R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("spatstat-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('spatstat')
Loading required package: mgcv
This is mgcv 1.3-1 
Loading required package: sm
Library `sm', version 2; Copyright (C) 1997, 2000 A.W.Bowman & A.Azzalini
type help(sm) for summary information
spatstat 1.6-9 
Type "demo(spatstat)" for a demonstration
See the Introduction and Quick Reference in
 /CRANPkg/check/spatstat.Rcheck/spatstat/doc 
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "DiggleGratton"
> 
> ### * DiggleGratton
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: DiggleGratton
> ### Title: Diggle-Gratton model
> ### Aliases: DiggleGratton
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(cells)
>    ppm(cells, ~1, DiggleGratton(0.05, 0.1))
Stationary Diggle-Gratton process

Trend:

First order term:
    beta 
264.2764 

Interaction:
Pairwise interaction family
Interaction: Diggle-Gratton process 
lower limit delta:	0.05
 upper limit rho:	0.1
Fitted exponent kappa:
[1] 9.05
> 
> 
> 
> cleanEx(); ..nameEx <- "Fest"
> 
> ### * Fest
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Fest
> ### Title: Estimate the empty space function F
> ### Aliases: Fest empty.space
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(cells)
>    Fc <- Fest(cells, 0.01)
> 
>    # Tip: don't use F for the left hand side!
>    # That's an abbreviation for FALSE
> 
>    plot(Fc)
     lty col
km     1   1
rs     2   2
theo   3   3
> 
>    # P-P style plot
>    plot(Fc, cbind(km, theo) ~ theo)
     lty col
km     1   1
theo   2   2
> 
>    # The empirical F is above the Poisson F
>    # indicating an inhibited pattern
> 
>    ## Not run: 
> ##D    plot(Fc, . ~ theo)
> ##D    plot(Fc, asin(sqrt(.)) ~ asin(sqrt(theo)))
> ##D    
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "Gcross"
> 
> ### * Gcross
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Gcross
> ### Title: Multitype Nearest Neighbour Distance Function (i-to-j)
> ### Aliases: Gcross
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     data(betacells)
>      # cat retina data
>     G01 <- Gcross(betacells, "off", "on") 
>     plot(G01)
     lty col
km     1   1
rs     2   2
theo   3   3
> 
>     # empty space function of `on' points
>     ## Not run: 
> ##D        F1 <- Fest(betacells[betacells == "on"], r = G01$r, eps=10.0)
> ##D        lines(F1$r, F1$km, lty=3)
> ##D     
> ## End(Not run)
> 
>     # synthetic example    
>     pp <- runifpoispp(50)
>     pp <- pp %mark% factor(sample(0:1, pp$n, replace=TRUE))
>     G <- Gcross(pp, "0", "1")   # note: "0" not 0
> 
> 
> 
> cleanEx(); ..nameEx <- "Gdot"
> 
> ### * Gdot
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Gdot
> ### Title: Multitype Nearest Neighbour Distance Function (i-to-any)
> ### Aliases: Gdot
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     data(betacells)
>      # cat retina data
>     G0. <- Gdot(betacells, "off") 
>     plot(G0.)
     lty col
km     1   1
rs     2   2
theo   3   3
> 
>     # synthetic example    
>     pp <- runifpoispp(50)
>     pp <- pp %mark% factor(sample(0:1, pp$n, replace=TRUE))
>     G <- Gdot(pp, "0") # note: "0" not 0
> 
> 
> 
> cleanEx(); ..nameEx <- "Gest"
> 
> ### * Gest
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Gest
> ### Title: Nearest Neighbour Distance Function G
> ### Aliases: Gest nearest.neighbour
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)
>   G <- Gest(cells)
>   plot(G)
     lty col
km     1   1
rs     2   2
theo   3   3
> 
>   # P-P style plot
>   plot(G, cbind(km,theo) ~ theo)
     lty col
km     1   1
theo   2   2
> 
>   # the empirical G is below the Poisson G,
>   # indicating an inhibited pattern
> 
>   ## Not run: 
> ##D      plot(G, . ~ r)
> ##D      plot(G, . ~ theo)
> ##D      plot(G, asin(sqrt(.)) ~ asin(sqrt(theo)))
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "Geyer"
> 
> ### * Geyer
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Geyer
> ### Title: Geyer's Saturation Point Process Model
> ### Aliases: Geyer
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(cells) 
>    ppm(cells, ~1, Geyer(r=0.07, sat=2), rbord=0.07)
Stationary Geyer saturation process

Trend:

First order term:
    beta 
126.1468 

Interaction:
Saturated pairwise interaction family
Interaction: Geyer saturation process 
interaction distance:	0.07
 saturation parameter:	2
Fitted interaction parameter gamma:
[1] 1e-04
>    # fit the stationary saturation process to `cells'
> 
> 
> 
> cleanEx(); ..nameEx <- "Gmulti"
> 
> ### * Gmulti
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Gmulti
> ### Title: Marked Nearest Neighbour Distance Function
> ### Aliases: Gmulti
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     data(longleaf)
>      # Longleaf Pine data: marks represent diameter
>     ## Don't show:
>       longleaf <- longleaf[seq(1,longleaf$n, by=50), ]
>     
> ## End Don't show
>     Gm <- Gmulti(longleaf, longleaf$marks <= 15, longleaf$marks >= 25)
>     plot(Gm)
     lty col
km     1   1
rs     2   2
theo   3   3
> 
> 
> 
> cleanEx(); ..nameEx <- "Iest"
> 
> ### * Iest
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Iest
> ### Title: Estimate the I-function
> ### Aliases: Iest
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(amacrine)
>    Ic <- Iest(amacrine)
>    plot(Ic, main="Amacrine Cells data")
     lty col
km     1   1
rs     2   2
un     3   3
theo   4   4
>    # values are below I= 0, suggesting negative association
>    # between 'on' and 'off' cells.
> 
> 
> 
> cleanEx(); ..nameEx <- "Jcross"
> 
> ### * Jcross
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Jcross
> ### Title: Multitype J Function (i-to-j)
> ### Aliases: Jcross
> ### Keywords: spatial
> 
> ### ** Examples
> 
>      # Lansing woods data: 6 types of trees
>     data(lansing)
> 
>     ## Don't show:
>        lansing <- lansing[seq(1,lansing$n, by=30), ]
>     
> ## End Don't show
>     Jhm <- Jcross(lansing, "hickory", "maple")
>     # diagnostic plot for independence between hickories and maples
>     plot(Jhm)
     lty col
un     1   1
km     2   2
rs     3   3
theo   4   4
> 
>     # synthetic example with two marks "a" and "b"
>     pp <- runifpoispp(50)
>     pp <- pp %mark% sample(c("a","b"), pp$n, replace=TRUE)
>     J <- Jcross(pp, "a", "b")
> 
> 
> 
> cleanEx(); ..nameEx <- "Jdot"
> 
> ### * Jdot
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Jdot
> ### Title: Multitype J Function (i-to-any)
> ### Aliases: Jdot
> ### Keywords: spatial
> 
> ### ** Examples
> 
>      # Lansing woods data: 6 types of trees
>     data(lansing)
> 
>     ## Don't show:
>         lansing <- lansing[seq(1,lansing$n, by=30), ]
>     
> ## End Don't show
>     Jh. <- Jdot(lansing, "hickory")
>     plot(Jh.)
     lty col
un     1   1
km     2   2
rs     3   3
theo   4   4
>     # diagnostic plot for independence between hickories and other trees
>     Jhh <- Jest(lansing[lansing$marks == "hickory", ])
>     plot(Jhh, add=TRUE)
     lty col
un     1   1
km     2   2
rs     3   3
theo   4   4
> 
>     # synthetic example with two marks "a" and "b"
>     pp <- runifpoispp(50)
>     pp <- pp %mark% sample(c("a","b"), pp$n, replace=TRUE)
>     J <- Jdot(pp, "a")
> 
> 
> 
> cleanEx(); ..nameEx <- "Jest"
> 
> ### * Jest
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Jest
> ### Title: Estimate the J-function
> ### Aliases: Jest
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(cells)
>    J <- Jest(cells, 0.01)
>    plot(J, main="cells data")
     lty col
un     1   1
km     2   2
rs     3   3
theo   4   4
>    # values are far above J= 1, indicating regular pattern
> 
>    data(redwood)
>    J <- Jest(redwood, 0.01)
>    plot(J, main="redwood data")
     lty col
un     1   1
km     2   2
rs     3   3
theo   4   4
>    # values are below J= 1, indicating clustered pattern
> 
> 
> 
> cleanEx(); ..nameEx <- "Jmulti"
> 
> ### * Jmulti
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Jmulti
> ### Title: Marked J Function
> ### Aliases: Jmulti
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     data(longleaf)
>      # Longleaf Pine data: marks represent diameter
>     ## Don't show:
>         longleaf <- longleaf[seq(1,longleaf$n, by=50), ]
>     
> ## End Don't show
>     Jm <- Jmulti(longleaf, longleaf$marks <= 15, longleaf$marks >= 25)
>     plot(Jm)
     lty col
un     1   1
km     2   2
rs     3   3
theo   4   4
> 
> 
> 
> cleanEx(); ..nameEx <- "Kcross"
> 
> ### * Kcross
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Kcross
> ### Title: Multitype K Function (Cross-type)
> ### Aliases: Kcross
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     data(betacells)
>      # cat retina data
>     K01 <- Kcross(betacells, "off", "on") 
>     plot(K01)
       lty col
iso      1   1
trans    2   2
border   3   3
theo     4   4
> 
>     K10 <- Kcross(betacells, "on", "off")
> 
>     # synthetic example    
>     pp <- runifpoispp(50)
>     pp <- pp %mark% factor(sample(0:1, pp$n, replace=TRUE))
>     K <- Kcross(pp, "0", "1") # note: "0" not 0
> 
> 
> 
> cleanEx(); ..nameEx <- "Kdot"
> 
> ### * Kdot
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Kdot
> ### Title: Multitype K Function (i-to-any)
> ### Aliases: Kdot
> ### Keywords: spatial
> 
> ### ** Examples
> 
>      # Lansing woods data: 6 types of trees
>     data(lansing)
> 
>     ## Not run: 
> ##D     Kh. <- Kdot(lansing, "hickory") 
> ##D     
> ## End(Not run)
>     ## Don't show:
>     sub <- lansing[seq(1,lansing$n, by=80), ]
>     Kh. <- Kdot(sub, "hickory") 
>     
> ## End Don't show
>     # diagnostic plot for independence between hickories and other trees
>     plot(Kh.)
       lty col
iso      1   1
trans    2   2
border   3   3
theo     4   4
> 
>     # synthetic example with two marks "a" and "b"
>     pp <- runifpoispp(50)
>     pp <- pp %mark% sample(c("a","b"), pp$n, replace=TRUE)
>     K <- Kdot(pp, "a")
> 
> 
> 
> cleanEx(); ..nameEx <- "Kest"
> 
> ### * Kest
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Kest
> ### Title: K-function
> ### Aliases: Kest
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  pp <- runifpoint(50)
>  K <- Kest(pp)
>  data(cells)
>  K <- Kest(cells, correction="isotropic")
>  plot(K)
     lty col
iso    1   1
theo   2   2
>  plot(K, main="K function for cells")
     lty col
iso    1   1
theo   2   2
>  # plot the L function
>  plot(K, sqrt(iso/pi) ~ r)
>  plot(K, sqrt(./pi) ~ r, ylab="L(r)", main="L function for cells")
     lty col
iso    1   1
theo   2   2
> 
> 
> 
> cleanEx(); ..nameEx <- "Kest.fft"
> 
> ### * Kest.fft
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Kest.fft
> ### Title: K-function using FFT
> ### Aliases: Kest.fft
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  pp <- runifpoint(10000)
>  ## Not run: 
> ##D  spatstat.options(npixel=512)
> ##D  
> ## End(Not run)
>  ## Don't show:
>   spatstat.options(npixel=256)
>  
> ## End Don't show
>  Kpp <- Kest.fft(pp, 0.01)
>  plot(Kpp)
       lty col
border   1   1
theo     2   2
> 
> 
> 
> cleanEx(); ..nameEx <- "Kinhom"
> 
> ### * Kinhom
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Kinhom
> ### Title: Inhomogeneous K-function
> ### Aliases: Kinhom
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(lansing)
>   # inhomogeneous pattern of maples
>   X <- unmark(lansing[lansing$marks == "maple",])
>   ## Don't show:
>      sub <- sample(c(TRUE,FALSE), X$n, replace=TRUE, prob=c(0.1,0.9))
>      X <- X[sub , ]
>   
> ## End Don't show
>   # fit spatial trend
>   fit <- ppm(X, ~ polynom(x,y,2), Poisson())
>   # predict intensity values at points themselves
>   lambda <- predict(fit, locations=X, type="trend")
>   # inhomogeneous K function
>   Ki <- Kinhom(X, lambda)
>   plot(Ki)
           lty col
iso          1   1
trans        2   2
bord.modif   3   3
border       4   4
theo         5   5
> 
>   # SIMULATED DATA
>   # known intensity function
>   lamfun <- function(x,y) { 100 * x }
>   # inhomogeneous Poisson process
>   Y <- rpoispp(lamfun, 100, owin())
>   # evaluate intensity at points of pattern
>   lambda <- lamfun(Y$x, Y$y)
>   # inhomogeneous K function
>   Ki <- Kinhom(Y, lambda)
>   plot(Ki)
           lty col
iso          1   1
trans        2   2
bord.modif   3   3
border       4   4
theo         5   5
> 
> 
> 
> cleanEx(); ..nameEx <- "Kmeasure"
> 
> ### * Kmeasure
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Kmeasure
> ### Title: Reduced Second Moment Measure
> ### Aliases: Kmeasure
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  data(cells)
>  image(Kmeasure(cells, 0.05))
>  # shows pronounced dip around origin consistent with strong inhibition
>  data(redwood)
>  image(Kmeasure(redwood, 0.03), col=grey(seq(1,0,length=32)))
>  # shows peaks at several places, reflecting clustering and ?periodicity
> 
> 
> 
> cleanEx(); ..nameEx <- "Kmulti"
> 
> ### * Kmulti
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Kmulti
> ### Title: Marked K-Function
> ### Aliases: Kmulti
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     data(longleaf)
>      # Longleaf Pine data: marks represent diameter
>     ## Don't show:
>         longleaf <- longleaf[seq(1,longleaf$n, by=50), ]
>     
> ## End Don't show
>     K <- Kmulti(longleaf, longleaf$marks <= 15, longleaf$marks >= 25)
>     plot(K)
       lty col
iso      1   1
trans    2   2
border   3   3
theo     4   4
> 
> 
> 
> cleanEx(); ..nameEx <- "LennardJones"
> 
> ### * LennardJones
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: LennardJones
> ### Title: The Lennard-Jones Potential
> ### Aliases: LennardJones
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    X <- rpoispp(100)
>    ppm(X, ~1, LennardJones(), correction="translate")
Stationary Lennard-Jones potential

Trend:

First order term:
    beta 
91.55748 

Interaction:
Pairwise interaction family
Interaction: Lennard-Jones potential 
:	
Fitted interaction parameters:
sigma   tau 
   NA    NA 
>    # Typically yields very small values for theta_1, theta_2
>    # so the values of sigma, tau may not be sensible
> ##########
>    # How to plot the pair potential function (exponentiated)
>    plotLJ <- function(sigma, tau) {
+         dmax <- 2 * sigma * max(1, tau)^(1/6)
+         d <- seq(dmax * 0.0001, dmax, length=1000)
+         plot(d, exp(- (sigma/d)^12 + tau * (sigma/d)^6), type="l",
+                 ylab="Lennard-Jones",
+                 main=substitute(list(sigma==s, tau==t),
+                      list(s=sigma,t=tau)))
+         abline(h=1, lty=2)
+    }
>    plotLJ(1,1)
> 
> 
> 
> cleanEx(); ..nameEx <- "MultiStrauss"
> 
> ### * MultiStrauss
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: MultiStrauss
> ### Title: The Multitype Strauss Point Process Model
> ### Aliases: MultiStrauss
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    r <- matrix(c(1,2,2,1), nrow=2,ncol=2)
>    MultiStrauss(1:2, r)
Multitype pairwise interaction family
Interaction:	 Multitype Strauss process 
2 types of points
Possible types: 
[1] "1" "2"
Interaction radii:
  1 2
1 1 2
2 2 1
>    # prints a sensible description of itself
>    data(betacells)
>    r <- 30.0 * matrix(c(1,2,2,1), nrow=2,ncol=2)
>    ppm(betacells, ~1, MultiStrauss(c("off","on"), r), rbord=60.0)
Stationary Multitype Strauss process
Possible marks: 
off on
Trend:

Fitted first order terms:
    beta_off      beta_on 
0.0001373652 0.0001373652 

Interaction:
Multitype pairwise interaction family
Interaction:	 Multitype Strauss process 
2 types of points
Possible types: 
[1] "off" "on" 
Interaction radii:
    off on
off  30 60
on   60 30
Fitted interaction parameters gamma_ij:
       off     on
off 0.0000 0.8303
on  0.8303 0.0000
>    # fit the stationary multitype Strauss process to `betacells'
>    ppm(betacells, ~polynom(x,y,3), MultiStrauss(c("off","on"), r), rbord=60.0)
Nonstationary Multitype Strauss process
Possible marks: 
off on
Trend:
Trend formula: ~polynom(x, y, 3)

Fitted coefficients for trend formula:
            (Intercept)     polynom(x, y, 3)[x]     polynom(x, y, 3)[y] 
          -1.024463e+01            1.527585e-02           -1.822493e-03 
  polynom(x, y, 3)[x^2]   polynom(x, y, 3)[x.y]   polynom(x, y, 3)[y^2] 
          -3.530505e-05           -7.962093e-06            7.862101e-06 
  polynom(x, y, 3)[x^3] polynom(x, y, 3)[x^2.y] polynom(x, y, 3)[x.y^2] 
           2.181347e-08            1.233072e-08           -2.606491e-09 
  polynom(x, y, 3)[y^3] 
          -4.201735e-09 

Interaction:
Multitype pairwise interaction family
Interaction:	 Multitype Strauss process 
2 types of points
Possible types: 
[1] "off" "on" 
Interaction radii:
    off on
off  30 60
on   60 30
Fitted interaction parameters gamma_ij:
       off     on
off 0.0000 0.7324
on  0.7324 0.0000
>    # fit a nonstationary Strauss process with log-cubic polynomial trend
> 
> 
> 
> cleanEx(); ..nameEx <- "MultiStraussHard"
> 
> ### * MultiStraussHard
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: MultiStraussHard
> ### Title: The Multitype/Hard Core Strauss Point Process Model
> ### Aliases: MultiStraussHard
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    r <- matrix(3, nrow=2,ncol=2)
>    h <- matrix(c(1,2,2,1), nrow=2,ncol=2)
>    MultiStraussHard(1:2, r, h)
Multitype pairwise interaction family
Interaction:	 Multitype Strauss Hardcore process 
2 types of points
Possible types: 
[1] "1" "2"
Interaction radii:
  1 2
1 3 3
2 3 3
Hardcore radii:
  1 2
1 1 2
2 2 1
>    # prints a sensible description of itself
>    data(betacells)
>    r <- 30.0 * matrix(c(1,2,2,1), nrow=2,ncol=2)
>    h <- 30.0 * matrix(c(NA,1,1,NA), nrow=2,ncol=2)
>    ppm(betacells, ~1, MultiStraussHard(c("off","on"), r, h), rbord=60.0)
Warning in mpl.prepare(Q, X, P, trend, interaction, covariates, want.trend,  : 
	 25 data point(s) are illegal (zero conditional intensity under the model)
Stationary Multitype Strauss Hardcore process
Possible marks: 
off on
Trend:

Fitted first order terms:
    beta_off      beta_on 
0.0001492623 0.0001492623 

Interaction:
Multitype pairwise interaction family
Interaction:	 Multitype Strauss Hardcore process 
2 types of points
Possible types: 
[1] "off" "on" 
Interaction radii:
    off on
off  30 60
on   60 30
Hardcore radii:
    off on
off  NA 30
on   30 NA
Fitted interaction parameters gamma_ij:
       off     on
off 0.0000 0.8291
on  0.8291 0.0000
>    # fit the stationary multitype hardcore Strauss process to `betacells'
> 
> 
> 
> cleanEx(); ..nameEx <- "PairPiece"
> 
> ### * PairPiece
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: PairPiece
> ### Title: The Piecewise Constant Pairwise Interaction Point Process Model
> ### Aliases: PairPiece
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    PairPiece(c(0.1,0.2))
Pairwise interaction family
Interaction: Piecewise constant pairwise interaction process 
interaction thresholds:	c(0.1, 0.2)
>    # prints a sensible description of itself
>    data(cells) 
>    ppm(cells, ~1, PairPiece(r = c(0.05, 0.1, 0.2)), rbord=0.2)
Stationary Piecewise constant pairwise interaction process

Trend:

First order term:
    beta 
1518.802 

Interaction:
Pairwise interaction family
Interaction: Piecewise constant pairwise interaction process 
interaction thresholds:	c(0.05, 0.1, 0.2)
Fitted interaction parameters gamma_i:
  [0,0.05) [0.05,0.1)  [0.1,0.2) 
    0.0000     0.0247     0.8748 
>    # fit a stationary piecewise constant pairwise interaction process
>    ppm(cells, ~polynom(x,y,3), PairPiece(c(0.05, 0.1)), rbord=0.1)
Nonstationary Piecewise constant pairwise interaction process

Trend:
Trend formula: ~polynom(x, y, 3)

Fitted coefficients for trend formula:
            (Intercept)     polynom(x, y, 3)[x]     polynom(x, y, 3)[y] 
               2.770327               16.329865               13.056614 
  polynom(x, y, 3)[x^2]   polynom(x, y, 3)[x.y]   polynom(x, y, 3)[y^2] 
             -29.257015              -17.982790              -18.098769 
  polynom(x, y, 3)[x^3] polynom(x, y, 3)[x^2.y] polynom(x, y, 3)[x.y^2] 
              17.555897                9.824152                9.385077 
  polynom(x, y, 3)[y^3] 
               7.482870 

