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> ### > attach(NULL, name = "CheckExEnv") > assign(".CheckExEnv", as.environment(2), pos = length(search())) # base > ## add some hooks to label plot pages for base and grid graphics > setHook("plot.new", ".newplot.hook") > setHook("persp", ".newplot.hook") > setHook("grid.newpage", ".gridplot.hook") > > assign("cleanEx", + function(env = .GlobalEnv) { + rm(list = ls(envir = env, all.names = TRUE), envir = env) + RNGkind("default", "default") + set.seed(1) + options(warn = 1) + delayedAssign("T", stop("T used instead of TRUE"), + assign.env = .CheckExEnv) + delayedAssign("F", stop("F used instead of FALSE"), + assign.env = .CheckExEnv) + sch <- search() + newitems <- sch[! sch %in% .oldSearch] + for(item in rev(newitems)) + eval(substitute(detach(item), list(item=item))) + missitems <- .oldSearch[! .oldSearch %in% sch] + if(length(missitems)) + warning("items ", paste(missitems, collapse=", "), + " have been removed from the search path") + }, + env = .CheckExEnv) > assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now > assign("ptime", proc.time(), env = .CheckExEnv) > grDevices::postscript("compositions-Examples.ps") > assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv) > options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly")) > options(warn = 1) > library('compositions') Attaching package: 'compositions' The following object(s) are masked from package:stats : cor cov dist var The following object(s) are masked from package:base : %*% > > assign(".oldSearch", search(), env = .CheckExEnv) > assign(".oldNS", loadedNamespaces(), env = .CheckExEnv) > cleanEx(); ..nameEx <- "Hydrochem" > > ### * Hydrochem > > flush(stderr()); flush(stdout()) > > ### Name: Hydrochem > ### Title: Hydrochemical composition data set of Llobregat river basin > ### water (NE Spain) > ### Aliases: Hydrochem > ### Keywords: datasets > > ### ** Examples > > data(Hydrochem) > biplot(princomp(rplus(Hydrochem))) Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped > biplot(princomp(rcomp(Hydrochem))) Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped Warning: zero-length arrow is of indeterminate angle and so skipped > > biplot(princomp(aplus(Hydrochem))) > biplot(princomp(acomp(Hydrochem))) > > > > cleanEx(); ..nameEx <- "SimulatedAmounts" > > ### * SimulatedAmounts > > flush(stderr()); flush(stdout()) > > ### Name: SimulatedAmounts > ### Title: Simulated amount datasets > ### Aliases: SimulatedAmounts sa.dirichlet sa.dirichlet.dil > ### sa.dirichlet.mix sa.dirichlet5 sa.dirichlet5.dil sa.dirichlet5.mix > ### sa.uniform sa.uniform.dil sa.uniform.mix sa.uniform5 sa.uniform5.dil > ### sa.uniform5.mix sa.lognormals sa.lognormals.dil sa.lognormals.mix > ### sa.lognormals5 sa.lognormals5.dil sa.lognormals5.mix sa.tnormals > ### sa.tnormals.dil sa.tnormals.mix sa.tnormals5 sa.tnormals5.dil > ### sa.tnormals5.mix sa.groups sa.groups.dil sa.groups.mix sa.groups5 > ### sa.groups5.dil sa.groups5.mix sa.groups.area sa.groups5.area > ### Keywords: datasets > > ### ** Examples > > data(SimulatedAmounts) > plot.acomp(sa.lognormals) > plot.acomp(sa.lognormals.dil) > plot.acomp(sa.lognormals.mix) > plot.acomp(sa.lognormals5) > plot.acomp(sa.lognormals5.dil) > plot.acomp(sa.lognormals5.mix) > > library(MASS) > plot.rcomp(sa.tnormals) > plot.rcomp(sa.tnormals.dil) > plot.rcomp(sa.tnormals.mix) > plot.rcomp(sa.tnormals5) > plot.rcomp(sa.tnormals5.dil) > plot.rcomp(sa.tnormals5.mix) > > plot.acomp(sa.groups,col=as.numeric(sa.groups.area),pch=20) > plot.acomp(sa.groups.dil,col=as.numeric(sa.groups.area),pch=20) > plot.acomp(sa.groups.mix,col=as.numeric(sa.groups.area),pch=20) > plot.acomp(sa.groups5,col=as.numeric(sa.groups.area),pch=20) > plot.acomp(sa.groups5.dil,col=as.numeric(sa.groups.area),pch=20) > plot.acomp(sa.groups5.mix,col=as.numeric(sa.groups.area),pch=20) > > plot.acomp(sa.uniform) > plot.acomp(sa.uniform.dil) > plot.acomp(sa.uniform.mix) > plot.acomp(sa.uniform5) > plot.acomp(sa.uniform5.dil) > plot.acomp(sa.uniform5.mix) > > plot.acomp(sa.dirichlet) > plot.acomp(sa.dirichlet.dil) > plot.acomp(sa.dirichlet.mix) > plot.acomp(sa.dirichlet5) > plot.acomp(sa.dirichlet5.dil) > plot.acomp(sa.dirichlet5.mix) > > # The data was simulated with the following commands: > > library(MASS) > dilution <- function(x) {clo(cbind(x,exp(rnorm(nrow(x),5,1))))[,1:ncol(x)]*1E6} > seqmix <- function(x) {clo(apply(x,2,cumsum))*1E6} > > vars <- c("Cu","Zn","Pb") > vars5 <- c("Cu","Zn","Pb","Cd","Co") > > sa.lognormals <- structure(exp(matrix(rnorm(3*60),ncol=3) %*% + chol(matrix(c(1,0.8,-0.2,0.8,1, + -0.2,-0.2,-0.2,1),ncol=3))+ + matrix(rep(c(1:3),each=60),ncol=3)), + dimnames=list(NULL,vars)) > > plot.acomp(sa.lognormals) > pairs(sa.lognormals) > > sa.lognormals.dil <- dilution(sa.lognormals) > plot.acomp(sa.lognormals.dil) > pairs(sa.lognormals.dil) > > sa.lognormals.mix <- seqmix(sa.lognormals.dil) > plot.acomp(sa.lognormals.mix) > pairs(sa.lognormals.mix) > > sa.lognormals5 <- structure(exp(matrix(rnorm(5*60),ncol=5) %*% + chol(matrix(c(1,0.8,-0.2,0,0, + 0.8,1,-0.2,0,0, + -0.2,-0.2,1,0,0, + 0,0,0,5,4.9, + 0,0,0,4.9,5),ncol=5))+ + matrix(rep(c(1:3,-2,-2),each=60),ncol=5)), + dimnames=list(NULL,vars5)) > > plot.acomp(sa.lognormals5) > pairs(sa.lognormals5) > > sa.lognormals5.dil <- dilution(sa.lognormals5) > plot.acomp(sa.lognormals5.dil) > pairs(sa.lognormals5.dil) > > sa.lognormals5.mix <- seqmix(sa.lognormals5.dil) > plot.acomp(sa.lognormals5.mix) > pairs(sa.lognormals5.mix) > > > sa.groups.area <- factor(rep(c("Upper","Middle","Lower"),each=20)) > sa.groups <- structure(exp(matrix(rnorm(3*20*3),ncol=3) %*% + chol(0.5*matrix(c(1,0.8,-0.2,0.8,1, + -0.2,-0.2,-0.2,1),ncol=3))+ + matrix(rep(c(1,2,2.5,2,2.9,5,4,2,5), + each=20),ncol=3)), + dimnames=list(NULL,c("clay","sand","gravel"))) > > plot.acomp(sa.groups,col=as.numeric(sa.groups.area),pch=20) > pairs(sa.lognormals,col=as.numeric(sa.groups.area),pch=20) > > sa.groups.dil <- dilution(sa.groups) > plot.acomp(sa.groups.dil,col=as.numeric(sa.groups.area),pch=20) > pairs(sa.groups.dil,col=as.numeric(sa.groups.area),pch=20) > > sa.groups.mix <- seqmix(sa.groups.dil) > plot.acomp(sa.groups.mix,col=as.numeric(sa.groups.area),pch=20) > pairs(sa.groups.mix,col=as.numeric(sa.groups.area),pch=20) > > > sa.groups5.area <- factor(rep(c("Upper","Middle","Lower"),each=20)) > sa.groups5 <- structure(exp(matrix(rnorm(5*20*3),ncol=5) %*% + chol(matrix(c(1,0.8,-0.2,0,0, + 0.8,1,-0.2,0,0, + -0.2,-0.2,1,0,0, + 0,0,0,5,4.9, + 0,0,0,4.9,5),ncol=5))+ + matrix(rep(c(1,2,2.5, + 2,2.9,5, + 4,2.5,0, + -2,-1,-1, + -1,-2,-3), + each=20),ncol=5)), + dimnames=list(NULL, + vars5)) > > plot.acomp(sa.groups5,col=as.numeric(sa.groups5.area),pch=20) > pairs(sa.groups5,col=as.numeric(sa.groups5.area),pch=20) > > sa.groups5.dil <- dilution(sa.groups5) > plot.acomp(sa.groups5.dil,col=as.numeric(sa.groups5.area),pch=20) > pairs(sa.groups5.dil,col=as.numeric(sa.groups5.area),pch=20) > > sa.groups5.mix <- seqmix(sa.groups5.dil) > plot.acomp(sa.groups5.mix,col=as.numeric(sa.groups5.area),pch=20) > pairs(sa.groups5.mix,col=as.numeric(sa.groups5.area),pch=20) > > > sa.tnormals <- structure(pmax(matrix(rnorm(3*60),ncol=3) %*% + chol(matrix(c(1,0.8,-0.2,0.8,1, + -0.2,-0.2,-0.2,1),ncol=3))+ + matrix(rep(c(0:2),each=60),ncol=3),0), + dimnames=list(NULL,c("clay","sand","gravel"))) > > plot.rcomp(sa.tnormals) > pairs(sa.tnormals) > > sa.tnormals.dil <- dilution(sa.tnormals) > plot.acomp(sa.tnormals.dil) Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values > pairs(sa.tnormals.dil) > > sa.tnormals.mix <- seqmix(sa.tnormals.dil) > plot.acomp(sa.tnormals.mix) Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values > pairs(sa.tnormals.mix) > > > sa.tnormals5 <- structure(pmax(matrix(rnorm(5*60),ncol=5) %*% + chol(matrix(c(1,0.8,-0.2,0,0, + 0.8,1,-0.2,0,0, + -0.2,-0.2,1,0,0, + 0,0,0,0.05,0.049, + 0,0,0,0.049,0.05),ncol=5))+ + matrix(rep(c(0:2,0.1,0.1),each=60),ncol=5),0), + dimnames=list(NULL, + vars5)) > > plot.rcomp(sa.tnormals5) > pairs(sa.tnormals5) > > sa.tnormals5.dil <- dilution(sa.tnormals5) > plot.acomp(sa.tnormals5.dil) Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values Warning in acomp(cbind(Rest = exp(log(Xm) %*% rep(1/NCOL(Xm), NCOL(Xm))), : Compositions has nonpositiv values Warning in acomp(tmp) : Compositions has nonpositiv values Warning in acomp(X, c(1, 2, 3)) : Compositions has nonpositiv values > pairs(sa.tnormals5.dil) > > sa.tnormals5.mix <- seqmix(sa.tnormals5.dil) > plot.acomp(sa.tnormals5.mix) > pairs(sa.tnormals5.mix) > > > sa.dirichlet <- sapply(c(clay=0.2,sand=2,gravel=3),rgamma,n=60) > colnames(sa.dirichlet) <- vars > > plot.acomp(sa.dirichlet) > pairs(sa.dirichlet) > > sa.dirichlet.dil <- dilution(sa.dirichlet) > plot.acomp(sa.dirichlet.dil) > pairs(sa.dirichlet.dil) > > sa.dirichlet.mix <- seqmix(sa.dirichlet.dil) > plot.acomp(sa.dirichlet.mix) > pairs(sa.dirichlet.mix) > > > sa.dirichlet5 <- sapply(c(clay=0.2,sand=2,gravel=3,humus=0.1,plant=0.1),rgamma,n=60) > colnames(sa.dirichlet5) <- vars5 > > plot.acomp(sa.dirichlet5) > pairs(sa.dirichlet5) > > sa.dirichlet5.dil <- dilution(sa.dirichlet5) > plot.acomp(sa.dirichlet5.dil) > pairs(sa.dirichlet5.dil) > > sa.dirichlet5.mix <- seqmix(sa.dirichlet5.dil) > plot.acomp(sa.dirichlet5.mix) > pairs(sa.dirichlet5.mix) > > sa.uniform <- sapply(c(clay=1,sand=1,gravel=1),rgamma,n=60) > colnames(sa.uniform) <- vars > > plot.acomp(sa.uniform) > pairs(sa.uniform) > > sa.uniform.dil <- dilution(sa.uniform) > plot.acomp(sa.uniform.dil) > pairs(sa.uniform.dil) > > sa.uniform.mix <- seqmix(sa.uniform.dil) > plot.acomp(sa.uniform.mix) > pairs(sa.uniform.mix) > > > sa.uniform5 <- sapply(c(clay=1,sand=1,gravel=1,humus=1,plant=1),rgamma,n=60) > colnames(sa.uniform5) <- vars5 > > plot.acomp(sa.uniform5) > pairs(sa.uniform5) > > sa.uniform5.dil <- dilution(sa.uniform5) > plot.acomp(sa.uniform5.dil) > pairs(sa.uniform5.dil) > > sa.uniform5.mix <- seqmix(sa.uniform5.dil) > plot.acomp(sa.uniform5.mix) > pairs(sa.uniform5.mix) > > objects(pattern="sa.*") [1] "sa.dirichlet" "sa.dirichlet.dil" "sa.dirichlet.mix" [4] "sa.dirichlet5" "sa.dirichlet5.dil" "sa.dirichlet5.mix" [7] "sa.groups" "sa.groups.area" "sa.groups.dil" [10] "sa.groups.mix" "sa.groups5" "sa.groups5.area" [13] "sa.groups5.dil" "sa.groups5.mix" "sa.lognormals" [16] "sa.lognormals.dil" "sa.lognormals.mix" "sa.lognormals5" [19] "sa.lognormals5.dil" "sa.lognormals5.mix" "sa.tnormals" [22] "sa.tnormals.dil" "sa.tnormals.mix" "sa.tnormals5" [25] "sa.tnormals5.dil" "sa.tnormals5.mix" "sa.uniform" [28] "sa.uniform.dil" "sa.uniform.mix" "sa.uniform5" [31] "sa.uniform5.dil" "sa.uniform5.mix" > > > > cleanEx(); ..nameEx <- "acomp" > > ### * acomp > > flush(stderr()); flush(stdout()) > > ### Name: acomp > ### Title: Aitchison compositions > ### Aliases: acomp > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > plot(acomp(sa.lognormals)) > > > > cleanEx(); ..nameEx <- "acomparith" > > ### * acomparith > > flush(stderr()); flush(stdout()) > > ### Name: acomparith > ### Title: Power transform in Aitchisons simplex > ### Aliases: power.acomp *.acomp /.acomp > ### Keywords: multivariate > > ### ** Examples > > acomp(1:5)* -1 + acomp(1:5) [1] 0.2 0.2 0.2 0.2 0.2 attr(,"class") [1] "acomp" > data(SimulatedAmounts) > cdata <- acomp(sa.lognormals) > plot( tmp <- (cdata-mean(cdata))/msd(cdata) ) > class(tmp) [1] "acomp" > mean(tmp) Cu Zn Pb 0.3333333 0.3333333 0.3333333 attr(,"class") [1] "acomp" > msd(tmp) [1] 1 > var(tmp) Cu Zn Pb Cu 0.4024702 0.2039003 -0.6063706 Zn 0.2039003 0.3936294 -0.5975298 Pb -0.6063706 -0.5975298 1.2039003 > > > > cleanEx(); ..nameEx <- "acompmargin" > > ### * acompmargin > > flush(stderr()); flush(stdout()) > > ### Name: acompmargin > ### Title: Marginal compositions in Aitchison Compositions > ### Aliases: acompmargin > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > plot.acomp(sa.lognormals5,margin="acomp") > plot.acomp(acompmargin(sa.lognormals5,c("Pb","Zn"))) > plot.acomp(acompmargin(sa.lognormals5,c(1,2))) > > > > cleanEx(); ..nameEx <- "alr" > > ### * alr > > flush(stderr()); flush(stdout()) > > ### Name: alr > ### Title: Additive log ratio transform > ### Aliases: alr alr.inv > ### Keywords: multivariate > > ### ** Examples > > (tmp <- alr(c(1,2,3))) [1] -1.0986123 -0.4054651 attr(,"class") [1] "rmult" > alr.inv(tmp) [1] 0.1666667 0.3333333 0.5000000 attr(,"class") [1] "acomp" > unclass(alr.inv(tmp)) - clo(c(1,2,3)) # 0 [1] 0 0 0 > data(Hydrochem) > cdata <- Hydrochem[,6:19] > pairs(alr(cdata)) > > > > cleanEx(); ..nameEx <- "aplus" > > ### * aplus > > flush(stderr()); flush(stdout()) > > ### Name: aplus > ### Title: Amounts analysed in log-scale > ### Aliases: aplus > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > plot(aplus(sa.lognormals)) > > > > cleanEx(); ..nameEx <- "aplusarithm" > > ### * aplusarithm > > flush(stderr()); flush(stdout()) > > ### Name: aplusarithm > ### Title: vectorial arithmetic for datasets with aplus class > ### Aliases: +.aplus -.aplus *.aplus /.aplus perturbe.aplus power.aplus > ### Keywords: multivariate > > ### ** Examples > > x <- aplus(matrix( sqrt(1:12), ncol= 3 )) > x [,1] [,2] [,3] [1,] 1.000000 2.236068 3.000000 [2,] 1.414214 2.449490 3.162278 [3,] 1.732051 2.645751 3.316625 [4,] 2.000000 2.828427 3.464102 attr(,"class") [1] "aplus" > x+x [,1] [,2] [,3] [1,] 1 5 9 [2,] 2 6 10 [3,] 3 7 11 [4,] 4 8 12 attr(,"class") [1] "aplus" > x + aplus(1:3) [,1] [,2] [,3] [1,] 1.000000 4.472136 9.000000 [2,] 1.414214 4.898979 9.486833 [3,] 1.732051 5.291503 9.949874 [4,] 2.000000 5.656854 10.392305 attr(,"class") [1] "aplus" > x * 1:4 [,1] [,2] [,3] [1,] 1.000000 2.236068 3.00000 [2,] 2.000000 6.000000 10.00000 [3,] 5.196152 18.520259 36.48287 [4,] 16.000000 64.000000 144.00000 attr(,"class") [1] "aplus" > 1:4 * x [,1] [,2] [,3] [1,] 1.000000 2.236068 3.00000 [2,] 2.000000 6.000000 10.00000 [3,] 5.196152 18.520259 36.48287 [4,] 16.000000 64.000000 144.00000 attr(,"class") [1] "aplus" > x / 1:4 [,1] [,2] [,3] [1,] 1.000000 2.236068 3.000000 [2,] 1.189207 1.565085 1.778279 [3,] 1.200937 1.383088 1.491301 [4,] 1.189207 1.296840 1.364262 attr(,"class") [1] "aplus" > x / 10 [,1] [,2] [,3] [1,] 1.000000 1.083798 1.116123 [2,] 1.035265 1.093724 1.122018 [3,] 1.056467 1.102186 1.127378 [4,] 1.071773 1.109569 1.132294 attr(,"class") [1] "aplus" > power.aplus(x,1:4) [,1] [,2] [,3] [1,] 1.000000 2.236068 3.00000 [2,] 2.000000 6.000000 10.00000 [3,] 5.196152 18.520259 36.48287 [4,] 16.000000 64.000000 144.00000 attr(,"class") [1] "aplus" > > > > cleanEx(); ..nameEx <- "apt" > > ### * apt > > flush(stderr()); flush(stdout()) > > ### Name: apt > ### Title: Additive planar transform > ### Aliases: apt apt.inv > ### Keywords: multivariate > > ### ** Examples > > (tmp <- apt(c(1,2,3))) [1] 0.1666667 0.3333333 attr(,"class") [1] "rmult" > apt.inv(tmp) [1] 0.1666667 0.3333333 0.5000000 attr(,"class") [1] "rcomp" > apt.inv(tmp) - clo(c(1,2,3)) # 0 [1] 0 0 0 attr(,"class") [1] "rmult" > data(Hydrochem) > cdata <- Hydrochem[,6:19] > pairs(apt(cdata)) > > > > cleanEx(); ..nameEx <- "asdataframe" > > ### * asdataframe > > flush(stderr()); flush(stdout()) > > ### Name: as.data.frame > ### Title: Convert "compositions" classes to data frames > ### Aliases: as.data.frame.acomp as.data.frame.rcomp as.data.frame.aplus > ### as.data.frame.rplus as.data.frame.rmult > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > as.data.frame(acomp(sa.groups)) clay sand gravel 1 0.238531790 0.45840899 0.30305922 2 0.044958879 0.20244343 0.75259769 3 0.031554884 0.10125397 0.86719115 4 0.248943729 0.40261884 0.34843743 5 0.053912442 0.13547960 0.81060796 6 0.063904398 0.11681811 0.81927749 7 0.017576687 0.11216958 0.87025373 8 0.027600609 0.11459239 0.85780700 9 0.039996070 0.08613840 0.87386553 10 0.015442768 0.10173437 0.88282287 11 0.028977134 0.08204979 0.88897307 12 0.052376585 0.11797465 0.82964877 13 0.078008162 0.24618533 0.67580651 14 0.113074778 0.31782412 0.56910110 15 0.028161241 0.04552202 0.92631674 16 0.042078087 0.13691199 0.82100992 17 0.087293940 0.27561998 0.63708609 18 0.015135459 0.05567816 0.92918638 19 0.019287534 0.04427458 0.93643789 20 0.148110584 0.34267370 0.50921571 21 0.133096867 0.27503661 0.59186652 22 0.306994576 0.65437585 0.03862957 23 0.228582791 0.64885813 0.12255908 24 0.386442602 0.59955634 0.01400106 25 0.168367367 0.64069088 0.19094175 26 0.241675531 0.55235849 0.20596598 27 0.341325186 0.52273849 0.13593632 28 0.138718747 0.51725483 0.34402642 29 0.477267941 0.43512723 0.08760483 30 0.315091909 0.46943783 0.21547026 31 0.414040458 0.43233859 0.15362095 32 0.091807828 0.53714174 0.37105043 33 0.177321745 0.60041342 0.22226484 34 0.277318127 0.57550273 0.14717915 35 0.210352616 0.65065525 0.13899214 36 0.129494801 0.23659708 0.63390812 37 0.227254739 0.72000368 0.05274158 38 0.361842695 0.43701056 0.20114675 39 0.099526510 0.51529507 0.38517842 40 0.432203387 0.42798528 0.13981133 41 0.028013932 0.56588947 0.40609660 42 0.063692489 0.78431761 0.15198990 43 0.046598995 0.68808427 0.26531674 44 0.005696019 0.06497758 0.92932640 45 0.050290757 0.44557477 0.50413448 46 0.054419718 0.68524046 0.26033982 47 0.053106987 0.52368407 0.42320895 48 0.022186090 0.26930296 0.70851095 49 0.016866567 0.18529288 0.79784055 50 0.063882077 0.74071679 0.19540113 51 0.030628346 0.42857897 0.54079269 52 0.012963274 0.19723355 0.78980318 53 0.057298948 0.81633573 0.12636532 54 0.065798656 0.39849533 0.53570602 55 0.042072151 0.48636964 0.47155821 56 0.050651296 0.51775951 0.43158920 57 0.106719047 0.53708079 0.35620016 58 0.033836695 0.55079286 0.41537045 59 0.009670684 0.13820359 0.85212573 60 0.046906231 0.21168173 0.74141204 > data.frame(acomp(sa.groups),groups=sa.groups.area) clay sand gravel groups 1 0.238531790 0.45840899 0.30305922 Upper 2 0.044958879 0.20244343 0.75259769 Upper 3 0.031554884 0.10125397 0.86719115 Upper 4 0.248943729 0.40261884 0.34843743 Upper 5 0.053912442 0.13547960 0.81060796 Upper 6 0.063904398 0.11681811 0.81927749 Upper 7 0.017576687 0.11216958 0.87025373 Upper 8 0.027600609 0.11459239 0.85780700 Upper 9 0.039996070 0.08613840 0.87386553 Upper 10 0.015442768 0.10173437 0.88282287 Upper 11 0.028977134 0.08204979 0.88897307 Upper 12 0.052376585 0.11797465 0.82964877 Upper 13 0.078008162 0.24618533 0.67580651 Upper 14 0.113074778 0.31782412 0.56910110 Upper 15 0.028161241 0.04552202 0.92631674 Upper 16 0.042078087 0.13691199 0.82100992 Upper 17 0.087293940 0.27561998 0.63708609 Upper 18 0.015135459 0.05567816 0.92918638 Upper 19 0.019287534 0.04427458 0.93643789 Upper 20 0.148110584 0.34267370 0.50921571 Upper 21 0.133096867 0.27503661 0.59186652 Middle 22 0.306994576 0.65437585 0.03862957 Middle 23 0.228582791 0.64885813 0.12255908 Middle 24 0.386442602 0.59955634 0.01400106 Middle 25 0.168367367 0.64069088 0.19094175 Middle 26 0.241675531 0.55235849 0.20596598 Middle 27 0.341325186 0.52273849 0.13593632 Middle 28 0.138718747 0.51725483 0.34402642 Middle 29 0.477267941 0.43512723 0.08760483 Middle 30 0.315091909 0.46943783 0.21547026 Middle 31 0.414040458 0.43233859 0.15362095 Middle 32 0.091807828 0.53714174 0.37105043 Middle 33 0.177321745 0.60041342 0.22226484 Middle 34 0.277318127 0.57550273 0.14717915 Middle 35 0.210352616 0.65065525 0.13899214 Middle 36 0.129494801 0.23659708 0.63390812 Middle 37 0.227254739 0.72000368 0.05274158 Middle 38 0.361842695 0.43701056 0.20114675 Middle 39 0.099526510 0.51529507 0.38517842 Middle 40 0.432203387 0.42798528 0.13981133 Middle 41 0.028013932 0.56588947 0.40609660 Lower 42 0.063692489 0.78431761 0.15198990 Lower 43 0.046598995 0.68808427 0.26531674 Lower 44 0.005696019 0.06497758 0.92932640 Lower 45 0.050290757 0.44557477 0.50413448 Lower 46 0.054419718 0.68524046 0.26033982 Lower 47 0.053106987 0.52368407 0.42320895 Lower 48 0.022186090 0.26930296 0.70851095 Lower 49 0.016866567 0.18529288 0.79784055 Lower 50 0.063882077 0.74071679 0.19540113 Lower 51 0.030628346 0.42857897 0.54079269 Lower 52 0.012963274 0.19723355 0.78980318 Lower 53 0.057298948 0.81633573 0.12636532 Lower 54 0.065798656 0.39849533 0.53570602 Lower 55 0.042072151 0.48636964 0.47155821 Lower 56 0.050651296 0.51775951 0.43158920 Lower 57 0.106719047 0.53708079 0.35620016 Lower 58 0.033836695 0.55079286 0.41537045 Lower 59 0.009670684 0.13820359 0.85212573 Lower 60 0.046906231 0.21168173 0.74141204 Lower > > > > cleanEx(); ..nameEx <- "barplot" > > ### * barplot > > flush(stderr()); flush(stdout()) > > ### Name: barplot.acomp > ### Title: Barcharts of amounts > ### Aliases: barplot.acomp barplot.rcomp barplot.aplus barplot.rplus > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > barplot(mean(acomp(sa.lognormals[1:10,]))) > barplot(mean(rcomp(sa.lognormals[1:10,]))) > barplot(mean(aplus(sa.lognormals[1:10,]))) > barplot(mean(rplus(sa.lognormals[1:10,]))) > > barplot(acomp(sa.lognormals[1:10,])) > barplot(rcomp(sa.lognormals[1:10,])) > barplot(aplus(sa.lognormals[1:10,])) > barplot(rplus(sa.lognormals[1:10,])) > > > > > cleanEx(); ..nameEx <- "boxplot" > > ### * boxplot > > flush(stderr()); flush(stdout()) > > ### Name: boxplot > ### Title: Displaying compositions and amounts by boxplots > ### Aliases: boxplot.acomp boxplot.rcomp boxplot.rplus boxplot.aplus > ### vp.boxplot vp.logboxplot > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > boxplot(acomp(sa.lognormals)) > boxplot(rcomp(sa.lognormals)) > boxplot(aplus(sa.lognormals)) > boxplot(rplus(sa.lognormals)) > > > > cleanEx(); ..nameEx <- "cdt" > > ### * cdt > > flush(stderr()); flush(stdout()) > > ### Name: cdt > ### Title: Centered default transform > ### Aliases: cdt cdt.default cdt.acomp cdt.rcomp cdt.aplus cdt.rplus > ### cdt.rmult cdt.factor > ### Keywords: multivariate > > ### ** Examples > > ## Not run: > ##D # the cdt is defined by > ##D cdt <- function(x) UseMethod("cdt",x) > ##D cdt.default <- function(x) x > ##D cdt.acomp <- clr > ##D cdt.rcomp <- cpt > ##D cdt.aplus <- ilt > ##D cdt.rplus <- iit > ## End(Not run) > cdt(acomp(1:5)) [1] -0.9574983 -0.2643512 0.1411139 0.4287960 0.6519396 attr(,"class") [1] "rmult" > cdt(rcomp(1:5)) [,1] [,2] [,3] [,4] [,5] [1,] -0.1333333 -0.06666667 0 0.06666667 0.1333333 attr(,"class") [1] "rmult" > > > > > cleanEx(); ..nameEx <- "clo" > > ### * clo > > flush(stderr()); flush(stdout()) > > ### Name: clo > ### Title: Closure of a composition > ### Aliases: clo > ### Keywords: multivariate > > ### ** Examples > > (tmp <- clo(c(1,2,3))) [1] 0.1666667 0.3333333 0.5000000 > clo(tmp,total=100) [1] 16.66667 33.33333 50.00000 > data(Hydrochem) > cdata <- Hydrochem[,6:19] > plot( clo(Hydrochem,8:9) ) # Giving points on a line > > > > > cleanEx(); ..nameEx <- "clr" > > ### * clr > > flush(stderr()); flush(stdout()) > > ### Name: clr > ### Title: Centered log ratio transform > ### Aliases: clr clr.inv > ### Keywords: multivariate > > ### ** Examples > > (tmp <- clr(c(1,2,3))) [1] -0.59725316 0.09589402 0.50135913 attr(,"class") [1] "rmult" > clr.inv(tmp) [1] 0.1666667 0.3333333 0.5000000 attr(,"class") [1] "acomp" > clr.inv(tmp) - clo(c(1,2,3)) # 0 [1] 0.3333333 0.3333333 0.3333333 attr(,"class") [1] "acomp" > data(Hydrochem) > cdata <- Hydrochem[,6:19] > pairs(clr(cdata)) > > > > cleanEx(); ..nameEx <- "clr2ilr" > > ### * clr2ilr > > flush(stderr()); flush(stdout()) > > ### Name: clr2ilr > ### Title: Convert between clr and ilr, and between cpt and ipt. Acts in > ### vectors and in bilinear forms. > ### Aliases: clr2ilr ilr2clr clrvar2ilr ilrvar2clr > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > ilr.inv(clr2ilr(clr(sa.lognormals)))-clo(sa.lognormals) Cu Zn Pb [1,] 0.3333333 0.3333333 0.3333333 [2,] 0.3333333 0.3333333 0.3333333 [3,] 0.3333333 0.3333333 0.3333333 [4,] 0.3333333 0.3333333 0.3333333 [5,] 0.3333333 0.3333333 0.3333333 [6,] 0.3333333 0.3333333 0.3333333 [7,] 0.3333333 0.3333333 0.3333333 [8,] 0.3333333 0.3333333 0.3333333 [9,] 0.3333333 0.3333333 0.3333333 [10,] 0.3333333 0.3333333 0.3333333 [11,] 0.3333333 0.3333333 0.3333333 [12,] 0.3333333 0.3333333 0.3333333 [13,] 