array( 初始值, 維度)

產生2x3陣列裡面元素為0

   1: > x<-array(0, dim=c(2,3))
   2: > x
   3:      [,1] [,2] [,3]
   4: [1,]    0    0    0
   5: [2,]    0    0    0

產生2x3陣列裡面元素為-1

   1: > x<-array(-1, dim=c(2,3))
   2: > x
   3:      [,1] [,2] [,3]
   4: [1,]   -1   -1   -1
   5: [2,]   -1   -1   -1

假設故意初始化一個長度超過指定陣列元素總數量, 聰明的R也可以自動判定, 儲存到總個數上限

   1: > x<-array(1:7, dim=c(2,3))
   2: > x
   3:      [,1] [,2] [,3]
   4: [1,]    1    3    5
   5: [2,]    2    4    6

將x進行轉置並存回

   1: > x=t(x)
   2: > x
   3:      [,1] [,2]
   4: [1,]    1    2
   5: [2,]    3    4
   6: [3,]    5    6

產生索引, 其中column 1為列的索引[1 2 3]’;而column 2 為行的索引[2 1 1]’

   1: > ind<-array(c(1:3, 2:1), dim=c(3,2))
   2: > ind
   3:      [,1] [,2]
   4: [1,]    1    2
   5: [2,]    2    1
   6: [3,]    3    1

所以取出對應ind的x數值, 也就是分別取出x(1,2), x(2,1) 和x(3,1)的意思

   1: > x[ind]
   2: [1] 2 3 5

同樣的, 若要將對應ind的x數值取代成-100

   1: > x[ind] = -100
   2: > x
   3:      [,1] [,2]
   4: [1,]    1 -100
   5: [2,] -100    4
   6: [3,] -100    6

array: array(data_vector, dim_vector)

產生2x2x3的向量

   1: > x <- array(1:12, dim=c(2,2,3))
   2: > x
   3: , , 1
   4:  
   5:      [,1] [,2]
   6: [1,]    1    3
   7: [2,]    2    4
   8:  
   9: , , 2
  10:  
  11:      [,1] [,2]
  12: [1,]    5    7
  13: [2,]    6    8
  14:  
  15: , , 3
  16:  
  17:      [,1] [,2]
  18: [1,]    9   11
  19: [2,]   10   12


matrix

   1: > x <-matrix(0, nrow=3, ncol=4)
   2: > x
   3:      [,1] [,2] [,3] [,4]
   4: [1,]    0    0    0    0
   5: [2,]    0    0    0    0
   6: [3,]    0    0    0    0

另一種方式

   1: > n=3;b=2
   2: > Xb <- matrix(0, n, b)
   3: > Xb
   4:      [,1] [,2]
   5: [1,]    0    0
   6: [2,]    0    0
   7: [3,]    0    0

Outer Product of Arrays

   1: > d <- outer(0:9, 0:9)
   2: > d
   3:       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
   4:  [1,]    0    0    0    0    0    0    0    0    0     0
   5:  [2,]    0    1    2    3    4    5    6    7    8     9
   6:  [3,]    0    2    4    6    8   10   12   14   16    18
   7:  [4,]    0    3    6    9   12   15   18   21   24    27
   8:  [5,]    0    4    8   12   16   20   24   28   32    36
   9:  [6,]    0    5   10   15   20   25   30   35   40    45
  10:  [7,]    0    6   12   18   24   30   36   42   48    54
  11:  [8,]    0    7   14   21   28   35   42   49   56    63
  12:  [9,]    0    8   16   24   32   40   48   56   64    72
  13: [10,]    0    9   18   27   36   45   54   63   72    81

產生2x2x3陣列

   1: > x <-array(1:12, c(2,2,3))
   2: > x
   3: , , 1
   4:  
   5:      [,1] [,2]
   6: [1,]    1    3
   7: [2,]    2    4
   8:  
   9: , , 2
  10:  
  11:      [,1] [,2]
  12: [1,]    5    7
  13: [2,]    6    8
  14:  
  15: , , 3
  16:  
  17:      [,1] [,2]
  18: [1,]    9   11
  19: [2,]   10   12

超過2維陣列轉置不可以使用t()

   1: > t(x)
   2: 錯誤在t.default(x) : 引數不是矩陣

要用令用aperm()

