787 lines (756 with data), 38.9 kB

R Under development (unstable) (2014-06-29 r66051) -- "Unsuffered Consequences"
Copyright (C) 2014 The R Foundation for Statistical Computing
Platform: x86_64-unknown-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> 
> set.seed(290875)
> library("party")
Loading required package: grid
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

Loading required package: sandwich
Loading required package: strucchange
Loading required package: modeltools
Loading required package: stats4
> library("survival")
Loading required package: splines
> 
> ### get rid of the NAMESPACE
> attach(asNamespace("party"))
The following objects are masked from package:party:

    cforest, cforest_classical, cforest_control, cforest_unbiased,
    conditionalTree, ctree, ctree_control, ctree_memory, edge_simple,
    mob, mob_control, node_barplot, node_bivplot, node_boxplot,
    node_density, node_hist, node_inner, node_scatterplot, node_surv,
    node_terminal, proximity, ptrafo, reweight, sctest.mob, varimp,
    varimpAUC

> 
> ### check nominal level printing
> set.seed(290875)
> x <- gl(5, 50)
> df <- data.frame(y = c(rnorm(50, 0), rnorm(50, 1), rnorm(50, 2), rnorm(50, 3), rnorm(50, 4)), 
+                  x = x, z = rnorm(250))
> ctree(y ~ x, data = df)

	 Conditional inference tree with 5 terminal nodes

Response:  y 
Input:  x 
Number of observations:  250 

1) x == {3, 4, 5}; criterion = 1, statistic = 159.215
  2) x == {4, 5}; criterion = 1, statistic = 54.696
    3) x == {5}; criterion = 1, statistic = 16.711
      4)*  weights = 50 
    3) x == {4}
      5)*  weights = 50 
  2) x == {3}
    6)*  weights = 50 
1) x == {1, 2}
  7) x == {2}; criterion = 1, statistic = 21.738
    8)*  weights = 50 
  7) x == {1}
    9)*  weights = 50 
> 
> ### check asymptotic vs. MonteCarlo, especially categorical splits after
> ### MonteCarlo resampling
> a <- ctree(y ~ x + z, data = df, control = ctree_control(stump = TRUE))
> b <- ctree(y ~ x + z, data = df,
+            control =  ctree_control(testtype = "Monte", stump = TRUE))
> stopifnot(isequal(a@tree$psplit, b@tree$psplit))  
> stopifnot(isequal(a@tree$criterion$statistic, b@tree$criterion$statistic))
> 
> ### we did not check the hyper parameters
> try(cforest_control(minsplit = -1))
Error in validObject(object@splitctrl) : 
  invalid class "SplitControl" object: FALSE
In addition: Warning message:
In validityMethod(object) :
  no negative values allowed in objects of class 'SplitControl'
> try(cforest_control(ntree = -1))
Error in validObject(RET) : invalid class "ForestControl" object: FALSE
In addition: Warning message:
In validityMethod(object) : 'ntree' must be equal or greater 1
> try(cforest_control(maxdepth = -1))
Error in validObject(object@tgctrl) : 
  invalid class "TreeGrowControl" object: FALSE
In addition: Warning message:
In validityMethod(object) : 'maxdepth' must be positive
> try(cforest_control(nresample = 10))
Error in validObject(object@gtctrl) : 
  invalid class "GlobalTestControl" object: FALSE
In addition: Warning message:
In validityMethod(object) : 'nresample' must be larger than 100
> 
> ### NA handling for factors and in random forest
> ### more than one (ordinal) response variable
> xo <- ordered(x)
> x[sample(1:length(x), 10)] <- NA
> cforest(y + xo ~ x + z, data = df, 
+         control = cforest_unbiased(ntree = 50))

	 Random Forest using Conditional Inference Trees

Number of trees:  50 

Responses: y, xo 
Inputs:  x, z 
Number of observations:  250 

There were 50 or more warnings (use warnings() to see the first 50)
> 
> ### make sure minsplit is OK in the presence of missing values
> ### spotted by Han Lee <Han.Lee@GeodeCapital.com>
> load("t1.RData")
> tr <- try(ctree(p ~., data = t1))
> stopifnot(!inherits(tr, "try-error"))
> 
> ### make sure number of surrogate splits exceeds number of inputs by 1
> ### spotted by Henric Nilsson <henric.nilsson@phadia.com>
> airq <- subset(airquality, !is.na(Ozone))
> tr <- try(ctree(Ozone ~ Wind, data = airq,
+           controls = ctree_control(maxsurrogate = 3)))
Error in model@fit(data, ...) : 
  cannot set up 3 surrogate splits with only 0 ordered input variable(s)
> stopifnot(inherits(tr, "try-error"))
> 
> ### ctree() used only the first of a multivariate response
> ### spotted by Henric Nilsson <henric.nilsson@phadia.com>
> airq <- subset(airquality, complete.cases(Ozone, Solar.R))
> airOzoSol1 <- ctree(Ozone + Solar.R ~ Wind + Temp + Month + Day,
+                     data = airq)
> airOzoSol2 <- ctree(Solar.R + Ozone ~ Wind + Temp + Month + Day,
+                     data = airq)
> stopifnot(isequal(airOzoSol1@where, airOzoSol2@where))
> 
> ### one variable with all values missing
> dat <- data.frame(y = rnorm(100), x1 = runif(100), x2 = rep(NA, 100))
> ctree(y ~ x1 + x2, data = dat)

	 Conditional inference tree with 1 terminal nodes

Response:  y 
Inputs:  x1, x2 
Number of observations:  100 

1)*  weights = 100 
> 
> ### one factor with only one level
> dat$x2 <- factor(rep(0, 100))
> try(ctree(y ~ x1 + x2, data = dat))