0.3333333 0.3333333 0.3333333 [14,] 0.3333333 0.3333333 0.3333333 [15,] 0.3333333 0.3333333 0.3333333 [16,] 0.3333333 0.3333333 0.3333333 [17,] 0.3333333 0.3333333 0.3333333 [18,] 0.3333333 0.3333333 0.3333333 [19,] 0.3333333 0.3333333 0.3333333 [20,] 0.3333333 0.3333333 0.3333333 [21,] 0.3333333 0.3333333 0.3333333 [22,] 0.3333333 0.3333333 0.3333333 [23,] 0.3333333 0.3333333 0.3333333 [24,] 0.3333333 0.3333333 0.3333333 [25,] 0.3333333 0.3333333 0.3333333 [26,] 0.3333333 0.3333333 0.3333333 [27,] 0.3333333 0.3333333 0.3333333 [28,] 0.3333333 0.3333333 0.3333333 [29,] 0.3333333 0.3333333 0.3333333 [30,] 0.3333333 0.3333333 0.3333333 [31,] 0.3333333 0.3333333 0.3333333 [32,] 0.3333333 0.3333333 0.3333333 [33,] 0.3333333 0.3333333 0.3333333 [34,] 0.3333333 0.3333333 0.3333333 [35,] 0.3333333 0.3333333 0.3333333 [36,] 0.3333333 0.3333333 0.3333333 [37,] 0.3333333 0.3333333 0.3333333 [38,] 0.3333333 0.3333333 0.3333333 [39,] 0.3333333 0.3333333 0.3333333 [40,] 0.3333333 0.3333333 0.3333333 [41,] 0.3333333 0.3333333 0.3333333 [42,] 0.3333333 0.3333333 0.3333333 [43,] 0.3333333 0.3333333 0.3333333 [44,] 0.3333333 0.3333333 0.3333333 [45,] 0.3333333 0.3333333 0.3333333 [46,] 0.3333333 0.3333333 0.3333333 [47,] 0.3333333 0.3333333 0.3333333 [48,] 0.3333333 0.3333333 0.3333333 [49,] 0.3333333 0.3333333 0.3333333 [50,] 0.3333333 0.3333333 0.3333333 [51,] 0.3333333 0.3333333 0.3333333 [52,] 0.3333333 0.3333333 0.3333333 [53,] 0.3333333 0.3333333 0.3333333 [54,] 0.3333333 0.3333333 0.3333333 [55,] 0.3333333 0.3333333 0.3333333 [56,] 0.3333333 0.3333333 0.3333333 [57,] 0.3333333 0.3333333 0.3333333 [58,] 0.3333333 0.3333333 0.3333333 [59,] 0.3333333 0.3333333 0.3333333 [60,] 0.3333333 0.3333333 0.3333333 attr(,"class") [1] "acomp" > clr.inv(ilr2clr(ilr(sa.lognormals)))-clo(sa.lognormals) Cu Zn Pb [1,] 0.3333333 0.3333333 0.3333333 [2,] 0.3333333 0.3333333 0.3333333 [3,] 0.3333333 0.3333333 0.3333333 [4,] 0.3333333 0.3333333 0.3333333 [5,] 0.3333333 0.3333333 0.3333333 [6,] 0.3333333 0.3333333 0.3333333 [7,] 0.3333333 0.3333333 0.3333333 [8,] 0.3333333 0.3333333 0.3333333 [9,] 0.3333333 0.3333333 0.3333333 [10,] 0.3333333 0.3333333 0.3333333 [11,] 0.3333333 0.3333333 0.3333333 [12,] 0.3333333 0.3333333 0.3333333 [13,] 0.3333333 0.3333333 0.3333333 [14,] 0.3333333 0.3333333 0.3333333 [15,] 0.3333333 0.3333333 0.3333333 [16,] 0.3333333 0.3333333 0.3333333 [17,] 0.3333333 0.3333333 0.3333333 [18,] 0.3333333 0.3333333 0.3333333 [19,] 0.3333333 0.3333333 0.3333333 [20,] 0.3333333 0.3333333 0.3333333 [21,] 0.3333333 0.3333333 0.3333333 [22,] 0.3333333 0.3333333 0.3333333 [23,] 0.3333333 0.3333333 0.3333333 [24,] 0.3333333 0.3333333 0.3333333 [25,] 0.3333333 0.3333333 0.3333333 [26,] 0.3333333 0.3333333 0.3333333 [27,] 0.3333333 0.3333333 0.3333333 [28,] 0.3333333 0.3333333 0.3333333 [29,] 0.3333333 0.3333333 0.3333333 [30,] 0.3333333 0.3333333 0.3333333 [31,] 0.3333333 0.3333333 0.3333333 [32,] 0.3333333 0.3333333 0.3333333 [33,] 0.3333333 0.3333333 0.3333333 [34,] 0.3333333 0.3333333 0.3333333 [35,] 0.3333333 0.3333333 0.3333333 [36,] 0.3333333 0.3333333 0.3333333 [37,] 0.3333333 0.3333333 0.3333333 [38,] 0.3333333 0.3333333 0.3333333 [39,] 0.3333333 0.3333333 0.3333333 [40,] 0.3333333 0.3333333 0.3333333 [41,] 0.3333333 0.3333333 0.3333333 [42,] 0.3333333 0.3333333 0.3333333 [43,] 0.3333333 0.3333333 0.3333333 [44,] 0.3333333 0.3333333 0.3333333 [45,] 0.3333333 0.3333333 0.3333333 [46,] 0.3333333 0.3333333 0.3333333 [47,] 0.3333333 0.3333333 0.3333333 [48,] 0.3333333 0.3333333 0.3333333 [49,] 0.3333333 0.3333333 0.3333333 [50,] 0.3333333 0.3333333 0.3333333 [51,] 0.3333333 0.3333333 0.3333333 [52,] 0.3333333 0.3333333 0.3333333 [53,] 0.3333333 0.3333333 0.3333333 [54,] 0.3333333 0.3333333 0.3333333 [55,] 0.3333333 0.3333333 0.3333333 [56,] 0.3333333 0.3333333 0.3333333 [57,] 0.3333333 0.3333333 0.3333333 [58,] 0.3333333 0.3333333 0.3333333 [59,] 0.3333333 0.3333333 0.3333333 [60,] 0.3333333 0.3333333 0.3333333 attr(,"class") [1] "acomp" > ilrvar2clr(var(ilr(sa.lognormals)))-var(clr(sa.lognormals)) Cu Zn Pb Cu 1.110223e-16 5.551115e-17 -2.220446e-16 Zn 1.110223e-16 4.440892e-16 -4.440892e-16 Pb -2.220446e-16 -5.551115e-16 2.220446e-16 > clrvar2ilr(var(cpt(sa.lognormals)))-var(ipt(sa.lognormals)) [,1] [,2] [1,] 3.469447e-18 -3.469447e-18 [2,] -6.938894e-18 0.000000e+00 > > > > > cleanEx(); ..nameEx <- "cor" > > ### * cor > > flush(stderr()); flush(stdout()) > > ### Name: cor.acomp > ### Title: Correlations of amounts and compositions > ### Aliases: cor cor.default cor.acomp cor.rcomp cor.aplus cor.rplus > ### cor.rmult > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > mean.col(sa.lognormals) Cu Zn Pb 5.392698 14.908465 38.319017 > cor(acomp(sa.lognormals5[,1:3]),acomp(sa.lognormals5[,4:5])) > cor(rcomp(sa.lognormals5[,1:3]),rcomp(sa.lognormals5[,4:5])) > cor(aplus(sa.lognormals5[,1:3]),aplus(sa.lognormals5[,4:5])) > cor(rplus(sa.lognormals5[,1:3]),rplus(sa.lognormals5[,4:5])) > cor(acomp(sa.lognormals5[,1:3]),aplus(sa.lognormals5[,4:5])) > > > > > cleanEx(); ..nameEx <- "cpt" > > ### * cpt > > flush(stderr()); flush(stdout()) > > ### Name: cpt > ### Title: Centered planar transform > ### Aliases: cpt cpt.inv > ### Keywords: multivariate > > ### ** Examples > > (tmp <- cpt(c(1,2,3))) [,1] [,2] [,3] [1,] -0.1666667 0 0.1666667 attr(,"class") [1] "rmult" > cpt.inv(tmp) [,1] [,2] [,3] [1,] 0.1666667 0.3333333 0.5 attr(,"class") [1] "rcomp" > cpt.inv(tmp) - clo(c(1,2,3)) # 0 [,1] [,2] [,3] [1,] 0 0 0 attr(,"class") [1] "rmult" > data(Hydrochem) > cdata <- Hydrochem[,6:19] > pairs(cpt(cdata)) > > > > cleanEx(); ..nameEx <- "dist" > > ### * dist > > flush(stderr()); flush(stdout()) > > ### Name: dist > ### Title: Distances in variouse approaches > ### Aliases: dist dist.default > ### Keywords: multivariate > > ### ** Examples > > data(iris) > dist(iris[,1:4]) 1 2 3 4 5 6 7 2 0.5385165 3 0.5099020 0.3000000 4 0.6480741 0.3316625 0.2449490 5 0.1414214 0.6082763 0.5099020 0.6480741 6 0.6164414 1.0908712 1.0862780 1.1661904 0.6164414 7 0.5196152 0.5099020 0.2645751 0.3316625 0.4582576 0.9949874 8 0.1732051 0.4242641 0.4123106 0.5000000 0.2236068 0.7000000 0.4242641 9 0.9219544 0.5099020 0.4358899 0.3000000 0.9219544 1.4594520 0.5477226 10 0.4690416 0.1732051 0.3162278 0.3162278 0.5291503 1.0099505 0.4795832 11 0.3741657 0.8660254 0.8831761 1.0000000 0.4242641 0.3464102 0.8660254 12 0.3741657 0.4582576 0.3741657 0.3741657 0.3464102 0.8124038 0.3000000 13 0.5916080 0.1414214 0.2645751 0.2645751 0.6403124 1.1618950 0.4898979 14 0.9949874 0.6782330 0.5000000 0.5196152 0.9746794 1.5716234 0.6164414 15 0.8831761 1.3601471 1.3638182 1.5297059 0.9165151 0.6782330 1.3601471 16 1.1045361 1.6278821 1.5874508 1.7146428 1.0862780 0.6164414 1.4933185 17 0.5477226 1.0535654 1.0099505 1.1661904 0.5477226 0.4000000 0.9539392 18 0.1000000 0.5477226 0.5196152 0.6557439 0.1732051 0.5916080 0.5099020 19 0.7416198 1.1747340 1.2369317 1.3228757 0.7937254 0.3316625 1.2083046 20 0.3316625 0.8366600 0.7549834 0.8660254 0.2645751 0.3872983 0.6480741 21 0.4358899 0.7071068 0.8306624 0.8774964 0.5385165 0.5385165 0.8602325 22 0.3000000 0.7615773 0.7000000 0.8062258 0.2645751 0.4123106 0.6000000 23 0.6480741 0.7810250 0.5099020 0.7071068 0.5656854 1.1224972 0.4582576 24 0.4690416 0.5567764 0.6480741 0.6480741 0.5291503 0.6782330 0.6244998 25 0.5916080 0.6480741 0.6403124 0.5385165 0.5744563 0.8306624 0.5477226 26 0.5477226 0.2236068 0.4690416 0.4242641 0.6324555 1.0099505 0.6082763 27 0.3162278 0.5000000 0.5099020 0.5477226 0.3464102 0.6480741 0.4582576 28 0.1414214 0.5916080 0.6164414 0.7211103 0.2449490 0.5291503 0.6244998 29 0.1414214 0.5000000 0.5477226 0.6782330 0.2828427 0.6480741 0.6082763 30 0.5385165 0.3464102 0.3000000 0.1732051 0.5385165 1.0148892 0.3162278 31 0.5385165 0.2449490 0.3316625 0.2236068 0.5744563 1.0246951 0.4242641 32 0.3872983 0.6782330 0.7810250 0.8774964 0.5000000 0.5385165 0.8124038 33 0.6244998 1.1489125 1.0535654 1.1704700 0.5567764 0.4582576 0.9486833 34 0.8062258 1.3416408 1.2845233 1.4247807 0.7810250 0.4795832 1.2083046 35 0.4582576 0.1414214 0.3000000 0.3000000 0.5196152 0.9848858 0.4472136 36 0.3741657 0.3000000 0.3162278 0.5099020 0.4472136 0.9695360 0.5000000 37 0.4123106 0.7874008 0.8544004 1.0049876 0.5196152 0.6082763 0.9165151 38 0.2449490 0.6082763 0.4690416 0.6000000 0.1414214 0.7211103 0.4123106 39 0.8660254 0.5099020 0.3605551 0.3000000 0.8544004 1.4177447 0.4690416 40 0.1414214 0.4582576 0.4898979 0.5830952 0.2449490 0.6480741 0.5196152 41 0.1732051 0.5291503 0.4358899 0.6082763 0.1732051 0.7000000 0.4242641 42 1.3490738 0.8185353 0.9273618 0.8366600 1.4000000 1.8814888 1.1090537 43 0.7681146 0.5477226 0.3000000 0.3000000 0.7280110 1.3000000 0.3162278 44 0.4582576 0.6782330 0.6557439 0.7000000 0.4582576 0.6082763 0.5477226 45 0.6164414 0.9848858 0.9591663 0.9695360 0.5830952 0.3741657 0.8185353 46 0.5916080 0.1414214 0.2645751 0.2645751 0.6403124 1.1269428 0.4472136 47 0.3605551 0.8485281 0.7810250 0.8660254 0.3000000 0.3872983 0.6782330 48 0.5830952 0.3605551 0.1414214 0.1414214 0.5656854 1.1224972 0.2236068 49 0.3000000 0.8124038 0.8062258 0.9219544 0.3316625 0.3605551 0.7745967 50 0.2236068 0.3162278 0.3316625 0.4582576 0.3000000 0.8062258 0.4242641 51 4.0037482 4.0963398 4.2766810 4.1773197 4.0607881 3.6124784 4.2308392 52 3.6166283 3.6864617 3.8496753 3.7336309 3.6633318 3.2465366 3.7854986 53 4.1641326 4.2367440 4.4158804 4.3058100 4.2190046 3.7868192 4.3669211 54 3.0935417 2.9698485 3.1543621 2.9849623 3.1480152 2.9444864 3.1272992 55 3.7920970 3.8118237 3.9974992 3.8729833 3.8496753 3.4698703 3.9560081 56 3.4161382 3.3911650 3.5510562 3.3926391 3.4568772 3.1543621 3.4899857 57 3.7854986 3.8600518 4.0112342 3.8897301 3.8249183 3.4073450 3.9344631 58 2.3452079 2.1470911 2.3065125 2.1118712 2.3874673 2.3280893 2.2781571 59 3.7496667 3.7881394 3.9749214 3.8548671 3.8078866 3.4146742 3.9357337 60 2.8879058 2.8053520 2.9495762 2.7784888 2.9223278 2.7055499 2.8827071 61 2.7037012 2.4617067 2.6476405 2.4515301 2.7586228 2.7147744 2.6495283 62 3.2280025 3.2449961 3.4029399 3.2680269 3.2710854 2.9189039 3.3361655 63 3.1464265 3.0413813 3.2588341 3.1080541 3.2186954 2.9832868 3.2634338 64 3.7000000 3.7121422 3.8794329 3.7376463 3.7456642 3.3896903 3.8209946 65 2.5806976 2.5592968 2.7202941 2.5806976 2.6267851 2.3366643 2.6627054 66 3.6276714 3.7000000 3.8807216 3.7762415 3.6851052 3.2588341 3.8353618 67 3.4351128 3.4336569 3.5749126 3.4205263 3.4669872 3.1464265 3.4942810 68 3.0099834 2.9715316 3.1527766 3.0000000 3.0626786 2.7784888 3.1160873 69 3.7682887 3.6918830 3.8961519 3.7496667 3.8340579 3.5468296 3.8794329 70 2.8827071 2.7928480 2.9782545 2.8160256 2.9376862 2.7073973 2.9495762 71 3.8535698 3.8935845 4.0311289 3.8923001 3.8845849 3.5085610 3.9420807 72 3.0757113 3.0740852 3.2588341 3.1304952 3.1336879 2.7928480 3.2202484 73 4.0472213 4.0187063 4.2071368 4.0620192 4.1036569 3.7709415 4.1701319 74 3.6578682 3.6565011 3.8314488 3.6851052 3.7067506 3.3674916 3.7828561 75 3.4161382 3.4467376 3.6318040 3.5114100 3.4741906 3.0935417 3.5916570 76 3.5972211 3.6510273 3.8340579 3.7229021 3.6551334 3.2465366 3.7907783 77 4.0472213 4.0804412 4.2731721 4.1545156 4.1085277 3.7121422 4.2391037 78 4.2449971 4.2953463 4.4698993 4.3497126 4.2965102 3.8832976 4.4147480 79 3.5312887 3.5383612 3.7027017 3.5623026 3.5763109 3.2264532 3.6414283 80 2.4939928 2.4186773 2.6153394 2.4698178 2.5573424 2.3194827 2.5980762 81 2.8178006 2.7000000 2.8879058 2.7202941 2.8740216 2.6758176 2.8653098 82 2.7018512 2.5787594 2.7712813 2.6038433 2.7604347 2.5729361 2.7549955 83 2.8948230 2.8548205 3.0364453 2.8913665 2.9495762 2.6608269 2.9983329 84 4.1352146 4.1170378 4.2825226 4.1279535 4.1785165 3.8470768 4.2225585 85 3.4117444 3.3985291 3.5298725 3.3674916 3.4380227 3.1400637 3.4423829 86 3.5199432 3.5972211 3.7322915 3.6069378 3.5510562 3.1448370 3.6414283 87 3.9115214 3.9786933 4.1545156 4.0422766 3.9648455 3.5411862 4.1024383 88 3.6180105 3.5580894 3.7669616 3.6262929 3.6864617 3.3867388 3.7549967 89 3.0000000 2.9983329 3.1464265 2.9966648 3.0364453 2.7239677 3.0740852 90 3.0215890 2.9291637 3.1032241 2.9376862 3.0708305 2.8407745 3.0626786 91 3.3120990 3.2434549 3.4073450 3.2357379 3.3541020 3.1032241 3.3555923 92 3.5958309 3.6221541 3.7854986 3.6482873 3.6400549 3.2726136 3.7229021 93 3.0099834 2.9546573 3.1400637 2.9899833 3.0659419 2.7892651 3.1064449 94 2.3874673 2.1794495 2.3537205 2.1633308 2.4372115 2.3748684 2.3388031 95 3.1527766 3.1032241 3.2680269 3.1080541 3.1968735 2.9223278 3.2140317 96 3.0740852 3.0789609 3.2326460 3.0838288 3.1128765 2.7910571 3.1654384 97 3.1256999 3.1144823 3.2726136 3.1224990 3.1670175 2.8548205 3.2093613 98 3.3451457 3.3645208 3.5425979 3.4132096 3.3985291 3.0347982 3.4957117 99 2.0904545 1.9131126 2.0856654 1.9157244 2.1424285 2.0566964 2.0639767 100 3.0577770 3.0298515 3.1953091 3.0446675 3.1032241 2.8053520 3.1400637 101 5.2848841 5.3385391 5.4726593 5.3357286 5.3131911 4.9061186 5.3758720 102 4.2083251 4.1809090 4.3347434 4.1773197 4.2461747 3.9255573 4.2638011 103 5.3018865 5.3572381 5.5290144 5.4064776 5.3507009 4.9223978 5.4680892 104 4.6904158 4.7085029 4.8682646 4.7222876 4.7307505 4.3566042 4.7989582 105 5.0566788 5.0911688 5.2469038 5.1097945 5.0960769 4.6978719 5.1710734 106 6.0950800 6.1595454 6.3364028 6.2153037 6.1457302 5.7052607 6.2801274 107 3.5916570 3.4799425 3.6083237 3.4205263 3.6166283 3.4263683 3.5312887 108 5.6364883 5.6868269 5.8660038 5.7384667 5.6877060 5.2659282 5.8137767 109 5.0477718 5.0408333 5.2249402 5.0813384 5.1009803 4.7349762 5.1797683 110 5.6391489 5.7471732 5.8940648 5.7844619 5.6762664 5.2057660 5.8077534 111 4.3566042 4.4192760 4.5738387 4.4519659 4.3977267 3.9774364 4.4977772 112 4.5199558 4.5210618 4.6936127 4.5530210 4.5683695 4.2011903 4.6368092 113 4.8538644 4.9020404 5.0695167 4.9457052 4.9010203 4.4833024 5.0049975 114 4.1904654 4.1340053 4.2918527 4.1303753 4.2308392 3.9370039 4.2272923 115 4.4170126 4.4022721 4.5442271 4.3965896 4.4508426 4.1146081 4.4609416 116 4.6260134 4.6808119 4.8270074 4.7010637 4.6626173 4.2497059 4.7423623 117 4.6454279 4.6829478 4.8456166 4.7095647 4.6882833 4.2918527 4.7780749 118 6.2401923 6.3694584 6.5207362 6.4140471 6.2785349 5.7913729 6.4397205 119 6.4984614 6.5314623 6.7178866 6.5901442 6.5536250 6.1343296 6.6708320 120 4.1412558 4.0620192 4.2508823 4.0877867 4.1964271 3.9179076 4.2190046 121 5.1215232 5.1903757 5.3488316 5.2297227 5.1643005 4.7275787 5.2744668 122 4.0286474 4.0024992 4.1436699 3.9862263 4.0607881 3.7483330 4.0620192 123 6.2112801 6.2617889 6.4467046 6.3229740 6.2657801 5.8360946 6.3992187 124 4.1097445 4.1060930 4.2813549 4.1436699 4.1605288 3.8013156 4.2284749 125 4.9699095 5.0428167 5.1942276 5.0695167 5.0079936 4.5760245 5.1137071 126 5.3122500 5.3898052 5.5587768 5.4387499 5.3591044 4.9173163 5.4963624 127 3.9774364 3.9812058 4.1496988 4.0124805 4.0249224 3.6633318 4.0902323 128 4.0074930 4.0311289 4.1856899 4.0472213 4.0472213 3.6742346 4.1121770 129 4.8404545 4.8518038 5.0149776 4.8733972 4.8836462 4.5066617 4.9477268 130 5.0970580 5.1584882 5.3385391 5.2172790 5.1497573 4.7222876 5.2886671 131 5.5461698 5.5919585 5.7775427 5.6550862 5.6017854 5.1788030 5.7314920 132 6.0141500 6.1546730 6.3126856 6.2153037 6.0572271 5.5596762 6.2401923 133 4.8805737 4.8918299 5.0537115 4.9132474 4.9234135 4.5453273 4.9849774 134 4.1605288 4.1689327 4.3416587 4.1988094 4.2083251 3.8457769 4.2871902 135 4.5705580 4.5475268 4.7169906 4.5552168 4.6141088 4.2883563 4.6626173 136 5.7887823 5.8600341 6.0406953 5.9321160 5.8438001 5.3916602 5.9883220 137 4.8918299 4.9598387 5.0921508 4.9628621 4.9203658 4.5022217 4.9939964 138 4.6065171 4.6508064 4.8062459 4.6690470 4.6454279 4.2473521 4.7318073 139 3.8961519 3.9153544 4.0669399 3.9268308 3.9344631 3.5693137 3.9912404 140 4.7968740 4.8600412 5.0269275 4.9101935 4.8445846 4.4124823 4.9618545 141 5.0199602 5.0724747 5.2287666 5.1048996 5.0616203 4.6411206 5.1526692 142 4.6368092 4.7021272 4.8682646 4.7602521 4.6861498 4.2497059 4.8031240 143 4.2083251 4.1809090 4.3347434 4.1773197 4.2461747 3.9255573 4.2638011 144 5.2573758 5.3207142 5.4753995 5.3497664 5.2971691 4.8682646 5.3972215 145 5.1361464 5.2067264 5.3535035 5.2325902 5.1730069 4.7391982 5.2678269 146 4.6540305 4.7000000 4.8641546 4.7455242 4.7010637 4.2848571 4.7968740 147 4.2766810 4.2497059 4.4305756 4.2883563 4.3301270 3.9887341 4.3840620 148 4.4598206 4.4988888 4.6615448 4.5332108 4.5044423 4.1024383 4.5934736 149 4.6508064 4.7180504 4.8487112 4.7191101 4.6786750 4.2649736 4.7497368 150 4.1400483 4.1533119 4.2988371 4.1496988 4.1737274 3.8183766 4.2178193 8 9 10 11 12 13 14 2 3 4 5 6 7 8 9 0.7874008 10 0.3316625 0.5567764 11 0.5000000 1.2845233 0.7874008 12 0.2236068 0.6708204 0.3464102 0.6782330 13 0.4690416 0.4242641 0.1732051 0.9327379 0.4582576 14 0.9055385 0.3464102 0.7280110 1.3674794 0.8185353 0.5830952 15 1.0440307 1.7916473 1.3114877 0.5830952 1.2328828 1.4317821 1.8083141 16 1.2369317 1.9974984 1.5556349 0.7874008 1.3638182 1.6941074 2.0420578 17 0.7000000 1.4317821 1.0099505 0.3464102 0.8602325 1.1269428 1.4662878 18 0.2000000 0.9273618 0.5000000 0.3872983 0.3872983 0.6164414 1.0099505 19 0.8366600 1.6124515 1.1000000 0.3872983 0.9949874 1.2569805 1.7320508 20 0.4242641 1.1489125 0.7549834 0.3316625 0.5196152 0.8831761 1.2165525 21 0.4472136 1.1575837 0.6244998 0.3605551 0.6082763 0.7874008 1.3190906 22 0.3741657 1.0862780 0.7000000 0.3605551 0.4795832 0.8246211 1.1747340 23 0.6708204 0.8306624 0.7745967 0.9486833 0.6633250 0.7549834 0.6855655 24 0.3872983 0.9110434 0.5291503 0.6164414 0.4472136 0.6557439 1.1180340 25 0.4472136 0.8124038 0.5196152 0.7810250 0.3000000 0.6480741 1.0295630 26 0.4123106 0.6403124 0.2000000 0.8124038 0.4472136 0.3000000 0.8660254 27 0.2236068 0.8306624 0.4472136 0.5477226 0.2828427 0.5744563 0.9949874 28 0.2236068 1.0049876 0.5099020 0.2828427 0.4242641 0.6557439 1.1090537 29 0.2236068 0.9433981 0.4472136 0.3741657 0.4472136 0.5744563 1.0344080 30 0.3741657 0.4690416 0.2645751 0.8660254 0.2236068 0.3162278 0.6782330 31 0.3741657 0.4898979 0.1732051 0.8544004 0.3000000 0.2449490 0.7211103 32 0.4472136 1.1401754 0.6557439 0.3605551 0.6403124 0.7874008 1.2727922 33 0.7348469 1.4491377 1.0440307 0.4582576 0.8185353 1.1747340 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1.8814888 0.6633250 0.6244998 113 114 115 116 117 118 119 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 1.3114877 115 1.1357817 0.5196152 116 0.5291503 1.0770330 0.7549834 117 0.4242641 1.0862780 1.0246951 0.5830952 118 1.7029386 2.9359837 2.6851443 2.0049938 1.9183326 119 1.7233688 2.7766887 2.6267851 2.1470911 1.9519221 1.2206556 120 1.3747727 0.6557439 1.1045361 1.3747727 1.1090537 2.9715316 2.7018512 121 0.3605551 1.5842980 1.3190906 0.6403124 0.7000000 1.4177447 1.5620499 122 1.3601471 0.3316625 0.4898979 1.0246951 1.1180340 2.9478806 2.9223278 123 1.5165751 2.6419690 2.5159491 1.9748418 1.7204651 1.0198039 0.4123106 124 0.8888194 0.6708204 0.8124038 0.8185353 0.7000000 2.5632011 2.4939928 125 0.3741657 1.4628739 1.2288206 0.5477226 0.5099020 1.5033296 1.7233688 126 0.7348469 1.9442222 1.8138357 1.1747340 0.8831761 1.1224972 1.2922848 127 0.9899495 0.6480741 0.7810250 0.8366600 0.7874008 2.6495283 2.6362853 128 0.9695360 0.6782330 0.7280110 0.7348469 0.7211103 2.5690465 2.6400758 129 0.4582576 0.9746794 0.8366600 0.5385165 0.3872983 1.9773720 1.8601075 130 0.7071068 1.8165902 1.7691806 1.1916375 0.7874008 1.4352700 1.4525839 131 0.8944272 2.0493902 1.9519221 1.4000000 1.1045361 1.2409674 0.9643651 132 1.6340135 2.9137605 2.6944387 1.9773720 1.8574176 0.4123106 1.3490738 133 0.4690416 0.9899495 0.8062258 0.5099020 0.4690416 1.9748418 1.8520259 134 0.9000000 0.8426150 1.0295630 0.9219544 0.5744563 2.4515301 2.4248711 135 1.0723805 0.9433981 1.1747340 1.1618950 0.7000000 2.4186773 2.2494444 136 1.1000000 2.3558438 2.1587033 1.5394804 1.4317821 1.0049876 0.8944272 137 0.7141428 1.3000000 0.9273618 0.3872983 0.7549834 1.8357560 2.0736441 138 0.5099020 1.0677078 0.9848858 0.5477226 0.1414214 1.9442222 2.0371549 139 1.1045361 0.6480741 0.7280110 0.8366600 0.8602325 2.7018512 2.7766887 140 0.1732051 1.4035669 1.2165525 0.5567764 0.5196152 1.6822604 1.7832555 141 0.3464102 1.3711309 1.0723805 0.4472136 0.6480741 1.6552945 1.7175564 142 0.4690416 1.3784049 1.1445523 0.5477226 0.7615773 1.9235384 2.0322401 143 1.1357817 0.2645751 0.5099020 0.9000000 0.8660254 2.7331301 2.6495283 144 0.4898979 1.6124515 1.3453624 0.7211103 0.7348469 1.3490738 1.4730920 145 0.5477226 1.5427249 1.1958261 0.5477226 0.8124038 1.5297059 1.7233688 146 0.3741657 1.1747340 0.9327379 0.3741657 0.6164414 1.9748418 2.0124612 147 0.8888194 0.6082763 0.7745967 0.8660254 0.7416198 2.5748786 2.3958297 148 0.4358899 0.9643651 0.8366600 0.3872983 0.3605551 2.0904545 2.1400935 149 0.7549834 1.1445523 0.7874008 0.3000000 0.7141428 2.0273135 2.2671568 150 1.0295630 0.5830952 0.6403124 0.7615773 0.7211103 2.5690465 2.6248809 120 121 122 123 124 125 126 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 1.7146428 122 0.8831761 1.6062378 123 2.5278449 1.3747727 2.7658633 124 0.6633250 1.2247449 0.7348469 2.2912878 125 1.5968719 0.3000000 1.4525839 1.5033296 1.1180340 126 1.8788294 0.6557439 1.9924859 0.9695360 1.5066519 0.6633250 127 0.7280110 1.3076697 0.6403124 2.4289916 0.1732051 1.1832160 1.6124515 128 0.8660254 1.2529964 0.5744563 2.4248711 0.3605551 1.0862780 1.5684387 129 1.1135529 0.6782330 1.0677078 1.7058722 0.7745967 0.5916080 1.0246951 130 1.6522712 0.7937254 1.8894444 1.1224972 1.3228757 0.7745967 0.3464102 131 1.9209373 0.8544004 2.1656408 0.6782330 1.6340135 0.9695360 0.4690416 132 2.8948230 1.3928388 2.9223278 1.0630146 2.4617067 1.4798649 1.0246951 133 1.1704700 0.6557439 1.0816654 1.7146428 0.8185353 0.6000000 1.0583005 134 0.6782330 1.2328828 0.8831761 2.1840330 0.3741657 1.0630146 1.3674794 135 0.7348469 1.3490738 1.0677078 2.0420578 0.8366600 1.1618950 1.3747727 136 2.3194827 0.9165151 2.4454039 0.7000000 1.9339080 1.1357817 0.7416198 137 1.6431677 0.6480741 1.2247449 1.9209373 1.1575837 0.5196152 1.1704700 138 1.1445523 0.7416198 1.0630146 1.8055470 0.7280110 0.5099020 0.9486833 139 0.8774964 1.3820275 0.5000000 2.5651511 0.4358899 1.2165525 1.7088007 140 1.4628739 0.3741657 1.4282857 1.5588457 0.9273618 0.4123106 0.7416198 141 1.5716234 0.2645751 1.3964240 1.5684387 1.0816654 0.3741657 0.8831761 142 1.5066519 0.6082763 1.3820275 1.8384776 0.9000000 0.6928203 1.0770330 143 0.6782330 1.4071247 0.3162278 2.4879711 0.5477226 1.2529964 1.7406895 144 1.7578396 0.2236068 1.6401219 1.3038405 1.3228757 0.3162278 0.6480741 145 1.7860571 0.3000000 1.5329710 1.5811388 1.2845233 0.4000000 0.9165151 146 1.3453624 0.5744563 1.1958261 1.8384776 0.7681146 0.6164414 1.0862780 147 0.5830952 1.2247449 0.7745967 2.2248595 0.2449490 1.1532563 1.5198684 148 1.0862780 0.7348469 0.9695360 1.9313208 0.5099020 0.6244998 1.1000000 149 1.5099669 0.7874008 1.0295630 2.0952327 1.0000000 0.6244998 1.2845233 150 0.8660254 1.2845233 0.4582576 2.4248711 0.5385165 1.0862780 1.5937377 127 128 129 130 131 132 133 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 0.2449490 129 0.8774964 0.8426150 130 1.4422205 1.4352700 0.9848858 131 1.7720045 1.7832555 1.1357817 0.5099020 132 2.5475478 2.4839485 1.9748418 1.2845233 1.1618950 133 0.9165151 0.8831761 0.1000000 1.0392305 1.1575837 1.9824228 134 0.4358899 0.4582576 0.7874008 1.1618950 1.5394804 2.3452079 0.8660254 135 0.9219544 0.9000000 0.7874008 1.2041595 1.4933185 2.3832751 0.8774964 136 2.0566964 2.0615528 1.4212670 0.9110434 0.5385165 0.9273618 1.4106736 137 1.1704700 1.0246951 0.6782330 1.2845233 1.4387495 1.8761663 0.6403124 138 0.7874008 0.6782330 0.4358899 0.8831761 1.2083046 1.8947295 0.5099020 139 0.2828427 0.1414214 0.9643651 1.5748016 1.9235384 2.6172505 1.0000000 140 1.0148892 0.9949874 0.6164414 0.7141428 0.9327379 1.5811388 0.6244998 141 1.1575837 1.1045361 0.5196152 0.9695360 1.0392305 1.6522712 0.4690416 142 0.9591663 0.9695360 0.7937254 1.0392305 1.2247449 1.8083141 0.7745967 143 