PUcopulaSynth: end-to-end workflow
Overview
PUcopulaFit provides a compact pipeline to:
preprocess a data frame (factor handling and dummy encoding),
fit a Partition-of-Unity (PU) copula dependence model,
estimate marginal distributions (logspline or empirical),
generate synthetic data, and
restore original factor structure.
No DataSHIELD and no Python dependencies.
Installation
A tiny example
We’ll create a small toy dataset with mixed types.
set.seed(1)
toy <- data.frame(
x = rnorm(200),
y = rpois(200, 2),
z = factor(sample(c("a","b","c"), 200, TRUE)),
w = ordered(sample(1:4, 200, TRUE))
)
str(toy)
#> 'data.frame': 200 obs. of 4 variables:
#> $ x: num -0.626 0.184 -0.836 1.595 0.33 ...
#> $ y: int 2 1 5 4 4 3 1 3 0 4 ...
#> $ z: Factor w/ 3 levels "a","b","c": 3 1 2 1 1 3 2 2 2 1 ...
#> $ w: Ord.factor w/ 4 levels "1"<"2"<"3"<"4": 1 2 3 4 3 2 1 4 4 4 ...1) Preprocess
Multi-level unordered factors become dummy variables (tagged with
.cat.).Multi-level ordered factors may become
.lev..Remaining factor columns are kept and renamed with
.oriname; their levels are recorded.
library(PUcopulaSynth)
pre <- preprocessData(toy)
names(pre$data)[1:6]
#> [1] "x.oriname" "y.oriname" "z.cat.1" "z.cat.2" "w.lev..L" "w.lev..Q"
str(pre$original_levels)
#> List of 2
#> $ dummies:List of 2
#> ..$ z.cat.: chr [1:3] "a" "b" "c"
#> ..$ w.lev.: chr [1:4] "1" "2" "3" "4"
#> $ oriname: list()2) Fit the PU copula
You can control:
driver_strength_factor(row-based scale for driver strength; scalar or per-variable),bin_size(rank-binning smoothness; scalar, vector or named list),jitter(FALSE, single numeric, or named list), andfamily(e.g."binom"or"nbinom").
cop <- fitPUcopula(
data = pre$data,
driver_strength_factor = 0.5,
bin_size = 3,
jitter = FALSE,
family = "binom"
)
cop
#> An object of class "PUCopula"
#> Slot "dim":
#> [1] 7
#>
#> Slot "family":
#> [1] "binom"
#>
#> Slot "par.factor":
#> [1] 1
#>
#> Slot "pars.a":
#> [1] 100 100 100 100 100 100 100
#>
#> Slot "patchpar":
#> [[1]]
#> NULL
#>
#>
#> Slot "p":
#> <0 x 0 matrix>
#>
#> Slot "phi":
#> function (u, s)
#> {
#> if (s%%1 != 0) {
#> warning(paste("non-integer value for s =", s))
#> return(rep(0, length(u)))
#> }
#> else dbinom(x = s, size = par.a - 1, prob = u)
#> }
#> <bytecode: 0x556c4aca1678>
#> <environment: 0x556c53746fc0>
#>
#> Slot "psy":
#> function (u, s)
#> {
#> if (s%%1 != 0) {
#> warning(paste("non-integer value for s =", s))
#> return(rep(0, length(u)))
#> }
#> else dbinom(x = s, size = par.a - 1, prob = u)
#> }
#> <bytecode: 0x556c4aca1678>
#> <environment: 0x556c53744af0>
#>
#> Slot "phis":
#> [[1]]
#> function (u, s)
#> {
#> if (s%%1 != 0) {
#> warning(paste("non-integer value for s =", s))
#> return(rep(0, length(u)))
#> }
#> else dbinom(x = s, size = par.a - 1, prob = u)
#> }
#> <environment: 0x556c4c51bb58>
#>
#> [[2]]
#> function (u, s)
#> {
#> if (s%%1 != 0) {
#> warning(paste("non-integer value for s =", s))
#> return(rep(0, length(u)))
#> }
#> else dbinom(x = s, size = par.a - 1, prob = u)
#> }
#> <bytecode: 0x556c4aca1678>
#> <environment: 0x556c4c51c488>
#>
#> [[3]]
#> function (u, s)
#> {
#> if (s%%1 != 0) {
#> warning(paste("non-integer value for s =", s))
#> return(rep(0, length(u)))
#> }
#> else dbinom(x = s, size = par.a - 1, prob = u)
#> }
#> <bytecode: 0x556c4aca1678>
#> <environment: 0x556c53744060>
#>
#> [[4]]
#> function (u, s)
#> {
#> if (s%%1 != 0) {
#> warning(paste("non-integer value for s =", s))
#> return(rep(0, length(u)))
#> }
#> else dbinom(x = s, size = par.a - 1, prob = u)
#> }
#> <bytecode: 0x556c4aca1678>
#> <environment: 0x556c53743960>
#>
#> [[5]]
#> function (u, s)
#> {
#> if (s%%1 != 0) {
#> warning(paste("non-integer value for s =", s))
#> return(rep(0, length(u)))
#> }
#> else dbinom(x = s, size = par.a - 1, prob = u)
#> }
#> <bytecode: 0x556c4aca1678>
#> <environment: 0x556c53743110>
#>
#> [[6]]
#> function (u, s)
#> {
#> if (s%%1 != 0) {
#> warning(paste("non-integer value for s =", s))
#> return(rep(0, length(u)))
#> }
#> else dbinom(x = s, size = par.a - 1, prob = u)
#> }
#> <bytecode: 0x556c4aca1678>
#> <environment: 0x556c53742a10>
#>
#> [[7]]
#> function (u, s)
#> {
#> if (s%%1 != 0) {
#> warning(paste("non-integer value for s =", s))
#> return(rep(0, length(u)))
#> }
#> else dbinom(x = s, size = par.a - 1, prob = u)
#> }
#> <bytecode: 0x556c4aca1678>
#> <environment: 0x556c53746140>
#>
#>
#> Slot "continuous":
#> [1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>
#> Slot "alph":
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c537523f0>
#>
#> Slot "beta":
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c53761b28>
#>
#> Slot "alphs":
#> [[1]]
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c53773da8>
#>
#> [[2]]
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c5377a198>
#>
#> [[3]]
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c53782550>
#>
#> [[4]]
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c53786a30>
#>
#> [[5]]
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c53794ac8>
#>
#> [[6]]
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c537cb430>
#>
#> [[7]]
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c537da538>
#>
#>
#> Slot "alphsCDF":
#> [[1]]
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c537e3f88>
#>
#> [[2]]
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c537ea420>
#>
#> [[3]]
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c537eca50>
#>
#> [[4]]
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c53810ca0>
#>
#> [[5]]
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c53817090>
#>
#> [[6]]
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c5381d4b8>
#>
#> [[7]]
#> function (s)
#> {
#> args <- lapply(as.list(match.call())[-1L], eval, parent.frame())
#> names <- names(args) %||% character(length(args))
#> dovec <- names %in% vectorize.args
#> do.call("mapply", c(FUN = FUN, args[dovec], MoreArgs = list(args[!dovec]),
#> SIMPLIFY = SIMPLIFY, USE.NAMES = USE.NAMES))
#> }
#> <environment: 0x556c53821a40>
#>
#>
#> Slot "opstart":
#> [[1]]
#> NULL
#>
#>
#> Slot "cdflim":
#> [[1]]
#> NULL
#>
#>
#> Slot "cdfdom":
#> [[1]]
#> NULL
#>
#>
#> Slot "alphsquantf":
#> [[1]]
#> NULL
#>
#>
#> Slot "cdfappx":
#> [[1]]
#> NULL
#>
#>
#> Slot "alphsobjective":
#> [[1]]
#> NULL
#>
#>
#> Slot "alphsquant":
#> [[1]]
#> NULL
#>
#>
#> Slot "fdens":
#> function (u, s)
#> return(.Object@phi(u, s)/.Object@alph(s))
#> <environment: 0x556c4cb38f20>
#>
#> Slot "gdens":
#> function (u, s)
#> {
#> .Object@psy(u, s)/.Object@beta(s)
#> }
#> <environment: 0x556c4cb38f20>
#>
#> Slot "fdenss":
#> [[1]]
#> function (u, s, log = FALSE)
#> {
#> if (log == FALSE) {
#> phis[[i]](u, s)/alphs[[i]](s)
#> }
#> else {
#> log(phis[[i]](u, s)/alphs[[i]](s))
#> }
#> }
#> <environment: 0x556c53836b88>
#>
#> [[2]]
#> function (u, s, log = FALSE)
#> {
#> if (log == FALSE) {
#> phis[[i]](u, s)/alphs[[i]](s)
#> }
#> else {
#> log(phis[[i]](u, s)/alphs[[i]](s))
#> }
#> }
#> <environment: 0x556c538368b0>
#>
#> [[3]]
#> function (u, s, log = FALSE)
#> {
#> if (log == FALSE) {
#> phis[[i]](u, s)/alphs[[i]](s)
#> }
#> else {
#> log(phis[[i]](u, s)/alphs[[i]](s))
#> }
#> }
#> <environment: 0x556c538365d8>
#>
#> [[4]]
#> function (u, s, log = FALSE)
#> {
#> if (log == FALSE) {
#> phis[[i]](u, s)/alphs[[i]](s)
#> }
#> else {
#> log(phis[[i]](u, s)/alphs[[i]](s))
#> }
#> }
#> <environment: 0x556c53836300>
#>
#> [[5]]
#> function (u, s, log = FALSE)
#> {
#> if (log == FALSE) {
#> phis[[i]](u, s)/alphs[[i]](s)
#> }
#> else {
#> log(phis[[i]](u, s)/alphs[[i]](s))
#> }
#> }
#> <environment: 0x556c53836028>
#>
#> [[6]]
#> function (u, s, log = FALSE)
#> {
#> if (log == FALSE) {
#> phis[[i]](u, s)/alphs[[i]](s)
#> }
#> else {
#> log(phis[[i]](u, s)/alphs[[i]](s))
#> }
#> }
#> <environment: 0x556c53835d50>
#>
#> [[7]]
#> function (u, s, log = FALSE)
#> {
#> if (log == FALSE) {
#> phis[[i]](u, s)/alphs[[i]](s)
#> }
#> else {
#> log(phis[[i]](u, s)/alphs[[i]](s))
#> }
#> }
#> <environment: 0x556c53835a78>
#>
#>
#> Slot "cpatch":
