Pertemuan 2 Komputasi Statistika

NAMA : ARINI NAJLA KHANIYAH

NIM : 2504220068

PRODI: KOMPUTASI STATISTIKA

2 Simple manipulations; numbers and vectors

2.1 Vectors and assignment

x <- c(10.4, 5.6, 3.1, 6.4, 21.7)
assign("x", c(10.4, 5.6, 3.1, 6.4, 21.7))
c(10.4, 5.6, 3.1, 6.4, 21.7)-> x
1/x

## [1] 0.09615385 0.17857143 0.32258065 0.15625000 0.04608295

y <- c(x, 0, x)

2.2 Vektor arithematic

v <- 2*x + y + 1

## Warning in 2 * x + y: longer object length is not a multiple of shorter object
## length

sum((x-mean(x))^2)/(length(x)-1)

## [1] 53.853

sort (x)

## [1]  3.1  5.6  6.4 10.4 21.7

sqrt(-17)

## Warning in sqrt(-17): NaNs produced

## [1] NaN

sqrt(-17+0i)

## [1] 0+4.123106i

2.3 Generating regular sequences

seq(-5, 5, by=.2)-> s3
s4 <- seq(length=51, from=-5, by=.2)
s5 <- rep(x, times=5)
s6 <- rep(x, each=5)

2.4 Logical vectors

temp <- x > 13
x

## [1] 10.4  5.6  3.1  6.4 21.7

2.5 Missing values

z <- c(1:3,NA); ind <- is.na(z)
0/0

## [1] NaN

2.6 Characters vectors

labs <- paste(c("X","Y"), 1:10, sep="")
labs

##  [1] "X1"  "Y2"  "X3"  "Y4"  "X5"  "Y6"  "X7"  "Y8"  "X9"  "Y10"

2.7 Index vectors

1. A logical vector

y <- x[!is.na(x)]
(x+1)[(!is.na(x)) & x>0]-> z
z

## [1] 11.4  6.6  4.1  7.4 22.7

2. A vector of positive integral quantities

### 2. A vector of positive integral quantities
x[1:10]

##  [1] 10.4  5.6  3.1  6.4 21.7   NA   NA   NA   NA   NA

c("x","y")[rep(c(1,2,2,1), times=4)]

##  [1] "x" "y" "y" "x" "x" "y" "y" "x" "x" "y" "y" "x" "x" "y" "y" "x"

3. A vector of negative integral quantities

y <- x[-(1:5)]

4. A vector of character strings

fruit <- c(5, 10, 1, 20) 
names(fruit) <- c("orange", "banana", "apple", "peach") 
lunch <- fruit[c("apple","orange")]
x[is.na(x)] <- 0
y[y < 0] <--y[y < 0]
y <- abs(y)

3 Objects, their modes and attributes

3.1 Intrinsic attributes: mode and length

z <- 0:9
digits <- as.character(z)
d <- as.integer(digits)

3.2 Changing the length of an object

e <- numeric()
e[3] <- 17
alpha <- c(10, 20, 30, 40, 50, 60, 70, 80, 90, 100)
alpha <- alpha[2 * 1:5]
length(alpha) <- 3
e

## [1] NA NA 17

3.3 Getting and setting attributes

z <- 1:100
attr(z, "dim") <- c(10,10)
z

##       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
##  [1,]    1   11   21   31   41   51   61   71   81    91
##  [2,]    2   12   22   32   42   52   62   72   82    92
##  [3,]    3   13   23   33   43   53   63   73   83    93
##  [4,]    4   14   24   34   44   54   64   74   84    94
##  [5,]    5   15   25   35   45   55   65   75   85    95
##  [6,]    6   16   26   36   46   56   66   76   86    96
##  [7,]    7   17   27   37   47   57   67   77   87    97
##  [8,]    8   18   28   38   48   58   68   78   88    98
##  [9,]    9   19   29   39   49   59   69   79   89    99
## [10,]   10   20   30   40   50   60   70   80   90   100

