# DirStats.R - a directional statistics package for analysis of directional # data in the R environment for statistical computing. # # Copyright P.R. Fisher. # Microbiology Dept., La Trobe University, VIC 3086, AUSTRALIA. # Email: fisher@lumi.latrobe.edu.au # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License version 2 # as published by the Free Software Foundation. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY FOR A PARTICULAR PURPOSE. See the GNU General Public # License for more details. # "load.libraries" <- function(){ # # Copyright P.R. Fisher. # Microbiology Dept., La Trobe University, VIC 3086, AUSTRALIA. # Email: fisher@lumi.latrobe.edu.au # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License version 2 # as published by the Free Software Foundation. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY FOR A PARTICULAR PURPOSE. See the GNU General Public # License for more details. # library(CircStats) library(circular) library(Bhat) } "acorn" <- function(file="",rose=T,stack=F,ml=F,shrink=1.2,kappa.alpha=0.1,mu.alpha=0.01,tracks=T, type = "n"){ # # Copyright P.R. Fisher. # Microbiology Dept., La Trobe University, VIC 3086, AUSTRALIA. # Email: fisher@lumi.latrobe.edu.au # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License version 2 # as published by the Free Software Foundation. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY FOR A PARTICULAR PURPOSE. See the GNU General Public # License for more details. # # If rose = F, no plot is produced # If stack = T, individual angles are plotted in the perimeter of the circle stacked in # 2 deg. wide bins # If ml = T, the mean direction (solid arrow) and confidence limits (dotted lines) are drawn # If tracks = T, a vector is drawn as a solid line representing each individual observation, # along with a scale bar. # If type = "n", the plot is produced but without the rose while type = "l" plots the rose. # kappa.alpha and mu.alpha are the level of confidence for maximum likelihood estimates # shrink will reduce the size of the plot (sometimes needed to accommodate stacks) # require("CircStats") require("circular") # # Set up plot parameters # if (rose) oldpar<-par( mai=c(0.2,0.2,0.2,0.2),fig=c(0,1,0,1) ) # # Get and convert data # data<-fetch(file=file,ncol=5) data.distances<-sqrt((data[,5]-data[,3])**2 + (data[,4]-data[,2])**2) # # remove data points where distance = 0 # data<-data[data.distances != 0,] data.distances<-data.distances[data.distances != 0] # # distance.stats<<-stat.desc(data.distances) data.sines<-(data[,5]-data[,3])/data.distances data.cosines<-(data[,4]-data[,2])/data.distances angles<-atan2(data.sines[data.distances > 0],data.cosines[data.distances > 0]) angles<-conversion.circular(angles,"degrees") angles[angles < 0] <- angles[angles < 0] + 360 sample.size<-length(angles) rbar<-sqrt(mean(data.sines)**2+mean(data.cosines)**2) sbar<-mean(data.sines) cbar<-mean(data.cosines) # # Calculate maximum likelihood estimates # mle<-mle.vonmises(angles) mu.mle<-mle$mu[[1]] if (mu.mle < 0) mu.mle<-mu.mle+360 kappa.mle<-mle$kappa[[1]] # # Calculate bootstrap confidence limits # # angles.bs<-mle.vonmises.bootstrap.ci(angles,mu.alpha=mu.alpha,kappa.alpha=kappa.alpha) # angles.bs$mu.ci[angles.bs$mu.ci < 0 ] <- angles.bs$mu.ci[angles.bs$mu.ci < 0 ] + 360 mu.bootstrap.limits<-paste(round(as.numeric(angles.bs$mu.ci),digits=2),collapse=", ") kappa.bootstrap.limits<-paste(round(as.numeric(angles.bs$kappa.ci),digits=2),collapse=", ") # # Calculate parametric confidence limits # # Calculate 99% limits on mu (mu.alpha= 0.01) and, based on that, if mu is accepted to be zero # mu.is.zero<-F # if ( sample.size <= 30 ) {delta<-APPEND2.7.read(n=sample.size,rbar=rbar)} else { k.prime<- sample.size*kappa.mle*rbar if ( k.prime > 10 ) delta<-180/pi*qnorm(p=0.01/2,sd=1/sqrt(k.prime-0.5),lower.tail=F) else delta<-180-APPEND2.6.read(k.prime) } mu.limits<-c(mle$mu[[1]]-delta,mle$mu[[1]]+delta) if ( ! (is.nan(delta) || is.na(delta)) && ((mu.limits[1] < 0) || ( mu.limits[2] > 360)) ) { mu.is.zero<-T mu.limits[mu.limits < 0]<-mu.limits[mu.limits < 0 ] + 360 mu.limits[mu.limits > 360]<-mu.limits[mu.limits > 360 ] - 360 } # # # Calculate 90% confidence limits on kappa (kappa.alpha=0.1) # if(mu.is.zero) { degrees.of.freedom<-sample.size resultant<-mean(data.cosines) if ( kappa.mle < 2 ) kappa.limits<-TABLE.read(sample.size,resultant,TABLE1) else { a<-sample.size*(1-resultant)/qchisq(p=0.95,df=degrees.of.freedom,lower.tail=F) b<-sample.size*(1-resultant)/qchisq(p=0.05,df=degrees.of.freedom,lower.tail=F) kappa.limits<-c( (1+sqrt(1+3*a))/4/a, (1+sqrt(1+3*b))/4/b ) } } else { degrees.of.freedom<-sample.size-1 resultant<-rbar if ( kappa.mle < 2 ) kappa.limits<-TABLE.read(sample.size,resultant,TABLE2) else { a<-sample.size*(1-resultant)/qchisq(p=0.95,df=degrees.of.freedom,lower.tail=F) b<-sample.size*(1-resultant)/qchisq(p=0.05,df=degrees.of.freedom,lower.tail=F) kappa.limits<-c( (1+sqrt(1+3*a))/4/a, (1+sqrt(1+3*b))/4/b ) } } # # Perform Raleigh test for uniformity # if(mu.is.zero) rtest<-rayleigh.test(angles,mu=0) else rtest<-rayleigh.test(angles) rtest[[1]]<-round(as.numeric(rtest[[1]]),digits=3) rtest[[2]]<-round(as.numeric(rtest[[2]]),digits=3) if(rtest[[1]] < 0 ) { rtest[[2]]<- 1 - rtest[[2]] } # # # Plot rose diagram with parameter estimates # if ( rose ) { rose.diag(angles,main=file,shrink=shrink,type=type) # # If stack is true, create a points stack on the perimeter of the plotting circle # if ( stack ) { # # Note: a "bug" in the points.circular routine is that it fails to plot points at exactly 0 # angles_for_plot<-angles angles_for_plot[angles == 0]<-angles[angles == 0]+0.00001 points.circular(angles_for_plot,stack=T,bins=180) } # # If ml is true, draw the directions for mu and its bootstrap confidence limits to the perimeter of the circle # if ( ml ) { arrows(0,0,cos(rad(mu.mle)),sin(rad(mu.mle)),lwd=4,angle=10) lines(c(0,cos(rad(angles.bs$mu.ci[[1]]))),c(0,sin(rad(angles.bs$mu.ci[[1]]))),lwd=2,lty=3) lines(c(0,cos(rad(angles.bs$mu.ci[[2]]))),c(0,sin(rad(angles.bs$mu.ci[[2]]))),lwd=2,lty=3) } # # If tracks is true, draw lines for each individual observation # if ( tracks ) traks(file, new=F) # # Round up and write results onto the plot # mu.mle<-round(mu.mle,digits=2) kappa.mle<-round(kappa.mle,digits=2) mu.limits<-round(mu.limits,digits=2) kappa.limits<-round(kappa.limits,digits=2) # text(-1,1.15,paste("Estimated mu =",mu.mle,"(",mu.bootstrap.limits,")","(",mu.limits[1],", ",mu.limits[2],")"),adj=0) text(-1,1.05,paste("Estimated kappa =",kappa.mle,"(",kappa.bootstrap.limits,")","(",kappa.limits[1],",",kappa.limits[2],")"),adj=0) text(-1,0.95,paste("n =",sample.size),adj=0) text(-1,-1.1,paste("Rayleigh test: Rbar =",rtest[[1]]," p =",rtest[[2]]),adj=0) } # # Return parameter estimates # return(round(c(sample.size,rbar,mu.mle,angles.bs$mu.ci,mu.limits,kappa.mle,angles.bs$kappa.ci,kappa.limits,rtest[[2]]),digits=3)) # # } "bimstat" <- function(file,alpha=1,kappa=1,kappa1,rose=T,stack=F,ml=F,tracks=T,shrink=1.2,type="n"){ # # Copyright P.R. Fisher. # Microbiology Dept., La Trobe University, VIC 3086, AUSTRALIA. # Email: fisher@lumi.latrobe.edu.au # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License version 2 # as published by the Free Software Foundation. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY FOR A PARTICULAR PURPOSE. See the GNU General Public # License for more details. # # require("circular") require("Bhat") # # If rose = F, no plot is produced # If stack = T, individual angles are plotted in the perimeter of the circle stacked in # 2 deg. wide bins # If ml = T, the mean directions (solid arrows) and confidence limits (dotted lines) are drawn # If tracks = T, a line is drawn representing each individual observation, # along with a scale bar. # If type = "n", the plot is produced but without the rose while type = "l" plots the rose. # kappa.alpha and mu.alpha are the level of confidence for maximum likelihood estimates # shrink will reduce the size of the plot (sometimes needed to accommodate stacks) # # Set up plot parameters # if (rose) oldpar<-par( mai=c(0.2,0.2,0.2,0.2),fig=c(0,1,0,1) ) ## # Get and convert data # data<-fetch(file=file,ncol=5) data.distances<-sqrt((data[,5]-data[,3])**2 + (data[,4]-data[,2])**2) # # Remove data points where distance = 0 # data<-data[data.distances != 0,] data.distances<-data.distances[data.distances != 0] data.sines<-(data[,5]-data[,3])/data.distances data.cosines<-(data[,4]-data[,2])/data.distances # # angles is put into the global environment so subsequent function calls can access it # angles<<-atan2(data.sines[data.distances > 0],data.cosines[data.distances > 0]) sample.size<-length(angles) # # Create initial input for functions finding minimum of negative Likelihood # input<-list(label=c("alpha","kappa"),est=c(alpha,kappa),low=c(0,0),upp=c(pi,1000)) # # Get first estimates using dfp, use dfp outputs as input for newton # dfp.output<-dfp(input,log.likelihood) input$est<-dfp.output$est newton.output<-newton(input,log.likelihood,itmax=1000,relax=1) # # Calculate -log likelihoods and LR test statistic for H0 that alpha=0, kappa=kappa1 # versus H1 that alpha and kappa equal the maximum likelihood estimates # H0.Likelihood<-log.likelihood(c(0,kappa1)) H1.Likelihood<-log.likelihood(newton.output$est) LR<- 2*(H0.Likelihood-H1.Likelihood) p<-round(pchisq(LR,df=1,lower.tail=F),digits=3) # # # round up results # alpha<-round(newton.output$est[1]/pi*180,digits=2) kappa<-round(newton.output$est[2],digits=2) alpha.limits<-round(c(newton.output$low[1],newton.output$upp[1])/pi*180,digits=2) kappa.limits<-round(c(newton.output$low[2],newton.output$upp[2]),digits=2) LR<-round(LR,digits=2) # ## # convert angles to degrees for plotting # angles<<-conversion.circular(angles,"degrees") angles[angles < 0] <<- angles[angles < 0] + 360 # # Plot rose diagram with parameter estimates # if ( rose ) { rose.diag(angles,main=file,shrink=shrink,type=type) # # If stack is true, create a points stack on the perimeter of the plotting circle # if ( stack ) { # # Note: a "bug" in the points.circular routine is that it fails to plot points at exactly 0 # angles_for_plot<<-angles angles_for_plot[angles == 0]<<-angles[angles == 0]+0.00001 points.circular(angles_for_plot,stack=T,bins=180) } # # If ml is true, draw the directions for =/- alpha and its maximum likelihood confidence # limits to the perimeter of the circle # if ( ml ) { arrows(c(0,0),c(0,0),cos(rad(c(alpha,-alpha))),sin(rad(c(alpha,-alpha))),lwd=4,angle=10) lines(c(0,cos(rad(alpha.limits[1]))),c(0,sin(rad(alpha.limits[1]))),lwd=2,lty=3) lines(c(0,cos(rad(-alpha.limits[1]))),c(0,sin(rad(-alpha.limits[1]))),lwd=2,lty=3) lines(c(0,cos(rad(alpha.limits[2]))),c(0,sin(rad(alpha.limits[2]))),lwd=2,lty=3) lines(c(0,cos(rad(-alpha.limits[2]))),c(0,sin(rad(-alpha.limits[2]))),lwd=2,lty=3) } # # If tracks is true, draw lines for each individual observation # if ( tracks ) traks(file, new=F) # # Write results onto the plot # # text(-1,1.15,paste("Estimated alpha ",alpha,"(",alpha.limits[1],",",alpha.limits[2],")"),adj=0) text(-1,1.05,paste("Estimated kappa ",kappa,"(",kappa.limits[1],",",kappa.limits[2],")"),adj=0) text(-1,0.95,paste("n =",sample.size),adj=0) text(-1,-1.1,paste("LR statistic = ",LR," p = ",p),adj=0) } # rm(angles,inherits=T) return(c(alpha,alpha.limits,kappa,kappa.limits,LR,p)) } "vmtests" <- function(sample.stats){ # # Copyright P.R. Fisher. # Microbiology Dept., La Trobe University, VIC 3086, AUSTRALIA. # Email: fisher@lumi.latrobe.edu.au # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License version 2 # as published by the Free Software Foundation. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY FOR A PARTICULAR PURPOSE. See the GNU General Public # License for more details. # # # # Performs tests for the equality of kappa in either the 2-sample or the multisample case # Input is a matrix (sample.stats) in which each row represents data from one sample and column 1 contains the size # of the sample while column 2 contains the value of Rbar for that sample. Additional columns may be present but # will be ignored. # Output from acorn is suitable as input for one row of the matrix. # See also vmtests.on.files which takes a vector of file names, runs acorn on them, stores the results in the matrix # by the input # name and tests them for equality of kappa # # number.of.samples <- length(sample.stats[,1]) n<-sample.stats[,1] rbar<-sample.stats[,2] rbar.mean<-sum(n*rbar)/sum(n) # if ( number.of.samples <= 1 ) return("ERROR - less than 2 samples") else if ( number.of.samples == 2 ) { if(rbar[1] > rbar[2] ) lower.tail=T else lower.tail=F if (rbar.mean < 0.45) { a<-sqrt(3/8) g<-asin(2*a*rbar) Q<-2/sqrt(3)*(g[1]-g[2])/sqrt(sum(1/(n-4))) probability<-1-pnorm(Q,lower.tail=lower.tail) } else if ( rbar.mean <= 0.7 ) { x<-(rbar-1.0894)/0.25789 g<-log(x+sqrt(x**2+1)) Q<-(g[1]-g[2])/0.89325/sqrt(sum(1/(n-3))) probability<-1-pnorm(Q,lower.tail=lower.tail) } else { Q<-(n[1]*(1-rbar[1])*(n[2]-1))/(n[2]*(1-rbar[2])*(n[1]-1)) probability<-pf(Q,n[1]-1,n[2]-1,lower.tail=lower.tail) } } else { if(rbar.mean < 0.45) { a<-sqrt(3/8) g<-asin(2*a*rbar) w<-4*(n-4)/3 Q<-sum(w*g**2) - (sum(w*g)**2)/sum(w) } else if (rbar.mean <= 0.7) { x<-(rbar-1.0894)/0.25789 g<-log(x+sqrt(x**2+1)) w<-(n-3)/0.7979 Q<-sum(w*g**2)-(sum(w*g))**2/sum(w) } else { v<-n-1 vee<-sum(v) d<-(sum(1/v)-1/vee)/3/(number.of.samples-1) Q<-(vee*log((sum(n)-sum(n*rbar))/vee)-sum(v*log((n-n*rbar)/v)))/(1+d) } probability<-1-pchisq(Q,number.of.samples-1) } return(c(rbar.mean,Q,probability)) } "vmtests.on.files" <- function(files,save=T){ # # Copyright P.R. Fisher. # Microbiology Dept., La Trobe University, VIC 3086, AUSTRALIA. # Email: fisher@lumi.latrobe.edu.au # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License version 2 # as published by the Free Software Foundation. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY FOR A PARTICULAR PURPOSE. See the GNU General Public # License for more details. # for (file in files) { if (file == files[1]) results<-acorn(file,rose=F) else results<-c(results,acorn(file,rose=F)) } ifelse (save, acorn.results<<-matrix(results,ncol=13,byrow=T), acorn.results<-matrix(results,ncol=13,byrow=T)) return(vmtests(acorn.results)) } "fetch" <- function(file, ncol = 4) # # Copyright P.R. Fisher. # Microbiology Dept., La Trobe University, VIC 3086, AUSTRALIA. # Email: fisher@lumi.latrobe.edu.au # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License version 2 # as published by the Free Software Foundation. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY FOR A PARTICULAR PURPOSE. See the GNU General Public # License for more details. # { matrix(scan(file, what = numeric()), byrow = T, ncol = ncol) } "traks" <- function(file = "tablet.dat",new=T) # # Copyright P.R. Fisher. # Microbiology Dept., La Trobe University, VIC 3086, AUSTRALIA. # Email: fisher@lumi.latrobe.edu.au # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License version 2 # as published by the Free Software Foundation. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY FOR A PARTICULAR PURPOSE. See the GNU General Public # License for more details. # { par(pty = "s") coords <- fetch(file, ncol = 5) x <- coords[, 4] - coords[, 2] y <- coords[, 5] - coords[, 3] if ( new ) { scale <- max(abs(c(x, y))) plot(c(-scale, scale), c(-scale, scale), pch = " ", xaxt = "n", yaxt = "n", xlab = "", ylab = "") lines(c(-scale/2,scale/2),c(-scale/2,-scale/2),lwd=5) text(0,-scale/1.8,paste(round(scale,digits=1),"mm")) } else { scale<-max(sqrt(x^2+y^2)) lines(c(-1/2,1/2),c(-1/2,-1/2),lwd=5) text(0,-1/1.8,paste(round(scale,digits=1),"mm")) } # # for(n in 1:length(x)) { if(new) lines(c(0, x[n]), c(0, y[n])) else lines(c(0, x[n]/scale), c(0, y[n])/scale) } par(pty = "m") title(file) } "mle.vonmises.bootstrap.ci" <- function (x, mu, bias = FALSE, mu.alpha = 0.05, kappa.alpha = 0.05, reps = 1000) { # # Copyright P.R. Fisher. # Microbiology Dept., La Trobe University, VIC 3086, AUSTRALIA. # Email: fisher@lumi.latrobe.edu.au # # This program is a modified form of the function of the same name # distributed in the package "circular" through # "The Comprehensive R Archive Network" # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License version 2 # as published by the Free Software Foundation. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY FOR A PARTICULAR PURPOSE. See the GNU General Public # License for more details. # if (require(boot)) { x <- as.circular(x) xcircularp <- circularp(x) units <- xcircularp$units x <- conversion.circular(x, units = "radians") if (missing(mu)) { sinr <- sum(sin(x)) cosr <- sum(cos(x)) mu <- atan2(sinr, cosr) } else { attr(mu, "circularp") <- xcircularp attr(mu, "class") <- "circular" mu <- conversion.circular(mu, units = "radians") } mle.vonmises.mu <- function(x, i) { sinr <- sum(sin(x[i])) cosr <- sum(cos(x[i])) mu <- atan2(sinr, cosr) return(mu) } mle.vonmises.kappa <- function(x, i, mu, bias) { n <- length(x[i]) V <- mean(cos(x[i] - mu)) if (V > 0) { kappa <- A1inv(V) } else { kappa <- 0 } if (bias == TRUE) { if (kappa < 2) { kappa <- max(kappa - 2 * (n * kappa)^-1, 0) } else { kappa <- ((n - 1)^3 * kappa)/(n^3 + n) } } return(kappa) } mean.bs <- boot(data = x, statistic = mle.vonmises.mu, R = reps, stype = "i") mean.reps <- mean.bs$t mean.reps <- sort(mean.reps%%(2 * pi)) B <- reps spacings <- c(diff(mean.reps), mean.reps[1] - mean.reps[B] + 2 * pi) max.spacing <- (1:B)[spacings == max(spacings)] off.set <- 2 * pi - mean.reps[max.spacing + 1] if (max.spacing != B) mean.reps2 <- mean.reps + off.set else mean.reps2 <- mean.reps mean.reps2 <- sort(mean.reps2%%(2 * pi)) mean.ci <- quantile(mean.reps2, c(mu.alpha/2, 1 - mu.alpha/2)) if (max.spacing != B) mean.ci <- mean.ci - off.set kappa.bs <- boot(data = x, statistic = mle.vonmises.kappa, R = reps, stype = "i", mu = mu, bias = bias) kappa.reps <- kappa.bs$t kappa.ci <- quantile(kappa.reps, c(kappa.alpha/2, 1 - kappa.alpha/2)) if (units == "degrees") { mean.reps <- mean.reps/pi * 180 mean.ci <- mean.ci/pi * 180 } attr(mean.reps, "circularp") <- xcircularp attr(mean.reps, "class") <- "circular" attr(mean.ci, "circularp") <- xcircularp attr(mean.ci, "class") <- "circular" result <- list() result$call <- match.call() result$mu.ci <- mean.ci result$mu <- c(mean.reps) result$kappa.ci <- kappa.ci result$kappa <- c(kappa.reps) result$mu.alpha <- mu.alpha result$kappa.alpha <- kappa.alpha class(result) <- "mle.vonmises.bootstrap.ci" return(result) } else { stop("To use this function you have to install the package 'boot' \n") } } "log.likelihood" <- function(input){ # # Copyright P.R. Fisher. # Microbiology Dept., La Trobe University, VIC 3086, AUSTRALIA. # Email: fisher@lumi.latrobe.edu.au # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License version 2 # as published by the Free Software Foundation. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY FOR A PARTICULAR PURPOSE. See the GNU General Public # License for more details. # # # Returns the negative logarithm of the likelihood function for a bidirectional von Mises # distribution. Minimizing this is equivalent to maximizing the likelihood. # alpha<-input[1] kappa<-input[2] f<-(exp(kappa*cos(angles+alpha)) + exp(kappa*cos(angles-alpha)))/4/pi/besselI(kappa,0) return(-sum(log(f))) } "TABLE.read" <- function(n,cbar,TABLE=TABLE1){ # kappa.limits<-c(NA,NA) # kappas<-TABLE[1,2:12] # row.number<-length(TABLE[TABLE[,1] <= n,1]) - 1 n1<-TABLE[row.number,1] n2<-TABLE[row.number+2,1] root1<-1/sqrt(n1) root2<-1/sqrt(n2) root.n<-1/sqrt(n) # # get the relevant rows from the table # row1<-TABLE[row.number,2:12] row2<-TABLE[row.number+1,2:12] row3<-TABLE[row.number+2,2:12] row4<-TABLE[row.number+3,2:12] # # Calculate values for the lower limits by interpolating in 1/sqrt(n) # lower.limits<-row1+(row3-row1)*(root.n-root1)/(root2-root1) upper.limits<-row2+(row4-row2)*(root.n-root1)/(root2-root1) # # column.lower.number<-length(lower.limits[lower.limits < cbar]) column.upper.number<-length(upper.limits[upper.limits < cbar]) if ( column.lower.number > 0 ) { kappal1<-kappas[column.lower.number] kappal2<-kappas[column.lower.number+1] kappa.limits[1]<-kappal1+(kappal2-kappal1)* (cbar-lower.limits[column.lower.number])/ (lower.limits[column.lower.number+1]-lower.limits[column.lower.number]) } if ( column.upper.number > 0 ) { kappau1<-kappas[column.upper.number] kappau2<-kappas[column.upper.number+1] kappa.limits[2]<-kappau1+(kappau2-kappau1)* (cbar-upper.limits[column.upper.number])/ (upper.limits[column.upper.number+1]-upper.limits[column.upper.number]) } # return(kappa.limits) } "TABLE1" <- structure(c(NA, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 12, 12, 16, 16, 20, 20, 30, 30, 40, 40, 60, 60, 100, 100, 200, 200, 1e+06, 1e+06, 0, 0.522, -0.522, 0.476, -0.476, 0.441, -0.441, 0.412, -0.412, 0.388, -0.388, 0.368, -0.368, 0.336, -0.336, 0.291, -0.291, 0.26, -0.26, 0.212, -0.212, 0.184, -0.184, 0.15, -0.15, 0.116, -0.116, 0.082, -0.082, 0, 0, 0.5, 0.716, -0.278, 0.677, -0.231, 0.647, -0.194, 0.622, -0.165, 0.601, -0.14, 0.583, -0.12, 0.554, -0.087, 0.514, -0.042, 0.486, -0.011, 0.442, 0.036, 0.416, 0.064, 0.384, 0.097, 0.353, 0.13, 0.321, 0.163, 0.243, 0.243, 1, 0.84, 0.003, 0.81, 0.025, 0.787, 0.049, 0.767, 0.076, 0.75, 0.099, 0.736, 0.118, 0.713, 0.148, 0.679, 0.19, 0.656, 0.218, 0.619, 0.262, 0.597, 0.287, 0.57, 0.317, 0.542, 0.347, 0.515, 0.376, 0.446, 0.446, 1.5, 0.904, 0.183, 0.883, 0.224, 0.866, 0.254, 0.852, 0.277, 0.84, 0.3, 0.829, 0.32, 0.811, 0.346, 0.785, 0.378, 0.767, 0.402, 0.738, 0.439, 0.72, 0.461, 0.698, 0.487, 0.676, 0.512, 0.653, 0.537, 0.596, 0.596, 2, 0.933, 0.352, 0.919, 0.386, 0.907, 0.412, 0.897, 0.433, 0.888, 0.45, 0.88, 0.464, 0.867, 0.486, 0.848, 0.515, 0.834, 0.537, 0.811, 0.568, 0.797, 0.587, 0.78, 0.608, 0.762, 0.629, 0.744, 0.649, 0.698, 0.698, 2.5, 0.947, 0.48, 0.938, 0.508, 0.929, 0.529, 0.922, 0.546, 0.915, 0.56, 0.909, 0.572, 0.899, 0.59, 0.884, 0.616, 0.873, 0.632, 0.856, 0.658, 0.845, 0.674, 0.831, 0.691, 0.817, 0.709, 0.802, 0.726, 0.765, 0.765, 3, 0.956, 0.574, 0.949, 0.597, 0.942, 0.615, 0.936, 0.629, 0.931, 0.64, 0.927, 0.65, 0.919, 0.665, 0.907, 0.686, 0.898, 0.7, 0.884, 0.721, 0.875, 0.734, 0.864, 0.749, 0.853, 0.763, 0.841, 0.777, 0.81, 0.81, 3.5, 0.963, 0.643, 0.957, 0.662, 0.951, 0.677, 0.946, 0.688, 0.942, 0.698, 0.938, 0.706, 0.932, 0.719, 0.922, 0.737, 0.915, 0.749, 0.903, 0.766, 0.896, 0.777, 0.886, 0.79, 0.877, 0.802, 0.867, 0.814, 0.841, 0.841, 4, 0.968, 0.694, 0.963, 0.71, 0.958, 0.723, 0.954, 0.733, 0.95, 0.741, 0.947, 0.748, 0.941, 0.759, 0.933, 0.774, 0.927, 0.784, 0.916, 0.8, 0.91, 0.808, 0.902, 0.819, 0.894, 0.83, 0.885, 0.84, 0.864, 0.864, 4.5, 0.972, 0.733, 0.967, 0.747, 0.963, 0.758, 0.959, 0.766, 0.956, 0.773, 0.953, 0.779, 0.948, 0.789, 0.941, 0.802, 0.935, 0.811, 0.927, 0.825, 0.921, 0.832, 0.914, 0.842, 0.907, 0.851, 0.9, 0.86, 0.88, 0.88, 5, 0.976, 0.762, 0.971, 0.775, 0.967, 0.784, 0.964, 0.792, 0.961, 0.798, 0.958, 0.804, 0.954, 0.812, 0.947, 0.824, 0.942, 0.832, 0.935, 0.844, 0.93, 0.851, 0.923, 0.859, 0.917, 0.867, 0.91, 0.875, 0.893, 0.893), .Dim = as.integer(c(31, 12))) "TABLE2" <- structure(c(NA, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 12, 12, 16, 16, 20, 20, 30, 30, 40, 40, 60, 60, 100, 100, 200, 200, 1e+06, 1e+06, 0, NA, NA, NA, NA, 0.642, NA, 0.602, NA, 0.569, NA, 0.54, NA, 0.494, NA, 0.429, NA, 0.385, NA, 0.315, NA, 0.273, NA, 0.223, NA, 0.173, NA, 0.122, NA, 0, 0, 0.5, 0.815, 0.145, 0.764, 0.127, 0.724, 0.116, 0.691, 0.107, 0.665, 0.102, 0.642, 0.097, 0.605, 0.092, 0.554, 0.088, 0.519, 0.088, 0.466, 0.097, 0.434, 0.107, 0.397, 0.123, 0.361, 0.144, 0.326, 0.17, 0.243, 0.243, 1, 0.864, 0.197, 0.844, 0.194, 0.828, 0.195, 0.809, 0.199, 0.789, 0.204, 0.772, 0.209, 0.742, 0.22, 0.694, 0.24, 0.663, 0.256, 0.626, 0.285, 0.606, 0.303, 0.577, 0.327, 0.547, 0.353, 0.517, 0.379, 0.446, 0.446, 1.5, 0.937, 0.306, 0.915, 0.321, 0.896, 0.334, 0.879, 0.345, 0.865, 0.356, 0.852, 0.365, 0.831, 0.382, 0.801, 0.406, 0.78, 0.424, 0.747, 0.453, 0.727, 0.471, 0.703, 0.493, 0.679, 0.516, 0.654, 0.539, 0.596, 0.596, 2, 0.956, 0.432, 0.941, 0.45, 0.928, 0.465, 0.917, 0.478, 0.906, 0.489, 0.897, 0.498, 0.882, 0.514, 0.859, 0.537, 0.843, 0.553, 0.818, 0.578, 0.802, 0.594, 0.783, 0.613, 0.764, 0.632, 0.745, 0.651, 0.698, 0.698, 2.5, 0.965, 0.537, 0.955, 0.571, 0.945, 0.6, 0.937, 0.601, 0.929, 0.599, 0.922, 0.601, 0.911, 0.612, 0.894, 0.632, 0.881, 0.645, 0.861, 0.667, 0.849, 0.68, 0.834, 0.695, 0.819, 0.711, 0.803, 0.727, 0.765, 0.765, 3, 0.972, 0.625, 0.963, 0.638, 0.956, 0.649, 0.949, 0.657, 0.943, 0.665, 0.937, 0.679, 0.928, 0.696, 0.915, 0.703, 0.905, 0.711, 0.888, 0.728, 0.879, 0.739, 0.866, 0.752, 0.854, 0.765, 0.841, 0.778, 0.81, 0.81, 3.5, 0.976, 0.688, 0.969, 0.698, 0.963, 0.706, 0.957, 0.714, 0.952, 0.72, 0.947, 0.726, 0.94, 0.735, 0.928, 0.748, 0.92, 0.759, 0.907, 0.772, 0.898, 0.782, 0.888, 0.792, 0.878, 0.803, 0.867, 0.814, 0.841, 0.841, 4, 0.98, 0.733, 0.973, 0.742, 0.968, 0.749, 0.963, 0.755, 0.959, 0.76, 0.955, 0.765, 0.948, 0.773, 0.938, 0.783, 0.931, 0.791, 0.92, 0.805, 0.913, 0.812, 0.904, 0.822, 0.895, 0.831, 0.886, 0.841, 0.864, 0.864, 4.5, 0.983, 0.767, 0.977, 0.775, 0.972, 0.781, 0.967, 0.786, 0.964, 0.79, 0.96, 0.794, 0.954, 0.801, 0.946, 0.811, 0.94, 0.817, 0.93, 0.829, 0.923, 0.836, 0.916, 0.844, 0.908, 0.852, 0.9, 0.86, 0.88, 0.88, 5, 0.985, 0.794, 0.979, 0.8, 0.975, 0.805, 0.971, 0.81, 0.968, 0.814, 0.965, 0.817, 0.959, 0.823, 0.952, 0.832, 0.946, 0.838, 0.937, 0.848, 0.932, 0.854, 0.925, 0.861, 0.918, 0.868, 0.911, 0.876, 0.893, 0.893 ), .Dim = as.integer(c(31, 12))) "APPEND2.3" <- structure(c(0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.6, 0.61, 0.62, 0.63, 0.64, 0.65, 0.66, 0.67, 0.68, 0.69, 0.7, 0.71, 0.72, 0.73, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79, 0.8, 1.01022, 1.03889, 1.0681, 1.09788, 1.12828, 1.15932, 1.19105, 1.2235, 1.25672, 1.29077, 1.3257, 1.36156, 1.39842, 1.43635, 1.47543, 1.51574, 1.55738, 1.60044, 1.64506, 1.69134, 1.73945, 1.78953, 1.84177, 1.89637, 1.95357, 2.01363, 2.07685, 2.14359, 2.21425, 2.2893, 2.3693, 2.4549, 2.54686, 2.64613, 2.75382, 2.87129), .Dim = as.integer(c(36, 2))) "APPEND2.6" <- structure(c(0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 3, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 4, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 5, 5.2, 5.4, 5.6, 5.8, 6, 6.2, 6.4, 6.6, 6.8, 7, 7.2, 7.4, 7.6, 7.8, 8, 8.2, 8.4, 8.6, 8.8, 9, 9.2, 9.4, 9.6, 9.8, 10, 10.5, 0.6, 2, 2.2, 2.5, 2.8, 3.2, 3.6, 