0.5196152 0.4795832 0.8124038 1.6217275 1.8894444 2.7055499 0.8426150 144 1.4071247 1.3341664 0.6708204 0.8366600 0.8485281 1.3820275 0.6480741 145 1.3416408 1.2569805 0.7141428 1.0770330 1.1224972 1.5588457 0.6633250 146 0.8366600 0.8366600 0.5744563 1.0488088 1.2247449 1.9000000 0.5477226 147 0.3872983 0.5567764 0.7071068 1.3379088 1.5842980 2.4939928 0.7416198 148 0.5744563 0.5385165 0.4690416 1.0049876 1.2922848 2.0099751 0.5000000 149 0.9848858 0.8185353 0.6928203 1.3453624 1.5652476 2.0346990 0.6708204 150 0.4690416 0.2828427 0.7937254 1.4899664 1.8165902 2.5238859 0.8366600 134 135 136 137 138 139 140 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 0.5830952 136 1.9078784 1.9442222 137 1.1916375 1.2961481 1.5427249 138 0.5916080 0.7141428 1.5198684 0.6855655 139 0.5567764 0.9848858 2.1977261 1.1180340 0.8124038 140 0.9486833 1.1916375 1.0862780 0.7615773 0.5916080 1.1269428 141 1.1445523 1.2688578 1.1269428 0.5000000 0.6782330 1.2247449 0.4123106 142 1.0440307 1.3964240 1.2845233 0.8426150 0.8124038 1.0770330 0.3605551 143 0.6480741 0.7745967 2.2045408 1.1135529 0.8306624 0.4795832 1.2247449 144 1.3000000 1.3228757 0.9433981 0.6244998 0.7615773 1.4628739 0.5567764 145 1.3304135 1.4387495 1.1357817 0.4358899 0.8124038 1.3711309 0.5744563 146 0.9219544 1.2206556 1.3453624 0.7000000 0.6633250 0.9486833 0.3605551 147 0.5099020 0.8124038 1.8920888 1.1916375 0.7937254 0.6244998 0.9591663 148 0.5830952 0.9165151 1.5297059 0.7211103 0.3872983 0.6708204 0.4690416 149 1.0488088 1.2247449 1.7029386 0.2449490 0.6244998 0.9000000 0.7874008 150 0.5385165 0.7810250 2.1189620 0.9643651 0.6480741 0.3162278 1.0908712 141 142 143 144 145 146 147 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 0.5477226 143 1.2124356 1.2369317 144 0.3464102 0.8124038 1.4317821 145 0.2449490 0.6928203 1.3747727 0.3162278 146 0.4242641 0.2449490 1.0344080 0.7348469 0.6164414 147 1.0630146 0.9433981 0.5477226 1.3076697 1.2845233 0.7810250 148 0.6082763 0.5196152 0.7745967 0.8426150 0.7937254 0.3605551 0.5830952 149 0.6244998 0.8185353 0.9486833 0.8062258 0.6244998 0.6708204 1.0677078 150 1.1224972 1.1224972 0.3316625 1.3190906 1.2569805 0.9486833 0.6557439 148 149 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 0.6164414 150 0.6403124 0.7681146 > data(SimulatedAmounts) > dist(acomp(sa.lognormals),method="manhattan") 1 2 3 4 5 6 2 3.36624897 3 1.81114583 1.86418197 4 0.73804360 3.57824221 2.53056379 5 1.25905801 2.10719096 1.44120189 1.47105125 6 0.84514677 4.21139574 2.65629260 0.67212476 2.10420478 7 2.44853793 2.28584120 2.59492003 1.92248757 1.54079822 2.59461233 8 3.16364855 0.37306257 2.03464411 3.37564179 1.90459054 4.00879532 9 1.06135645 3.99199644 2.85387664 0.41375423 1.88480548 0.58168339 10 2.91533131 1.85090903 2.89670566 2.75985687 2.00759159 3.39301041 11 0.48564424 3.85189321 2.29679007 0.74772973 1.74470225 0.43510751 12 2.50258173 1.27904564 2.27956036 2.71457497 1.39044630 3.34772850 13 1.72140578 1.64484320 1.59084756 1.93339901 0.61199344 2.56655255 14 2.76723921 6.13348819 4.57838505 2.55524598 4.02629722 1.92209244 15 1.53437749 4.52395161 3.32689767 0.94570940 2.41676065 0.83530512 16 3.37034225 6.01527171 5.16286244 2.63229865 3.90808075 2.67126988 17 1.28264370 2.08360528 1.51146051 1.49463693 0.09384430 2.12779047 18 0.55941389 3.92566286 2.37055972 0.57892825 1.81847190 0.28573288 19 0.44996212 3.49237928 2.24248230 0.28808148 1.38518832 0.71901646 20 0.30336505 3.66961403 2.11451089 0.58851244 1.56242306 0.54178172 21 3.70122634 0.48463974 1.89008051 3.91321958 2.44216833 4.54637311 22 3.01006973 0.44310494 1.42107702 3.22206297 1.75101172 3.85521650 23 1.33506841 2.65852315 2.41986278 0.91971906 0.97866089 1.55287259 24 2.82185208 1.42293769 2.74272277 3.03384532 1.85360870 3.66699885 25 1.44416945 4.65920884 3.23668964 1.08096662 2.55201787 0.74509708 26 0.65683267 2.70941630 1.45018952 1.08037427 0.60222534 1.50197945 27 1.89244677 1.47380221 1.74504328 2.10444000 0.85592921 2.73759354 28 2.95076014 0.99253504 2.44122818 3.16275338 1.69170213 3.79590691 29 3.59750470 0.23125573 1.98506708 3.80949794 2.33844669 4.44265147 30 1.50189354 4.38572155 3.29441373 0.80747934 2.27853059 0.80282117 31 1.68660979 1.67963918 0.49566015 2.03490363 0.94554174 2.53175656 32 3.44216651 6.80841549 5.25331235 3.37446547 4.70122452 2.70234071 33 3.76361906 1.04052166 2.90470362 3.97561229 2.50456105 4.60876583 34 2.09162480 1.48005276 2.06961055 2.30361803 1.18049648 2.93677157 35 2.57673216 5.50861366 4.36925235 1.93037145 3.40142270 1.87765979 36 2.56767492 0.79857405 1.24803068 2.77966816 1.30861691 3.41282169 37 2.12218072 5.48842969 3.93332656 1.91018748 3.38123873 1.27703395 38 0.55730762 3.92355659 2.36845345 0.71968252 1.81636563 0.33539691 39 2.32251784 5.68876681 4.13366367 2.11052460 3.58157585 1.47737107 40 1.80962812 1.55662085 0.38941297 2.14115081 1.05178892 2.65477490 41 1.13022038 4.49646935 2.94136621 1.24576110 2.38927839 0.57363634 42 2.19103525 1.17521372 1.17872021 2.40302849 0.93197724 3.03618202 43 1.09053222 4.45678119 2.90167805 0.90308258 2.34959023 0.24538545 44 0.59305405 3.95930302 2.40419988 0.82217327 1.85211206 0.40214123 45 1.37263428 4.14512826 3.16515447 0.63459068 2.03793730 0.73982939 46 3.56710166 0.20085269 1.88213381 3.77909490 2.30804365 4.41224843 47 1.38655312 4.75280209 3.19769895 1.17455988 2.64561113 0.65787913 48 5.09405698 8.46030595 6.90520281 4.88206374 6.35311499 4.24891021 49 0.91073036 2.45551861 1.16586748 1.36469631 0.62366206 1.75587713 50 1.91267985 2.32204040 0.45785843 2.65072344 1.56136155 2.61175222 51 1.83783794 5.20408691 3.64898377 1.62584470 3.09689595 0.99269116 52 1.31309181 2.05315716 1.36305759 1.52508505 0.07814430 2.15823858 53 7.57790123 4.21165225 5.76675539 7.78989446 6.31884321 8.42304800 54 3.88407474 0.51782576 2.20708118 4.09606797 2.62501673 4.72922151 55 2.79059462 0.57565435 1.84420483 3.00258786 1.53153661 3.63574139 56 0.51935093 3.88559990 2.33049676 0.54295103 1.77840894 0.32579584 57 1.96933849 1.39691049 0.72830248 2.18133172 0.87109206 2.81448526 58 2.20106395 1.16518503 1.84062782 2.41305718 0.95151375 3.04621072 59 0.37154027 2.99470871 1.67622999 0.85433380 0.88751774 1.21668704 60 1.71873237 1.83739805 1.98240163 1.74084416 0.81099266 2.37399770 7 8 9 10 11 12 2 3 4 5 6 7 8 1.91277864 9 2.27188556 3.78939602 10 0.90172555 1.47784647 3.17361110 11 2.67021730 3.64929279 0.79739159 3.13701068 12 1.00679556 0.90598307 3.12832920 0.61714530 2.98822597 13 1.00407247 1.44224278 2.34715324 1.39559816 2.20705001 0.78117595 14 4.41337730 5.93088776 2.14149175 5.31510285 2.28159498 5.26982094 15 2.80384073 4.32135119 0.53195517 3.70556628 1.27041262 3.66028437 16 4.29516083 5.81267129 2.30898580 5.19688637 3.10637739 5.15160447 17 1.44695391 1.88100486 1.90839116 1.91374729 1.76828793 1.29660199 18 2.50141582 3.72306244 0.55482045 3.10727753 0.24257114 3.06199562 19 2.12470612 3.28977886 0.61139434 2.67399395 0.54551118 2.62871204 20 2.51100001 3.46701360 0.82045348 2.97779338 0.18227918 2.80594678 21 2.77048094 0.85770230 4.32697381 2.33554877 4.18687058 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2.69964493 6.40714879 53 8.66843344 8.17095528 8.35678052 4.01079956 8.96445434 12.67195820 54 4.97460695 4.47712879 4.66295403 0.32494736 5.27062785 8.97813171 55 3.88112684 3.38364867 3.56947391 0.77650704 4.17714774 7.88465160 56 0.57118129 0.27922224 0.87018402 4.08645259 0.86720219 4.57470605 57 3.05987070 2.56239254 2.74821778 1.59776318 3.35589160 7.06339546 58 3.29159616 2.79411800 2.97994324 1.36603772 3.58761706 7.29512092 59 1.46207249 0.96459432 1.48892448 3.19556139 1.75809338 5.46559724 60 2.61938314 2.12190498 2.30773022 2.03825074 2.91540404 6.62290790 49 50 51 52 53 54 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 1.28602714 51 2.74856829 3.31128500 52 0.59955156 1.48321725 3.15092975 53 6.66717087 6.10445416 9.41573916 6.26480941 54 2.97334438 2.66493961 5.72191267 2.57098292 3.69382649 55 1.87986426 2.30206326 4.62843256 1.47750281 4.78730660 1.09348011 56 1.43008129 2.41513010 1.31848701 1.83244274 8.09725215 4.40342566 57 1.05860813 1.18616091 3.80717642 0.79294777 5.60856274 1.91473625 58 1.57517581 2.29848625 4.03890188 0.97562425 5.37683728 1.68301079 59 0.53919009 1.79638965 2.20937820 0.94155154 7.20636096 3.51253447 60 1.43465472 2.15796516 3.36668886 0.83510315 6.04905030 2.35522381 55 56 57 58 59 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 3.30994555 57 1.11590235 2.48868941 58 0.58953068 2.72041487 1.11232534 59 2.41905435 0.89089119 1.59779822 1.82952368 60 1.26174370 2.04820185 1.41229181 0.67221302 1.46348230 > dist(rcomp(sa.lognormals)) 1 2 3 4 5 6 2 0.547597799 3 0.296044440 0.256753687 4 0.082688869 0.527586789 0.291893448 5 0.307821646 0.240591024 0.054345364 0.288691663 6 0.168002121 0.711698954 0.463289794 0.192497727 0.471110856 7 0.435886564 0.147711059 0.182047562 0.401536415 0.139324381 0.591973623 8 0.542164226 0.007677638 0.252220317 0.521403434 0.234862606 0.705954772 9 0.123939394 0.614526223 0.380495718 0.088674752 0.376692683 0.126439565 10 0.520779819 0.055169288 0.240437538 0.493778689 0.213624731 0.681601650 11 0.114253916 0.661812960 0.409893310 0.159031193 0.421829688 0.061623781 12 0.507840337 0.049189994 0.223299583 0.483843943 0.200036442 0.670121205 13 0.408056211 0.143428562 0.131396200 0.384418514 0.100536799 0.570105140 14 0.463319526 0.998733765 0.756304236 0.471171006 0.759185647 0.295878292 15 0.227086421 0.718726109 0.490480264 0.198853888 0.483741983 0.129357045 16 0.600749383 0.988823036 0.811323654 0.547761929 0.786151393 0.501623707 17 0.318964532 0.230060934 0.062362730 0.298371656 0.011869143 0.481764599 18 0.108338290 0.652260273 0.403394933 0.138425315 0.411711294 0.059895789 19 0.048583393 0.530928735 0.287200674 0.034424451 0.290453873 0.181530196 20 0.062396375 0.609128730 0.358381029 0.110435952 0.368917926 0.105853327 21 0.558129543 0.011449658 0.266554800 0.538665913 0.251393787 0.722466794 22 0.513497335 0.034367816 0.222399933 0.494551507 0.206888151 0.677904722 23 0.268462313 0.303783944 0.126553534 0.229496147 0.085730927 0.420352875 24 0.536940968 0.032042116 0.251733040 0.512530105 0.229139832 0.699113663 25 0.242158428 0.756398183 0.521213928 0.230305070 0.518738801 0.107400848 26 0.153947807 0.393667325 0.144201660 0.151243867 0.154444037 0.319754705 27 0.437984440 0.115486136 0.159442194 0.413459928 0.130514147 0.599756178 28 0.539758478 0.019894553 0.252092950 0.517102049 0.232012746 0.702743534 29 0.560708910 0.013119125 0.269664684 0.540622768 0.253705846 0.724814878 30 0.207603002 0.687454100 0.461649382 0.171104956 0.453408819 0.136987176 31 0.317742941 0.231650158 0.028205034 0.307940212 0.037956414 0.484013051 32 0.672023906 1.211413340 0.954717303 0.718830444 0.976228692 0.528732268 33 0.581383406 0.035005460 0.291516605 0.559699322 0.273895609 0.744894663 34 0.468972443 0.088447744 0.189404944 0.443491527 0.161602098 0.630402306 35 0.443324459 0.890383770 0.685272721 0.402783339 0.668796731 0.328295131 36 0.474452622 0.073221129 0.184096585 0.455922114 0.167938447 0.638885951 37 0.380465430 0.910248235 0.670390778 0.382779989 0.671337410 0.215925742 38 0.122913553 0.670060700 0.418910689 0.162646227 0.429838061 0.050082724 39 0.408018494 0.937369482 0.697912494 0.410005008 0.698624535 0.243165475 40 0.335138758 0.214389193 0.043527064 0.324602512 0.045978248 0.501337252 41 0.283169137 0.830274569 0.576309187 0.323841107 0.590946713 0.134431581 42 0.437810425 0.109792785 0.149282201 0.419158517 0.131079362 0.602060607 43 0.232148939 0.778656982 0.528183799 0.261654252 0.538195371 0.069159650 44 0.142333218 0.689929012 0.437664692 0.185290307 0.450012179 0.045137347 45 0.170860782 0.634795095 0.410256032 0.121946054 0.400986052 0.150175655 46 0.556974569 0.009503115 0.265813680 0.537088820 0.250045708 0.721148448 47 0.258301612 0.785674018 0.545729646 0.258097068 0.546523215 0.102668059 48 0.665074729 1.211088934 0.955686501 0.702940661 0.972583765 0.510469379 49 0.192386101 0.355871447 0.104676491 0.189541972 0.118772275 0.358938065 50 0.195455658 0.365436109 0.108735440 0.210792602 0.140830724 0.363330766 51 0.357239228 0.901672135 0.653131308 0.378320748 0.661086744 0.190137725 52 0.313170473 0.234903006 0.052698860 0.294846196 0.006538361 0.476811939 53 0.630254697 0.082716431 0.338363942 0.609881049 0.323293922 0.794404730 54 0.575705649 0.028108497 0.284560547 0.555424914 0.268661847 0.739772693 55 0.515181591 0.033428596 0.226144250 0.494301852 0.207771442 0.678846290 56 0.097944815 0.640893367 0.392403911 0.127098984 0.400327099 0.070978199 57 0.383731319 0.164409130 0.093776006 0.368757086 0.080423493 0.548973172 58 0.470703565 0.081087798 0.186904301 0.447562370 0.162884719 0.633249443 59 0.098229102 0.449574365 0.200346074 0.102493962 0.209600408 0.263349711 60 0.396803113 0.161646312 0.132734204 0.368965154 0.092939880 0.556689748 7 8 9 10 11 12 2 3 4 5 6 7 8 0.140136571 9 0.484959089 0.608202890 10 0.099211971 0.047744508 0.579096953 11 0.547818050 0.656347882 0.121148439 0.634371327 12 0.098531827 0.041654074 0.570021224 0.022325470 0.621768670 13 0.060684897 0.137065578 0.471137985 0.113105254 0.521874565 0.100024993 14 0.870151158 0.992571070 0.385312035 0.964332671 0.355058450 0.954902902 15 0.584212264 0.712156111 0.111201859 0.680615236 0.170500929 0.672990185 16 0.841407691 0.981328814 0.476858440 0.939635343 0.551719611 0.939677157 17 0.127561416 0.224216083 0.386123686 0.202162790 0.432878792 0.188892861 18 0.534173537 0.646573593 0.092355183 0.622821984 0.029125654 0.611027574 19 0.410829949 0.525054495 0.099780563 0.500091182 0.139148703 0.488799800 20 0.494493808 0.603595649 0.099235408 0.581209326 0.053325794 0.568760234 21 0.158921435 0.018809740 0.625687041 0.064878806 0.672363512 0.060462550 22 0.124524006 0.030203067 0.581791834 0.051373739 0.627731486 0.032661176 23 0.172040497 0.297081019 0.313514611 0.265754043 0.378031230 0.257672307 24 0.122267970 0.025244517 0.598490676 0.024402449 0.650859698 0.029103637 25 0.625092384 0.750025136 0.142062812 0.720219707 0.161865053 0.711593271 26 0.287161567 0.388271701 0.238827196 0.367989305 0.268193422 0.354397606 27 0.054128908 0.108788698 0.499825017 0.083149622 0.551758890 0.070447921 28 0.130924156 0.013033195 0.603485415 0.035538045 0.653829617 0.033810062 29 0.158818001 0.019474300 0.627511105 0.063389387 0.674926131 0.060664996 30 0.552265098 0.680836372 0.086175711 0.648898109 0.167335900 0.641503850 31 0.154219839 0.226801242 0.396581419 0.213110231 0.431928331 0.196502198 32 1.107746081 1.206705678 0.653195747 1.189801789 0.562449067 1.175261472 33 0.171844612 0.039377359 0.646181510 0.073030754 0.695541206 0.076489796 34 0.062815701 0.081256258 0.529467636 0.052059396 0.582684925 0.040741476 35 0.746715773 0.883241852 0.322115777 0.845861724 0.381417704 0.842203302 36 0.100599436 0.068226535 0.543349716 0.066799973 0.588684065 0.045000432 37 0.780392721 0.903994546 0.295992451 0.875054532 0.277068858 0.865986721 38 0.554701603 0.664528542 0.118156213 0.641992631 0.011679092 0.629645972 39 0.807012534 0.931091210 0.322960454 0.901910614 0.304155585 0.892981212 40 0.142687882 0.209607898 0.413199817 0.196910512 0.449329922 0.179871580 41 0.717704650 0.824967938 0.260532901 0.803920312 0.169893800 0.790980977 42 0.085464182 0.104421713 0.506683590 0.093015595 0.552021194 0.074308277 43 0.660598378 0.773031634 0.192543297 0.749527450 0.118743094 0.737673356 44 0.575988736 0.684483173 0.138598297 0.662595250 0.028227837 0.649967490 45 0.499935050 0.628181614 0.048069829 0.596373735 0.160642869 0.588880418 46 0.156302668 0.016384376 0.624028226 0.061829518 0.671196839 0.057936283 47 0.657142003 0.779468240 0.172185041 0.751093306 0.163415472 0.741684686 48 1.099762735 1.205954482 0.630305476 1.185832122 0.552007682 1.172586511 49 0.255228248 0.350653727 0.277629430 0.332127613 0.306587966 0.317735919 50 0.280153604 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0.063225802 0.918713858 0.637803354 0.910762419 0.151793954 0.574085017 59 0.309835720 0.556020606 0.298049838 0.649042306 0.220735911 0.203521282 60 0.024761876 0.839804006 0.557627638 0.833179827 0.081074811 0.498015173 19 20 21 22 23 24 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0.086917542 21 0.541800017 0.619736909 22 0.497333523 0.575110976 0.044632218 23 0.239802991 0.324849939 0.315139273 0.272416806 24 0.517753513 0.597841849 0.040873988 0.040885652 0.285720106 25 0.235291170 0.188235624 0.767584815 0.723763260 0.454465958 0.739941615 26 0.143243913 0.215753198 0.404183983 0.359551910 0.132227139 0.383498380 27 0.418390632 0.498677201 0.126858334 0.085004043 0.188305079 0.099363413 28 0.521568731 0.600929683 0.029372865 0.034228643 0.291394168 0.012226674 29 0.544032313 0.622245902 0.004829044 0.047371183 0.316539366 0.039087944 30 0.185853741 0.169481077 0.698766083 0.655550238 0.383849455 0.669411924 31 0.305802631 0.379841305 0.241750135 0.197296094 0.121593772 0.225165846 32 0.701580219 0.615283974 1.221271941 1.177046604 0.939864459 1.204257940 33 0.563852089 0.642741499 0.027079419 0.069172603 0.334138337 0.049619747 34 0.448965057 0.529572333 0.099892813 0.062026987 0.216942639 0.069047002 35 0.421212160 0.399386093 0.901833409 0.860838749 0.590418540 0.868331937 36 0.458391743 0.536058991 0.083680890 0.039051988 0.235373299 0.069946358 37 0.383222266 0.319914565 0.921362686 0.877309930 0.609377303 0.894479210 38 0.144804500 0.060933064 0.680665069 0.636038207 0.384369398 0.658722809 39 0.410729826 0.347389976 0.948498558 0.904484506 0.636188281 0.921434815 40 0.322914734 0.397223195 0.224440177 0.180026598 0.131697494 0.208403755 41 0.308025725 0.223219374 0.840686087 0.796072122 0.547625139 0.820083614 42 0.421533016 0.499341434 0.120427877 0.075844147 0.200012892 0.102468406 43 0.249825844 0.169907609 0.789331105 0.744721491 0.489170045 0.766711849 44 0.166821121 0.081522574 0.700462494 0.655830304 0.406049915 0.679060126 45 0.141301775 0.146172327 0.646105772 0.602890473 0.331215931 0.616819275 46 0.540401997 0.618531305 0.003187550 0.043568550 0.313229590 0.037757462 47 0.258529150 0.199684242 0.796760590 0.752643286 0.485646561 0.770263984 48 0.689476983 0.605328602 1.221340989 1.176794697 0.929277177 1.201687997 49 0.182743869 0.254501644 0.366247353 0.321640240 0.114810966 0.346793507 50 0.196997339 0.257490308 0.375151776 0.331095259 0.156437294 0.360179184 51 0.370932630 0.294843719 0.912475497 0.867936192 0.607761958 0.888664710 52 0.296306906 0.374399817 0.245655221 0.201107621 0.091907177 0.223915556 53 0.613576047 0.691826274 0.072144055 0.116767671 0.384698916 0.099846992 54 0.558956678 0.637235609 0.018121700 0.062350085 0.330962943 0.049743662 55 0.497924938 0.576561547 0.044757931 0.012173061 0.270381361 0.030398636 56 0.111771952 0.037668917 0.651633830 0.607056107 0.351495118 0.628595283 57 0.369279023 0.445549793 0.174668588 0.130101950 0.159030416 0.157973997 58 0.452017951 0.531688983 0.092478319 0.051632810 0.222723480 0.066285686 59 0.088602361 0.159576923 0.460165924 0.415538269 0.175181469 0.438712372 60 0.375164690 0.456769778 0.173046522 0.131224889 0.142344744 0.143736819 25 26 27 28 29 30 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 0.378097220 27 0.641518069 0.284932686 28 0.745135910 0.386041989 0.103672827 29 0.769361716 0.406776118 0.128238939 0.028254439 30 0.081335715 0.322347041 0.572050585 0.675240297 0.700275823 31 0.538103978 0.164267563 0.131567687 0.226045586 0.244664318 0.475997287 32 0.547534204 0.822188634 1.106652895 1.205815267 1.224358251 0.626865150 33 0.787860176 0.427523385 0.146356814 0.042750778 0.022854762 0.717980960 34 0.670970245 0.316006758 0.031095538 0.074523851 0.100652202 0.600766034 35 0.220967460 0.552203286 0.775853894 0.875844601 0.902627500 0.236207601 36 0.685369065 0.320509170 0.051825357 0.068396997 0.086306619 0.617718329 37 0.155558736 0.526270844 0.795745729 0.899416508 0.923261917 0.233306819 38 0.150576377 0.276631323 0.559528397 0.661847242 0.683177738 0.158973989 39 0.181939325 0.553807129 0.822777489 0.926441959 0.950373941 0.258457098 40 0.554845457 0.181610015 0.116197891 0.209045891 0.227386908 0.492169100 41 0.185855002 0.436753653 0.721153352 0.822786331 0.843370355 0.251867544 42 0.648722866 0.283889150 0.031536521 0.103084909 0.122907798 0.581451161 43 0.121995743 0.385606595 0.667400065 0.770099906 0.791776102 0.182389671 44 0.152081295 0.296279332 0.579972133 0.682003431 0.703040634 0.171391810 45 0.128290657 0.272551945 0.519397168 0.622609929 0.647619601 0.052661987 46 0.765898074 0.403037245 0.124925489 0.026369530 0.003893106 0.696922519 47 0.041390340 0.401700063 0.671370242 0.775039757 0.798704113 0.121696821 48 0.512284693 0.818190229 1.102952328 1.204122557 1.224153525 0.593356162 49 0.417401354 0.039546317 0.248980032 0.348873880 0.368958302 0.360457607 50 0.431575218 0.064679088 0.265801995 0.360771266 0.378317773 0.381039284 51 0.177382674 0.509837655 0.789305647 0.892493949 0.914784572 0.258128657 52 0.524949293 0.159582824 0.125612133 0.226590241 0.248021123 0.459791739 53 0.838275191 0.476312441 0.196763740 0.093307383 0.069597528 0.768546642 54 0.784049528 0.421773956 0.142722394 0.040630437 0.014999300 0.714763833 55 0.723010380 0.361320421 0.082107411 0.026396270 0.046352337 0.654027847 56 0.151322242 0.248781981 0.529261173 0.632094150 0.654011053 0.140707669 57 0.598947464 0.229818055 0.068832310 0.158618426 0.177463385 0.533816703 58 0.675836964 0.317215437 0.034422760 0.069588810 0.093817103 0.606471751 59 0.323873230 0.056405191 0.339770791 0.441566902 0.462690245 0.272025418 60 0.596232469 0.245225377 0.046294627 0.149072874 0.174306728 0.526191906 31 32 33 34 35 36 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 0.979927904 33 0.266173228 1.246064882 34 0.161776354 1.137746832 0.117230744 35 0.696026590 0.635168414 0.917901284 0.801986112 36 0.158575572 1.138481912 0.107597794 0.041156840 0.824990881 37 0.688797074 0.428872314 0.942092556 0.825451484 0.218444254 0.838701656 38 0.440627098 0.557080140 0.703672137 0.590401146 0.370469950 0.596986287 39 0.716248132 0.417974808 0.969132126 0.852419526 0.220867189 0.865908083 40 0.017408118 0.997097807 0.248969941 0.145946874 0.711055405 0.141384839 41 0.599410348 0.395113862 0.864249657 0.752136850 0.371880561 0.757065938 42 0.122971683 1.102760048 0.143746837 0.047022370 0.790247511 0.036859441 43 0.549746072 0.460764775 0.812090396 0.698153872 0.326814486 0.705674091 44 0.459880712 0.534813774 0.723688470 0.610902766 0.373047570 0.616785821 45 0.424047545 0.664350120 0.665353009 0.548144721 0.281012243 0.565072962 46 0.240847701 1.220513702 0.026703539 0.097633309 0.899615700 0.082544397 47 0.563956756 0.506172712 0.817680022 0.701218977 0.235203126 0.713986339 48 0.979649979 0.087583809 1.245298599 1.133976031 0.573303774 1.137875370 49 0.125358103 0.857697678 0.389985404 0.280068437 0.588604956 0.282652168 50 0.135067744 0.846211043 0.400232491 0.296417754 0.613461133 0.292831343 51 0.674105031 0.371279895 0.934740438 0.819826551 0.301488519 0.828931948 52 0.033453144 0.981040843 0.268346598 0.156706614 0.675328901 0.162116748 53 0.313807861 1.293021476 0.050586355 0.167813357 0.968110261 0.155803458 54 0.259629119 1.239269596 0.011143997 0.114594711 0.916355480 0.101304891 55 0.200367567 1.180281905 0.066203502 0.056060907 0.857433734 0.042145180 56 0.413036628 0.591862571 0.674176487 0.559982003 0.365275542 0.568027341 57 0.067443134 1.047353943 0.198809316 0.096979680 0.747820637 0.091231263 58 0.159806684 1.138111592 0.112138821 0.013853933 0.809803785 0.027307280 59 0.220667753 0.768946559 0.483260525 0.370771590 0.505190365 0.376486449 60 0.104793192 1.067361721 0.191822965 0.074738083 0.729615473 0.096343694 37 38 39 40 41 42 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 0.265765164 39 0.027584751 0.292906047 40 0.705800930 0.458017658 0.733237244 41 0.181665486 0.163263904 0.201187591 0.616811770 42 0.801936902 0.560272638 0.829158146 0.106040798 0.720553334 43 