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##
## hierstrhard.R
##
## $Revision: 1.6 $ $Date: 2022/03/07 02:07:02 $
##
## The hierarchical Strauss-hard core process
##
## -------------------------------------------------------------------
##
HierStraussHard <- local({
# ......... define interaction potential
HSHpotential <- function(d, tx, tu, par) {
# arguments:
# d[i,j] distance between points X[i] and U[j]
# tx[i] type (mark) of point X[i]
# tu[j] type (mark) of point U[j]
#
# get matrices of interaction radii
r <- par$iradii
h <- par$hradii
#
# get possible marks and validate
if(!is.factor(tx) || !is.factor(tu))
stop("marks of data and dummy points must be factor variables")
lx <- levels(tx)
lu <- levels(tu)
if(length(lx) != length(lu) || any(lx != lu))
stop("marks of data and dummy points do not have same possible levels")
if(!identical(lx, par$types))
stop("data and model do not have the same possible levels of marks")
if(!identical(lu, par$types))
stop("dummy points and model do not have the same possible levels of marks")
# ensure factor levels are acceptable for column names (etc)
lxname <- make.names(lx, unique=TRUE)
## list all ordered pairs of types to be checked
uptri <- par$archy$relation & !is.na(r)
mark1 <- (lx[row(r)])[uptri]
mark2 <- (lx[col(r)])[uptri]
## corresponding names
mark1name <- (lxname[row(r)])[uptri]
mark2name <- (lxname[col(r)])[uptri]
vname <- apply(cbind(mark1name,mark2name), 1, paste, collapse="x")
vname <- paste("mark", vname, sep="")
npairs <- length(vname)
## create logical array for result
z <- array(FALSE, dim=c(dim(d), npairs),
dimnames=list(character(0), character(0), vname))
# go....
if(length(z) > 0) {
## assemble the relevant interaction distance for each pair of points
rxu <- r[ tx, tu ]
## apply relevant threshold to each pair of points
str <- (d <= rxu)
# and the relevant hard core distance
hxu <- h[ tx, tu ]
forbid <- (d < hxu)
forbid[is.na(forbid)] <- FALSE
# form the potential
value <- str
value[forbid] <- -Inf
## score
for(i in 1:npairs) {
# data points with mark m1
Xsub <- (tx == mark1[i])
# quadrature points with mark m2
Qsub <- (tu == mark2[i])
# assign
z[Xsub, Qsub, i] <- value[Xsub, Qsub]
}
}
return(z)
}
#### end of 'pot' function ####
# ........ auxiliary functions ..............
delHSH <- function(which, types, iradii, hradii, archy, ihc) {
iradii[which] <- NA
if(any(!is.na(iradii))) {
# some gamma interactions left
# return modified HierStraussHard with fewer gamma parameters
return(HierStraussHard(types=types, iradii=iradii, hradii=hradii,
archy=archy))
} else if(any(!ihc)) {
# ihc = inactive hard cores
# no gamma interactions left, but some active hard cores
return(HierHard(types=types, hradii=hradii, archy=archy))
} else return(Poisson())
}
# Set up basic object except for family and parameters
BlankHSHobject <-
list(
name = "Hierarchical Strauss-hard core process",
creator = "HierStraussHard",
family = "hierpair.family", # evaluated later
pot = HSHpotential,
par = list(types=NULL, iradii=NULL, hradii=NULL, archy=NULL),
parnames = c("possible types",
"interaction distances",
"hardcore distances",
"hierarchical order"),
pardesc = c("vector of possible types",
"matrix of interaction distances",
"matrix of hardcore distances",
"hierarchical order"),
hasInf = TRUE,
selfstart = function(X, self) {
types <- self$par$types
hradii <- self$par$hradii
archy <- self$par$archy
if(!is.null(types) && !is.null(hradii) && !is.null(archy)) return(self)
if(is.null(types)) types <- levels(marks(X))
if(is.null(archy))
archy <- seq_len(length(types))
if(!inherits(archy, "hierarchicalordering"))
archy <- hierarchicalordering(archy, types)
if(is.null(hradii)) {
marx <- marks(X)
d <- nndist(X, by=marx)
h <- aggregate(d, by=list(from=marx), min)
h <- as.matrix(h[, -1L, drop=FALSE])
m <- table(marx)
mm <- outer(m, m, pmin)
hradii <- h * mm/(mm+1)
dimnames(hradii) <- list(types, types)
h[!(archy$relation)] <- NA
}
HierStraussHard(types=types,hradii=hradii,
iradii=self$par$iradii, archy=archy)
},
init = function(self) {
types <- self$par$types
iradii <- self$par$iradii
hradii <- self$par$hradii
## hradii could be NULL
if(!is.null(types)) {
if(!is.null(dim(types)))
stop(paste("The", sQuote("types"),
"argument should be a vector"))
if(length(types) == 0)
stop(paste("The", sQuote("types"),"argument should be",
"either NULL or a vector of all possible types"))
if(anyNA(types))
stop("NA's not allowed in types")
if(is.factor(types)) {
types <- levels(types)
} else {
types <- levels(factor(types, levels=types))
}
nt <- length(types)
MultiPair.checkmatrix(iradii, nt, sQuote("iradii"), asymmok=TRUE)
if(!is.null(hradii))
MultiPair.checkmatrix(hradii, nt, sQuote("hradii"), asymmok=TRUE)