#> function (s, t)
#> {
#> copula::dCopula(u = c(s, t), copula = copula::normalCopula(0.8,
#> dim = 2))
#> }
#> <environment: 0x556c4cb38f20>
#>
#> Slot "PUdens":
#> function (u, v)
#> {
#> integrate(function(t) {
#> sapply(t, function(t) {
#> integrate(function(s) {
#> sapply(s, function(s) return(.Object@cpatch(.Object@alph(s),
#> .Object@beta(t)) * .Object@phi(u, s) * .Object@psy(v,
#> t)))
#> }, 0, 100, rel.tol = 1e-07)$value
#> })
#> }, 0, 100, rel.tol = 1e-04)
#> }
#> <environment: 0x556c4cb38f20>
#>
#> Slot "fq":
#> function ()
#> NULL
#> <bytecode: 0x556c4fb32d38>
#>
#> Slot "gq":
#> function ()
#> NULL
#> <bytecode: 0x556c4fb32e88>
#>
#> Slot "patch":
#> [1] "rook"
#>
#> Slot "dPWork":
#> function (u, v)
#> {
#> n <- dim(.Object@data)[1]
#> getpatch <- (u <= (.Object@ranks[, 1]/n)) * (u > ((.Object@ranks[,
#> 1] - 1)/n)) * (v <= (.Object@ranks[, 2]/n)) * (v > ((.Object@ranks[,
#> 2] - 1)/n))
#> k <- which(getpatch == 1)
#> if (length(k) == 0)
#> return(0)
#> else {
#> return(copula::dCopula(c(n * u - .Object@ranks[k, 1] +
#> 1, n * v - .Object@ranks[k, 2] + 1), copula::normalCopula(0.8,
#> dim = 2)))
#> }
#> }
#> <environment: 0x556c4cb38f20>
#>
#> Slot "data":
#> x.oriname y.oriname z.cat.1 z.cat.2 w.lev..L w.lev..Q w.lev..C
#> [1,] 47.0 103.5000 31.5 31.50000 27.00000 124 69.00000
#> [2,] 117.0 27.5000 120.5 53.16667 45.00000 49 173.00000
#> [3,] 32.0 192.0000 53.5 165.50000 97.16667 49 21.50000
#> [4,] 189.0 178.5000 166.5 96.50000 144.83333 124 86.16667
#> [5,] 123.0 178.5000 166.5 96.50000 129.50000 49 21.50000
#> [6,] 32.0 134.8333 31.5 31.50000 81.00000 49 173.00000
#> [7,] 141.0 52.5000 97.5 165.50000 27.00000 124 69.00000
#> [8,] 156.0 134.8333 97.5 165.50000 175.50000 149 120.50000
#> [9,] 147.0 15.0000 97.5 165.50000 175.50000 149 120.50000
#> [10,] 74.0 178.5000 166.5 96.50000 175.50000 149 120.50000
#> [11,] 189.0 198.5000 31.5 31.50000 27.00000 149 69.00000
#> [12,] 132.0 52.5000 31.5 31.50000 27.00000 149 69.00000
#> [13,] 47.0 150.5000 31.5 31.50000 175.50000 149 120.50000
#> [14,] 2.0 150.5000 97.5 165.50000 175.50000 149 120.50000
#> [15,] 174.0 150.5000 97.5 165.50000 81.00000 49 173.00000
#> [16,] 102.0 103.5000 97.5 165.50000 27.00000 149 69.00000
#> [17,] 105.0 103.5000 166.5 96.50000 175.50000 149 120.50000
#> [18,] 168.0 52.5000 31.5 31.50000 129.50000 49 21.50000
#> [19,] 162.0 150.5000 31.5 31.50000 81.00000 49 173.00000
#> [20,] 147.0 150.5000 166.5 96.50000 81.00000 49 173.00000
#> [21,] 168.0 103.5000 31.5 31.50000 129.50000 49 21.50000
#> [22,] 159.0 103.5000 31.5 31.50000 129.50000 49 21.50000
#> [23,] 114.0 103.5000 166.5 96.50000 129.50000 49 21.50000
#> [24,] 2.0 52.5000 97.5 165.50000 129.50000 49 21.50000
#> [25,] 150.0 52.5000 166.5 96.50000 27.00000 149 69.00000
#> [26,] 98.5 52.5000 97.5 165.50000 27.00000 149 69.00000
#> [27,] 89.0 15.0000 31.5 31.50000 175.50000 149 120.50000
#> [28,] 11.0 178.5000 31.5 31.50000 175.50000 149 120.50000
#> [29,] 59.0 150.5000 97.5 165.50000 27.00000 149 69.00000
#> [30,] 135.0 178.5000 97.5 165.50000 81.00000 49 173.00000
#> [31,] 183.0 178.5000 97.5 165.50000 81.00000 49 173.00000
#> [32,] 92.0 15.0000 166.5 96.50000 175.50000 149 120.50000
#> [33,] 129.0 52.5000 97.5 165.50000 129.50000 49 21.50000
#> [34,] 98.5 103.5000 166.5 96.50000 175.50000 149 120.50000
#> [35,] 14.0 15.0000 166.5 96.50000 175.50000 149 120.50000
#> [36,] 65.0 150.5000 97.5 165.50000 27.00000 149 69.00000
#> [37,] 65.0 150.5000 97.5 165.50000 175.50000 149 120.50000
#> [38,] 98.5 15.0000 97.5 165.50000 175.50000 149 120.50000
#> [39,] 174.0 103.5000 31.5 31.50000 81.00000 49 173.00000
#> [40,] 159.0 178.5000 166.5 96.50000 81.00000 49 173.00000
#> [41,] 86.0 15.0000 31.5 31.50000 81.00000 49 173.00000
#> [42,] 80.0 52.5000 97.5 165.50000 175.50000 149 120.50000
#> [43,] 153.0 103.5000 31.5 31.50000 129.50000 49 21.50000
#> [44,] 144.0 103.5000 31.5 31.50000 27.00000 149 69.00000
#> [45,] 41.0 52.5000 31.5 31.50000 175.50000 149 120.50000
#> [46,] 38.0 103.5000 97.5 165.50000 175.50000 149 120.50000
#> [47,] 126.0 52.5000 97.5 165.50000 175.50000 149 120.50000
#> [48,] 159.0 178.5000 166.5 96.50000 27.00000 149 69.00000
#> [49,] 92.0 15.0000 31.5 31.50000 81.00000 49 173.00000
#> [50,] 165.0 15.0000 97.5 165.50000 27.00000 149 69.00000
#> [51,] 132.0 192.0000 31.5 31.50000 175.50000 149 120.50000
#> [52,] 50.0 103.5000 166.5 96.50000 81.00000 49 173.00000
#> [53,] 126.0 52.5000 97.5 165.50000 129.50000 49 21.50000
#> [54,] 23.0 52.5000 97.5 165.50000 27.00000 149 69.00000
#> [55,] 183.0 15.0000 31.5 31.50000 175.50000 149 120.50000
#> [56,] 195.0 103.5000 166.5 96.50000 81.00000 49 173.00000
#> [57,] 68.0 103.5000 97.5 165.50000 27.00000 149 69.00000
#> [58,] 26.0 198.5000 166.5 96.50000 81.00000 49 173.00000
#> [59,] 147.0 103.5000 166.5 96.50000 27.00000 149 69.00000
#> [60,] 92.0 15.0000 97.5 165.50000 27.00000 149 69.00000
#> [61,] 198.5 52.5000 31.5 31.50000 129.50000 49 21.50000
#> [62,] 102.0 103.5000 97.5 165.50000 175.50000 149 120.50000
#> [63,] 153.0 15.0000 166.5 96.50000 27.00000 149 69.00000
#> [64,] 108.0 103.5000 31.5 31.50000 129.50000 49 21.50000
#> [65,] 35.0 52.5000 166.5 96.50000 81.00000 49 173.00000
#> [66,] 117.0 178.5000 31.5 31.50000 27.00000 149 69.00000
#> [67,] 5.0 150.5000 97.5 165.50000 129.50000 49 21.50000
#> [68,] 186.0 52.5000 31.5 31.50000 81.00000 49 173.00000
#> [69,] 114.0 103.5000 31.5 31.50000 81.00000 49 173.00000
#> [70,] 198.5 150.5000 166.5 96.50000 175.50000 149 120.50000
#> [71,] 138.0 103.5000 97.5 165.50000 81.00000 49 173.00000
#> [72,] 38.0 192.0000 31.5 31.50000 129.50000 49 21.50000
#> [73,] 150.0 150.5000 31.5 31.50000 81.00000 49 173.00000
#> [74,] 29.0 52.5000 97.5 165.50000 129.50000 49 21.50000
#> [75,] 17.0 15.0000 166.5 96.50000 175.50000 149 120.50000
#> [76,] 123.0 52.5000 166.5 96.50000 27.00000 149 69.00000
#> [77,] 62.0 178.5000 31.5 31.50000 81.00000 49 173.00000
#> [78,] 108.0 103.5000 166.5 96.50000 129.50000 49 21.50000
#> [79,] 111.0 103.5000 97.5 165.50000 81.00000 49 173.00000
#> [80,] 53.0 150.5000 166.5 96.50000 27.00000 149 69.00000
#> [81,] 56.0 150.5000 166.5 96.50000 27.00000 149 69.00000
#> [82,] 89.0 52.5000 31.5 31.50000 81.00000 49 173.00000
#> [83,] 177.0 150.5000 31.5 31.50000 27.00000 149 69.00000
#> [84,] 8.0 178.5000 97.5 165.50000 81.00000 49 173.00000
#> [85,] 150.0 103.5000 31.5 31.50000 175.50000 149 120.50000
#> [86,] 126.0 103.5000 97.5 165.50000 27.00000 149 69.00000
#> [87,] 174.0 52.5000 166.5 96.50000 81.00000 49 173.00000
#> [88,] 74.0 15.0000 97.5 165.50000 81.00000 49 173.00000
#> [89,] 129.0 178.5000 97.5 165.50000 129.50000 49 21.50000
#> [90,] 120.0 15.0000 166.5 96.50000 81.00000 49 173.00000
#> [91,] 56.0 15.0000 31.5 31.50000 27.00000 149 69.00000
#> [92,] 180.0 178.5000 31.5 31.50000 129.50000 49 21.50000
#> [93,] 177.0 52.5000 97.5 165.50000 175.50000 149 120.50000
#> [94,] 153.0 52.5000 166.5 96.50000 81.00000 49 173.00000
#> [95,] 189.0 52.5000 166.5 96.50000 81.00000 49 173.00000
#> [96,] 144.0 103.5000 166.5 96.50000 175.50000 149 120.50000
#> [97,] 17.0 103.5000 166.5 96.50000 129.50000 49 21.50000
#> [98,] 53.0 103.5000 97.5 165.50000 27.00000 149 69.00000
#> [99,] 20.0 150.5000 97.5 165.50000 27.00000 149 69.00000
#> [100,] 59.0 15.0000 31.5 31.50000 175.50000 149 120.50000
#> [101,] 50.0 103.5000 31.5 31.50000 81.00000 49 173.00000
#> [102,] 111.0 150.5000 31.5 31.50000 81.00000 49 173.00000
#> [103,] 32.0 103.5000 97.5 165.50000 175.50000 149 120.50000
#> [104,] 117.0 103.5000 166.5 96.50000 175.50000 149 120.50000
#> [105,] 41.0 103.5000 31.5 31.50000 175.50000 149 120.50000
#> [106,] 192.0 192.0000 31.5 31.50000 81.00000 49 173.00000
#> [107,] 156.0 52.5000 97.5 165.50000 27.00000 149 69.00000
#> [108,] 165.0 150.5000 166.5 96.50000 27.00000 149 69.00000
#> [109,] 129.0 150.5000 166.5 96.50000 81.00000 49 173.00000
#> [110,] 192.0 103.5000 97.5 165.50000 81.00000 49 173.00000
#> [111,] 44.0 178.5000 31.5 31.50000 175.50000 149 120.50000
