TDA (version 1.0)

distFct: Distance function

Description

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

Usage

distFct(X, Grid)

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.

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.

Value

• Returns a numeric vector of length $n$, where $n$ is the number of points stored in Grid.

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
by=0.065
Xseq=seq(-1.6, 1.6, by=by)
Yseq=seq(-1.7, 1.7, by=by)
Grid=expand.grid(Xseq,Yseq)

## distance fct
distance= distFct(X, Grid)