Interaction:
Pairwise interaction family
Interaction: Piecewise constant pairwise interaction process 
interaction thresholds:	c(0.05, 0.1)
Fitted interaction parameters gamma_i:
  [0,0.05) [0.05,0.1) 
    0.0000     0.0155 
>    # nonstationary process with log-cubic polynomial trend
> 
> 
> 
> cleanEx(); ..nameEx <- "Pairwise"
> 
> ### * Pairwise
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Pairwise
> ### Title: Generic Pairwise Interaction model
> ### Aliases: Pairwise
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    #This is the same as StraussHard(r=0.7,h=0.2)
>    strpot <- function(t,par) {
+          r <- par$r
+          h <- par$h
+          value <- (t <= r)
+          value[t < h] <- -Inf
+          value
+    }
>    mySH <- Pairwise(strpot, "StraussHard", list(r=0.7,h=0.2),
+            c("interaction distance r", "hard core distance c"))
>    data(cells)
>    ppm(cells, ~ 1, mySH)
Warning in mpl.prepare(Q, X, P, trend, interaction, covariates, want.trend,  : 
	 42 data point(s) are illegal (zero conditional intensity under the model)
Stationary StraussHard

Trend:

First order term:
        beta 
3.059023e-08 

Interaction:
StraussHard 
Potential function:
function (t, par) 
{
    r <- par$r
    h <- par$h
    value <- (t <= r)
    value[t < h] <- -Inf
    value
}
Fitted interaction terms:
Interaction 
          1 
> 
> 
> 
> cleanEx(); ..nameEx <- "Poisson"
> 
> ### * Poisson
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Poisson
> ### Title: Poisson Point Process Model
> ### Aliases: Poisson
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  data(nztrees)
>  ppm(nztrees, ~1, Poisson())
Stationary Poisson process

Intensity:

Uniform intensity:
[1] 0.005916753
>  # fit the stationary Poisson process to 'nztrees'
>  # no edge correction needed
> 
>  data(longleaf)
>  ## Don't show:
>    longleaf <- longleaf[seq(1, longleaf$n, by=50)]
>  
> ## End Don't show
>  longadult <- longleaf[longleaf$marks >= 30, ]
>  longadult <- unmark(longadult)
>  ppm(longadult, ~ x, Poisson())
Nonstationary Poisson process

Intensity:
Trend formula: ~x

Fitted coefficients for trend formula:
 (Intercept)            x 
-8.052377176 -0.003696828 
>  # fit the nonstationary Poisson process 
>  # with intensity lambda(x,y) = exp( a + bx)
> 
>  data(lansing)
>  # trees marked by species
>  ## Don't show:
>      lansing <- lansing[seq(1,lansing$n, by=30), ]
>  
> ## End Don't show
>  ppm(lansing, ~ marks, Poisson())
Stationary multitype Poisson process
Possible marks: 
blackoak hickory maple misc redoak whiteoak
Intensity:
Trend formula: ~marks

Fitted intensities:
beta_blackoak  beta_hickory    beta_maple     beta_misc   beta_redoak 
            5            23            18             3            12 
beta_whiteoak 
           15 
>  # fit stationary marked Poisson process
>  # with different intensity for each species
> 
> ## Not run: 
> ##D  ppm(lansing, ~ marks * polynom(x,y,3), Poisson())
> ## End(Not run)
>  # fit nonstationary marked Poisson process
>  # with different log-cubic trend for each species
> ## Don't show:
>  # equivalent functionality - smaller dataset
>  data(betacells)
>  ppm(betacells, ~ marks * polynom(x,y,2), Poisson())
Nonstationary multitype Poisson process
Possible marks: 
off on
Intensity:
Trend formula: ~marks * polynom(x, y, 2)

Fitted coefficients for trend formula:
                  (Intercept)                       markson 
                -9.414097e+00                  7.140810e-01 
          polynom(x, y, 2)[x]           polynom(x, y, 2)[y] 
                -8.360216e-04                  1.595380e-03 
        polynom(x, y, 2)[x^2]         polynom(x, y, 2)[x.y] 
                 5.373429e-07                 -7.688609e-07 
        polynom(x, y, 2)[y^2]   markson:polynom(x, y, 2)[x] 
                -9.123127e-07                 -2.244465e-03 
  markson:polynom(x, y, 2)[y] markson:polynom(x, y, 2)[x^2] 
                -1.894023e-03                  1.618490e-06 
markson:polynom(x, y, 2)[x.y] markson:polynom(x, y, 2)[y^2] 
                 1.823315e-06                  1.075783e-06 
> ## End Don't show
> 
> 
> 
> cleanEx(); ..nameEx <- "Softcore"
> 
> ### * Softcore
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Softcore
> ### Title: The Soft Core Point Process Model
> ### Aliases: Softcore
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(cells) 
>    ppm(cells, ~1, Softcore(kappa=0.5), rbord=0)
Stationary Soft core process

Trend:

First order term:
    beta 
430.7452 

Interaction:
Pairwise interaction family
Interaction: Soft core process 
Exponent kappa:	0.5
Fitted interaction parameter sigma:
[1] 0.09291655
>    # fit the stationary Soft Core process to `cells'
> 
> 
> 
> cleanEx(); ..nameEx <- "Strauss"
> 
> ### * Strauss
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Strauss
> ### Title: The Strauss Point Process Model
> ### Aliases: Strauss
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    Strauss(r=0.1)
Pairwise interaction family
Interaction: Strauss process 
interaction distance:	0.1
>    # prints a sensible description of itself
>    data(cells) 
>    ppm(cells, ~1, Strauss(r=0.07), rbord=0.07)
Stationary Strauss process

Trend:

First order term:
    beta 
126.1468 

Interaction:
Pairwise interaction family
Interaction: Strauss process 
interaction distance:	0.07
Fitted interaction parameter gamma:
[1] 0
>    # fit the stationary Strauss process to `cells'
>    ppm(cells, ~polynom(x,y,3), Strauss(r=0.07), rbord=0.1)
Nonstationary Strauss process

Trend:
Trend formula: ~polynom(x, y, 3)

Fitted coefficients for trend formula:
            (Intercept)     polynom(x, y, 3)[x]     polynom(x, y, 3)[y] 
             0.05106119             32.80566353              0.12842709 
  polynom(x, y, 3)[x^2]   polynom(x, y, 3)[x.y]   polynom(x, y, 3)[y^2] 
           -67.33464677             -5.36337896              6.19537368 
  polynom(x, y, 3)[x^3] polynom(x, y, 3)[x^2.y] polynom(x, y, 3)[x.y^2] 
            41.28159446             10.00958702             -4.28944313 
  polynom(x, y, 3)[y^3] 
            -5.82298495 

Interaction:
Pairwise interaction family
Interaction: Strauss process 
interaction distance:	0.07
Fitted interaction parameter gamma:
[1] 0
>    # fit a nonstationary Strauss process with log-cubic polynomial trend
> 
> 
> 
> cleanEx(); ..nameEx <- "StraussHard"
> 
> ### * StraussHard
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: StraussHard
> ### Title: The Strauss / Hard Core Point Process Model
> ### Aliases: StraussHard
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    StraussHard(r=1,hc=0.02)
Pairwise interaction family
Interaction: Strauss - hard core process 
interaction distance:	1
 hard core distance:	0.02
>    # prints a sensible description of itself
> 
>    data(cells) 
>    ppm(cells, ~1, StraussHard(r=0.1, hc=0.05), rbord=0.1)
Stationary Strauss - hard core process

Trend:

First order term:
   beta 
763.276 

Interaction:
Pairwise interaction family
Interaction: Strauss - hard core process 
interaction distance:	0.1
 hard core distance:	0.05
Fitted interaction parameter gamma:
[1] 0.0145
>    # fit the stationary Strauss/hard core  process to `cells'
> 
>    ppm(cells, ~ polynom(x,y,3), StraussHard(r=0.1, hc=0.05), rbord=0.1)
Nonstationary Strauss - hard core process

Trend:
Trend formula: ~polynom(x, y, 3)

Fitted coefficients for trend formula:
            (Intercept)     polynom(x, y, 3)[x]     polynom(x, y, 3)[y] 
               2.770327               16.329865               13.056614 
  polynom(x, y, 3)[x^2]   polynom(x, y, 3)[x.y]   polynom(x, y, 3)[y^2] 
             -29.257015              -17.982790              -18.098769 
  polynom(x, y, 3)[x^3] polynom(x, y, 3)[x^2.y] polynom(x, y, 3)[x.y^2] 
              17.555897                9.824152                9.385077 
  polynom(x, y, 3)[y^3] 
               7.482870 

Interaction:
Pairwise interaction family
Interaction: Strauss - hard core process 
interaction distance:	0.1
 hard core distance:	0.05
Fitted interaction parameter gamma:
[1] 0.0155
>    # fit a nonstationary Strauss/hard core process
>    # with log-cubic polynomial trend
>    
> 
> 
> cleanEx(); ..nameEx <- "affine"
> 
> ### * affine
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: affine
> ### Title: Apply Affine Transformation
> ### Aliases: affine
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)
>   # shear transformation
>   X <- affine(cells, matrix(c(1,0,0.6,1),ncol=2))
>   ## Not run: 
> ##D   plot(X)
> ##D   # rescale y coordinates by factor 1.3
> ##D   plot(affine(cells, diag(c(1,1.3))))
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "affine.owin"
> 
> ### * affine.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: affine.owin
> ### Title: Apply Affine Transformation To Window
> ### Aliases: affine.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   # shear transformation
>   X <- affine(owin(), matrix(c(1,0,0.6,1),ncol=2))
>   ## Not run: 
> ##D   plot(X)
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "affine.ppp"
> 
> ### * affine.ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: affine.ppp
> ### Title: Apply Affine Transformation To Point Pattern
> ### Aliases: affine.ppp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)
>   # shear transformation
>   X <- affine(cells, matrix(c(1,0,0.6,1),ncol=2))
>   ## Not run: 
> ##D   plot(X)
> ##D   # rescale y coordinates by factor 1.3
> ##D   plot(affine(cells, diag(c(1,1.3))))
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "allstats"
> 
> ### * allstats
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: allstats
> ### Title: Calculate four standard summary functions of a point pattern.
> ### Aliases: allstats
> ### Keywords: spatial
> 
> ### ** Examples
> 
>         data(swedishpines)
>         a <- allstats(swedishpines,dataname="Swedish Pines")
>         ## Not run: 
> ##D         plot(a)
> ##D         plot(a, subset=list("r<=15","r<=15","r<=15","r<=50"))
> ##D         
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "alltypes"
> 
> ### * alltypes
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: alltypes
> ### Title: Calculate Statistic for All Types in a Multitype Point Pattern
> ### Aliases: alltypes
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    # bramblecanes (3 marks).
>    data(bramblecanes)
>    ## Not run: 
> ##D    X.F <- alltypes(bramblecanes,fun="F",verb=TRUE)
> ##D    plot(X.F) 
> ##D    X.G <- alltypes(bramblecanes,fun="G",verb=TRUE)
> ##D    X.J <- alltypes(bramblecanes,fun="J",verb=TRUE)
> ##D    X.K <- alltypes(bramblecanes,fun="K",verb=TRUE)
> ##D    X.Gd <- alltypes(bramblecanes,fun="Gdot",verb=TRUE)
> ##D    X.Jd <- alltypes(bramblecanes,fun="Jdot",verb=TRUE)
> ##D    X.Kd <- alltypes(bramblecanes,fun="Kdot",verb=TRUE)
> ##D    
> ## End(Not run)
>    ## Don't show:
>       # smaller dataset
>       bram <- bramblecanes[seq(1, bramblecanes$n, by=20), ]
>       X.F <- alltypes(bram,fun="F",verb=TRUE)
i = 1 j = 1 
i = 2 j = 1 
i = 3 j = 1 
>       X.G <- alltypes(bram,fun="G",verb=TRUE)
i = 1 j = 1 
i = 1 j = 2 
i = 1 j = 3 
i = 2 j = 1 
i = 2 j = 2 
i = 2 j = 3 
i = 3 j = 1 
i = 3 j = 2 
i = 3 j = 3 
>       X.J <- alltypes(bram,fun="J",verb=TRUE)
i = 1 j = 1 
i = 1 j = 2 
i = 1 j = 3 
i = 2 j = 1 
i = 2 j = 2 
i = 2 j = 3 
i = 3 j = 1 
i = 3 j = 2 
i = 3 j = 3 
>       X.K <- alltypes(bram,fun="K",verb=TRUE)
i = 1 j = 1 
i = 1 j = 2 
i = 1 j = 3 
i = 2 j = 1 
i = 2 j = 2 
i = 2 j = 3 
i = 3 j = 1 
i = 3 j = 2 
i = 3 j = 3 
>       X.Gd <- alltypes(bram,fun="Gdot",verb=TRUE)
i = 1 j = 1 
i = 2 j = 1 
i = 3 j = 1 
>       X.Jd <- alltypes(bram,fun="Jdot",verb=TRUE)
i = 1 j = 1 
i = 2 j = 1 
i = 3 j = 1 
>       X.Kd <- alltypes(bram,fun="Kdot",verb=TRUE)
i = 1 j = 1 
i = 2 j = 1 
i = 3 j = 1 
>    
> ## End Don't show
>    
>    # Swedishpines (unmarked).
>    data(swedishpines)
>    ## Don't show:
>         swedishpines <- swedishpines[1:25]
>    
> ## End Don't show
>    X.K <- alltypes(swedishpines,fun="K")
>    X.F <- alltypes(swedishpines,fun="F")
>    X.G <- alltypes(swedishpines,fun="G")
>    X.J <- alltypes(swedishpines,fun="J")
> 
>    # simulated data
>    ## Not run: 
> ##D    pp <- runifpoint(350, owin(c(0,1),c(0,1)))
> ##D    pp$marks <- factor(c(rep(1,50),rep(2,100),rep(3,200)))
> ##D    X.F <- alltypes(pp,fun="F",verb=TRUE,dataname="Fake Data")
> ##D    X.G <- alltypes(pp,fun="G",verb=TRUE,dataname="Fake Data")
> ##D    X.J <- alltypes(pp,fun="J",verb=TRUE,dataname="Fake Data")
> ##D    X.K <- alltypes(pp,fun="K",verb=TRUE,dataname="Fake Data")
> ##D    
> ## End(Not run)
> 
>    # A setting where you might REALLY want to use dataname:
>    ## Not run: 
> ##D    xxx <- alltypes(ppp(Melvin$x,Melvin$y,
> ##D                 window=as.owin(c(5,20,15,50)),marks=clyde),
> ##D                 fun="F",verb=TRUE,dataname="Melvin")
> ##D    
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "anova.ppm"
> 
> ### * anova.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: anova.ppm
> ### Title: ANOVA for Fitted Point Process Models
> ### Aliases: anova.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  data(swedishpines)
>  mod0 <- ppm(swedishpines, ~1, Poisson())
>  modx <- ppm(swedishpines, ~x, Poisson())
>  anova.ppm(modx, mod0, test="Chi")
Analysis of Deviance Table

Model 1: .mpl.Y ~ x
Model 2: .mpl.Y ~ 1
  Resid. Df Resid. Dev  Df Deviance P(>|Chi|)
1       698     406.94                       
2       699     408.10  -1    -1.15      0.28
> 
> 
> 
> cleanEx(); ..nameEx <- "ants"
> 
> ### * ants
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ants
> ### Title: Harkness-Isham ants' nests data
> ### Aliases: ants ants.extra
> ### Keywords: datasets
> 
> ### ** Examples
> 
> 
>   # Equivalent to Figure 1 of Harkness and Isham (1983)
> 
>   data(ants)
>   ants.extra$plot()
> 
>   # Data in subrectangle A, rotated 
>   # Approximate data used by Sarkka (1993)
> 
>   angle <- atan(diff(ants.extra$fieldscrub$y)/diff(ants.extra$fieldscrub$x))
>   plot(rotate(ants.extra$A, -angle))
Cataglyphis      Messor 
          1           2 
> 
>   # Approximate window used by Takacs and Fiksel (1986)
> 
>   tfwindow <- bounding.box(ants$window)
>   antsTF <- ppp(ants$x, ants$y, window=tfwindow)
>   plot(antsTF)
> 
> 
> 
> cleanEx(); ..nameEx <- "applynbd"
> 
> ### * applynbd
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: applynbd
> ### Title: Apply Function to Every Neighbourhood in a Point Pattern
> ### Aliases: applynbd
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(redwood)
> 
>   # count the number of points within radius 0.2 of each point of X
>   nneighbours <- applynbd(redwood, R=0.2, function(Y, ...){Y$n-1})
>   # equivalent to:
>   nneighbours <- applynbd(redwood, R=0.2, function(Y, ...){Y$n}, exclude=TRUE)
> 
>   # compute the distance to the second nearest neighbour of each point
>   secondnndist <- applynbd(redwood, N = 2,
+                            function(dists, ...){max(dists)},
+                            exclude=TRUE)
> 
>   # marked point pattern
>   data(longleaf)
>   ## Don't show:
>         # smaller dataset
>         longleaf <- longleaf[seq(1, longleaf$n, by=80)]
>   
> ## End Don't show
>   # compute the median of the marks of all neighbours of a point
>   dbh.med <- applynbd(longleaf, R=40, exclude=TRUE,
+                  function(Y, ...) { median(Y$marks)})
> 
>   # ANIMATION explaining the definition of the K function
>   # (arguments `fullpicture' and 'rad' are passed to FUN)
> 
>   showoffK <- function(Y, current, dists, dranks, fullpicture,rad) { 
+         plot(fullpicture, main="")
+         points(Y, cex=2)
+         u <- current
+         points(u[1],u[2],pch="+",cex=3)
+         theta <- seq(0,2*pi,length=100)
+         polygon(u[1]+ rad * cos(theta),u[2]+rad*sin(theta))
+         text(u[1]+rad/3,u[2]+rad/2,Y$n,cex=3)
+         Sys.sleep(if(runif(1) < 0.1) 1.5 else 0.3)
+         return(Y$n - 1)
+   }
>   applynbd(redwood, R=0.2, showoffK, fullpicture=redwood, rad=0.2, exclude=TRUE)
 [1]  3  3  3  3  3 12 10 12  7 10  7  7  7  8 10  7 10  6  6  6  8  8 10 10 11
[26] 11 11  9 11 12 12 12 11 11 11  6  7  5  0  0  6  6 13 13 10 12  2  4 11  9
[51]  8  3 10  9 11 12  7 11  8  1  4  2
> 
>   # animation explaining the definition of the G function
> 
>   showoffG <- function(Y, current, dists, dranks, fullpicture) { 
+         plot(fullpicture, main="")
+         points(Y, cex=2)
+         u <- current
+         points(u[1],u[2],pch="+",cex=3)
+         v <- c(Y$x[1],Y$y[1])
+         segments(u[1],u[2],v[1],v[2],lwd=2)
+         w <- (u + v)/2
+         nnd <- dists[1]
+         text(w[1],w[2],round(nnd,3),cex=2)
+         Sys.sleep(if(runif(1) < 0.1) 1.5 else 0.3)
+         return(nnd)
+   }
> 
>   data(cells)
>   applynbd(cells, N=1, showoffG, exclude=TRUE, fullpicture=cells)
 [1] 0.14583895 0.11486514 0.14024621 0.11180340 0.11180340 0.15449595
 [7] 0.15449595 0.11486514 0.14577380 0.14243595 0.15206906 0.12356780
[13] 0.12356780 0.12500000 0.12356780 0.14313630 0.13036104 0.13036104
[19] 0.10697663 0.13861097 0.12224974 0.15206906 0.13861097 0.08363014
[25] 0.13036104 0.11200000 0.12224974 0.15089400 0.15037619 0.10662551
[31] 0.11819052 0.08363014 0.13462912 0.11200000 0.10662551 0.13852076
[37] 0.14313630 0.14313630 0.13953136 0.12801562 0.12801562 0.13852076
> 
> 
> 
> cleanEx(); ..nameEx <- "area.owin"
> 
> ### * area.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: area.owin
> ### Title: Area of a Window
> ### Aliases: area.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- unit.square()
>   area.owin(w)
[1] 1
>        # returns 1.00000
> 
>   k <- 6
>   theta <- 2 * pi * (0:(k-1))/k
>   co <- cos(theta)
>   si <- sin(theta)
>   mas <- owin(c(-1,1), c(-1,1), poly=list(x=co, y=si))
>   area.owin(mas)
[1] 2.598076
>       # returns approx area of k-gon
>   
>   mas <- as.mask(w, eps=0.01)
>   X <- raster.x(mas)
>   Y <- raster.y(mas)
>   mas$m <- ((X - 0.5)^2 + (Y - 0.5)^2 <= 1)
>   area.owin(mas)
[1] 1
>        # returns 3.14 approx     
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "as.im"
> 
> ### * as.im
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: as.im
> ### Title: Convert to Pixel Image
> ### Aliases: as.im
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(demopat)
>   # window object
>   W <- demopat$window
>   plot(W)
>   Z <- as.im(W)
>   image(Z)
>   # function
>   Z <- as.im(function(x,y) {x^2 + y^2}, unit.square())
>   image(Z)
>   # function with extra arguments
>   f <- function(x, y, x0, y0) {
+       sqrt((x - x0)^2 + (y-y0)^2)
+   }
>   Z <- as.im(f, unit.square(), x0=0.5, y0=0.5)
>   image(Z)
>   # Revisit the Sixties
>   data(letterR)
>   Z <- as.im(f, letterR, x0=2.5, y0=2)
>   image(Z)  
> 
> 
> 
> cleanEx(); ..nameEx <- "as.mask"
> 
> ### * as.mask
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: as.mask
> ### Title: Pixel Image Approximation of a Window
> ### Aliases: as.mask
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- owin(c(0,10),c(0,10), poly=list(x=c(1,2,3,2,1), y=c(2,3,4,6,7)))
>   ## Not run: plot(w)
>   m <- as.mask(w)
>   ## Not run: plot(m)
>   x <- 1:9
>   y <- seq(0.25, 9.75, by=0.5)
>   m <- as.mask(w, xy=list(x=x, y=y))
> 
> 
> 
> cleanEx(); ..nameEx <- "as.owin"
> 
> ### * as.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: as.owin
> ### Title: Convert Data To Class owin
> ### Aliases: as.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  w <- as.owin(c(0,1,0,1))
>  w <- as.owin(list(xrange=c(0,5),yrange=c(0,10)))
>  # point pattern
>  data(demopat)
>  w <- as.owin(demopat)
>  # image
>  Z <- as.im(function(x,y) { x + 3}, unit.square())
>  w <- as.owin(Z)
> 
>  # Venables & Ripley 'spatial' package
>  require(spatial)
Loading required package: spatial

