Looping in R
Ankan Basu / Learning from Example codes from coursera!
Wednesday, August 13, 2014
VARIOUS LOOPING TECHNIQUES in R with EXAMPLES
In this text, we are going to over some of the most extraordinary functions to help us loop in R. Mastering these tools (functions) would make a more efficient R-programmer. I use R for various geologic/geochemical and hydrogeologic investigations and I use the functions discussed here a lot. Although, the examples used in this write up do not produce any graphs, you can easily produce graphs with the looping functions in R.
lapply(X, FUN, …)
sapply(X, FUN, …,
simplify = TRUE, USE.NAMES = TRUE)
vapply(X, FUN, FUN.VALUE,
…, USE.NAMES = TRUE)
replicate(n, expr,
simplify = “array”)
simplify2array(x, higher
= TRUE)
lapply
Apply a Function over a
List or Vector. loop over a list, item by item. Actual looping is done
in C language.
str(lapply)## function (X, FUN, ...)object=list(a=1:10, b=rnorm(10))
object## $a
## [1] 1 2 3 4 5 6 7 8 9 10
##
## $b
## [1] -0.45736 -1.00367 1.61543 0.12046 -0.03302 -0.49324 -0.74551
## [8] 0.85625 -0.81216 -0.18206lapply(object, sd)## $a
## [1] 3.028
##
## $b
## [1] 0.8123lapply returns a list of
the same length as X, each element of which is the result of applying
FUN to the corresponding element of X.
object=1:10
object## [1] 1 2 3 4 5 6 7 8 9 10lapply(object, runif, min=0, max=10) #runif generates random deviates.## [[1]]
## [1] 8.837
##
## [[2]]
## [1] 8.957 3.166
##
## [[3]]
## [1] 4.177 3.054 2.045
##
## [[4]]
## [1] 8.055 7.978 7.803 2.051
##
## [[5]]
## [1] 5.077 4.916 1.499 8.946 5.967
##
## [[6]]
## [1] 3.674 1.465 3.482 2.330 7.211 4.193
##
## [[7]]
## [1] 3.925 2.792 6.544 3.256 6.603 4.842 1.278
##
## [[8]]
## [1] 5.086 1.168 2.051 3.887 2.210 5.409 8.314 7.609
##
## [[9]]
## [1] 6.3217 9.3295 0.8053 8.2122 7.5664 6.2449 7.9882 4.4039 6.1933
##
## [[10]]
## [1] 1.2048 4.7770 0.1617 4.6686 6.4722 2.3602 5.1982 0.5486 4.4962 4.0775Example of annonymous
fuctions within lapply
object=list(a=matrix(1:4,2,2), b=matrix(1:6, 3,2))
object## $a
## [,1] [,2]
## [1,] 1 3
## [2,] 2 4
##
## $b
## [,1] [,2]
## [1,] 1 4
## [2,] 2 5
## [3,] 3 6lapply(object, function(firstcolumn) firstcolumn[,1]) ## $a
## [1] 1 2
##
## $b
## [1] 1 2 3lapply(object, function(firstrow) firstrow[1,]) ## $a
## [1] 1 3
##
## $b
## [1] 1 4sapply
sapply is a user-friendly
version and wrapper of lapply by default returning a vector, matrix or,
if simplify = “array”, an array.
similar to lapply,
simplified, loop over a list, item by item
str(sapply)## function (X, FUN, ..., simplify = TRUE, USE.NAMES = TRUE)object=list(a=1:10, b=rnorm(10))
object## $a
## [1] 1 2 3 4 5 6 7 8 9 10
##
## $b
## [1] 0.5605 0.8882 0.3827 0.5794 -0.2564 -1.0797 1.1774 0.7096
## [9] -0.3987 -0.9082loutput=lapply(object, sd)
loutput## $a
## [1] 3.028
##
## $b
## [1] 0.7758class(loutput)## [1] "list"soutput=sapply(object,sd) # notice difference
soutput## a b
## 3.0277 0.7758class(soutput)## [1] "numeric"vapply
vapply is similar to
sapply, but has a pre-specified type of return value, so it can be
safer (and sometimes faster) to use.