3.4 The class of an object

datasets::attitude

##    rating complaints privileges learning raises critical advance
## 1      43         51         30       39     61       92      45
## 2      63         64         51       54     63       73      47
## 3      71         70         68       69     76       86      48
## 4      61         63         45       47     54       84      35
## 5      81         78         56       66     71       83      47
## 6      43         55         49       44     54       49      34
## 7      58         67         42       56     66       68      35
## 8      71         75         50       55     70       66      41
## 9      72         82         72       67     71       83      31
## 10     67         61         45       47     62       80      41
## 11     64         53         53       58     58       67      34
## 12     67         60         47       39     59       74      41
## 13     69         62         57       42     55       63      25
## 14     68         83         83       45     59       77      35
## 15     77         77         54       72     79       77      46
## 16     81         90         50       72     60       54      36
## 17     74         85         64       69     79       79      63
## 18     65         60         65       75     55       80      60
## 19     65         70         46       57     75       85      46
## 20     50         58         68       54     64       78      52
## 21     50         40         33       34     43       64      33
## 22     64         61         52       62     66       80      41
## 23     53         66         52       50     63       80      37
## 24     40         37         42       58     50       57      49
## 25     63         54         42       48     66       75      33
## 26     66         77         66       63     88       76      72
## 27     78         75         58       74     80       78      49
## 28     48         57         44       45     51       83      38
## 29     85         85         71       71     77       74      55
## 30     82         82         39       59     64       78      39

unclass(attitude)

## $rating
##  [1] 43 63 71 61 81 43 58 71 72 67 64 67 69 68 77 81 74 65 65 50 50 64 53 40 63
## [26] 66 78 48 85 82
## 
## $complaints
##  [1] 51 64 70 63 78 55 67 75 82 61 53 60 62 83 77 90 85 60 70 58 40 61 66 37 54
## [26] 77 75 57 85 82
## 
## $privileges
##  [1] 30 51 68 45 56 49 42 50 72 45 53 47 57 83 54 50 64 65 46 68 33 52 52 42 42
## [26] 66 58 44 71 39
## 
## $learning
##  [1] 39 54 69 47 66 44 56 55 67 47 58 39 42 45 72 72 69 75 57 54 34 62 50 58 48
## [26] 63 74 45 71 59
## 
## $raises
##  [1] 61 63 76 54 71 54 66 70 71 62 58 59 55 59 79 60 79 55 75 64 43 66 63 50 66
## [26] 88 80 51 77 64
## 
## $critical
##  [1] 92 73 86 84 83 49 68 66 83 80 67 74 63 77 77 54 79 80 85 78 64 80 80 57 75
## [26] 76 78 83 74 78
## 
## $advance
##  [1] 45 47 48 35 47 34 35 41 31 41 34 41 25 35 46 36 63 60 46 52 33 41 37 49 33
## [26] 72 49 38 55 39
## 
## attr(,"row.names")
##  [1]  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] 26 27 28 29 30

4 Ordered and unordered factors

4.1 A specific example

state <- c("tas", "sa", "qld", "nsw", "nsw", "nt", "wa", "wa", "qld", "vic", "nsw", "vic", "qld", "qld", "sa", "tas", "sa", "nt", "wa", "vic", "qld", "nsw", "nsw", "wa", "sa", "act", "nsw", "vic", "vic", "act")
statef <- factor(state)
statef 

##  [1] tas sa  qld nsw nsw nt  wa  wa  qld vic nsw vic qld qld sa  tas sa  nt  wa 
## [20] vic qld nsw nsw wa  sa  act nsw vic vic act
## Levels: act nsw nt qld sa tas vic wa

levels(statef)

## [1] "act" "nsw" "nt"  "qld" "sa"  "tas" "vic" "wa"

4.2 The function tapply() and ragged arrays

incomes <- c(60, 49, 40, 61, 64, 60, 59, 54, 62, 69, 70, 42, 56, 61, 61, 61, 58, 51, 48, 65, 49, 49, 41, 48, 52, 46, 59, 46, 58, 43)
incmeans <- tapply(incomes, statef, mean)
stdError <- function(x) sqrt(var(x)/length(x))
incster <- tapply(incomes, statef, stdError)
incster

##      act      nsw       nt      qld       sa      tas      vic       wa 
## 1.500000 4.310195 4.500000 4.106093 2.738613 0.500000 5.244044 2.657536