   1: > x
   2: , , 1
   3:  
   4:      [,1] [,2]
   5: [1,]    1    3
   6: [2,]    2    4
   7:  
   8: , , 2
   9:  
  10:      [,1] [,2]
  11: [1,]    5    7
  12: [2,]    6    8
  13:  
  14: , , 3
  15:  
  16:      [,1] [,2]
  17: [1,]    9   11
  18: [2,]   10   12
  19:  
  20: > aperm(x)
  21: , , 1
  22:  
  23:      [,1] [,2]
  24: [1,]    1    3
  25: [2,]    5    7
  26: [3,]    9   11
  27:  
  28: , , 2
  29:  
  30:      [,1] [,2]
  31: [1,]    2    4
  32: [2,]    6    8
  33: [3,]   10   12
  34: 

矩陣 A*B

語法: A %*% B

   1: > A
   2:      [,1] [,2]
   3: [1,]    1    3
   4: [2,]    2    4
   5: > B<-array(c(1,2,3,4), dim=c(2,2))
   6: > B
   7:      [,1] [,2]
   8: [1,]    1    3
   9: [2,]    2    4
  10: > A %*% B
  11:      [,1] [,2]
  12: [1,]    7   15
  13: [2,]   10   22

A .* B 對應元素位置相乘

語法: A*B

   1: > A*B
   2:      [,1] [,2]
   3: [1,]    1    9
   4: [2,]    4   16

The inverse of A

語法: solve( A )

   1: > solve(A)
   2:      [,1] [,2]
   3: [1,]   -2  1.5
   4: [2,]    1 -0.5

假設 Ax = b, 則 x = inv( A )*b

語法 x = solve(A, b)

   1: > b = array(1:2, dim=c(2,1))
   2: > b
   3:      [,1]
   4: [1,]    1
   5: [2,]    2
   6: > solve(A, b)
   7:      [,1]
   8: [1,]    1
   9: [2,]    0

List 是一種有順序性收納(an ordered collection)資料型態, 可以收集許多物件也就是它的組成元素 

   1: > Lst <- list(name="Fred", wife="Mary", no.children=3,
   2: + child.ages=c(4,7,9))
   3: > Lst
   4: $name
   5: [1] "Fred"
   6:  
   7: $wife
   8: [1] "Mary"
   9:  
  10: $no.children
  11: [1] 3
  12:  
  13: $child.ages
  14: [1] 4 7 9

甚麼是有順序性?由下列範例可以知道:

   1: > Lst[1]
   2: $name
   3: [1] "Fred"
   4:  
   5: > Lst[2]
   6: $wife
   7: [1] "Mary"
   8:  
   9: > Lst[3]
  10: $no.children
  11: [1] 3
  12:  
  13: > Lst[4]
  14: $child.ages
  15: [1] 4 7 9

Lst筆數

   1: > length(Lst)
   2: [1] 4

取出Lst對應不同欄位的數值, 語法: 變數名稱.$欄位名稱

   1: > Lst$name
   2: [1] "Fred"
   3: > Lst$wife
   4: [1] "Mary"
   5: > Lst$child.ages[0]
   6: numeric(0)
   7: > Lst$child.ages[1]
   8: [1] 4
   9: > Lst$child.ages[2]
  10: [1] 7
  11: > Lst$child.ages[3]
  12: [1] 9

另外, 也可以 變數名稱[“欄位名稱”]

   1: > Lst["name"]
   2: $name
   3: [1] "Fred"
   4:  
   5: > Lst["wife"]
   6: $wife
   7: [1] "Mary"

可是卻沒有辦法取出

   1: > Lst["child"]
   2: $<NA>
   3: NULL
   4: 

反而要像這樣

   1: > Lst["child.ages"]
   2: $child.ages
   3: [1] 4 7 9

也可以用剛才索引的方式取出

   1: > Lst[4][1]
   2: $child.ages
   3: [1] 4 7 9

若要個別物件取出則需要兩層[]

   1: > Lst[[1]]
   2: [1] "Fred"
   3: > Lst[[2]]
   4: [1] "Mary"
   5: > Lst[[3]]
   6: [1] 3
   7: > Lst[[4]]
   8: [1] 4 7 9

其中第4個物件有三個元素

   1: > Lst[[4]][1]
   2: [1] 4
   3: > Lst[[4]][2]
   4: [1] 7
   5: > Lst[[4]][3]
   6: [1] 9
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