#> [112,] 62.0 103.5000 97.5 165.50000 27.00000 149 69.00000
#> [113,] 183.0 15.0000 97.5 165.50000 175.50000 149 120.50000
#> [114,] 44.0 150.5000 31.5 31.50000 129.50000 49 21.50000
#> [115,] 83.0 150.5000 97.5 165.50000 175.50000 149 120.50000
#> [116,] 68.0 52.5000 31.5 31.50000 27.00000 149 69.00000
#> [117,] 71.0 103.5000 31.5 31.50000 81.00000 49 173.00000
#> [118,] 77.0 103.5000 166.5 96.50000 129.50000 49 21.50000
#> [119,] 141.0 52.5000 31.5 31.50000 27.00000 149 69.00000
#> [120,] 83.0 103.5000 97.5 165.50000 129.50000 49 21.50000
#> [121,] 59.0 150.5000 97.5 165.50000 129.50000 49 21.50000
#> [122,] 180.0 150.5000 31.5 31.50000 175.50000 149 120.50000
#> [123,] 80.0 52.5000 31.5 31.50000 27.00000 149 69.00000
#> [124,] 83.0 15.0000 97.5 165.50000 27.00000 149 69.00000
#> [125,] 95.0 52.5000 166.5 96.50000 27.00000 149 69.00000
#> [126,] 156.0 178.5000 166.5 96.50000 27.00000 149 69.00000
#> [127,] 95.0 150.5000 97.5 165.50000 129.50000 49 21.50000
#> [128,] 102.0 150.5000 166.5 96.50000 27.00000 149 69.00000
#> [129,] 41.0 192.0000 97.5 165.50000 129.50000 49 21.50000
#> [130,] 71.0 198.5000 166.5 96.50000 81.00000 49 173.00000
#> [131,] 111.0 103.5000 166.5 96.50000 129.50000 49 21.50000
#> [132,] 53.0 15.0000 166.5 96.50000 129.50000 49 21.50000
#> [133,] 144.0 52.5000 31.5 31.50000 129.50000 49 21.50000
#> [134,] 8.0 52.5000 97.5 165.50000 175.50000 149 120.50000
#> [135,] 123.0 15.0000 166.5 96.50000 175.50000 149 120.50000
#> [136,] 8.0 15.0000 97.5 165.50000 129.50000 49 21.50000
#> [137,] 77.0 52.5000 166.5 96.50000 129.50000 49 21.50000
#> [138,] 56.0 52.5000 31.5 31.50000 27.00000 149 69.00000
#> [139,] 44.0 52.5000 166.5 96.50000 129.50000 49 21.50000
#> [140,] 98.5 103.5000 97.5 165.50000 175.50000 149 120.50000
#> [141,] 2.0 52.5000 166.5 96.50000 175.50000 149 120.50000
#> [142,] 177.0 192.0000 166.5 96.50000 27.00000 149 69.00000
#> [143,] 5.0 103.5000 31.5 31.50000 81.00000 49 173.00000
#> [144,] 62.0 52.5000 97.5 165.50000 27.00000 149 69.00000
#> [145,] 23.0 52.5000 166.5 96.50000 175.50000 149 120.50000
#> [146,] 35.0 15.0000 166.5 96.50000 81.00000 49 173.00000
#> [147,] 195.0 198.5000 31.5 31.50000 81.00000 49 173.00000
#> [148,] 108.0 52.5000 166.5 96.50000 81.00000 49 173.00000
#> [149,] 17.0 103.5000 166.5 96.50000 81.00000 49 173.00000
#> [150,] 5.0 150.5000 97.5 165.50000 81.00000 49 173.00000
#> [151,] 138.0 178.5000 166.5 96.50000 129.50000 49 21.50000
#> [152,] 105.0 103.5000 97.5 165.50000 81.00000 49 173.00000
#> [153,] 74.0 15.0000 31.5 31.50000 129.50000 49 21.50000
#> [154,] 29.0 178.5000 166.5 96.50000 175.50000 149 120.50000
#> [155,] 11.0 150.5000 166.5 96.50000 81.00000 49 173.00000
#> [156,] 23.0 52.5000 31.5 31.50000 129.50000 49 21.50000
#> [157,] 171.0 15.0000 166.5 96.50000 27.00000 149 69.00000
#> [158,] 47.0 15.0000 31.5 31.50000 81.00000 49 173.00000
#> [159,] 14.0 150.5000 166.5 96.50000 129.50000 49 21.50000
#> [160,] 192.0 150.5000 31.5 31.50000 81.00000 49 173.00000
#> [161,] 135.0 103.5000 166.5 96.50000 129.50000 49 21.50000
#> [162,] 80.0 15.0000 166.5 96.50000 27.00000 149 69.00000
#> [163,] 171.0 52.5000 166.5 96.50000 175.50000 149 120.50000
#> [164,] 165.0 150.5000 166.5 96.50000 129.50000 49 21.50000
#> [165,] 50.0 178.5000 97.5 165.50000 81.00000 49 173.00000
#> [166,] 198.5 150.5000 166.5 96.50000 27.00000 149 69.00000
#> [167,] 77.0 52.5000 97.5 165.50000 27.00000 149 69.00000
#> [168,] 14.0 103.5000 97.5 165.50000 81.00000 49 173.00000
#> [169,] 89.0 52.5000 31.5 31.50000 27.00000 149 69.00000
#> [170,] 120.0 192.0000 97.5 165.50000 27.00000 149 69.00000
#> [171,] 198.5 52.5000 31.5 31.50000 81.00000 49 173.00000
#> [172,] 114.0 103.5000 97.5 165.50000 27.00000 149 69.00000
#> [173,] 138.0 52.5000 97.5 165.50000 81.00000 49 173.00000
#> [174,] 95.0 15.0000 97.5 165.50000 175.50000 149 120.50000
#> [175,] 71.0 150.5000 31.5 31.50000 81.00000 49 173.00000
#> [176,] 105.0 103.5000 97.5 165.50000 81.00000 49 173.00000
#> [177,] 162.0 103.5000 97.5 165.50000 175.50000 149 120.50000
#> [178,] 195.0 103.5000 166.5 96.50000 27.00000 149 69.00000
#> [179,] 171.0 150.5000 31.5 31.50000 27.00000 149 69.00000
#> [180,] 180.0 150.5000 97.5 165.50000 175.50000 149 120.50000
#> [181,] 20.0 52.5000 31.5 31.50000 81.00000 49 173.00000
#> [182,] 168.0 192.0000 166.5 96.50000 27.00000 149 69.00000
#> [183,] 120.0 103.5000 166.5 96.50000 27.00000 149 69.00000
#> [184,] 11.0 27.5000 31.5 31.50000 81.00000 49 173.00000
#> [185,] 141.0 103.5000 31.5 31.50000 27.00000 149 69.00000
#> [186,] 86.0 103.5000 97.5 165.50000 129.50000 49 21.50000
#> [187,] 186.0 27.5000 166.5 96.50000 175.50000 149 120.50000
#> [188,] 35.0 103.5000 166.5 96.50000 175.50000 149 120.50000
#> [189,] 65.0 192.0000 97.5 165.50000 129.50000 49 21.50000
#> [190,] 29.0 150.5000 166.5 96.50000 175.50000 149 120.50000
#> [191,] 86.0 103.5000 97.5 165.50000 129.50000 49 21.50000
#> [192,] 132.0 52.5000 97.5 165.50000 45.00000 149 86.16667
#> [193,] 38.0 150.5000 97.5 165.50000 97.16667 49 173.00000
#> [194,] 162.0 103.5000 120.5 165.50000 175.50000 149 120.50000
#> [195,] 20.0 150.5000 31.5 31.50000 97.16667 49 173.00000
#> [196,] 26.0 103.5000 120.5 165.50000 175.50000 149 120.50000
#> [197,] 186.0 103.5000 166.5 96.50000 175.50000 149 120.50000
#> [198,] 26.0 103.5000 53.5 53.16667 45.00000 149 86.16667
#> [199,] 135.0 52.5000 166.5 96.50000 144.83333 49 21.50000
#> [200,] 68.0 134.8333 53.5 53.16667 144.83333 124 21.50000
#>
#> Slot "ranks":
#> x.oriname y.oriname z.cat.1 z.cat.2 w.lev..L w.lev..Q w.lev..C
#> [1,] 47.0 103.0 30.5 30.5 26.0 98.5 68.0
#> [2,] 117.0 29.0 132.0 62.0 53.0 48.5 173.0
#> [3,] 32.0 192.0 62.0 165.5 108.0 48.5 21.5
#> [4,] 189.0 178.5 167.0 97.0 150.0 98.5 95.0
#> [5,] 123.0 178.5 167.0 97.0 129.0 48.5 21.5
#> [6,] 32.0 132.0 30.5 30.5 80.5 48.5 173.0
#> [7,] 141.0 53.0 97.0 165.5 26.0 98.5 68.0
#> [8,] 156.0 132.0 97.0 165.5 176.0 150.5 121.0
#> [9,] 147.0 14.0 97.0 165.5 176.0 150.5 121.0
#> [10,] 74.0 178.5 167.0 97.0 176.0 150.5 121.0
#> [11,] 189.0 198.5 30.5 30.5 26.0 150.5 68.0
#> [12,] 132.0 53.0 30.5 30.5 26.0 150.5 68.0
#> [13,] 47.0 151.5 30.5 30.5 176.0 150.5 121.0
#> [14,] 2.0 151.5 97.0 165.5 176.0 150.5 121.0
#> [15,] 174.0 151.5 97.0 165.5 80.5 48.5 173.0
#> [16,] 102.0 103.0 97.0 165.5 26.0 150.5 68.0
#> [17,] 105.0 103.0 167.0 97.0 176.0 150.5 121.0
#> [18,] 168.0 53.0 30.5 30.5 129.0 48.5 21.5
#> [19,] 162.0 151.5 30.5 30.5 80.5 48.5 173.0
#> [20,] 147.0 151.5 167.0 97.0 80.5 48.5 173.0
#> [21,] 168.0 103.0 30.5 30.5 129.0 48.5 21.5
#> [22,] 159.0 103.0 30.5 30.5 129.0 48.5 21.5
#> [23,] 114.0 103.0 167.0 97.0 129.0 48.5 21.5
#> [24,] 2.0 53.0 97.0 165.5 129.0 48.5 21.5
#> [25,] 150.0 53.0 167.0 97.0 26.0 150.5 68.0
#> [26,] 98.5 53.0 97.0 165.5 26.0 150.5 68.0
#> [27,] 89.0 14.0 30.5 30.5 176.0 150.5 121.0
#> [28,] 11.0 178.5 30.5 30.5 176.0 150.5 121.0
#> [29,] 59.0 151.5 97.0 165.5 26.0 150.5 68.0
#> [30,] 135.0 178.5 97.0 165.5 80.5 48.5 173.0
#> [31,] 183.0 178.5 97.0 165.5 80.5 48.5 173.0
#> [32,] 92.0 14.0 167.0 97.0 176.0 150.5 121.0
#> [33,] 129.0 53.0 97.0 165.5 129.0 48.5 21.5
#> [34,] 98.5 103.0 167.0 97.0 176.0 150.5 121.0
#> [35,] 14.0 14.0 167.0 97.0 176.0 150.5 121.0
#> [36,] 65.0 151.5 97.0 165.5 26.0 150.5 68.0
#> [37,] 65.0 151.5 97.0 165.5 176.0 150.5 121.0
#> [38,] 98.5 14.0 97.0 165.5 176.0 150.5 121.0
#> [39,] 174.0 103.0 30.5 30.5 80.5 48.5 173.0
#> [40,] 159.0 178.5 167.0 97.0 80.5 48.5 173.0
#> [41,] 86.0 14.0 30.5 30.5 80.5 48.5 173.0
#> [42,] 80.0 53.0 97.0 165.5 176.0 150.5 121.0
#> [43,] 153.0 103.0 30.5 30.5 129.0 48.5 21.5
#> [44,] 144.0 103.0 30.5 30.5 26.0 150.5 68.0
#> [45,] 41.0 53.0 30.5 30.5 176.0 150.5 121.0
#> [46,] 38.0 103.0 97.0 165.5 176.0 150.5 121.0
#> [47,] 126.0 53.0 97.0 165.5 176.0 150.5 121.0
#> [48,] 159.0 178.5 167.0 97.0 26.0 150.5 68.0
#> [49,] 92.0 14.0 30.5 30.5 80.5 48.5 173.0
#> [50,] 165.0 14.0 97.0 165.5 26.0 150.5 68.0
#> [51,] 132.0 192.0 30.5 30.5 176.0 150.5 121.0
#> [52,] 50.0 103.0 167.0 97.0 80.5 48.5 173.0
#> [53,] 126.0 53.0 97.0 165.5 129.0 48.5 21.5