Attaching package: 'spatial'


	The following object(s) are masked from package:spatstat :

	 Strauss 

[1] TRUE
>  towns <- ppinit("towns.dat")
>  w <- as.owin(towns)
>  detach(package:spatial)
> 
> 
> 
> cleanEx(); ..nameEx <- "as.ppp"
> 
> ### * as.ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: as.ppp
> ### Title: Convert Data To Class ppp
> ### Aliases: as.ppp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  ## Not run: 
> ##D  plot(c(0,1),c(0,1),type="n")
> ##D  xy <- locator(20) # click on 20 points in plot window
> ##D  pp <- as.ppp(xy, c(0,1,0,1))
> ##D  
> ##D  w <- owin(c(0,1),c(0,1))
> ##D  plot(w)                      # neater
> ##D  xy <- locator(20)            # click on 20 points in plot window
> ##D  pp <- as.ppp(xy, w)
> ##D  
> ## End(Not run) 
>  
>  xy <- matrix(runif(40), ncol=2)
>  pp <- as.ppp(xy, c(0,1,0,1))
>  
>  # Venables-Ripley format
>  require(spatial)
Loading required package: spatial

Attaching package: 'spatial'


	The following object(s) are masked from package:spatstat :

	 Strauss 

[1] TRUE
>  towns <- ppinit("towns.dat")
>  pp <- as.ppp(towns)   # converted to our format
>  detach(package:spatial)
> 
> 
> 
> cleanEx(); ..nameEx <- "as.rectangle"
> 
> ### * as.rectangle
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: as.rectangle
> ### Title: Window Frame
> ### Aliases: as.rectangle
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- owin(c(0,10),c(0,10), poly=list(x=c(1,2,3,2,1), y=c(2,3,4,6,7)))
>   r <- as.rectangle(w)
>   # returns a 10 x 10 rectangle
> 
> 
> 
> cleanEx(); ..nameEx <- "bdist.pixels"
> 
> ### * bdist.pixels
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: bdist.pixels
> ### Title: Distance to Boundary of Window
> ### Aliases: bdist.pixels
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   u <- owin(c(0,1),c(0,1))
>   d <- bdist.pixels(u, eps=0.01)
>   image(d)
>   d <- bdist.pixels(u, eps=0.01, coords=FALSE)
>   mean(d >= 0.1)
[1] 0.64
>   # value is approx (1 - 2 * 0.1)^2 = 0.64
> 
> 
> 
> cleanEx(); ..nameEx <- "bdist.points"
> 
> ### * bdist.points
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: bdist.points
> ### Title: Distance to Boundary of Window
> ### Aliases: bdist.points
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)
>   d <- bdist.points(cells)
> 
> 
> 
> cleanEx(); ..nameEx <- "betacells"
> 
> ### * betacells
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: betacells
> ### Title: Beta Ganglion Cells in Cat Retina
> ### Aliases: betacells betacells.extra
> ### Keywords: datasets
> 
> ### ** Examples
> 
>    data(betacells)
>    plot(betacells)
off  on 
  1   2 
>    plot(betacells$window, main="beta cells")
>    symbols(betacells$x, betacells$y,
+        circles=sqrt(betacells.extra$area/pi),
+        inches=FALSE, add=TRUE)
> 
> 
> 
> cleanEx(); ..nameEx <- "bounding.box"
> 
> ### * bounding.box
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: bounding.box
> ### Title: Bounding Box of a Window
> ### Aliases: bounding.box
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- owin(c(0,10),c(0,10), poly=list(x=c(1,2,3,2,1), y=c(2,3,4,6,7)))
>   r <- bounding.box(w)
>   # returns rectangle [1,3] x [2,7]
> 
>   w2 <- unit.square()
>   r <- bounding.box(w, w2)
>   # returns rectangle [0,3] x [0,7]
> 
> 
> 
> cleanEx(); ..nameEx <- "centroid.owin"
> 
> ### * centroid.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: centroid.owin
> ### Title: Centroid of a window
> ### Aliases: centroid.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- owin(c(0,1),c(0,1))
>   centroid.owin(w) 
$x
[1] 0.5

$y
[1] 0.5

>   # returns 0.5, 0.5
> 
>   data(demopat)
>   w <- demopat$window
>   # an irregular window
>   ## Not run: 
> ##D   plot(w)
> ##D   # plot the window
> ##D   points(centroid.owin(w))
> ##D   # mark its centroid 
> ##D   
> ## End(Not run)
> 
>   wapprox <- as.mask(w)
>   # pixel approximation of window
>   ## Not run: 
> ##D   points(centroid.owin(wapprox))
> ##D   # should be indistinguishable 
> ##D   
> ## End(Not run)
>   ## Don't show:
>   centroid.owin(w)
$x
[1] 5733.019

$y
[1] 3634.136

>   centroid.owin(wapprox)
$x
[1] 5732.25

$y
[1] 3634.436

>   
> ## End Don't show     
> 
> 
> 
> cleanEx(); ..nameEx <- "coef.ppm"
> 
> ### * coef.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: coef.ppm
> ### Title: Coefficients of Fitted Point Process Model
> ### Aliases: coef.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     data(cells)
> 
>     poi <- ppm(cells, ~1, Poisson())
>     coef(poi)
$"log(lambda)"
[1] 3.737670

>     # This is the log of the fitted intensity of the Poisson process
> 
>     stra <- ppm(cells, ~1, Strauss(r=0.07), rbord=0.07)
>     coef(stra)
(Intercept) Interaction 
   4.837446  -19.283583 
> 
>     # The two entries "(Intercept)" and "Interaction"
>     # are respectively log(beta) and log(gamma)
>     # in the usual notation for Strauss(beta, gamma, r)
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "complement.owin"
> 
> ### * complement.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: complement.owin
> ### Title: Take Complement of a Window
> ### Aliases: complement.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    # polygonal
>    data(demopat)
>    w <- demopat$window
>    outside <- complement.owin(w)
>    # mask
>    w <- as.mask(demopat$window)
>    outside <- complement.owin(w)
> 
> 
> 
> cleanEx(); ..nameEx <- "concatxy"
> 
> ### * concatxy
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: concatxy
> ### Title: Concatenate x,y Coordinate Vectors
> ### Aliases: concatxy
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   dat <- runifrect(30)
>   xy <- list(x=runif(10),y=runif(10))
>   new <- concatxy(dat, xy)
> 
> 
> 
> cleanEx(); ..nameEx <- "copper"
> 
> ### * copper
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: copper
> ### Title: Berman-Huntington points and lines data
> ### Aliases: copper
> ### Keywords: datasets
> 
> ### ** Examples
> 
> 
>   data(copper)
> 
>   # Plot full dataset
> 
>   plot(copper$points)
>   cl <- copper$lines
>   segments(cl[,1], cl[,2], cl[,3], cl[,4])
> 
>   # Plot southern half of data
>   plot(copper$SouthPoints)
>   cl <- copper$SouthLines
>   segments(cl[,1], cl[,2], cl[,3], cl[,4])
> 
>   ## Not run: 
> ##D     Z <- copper$SouthDistance()
> ##D     plot(Z)
> ##D     X <- copper$SouthPoints
> ##D     ppm(X, ~D, covariates=list(D=Z))
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "corners"
> 
> ### * corners
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: corners
> ### Title: Corners of a rectangle
> ### Aliases: corners
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- unit.square()
>   corners(w)
$x
[1] 0 1 0 1

$y
[1] 0 0 1 1

>        # returns list(x=c(0,1,0,1),y=c(0,0,1,1))
> 
> 
> 
> cleanEx(); ..nameEx <- "crossdist"
> 
> ### * crossdist
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: crossdist
> ### Title: Pairwise distances between two different point patterns
> ### Aliases: crossdist crossdist.ppp crossdist.default
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(cells)
>    d <- crossdist(cells, runifpoint(6))
>    
>    d <- crossdist(runif(7), runif(7), runif(12), runif(12))
> 
> 
> 
> cleanEx(); ..nameEx <- "cut.ppp"
> 
> ### * cut.ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: cut.ppp
> ### Title: Convert Point Pattern Marks from Numeric to Factor
> ### Aliases: cut.ppp cut
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  data(longleaf)
>  # Longleaf Pines data
>  # the marks are positive real numbers indicating tree diameters.
> 
>  ## Don't show:
>         # smaller dataset
>         longleaf <- longleaf[seq(1, longleaf$n, by=80)]
>  
> ## End Don't show
>  ## Not run: 
> ##D  plot(longleaf)
> ##D  
> ## End(Not run)
> 
>  # cut the range of tree diameters into three intervals
>  long3 <- cut(longleaf, 3)
>  ## Not run: 
> ##D  plot(long3)
> ##D  
> ## End(Not run)
> 
>  # adult trees defined to have diameter at least 30 cm
>  long2 <- cut(longleaf, breaks=c(0,30,100), labels=c("Sapling", "Adult"))
>  plot(long2)
Sapling   Adult 
      1       2 
>  plot(long2, cols=c("green","blue"))
Sapling   Adult 
      1       2 
> 
> 
> 
> cleanEx(); ..nameEx <- "data.ppm"
> 
> ### * data.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: data.ppm
> ### Title: Extract Original Data from a Fitted Point Process Model
> ### Aliases: data.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  data(cells)
>  fit <- ppm(cells, ~1, Strauss(r=0.1), rbord=0.1)
>  X <- data.ppm(fit)
>  # 'X' is identical to 'cells'
> 
> 
> 
> cleanEx(); ..nameEx <- "default.dummy"
> 
> ### * default.dummy
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: default.dummy
> ### Title: Generate a Default Pattern of Dummy Points
> ### Aliases: default.dummy
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(simdat)
>   P <- simdat
>   D <- default.dummy(P, 100)
>   ## Not run: plot(D)
>   Q <- quadscheme(P, D, "grid")
>   ## Not run: plot(union.quad(Q))
> 
> 
> 
> cleanEx(); ..nameEx <- "diagnose.ppm"
> 
> ### * diagnose.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: diagnose.ppm
> ### Title: Diagnostic Plots for Fitted Point Process Model
> ### Aliases: diagnose.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     data(cells)
>     fit <- ppm(cells, ~x, Strauss(r=0.15), rbord=0.15)
>     diagnose.ppm(fit, rbord=0.15)
Model diagnostics (raw residuals)
Diagnostics available:
	four-panel plot
	mark plot 
	smoothed residual field
	x cumulative residuals
	y cumulative residuals
	sum of all residuals
sum of raw residuals in clipped window = -9.558e-09 
area of clipped window = 0.49 
range of smoothed field = [ -51.05,37.61 ]
>     diagnose.ppm(fit, type="pearson", rbord=0.15)
Model diagnostics (Pearson residuals)
Diagnostics available:
	four-panel plot
	mark plot 
	smoothed residual field
	x cumulative residuals
	y cumulative residuals
	sum of all residuals
sum of Pearson residuals in clipped window = 0.1981 
area of clipped window = 0.49 
range of smoothed field = [ -5.18,16.05 ]
>     diagnose.ppm(fit, rbord=0.15, which="marks")
Model diagnostics (raw residuals)
Diagnostics available:
	mark plot 
>     diagnose.ppm(fit, rbord=0.15, type="raw", plot.neg="discrete")
Model diagnostics (raw residuals)
Diagnostics available:
	four-panel plot
	mark plot (discrete representation only)
	smoothed residual field
	x cumulative residuals
	y cumulative residuals
	sum of all residuals
sum of raw residuals in clipped window = -9.558e-09 
area of clipped window = 0.49 
range of smoothed field = [ -51.05,37.61 ]
> 
>     # save the diagnostics and plot them later
>     u <- diagnose.ppm(fit, rbord=0.15, plot.it=FALSE)
>     plot(u)
>     plot(u, which="marks") 
> 
> 
> 
> cleanEx(); ..nameEx <- "diameter"
> 
> ### * diameter
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: diameter
> ### Title: Diameter of a Window Frame
> ### Aliases: diameter
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- owin(c(0,1),c(0,1))
>   diameter(w) 
[1] 1.414214
>   # returns sqrt(2)
> 
> 
> 
> cleanEx(); ..nameEx <- "dirichlet.weights"
> 
> ### * dirichlet.weights
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dirichlet.weights
> ### Title: Compute Quadrature Weights Based on Dirichlet Tessellation
> ### Aliases: dirichlet.weights
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   Q <- quadscheme(runifpoispp(10))
>   X <- as.ppp(Q) # data and dummy points together
>   w <- dirichlet.weights(X, exact=FALSE)
> 
> 
> 
> cleanEx(); ..nameEx <- "distmap"
> 
> ### * distmap
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: distmap
> ### Title: Distance Map
> ### Aliases: distmap
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)
>   U <- distmap(cells)
>   data(letterR)
>   V <- distmap(letterR)
>   ## Not run: 
> ##D   plot(U)
> ##D   plot(V)
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "distmap.owin"
> 
> ### * distmap.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: distmap.owin
> ### Title: Distance Map of Window
> ### Aliases: distmap.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(letterR)
>   U <- distmap(letterR)
>   ## Not run: 
> ##D   plot(U)
> ##D   plot(attr(U, "bdry"))
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "distmap.ppp"
> 
> ### * distmap.ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: distmap.ppp
> ### Title: Distance Map of Point Pattern
> ### Aliases: distmap.ppp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)
>   U <- distmap(cells)
>   ## Not run: 
> ##D   plot(U)
> ##D   plot(attr(U, "bdry"))
> ##D   plot(attr(U, "index"))
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "dummy.ppm"
> 
> ### * dummy.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dummy.ppm
> ### Title: Extract Dummy Points Used to Fit a Point Process Model
> ### Aliases: dummy.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  data(cells)
>  fit <- ppm(cells, ~1, Strauss(r=0.1), rbord=0.1)
>  X <- dummy.ppm(fit)
>  X$n
[1] 629
>  # this is the number of dummy points in the quadrature scheme
> 
> 
> 
> cleanEx(); ..nameEx <- "eem"
> 
> ### * eem
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: eem
> ### Title: Exponential Energy Marks
> ### Aliases: eem
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     data(cells)
>     fit <- ppm(cells, ~x, Strauss(r=0.15), rbord=0.15)
>     ee <- eem(fit)
>     sum(ee)/area.owin(cells$window) # should be about 1 if model is correct
[1] 0.8578947
>     Y <- setmarks(cells, ee)
>     plot(Y, main="Cells data\n Exponential energy marks")
         0       0.05        0.1       0.15        0.2 
0.00000000 0.02999414 0.05998828 0.08998241 0.11997655 
> 
> 
> 
> cleanEx(); ..nameEx <- "envelope"
> 
> ### * envelope
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: envelope
> ### Title: Simulation envelopes of summary function
> ### Aliases: envelope
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  X <- rpoispp(42)
> 
>  # Envelope of K function under CSR
>  ## Not run: 
> ##D  plot(envelope(X))
> ##D  
> ## End(Not run)
>  ## Don't show:
>   plot(envelope(X, nsim=5))
Generating 5 simulations of CSR ...
1, 2, 3, 4, 5.
Done.
     lty col
obs    1   1
theo   2   2
lo     3   3
hi     4   4
>  
> ## End Don't show
> 
>  # Translation edge correction (this is also FASTER):
>  ## Not run: 
> ##D  plot(envelope(X, correction="translate"))
> ##D  
> ## End(Not run)
>  ## Don't show:
>   plot(envelope(X, nsim=5, correction="translate"))
Generating 5 simulations of CSR ...
1, 2, 3, 4, 5.
Done.
     lty col
obs    1   1
theo   2   2
lo     3   3
hi     4   4
>  
> ## End Don't show
> 
>  # Envelope of K function for simulations from model 
>  data(cells)
>  fit <- ppm(cells, ~1, Strauss(0.05))
>  ## Not run: 
> ##D  plot(envelope(fit))
> ##D  
> ## End(Not run)
>  ## Don't show:
>   plot(envelope(fit, nsim=4))
Generating 4 simulations of model ...
1, 2, 3, 4.
Done.
      lty col
obs     1   1
mmean   2   2
lo      3   3
hi      4   4
>  
> ## End Don't show
> 
>  # Envelope of G function under CSR
>  ## Not run: 
> ##D  plot(envelope(X, Gest))
> ##D  
> ## End(Not run)
>  ## Don't show:
>   plot(envelope(X, Gest, nsim=5))
Generating 5 simulations of CSR ...
1, 2, 3, 4, 5.
Done.
     lty col
obs    1   1
theo   2   2
lo     3   3
hi     4   4
>  
> ## End Don't show
> 
>  # Use of `simulate'
>  ## Not run: 
> ##D  plot(envelope(X, Gest, simulate=expression(runifpoint(42))))
> ##D  plot(envelope(X, Gest, simulate=expression(rMaternI(100,0.02))))
> ##D  
> ## End(Not run)
>  ## Don't show:
>   plot(envelope(X, Gest, simulate=expression(runifpoint(42)), nsim=5))
Generating 5 simulations  ...
1, 2, 3, 4, 5.
Done.
      lty col
obs     1   1
mmean   2   2
lo      3   3
hi      4   4
>   plot(envelope(X, Gest, simulate=expression(rMaternI(100, 0.02)), nsim=5))
Generating 5 simulations  ...
1, 2, 3, 4, 5.
Done.
      lty col
obs     1   1
mmean   2   2
lo      3   3
hi      4   4
>  
> ## End Don't show
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "erode.owin"
> 
> ### * erode.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: erode.owin
> ### Title: Erode a Window
> ### Aliases: erode.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- owin(c(0,1),c(0,1))
>   v <- erode.owin(w, 0.1) 
>   # returns rectangle [0.1, 0.9] x [0.1,0.9]
>   ## Not run: 
> ##D   v <- erode.owin(w, 0.6)
> ##D   #fails - erosion is empty
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "eroded.areas"
> 
> ### * eroded.areas
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: eroded.areas
> ### Title: Areas of Morphological Erosions
> ### Aliases: eroded.areas
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- owin(c(0,1),c(0,1))
>   a <- eroded.areas(w, seq(0.01,0.49,by=0.01))
> 
> 
> 
> cleanEx(); ..nameEx <- "expand.owin"
> 
> ### * expand.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: expand.owin
> ### Title: Expand Window By Factor
> ### Aliases: expand.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- square(1)
>   expand.owin(w, 9)
window: rectangle = [ -1 , 2 ] x [ -1 , 2 ]
>   # returns the square [-1,2] x [-1,2]
> 
> 
> 
> cleanEx(); ..nameEx <- "fasp.object"
> 
> ### * fasp.object
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: fasp.object
> ### Title: Function Arrays for Spatial Patterns
> ### Aliases: fasp.object
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   # unmarked point pattern
>   data(swedishpines)
>   ## Don't show:
>         # smaller dataset
>         swedishpines <- swedishpines[1:30]
>   
> ## End Don't show
>   a <- allstats(swedishpines,dataname="Swedish Pines")
>   a
Function array (class "fasp")
Dimensions:  2 x 2 
Title: Four summary functions for Swedish Pines. 
>   plot(a)
>   plot(a[1,])
> 
>   # multitype point pattern
>   data(amacrine)
>   a <- alltypes(amacrine, "G")
>   plot(a)
> 
>   # select the row corresponding to cells of type "on"
>   b <- a["on", ]
>   plot(b)
> 
> 
> 
> cleanEx(); ..nameEx <- "finpines"
> 
> ### * finpines
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: finpines
> ### Title: Pine saplings in Finland.
> ### Aliases: finpines finpines.extra
> ### Keywords: datasets
> 
> ### ** Examples
> 
>     data(finpines)
>     plot(unmark(finpines), main="Finnish pines: locations")
>     plot(finpines, main="locations and heights")
        0         1         2         3         4         5         6 
0.0000000 0.1303089 0.2606178 0.3909267 0.5212356 0.6515445 0.7818534 
>     plot(finpines %mark% finpines.extra$diameter, main="diameters")
       0        1        2        3        4        5        6        7 
0.000000 0.100524 0.201048 0.301572 0.402096 0.502620 0.603144 0.703668 
> 
> 
> 
> cleanEx(); ..nameEx <- "fitted.ppm"
> 
> ### * fitted.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: fitted.ppm
> ### Title: Fitted Conditional Intensity for Point Process Model
> ### Aliases: fitted.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     data(cells)
>     str <- ppm(cells, ~x, Strauss(r=0.15), rbord=0.15)
>     lambda <- fitted(str)
> 
>     # extract quadrature points in corresponding order
>     quadpoints <- union.quad(quad.ppm(str))
> 
>     # plot conditional intensity values
>     # as circles centred on the quadrature points 
>     quadmarked <- setmarks(quadpoints, lambda)
>     plot(quadmarked)
          0        1000        2000        3000        4000        5000 
0.000000000 0.006575748 0.013151497 0.019727245 0.026302994 0.032878742 
> 
> 
> 
> cleanEx(); ..nameEx <- "fv.object"
> 
> ### * fv.object
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: fv.object
> ### Title: Data Frames of Function Values
> ### Aliases: fv.object
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     data(cells)
>     K <- Kest(cells)
> 
>     class(K)
[1] "fv"         "data.frame"
> 
>     K  # prints a sensible summary
Function value object (class "fv")
for the function r -> K(r) 
Entries:
id	label      description
--	-----      -----------
r	r          distance argument r
theo	Kpois(r)   theoretical Poisson K(r)
border	Kbord(r)   border-corrected estimate of K(r)
trans	Ktrans(r)  translation-corrected estimate of K(r)
iso	Kiso(r)    Ripley isotropic correction estimate of K(r)
--------------------------------------

