TDA (version 1.9.1)

distFct: Distance function

Description

The function distFct computes the distance between each point of a set Grid and the corresponding closest point of another set X.

Usage

distFct(X, Grid)

Value

The function distFct returns a numeric vector of length \(n\), where \(n\) is the number of points stored in Grid. Each value in V corresponds to the distance between a point in G and the nearest point in X.

Arguments

X

a numeric \(m\) by \(d\) matrix of coordinates in the space, where \(m\) is the number of points in X and \(d\) is the dimension of the space. X is the set of points whose distance is being measured from a base grid.

Grid

a numeric \(n\) by \(d\) matrix of coordinates in the space, where \(n\) is the number of points in Grid and \(d\) is the dimension of the space. Grid is the base set from which each point is compared to the closest point in X.

Author

Fabrizio Lecci

Details

Given a set of points X, the distance function computed at \(g\) is defined as $$ d(g) = \inf_{x \in X} \| x-g \|_2 $$

See Also

kde,kernelDist, dtm

Examples

## Generate Data from the unit circle
n <- 300
X <- circleUnif(n)

## Construct a grid of points over which we evaluate the function
interval <- 0.065
Xseq <- seq(-1.6, 1.6, by = interval)
Yseq <- seq(-1.7, 1.7, by = interval)
Grid <- expand.grid(Xseq, Yseq)

## distance fct
distance <- distFct(X, Grid)