	 Conditional inference tree with 1 terminal nodes

Response:  y 
Inputs:  x1, x2 
Number of observations:  100 

1)*  weights = 100 
> 
> ### weights for sampling without replacement for cforest
> ### spotted by Carolin Strobl <carolin.strol@stat.uni-muenchen.de>
> airq <- subset(airquality, !is.na(Ozone))
> cctrl <- cforest_control(replace = FALSE, fraction = 0.5)
> n <- nrow(airq)
> w <- double(n)
> 
> 
> if (FALSE) {
+ ### forest objects have weights remove in 0.9-13
+ 
+ ### case weights
+ x <- runif(w)
+ w[x > 0.5] <- 1
+ w[x > 0.9] <- 2
+ 
+ rf <- cforest(Ozone ~ .,data = airq, weights = w, control = cctrl)
+ rfw <- sapply(rf@ensemble, function(x) x[[2]])
+ stopifnot(all(colSums(rfw) == ceiling(sum(w) / 2)))
+ stopifnot(max(abs(rfw[w == 0,])) == 0)
+ 
+ ### real weights
+ w <- runif(n)
+ w[1:10] <- 0
+ rf <- cforest(Ozone ~ .,data = airq, weights = w, control = cctrl)
+ rfw <- sapply(rf@ensemble, function(x) x[[2]])
+ stopifnot(all(colSums(rfw) == ceiling(sum(w > 0) / 2)))
+ stopifnot(max(abs(rfw[w == 0,])) == 0)
+ }
> 
> ### cforest with multivariate response
> df <- data.frame(y1 = rnorm(100), y2 = rnorm(100), x1 = runif(100), x2 = runif(100))
> df$y1[df$x1 < 0.5] <- df$y1[df$x1 < 0.5] + 1
> cf <- cforest(y1 + y2 ~ x1 + x2, data = df)
There were 50 or more warnings (use warnings() to see the first 50)
> pr <- predict(cf)
> stopifnot(length(pr) == nrow(df) || lengthl(pr[[1]]) != 2)
> 
> ### varimp with ordered response
> ### spotted by Max Kuhn <Max.Kuhn@pfizer.com>
> data("mammoexp", package = "TH.data")
> test <- cforest(ME ~ ., data = mammoexp, control = cforest_unbiased(ntree = 50))
> stopifnot(sum(abs(varimp(test))) > 0)
> 
> ### missing values in factors lead to segfaults on 64 bit systems
> ### spotted by Carolin Strobl <carolin.strobl@lme.de>
> y <- rnorm(100)
> x <- gl(2, 50)
> z <- gl(2, 50)[sample(1:100)]
> y <- y + (x == "1") * 3
> xNA <- x
> xNA[1:2] <- NA
> ctree(y ~ xNA )

	 Conditional inference tree with 2 terminal nodes

Response:  y 
Input:  xNA 
Number of observations:  100 

1) xNA == {1}; criterion = 1, statistic = 72.566
  2)*  weights = 48 
1) xNA == {2}
  3)*  weights = 52 
> 
> 
> y <- rnorm(100)
> x <- y + rnorm(100, sd = 0.1)
> 
> tmp <- data.frame(x, y)
> 
> x[sample(1:100)[1:10]] <- NA
> 
> ct1 <- ctree(y ~ x, data = tmp)
> ct2 <- ctree(y ~ x, data = tmp[complete.cases(tmp),])
> w <- as.double(complete.cases(tmp))
> ct3 <- ctree(y ~ x, data = tmp, weights = w)
> 
> xx <- data.frame(x = rnorm(100))
> t1 <- max(abs(predict(ct2, newdata = xx) - predict(ct3, newdata = xx))) == 0
> t2 <- nterminal(ct1@tree) == nterminal(ct2@tree)
> t3 <- nterminal(ct3@tree) == nterminal(ct1@tree)
> t4 <- all.equal(ct2@tree$psplit, ct1@tree$psplit)
> stopifnot(t1 && t2 && t3 && t4)
> 
> y <- rnorm(100)
> x <- cut(y, c(-Inf, -1, 0, 1, Inf))
> 
> tmp <- data.frame(x, y)
> 
> x[sample(1:100)[1:10]] <- NA
> 
> ct1 <- ctree(y ~ x, data = tmp)
> ct2 <- ctree(y ~ x, data = tmp[complete.cases(tmp),])
> w <- as.double(complete.cases(tmp))
> ct3 <- ctree(y ~ x, data = tmp, weights = w)
> 
> stopifnot(all.equal(ct2@tree$psplit, ct1@tree$psplit))
> stopifnot(all.equal(ct2@tree$psplit, ct3@tree$psplit))
> 
> ### predictions for obs with zero weights
> ### spotted by Mark Difford <mark_difford@yahoo.co.uk>
> airq <- subset(airquality, !is.na(Ozone))
> w <- rep(1, nrow(airq))
> w[1:5] <- 0
> 
> ctw <- ctree(Ozone ~ ., data = airq, weights = w)
> stopifnot(all.equal(predict(ctw)[1:5], predict(ctw, newdata = airq)[1:5]))
> rfw <- cforest(Ozone ~ ., data = airq, weights = w)
> stopifnot(all.equal(predict(rfw)[1:5], predict(rfw, newdata = airq)[1:5]))
> 
> ### more surrogate splits than available requested
> ### spotted by Henric Nilsson <henric.nilsson@sorch.se>
> airq <- data.frame(airq,
+                     x1 = factor(ifelse(runif(nrow(airq)) < 0.5, 0, 1)),
+                     x2 = factor(ifelse(runif(nrow(airq)) < 0.5, 0, 1)),
+                     x3 = factor(ifelse(runif(nrow(airq)) < 0.5, 0, 1)))
> 
> foo <- function(nm) 
+     ctree(Ozone ~ ., data = airq,
+           controls = ctree_control(maxsurrogate = nm))
> foo(4)