Default plot formula:
	. ~ r

Recommended range of argument r: [0, 0.25]
> 
>     plot(K)
       lty col
iso      1   1
trans    2   2
border   3   3
theo     4   4
> 
> 
> 
> cleanEx(); ..nameEx <- "gridcentres"
> 
> ### * gridcentres
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: gridcentres
> ### Title: Rectangular grid of points
> ### Aliases: gridcentres gridcenters
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- unit.square()
>   xy <- gridcentres(w, 10,15)
>   ## Not run: 
> ##D   plot(w)
> ##D   points(xy)
> ##D   
> ## End(Not run)
> 
>   bdry <- list(x=c(0.1,0.3,0.7,0.4,0.2),
+                y=c(0.1,0.1,0.5,0.7,0.3))
>   w <- owin(c(0,1), c(0,1), poly=bdry)
>   xy <- gridcentres(w, 30, 30)
>   ok <- inside.owin(xy$x, xy$y, w)
>   ## Not run: 
> ##D   plot(w)
> ##D   points(xy$x[ok], xy$y[ok])
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "gridweights"
> 
> ### * gridweights
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: gridweights
> ### Title: Compute Quadrature Weights Based on Grid Counts
> ### Aliases: gridweights
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   Q <- quadscheme(runifpoispp(10))
>   X <- as.ppp(Q) # data and dummy points together
>   w <- gridweights(X, 10)
>   w <- gridweights(X, c(10, 10))
> 
> 
> 
> cleanEx(); ..nameEx <- "harmonic"
> 
> ### * harmonic
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: harmonic
> ### Title: Basis for Harmonic Functions
> ### Aliases: harmonic
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(longleaf)
>    X <- unmark(longleaf)
>    # inhomogeneous point pattern
>    ## Don't show:
>         # smaller dataset
>         longleaf <- longleaf[seq(1,longleaf$n, by=50)]
>    
> ## End Don't show
> 
>    # fit Poisson point process with log-cubic intensity
>    fit.3 <- ppm(X, ~ polynom(x,y,3), Poisson())
> 
>    # fit Poisson process with log-cubic-harmonic intensity
>    fit.h <- ppm(X, ~ harmonic(x,y,3), Poisson())
> 
>    # Likelihood ratio test
>    lrts <- 2 * (fit.3$maxlogpl - fit.h$maxlogpl)
>    x <- X$x
>    y <- X$y
>    df <- ncol(polynom(x,y,3)) - ncol(harmonic(x,y,3))
>    pval <- 1 - pchisq(lrts, df=df)
> 
> 
> 
> cleanEx(); ..nameEx <- "im"
> 
> ### * im
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: im
> ### Title: Create a Pixel Image Object
> ### Aliases: im
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    whitenoise <- im(matrix(rnorm(10000), 100, 100))
>    image(whitenoise)
> 
> 
> 
> cleanEx(); ..nameEx <- "inside.owin"
> 
> ### * inside.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: inside.owin
> ### Title: Test Whether Points Are Inside A Window
> ### Aliases: inside.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   # hexagonal window
>   k <- 6
>   theta <- 2 * pi * (0:(k-1))/k
>   co <- cos(theta)
>   si <- sin(theta)
>   mas <- owin(c(-1,1), c(-1,1), poly=list(x=co, y=si))
>   ## Not run: 
> ##D   plot(mas)
> ##D   
> ## End(Not run)
> 
>   # random points in rectangle
>   x <- runif(30,min=-1, max=1)
>   y <- runif(30,min=-1, max=1)
> 
>   ok <- inside.owin(x, y, mas)
> 
>   ## Not run: 
> ##D   points(x[ok], y[ok])
> ##D   points(x[!ok], y[!ok], pch="x")
> ##D   
> ## End(Not run)  
> 
> 
> 
> cleanEx(); ..nameEx <- "intersect.owin"
> 
> ### * intersect.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: intersect.owin
> ### Title: Intersection or Union of Two Windows
> ### Aliases: intersect.owin union.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
> # rectangles
>    u <- unit.square()
>    v <- owin(c(0.5,3.5), c(0.4,2.5))
> # polygon
>    data(letterR)
> # mask
>    m <- as.mask(letterR)
> 
> # two rectangles
>    intersect.owin(u, v) 
window: rectangle = [ 0.5 , 1 ] x [ 0.4 , 1 ]
>    union.owin(u,v)
window: binary image mask
enclosing rectangle: [ 0 , 3.5 ] x [ 0 , 2.5 ]
> 
> # polygon and rectangle
>    intersect.owin(letterR, v)
window: binary image mask
enclosing rectangle: [ 2.017 , 3.5 ] x [ 0.645 , 2.5 ]
>    union.owin(letterR,v)
window: binary image mask
enclosing rectangle: [ 0.5 , 3.93 ] x [ 0.4 , 3.278 ]
> 
> # mask and rectangle
>    intersect.owin(m, v)
window: binary image mask
enclosing rectangle: [ 2.017 , 3.5 ] x [ 0.645 , 2.5 ]
>    union.owin(m,v)
window: binary image mask
enclosing rectangle: [ 0.5 , 3.93 ] x [ 0.4 , 3.278 ]
> #
>    A <- letterR
>    B <- rotate(letterR, 0.2)
>    plot(bounding.box(A,B), main="intersection")
>    w <- intersect.owin(A, B)
>    plot(w, add=TRUE)
>    plot(A, add=TRUE)
>    plot(B, add=TRUE)
> 
>    plot(bounding.box(A,B), main="union")
>    w <- union.owin(A,B)
>    plot(w, add=TRUE)   
>    plot(A, add=TRUE)
>    plot(B, add=TRUE)
> 
> 
> 
> cleanEx(); ..nameEx <- "is.marked.ppm"
> 
> ### * is.marked.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: is.marked.ppm
> ### Title: Test Whether A Point Process Model is Marked
> ### Aliases: is.marked.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(lansing)
>    # Multitype point pattern --- trees marked by species
> 
>    ## Don't show:
>       # Smaller dataset
>       data(betacells)
>       lansing <- betacells[seq(2, 135, by=3), ]
>    
> ## End Don't show
> 
>   fit1 <- ppm(lansing, ~ marks, Poisson())
>   is.marked(fit1)
[1] TRUE
>   # TRUE
> 
>   fit2 <- ppm(lansing, ~ 1, Poisson())
>   is.marked(fit2)
[1] TRUE
>   # TRUE
> 
>   data(cells)
>   # Unmarked point pattern
> 
>   fit3 <- ppm(cells, ~ 1, Poisson())
>   is.marked(fit3)
[1] FALSE
>   # FALSE
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "is.marked.ppp"
> 
> ### * is.marked.ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: is.marked.ppp
> ### Title: Test Whether A Point Pattern is Marked
> ### Aliases: is.marked.ppp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(cells)
>    is.marked(cells)  #FALSE
[1] FALSE
>    data(longleaf)
>    is.marked(longleaf) #TRUE
[1] TRUE
> 
> 
> 
> cleanEx(); ..nameEx <- "is.subset.owin"
> 
> ### * is.subset.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: is.subset.owin
> ### Title: Determine Whether One Window is Contained In Another
> ### Aliases: is.subset.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    w1 <- as.owin(c(0,1,0,1))
>    w2 <- as.owin(c(-1,2,-1,2))
>    is.subset.owin(w1,w2)  # Returns TRUE.
[1] TRUE
>    is.subset.owin(w2,w1)  # Returns FALSE.
[1] FALSE
> 
> 
> 
> cleanEx(); ..nameEx <- "ksmooth.ppp"
> 
> ### * ksmooth.ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ksmooth.ppp
> ### Title: Kernel Smoothed Intensity of Point Pattern
> ### Aliases: ksmooth.ppp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)
>   Z <- ksmooth.ppp(cells, 0.05)
>   plot(Z)
> 
> 
> 
> cleanEx(); ..nameEx <- "lurking"
> 
> ### * lurking
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: lurking
> ### Title: Lurking variable plot
> ### Aliases: lurking
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(nztrees)
>   fit <- ppm(nztrees, ~x, Poisson())
>   lurking(fit, expression(x))
>   lurking(fit, expression(x), cumulative=FALSE)
> 
> 
> 
> cleanEx(); ..nameEx <- "markcorr"
> 
> ### * markcorr
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: markcorr
> ### Title: Mark Correlation Function
> ### Aliases: markcorr
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     # CONTINUOUS-VALUED MARKS:
>     # (1) Longleaf Pine data
>     # marks represent tree diameter
>     data(longleaf)
>     # Subset of this large pattern
>     swcorner <- owin(c(0,100),c(0,100))
>     sub <- longleaf[ , swcorner]
>     # mark correlation function
>     mc <- markcorr(sub)
>     plot(mc)
       lty col
iso      1   1
trans    2   2
border   3   3
theo     4   4
> 
>     # (2) simulated data with independent marks
>     X <- rpoispp(100)
>     X <- X %mark% runif(X$n)
>     Xc <- markcorr(X)
>     plot(Xc)
       lty col
iso      1   1
trans    2   2
border   3   3
theo     4   4
>     
>     # MULTITYPE DATA:
>     # Hughes' amacrine data
>     # Cells marked as 'on'/'off'
>     data(amacrine)
>     # (3) Kernel density estimate with Epanecnikov kernel
>     # (as proposed by Stoyan & Stoyan)
>     M <- markcorr(amacrine, function(m1,m2) {m1==m2},
+                   correction="translate", method="density",
+                   kernel="epanechnikov")
>     plot(M)
      lty col
trans   1   1
theo    2   2
>     # Note: kernel="epanechnikov" comes from help(density)
> 
>     # (4) Same again with explicit control over bandwidth
>     M <- markcorr(amacrine, function(m1,m2) {m1==m2},
+                   correction="translate", method="density",
+                   kernel="epanechnikov", bw=0.02)
>     # see help(density) for correct interpretation of 'bw'
> 
>    ## Don't show:
>     data(betacells)
>     betacells <- betacells[seq(1,betacells$n,by=3)]
>     niets <- markcorr(betacells, function(m1,m2){m1 == m2}, method="loess")
>     niets <- markcorr(X, correction="isotropic", method="smrep")
>     
> ## End Don't show
> 
> 
> 
> cleanEx(); ..nameEx <- "nearest.raster.point"
> 
> ### * nearest.raster.point
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: nearest.raster.point
> ### Title: Find Pixel Nearest to a Given Point
> ### Aliases: nearest.raster.point
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- owin(c(0,1), c(0,1), mask=matrix(TRUE, 100,100))  # 100 x 100 grid
>   nearest.raster.point(0.5, 0.3, w)
$row
[1] 30

$col
[1] 51

>   nearest.raster.point(0.5, 0.3, w, indices=FALSE)
$x
[1] 0.505

$y
[1] 0.295

> 
> 
> 
> cleanEx(); ..nameEx <- "nndist"
> 
> ### * nndist
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: nndist
> ### Title: Nearest neighbour distances
> ### Aliases: nndist nndist.ppp nndist.default
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(cells)
>    d <- nndist(cells)
> 
>    x <- runif(100)
>    y <- runif(100)
>    d <- nndist(x, y)
> 
>    # Stienen diagram
>    plot(cells %mark% (nndist(cells)/2), markscale=1)
0.04 0.05 0.06 0.07 0.08 
0.04 0.05 0.06 0.07 0.08 
> 
> 
> 
> cleanEx(); ..nameEx <- "owin"
> 
> ### * owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: owin
> ### Title: Create a Window
> ### Aliases: owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- owin()
>   w <- owin(c(0,1), c(0,1))
>   # the unit square
> 
>   w <- owin(c(10,20), c(10,30))
>   # a rectangle of dimensions 10 x 20 units
>   # with lower left corner at (10,10)
> 
>   # polygon (diamond shape)
>   w <- owin(poly=list(x=c(0.5,1,0.5,0),y=c(0,1,2,1)))
>   w <- owin(c(0,1), c(0,2), poly=list(x=c(0.5,1,0.5,0),y=c(0,1,2,1)))
> 
>   # polygon with hole
>   ho <- owin(poly=list(list(x=c(0,1,1,0), y=c(0,0,1,1)),
+                        list(x=c(0.6,0.4,0.4,0.6), y=c(0.2,0.2,0.4,0.4))))
>   
>   w <- owin(c(-1,1), c(-1,1), mask=matrix(TRUE, 100,100))
>           # 100 x 100 image, all TRUE
>   X <- raster.x(w)
>   Y <- raster.y(w)
>   wm <- owin(w$xrange, w$yrange, mask=(X^2 + Y^2 <= 1))
>           # discrete approximation to the unit disc
> 
>   ## Not run: 
> ##D   plot(c(0,1),c(0,1),type="n")
> ##D   bdry <- locator()
> ##D   # click the vertices of a polygon (anticlockwise)
> ##D   
> ## End(Not run)
>   ## Don't show:
>   bdry <- list(x=c(0.1,0.3,0.7,0.4,0.2),
+                y=c(0.1,0.1,0.5,0.7,0.3))
>   
> ## End Don't show
>   w <- owin(poly=bdry)
>   ## Not run: plot(w)
>  
>  ## Not run: 
> ##D  im <- as.logical(matrix(scan("myfile"), nrow=128, ncol=128))
> ##D  # read in an arbitrary 128 x 128 digital image from text file
> ##D  rim <- im[, 128:1]
> ##D  # Assuming it was given in row-major order in the file
> ##D  # i.e. scanning left-to-right in rows from top-to-bottom,
> ##D  # the use of matrix() has effectively transposed rows & columns,
> ##D  # so to convert it to our format just reverse the column order.
> ##D  w <- owin(mask=rim)
> ##D  plot(w)
> ##D  # display it to check!
> ##D  
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "owin.object"
> 
> ### * owin.object
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: owin.object
> ### Title: Class owin
> ### Aliases: owin.object
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  w <- owin()
>  w <- owin(c(0,1), c(0,1))
>  # the unit square
>   
>  w <- owin(c(0,1), c(0,2))
>  ## Not run: 
> ##D  plot(w)
> ##D  # plots edges of a box 1 unit x 2 units
> ##D  v <- locator() 
> ##D  # click on points in the plot window
> ##D  # to be the vertices of a polygon 
> ##D  # traversed in anticlockwise order 
> ##D  u <- owin(c(0,1), c(0,2), poly=v)
> ##D  plot(u)
> ##D  # plots polygonal boundary using polygon()
> ##D  plot(as.mask(u, eps=0.02))
> ##D  # plots discrete pixel approximation to polygon
> ##D  
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "pairdist"
> 
> ### * pairdist
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: pairdist
> ### Title: Pairwise distances
> ### Aliases: pairdist pairdist.ppp pairdist.default
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(cells)
>    d <- pairdist(cells)
> 
>    x <- runif(100)
>    y <- runif(100)
>    d <- pairdist(x, y)
> 
> 
> 
> cleanEx(); ..nameEx <- "pcf"
> 
> ### * pcf
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: pcf
> ### Title: Pair Correlation Function
> ### Aliases: pcf
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   # ppp object
>   data(simdat)
>   ## Don't show:
>     simdat <- simdat[seq(1,simdat$n, by=4)]
>   
> ## End Don't show
>   p <- pcf(simdat)
>   plot(p)
      lty col
ripl    1   1
trans   2   2
theo    3   3
> 
>   # fv object
>   K <- Kest(simdat)
>   p2 <- pcf(K)
>   plot(p2)
     lty col
pcf    1   1
theo   2   2
> 
>   # multitype pattern; fasp object
>   data(betacells)
>   ## Don't show:
>      betacells <- betacells[seq(1,betacells$n, by=10)]
>   
> ## End Don't show
>   p <- pcf(alltypes(betacells, "K"))
>   plot(p)
> 
> 
> 
> cleanEx(); ..nameEx <- "pcf.fasp"
> 
> ### * pcf.fasp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: pcf.fasp
> ### Title: Pair Correlation Function obtained from array of K functions
> ### Aliases: pcf.fasp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   # multitype point pattern
>   data(betacells)
>   ## Don't show:
>      betacells <- betacells[seq(1,betacells$n, by=10)]
>   
> ## End Don't show
>   KK <- alltypes(betacells, "K")
>   p <- pcf.fasp(KK, spar=0.5, method="b")
>   plot(p)
>   # short range inhibition between all types
>   # strong inhibition between "on" and "off"
> 
> 
> 
> cleanEx(); ..nameEx <- "pcf.fv"
> 
> ### * pcf.fv
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: pcf.fv
> ### Title: Pair Correlation Function obtained from K Function
> ### Aliases: pcf.fv
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   # univariate point pattern
>   data(simdat)
>   ## Don't show:
>     simdat <- simdat[seq(1,simdat$n, by=4)]
>   
> ## End Don't show
>   K <- Kest(simdat)
>   p <- pcf.fv(K, spar=0.5, method="b")
>   plot(p, main="pair correlation function for simdat")
     lty col
pcf    1   1
theo   2   2
>   # indicates inhibition at distances r < 0.3
> 
> 
> 
> cleanEx(); ..nameEx <- "pcf.ppp"
> 
> ### * pcf.ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: pcf.ppp
> ### Title: Pair Correlation Function of Point Pattern
> ### Aliases: pcf.ppp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(simdat)
>   p <- pcf(simdat)
>   ## Don't show:
>     simdat <- simdat[seq(1,simdat$n, by=4)]
>   
> ## End Don't show
>   plot(p, main="pair correlation function for simdat")
      lty col
ripl    1   1
trans   2   2
theo    3   3
>   # indicates inhibition at distances r < 0.3
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.fasp"
> 
> ### * plot.fasp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.fasp
> ### Title: Plot a Function Array
> ### Aliases: plot.fasp plot
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    ## Not run: 
> ##D    # Bramble Canes data.
> ##D    data(bramblecanes)
> ##D 
> ##D    X.G <- alltypes(bramblecanes,type="G",dataname="Bramblecanes",verb=TRUE)
> ##D    plot(X.G)
> ##D    plot(X.G,subset="r<=0.2")
> ##D    plot(X.G,formule=cbind(asin(sqrt(km)),
> ##D                     asin(sqrt(theo))) ~ asin(sqrt(theo)))
> ##D        plot(X.G,fo=cbind(km-theo,0)~r,"r<=0.2")
> ##D 
> ##D    # Swedish pines.
> ##D    data(swedishpines)
> ##D    X <- allstats(swedishpines,dataname="Swedish Pines")
> ##D    plot(X,subset=list("r<=20","r<=20","r<=20","r<=50"))
> ##D 
> ##D    # Simulated data.
> ##D    pp <- runifpoint(350, owin(c(0,1),c(0,1)))
> ##D    pp$marks <- factor(c(rep(1,50),rep(2,100),rep(3,200)))
> ##D    X.K <- alltypes(pp,type="K",verb=TRUE,dataname="Fake Data")
> ##D    plot(X.K,fo=cbind(border,theo)~theo,"theo<=0.75")
> ##D    
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.fv"
> 
> ### * plot.fv
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.fv
> ### Title: Plot Function Valuesn
> ### Aliases: plot.fv
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(cells)
>    K <- Kest(cells)
>    # K is an object of class "fv"
> 
>    plot(K, iso ~ r)                # plots iso against r
> 
>    plot(K, sqrt(iso/pi) ~ r)   # plots sqrt(iso/r)  against r
> 
>    plot(K, cbind(iso,theo) ~ r)   # plots iso against r  AND theo against r
     lty col
iso    1   1
theo   2   2
> 
>    plot(K, .  ~ r)            # plots all available estimates of K against r
       lty col
iso      1   1
trans    2   2
border   3   3
theo     4   4
> 
>    plot(K, sqrt(./pi) ~ r)   # plots all estimates of L-function
       lty col
iso      1   1
trans    2   2
border   3   3
theo     4   4
>                              # L(r) = sqrt(K(r)/pi)
> 
>    plot(K, cbind(iso,theo) ~ r, col=c(2,3))
     lty col
iso    1   2
theo   2   3
>                                    # plots iso against r  in colour 2
>                                    # and theo against r in colour 3
> 
>    plot(K, iso ~ r, subset=quote(r < 0.2))
>                                    # plots iso against r for r < 10
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.im"
> 
> ### * plot.im
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.im
> ### Title: Plot a Pixel Image
> ### Aliases: plot.im image.im
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    # an image
>    Z <- setcov(owin())
>    plot(Z)
>    plot(Z, col=terrain.colors(128), axes=FALSE)
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.owin"
> 
> ### * plot.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.owin
> ### Title: Plot a Spatial Window
> ### Aliases: plot.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
> ## Not run: 
> ##D   # rectangular window
> ##D    data(nztrees)
> ##D    plot(nztrees$window)
> ##D    abline(v=148, lty=2)
> ##D 
> ##D   # polygonal window
> ##D   plot(c(0,1),c(0,1),type="n")
> ##D   bdry <- locator()
> ##D   # click the vertices of a polygon (anticlockwise)
> ##D   w <- owin(c(0,1), c(0,1), poly=bdry)
> ##D   plot(w)
> ##D 
> ##D   # binary mask
> ##D   we <- erode.owin(w, 0.05, FALSE)
> ##D   plot(we)
> ##D   spatstat.options(par.binary=list(col=grey(c(0.5,1))))
> ##D   plot(we)
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.plotppm"
> 
> ### * plot.plotppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.plotppm
> ### Title: Plot a plotppm Object Created by plot.ppm
> ### Aliases: plot.plotppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  ## Not run: 
> ##D  data(cells)
> ##D  Q <- quadscheme(cells)
> ##D  m <- ppm(Q, ~1, Strauss(0.05))
> ##D  mpic <- plot(m)
> ##D  # Perspective plot only, with altered parameters:
> ##D   plot(mpic,how="persp", theta=-30,phi=40,d=4)
> ##D  # All plots, with altered parameters for perspective plot:
> ##D  spatstat.options(par.persp=list(theta=-30,phi=40,d=4))
> ##D  plot(mpic)
> ##D  
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.ppm"
> 
> ### * plot.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.ppm
> ### Title: plot a Fitted Point Process Model
> ### Aliases: plot.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  ## Not run: 
> ##D  data(cells)
> ##D  m <- ppm(cells, ~1, Strauss(0.05))
> ##D  pm <- plot(m) # The object ``pm'' will be plotted as well as saved
> ##D                # for future plotting.
> ##D  
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.ppp"
> 
> ### * plot.ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.ppp
> ### Title: plot a Spatial Point Pattern
> ### Aliases: plot.ppp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(cells)
>    plot(cells)
> 
>    # make the plotting symbols larger (for publication at reduced scale)
>    plot(cells, cex=2)
> 
>    # multitype 
>    data(lansing)
>    plot(lansing)
blackoak  hickory    maple     misc   redoak whiteoak 
       1        2        3        4        5        6 
> 
>    # marked by a real number
>    data(longleaf)
>    plot(longleaf)
       0       20       40       60       80 
0.000000 1.722522 3.445045 5.167567 6.890090 
> 
>    # just plot the points
>    plot(longleaf, use.marks=FALSE)
>    plot(unmark(longleaf)) # equivalent
> 
>    # controlling COLOURS of points
>    plot(cells, cols="blue")
>    plot(lansing, cols=c("black", "yellow", "green", 
+                         "blue","red","pink"))
blackoak  hickory    maple     misc   redoak whiteoak 
       1        2        3        4        5        6 
>    plot(longleaf, fg="blue")
       0       20       40       60       80 
0.000000 1.722522 3.445045 5.167567 6.890090 
> 
>    # make points and window purple
>    plot(lansing, col="purple")
blackoak  hickory    maple     misc   redoak whiteoak 
       1        2        3        4        5        6 
>    # make everything purple
>    plot(lansing, col="purple", col.main="purple")
blackoak  hickory    maple     misc   redoak whiteoak 
       1        2        3        4        5        6 
>  
>    # controlling PLOT CHARACTERS
>    plot(lansing, chars = 11:16)
blackoak  hickory    maple     misc   redoak whiteoak 
      11       12       13       14       15       16 
>    plot(lansing, chars = c("o","h","m",".","o","o"))
blackoak  hickory    maple     misc   redoak whiteoak 
     "o"      "h"      "m"      "."      "o"      "o" 
> 
>    # controlling MARK SCALE
>    plot(longleaf, markscale=0.1)
 0 20 40 60 80 
 0  2  4  6  8 
> 
>    # draw circles of diameter equal to nearest neighbour distance
>    plot(cells %mark% (nndist(cells)/2), markscale=1)
0.04 0.05 0.06 0.07 0.08 
0.04 0.05 0.06 0.07 0.08 
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.quad"
> 
> ### * plot.quad
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.quad
> ### Title: plot a Spatial Quadrature Scheme
> ### Aliases: plot.quad
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(nztrees)
>    Q <- quadscheme(nztrees)
> 
>    plot(Q, main="NZ trees: quadrature scheme")
> 
>    par(mfrow=c(2,1))
>    plot(Q, main="NZ trees", dum=list(add=FALSE))
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "plot.splitppp"
> 
> ### * plot.splitppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.splitppp
> ### Title: Plot a List of Point Patterns
> ### Aliases: plot.splitppp
> ### Keywords: spatial
> 
> ### ** Examples
> 
> # Multitype point pattern
>  data(amacrine)
>  plot(split(amacrine))
> 
> 
> 
> cleanEx(); ..nameEx <- "ppm"
> 
> ### * ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ppm
> ### Title: Fit Point Process Model to Data
> ### Aliases: ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  data(nztrees)
>  ppm(nztrees)
Stationary Poisson process

