrix. Function `Euclid` can also be provided two data matrices (arguments `x` and `y`) and output a rectangular matrix of the Euclidean distances.

### Value

A 'dist-class' object or, whenever `y` is provided, a `matrix` with as many rows as the number of rows in `x` and as many columns as the number of rows in `y`.

### Author(s)

Guillaume Guenard and Pierre Legendre, Bertrand Pages Maintainer: Guillaume Guenard <guillaume.guenard@gmail.com>

The 'dist-class' and associated methods.

### Examples

``````## A set of reference points:
x <- cbind(c(1,4,5,2,8,4), c(3,6,7,1,3,2))
dimnames(x) <- list(LETTERS[1:6], c("x", "y"))

## The pairwise Euclidean distances among the reference points:
d1 <- Euclid(x)
d1

## That result is the same as that obtained from function dist:
d2 <- dist(x, method = "euclidean")
all(d1 == d2)

## A second set of points:
y <- cbind(c(3,5,7), c(3,6,8))
dimnames(y) <- list(LETTERS[7:9], c("x", "y"))

## The distances between the points in y (rows) and x (columns):
Euclid(x, y)

``````

guenardg/codep documentation built on April 15, 2023, 6:47 a.m.