5 Arrays and matrices

5.1 Arrays

z <- 1:(3*5*100)
dim(z) <- c(3,5,100)
z

## , , 1
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]    1    4    7   10   13
## [2,]    2    5    8   11   14
## [3,]    3    6    9   12   15
## 
## , , 2
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]   16   19   22   25   28
## [2,]   17   20   23   26   29
## [3,]   18   21   24   27   30
## 
## , , 3
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]   31   34   37   40   43
## [2,]   32   35   38   41   44
## [3,]   33   36   39   42   45
## 
## , , 4
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]   46   49   52   55   58
## [2,]   47   50   53   56   59
## [3,]   48   51   54   57   60
## 
## , , 5
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]   61   64   67   70   73
## [2,]   62   65   68   71   74
## [3,]   63   66   69   72   75
## 
## , , 6
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]   76   79   82   85   88
## [2,]   77   80   83   86   89
## [3,]   78   81   84   87   90
## 
## , , 7
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]   91   94   97  100  103
## [2,]   92   95   98  101  104
## [3,]   93   96   99  102  105
## 
## , , 8
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  106  109  112  115  118
## [2,]  107  110  113  116  119
## [3,]  108  111  114  117  120
## 
## , , 9
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  121  124  127  130  133
## [2,]  122  125  128  131  134
## [3,]  123  126  129  132  135
## 
## , , 10
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  136  139  142  145  148
## [2,]  137  140  143  146  149
## [3,]  138  141  144  147  150
## 
## , , 11
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  151  154  157  160  163
## [2,]  152  155  158  161  164
## [3,]  153  156  159  162  165
## 
## , , 12
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  166  169  172  175  178
## [2,]  167  170  173  176  179
## [3,]  168  171  174  177  180
## 
## , , 13
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  181  184  187  190  193
## [2,]  182  185  188  191  194
## [3,]  183  186  189  192  195
## 
## , , 14
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  196  199  202  205  208
## [2,]  197  200  203  206  209
## [3,]  198  201  204  207  210
## 
## , , 15
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  211  214  217  220  223
## [2,]  212  215  218  221  224
## [3,]  213  216  219  222  225
## 
## , , 16
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  226  229  232  235  238
## [2,]  227  230  233  236  239
## [3,]  228  231  234  237  240
## 
## , , 17
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  241  244  247  250  253
## [2,]  242  245  248  251  254
## [3,]  243  246  249  252  255
## 
## , , 18
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  256  259  262  265  268
## [2,]  257  260  263  266  269
## [3,]  258  261  264  267  270
## 
## , , 19
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  271  274  277  280  283
## [2,]  272  275  278  281  284
## [3,]  273  276  279  282  285
## 
## , , 20
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  286  289  292  295  298
## [2,]  287  290  293  296  299
## [3,]  288  291  294  297  300
## 
## , , 21
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  301  304  307  310  313
## [2,]  302  305  308  311  314
## [3,]  303  306  309  312  315
## 
## , , 22
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  316  319  322  325  328
## [2,]  317  320  323  326  329
## [3,]  318  321  324  327  330
## 
## , , 23
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  331  334  337  340  343
## [2,]  332  335  338  341  344
## [3,]  333  336  339  342  345
## 
## , , 24
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  346  349  352  355  358
## [2,]  347  350  353  356  359
## [3,]  348  351  354  357  360
## 
## , , 25
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  361  364  367  370  373
## [2,]  362  365  368  371  374
## [3,]  363  366  369  372  375
## 
## , , 26
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  376  379  382  385  388
## [2,]  377  380  383  386  389
## [3,]  378  381  384  387  390
## 
## , , 27
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  391  394  397  400  403
## [2,]  392  395  398  401  404
## [3,]  393  396  399  402  405
## 
## , , 28
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  406  409  412  415  418
## [2,]  407  410  413  416  419
## [3,]  408  411  414  417  420
## 
## , , 29
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  421  424  427  430  433
## [2,]  422  425  428  431  434
## [3,]  423  426  429  432  435
## 
## , , 30
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  436  439  442  445  448
## [2,]  437  440  443  446  449
## [3,]  438  441  444  447  450
## 
## , , 31
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  451  454  457  460  463
## [2,]  452  455  458  461  464
## [3,]  453  456  459  462  465
## 
## , , 32
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  466  469  472  475  478
## [2,]  467  470  473  476  479
## [3,]  468  471  474  477  480
## 
## , , 33
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  481  484  487  490  493