Intensity:

Uniform intensity:
[1] 0.005916753
>  # fit the stationary Poisson process
>  # to point pattern 'nztrees'
> 
>  Q <- quadscheme(nztrees) 
>  ppm(Q) 
Stationary Poisson process

Intensity:

Uniform intensity:
[1] 0.005916753
>  # equivalent.
> 
>  ppm(nztrees, ~ x)
Nonstationary Poisson process

Intensity:
Trend formula: ~x

Fitted coefficients for trend formula:
 (Intercept)            x 
-5.335350623  0.002598965 
>  # fit the nonstationary Poisson process 
>  # with intensity function lambda(x,y) = exp(a + bx)
>  # where x,y are the Cartesian coordinates
>  # and a,b are parameters to be estimated
> 
>  ppm(nztrees, ~ polynom(x,2))
Nonstationary Poisson process

Intensity:
Trend formula: ~polynom(x, 2)

Fitted coefficients for trend formula:
       (Intercept)   polynom(x, 2)[x] polynom(x, 2)[x^2] 
     -4.8734315562      -0.0154824569       0.0001155524 
>  # fit the nonstationary Poisson process 
>  # with intensity function lambda(x,y) = exp(a + bx + cx^2)
> 
>  library(splines)
>  ppm(nztrees, ~ bs(x,df=3))
Nonstationary Poisson process

Intensity:
Trend formula: ~bs(x, df = 3)

Fitted coefficients for trend formula:
   (Intercept) bs(x, df = 3)1 bs(x, df = 3)2 bs(x, df = 3)3 
    -4.9411986     -0.5037808     -0.8175941      0.4621456 
>  #       WARNING: do not use predict.ppm() on this result
>  # Fits the nonstationary Poisson process 
>  # with intensity function lambda(x,y) = exp(B(x))
>  # where B is a B-spline with df = 3
>  
>  ppm(nztrees, ~1, Strauss(r=10), rbord=10)
Stationary Strauss process

Trend:

First order term:
       beta 
0.005770516 

Interaction:
Pairwise interaction family
Interaction: Strauss process 
interaction distance:	10
Fitted interaction parameter gamma:
[1] 0.999
>  # Fit the stationary Strauss process with interaction range r=10
>  # using the border method with margin rbord=10
>   
>  ppm(nztrees, ~ x, Strauss(13), correction="periodic")
Nonstationary Strauss process

Trend:
Trend formula: ~x

Fitted coefficients for trend formula:
 (Intercept)            x 
-5.533989737  0.002111864 

Interaction:
Pairwise interaction family
Interaction: Strauss process 
interaction distance:	13
Fitted interaction parameter gamma:
[1] 1.0768
>  # Fit the nonstationary Strauss process with interaction range r=13
>  # and exp(first order potential) =  activity = beta(x,y) = exp(a+bx)
>  # using the periodic correction.
> 
> # Huang-Ogata fit:
> ## Not run: ppm(nztrees, ~1, Strauss(r=10), rbord=10, method="mpl")
> 
>  # COVARIATES
>  #
>  X <- rpoispp(42)
>  weirdfunction <- function(x,y){ 10 * x^2 + runif(length(x))}
>  Zimage <- as.im(weirdfunction, unit.square())
>  #
>  # (a) covariate values in pixel image
>  ppm(X, ~ y + Z, covariates=list(Z=Zimage))
Nonstationary Poisson process

Intensity:
Trend formula: ~y + Z

Fitted coefficients for trend formula:
(Intercept)           y           Z 
 3.35131101  0.27434643  0.03007803 
>  #
>  # (b) covariate values in data frame
>  Q <- quadscheme(X)
>  xQ <- x.quad(Q)
>  yQ <- y.quad(Q)
>  Zvalues <- weirdfunction(xQ,yQ)
>  ppm(Q, ~ y + Z, covariates=data.frame(Z=Zvalues))
Nonstationary Poisson process

Intensity:
Trend formula: ~y + Z

Fitted coefficients for trend formula:
(Intercept)           y           Z 
 3.39489845  0.27462019  0.01932311 
>  # Note Q not X
> 
>  ## MULTITYPE POINT PROCESSES ### 
>  data(lansing)
>  # Multitype point pattern --- trees marked by species
> ## Don't show:
>  # equivalent functionality - smaller dataset
>  data(betacells)
>  
> ## End Don't show
> 
>  # fit stationary marked Poisson process
>  # with different intensity for each species
> ## Not run: ppm(lansing, ~ marks, Poisson())
> ## Don't show:
> ppm(betacells, ~ marks, Poisson())
Stationary multitype Poisson process
Possible marks: 
off on
Intensity:
Trend formula: ~marks

Fitted intensities:
    beta_off      beta_on 
9.419807e-05 8.746964e-05 
> ## End Don't show
> 
>  # fit nonstationary marked Poisson process
>  # with different log-cubic trend for each species
> ## Not run: ppm(lansing, ~ marks * polynom(x,y,3), Poisson())
> ## Don't show:
> ppm(betacells, ~ marks * polynom(x,y,2), Poisson())
Nonstationary multitype Poisson process
Possible marks: 
off on
Intensity:
Trend formula: ~marks * polynom(x, y, 2)

Fitted coefficients for trend formula:
                  (Intercept)                       markson 
                -9.414097e+00                  7.140810e-01 
          polynom(x, y, 2)[x]           polynom(x, y, 2)[y] 
                -8.360216e-04                  1.595380e-03 
        polynom(x, y, 2)[x^2]         polynom(x, y, 2)[x.y] 
                 5.373429e-07                 -7.688609e-07 
        polynom(x, y, 2)[y^2]   markson:polynom(x, y, 2)[x] 
                -9.123127e-07                 -2.244465e-03 
  markson:polynom(x, y, 2)[y] markson:polynom(x, y, 2)[x^2] 
                -1.894023e-03                  1.618490e-06 
markson:polynom(x, y, 2)[x.y] markson:polynom(x, y, 2)[y^2] 
                 1.823315e-06                  1.075783e-06 
> ## End Don't show
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "ppm.object"
> 
> ### * ppm.object
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ppm.object
> ### Title: Class of Fitted Point Process Models
> ### Aliases: ppm.object
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)
>   fit <- ppm(cells, ~ x, Strauss(0.1), correction="periodic")
>   fit
Nonstationary Strauss process

Trend:
Trend formula: ~x

Fitted coefficients for trend formula:
(Intercept)           x 
 5.74292851  0.08449064 