4.1, 4.7, 5.4, 6.2, 7.2, 8.3, 9.6, 11.2, 13.1, 15.3, 17.9, 20.8, 24.2, 28, 32.1, 36.6, 41.2, 46, 50.7, 55.2, 59.6, 63.6, 67.4, 70.9, 74.2, 77.1, 79.9, 82.4, 84.8, 86.9, 89, 90.8, 92.6, 94.3, 95.8, 97.3, 98.7, 100, 101.2, 102.4, 103.5, 104.6, 105.6, 106.6, 108.4, 110.1, 111.7, 113.2, 114.5, 115.8, 117, 118.2, 119.2, 120.3, 121.2, 122.2, 123, 123.9, 124.7, 125.5, 126.2, 126.9, 127.6, 128.2, 128.9, 129, 130.1, 130.6, 131.2, 132.5, 0.1, 0.2, 0.2, 0.2, 0.3, 0.3, 0.4, 0.4, 0.5, 0.5, 0.6, 0.7, 0.8, 1, 1.1, 1.3, 1.6, 1.8, 2.2, 2.6, 3, 3.6, 4.3, 5.1, 6, 7.2, 8.5, 10.1, 12.1, 14.3, 16.9, 19.9, 23.2, 26.9, 30.8, 34.9, 39.1, 43.2, 47.1, 50.9, 54.5, 57.8, 60.9, 63.7, 66.3, 68.8, 71.1, 73.2, 75.2, 77.1, 78.8, 82, 84.9, 87.5, 89.8, 92, 94, 95.8, 97.6, 99.2, 100.7, 102.1, 103.5, 104.7, 105.9, 107.1, 108.2, 109.2, 110.2, 111.2, 112.1, 113, 113.8, 114.7, 115.4, 116.2, 118), .Dim = as.integer(c(77, 3))) "APPEND2.6.read" <- function(k.prime){ # # Copyright P.R. Fisher. # Microbiology Dept., La Trobe University, VIC 3086, AUSTRALIA. # Email: fisher@lumi.latrobe.edu.au # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License version 2 # as published by the Free Software Foundation. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY FOR A PARTICULAR PURPOSE. See the GNU General Public # License for more details. # if(k.prime > 10)return(delta) row1<-length(APPEND2.6[APPEND2.6[,1] <= k.prime,1]) row2<-row1+1 kappa1<-APPEND2.6[row1,1] kappa2<-APPEND2.6[row2,1] delta1<-APPEND2.6[row1,2] delta2<-APPEND2.6[row2,2] delta<-delta1+(delta2-delta1)*(k.prime-kappa1)/(kappa2-kappa1) return(delta) } "APPEND2.7.read" <- function(n,rbar){ # # Copyright P.R. Fisher. # Microbiology Dept., La Trobe University, VIC 3086, AUSTRALIA. # Email: fisher@lumi.latrobe.edu.au # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License version 2 # as published by the Free Software Foundation. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY FOR A PARTICULAR PURPOSE. See the GNU General Public # License for more details. # # rbar<-round(rbar,digits=3) # # if ( n < 8 ) return(delta) # else if ( n <= 10 ) { delta1<-mean(APPEND2.71[APPEND2.71[,1] == rbar,2]) delta2<-mean(APPEND2.72[APPEND2.72[,1] == rbar,2]) delta<-delta1+(delta2-delta1)*(n-8)/2 } else if ( n <= 12 ) { delta1<-mean(APPEND2.72[APPEND2.72[,1] == rbar,2]) delta2<-mean(APPEND2.73[APPEND2.73[,1] == rbar,2]) delta<-delta1+(delta2-delta1)*(n-10)/2 } else if ( n <= 14 ) { delta1<-mean(APPEND2.73[APPEND2.73[,1] == rbar,2]) delta2<-mean(APPEND2.74[APPEND2.74[,1] == rbar,2]) delta<-delta1+(delta2-delta1)*(n-12)/2 } else if ( n <= 16 ) { delta1<-mean(APPEND2.74[APPEND2.74[,1] == rbar,2]) delta2<-mean(APPEND2.75[APPEND2.75[,1] == rbar,2]) delta<-delta1+(delta2-delta1)*(n-14)/2 } else if ( n <= 18 ) { delta1<-mean(APPEND2.75[APPEND2.75[,1] == rbar,2]) delta2<-mean(APPEND2.76[APPEND2.76[,1] == rbar,2]) delta<-delta1+(delta2-delta1)*(n-16)/2 } else if ( n <= 20 ) { delta1<-mean(APPEND2.76[APPEND2.76[,1] == rbar,2]) delta2<-mean(APPEND2.77[APPEND2.77[,1] == rbar,2]) delta<-delta1+(delta2-delta1)*(n-18)/2 } else { delta1<-mean(APPEND2.77[APPEND2.77[,1] == rbar,2]) delta2<-mean(APPEND2.78[APPEND2.78[,1] == rbar,2]) delta<-delta1+(delta2-delta1)*(n-20)/10 } return(delta) } "APPEND2.71" <- structure(c(1, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.998, 0.998, 0.999, 0.999, 0.999, 0.998, 0.998, 0.997, 0.997, 0.997, 0.997, 0.997, 0.997, 0.996, 0.996, 0.996, 0.996, 0.996, 0.995, 0.995, 0.995, 0.994, 0.994, 0.994, 0.993, 0.993, 0.993, 0.992, 0.992, 0.993, 0.992, 0.992, 0.992, 0.991, 0.991, 0.99, 0.99, 0.989, 0.989, 0.989, 0.988, 0.988, 0.988, 0.988, 0.988, 0.987, 0.987, 0.986, 0.986, 0.986, 0.985, 0.985, 0.985, 0.985, 0.984, 0.984, 0.984, 0.983, 0.983, 0.983, 0.982, 0.981, 0.982, 0.981, 0.981, 0.981, 0.981, 0.981, 0.98, 0.98, 0.979, 0.979, 0.979, 0.978, 0.978, 0.977, 0.976, 0.976, 0.976, 0.975, 0.975, 0.975, 0.974, 0.973, 0.972, 0.972, 0.972, 0.971, 0.971, 0.97, 0.97, 0.97, 0.969, 0.969, 0.968, 0.967, 0.967, 0.966, 0.966, 0.965, 0.964, 0.964, 0.963, 0.962, 0.961, 0.96, 0.96, 0.959, 0.958, 0.957, 0.957, 0.956, 0.956, 0.955, 0.955, 0.954, 0.953, 0.952, 0.952, 0.951, 0.95, 0.949, 0.948, 0.947, 0.947, 0.946, 0.944, 0.944, 0.943, 0.942, 0.941, 0.94, 0.939, 0.937, 0.936, 0.935, 0.933, 0.933, 0.931, 0.93, 0.928, 0.927, 0.926, 0.924, 0.923, 0.922, 0.921, 0.919, 0.918, 0.916, 0.915, 0.913, 0.912, 0.911, 0.909, 0.908, 0.906, 0.905, 0.904, 0.902, 0.902, 0.901, 0.899, 0.898, 0.897, 0.896, 0.894, 0.893, 0.891, 0.889, 0.888, 0.886, 0.885, 0.884, 0.882, 0.881, 0.879, 0.877, 0.876, 0.874, 0.872, 0.871, 0.869, 0.868, 0.866, 0.865, 0.863, 0.862, 0.861, 0.859, 0.857, 0.856, 0.854, 0.852, 0.85, 0.849, 0.847, 0.846, 0.844, 0.842, 0.841, 0.839, 0.838, 0.836, 0.835, 0.833, 0.832, 0.83, 0.829, 0.827, 0.826, 0.824, 0.824, 0.822, 0.821, 0.819, 0.818, 0.816, 0.815, 0.814, 0.812, 0.811, 0.809, 0.808, 0.806, 0.805, 0.804, 0.802, 0.801, 0.8, 0.799, 0.798, 0.797, 0.795, 0.794, 0.793, 0.791, 0.79, 0.789, 0.787, 0.784, 0.783, 0.782, 0.781, 0.78, 0.778, 0.777, 0.775, 0.775, 0.774, 0.773, 0.772, 0.77, 0.769, 0.768, 0.767, 0.765, 0.764, 0.763, 0.762, 0.761, 0.76, 0.759, 0.757, 0.756, 0.755, 0.753, 0.752, 0.75, 0.75, 0.749, 0.747, 0.747, 0.746, 0.744, 0.743, 0.742, 0.741, 0.74, 0.738, 0.737, 0.736, 0.735, 0.734, 0.732, 0.731, 0.73, 0.729, 0.728, 0.726, 0.725, 0.724, 0.722, 0.721, 0.719, 0.719, 0.717, 0.716, 0.715, 0.714, 0.713, 0.712, 0.711, 0.711, 0.709, 0.708, 0.707, 0.705, 0.704, 0.703, 0.702, 0.701, 0.699, 0.699, 0.698, 0.697, 0.696, 0.695, 0.695, 0.694, 0.693, 0.692, 0.691, 0.69, 0.69, 0.689, 0.689, 0.688, 0.687, 0.685, 0.685, 0.685, 0.684, 0.683, 0.682, 0.682, 0.681, 0.68, 0.679, 0.678, 0.677, 0.676, 0.676, 0.675, 0.674, 0.674, 0.673, 0.672, 0.672, 0.671, 0.671, 0.67, 0.67, 0.669, 0.668, 0.667, 0.667, 0.666, 0.666, 0.666, 0.665, 0.665, 0.664, 0.663, 0.663, 0.663, 0.662, 0.661, 0.661, 0.66, 0.66, 0.659, 0.659, 0.658, 0.658, 0.657, 0.657, 0.657, 0.656, 0.656, 0.655, 0.655, 0.654, 0.654, 0.654, 0.653, 0.653, 0.653, 0.652, 0.653, 0.652, 0.652, 0.651, 0.65, 0.65, 0.649, 0.649, 0.649, 0.649, 0.649, 0.648, 0.647, 0.648, 0.647, 0.647, 0.647, 0.647, 0.646, 0.646, 0.646, 0.646, 0.645, 0.645, 0.645, 0.645, 0.645, 0.644, 0.644, 0.643, 0.643, 0.643, 0.643, 0.643, 0.643, 0.642, 0.642, 0.642, 0.641, 0.641, 0.641, 0.641, 0.641, 0.641, 0.641, 0.64, 0.64, 0.64, 0.64, 0.639, 0.639, 0.639, 0.639, 0.639, 0.639, 0.639, 0.638, 0.4, 0.8, 1, 1.2, 1.4, 1.6, 1.8, 2, 2.2, 2.4, 2.6, 2.8, 3, 3.2, 3.4, 3.6, 3.8, 4, 4.2, 4.4, 4.6, 4.8, 5, 5.2, 5.4, 5.6, 5.8, 6, 6.2, 6.4, 6.6, 6.8, 7, 7.2, 7.4, 7.6, 8, 8.2, 8.4, 8.6, 8.8, 9, 9.2, 9.4, 9.6, 9.8, 10, 10.2, 