	 Conditional inference tree with 6 terminal nodes

Response:  Ozone 
Inputs:  Solar.R, Wind, Temp, Month, Day, x1, x2, x3 
Number of observations:  116 

1) Temp <= 82; criterion = 1, statistic = 56.086
  2) Wind <= 6.9; criterion = 0.997, statistic = 12.969
    3)*  weights = 10 
  2) Wind > 6.9
    4) Temp <= 77; criterion = 0.995, statistic = 11.599
      5)*  weights = 48 
    4) Temp > 77
      6)*  weights = 21 
1) Temp > 82
  7) Wind <= 10.3; criterion = 0.995, statistic = 11.712
    8) x1 == {1}; criterion = 0.961, statistic = 7.877
      9)*  weights = 15 
    8) x1 == {0}
      10)*  weights = 15 
  7) Wind > 10.3
    11)*  weights = 7 
> try(foo(5))
Error in model@fit(data, ...) : 
  cannot set up 5 surrogate splits with only 4 ordered input variable(s)
> try(foo(6))
Error in model@fit(data, ...) : 
  cannot set up 6 surrogate splits with only 4 ordered input variable(s)
> 
> ### variance = 0 due to constant variables
> ### spotted by Sebastian Wietzke <Sebastian.Wietzke@axa.de>
> v <- rep(0,20)
> w <- rep(0,20)
> x <- 1:20
> y <- rep(1,20)
> z <- c(4,5,8,2,6,1,3,6,8,2,5,8,9,3,5,8,9,4,6,8)
> tmp <- ctree(z ~ v+w+x+y,controls = ctree_control(mincriterion = 0.80,
+              minsplit = 2, minbucket = 1, testtype = "Univariate", teststat = "quad"))
> stopifnot(all(tmp@tree$criterion$criterion[c(1,2,4)] == 0))
> 
> ### optimal split in last observation lead to selection of suboptimal split
> data("GlaucomaM", package = "TH.data")
> tmp <- subset(GlaucomaM, vari <= 0.059)
> weights <- rep(1.0, nrow(tmp))
> stopifnot(all.equal(Split(tmp$vasg, tmp$Class, weights, 
+                     ctree_control()@splitctrl)[[1]], 0.066))
> 
> ### model.matrix.survReg was missing from modeltools
> data("GBSG2", package = "TH.data")
> nloglik <- function(x) -logLik(x)
> GBSG2$time <- GBSG2$time/365
> mobGBSG2 <- mob(Surv(time, cens) ~ horTh + pnodes | progrec + menostat +
+   estrec + menostat + age + tsize + tgrade, data = GBSG2, model = survReg,
+   control = mob_control(objfun = nloglik, minsplit = 40))
> plot(mobGBSG2, terminal = node_scatterplot, tp_args = list(yscale = c(-0.1, 11)))
> 
> ### factors were evaluated for surrogate splits
> data("Ozone", package = "mlbench")
> Ozone$V2 <- ordered(Ozone$V2)
> Ozone <- subset(Ozone, !is.na(V4))
> rf <- cforest(V4 ~ ., data = Ozone, control = cforest_unbiased(maxsurrogate = 7))
> 
> ### scores for response
> ### spotted and fixed by Silke Janitza <janitza@ibe.med.uni-muenchen.de>
> tmp <- data.frame(y = gl(3, 10, ordered = TRUE), x = gl(3, 10, ordered = TRUE))
> ct <- ctree(y ~ x, data = tmp, scores = list(y = c(0, 10, 11), x = c(1, 2, 5)))
> stopifnot(isTRUE(all.equal(ct@responses@scores, list(y = c(0, 10, 11)))))
> 
> ### deal with empty levels for teststat = "quad" by
> ### removing elements of the teststatistic with zero variance  
> ### reported by Wei-Yin Loh <loh@stat.wisc.edu>
> tdata <-
+ structure(list(ytrain = structure(c(3L, 7L, 3L, 2L, 1L, 6L, 2L, 
+ 1L, 1L, 2L, 1L, 2L, 3L, 3L, 2L, 1L, 2L, 6L, 2L, 4L, 6L, 1L, 2L, 
+ 3L, 7L, 6L, 4L, 6L, 2L, 2L, 1L, 2L, 6L, 1L, 7L, 1L, 3L, 6L, 2L, 
+ 1L, 7L, 2L, 7L, 2L, 3L, 2L, 1L, 1L, 3L, 1L, 6L, 2L, 2L, 2L, 2L, 
+ 2L, 1L, 1L, 6L, 6L, 7L, 2L, 2L, 2L, 2L, 2L, 1L, 3L, 6L, 5L, 1L, 
+ 1L, 4L, 7L, 2L, 3L, 3L, 3L, 1L, 8L, 1L, 6L, 2L, 8L, 3L, 4L, 6L, 
+ 2L, 7L, 3L, 6L, 6L, 1L, 1L, 2L, 6L, 3L, 3L, 1L, 2L, 3L, 1L, 2L, 
+ 7L, 2L, 3L, 6L, 2L, 5L, 2L, 2L, 2L, 1L, 3L, 3L, 7L, 3L, 2L, 3L, 
+ 3L, 1L, 6L, 1L, 1L, 1L, 7L, 1L, 3L, 7L, 6L, 1L, 3L, 3L, 6L, 4L, 
+ 2L, 3L, 2L, 8L, 3L, 4L, 2L, 2L, 2L, 3L, 2L, 2L, 2L, 3L, 4L, 6L, 
+ 4L, 8L, 2L, 2L, 3L, 3L, 2L, 3L, 6L, 2L, 1L, 2L, 2L, 7L, 2L, 1L, 
+ 1L, 7L, 2L, 7L, 6L, 6L, 6L), .Label = c("0", "1", "2", "3", "4", 
+ "5", "6", "7"), class = "factor"), landmass = c(5L, 3L, 4L, 6L, 
+ 3L, 4L, 1L, 2L, 2L, 6L, 3L, 1L, 5L, 5L, 1L, 3L, 1L, 4L, 1L, 5L, 
+ 4L, 2L, 1L, 5L, 3L, 4L, 5L, 4L, 4L, 1L, 4L, 1L, 4L, 2L, 5L, 2L, 
+ 4L, 4L, 6L, 1L, 1L, 3L, 3L, 3L, 4L, 1L, 1L, 2L, 4L, 1L, 4L, 4L, 
+ 3L, 2L, 6L, 3L, 3L, 2L, 4L, 4L, 3L, 3L, 3L, 3L, 1L, 6L, 1L, 4L, 
+ 4L, 2L, 1L, 1L, 5L, 3L, 3L, 6L, 5L, 5L, 3L, 5L, 3L, 4L, 1L, 5L, 
+ 5L, 5L, 4L, 6L, 5L, 5L, 4L, 4L, 3L, 3L, 4L, 4L, 5L, 5L, 3L, 6L, 
