# rinter: Generate interaction point patterns In stpp: Space-Time Point Pattern Simulation, Visualisation and Analysis

## Description

Generate one (or several) realisation(s) of the inhibition or contagious process in a region S x T.

## Usage

 ```1 2 3``` ``` rinter(npoints,s.region,t.region,hs="step",gs="min",thetas=0, deltas,ht="step",gt="min",thetat=1,deltat,recent="all",nsim=1, discrete.time=FALSE,replace=FALSE,inhibition=TRUE,...) ```

## Arguments

 `npoints` Number of points to simulate. `s.region` Two-column matrix specifying polygonal region containing all data locations. If `s.region` is missing, the unit square is considered. `t.region` Vector containing the minimum and maximum values of the time interval. If `t.region` is missing, the interval [0,1] is considered. `hs, ht` Function which depends on the distance between points and `theta`. Can be chosen among "`step`" and "`gaussian`" or can refer to a user defined function which only depend on d, theta, and delta (see details). If `inhibition=TRUE`, `h` is monotone, increasing, and must tend to 1 when the distance tends to infinity. 0 <=`h(d,theta)`<= 1. Otherwise, `h` is monotone, decreasing, and must tend to 1 when the distance tends to 0. `thetas, thetat` Parameters of `hs` and `ht` functions. `deltas, deltat` Spatial and temporal distance of inhibition. `gs, gt` Compute the probability of acceptance of a new point from `hs` or `ht` and `recent`. Must be choosen among "`min`", "`max`" and "`prod`". `recent` If “`all`” consider all previous events. If is an integer, say N, consider only the N most recent events. `nsim` Number of simulations to generate. Default is 1. `discrete.time` If TRUE, times belong to N, otherwise belong to R^+. `replace` Logical. If TRUE allows times repeat. `inhibition` Logical. If TRUE, an inhibition process is generated. Otherwise, it is a contagious process. `...` Additional parameters if `hs` and `ht` are defined by the user.

## Value

A list containing:

 `xyt` Matrix (or list of matrices if `nsim`>1) containing the points (x,y,t) of the simulated point pattern. `xyt` (or any element of the list if `nsim`>1) is an object of the class `stpp`. `s.region, t.region` Parameters passed in argument.

## Author(s)

Edith Gabriel <[email protected]>, Peter J Diggle.

`plot.stpp`, `animation` and `stan` for plotting space-time point patterns.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49``` ```# simple inhibition process inh1 = rinter(npoints=200,thetas=0,deltas=0.05,thetat=0,deltat=0.001, inhibition=TRUE) plot(inh1\$xyt,style="elegant") # inhibition process using hs and ht defined by the user hs = function(d,theta,delta,mus=0.1) { res=NULL a=(1-theta)/mus b=theta-a*delta for(i in 1:length(d)) { if (d[i]<=delta) res=c(res,theta) if (d[i]>(delta+mus)) res=c(res,1) if (d[i]>delta & d[i]<=(delta+mus)) res=c(res,a*d[i]+b) } return(res) } ht = function(d,theta,delta,mut=0.3) { res=NULL a=(1-theta)/mut b=theta-a*delta for(i in 1:length(d)) { if (d[i]<=delta) res=c(res,theta) if (d[i]>(delta+mut)) res=c(res,1) if (d[i]>delta & d[i]<=(delta+mut)) res=c(res,a*d[i]+b) } return(res) } d=seq(0,1,length=100) plot(d,hs(d,theta=0.2,delta=0.1,mus=0.1),xlab="",ylab="",type="l", ylim=c(0,1),lwd=2,las=1) lines(d,ht(d,theta=0.1,delta=0.05,mut=0.3),col=2,lwd=2) legend("bottomright",col=1:2,lty=1,lwd=2,legend=c(expression(h[s]), expression(h[t])),bty="n",cex=2) inh2 = rinter(npoints=100, hs=hs, gs="min", thetas=0.2, deltas=0.1, ht=ht, gt="min", thetat=0.1, deltat=0.05, inhibition=TRUE) animation(inh2\$xyt, runtime=15, cex=0.8) # simple contagious process for given spatial and temporal regions data(northcumbria) cont1 = rinter(npoints=100, s.region=northcumbria, t.region=c(1,200), thetas=0, deltas=10000, thetat=0, deltat=10, recent=1, inhibition=FALSE) plot(cont1\$xyt,pch=19,s.region=cont1\$s.region,mark=TRUE,mark.col=4) ```