Interaction:
Pairwise interaction family
Interaction: Strauss process 
interaction distance:	0.1
Fitted interaction parameter gamma:
[1] 0.0237
>   coef(fit)
(Intercept)           x Interaction 
 5.74292851  0.08449064 -3.74186444 
>   ## Not run: 
> ##D   pred <- predict(fit)
> ##D   
> ## End(Not run)
>   pred <- predict(fit, ngrid=20, type="trend")
>   ## Not run: 
> ##D   plot(fit)
> ##D   
> ## End(Not run)  
> 
> 
> 
> cleanEx(); ..nameEx <- "ppp"
> 
> ### * ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ppp
> ### Title: Create a Point Pattern
> ### Aliases: ppp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   # some arbitrary coordinates in [0,1]
>   x <- runif(20)
>   y <- runif(20)
> 
>   # the following are equivalent
>   X <- ppp(x, y, c(0,1), c(0,1))
>   X <- ppp(x, y)
>   X <- ppp(x, y, window=owin(c(0,1),c(0,1)))
> 
>   ## Not run: plot(X)
> 
>   # marks
>   m <- sample(1:2, 20, replace=TRUE)
>   m <- factor(m, levels=1:2)
>   X <- ppp(x, y, c(0,1), c(0,1), marks=m)
>   ## Not run: plot(X)
> 
>   # polygonal window
>   X <- ppp(x, y, poly=list(x=c(0,10,0), y=c(0,0,10)))
>   ## Not run: plot(X)
> 
>   # copy the window from another pattern
>   data(cells)
>   X <- ppp(x, y, window=cells$window)
> 
> 
> 
> cleanEx(); ..nameEx <- "ppp.object"
> 
> ### * ppp.object
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ppp.object
> ### Title: Class of Point Patterns
> ### Aliases: ppp.object
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   x <- runif(100)
>   y <- runif(100)
>   X <- ppp(x, y, c(0,1),c(0,1))
>   X
 planar point pattern: 100 points
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
>   ## Not run: plot(X)
>   mar <- sample(1:3, 100, replace=TRUE)
>   mm <- ppp(x, y, c(0,1), c(0,1), marks=mar)
>   ## Not run: plot(mm)
>   # points with mark equal to 2
>   ss <- mm[ mm$marks == 2 , ]
>   ## Not run: plot(ss)
>   # left half of pattern 'mm'
>   lu <- owin(c(0,0.5),c(0,1))
>   mmleft <- mm[ , lu]
>   ## Not run: plot(mmleft)
>   ## Not run: 
> ##D   # input data from file
> ##D   qq <- scanpp("my.table", unit.square())
> ##D 
> ##D   # interactively build a point pattern
> ##D   plot(unit.square())
> ##D   X <- as.ppp(locator(10), unit.square())
> ##D   plot(X)
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "predict.ppm"
> 
> ### * predict.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: predict.ppm
> ### Title: Prediction from a Fitted Point Process Model
> ### Aliases: predict.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)
>   m <- ppm(cells, ~ polynom(x,y,2), Strauss(0.05), rbord=0.05)
>   trend <- predict(m, type="trend")
>   ## Not run: 
> ##D   image(trend)
> ##D   points(cells)
> ##D   
> ## End(Not run)
>   cif <- predict(m, type="cif")
>   ## Not run: 
> ##D   persp(cif)
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "print.im"
> 
> ### * print.im
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: print.im
> ### Title: Print Brief Details of an Image
> ### Aliases: print.im
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(letterR)
>   U <- as.im(letterR)
>   U
Pixel image
256 x 256 pixel array
enclosing rectangle: [ 2.017, 3.93 ] x [ 0.645, 3.278 ]
> 
> 
> 
> cleanEx(); ..nameEx <- "print.owin"
> 
> ### * print.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: print.owin
> ### Title: Print Brief Details of a Spatial Window
> ### Aliases: print.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   owin()  # the unit square
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> 
>   data(demopat)
>   W <- demopat$window  
>   W                    # just says it is polygonal
window: polygonal boundary
enclosing rectangle: [ 525 , 10575 ] x [ 450 , 7125 ]
>   as.mask(W)           # just says it is a binary image 
window: binary image mask
enclosing rectangle: [ 525 , 10575 ] x [ 450 , 7125 ]
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "print.ppm"
> 
> ### * print.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: print.ppm
> ### Title: Print a Fitted Point Process Model
> ### Aliases: print.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  ## Not run: 
> ##D  data(cells)
> ##D  Q <- quadscheme(cells)
> ##D  m <- ppm(Q, ~1, Strauss(0.05))
> ##D  m
> ##D  
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "print.ppp"
> 
> ### * print.ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: print.ppp
> ### Title: Print Brief Details of a Point Pattern Dataset
> ### Aliases: print.ppp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)      # plain vanilla point pattern
>   cells
 planar point pattern: 42 points
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> 
>   data(lansing)    # multitype point pattern
>   lansing          
marked planar point pattern: 2251 points
multitype, with levels = blackoak	hickory	maple	misc	redoak	whiteoak 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
>   
>   data(longleaf)    # numeric marks
>   longleaf          
marked planar point pattern: 584 points
marks are numeric, of type "double"
window: rectangle = [ 0 , 200 ] x [ 0 , 200 ]
> 
>   data(demopat)     # weird polygonal window
>   demopat
marked planar point pattern: 112 points
multitype, with levels = A	B 
window: polygonal boundary
enclosing rectangle: [ 525 , 10575 ] x [ 450 , 7125 ]
> 
> 
> 
> cleanEx(); ..nameEx <- "print.quad"
> 
> ### * print.quad
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: print.quad
> ### Title: Print a Quadrature Scheme
> ### Aliases: print.quad
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  data(cells)
>  Q <- quadscheme(cells)
>  Q
Quadrature scheme
42 data points,  629 dummy points
Total weight  1.00000000000001 
> 
> 
> 
> cleanEx(); ..nameEx <- "qqplot.ppm"
> 
> ### * qqplot.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: qqplot.ppm
> ### Title: Q-Q Plot of Residuals from Fitted Point Process Model
> ### Aliases: qqplot.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     data(cells)
> 
>     fit <- ppm(cells, ~1, Poisson())
>     diagnose.ppm(fit)  # no suggestion of departure from stationarity
Model diagnostics (raw residuals)
Diagnostics available:
	four-panel plot
	mark plot 
	smoothed residual field
	x cumulative residuals
	y cumulative residuals
	sum of all residuals
sum of raw residuals in entire window = 1.562e-13 
area of entire window = 1 
range of smoothed field = [ -26.69,15.74 ]
>     ## Not run: qqplot.ppm(fit, 80)  # strong evidence of non-Poisson interaction
>     ## Don't show:
> qqplot.ppm(fit, 5)
Extracting model information...Evaluating trend...done.
Simulating 5 realisations... 1, 2, 3, 4, 5, Calculating quantiles...averaging.....Done.
> ## End Don't show
> 
>     ## Not run: 
> ##D diagnose.ppm(fit, type="pearson")  
> ##D     qqplot.ppm(fit, type="pearson")
> ## End(Not run)
>     ## Don't show:
> qqplot.ppm(fit, 5, type="pearson")
Extracting model information...Evaluating trend...done.
Simulating 5 realisations... 1, 2, 3, 4, 5, Calculating quantiles...averaging.....Done.
> ## End Don't show
> 
>     ###########################################
>     ## oops, I need the plot coordinates
>     mypreciousdata <- .Last.value
>     ## Not run: mypreciousdata <- qqplot.ppm(fit, type="pearson")
>     ## Don't show:
> mypreciousdata <- qqplot.ppm(fit, 5, type="pearson")
Extracting model information...Evaluating trend...done.
Simulating 5 realisations... 1, 2, 3, 4, 5, Calculating quantiles...averaging.....Done.
> ## End Don't show
>     plot(mypreciousdata)
> 
>     ######################################################
>     # Q-Q plots based on fixed n
>     # The above QQ plots used simulations from the (fitted) Poisson process.
>     # But I want to simulate conditional on n, instead of Poisson
>     # Do this by setting rmhcontrol(p=1)
>     fixit <- list(p=1)
>     ## Not run: qqplot.ppm(fit, 100, control=fixit)
>     ## Don't show:
> qqplot.ppm(fit, 5, control=fixit)
Extracting model information...Evaluating trend...done.
Simulating 5 realisations... 1, 2, 3, 4, 5, Calculating quantiles...averaging.....Done.
> ## End Don't show
> 
>     ######################################################
>     # Inhomogeneous Poisson data
>     X <- rpoispp(function(x,y){1000 * exp(-3*x)}, 1000)
>     plot(X)
>     # Inhomogeneous Poisson model
>     fit <- ppm(X, ~x, Poisson())
>     ## Not run: qqplot.ppm(fit, 100)
>     ## Don't show:
> qqplot.ppm(fit, 10)
Extracting model information...Evaluating trend...done.
Simulating 10 realisations... 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Calculating quantiles...averaging.....Done.
> ## End Don't show
>     # conclusion: fitted inhomogeneous Poisson model looks OK
> 
>     ######################################################
>     # Advanced use of 'expr' argument
>     # 
>     # set the initial conditions in Metropolis-Hastings algorithm
>     # 
>     expr <- expression(rmh(fit, start=list(n.start=42), verbose=FALSE))
>     ## Not run: qqplot.ppm(fit, 100, expr)
>     ## Don't show:
> qqplot.ppm(fit, 5, expr)
Simulating 5 realisations... 1, 2, 3, 4, 5, Calculating quantiles...averaging.....Done.
> ## End Don't show
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "quad.ppm"
> 
> ### * quad.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: quad.ppm
> ### Title: Extract Quadrature Scheme Used to Fit a Point Process Model
> ### Aliases: quad.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  data(cells)
>  fit <- ppm(cells, ~1, Strauss(r=0.1), rbord=0.1)
>  Q <- quad.ppm(fit)
>  ## Not run: plot(Q)
>  Q$data$n
[1] 42
>  Q$dummy$n
[1] 629
> 
> 
> 
> cleanEx(); ..nameEx <- "quadratcount"
> 
> ### * quadratcount
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: quadratcount
> ### Title: Quadrat counting for a point pattern
> ### Aliases: quadratcount
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  X <- runifpoint(50)
>  quadratcount(X)
           y
x           [0,0.2] (0.2,0.4] (0.4,0.6] (0.6,0.8] (0.8,1]
  [0,0.2]         1         3         2         0       1
  (0.2,0.4]       2         2         2         0       5
  (0.4,0.6]       1         2         3         2       1
  (0.6,0.8]       1         3         3         6       2
  (0.8,1]         1         4         0         3       0
>  quadratcount(X, 4, 5)
            y
x            [0,0.25] (0.25,0.5] (0.5,0.75] (0.75,1]
  [0,0.25]          2          5          0        3
  (0.25,0.5]        2          8          0        3
  (0.5,0.75]        3          4          4        3
  (0.75,1]          3          2          3        5
>  quadratcount(X, xbreaks=c(0, 0.3, 1), ybreaks=c(0, 0.4, 0.8, 1))
         y
x         [0,0.4] (0.4,0.8] (0.8,1]
  [0,0.3]       5         4       3
  (0.3,1]      15        17       6
> 
> 
> 
> cleanEx(); ..nameEx <- "quadscheme"
> 
> ### * quadscheme
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: quadscheme
> ### Title: Generate a Quadrature Scheme from a Point Pattern
> ### Aliases: quadscheme
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(simdat)
> 
>   # grid weights
>   Q <- quadscheme(simdat)
>   Q <- quadscheme(simdat, method="grid")
>   Q <- quadscheme(simdat, nd=50)           # 1 dummy point per tile
>   Q <- quadscheme(simdat, ntile=25, nd=50) # 4 dummy points per tile
> 
>   # Dirichlet weights
>   Q <- quadscheme(simdat, method="dirichlet", exact=FALSE)
> 
>   # random dummy pattern
>   ## Not run: 
> ##D   D <- runifpoint(250, simdat$window)
> ##D   Q <- quadscheme(simdat, D, method="dirichlet", exact=FALSE)
> ##D   
> ## End(Not run)
> 
>   # polygonal window
>   data(demopat)
>   X <- unmark(demopat)
>   Q <- quadscheme(X)
> 
>   # mask window
>   X$window <- as.mask(X$window)
>   Q <- quadscheme(X)
>   
> 
> 
> 
> cleanEx(); ..nameEx <- "rMatClust"
> 
> ### * rMatClust
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rMatClust
> ### Title: Simulate Matern Cluster Process
> ### Aliases: rMatClust
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  pp <- rMatClust(10, 0.05, 4)
> 
> 
> 
> cleanEx(); ..nameEx <- "rMaternI"
> 
> ### * rMaternI
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rMaternI
> ### Title: Simulate Matern Model I
> ### Aliases: rMaternI
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  pp <- rMaternI(20, 0.05)
> 
> 
> 
> cleanEx(); ..nameEx <- "rMaternII"
> 
> ### * rMaternII
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rMaternII
> ### Title: Simulate Matern Model II
> ### Aliases: rMaternII
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  pp <- rMaternII(20, 0.05)
> 
> 
> 
> cleanEx(); ..nameEx <- "rNeymanScott"
> 
> ### * rNeymanScott
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rNeymanScott
> ### Title: Simulate Neyman-Scott Process
> ### Aliases: rNeymanScott
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   nclust <-  function(x0, y0, radius, n) {
+                            return(runifdisc(n, radius, x0, y0))
+                          }
>   X <- rNeymanScott(10, 0.2, nclust, radius=0.2, n=5)
> 
> 
> 
> cleanEx(); ..nameEx <- "rSSI"
> 
> ### * rSSI
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rSSI
> ### Title: Simple Sequential Inhibition
> ### Aliases: rSSI
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  pp <- rSSI(0.05, 200)
>  ## Not run: plot(pp)
> 
> 
> 
> cleanEx(); ..nameEx <- "rThomas"
> 
> ### * rThomas
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rThomas
> ### Title: Simulate Thomas Process
> ### Aliases: rThomas
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   X <- rThomas(10, 0.2, 5)
> 
> 
> 
> cleanEx(); ..nameEx <- "raster.x"
> 
> ### * raster.x
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: raster.x
> ### Title: Cartesian Coordinates for a Pixel Raster
> ### Aliases: raster.x raster.y
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   u <- owin(c(-1,1),c(-1,1)) # square of side 2
>   w <- as.mask(u, eps=0.01) # 200 x 200 grid
>   X <- raster.x(w)
>   Y <- raster.y(w)
>   disc <- owin(c(-1,1), c(-1,1), mask=(X^2 + Y^2 <= 1))
>   ## Not run: plot(disc)
>   # approximation to the unit disc
> 
> 
> 
> cleanEx(); ..nameEx <- "reach"
> 
> ### * reach
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: reach
> ### Title: Interaction Distance of a Point Process
> ### Aliases: reach reach.ppm reach.interact
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     reach(Poisson())
[1] 0
>     # returns 0
> 
>     reach(Strauss(r=7))
[1] 7
>     # returns 7
>     data(swedishpines)
>     fit <- ppm(swedishpines, ~1, Strauss(r=7))
>     reach(fit)
[1] 7
>     # returns 7
> 
>     reach(OrdThresh(42))
[1] Inf
>     # returns Inf
>     
>     reach(MultiStrauss(1:2, matrix(c(1,3,3,1),2,2)))
[1] 3
>     # returns 3
> 
> 
> 
> cleanEx(); ..nameEx <- "redwoodfull"
> 
> ### * redwoodfull
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: redwoodfull
> ### Title: California Redwoods Point Pattern (Entire Dataset)
> ### Aliases: redwoodfull redwoodfull.extra
> ### Keywords: datasets
> 
> ### ** Examples
> 
>        data(redwoodfull)
>        plot(redwoodfull)
>        redwoodfull.extra$plot()
>        # extract the pattern in region II 
>        redwoodII <- redwoodfull[, redwoodfull.extra$regionII]
> 
> 
> 
> cleanEx(); ..nameEx <- "rescue.rectangle"
> 
> ### * rescue.rectangle
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rescue.rectangle
> ### Title: Convert Window Back To Rectangle
> ### Aliases: rescue.rectangle
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- owin(poly=list(x=c(0,1,1,0),y=c(0,0,1,1)))
>   rw <- rescue.rectangle(w)
> 
>   w <- as.mask(unit.square())
>   rw <- rescue.rectangle(w)
> 
> 
> 
> cleanEx(); ..nameEx <- "residuals.ppm"
> 
> ### * residuals.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: residuals.ppm
> ### Title: Residuals for Fitted Point Process Model
> ### Aliases: residuals.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     data(cells)
>     fit <- ppm(cells, ~x, Strauss(r=0.15), rbord=0.15)
> 
>     rp <- residuals.ppm(fit, type="pe")
>     sum(rp) # should be close to 0
[1] -5.693327
> 
>     # extract quadrature points to which the residuals correspond
>     quadpoints <- union.quad(quad.ppm(fit))
> 
>     # plot residuals as marks attached to the quadrature points 
>     quadmarked <- setmarks(quadpoints, rp)
>     plot(quadmarked)
        -0.2         -0.1            0          0.1          0.2          0.3 
-0.015085475 -0.007542737  0.000000000  0.007542737  0.015085475  0.022628212 
         0.4          0.5 
 0.030170950  0.037713687 
> 
> 
> 
> cleanEx(); ..nameEx <- "residualspaper"
> 
> ### * residualspaper
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: residualspaper
> ### Title: Data and Code From JRSS Discussion Paper on Residuals
> ### Aliases: residualspaper
> ### Keywords: datasets
> 
> ### ** Examples
> 
> 
> ## Not run: 
> ##D   data(residualspaper)
> ##D   
> ##D   X <- residualspaper$Fig4a
> ##D   summary(X)
> ##D   plot(X)
> ##D 
> ##D   # reproduce all Figures
> ##D   residualspaper$plotfig()
> ##D 
> ##D   # reproduce Figures 1 to 10
> ##D   residualspaper$plotfig(1:10)
> ##D 
> ##D   # reproduce Figure 7 (a)
> ##D   residualspaper$plotfig("7a")
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "ripras"
> 
> ### * ripras
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ripras
> ### Title: Estimate window from points alone
> ### Aliases: ripras
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   ## Not run: 
> ##D   plot(owin())
> ##D   
> ## End(Not run)
>   x <- runif(30)
>   y <- runif(30)
>   ## Not run: points(x,y)
>   w <- ripras(x,y)
>   ## Not run: 
> ##D   plot(w, box=FALSE)
> ##D   points(x,y)
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "rlabel"
> 
> ### * rlabel
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rlabel
> ### Title: Random Re-Labelling of Point Pattern
> ### Aliases: rlabel
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(amacrine)
> 
>    # Randomly permute the marks "on" and "off"
>    # Result always has 142 "off" and 152 "on"
>    Y <- rlabel(amacrine)
> 
>    # randomly allocate marks "on" and "off"
>    # with probabilities p(off) = 0.48, p(on) = 0.52
>    Y <- rlabel(amacrine, permute=FALSE)
> 
>    # randomly allocate marks "A" and "B" with equal probability
>    data(cells)
>    Y <- rlabel(cells, labels=factor(c("A", "B")), permute=FALSE)
> 
> 
> 
> cleanEx(); ..nameEx <- "rmh"
> 
> ### * rmh
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rmh
> ### Title: Simulate point patterns using the Metropolis-Hastings algorithm.
> ### Aliases: rmh
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     # See examples in rmh.default and rmh.ppm
> 
> 
> 
> cleanEx(); ..nameEx <- "rmh.default"
> 
> ### * rmh.default
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rmh.default
> ### Title: Simulate Point Process Models using the Metropolis-Hastings
> ###   Algorithm.
> ### Aliases: rmh.default
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    ## Not run: 
> ##D    nr   <- 1e5
> ##D    nv  <- 5000
> ##D    
> ## End(Not run)
>    ## Don't show:
>    nr  <- 10
>    nv <- 5
>    
> ## End Don't show
>    set.seed(961018)
>    
>    # Strauss process.
>    mod01 <- list(cif="strauss",par=c(beta=2,gamma=0.2,r=0.7),
+                  w=c(0,10,0,10))
>    X1.strauss <- rmh(model=mod01,start=list(n.start=80),
+                      control=list(nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Strauss process, conditioning on n = 80:
>    X2.strauss <- rmh(model=mod01,start=list(n.start=80),
+                      control=list(p=1,nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Strauss process equal to pure hardcore:
>    mod02 <- list(cif="strauss",par=c(beta=2,gamma=0,r=0.7),w=c(0,10,0,10))
>    X3.strauss <- rmh(model=mod02,start=list(n.start=60,iseed=c(42,17,69)),
+                      control=list(nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Strauss process in a polygonal window.
>    x     <- c(0.55,0.68,0.75,0.58,0.39,0.37,0.19,0.26,0.42)
>    y     <- c(0.20,0.27,0.68,0.99,0.80,0.61,0.45,0.28,0.33)
>    mod03 <- list(cif="strauss",par=c(beta=2000,gamma=0.6,r=0.07),
+                 w=owin(poly=list(x=x,y=y)))
>    X4.strauss <- rmh(model=mod03,start=list(n.start=90),
+                      control=list(nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Strauss process in a polygonal window, conditioning on n = 80.
>    X5.strauss <- rmh(model=mod03,start=list(n.start=90),
+                      control=list(p=1,nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Strauss process, starting off from X4.strauss, but with the
>    # polygonal window replace by a rectangular one.  At the end,
>    # the generated pattern is clipped to the original polygonal window.
>    xxx <- X4.strauss
>    xxx$window <- as.owin(c(0,1,0,1))
>    X6.strauss <- rmh(model=mod03,start=list(x.start=xxx),
+                      control=list(nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Strauss with hardcore:
>    mod04 <- list(cif="straush",par=c(beta=2,gamma=0.2,r=0.7,hc=0.3),
+                 w=c(0,10,0,10))
>    X1.straush <- rmh(model=mod04,start=list(n.start=70),
+                      control=list(nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Another Strauss with hardcore (with a perhaps surprising result):
>    mod05 <- list(cif="straush",par=c(beta=80,gamma=0.36,r=45,hc=2.5),
+                 w=c(0,250,0,250))
>    X2.straush <- rmh(model=mod05,start=list(n.start=250),
+                      control=list(nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Pure hardcore (identical to X3.strauss).
>    mod06 <- list(cif="straush",par=c(beta=2,gamma=1,r=1,hc=0.7),
+                 w=c(0,10,0,10))
>    X3.straush <- rmh(model=mod06,start=list(n.start=60, iseed=c(42,17,69)),
+                      control=list(nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Soft core:
>    par3 <- c(0.8,0.1,0.5)
>    w    <- c(0,10,0,10)
>    mod07 <- list(cif="sftcr",par=c(beta=0.8,sigma=0.1,kappa=0.5),
+                 w=c(0,10,0,10))
>    X.sftcr <- rmh(model=mod07,start=list(n.start=70),
+                   control=list(nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Multitype Strauss:
>    beta <- c(0.027,0.008)
>    gmma <- matrix(c(0.43,0.98,0.98,0.36),2,2)
>    r    <- matrix(c(45,45,45,45),2,2)
>    mod08 <- list(cif="straussm",par=list(beta=beta,gamma=gmma,radii=r),
+                 w=c(0,250,0,250))
>    X1.straussm <- rmh(model=mod08,start=list(n.start=80),
+                       control=list(ptypes=c(0.75,0.25),nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Multitype Strauss conditioning upon the total number
>    # of points being 80:
>    X2.straussm <- rmh(model=mod08,start=list(n.start=80),
+                       control=list(p=1,ptypes=c(0.75,0.25),nrep=nr,
+                                    nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Conditioning upon the number of points of type 1 being 60
>    # and the number of points of type 2 being 20:
>    X3.straussm <- rmh(model=mod08,start=list(n.start=c(60,20)),
+                       control=list(fixall=TRUE,p=1,ptypes=c(0.75,0.25),
+                                    nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Multitype Strauss hardcore:
>    rhc  <- matrix(c(9.1,5.0,5.0,2.5),2,2)
>    mod09 <- list(cif="straushm",par=list(beta=beta,gamma=gmma,
+                 iradii=r,hradii=rhc),w=c(0,250,0,250))
>    X.straushm <- rmh(model=mod09,start=list(n.start=80),
+                      control=list(ptypes=c(0.75,0.25),nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Multitype Strauss hardcore with trends for each type:
>    beta  <- c(0.27,0.08)
>    tr3   <- function(x,y){x <- x/250; y <- y/250;
+                            exp((6*x + 5*y - 18*x^2 + 12*x*y - 9*y^2)/6)
+                          }
>                          # log quadratic trend
>    tr4   <- function(x,y){x <- x/250; y <- y/250;
+                          exp(-0.6*x+0.5*y)}
>                         # log linear trend
>    mod10 <- list(cif="straushm",par=list(beta=beta,gamma=gmma,
+                  iradii=r,hradii=rhc),w=c(0,250,0,250),
+                  trend=list(tr3,tr4))
>    X1.straushm.trend <- rmh(model=mod10,start=list(n.start=350),
+                             control=list(ptypes=c(0.75,0.25),
+                             nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Evaluating trend integral...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
irep/nverb=
[1] 2
>    
>    # Multitype Strauss hardcore with trends for each type, given as images:
>    x <- seq(0,250,length=51)
>    xy <- expand.grid(x=x,y=x)
>    i1 <- im(matrix(tr3(xy$x,xy$y),nrow=51),x,x)
>    i2 <- im(matrix(tr4(xy$x,xy$y),nrow=51),x,x)
>    mod11 <- list(cif="straushm",par=list(beta=beta,gamma=gmma,
+                  iradii=r,hradii=rhc),w=c(0,250,0,250),
+                  trend=list(i1,i2))
>    X2.straushm.trend <- rmh(model=mod11,start=list(n.start=350),
+                             control=list(ptypes=c(0.75,0.25),expand=1,
+                             nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Evaluating trend integral...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 1
irep/nverb=
[1] 1
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Diggle, Gates, and Stibbard:
>    mod12 <- list(cif="dgs",par=c(beta=3600,rho=0.08),w=c(0,1,0,1))
>    X.dgs <- rmh(model=mod12,start=list(n.start=300),
+                 control=list(nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Diggle-Gratton:
>    mod13 <- list(cif="diggra",
+                  par=c(beta=1800,kappa=3,delta=0.02,rho=0.04),
+                  w=square(1))
>    X.diggra <- rmh(model=mod13,start=list(n.start=300),
+                    control=list(nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Geyer:
>    mod14 <- list(cif="geyer",par=c(beta=1.25,gamma=1.6,r=0.2,sat=4.5),
+                  w=c(0,10,0,10))
>    X1.geyer <- rmh(model=mod14,start=list(n.start=200),
+                    control=list(nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Geyer; same as a Strauss process with parameters
>    # (beta=2.25,gamma=0.16,r=0.7):
>    
>    mod15 <- list(cif="geyer",par=c(beta=2.25,gamma=0.4,r=0.7,sat=10000),
+                  w=c(0,10,0,10))
>    X2.geyer <- rmh(model=mod15,start=list(n.start=200),
+                    control=list(nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    mod16 <- list(cif="geyer",par=c(beta=8.1,gamma=2.2,r=0.08,sat=3))
>    data(redwood)
>    X3.geyer <- rmh(model=mod16,start=list(x.start=redwood),
+                    control=list(periodic=TRUE,nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>    
>    # Geyer, starting from the redwood data set, simulating
>    # on a torus, and conditioning on n:
>    X4.geyer <- rmh(model=mod16,start=list(x.start=redwood),
+                    control=list(p=1,periodic=TRUE,nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
> 
>    # Lookup (interaction function h_2 from page 76, Diggle (2003)):
>       r <- seq(from=0,to=0.2,length=101)[-1] # Drop 0.
>       h <- 20*(r-0.05)
>       h[r<0.05] <- 0
>       h[r>0.10] <- 1
>       mod17 <- list(cif="lookup",par=list(beta=4000,h=h,r=r),w=c(0,1,0,1))
>       X.lookup <- rmh(model=mod17,start=list(n.start=100),
+                       control=list(nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
>                    
>    # Strauss with trend
>    tr <- function(x,y){x <- x/250; y <- y/250;
+                            exp((6*x + 5*y - 18*x^2 + 12*x*y - 9*y^2)/6)
+                          }
>    beta <- 0.3
>    gmma <- 0.5
>    r    <- 45
>    mod17 <- list(cif="strauss",par=c(beta=beta,gamma=gmma,r=r),w=c(0,250,0,250),
+                  trend=tr3)
>    X1.strauss.trend <- rmh(model=mod17,start=list(n.start=90),
+                            control=list(nrep=nr,nverb=nv))
Checking arguments..determining simulation windows...Evaluating trend integral...Starting simulation.
Initial state...Proposal points...Start simulation.
irep/nverb=
[1] 1
irep/nverb=
[1] 2
> 
> 
> 
> cleanEx(); ..nameEx <- "rmh.ppm"
> 
> ### * rmh.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rmh.ppm
> ### Title: Simulate from a Fitted Point Process Model
> ### Aliases: rmh.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(swedishpines)
>    X <- swedishpines
>    plot(X, main="Swedish Pines data")
> 
>    # Poisson process
>    fit <- ppm(X, ~1, Poisson())
>    Xsim <- rmh(fit)
Extracting model information...Evaluating trend...done.
Checking arguments..determining simulation windows...>    plot(Xsim, main="simulation from fitted Poisson model")
> 
>    # Strauss process   
>    fit <- ppm(X, ~1, Strauss(r=7), rbord=7)
>    Xsim <- rmh(fit, control=list(nrep=1e3))
Extracting model information...Evaluating trend...done.
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
>    plot(Xsim, main="simulation from fitted Strauss model")
> 
>    # Strauss process simulated on a larger window
>    # then clipped to original window
>    Xsim <- rmh(fit, control=list(nrep=1e3, expand=2, periodic=TRUE))
Extracting model information...Evaluating trend...done.
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
>    
>    # Strauss - hard core process
>    fit <- ppm(X, ~1, StraussHard(r=7,hc=2), rbord=7)
>    Xsim <- rmh(fit, start=list(n.start=X$n), control=list(nrep=1e3))
Extracting model information...Evaluating trend...done.
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
>    plot(Xsim, main="simulation from fitted Strauss hard core model")
> 
>    # Geyer saturation process
>    fit <- ppm(X, ~1, Geyer(r=7,sat=2), rbord=7)
>    Xsim <- rmh(fit, start=list(n.start=X$n), control=list(nrep=1e3))
Extracting model information...Evaluating trend...done.
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
>    plot(Xsim, main="simulation from fitted Geyer model")
> 
>    # soft core interaction process
>    Q <- quadscheme(X, nd=50)
>    fit <- ppm(Q, ~1, Softcore(kappa=0.1))
>    Xsim <- rmh(fit, start=list(n.start=X$n), control=list(nrep=1e3))
Extracting model information...Evaluating trend...done.
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
>    plot(Xsim, main="simulation from fitted Soft Core model")
> 
>    data(cells)
>    plot(cells)
>    # Diggle-Gratton pairwise interaction model
>    fit <- ppm(cells, ~1, DiggleGratton(0.05, 0.1))
>    Xsim <- rmh(fit, start=list(n.start=cells$n), control=list(nrep=1e3))
Extracting model information...Evaluating trend...done.
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
>    plot(Xsim, main="simulation from fitted Diggle-Gratton model")
> 
>    ## Not run: 
> ##D    X <- rSSI(0.05, 100)
> ##D    plot(X, main="new data")
> ##D 
> ##D    # piecewise-constant pairwise interaction function
> ##D    fit <- ppm(X, ~1, PairPiece(seq(0.02, 0.1, by=0.01)))