#> [54,] 23.0 53.0 97.0 165.5 26.0 150.5 68.0
#> [55,] 183.0 14.0 30.5 30.5 176.0 150.5 121.0
#> [56,] 195.0 103.0 167.0 97.0 80.5 48.5 173.0
#> [57,] 68.0 103.0 97.0 165.5 26.0 150.5 68.0
#> [58,] 26.0 198.5 167.0 97.0 80.5 48.5 173.0
#> [59,] 147.0 103.0 167.0 97.0 26.0 150.5 68.0
#> [60,] 92.0 14.0 97.0 165.5 26.0 150.5 68.0
#> [61,] 198.5 53.0 30.5 30.5 129.0 48.5 21.5
#> [62,] 102.0 103.0 97.0 165.5 176.0 150.5 121.0
#> [63,] 153.0 14.0 167.0 97.0 26.0 150.5 68.0
#> [64,] 108.0 103.0 30.5 30.5 129.0 48.5 21.5
#> [65,] 35.0 53.0 167.0 97.0 80.5 48.5 173.0
#> [66,] 117.0 178.5 30.5 30.5 26.0 150.5 68.0
#> [67,] 5.0 151.5 97.0 165.5 129.0 48.5 21.5
#> [68,] 186.0 53.0 30.5 30.5 80.5 48.5 173.0
#> [69,] 114.0 103.0 30.5 30.5 80.5 48.5 173.0
#> [70,] 198.5 151.5 167.0 97.0 176.0 150.5 121.0
#> [71,] 138.0 103.0 97.0 165.5 80.5 48.5 173.0
#> [72,] 38.0 192.0 30.5 30.5 129.0 48.5 21.5
#> [73,] 150.0 151.5 30.5 30.5 80.5 48.5 173.0
#> [74,] 29.0 53.0 97.0 165.5 129.0 48.5 21.5
#> [75,] 17.0 14.0 167.0 97.0 176.0 150.5 121.0
#> [76,] 123.0 53.0 167.0 97.0 26.0 150.5 68.0
#> [77,] 62.0 178.5 30.5 30.5 80.5 48.5 173.0
#> [78,] 108.0 103.0 167.0 97.0 129.0 48.5 21.5
#> [79,] 111.0 103.0 97.0 165.5 80.5 48.5 173.0
#> [80,] 53.0 151.5 167.0 97.0 26.0 150.5 68.0
#> [81,] 56.0 151.5 167.0 97.0 26.0 150.5 68.0
#> [82,] 89.0 53.0 30.5 30.5 80.5 48.5 173.0
#> [83,] 177.0 151.5 30.5 30.5 26.0 150.5 68.0
#> [84,] 8.0 178.5 97.0 165.5 80.5 48.5 173.0
#> [85,] 150.0 103.0 30.5 30.5 176.0 150.5 121.0
#> [86,] 126.0 103.0 97.0 165.5 26.0 150.5 68.0
#> [87,] 174.0 53.0 167.0 97.0 80.5 48.5 173.0
#> [88,] 74.0 14.0 97.0 165.5 80.5 48.5 173.0
#> [89,] 129.0 178.5 97.0 165.5 129.0 48.5 21.5
#> [90,] 120.0 14.0 167.0 97.0 80.5 48.5 173.0
#> [91,] 56.0 14.0 30.5 30.5 26.0 150.5 68.0
#> [92,] 180.0 178.5 30.5 30.5 129.0 48.5 21.5
#> [93,] 177.0 53.0 97.0 165.5 176.0 150.5 121.0
#> [94,] 153.0 53.0 167.0 97.0 80.5 48.5 173.0
#> [95,] 189.0 53.0 167.0 97.0 80.5 48.5 173.0
#> [96,] 144.0 103.0 167.0 97.0 176.0 150.5 121.0
#> [97,] 17.0 103.0 167.0 97.0 129.0 48.5 21.5
#> [98,] 53.0 103.0 97.0 165.5 26.0 150.5 68.0
#> [99,] 20.0 151.5 97.0 165.5 26.0 150.5 68.0
#> [100,] 59.0 14.0 30.5 30.5 176.0 150.5 121.0
#> [101,] 50.0 103.0 30.5 30.5 80.5 48.5 173.0
#> [102,] 111.0 151.5 30.5 30.5 80.5 48.5 173.0
#> [103,] 32.0 103.0 97.0 165.5 176.0 150.5 121.0
#> [104,] 117.0 103.0 167.0 97.0 176.0 150.5 121.0
#> [105,] 41.0 103.0 30.5 30.5 176.0 150.5 121.0
#> [106,] 192.0 192.0 30.5 30.5 80.5 48.5 173.0
#> [107,] 156.0 53.0 97.0 165.5 26.0 150.5 68.0
#> [108,] 165.0 151.5 167.0 97.0 26.0 150.5 68.0
#> [109,] 129.0 151.5 167.0 97.0 80.5 48.5 173.0
#> [110,] 192.0 103.0 97.0 165.5 80.5 48.5 173.0
#> [111,] 44.0 178.5 30.5 30.5 176.0 150.5 121.0
#> [112,] 62.0 103.0 97.0 165.5 26.0 150.5 68.0
#> [113,] 183.0 14.0 97.0 165.5 176.0 150.5 121.0
#> [114,] 44.0 151.5 30.5 30.5 129.0 48.5 21.5
#> [115,] 83.0 151.5 97.0 165.5 176.0 150.5 121.0
#> [116,] 68.0 53.0 30.5 30.5 26.0 150.5 68.0
#> [117,] 71.0 103.0 30.5 30.5 80.5 48.5 173.0
#> [118,] 77.0 103.0 167.0 97.0 129.0 48.5 21.5
#> [119,] 141.0 53.0 30.5 30.5 26.0 150.5 68.0
#> [120,] 83.0 103.0 97.0 165.5 129.0 48.5 21.5
#> [121,] 59.0 151.5 97.0 165.5 129.0 48.5 21.5
#> [122,] 180.0 151.5 30.5 30.5 176.0 150.5 121.0
#> [123,] 80.0 53.0 30.5 30.5 26.0 150.5 68.0
#> [124,] 83.0 14.0 97.0 165.5 26.0 150.5 68.0
#> [125,] 95.0 53.0 167.0 97.0 26.0 150.5 68.0
#> [126,] 156.0 178.5 167.0 97.0 26.0 150.5 68.0
#> [127,] 95.0 151.5 97.0 165.5 129.0 48.5 21.5
#> [128,] 102.0 151.5 167.0 97.0 26.0 150.5 68.0
#> [129,] 41.0 192.0 97.0 165.5 129.0 48.5 21.5
#> [130,] 71.0 198.5 167.0 97.0 80.5 48.5 173.0
#> [131,] 111.0 103.0 167.0 97.0 129.0 48.5 21.5
#> [132,] 53.0 14.0 167.0 97.0 129.0 48.5 21.5
#> [133,] 144.0 53.0 30.5 30.5 129.0 48.5 21.5
#> [134,] 8.0 53.0 97.0 165.5 176.0 150.5 121.0
#> [135,] 123.0 14.0 167.0 97.0 176.0 150.5 121.0
#> [136,] 8.0 14.0 97.0 165.5 129.0 48.5 21.5
#> [137,] 77.0 53.0 167.0 97.0 129.0 48.5 21.5
#> [138,] 56.0 53.0 30.5 30.5 26.0 150.5 68.0
#> [139,] 44.0 53.0 167.0 97.0 129.0 48.5 21.5
#> [140,] 98.5 103.0 97.0 165.5 176.0 150.5 121.0
#> [141,] 2.0 53.0 167.0 97.0 176.0 150.5 121.0
#> [142,] 177.0 192.0 167.0 97.0 26.0 150.5 68.0
#> [143,] 5.0 103.0 30.5 30.5 80.5 48.5 173.0
#> [144,] 62.0 53.0 97.0 165.5 26.0 150.5 68.0
#> [145,] 23.0 53.0 167.0 97.0 176.0 150.5 121.0
#> [146,] 35.0 14.0 167.0 97.0 80.5 48.5 173.0
#> [147,] 195.0 198.5 30.5 30.5 80.5 48.5 173.0
#> [148,] 108.0 53.0 167.0 97.0 80.5 48.5 173.0
#> [149,] 17.0 103.0 167.0 97.0 80.5 48.5 173.0
#> [150,] 5.0 151.5 97.0 165.5 80.5 48.5 173.0
#> [151,] 138.0 178.5 167.0 97.0 129.0 48.5 21.5
#> [152,] 105.0 103.0 97.0 165.5 80.5 48.5 173.0
#> [153,] 74.0 14.0 30.5 30.5 129.0 48.5 21.5
#> [154,] 29.0 178.5 167.0 97.0 176.0 150.5 121.0
#> [155,] 11.0 151.5 167.0 97.0 80.5 48.5 173.0
#> [156,] 23.0 53.0 30.5 30.5 129.0 48.5 21.5
#> [157,] 171.0 14.0 167.0 97.0 26.0 150.5 68.0
#> [158,] 47.0 14.0 30.5 30.5 80.5 48.5 173.0
#> [159,] 14.0 151.5 167.0 97.0 129.0 48.5 21.5
#> [160,] 192.0 151.5 30.5 30.5 80.5 48.5 173.0
#> [161,] 135.0 103.0 167.0 97.0 129.0 48.5 21.5
#> [162,] 80.0 14.0 167.0 97.0 26.0 150.5 68.0
#> [163,] 171.0 53.0 167.0 97.0 176.0 150.5 121.0
#> [164,] 165.0 151.5 167.0 97.0 129.0 48.5 21.5
#> [165,] 50.0 178.5 97.0 165.5 80.5 48.5 173.0
#> [166,] 198.5 151.5 167.0 97.0 26.0 150.5 68.0
#> [167,] 77.0 53.0 97.0 165.5 26.0 150.5 68.0
#> [168,] 14.0 103.0 97.0 165.5 80.5 48.5 173.0
#> [169,] 89.0 53.0 30.5 30.5 26.0 150.5 68.0
#> [170,] 120.0 192.0 97.0 165.5 26.0 150.5 68.0
#> [171,] 198.5 53.0 30.5 30.5 80.5 48.5 173.0
#> [172,] 114.0 103.0 97.0 165.5 26.0 150.5 68.0
#> [173,] 138.0 53.0 97.0 165.5 80.5 48.5 173.0
#> [174,] 95.0 14.0 97.0 165.5 176.0 150.5 121.0
#> [175,] 71.0 151.5 30.5 30.5 80.5 48.5 173.0
#> [176,] 105.0 103.0 97.0 165.5 80.5 48.5 173.0
#> [177,] 162.0 103.0 97.0 165.5 176.0 150.5 121.0
#> [178,] 195.0 103.0 167.0 97.0 26.0 150.5 68.0
#> [179,] 171.0 151.5 30.5 30.5 26.0 150.5 68.0
#> [180,] 180.0 151.5 97.0 165.5 176.0 150.5 121.0
#> [181,] 20.0 53.0 30.5 30.5 80.5 48.5 173.0
#> [182,] 168.0 192.0 167.0 97.0 26.0 150.5 68.0
#> [183,] 120.0 103.0 167.0 97.0 26.0 150.5 68.0
#> [184,] 11.0 29.0 30.5 30.5 80.5 48.5 173.0
#> [185,] 141.0 103.0 30.5 30.5 26.0 150.5 68.0
#> [186,] 86.0 103.0 97.0 165.5 129.0 48.5 21.5
#> [187,] 186.0 29.0 167.0 97.0 176.0 150.5 121.0
#> [188,] 35.0 103.0 167.0 97.0 176.0 150.5 121.0
#> [189,] 65.0 192.0 97.0 165.5 129.0 48.5 21.5
#> [190,] 29.0 151.5 167.0 97.0 176.0 150.5 121.0
#> [191,] 86.0 103.0 97.0 165.5 129.0 48.5 21.5
#> [192,] 132.0 53.0 97.0 165.5 53.0 150.5 95.0
#> [193,] 38.0 151.5 97.0 165.5 108.0 48.5 173.0
#> [194,] 162.0 103.0 132.0 165.5 176.0 150.5 121.0
#> [195,] 20.0 151.5 30.5 30.5 108.0 48.5 173.0
#> [196,] 26.0 103.0 132.0 165.5 176.0 150.5 121.0
#> [197,] 186.0 103.0 167.0 97.0 176.0 150.5 121.0
#> [198,] 26.0 103.0 62.0 62.0 53.0 150.5 95.0
#> [199,] 135.0 53.0 167.0 97.0 150.0 48.5 21.5
#> [200,] 68.0 132.0 62.0 62.0 150.0 98.5 21.5
#>
#> Slot "relRanks":
#> x.oriname y.oriname z.cat.1 z.cat.2 w.lev..L w.lev..Q w.lev..C
#> [1,] 0.233830846 0.51243781 0.1517413 0.1517413 0.1293532 0.4900498 0.3383085
#> [2,] 0.582089552 0.14427861 0.6567164 0.3084577 0.2636816 0.2412935 0.8606965
#> [3,] 0.159203980 0.95522388 0.3084577 0.8233831 0.5373134 0.2412935 0.1069652
#> [4,] 0.940298507 0.88805970 0.8308458 0.4825871 0.7462687 0.4900498 0.4726368
#> [5,] 0.611940299 0.88805970 0.8308458 0.4825871 0.6417910 0.2412935 0.1069652
#> [6,] 0.159203980 0.65671642 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [7,] 0.701492537 0.26368159 0.4825871 0.8233831 0.1293532 0.4900498 0.3383085
#> [8,] 0.776119403 0.65671642 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [9,] 0.731343284 0.06965174 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [10,] 0.368159204 0.88805970 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [11,] 0.940298507 0.98756219 0.1517413 0.1517413 0.1293532 0.7487562 0.3383085