apply
apply a function of your
choice over an array; not really looping
str(apply)## function (X, MARGIN, FUN, ...)#MARGIN is a vector giving the subscripts which the function will be applied over; for a matrix 1 indicates rows, 2 indicates columns
my_matrix<-matrix(rnorm(30), 10, 3)
apply(my_matrix, 2, mean) # apply mean on columns## [1] -0.38317 -0.13071 -0.02697apply(my_matrix, 1, mean) # apply mean on rows## [1] 9.349e-06 1.120e-01 -1.958e+00 1.879e-01 4.237e-01 6.855e-01
## [7] -2.568e-01 -2.324e-01 4.607e-01 -1.226e+00rowSums = apply(my_matrix, 1, sum)
rowSums## [1] 2.805e-05 3.360e-01 -5.873e+00 5.638e-01 1.271e+00 2.056e+00
## [7] -7.704e-01 -6.973e-01 1.382e+00 -3.677e+00rowMeans = apply(my_matrix, 1, mean)
rowMeans## [1] 9.349e-06 1.120e-01 -1.958e+00 1.879e-01 4.237e-01 6.855e-01
## [7] -2.568e-01 -2.324e-01 4.607e-01 -1.226e+00colSums = apply(my_matrix, 2, sum)
colSums## [1] -3.8317 -1.3071 -0.2697colMeans = apply(my_matrix, 2, mean)
colMeans## [1] -0.38317 -0.13071 -0.02697apply(my_matrix, 1, quantile, probs = c(0.25, 0.75))## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
## 25% -0.2612 -0.417 -2.323 -0.1307 0.3783 0.1301 -0.6924 -0.9489 -0.02951
## 75% 0.4376 0.423 -1.651 0.4127 0.4870 1.1369 0.2504 0.4258 0.87513
## [,10]
## 25% -1.7341
## 75% -0.9402 a <- array(data=rnorm(2 * 2 * 10), dim=c(2, 2, 10)) #generate 40 random numbers and assign 2x2x10 dimentions
a## , , 1
##
## [,1] [,2]
## [1,] -0.4396 -0.184
## [2,] 1.0707 1.776
##
## , , 2
##
## [,1] [,2]
## [1,] -0.2107 0.1165
## [2,] 0.4991 -0.8378
##
## , , 3
##
## [,1] [,2]
## [1,] 1.6221 0.4075
## [2,] 0.1481 -0.4790
##
## , , 4
##
## [,1] [,2]
## [1,] -0.4467 1.560
## [2,] -0.3858 2.175
##
## , , 5
##
## [,1] [,2]
## [1,] -0.8019 1.474
## [2,] -0.3677 1.580
##
## , , 6
##
## [,1] [,2]
## [1,] 0.1808 -1.560
## [2,] -0.4412 2.058
##
## , , 7
##
## [,1] [,2]
## [1,] 0.8715 -0.01511
## [2,] 0.2059 -0.61433
##
## , , 8
##
## [,1] [,2]
## [1,] 0.6668 -0.4581
## [2,] -0.9788 -2.3214
##
## , , 9
##
## [,1] [,2]
## [1,] -0.4312 0.3950
## [2,] -0.5110 -0.8342
##
## , , 10
##
## [,1] [,2]
## [1,] 0.5953 -0.2219
## [2,] 0.2690 -0.4078tapply
apply a function of your
choice over any subset of a vector Apply a function to each cell of a
ragged array, that is to each (non-empty) group of values given by a
unique combination of the levels of certain factors.
str(tapply)## function (X, INDEX, FUN = NULL, ..., simplify = TRUE)require(stats)
groups <- as.factor(rbinom(100, n = 5, prob = 0.8)) #rbinom(n, size, prob)
groups## [1] 81 83 83 81 84
## Levels: 81 83 84tapply(groups, groups, length) #- is almost the same as## 81 83 84
## 2 2 1table(groups)## groups
## 81 83 84
## 2 2 1x <- c(rnorm(10), runif(10), rnorm(10, 1))
x## [1] 0.14386 -0.21274 -0.31354 -0.32914 -0.74218 -0.41923 0.32376
## [8] 0.57782 1.29516 0.51849 0.09856 0.74341 0.64724 0.40818
## [15] 0.80790 0.46450 0.92045 0.65810 0.96937 0.53147 -0.54966
## [22] 1.03216 1.40758 1.18356 3.07369 1.99872 -0.30349 2.04159
## [29] 0.87591 0.73995f <- gl(3, 10) # generate 3 levels with 10 repetitions
#gl(n, k, length = n*k, labels = 1:n, ordered = FALSE)
#Generate factors by specifying the pattern of their levels.