10.4, 10.6, 10.8, 11, 11.2, 11.4, 11.6, 11.8, 12, 12.2, 12.4, 12.6, 12.8, 13, 13.2, 13.4, 13.6, 13.8, 14, 14.2, 14.4, 14.6, 14.8, 15, 15.2, 15.4, 15.7, 15.9, 16.1, 16.3, 16.5, 16.7, 17, 17.2, 17.4, 17.6, 17.8, 18, 18.2, 18.4, 18.6, 18.8, 19, 19.2, 19.4, 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51.9, 52.1, 52.3, 52.5, 52.6, 52.8, 53, 53.2, 53.4, 53.6, 53.8, 53.9, 54.1, 54.3, 54.5, 54.7, 54.8, 55, 55.2, 55.4, 55.6, 55.8, 56, 56.2, 56.4, 56.6, 56.8, 57, 57.2, 57.4, 57.6, 57.8, 58, 58.2, 58.4, 58.6, 58.8, 59, 59.2, 59.4, 59.5, 59.7, 59.8, 60, 60.1, 60.3, 60.5, 60.7, 60.9, 61.1, 61.3, 61.5, 61.6, 61.8, 62, 62.2, 62.4, 62.6, 62.8, 63, 63.1, 63.3, 63.5, 63.7, 63.9, 64.1, 64.3, 64.5, 64.7, 64.9, 65.1, 65.3, 65.5, 65.7, 65.9, 66.1, 66.3, 66.4, 66.6, 66.8, 67, 67.2, 67.4, 67.6, 67.8, 68, 68.2, 68.4, 68.6, 68.8, 69, 69.2, 69.4, 69.6, 69.8, 70, 70.2, 70.4, 70.6, 70.8, 71, 71.2, 71.6, 71.8, 72, 72.2, 72.4, 72.6, 72.8, 73, 73.2, 73.4, 73.6, 73.8, 74, 74.2, 74.5, 74.7, 74.9, 75.1, 75.3, 75.5, 75.7, 75.9, 76.1, 76.3, 76.5, 76.7, 76.9, 77.1, 77.3, 77.5, 77.7, 77.9, 78.1, 78.3, 78.5, 78.7, 78.9, 79.1, 79.3, 79.5, 79.7, 79.9, 80.1, 80.3, 80.5, 80.8, 81, 81.2, 81.4, 81.6, 81.8, 82, 82.2, 82.4, 82.6, 82.8, 83, 83.2, 83.4, 83.6, 83.8, 84, 84.2, 84.4, 84.6, 84.8, 85, 85.2, 85.4, 85.6, 85.8, 86, 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89.8, 90), .Dim = as.integer(c(466, 2))) "APPEND2.73" <- structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 0.999, 0.999, 0.999, 0.998, 0.998, 0.998, 0.998, 0.997, 0.997, 0.997, 0.996, 0.995, 0.995, 0.994, 0.994, 0.994, 0.993, 0.993, 0.992, 0.992, 0.991, 0.99, 0.99, 0.99, 0.989, 0.989, 0.989, 0.989, 0.988, 0.988, 0.987, 0.986, 0.986, 0.985, 0.985, 0.984, 0.984, 0.983, 0.983, 0.982, 0.982, 0.981, 0.981, 0.98, 0.979, 0.978, 0.978, 0.977, 0.977, 0.975, 0.975, 0.974, 0.973, 0.972, 0.971, 0.97, 0.969, 0.967, 0.967, 0.967, 0.966, 0.965, 0.964, 0.963, 0.962, 0.961, 0.959, 0.959, 0.957, 0.956, 0.956, 0.954, 0.953, 0.952, 0.95, 0.949, 0.948, 0.948, 0.947, 0.945, 0.944, 0.943, 0.942, 0.941, 0.94, 0.938, 0.938, 0.937, 0.935, 0.934, 0.933, 0.932, 0.93, 0.929, 0.928, 0.926, 0.925, 0.923, 0.923, 0.921, 0.92, 0.919, 0.917, 0.916, 0.914, 0.913, 0.912, 0.91, 0.909, 0.907, 0.905, 0.904, 0.902, 0.9, 0.899, 0.897, 0.896, 0.895, 0.893, 0.892, 0.89, 0.889, 0.887, 0.886, 0.885, 0.883, 0.881, 0.88, 0.878, 0.877, 0.875, 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26.4, 26.6, 26.7, 26.9, 27, 27.2, 27.4, 27.6, 27.6, 27.8, 28, 28.2, 28.4, 28.5, 28.7, 28.8, 29, 29.1, 29.2, 29.4, 29.9, 30.1, 30.2, 30.4, 30.5, 30.7, 30.8, 31, 31.1, 31.3, 31.5, 31.7, 31.9, 32, 32.2, 32.4, 32.6, 32.8, 32.9, 33.1, 33.3, 33.5, 33.7, 33.8, 34, 34.1, 34.3, 34.5, 34.6, 34.8, 35, 35.2, 35.3, 35.5, 35.6, 35.8, 35.9, 36.1, 36.3, 36.5, 36.7, 36.9, 37, 37.2, 37.3, 37.5, 37.7, 37.9, 38.1, 38.3, 38.5, 38.6, 38.7, 38.9, 39, 39.2, 39.4, 39.5, 39.7, 39.9, 40, 40.2, 40.4, 40.5, 40.7, 40.9, 41, 41.2, 41.3, 41.5, 41.6, 41.8, 41.9, 42.1, 42.2, 42.4, 42.6, 42.7, 42.9, 43.1, 43.2, 43.4, 43.6, 43.8, 43.9, 44.1, 44.2, 44.4, 44.6, 44.7, 44.9, 45.1, 45.2, 45.4, 45.5, 45.7, 45.9, 46.1, 46.2, 46.4, 46.6, 46.8, 46.9, 47.1, 47.3, 47.6, 47.7, 47.9, 48.1, 48.3, 48.5, 48.7, 48.9, 49.1, 49.3, 49.5, 49.6, 49.8, 49.9, 50.1, 50.3, 50.5, 50.7, 50.9, 51.1, 51.3, 51.5, 51.7, 51.9, 52.1, 52.2, 52.4, 52.6, 52.8, 53, 53.2, 53.4, 53.6, 53.8, 54, 54.2, 54.4, 54.6, 54.8, 55, 55.2, 55.4, 55.6, 55.7, 55.9, 56.1, 56.3, 56.5, 56.7, 57, 57.2, 57.4, 57.6, 57.8, 58, 58.2, 58.4, 58.6, 58.8, 59, 59.2, 59.4, 59.6, 59.8, 60, 60.2, 60.4, 60.6, 60.8, 61, 61.2, 61.4, 61.6, 61.8, 62, 62.2, 62.5, 62.6, 62.8, 63, 63.2, 63.4, 63.6, 63.8, 64, 64.2, 64.4, 64.6, 64.8, 65, 65.2, 65.4, 65.6, 65.8, 66, 66.2, 66.4, 66.6, 66.8, 67, 67.2, 67.4, 67.6, 67.8, 68, 68.2, 68.4, 68.6, 68.8, 69, 69.2, 69.4, 69.6, 69.8, 70, 70.2, 70.4, 70.6, 70.8, 71, 71.2, 71.4, 71.7, 71.9, 72.1, 72.3, 72.5, 72.7, 72.9, 73.1, 73.3, 73.5, 73.8, 74, 74.2, 74.4, 74.6, 74.8, 75, 75.2, 75.4, 75.6, 75.8, 76, 76.2, 76.4, 76.6, 76.8, 77, 77.2, 77.4, 77.6, 77.8, 78, 78.2, 78.4, 78.6, 78.8, 79, 79.3, 79.5, 79.7, 79.9, 80.1, 80.3, 80.5, 80.7, 80.9, 81.1, 81.3, 81.5, 81.7, 81.9, 82.1, 82.3, 82.5, 82.7, 83, 83.2, 83.4, 83.6, 83.8, 84, 84.2, 84.5, 84.7, 84.9, 85.1, 85.3, 85.5, 85.7, 85.9, 86.1, 86.3, 86.5, 86.7, 86.9, 87.1, 87.3, 87.5, 87.7, 88, 88.2, 88.4, 88.6, 88.8, 89.2, 89.4, 89.6, 89.8, 90), .Dim = as.integer(c(471, 2))) "APPEND2.74" <- 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24.6, 24.8, 25, 25, 25.2, 25.3, 25.5, 25.6, 25.8, 26, 26.2, 26.3, 26.5, 26.7, 26.8, 27, 27.1, 27.3, 27.5, 27.6, 27.8, 27.9, 28.1, 28.2, 28.4, 28.6, 28.7, 28.9, 29, 29.2, 29.3, 29.5, 29.7, 29.9, 30, 30.2, 30.3, 30.5, 30.6, 30.7, 30.9, 31.1, 31.2, 31.4, 31.6, 31.8, 31.9, 32.1, 32.2, 32.4, 32.6, 32.6, 32.8, 32.9, 33.1, 33.2, 33.4, 33.5, 33.7, 33.9, 34.1, 34.2, 34.4, 34.5, 34.6, 34.8, 35, 35.1, 35.3, 35.5, 35.6, 35.8, 35.9, 36, 36.2, 36.3, 36.5, 36.6, 36.8, 37, 37.2, 37.3, 37.5, 37.6, 37.8, 37.9, 38, 38.2, 38.2, 38.4, 38.5, 38.7, 38.8, 38.9, 39.1, 39.1, 39.3, 39.4, 39.6, 39.7, 39.9, 40.1, 40.3, 40.5, 40.6, 40.8, 41, 41.2, 41.3, 41.5, 41.6, 41.8, 41.9, 42.1, 42.3, 42.5, 42.7, 42.9, 43.1, 43.3, 43.5, 43.6, 43.7, 43.9, 44.1, 44.3, 44.5, 44.7, 44.9, 45.1, 45.2, 45.4, 45.5, 45.7, 45.9, 46.1, 46.3, 46.4, 46.6, 46.8, 47, 47.2, 47.3, 47.5, 47.7, 47.8, 48, 48.2, 48.4, 48.6, 48.8, 48.9, 49.1, 49.3, 49.5, 49.6, 49.8, 50, 50.1, 50.4, 50.7, 50.9, 51.1, 51.3, 51.5, 51.9, 52.1, 52.3, 52.5, 52.7, 52.9, 53.1, 53.3, 53.4, 53.6, 53.8, 54, 54.2, 54.4, 54.6, 54.8, 55, 55.1, 55.3, 55.4, 55.6, 55.9, 56.1, 56.3, 56.5, 56.7, 56.9, 57.1, 57.3, 57.5, 57.7, 57.9, 58.1, 58.3, 58.5, 58.7, 58.9, 59, 59.2, 59.4, 59.6, 59.8, 60, 60.2, 60.4, 60.6, 60.8, 61, 61.2, 61.4, 61.6, 61.8, 62, 62.2, 62.4, 62.6, 62.8, 63, 63.2, 63.4, 63.6, 63.8, 64.1, 64.3, 64.6, 64.8, 65, 65.2, 65.4, 65.6, 65.8, 66, 66.2, 66.4, 66.6, 66.8, 67, 67.2, 67.4, 67.6, 67.8, 68, 68.2, 68.4, 68.6, 68.8, 69, 69.2, 69.4, 69.6, 69.8, 70, 70.2, 70.4, 70.7, 70.9, 71.1, 71.3, 71.5, 71.7, 71.9, 72.1, 72.3, 72.5, 72.7, 72.9, 73.1, 73.3, 73.5, 73.7, 73.9, 74.1, 74.3, 74.5, 74.7, 74.9, 75.2, 75.4, 75.6, 75.8, 76, 76.2, 76.4, 76.6, 76.8, 77.1, 77.3, 77.5, 77.7, 77.9, 78.1, 78.3, 78.5, 78.7, 78.9, 79.1, 79.3, 79.5, 79.7, 79.9, 80.1, 80.3, 80.5, 80.7, 80.9, 81.1, 81.3, 81.9, 82.1, 82.3, 82.5, 82.7, 82.9, 83.2, 83.4, 83.6, 83.8, 84, 84.2, 84.4, 84.6, 84.8, 85, 85.2, 85.4, 85.6, 85.8, 86, 86.2, 86.4, 86.6, 86.8, 87, 87.2, 87.4, 87.6, 87.8, 88, 88.2, 88.4, 88.6, 88.8, 89, 89.2, 89.4, 89.6, 89.8, 90), .Dim = as.integer(c(481, 2))) "APPEND2.75" <- structure(c(1, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.998, 