#> [12,] 0.656716418 0.26368159 0.1517413 0.1517413 0.1293532 0.7487562 0.3383085
#> [13,] 0.233830846 0.75373134 0.1517413 0.1517413 0.8756219 0.7487562 0.6019900
#> [14,] 0.009950249 0.75373134 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [15,] 0.865671642 0.75373134 0.4825871 0.8233831 0.4004975 0.2412935 0.8606965
#> [16,] 0.507462687 0.51243781 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [17,] 0.522388060 0.51243781 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [18,] 0.835820896 0.26368159 0.1517413 0.1517413 0.6417910 0.2412935 0.1069652
#> [19,] 0.805970149 0.75373134 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [20,] 0.731343284 0.75373134 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [21,] 0.835820896 0.51243781 0.1517413 0.1517413 0.6417910 0.2412935 0.1069652
#> [22,] 0.791044776 0.51243781 0.1517413 0.1517413 0.6417910 0.2412935 0.1069652
#> [23,] 0.567164179 0.51243781 0.8308458 0.4825871 0.6417910 0.2412935 0.1069652
#> [24,] 0.009950249 0.26368159 0.4825871 0.8233831 0.6417910 0.2412935 0.1069652
#> [25,] 0.746268657 0.26368159 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [26,] 0.490049751 0.26368159 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [27,] 0.442786070 0.06965174 0.1517413 0.1517413 0.8756219 0.7487562 0.6019900
#> [28,] 0.054726368 0.88805970 0.1517413 0.1517413 0.8756219 0.7487562 0.6019900
#> [29,] 0.293532338 0.75373134 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [30,] 0.671641791 0.88805970 0.4825871 0.8233831 0.4004975 0.2412935 0.8606965
#> [31,] 0.910447761 0.88805970 0.4825871 0.8233831 0.4004975 0.2412935 0.8606965
#> [32,] 0.457711443 0.06965174 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [33,] 0.641791045 0.26368159 0.4825871 0.8233831 0.6417910 0.2412935 0.1069652
#> [34,] 0.490049751 0.51243781 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [35,] 0.069651741 0.06965174 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [36,] 0.323383085 0.75373134 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [37,] 0.323383085 0.75373134 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [38,] 0.490049751 0.06965174 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [39,] 0.865671642 0.51243781 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [40,] 0.791044776 0.88805970 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [41,] 0.427860697 0.06965174 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [42,] 0.398009950 0.26368159 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [43,] 0.761194030 0.51243781 0.1517413 0.1517413 0.6417910 0.2412935 0.1069652
#> [44,] 0.716417910 0.51243781 0.1517413 0.1517413 0.1293532 0.7487562 0.3383085
#> [45,] 0.203980100 0.26368159 0.1517413 0.1517413 0.8756219 0.7487562 0.6019900
#> [46,] 0.189054726 0.51243781 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [47,] 0.626865672 0.26368159 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [48,] 0.791044776 0.88805970 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [49,] 0.457711443 0.06965174 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [50,] 0.820895522 0.06965174 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [51,] 0.656716418 0.95522388 0.1517413 0.1517413 0.8756219 0.7487562 0.6019900
#> [52,] 0.248756219 0.51243781 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [53,] 0.626865672 0.26368159 0.4825871 0.8233831 0.6417910 0.2412935 0.1069652
#> [54,] 0.114427861 0.26368159 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [55,] 0.910447761 0.06965174 0.1517413 0.1517413 0.8756219 0.7487562 0.6019900
#> [56,] 0.970149254 0.51243781 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [57,] 0.338308458 0.51243781 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [58,] 0.129353234 0.98756219 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [59,] 0.731343284 0.51243781 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [60,] 0.457711443 0.06965174 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [61,] 0.987562189 0.26368159 0.1517413 0.1517413 0.6417910 0.2412935 0.1069652
#> [62,] 0.507462687 0.51243781 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [63,] 0.761194030 0.06965174 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [64,] 0.537313433 0.51243781 0.1517413 0.1517413 0.6417910 0.2412935 0.1069652
#> [65,] 0.174129353 0.26368159 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [66,] 0.582089552 0.88805970 0.1517413 0.1517413 0.1293532 0.7487562 0.3383085
#> [67,] 0.024875622 0.75373134 0.4825871 0.8233831 0.6417910 0.2412935 0.1069652
#> [68,] 0.925373134 0.26368159 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [69,] 0.567164179 0.51243781 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [70,] 0.987562189 0.75373134 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [71,] 0.686567164 0.51243781 0.4825871 0.8233831 0.4004975 0.2412935 0.8606965
#> [72,] 0.189054726 0.95522388 0.1517413 0.1517413 0.6417910 0.2412935 0.1069652
#> [73,] 0.746268657 0.75373134 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [74,] 0.144278607 0.26368159 0.4825871 0.8233831 0.6417910 0.2412935 0.1069652
#> [75,] 0.084577114 0.06965174 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [76,] 0.611940299 0.26368159 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [77,] 0.308457711 0.88805970 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [78,] 0.537313433 0.51243781 0.8308458 0.4825871 0.6417910 0.2412935 0.1069652
#> [79,] 0.552238806 0.51243781 0.4825871 0.8233831 0.4004975 0.2412935 0.8606965
#> [80,] 0.263681592 0.75373134 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [81,] 0.278606965 0.75373134 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [82,] 0.442786070 0.26368159 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [83,] 0.880597015 0.75373134 0.1517413 0.1517413 0.1293532 0.7487562 0.3383085
#> [84,] 0.039800995 0.88805970 0.4825871 0.8233831 0.4004975 0.2412935 0.8606965
#> [85,] 0.746268657 0.51243781 0.1517413 0.1517413 0.8756219 0.7487562 0.6019900
#> [86,] 0.626865672 0.51243781 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [87,] 0.865671642 0.26368159 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [88,] 0.368159204 0.06965174 0.4825871 0.8233831 0.4004975 0.2412935 0.8606965
#> [89,] 0.641791045 0.88805970 0.4825871 0.8233831 0.6417910 0.2412935 0.1069652
#> [90,] 0.597014925 0.06965174 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [91,] 0.278606965 0.06965174 0.1517413 0.1517413 0.1293532 0.7487562 0.3383085
#> [92,] 0.895522388 0.88805970 0.1517413 0.1517413 0.6417910 0.2412935 0.1069652
#> [93,] 0.880597015 0.26368159 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [94,] 0.761194030 0.26368159 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [95,] 0.940298507 0.26368159 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [96,] 0.716417910 0.51243781 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [97,] 0.084577114 0.51243781 0.8308458 0.4825871 0.6417910 0.2412935 0.1069652
#> [98,] 0.263681592 0.51243781 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [99,] 0.099502488 0.75373134 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [100,] 0.293532338 0.06965174 0.1517413 0.1517413 0.8756219 0.7487562 0.6019900
#> [101,] 0.248756219 0.51243781 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [102,] 0.552238806 0.75373134 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [103,] 0.159203980 0.51243781 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [104,] 0.582089552 0.51243781 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [105,] 0.203980100 0.51243781 0.1517413 0.1517413 0.8756219 0.7487562 0.6019900
#> [106,] 0.955223881 0.95522388 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [107,] 0.776119403 0.26368159 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [108,] 0.820895522 0.75373134 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [109,] 0.641791045 0.75373134 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [110,] 0.955223881 0.51243781 0.4825871 0.8233831 0.4004975 0.2412935 0.8606965