> ##D    Xsim <- rmh(fit, control=list(nrep=1e3))
> ##D    plot(Xsim, main="simulation from fitted pairwise model")
> ##D    
> ## End(Not run)
> 
>    # marked point pattern
>    data(amacrine)
>    Y <- amacrine
>    plot(Y, main="Amacrine data")
off  on 
  1   2 
> 
>    # marked Poisson models 
>    fit <- ppm(Y)
>    Ysim <- rmh(fit)
Extracting model information...Evaluating trend...done.
Checking arguments..determining simulation windows...>    plot(Ysim, main="simulation from ppm(Y)")
off  on 
  1   2 
> 
>    fit <- ppm(Y,~marks)
>    Ysim <- rmh(fit)
Extracting model information...Evaluating trend...done.
Checking arguments..determining simulation windows...>    plot(Ysim, main="simulation from ppm(Y, ~marks)")
off  on 
  1   2 
> 
>    fit <- ppm(Y,~polynom(x,y,2))
>    Ysim <- rmh(fit)
Extracting model information...Evaluating trend...done.
Checking arguments..determining simulation windows...>    plot(Ysim, main="simulation from ppm(Y, ~polynom(x,y,2))")
off  on 
  1   2 
> 
>    fit <- ppm(Y,~marks+polynom(x,y,2))
>    Ysim <- rmh(fit)
Extracting model information...Evaluating trend...done.
Checking arguments..determining simulation windows...>    plot(Ysim, main="simulation from ppm(Y, ~marks+polynom(x,y,2))")
off  on 
  1   2 
> 
>    fit <- ppm(Y,~marks*polynom(x,y,2))
>    Ysim <- rmh(fit)
Extracting model information...Evaluating trend...done.
Checking arguments..determining simulation windows...>    plot(Ysim, main="simulation from ppm(Y, ~marks*polynom(x,y,2))")
off  on 
  1   2 
> 
>    # multitype Strauss models
>    MS <- MultiStrauss(types = levels(Y$marks),
+                       radii=matrix(0.07, ncol=2, nrow=2))
>    fit <- ppm(Y, ~marks, MS)
>    Ysim <- rmh(fit, control=list(nrep=1e3))
Extracting model information...Model is invalid - projecting it
Evaluating trend...done.
Checking arguments..determining simulation windows...Starting simulation.
Initial state...Proposal points...Start simulation.
>    plot(Ysim, main="simulation from fitted Multitype Strauss")
off  on 
  1   2 
> 
>    fit <- ppm(Y,~marks*polynom(x,y,2), MS)
>    Ysim <- rmh(fit, control=list(nrep=1e3))
Extracting model information...Evaluating trend...done.
Checking arguments..determining simulation windows...Evaluating trend integral...Starting simulation.
Initial state...Proposal points...Start simulation.
>    plot(Ysim, main="simulation from fitted inhomogeneous Multitype Strauss")
off  on 
  1   2 
> 
> 
> 
> cleanEx(); ..nameEx <- "rmhcontrol"
> 
> ### * rmhcontrol
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rmhcontrol
> ### Title: Set Control Parameters for Metropolis-Hastings Algorithm.
> ### Aliases: rmhcontrol rmhcontrol.default
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    # parameters given as named arguments
>    c1 <- rmhcontrol(p=0.3,periodic=TRUE,nrep=1e6,nverb=1e5)
> 
>    # parameters given as a list
>    liz <- list(p=0.9, nrep=1e4)
>    c2 <- rmhcontrol(liz)
> 
>    # parameters given in rmhcontrol object
>    c3 <- rmhcontrol(c1)
> 
> 
> 
> cleanEx(); ..nameEx <- "rmhmodel"
> 
> ### * rmhmodel
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rmhmodel
> ### Title: Define Point Process Model for Metropolis-Hastings Simulation.
> ### Aliases: rmhmodel rmhmodel.default
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    # Strauss process:
>    mod01 <- rmhmodel(cif="strauss",par=c(beta=2,gamma=0.2,r=0.7),
+                  w=c(0,10,0,10))
>    # Equivalent to:
>    a <- list(cif="strauss",par=c(beta=2,gamma=0.2,r=0.7),
+                  w=c(0,10,0,10))
>    mod01 <- rmhmodel(a)
> 
>    # Strauss with hardcore:
>    mod04 <- list(cif="straush",par=c(beta=2,gamma=0.2,r=0.7,hc=0.3),
+                 w=owin(c(0,10),c(0,5)))
>    mod04 <- rmhmodel(mod04)
> 
>    # Soft core:
>    par3 <- c(0.8,0.1,0.5)
>    w    <- square(10)
>    mod07 <- rmhmodel(cif="sftcr",
+                      par=c(beta=0.8,sigma=0.1,kappa=0.5),
+                      w=w)
>    
>    # Multitype Strauss:
>    beta <- c(0.027,0.008)
>    gmma <- matrix(c(0.43,0.98,0.98,0.36),2,2)
>    r    <- matrix(c(45,45,45,45),2,2)
>    mod08 <- rmhmodel(cif="straussm",
+                      par=list(beta=beta,gamma=gmma,radii=r),
+                      w=square(250))
>    # specify types
>    mod09 <- rmhmodel(cif="straussm",
+                      par=list(beta=beta,gamma=gmma,radii=r),
+                      w=square(250),
+                      types=c("A", "B"))
> 
>    
>    # Multitype Strauss hardcore with trends for each type:
>    beta  <- c(0.27,0.08)
>    ri    <- matrix(c(45,45,45,45),2,2)
>    rhc  <- matrix(c(9.1,5.0,5.0,2.5),2,2)
>    tr3   <- function(x,y){x <- x/250; y <- y/250;
+                            exp((6*x + 5*y - 18*x^2 + 12*x*y - 9*y^2)/6)
+                          }
>                          # log quadratic trend
>    tr4   <- function(x,y){x <- x/250; y <- y/250;
+                          exp(-0.6*x+0.5*y)}
>                         # log linear trend
>    mod10 <- rmhmodel(cif="straushm",par=list(beta=beta,gamma=gmma,
+                  iradii=ri,hradii=rhc),w=c(0,250,0,250),
+                  trend=list(tr3,tr4))
> 
>    # Lookup (interaction function h_2 from page 76, Diggle (2003)):
>       r <- seq(from=0,to=0.2,length=101)[-1] # Drop 0.
>       h <- 20*(r-0.05)
>       h[r<0.05] <- 0
>       h[r>0.10] <- 1
>       mod17 <- rmhmodel(cif="lookup",par=list(beta=4000,h=h,r=r),w=c(0,1,0,1))
> 
> 
> 
> cleanEx(); ..nameEx <- "rmhstart"
> 
> ### * rmhstart
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rmhstart
> ### Title: Determine Initial State for Metropolis-Hastings Simulation.
> ### Aliases: rmhstart rmhstart.default
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    # 30 random points
>    a <- rmhstart(n.start=30)
> 
>    # a particular point pattern
>    data(cells)
>    b <- rmhstart(x.start=cells)
> 
>    # set the seed
>    d <- rmhstart(n.start=30, iseed=c(42, 4, 2))
> 
> 
> 
> cleanEx(); ..nameEx <- "rmpoint"
> 
> ### * rmpoint
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rmpoint
> ### Title: Generate N Random Multitype Points
> ### Aliases: rmpoint
> ### Keywords: spatial
> 
> ### ** Examples
> 
> 
> abc <- c("a","b","c")
> 
> ##### Model I
> 
> rmpoint(25, types=abc)
marked planar point pattern: 25 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> rmpoint(25, 1, types=abc)
marked planar point pattern: 25 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> # 25 points, equal probability for each type, uniformly distributed locations
> 
> rmpoint(25, function(x,y,m) {rep(1, length(x))}, types=abc)
marked planar point pattern: 25 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> # same as above
> rmpoint(25, list(function(x,y){rep(1, length(x))},
+                  function(x,y){rep(1, length(x))},
+                  function(x,y){rep(1, length(x))}),
+              types=abc)
marked planar point pattern: 25 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> # same as above
> 
> rmpoint(25, function(x,y,m) { x }, types=abc)
marked planar point pattern: 25 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> # 25 points, equal probability for each type,
> # locations nonuniform with density proportional to x
> 
> rmpoint(25, function(x,y,m) { ifelse(m == "a", 1, x) }, types=abc)
marked planar point pattern: 25 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> rmpoint(25, list(function(x,y) { rep(1, length(x)) },
+                 function(x,y) { x },
+                 function(x,y) { x }),
+                 types=abc)
marked planar point pattern: 25 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> # 25 points, UNEQUAL probabilities for each type,
> # type "a" points uniformly distributed,
> # type "b" and "c" points nonuniformly distributed.
> 
> ##### Model II
> 
> rmpoint(25, 1, types=abc, ptypes=rep(1,3)/3)
marked planar point pattern: 25 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> rmpoint(25, 1, types=abc, ptypes=rep(1,3))
marked planar point pattern: 25 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> # 25 points, equal probability for each type,
> # uniformly distributed locations
> 
> rmpoint(25, function(x,y,m) {rep(1, length(x))}, types=abc, ptypes=rep(1,3))
marked planar point pattern: 25 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> # same as above
> rmpoint(25, list(function(x,y){rep(1, length(x))},
+                  function(x,y){rep(1, length(x))},
+                  function(x,y){rep(1, length(x))}),
+              types=abc, ptypes=rep(1,3))
marked planar point pattern: 25 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> # same as above
> 
> rmpoint(25, function(x,y,m) { x }, types=abc, ptypes=rep(1,3))
marked planar point pattern: 25 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> # 25 points, equal probability for each type,
> # locations nonuniform with density proportional to x
> 
> rmpoint(25, function(x,y,m) { ifelse(m == "a", 1, x) }, types=abc, ptypes=rep(1,3))
marked planar point pattern: 25 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> # 25 points, EQUAL probabilities for each type,
> # type "a" points uniformly distributed,
> # type "b" and "c" points nonuniformly distributed.
> 
> ###### Model III
> 
> rmpoint(c(12, 8, 4), 1, types=abc)
marked planar point pattern: 24 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> # 12 points of type "a",
> # 8 points of type "b",
> # 4 points of type "c",
> # each uniformly distributed
> 
> rmpoint(c(12, 8, 4), function(x,y,m) { ifelse(m=="a", 1, x)}, types=abc)
marked planar point pattern: 24 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> rmpoint(c(12, 8, 4), list(function(x,y) { rep(1, length(x)) },
+                                function(x,y) { x },
+                                function(x,y) { x }),
+              types=abc)
marked planar point pattern: 24 points
multitype, with levels = a	b	c 
window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
> 
> # 12 points of type "a", uniformly distributed
> # 8 points of type "b", nonuniform
> # 4 points of type "c", nonuniform
> 
> #########
> 
> ## Randomising an existing point pattern:
> data(demopat)
> X <- demopat
> 
> # same numbers of points of each type, uniform random locations (Model III)
> rmpoint(table(X$marks), 1, types=levels(X$marks), win=X$window)
marked planar point pattern: 112 points
multitype, with levels = A	B 
window: polygonal boundary
enclosing rectangle: [ 525 , 10575 ] x [ 450 , 7125 ]
> 
> # same total number of points, distribution of types estimated from X,
> # uniform random locations (Model II)
> rmpoint(X$n, 1, types=levels(X$marks), win=X$window,
+        ptypes=table(X$marks))
marked planar point pattern: 112 points
multitype, with levels = A	B 
window: polygonal boundary
enclosing rectangle: [ 525 , 10575 ] x [ 450 , 7125 ]
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "rmpoispp"
> 
> ### * rmpoispp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rmpoispp
> ### Title: Generate Multitype Poisson Point Pattern
> ### Aliases: rmpoispp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  # uniform bivariate Poisson process with total intensity 100 in unit square
>  pp <- rmpoispp(50, types=c("a","b"))
>  
>  # stationary bivariate Poisson process with intensity A = 30, B = 70
>  pp <- rmpoispp(c(30,70), types=c("A","B"))
>  pp <- rmpoispp(c(30,70))
> 
>  # works in any window
>  data(letterR)
>  pp <- rmpoispp(c(30,70), win=letterR, types=c("A","B"))
> 
>  # inhomogeneous lambda(x,y,m)
>  # note argument 'm' is a factor 
>  lam <- function(x,y,m) { 50 * (x^2 + y^3) * ifelse(m=="A", 2, 1)}
>  pp <- rmpoispp(lam, win=letterR, types=c("A","B"))
>  # extra arguments
>  lam <- function(x,y,m,scal) { scal * (x^2 + y^3) * ifelse(m=="A", 2, 1)}
>  pp <- rmpoispp(lam, win=letterR, types=c("A","B"), scal=50)
> 
>  # list of functions lambda[[i]](x,y)
>  lams <- list(function(x,y){50 * x^2}, function(x,y){20 * abs(y)})
>  pp <- rmpoispp(lams, win=letterR, types=c("A","B"))
>  pp <- rmpoispp(lams, win=letterR)
>  # functions with extra arguments
>  lams <- list(function(x,y,scal){5 * scal * x^2},
+               function(x,y, scal){2 * scal * abs(y)})
>  pp <- rmpoispp(lams, win=letterR, types=c("A","B"), scal=10)
>  pp <- rmpoispp(lams, win=letterR, scal=10)
> 
>  # florid example
>  lams <- list(function(x,y){
+                            100*exp((6*x + 5*y - 18*x^2 + 12*x*y - 9*y^2)/6)
+                          }
+                          # log quadratic trend
+               ,
+               function(x,y){
+                                    100*exp(-0.6*x+0.5*y)
+                          }
+                         # log linear trend
+               )
>   X <- rmpoispp(lams, win=unit.square(), types=c("on", "off"))   
> 
>  # pixel image
>  Z <- as.im(function(x,y){30 * (x^2 + y^3)}, letterR)
>  pp <- rmpoispp(Z, types=c("A","B"))
> 
>  # list of pixel images
>  ZZ <- list(
+           as.im(function(x,y){20 * (x^2 + y^3)}, letterR),
+           as.im(function(x,y){40 * (x^3 + y^2)}, letterR))
>  pp <- rmpoispp(ZZ, types=c("A","B"))
>  pp <- rmpoispp(ZZ)
>  
> 
> 
> 
> cleanEx(); ..nameEx <- "rotate"
> 
> ### * rotate
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rotate
> ### Title: Rotate
> ### Aliases: rotate
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)
>   X <- rotate(cells, pi/3)
>   ## Not run: 
> ##D   plot(X)
> ##D   plot(rotate(cells$window, pi/4))
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "rotate.owin"
> 
> ### * rotate.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rotate.owin
> ### Title: Rotate a Window
> ### Aliases: rotate.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- owin(c(0,1),c(0,1))
>   v <- rotate(w, pi/3)
>   ## Not run: 
> ##D   plot(v)
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "rotate.ppp"
> 
> ### * rotate.ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rotate.ppp
> ### Title: Rotate a Point Pattern
> ### Aliases: rotate.ppp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)
>   X <- rotate(cells, pi/3)
>   ## Not run: 
> ##D   plot(X)
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "rpoint"
> 
> ### * rpoint
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rpoint
> ### Title: Generate N Random Points
> ### Aliases: rpoint
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  # 100 uniform random points in the unit square
>  X <- rpoint(100)
> 
>  # 100 random points with probability density proportional to x^2 + y^2
>  X <- rpoint(100, function(x,y) { x^2 + y^2}, 1)
> 
>  # `fmax' may be omitted
>  X <- rpoint(100, function(x,y) { x^2 + y^2})
> 
>  # irregular window
>  data(letterR)
>  X <- rpoint(100, function(x,y) { x^2 + y^2}, win=letterR)
> 
>  # make a pixel image 
>  Z <- setcov(letterR)
>  # 100 points with density proportional to pixel values
>  X <- rpoint(100, Z)
> 
> 
> 
> cleanEx(); ..nameEx <- "rpoispp"
> 
> ### * rpoispp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rpoispp
> ### Title: Generate Poisson Point Pattern
> ### Aliases: rpoispp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  # uniform Poisson process with intensity 100 in the unit square
>  pp <- rpoispp(100)
>  
>  # uniform Poisson process with intensity 1 in a 10 x 10 square
>  pp <- rpoispp(1, win=owin(c(0,10),c(0,10)))
>  # plots should look similar !
>  
>  # inhomogeneous Poisson process in unit square
>  # with intensity lambda(x,y) = 100 * exp(-3*x)
>  # Intensity is bounded by 100
>  pp <- rpoispp(function(x,y) {100 * exp(-3*x)}, 100)
> 
>  # How to tune the coefficient of x
>  lamb <- function(x,y,a) { 100 * exp( - a * x)}
>  pp <- rpoispp(lamb, 100, a=3)
> 
>  # pixel image
>  Z <- as.im(function(x,y){100 * sqrt(x+y)}, unit.square())
>  pp <- rpoispp(Z)
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "rtoro"
> 
> ### * rtoro
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: rtoro
> ### Title: Random Toroidal Shift of Point Pattern
> ### Aliases: rtoro
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(amacrine)
> 
>    # point patterns:
>    # shift all points simultaneously
>    X <- rtoro(amacrine)
>    # shift "on" and "off" points separately
>    X <- rtoro(amacrine, which=amacrine$marks)
>    # shift "on" points and leave "off" points fixed
>    X <- rtoro(amacrine, which="on")
> 
>    # splitppp objects:
>    Y <- split(amacrine)
>    # shift "on" and "off" points separately
>    Z <- rtoro(Y)
>    # shift "on" points and leave "off" points fixed
>    Z <- rtoro(Y, "on")
>    # shift all points simultaneously
>    Z <- split(rtoro(superimpose(Y)))
>    
> 
> 
> 
> cleanEx(); ..nameEx <- "runifpoint"
> 
> ### * runifpoint
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: runifpoint
> ### Title: Generate N Uniform Random Points
> ### Aliases: runifpoint
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  # 100 random points in the unit square
>  pp <- runifpoint(100)
>  # irregular window
>  data(letterR)
>  # polygonal
>  pp <- runifpoint(100, letterR)
>  # binary image mask
>  pp <- runifpoint(100, as.mask(letterR))
> 
> 
> 
> cleanEx(); ..nameEx <- "setcov"
> 
> ### * setcov
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: setcov
> ### Title: Set Covariance of a Window
> ### Aliases: setcov
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- owin(c(0,1),c(0,1))
>   v <- setcov(w)
>   plot(v)
> 
> 
> 
> cleanEx(); ..nameEx <- "setmarks"
> 
> ### * setmarks
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: setmarks
> ### Title: Set or Reset the Marks in a Point Pattern
> ### Aliases: setmarks \%mark\%
> ### Keywords: spatial
> 
> ### ** Examples
> 
>    data(cells)
> 
>    m <- runif(cells$n)
> 
>    Y <- setmarks(cells, m)
>    Y <- cells %mark% m
>    # equivalent
> 
>    ## Not run: plot(Y)
>    is.marked(Y)  #TRUE
[1] TRUE
> 
> 
> 
> cleanEx(); ..nameEx <- "shift"
> 
> ### * shift
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: shift
> ### Title: Apply Vector Translation
> ### Aliases: shift
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)
>   X <- shift(cells, c(2,3))
>   ## Not run: 
> ##D   plot(X)
> ##D   # no discernible difference except coordinates are different
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "shift.im"
> 
> ### * shift.im
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: shift.im
> ### Title: Apply Vector Translation To Pixel Image
> ### Aliases: shift.im
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  # make up an image
>  X <- setcov(unit.square())
>  plot(X)
> 
>  Y <- shift(X, c(10,10))
>  plot(Y)
>  # no discernible difference except coordinates are different
>   
> 
> 
> cleanEx(); ..nameEx <- "shift.owin"
> 
> ### * shift.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: shift.owin
> ### Title: Apply Vector Translation To Window
> ### Aliases: shift.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   W <- owin(c(0,1),c(0,1))
>   X <- shift(W, c(2,3))
>   ## Not run: 
> ##D   plot(W)
> ##D   # no discernible difference except coordinates are different
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "shift.ppp"
> 
> ### * shift.ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: shift.ppp
> ### Title: Apply Vector Translation To Point Pattern
> ### Aliases: shift.ppp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)
>   X <- shift(cells, c(2,3))
>   ## Not run: 
> ##D   plot(X)
> ##D   # no discernible difference except coordinates are different
> ##D   
> ## End(Not run)
>   Y <- superimpose(cells, shift(cells, c(0.1,0.1)))
>   ## Not run: plot(Y)
> 
> 
> 
> cleanEx(); ..nameEx <- "spatstat.options"
> 
> ### * spatstat.options
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: spatstat.options
> ### Title: Internal Options in Spatstat Package
> ### Aliases: spatstat.options
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   spatstat.options(npixel=150)
>   spatstat.options(npixel=c(100,200))
> 
>   spatstat.options(par.binary=list(col=grey(c(0.5,1))))
> 
>   spatstat.options(par.persp=list(theta=-30,phi=40,d=4))
>   # see help(persp.default) for other options
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "split.ppp"
> 
> ### * split.ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: split.ppp
> ### Title: Divide Point Pattern into Sub-patterns
> ### Aliases: split.ppp split<-.ppp split split<-
> ### Keywords: spatial
> 
> ### ** Examples
> 
> 
> # Multitype point pattern: separate into types
>  data(amacrine)
>  u <- split(amacrine)
> 
> # the following are equivalent:
>  amon <- amacrine[amacrine$marks == "on"]
>  amon <- split(amacrine)$on
>    
> # plot them
>  plot(split(amacrine))
> 
> # Scramble the locations of the 'on' cells
>  u <- unmark(split(amacrine))
>  u$on <- runifpoint(amon$n, amon$window)
>  split(amacrine) <- u
> 
> # Point pattern with continuous marks
>  data(longleaf)
>  ## Don't show:
>         # smaller dataset
>         longleaf <- longleaf[seq(1, longleaf$n, by=80)]
>  
> ## End Don't show
>  # cut the range of tree diameters into three intervals
>  long3 <- cut.ppp(longleaf, 3)
>  # now split them
>  long3split <- split(long3)
> 
> # Unmarked point pattern
>   data(swedishpines)
> # cut & split according to nearest neighbour distance
>   f <- cut(nndist(swedishpines), 3)
>   u <- split(swedishpines, f)
> 
> 
> 
> cleanEx(); ..nameEx <- "spokes"
> 
> ### * spokes
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: spokes
> ### Title: Spokes pattern of dummy points
> ### Aliases: spokes
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   dat <- runifrect(10)
>   ## Not run: 
> ##D   plot(dat)
> ##D   
> ## End(Not run)
>   dum <- spokes(dat$x, dat$y)
>   ## Not run: 
> ##D   points(dum$x, dum$y, pch=".")
> ##D   
> ## End(Not run)
>   Q <- quadscheme(dat, dum)
Warning in countingweights(id, areas) : some tiles with positive area do not contain any points
> 
> 
> 
> cleanEx(); ..nameEx <- "spruces"
> 
> ### * spruces
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: spruces
> ### Title: Spruces Point Pattern
> ### Aliases: spruces
> ### Keywords: datasets
> 
> ### ** Examples
> 
>      data(spruces)
>      plot(spruces)
    0.15      0.2     0.25      0.3     0.35      0.4 
1.276075 1.701433 2.126791 2.552149 2.977507 3.402865 
>      # To reproduce Goulard et al. Figure 3
>      plot(spruces, maxsize=5*max(spruces$marks))
0.15  0.2 0.25  0.3 0.35  0.4 
0.75 1.00 1.25 1.50 1.75 2.00 
>      plot(unmark(spruces), add=TRUE)
> 
> 
> 
> cleanEx(); ..nameEx <- "square"
> 
> ### * square
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: square
> ### Title: Square Window
> ### Aliases: square unit.square
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  W <- square(10)
> 
> 
> 
> cleanEx(); ..nameEx <- "stratrand"
> 
> ### * stratrand
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: stratrand
> ### Title: Stratified random point pattern
> ### Aliases: stratrand
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   w <- unit.square()
>   xy <- stratrand(w, 10, 10)
>   ## Not run: 
> ##D   plot(w)
> ##D   points(xy)
> ##D   
> ## End(Not run)
> 
>   # polygonal boundary
>   bdry <- list(x=c(0.1,0.3,0.7,0.4,0.2),
+                y=c(0.1,0.1,0.5,0.7,0.3))
>   w <- owin(c(0,1), c(0,1), poly=bdry)
>   xy <- stratrand(w, 10, 10, 3)
>   ## Not run: 
> ##D   plot(w)
> ##D   points(xy)
> ##D   
> ## End(Not run)
>   # determine which grid points are inside polygon
>   ok <- inside.owin(xy$x, xy$y, w)
>   ## Not run: 
> ##D   plot(w)
> ##D   points(xy$x[ok], xy$y[ok])
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "subset.fasp"
> 
> ### * subset.fasp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: subset.fasp
> ### Title: Extract Subset of Function Array
> ### Aliases: subset.fasp [.fasp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  # Lansing woods data - multitype points with 6 types
>  data(lansing)
>  ## Not run: 
> ##D  # compute 6 x 6 array of all cross-type K functions
> ##D    a <- alltypes(lansing, "K")
> ##D    plot(a)
> ##D  
> ## End(Not run)
>  ## Don't show:
>  # smaller dataset
>    sub <- lansing[ seq(1,lansing$n,by=40), ]
>    a <- alltypes(sub, "K")
>  
> ## End Don't show
>  # first three marks only
>  b <- a[1:3,1:3]
>  ## Not run: plot(b)
>  # subset pertaining to hickories
>  h <- a[levels(lansing$marks) == "hickory", ]
>  ## Not run: plot(h)
> 
> 
> 
> cleanEx(); ..nameEx <- "subset.fv"
> 
> ### * subset.fv
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: subset.fv
> ### Title: Extract Subset of Function Values
> ### Aliases: subset.fv [.fv
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  data(cells)
>  K <- Kest(cells)
> 
>  # discard the estimates of K(r) for r  > 0.1
>  Ksub <- K[K$r <= 0.1, ]
> 
>  # discard the border method estimator
>  Ksub <- K[ , names(K) != "border"]
>  
> 
> 
> 
> cleanEx(); ..nameEx <- "subset.im"
> 
> ### * subset.im
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: subset.im
> ### Title: Extract Subset of Image
> ### Aliases: subset.im [.im
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  # make up an image
>  X <- setcov(unit.square())
>  plot(X)
> 
>  # a rectangular subset
>  W <- owin(c(0,0.5),c(0.2,0.8))
>  Y <- X[W]
>  plot(Y)
> 
>  # a polygonal subset
>  data(letterR)
>  R <- affine(letterR, diag(c(1,1)/2), c(-2,-0.7))
>  Y <- X[R, drop=FALSE]
>  plot(Y)
> 
>  # a point pattern
>  P <- rpoispp(20)
>  Y <- X[P]
> 
> 
> 
> cleanEx(); ..nameEx <- "subset.ppp"
> 
> ### * subset.ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: subset.ppp
> ### Title: Extract or Replace Subset of Point Pattern
> ### Aliases: subset.ppp [.ppp [<-.ppp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>  data(longleaf)
>  # Longleaf pines data
>  ## Not run: 
> ##D  plot(longleaf)
> ##D  
> ## End(Not run)
>  ## Don't show:
>         longleaf <- longleaf[seq(1,longleaf$n,by=10)]
>  
> ## End Don't show
>  # adult trees defined to have diameter at least 30 cm
>  adult <- (longleaf$marks >= 30)
>  longadult <- longleaf[adult]
>  # equivalent to: longadult <- subset.ppp(longleaf, subset=adult)
>  ## Not run: 
> ##D  plot(longadult)
> ##D  
> ## End(Not run)
>  # note that the marks are still retained.
>  # Use unmark(longadult) to remove the marks
>  
>  # New Zealand trees data
>  data(nztrees)
>  ## Not run: 
> ##D  plot(nztrees)          # plot shows a line of trees at the far right
> ##D  abline(v=148, lty=2)   # cut along this line
> ##D  
> ## End(Not run)
>  nzw <- owin(c(0,148),c(0,95)) # the subwindow
>  # trim dataset to this subwindow
>  nzsub <- nztrees[,nzw]
>  # equivalent to: nzsub <- subset.ppp(nztrees, window=nzw)
>  ## Not run: 
> ##D  plot(nzsub)
> ##D  
> ## End(Not run)
> 
>  # Redwood data
>  data(redwood) 
>  ## Not run: 
> ##D  plot(redwood)
> ##D  
> ## End(Not run)
>  # Random thinning: delete 60% of data
>  retain <- (runif(redwood$n) < 0.4)
>  thinred <- redwood[retain]
>  ## Not run: 
> ##D  plot(thinred)
> ##D  
> ## End(Not run)
>  # Scramble 60% of data
>  modif <- (runif(redwood$n) < 0.6)
>  scramble <- function(x) { runifpoint(x$n, x$window) }
>  redwood[modif] <- scramble(redwood[modif])
> 
>  # Lansing woods data - multitype points
>  data(lansing)
>  ## Don't show:
>     lansing <- lansing[seq(1, lansing$n, length=100)]
>  
> ## End Don't show
>  # hickory trees only
>  hick <- lansing[lansing$marks == "hickory", ]
>  # still a marked pattern -- remove marks
>  hick <- unmark(hick)
> 
>  # scramble the hickories
>  lansing[lansing$marks == "hickory"] <- scramble(hick)
>   
> 
> 
> 
> cleanEx(); ..nameEx <- "suffstat"
> 
> ### * suffstat
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: suffstat
> ### Title: Sufficient Statistic of Point Process Model
> ### Aliases: suffstat
> ### Keywords: spatial
> 
> ### ** Examples
> 
>     data(swedishpines)
>     fitS <- ppm(swedishpines, ~1, Strauss(7))
>     X <- rpoispp(summary(swedishpines)$intensity, win=swedishpines$window)
>     suffstat(fitS, X)
(Intercept) Interaction 
         65          31 
> 
> 
> 
> cleanEx(); ..nameEx <- "summary.im"
> 
> ### * summary.im
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: summary.im
> ### Title: Summarizing a Pixel Image
> ### Aliases: summary.im print.summary.im
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   # make an image
>   X <- as.im(function(x,y) {x^2}, unit.square())
>   # summarize it
>   summary(X)
Pixel image
200 x 100 pixel array
enclosing rectangle: [ 8.67361737988404e-19, 1 ] x [ 4.33680868994202e-19, 1 ]
dimensions of each pixel: 0.01 x 0.005 
Image is defined on the full rectangular grid
Frame area =  1 
Pixel values :
	range = [2.5e-05,0.990025]
	integral = 0.333325000000017
	mean = 0.333325000000017
>   # save the summary
>   s <- summary(X)
>   # print it
>   print(X)
Pixel image
200 x 100 pixel array
enclosing rectangle: [ 8.67361737988404e-19, 1 ] x [ 4.33680868994202e-19, 1 ]
>   s
Pixel image
200 x 100 pixel array
enclosing rectangle: [ 8.67361737988404e-19, 1 ] x [ 4.33680868994202e-19, 1 ]
dimensions of each pixel: 0.01 x 0.005 
Image is defined on the full rectangular grid
Frame area =  1 
Pixel values :
	range = [2.5e-05,0.990025]
	integral = 0.333325000000017
	mean = 0.333325000000017
>   # extract stuff
>   X$dim
[1] 200 100
>   X$range
NULL
>   X$integral
NULL
> 
> 
> 
> cleanEx(); ..nameEx <- "summary.owin"
> 
> ### * summary.owin
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: summary.owin
> ### Title: Summary of a Spatial Window
> ### Aliases: summary.owin
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   summary(owin())  # the unit square
Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 
> 
>   data(demopat)
>   W <- demopat$window  # weird polygonal window
>   summary(W)           # describes it
Window: polygonal boundary
2 separate polygons (1 hole)
                 vertices     area relative.area
polygon 1              32 52711875         1.110
polygon 2 (hole)       12 -5127188        -0.108
enclosing rectangle: [ 525 , 10575 ] x [ 450 , 7125 ]
Window area =  47584687.5 
> 
>   summary(as.mask(W))  # demonstrates current pixel resolution
Window: binary image mask
200 x 100 pixel array
enclosing rectangle: [ 525 , 10575 ] x [ 450 , 7125 ]
Window area =  47545607.8125 
> 
> 
> 
> cleanEx(); ..nameEx <- "summary.ppm"
> 
> ### * summary.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: summary.ppm
> ### Title: Summarizing a Fitted Point Process Model
> ### Aliases: summary.ppm print.summary.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   # invent some data
>   X <- rpoispp(42)
>   # fit a model to it
>   fit <- ppm(X, ~x, Strauss(r=0.1))
>   # summarize the fitted model
>   summary(fit)
Point process model
fitted by maximum pseudolikelihood
Call:
ppm(Q = X, trend = ~x, interaction = Strauss(r = 0.1))
Edge correction: 'border'