## [2,]  482  485  488  491  494
## [3,]  483  486  489  492  495
## 
## , , 34
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  496  499  502  505  508
## [2,]  497  500  503  506  509
## [3,]  498  501  504  507  510
## 
## , , 35
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  511  514  517  520  523
## [2,]  512  515  518  521  524
## [3,]  513  516  519  522  525
## 
## , , 36
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  526  529  532  535  538
## [2,]  527  530  533  536  539
## [3,]  528  531  534  537  540
## 
## , , 37
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  541  544  547  550  553
## [2,]  542  545  548  551  554
## [3,]  543  546  549  552  555
## 
## , , 38
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  556  559  562  565  568
## [2,]  557  560  563  566  569
## [3,]  558  561  564  567  570
## 
## , , 39
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  571  574  577  580  583
## [2,]  572  575  578  581  584
## [3,]  573  576  579  582  585
## 
## , , 40
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  586  589  592  595  598
## [2,]  587  590  593  596  599
## [3,]  588  591  594  597  600
## 
## , , 41
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  601  604  607  610  613
## [2,]  602  605  608  611  614
## [3,]  603  606  609  612  615
## 
## , , 42
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  616  619  622  625  628
## [2,]  617  620  623  626  629
## [3,]  618  621  624  627  630
## 
## , , 43
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  631  634  637  640  643
## [2,]  632  635  638  641  644
## [3,]  633  636  639  642  645
## 
## , , 44
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  646  649  652  655  658
## [2,]  647  650  653  656  659
## [3,]  648  651  654  657  660
## 
## , , 45
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  661  664  667  670  673
## [2,]  662  665  668  671  674
## [3,]  663  666  669  672  675
## 
## , , 46
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  676  679  682  685  688
## [2,]  677  680  683  686  689
## [3,]  678  681  684  687  690
## 
## , , 47
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  691  694  697  700  703
## [2,]  692  695  698  701  704
## [3,]  693  696  699  702  705
## 
## , , 48
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  706  709  712  715  718
## [2,]  707  710  713  716  719
## [3,]  708  711  714  717  720
## 
## , , 49
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  721  724  727  730  733
## [2,]  722  725  728  731  734
## [3,]  723  726  729  732  735
## 
## , , 50
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  736  739  742  745  748
## [2,]  737  740  743  746  749
## [3,]  738  741  744  747  750
## 
## , , 51
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  751  754  757  760  763
## [2,]  752  755  758  761  764
## [3,]  753  756  759  762  765
## 
## , , 52
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  766  769  772  775  778
## [2,]  767  770  773  776  779
## [3,]  768  771  774  777  780
## 
## , , 53
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  781  784  787  790  793
## [2,]  782  785  788  791  794
## [3,]  783  786  789  792  795
## 
## , , 54
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  796  799  802  805  808
## [2,]  797  800  803  806  809
## [3,]  798  801  804  807  810
## 
## , , 55
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  811  814  817  820  823
## [2,]  812  815  818  821  824
## [3,]  813  816  819  822  825
## 
## , , 56
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  826  829  832  835  838
## [2,]  827  830  833  836  839
## [3,]  828  831  834  837  840
## 
## , , 57
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  841  844  847  850  853
## [2,]  842  845  848  851  854
## [3,]  843  846  849  852  855
## 
## , , 58
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  856  859  862  865  868
## [2,]  857  860  863  866  869
## [3,]  858  861  864  867  870
## 
## , , 59
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  871  874  877  880  883
## [2,]  872  875  878  881  884
## [3,]  873  876  879  882  885
## 
## , , 60
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  886  889  892  895  898
## [2,]  887  890  893  896  899
## [3,]  888  891  894  897  900
## 
## , , 61
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  901  904  907  910  913
## [2,]  902  905  908  911  914
## [3,]  903  906  909  912  915
## 
## , , 62
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  916  919  922  925  928
## [2,]  917  920  923  926  929
## [3,]  918  921  924  927  930
## 
## , , 63
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  931  934  937  940  943
## [2,]  932  935  938  941  944
## [3,]  933  936  939  942  945
## 
## , , 64
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  946  949  952  955  958
## [2,]  947  950  953  956  959
## [3,]  948  951  954  957  960
## 
## , , 65
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  961  964  967  970  973
## [2,]  962  965  968  971  974
## [3,]  963  966  969  972  975
## 
## , , 66
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  976  979  982  985  988
## [2,]  977  980  983  986  989
## [3,]  978  981  984  987  990
## 
## , , 67
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,]  991  994  997 1000 1003