#> [111,] 0.218905473 0.88805970 0.1517413 0.1517413 0.8756219 0.7487562 0.6019900
#> [112,] 0.308457711 0.51243781 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [113,] 0.910447761 0.06965174 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [114,] 0.218905473 0.75373134 0.1517413 0.1517413 0.6417910 0.2412935 0.1069652
#> [115,] 0.412935323 0.75373134 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [116,] 0.338308458 0.26368159 0.1517413 0.1517413 0.1293532 0.7487562 0.3383085
#> [117,] 0.353233831 0.51243781 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [118,] 0.383084577 0.51243781 0.8308458 0.4825871 0.6417910 0.2412935 0.1069652
#> [119,] 0.701492537 0.26368159 0.1517413 0.1517413 0.1293532 0.7487562 0.3383085
#> [120,] 0.412935323 0.51243781 0.4825871 0.8233831 0.6417910 0.2412935 0.1069652
#> [121,] 0.293532338 0.75373134 0.4825871 0.8233831 0.6417910 0.2412935 0.1069652
#> [122,] 0.895522388 0.75373134 0.1517413 0.1517413 0.8756219 0.7487562 0.6019900
#> [123,] 0.398009950 0.26368159 0.1517413 0.1517413 0.1293532 0.7487562 0.3383085
#> [124,] 0.412935323 0.06965174 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [125,] 0.472636816 0.26368159 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [126,] 0.776119403 0.88805970 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [127,] 0.472636816 0.75373134 0.4825871 0.8233831 0.6417910 0.2412935 0.1069652
#> [128,] 0.507462687 0.75373134 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [129,] 0.203980100 0.95522388 0.4825871 0.8233831 0.6417910 0.2412935 0.1069652
#> [130,] 0.353233831 0.98756219 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [131,] 0.552238806 0.51243781 0.8308458 0.4825871 0.6417910 0.2412935 0.1069652
#> [132,] 0.263681592 0.06965174 0.8308458 0.4825871 0.6417910 0.2412935 0.1069652
#> [133,] 0.716417910 0.26368159 0.1517413 0.1517413 0.6417910 0.2412935 0.1069652
#> [134,] 0.039800995 0.26368159 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [135,] 0.611940299 0.06965174 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [136,] 0.039800995 0.06965174 0.4825871 0.8233831 0.6417910 0.2412935 0.1069652
#> [137,] 0.383084577 0.26368159 0.8308458 0.4825871 0.6417910 0.2412935 0.1069652
#> [138,] 0.278606965 0.26368159 0.1517413 0.1517413 0.1293532 0.7487562 0.3383085
#> [139,] 0.218905473 0.26368159 0.8308458 0.4825871 0.6417910 0.2412935 0.1069652
#> [140,] 0.490049751 0.51243781 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [141,] 0.009950249 0.26368159 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [142,] 0.880597015 0.95522388 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [143,] 0.024875622 0.51243781 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [144,] 0.308457711 0.26368159 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [145,] 0.114427861 0.26368159 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [146,] 0.174129353 0.06965174 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [147,] 0.970149254 0.98756219 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [148,] 0.537313433 0.26368159 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [149,] 0.084577114 0.51243781 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [150,] 0.024875622 0.75373134 0.4825871 0.8233831 0.4004975 0.2412935 0.8606965
#> [151,] 0.686567164 0.88805970 0.8308458 0.4825871 0.6417910 0.2412935 0.1069652
#> [152,] 0.522388060 0.51243781 0.4825871 0.8233831 0.4004975 0.2412935 0.8606965
#> [153,] 0.368159204 0.06965174 0.1517413 0.1517413 0.6417910 0.2412935 0.1069652
#> [154,] 0.144278607 0.88805970 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [155,] 0.054726368 0.75373134 0.8308458 0.4825871 0.4004975 0.2412935 0.8606965
#> [156,] 0.114427861 0.26368159 0.1517413 0.1517413 0.6417910 0.2412935 0.1069652
#> [157,] 0.850746269 0.06965174 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [158,] 0.233830846 0.06965174 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [159,] 0.069651741 0.75373134 0.8308458 0.4825871 0.6417910 0.2412935 0.1069652
#> [160,] 0.955223881 0.75373134 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [161,] 0.671641791 0.51243781 0.8308458 0.4825871 0.6417910 0.2412935 0.1069652
#> [162,] 0.398009950 0.06965174 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [163,] 0.850746269 0.26368159 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [164,] 0.820895522 0.75373134 0.8308458 0.4825871 0.6417910 0.2412935 0.1069652
#> [165,] 0.248756219 0.88805970 0.4825871 0.8233831 0.4004975 0.2412935 0.8606965
#> [166,] 0.987562189 0.75373134 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [167,] 0.383084577 0.26368159 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [168,] 0.069651741 0.51243781 0.4825871 0.8233831 0.4004975 0.2412935 0.8606965
#> [169,] 0.442786070 0.26368159 0.1517413 0.1517413 0.1293532 0.7487562 0.3383085
#> [170,] 0.597014925 0.95522388 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [171,] 0.987562189 0.26368159 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [172,] 0.567164179 0.51243781 0.4825871 0.8233831 0.1293532 0.7487562 0.3383085
#> [173,] 0.686567164 0.26368159 0.4825871 0.8233831 0.4004975 0.2412935 0.8606965
#> [174,] 0.472636816 0.06965174 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [175,] 0.353233831 0.75373134 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [176,] 0.522388060 0.51243781 0.4825871 0.8233831 0.4004975 0.2412935 0.8606965
#> [177,] 0.805970149 0.51243781 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [178,] 0.970149254 0.51243781 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [179,] 0.850746269 0.75373134 0.1517413 0.1517413 0.1293532 0.7487562 0.3383085
#> [180,] 0.895522388 0.75373134 0.4825871 0.8233831 0.8756219 0.7487562 0.6019900
#> [181,] 0.099502488 0.26368159 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [182,] 0.835820896 0.95522388 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [183,] 0.597014925 0.51243781 0.8308458 0.4825871 0.1293532 0.7487562 0.3383085
#> [184,] 0.054726368 0.14427861 0.1517413 0.1517413 0.4004975 0.2412935 0.8606965
#> [185,] 0.701492537 0.51243781 0.1517413 0.1517413 0.1293532 0.7487562 0.3383085
#> [186,] 0.427860697 0.51243781 0.4825871 0.8233831 0.6417910 0.2412935 0.1069652
#> [187,] 0.925373134 0.14427861 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [188,] 0.174129353 0.51243781 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [189,] 0.323383085 0.95522388 0.4825871 0.8233831 0.6417910 0.2412935 0.1069652
#> [190,] 0.144278607 0.75373134 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [191,] 0.427860697 0.51243781 0.4825871 0.8233831 0.6417910 0.2412935 0.1069652
#> [192,] 0.656716418 0.26368159 0.4825871 0.8233831 0.2636816 0.7487562 0.4726368
#> [193,] 0.189054726 0.75373134 0.4825871 0.8233831 0.5373134 0.2412935 0.8606965
#> [194,] 0.805970149 0.51243781 0.6567164 0.8233831 0.8756219 0.7487562 0.6019900
#> [195,] 0.099502488 0.75373134 0.1517413 0.1517413 0.5373134 0.2412935 0.8606965
#> [196,] 0.129353234 0.51243781 0.6567164 0.8233831 0.8756219 0.7487562 0.6019900
#> [197,] 0.925373134 0.51243781 0.8308458 0.4825871 0.8756219 0.7487562 0.6019900
#> [198,] 0.129353234 0.51243781 0.3084577 0.3084577 0.2636816 0.7487562 0.4726368
#> [199,] 0.671641791 0.26368159 0.8308458 0.4825871 0.7462687 0.2412935 0.1069652
#> [200,] 0.338308458 0.65671642 0.3084577 0.3084577 0.7462687 0.4900498 0.1069652
#>
#> Slot "rpatch":
#> function (n = 1, patch = .Object@patch, patchpar = NULL, keep_ties = NULL,
#> return_extra_objects = FALSE)
#> {
#> rsims.index <- ceiling(runif(n) * dim(.Object@ranks)[1])
#> rsims <- as.matrix(.Object@ranks[rsims.index, , drop = FALSE])
#> obj_ties <- apply(.Object@ranks, 2, function(x) {