----------------------------------------------------
Quadrature scheme = data + dummy + weights
Data pattern:
Planar point pattern: 37 points
Average intensity 37 points per unit area

Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 


Dummy quadrature points:
( 25 x 25 grid, plus 4 corner points)
Planar point pattern: 629 points
Average intensity 629 points per unit area

Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 


Quadrature weights:
(counting weights based on 25 x 25 array of rectangular tiles)
All weights:
	range: [0.000533, 0.0016]	total: 1
Weights on data points:
	range: [0.000533, 8e-04]	total: 0.0285
Weights on dummy points:
	range: [0.000533, 0.0016]	total: 0.971

----------------------------------------------------
FITTED MODEL:

Nonstationary Strauss process


 ---- Trend: ----

Trend formula: ~x

Fitted coefficients for trend formula:
(Intercept)           x 
  3.5880605   0.3130043 


 ---- Interaction: -----

Pairwise interaction family
Interaction: Strauss process 
interaction distance:	0.1
Fitted interaction parameter gamma:
[1] 0.8756


----------- gory details -----

Fitted regular parameters (theta): 
(Intercept)           x Interaction 
  3.5880605   0.3130043  -0.1328183 

Fitted exp(theta): 
(Intercept)           x Interaction 
 36.1638690   1.3675274   0.8756242 
>   # `quick' option
>   summary(fit, quick=TRUE)
Nonstationary Strauss process 
> 
>   # save the full summary
>   s <- summary(fit)
>   # print it
>   print(s)
Point process model
fitted by maximum pseudolikelihood
Call:
ppm(Q = X, trend = ~x, interaction = Strauss(r = 0.1))
Edge correction: 'border'

----------------------------------------------------
Quadrature scheme = data + dummy + weights
Data pattern:
Planar point pattern: 37 points
Average intensity 37 points per unit area

Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 


Dummy quadrature points:
( 25 x 25 grid, plus 4 corner points)
Planar point pattern: 629 points
Average intensity 629 points per unit area

Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 


Quadrature weights:
(counting weights based on 25 x 25 array of rectangular tiles)
All weights:
	range: [0.000533, 0.0016]	total: 1
Weights on data points:
	range: [0.000533, 8e-04]	total: 0.0285
Weights on dummy points:
	range: [0.000533, 0.0016]	total: 0.971

----------------------------------------------------
FITTED MODEL:

Nonstationary Strauss process


 ---- Trend: ----

Trend formula: ~x

Fitted coefficients for trend formula:
(Intercept)           x 
  3.5880605   0.3130043 


 ---- Interaction: -----

Pairwise interaction family
Interaction: Strauss process 
interaction distance:	0.1
Fitted interaction parameter gamma:
[1] 0.8756


----------- gory details -----

Fitted regular parameters (theta): 
(Intercept)           x Interaction 
  3.5880605   0.3130043  -0.1328183 

Fitted exp(theta): 
(Intercept)           x Interaction 
 36.1638690   1.3675274   0.8756242 
>   s
Point process model
fitted by maximum pseudolikelihood
Call:
ppm(Q = X, trend = ~x, interaction = Strauss(r = 0.1))
Edge correction: 'border'

----------------------------------------------------
Quadrature scheme = data + dummy + weights
Data pattern:
Planar point pattern: 37 points
Average intensity 37 points per unit area

Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 


Dummy quadrature points:
( 25 x 25 grid, plus 4 corner points)
Planar point pattern: 629 points
Average intensity 629 points per unit area

Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 


Quadrature weights:
(counting weights based on 25 x 25 array of rectangular tiles)
All weights:
	range: [0.000533, 0.0016]	total: 1
Weights on data points:
	range: [0.000533, 8e-04]	total: 0.0285
Weights on dummy points:
	range: [0.000533, 0.0016]	total: 0.971

----------------------------------------------------
FITTED MODEL:

Nonstationary Strauss process


 ---- Trend: ----

Trend formula: ~x

Fitted coefficients for trend formula:
(Intercept)           x 
  3.5880605   0.3130043 


 ---- Interaction: -----

Pairwise interaction family
Interaction: Strauss process 
interaction distance:	0.1
Fitted interaction parameter gamma:
[1] 0.8756


----------- gory details -----

Fitted regular parameters (theta): 
(Intercept)           x Interaction 
  3.5880605   0.3130043  -0.1328183 

Fitted exp(theta): 
(Intercept)           x Interaction 
 36.1638690   1.3675274   0.8756242 
>   # extract stuff
>   names(s)
 [1] "antiquated"  "no.trend"    "stationary"  "poisson"     "marked"     
 [6] "multitype"   "name"        "has.covars"  "args"        "entries"    
[11] "data"        "quad"        "trend"       "interaction"
>   s$args$correction
[1] "border"
>   s$name
[1] "Nonstationary Strauss process"
>   s$trend$value
(Intercept)           x 
  3.5880605   0.3130043 
> 
>   # multitype pattern
>   data(demopat)
>   fit <- ppm(demopat, ~marks, Poisson())
>   summary(fit)
Point process model
fitted by maximum pseudolikelihood
Call:
ppm(Q = demopat, trend = ~marks, interaction = Poisson())
Edge correction: 'border'

----------------------------------------------------
Quadrature scheme = data + dummy + weights
Data pattern:
Marked planar point pattern: 112 points
Average intensity 2.35e-06 points per unit area
Marks:
  frequency proportion intensity
A        45      0.402  9.46e-07
B        67      0.598  1.41e-06

Window: polygonal boundary
2 separate polygons (1 hole)
                 vertices     area relative.area
polygon 1              32 52711875         1.110
polygon 2 (hole)       12 -5127188        -0.108
enclosing rectangle: [ 525 , 10575 ] x [ 450 , 7125 ]
Window area =  47584687.5 


Dummy quadrature points:
( 50 x 40 grid, plus 4 corner points)
Marked planar point pattern: 3156 points
Average intensity 6.63e-05 points per unit area
Marks:
  frequency proportion intensity
A      1590      0.503  3.34e-05
B      1570      0.497  3.29e-05

Window: polygonal boundary
2 separate polygons (1 hole)
                 vertices     area relative.area
polygon 1              32 52711875         1.110
polygon 2 (hole)       12 -5127188        -0.108
enclosing rectangle: [ 525 , 10575 ] x [ 450 , 7125 ]
Window area =  47584687.5 


Quadrature weights:
(counting weights based on 50 x 40 array of rectangular tiles)
All weights:
	range: [3350, 33500]	total: 95100000
Weights on data points:
	range: [5590, 16800]	total: 1730000
Weights on dummy points:
	range: [3350, 33500]	total: 93400000

----------------------------------------------------
FITTED MODEL:

Stationary multitype Poisson process
Possible marks: 
A B

 ---- Intensity: ----

Trend formula: ~marks

Fitted intensities:
      beta_A       beta_B 
9.464597e-07 1.409173e-06 


----------- gory details -----

Fitted regular parameters (theta): 
(Intercept)      marksB 
-13.8705375   0.3980301 

Fitted exp(theta): 
 (Intercept)       marksB 
9.464597e-07 1.488889e+00 
> 
> 
> 
> cleanEx(); ..nameEx <- "summary.ppp"
> 
> ### * summary.ppp
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: summary.ppp
> ### Title: Summary of a Point Pattern Dataset
> ### Aliases: summary.ppp
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(cells)      # plain vanilla point pattern
>   summary(cells)  
Planar point pattern: 42 points
Average intensity 42 points per unit area

Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 
> 
>   data(lansing)    # multitype point pattern
>   summary(lansing) # tabulates frequences of each mark
Marked planar point pattern: 2251 points
Average intensity 2250 points per unit area
Marks:
         frequency proportion intensity
blackoak       135     0.0600       135
hickory        703     0.3120       703
maple          514     0.2280       514
misc           105     0.0466       105
redoak         346     0.1540       346
whiteoak       448     0.1990       448

Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 
>   
>   data(longleaf)    # numeric marks
>   summary(longleaf) # prints summary.default(x$marks)
Marked planar point pattern: 584 points
Average intensity 0.0146 points per unit area
marks are numeric, of type "double"
summary:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   2.00    9.10   26.15   26.84   42.13   75.90 

Window: rectangle = [ 0 , 200 ] x [ 0 , 200 ]
Window area =  40000 
> 
>   data(demopat)     # weird polygonal window
>   summary(demopat)  # describes it
Marked planar point pattern: 112 points
Average intensity 2.35e-06 points per unit area
Marks:
  frequency proportion intensity
A        45      0.402  9.46e-07
B        67      0.598  1.41e-06

Window: polygonal boundary
2 separate polygons (1 hole)
                 vertices     area relative.area
polygon 1              32 52711875         1.110
polygon 2 (hole)       12 -5127188        -0.108
enclosing rectangle: [ 525 , 10575 ] x [ 450 , 7125 ]
Window area =  47584687.5 
> 
> 
> 
> cleanEx(); ..nameEx <- "summary.quad"
> 
> ### * summary.quad
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: summary.quad
> ### Title: Summarizing a Quadrature Scheme
> ### Aliases: summary.quad print.summary.quad
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   # make a quadrature scheme
>   Q <- quadscheme(rpoispp(42))
>   # summarize it
>   summary(Q)
Quadrature scheme = data + dummy + weights
Data pattern:
Planar point pattern: 37 points
Average intensity 37 points per unit area

Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 


Dummy quadrature points:
( 25 x 25 grid, plus 4 corner points)
Planar point pattern: 629 points
Average intensity 629 points per unit area

Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 


Quadrature weights:
(counting weights based on 25 x 25 array of rectangular tiles)
All weights:
	range: [0.000533, 0.0016]	total: 1
Weights on data points:
	range: [0.000533, 8e-04]	total: 0.0285
Weights on dummy points:
	range: [0.000533, 0.0016]	total: 0.971
>   # save the summary
>   s <- summary(Q)
>   # print it
>   print(s)
Quadrature scheme = data + dummy + weights
Data pattern:
Planar point pattern: 37 points
Average intensity 37 points per unit area

Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 


Dummy quadrature points:
( 25 x 25 grid, plus 4 corner points)
Planar point pattern: 629 points
Average intensity 629 points per unit area

Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 


Quadrature weights:
(counting weights based on 25 x 25 array of rectangular tiles)
All weights:
	range: [0.000533, 0.0016]	total: 1
Weights on data points:
	range: [0.000533, 8e-04]	total: 0.0285
Weights on dummy points:
	range: [0.000533, 0.0016]	total: 0.971
>   s
Quadrature scheme = data + dummy + weights
Data pattern:
Planar point pattern: 37 points
Average intensity 37 points per unit area

Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 


Dummy quadrature points:
( 25 x 25 grid, plus 4 corner points)
Planar point pattern: 629 points
Average intensity 629 points per unit area

Window: rectangle = [ 0 , 1 ] x [ 0 , 1 ]
Window area =  1 


Quadrature weights:
(counting weights based on 25 x 25 array of rectangular tiles)
All weights:
	range: [0.000533, 0.0016]	total: 1
Weights on data points:
	range: [0.000533, 8e-04]	total: 0.0285
Weights on dummy points:
	range: [0.000533, 0.0016]	total: 0.971
>   # extract total quadrature weight
>   s$w$all$sum
[1] 1
> 
> 
> 
> cleanEx(); ..nameEx <- "superimpose"
> 
> ### * superimpose
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: superimpose
> ### Title: Superimpose Several Point Patterns
> ### Aliases: superimpose
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   dat <- runifrect(30)
>   xy <- list(x=runif(10),y=runif(10))
>   new <- superimpose(dat, xy)
>   ## Not run: plot(new)
> 
>   # how to make a 2-type point pattern with types "a" and "b"
>   u <- superimpose(a = rpoispp(10), b = rpoispp(20))
> 
>   # how to make a 2-type point pattern with types 1 and 2
>   u <- superimpose("1" = rpoispp(10), "2" = rpoispp(20))
> 
> 
> 
> cleanEx(); ..nameEx <- "union.quad"
> 
> ### * union.quad
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: union.quad
> ### Title: Union of Data and Dummy Points
> ### Aliases: union.quad
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(simdat)
>   Q <- quadscheme(simdat, default.dummy(simdat))
>   U <- union.quad(Q)
>   ## Not run: plot(U)
>   # equivalent:
>   U <- as.ppp(Q)
> 
> 
> 
> cleanEx(); ..nameEx <- "unmark"
> 
> ### * unmark
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: unmark
> ### Title: Remove Marks from a Marked Point Pattern
> ### Aliases: unmark
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(lansing)
>   hicks <- lansing[lansing$marks == "hickory", ]
>   ## Not run: 
> ##D   plot(hicks)  # still a marked point pattern, but only 1 value of marks
> ##D   plot(unmark(hicks)) # unmarked
> ##D   
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "update.ppm"
> 
> ### * update.ppm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: update.ppm
> ### Title: Update a Fitted Point Process Model
> ### Aliases: update.ppm
> ### Keywords: spatial
> 
> ### ** Examples
> 
>   data(nztrees)
>   data(cells)
> 
>   # fit the stationary Poisson process
>   fit <- ppm(nztrees, ~ 1)
> 
>   # fit a nonstationary Poisson process
>   fitP <- update(fit, trend=~x)
>   fitP <- update(fit, ~x)
> 
>   # fit a stationary Strauss process
>   fitS <- update(fit, interaction=Strauss(13))
>   fitS <- update(fit, Strauss(13))
> 
>   # oops, forgot the edge correction
>   fitS <- update(fitS, rbord=13)
> 
>   # re-fit the model to a subset
>   # of the original point pattern
>   nzw <- owin(c(0,148),c(0,95))
>   nzsub <- nztrees[,nzw]
>   fut <- update(fitS, Q=nzsub)
>   fut <- update(fitS, nzsub)
> 
>   # WARNING: the point pattern argument is called 'Q'
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  237.79 45.64 322.85 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')