## [2,]  992  995  998 1001 1004
## [3,]  993  996  999 1002 1005
## 
## , , 68
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1006 1009 1012 1015 1018
## [2,] 1007 1010 1013 1016 1019
## [3,] 1008 1011 1014 1017 1020
## 
## , , 69
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1021 1024 1027 1030 1033
## [2,] 1022 1025 1028 1031 1034
## [3,] 1023 1026 1029 1032 1035
## 
## , , 70
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1036 1039 1042 1045 1048
## [2,] 1037 1040 1043 1046 1049
## [3,] 1038 1041 1044 1047 1050
## 
## , , 71
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1051 1054 1057 1060 1063
## [2,] 1052 1055 1058 1061 1064
## [3,] 1053 1056 1059 1062 1065
## 
## , , 72
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1066 1069 1072 1075 1078
## [2,] 1067 1070 1073 1076 1079
## [3,] 1068 1071 1074 1077 1080
## 
## , , 73
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1081 1084 1087 1090 1093
## [2,] 1082 1085 1088 1091 1094
## [3,] 1083 1086 1089 1092 1095
## 
## , , 74
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1096 1099 1102 1105 1108
## [2,] 1097 1100 1103 1106 1109
## [3,] 1098 1101 1104 1107 1110
## 
## , , 75
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1111 1114 1117 1120 1123
## [2,] 1112 1115 1118 1121 1124
## [3,] 1113 1116 1119 1122 1125
## 
## , , 76
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1126 1129 1132 1135 1138
## [2,] 1127 1130 1133 1136 1139
## [3,] 1128 1131 1134 1137 1140
## 
## , , 77
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1141 1144 1147 1150 1153
## [2,] 1142 1145 1148 1151 1154
## [3,] 1143 1146 1149 1152 1155
## 
## , , 78
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1156 1159 1162 1165 1168
## [2,] 1157 1160 1163 1166 1169
## [3,] 1158 1161 1164 1167 1170
## 
## , , 79
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1171 1174 1177 1180 1183
## [2,] 1172 1175 1178 1181 1184
## [3,] 1173 1176 1179 1182 1185
## 
## , , 80
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1186 1189 1192 1195 1198
## [2,] 1187 1190 1193 1196 1199
## [3,] 1188 1191 1194 1197 1200
## 
## , , 81
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1201 1204 1207 1210 1213
## [2,] 1202 1205 1208 1211 1214
## [3,] 1203 1206 1209 1212 1215
## 
## , , 82
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1216 1219 1222 1225 1228
## [2,] 1217 1220 1223 1226 1229
## [3,] 1218 1221 1224 1227 1230
## 
## , , 83
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1231 1234 1237 1240 1243
## [2,] 1232 1235 1238 1241 1244
## [3,] 1233 1236 1239 1242 1245
## 
## , , 84
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1246 1249 1252 1255 1258
## [2,] 1247 1250 1253 1256 1259
## [3,] 1248 1251 1254 1257 1260
## 
## , , 85
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1261 1264 1267 1270 1273
## [2,] 1262 1265 1268 1271 1274
## [3,] 1263 1266 1269 1272 1275
## 
## , , 86
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1276 1279 1282 1285 1288
## [2,] 1277 1280 1283 1286 1289
## [3,] 1278 1281 1284 1287 1290
## 
## , , 87
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1291 1294 1297 1300 1303
## [2,] 1292 1295 1298 1301 1304
## [3,] 1293 1296 1299 1302 1305
## 
## , , 88
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1306 1309 1312 1315 1318
## [2,] 1307 1310 1313 1316 1319
## [3,] 1308 1311 1314 1317 1320
## 
## , , 89
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1321 1324 1327 1330 1333
## [2,] 1322 1325 1328 1331 1334
## [3,] 1323 1326 1329 1332 1335
## 
## , , 90
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1336 1339 1342 1345 1348
## [2,] 1337 1340 1343 1346 1349
## [3,] 1338 1341 1344 1347 1350
## 
## , , 91
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1351 1354 1357 1360 1363
## [2,] 1352 1355 1358 1361 1364
## [3,] 1353 1356 1359 1362 1365
## 
## , , 92
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1366 1369 1372 1375 1378
## [2,] 1367 1370 1373 1376 1379
## [3,] 1368 1371 1374 1377 1380
## 
## , , 93
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1381 1384 1387 1390 1393
## [2,] 1382 1385 1388 1391 1394
## [3,] 1383 1386 1389 1392 1395
## 
## , , 94
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1396 1399 1402 1405 1408
## [2,] 1397 1400 1403 1406 1409
## [3,] 1398 1401 1404 1407 1410
## 
## , , 95
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1411 1414 1417 1420 1423
## [2,] 1412 1415 1418 1421 1424
## [3,] 1413 1416 1419 1422 1425
## 
## , , 96
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1426 1429 1432 1435 1438
## [2,] 1427 1430 1433 1436 1439
## [3,] 1428 1431 1434 1437 1440
## 
## , , 97
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1441 1444 1447 1450 1453
## [2,] 1442 1445 1448 1451 1454
## [3,] 1443 1446 1449 1452 1455
## 
## , , 98
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1456 1459 1462 1465 1468
## [2,] 1457 1460 1463 1466 1469
## [3,] 1458 1461 1464 1467 1470
## 
## , , 99
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1471 1474 1477 1480 1483
## [2,] 1472 1475 1478 1481 1484
## [3,] 1473 1476 1479 1482 1485
## 
## , , 100
## 
##      [,1] [,2] [,3] [,4] [,5]
## [1,] 1486 1489 1492 1495 1498
## [2,] 1487 1490 1493 1496 1499
## [3,] 1488 1491 1494 1497 1500