f## [1] 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3
## Levels: 1 2 3tapply(x, f, mean) #get the mean for each level in x## 1 2 3
## 0.08423 0.62492 1.15000tapply(x, f, mean, simplify = FALSE) #group means without simplification## $`1`
## [1] 0.08423
##
## $`2`
## [1] 0.6249
##
## $`3`
## [1] 1.15tapply(x, f, range) # check group ranges## $`1`
## [1] -0.7422 1.2952
##
## $`2`
## [1] 0.09856 0.96937
##
## $`3`
## [1] -0.5497 3.0737tapply(x, f, min) # check group min## 1 2 3
## -0.74218 0.09856 -0.54966split
Divide into Groups and
Reassemble. split divides the data in the vector x into the groups
defined by f.
The replacement forms
replace values corresponding to such a division.
unsplit reverses the
effect of split. Usage
split(x, f, drop = FALSE,
…) split(x, f, drop = FALSE, …) <- value unsplit(value, f, drop
= FALSE
x <- c(rnorm(10), runif(10), rnorm(10, 1))
f <- gl(3, 10)
x # no splitting in the data## [1] -0.64199 1.24759 0.94857 -1.91172 0.17663 0.10583 0.08753
## [8] 0.44691 0.88841 -0.24475 0.61367 0.93486 0.74584 0.74547
## [15] 0.45167 0.36987 0.54612 0.66831 0.36644 0.44551 1.18085
## [22] 0.03665 -0.02822 2.46721 0.60715 1.50149 2.13073 1.17925
## [29] -0.27713 -0.75292split(x,f) #splitted data by factors## $`1`
## [1] -0.64199 1.24759 0.94857 -1.91172 0.17663 0.10583 0.08753
## [8] 0.44691 0.88841 -0.24475
##
## $`2`
## [1] 0.6137 0.9349 0.7458 0.7455 0.4517 0.3699 0.5461 0.6683 0.3664 0.4455
##
## $`3`
## [1] 1.18085 0.03665 -0.02822 2.46721 0.60715 1.50149 2.13073
## [8] 1.17925 -0.27713 -0.75292lapply(split(x, f), mean) # is same as:## $`1`
## [1] 0.1103
##
## $`2`
## [1] 0.5888
##
## $`3`
## [1] 0.8045sapply(split(x, f), mean) #is same as :## 1 2 3
## 0.1103 0.5888 0.8045tapply(x, f, mean)## 1 2 3
## 0.1103 0.5888 0.8045You can also split a data
frame
library(datasets)
head(airquality, 2)## Ozone Solar.R Wind Temp Month Day
## 1 41 190 7.4 67 5 1
## 2 36 118 8.0 72 5 2#Split air Quality data by month
s <- split(airquality, airquality$Month)
s## $`5`
## Ozone Solar.R Wind Temp Month Day
## 1 41 190 7.4 67 5 1
## 2 36 118 8.0 72 5 2
## 3 12 149 12.6 74 5 3
## 4 18 313 11.5 62 5 4
## 5 NA NA 14.3 56 5 5
## 6 28 NA 14.9 66 5 6
## 7 23 299 8.6 65 5 7
## 8 19 99 13.8 59 5 8
## 9 8 19 20.1 61 5 9
## 10 NA 194 8.6 69 5 10
## 11 7 NA 6.9 74 5 11
## 12 16 256 9.7 69 5 12
## 13 11 290 9.2 66 5 13
## 14 14 274 10.9 68 5 14
## 15 18 65 13.2 58 5 15
## 16 14 334 11.5 64 5 16
## 17 34 307 12.0 66 5 17
## 18 6 78 18.4 57 5 18
## 19 30 322 11.5 68 5 19
## 20 11 44 9.7 62 5 20
## 21 1 8 9.7 59 5 21
## 22 11 320 16.6 73 5 22
## 23 4 25 9.7 61 5 23
## 24 32 92 12.0 61 