+ 4L, 1L, 6L, 5L, 1L, 4L, 4L, 6L, 5L, 3L, 1L, 6L, 1L, 4L, 4L, 5L, 
+ 5L, 3L, 5L, 5L, 2L, 6L, 2L, 2L, 6L, 3L, 1L, 5L, 3L, 4L, 4L, 5L, 
+ 4L, 4L, 5L, 6L, 4L, 4L, 5L, 5L, 5L, 1L, 1L, 1L, 4L, 2L, 3L, 3L, 
+ 5L, 5L, 4L, 5L, 4L, 6L, 2L, 4L, 5L, 1L, 5L, 4L, 3L, 2L, 1L, 1L, 
+ 5L, 6L, 3L, 2L, 5L, 6L, 3L, 4L, 4L, 4L), zone = c(1L, 1L, 1L, 
+ 3L, 1L, 2L, 4L, 3L, 3L, 2L, 1L, 4L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, 
+ 1L, 2L, 3L, 4L, 1L, 1L, 4L, 1L, 2L, 1L, 4L, 4L, 4L, 1L, 3L, 1L, 
+ 4L, 2L, 2L, 3L, 4L, 4L, 1L, 1L, 1L, 1L, 4L, 4L, 3L, 1L, 4L, 1L, 
+ 1L, 4L, 3L, 2L, 1L, 1L, 4L, 2L, 4L, 1L, 1L, 4L, 1L, 4L, 1L, 4L, 
+ 4L, 4L, 4L, 4L, 4L, 1L, 1L, 4L, 2L, 1L, 1L, 4L, 1L, 1L, 4L, 4L, 
+ 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 4L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 
+ 1L, 4L, 4L, 1L, 1L, 4L, 4L, 2L, 2L, 1L, 1L, 4L, 2L, 4L, 1L, 1L, 
+ 1L, 1L, 1L, 1L, 1L, 4L, 2L, 3L, 3L, 1L, 1L, 4L, 1L, 1L, 2L, 1L, 
+ 1L, 4L, 4L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 4L, 4L, 4L, 1L, 4L, 1L, 
+ 1L, 1L, 1L, 2L, 1L, 1L, 2L, 4L, 1L, 1L, 4L, 1L, 1L, 4L, 3L, 4L, 
+ 4L, 1L, 2L, 1L, 4L, 1L, 3L, 1L, 2L, 2L, 2L), area = c(648L, 29L, 
+ 2388L, 0L, 0L, 1247L, 0L, 2777L, 2777L, 7690L, 84L, 19L, 1L, 
+ 143L, 0L, 31L, 23L, 113L, 0L, 47L, 600L, 8512L, 0L, 6L, 111L, 
+ 274L, 678L, 28L, 474L, 9976L, 4L, 0L, 623L, 757L, 9561L, 1139L, 
+ 2L, 342L, 0L, 51L, 115L, 9L, 128L, 43L, 22L, 0L, 49L, 284L, 1001L, 
+ 21L, 28L, 1222L, 1L, 12L, 18L, 337L, 547L, 91L, 268L, 10L, 108L, 
+ 249L, 0L, 132L, 0L, 0L, 109L, 246L, 36L, 215L, 28L, 112L, 1L, 
+ 93L, 103L, 1904L, 1648L, 435L, 70L, 21L, 301L, 323L, 11L, 372L, 
+ 98L, 181L, 583L, 0L, 236L, 10L, 30L, 111L, 0L, 3L, 587L, 118L, 
+ 333L, 0L, 0L, 0L, 1031L, 1973L, 1L, 1566L, 0L, 447L, 783L, 0L, 
+ 140L, 41L, 0L, 268L, 128L, 1267L, 925L, 121L, 195L, 324L, 212L, 
+ 804L, 76L, 463L, 407L, 1285L, 300L, 313L, 9L, 11L, 237L, 26L, 
+ 0L, 2150L, 196L, 72L, 1L, 30L, 637L, 1221L, 99L, 288L, 66L, 0L, 
+ 0L, 0L, 2506L, 63L, 450L, 41L, 185L, 36L, 945L, 514L, 57L, 1L, 
+ 5L, 164L, 781L, 0L, 84L, 236L, 245L, 178L, 0L, 9363L, 22402L, 
+ 15L, 0L, 912L, 333L, 3L, 256L, 905L, 753L, 391L), population = c(16L, 
+ 3L, 20L, 0L, 0L, 7L, 0L, 28L, 28L, 15L, 8L, 0L, 0L, 90L, 0L, 
+ 10L, 0L, 3L, 0L, 1L, 1L, 119L, 0L, 0L, 9L, 7L, 35L, 4L, 8L, 24L, 
+ 0L, 0L, 2L, 11L, 1008L, 28L, 0L, 2L, 0L, 2L, 10L, 1L, 15L, 5L, 
+ 0L, 0L, 6L, 8L, 47L, 5L, 0L, 31L, 0L, 0L, 1L, 5L, 54L, 0L, 1L, 
+ 1L, 17L, 61L, 0L, 10L, 0L, 0L, 8L, 6L, 1L, 1L, 6L, 4L, 5L, 11L, 
+ 0L, 157L, 39L, 14L, 3L, 4L, 57L, 7L, 2L, 118L, 2L, 6L, 17L, 0L, 
+ 3L, 3L, 1L, 1L, 0L, 0L, 9L, 6L, 13L, 0L, 0L, 0L, 2L, 77L, 0L, 
+ 2L, 0L, 20L, 12L, 0L, 16L, 14L, 0L, 2L, 3L, 5L, 56L, 18L, 9L, 
+ 4L, 1L, 84L, 2L, 3L, 3L, 14L, 48L, 36L, 3L, 0L, 22L, 5L, 0L, 
+ 9L, 6L, 3L, 3L, 0L, 5L, 29L, 39L, 2L, 15L, 0L, 0L, 0L, 20L, 0L, 
+ 8L, 6L, 10L, 18L, 18L, 49L, 2L, 0L, 1L, 7L, 45L, 0L, 1L, 13L, 
+ 56L, 3L, 0L, 231L, 274L, 0L, 0L, 15L, 60L, 0L, 22L, 28L, 6L, 
+ 8L), language = structure(c(10L, 6L, 8L, 1L, 6L, 10L, 1L, 2L, 
+ 2L, 1L, 4L, 1L, 8L, 6L, 1L, 6L, 1L, 3L, 1L, 10L, 10L, 6L, 1L, 
+ 10L, 5L, 3L, 10L, 10L, 3L, 1L, 6L, 1L, 10L, 2L, 7L, 2L, 3L, 10L, 
+ 1L, 2L, 2L, 6L, 5L, 6L, 3L, 1L, 2L, 2L, 8L, 2L, 10L, 10L, 6L, 
+ 1L, 1L, 9L, 3L, 3L, 10L, 1L, 4L, 4L, 1L, 6L, 1L, 1L, 2L, 3L, 
+ 6L, 1L, 3L, 2L, 7L, 9L, 6L, 10L, 6L, 8L, 1L, 10L, 6L, 3L, 1L, 
+ 9L, 8L, 10L, 10L, 1L, 10L, 8L, 10L, 10L, 4L, 4L, 10L, 10L, 10L, 
+ 10L, 10L, 10L, 8L, 2L, 10L, 10L, 1L, 8L, 10L, 10L, 10L, 6L, 6L, 
+ 1L, 2L, 3L, 10L, 10L, 8L, 6L, 8L, 6L, 2L, 1L, 2L, 2L, 10L, 5L, 
+ 2L, 8L, 6L, 10L, 6L, 8L, 3L, 1L, 7L, 1L, 10L, 6L, 10L, 8L, 10L, 
+ 1L, 1L, 1L, 8L, 6L, 6L, 4L, 8L, 7L, 10L, 10L, 3L, 10L, 1L, 8L, 
+ 9L, 1L, 8L, 10L, 1L, 2L, 1L, 1L, 5L, 6L, 6L, 2L, 10L, 1L, 6L, 
+ 10L, 10L, 10L), .Label = c("1", "2", "3", "4", "5", "6", "7", 
+ "8", "9", "10"), class = "factor"), bars = c(0L, 0L, 2L, 0L, 
+ 3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 3L, 0L, 0L, 0L, 0L, 
+ 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 2L, 1L, 0L, 1L, 0L, 0L, 0L, 
+ 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+ 0L, 0L, 0L, 0L, 3L, 3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 3L, 