5.2 Array indexing. Subsections of an array

a <- array(1:24, dim = c(4,3,2))
a[2,,]

##      [,1] [,2]
## [1,]    2   14
## [2,]    6   18
## [3,]   10   22

5.3 Index matrices

x <- array(1:20, dim=c(4,5))
x

##      [,1] [,2] [,3] [,4] [,5]
## [1,]    1    5    9   13   17
## [2,]    2    6   10   14   18
## [3,]    3    7   11   15   19
## [4,]    4    8   12   16   20

i <- array(c(1:3,3:1), dim=c(3,2))
i

##      [,1] [,2]
## [1,]    1    3
## [2,]    2    2
## [3,]    3    1

x[i] <- 0 
x

##      [,1] [,2] [,3] [,4] [,5]
## [1,]    1    5    0   13   17
## [2,]    2    0   10   14   18
## [3,]    0    7   11   15   19
## [4,]    4    8   12   16   20

5.4 The array() function

data_vector <- 1:24
dim_vector <- c(3,4,2)
h <- 1:24

Z <- array(data_vector, dim_vector)
Z <- array(h, dim=c(3,4,2))
Z <- h ; dim(Z) <- c(3,4,2)

A <- 1:5
B <- 6:10
C <- 11:15
D <- 2*A*B + C + 1
Z

## , , 1
## 
##      [,1] [,2] [,3] [,4]
## [1,]    1    4    7   10
## [2,]    2    5    8   11
## [3,]    3    6    9   12
## 
## , , 2
## 
##      [,1] [,2] [,3] [,4]
## [1,]   13   16   19   22
## [2,]   14   17   20   23
## [3,]   15   18   21   24