0.998, 0.998, 0.998, 0.997, 0.997, 0.996, 0.996, 0.996, 0.996, 0.995, 0.995, 0.994, 0.993, 0.993, 0.992, 0.991, 0.991, 0.99, 0.989, 0.988, 0.988, 0.987, 0.986, 0.986, 0.984, 0.984, 0.983, 0.981, 0.98, 0.98, 0.979, 0.978, 0.978, 0.976, 0.976, 0.974, 0.974, 0.973, 0.972, 0.971, 0.97, 0.969, 0.968, 0.967, 0.966, 0.965, 0.964, 0.963, 0.961, 0.961, 0.96, 0.958, 0.957, 0.956, 0.955, 0.953, 0.952, 0.951, 0.95, 0.949, 0.948, 0.947, 0.946, 0.944, 0.944, 0.942, 0.941, 0.94, 0.939, 0.937, 0.935, 0.934, 0.933, 0.931, 0.93, 0.929, 0.927, 0.926, 0.924, 0.923, 0.921, 0.92, 0.918, 0.917, 0.915, 0.913, 0.912, 0.91, 0.908, 0.907, 0.905, 0.903, 0.901, 0.9, 0.898, 0.896, 0.895, 0.893, 0.891, 0.889, 0.888, 0.886, 0.885, 0.883, 0.882, 0.88, 0.878, 0.876, 0.875, 0.873, 0.872, 0.869, 0.867, 0.865, 0.864, 0.862, 0.86, 0.858, 0.857, 0.855, 0.853, 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18.5, 18.7, 18.9, 19.1, 19.3, 19.5, 19.7, 19.9, 20.1, 20.2, 20.3, 20.5, 20.6, 20.8, 20.9, 21.1, 21.2, 21.4, 21.4, 21.6, 21.7, 21.9, 22, 22.2, 22.3, 22.5, 22.7, 22.9, 23, 23.2, 23.4, 23.5, 23.6, 23.8, 23.9, 24.1, 24.2, 24.3, 24.4, 24.6, 24.7, 24.9, 25, 25.2, 25.3, 25.4, 25.6, 25.8, 26, 26.2, 26.3, 26.5, 26.6, 26.7, 26.9, 27.1, 27.2, 27.3, 27.4, 27.5, 27.7, 27.8, 28, 28.1, 28.2, 28.4, 28.5, 28.7, 28.8, 28.9, 29.1, 29.2, 29.4, 29.5, 29.7, 29.8, 29.9, 30.1, 30.3, 30.4, 30.5, 30.7, 30.8, 30.9, 31.1, 31.2, 31.4, 31.5, 31.6, 31.8, 31.9, 32, 32.2, 32.3, 32.6, 32.8, 32.9, 33.1, 33.2, 33.4, 33.6, 33.7, 33.8, 34, 34, 34.1, 34.3, 34.4, 34.6, 34.7, 34.8, 35, 35.1, 35.3, 35.4, 35.6, 35.7, 35.8, 36, 36.1, 36.3, 36.5, 36.7, 36.8, 36.9, 37.1, 37.2, 37.4, 37.6, 37.7, 37.9, 38, 38.2, 38.3, 38.5, 38.7, 38.9, 39, 39.2, 39.3, 39.5, 39.7, 39.9, 40, 40.2, 40.4, 40.6, 40.7, 40.9, 41.1, 41.3, 41.4, 41.6, 41.7, 41.9, 42.1, 42.3, 42.5, 42.6, 42.7, 42.9, 43, 43.2, 43.4, 43.6, 43.8, 44, 44.1, 44.3, 44.5, 44.6, 44.8, 45, 45.2, 45.4, 45.6, 45.8, 46, 46.2, 46.3, 46.5, 46.7, 46.9, 47.1, 47.2, 47.4, 47.6, 47.8, 48, 48.1, 48.3, 48.5, 48.7, 48.9, 49, 49.2, 49.4, 49.6, 49.8, 50, 50.2, 50.4, 50.6, 50.8, 51, 51.2, 51.4, 51.5, 51.7, 51.9, 52.1, 52.3, 52.5, 52.7, 52.9, 53.1, 53.3, 53.5, 53.7, 53.9, 54.1, 54.4, 54.6, 54.8, 55, 55.2, 55.4, 55.6, 55.8, 56, 56.2, 56.4, 56.6, 56.8, 57, 57.2, 57.4, 57.6, 57.8, 58, 58.2, 58.4, 58.6, 58.8, 59, 59.2, 59.4, 59.6, 59.8, 60, 60.2, 60.4, 60.6, 60.8, 61, 61.2, 61.4, 61.6, 61.8, 62, 62.2, 62.4, 62.6, 62.8, 63, 63.2, 63.4, 63.6, 63.8, 64, 64.2, 64.4, 64.6, 64.8, 64.9, 65.1, 65.3, 65.5, 65.7, 65.9, 66.1, 66.3, 66.5, 66.7, 66.9, 67.1, 67.3, 67.5, 67.7, 67.9, 68.1, 68.3, 68.5, 68.7, 68.9, 69.2, 69.5, 70.1, 70.3, 70.4, 70.6, 70.8, 71, 71.2, 71.4, 71.6, 71.8, 72, 72.2, 72.4, 72.6, 72.8, 73, 73.2, 73.4, 73.6, 73.8, 74, 74.2, 74.4, 74.6, 74.8, 75, 75.2, 75.4, 75.6, 75.8, 76, 76.2, 76.4, 76.6, 76.8, 77, 77.2, 77.4, 77.6, 77.8, 78, 78.2, 78.4, 78.6, 78.8, 79, 79.2, 79.4, 79.6, 79.8, 80, 80.2, 80.4, 80.6, 80.8, 81, 81.2, 81.4, 81.6, 81.8, 82, 82.2, 82.4, 82.6, 82.8, 83, 83.2, 83.4, 83.6, 83.8, 84, 84.2, 84.4, 84.6, 84.8, 85, 85.2, 85.4, 85.6, 85.8, 86, 86.2, 86.4, 86.6, 86.8, 87, 87.2, 87.4, 87.6, 87.8, 88, 88.2, 88.4, 88.6, 88.8, 89, 89.2, 89.4, 89.6, 89.8, 90), .Dim = as.integer(c(492, 2))) "APPEND2.76" <- structure(c(1, 1, 1, 1, 1, 1, 0.999, 0.999, 0.999, 0.998, 0.998, 0.998, 0.998, 0.997, 0.996, 0.996, 0.995, 0.994, 0.994, 0.993, 0.992, 0.991, 0.99, 0.99, 0.989, 0.988, 0.987, 0.987, 0.986, 0.985, 0.984, 0.984, 0.983, 0.982, 0.981, 0.981, 0.98, 0.979, 0.978, 0.977, 0.976, 0.976, 0.974, 0.973, 0.972, 0.971, 0.97, 0.969, 0.968, 0.967, 0.965, 0.964, 0.963, 0.962, 0.961, 0.96, 0.958, 0.957, 0.955, 0.954, 0.953, 0.951, 0.95, 0.949, 0.948, 0.946, 0.945, 0.944, 0.942, 0.94, 0.939, 0.938, 0.936, 0.935, 0.933, 0.932, 0.931, 0.929, 0.928, 0.926, 0.924, 0.922, 0.921, 0.919, 0.918, 0.916, 0.914, 0.913, 0.911, 0.91, 0.908, 0.907, 0.905, 0.904, 0.902, 0.901, 0.899, 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2))) "APPEND2.78" <- structure(c(1, 0.999, 0.999, 0.998, 0.998, 0.997, 0.997, 0.996, 0.995, 0.994, 0.993, 0.992, 0.991, 0.99, 0.989, 0.988, 0.987, 0.986, 0.985, 0.984, 0.983, 0.983, 0.981, 0.98, 0.98, 0.979, 0.977, 0.977, 0.976, 0.974, 0.973, 0.972, 0.971, 0.97, 0.968, 0.968, 0.966, 0.965, 0.964, 0.962, 0.96, 0.959, 0.957, 0.955, 0.953, 0.951, 0.949, 0.947, 0.945, 0.944, 0.942, 0.94, 0.939, 0.937, 0.936, 0.934, 0.932, 0.93, 0.929, 0.927, 0.925, 0.923, 0.922, 0.92, 0.918, 0.917, 0.915, 0.913, 0.911, 0.909, 0.907, 0.905, 0.903, 0.901, 0.899, 0.897, 0.895, 0.893, 0.891, 0.889, 0.887, 0.886, 0.884, 0.882, 0.88, 0.878, 0.876, 0.874, 0.872, 0.87, 0.868, 0.866, 0.864, 0.862, 0.86, 0.858, 0.856, 0.854, 0.852, 0.85, 0.848, 0.846, 0.844, 0.842, 0.84, 0.838, 0.836, 0.834, 0.832, 0.831, 0.828, 0.826, 0.824, 0.822, 0.82, 0.819, 0.817, 0.815, 0.813, 0.81, 0.808, 0.806, 0.804, 0.802, 0.8, 0.798, 0.796, 0.794, 0.792, 0.79, 0.788, 0.786, 0.784, 0.782, 0.78, 0.779, 0.777, 0.775, 0.773, 0.771, 0.769, 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0.363, 0.363, 0.363, 0.363, 0.362, 0.361, 0.361, 0.36, 0.36, 0.36, 0.359, 0.359, 0.359, 0.358, 0.358, 0.358, 0.357, 0.356, 0.355, 0.355, 0.354, 0.354, 0.354, 0.354, 0.353, 0.353, 0.353, 0.353, 0.353, 0.353, 0.352, 0.352, 0.351, 0.351, 0.351, 0.351, 0.351, 0.35, 0.35, 0.35, 0.349, 0.349, 0.349, 0.348, 0.349, 0.349, 0.348, 0.349, 0.349, 0.348, 0.349, 0.348, 0.348, 0.348, 0.348, 0.347, 0.347, 0.347, 0.347, 0.346, 0.346, 0.346, 0.346, 0.346, 0.346, 0.346, 0.345, 0.345, 0.345, 0.345, 0.345, 0.345, 0.345, 0.345, 0.345, 0.345, 0.344, 0.344, 0.344, 0.344, 0.344, 0.344, 0.344, 0.344, 0.344, 0.344, 0.343, 0.343, 0.343, 0.343, 0.343, 0.343, 0.343, 0.343, 0.343, 0.343, 0.8, 1, 1.2, 1.4, 1.6, 1.8, 2, 2.2, 2.4, 2.6, 2.8, 3, 3.2, 3.4, 3.6, 3.8, 4, 4.2, 4.4, 4.6, 4.8, 5, 5, 5.2, 5.4, 5.6, 5.7, 5.9, 6.1, 6.3, 6.5, 6.7, 6.9, 7.1, 7.1, 7.3, 7.4, 7.6, 7.8, 8, 8.1, 8.3, 8.5, 8.7, 8.9, 9.1, 9.3, 9.5, 9.6, 9.8, 9.9, 10.1, 10.3, 10.3, 10.5, 10.6, 10.8, 10.9, 11.1, 11.2, 11.3, 11.5, 11.7, 11.8, 11.9, 12.1, 12.2, 12.4, 12.5, 12.7, 12.8, 12.9, 13, 13.2, 13.3, 13.5, 13.6, 13.8, 13.9, 14, 14.1, 14.3, 14.4, 14.5, 14.7, 14.8, 14.9, 15, 15.2, 15.3, 15.4, 15.5, 15.6, 15.7, 15.9, 16, 16.1, 16.2, 16.3, 16.5, 16.6, 16.7, 16.9, 17, 17.1, 17.2, 17.3, 17.4, 17.5, 17.7, 17.8, 18, 18.1, 18.2, 18.3, 18.5, 18.6, 18.7, 18.8, 19, 19.1, 19.3, 19.3, 19.5, 19.6, 19.7, 19.8, 19.9, 20.1, 20.2, 20.3, 20.4, 20.6, 20.7, 20.7, 20.9, 21, 21.1, 21.2, 21.3, 21.5, 21.6, 21.7, 21.8, 22, 22.1, 22.2, 22.4, 22.5, 22.5, 22.6, 22.7, 22.8, 22.9, 23, 23.1, 23.2, 23.4, 23.4, 23.5, 23.7, 23.8, 24, 24.1, 24.2, 24.3, 24.4, 24.5, 24.6, 24.8, 24.8, 25, 25.1, 25.2, 25.3, 25.4, 25.6, 25.6, 