R version 2.12.0 (2010-10-15)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: i486-pc-linux-gnu (32-bit)

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

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

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

> x <- c(61,81,87,87,136,147,168,185,137,125,64,45,35,-4,88,85,95,128,186,182,151,106,60,44,30,54,72,88,153,168,181,180,149,84,85,42,54,30,96,110,141,159,164,155,135,93,28,56,56,22,76,83,121,151,208,179,139,99,103,57,44,70,58,91,126,146,199,194,145,131,74,-3,7,10,34,94,105,151,162,175,128,115,62,11,-7,64,80,77,127,158,173,206,147,103,73,52,52,68,77,94,147,160,166,167,155,104,44,53,56,36,76,99,142,150,190,176,175,112,73,52,48,61,68,97,146,160,155,175,163,117,82,55,32,48,53,82,139,150,184,185,138,147,77,32,48,72,76,94,133,164,174,187,149,102,86,35,31,28,75,102,133,178,190,190,147,83,83,46,40,50,61,102,117,158,170,190,155,117,68,40,56,28,66,103,122,166,176,164,160,139,75,44,22,32,42,86,140,163,222,166,183,140,98,69,75,63,81,126,139,171,170,173,144,105,75,41,68,53,61,87,155,159,180,175,138,105,73,26,12,35,64,115,138,138,182,191,155,113,98,29)
> ylimmax = ''
> ylimmin = ''
> main = 'Robustness of Central Tendency'
> #'GNU S' R Code compiled by R2WASP v. 1.0.44 ()
> #Author: Prof. Dr. P. Wessa
> #To cite this work: AUTHOR(S), (YEAR), YOUR SOFTWARE TITLE (vNUMBER) in Free Statistics Software (v$_version), Office for Research Development and Education, URL http://www.wessa.net/rwasp_YOURPAGE.wasp/
> #Source of accompanying publication: Office for Research, Development, and Education
> #Technical description: Write here your technical program description (don't use hard returns!)
> geomean <- function(x) {
+ return(exp(mean(log(x))))
+ }
> harmean <- function(x) {
+ return(1/mean(1/x))
+ }
> quamean <- function(x) {
+ return(sqrt(mean(x*x)))
+ }
> winmean <- function(x) {
+ x <-sort(x[!is.na(x)])
+ n<-length(x)
+ denom <- 3
+ nodenom <- n/denom
+ if (nodenom>40) denom <- n/40
+ sqrtn = sqrt(n)
+ roundnodenom = floor(nodenom)
+ win <- array(NA,dim=c(roundnodenom,2))
+ for (j in 1:roundnodenom) {
+ win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
+ win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
+ }
+ return(win)
+ }
> trimean <- function(x) {
+ x <-sort(x[!is.na(x)])
+ n<-length(x)
+ denom <- 3
+ nodenom <- n/denom
+ if (nodenom>40) denom <- n/40
+ sqrtn = sqrt(n)
+ roundnodenom = floor(nodenom)
+ tri <- array(NA,dim=c(roundnodenom,2))
+ for (j in 1:roundnodenom) {
+ tri[j,1] <- mean(x,trim=j/n)
+ tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
+ }
+ return(tri)
+ }
> midrange <- function(x) {
+ return((max(x)+min(x))/2)
+ }
> q1 <- function(data,n,p,i,f) {
+ np <- n*p;
+ i <<- floor(np)
+ f <<- np - i
+ qvalue <- (1-f)*data[i] + f*data[i+1]
+ }
> q2 <- function(data,n,p,i,f) {
+ np <- (n+1)*p
+ i <<- floor(np)
+ f <<- np - i
+ qvalue <- (1-f)*data[i] + f*data[i+1]
+ }
> q3 <- function(data,n,p,i,f) {
+ np <- n*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- data[i]
+ } else {
+ qvalue <- data[i+1]
+ }
+ }
> q4 <- function(data,n,p,i,f) {
+ np <- n*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- (data[i]+data[i+1])/2
+ } else {
+ qvalue <- data[i+1]
+ }
+ }
> q5 <- function(data,n,p,i,f) {