5.5 The outer product of two arrays

a <- 1:5
b <- 6:10

ab <- a %o% b
ab <- outer(a, b, "*")

x <- 1:5
y <- 1:5
f <- function(x, y) cos(y)/(1 + x^2)

z <- outer(x, y, f)
z

##            [,1]        [,2]        [,3]        [,4]       [,5]
## [1,] 0.27015115 -0.20807342 -0.49499625 -0.32682181 0.14183109
## [2,] 0.10806046 -0.08322937 -0.19799850 -0.13072872 0.05673244
## [3,] 0.05403023 -0.04161468 -0.09899925 -0.06536436 0.02836622
## [4,] 0.03178249 -0.02447923 -0.05823485 -0.03844962 0.01668601
## [5,] 0.02078086 -0.01600565 -0.03807663 -0.02514014 0.01091008

5.6 Generalized transpose of an array

A <- array(1:6, dim = c(2,3))
B <- aperm(A, c(2,1))
B <- t(A)
A

##      [,1] [,2] [,3]
## [1,]    1    3    5
## [2,]    2    4    6

5.7 Matrix facilities

5.7.1 Matrix multiplication

A <- matrix(1:6, nrow = 2, ncol = 3)
B <- matrix(7:12, nrow = 2, ncol = 3)
A * B

##      [,1] [,2] [,3]
## [1,]    7   27   55
## [2,]   16   40   72

A %*% t(B)

##      [,1] [,2]
## [1,]   89   98
## [2,]  116  128

x <- c(1,2,3)
M <- matrix(1:9, nrow = 3, ncol = 3)
t(x) %*% M %*% x

##      [,1]
## [1,]  228

5.7.2 Linear equations and inversion

A <- matrix(c(2,1,1,3), nrow = 2, ncol = 2)
x <- c(1,2)
b <- A %*% x
solve(A, b)

##      [,1]
## [1,]    1
## [2,]    2

5.7.3 Eigenvalues and eigenvectors

Sm <- matrix(c(4,2,2,3), nrow = 2, ncol = 2)
ev <- eigen(Sm)
evals <- eigen(Sm)$values
eigen(Sm)

## eigen() decomposition
## $values
## [1] 5.561553 1.438447
## 
## $vectors
##            [,1]       [,2]
## [1,] -0.7882054  0.6154122
## [2,] -0.6154122 -0.7882054

evals <- eigen(Sm, only.values = TRUE)$values

5.7.4 Singular value decomposition and determinants

M <- matrix(c(2,4,1,3), nrow = 2, ncol = 2)
absdetM <- prod(svd(M)$d)
absdet <- function(M) prod(svd(M)$d)
M

##      [,1] [,2]
## [1,]    2    1
## [2,]    4    3

5.7.5 Least squares fitting and the QR decomposition

X <- matrix(c(1,2,3,4,5,6), nrow = 3, ncol = 2)
y <- c(7,8,9)

ans <- lsfit(X, y)

## Warning in lsfit(X, y): 'X' matrix was collinear

Xplus <- qr(X)
b <- qr.coef(Xplus, y)
fit <- qr.fitted(Xplus, y)
res <- qr.resid(Xplus, y)

5.8 Forming partitioned matrices, cbind() and rbind()

X1 <- 1:5
X2 <- 6:10
X <- cbind(1, X1, X2)
X

##        X1 X2
## [1,] 1  1  6
## [2,] 1  2  7
## [3,] 1  3  8
## [4,] 1  4  9
## [5,] 1  5 10

5.9 The concatenation function, c(), with arrays

vec <- as.vector(X)
vec <- c(X)
vec

##  [1]  1  1  1  1  1  1  2  3  4  5  6  7  8  9 10

5.10 Frequency tables from factors

statefr <- table(statef)
statefr <- tapply(statef, statef, length)
factor(cut(incomes, breaks = 35+10*(0:7)))-> incomef
table(incomef,statef)

##          statef
## incomef   act nsw nt qld sa tas vic wa
##   (35,45]   1   1  0   1  0   0   1  0
##   (45,55]   1   1  1   1  2   0   1  3
##   (55,65]   0   3  1   3  2   2   2  1
##   (65,75]   0   1  0   0  0   0   1  0

statef

##  [1] tas sa  qld nsw nsw nt  wa  wa  qld vic nsw vic qld qld sa  tas sa  nt  wa 
## [20] vic qld nsw nsw wa  sa  act nsw vic vic act
## Levels: act nsw nt qld sa tas vic wa