0.170434041 0.109292260 0.195739380 0.567125526 0.070190416 0.668905850 44 0.254892880 0.022694638 0.281605841 0.477285769 0.141716632 0.580140047 45 0.283225482 0.155353023 0.308996165 0.440100375 0.278768908 0.528824659 46 0.919751340 0.679462351 0.946872524 0.223563547 0.839609640 0.119189956 47 0.124875156 0.151736546 0.152292381 0.580945253 0.150082750 0.677201425 48 0.378678998 0.545083852 0.363481395 0.997006542 0.382128379 1.101552736 49 0.565815270 0.315270189 0.593350247 0.142752673 0.474442942 0.246238927 50 0.575282680 0.316786953 0.602864103 0.151792174 0.470636029 0.257828672 51 0.087013605 0.234871528 0.099500152 0.691440322 0.107096826 0.792094334 52 0.677434669 0.435328689 0.704735401 0.039964985 0.596240243 0.125268768 53 0.992396789 0.752757066 1.019464908 0.296473578 0.912829871 0.192485322 54 0.938024737 0.698167737 0.965122146 0.242342417 0.858369397 0.137901241 55 0.876919847 0.637493470 0.904027148 0.183266696 0.798051107 0.077622632 56 0.282787243 0.036300735 0.310307481 0.430359442 0.197140775 0.531214428 57 0.751156940 0.506444237 0.778495398 0.050457090 0.666057095 0.055584035 58 0.829975584 0.592586675 0.857030558 0.143392263 0.753830162 0.039574667 59 0.470588190 0.220500512 0.498149148 0.238002625 0.381391088 0.339782700 60 0.750743945 0.517454527 0.777698406 0.093221886 0.679745784 0.065549601 43 44 45 46 47 48 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 0.092000165 45 0.208695013 0.173135630 46 0.788080578 0.699307221 0.644264233 47 0.092894994 0.147016643 0.165679375 0.795176486 48 0.441312531 0.523808449 0.635321581 1.220362737 0.471682314 49 0.424409253 0.334568183 0.310067899 0.365188698 0.441231147 0.855320991 50 0.425809271 0.334243454 0.332738036 0.374459348 0.451915177 0.848380312 51 0.126107714 0.218103836 0.300331713 0.911130939 0.136438401 0.335368838 52 0.543785563 0.455417224 0.407385340 0.244344162 0.552606180 0.977772750 53 0.861371931 0.772587893 0.715914813 0.073295632 0.867919758 1.293441053 54 0.806755257 0.718037067 0.662112897 0.018782680 0.813493941 1.239142434 55 0.745957669 0.657489444 0.601368519 0.042911172 0.752375226 1.179149415 56 0.138222462 0.058912707 0.127201887 0.650335365 0.162030927 0.577880978 57 0.615338864 0.526036690 0.481372768 0.173670036 0.626297182 1.046692759 58 0.700703051 0.612861382 0.553817736 0.090514662 0.705543774 1.135405644 59 0.329330767 0.240441092 0.224210121 0.458970385 0.346243870 0.763220729 60 0.624717514 0.538238655 0.473554090 0.171053417 0.626561472 1.061816098 49 50 51 52 53 54 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 0.045168828 51 0.548943774 0.551652364 52 0.123391018 0.143847900 0.666829044 53 0.438390153 0.446815970 0.984361297 0.317617759 54 0.383955842 0.393187771 0.929730627 0.262990243 0.054632176 55 0.323828473 0.334867113 0.868753445 0.202182328 0.115676778 0.061125892 56 0.287991482 0.293358558 0.261106242 0.405991280 0.723606400 0.668976529 57 0.191618108 0.202247686 0.739104805 0.074091247 0.246800505 0.192450210 58 0.280550011 0.294856181 0.822949310 0.157633074 0.162444244 0.108311179 59 0.095719527 0.109048296 0.453438419 0.214977764 0.532263603 0.477682410 60 0.211149911 0.233062660 0.745812930 0.089309416 0.242367565 0.188653155 55 56 57 58 59 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 0.608091343 57 0.132930044 0.478028411 58 0.047759581 0.562644962 0.093350823 59 0.417066043 0.192376809 0.286009775 0.372478368 60 0.128326437 0.486495962 0.061483035 0.080571038 0.298861208 > dist(aplus(sa.lognormals)) 1 2 3 4 5 6 7 2 3.5158770 3 2.1913087 1.6201216 4 2.6181991 2.2286338 1.8216846 5 2.4079521 1.4125652 1.0164013 0.9830595 6 2.3254439 2.6452363 1.8839353 0.5608510 1.2886337 7 2.5487394 1.6656967 1.7978119 1.4410941 1.0090564 1.8125709 8 3.1790586 0.4149847 1.4562521 2.0717396 1.1957933 2.4704024 1.3191691 9 2.2914601 2.5586995 1.9326744 0.4642329 1.2035748 0.3651341 1.5312580 10 3.5646845 1.1449244 2.2025518 1.8800715 1.4363429 2.4041523 1.0973613 11 3.6372065 2.4877237 2.4050349 1.1463080 1.7330029 1.3956741 2.3463765 12 3.2522959 0.8024754 1.7396939 1.6992324 1.0602238 2.1822943 0.9891517 13 2.0757822 1.5396577 1.0960035 1.4576634 0.6716268 1.6812692 0.7530200 14 1.8395149 5.0771213 3.8072909 3.5029931 3.7620472 3.0628084 3.8130154 15 0.9795722 4.0215378 2.8734198 2.6711440 2.7714372 2.3375914 2.7235325 16 2.4180887 4.2964004 3.5047689 2.3510169 2.9598973 2.0550103 2.8224424 17 2.7548972 1.2991388 1.2638266 0.9366627 0.3605482 1.3556892 1.0939568 18 3.2541697 2.4350662 2.1972851 0.7464479 1.4703379 0.9896605 2.0554840 19 2.1958162 2.2442397 1.5409033 0.4383465 0.8570452 0.4545095 1.4014026 20 1.3093907 2.7310319 1.5464388 1.3392965 1.3747429 1.0281206 1.7775933 21 3.2068285 0.6526552 1.3675636 2.4736827 1.5214736 2.7979888 1.7761089 22 1.8452627 2.9306724 2.0775916 3.3391896 2.5895348 3.3261650 2.5659603 23 3.7815475 1.9167117 2.4179750 1.2737747 1.5412881 1.7908147 1.8080724 24 2.7514200 1.2786657 1.7040597 2.0360273 1.2718714 2.3950819 0.7558502 25 1.0190970 4.2713758 3.0650434 2.9596366 3.0373787 2.6052710 3.0135466 26 1.9553546 1.9085859 0.9475450 0.9650196 0.5546829 1.0036361 1.3140163 27 4.0354961 1.4002329 2.3692806 1.7970356 1.6420710 2.3239792 1.8781219 28 3.3480192 0.6209310 1.7713271 1.9588684 1.2380839 2.4243033 1.1499624 29 2.4430445 1.8041899 1.5282634 2.8063553 1.8862535 2.9790055 1.8502689 30 1.0597515 3.6147485 2.5374756 2.1583396 2.3186034 1.8417237 2.2939521 31 3.0745499 1.1280166 1.1398766 1.4254701 0.8383209 1.7475140 1.6927120 32 2.2536174 5.1408162 3.6880560 3.4877626 3.8077348 2.9451226 4.2081890 33 3.5095738 0.7106506 1.9661553 2.4519520 1.6481158 2.8876116 1.4507958 34 3.4000147 1.0057918 1.8780883 1.5198560 1.0840040 2.0427869 1.1359485 35 2.2634452 3.7447800 2.9664565 1.7100841 2.3831220 1.3973233 2.3819469 36 2.9073656 0.6496322 1.0158640 1.7678743 0.8459670 2.1084993 1.3537201 37 1.4097444 4.5626030 3.3292340 3.0318089 3.2546948 2.6169475 3.2941531 38 3.0260837 2.4094651 2.0180641 0.6155913 1.3393553 0.7798460 1.9854436 39 1.6036447 4.1977460 3.0455232 2.4191938 2.8177147 1.9748031 2.9289862 40 2.1412263 1.4992706 0.2752391 1.6666038 0.8003176 1.7763286 1.5242901 41 1.5913616 3.1063275 1.9073158 1.3938505 1.7165510 0.9011648 2.2017331 42 2.6938878 0.8846461 0.9207214 1.5376633 0.5874869 1.8649292 1.1659461 43 1.5044916 3.1151848 1.9767717 1.3852021 1.7148643 0.9311770 2.0869324 44 2.1417818 2.5371216 1.6336523 0.6861851 1.1624000 0.2895211 1.7904651 45 2.5487338 2.6350166 2.1567876 0.4598817 1.3503781 0.5223405 1.5954389 46 2.8037353 1.0974352 1.2888627 2.4823039 1.5092642 2.7506629 1.6129643 47 2.0585240 3.1044433 2.2444973 1.0473050 1.7052715 0.6174168 1.9903615 48 3.3649359 5.4419580 4.2789705 3.3563947 4.0546866 2.8362956 4.4399236 49 0.9977626 2.5368320 1.2207141 1.9713433 1.5037858 1.8250291 1.8186693 50 3.0426601 1.5143811 1.0428185 1.6561624 1.1559711 1.8294878 2.1189936 51 2.5988231 3.2290932 2.4547786 1.0484031 1.8976240 0.6131034 2.3420846 52 1.3096693 2.2149806 1.1373580 1.8366112 1.2524281 1.8108798 1.4338363 53 5.6701103 2.6114929 3.9059680 4.8267185 3.9922041 5.2533591 3.9557950 54 3.0520436 0.9963707 1.5201178 2.6090899 1.6496852 2.9179348 1.6724876 55 4.0581113 0.9135337 2.1961384 2.1403511 1.6847956 2.6373207 1.9512235 56 2.0044364 2.5347378 1.6463532 0.6907377 1.1301825 0.3504177 1.6489431 57 1.6371561 1.9725425 0.8331004 2.0878926 1.3079331 2.1114710 1.6333616 58 2.2852714 1.3525628 1.1880308 1.6878710 0.8397539 1.9593409 0.7522929 59 1.3032971 2.4108954 1.2186120 1.4002801 1.1392689 1.2368406 1.5468654 60 1.9222258 1.8055774 1.3361511 1.5061420 0.8925985 1.6922296 0.6946095 8 9 10 11 12 13 14 2 3 4 5 6 7 8 9 2.3482863 10 1.0324082 2.1912633 11 2.5228151 1.5208478 2.2737092 12 0.6356049 2.0112660 0.4734959 2.1455107 13 1.1805053 1.5135198 1.5261592 2.3737582 1.1815784 14 4.7479605 3.0512659 4.8650577 4.4310492 4.6455865 3.5738481 15 3.6698256 2.2459551 3.7994981 3.7282159 3.5813803 2.4911972 1.1449265 16 3.9974272 1.9153609 3.7317997 3.2226624 3.6580230 2.9272626 1.9017588 17 1.1618321 1.2757895 1.2450160 1.4911740 0.9024030 0.9644221 4.0419811 18 2.4012892 1.1002567 2.1635617 0.4213713 2.0160382 2.0763745 4.0339556 19 2.0408701 0.3991731 2.0309341 1.4869685 1.7782142 1.2330383 3.1821734 20 2.4555535 1.0341074 2.6681986 2.3335564 2.3647581 1.3733832 2.4198734 21 0.5790404 2.7204699 1.6014773 2.9029684 1.2128534 1.4365553 4.8940679 22 2.5998515 3.2300220 3.3010156 4.2723615 2.9663911 2.0295107 3.6051776 23 1.9535704 1.7119996 1.4085298 0.9996998 1.4344592 2.0738322 4.7589194 24 0.8768640 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1.9128865 1.6396513 2.5846145 27 4.0025885 0.7460956 2.0242639 4.5655516 2.1355673 28 2.8999370 1.6762539 0.8585916 3.9992731 1.7720923 1.2743234 29 1.1898123 3.2301659 1.2802845 3.3123753 2.0048160 2.9973406 1.8167258 30 2.6391258 3.3711740 2.7620767 0.8257755 1.8929379 3.7802822 3.3059563 31 3.0715312 1.4321647 1.7422228 3.7747645 1.1935950 1.3094767 1.2863933 32 4.0223350 4.7334939 4.6373648 1.9159596 3.2604986 5.2219049 5.0084959 33 2.7674900 2.1967561 0.8786468 4.2106088 2.1381763 1.7251232 0.5339663 34 3.2789308 1.0568340 1.2490083 3.9582870 1.6275950 0.7859920 0.6228402 35 3.6985868 2.8215691 3.0694524 1.9504934 2.0636346 3.4212179 3.3710291 36 2.5320935 1.8301750 1.1132592 3.6729413 1.2853859 1.5538002 0.7989643 37 3.1934123 4.2830902 3.7332821 0.5189343 2.7763681 4.7316684 4.2893967 38 3.7759756 1.2132798 2.5040660 3.3802266 1.3234842 1.7844798 2.2572250 39 3.3680879 3.6683962 3.4687847 1.0501421 2.3475595 4.1817034 3.9108124 40 2.0323384 2.2665327 1.4515908 2.9791405 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52 1.3992194 1.6168029 1.9318020 3.2351030 2.2129276 2.1736455 2.3516035 53 3.2890357 5.9704154 3.6590249 7.5585103 2.5088483 3.4141544 6.2692934 54 0.8755011 3.3553579 1.7422226 4.9788674 0.8381790 1.6847833 3.8108202 55 2.6724915 3.9573791 1.2255210 5.4195547 1.3350556 0.8444314 3.7852563 56 2.6857096 1.6020431 1.6997032 2.8424620 2.7429118 2.0162576 1.4148078 57 1.0461437 2.1142822 1.7985572 3.5500661 2.0302255 2.1672067 2.8335375 58 1.1843094 2.3540466 1.4391996 4.1089892 1.2483958 1.3134461 2.7241050 59 1.9918788 1.3331885 1.8252776 2.8013344 2.5247894 2.1794952 1.8577307 60 1.4583525 1.8789431 1.6727831 3.7196179 1.6990109 1.5645258 2.2819028 36 37 38 39 40 41 42 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 3.9516290 38 1.9954186 3.3941776 39 3.5922988 0.7627429 2.7375032 40 0.8662991 3.2551807 1.9315287 2.9591180 41 2.4841412 1.8598584 1.6247848 1.3137743 1.8537428 42 0.2692740 3.6996374 1.8119925 3.3292539 0.7231128 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1.8460224 1.5293101 0.7165960 1.7019782 57 1.4085454 2.9072167 2.4700294 2.7730344 0.7338546 1.9282160 1.2707890 58 0.9018954 3.3096324 2.1491436 3.0322675 0.9211616 2.1661403 0.7346327 59 1.7791069 2.1891892 1.8152841 1.8710580 1.0966234 0.9446090 1.5329034 60 1.3043980 2.8490942 2.0414818 2.5684997 1.0735769 1.8105507 1.0788960 43 44 45 46 47 48 49 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 0.8345747 45 1.2235571 0.7632865 46 2.8821504 2.5735151 2.8070819 47 0.6156491 0.7370299 0.7329568 3.0585797 48 2.4853352 2.9060011 3.0493085 5.3415739 2.4590901 49 1.3544737 1.5915061 2.0627535 1.8884410 1.8226260 3.7034458 50 2.3337200 1.6573891 2.0921271 1.8809255 2.3870152 4.3470258 2.1184872 51 1.0947147 0.8256627 0.8024719 3.3626671 0.6327923 2.3317611 2.2899776 52 1.5072297 1.6047885 1.9602390 1.5654778 1.8599365 3.9530943 0.4256537 53 5.6420874 5.1351684 5.2148816 2.8782171 5.6833577 8.0309493 4.7625407 54 3.0982638 2.7568956 2.9413666 0.2700466 3.2399048 5.5589133 2.1430907 55 3.3301249 2.6116839 2.5495261 1.9840037 3.1600720 5.4408711 3.1043920 56 0.7213673 0.2253449 0.6981628 2.5132947 0.6284347 2.9314718 1.4773017 57 1.9118639 1.8771260 2.3013011 1.2073365 2.2692878 4.3288877 0.7061159 58 2.1014570 1.8259843 1.9401472 0.9516525 2.1985503 4.5714561 1.3979419 59 0.9000910 1.0186204 1.4746694 2.0135939 1.2727776 3.3628666 0.5943265 60 1.7087012 1.5723670 1.6586062 1.3985778 1.8185311 4.1762453 1.1372941 50 51 52 53 54 55 56 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 2.3324265 52 2.0254153 2.3332708 53 3.8960772 5.8397263 4.4389627 54 2.0057170 3.5302600 1.8044562 2.6356960 55 1.6668337 3.1344644 2.8003259 2.9652470 1.8912145 56 1.7765371 0.8857398 1.4705534 5.1217577 2.6975901 2.6465642 57 1.8406808 2.6688413 0.5242914 4.0705176 1.4707023 2.6672592 1.7909590 58 1.7627870 2.5558002 0.9956639 3.6329426 1.0925147 1.9450500 1.7177643 59 1.8672673 1.7213392 0.6426930 4.8347912 2.2435646 2.8204460 0.8875264 60 1.9558335 2.2539724 0.7403795 4.1151086 1.5614297 2.2905513 1.4194985 57 58 59 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 0.9835398 59 1.0197468 1.3139235 60 0.9896319 0.4907135 0.9791275 > dist(rplus(sa.lognormals)) 1 2 3 4 5 6 2 33.5349005 3 24.5211943 12.1937586 4 47.0837320 38.6880156 31.9043599 5 37.5744352 24.8696283 18.5297348 13.8934097 6 45.5288877 40.4471547 32.5310286 4.3506207 15.6801524 7 35.1134939 15.9441316 12.7750574 23.0915631 9.6673654 25.0685638 8 33.7817549 4.9794668 15.4481959 43.5776221 29.7339488 45.2399820 9 45.7169031 38.8737265 31.5673513 2.2851583 14.0599511 2.7662100 10 38.2313545 18.6372210 15.7855965 20.4700126 7.5705726 22.8895047 11 51.9149211 43.4217769 36.9050874 5.3056513 18.8021351 6.9213441 12 36.3044592 15.4493766 13.0722638 23.4096470 9.9382927 25.5720474 13 30.2504241 8.7295185 6.6060668 30.7314784 16.8935079 32.1717078 14 52.4942690 81.7847562 70.8069396 71.5886721 72.1287280 67.7599581 15 23.1172244 39.1344377 28.6659373 33.0482563 29.2419189 30.6376675 16 48.0427642 49.3113607 41.8456465 24.1330818 29.8742339 22.6216764 17 41.2072607 28.7772361 22.8116286 9.9619644 4.3055973 12.4127079 18 50.6660190 42.5472572 35.8505021 4.1461150 17.8286723 5.6922776 19 43.2922114 36.0997808 28.6281011 3.7988659 11.2720709 4.4636793 20 32.8807676 32.7822141 22.6441081 14.6085470 12.3486746 12.6501592 21 46.0780039 31.1154236 39.2602080 69.6252549 55.7475682 71.0486799 22 170.5336776 168.4000114 175.0375263 206.4957771 192.6692370 207.4597373 23 50.9866417 40.0550330 34.3780059 4.5049864 15.9219418 8.3712136 24 36.6369143 14.5702973 23.7281916 53.0019010 39.1725344 54.5677174 25 21.7823833 45.9629517 35.4187397 42.4476143 38.6965694 39.6683178 26 35.9158281 27.7182470 19.6323899 12.4084274 4.4787348 12.9887143 27 47.6464162 34.8077904 29.6016378 6.1449151 11.1455703 10.2355348 28 34.1459681 6.3899560 10.3643329 32.4183413 18.6931192 34.3397227 29 109.5693139 103.8876317 111.1701979 142.2685105 128.4032795 143.4667249 30 29.4171096 35.1591202 24.9928746 21.7200242 19.2428282 19.5820936 31 40.0153744 27.7031491 21.4680342 11.1201319 3.1904416 13.2337145 32 118.2049107 150.2476292 138.9557692 141.3671046 142.3005806 137.1780323 33 41.4502967 21.6522653 30.7555702 60.2786480 46.4347834 61.8782884 34 41.2669858 25.5259727 20.9828267 13.6382952 4.0326685 16.4232863 35 45.9237832 44.0616535 36.0592073 12.2871797 20.9669168 10.2412723 36 32.0462169 7.6693786 7.9018815 31.1415608 17.2723846 32.7973966 37 34.1957715 58.8116919 47.6686184 47.5101592 47.4806062 43.9170718 38 49.3254361 41.9028537 34.8904267 3.4366886 17.0874999 4.2807993 39 36.3197208 50.0509889 39.0127201 29.4494389 32.4848156 25.6627763 40 26.6579811 10.7333750 2.3305811 31.1377403 17.4843538 32.0590589 41 37.0858169 41.4258355 30.8708717 16.2258575 20.1055209 12.3367588 42 32.6910812 12.3927702 8.8989662 26.3913743 12.5162570 28.0570115 43 37.2095156 39.6784993 29.5263376 14.0692009 17.8186658 10.4287437 44 43.0102201 38.9345340 30.5192490 5.9979469 14.4667758 2.6504447 45 47.9085300 40.3922383 33.4727824 2.2008693 15.6259397 3.8962896 46 61.6533590 51.3618358 59.0388377 89.8062395 75.9316223 91.1266091 47 44.1973819 41.3023326 32.8626277 7.2759466 16.9831555 3.5072103 48 59.4955982 86.4740013 74.3847622 69.8820324 72.9147596 65.5929795 49 16.8601261 16.8920961 8.4536978 38.0638372 25.5720161 37.9779781 50 38.3976208 29.2401108 21.6624581 10.4743579 5.0179427 11.4739522 51 47.2623800 44.2478343 35.9120073 7.8390102 19.6102469 4.0700814 52 23.3641895 10.4428809 8.9239229 40.2774673 26.7626338 40.9753768 53 266.4475461 262.1708257 269.6708561 300.7011998 286.8308543 301.9708769 54 68.8322812 58.9388724 66.7310522 97.4421480 83.5692628 98.7960847 55 41.7669118 25.5110733 21.1962834 13.9010255 4.6258514 16.7795956 56 42.2790050 37.5944443 29.3269247 5.6768738 13.1037170 3.3677012 57 30.2242337 20.3436123 24.7945868 56.3944720 42.6796892 57.2141737 58 31.0183700 3.5898701 11.9266115 40.4602975 26.6081444 41.9442322 59 28.6614545 24.8291669 14.6306888 19.1356692 9.5114654 18.7494348 60 29.9102586 8.6227608 6.8706274 31.2729988 17.5033322 32.6839480 7 8 9 10 11 12 2 3 4 5 6 7 8 20.7553557 9 23.2531340 43.7038154 10 4.0576055 23.5811148 20.9615014 11 27.9533130 48.3547289 6.6010706 25.0351492 12 2.6252337 20.3950338 23.7791888 3.2542493 28.0633551 13 8.4427405 13.1881349 30.6975555 11.8098419 35.6790699 8.6781495 14 75.2587895 83.4339180 69.3447793 77.0905370 74.0237584 77.1093134 15 30.9680922 41.7199968 31.0377471 33.0960506 37.3649645 33.0362529 16 35.0392729 53.2777529 22.3735298 34.9489568 26.0230437 36.9986256 17 13.3872753 33.6937019 10.5193224 10.6256026 14.6786509 13.4892721 18 27.0381026 47.4649540 5.3170693 24.2225914 1.2957554 27.2176884 19 20.6621274 40.9223496 3.0620522 18.4263260 8.8401284 21.1288174 20 19.4759442 37.0908962 13.0591563 19.1496806 19.1537594 20.5038024 21 46.8029734 26.1538087 69.6387411 49.7289322 74.4565849 46.5483756 22 183.8674761 163.4304950 206.2763883 186.9809457 211.4644209 183.7842905 23 24.6068426 45.0095966 6.6662727 21.4948281 4.2847617 24.6241389 24 30.0566086 9.6132162 53.0454009 33.0416396 57.8460052 29.8841958 25 39.9615426 47.8277854 40.3853864 42.3317958 46.5117073 41.9267798 26 13.0874692 32.4279409 11.9696862 11.7672884 17.4833559 13.6748454 27 19.5091688 39.7707813 8.0025669 16.2539759 9.1714649 19.3913740 28 9.6878956 11.3271743 32.6678119 12.2561480 37.1262750 9.0879446 29 119.4655099 98.9201663 142.1626501 122.4815605 147.1692972 119.3073366 30 23.2696433 38.8208847 19.7488723 24.3773885 26.1796399 25.1861842 31 12.5833956 32.6102820 11.5720775 9.9052295 15.8246228 12.5808639 32 146.1832866 151.2914786 139.4406610 147.5648076 142.7874495 147.2848876 33 37.3565186 16.7145475 60.3678365 40.2058538 65.0641818 37.0586263 34 10.2875477 30.4789587 14.3741660 6.9845239 18.0632302 10.0887066 35 28.6064868 48.5698428 10.3680226 27.4460105 14.1889940 29.9377480 36 8.7932529 12.4792187 31.2749937 11.5883068 35.9403973 8.3362747 37 50.8408304 61.0870972 45.2726921 52.5174001 50.4501292 52.7116212 38 26.4229783 46.7989604 4.2223224 23.7292129 2.6755869 26.6550781 39 38.2545127 53.5513420 27.1877360 38.8071386 31.9105616 39.9221262 40 10.8842000 14.4996411 30.9194661 13.9794367 36.1247894 11.1039748 41 28.0933671 45.6700616 14.2784109 27.3999245 18.9323364 29.0217903 42 4.7279368 17.2280385 26.5232539 7.3551753 31.2140712 4.2926818 43 25.8653639 44.0081723 12.0373685 25.1244986 17.2683360 26.8733940 44 23.8505249 43.6653806 4.3148409 21.9159536 9.3292441 24.3964374 45 24.6756238 45.2543022 2.2259612 22.2084473 4.8511666 25.1450382 46 66.9862874 46.3954400 89.7632089 69.9639005 94.6725319 66.7859867 47 25.9759364 45.9809962 5.1183415 24.2681345 9.7582217 26.7892234 48 78.3675306 88.8988287 67.8941260 79.1362976 71.0185897 79.5976937 49 20.4334087 17.9939042 37.3465254 23.7712589 43.1631288 21.1948234 50 14.5386847 34.0474554 10.4200570 12.4700159 15.2975423 14.7262467 51 28.9211884 48.9921122 6.4039897 26.8827841 8.0800193 29.5174652 52 19.2901535 10.6070236 39.8929051 22.8129457 45.3712416 19.7460559 53 277.8027982 257.2205201 300.6363846 280.7366948 305.5569229 277.5943651 54 74.5817499 53.9777477 97.4152135 77.5319422 102.2939719 74.3664911 55 10.5615869 30.4785120 14.7552126 7.0333639 18.1618688 10.1281868 56 22.4106039 42.3280621 3.9395623 20.5272747 9.7867343 23.0173248 57 34.5311050 16.0393941 56.1085190 37.8432908 61.4130868 34.6144703 58 17.7168002 3.9050011 40.4633267 20.8539339 45.3541050 17.6403070 59 12.9696545 29.0441113 18.2324579 13.7696595 24.2108498 14.0856847 60 8.8804833 12.8865182 31.1893641 12.4456509 36.2664445 9.3778565 13 14 15 16 17 18 2 3 4 5 6 7 8 9 10 11 12 13 14 75.2859159 15 31.7650272 44.6170535 16 41.1208161 58.5040065 26.1203819 17 21.0307985 73.1708378 31.1532316 28.4625517 18 34.7122863 73.0024273 36.0917458 25.2387209 13.7728789 19 27.9065654 69.1056563 29.7967454 23.7969481 7.9874154 7.6099484 20 24.1611834 60.6375142 20.3862769 24.5680351 12.8772621 17.8948377 21 38.9428155 97.2383116 61.4662570 76.9935091 59.7888618 73.5444815 22 175.8254912 208.5015312 190.3929271 210.0242248 196.8300413 210.4864114 23 32.5733312 75.9300248 37.3852460 26.7859865 11.6354744 4.2062232 24 22.3972189 87.4922389 47.7840201 61.0420868 43.1719583 56.9359318 25 39.4515357 36.1069442 10.0780341 34.0520040 40.7578660 45.2594885 26 19.3421223 68.2203128 26.1881178 27.6410777 5.7029141 16.3564444 27 27.4865558 76.2566201 35.7993037 28.1951795 6.8711797 8.6615465 28 4.4558984 79.7314496 36.0892123 43.9446308 22.5011855 36.2644281 29 111.5391989 153.0448928 128.6676094 147.0084997 132.5010072 146.2289248 30 26.7028457 53.5839492 11.3848895 19.8338530 20.4004846 24.8964393 31 19.9259948 72.8472138 30.7382922 29.4220763 1.6152404 14.9047131 32 144.9250790 79.9044416 119.2490850 134.6034288 143.2862115 141.9881528 33 29.7198378 92.7927814 54.4460728 68.3575912 50.4040648 64.1762906 34 18.2563448 75.7624545 32.8086461 30.9683027 4.0883762 17.2794537 35 35.5345989 62.6912398 26.8835471 12.4543647 18.5867385 13.2692636 36 2.3928886 77.4342325 33.9727080 42.6980049 21.2755666 35.0313553 37 51.6413054 24.7512701 20.4805656 36.2414173 48.5424002 49.3399654 38 33.9598131 71.7453625 34.7912114 24.7577353 13.1669167 1.4576650 39 41.6623315 42.2528864 15.9000515 21.2650173 32.4017580 30.8583610 40 4.3242508 72.4483754 29.7398359 41.4908661 21.7630528 35.1013317 41 32.8523301 56.4543179 21.8437208 23.2831728 19.2776417 17.8307755 42 4.7847482 75.5471985 31.7480093 38.7947011 16.5482178 30.2919305 43 31.0339367 58.0788132 21.6398544 21.6644369 16.8960062 16.0884706 44 30.5629562 66.1474138 28.6354939 23.0312466 11.7363038 8.1050925 45 32.3376446 70.7604823 32.8927106 22.4699522 11.8145366 3.6541605 46 59.0860952 110.7082562 79.1158677 96.0132941 80.0022243 93.7465886 47 32.8067145 64.6049821 27.9987332 19.7384637 14.2598148 8.5928493 48 79.3504772 25.3273719 51.8775424 63.1264057 73.1546578 70.2462620 49 13.9441372 66.1149009 26.5292803 44.5792938 29.7906971 42.0153386 50 21.1408287 69.9631460 28.6059953 28.4226116 4.2254743 14.2477339 51 35.8672214 66.0253384 31.1422785 21.5919533 16.4655610 7.2204642 52 11.1397172 73.0284613 32.4109162 47.7364616 31.0590378 44.3071565 53 269.9764987 304.0806776 286.0096810 304.6796936 290.8867872 304.6413315 54 66.7290257 117.1840041 86.5360370 103.4892768 87.6227929 101.3763029 55 18.4231128 76.5175026 33.6297131 31.7945733 4.5054699 17.4251414 56 29.2083943 66.3911083 28.0525198 22.7088511 10.4361198 8.5153306 57 26.1572277 81.9815898 45.7797537 63.1187271 46.9308872 60.3897901 58 9.7749115 79.9141118 37.8828381 49.6317345 30.6780317 44.4155799 59 16.2567781 63.9230359 21.1869890 29.4389234 12.6306694 23.0132262 60 1.1720087 74.9884530 31.4353596 40.9699082 21.6411707 35.2854528 19 20 21 22 23 24 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 10.9029177 21 66.8231426 61.7604227 22 203.4425673 196.8097724 137.3331570 23 7.9831281 18.8732755 71.1596643 208.3375535 24 50.2859877 45.8692900 16.8047532 153.9822595 54.4984352 25 39.1849802 29.2968081 64.5687458 188.7879144 46.8755509 52.6611219 26 9.0000908 7.9517025 58.1033232 194.5361052 15.5102613 41.7152257 27 7.2958727 17.0062113 65.9216387 203.1481834 5.3082816 49.2747369 28 29.9463363 27.5119275 37.4754159 174.7485105 33.7085348 20.8290395 29 139.3422251 133.3228522 72.7747033 64.8295853 143.9182874 89.4554080 30 18.5127219 10.2409853 