5 24
## 25 NA 66 16.6 57 5 25
## 26 NA 266 14.9 58 5 26
## 27 NA NA 8.0 57 5 27
## 28 23 13 12.0 67 5 28
## 29 45 252 14.9 81 5 29
## 30 115 223 5.7 79 5 30
## 31 37 279 7.4 76 5 31
##
## $`6`
## Ozone Solar.R Wind Temp Month Day
## 32 NA 286 8.6 78 6 1
## 33 NA 287 9.7 74 6 2
## 34 NA 242 16.1 67 6 3
## 35 NA 186 9.2 84 6 4
## 36 NA 220 8.6 85 6 5
## 37 NA 264 14.3 79 6 6
## 38 29 127 9.7 82 6 7
## 39 NA 273 6.9 87 6 8
## 40 71 291 13.8 90 6 9
## 41 39 323 11.5 87 6 10
## 42 NA 259 10.9 93 6 11
## 43 NA 250 9.2 92 6 12
## 44 23 148 8.0 82 6 13
## 45 NA 332 13.8 80 6 14
## 46 NA 322 11.5 79 6 15
## 47 21 191 14.9 77 6 16
## 48 37 284 20.7 72 6 17
## 49 20 37 9.2 65 6 18
## 50 12 120 11.5 73 6 19
## 51 13 137 10.3 76 6 20
## 52 NA 150 6.3 77 6 21
## 53 NA 59 1.7 76 6 22
## 54 NA 91 4.6 76 6 23
## 55 NA 250 6.3 76 6 24
## 56 NA 135 8.0 75 6 25
## 57 NA 127 8.0 78 6 26
## 58 NA 47 10.3 73 6 27
## 59 NA 98 11.5 80 6 28
## 60 NA 31 14.9 77 6 29
## 61 NA 138 8.0 83 6 30
##
## $`7`
## Ozone Solar.R Wind Temp Month Day
## 62 135 269 4.1 84 7 1
## 63 49 248 9.2 85 7 2
## 64 32 236 9.2 81 7 3
## 65 NA 101 10.9 84 7 4
## 66 64 175 4.6 83 7 5
## 67 40 314 10.9 83 7 6
## 68 77 276 5.1 88 7 7
## 69 97 267 6.3 92 7 8
## 70 97 272 5.7 92 7 9
## 71 85 175 7.4 89 7 10
## 72 NA 139 8.6 82 7 11
## 73 10 264 14.3 73 7 12
## 74 27 175 14.9 81 7 13
## 75 NA 291 14.9 91 7 14
## 76 7 48 14.3 80 7 15
## 77 48 260 6.9 81 7 16
## 78 35 274 10.3 82 7 17
## 79 61 285 6.3 84 7 18
## 80 79 187 5.1 87 7 19
## 81 63 220 11.5 85 7 20
## 82 16 7 6.9 74 7 21
## 83 NA 258 9.7 81 7 22
## 84 NA 295 11.5 82 7 23
## 85 80 294 8.6 86 7 24
## 86 108 223 8.0 85 7 25
## 87 20 81 8.6 82 7 26
## 88 52 82 12.0 86 7 27
## 89 82 213 7.4 88 7 28
## 90 50 275 7.4 86 7 29
## 91 64 253 7.4 83 7 30
## 92 59 254 9.2 81 7 31
##
## $`8`
## Ozone Solar.R Wind Temp Month Day
## 93 39 83 6.9 81 8 1
## 94 9 24 13.8 81 8 2
## 95 16 77 7.4 82 8 3
## 96 78 NA 6.9 86 8 4
## 97 35 NA 7.4 85 8 5
## 98 66 NA 4.6 87 8 6
## 99 122 255 4.0 89 8 7
## 100 89 229 10.3 90 8 8
## 101 110 207 8.0 90 8 9
## 102 NA 222 8.6 92 8 10
## 103 NA 137 11.5 86 8 11
## 104 44 192 11.5 86 8 12
## 105 28 273 11.5 82 8 13
## 106 65 157 9.7 80 8 14
## 107 NA 64 11.5 79 8 15
## 108 22 71 10.3 77 8 16
## 109 59 51 6.3 79 8 17
## 110 23 115 7.4 76 8 18
## 111 31 244 10.9 78 8 19
## 112 44 190 10.3 78 8 20
## 113 21 259 15.5 77 8 21
## 114 9 36 14.3 72 8 22
## 115 NA 255 12.6 75 8 23
## 116 45 212 9.7 79 8 24
## 117 168 238 3.4 81 8 25
## 118 73 215 8.0 86 8 26
## 119 NA 153 5.7 88 8 27
## 120 76 203 9.7 97 8 28
## 121 118 225 2.3 94 8 29
## 122 84 237 6.3 96 8 30
## 