+ np <- (n-1)*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- data[i+1]
+ } else {
+ qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
+ }
+ }
> q6 <- function(data,n,p,i,f) {
+ np <- n*p+0.5
+ i <<- floor(np)
+ f <<- np - i
+ qvalue <- data[i]
+ }
> q7 <- function(data,n,p,i,f) {
+ np <- (n+1)*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- data[i]
+ } else {
+ qvalue <- f*data[i] + (1-f)*data[i+1]
+ }
+ }
> q8 <- function(data,n,p,i,f) {
+ np <- (n+1)*p
+ i <<- floor(np)
+ f <<- np - i
+ if (f==0) {
+ qvalue <- data[i]
+ } else {
+ if (f == 0.5) {
+ qvalue <- (data[i]+data[i+1])/2
+ } else {
+ if (f < 0.5) {
+ qvalue <- data[i]
+ } else {
+ qvalue <- data[i+1]
+ }
+ }
+ }
+ }
> midmean <- function(x,def) {
+ x <-sort(x[!is.na(x)])
+ n<-length(x)
+ if (def==1) {
+ qvalue1 <- q1(x,n,0.25,i,f)
+ qvalue3 <- q1(x,n,0.75,i,f)
+ }
+ if (def==2) {
+ qvalue1 <- q2(x,n,0.25,i,f)
+ qvalue3 <- q2(x,n,0.75,i,f)
+ }
+ if (def==3) {
+ qvalue1 <- q3(x,n,0.25,i,f)
+ qvalue3 <- q3(x,n,0.75,i,f)
+ }
+ if (def==4) {
+ qvalue1 <- q4(x,n,0.25,i,f)
+ qvalue3 <- q4(x,n,0.75,i,f)
+ }
+ if (def==5) {
+ qvalue1 <- q5(x,n,0.25,i,f)
+ qvalue3 <- q5(x,n,0.75,i,f)
+ }
+ if (def==6) {
+ qvalue1 <- q6(x,n,0.25,i,f)
+ qvalue3 <- q6(x,n,0.75,i,f)
+ }
+ if (def==7) {
+ qvalue1 <- q7(x,n,0.25,i,f)
+ qvalue3 <- q7(x,n,0.75,i,f)
+ }
+ if (def==8) {
+ qvalue1 <- q8(x,n,0.25,i,f)
+ qvalue3 <- q8(x,n,0.75,i,f)
+ }
+ midm <- 0
+ myn <- 0
+ roundno4 <- round(n/4)
+ round3no4 <- round(3*n/4)
+ for (i in 1:n) {
+ if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
+ midm = midm + x[i]
+ myn = myn + 1
+ }
+ }
+ midm = midm / myn
+ return(midm)
+ }
> (arm <- mean(x))
[1] 106.3708
> sqrtn <- sqrt(length(x))
> (armse <- sd(x) / sqrtn)
[1] 3.427863
> (armose <- arm / armse)
[1] 31.03124
> (geo <- geomean(x))
[1] NaN
Warning message:
In log(x) : NaNs produced
> (har <- harmean(x))
[1] 93.68706
> (qua <- quamean(x))
[1] 118.8405
> (win <- winmean(x))
          [,1]     [,2]
 [1,] 106.3250 3.418407
 [2,] 106.3167 3.415232
 [3,] 106.3542 3.388843
 [4,] 106.3208 3.373491
 [5,] 106.2792 3.364322
 [6,] 106.2792 3.358751
 [7,] 106.5708 3.326101
 [8,] 106.5708 3.326101
 [9,] 106.7208 3.310470
[10,] 106.6792 3.289083
[11,] 106.6333 3.284424
[12,] 106.5833 3.279395
[13,] 106.6375 3.273993
[14,] 106.6375 3.262417
[15,] 106.5750 3.256248
[16,] 106.5750 3.243201
[17,] 106.6458 3.236330
[18,] 106.5708 3.229060
[19,] 106.4917 3.221463
[20,] 106.6583 3.205497
[21,] 106.6583 3.188893
[22,] 106.5667 3.180235
[23,] 106.3750 3.162400
[24,] 106.4750 3.153002
[25,] 106.7875 3.105171
[26,] 106.7875 3.105171
[27,] 106.9000 3.095098
[28,] 107.0167 3.084757
[29,] 106.8958 3.073667
[30,] 107.0208 3.040398
[31,] 107.0208 3.040398
[32,] 106.7542 3.016408
[33,] 106.6167 3.004212
[34,] 106.7583 2.991917
[35,] 106.6125 2.953779
[36,] 106.9125 2.928272
[37,] 106.7583 2.914878
[38,] 106.6000 2.901250
[39,] 106.9250 2.874049
[40,] 107.2583 2.846699
[41,] 106.9167 2.817466
[42,] 106.9167 2.817466
[43,] 107.0958 2.802926
[44,] 106.9125 2.787422
[45,] 106.9125 2.787422
[46,] 106.9125 2.755884
[47,] 106.5208 2.723413
[48,] 106.7208 2.707351
[49,] 106.9250 2.691108
[50,] 106.7167 2.673990
[51,] 106.7167 2.673990
[52,] 106.5000 2.656339