61.9273994 194.9944531 26.0178309 46.5370140 31 8.8335684 12.4002787 58.6629445 195.6551199 12.9439549 42.1089807 32 139.0074961 130.6138211 160.0370024 244.3873562 145.4207627 154.2878904 33 57.5894185 53.1243502 9.6981652 146.9453095 61.6796727 7.4309539 34 12.0119525 15.8252924 56.6319728 193.8485744 14.5362339 39.9690889 35 12.1803846 15.8025313 73.7930830 209.1818001 15.4516678 57.3359034 36 28.4695916 25.3668531 38.5166075 175.6357816 32.7118345 21.9799519 37 44.8324046 36.1869130 78.4456431 200.6878755 51.9255545 66.4203921 38 6.4872225 16.5173547 72.8293803 209.6630915 4.9848356 56.2530847 39 27.2473073 20.7676113 75.5461082 205.7919657 33.7286650 60.9285251 40 28.0057299 22.8304563 39.2149969 175.5020566 33.3909109 23.2549658 41 13.6986128 8.7495724 69.9504800 204.0976552 20.5514861 54.3294644 42 23.7178592 21.1454597 43.2527752 180.3091066 28.0440516 26.7001233 43 11.3625248 6.9337014 68.6065955 203.2444101 18.5086957 52.7576593 44 4.1605372 10.1441316 69.3080109 205.4824277 10.3083033 52.9397820 45 5.0745560 15.2686741 71.2659848 208.0382246 5.2689272 54.6179985 46 86.9451154 81.4312529 20.2495061 117.1190265 91.3976705 36.9626705 47 6.5170073 11.6947758 71.5464967 207.5176502 11.3712735 55.1268587 48 67.8740861 60.6552158 105.4187563 221.3623783 73.8529117 94.5071622 49 34.5079740 26.5114358 37.1003604 170.3735328 41.0753571 23.5274874 50 7.3811763 9.3344868 59.8698755 196.5116775 13.2607383 43.4689463 51 8.4863686 14.7385593 74.6688821 210.7903054 10.9922831 58.2491576 52 37.0429754 30.7594367 31.1674614 166.4957836 42.6774334 16.3346264 53 297.8250856 291.7906064 231.1006402 96.1043747 302.2157323 247.7585070 54 94.6035727 89.1220090 27.8413882 109.6894760 98.9867028 44.5333173 55 12.4086477 16.4375829 56.6262913 193.8792042 14.5829409 39.9975758 56 3.0367444 9.4259008 68.0060747 204.2469631 10.1341507 51.5926551 57 53.2366351 46.8859271 16.3053466 150.2625057 58.5573185 10.4147300 58 37.6784241 33.4549213 29.1923982 166.2162391 42.1298269 12.6352081 59 15.4464256 8.0880800 53.7135374 189.1512375 22.6212810 37.7945038 60 28.4334870 24.5446267 38.4956977 175.2964414 33.1623234 21.9196362 25 26 27 28 29 30 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 35.5335697 27 45.4544425 11.7398422 28 43.8642908 21.8297149 28.4627467 29 128.4436031 130.5066267 138.6902090 110.2368272 30 21.1549692 15.8847872 24.5286418 30.6145552 132.0840385 31 40.2240710 4.8134304 8.2145944 21.4917082 131.3582964 20.2103827 32 110.6114981 138.1504812 146.0717271 149.1770659 200.6735277 127.0047709 33 58.6777690 49.0041088 56.4261007 27.9717324 82.3206745 53.7524549 34 42.4184883 7.9877659 9.3136609 19.1726527 129.3925708 22.5699712 35 35.8798603 18.2752060 17.3813270 38.1337782 145.5118628 16.7730940 36 41.6815731 20.0524073 27.5253180 2.6746937 111.2440137 28.5735494 37 14.0281584 43.6343956 51.8565959 56.0483413 141.3178026 28.8350365 38 43.9126869 15.3261572 8.7003729 35.6572816 145.4669479 23.6278638 39 19.9816465 28.3458640 34.4147991 45.6699367 143.9616690 15.4394748 40 36.8913260 19.0773171 28.4818017 8.1441372 111.4647809 25.4239690 41 29.4216540 15.6908093 20.9005630 36.2167817 140.9855115 13.2449174 42 40.0744120 15.3895713 22.9021296 6.4941940 115.9570387 25.1259685 43 29.9160023 13.4852677 18.6219902 34.2983990 139.9429252 11.9228877 44 37.5883283 11.2414148 11.0581366 32.9523909 141.5940826 17.6714269 45 42.2482075 13.9269708 7.9834268 34.1234934 143.8530813 21.6171831 46 80.7664011 78.1656302 86.1655061 57.7148767 52.5261641 80.9393741 47 36.9341917 13.8042424 13.0568475 35.3084111 143.7030709 17.1488087 48 45.8033346 68.5187831 75.0694931 83.6481924 164.7974499 57.3226385 49 31.2306547 25.7013435 36.6547793 17.4794284 107.1608951 26.4011906 50 37.8947936 2.8591087 9.4857824 23.2384857 132.3964016 18.0549617 51 39.7447578 16.6199063 13.9415265 38.1988761 146.9335062 20.5799423 52 37.7297475 28.1154055 37.8033755 13.1388609 102.6782873 31.1800821 53 284.6660383 289.0080460 296.9568836 268.5078068 158.5163743 290.2319188 54 87.9370548 85.8387983 93.7443275 65.2863086 44.9836567 88.5490145 55 43.1994397 8.5617161 9.3035174 19.1735067 129.3979992 23.4068110 56 37.1928605 9.9444775 10.2676890 31.5868017 140.3226357 16.9315788 57 48.8209303 44.2933024 53.5247849 26.1796266 86.4730580 46.6941635 58 44.1860088 29.0802158 36.9581383 8.8805557 101.8406383 34.9365988 59 30.0019174 7.2704763 18.9899211 19.8605736 125.4813490 13.0252148 60 39.0719173 19.8949544 28.1051237 4.8373866 111.0289756 26.6368846 31 32 33 34 35 36 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 142.6216025 33 49.3240885 158.0071231 34 4.0010370 146.1166070 47.1438856 35 19.5843897 135.3368147 64.7651777 21.9734538 36 20.1554930 146.6003814 29.1806676 18.2528206 36.6818987 37 48.2401733 100.7479760 72.5329007 51.0690005 39.1096029 53.7645860 38 14.2212860 140.7277947 63.5086684 16.8479753 12.5809580 34.3395872 39 32.4186541 115.1925192 67.9279789 35.5917521 20.8896022 43.4690684 40 20.4737894 141.0643897 30.4172579 19.6056035 35.6455650 5.6345519 41 19.1843779 125.3386420 61.5194287 22.9671290 14.2394418 34.0397659 42 15.4220542 145.1571707 33.9289838 13.6727894 32.1756875 4.7569501 43 16.9076732 127.8335860 60.0194423 20.5794362 12.2019255 32.2201473 44 12.2842695 135.4307766 60.2398626 15.8168899 10.9392835 31.2666121 45 13.0109452 140.8669867 61.9304133 15.4588837 10.5496030 32.8444195 46 78.8689120 169.1085302 29.8327866 76.8707808 93.5533785 58.7352751 47 15.0107177 134.7956101 62.4877867 18.2263829 7.4717661 33.6694402 48 72.7753181 72.6002300 100.1900682 76.4339339 63.2025900 81.0672693 49 28.4821399 133.5853580 29.8763425 28.5131275 40.2889331 15.4996940 50 3.4487611 139.2900623 50.6994300 7.3882043 18.1731736 21.5889420 51 17.2601967 135.1128338 65.5754194 20.4759218 9.3117914 36.5889164 52 29.8317579 140.9169492 23.1314559 28.8401122 43.5251618 12.1386460 53 289.7603071 335.5722820 240.5362933 287.6801568 303.8667495 269.6170860 54 86.4985280 174.2128270 37.3450235 84.4539542 101.1850013 66.3540197 55 4.3517430 146.6210268 47.1288637 0.9445371 22.6450034 18.2999311 56 11.0153595 136.1069386 58.9093520 14.4922708 10.8634883 29.9320248 57 45.6955966 146.2249213 11.8000272 44.3558001 59.7239074 26.3236755 58 29.5828960 148.3948170 19.9581768 27.6547043 45.0130479 9.5314338 59 11.5238923 133.8845713 45.0408079 13.5130593 22.0894141 17.5783370 60 20.5789165 144.9215026 29.2888132 18.8863168 35.7273470 3.2794309 37 38 39 40 41 42 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 48.0426053 39 18.8331510 29.6214981 40 49.0841498 34.2109013 39.8263790 41 32.8083074 16.4093596 15.5907884 31.2779914 42 51.4676113 29.5891048 39.9499868 6.8469611 29.8202129 43 34.0901363 14.6627576 16.6818474 29.7593579 2.8635290 27.8972498 44 42.1850341 6.6598359 24.2518012 30.1789805 10.2674353 26.5671745 45 46.8188315 3.0014348 28.5265373 32.7412053 16.0030573 28.0965065 46 94.4432621 93.0096421 93.8717698 59.1742357 89.4064372 63.4592189 47 40.7863445 7.3343385 22.4062724 32.5301107 10.2466216 28.9903428 48 33.7187798 69.0474763 43.8405478 76.0781791 54.2582880 78.4666619 49 44.2844009 40.9092828 39.0465271 10.4399405 33.8305516 17.1003784 50 45.4599391 13.2865636 29.5670078 21.0207290 15.9439862 16.8794640 51 42.6820829 6.1542385 24.0459479 35.5744252 11.8262287 31.8706482 52 51.0642983 43.3769742 45.0269348 9.5197202 38.8429125 15.5913136 53 296.6522887 303.9099433 301.4902023 269.9659062 299.3340064 274.3503493 54 101.5429033 100.6515653 101.3998484 66.8581436 97.0884018 71.0855905 55 51.8400530 17.0341594 36.3319657 19.7941146 23.4933542 13.7739385 56 42.2580647 7.1325594 24.5080079 28.9290722 10.7843161 25.2253385 57 62.5688658 59.5006989 59.7203852 25.3075887 54.7089807 30.7020962 58 57.3557687 43.6933591 49.6661436 10.9563004 42.0230417 14.1762422 59 39.5114168 21.8354314 26.6693990 14.7568581 16.6455050 13.7091130 60 51.3974253 34.5286939 41.6663448 4.7314283 33.2394303 5.6771347 43 44 45 46 47 48 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 8.2856936 45 13.8668510 6.1566745 46 88.1916697 89.3253140 91.4201116 47 8.2115577 3.7104163 6.2429076 91.5041652 48 56.7316776 64.1100977 69.1293124 120.4043523 63.0317036 49 32.9140225 35.7278240 39.3983853 55.8669303 37.6950689 71.2394152 50 13.8124545 9.9759031 12.2464141 79.9950924 12.9581256 69.4177463 51 10.5169852 5.4711459 6.5369595 94.6798442 3.7530612 63.1878636 52 37.5288225 39.0003882 41.7568490 50.6780430 41.0854467 78.7500679 53 298.3615301 300.1081682 302.2969297 210.9003126 302.2108309 317.2444956 54 95.8783418 97.0057426 99.0585533 7.6936478 99.1810386 127.2508711 55 21.1527888 16.2141888 15.7833061 76.8723643 18.7221190 76.9881786 56 8.5252118 1.5564088 6.0717616 88.0352723 4.2696310 64.8749232 57 53.5784293 55.2345384 57.9364307 34.7376240 57.3799510 89.3710265 58 40.3604342 40.3070194 42.0774939 49.3582582 42.5334505 85.3657941 59 15.0092479 16.5221707 20.3527064 73.4605477 18.5737529 65.5392294 60 31.3993710 31.0785012 32.8295685 58.6026866 33.2222586 79.4301789 49 50 51 52 53 54 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 28.0524588 51 40.9004254 15.3036681 52 7.5971486 30.2719436 44.3088563 53 265.5113728 290.8664993 305.4490850 261.1883059 54 63.5127095 87.6567668 102.3586297 58.3669346 203.2651335 55 28.8480957 7.7553314 20.8449930 29.0677199 287.6565516 84.4469179 56 34.6336303 8.7943992 6.6764262 37.7519011 298.8356419 95.7122640 57 21.1658164 46.3185809 60.5740054 16.3034091 244.9669018 42.4047339 58 14.8268773 30.8546497 45.6247264 7.6660560 260.2432631 56.9869501 59 19.2339410 9.8822549 21.7307948 22.8238331 283.9814810 81.1525014 60 13.6654888 21.7825984 36.3476316 10.6391252 269.4684504 66.2440422 55 56 57 58 59 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 14.9364905 57 44.4741803 54.0041601 58 27.7334901 38.9636594 17.4172639 59 14.0952377 15.4012637 39.0268640 25.3965506 60 19.0942081 29.7054006 25.6756222 9.3517042 16.6367070 > > > > cleanEx(); ..nameEx <- "ellipses" > > ### * ellipses > > flush(stderr()); flush(stdout()) > > ### Name: ellipses > ### Title: Draw ellipses > ### Aliases: ellipses ellipses.rmult ellipses.acomp ellipses.rcomp > ### ellipses.aplus ellipses.rplus > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > > plot(acomp(sa.lognormals)) > tt<-acomp(sa.lognormals); ellipses(mean(tt),var(tt),r=2,col="red") > tt<-rcomp(sa.lognormals); ellipses(mean(tt),var(tt),r=2,col="blue") > > plot(aplus(sa.lognormals[,1:2])) > tt<-aplus(sa.lognormals[,1:2]); ellipses(mean(tt),var(tt),r=2,col="red") > tt<-rplus(sa.lognormals[,1:2]); ellipses(mean(tt),var(tt),r=2,col="blue") > > plot(rplus(sa.lognormals[,1:2])) > tt<-aplus(sa.lognormals[,1:2]); ellipses(mean(tt),var(tt),r=2,col="red") > tt<-rplus(sa.lognormals[,1:2]); ellipses(mean(tt),var(tt),r=2,col="blue") > tt<-rmult(sa.lognormals[,1:2]); ellipses(mean(tt),var(tt),r=2,col="green") > > > > > cleanEx(); ..nameEx <- "endpointCoordinates" > > ### * endpointCoordinates > > flush(stderr()); flush(stdout()) > > ### Name: endpointCoordinates > ### Title: Amounts in barytic-coordinates > ### Aliases: endpointCoordinates endpointCoordinates.inv > ### endpointCoordinates.default endpointCoordinates.acomp > ### endpointCoordinates.aplus endpointCoordinates.rplus > ### endpointCoordinatesInv endpointCoordinatesInv.rmult > ### endpointCoordinatesInv.acomp endpointCoordinatesInv.aplus > ### endpointCoordinatesInv.rcomp endpointCoordinatesInv.rplus > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > ep <- aplus(rbind(c(2,1,2),c(2,2,1),c(1,2,2))) > dat <- endpointCoordinatesInv(acomp(sa.lognormals),acomp(ep)) > plot(dat) > plot( acomp(endpointCoordinates(dat,acomp(ep)))) > > dat <- endpointCoordinatesInv(rcomp(sa.lognormals),rcomp(ep)) > plot(dat) > plot( rcomp(endpointCoordinates(dat,rcomp(ep)))) > > dat <- endpointCoordinatesInv(aplus(sa.lognormals),aplus(ep)) > plot(dat) > plot( endpointCoordinates(dat,aplus(ep))) > > dat <- endpointCoordinatesInv(rplus(sa.lognormals),rplus(ep)) > plot(dat) > plot(endpointCoordinates(rplus(dat),rplus(ep))) > > > > > cleanEx(); ..nameEx <- "geometricmean" > > ### * geometricmean > > flush(stderr()); flush(stdout()) > > ### Name: geometricmean > ### Title: The geometric mean > ### Aliases: geometricmean geometricmean.row geometricmean.col > ### Keywords: univar > > ### ** Examples > > geometricmean(1:10) [1] 4.528729 > > > > > cleanEx(); ..nameEx <- "groupparts" > > ### * groupparts > > flush(stderr()); flush(stdout()) > > ### Name: groupparts > ### Title: Group amounts of parts > ### Aliases: groupparts groupparts.acomp groupparts.rcomp groupparts.aplus > ### groupparts.rplus > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > groupparts(acomp(sa.lognormals5),A=c(1,2),B=c(3,4),C=5) A B C [1,] 0.9461005 0.047775050 6.124410e-03 [2,] 0.9759236 0.023988940 8.748620e-05 [3,] 0.7098493 0.287295857 2.854837e-03 [4,] 0.4911195 0.458448121 5.043240e-02 [5,] 0.6650760 0.315007582 1.991637e-02 [6,] 0.7979965 0.198554017 3.449516e-03 [7,] 0.2638660 0.641393821 9.474014e-02 [8,] 0.9131371 0.082012750 4.850188e-03 [9,] 0.5774547 0.362879457 5.966586e-02 [10,] 0.6933675 0.205048097 1.015844e-01 [11,] 0.7338189 0.252442240 1.373882e-02 [12,] 0.9988602 0.001112986 2.682950e-05 [13,] 0.9706307 0.027218541 2.150751e-03 [14,] 0.8847850 0.094554144 2.066082e-02 [15,] 0.6035009 0.380556581 1.594254e-02 [16,] 0.8217218 0.163643632 1.463461e-02 [17,] 0.3873727 0.570673220 4.195405e-02 [18,] 0.4828122 0.423240840 9.394697e-02 [19,] 0.9444049 0.049272352 6.322731e-03 [20,] 0.8805485 0.079409523 4.004201e-02 [21,] 0.3447736 0.577759938 7.746649e-02 [22,] 0.6064969 0.370802563 2.270052e-02 [23,] 0.7631062 0.216237904 2.065585e-02 [24,] 0.9477233 0.042550881 9.725849e-03 [25,] 0.9959176 0.004029037 5.331368e-05 [26,] 0.9247415 0.073633964 1.624563e-03 [27,] 0.2129205 0.554583902 2.324956e-01 [28,] 0.1954212 0.579586821 2.249920e-01 [29,] 0.4875011 0.471663937 4.083500e-02 [30,] 0.9469745 0.049613173 3.412324e-03 [31,] 0.3531533 0.548110946 9.873576e-02 [32,] 0.9069817 0.071312486 2.170577e-02 [33,] 0.8290611 0.155477715 1.546122e-02 [34,] 0.9637292 0.032711221 3.559538e-03 [35,] 0.4374266 0.291312686 2.712607e-01 [36,] 0.2160422 0.590252103 1.937057e-01 [37,] 0.9910054 0.008631553 3.630164e-04 [38,] 0.6121552 0.377381675 1.046310e-02 [39,] 0.4413518 0.275853438 2.827948e-01 [40,] 0.3517672 0.644137425 4.095386e-03 [41,] 0.4148337 0.506838873 7.832744e-02 [42,] 0.9113990 0.085336435 3.264608e-03 [43,] 0.9850240 0.014797763 1.782807e-04 [44,] 0.6038030 0.361499167 3.469785e-02 [45,] 0.7947808 0.190491853 1.472735e-02 [46,] 0.8245512 0.158098710 1.735009e-02 [47,] 0.6228634 0.297209624 7.992697e-02 [48,] 0.6584099 0.308287744 3.330235e-02 [49,] 0.7850687 0.207587565 7.343738e-03 [50,] 0.6902642 0.219238716 9.049708e-02 [51,] 0.8458306 0.151311882 2.857518e-03 [52,] 0.7513083 0.229679452 1.901229e-02 [53,] 0.7230675 0.222936180 5.399630e-02 [54,] 0.7277685 0.258269614 1.396186e-02 [55,] 0.3258454 0.652417822 2.173681e-02 [56,] 0.5733861 0.356617768 6.999610e-02 [57,] 0.4323916 0.401254390 1.663541e-01 [58,] 0.4279511 0.528043692 4.400518e-02 [59,] 0.9039781 0.087572816 8.449088e-03 [60,] 0.7748226 0.201605531 2.357187e-02 attr(,"class") [1] "acomp" > groupparts(aplus(sa.lognormals5),B=c(3,4),C=5) B C Cu Zn [1,] 0.40365574 0.0517456966 8.0428875 7.9447925 [2,] 0.13114460 0.0004782764 5.0038487 5.6886102 [3,] 0.18617978 0.0018500542 0.3351019 0.6314831 [4,] 0.62534556 0.0687922422 0.5289819 0.8483855 [5,] 2.11925750 0.1339901836 3.5852145 5.5840964 [6,] 0.80304933 0.0139515269 1.5636165 6.6619105 [7,] 10.38677905 1.5342289231 3.4833151 5.2418726 [8,] 0.69174781 0.0409095764 4.2414755 13.9858158 [9,] 1.96995473 0.3239065799 1.0045703 9.7823499 [10,] 1.97150985 0.9767205910 4.3858923 10.1334048 [11,] 3.34025685 0.1817889041 9.2194750 10.2260360 [12,] 0.05562339 0.0013408510 19.7688675 126.0559578 [13,] 0.83824634 0.0662364282 22.0252058 40.5696942 [14,] 0.98727705 0.2157277753 5.6051911 15.2265694 [15,] 1.66848388 0.0698972908 1.2864930 5.4419426 [16,] 1.19001888 0.1064230800 2.8359015 12.5912231 [17,] 1.92030902 0.1411749178 0.8899305 1.9092782 [18,] 2.45168465 0.5442016018 2.4601441 3.1794353 [19,] 0.39435971 0.0506050592 7.3793324 7.7424410 [20,] 0.92881377 0.4683514841 6.3437767 16.7213278 [21,] 2.02643684 0.2717061764 0.7012141 2.0853964 [22,] 1.88134790 0.1151760699 1.4808674 6.3943113 [23,] 1.15984174 0.1107924175 3.3874451 4.9457433 [24,] 0.63751243 0.1457161221 12.3607821 16.3108782 [25,] 0.10881458 0.0014398743 24.3812613 29.6730694 [26,] 0.92924944 0.0205017335 4.9670310 27.4190278 [27,] 9.59341394 4.0218011385 2.0029717 6.7728607 [28,] 5.31960493 2.0650372263 1.7731193 1.8143757 [29,] 3.81797076 0.3305464286 1.4426845 10.7939309 [30,] 1.70154086 0.1170295689 11.9156365 88.5217705 [31,] 13.84939947 2.4948068491 6.8529647 11.6191129 [32,] 1.33977209 0.4077937817 9.8936559 29.3474918 [33,] 1.57410369 0.1565341023 6.3936467 11.0193197 [34,] 0.38025432 0.0413781470 10.7383205 11.6876853 [35,] 5.35584733 4.9871874791 6.3460747 10.1916095 [36,] 6.65885466 2.1852660304 1.6734404 3.5496952 [37,] 0.13430810 0.0056485834 9.0223298 26.3548127 [38,] 1.76409893 0.0489105288 1.7595898 4.6536739 [39,] 2.79500915 2.8653406315 2.7640328 7.2349610 [40,] 4.50438705 0.0286386159 1.9959244 3.0316628 [41,] 2.92651186 0.4522663529 1.2614974 4.5480207 [42,] 0.78376661 0.0299835688 6.9569688 10.0716707 [43,] 0.20595033 0.0024812516 4.2902161 43.8073819 [44,] 2.99788035 0.2877462055 4.0106287 6.2516122 [45,] 0.70649984 0.0546210707 1.4945243 5.8138399 [46,] 1.54154120 0.1691720625 3.2775534 19.7214617 [47,] 3.60436319 0.9693017926 6.3650857 8.9642247 [48,] 2.19033696 0.2366080873 1.8868680 11.5973971 [49,] 0.55087541 0.0194880883 1.0606563 4.0920859 [50,] 3.10075690 1.2799264536 6.8003114 14.0153142 [51,] 0.56280801 0.0106286056 2.4449945 4.0482131 [52,] 2.51730507 0.2083762590 4.1475780 16.3481709 [53,] 1.54484011 0.3741683133 1.5150460 16.5705854 [54,] 1.54998254 0.0837908775 1.5011029 12.7081714 [55,] 2.59694586 0.0865232504 1.1427600 1.4721167 [56,] 1.22136742 0.2397271320 1.4430373 2.6724127 [57,] 5.58820976 2.3167879368 3.0420067 11.9206532 [58,] 1.66775703 0.1389846273 0.7160270 2.5514367 [59,] 1.42780413 0.1377555693 13.8389529 15.6968036 [60,] 2.10869108 0.2465497816 3.1480246 20.8635147 attr(,"class") [1] "aplus" > groupparts(rcomp(sa.lognormals5),A=c("Cu","Pb"),B=c(2,5)) A B Cd [1,] 0.5747932 0.422182276 3.024494e-03 [2,] 0.8785542 0.121435680 1.015393e-05 [3,] 0.9718098 0.028118835 7.140262e-05 [4,] 0.9345453 0.063375428 2.079226e-03 [5,] 0.9253908 0.073759122 8.500361e-04 [6,] 0.8492698 0.150328512 4.016947e-04 [7,] 0.8278423 0.124487564 4.767018e-02 [8,] 0.5081864 0.490190060 1.623520e-03 [9,] 0.5461404 0.439268837 1.459072e-02 [10,] 0.5402803 0.442824181 1.689556e-02 [11,] 0.9009034 0.097884468 1.212101e-03 [12,] 0.1517539 0.848238640 7.479854e-06 [13,] 0.4596310 0.539627663 7.413375e-04 [14,] 0.3858457 0.605147580 9.006760e-03 [15,] 0.8864469 0.112211909 1.341223e-03 [16,] 0.5998738 0.397412151 2.714092e-03 [17,] 0.9162321 0.077758530 6.009412e-03 [18,] 0.7709425 0.201470280 2.758726e-02 [19,] 0.5922366 0.405737049 2.026352e-03 [20,] 0.3505051 0.639093910 1.040103e-02 [21,] 0.7177990 0.224812659 5.738830e-02 [22,] 0.8017852 0.194062689 4.152097e-03 [23,] 0.7679792 0.227593188 4.427656e-03 [24,] 0.4540093 0.537386761 8.603893e-03 [25,] 0.5621093 0.437877986 1.274191e-05 [26,] 0.6774446 0.322362871 1.925070e-04 [27,] 0.7469896 0.205810640 4.719974e-02 [28,] 0.7350837 0.175973585 8.894268e-02 [29,] 0.8157653 0.179448537 4.786193e-03 [30,] 0.2919486 0.707115566 9.358159e-04 [31,] 0.8535694 0.126863392 1.956725e-02 [32,] 0.3319352 0.660204162 7.860660e-03 [33,] 0.7662854 0.232028738 1.685826e-03 [34,] 0.5413984 0.456820727 1.780845e-03 [35,] 0.4050952 0.466177901 1.287269e-01 [36,] 0.7437160 0.187497175 6.878681e-02 [37,] 0.3187675 0.681091923 1.405961e-04 [38,] 0.9446640 0.054877402 4.585921e-04 [39,] 0.4450232 0.494510579 6.046626e-02 [40,] 0.9925083 0.007372506 1.192198e-04 [41,] 0.7037628 0.259963416 3.627383e-02 [42,] 0.7128805 0.286163802 9.557318e-04 [43,] 0.3987505 0.601225991 2.350386e-05 [44,] 0.8010365 0.188116723 1.084681e-02 [45,] 0.7421344 0.256457174 1.408415e-03 [46,] 0.6297614 0.368802781 1.435808e-03 [47,] 0.7265357 0.257867153 1.559715e-02 [48,] 0.6054198 0.385234458 9.345718e-03 [49,] 0.7636723 0.234918631 1.409050e-03 [50,] 0.4779424 0.485167143 3.689045e-02 [51,] 0.8762945 0.123340745 3.647182e-04 [52,] 0.6116901 0.381780593 6.529318e-03 [53,] 0.3128313 0.672302907 1.486575e-02 [54,] 0.5591376 0.435384437 5.477996e-03 [55,] 0.9675958 0.029797907 2.606334e-03 [56,] 0.7023299 0.274303179 2.336696e-02 [57,] 0.4484285 0.458953502 9.261796e-02 [58,] 0.8813016 0.112940414 5.757975e-03 [59,] 0.6150866 0.380738731 4.174645e-03 [60,] 0.3728819 0.613758687 1.335939e-02 attr(,"class") [1] "rcomp" > groupparts(rplus(sa.lognormals5),1:5) [,1] [1,] 18.94096 [2,] 46.84857 [3,] 22.52345 [4,] 14.47213 [5,] 77.52379 [6,] 44.40849 [7,] 54.43196 [8,] 28.61487 [9,] 23.00700 [10,] 25.08925 [11,] 106.32764 [12,] 148.61065 [13,] 75.30365 [14,] 25.51823 [15,] 49.11992 [16,] 31.95083 [17,] 26.36949 [18,] 18.48231 [19,] 19.20713 [20,] 26.89695 [21,] 10.48474 [22,] 33.54322 [23,] 22.21743 [24,] 30.62337 [25,] 67.76890 [26,] 85.12001 [27,] 52.44948 [28,] 22.04543 [29,] 61.99258 [30,] 125.35264 [31,] 111.25290 [32,] 45.06982 [33,] 48.16582 [34,] 25.67542 [35,] 32.56010 [36,] 30.58692 [37,] 38.70324 [38,] 85.69255 [39,] 20.42484 [40,] 415.09649 [41,] 19.23458 [42,] 35.30025 [43,] 72.86755 [44,] 34.76224 [45,] 22.88281 [46,] 53.93298 [47,] 38.52188 [48,] 30.71897 [49,] 17.50212 [50,] 31.52571 [51,] 32.90755 [52,] 43.36665 [53,] 25.20405 [54,] 29.38084 [55,] 52.30703 [56,] 10.61650 [57,] 31.02153 [58,] 23.82160 [59,] 41.58904 [60,] 34.39473 attr(,"class") [1] "rplus" > > > > cleanEx(); ..nameEx <- "gsiadd" > > ### * gsiadd > > flush(stderr()); flush(stdout()) > > ### Name: gsi.add > ### Title: Internal functions: Parallel operations of single and multiple > ### datasets > ### Aliases: gsi.add gsi.sub gsi.mul gsi.div > > > ### ** Examples > > tmp1 <- matrix(1:12,ncol=3) > tmp2 <- 1:3 > gsi.add(tmp1,tmp2) [,1] [,2] [,3] [1,] 2 7 12 [2,] 3 8 13 [3,] 4 9 14 [4,] 5 10 15 > gsi.sub(tmp1,tmp2) [,1] [,2] [,3] [1,] 0 3 6 [2,] 1 4 7 [3,] 2 5 8 [4,] 3 6 9 > gsi.mul(tmp1,tmp2) [,1] [,2] [,3] [1,] 1 10 27 [2,] 2 12 30 [3,] 3 14 33 [4,] 4 16 36 > gsi.div(tmp1,tmp2) [,1] [,2] [,3] [1,] 1 2.5 3.000000 [2,] 2 3.0 3.333333 [3,] 3 3.5 3.666667 [4,] 4 4.0 4.000000 > > gsi.add(tmp2,tmp2) [1] 2 4 6 > gsi.sub(tmp2,tmp2) [1] 0 0 0 > gsi.mul(tmp2,tmp2) [1] 1 4 9 > gsi.div(tmp2,tmp2) [1] 1 1 1 > > gsi.add(tmp1,tmp1) [,1] [,2] [,3] [1,] 2 10 18 [2,] 4 12 20 [3,] 6 14 22 [4,] 8 16 24 > gsi.sub(tmp1,tmp1) [,1] [,2] [,3] [1,] 0 0 0 [2,] 0 0 0 [3,] 0 0 0 [4,] 0 0 0 > gsi.mul(tmp1,tmp1) [,1] [,2] [,3] [1,] 1 25 81 [2,] 4 36 100 [3,] 9 49 121 [4,] 16 64 144 > gsi.div(tmp1,tmp1) [,1] [,2] [,3] [1,] 1 1 1 [2,] 1 1 1 [3,] 1 1 1 [4,] 1 1 1 > > > > > cleanEx(); ..nameEx <- "gsiaddclass" > > ### * gsiaddclass > > flush(stderr()); flush(stdout()) > > ### Name: gsi.addclass > ### Title: Internal function: give an object a derived subclass > ### Aliases: gsi.addclass > > > ### ** Examples > > gsi.addclass(1:10,"goofy") [1] 1 2 3 4 5 6 7 8 9 10 attr(,"class") [1] "goofy" > > > > cleanEx(); ..nameEx <- "gsicall" > > ### * gsicall > > flush(stderr()); flush(stdout()) > > ### Name: gsicall > ### Title: Internal functions of the compositions package > ### Aliases: gsi.call > > > ### ** Examples > > mypars <- list(x=3) > do.call("gsi.call",c(list(function(x){x}),mypars)) [1] 3 > > > > cleanEx(); ..nameEx <- "gsiclosespread" > > ### * gsiclosespread > > flush(stderr()); flush(stdout()) > > ### Name: gsiinternal1 > ### Title: Internal functions of the compositions package > ### Aliases: gsi.closespread > > > ### ** Examples > > > > > cleanEx(); ..nameEx <- "gsidiagExtract" > > ### * gsidiagExtract > > flush(stderr()); flush(stdout()) > > ### Name: gsi.diagExtract > ### Title: Internal functions: Get the diagonal of a matrix > ### Aliases: gsi.diagExtract > > > ### ** Examples > > data(SimulatedAmounts) > gsi.diagExtract(var(acomp(sa.lognormals,c(1,2)))) Cu Zn 0.1011749 0.1011749 > gsi.diagExtract(var(ilr(acomp(sa.lognormals,c(1,2))))) [1] 0.2023497 > gsi.diagExtract(var(ilt(aplus(sa.lognormals,c(1))))) [1] 1.087208 > > > > cleanEx(); ..nameEx <- "gsidiagGenerate" > > ### * gsidiagGenerate > > flush(stderr()); flush(stdout()) > > ### Name: gsi.diagGenerate > ### Title: Internal functions: Generate a diagonal matrix > ### Aliases: gsi.diagGenerate > > > ### ** Examples > > diag(1:3) [,1] [,2] [,3] [1,] 1 0 0 [2,] 0 2 0 [3,] 0 0 3 > gsi.diagGenerate(1:3) [,1] [,2] [,3] [1,] 1 0 0 [2,] 0 2 0 [3,] 0 0 3 > gsi.diagGenerate(3) [,1] [1,] 3 > diag(3) [,1] [,2] [,3] [1,] 1 0 0 [2,] 0 1 0 [3,] 0 0 1 > > > > cleanEx(); ..nameEx <- "gsidrop" > > ### * gsidrop > > flush(stderr()); flush(stdout()) > > ### Name: gsi.drop > ### Title: Internal functions: A conditional drop > ### Aliases: gsi.drop > > > ### ** Examples > > > > > > cleanEx(); ..nameEx <- "gsieps" > > ### * gsieps > > flush(stderr()); flush(stdout()) > > ### Name: gsi.eps > ### Title: Internal variable: Negligible differences > ### Aliases: gsi.eps > > > ### ** Examples > > > > > cleanEx(); ..nameEx <- "gsiexpandrcomp" > > ### * gsiexpandrcomp > > flush(stderr()); flush(stdout()) > > ### Name: gsi.expandrcomp > ### Title: Internal function: Scaling rcomp > ### Aliases: gsi.expandrcomp > ### Keywords: multivariate > > ### ** Examples > > gsi.expandrcomp(rcomp(1:3),0.5) [,1] [,2] [,3] [1,] 0.25 0.3333333 0.4166667 attr(,"class") [1] "rcomp" > > > > cleanEx(); ..nameEx <- "gsigetD" > > ### * gsigetD > > flush(stderr()); flush(stdout()) > > ### Name: gsi.getD > ### Title: Interal function: Get number of samples and number of parts in a > ### compositional object > ### Aliases: gsi.getD gsi.getN > ### Keywords: multivariate > > ### ** Examples > > gsi.getD(1:5) [1] 5 > gsi.getN(1:5) [1] 1 > NCOL(1:5) [1] 1 > NROW(1:5) [1] 5 > data(SimulatedAmounts) > gsi.getD(sa.lognormals5) [1] 5 > gsi.getN(sa.lognormals5) [1] 60 > > > > cleanEx(); ..nameEx <- "gsiinternal" > > ### * gsiinternal > > flush(stderr()); flush(stdout()) > > ### Name: gsiinternal > ### Title: Internal functions of the compositions package > ### Aliases: gsi > > > ### ** Examples > > > > > cleanEx(); ..nameEx <- "gsiinvperm" > > ### * gsiinvperm > > flush(stderr()); flush(stdout()) > > ### Name: gsi2.invperm > ### Title: Internal function: Invert a permutation > ### Aliases: gsi2.invperm > > > ### ** Examples > > gsi2.invperm(c(2,3),10) [1] 3 1 2 4 5 6 7 8 9 10 > > > > cleanEx(); ..nameEx <- "gsiisSingleRow" > > ### * gsiisSingleRow > > flush(stderr()); flush(stdout()) > > ### Name: gsi.isSingleRow > ### Title: Internal function: Can something be considered as a single > ### multivariate data item? > ### Aliases: gsi.isSingleRow > > > ### ** Examples > > gsi.isSingleRow(1:10) [1] TRUE > > > > cleanEx(); ..nameEx <- "gsimap01" > > ### * gsimap01 > > flush(stderr()); flush(stdout()) > > ### Name: gsi.mapin01 > ### Title: Internal functions: Storing integers as reals > ### Aliases: gsi.mapin01 gsi.mapfrom01 gsi.mapmin gsi.mapmax > > > ### ** Examples > > gsi.mapin01(5) [1] 0.0 0.2 1.0 > > > > cleanEx(); ..nameEx <- "gsimargin" > > ### * gsimargin > > flush(stderr()); flush(stdout()) > > ### Name: gsi.margin > ### Title: Internal function: Compute a desired compositional margin > ### Aliases: gsi.margin gsi.margin.acomp gsi.margin.rcomp gsi.margin.aplus > ### gsi.margin.rplus > > > ### ** Examples > > data(SimulatedAmounts) > plot(gsi.margin(acomp(sa.lognormals5),c("Cd","Cu"))) > > > > cleanEx(); ..nameEx <- "gsipairrelativeMatrix" > > ### * gsipairrelativeMatrix > > flush(stderr()); flush(stdout()) > > ### Name: gsiinternal2 > ### Title: Internal functions of the compositions package > ### Aliases: gsi.pairrelativeMatrix > > > ### ** Examples > > gsi.pairrelativeMatrix(c("a","b","c")) a b c a/b 1 -1 0 a/c 1 0 -1 b/c 0 1 -1 > > > > cleanEx(); ..nameEx <- "gsipairs" > > ### * gsipairs > > flush(stderr()); flush(stdout()) > > ### Name: gsipairs > ### Title: Internal functions of the compositions package > ### Aliases: gsi.pairs gsi.add2pairs gsi.plots > > > ### ** Examples > > > > > cleanEx(); ..nameEx <- "gsiplain" > > ### * gsiplain > > flush(stderr()); flush(stdout()) > > ### Name: gsi.plain > ### Title: Internal function: Convert to plain vector or matrix > ### Aliases: gsi.plain > > > ### ** Examples > > gsi.plain(acomp(c(12,3,4))) [1] 0.6315789 0.1578947 0.2105263 > > > > cleanEx(); ..nameEx <- "gsiplotmargin" > > ### * gsiplotmargin > > flush(stderr()); flush(stdout()) > > ### Name: gsiinternal > ### Title: Internal functions of the compositions package > ### Aliases: gsi.plotmargin > > > ### ** Examples > > > > > cleanEx(); ..nameEx <- "gsisimshape" > > ### * gsisimshape > > flush(stderr()); flush(stdout()) > > ### Name: gsi.simshape > ### Title: Internal function: Reshape an object to the shape type of > ### another > ### Aliases: gsi.simshape > > > ### ** Examples > > gsi.simshape(matrix(1:4,nrow=1),1:3) [1] 1 2 3 4 > > > > cleanEx(); ..nameEx <- "gsispreadToIsoSpace" > > ### * gsispreadToIsoSpace > > flush(stderr()); flush(stdout()) > > ### Name: gsiinternal3 > ### Title: Internal functions of the compositions package > ### Aliases: gsi.spreadToIsoSpace > > > ### ** Examples > > > > > cleanEx(); ..nameEx <- "gsitextpanel" > > ### * gsitextpanel > > flush(stderr()); flush(stdout()) > > ### Name: gsi.textpanel > ### Title: Internal function: A panel displaying a label only > ### Aliases: gsi.textpanel > > > ### ** Examples > > data(iris) > pairs(iris,text.panel=gsi.textpanel) > > > > cleanEx(); ..nameEx <- "idt" > > ### * idt > > flush(stderr()); flush(stdout()) > > ### Name: idt > ### Title: Isometric default transform > ### Aliases: idt idt.default idt.acomp idt.rcomp idt.aplus idt.rplus > ### idt.rmult idt.factor > ### Keywords: multivariate > > ### ** Examples > > ## Not run: > ##D # the idt is defined by > ##D idt <- function(x) UseMethod("idt",x) > ##D idt.default <- function(x) x > ##D idt.acomp <- function(x) ilr(x) > ##D idt.rcomp <- function(x) ipt(x) > ##D idt.aplus <- ilt > ##D idt.rplus <- iit > ## End(Not run) > idt(acomp(1:5)) [,1] [,2] [,3] [,4] [1,] -1.070516 -0.5816524 -0.3259894 -0.1577863 attr(,"class") [1] "rmult" > idt(rcomp(1:5)) [,1] [,2] [,3] [,4] [1,] -0.1490712 -0.1154701 -0.08164966 -0.04714045 attr(,"class") [1] "rmult" > > > > > cleanEx(); ..nameEx <- "iit" > > ### * iit > > flush(stderr()); flush(stdout()) > > ### Name: iit > ### Title: Isometric identity transform > ### Aliases: iit iit.inv > ### Keywords: multivariate > > ### ** Examples > > (tmp <- iit(c(1,2,3))) [1] 1 2 3 attr(,"class") [1] "rmult" > iit.inv(tmp) [1] 1 2 3 attr(,"class") [1] "rplus" > iit.inv(tmp) - c(1,2,3) # 0 [1] 0 0 0 attr(,"class") [1] "rmult" > data(Hydrochem) > cdata <- Hydrochem[,6:19] > pairs(iit(cdata)) > > > > cleanEx(); ..nameEx <- "ilr" > > ### * ilr > > flush(stderr()); flush(stdout()) > > ### Name: ilr > ### Title: Isometric log ratio transform > ### Aliases: ilr ilr.inv > ### Keywords: multivariate > > ### ** Examples > > (tmp <- ilr(c(1,2,3))) [,1] [,2] [1,] -0.7314827 -0.2867071 attr(,"class") [1] "rmult" > ilr.inv(tmp) [,1] [,2] [,3] [1,] 0.1666667 0.3333333 0.5 attr(,"class") [1] "acomp" > ilr.inv(tmp) - clo(c(1,2,3)) # 0 [,1] [,2] [,3] [1,] 0.3333333 0.3333333 0.3333333 attr(,"class") [1] "acomp" > data(Hydrochem) > cdata <- Hydrochem[,6:19] > pairs(ilr(cdata)) > ilrBase(D=3) [,1] [,2] [1,] 0.8164966 7.850462e-17 [2,] -0.4082483 7.071068e-01 [3,] -0.4082483 -7.071068e-01 > > > > cleanEx(); ..nameEx <- "ilrBase" > > ### * ilrBase > > flush(stderr()); flush(stdout()) > > ### Name: ilrBase > ### Title: The canonical basis in the clr plane used for ilr and ipt > ### transforms. > ### Aliases: ilrBase gsi.ilrBase ilrBaseList > ### Keywords: multivariate > > ### ** Examples > > ilr(c(1,2,3)) [,1] [,2] [1,] -0.7314827 -0.2867071 attr(,"class") [1] "rmult" > ilrBase(D=2) [1] 0.7071068 -0.7071068 > ilrBase(c(1,2,3)) [,1] [,2] [1,] 0.8164966 7.850462e-17 [2,] -0.4082483 7.071068e-01 [3,] -0.4082483 -7.071068e-01 > ilrBase(z= ilr(c(1,2,3)) ) [,1] [,2] [1,] 0.8164966 7.850462e-17 [2,] -0.4082483 7.071068e-01 [3,] -0.4082483 -7.071068e-01 > round(ilrBase(D=7),digits= 3) [,1] [,2] [,3] [,4] [,5] [,6] [1,] 0.926 0.000 0.000 0.000 0.000 0.000 [2,] -0.154 0.913 0.000 0.000 0.000 0.000 [3,] -0.154 -0.183 0.894 0.000 0.000 0.000 [4,] -0.154 -0.183 -0.224 0.866 0.000 0.000 [5,] -0.154 -0.183 -0.224 -0.289 0.816 0.000 [6,] -0.154 -0.183 -0.224 -0.289 -0.408 0.707 [7,] -0.154 -0.183 -0.224 -0.289 -0.408 -0.707 > > > > cleanEx(); ..nameEx <- "ilt" > > ### * ilt > > flush(stderr()); flush(stdout()) > > ### Name: ilt > ### Title: Isometric log transform > ### Aliases: ilt ilt.inv > ### Keywords: multivariate > > ### ** Examples > > (tmp <- ilt(c(1,2,3))) [1] 0.0000000 0.6931472 1.0986123 attr(,"class") [1] "rmult" > ilt.inv(tmp) [1] 1 2 3 attr(,"class") [1] "aplus" > ilt.inv(tmp) - c(1,2,3) # 0 [1] 1 1 1 attr(,"class") [1] "aplus" > data(Hydrochem) > cdata <- Hydrochem[,6:19] > pairs(ilt(cdata)) > > > > cleanEx(); ..nameEx <- "ipt" > > ### * ipt > > flush(stderr()); flush(stdout()) > > ### Name: ipt > ### Title: Isometric planar transform > ### Aliases: ipt ipt.inv ucipt.inv > ### Keywords: multivariate > > ### ** Examples > > (tmp <- ipt(c(1,2,3))) [,1] [,2] [1,] -0.2041241 -0.1178511 attr(,"class") [1] "rmult" > ipt.inv(tmp) [,1] [,2] [,3] [1,] 0.1666667 0.3333333 0.5 attr(,"class") [1] "rcomp" > ipt.inv(tmp) - clo(c(1,2,3)) # 0 [,1] [,2] [,3] [1,] 0 0 1.110223e-16 attr(,"class") [1] "rmult" > data(Hydrochem) > cdata <- Hydrochem[,6:19] > pairs(ipt(cdata)) > > > > cleanEx(); ..nameEx <- "isAcomp" > > ### * isAcomp > > flush(stderr()); flush(stdout()) > > ### Name: is.acomp > ### Title: Check for compositional data type > ### Aliases: is.acomp is.aplus is.rcomp is.rplus is.rmult > > > ### ** Examples > > is.acomp(1:3) [1] FALSE > is.acomp(acomp(1:3)) [1] TRUE > is.rcomp(acomp(1:3)) [1] FALSE > is.acomp(acomp(1:3)+acomp(1:3)) [1] TRUE > > > > cleanEx(); ..nameEx <- "lines" > > ### * lines > > flush(stderr()); flush(stdout()) > > ### Name: lines > ### Title: Draws connected lines from point to point. > ### Aliases: lines.rmult lines.acomp lines.rcomp lines.aplus lines.rplus > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > > plot(acomp(sa.lognormals)) > lines(acomp(sa.lognormals),col="red") > lines(rcomp(sa.lognormals),col="blue") > > plot(aplus(sa.lognormals[,1:2])) > lines(aplus(sa.lognormals[,1:2]),col="red") > lines(rplus(sa.lognormals)[,1:2],col="blue") > > plot(rplus(sa.lognormals[,1:2])) > tt<-aplus(sa.lognormals[,1:2]); ellipses(mean(tt),var(tt),r=2,col="red") > tt<-rplus(sa.lognormals[,1:2]); ellipses(mean(tt),var(tt),r=2,col="blue") > tt<-rmult(sa.lognormals[,1:2]); ellipses(mean(tt),var(tt),r=2,col="green") > > > > > cleanEx(); ..nameEx <- "matmult" > > ### * matmult > > flush(stderr()); flush(stdout()) > > ### Name: matmult > ### Title: inner product for matrices and vectors > ### Aliases: \%*\% \%*\%.default > ### Keywords: multivariate > > ### ** Examples > > M <- matrix(c( + 0.2,0.1,0.0, + 0.1,0.2,0.0, + 0.0,0.0,0.2),byrow=TRUE,nrow=3) > x <- c(1,1,2) > M %*% x [,1] [1,] 0.3 [2,] 0.3 [3,] 0.4 > x %*% M [,1] [,2] [,3] [1,] 0.3 0.3 0.4 > x %*% x [,1] [1,] 6 > M %*% M [,1] [,2] [,3] [1,] 0.05 0.04 0.00 [2,] 0.04 0.05 0.00 [3,] 0.00 0.00 0.04 > t(x) %*% M [,1] [,2] [,3] [1,] 0.3 0.3 0.4 > > > > > cleanEx(); ..nameEx <- "matmultacomp" > > ### * matmultacomp > > flush(stderr()); flush(stdout()) > > ### Name: acompscalarproduct > ### Title: inner product for datasets with a vector space structure > ### Aliases: \%*\%.acomp \%*\%.aplus > ### Keywords: multivariate > > ### ** Examples > > x <- acomp(matrix( sqrt(1:12), ncol= 3 )) > x%*%x [1] 0.6469650 0.3381818 0.2175284 0.1543170 > A <- matrix( 1:9,nrow=3) > x %*% A %*% x [1] 3.091984e-16 -9.151700e-16 1.442494e-16 -3.937424e-16 > x %*% A [,1] [,2] [,3] [1,] 0.3333333 0.3333333 0.3333333 [2,] 0.3333333 0.3333333 0.3333333 [3,] 0.3333333 0.3333333 0.3333333 [4,] 0.3333333 0.3333333 0.3333333 attr(,"class") [1] "acomp" > A %*% x [,1] [,2] [,3] [1,] 0.3333333 0.3333333 0.3333333 [2,] 0.3333333 0.3333333 0.3333333 [3,] 0.3333333 0.3333333 0.3333333 [4,] 0.3333333 0.3333333 0.3333333 attr(,"class") [1] "acomp" > A <- matrix( 1:4,nrow=2) > x %*% A %*% x [1] 1.5839151 0.9352057 0.6442363 0.4781194 > x %*% A [,1] [,2] [,3] [1,] 0.02393516 0.01102243 0.9650424 [2,] 0.05536969 0.03149999 0.9131303 [3,] 0.08543044 0.05428763 0.8602819 [4,] 0.11200725 0.07642630 0.8115665 attr(,"class") [1] "acomp" > A %*% x [,1] [,2] [,3] [1,] 0.03120125 0.03210480 0.9366939 [2,] 0.06262929 0.06571027 0.8716604 [3,] 0.09060035 0.09544972 0.8139499 [4,] 0.11465830 0.12077259 0.7645691 attr(,"class") [1] "acomp" > x <- aplus(matrix( sqrt(1:12), ncol= 3 )) > x%*%x [1] 1.854522 2.248188 2.685854 3.105163 > A <- matrix( 1:9,nrow=3) > x %*% A %*% x [1] 26.47744 36.35527 44.09613 50.80013 > x %*% A [,1] [,2] [,3] [1,] 135.0000 40752.34 12301875 [2,] 268.3282 352726.52 463671056 [3,] 442.3313 1552979.29 5452348849 [4,] 665.1075 5004822.60 37660451716 attr(,"class") [1] "aplus" > A %*% x [,1] [,2] [,3] [1,] 54675.0 366771.1 2460375 [2,] 160996.9 1763632.6 19319627 [3,] 374654.6 5694257.4 86545220 [4,] 766203.9 15014467.8 294222279 attr(,"class") [1] "aplus" > > > > cleanEx(); ..nameEx <- "meanAcomp" > > ### * meanAcomp > > flush(stderr()); flush(stdout()) > > ### Name: mean.acomp > ### Title: Mean amounts and mean compositions > ### Aliases: mean.acomp mean.rcomp mean.aplus mean.rplus mean.rmult > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > mean.col(sa.lognormals) Cu Zn Pb 5.392698 14.908465 38.319017 > mean(acomp(sa.lognormals)) Cu Zn Pb 0.08918175 0.23949922 0.67131903 attr(,"class") [1] "acomp" > mean(rcomp(sa.lognormals)) Cu Zn Pb 0.1112224 0.2762183 0.6125594 attr(,"class") [1] "rcomp" > mean(aplus(sa.lognormals)) Cu Zn Pb 3.018042 8.105008 22.718430 attr(,"class") [1] "aplus" > mean(rplus(sa.lognormals)) Cu Zn Pb 5.392698 14.908465 38.319017 attr(,"class") [1] "rplus" > mean(rmult(sa.lognormals)) Cu Zn Pb 5.392698 14.908465 38.319017 attr(,"class") [1] "rmult" > > > > cleanEx(); ..nameEx <- "meanrow" > > ### * meanrow > > flush(stderr()); flush(stdout()) > > ### Name: meanrow > ### Title: The arithmetic mean of rows or columns > ### Aliases: mean.row mean.col > ### Keywords: univar > > ### ** Examples > > data(SimulatedAmounts) > mean.col(sa.tnormals) clay sand gravel 0.3442712 1.0790201 2.0935988 > mean.row(sa.tnormals) [1] 1.0894352 2.4032841 1.0227738 1.2345591 1.2929267 1.0421369 0.8081017 [8] 1.0791940 1.2425931 0.9205721 1.4313944 0.8578415 1.0254484 1.2961104 [15] 1.5306312 0.4563095 1.5424136 0.2559007 0.7626727 1.7732329 1.7621865 [22] 1.4864593 1.2088910 1.5900434 0.8127302 1.2118821 1.9412685 1.2550854 [29] 0.3627439 0.9202394 1.8175552 1.0620058 0.8181015 0.7156372 1.0320648 [36] 1.8476012 1.2047013 0.5160420 1.2715755 1.2263230 0.6827358 1.3595707 [43] 1.1511512 1.1279994 2.1310195 1.3367617 1.4326856 0.7324932 1.1272941 [50] 1.9253702 0.5959185 0.9535205 0.5232318 1.3948077 0.7285579 1.0565911 [57] 1.6888305 1.1480951 1.5077177 0.6027821 > > > > > cleanEx(); ..nameEx <- "mvar" > > ### * mvar > > flush(stderr()); flush(stdout()) > > ### Name: mvar > ### Title: Metric summary statistics of real, amount or compositional data > ### Aliases: mvar mvar.default mcov mcov.default mcor mcor.default msd > ### msd.default > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > mvar(acomp(sa.lognormals)) [1] 2.084473 > mvar(rcomp(sa.lognormals)) [1] 0.1340421 > mvar(aplus(sa.lognormals)) [1] 3.236377 > mvar(rplus(sa.lognormals)) [1] 3186.038 > > msd(acomp(sa.lognormals)) [1] 1.0209 > msd(rcomp(sa.lognormals)) [1] 0.2588842 > msd(aplus(sa.lognormals)) [1] 1.038649 > msd(rplus(sa.lognormals)) [1] 32.58854 > > mcov(acomp(sa.lognormals5[,1:3]),acomp(sa.lognormals5[,4:5])) [1] 0.02477656 > mcor(acomp(sa.lognormals5[,1:3]),acomp(sa.lognormals5[,4:5])) [1] 0.09830424 > mcov(rcomp(sa.lognormals5[,1:3]),rcomp(sa.lognormals5[,4:5])) [1] 0.001887371 > mcor(rcomp(sa.lognormals5[,1:3]),rcomp(sa.lognormals5[,4:5])) [1] 0.05397564 > > mcov(aplus(sa.lognormals5[,1:3]),aplus(sa.lognormals5[,4:5])) [1] 0.5439218 > mcor(aplus(sa.lognormals5[,1:3]),aplus(sa.lognormals5[,4:5])) [1] 0.2974957 > mcov(rplus(sa.lognormals5[,1:3]),rplus(sa.lognormals5[,4:5])) [1] 5.441885 > mcor(rplus(sa.lognormals5[,1:3]),rplus(sa.lognormals5[,4:5])) [1] 0.193851 > > mcov(acomp(sa.lognormals5[,1:3]),aplus(sa.lognormals5[,4:5])) [1] 0.2136284 > mcor(acomp(sa.lognormals5[,1:3]),aplus(sa.lognormals5[,4:5])) [1] 0.1539326 > > > > cleanEx(); ..nameEx <- "names" > > ### * names > > flush(stderr()); flush(stdout()) > > ### Name: names > ### Title: The names of the parts > ### Aliases: names.acomp names.aplus names.rcomp names.rplus names.rmult > ### names<-.acomp names<-.aplus names<-.rcomp names<-.rplus names<-.rmult > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > tmp <- acomp(sa.lognormals) > names(tmp) [1] "Cu" "Zn" "Pb" > names(tmp) <- c("x","y","z") > tmp x y z [1,] 0.097971136 0.391326782 0.51070208 [2,] 0.015828238 0.051778890 0.93239287 [3,] 0.023646054 0.229295970 0.74705798 [4,] 0.157117191 0.333557432 0.50932538 [5,] 0.063751759 0.192800530 0.74344771 [6,] 0.155329691 0.470558827 0.37411148 [7,] 0.102725807 0.080758608 0.81651559 [8,] 0.020979121 0.052297696 0.92672318 [9,] 0.194852953 0.368202307 0.43694474 [10,] 0.057866882 0.044773472 0.89735965 [11,] 0.117728338 0.460405248 0.42186641 [12,] 0.044286404 0.062094203 0.89361939 [13,] 0.059874363 0.123728325 0.81639731 [14,] 0.278235681 0.589224043 0.13254028 [15,] 0.256873029 0.394621002 0.34850597 [16,] 0.563893885 0.291169413 0.14493670 [17,] 0.065882158 0.183547882 0.75056996 [18,] 0.138067296 0.439563517 0.42236919 [19,] 0.131217406 0.355963659 0.51281894 [20,] 0.115952571 0.423617474 0.46042996 [21,] 0.010611522 0.047668860 0.94171962 [22,] 0.017620801 0.075134689 0.90724451 [23,] 0.126201118 0.188961139 0.68483774 [24,] 0.041558370 0.043014903 0.91542673 [25,] 0.242399802 0.436055266 0.32154493 [26,] 0.073307860 0.296916882 0.62977526 [27,] 0.058531896 0.103233805 0.83823430 [28,] 0.031617947 0.047187132 0.92119492 [29,] 0.013489158 0.043895682 0.94261516 [30,] 0.252613941 0.374119482 0.37326658 [31,] 0.032833821 0.206414094 0.76075209 [32,] 0.071301394 0.879292677 0.04940593 [33,] 0.018347073 0.025863181 0.95578975 [34,] 0.057911915 0.081562486 0.86052560 [35,] 0.420392036 0.372600928 0.20700704 [36,] 0.024311095 0.098788780 0.87690012 [37,] 0.269222425 0.530159861 0.20061771 [38,] 0.125661816 0.461020597 0.41331759 [39,] 0.280690822 0.541213043 0.17809613 [40,] 0.029798911 0.195906023 0.77429507 [41,] 0.123841669 0.577364922 0.29879341 [42,] 0.033079477 0.119337415 0.84758311 [43,] 0.154061768 0.520083716 0.32585452 [44,] 0.120002000 0.479131152 0.40086685 [45,] 0.234077420 0.349788033 0.41613455 [46,] 0.013171842 0.046793430 0.94003473 [47,] 0.228353522 0.469698072 0.30194841 [48,] 0.142484163 0.837766482 0.01974936 [49,] 0.058878119 0.279115907 0.66200597 [50,] 0.023649744 0.306181692 0.67016856 [51,] 0.199613632 0.577278707 0.22310766 [52,] 0.060091725 0.191264809 0.74864347 [53,] 0.000728883 0.002319699 0.99695142 [54,] 0.011454976 0.034453992 0.95409103 [55,] 0.027055777 0.067710243 0.90523398 [56,] 0.137726613 0.431542471 0.43073092 [57,] 0.031467245 0.159422572 0.80911018 [58,] 0.046600419 0.087161098 0.86623848 [59,] 0.087881617 0.327464869 0.58465351 [60,] 0.078617049 0.120922730 0.80046022 attr(,"class") [1] "acomp" > > > > cleanEx(); ..nameEx <- "norm" > > ### * norm > > flush(stderr()); flush(stdout()) > > ### Name: norm > ### Title: Vector space norm > ### Aliases: norm norm.default norm.acomp norm.aplus norm.rcomp norm.rplus > ### norm.rmult > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > tmp <- acomp(sa.lognormals) > mvar(tmp) [1] 2.084473 > sum(norm( tmp - mean(tmp) )^2)/(nrow(tmp)-1) [1] 2.084473 > > > > > cleanEx(); ..nameEx <- "normalize" > > ### * normalize > > flush(stderr()); flush(stdout()) > > ### Name: normalize > ### Title: Normalize vectors to norm 1 > ### Aliases: normalize normalize.default > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > normalize(c(1,2,3)) [1] 0.2672612 0.5345225 0.8017837 > normalize(acomp(c(1,2,3))) [1] 0.1339635 0.3236980 0.5423385 attr(,"class") [1] "acomp" > norm(normalize(acomp(sa.groups))) [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [39] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 > > > > cleanEx(); ..nameEx <- "oneOrDataset" > > ### * oneOrDataset > > flush(stderr()); flush(stdout()) > > ### Name: oneOrDataset > ### Title: Treating single compositions as one-row datasets > ### Aliases: oneOrDataset > ### Keywords: multivariate > > ### ** Examples > > oneOrDataset(c(1,2,3)) [,1] [,2] [,3] [1,] 1 2 3 > oneOrDataset(c(1,2,3),matrix(1:12,nrow=4)) [,1] [,2] [,3] [1,] 1 2 3 [2,] 1 2 3 [3,] 1 2 3 [4,] 1 2 3 > oneOrDataset(data.frame(matrix(1:12,nrow=4))) X1 X2 X3 1 1 5 9 2 2 6 10 3 3 7 11 4 4 8 12 > > > > cleanEx(); ..nameEx <- "perturbe" > > ### * perturbe > > flush(stderr()); flush(stdout()) > > ### Name: perturbe > ### Title: Perturbation of compositions > ### Aliases: perturbe +.acomp -.acomp > ### Keywords: multivariate > > ### ** Examples > > tmp <- -acomp(1:3) > tmp + acomp(1:3) [1] 0.3333333 0.3333333 0.3333333 attr(,"class") [1] "acomp" > > > > > cleanEx(); ..nameEx <- "plot" > > ### * plot > > flush(stderr()); flush(stdout()) > > ### Name: plot.acomp > ### Title: Displaying compositions in ternary diagrams > ### Aliases: plot.acomp plot.rcomp > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > plot(acomp(sa.lognormals)) > plot(rcomp(sa.lognormals)) > plot(acomp(sa.lognormals5),pca=TRUE) > plot(rcomp(sa.lognormals5),pca=TRUE) > > > > cleanEx(); ..nameEx <- "plotpos" > > ### * plotpos > > flush(stderr()); flush(stdout()) > > ### Name: plot.aplus > ### Title: Displaying amounts in scatterplots > ### Aliases: plot.aplus plot.rplus plot.rmult > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > plot(aplus(sa.lognormals)) > plot(rplus(sa.lognormals)) > plot(aplus(sa.lognormals5)) > plot(rplus(sa.lognormals5)) > > > > cleanEx(); ..nameEx <- "powerofmatrix" > > ### * powerofmatrix > > flush(stderr()); flush(stdout()) > > ### Name: powerofpsdmatrix > ### Title: power transform of a matrix > ### Aliases: powerofpsdmatrix > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > d <- ilr(sa.lognormals) > var( d %*% powerofpsdmatrix(var(d),-1/2)) # Unit matrix [,1] [,2] [1,] 1.000000e+00 4.385602e-16 [2,] 4.385602e-16 1.000000e+00 > > > > cleanEx(); ..nameEx <- "princompacomp" > > ### * princompacomp > > flush(stderr()); flush(stdout()) > > ### Name: princomp.acomp > ### Title: Principal component analysis for Aitchison compositions > ### Aliases: princomp.acomp print.princomp.acomp plot.princomp.acomp > ### plot.princomp.acomp predict.princomp.acomp > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > pc <- princomp(acomp(sa.lognormals5)) > pc Call: princomp.acomp(x = acomp(sa.lognormals5)) Standard deviations: Comp.1 Comp.2 Comp.3 Comp.4 2.4242076 1.2527537 0.4673169 0.2667648 5 variables and 60 observations. Mean (compositional): Cu Zn Pb Cd Co 0.117710525 0.306222405 0.567371204 0.004239147 0.004456718 attr(,"class") [1] "acomp" +Loadings (compositional): Cu Zn Pb Cd Co Comp.1 0.6068998 0.5985836 0.6809203 1.5692975 1.5442987 Comp.2 1.3189309 1.3440242 0.3936868 0.9642938 0.9790643 Comp.3 1.8475861 0.4506335 0.8975793 0.8601707 0.9440304 Comp.4 0.8563030 0.9394475 0.9110133 0.4496577 1.8435786 attr(,"class") [1] "acomp" -Loadings (compositional): Cu Zn Pb Cd Co Comp.1 1.3568839 1.3757353 1.2093816 0.5247523 0.5332469 Comp.2 0.6213931 0.6097915 2.0817934 0.8499221 0.8370999 Comp.3 0.4439141 