123 85 188 6.3 94 8 31
##
## $`9`
## Ozone Solar.R Wind Temp Month Day
## 124 96 167 6.9 91 9 1
## 125 78 197 5.1 92 9 2
## 126 73 183 2.8 93 9 3
## 127 91 189 4.6 93 9 4
## 128 47 95 7.4 87 9 5
## 129 32 92 15.5 84 9 6
## 130 20 252 10.9 80 9 7
## 131 23 220 10.3 78 9 8
## 132 21 230 10.9 75 9 9
## 133 24 259 9.7 73 9 10
## 134 44 236 14.9 81 9 11
## 135 21 259 15.5 76 9 12
## 136 28 238 6.3 77 9 13
## 137 9 24 10.9 71 9 14
## 138 13 112 11.5 71 9 15
## 139 46 237 6.9 78 9 16
## 140 18 224 13.8 67 9 17
## 141 13 27 10.3 76 9 18
## 142 24 238 10.3 68 9 19
## 143 16 201 8.0 82 9 20
## 144 13 238 12.6 64 9 21
## 145 23 14 9.2 71 9 22
## 146 36 139 10.3 81 9 23
## 147 7 49 10.3 69 9 24
## 148 14 20 16.6 63 9 25
## 149 30 193 6.9 70 9 26
## 150 NA 145 13.2 77 9 27
## 151 14 191 14.3 75 9 28
## 152 18 131 8.0 76 9 29
## 153 20 223 11.5 68 9 30lapply(s, function(x) colMeans(x[, c("Ozone", "Solar.R", "Wind")]))## $`5`
## Ozone Solar.R Wind
## NA NA 11.62
##
## $`6`
## Ozone Solar.R Wind
## NA 190.17 10.27
##
## $`7`
## Ozone Solar.R Wind
## NA 216.484 8.942
##
## $`8`
## Ozone Solar.R Wind
## NA NA 8.794
##
## $`9`
## Ozone Solar.R Wind
## NA 167.43 10.18colMeans(airquality) # for all columns## Ozone Solar.R Wind Temp Month Day
## NA NA 9.958 77.882 6.993 15.804sapply(s, function(x) colMeans(x[, c("Ozone", "Solar.R", "Wind")]))## 5 6 7 8 9
## Ozone NA NA NA NA NA
## Solar.R NA 190.17 216.484 NA 167.43
## Wind 11.62 10.27 8.942 8.794 10.18#Now try removing NAs from the dataset
sapply(s, function(x) colMeans(x[, c("Ozone", "Solar.R", "Wind")], na.rm = TRUE))## 5 6 7 8 9
## Ozone 23.62 29.44 59.115 59.962 31.45
## Solar.R 181.30 190.17 216.484 171.857 167.43
## Wind 11.62 10.27 8.942 8.794 10.18You can also split more
than one level with SPLIT command
x=rnorm(20)
x## [1] 2.48597 1.34398 0.57253 1.69531 0.75884 0.17921 0.14734
## [8] 1.09718 0.07409 -2.00592 -1.49990 -2.23533 0.31148 0.68989
## [15] 2.61388 -1.32126 1.75524 0.36550 -0.76513 0.24786factor1=gl(4,5)
factor1## [1] 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4
## Levels: 1 2 3 4factor2=gl(5,4)
factor2## [1] 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5
## Levels: 1 2 3 4 5interaction(factor1, factor2)## [1] 1.1 1.1 1.1 1.1 1.2 2.2 2.2 2.2 2.3 2.3 3.3 3.3 3.4 3.4 3.4 4.4 4.5
## [18] 4.5 4.5 4.5
## 20 Levels: 1.1 2.1 3.1 4.1 1.2 2.2 3.2 4.2 1.3 2.3 3.3 4.3 1.4 2.4 ... 