# R/connectivity-function.R In SGCS: Spatial Graph Based Clustering Summaries for Spatial Point Patterns

#### Documented in confun

```#' Connectivity function and cumulative connectivity function.
#'
#' Amount of network connected pairs as a function of distance.
#'
#' @param x Point pattern
#' @param r Vector of distances to estimate the function
#' @param R The radius for generating the network, as geometric graph.
#' @param h Smoothing parameter. h=0 and h>0 mean different things, see Details.
#' @param preGraph Precomputed network/graph, as a spatgraph-object. Alternative to R.
#' @param ... ignored.
#'
#' @details
#' If h=0 we compute the cumulative version of the connecitivity function,
#' corresponding to Ripley's K-function under the condition that the points
#' in each pair must belong to the same component in an underlying network.
#'
#' The underlying network can be given, or it will be computed as a geometric graph with
#' parameter 'R'. If given as 'preGraph', it must be a \pkg{spatgraphs}-object, with same
#' dimensions as the point pattern.
#'
#' If h>0: Compute the probability of a pair being in the same component given their distance is ~ r.
#' Uses kernel smoothing with bandwidth h.
#'
#' Sensible defaults are computed for h and R if not given.
#'
#' Border correction is done via translation correction. The bias is unknown as the network censoring
#' is quite complex.
#'
#' Theoretical values are unknown due to the graph conditioning.
#'
#' @return
#' fv-object, see \link{spatstat} for more. Theoretical values unknown.
#'
#' @examples
#' \dontrun{
#' x <- rMatClust(10, 0.1, 10)
#' plot(Cx<-confun(x,h=0, R=0.1))
#'
#' # fit wrong model
#' ftho <- thomas.estpcf(x)
#' yf <- function()rThomas(ftho\$par[1], ftho\$par[2], x\$n/ftho\$par[1])
#' CC <- envelope(x, fun=confun, h=0, sim=yf, R=0.1)
#' C <- envelope(x, fun=confun, sim=yf, R=0.1)
#'
#' plot(CC)
#' plot(C)
#' }
#'
#' @useDynLib SGCS
#' @import spatstat
#' @export

confun <- function(x, r, R, h, adjust=1, preGraph=NULL, ...) {
### prepare data
x <- internalise_pp(x)
### default range for generating the component network
if(missing(R)) R <- 1/(x\$n/x\$area)^(1/x\$dim)
### default smoothing
if(missing(h)) h <- 0.15*R
### range
r <- default_r(x, r)

### Translation weights for correction
x\$weights <- translation_weights(x)
### Distances for speed
x\$pairwise_distances <- pairwise_distances(x)

### check preGraph
if(!is.null(preGraph)) if(class(preGraph) != "sg") stop("preGraph is not of class 'sg' (see package 'spatgraphs')")
### Compute:
res <- .External("SGCS_confun_c",
x,
r,
c(R,h), # function parameters
preGraph,
PACKAGE="SGCS"
)

# scale if needed
cumu <- NULL
if(h==0){
res <- res / (x\$n/x\$area)^2
cumu <- "Cumulative"
}
# paramaeters
pars <- paste0("(", ifelse(h==0, "", paste0("h=",h, ", ")), "R=", R, ")")

# make fv suitable
C.final<-fv( data.frame(r=r, C=res),
argu = "r",
alim = range(r),
ylab = substitute(C(r), NULL),
desc = c("distance argument r", paste(cumu, "Connectivity Function", pars)),
valu = "C",
fmla = ".~r",
fname="C"
)

C.final
}
```

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SGCS documentation built on May 29, 2017, 12:59 p.m.