1.8200368 0.9137572 0.9534962 0.8687957 Comp.4 0.9578058 0.8730365 0.9002854 1.8239920 0.4448804 attr(,"class") [1] "acomp" > summary(pc) Importance of components: Comp.1 Comp.2 Comp.3 Comp.4 Standard deviation 2.424208 1.2527537 0.46731693 0.266764829 Proportion of Variance 0.759694 0.2028759 0.02823073 0.009199331 Cumulative Proportion 0.759694 0.9625699 0.99080067 1.000000000 > plot(pc) #plot(pc,type="screeplot") > plot(pc,type="v") > plot(pc,type="biplot") > plot(pc,choice=c(1,3),type="biplot") > plot(pc,type="loadings") > plot(pc,type="loadings",scale.sdev=-1) # Downward > plot(pc,type="relative",scale.sdev=NA) # The directions > plot(pc,type="relative",scale.sdev=1) # one sigma Upward > plot(pc,type="relative",scale.sdev=-1) # one sigma Downward > biplot(pc) > screeplot(pc) > loadings(pc) Loadings: Comp.1 Comp.2 Comp.3 Comp.4 Cu -0.397 0.360 0.714 Zn -0.411 0.379 -0.697 Pb -0.282 -0.849 Cd 0.553 -0.700 Co 0.537 0.711 Comp.1 Comp.2 Comp.3 Comp.4 SS loadings 1.0 1.0 1.0 1.0 Proportion Var 0.2 0.2 0.2 0.2 Cumulative Var 0.2 0.4 0.6 0.8 > relativeLoadings(pc,mult=FALSE) Comp.1 Comp.2 Comp.3 Comp.4 Cu/Zn 4.10 Cu/Pb 0.89 3.35 2.06 Zn/Pb 0.88 3.41 0.50 Cu/Cd 0.39 1.37 2.15 1.90 Zn/Cd 0.38 1.39 0.52 2.09 Pb/Cd 0.43 0.41 2.03 Cu/Co 0.39 1.35 1.96 0.46 Zn/Co 0.39 1.37 0.48 0.51 Pb/Co 0.44 0.40 0.49 Cd/Co 0.24 attr(,"cutoff") [1] 0.1 attr(,"scale") [1] 1 1 1 1 attr(,"log") [1] FALSE > relativeLoadings(pc) Comp.1 Comp.2 Comp.3 Comp.4 Cu/Zn 4.10 Cu/Pb 0.89 3.35 2.06 Zn/Pb 0.88 3.41 0.50 Cu/Cd 0.39 1.37 2.15 1.90 Zn/Cd 0.38 1.39 0.52 2.09 Pb/Cd 0.43 0.41 2.03 Cu/Co 0.39 1.35 1.96 0.46 Zn/Co 0.39 1.37 0.48 0.51 Pb/Co 0.44 0.40 0.49 Cd/Co 0.24 attr(,"cutoff") [1] 0.1 attr(,"scale") [1] 1 1 1 1 attr(,"log") [1] FALSE > relativeLoadings(pc,scale.sdev=1) Comp.1 Comp.2 Comp.3 Comp.4 Cu/Zn 1.934 Cu/Pb 0.757 4.548 1.401 Zn/Pb 0.732 4.656 0.725 Cu/Cd 0.100 1.480 1.429 1.187 Zn/Cd 0.097 1.516 0.739 1.217 Pb/Cd 0.132 0.326 1.207 Cu/Co 0.104 1.453 1.369 0.815 Zn/Co 0.101 1.487 0.708 0.835 Pb/Co 0.137 0.319 0.829 Cd/Co 0.686 attr(,"cutoff") [1] 0.1 attr(,"scale") Comp.1 Comp.2 Comp.3 Comp.4 2.4242076 1.2527537 0.4673169 0.2667648 attr(,"log") [1] FALSE > relativeLoadings(pc,scale.sdev=2) Comp.1 Comp.2 Comp.3 Comp.4 Cu/Zn 3.7387 Cu/Pb 0.5724 20.6809 1.9635 Zn/Pb 0.5353 21.6809 0.5252 Cu/Cd 0.0100 2.1917 2.0432 1.4101 Zn/Cd 0.0093 2.2977 0.5465 1.4816 Pb/Cd 0.0175 0.1060 1.4575 Cu/Co 0.0108 2.1098 1.8731 0.6642 Zn/Co 0.0101 2.2118 0.5010 0.6979 Pb/Co 0.0189 0.1020 0.6865 Cd/Co 0.4710 attr(,"cutoff") [1] 0.1 attr(,"scale") Comp.1 Comp.2 Comp.3 Comp.4 4.8484151 2.5055074 0.9346339 0.5335297 attr(,"log") [1] FALSE > > pc$Loadings Cu Zn Pb Cd Co Comp.1 0.6068998 0.5985836 0.6809203 1.5692975 1.5442987 Comp.2 1.3189309 1.3440242 0.3936868 0.9642938 0.9790643 Comp.3 1.8475861 0.4506335 0.8975793 0.8601707 0.9440304 Comp.4 0.8563030 0.9394475 0.9110133 0.4496577 1.8435786 attr(,"class") [1] "acomp" > pc$DownLoadings Cu Zn Pb Cd Co Comp.1 1.3568839 1.3757353 1.2093816 0.5247523 0.5332469 Comp.2 0.6213931 0.6097915 2.0817934 0.8499221 0.8370999 Comp.3 0.4439141 1.8200368 0.9137572 0.9534962 0.8687957 Comp.4 0.9578058 0.8730365 0.9002854 1.8239920 0.4448804 attr(,"class") [1] "acomp" > barplot(pc$Loadings) > pc$sdev^2 Comp.1 Comp.2 Comp.3 Comp.4 5.87678231 1.56939188 0.21838511 0.07116347 > cov(predict(pc,sa.lognormals5)) Comp.1 Comp.2 Comp.3 Comp.4 Comp.1 5.976389e+00 5.048189e-16 -1.429709e-16 -3.196114e-16 Comp.2 5.048189e-16 1.595992e+00 3.028745e-16 3.381036e-17 Comp.3 -1.429709e-16 3.028745e-16 2.220866e-01 -1.060598e-16 Comp.4 -3.196114e-16 3.381036e-17 -1.060598e-16 7.236963e-02 > > > > cleanEx(); ..nameEx <- "princompaplus" > > ### * princompaplus > > flush(stderr()); flush(stdout()) > > ### Name: princomp.aplus > ### Title: Principal component analysis for amounts in log geometry > ### Aliases: princomp.aplus print.princomp.aplus plot.princomp.aplus > ### plot.princomp.aplus predict.princomp.aplus > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > pc <- princomp(aplus(sa.lognormals5)) > pc Call: princomp.aplus(x = aplus(sa.lognormals5)) Standard deviations: Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 2.8717397 1.3554503 0.9120868 0.4661378 0.2641545 5 variables and 60 observations. Mean (compositional): Cu Zn Pb Cd Co 3.2669025 8.4988046 15.7466498 0.1176520 0.1236904 attr(,"class") [1] "aplus" +Loadings (compositional): Cu Zn Pb Cd Co Comp.1 0.9508691 0.9445919 0.9876193 2.0323883 2.0153007 Comp.2 0.5399493 0.5220631 1.5521695 0.9714872 0.9416861 Comp.3 0.7554872 0.7148647 0.4076028 0.9935220 0.9447465 Comp.4 2.0749626 0.5071282 1.0232480 0.9475488 1.0535653 Comp.5 0.9241393 1.0247031 0.9761420 0.4954403 2.0271974 attr(,"class") [1] "aplus" -Loadings (compositional): Cu Zn Pb Cd Co Comp.1 1.0516695 1.0586583 1.0125359 0.492032 0.4962039 Comp.2 1.8520256 1.9154773 0.6442595 1.029350 1.0619250 Comp.3 1.3236492 1.3988661 2.4533688 1.006520 1.0584850 Comp.4 0.4819364 1.9718880 0.9772802 1.055355 0.9491581 Comp.5 1.0820880 0.9758924 1.0244411 2.018407 0.4932919 attr(,"class") [1] "aplus" > summary(pc) Importance of components: Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Standard deviation 2.8717397 1.3554503 0.91208676 0.46613779 0.264154533 Proportion of Variance 0.7361257 0.1639944 0.07425644 0.01939503 0.006228421 Cumulative Proportion 0.7361257 0.9001201 0.97437655 0.99377158 1.000000000 > plot(pc) #plot(pc,type="screeplot") > plot(pc,type="v") > plot(pc,type="biplot") > plot(pc,choice=c(1,3),type="biplot") > plot(pc,type="loadings") > plot(pc,type="loadings",scale.sdev=-1) # Downward > plot(pc,type="relative",scale.sdev=NA) # The directions > plot(pc,type="relative",scale.sdev=1) # one sigma Upward > plot(pc,type="relative",scale.sdev=-1) # one sigma Downward > biplot(pc) > screeplot(pc) > loadings(pc) Loadings: Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Cu -0.616 -0.280 0.730 Zn -0.650 -0.336 -0.679 Pb 0.440 -0.897 Cd 0.709 -0.702 Co 0.701 0.707 Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 SS loadings 1.0 1.0 1.0 1.0 1.0 Proportion Var 0.2 0.2 0.2 0.2 0.2 Cumulative Var 0.2 0.4 0.6 0.8 1.0 > relativeLoadings(pc,mult=FALSE) Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Cu/Zn 4.09 0.90 Cu/Pb 0.35 1.85 2.03 Zn/Pb 0.34 1.75 0.50 Cu/Cd 0.47 0.56 0.76 2.19 1.87 Zn/Cd 0.46 0.54 0.72 0.54 2.07 Pb/Cd 0.49 1.60 0.41 1.97 Cu/Co 0.47 0.57 0.80 1.97 0.46 Zn/Co 0.47 0.55 0.76 0.48 0.51 Pb/Co 0.49 1.65 0.43 0.48 Cd/Co 0.90 0.24 attr(,"cutoff") [1] 0.1 attr(,"scale") [1] 1 1 1 1 1 attr(,"log") [1] FALSE > relativeLoadings(pc) Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Cu/Zn 4.09 0.90 Cu/Pb 0.35 1.85 2.03 Zn/Pb 0.34 1.75 0.50 Cu/Cd 0.47 0.56 0.76 2.19 1.87 Zn/Cd 0.46 0.54 0.72 0.54 2.07 Pb/Cd 0.49 1.60 0.41 1.97 Cu/Co 0.47 0.57 0.80 1.97 0.46 Zn/Co 0.47 0.55 0.76 0.48 0.51 Pb/Co 0.49 1.65 0.43 0.48 Cd/Co 0.90 0.24 attr(,"cutoff") [1] 0.1 attr(,"scale") [1] 1 1 1 1 1 attr(,"log") [1] FALSE > relativeLoadings(pc,scale.sdev=1) Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Cu/Zn 1.93 Cu/Pb 0.90 0.24 1.76 1.39 Zn/Pb 0.88 0.23 1.67 0.72 Cu/Cd 0.11 0.45 0.78 1.44 1.18 Zn/Cd 0.11 0.43 0.74 0.75 1.21 Pb/Cd 0.13 1.89 0.44 1.20 Cu/Co 0.12 0.47 0.82 1.37 0.81 Zn/Co 0.11 0.45 0.78 0.71 0.84 Pb/Co 0.13 1.97 0.46 0.82 Cd/Co 0.69 attr(,"cutoff") [1] 0.1 attr(,"scale") Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 2.8717397 1.3554503 0.9120868 0.4661378 0.2641545 attr(,"log") [1] FALSE > relativeLoadings(pc,scale.sdev=2) Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Cu/Zn 1.106 3.719 Cu/Pb 0.804 0.057 3.082 1.933 Zn/Pb 0.774 0.052 2.787 0.520 Cu/Cd 0.013 0.203 0.607 2.077 1.390 Zn/Cd 0.012 0.186 0.549 0.558 1.468 Pb/Cd 0.016 3.562 0.197 1.431 Cu/Co 0.013 0.221 0.665 1.881 0.660 Zn/Co 0.013 0.202 0.601 0.506 0.697 Pb/Co 0.017 3.876 0.216 0.680 Cd/Co 0.475 attr(,"cutoff") [1] 0.1 attr(,"scale") Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 5.7434794 2.7109006 1.8241735 0.9322756 0.5283091 attr(,"log") [1] FALSE > > pc$Loadings Cu Zn Pb Cd Co Comp.1 0.9508691 0.9445919 0.9876193 2.0323883 2.0153007 Comp.2 0.5399493 0.5220631 1.5521695 0.9714872 0.9416861 Comp.3 0.7554872 0.7148647 0.4076028 0.9935220 0.9447465 Comp.4 2.0749626 0.5071282 1.0232480 0.9475488 1.0535653 Comp.5 0.9241393 1.0247031 0.9761420 0.4954403 2.0271974 attr(,"class") [1] "aplus" > pc$DownLoadings Cu Zn Pb Cd Co Comp.1 1.0516695 1.0586583 1.0125359 0.492032 0.4962039 Comp.2 1.8520256 1.9154773 0.6442595 1.029350 1.0619250 Comp.3 1.3236492 1.3988661 2.4533688 1.006520 1.0584850 Comp.4 0.4819364 1.9718880 0.9772802 1.055355 0.9491581 Comp.5 1.0820880 0.9758924 1.0244411 2.018407 0.4932919 attr(,"class") [1] "aplus" > barplot(pc$Loadings) > pc$sdev^2 Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 8.24688902 1.83724548 0.83190226 0.21728444 0.06977762 > cov(predict(pc,sa.lognormals5)) Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.1 8.386667e+00 5.720280e-16 3.209053e-16 -6.138692e-16 -1.971603e-15 Comp.2 5.720280e-16 1.868385e+00 1.253665e-16 2.967794e-16 1.900788e-16 Comp.3 3.209053e-16 1.253665e-16 8.460023e-01 2.196520e-16 -9.017914e-17 Comp.4 -6.138692e-16 2.967794e-16 2.196520e-16 2.209672e-01 1.033568e-16 Comp.5 -1.971603e-15 1.900788e-16 -9.017914e-17 1.033568e-16 7.096029e-02 > > > > cleanEx(); ..nameEx <- "princomprcomp" > > ### * princomprcomp > > flush(stderr()); flush(stdout()) > > ### Name: princomp.rcomp > ### Title: Principal component analysis for real compositions > ### Aliases: princomp.rcomp print.princomp.rcomp plot.princomp.rcomp > ### predict.princomp.rcomp > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > pc <- princomp(rcomp(sa.lognormals5)) > pc Call: princomp.rcomp(x = rcomp(sa.lognormals5)) Standard deviations: Comp.1 Comp.2 Comp.3 Comp.4 0.344585815 0.097415595 0.050739773 0.008331254 5 variables and 60 observations. > summary(pc) Importance of components: Comp.1 Comp.2 Comp.3 Comp.4 Standard deviation 0.3445858 0.09741559 0.05073977 0.0083312538 Proportion of Variance 0.9072863 0.07251144 0.01967191 0.0005303594 Cumulative Proportion 0.9072863 0.97979773 0.99946964 1.0000000000 > plot(pc) #plot(pc,type="screeplot") > plot(pc,type="v") > plot(pc,type="biplot") > plot(pc,choice=c(1,3),type="biplot") > plot(pc,type="loadings") > plot(pc,type="loadings",scale.sdev=-1) # Downward > plot(pc,type="relative",scale.sdev=NA) # The directions > plot(pc,type="relative",scale.sdev=1) # one sigma Upward > plot(pc,type="relative",scale.sdev=-1) # one sigma Downward > biplot(pc) > screeplot(pc) > loadings(pc) Loadings: Comp.1 Comp.2 Comp.3 Comp.4 Cu -0.227 0.737 0.453 Zn -0.563 -0.628 0.297 Pb 0.795 -0.234 0.335 Cd -0.489 -0.747 Co -0.596 0.663 Comp.1 Comp.2 Comp.3 Comp.4 SS loadings 1.0 1.0 1.0 1.0 Proportion Var 0.2 0.2 0.2 0.2 Cumulative Var 0.2 0.4 0.6 0.8 > relativeLoadings(pc,mult=FALSE) Comp.1 Comp.2 Comp.3 Comp.4 Cu/Zn 0.3365 1.3647 0.1565 Cu/Pb -1.0213 0.9711 0.1175 Zn/Pb -1.3578 -0.3935 Cu/Cd -0.2258 0.6823 0.9415 0.7727 Zn/Cd -0.5622 -0.6824 0.7851 0.7758 Pb/Cd 0.7956 -0.2889 0.8240 0.7776 Cu/Co -0.2222 0.6658 1.0494 -0.6373 Zn/Co -0.5587 -0.6988 0.8929 -0.6342 Pb/Co 0.7991 -0.3053 0.9318 -0.6324 Cd/Co 0.1078 -1.4100 attr(,"cutoff") [1] 0.1 attr(,"scale") [1] 1 1 1 1 > relativeLoadings(pc) Comp.1 Comp.2 Comp.3 Comp.4 Cu/Zn 0.3365 1.3647 0.1565 Cu/Pb -1.0213 0.9711 0.1175 Zn/Pb -1.3578 -0.3935 Cu/Cd -0.2258 0.6823 0.9415 0.7727 Zn/Cd -0.5622 -0.6824 0.7851 0.7758 Pb/Cd 0.7956 -0.2889 0.8240 0.7776 Cu/Co -0.2222 0.6658 1.0494 -0.6373 Zn/Co -0.5587 -0.6988 0.8929 -0.6342 Pb/Co 0.7991 -0.3053 0.9318 -0.6324 Cd/Co 0.1078 -1.4100 attr(,"cutoff") [1] 0.1 attr(,"scale") [1] 1 1 1 1 > relativeLoadings(pc,scale.sdev=1) Comp.1 Comp.2 Comp.3 Comp.4 Cu/Zn 1.2e-01 1.3e-01 Cu/Pb -3.5e-01 Zn/Pb -4.7e-01 Cu/Cd Zn/Cd -1.9e-01 Pb/Cd 2.7e-01 Cu/Co Zn/Co -1.9e-01 Pb/Co 2.8e-01 Cd/Co attr(,"cutoff") [1] 0.1 attr(,"scale") Comp.1 Comp.2 Comp.3 Comp.4 0.344585815 0.097415595 0.050739773 0.008331254 > relativeLoadings(pc,scale.sdev=2) Comp.1 Comp.2 Comp.3 Comp.4 Cu/Zn 2.3e-01 2.7e-01 Cu/Pb -7.0e-01 1.9e-01 Zn/Pb -9.4e-01 Cu/Cd -1.6e-01 1.3e-01 Zn/Cd -3.9e-01 -1.3e-01 Pb/Cd 5.5e-01 Cu/Co -1.5e-01 1.3e-01 1.1e-01 Zn/Co -3.9e-01 -1.4e-01 Pb/Co 5.5e-01 Cd/Co attr(,"cutoff") [1] 0.1 attr(,"scale") Comp.1 Comp.2 Comp.3 Comp.4 0.68917163 0.19483119 0.10147955 0.01666251 > > pc$sdev^2 Comp.1 Comp.2 Comp.3 Comp.4 1.187394e-01 9.489798e-03 2.574525e-03 6.940979e-05 > cov(predict(pc,sa.lognormals5)) Comp.1 Comp.2 Comp.3 Comp.4 Comp.1 1.207519e-01 1.402847e-17 -8.224473e-18 1.967580e-19 Comp.2 1.402847e-17 9.650642e-03 1.415728e-17 1.235024e-18 Comp.3 -8.224473e-18 1.415728e-17 2.618161e-03 -4.402912e-19 Comp.4 1.967580e-19 1.235024e-18 -4.402912e-19 7.058623e-05 > > > > cleanEx(); ..nameEx <- "princomprmult" > > ### * princomprmult > > flush(stderr()); flush(stdout()) > > ### Name: princomp.rmult > ### Title: Principle component analysis for Real data > ### Aliases: princomp.rmult > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > pc <- princomp(rmult(sa.lognormals5)) > pc Call: princomp(x = unclass(x)) Standard deviations: Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 53.6291886 19.8699154 3.8694564 1.2717521 0.2305226 5 variables and 60 observations. > summary(pc) Importance of components: Comp.1 Comp.2 Comp.3 Comp.4 Standard deviation 53.6291886 19.8699154 3.869456357 1.2717520946 Proportion of Variance 0.8748438 0.1200937 0.004554367 0.0004919636 Cumulative Proportion 0.8748438 0.9949375 0.999491872 0.9999838358 Comp.5 Standard deviation 2.305226e-01 Proportion of Variance 1.616424e-05 Cumulative Proportion 1.000000e+00 > plot(pc) > screeplot(pc) > screeplot(pc,type="l") > biplot(pc) > biplot(pc,choice=c(1,3)) > loadings(pc) Loadings: Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Cu -0.164 0.986 Zn -0.985 -0.165 Pb -0.999 Cd -0.642 -0.766 Co -0.766 0.642 Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 SS loadings 1.0 1.0 1.0 1.0 1.0 Proportion Var 0.2 0.2 0.2 0.2 0.2 Cumulative Var 0.2 0.4 0.6 0.8 1.0 > plot(loadings(pc)) > pc$sdev^2 Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 2.876090e+03 3.948135e+02 1.497269e+01 1.617353e+00 5.314068e-02 > cov(predict(pc,sa.lognormals5)) Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.1 2.924837e+03 1.405736e-13 5.190998e-14 4.358202e-15 -1.564210e-16 Comp.2 1.405736e-13 4.015053e+02 -5.905196e-14 2.736511e-15 1.248384e-15 Comp.3 5.190998e-14 -5.905196e-14 1.522647e+01 -1.631592e-18 2.173756e-16 Comp.4 4.358202e-15 2.736511e-15 -1.631592e-18 1.644766e+00 -1.227449e-15 Comp.5 -1.564210e-16 1.248384e-15 2.173756e-16 -1.227449e-15 5.404137e-02 > > > > cleanEx(); ..nameEx <- "princomprplus" > > ### * princomprplus > > flush(stderr()); flush(stdout()) > > ### Name: princomp.rplus > ### Title: Principal component analysis for real amounts > ### Aliases: princomp.rplus print.princomp.rplus plot.princomp.rplus > ### predict.princomp.rplus > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > pc <- princomp(rplus(sa.lognormals5)) > pc Call: princomp.rplus(x = rplus(sa.lognormals5)) Standard deviations: Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 53.6291886 19.8699154 3.8694564 1.2717521 0.2305226 5 variables and 60 observations. Mean: Cu Zn Pb Cd Co 5.0364342 14.2220517 28.5421272 0.4922757 0.5459743 attr(,"class") [1] "rplus" Loadings: Cu Zn Pb Cd Co Comp.1 0.013874129 5.263593e-02 -9.985167e-01 0.0007384299 0.0009073729 Comp.2 -0.164251970 -9.848766e-01 -5.418726e-02 0.0067959674 0.0075432478 Comp.3 0.986250097 -1.648617e-01 5.001249e-03 -0.0077969942 -0.0067498736 Comp.4 -0.011693312 -8.253912e-03 -1.768939e-03 -0.6423310866 -0.7662915799 Comp.5 -0.001676522 -8.762424e-05 -1.088185e-05 -0.7663571306 0.6424125854 attr(,"class") [1] "rmult" > summary(pc) Importance of components: Comp.1 Comp.2 Comp.3 Comp.4 Standard deviation 53.6291886 19.8699154 3.869456357 1.2717520946 Proportion of Variance 0.8748438 0.1200937 0.004554367 0.0004919636 Cumulative Proportion 0.8748438 0.9949375 0.999491872 0.9999838358 Comp.5 Standard deviation 2.305226e-01 Proportion of Variance 1.616424e-05 Cumulative Proportion 1.000000e+00 > plot(pc) #plot(pc,type="screeplot") > plot(pc,type="v") > plot(pc,type="biplot") > plot(pc,choice=c(1,3),type="biplot") > plot(pc,type="loadings") > plot(pc,type="loadings",scale.sdev=-1) # Downward > plot(pc,type="relative",scale.sdev=NA) # The directions > plot(pc,type="relative",scale.sdev=1) # one sigma Upward > plot(pc,type="relative",scale.sdev=-1) # one sigma Downward > biplot(pc) > screeplot(pc) > loadings(pc) Loadings: Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Cu -0.164 0.986 Zn -0.985 -0.165 Pb -0.999 Cd -0.642 -0.766 Co -0.766 0.642 Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 SS loadings 1.0 1.0 1.0 1.0 1.0 Proportion Var 0.2 0.2 0.2 0.2 0.2 Cumulative Var 0.2 0.4 0.6 0.8 1.0 > relativeLoadings(pc,mult=FALSE) Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Cu/Zn 8.2e-01 1.2e+00 Cu/Pb 1.0e+00 -1.1e-01 9.8e-01 Zn/Pb 1.1e+00 -9.3e-01 -1.7e-01 Cu/Cd -1.7e-01 9.9e-01 6.3e-01 7.6e-01 Zn/Cd -9.9e-01 -1.6e-01 6.3e-01 7.7e-01 Pb/Cd -1.0e+00 6.4e-01 7.7e-01 Cu/Co -1.7e-01 9.9e-01 7.5e-01 -6.4e-01 Zn/Co -9.9e-01 -1.6e-01 7.6e-01 -6.4e-01 Pb/Co -1.0e+00 7.6e-01 -6.4e-01 Cd/Co 1.2e-01 -1.4e+00 attr(,"cutoff") [1] 0.1 attr(,"scale") [1] 1 1 1 1 1 > relativeLoadings(pc) Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Cu/Zn 8.2e-01 1.2e+00 Cu/Pb 1.0e+00 -1.1e-01 9.8e-01 Zn/Pb 1.1e+00 -9.3e-01 -1.7e-01 Cu/Cd -1.7e-01 9.9e-01 6.3e-01 7.6e-01 Zn/Cd -9.9e-01 -1.6e-01 6.3e-01 7.7e-01 Pb/Cd -1.0e+00 6.4e-01 7.7e-01 Cu/Co -1.7e-01 9.9e-01 7.5e-01 -6.4e-01 Zn/Co -9.9e-01 -1.6e-01 7.6e-01 -6.4e-01 Pb/Co -1.0e+00 7.6e-01 -6.4e-01 Cd/Co 1.2e-01 -1.4e+00 attr(,"cutoff") [1] 0.1 attr(,"scale") [1] 1 1 1 1 1 > relativeLoadings(pc,scale.sdev=1) Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Cu/Zn -2.1e+00 1.6e+01 4.5e+00 Cu/Pb 5.4e+01 -2.2e+00 3.8e+00 Zn/Pb 5.6e+01 -1.8e+01 -6.6e-01 Cu/Cd 7.0e-01 -3.4e+00 3.8e+00 8.0e-01 1.8e-01 Zn/Cd 2.8e+00 -2.0e+01 -6.1e-01 8.1e-01 1.8e-01 Pb/Cd -5.4e+01 -1.2e+00 8.1e-01 1.8e-01 Cu/Co 7.0e-01 -3.4e+00 3.8e+00 9.6e-01 -1.5e-01 Zn/Co 2.8e+00 -2.0e+01 -6.1e-01 9.6e-01 -1.5e-01 Pb/Co -5.4e+01 -1.2e+00 9.7e-01 -1.5e-01 Cd/Co 1.6e-01 -3.2e-01 attr(,"cutoff") [1] 0.1 attr(,"scale") Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 53.6291886 19.8699154 3.8694564 1.2717521 0.2305226 > relativeLoadings(pc,scale.sdev=2) Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Cu/Zn -4.2e+00 3.3e+01 8.9e+00 Cu/Pb 1.1e+02 -4.4e+00 7.6e+00 Zn/Pb 1.1e+02 -3.7e+01 -1.3e+00 Cu/Cd 1.4e+00 -6.8e+00 7.7e+00 1.6e+00 3.5e-01 Zn/Cd 5.6e+00 -3.9e+01 -1.2e+00 1.6e+00 3.5e-01 Pb/Cd -1.1e+02 -2.4e+00 1.6e+00 3.5e-01 Cu/Co 1.4e+00 -6.8e+00 7.7e+00 1.9e+00 -3.0e-01 Zn/Co 5.5e+00 -3.9e+01 -1.2e+00 1.9e+00 -3.0e-01 Pb/Co -1.1e+02 -2.5e+00 1.9e+00 -3.0e-01 Cd/Co 3.2e-01 -6.5e-01 attr(,"cutoff") [1] 0.1 attr(,"scale") Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 107.2583771 39.7398308 7.7389127 2.5435042 0.4610452 > > pc$sdev^2 Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 2.876090e+03 3.948135e+02 1.497269e+01 1.617353e+00 5.314068e-02 > cov(predict(pc,sa.lognormals5)) Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.1 2.924837e+03 1.405736e-13 5.190998e-14 4.358202e-15 -1.564210e-16 Comp.2 1.405736e-13 4.015053e+02 -5.905196e-14 2.736511e-15 1.248384e-15 Comp.3 5.190998e-14 -5.905196e-14 1.522647e+01 -1.631592e-18 2.173756e-16 Comp.4 4.358202e-15 2.736511e-15 -1.631592e-18 1.644766e+00 -1.227449e-15 Comp.5 -1.564210e-16 1.248384e-15 2.173756e-16 -1.227449e-15 5.404137e-02 > > > > cleanEx(); ..nameEx <- "qqnorm" > > ### * qqnorm > > flush(stderr()); flush(stdout()) > > ### Name: qqnorm > ### Title: Normal quantile plots for compositions and amounts > ### Aliases: qqnorm.acomp qqnorm.rcomp qqnorm.rplus qqnorm.aplus vp.qqnorm > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > qqnorm(acomp(sa.lognormals),alpha=0.05) > qqnorm(rcomp(sa.lognormals),alpha=0.05) > qqnorm(aplus(sa.lognormals),alpha=0.05) > qqnorm(rplus(sa.lognormals),alpha=0.05) > > > > cleanEx(); ..nameEx <- "rDirichlet" > > ### * rDirichlet > > flush(stderr()); flush(stdout()) > > ### Name: rDirichlet > ### Title: Dirichlet distribution > ### Aliases: rDirichlet rDirichlet.acomp rDirichlet.rcomp > ### Keywords: multivariate > > ### ** Examples > > tmp <- rDirichlet.acomp(10,alpha=c(A=2,B=0.2,C=0.2)) > plot(tmp) > > > > cleanEx(); ..nameEx <- "ratioLoadings" > > ### * ratioLoadings > > flush(stderr()); flush(stdout()) > > ### Name: ratioLoadings > ### Title: Loadings of relations of two amounts > ### Aliases: relativeLoadings relativeLoadings.princomp.acomp > ### relativeLoadings.princomp.aplus relativeLoadings.princomp.rcomp > ### relativeLoadings.princomp.rplus print.relativeLoadings.princomp.acomp > ### print.relativeLoadings.princomp.aplus > ### print.relativeLoadings.princomp.rcomp > ### print.relativeLoadings.princomp.rplus > ### plot.relativeLoadings.princomp.acomp > ### plot.relativeLoadings.princomp.aplus > ### plot.relativeLoadings.princomp.rcomp > ### plot.relativeLoadings.princomp.rplus > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > pc <- princomp(acomp(sa.lognormals5)) > pc Call: princomp.acomp(x = acomp(sa.lognormals5)) Standard deviations: Comp.1 Comp.2 Comp.3 Comp.4 2.4242076 1.2527537 0.4673169 0.2667648 5 variables and 60 observations. Mean (compositional): Cu Zn Pb Cd Co 0.117710525 0.306222405 0.567371204 0.004239147 0.004456718 attr(,"class") [1] "acomp" +Loadings (compositional): Cu Zn Pb Cd Co Comp.1 0.6068998 0.5985836 0.6809203 1.5692975 1.5442987 Comp.2 1.3189309 1.3440242 0.3936868 0.9642938 0.9790643 Comp.3 1.8475861 0.4506335 0.8975793 0.8601707 0.9440304 Comp.4 0.8563030 0.9394475 0.9110133 0.4496577 1.8435786 attr(,"class") [1] "acomp" -Loadings (compositional): Cu Zn Pb Cd Co Comp.1 1.3568839 1.3757353 1.2093816 0.5247523 0.5332469 Comp.2 0.6213931 0.6097915 2.0817934 0.8499221 0.8370999 Comp.3 0.4439141 1.8200368 0.9137572 0.9534962 0.8687957 Comp.4 0.9578058 0.8730365 0.9002854 1.8239920 0.4448804 attr(,"class") [1] "acomp" > summary(pc) Importance of components: Comp.1 Comp.2 Comp.3 Comp.4 Standard deviation 2.424208 1.2527537 0.46731693 0.266764829 Proportion of Variance 0.759694 0.2028759 0.02823073 0.009199331 Cumulative Proportion 0.759694 0.9625699 0.99080067 1.000000000 > relativeLoadings(pc,log=TRUE) Comp.1 Comp.2 Comp.3 Comp.4 Cu/Zn 1.411 Cu/Pb -0.115 1.209 0.722 Zn/Pb -0.129 1.228 -0.689 Cu/Cd -0.950 0.313 0.765 0.644 Zn/Cd -0.964 0.332 -0.646 0.737 Pb/Cd -0.835 -0.896 0.706 Cu/Co -0.934 0.298 0.671 -0.767 Zn/Co -0.948 0.317 -0.740 -0.674 Pb/Co -0.819 -0.911 -0.705 Cd/Co -1.411 attr(,"cutoff") [1] 0.1 attr(,"scale") [1] 1 1 1 1 attr(,"log") [1] TRUE > relativeLoadings(pc) Comp.1 Comp.2 Comp.3 Comp.4 Cu/Zn 4.10 Cu/Pb 0.89 3.35 2.06 Zn/Pb 0.88 3.41 0.50 Cu/Cd 0.39 1.37 2.15 1.90 Zn/Cd 0.38 1.39 0.52 2.09 Pb/Cd 0.43 0.41 2.03 Cu/Co 0.39 1.35 1.96 0.46 Zn/Co 0.39 1.37 0.48 0.51 Pb/Co 0.44 0.40 0.49 Cd/Co 0.24 attr(,"cutoff") [1] 0.1 attr(,"scale") [1] 1 1 1 1 attr(,"log") [1] FALSE > relativeLoadings(pc,scale.sdev=1) Comp.1 Comp.2 Comp.3 Comp.4 Cu/Zn 1.934 Cu/Pb 0.757 4.548 1.401 Zn/Pb 0.732 4.656 0.725 Cu/Cd 0.100 1.480 1.429 1.187 Zn/Cd 0.097 1.516 0.739 1.217 Pb/Cd 0.132 0.326 1.207 Cu/Co 0.104 1.453 1.369 0.815 Zn/Co 0.101 1.487 0.708 0.835 Pb/Co 0.137 0.319 0.829 Cd/Co 0.686 attr(,"cutoff") [1] 0.1 attr(,"scale") Comp.1 Comp.2 Comp.3 Comp.4 2.4242076 1.2527537 0.4673169 0.2667648 attr(,"log") [1] FALSE > relativeLoadings(pc,scale.sdev=2) Comp.1 Comp.2 Comp.3 Comp.4 Cu/Zn 3.7387 Cu/Pb 0.5724 20.6809 1.9635 Zn/Pb 0.5353 21.6809 0.5252 Cu/Cd 0.0100 2.1917 2.0432 1.4101 Zn/Cd 0.0093 2.2977 0.5465 1.4816 Pb/Cd 0.0175 0.1060 1.4575 Cu/Co 0.0108 2.1098 1.8731 0.6642 Zn/Co 0.0101 2.2118 0.5010 0.6979 Pb/Co 0.0189 0.1020 0.6865 Cd/Co 0.4710 attr(,"cutoff") [1] 0.1 attr(,"scale") Comp.1 Comp.2 Comp.3 Comp.4 4.8484151 2.5055074 0.9346339 0.5335297 attr(,"log") [1] FALSE > > plot(relativeLoadings(pc,log=TRUE)) > plot(relativeLoadings(pc)) > plot(relativeLoadings(pc,scale.sdev=1)) > plot(relativeLoadings(pc,scale.sdev=2)) > > > > > cleanEx(); ..nameEx <- "rcomp" > > ### * rcomp > > flush(stderr()); flush(stdout()) > > ### Name: rcomp > ### Title: Compositions as elements of the Simplex embedded in the > ### D-dimensional real space > ### Aliases: rcomp > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > plot(rcomp(sa.tnormals)) > > > > cleanEx(); ..nameEx <- "rcomparithm" > > ### * rcomparithm > > flush(stderr()); flush(stdout()) > > ### Name: rcomparithm > ### Title: Arithmetic operations for composition in real geometry > ### Aliases: +.rcomp -.rcomp *.rcomp /.rcomp convex.rcomp > ### Keywords: multivariate > > ### ** Examples > > rcomp(1:5)* -1 + rcomp(1:5) Warning: Incompatible methods ("+.rmult", "+.rcomp") for "+" [1] 0 0 0 0 0 attr(,"class") [1] "rmult" > data(SimulatedAmounts) > cdata <- rcomp(sa.lognormals) > plot( tmp <- (cdata-mean(cdata))/msd(cdata) ) > class(tmp) [1] "rmult" > mean(tmp) Cu Zn Pb -1.272131e-16 -8.326673e-17 -2.405483e-16 attr(,"class") [1] "rmult" > msd(tmp) [1] 0.8164966 > var(tmp) Cu Zn Pb Cu 0.1720499 0.1812180 -0.3532679 Zn 0.1812180 0.6467321 -0.8279501 Pb -0.3532679 -0.8279501 1.1812180 > plot(convex.rcomp(rcomp(c(1,1,1)),sa.lognormals,0.1)) > > > > cleanEx(); ..nameEx <- "rcompmargin" > > ### * rcompmargin > > flush(stderr()); flush(stdout()) > > ### Name: rcompmargin > ### Title: Marginal compositions in real geometry > ### Aliases: rcompmargin > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > plot.rcomp(sa.tnormals5,margin="rcomp") > plot.rcomp(rcompmargin(sa.tnormals5,c("Cd","Zn"))) > plot.rcomp(rcompmargin(sa.tnormals5,c(1,2))) > > > > > cleanEx(); ..nameEx <- "rlnorm" > > ### * rlnorm > > flush(stderr()); flush(stdout()) > > ### Name: rlnorm > ### Title: The multivariate lognormal distribution > ### Aliases: rlnorm.rplus dlnorm.rplus > ### Keywords: multivariate > > ### ** Examples > > MyVar <- matrix(c( + 0.2,0.1,0.0, + 0.1,0.2,0.0, + 0.0,0.0,0.2),byrow=TRUE,nrow=3) > MyMean <- c(1,1,2) > > plot(rlnorm.rplus(100,log(MyMean),MyVar)) > plot(rnorm.aplus(100,MyMean,MyVar)) > x <- rnorm.aplus(5,MyMean,MyVar) > dnorm.aplus(x,MyMean,MyVar) [1] 0.39988743 0.08186178 0.64563859 0.03588271 0.02209225 > dlnorm.rplus(x,log(MyMean),MyVar) [1] 2.27891103 0.14442964 1.84338223 0.06746114 0.02109734 > > > > > cleanEx(); ..nameEx <- "rmult" > > ### * rmult > > flush(stderr()); flush(stdout()) > > ### Name: rmult > ### Title: Simple treatment of real vectors > ### Aliases: rmult > ### Keywords: multivariate > > ### ** Examples > > plot(rnorm.rmult(30,mean=0:4,var=diag(1:5)+10)) > > > > > cleanEx(); ..nameEx <- "rmultarithm" > > ### * rmultarithm > > flush(stderr()); flush(stdout()) > > ### Name: rmultarithm > ### Title: vectorial arithmetic for datasets in a classical vector scale > ### Aliases: +.rmult -.rmult *.rmult /.rmult > ### Keywords: multivariate > > ### ** Examples > > x <- rmult(matrix( sqrt(1:12), ncol= 3 )) > x [,1] [,2] [,3] [1,] 1.000000 2.236068 3.000000 [2,] 1.414214 2.449490 3.162278 [3,] 1.732051 2.645751 3.316625 [4,] 2.000000 2.828427 3.464102 attr(,"class") [1] "rmult" > x+x [,1] [,2] [,3] [1,] 2.000000 4.472136 6.000000 [2,] 2.828427 4.898979 6.324555 [3,] 3.464102 5.291503 6.633250 [4,] 4.000000 5.656854 6.928203 attr(,"class") [1] "rmult" > x + rmult(1:3) [,1] [,2] [,3] [1,] 2.000000 4.236068 6.000000 [2,] 2.414214 4.449490 6.162278 [3,] 2.732051 4.645751 6.316625 [4,] 3.000000 4.828427 6.464102 attr(,"class") [1] "rmult" > x * 1:4 [,1] [,2] [,3] [1,] 1.000000 2.236068 3.000000 [2,] 2.828427 4.898979 6.324555 [3,] 5.196152 7.937254 9.949874 [4,] 8.000000 11.313708 13.856406 attr(,"class") [1] "rmult" > 1:4 * x [,1] [,2] [,3] [1,] 1.000000 2.236068 3.000000 [2,] 2.828427 4.898979 6.324555 [3,] 5.196152 7.937254 9.949874 [4,] 8.000000 11.313708 13.856406 attr(,"class") [1] "rmult" > x / 1:4 [,1] [,2] [,3] [1,] 1.0000000 2.2360680 3.0000000 [2,] 0.7071068 1.2247449 1.5811388 [3,] 0.5773503 0.8819171 1.1055416 [4,] 0.5000000 0.7071068 0.8660254 attr(,"class") [1] "rmult" > x / 10 [,1] [,2] [,3] [1,] 0.1000000 0.2236068 0.3000000 [2,] 0.1414214 0.2449490 0.3162278 [3,] 0.1732051 0.2645751 0.3316625 [4,] 0.2000000 0.2828427 0.3464102 attr(,"class") [1] "rmult" > > > > cleanEx(); ..nameEx <- "rmultmatmult" > > ### * rmultmatmult > > flush(stderr()); flush(stdout()) > > ### Name: rmultmatmult > ### Title: inner product for datasets with vector scale > ### Aliases: \%*\%.rmult > ### Keywords: multivariate > > ### ** Examples > > x <- rmult(matrix( sqrt(1:12), ncol= 3 )) > x%*%x [1] 15 18 21 24 > A <- matrix( 1:9,nrow=3) > x %*% A %*% x [1] 244.3313 295.9495 344.7906 392.3946 > x %*% A [,1] [,2] [,3] [1,] 14.47214 33.18034 51.88854 [2,] 15.80003 36.87797 57.95591 [3,] 16.97343 40.05671 63.13999 [4,] 18.04916 42.92675 67.80433 attr(,"class") [1] "rmult" > A %*% x [,1] [,2] [,3] [1,] 30.94427 37.18034 43.41641 [2,] 33.34812 40.37410 47.40008 [3,] 35.53143 43.22586 50.92028 [4,] 37.56242 45.85495 54.14748 attr(,"class") [1] "rmult" > x %*% 1:3 [1] 14.47214 15.80003 16.97343 18.04916 > x %*% 1:3 [1] 14.47214 15.80003 16.97343 18.04916 > 1:3 %*% x [1] 14.47214 15.80003 16.97343 18.04916 > > > > > cleanEx(); ..nameEx <- "rnorm" > > ### * rnorm > > flush(stderr()); flush(stdout()) > > ### Name: rnorm > ### Title: Normal distributions on special spaces > ### Aliases: rnorm.acomp rnorm.rcomp rnorm.aplus rnorm.rplus rnorm.rmult > ### dnorm.acomp dnorm.aplus dnorm.rmult > ### Keywords: multivariate > > ### ** Examples > > MyVar <- matrix(c( + 0.2,0.1,0.0, + 0.1,0.2,0.0, + 0.0,0.0,0.2),byrow=TRUE,nrow=3) > MyMean <- c(1,1,2) > > plot(rnorm.acomp(100,MyMean,MyVar)) > plot(rnorm.rcomp(100,MyMean,MyVar)) > plot(rnorm.aplus(100,MyMean,MyVar)) > plot(rnorm.rplus(100,MyMean,MyVar)) > plot(rnorm.rmult(100,MyMean,MyVar)) > x <- rnorm.aplus(5,MyMean,MyVar) > dnorm.acomp(x,MyMean,MyVar) [1] 0.4497669 1.2175797 0.3637434 1.8717174 2.2066608 > dnorm.aplus(x,MyMean,MyVar) [1] 0.1112192 0.3467846 0.1092977 0.5128225 0.5866643 > dnorm.rmult(x,MyMean,MyVar) [1] 0.021789382 0.388381514 0.009368914 0.552242629 0.508924875 > > > > cleanEx(); ..nameEx <- "rplus" > > ### * rplus > > flush(stderr()); flush(stdout()) > > ### Name: rplus > ### Title: Amounts i.e. positive numbers analysed as objects of the real > ### vector space > ### Aliases: rplus > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > plot(rplus(sa.lognormals)) > > > > > cleanEx(); ..nameEx <- "rplusarithm" > > ### * rplusarithm > > flush(stderr()); flush(stdout()) > > ### Name: rplusarithm > ### Title: Arithmetik of rplus-scale > ### Aliases: +.rplus -.rplus *.rplus /.rplus mul.rplus > ### Keywords: multivariate > > ### ** Examples > > rplus(1:5)* -1 + rplus(1:5) Warning: Incompatible methods ("+.rmult", "+.rplus") for "+" [1] 0 0 0 0 0 attr(,"class") [1] "rmult" > data(SimulatedAmounts) > cdata <- rplus(sa.lognormals) > plot( tmp <- (cdata-mean(cdata))/msd(cdata) ) > class(tmp) [1] "rmult" > mean(tmp) Cu Zn Pb 1.052399e-17 3.053113e-17 -2.646032e-16 attr(,"class") [1] "rmult" > msd(tmp) [1] 1 > var(tmp) Cu Zn Pb Cu 0.04615345 0.08993804 -0.07507615 Zn 0.08993804 0.49178735 -0.19163713 Pb -0.07507615 -0.19163713 2.46205919 > > > > cleanEx(); ..nameEx <- "runif" > > ### * runif > > flush(stderr()); flush(stdout()) > > ### Name: runif > ### Title: The uniform distribution on the simplex > ### Aliases: runif.acomp runif.rcomp > ### Keywords: multivariate > > ### ** Examples > > plot(runif.acomp(10,3)) > plot(runif.rcomp(10,3)) > > > > cleanEx(); ..nameEx <- "scalar" > > ### * scalar > > flush(stderr()); flush(stdout()) > > ### Name: scalar > ### Title: Parallel scalar products > ### Aliases: scalar scalar.default > ### Keywords: multivariate > > ### ** Examples > > scalar function (x, y) UseMethod("scalar") > > > > > cleanEx(); ..nameEx <- "scale" > > ### * scale > > flush(stderr()); flush(stdout()) > > ### Name: scale > ### Title: Normalizing datasets by centering and scaling > ### Aliases: scale.acomp scale.aplus scale.rcomp scale.rplus scale.rmult > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > plot(scale(acomp(sa.groups))) > ## Not run: > ##D plot(scale(rcomp(sa.groups))) > ## End(Not run) > plot(scale(aplus(sa.groups))) > ## Not run: > ##D plot(scale(rplus(sa.groups))) > ## End(Not run) > plot(scale(rmult(sa.groups))) > > > > > cleanEx(); ..nameEx <- "segments" > > ### * segments > > flush(stderr()); flush(stdout()) > > ### Name: segments > ### Title: Draws straight lines from point to point. > ### Aliases: segments.rmult segments.acomp segments.rcomp segments.aplus > ### segments.rplus > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > > plot(acomp(sa.lognormals)) > segments.acomp(acomp(c(1,2,3)),acomp(c(2,3,1)),col="red") > segments.rcomp(acomp(c(1,2,3)),acomp(c(2,3,1)),col="blue") > > plot(aplus(sa.lognormals[,1:2])) > segments.aplus(aplus(c(10,20)),aplus(c(20,10)),col="red") > segments.rplus(rplus(c(10,20)),rplus(c(20,10)),col="blue") > > plot(rplus(sa.lognormals[,1:2])) > segments.aplus(aplus(c(10,20)),aplus(c(20,10)),col="red") > segments.rplus(rplus(c(10,20)),rplus(c(20,10)),col="blue") > > > > > > > cleanEx(); ..nameEx <- "split" > > ### * split > > flush(stderr()); flush(stdout()) > > ### Name: split > ### Title: Spliting datasets in groups given by factors > ### Aliases: split.acomp split.aplus split.rcomp split.rplus split.rmult > > > ### ** Examples > > data(SimulatedAmounts) > split(acomp(sa.groups),sa.groups.area) $Lower clay sand gravel [1,] 0.028013932 0.56588947 0.4060966 [2,] 0.063692489 0.78431761 0.1519899 [3,] 0.046598995 0.68808427 0.2653167 [4,] 0.005696019 0.06497758 0.9293264 [5,] 0.050290757 0.44557477 0.5041345 [6,] 0.054419718 0.68524046 0.2603398 [7,] 0.053106987 0.52368407 0.4232089 [8,] 0.022186090 0.26930296 0.7085109 [9,] 0.016866567 0.18529288 0.7978406 [10,] 0.063882077 0.74071679 0.1954011 [11,] 0.030628346 0.42857897 0.5407927 [12,] 0.012963274 0.19723355 0.7898032 [13,] 0.057298948 0.81633573 0.1263653 [14,] 0.065798656 0.39849533 0.5357060 [15,] 0.042072151 0.48636964 0.4715582 [16,] 0.050651296 0.51775951 0.4315892 [17,] 0.106719047 0.53708079 0.3562002 [18,] 0.033836695 0.55079286 0.4153704 [19,] 0.009670684 0.13820359 0.8521257 [20,] 0.046906231 0.21168173 0.7414120 attr(,"class") [1] "acomp" $Middle clay sand gravel [1,] 0.13309687 0.2750366 0.59186652 [2,] 0.30699458 0.6543759 0.03862957 [3,] 0.22858279 0.6488581 0.12255908 [4,] 0.38644260 0.5995563 0.01400106 [5,] 0.16836737 0.6406909 0.19094175 [6,] 0.24167553 0.5523585 0.20596598 [7,] 0.34132519 0.5227385 0.13593632 [8,] 0.13871875 0.5172548 0.34402642 [9,] 0.47726794 0.4351272 0.08760483 [10,] 0.31509191 0.4694378 0.21547026 [11,] 0.41404046 0.4323386 0.15362095 [12,] 0.09180783 0.5371417 0.37105043 [13,] 0.17732175 0.6004134 0.22226484 [14,] 0.27731813 0.5755027 0.14717915 [15,] 0.21035262 0.6506552 0.13899214 [16,] 0.12949480 0.2365971 0.63390812 [17,] 0.22725474 0.7200037 0.05274158 [18,] 0.36184270 0.4370106 0.20114675 [19,] 0.09952651 0.5152951 0.38517842 [20,] 0.43220339 0.4279853 0.13981133 attr(,"class") [1] "acomp" $Upper clay sand gravel [1,] 0.23853179 0.45840899 0.3030592 [2,] 0.04495888 0.20244343 0.7525977 [3,] 0.03155488 0.10125397 0.8671911 [4,] 0.24894373 0.40261884 0.3484374 [5,] 0.05391244 0.13547960 0.8106080 [6,] 0.06390440 0.11681811 0.8192775 [7,] 0.01757669 0.11216958 0.8702537 [8,] 0.02760061 0.11459239 0.8578070 [9,] 0.03999607 0.08613840 0.8738655 [10,] 0.01544277 0.10173437 0.8828229 [11,] 0.02897713 0.08204979 0.8889731 [12,] 0.05237658 0.11797465 0.8296488 [13,] 0.07800816 0.24618533 0.6758065 [14,] 0.11307478 0.31782412 0.5691011 [15,] 0.02816124 0.04552202 0.9263167 [16,] 0.04207809 0.13691199 0.8210099 [17,] 0.08729394 0.27561998 0.6370861 [18,] 0.01513546 0.05567816 0.9291864 [19,] 0.01928753 0.04427458 0.9364379 [20,] 0.14811058 0.34267370 0.5092157 attr(,"class") [1] "acomp" > > > > cleanEx(); ..nameEx <- "straight" > > ### * straight > > flush(stderr()); flush(stdout()) > > ### Name: straight > ### Title: Draws infinite straight lines. > ### Aliases: straight straight.rmult straight.acomp straight.rcomp > ### straight.aplus straight.rplus > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > > plot(acomp(sa.lognormals)) > straight(mean(acomp(sa.lognormals)),princomp(acomp(sa.lognormals))$Loadings[1,],col="red") > straight(mean(rcomp(sa.lognormals)),princomp(rcomp(sa.lognormals))$loadings[,1],col="blue") > > plot(aplus(sa.lognormals[,1:2])) > straight(mean(aplus(sa.lognormals[,1:2])),princomp(aplus(sa.lognormals[,1:2]))$Loadings[1,],col="red") > straight(mean(rplus(sa.lognormals[,1:2])),princomp(rplus(sa.lognormals[,1:2]))$loadings[,1],col="blue") > > plot(rplus(sa.lognormals[,1:2])) > straight(mean(aplus(sa.lognormals[,1:2])),princomp(aplus(sa.lognormals[,1:2]))$Loadings[1,],col="red") > straight(mean(rplus(sa.lognormals[,1:2])),princomp(rplus(sa.lognormals[,1:2]))$loadings[,1],col="blue") > > > > > > cleanEx(); ..nameEx <- "summaryAcomp" > > ### * summaryAcomp > > flush(stderr()); flush(stdout()) > > ### Name: summary.acomp > ### Title: Summarizing a compositional dataset in terms of ratios > ### Aliases: summary.acomp > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > summary(acomp(sa.lognormals)) $mean Cu Zn Pb 0.08918175 0.23949922 0.67131903 attr(,"class") [1] "acomp" $mean.ratio Cu Zn Pb Cu 1.000000 0.3723676 0.1328455 Zn 2.685518 1.0000000 0.3567592 Pb 7.527539 2.8030114 1.0000000 $variation Cu Zn Pb Cu 0.0000000 0.4046994 2.938182 Zn 0.4046994 0.0000000 2.910539 Pb 2.9381816 2.9105389 0.000000 $expsd Cu Zn Pb Cu 1.000000 1.889212 5.551746 Zn 1.889212 1.000000 5.507056 Pb 5.551746 5.507056 1.000000 $min Cu Zn Pb Cu 1.0000000 0.07724088 0.0007311118 Zn 0.5163550 1.00000000 0.0023267923 Pb 0.1386074 0.02357382 1.0000000000 $q1 Cu Zn Pb Cu 1.000000 0.2543938 0.03878968 Zn 1.790112 1.0000000 0.09787533 Pb 2.366983 0.8931808 1.00000000 $med Cu Zn Pb Cu 1.000000 0.3315667 0.1073090 Zn 3.016007 1.0000000 0.3642767 Pb 9.386296 2.8149235 1.0000000 $q3 Cu Zn Pb Cu 1.00000 0.5586652 0.4228832 Zn 3.93123 1.0000000 1.1196417 Pb 25.78058 10.2205546 1.0000000 $max Cu Zn Pb Cu 1.00000 1.936652 7.214623 Zn 12.94651 1.000000 42.419940 Pb 1367.77979 429.776229 1.000000 attr(,"class") [1] "summary.acomp" > > > > > cleanEx(); ..nameEx <- "summaryAplus" > > ### * summaryAplus > > flush(stderr()); flush(stdout()) > > ### Name: summary.aplus > ### Title: Summaries of amounts > ### Aliases: summary.aplus summary.rplus summary.rmult > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > summary(aplus(sa.lognormals)) Cu Zn Pb Min. 0.2266 0.7212 1.765 1st Qu. 1.4150 4.4030 10.440 Median 2.8510 7.4950 22.300 Mean 3.0180 8.1050 22.720 3rd Qu. 4.4450 13.6500 42.350 Max. 33.3200 147.2000 310.000 attr(,"class") [1] "summary.aplus" "matrix" > summary(rplus(sa.lognormals)) Cu Zn Pb Min. 0.2266 0.7212 1.765 1st Qu. 1.4150 4.4100 10.450 Median 2.8510 7.5090 22.300 Mean 5.3930 14.9100 38.320 3rd Qu. 4.4470 13.6600 42.380 Max. 33.3200 147.2000 310.000 attr(,"class") [1] "summary.rplus" "matrix" > summary(rmult(sa.lognormals)) Cu Zn Pb Min. 0.2266 0.7212 1.765 1st Qu. 1.4150 4.4100 10.450 Median 2.8510 7.5090 22.300 Mean 5.3930 14.9100 38.320 3rd Qu. 4.4470 13.6600 42.380 Max. 33.3200 147.2000 310.000 attr(,"class") [1] "summary.rmult" "matrix" > > > > > cleanEx(); ..nameEx <- "summaryRcomp" > > ### * summaryRcomp > > flush(stderr()); flush(stdout()) > > ### Name: summary.rcomp > ### Title: Summary of compositions in real geometry > ### Aliases: summary.rcomp > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > summary(rcomp(sa.lognormals)) Cu Zn Pb Min. 0.0007289 0.00232 0.01975 1st Qu. 0.0315800 0.08136 0.39420 Median 0.0723000 0.25420 0.67750 Mean 0.1112000 0.27620 0.61260 3rd Qu. 0.1454000 0.43270 0.86890 Max. 0.5639000 0.87930 0.99700 attr(,"class") [1] "summary.rcomp" "matrix" > > > > > cleanEx(); ..nameEx <- "totals" > > ### * totals > > flush(stderr()); flush(stdout()) > > ### Name: totals > ### Title: Total sum of amounts > ### Aliases: totals totals.acomp totals.aplus totals.rcomp totals.rplus > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > totals(acomp(sa.lognormals)) [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [39] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 > totals(rcomp(sa.lognormals,total=100)) [1] 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 [20] 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 [39] 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 [58] 100 100 100 > totals(aplus(sa.lognormals)) [1] 89.86653 51.27057 54.28445 18.31066 31.19352 21.82243 39.43808 [8] 56.93021 21.61490 32.58061 10.52452 36.23536 49.06616 119.76415 [15] 74.72095 45.67224 25.46203 12.71097 23.90380 40.56176 83.77316 [22] 237.51461 11.32728 67.98170 89.21379 33.52859 15.52377 45.01314 [29] 160.81818 55.62151 26.61455 167.38491 72.64818 25.90670 31.83482 [36] 46.04734 89.89735 14.81478 59.32474 51.87925 38.25728 42.06449 [43] 37.60260 25.16122 18.63411 105.43474 26.63836 89.37634 68.14808 [50] 28.66861 21.36047 65.54905 310.91520 111.86470 24.64854 26.32865 [57] 80.72172 57.45639 45.08284 50.69511 > totals(rplus(sa.lognormals)) [1] 89.86653 51.27057 54.28445 18.31066 31.19352 21.82243 39.43808 [8] 56.93021 21.61490 32.58061 10.52452 36.23536 49.06616 119.76415 [15] 74.72095 45.67224 25.46203 12.71097 23.90380 40.56176 83.77316 [22] 237.51461 11.32728 67.98170 89.21379 33.52859 15.52377 45.01314 [29] 160.81818 55.62151 26.61455 167.38491 72.64818 25.90670 31.83482 [36] 46.04734 89.89735 14.81478 59.32474 51.87925 38.25728 42.06449 [43] 37.60260 25.16122 18.63411 105.43474 26.63836 89.37634 68.14808 [50] 28.66861 21.36047 65.54905 310.91520 111.86470 24.64854 26.32865 [57] 80.72172 57.45639 45.08284 50.69511 > aplus(acomp(sa.lognormals),total=totals(aplus(sa.lognormals))) Cu Zn Pb [1,] 8.8043262 35.1671810 45.895025 [2,] 0.8115227 2.6547329 47.804310 [3,] 1.2836130 12.4472047 40.553628 [4,] 2.8769188 6.1076554 9.326082 [5,] 1.9886417 6.0141272 23.190751 [6,] 3.3896714 10.2687372 8.164022 [7,] 4.0513090 3.1849648 32.201811 [8,] 1.1943458 2.9773189 52.758548 [9,] 4.2117276 7.9586570 9.444518 [10,] 1.8853385 1.4587471 29.236527 [11,] 1.2390347 4.8455459 4.439943 [12,] 1.6047337 2.2500057 32.380618 [13,] 2.9378049 6.0708733 40.057478 [14,] 33.3226595 70.5679160 15.873573 [15,] 19.1937971 29.4864567 26.040698 [16,] 25.7542941 13.2983579 6.619583 [17,] 1.6774935 4.6735018 19.111035 [18,] 1.7549689 5.5872775 5.368721 [19,] 3.1365953 8.5088858 12.258324 [20,] 4.7032409 17.1826723 18.675852 [21,] 0.8889607 3.9933710 78.890828 [22,] 4.1851977 17.8455863 215.483826 [23,] 1.4295150 2.1404152 7.757347 [24,] 2.8252088 2.9242264 62.232269 [25,] 21.6254051 38.9021430 28.686242 [26,] 2.4579094 9.9552051 21.115478 [27,] 0.9086360 1.6025783 13.012560 [28,] 1.4232231 2.1240410 41.465877 [29,] 2.1693018 7.0592234 151.589650 [30,] 14.0507698 20.8090919 20.761652 [31,] 0.8738573 5.4936177 20.247072 [32,] 11.9347773 147.1803237 8.269807 [33,] 1.3328815 1.8789131 69.436389 [34,] 1.5003069 2.1130152 22.293382 [35,] 13.3831060 11.8616845 6.590032 [36,] 1.1194612 4.5489605 40.378918 [37,] 24.2023825 47.6599664 18.035001 [38,] 1.8616519 6.8299177 6.123208 [39,] 16.6519113 32.1073256 10.565508 [40,] 1.5459451 10.1634574 40.169847 [41,] 4.7378458 22.0884132 11.431024 [42,] 1.3914715 5.0198681 35.653155 [43,] 5.7931233 19.5565009 12.252978 [44,] 3.0193966 12.0555237 10.086298 [45,] 4.3618242 6.5179884 7.754297 [46,] 1.3887697 4.9336531 99.112316 [47,] 6.0829625 12.5119847 8.043409 [48,] 12.7347130 74.8765021 1.765125 [49,] 4.0124308 19.0212134 45.114437 [50,] 0.6780054 8.7778043 19.212803 [51,] 4.2638402 12.3309421 4.765684 [52,] 3.9389555 12.5372267 49.072869 [53,] 0.2266208 0.7212296 309.967353 [54,] 1.2814074 3.8541853 106.729102 [55,] 0.6668855 1.6689589 22.312699 [56,] 3.6261557 11.3619303 11.340563 [57,] 2.5400903 12.8688647 65.312768 [58,] 2.6774921 5.0079625 49.770940 [59,] 3.9619526 14.7630454 26.357839 [60,] 3.9854998 6.1301909 40.579417 attr(,"class") [1] "aplus" > > > > cleanEx(); ..nameEx <- "ult" > > ### * ult > > flush(stderr()); flush(stdout()) > > ### Name: ult > ### Title: Uncentered log transform > ### Aliases: ult ult.inv Kappa > ### Keywords: multivariate > > ### ** Examples > > (tmp <- ult(c(1,2,3))) [1] -1.7917595 -1.0986123 -0.6931472 attr(,"class") [1] "rmult" > ult.inv(tmp) [1] 0.1666667 0.3333333 0.5000000 attr(,"class") [1] "acomp" > ult.inv(tmp) - clo(c(1,2,3)) # 0 [1] 0.3333333 0.3333333 0.3333333 attr(,"class") [1] "acomp" > data(Hydrochem) > cdata <- Hydrochem[,6:19] > pairs(ult(cdata)) > Kappa(c(1,2,3)) [1] 1.194506 > > > > cleanEx(); ..nameEx <- "varAcomp" > > ### * varAcomp > > flush(stderr()); flush(stdout()) > > ### Name: var.acomp > ### Title: Variances and covariances of amounts and compositions > ### Aliases: var var.default var.acomp var.rcomp var.aplus var.rplus > ### var.rmult cov cov.default cov.acomp cov.rcomp cov.aplus cov.rplus > ### cov.rmult > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > mean.col(sa.lognormals) Cu Zn Pb 5.392698 14.908465 38.319017 > var(acomp(sa.lognormals)) Cu Zn Pb Cu 0.4194692 0.2125124 -0.6319817 Zn 0.2125124 0.4102550 -0.6227674 Pb -0.6319817 -0.6227674 1.2547491 > var(rcomp(sa.lognormals)) Cu Zn Pb Cu 0.01153096 0.01214542 -0.02367638 Zn 0.01214542 0.04334466 -0.05549008 Pb -0.02367638 -0.05549008 0.07916646 > var(aplus(sa.lognormals)) Cu Zn Pb Cu 1.0872077 0.9063050 -0.4159529 Zn 0.9063050 1.1301017 -0.3806846 Pb -0.4159529 -0.3806846 1.0190681 > var(rplus(sa.lognormals)) Cu Zn Pb Cu 49.01556 95.51535 -79.73183 Zn 95.51535 522.28445 -203.52108 Pb -79.73183 -203.52108 2614.73830 > cov(acomp(sa.lognormals5[,1:3]),acomp(sa.lognormals5[,4:5])) Cd Co Cu -0.011145828 0.011145828 Zn -0.002192223 0.002192223 Pb 0.013338051 -0.013338051 > cov(rcomp(sa.lognormals5[,1:3]),rcomp(sa.lognormals5[,4:5])) Cd Co Cu -0.0005588028 0.0005588028 Zn -0.0005307509 0.0005307509 Pb 0.0010895537 -0.0010895537 > cov(aplus(sa.lognormals5[,1:3]),aplus(sa.lognormals5[,4:5])) Cd Co Cu -0.26955832 -0.2089565 Zn -0.29520390 -0.2525093 Pb -0.09199686 -0.0803628 > cov(rplus(sa.lognormals5[,1:3]),rplus(sa.lognormals5[,4:5])) Cd Co Cu -0.5228806 -0.5473254 Zn -2.5453723 -2.8158151 Pb -2.3031642 -2.8123807 > cov(acomp(sa.lognormals5[,1:3]),aplus(sa.lognormals5[,4:5])) Cd Co Cu -0.05063863 -0.02834697 Zn -0.07628420 -0.07189976 Pb 0.12692283 0.10024673 > > svd(var(acomp(sa.lognormals))) $d [1] 1.882162e+00 2.023118e-01 1.936200e-16 $u [,1] [,2] [,3] [1,] -0.4116027 0.705159487 0.5773503 [2,] -0.4048847 -0.709038119 0.5773503 [3,] 0.8164874 0.003878633 0.5773503 $v [,1] [,2] [,3] [1,] -0.4116027 0.705159487 0.5773503 [2,] -0.4048847 -0.709038119 0.5773503 [3,] 0.8164874 0.003878633 0.5773503 > > > > > cleanEx(); ..nameEx <- "variation" > > ### * variation > > flush(stderr()); flush(stdout()) > > ### Name: variation > ### Title: Variation matrices of amounts and compositions > ### Aliases: variation variation.default variation.acomp variation.rcomp > ### variation.aplus variation.rplus variation.rmult > ### Keywords: multivariate > > ### ** Examples > > data(SimulatedAmounts) > mean.col(sa.lognormals) Cu Zn Pb 5.392698 14.908465 38.319017 > variation(acomp(sa.lognormals)) Cu Zn Pb Cu 0.0000000 0.4046994 2.938182 Zn 0.4046994 0.0000000 2.910539 Pb 2.9381816 2.9105389 0.000000 > variation(rcomp(sa.lognormals)) Cu Zn Pb Cu 0.00000000 0.03058478 0.1380502 Zn 0.03058478 0.00000000 0.2334913 Pb 0.13805018 0.23349126 0.0000000 > variation(aplus(sa.lognormals)) Cu Zn Pb Cu 0.0000000 0.4046994 2.938182 Zn 0.4046994 0.0000000 2.910539 Pb 2.9381816 2.9105389 0.000000 > variation(rplus(sa.lognormals)) Cu Zn Pb Cu 0.0000 380.2693 2823.218 Zn 380.2693 0.0000 3544.065 Pb 2823.2175 3544.0649 0.000 > variation(rmult(sa.lognormals)) Cu Zn Pb Cu 0.0000 380.2693 2823.218 Zn 380.2693 0.0000 3544.065 Pb 2823.2175 3544.0649 0.000 > > > > > ### *