#> ave(x, x, FUN = length)
#> })
#> obj_ties[, keep_ties] <- 0
#> rsims.ties <- as.matrix(obj_ties[rsims.index, , drop = FALSE])
#> usims <- matrix(runif(.Object@dim * n), nrow = n, ncol = .Object@dim)
#> if (is.null(patchpar))
#> patchpar <- .Object@patchpar
#> if (is.list(patchpar)) {
#> par.m <- patchpar$m
#> par.K <- patchpar$K
#> par.rho <- patchpar$rho
#> }
#> if (is.null(par.m))
#> par.m <- as.numeric(colSums(!is.na(.Object@ranks)))
#> if (is.null(par.K))
#> par.K <- dim(.Object@ranks)[1]
#> switch(patch, none = {
#> Z <- sweep((rsims - 0.5), 2, par.m, "/")
#> }, rook = {
#> Z <- sweep((rsims - 0.5 + 0.5 * rsims.ties - usims *
#> rsims.ties), 2, par.m, "/")
#> }, lFrechet = {
#> Z <- sweep(cbind(rsims[, 1] + 0.5 * rsims.ties[, 1] -
#> usims[, 1] * rsims.ties[, 1], rsims[, 2] + usims[,
#> 1] * rsims.ties[, 2] - 0.5 * rsims.ties[, 2] - 1),
#> 2, par.m, "/")
#> }, uFrechet = {
#> Z <- sweep((rsims - 0.5 + 0.5 * rsims.ties - usims[,
#> rep(1, .Object@dim)] * rsims.ties), 2, par.m, "/")
#> }, Bernstein = {
#> J <- floor(runif(n) * par.K)
#> new_usims <- matrix(runif(.Object@dim * n), nrow = n,
#> ncol = .Object@dim)
#> rsims <- rsims - 0.5 + 0.5 * rsims.ties - floor(new_usims *
#> rsims.ties)
#> Z <- qbeta(usims, sweep(par.K * (rsims - 1) + 1, 1, J,
#> "+"), sweep(sweep(-par.K * (rsims - 1), 2, par.K *
#> par.m, "+"), 1, J, "-"))
#> }, Gauss = {
#> if (is.numeric(patchpar)) par.rho = patchpar
#> if (is.null(par.rho)) warning("patchpar$rho must not be NULL when patch is Gauss")
#> if (!require(copula)) stop("The package copula is required for using of the Gauss copula driver, but it is not installed.")
#> tryCatch(norm_cop <- copula::normalCopula(par.rho, dim = .Object@dim),
#> error = function(e) stop(paste0("Gauss copula driver cannot be created for your chosen parameter par_rho=",
#> par.rho, ". Adapt the value to ensure a positive semidefinite correlation matrix.")))
#> Z <- sweep((rsims - 0.5 + copula::rCopula(n, norm_cop) *
#> rsims.ties - 0.5 * rsims.ties), 2, par.m, "/")
#> }, sample = {
#> ranks <- rsims
#> rel.ranks <- as.matrix(.Object@relRanks[rsims.index,
#> , drop = FALSE])
#> if (length(par.m) < dim(.Object@ranks)[2]) par.m <- rep_len(par.m,
#> dim(.Object@ranks)[2])
#> if (max(par.m) > dim(.Object@ranks)[1]) warning("in order to create a valid sample copula par.m must not be larger than the number of non-missing observations for each variable")
#> sij <- lapply(1:dim(.Object@ranks)[2], function(i) cumsum(prop.table(table(cut(.Object@relRanks[,
#> i], breaks = seq(0, 1, length.out = par.m[i] + 1),
#> include.lowest = T)))))
#> sij <- lapply(sij, function(x) c(0, x))
#> interim <- lapply(1:dim(ranks)[2], function(i) cut(rel.ranks[,
#> i], breaks = unique(sij[[i]]), include.lowest = T))
#> d <- as.data.frame(lapply(interim, as.numeric))
#> Z <- as.matrix(as.data.frame(lapply(1:dim(ranks)[2],
#> function(i) runif(length(d[[i]]), min = sij[[i]][!duplicated(sij[[i]])][d[[i]]],
#> max = sij[[i]][!duplicated(sij[[i]])][d[[i]] +
#> 1]))))
#> })
#> colnames(Z) <- colnames(.Object@ranks)
#> if (return_extra_objects) {
#> return(list(Z = Z, rsims = rsims, usims = usims, rsims.index = rsims.index))
#> }
#> else {
#> return(Z)
#> }
#> }
#> <environment: 0x556c4cb38f20>
#>
#> Slot "rand":
#> function (n = 1, patch = .Object@patch, patchpar = NULL, keep_ties = NULL,
#> return_extra_objects = F)
#> {
#> tmp <- .Object@rpatch(n, patch, patchpar, keep_ties, return_extra_objects = TRUE)
#> Z <- tmp$Z
#> rsims <- tmp$rsims
#> usims <- tmp$usims
#> if (!numericCDF) {
#> switch(.Object@family, binom = {
#> d <- ceiling(sweep(Z, 2, [email protected], "*"))
#> }, nbinom = {
#> d <- floor(sweep(Z/(1 - Z), 2, [email protected], "*"))
#> }, sample = {
#> rr <- t(matrixStats::colRanks(Z) - 0.5)/dim(Z)[1]
#> foo <- function(rrx, n) {
#> table(cut(rrx, breaks = seq(0, 1, length.out = n +
#> 1), ordered_result = FALSE))
#> }
#> rsims <- Z
#> ranks <- apply(rsims, 2, rank)
#> ranks
#> rel.ranks <- (ranks - 0.5)/dim(ranks)[1]
#> rel.ranks
#> if (length([email protected]) < dim(ranks)[2]) [email protected] <- rep_len([email protected],
#> dim(ranks)[2])
#> if (max([email protected]) > dim(ranks)[1]) warning("in order to create a valid sample copula pars.a must not be larger than the number of non-missing observations for each variable")
#> sij <- lapply(1:dim(ranks)[2], function(i) cumsum(prop.table(table(cut(rel.ranks[,
#> i], breaks = seq(0, 1, length.out = [email protected][i] +
#> 1), include.lowest = T)))))
#> print("done")
#> print("sij[[1]]")
#> print(sij)
#> sij <- lapply(sij, function(x) c(0, x))
#> print("sij[[1]]")
#> print(sij)
#> interim <- lapply(1:dim(ranks)[2], function(i) cut(rel.ranks[,
#> i], breaks = unique(sij[[i]]), include.lowest = T))
#> d2 <- as.data.frame(lapply(interim, as.numeric))
#> d <- d2
#> }, gamma = {
#> d <- 1/(1 - sweep(Z, 2, 1/[email protected], "^")) -
#> 1
#> }, beta = {
#> d <- floor(sweep(Z, 2, [email protected], "*"))
#> }, betaalt = {
#> d <- exp(1 - (1/Z))
#> }, power = {
#> d <- Z
#> for (j in 1:.Object@dim) {
#> cat(paste("for", j))
#> d[, j] <- .Object@alphsquantf[[j]](Z[, j])
#> }
#> }, poisson = {
#> d <- floor(sweep(-log(1 - Z), 2, (log([email protected] +
#> 1) - log([email protected])), "/"))
#> })
#> switch(.Object@family, binom = {
#> rslt <- qbeta(matrix(runif(n * .Object@dim), nrow = n,
#> ncol = .Object@dim), d, matrix([email protected] +
#> 1, nrow = n, ncol = .Object@dim, byrow = TRUE) -
#> d)
#> }, nbinom = {
#> rslt <- qbeta(matrix(runif(n * .Object@dim), nrow = n,
#> ncol = .Object@dim), d + 1, matrix([email protected] +
#> 1, nrow = n, ncol = .Object@dim, byrow = TRUE))
#> }, sample = {
#> rslt <- as.data.frame(lapply(1:dim(ranks)[2], function(i) runif(length(d[[i]]),
#> min = sij[[i]][!duplicated(sij[[i]])][d[[i]]],
#> max = sij[[i]][!duplicated(sij[[i]])][d[[i]] +
#> 1])))
#> }, gamma = {
#> rslt <- exp(-qgamma(matrix(runif(n * .Object@dim),
#> nrow = n, ncol = .Object@dim), matrix([email protected],
#> nrow = n, ncol = .Object@dim, byrow = T), 1 +
#> d))
#> }, beta = {
#> rslt <- qbeta(matrix(runif(n * .Object@dim), nrow = n,
#> ncol = .Object@dim), d, matrix([email protected] +
#> 1, nrow = n, ncol = .Object@dim, byrow = TRUE) -
#> d)
#> }, betaalt = {
#> rslt <- exp(-qgamma(matrix(runif(n * .Object@dim),
#> nrow = n, ncol = .Object@dim), 2, 1/(1 - log(d))))
#> }, poisson = {
#> rslt <- 1 - exp(-qgamma(matrix(runif(n * .Object@dim),
#> nrow = n, ncol = .Object@dim), shape = d + 1,
#> rate = 1 + matrix([email protected] + 1, nrow = n,
#> ncol = .Object@dim, byrow = TRUE)))
#> }, power = {
#> beta <- matrix([email protected], nrow = n, ncol = .Object@dim,
#> byrow = T)
#> smat <- d
#> umat <- matrix(runif(n * .Object@dim), nrow = n,
#> ncol = .Object@dim)
#> Fk <- function(s, beta) {
#> ifelse(1 < s, 1, ifelse(s < 0, 0, (1 - (1 - s)^(beta -
#> 1) - s)/(1 - s^(beta - 1) - (1 - s)^(beta -
#> 1))))
#> }
#> cond <- umat <= Fk(smat, beta)
#> fcase1 <- function(s, u, beta) {
#> 1 - (((1 - s)^(beta - 1))/((1 - s)^(beta - 1) +
#> u * (1 - s^(beta - 1) - (1 - s)^(beta - 1))))^(1/(beta -
#> 2))
#> }
#> fcase2 <- function(s, u, beta) {
#> (((s)^(beta - 1))/(1 - (1 - s)^(beta - 1) - u *
#> (1 - s^(beta - 1) - (1 - s)^(beta - 1))))^(1/(beta -
#> 2))
#> }
#> print("IFELSE")
#> rslt <- ifelse(umat > 1 | umat < 0, 0, ifelse(matrix(runif(n *
#> .Object@dim), nrow = n, ncol = .Object@dim) <=
#> smat, fcase1(smat, umat, beta), fcase2(smat,
#> umat, beta)))
#> })
#> colnames(rslt) <- colnames(.Object@ranks)
#> if (return_extra_objects) {
#> return(list(result = rslt, rsims = rsims, usims = usims,
#> Z = Z, d = d))
#> }
#> else return(rslt)
#> }
#> else {
#> d <- Z
#> print("Z")
#> print(Z)
#> for (i in 1:.Object@dim) d[, i] <- .Object@alphsquantf[[i]](Z[,
#> i])
#> rs <- d
#> print(paste("d", d))
#> for (i in 1:.Object@dim) for (j in 1:n) {
#> print(paste("i", i, "j", j, "d[j,i]", d[j, i]))
#> if (!require(armspp))
#> stop("numerically determining the CDF requires the armspp package, which is not installed.")