[53,] 106.7208 2.638851
[54,] 106.2708 2.566872
[55,] 106.7292 2.531136
[56,] 106.9625 2.513196
[57,] 106.9625 2.513196
[58,] 106.9625 2.513196
[59,] 106.9625 2.513196
[60,] 106.7125 2.454379
[61,] 106.4583 2.395208
[62,] 106.7167 2.375684
[63,] 106.7167 2.375684
[64,] 106.4500 2.354968
[65,] 106.9917 2.314468
[66,] 107.2667 2.252679
[67,] 107.2667 2.252679
[68,] 106.7000 2.209086
[69,] 106.7000 2.209086
[70,] 106.9917 2.187801
[71,] 107.2875 2.166400
[72,] 107.8875 2.123579
[73,] 107.5833 2.100219
[74,] 107.8917 2.078461
[75,] 107.5792 2.054566
[76,] 107.2625 2.030514
[77,] 106.9417 1.959595
[78,] 106.9417 1.912537
[79,] 106.6125 1.888096
[80,] 106.6125 1.888096
> (tri <- trimean(x))
          [,1]     [,2]
 [1,] 106.3613 3.388817
 [2,] 106.3983 3.357690
 [3,] 106.4402 3.326646
 [4,] 106.4698 3.303670
 [5,] 106.5087 3.283768
 [6,] 106.5570 3.264869
 [7,] 106.6062 3.246000
 [8,] 106.6116 3.231627
 [9,] 106.6171 3.216396
[10,] 106.6045 3.202403
[11,] 106.5963 3.190238
[12,] 106.5926 3.177833
[13,] 106.5935 3.165175
[14,] 106.5896 3.152249
[15,] 106.5857 3.139605
[16,] 106.5865 3.126693
[17,] 106.5874 3.114075
[18,] 106.5833 3.101185
[19,] 106.5842 3.088011
[20,] 106.5900 3.074536
[21,] 106.5859 3.061363
[22,] 106.5816 3.048508
[23,] 106.5825 3.035363
[24,] 106.5938 3.022541
[25,] 106.6000 3.009433
[26,] 106.5904 2.998613
[27,] 106.5806 2.986929
[28,] 106.5652 2.974985
[29,] 106.5440 2.962760
[30,] 106.5278 2.950275
[31,] 106.5056 2.938884
[32,] 106.4830 2.926535
[33,] 106.4713 2.914657
[34,] 106.4651 2.902519
[35,] 106.4529 2.890086
[36,] 106.4464 2.878885
[37,] 106.4277 2.868180
[38,] 106.4146 2.857270
[39,] 106.4074 2.846137
[40,] 106.3875 2.835534
[41,] 106.3544 2.825462
[42,] 106.3333 2.816079
[43,] 106.3117 2.805686
[44,] 106.2829 2.795041
[45,] 106.2600 2.784190
[46,] 106.2365 2.772182
[47,] 106.2123 2.760786
[48,] 106.2014 2.750090
[49,] 106.1831 2.739126
[50,] 106.1571 2.727864
[51,] 106.1377 2.716344
[52,] 106.1176 2.703485
[53,] 106.1045 2.690258
[54,] 106.0833 2.676589
[55,] 106.0769 2.665816
[56,] 106.0547 2.655830
[57,] 106.0238 2.645570
[58,] 105.9919 2.633892
[59,] 105.9590 2.620653
[60,] 105.9250 2.605697
[61,] 105.8983 2.592778
[62,] 105.8793 2.582032
[63,] 105.8509 2.570938
[64,] 105.8214 2.558147
[65,] 105.8000 2.544936
[66,] 105.7593 2.532546
[67,] 105.7075 2.522530
[68,] 105.6538 2.510723
[69,] 105.6176 2.500206
[70,] 105.5800 2.487755
[71,] 105.5306 2.474707
[72,] 105.4688 2.460965
[73,] 105.3830 2.448000
[74,] 105.3043 2.434608
[75,] 105.2111 2.420341
[76,] 105.1250 2.405519
[77,] 105.0465 2.390068
[78,] 104.9762 2.378063
[79,] 104.9024 2.367577
[80,] 104.8375 2.356814
> (midr <- midrange(x))
[1] 107.5
> midm <- array(NA,dim=8)
> for (j in 1:8) midm[j] <- midmean(x,j)
> midm
[1] 104.4758 105.9250 104.4758 105.9250 105.9250 104.4758 105.9250 106.8077
> postscript(file="/var/www/rcomp/tmp/1n5z31321536146.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> lb <- win[,1] - 2*win[,2]
> ub <- win[,1] + 2*win[,2]
> if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
> lines(ub,lty=3)
> lines(lb,lty=3)
> grid()
> dev.off()
null device 
          1 
> postscript(file="/var/www/rcomp/tmp/22ei31321536146.ps",horizontal=F,onefile=F,pagecentre=F,paper="special",width=8.3333333333333,height=5.5555555555556) 