}
ina <- is.na(iradii)
if(all(ina))
stop(paste("All entries of", sQuote("iradii"), "are NA"))
if(!is.null(hradii)) {
hna <- is.na(hradii)
both <- !ina & !hna
if(any(iradii[both] <= hradii[both]))
stop("iradii must be larger than hradii")
}
},
update = NULL, # default OK
print = function(self) {
iradii <- self$par$iradii
hradii <- self$par$hradii
types <- self$par$types
archy <- self$par$archy
if(waxlyrical('gory'))
splat(nrow(iradii), "types of points")
if(!is.null(types) && !is.null(archy)) {
if(waxlyrical('space')) {
splat("Possible types and ordering:")
} else cat("Hierarchy: ")
print(archy)
} else if(!is.null(types)) {
(if(waxlyrical('space')) splat else cat)("Possible types: ")
print(types)
} else if(waxlyrical('gory'))
splat("Possible types:\t not yet determined")
splat("Interaction radii:")
dig <- getOption("digits")
print(hiermat(signif(iradii, dig), archy))
if(!is.null(hradii)) {
splat("Hardcore radii:")
print(hiermat(signif(hradii, dig), archy))
} else splat("Hardcore radii: not yet determined")
invisible(NULL)
},
interpret = function(coeffs, self) {
# get possible types
typ <- self$par$types
ntypes <- length(typ)
## get matrices of interaction radii
r <- self$par$iradii
h <- self$par$hradii
## list all unordered pairs of types
uptri <- self$par$archy$relation & !is.na(r)
index1 <- (row(r))[uptri]
index2 <- (col(r))[uptri]
npairs <- length(index1)
# extract canonical parameters; shape them into a matrix
gammas <- matrix(NA, ntypes, ntypes)
dimnames(gammas) <- list(typ, typ)
gammas[ cbind(index1, index2) ] <- exp(coeffs)
#
return(list(param=list(gammas=gammas),
inames="interaction parameters gamma_ij",
printable=hiermat(dround(gammas), self$par$archy)))
},
valid = function(coeffs, self) {
# interaction radii r[i,j]
iradii <- self$par$iradii
# hard core radii r[i,j]
hradii <- self$par$hradii
# interaction parameters gamma[i,j]
gamma <- (self$interpret)(coeffs, self)$param$gammas
# parameters to estimate
required <- !is.na(iradii) & self$par$archy$relation
# all required parameters must be finite
if(!all(is.finite(gamma[required]))) return(FALSE)
# DIAGONAL interactions must be non-explosive
d <- diag(rep(TRUE, nrow(iradii)))
activehard <- !is.na(hradii) & (hradii > 0)
return(all(gamma[required & d & !activehard] <= 1))
},
project = function(coeffs, self) {
# interaction parameters gamma[i,j]
gamma <- (self$interpret)(coeffs, self)$param$gammas
# interaction radii
iradii <- self$par$iradii
# hard core radii r[i,j]
hradii <- self$par$hradii
types <- self$par$types
archy <- self$par$archy
# active hard cores
activehard <- !is.na(hradii) & (hradii > 0)
ihc <- !activehard
# problems?
uptri <- archy$relation
required <- !is.na(iradii) & uptri
offdiag <- !diag(nrow(iradii))
gammavalid <- is.finite(gamma) & (activehard | offdiag | (gamma <= 1))
naughty <- required & !gammavalid
#
if(!any(naughty))
return(NULL)
if(spatstat.options("project.fast")) {
# remove ALL naughty terms simultaneously
return(delHSH(naughty, types, iradii, hradii, archy, ihc))
} else {
# present a list of candidates
rn <- row(naughty)
cn <- col(naughty)
ord <- self$par$archy$ordering
uptri <- (ord[rn] <= ord[cn])
upn <- uptri & naughty
rowidx <- as.vector(rn[upn])
colidx <- as.vector(cn[upn])
mats <- lapply(as.data.frame(rbind(rowidx, colidx)),
matrix, ncol=2)
inters <- lapply(mats, delHSH, types=types,
iradii=iradii, hradii=hradii,
archy=archy, ihc=ihc)
return(inters)
}
},
irange = function(self, coeffs=NA, epsilon=0, ...) {
r <- self$par$iradii
h <- self$par$hradii
ractive <- !is.na(r) & self$par$archy$relation
hactive <- !is.na(h) & self$par$archy$relation
if(any(!is.na(coeffs))) {
gamma <- (self$interpret)(coeffs, self)$param$gammas
gamma[is.na(gamma)] <- 1
ractive <- ractive & (abs(log(gamma)) > epsilon)
}
if(!any(c(ractive,hactive)))
return(0)
else
return(max(c(r[ractive],h[hactive])))
},
hardcore = function(self, coeffs=NA, epsilon=0, ...) {
h <- self$par$hradii
active <- !is.na(h) & self$par$archy$relation
h[!active] <- 0
return(h)
},
version=NULL # to be added
)
class(BlankHSHobject) <- "interact"
# finally create main function
HierStraussHard <- function(iradii, hradii=NULL, types=NULL, archy=NULL) {
if(!is.null(types)) {
if(is.null(archy)) archy <- seq_len(length(types))
archy <- hierarchicalordering(archy, types)
}
iradii[iradii == 0] <- NA
out <- instantiate.interact(BlankHSHobject,
list(types=types,
iradii=iradii,
hradii=hradii,
archy=archy))
if(!is.null(types)) {
dn <- list(types, types)
dimnames(out$par$iradii) <- dn
if(!is.null(out$par$hradii)) dimnames(out$par$hradii) <- dn
}
return(out)
}
HierStraussHard <- intermaker(HierStraussHard, BlankHSHobject)
HierStraussHard
})
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