+ 1L, 0L, 2L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 0L, 3L, 3L, 0L, 0L, 
+ 0L, 0L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 2L, 0L, 
+ 0L, 3L, 0L, 3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 0L, 
+ 0L, 0L, 0L, 1L, 0L, 0L, 0L, 3L, 0L, 0L, 0L, 0L, 3L, 3L, 0L, 0L, 
+ 3L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 5L, 0L, 0L, 0L, 0L, 
+ 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 
+ 0L, 0L, 2L, 0L, 0L, 0L, 0L, 0L, 3L, 0L), stripes = c(3L, 0L, 
+ 0L, 0L, 0L, 2L, 1L, 3L, 3L, 0L, 3L, 3L, 0L, 0L, 0L, 0L, 2L, 0L, 
+ 0L, 0L, 5L, 0L, 0L, 0L, 3L, 2L, 0L, 0L, 0L, 0L, 2L, 0L, 0L, 2L, 
+ 0L, 3L, 0L, 0L, 0L, 5L, 5L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 3L, 3L, 
+ 3L, 3L, 0L, 0L, 0L, 0L, 0L, 0L, 3L, 5L, 3L, 3L, 1L, 9L, 0L, 0L, 
+ 0L, 0L, 2L, 0L, 0L, 3L, 0L, 3L, 0L, 2L, 3L, 3L, 0L, 2L, 0L, 0L, 
+ 0L, 0L, 3L, 0L, 5L, 0L, 3L, 2L, 0L, 11L, 2L, 3L, 2L, 3L, 14L, 
+ 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 5L, 3L, 0L, 3L, 1L, 0L, 3L, 
+ 3L, 0L, 5L, 3L, 0L, 2L, 0L, 0L, 0L, 3L, 0L, 0L, 2L, 5L, 0L, 0L, 
+ 0L, 3L, 0L, 0L, 3L, 2L, 0L, 0L, 3L, 0L, 3L, 0L, 0L, 0L, 0L, 3L, 
+ 5L, 0L, 0L, 3L, 0L, 0L, 5L, 5L, 0L, 0L, 0L, 0L, 0L, 3L, 6L, 0L, 
+ 9L, 0L, 13L, 0L, 0L, 0L, 3L, 0L, 0L, 3L, 0L, 0L, 7L), colours = c(5L, 
+ 3L, 3L, 5L, 3L, 3L, 3L, 2L, 3L, 3L, 2L, 3L, 2L, 2L, 3L, 3L, 8L, 
+ 2L, 6L, 4L, 3L, 4L, 6L, 4L, 5L, 3L, 3L, 3L, 3L, 2L, 5L, 6L, 5L, 
+ 3L, 2L, 3L, 2L, 3L, 4L, 3L, 3L, 3L, 3L, 2L, 4L, 6L, 3L, 3L, 4L, 
+ 2L, 4L, 3L, 3L, 6L, 7L, 2L, 3L, 3L, 3L, 4L, 3L, 3L, 3L, 2L, 3L, 
+ 7L, 2L, 3L, 4L, 5L, 2L, 2L, 6L, 3L, 3L, 2L, 3L, 4L, 3L, 2L, 3L, 
+ 3L, 3L, 2L, 4L, 2L, 4L, 4L, 3L, 4L, 4L, 3L, 3L, 3L, 3L, 3L, 4L, 
+ 3L, 3L, 3L, 2L, 4L, 2L, 3L, 7L, 2L, 5L, 3L, 3L, 3L, 3L, 3L, 2L, 
+ 3L, 2L, 3L, 4L, 3L, 3L, 2L, 3L, 4L, 6L, 2L, 4L, 2L, 3L, 2L, 7L, 
+ 4L, 4L, 2L, 3L, 3L, 2L, 4L, 2L, 5L, 4L, 4L, 4L, 5L, 4L, 4L, 4L, 
+ 4L, 2L, 2L, 4L, 3L, 4L, 3L, 4L, 2L, 3L, 2L, 2L, 6L, 4L, 5L, 3L, 
+ 3L, 6L, 3L, 2L, 4L, 4L, 7L, 2L, 3L, 4L, 4L, 4L, 5L), red = c(1L, 
+ 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 
+ 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
+ 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
+ 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 
+ 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 
+ 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
+ 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 
+ 0L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 
+ 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 
+ 1L, 0L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
+ 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), green = c(1L, 
+ 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 
+ 1L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 
+ 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 
+ 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 
+ 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 
+ 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 
+ 1L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 
+ 1L, 1L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 
+ 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 
+ 1L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 
+ 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L), blue = c(0L, 
+ 0L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 
+ 0L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 
+ 1L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 
+ 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 
+ 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 
+ 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 
+ 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 
+ 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 1L, 
+ 0L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 
+ 0L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 
+ 1L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L), gold = c(1L, 
+ 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 
+ 0L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 