> lb <- tri[,1] - 2*tri[,2]
> ub <- tri[,1] + 2*tri[,2]
> if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
> lines(ub,lty=3)
> lines(lb,lty=3)
> grid()
> dev.off()
null device 
          1 
> 
> #Note: the /var/www/rcomp/createtable file can be downloaded at http://www.wessa.net/cretab
> load(file="/var/www/rcomp/createtable")
> 
> a<-table.start()
> a<-table.row.start(a)
> a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Measure',header=TRUE)
> a<-table.element(a,'Value',header=TRUE)
> a<-table.element(a,'S.E.',header=TRUE)
> a<-table.element(a,'Value/S.E.',header=TRUE)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
> a<-table.element(a,arm)
> a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
> a<-table.element(a,armose)
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
> a<-table.element(a,geo)
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
> a<-table.element(a,har)
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
> a<-table.element(a,qua)
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> for (j in 1:length(win[,1])) {
+ a<-table.row.start(a)
+ mylabel <- paste('Winsorized Mean (',j)
+ mylabel <- paste(mylabel,'/')
+ mylabel <- paste(mylabel,length(win[,1]))
+ mylabel <- paste(mylabel,')')
+ a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
+ a<-table.element(a,win[j,1])
+ a<-table.element(a,win[j,2])
+ a<-table.element(a,win[j,1]/win[j,2])
+ a<-table.row.end(a)
+ }
> for (j in 1:length(tri[,1])) {
+ a<-table.row.start(a)
+ mylabel <- paste('Trimmed Mean (',j)
+ mylabel <- paste(mylabel,'/')
+ mylabel <- paste(mylabel,length(tri[,1]))
+ mylabel <- paste(mylabel,')')
+ a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
+ a<-table.element(a,tri[j,1])
+ a<-table.element(a,tri[j,2])
+ a<-table.element(a,tri[j,1]/tri[j,2])
+ a<-table.row.end(a)
+ }
> a<-table.row.start(a)
> a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
> a<-table.element(a,median(x))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
> a<-table.element(a,midr)
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[1])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[2])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[3])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[4])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[5])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[6])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[7])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
> mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ')
> a<-table.element(a,mylabel,header=TRUE)
> a<-table.element(a,midm[8])
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.row.start(a)
> a<-table.element(a,'Number of observations',header=TRUE)
> a<-table.element(a,length(x))
> a<-table.element(a,'')
> a<-table.element(a,'')
> a<-table.row.end(a)
> a<-table.end(a)
> table.save(a,file="/var/www/rcomp/tmp/39fmq1321536146.tab") 
> 
> try(system("convert tmp/1n5z31321536146.ps tmp/1n5z31321536146.png",intern=TRUE))
character(0)
> try(system("convert tmp/22ei31321536146.ps tmp/22ei31321536146.png",intern=TRUE))
character(0)
> 
> 
> proc.time()
   user  system elapsed 
  1.580   0.060   1.633