#> smpl <- armspp::arms(5000, function(theta) {
#> return(.Object@fdenss[[i]](u = theta, s = d[j,
#> i], log = F))
#> }, 0, 1)
#> rs[j, i] <- smpl[length(smpl)]
#> }
#> colnames(rs) <- colnames(.Object@ranks)
#> if (return_extra_objects) {
#> return(list(result = rs, rsims = rsims, usims = usims,
#> Z = Z, d = d))
#> }
#> else return(rs)
#> }
#> }
#> <environment: 0x556c4cb38f20>3) Estimate marginals
Numeric/ordered variables use logspline by default.
Binary/trivial variables fall back to empirical probability tables.
Optional k-NN smoothing via
k.
marg <- estimateMarginals(pre$data, method = "spline", k = 3)
#> Warning in (function (x, lbound, ubound, maxknots = 0, knots, nknots = 0, : too
#> much data close together
#> possible infinite density at lower end
#> running program with fewer knots
#> running with maximum degrees of freedom
#> Warning in (function (x, lbound, ubound, maxknots = 0, knots, nknots = 0, :
#> re-ran with oldlogspline
#> Warning in (function (x, lbound, ubound, maxknots = 0, knots, nknots = 0, : too
#> many knots beyond data
#> running with maximum degrees of freedom
#> Warning in (function (x, lbound, ubound, maxknots = 0, knots, nknots = 0, :
#> re-ran with oldlogspline
#> Warning in (function (x, lbound, ubound, maxknots = 0, knots, nknots = 0, : too
#> many knots beyond data
#> running with maximum degrees of freedom
#> Warning in (function (x, lbound, ubound, maxknots = 0, knots, nknots = 0, :
#> re-ran with oldlogspline
names(marg)
#> [1] "x.oriname" "y.oriname" "z.cat.1" "z.cat.2" "w.lev..L" "w.lev..Q"
#> [7] "w.lev..C"4) Generate synthetic data
Combines copula draws with the marginals’ inverse transformations.
Optionally restores factor structure using
original_levels,original_varnames, andoriginal_classes.
syn <- generateSynthetic(
n = 1000,
copula = cop,
marginals = marg,
original_levels = pre$original_levels,
original_varnames = names(toy),
original_classes = sapply(toy, class)
)
str(syn)
#> 'data.frame': 1000 obs. of 4 variables:
#> $ x: num -1.422 0.697 -1.33 0.373 -0.183 ...
#> $ y: int 2 1 3 4 1 3 5 3 0 2 ...
#> $ z: Factor w/ 3 levels "a","b","c": 2 2 1 2 2 2 2 2 1 2 ...
#> $ w: Factor w/ 4 levels "1","2","3","4": 2 3 4 1 1 2 2 4 2 4 ...
head(syn)
#> x y z w
#> 1 -1.4224888 2 b 2
#> 2 0.6966695 1 b 3
#> 3 -1.3296761 3 a 4
#> 4 0.3727409 4 b 1
#> 5 -0.1833070 1 b 1
#> 6 -0.4273024 3 b 25) Quick checks
Compare simple summaries between original and synthetic.
summary(toy)
#> x y z w
#> Min. :-2.21470 Min. :0.00 a:68 1:53
#> 1st Qu.:-0.61383 1st Qu.:1.00 b:70 2:55
#> Median :-0.04937 Median :2.00 c:62 3:42
#> Mean : 0.03554 Mean :2.07 4:50
#> 3rd Qu.: 0.61300 3rd Qu.:3.00
#> Max. : 2.40162 Max. :7.00
summary(syn)
#> x y z w
#> Min. :-3.31644 Min. :-2.000 a:477 1:273
#> 1st Qu.:-0.62439 1st Qu.: 1.000 b:523 2:266
#> Median :-0.06628 Median : 2.000 c: 0 3:209
#> Mean :-0.01204 Mean : 2.077 4:252
#> 3rd Qu.: 0.52590 3rd Qu.: 3.000
#> Max. : 3.50072 Max. :10.000You can also visualize marginal distributions:
op <- par(mfrow = c(1,2))
hist(toy$x, main = "Original x", xlab = "x")
hist(syn$x, main = "Synthetic x", xlab = "x")
Tips & notes
If your factors have only 2 levels, they’re treated as binary and modeled via empirical probabilities.
For small samples, consider slightly larger
bin_sizeor modestjitterto stabilise fits.For integers in the original data,
generateSynthetic()rounds and casts back tointeger.
Session info
sessionInfo()
#> R version 4.6.1 (2026-06-24)
#> Platform: x86_64-pc-linux-gnu
#> Running under: Ubuntu 26.04 LTS
#>
#> Matrix products: default
#> BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.32.so; LAPACK version 3.12.0
#>
#> locale:
#> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
#> [3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
#> [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
#> [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
#> [9] LC_ADDRESS=C LC_TELEPHONE=C
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
#>
#> time zone: Etc/UTC
#> tzcode source: system (glibc)
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] PUcopulaSynth_0.1.0 rmarkdown_2.31
#>
#> loaded via a namespace (and not attached):
#> [1] gtable_0.3.6 xfun_0.59 bslib_0.11.0
#> [4] ggplot2_4.0.3 recipes_1.3.3 logspline_2.1.22
#> [7] lattice_0.22-9 vctrs_0.7.3 tools_4.6.1
#> [10] generics_0.1.4 stats4_4.6.1 parallel_4.6.1
#> [13] tibble_3.3.1 ModelMetrics_1.2.2.2 pkgconfig_2.0.3
#> [16] Matrix_1.7-5 data.table_1.18.4 RColorBrewer_1.1-3
#> [19] S7_0.2.2 lifecycle_1.0.5 compiler_4.6.1
#> [22] farver_2.1.2 stringr_1.6.0 codetools_0.2-20
#> [25] htmltools_0.5.9 sys_3.4.3 buildtools_1.0.0
#> [28] class_7.3-23 sass_0.4.10 yaml_2.3.12
#> [31] pracma_2.4.6 prodlim_2026.03.11 tidyr_1.3.2
#> [34] pillar_1.11.1 jquerylib_0.1.4 MASS_7.3-65
#> [37] cachem_1.1.0 gower_1.0.2 iterators_1.0.14
#> [40] rpart_4.1.27 foreach_1.5.2 nlme_3.1-169
#> [43] parallelly_1.48.0 lava_1.9.2 tidyselect_1.2.1
#> [46] digest_0.6.39 stringi_1.8.7 future_1.70.0
#> [49] dplyr_1.2.1 reshape2_1.4.5 purrr_1.2.2
#> [52] listenv_1.0.0 maketools_1.3.2 splines_4.6.1
#> [55] fastmap_1.2.0 grid_4.6.1 cli_3.6.6
#> [58] magrittr_2.0.5 survival_3.8-6 future.apply_1.20.2
#> [61] withr_3.0.3 scales_1.4.0 lubridate_1.9.5
#> [64] timechange_0.4.0 matrixStats_1.5.0 globals_0.19.1
#> [67] otel_0.2.0 nnet_7.3-20 timeDate_4052.112
#> [70] RANN_2.6.2 evaluate_1.0.5 knitr_1.51
#> [73] hardhat_1.4.3 caret_7.0-1 rlang_1.3.0
#> [76] Rcpp_1.1.2 glue_1.8.1 pROC_1.19.0.1
#> [79] ipred_0.9-15 PUcopula_0.1.1 jsonlite_2.0.0
#> [82] R6_2.6.1 plyr_1.8.9