+ 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 
+ 0L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 0L, 1L, 
+ 1L, 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+ 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 
+ 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 
+ 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 
+ 1L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 1L, 1L, 0L, 
+ 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 
+ 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L), white = c(1L, 
+ 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 
+ 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, 
+ 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 
+ 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 
+ 1L, 1L, 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
+ 1L, 0L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 
+ 1L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
+ 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
+ 0L, 0L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 
+ 1L, 0L, 1L, 1L, 1L, 0L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 
+ 1L, 1L, 1L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 0L, 1L), black = c(1L, 
+ 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 1L, 
+ 0L, 1L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 
+ 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 
+ 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 
+ 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
+ 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 
+ 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 
+ 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 
+ 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 1L, 0L, 1L, 
+ 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L, 
+ 0L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 1L, 1L), orange = c(0L, 
+ 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 
+ 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 
+ 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+ 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+ 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 
+ 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+ 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 
+ 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 
+ 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 
+ 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
+ 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 0L), mainhue = structure(c(5L, 
+ 7L, 5L, 2L, 4L, 7L, 8L, 2L, 2L, 2L, 7L, 2L, 7L, 5L, 2L, 4L, 2L, 
+ 5L, 7L, 6L, 2L, 5L, 2L, 4L, 7L, 7L, 7L, 7L, 4L, 7L, 4L, 2L, 4L, 
+ 7L, 7L, 4L, 5L, 7L, 2L, 2L, 2L, 8L, 8L, 7L, 2L, 5L, 2L, 4L, 1L, 
+ 2L, 5L, 5L, 8L, 2L, 2L, 8L, 8L, 8L, 5L, 7L, 4L, 1L, 8L, 2L, 4L, 
+ 2L, 2L, 4L, 4L, 5L, 1L, 2L, 2L, 7L, 2L, 7L, 7L, 7L, 8L, 8L, 8L, 
+ 8L, 5L, 8L, 1L, 7L, 7L, 7L, 7L, 7L, 2L, 7L, 7L, 7L, 7L, 7L, 7L, 
+ 7L, 7L, 2L, 5L, 5L, 2L, 7L, 2L, 7L, 4L, 2L, 3L, 7L, 8L, 2L, 2L, 
+ 6L, 5L, 2L, 7L, 7L, 7L, 5L, 7L, 1L, 7L, 7L, 2L, 8L, 7L, 3L, 7L, 
+ 7L, 5L, 5L, 5L, 5L, 8L, 5L, 2L, 6L, 8L, 7L, 4L, 5L, 2L, 5L, 7L, 
+ 7L, 2L, 7L, 7L, 7L, 5L, 7L, 5L, 7L, 7L, 7L, 7L, 2L, 5L, 4L, 7L, 
+ 8L, 8L, 8L, 7L, 7L, 4L, 7L, 7L, 7L, 7L, 5L, 5L, 5L), .Label = c("black", 
+ "blue", "brown", "gold", "green", "orange", "red", "white"), class = "factor"), 
+     circles = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 1L, 0L, 0L, 1L, 0L, 1L, 4L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 
+     1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 
+     0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 2L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L), crosses = c(0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 
+     1L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 2L, 1L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 2L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 
+     0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), saltires = c(0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L), quarters = c(0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 