25.7, 25.8, 26, 26.1, 26.2, 26.5, 26.6, 26.8, 27, 27.1, 27.2, 27.3, 27.4, 27.5, 27.7, 27.7, 27.8, 27.9, 28.1, 28.2, 28.3, 28.5, 28.6, 28.8, 28.9, 29.1, 29.2, 29.4, 29.5, 29.6, 29.7, 29.8, 30, 30.1, 30.2, 30.3, 30.5, 30.6, 30.8, 31, 31.1, 31.2, 31.4, 31.5, 31.6, 31.7, 31.8, 32, 32.1, 32.2, 32.4, 32.4, 32.6, 32.6, 32.8, 32.8, 33, 33.1, 33.2, 33.4, 33.5, 33.7, 33.8, 33.9, 34.1, 34.2, 34.4, 34.6, 34.8, 34.9, 35.1, 35.3, 35.4, 35.6, 35.7, 35.8, 36, 36.1, 36.3, 36.3, 36.5, 36.7, 36.8, 37, 37.2, 37.3, 37.5, 37.7, 37.8, 38, 38.2, 38.4, 38.5, 38.7, 38.8, 39, 39.1, 39.3, 39.4, 39.6, 39.7, 39.9, 40.1, 40.3, 40.5, 40.6, 40.8, 41, 41.2, 41.3, 41.5, 41.7, 41.9, 42.1, 42.3, 42.5, 42.7, 42.9, 43.1, 43.2, 43.4, 43.6, 43.8, 44, 44.2, 44.4, 44.5, 44.7, 44.9, 45.1, 45.3, 45.5, 45.7, 45.9, 46.1, 46.3, 46.5, 46.7, 46.9, 47.1, 47.3, 47.5, 47.7, 47.9, 48.1, 48.3, 48.5, 48.7, 48.9, 49.1, 49.3, 49.5, 49.7, 49.9, 50.1, 50.3, 50.5, 50.7, 50.9, 51, 51.2, 51.4, 51.6, 51.8, 52, 52.2, 52.4, 52.6, 52.8, 53, 53.2, 53.4, 53.6, 53.7, 53.9, 54.1, 54.3, 54.5, 54.7, 54.9, 55.1, 55.3, 55.5, 55.7, 55.9, 56.1, 56.3, 56.5, 56.7, 56.9, 57.1, 57.3, 57.5, 57.7, 57.9, 58.1, 58.3, 58.5, 58.7, 58.9, 59.1, 59.3, 59.5, 59.7, 59.9, 60.1, 60.3, 60.5, 60.7, 60.9, 61.1, 61.3, 61.5, 61.7, 61.9, 62.1, 62.3, 62.5, 62.7, 62.9, 63.1, 63.3, 63.5, 63.7, 63.9, 64.1, 64.3, 64.5, 64.7, 64.9, 65.1, 65.3, 65.5, 65.7, 65.9, 66.2, 66.4, 66.6, 66.8, 67, 67.2, 67.4, 67.6, 67.8, 68, 68.2, 68.4, 68.6, 68.8, 69, 69.3, 69.5, 69.7, 69.9, 70.1, 70.4, 70.6, 70.8, 71, 71.2, 71.4, 71.6, 71.8, 72, 72.2, 72.4, 72.7, 72.9, 73.1, 73.7, 73.9, 74.1, 74.3, 74.5, 74.7, 75, 75.3, 75.5, 75.7, 75.9, 76.1, 76.3, 76.5, 76.7, 76.9, 77.1, 77.3, 77.5, 77.7, 78, 78.3, 78.5, 78.7, 78.9, 79.1, 79.3, 79.5, 79.7, 80, 80.2, 80.4, 80.6, 80.8, 81, 81.2, 81.4, 81.6, 81.8, 82, 82.2, 82.4, 82.6, 82.8, 83, 83.3, 83.5, 83.7, 83.9, 84.1, 84.4, 84.6, 84.8, 85, 85.2, 85.4, 85.6, 85.8, 86, 86.2, 86.4, 86.6, 86.8, 87, 87.2, 87.4, 87.6, 87.8, 88, 88.2, 88.4, 88.6, 88.8, 89, 89.2, 89.4, 89.6, 89.8, 90), .Dim = as.integer(c(526, 2))) "phototaxis_demo" <- structure(c(1, 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, 69.1, 71.4, 70.2, 71.6, 72, 72.5, 72.2, 71.9, 70.3, 73.5, 69.5, 68.9, 70.1, 71.3, 68.5, 71, 71.1, 71.1, 71.3, 72, 72.7, 70.9, 73.2, 72.7, 72, 71.9, 72.3, 69.4, 70, 70.4, 71.9, 62.2, 71.3, 71.2, 71.6, 70.2, 70.3, 72, 70.3, 68.6, 70.6, 71.7, 72.4, 70.5, 71.1, 71.2, 68, 70.3, 65.7, 65.8, 66.9, 72.2, 72.4, 71.6, 72.3, 71.5, 69.5, 70.1, 72.2, 70.8, 71.2, 70.3, 71.5, 65.3, 64.5, 64.4, 63.7, 63.6, 62.6, 61.3, 62.2, 61.6, 61.8, 60.9, 60.3, 60.2, 55.2, 55.8, 56.8, 56.8, 57.7, 58, 58, 57.7, 57.8, 59.5, 58.4, 61.6, 60.9, 60.5, 60.1, 60.1, 60.6, 56.3, 58.1, 58.5, 57.3, 56.6, 56.8, 53, 56.1, 54.7, 54.3, 55.8, 50.2, 50.7, 52, 53, 53.7, 53.9, 49.8, 48.4, 49.3, 49.3, 49.2, 48.2, 50.9, 50.3, 52.3, 51.8, 52.5, 53.6, 52.6, 53, 52.1, 53.5, 91, 76.7, 88.7, 85.7, 77.1, 74.8, 81, 88.4, 92.2, 89.1, 91.9, 92.3, 98.1, 80.8, 73.3, 88.2, 90.7, 89.6, 97.4, 90.5, 77.2, 77.2, 76.8, 77.2, 80.5, 76.9, 83.3, 86.5, 88.1, 82.2, 83, 64.2, 76.5, 74.6, 76.1, 82.9, 95.9, 98.1, 93, 93.3, 94.8, 93.3, 90.7, 89.7, 84, 86.7, 96, 92.5, 79.7, 81, 75.7, 87.4, 85.1, 92.5, 93.5, 89.9, 88.6, 91.1, 91, 88.1, 83.6, 84.2, 84.3, 65.3, 64.6, 64.2, 64.3, 63, 62.7, 62.8, 62, 62, 61.3, 60.8, 60, 59.7, 52.8, 55.5, 54.9, 55.8, 57.1, 57.1, 58, 58.2, 57.8, 59.5, 59.3, 59.5, 61.9, 60.3, 61.1, 62.2, 62.4, 55.7, 58.5, 58, 57.6, 56.6, 56.9, 57.5, 54.7, 56.7, 55.2, 53.5, 54.5, 53.8, 53.7, 53.5, 54.2, 57.7, 48.3, 45.7, 45.1, 47.6, 47.7, 49, 48.7, 51.6, 52.3, 53.5, 52.5, 54.3, 55.5, 53.1, 52.2, 56.7), .Dim = as.integer(c(63, 5))) "bimodal_demo" <- structure(c(1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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0.9503082, 0.9875089, 0.9843338, 0.9922843, 0.9027334, 0.9921724, 0.9988778, 0.9802026, 0.994327, 0.9917338, 0.9906628, 0.9848231, 0.9842737, 0.991148, 0.9616098, 0.9798577, 0.9457795, 0.9946663, 0.9290458, 0.9747883, 0.945298, 0.9880403, 0.9280227, 0.986598, 0.9883315, 0.9624655, 0.9736748, 0.998254, 0.981724, 0.9395329, 0.9812735, 0.9563509, 0.9956744, 0.9184491, 0.9569777, 0.9614015, 0.9918642, 0.9576335, 0.9834852, 0.9487517, 0.9815919, 0.942859, 0.9821237, 0.9777274, 0.9702888, 0.998808, 0.987192, 0.985495, 0.9750822, 0.9618256, 0.9995254, 0.9868717, 0.9806897, -0.1389574, -0.0201768, 0.2903452, 0.2492035, -0.1625754, -0.06129321, 0.2809264, -0.06337033, -0.2572124, 0.2121976, 0.1679816, 0.05765284, -0.2054647, 0.2553332, -0.2655355, -0.09041881, 0.1443193, -0.0241984, -0.2839996, 0.2707846, 0.1970239, 0.166132, 0.2592, 0.284622, 0.3190978, -0.1382914, -0.2111237, -0.0621207, 0.08788233, 0.1913446, -0.1133171, 0.2938877, -0.3156774, 0.08591024, -0.1747777, 0.2104317, -0.1078679, 0.0441943, -0.1911965, -0.1609678, -0.1012619, 0.1458881, 0.1131667, 0.2072626, -0.257945, 0.1257734, -0.2809353, 0.3113108, 0.1575633, -0.1763152, -0.1239835, -0.4302004, 0.1248756, -0.04736116, -0.197997, -0.1063671, 0.1283127, -0.1363349, -0.1735609, 0.1766504, 0.1327615, -0.2744203, -0.1996969, 0.3248093, 0.1031456, -0.3699647, 0.2231318, -0.3262079, -0.1541956, -0.3725236, -0.1631692, 0.1523185, -0.271404, -0.2279416, 0.05906845, -0.1903101, -0.3424587, 0.1926194, 0.2922208, 0.09291133, -0.3955391, 0.2901615, -0.2751494, 0.1273004, -0.2879897, -0.1809883, -0.3160225, 0.1909907, 0.3331921, 0.1882368, 0.209879, 0.2419499, 0.04881291, -0.1595362, -0.1697049, -0.221844, 0.2736632, 0.03080508, -0.1615062, 0.1955702), .Dim = as.integer(c(100, 5))) write(file="bimodal_demo",t(bimodal_demo)) write(file="phototaxis_demo",t(phototaxis_demo)) rm(list=c("bimodal_demo","phototaxis_demo")) "DirStats.demo" <- function(){ # # Copyright P.R. Fisher. # Microbiology Dept., La Trobe University, VIC 3086, AUSTRALIA. # Email: fisher@lumi.latrobe.edu.au # # This program is free software; you can redistribute it and/or modify # it under the terms of the GNU General Public License version 2 # as published by the Free Software Foundation. # # This program is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY FOR A PARTICULAR PURPOSE. See the GNU General Public # License for more details. # acorn("phototaxis_demo") text(0,-0.25,"acorn(\"phototaxis_demo\")",adj=0.5) cat("Type a carriage return for next demonstration plot\n") readLines(n=1) bimstat("bimodal_demo",kappa1=21.68,ml=T,tracks=F,type="l") text(0,-0.25,"bimstat(\"bimodal_demo\",kappa1=21.68,ml=T,tracks=F,type=\"l\")",adj=0.5,cex=0.75) } cat("DirStats package installed\n\ Demonstration data files are: \"phototaxis_demo\" and \"bimodal_demo\"\n\ Type DirStats.demo\(\) for a demonstration\n")