4.5str(split(x, list(factor1, factor2))) # this creates empty levels which can be dropped using## List of 20
## $ 1.1: num [1:4] 2.486 1.344 0.573 1.695
## $ 2.1: num(0)
## $ 3.1: num(0)
## $ 4.1: num(0)
## $ 1.2: num 0.759
## $ 2.2: num [1:3] 0.179 0.147 1.097
## $ 3.2: num(0)
## $ 4.2: num(0)
## $ 1.3: num(0)
## $ 2.3: num [1:2] 0.0741 -2.0059
## $ 3.3: num [1:2] -1.5 -2.24
## $ 4.3: num(0)
## $ 1.4: num(0)
## $ 2.4: num(0)
## $ 3.4: num [1:3] 0.311 0.69 2.614
## $ 4.4: num -1.32
## $ 1.5: num(0)
## $ 2.5: num(0)
## $ 3.5: num(0)
## $ 4.5: num [1:4] 1.755 0.365 -0.765 0.248str(split(x, list(factor1, factor2), drop = TRUE))## List of 8
## $ 1.1: num [1:4] 2.486 1.344 0.573 1.695
## $ 1.2: num 0.759
## $ 2.2: num [1:3] 0.179 0.147 1.097
## $ 2.3: num [1:2] 0.0741 -2.0059
## $ 3.3: num [1:2] -1.5 -2.24
## $ 3.4: num [1:3] 0.311 0.69 2.614
## $ 4.4: num -1.32
## $ 4.5: num [1:4] 1.755 0.365 -0.765 0.248mapply
this is the multivariate
version of tapply. Apply a Function to Multiple List or Vector
Arguments.
mapply is a multivariate
version of sapply. mapply applies FUN to the first elements of each …
argument, the second elements, the third elements, and so on. Arguments
are recycled if necessary.
mapply(rep, 1:4, 4:1)## [[1]]
## [1] 1 1 1 1
##
## [[2]]
## [1] 2 2 2
##
## [[3]]
## [1] 3 3
##
## [[4]]
## [1] 4mapply(rep, times = 1:4, x = 4:1)## [[1]]
## [1] 4
##
## [[2]]
## [1] 3 3
##
## [[3]]
## [1] 2 2 2
##
## [[4]]
## [1] 1 1 1 1More
Examples
require(stats); require(graphics)
x <- list(a = 1:10, beta = exp(-3:3), logic = c(TRUE,FALSE,FALSE,TRUE))
# compute the list mean for each list element
lapply(x, mean)## $a
## [1] 5.5
##
## $beta
## [1] 4.535
##
## $logic
## [1] 0.5# median and quartiles for each list element
x## $a
## [1] 1 2 3 4 5 6 7 8 9 10
##
## $beta
## [1] 0.04979 0.13534 0.36788 1.00000 2.71828 7.38906 20.08554
##
## $logic
## [1] TRUE FALSE FALSE TRUElapply(x, quantile, probs = 1:3/4)## $a
## 25% 50% 75%
## 3.25 5.50 7.75
##
## $beta
## 25% 50% 75%
## 0.2516 1.0000 5.0537
##
## $logic
## 25% 50% 75%
## 0.0 0.5 1.0x## $a
## [1] 1 2 3 4 5 6 7 8 9 10
##
## $beta
## [1] 0.04979 0.13534 0.36788 1.00000 2.71828 7.38906 20.08554
##
## $logic
## [1] TRUE FALSE FALSE TRUEsapply(x, quantile)## a beta logic
## 0% 1.00 0.04979 0.0
## 25% 3.25 0.25161 0.0
## 50% 5.50 1.00000 0.5
## 75% 7.75 5.05367 1.0
## 100% 10.00 20.08554 1.0i39 <- sapply(3:9, seq) # list of vectors
i39## [[1]]
## [1] 1 2 3
##
## [[2]]
## [1] 1 2 3 4
##
## [[3]]
## [1] 1 2 3 4 5
##
## [[4]]
## [1] 1 2 3 4 5 6
##
## [[5]]
## [1] 1 2 3 4 5 6 7
##
## [[6]]
## [1] 1 2 3 4 5 6 7 8
##
## [[7]]
## [1] 1 2 3 4 5 6 7 8 9sapply(i39, fivenum)## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## [1,] 1.0 1.0 1 1.0 1.0 1.0 1
## [2,] 1.5 1.5 2 2.0 2.5 2.5 3
## [3,] 2.0 2.5 3 3.5 4.0 4.5 5
## [4,] 2.5 3.5 4 5.0 5.5 6.5 7
## [5,] 3.0 4.0 5 6.0 7.0 8.0 9