+     0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 
+     0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
+     0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 4L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 1L, 0L, 
+     0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 
+     0L, 0L, 0L, 0L), sunstars = c(1L, 1L, 1L, 0L, 0L, 1L, 0L, 
+     0L, 1L, 6L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 22L, 
+     0L, 0L, 1L, 1L, 14L, 3L, 1L, 0L, 1L, 4L, 1L, 1L, 5L, 0L, 
+     4L, 1L, 15L, 0L, 1L, 0L, 0L, 0L, 1L, 10L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 7L, 
+     0L, 0L, 0L, 1L, 0L, 0L, 5L, 0L, 0L, 0L, 0L, 0L, 3L, 0L, 1L, 
+     0L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
+     1L, 1L, 0L, 0L, 1L, 1L, 0L, 4L, 1L, 0L, 1L, 1L, 1L, 2L, 0L, 
+     6L, 4L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 1L, 2L, 5L, 1L, 0L, 4L, 
+     0L, 1L, 0L, 2L, 0L, 2L, 0L, 1L, 0L, 5L, 5L, 1L, 0L, 0L, 1L, 
+     0L, 2L, 0L, 0L, 0L, 1L, 0L, 0L, 2L, 1L, 0L, 0L, 1L, 0L, 0L, 
+     1L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 50L, 1L, 0L, 0L, 7L, 1L, 
+     5L, 1L, 0L, 0L, 1L), crescent = c(0L, 0L, 1L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     1L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 
+     1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L), triangle = c(0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
+     0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 
+     0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 
+     0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 1L, 1L, 
+     0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     1L), icon = c(1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 1L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L, 0L, 
+     1L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
+     1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 
+     0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 
+     1L, 1L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 
+     0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 
+     1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
+     0L, 1L, 0L, 1L, 0L, 1L, 1L, 0L, 0L, 0L, 1L, 0L, 1L), animate = c(0L, 
+     1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     1L, 0L, 1L, 1L, 0L, 0L, 1L, 1L, 1L, 0L, 1L, 0L, 0L, 1L, 1L, 
+     1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 
+     0L, 0L, 1L, 0L, 0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     1L, 1L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 1L, 0L, 0L, 1L, 0L, 0L, 1L, 
+     0L, 1L, 0L, 0L, 0L, 1L, 1L, 1L), text = c(0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 
+     0L, 0L, 1L, 1L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 
+     0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 1L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 
+     0L, 0L, 0L, 0L, 1L, 1L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 1L, 0L, 0L, 0L, 0L, 0L, 0L, 
+     0L, 0L, 0L, 0L, 0L), topleft = structure(c(1L, 6L, 4L, 2L, 
+     2L, 6L, 7L, 2L, 2L, 7L, 6L, 2L, 7L, 4L, 2L, 1L, 6L, 4L, 7L, 
+     5L, 2L, 4L, 7L, 7L, 7L, 6L, 2L, 7L, 4L, 6L, 6L, 7L, 2L, 2L, 
+     6L, 3L, 4L, 6L, 7L, 2L, 2L, 7L, 7L, 6L, 7L, 4L, 2L, 3L, 6L, 
+     2L, 4L, 4L, 7L, 7L, 7L, 7L, 2L, 2L, 4L, 6L, 1L, 1L, 7L, 2L, 
+     6L, 6L, 2L, 6L, 6L, 1L, 1L, 2L, 7L, 6L, 2L, 6L, 4L, 6L, 4L, 
+     2L, 4L, 6L, 3L, 7L, 1L, 6L, 1L, 6L, 6L, 6L, 4L, 2L, 2L, 6L, 
+     7L, 1L, 2L, 6L, 7L, 2L, 4L, 4L, 2L, 6L, 7L, 6L, 4L, 2L, 2L, 
+     6L, 7L, 7L, 2L, 5L, 4L, 2L, 6L, 6L, 6L, 7L, 7L, 6L, 6L, 6L, 
+     2L, 7L, 6L, 7L, 2L, 6L, 4L, 4L, 4L, 4L, 6L, 2L, 2L, 5L, 7L, 
+     6L, 3L, 4L, 2L, 2L, 6L, 4L, 2L, 6L, 6L, 2L, 4L, 6L, 6L, 7L, 
+     7L, 6L, 6L, 7L, 6L, 1L, 7L, 7L, 7L, 2L, 6L, 1L, 3L, 3L, 6L, 
+     2L, 2L, 4L, 4L, 4L), .Label = c("black", "blue", "gold", 
+     "green", "orange", "red", "white"), class = "factor"), botright = structure(c(5L, 
+     7L, 8L, 7L, 7L, 1L, 2L, 2L, 2L, 2L, 7L, 2L, 7L, 5L, 2L, 7L, 
+     7L, 5L, 7L, 7L, 2L, 5L, 2L, 4L, 7L, 5L, 7L, 8L, 4L, 7L, 5L, 
+     2L, 4L, 7L, 7L, 7L, 5L, 7L, 2L, 2L, 2L, 8L, 7L, 7L, 5L, 5L, 
+     2L, 7L, 1L, 2L, 7L, 7L, 8L, 2L, 2L, 8L, 7L, 7L, 2L, 5L, 4L, 
+     4L, 7L, 2L, 7L, 7L, 2L, 5L, 5L, 5L, 7L, 2L, 2L, 5L, 2L, 8L, 
+     7L, 1L, 6L, 2L, 7L, 5L, 4L, 8L, 5L, 7L, 5L, 2L, 7L, 7L, 2L, 
+     7L, 7L, 2L, 5L, 5L, 8L, 7L, 7L, 2L, 5L, 7L, 2L, 7L, 2L, 7L, 
+     4L, 2L, 2L, 2L, 8L, 2L, 2L, 5L, 5L, 2L, 1L, 7L, 5L, 5L, 8L, 
+     1L, 2L, 7L, 7L, 7L, 7L, 3L, 7L, 5L, 5L, 5L, 7L, 2L, 8L, 5L, 
+     2L, 2L, 8L, 1L, 4L, 7L, 2L, 5L, 1L, 5L, 2L, 7L, 1L, 7L, 2L, 
+     7L, 5L, 7L, 8L, 7L, 7L, 2L, 1L, 7L, 7L, 8L, 8L, 7L, 7L, 5L, 
+     8L, 7L, 7L, 7L, 7L, 5L, 3L, 5L), .Label = c("black", "blue", 
+     "brown", "gold", "green", "orange", "red", "white"), class = "factor")), .Names = c("ytrain", 
+ "landmass", "zone", "area", "population", "language", "bars", 
+ "stripes", "colours", "red", "green", "blue", "gold", "white", 
+ "black", "orange", "mainhue", "circles", "crosses", "saltires", 
+ "quarters", "sunstars", "crescent", "triangle", "icon", "animate", 
+ "text", "topleft", "botright"), row.names = c(NA, -174L), class = "data.frame")
> tdata$language <-  factor(tdata$language)
> tdata$ytrain <- factor(tdata$ytrain)
> 
> library("coin")
> 
> m <- ctree(ytrain ~ language, data = subset(tdata, language != "8"), 
+     control = ctree_control(testtype = "Univariate", maxdepth = 1L))
> it <- independence_test(ytrain ~ language, data = subset(tdata, language != "8"), 
+                         teststat = "quad")
> stopifnot(isTRUE(all.equal(m@tree$criterion$statistic, 
+                            statistic(it), check.attributes = FALSE)))
> 
> ### easier example
> levels(tdata$language) <- c(1, 1, 1, 1, 1, 1, 2, 8, 1, 1)
> levels(tdata$ytrain) <- c(1, 1, 2, 2, 3, 3, 4, 4, 5, 6)
> m <- ctree(ytrain ~ language, data = subset(tdata, language != "8"),
+     control = ctree_control(testtype = "Univariate", maxdepth = 1L))
> it <- independence_test(ytrain ~ language, data = subset(tdata, language != "8"), 
+                         teststat = "quad")
> stopifnot(isTRUE(all.equal(m@tree$criterion$statistic, 
+                            statistic(it), check.attributes = FALSE)))
> 
> ## the whole exercise manually
> Y <- model.matrix(~ language - 1, data = subset(tdata, language != "8"))
> X <- model.matrix(~ ytrain -1, data = subset(tdata, language != "8"))
> w <- rep(1, nrow(X))
> 
> lin <- coin:::LinearStatistic(Y, X, weights = w)
> expcov <- coin:::ExpectCovarLinearStatistic(Y, X, weights = w)
> 
> tmp <- new("LinStatExpectCovar", ncol(Y), ncol(X))
> tmp@linearstatistic <- lin
> tmp@expectation <- expcov@expectation
> tmp@covariance <- expcov@covariance
> 
> a <- .Call("R_linexpcovReduce", tmp)
> 
> u <- matrix(tmp@linearstatistic - tmp@expectation, nc = 1)
> d <- tmp@dimension
> u <- matrix(tmp@linearstatistic - tmp@expectation, nc = 1)[1:d,,drop = FALSE]
> S <- coin:::MPinv(matrix(as.vector(tmp@covariance[1:d^2]), ncol = d))
> 
> stat <- t(u) %*% S$MPinv %*% u
> stopifnot(isTRUE(all.equal(stat[1,1], statistic(it), 
+                            check.attributes = FALSE)))
> 
> x <- matrix(as.vector(tmp@covariance[1:d^2]), ncol = d)
> s <- svd(x)
> 
> m <- new("svd_mem", 18L)
> m@p <- as.integer(d)
> 
> s2 <- .Call("R_svd", x, m)
> 
> stopifnot(max(abs(s$d - m@s[1:d])) < sqrt(.Machine$double.eps))
> stopifnot(max(abs(s$v - t(matrix(m@v[1:d^2], nrow = d)))) < sqrt(.Machine$double.eps))
> stopifnot(max(abs(s$u - matrix(m@u[1:d^2], nrow = d))) < sqrt(.Machine$double.eps))
> 
> s2 <- .Call("R_svd", tmp@covariance, m)
> 
> stopifnot(max(abs(s$d - m@s[1:d])) < sqrt(.Machine$double.eps))
> stopifnot(max(abs(s$v - t(matrix(m@v[1:d^2], nrow = d)))) < sqrt(.Machine$double.eps))
> stopifnot(max(abs(s$u - matrix(m@u[1:d^2], nrow = d))) < sqrt(.Machine$double.eps))
> 
> a <- .Call("R_MPinv", tmp@covariance, sqrt(.Machine$double.eps), m)
> 
> stat <- t(u) %*% matrix(a@MPinv[1:d^2], ncol = d) %*% u  
> stopifnot(isTRUE(all.equal(stat[1,1], statistic(it), 
+                            check.attributes = FALSE)))
> 
> proc.time()
   user  system elapsed 
  8.260   0.284   8.560