Matrices and arrays

TODO

• link to matrixArithmetic

Matrices

Create a matrix using matrix()

age <- c(17, 30, 30, 25, 23, 21)
matrix(age, nrow=3, ncol=2, byrow=FALSE)

     [,1] [,2]
[1,]   17   25
[2,]   30   23
[3,]   30   21

(ageMat <- matrix(age, nrow=2, ncol=3, byrow=TRUE))

     [,1] [,2] [,3]
[1,]   17   30   30
[2,]   25   23   21

Combine rows and columns to a matrix

age    <- c(19, 19, 31, 19, 24)
weight <- c(95, 76, 94, 76, 76)
height <- c(197, 178, 189, 184, 173)
rbind(age, weight, height)

       [,1] [,2] [,3] [,4] [,5]
age      19   19   31   19   24
weight   95   76   94   76   76
height  197  178  189  184  173

cbind(age, weight, height)

     age weight height
[1,]  19     95    197
[2,]  19     76    178
[3,]  31     94    189
[4,]  19     76    184
[5,]  24     76    173

Information about matrices

dim(ageMat)

[1] 2 3

nrow(ageMat)

[1] 2

ncol(ageMat)

[1] 3

prod(dim(ageMat))

[1] 6

Transpose matrices

t(ageMat)

     [,1] [,2]
[1,]   17   25
[2,]   30   23
[3,]   30   21

as.matrix(1:3)

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

c(ageMat)

[1] 17 25 30 23 30 21

Rows and columns

P       <- 2
Q       <- 3
(pqMat  <- matrix(1:(P*Q), nrow=P, ncol=Q))

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

(rowMat <- row(pqMat))

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

(colMat <- col(pqMat))

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

cbind(rowIdx=c(rowMat), colIdx=c(colMat), val=c(pqMat))

     rowIdx colIdx val
[1,]      1      1   1
[2,]      2      1   2
[3,]      1      2   3
[4,]      2      2   4
[5,]      1      3   5
[6,]      2      3   6

mat <- matrix(sample(1:10, 16, replace=TRUE), 4, 4)
upper.tri(mat)

      [,1]  [,2]  [,3]  [,4]
[1,] FALSE  TRUE  TRUE  TRUE
[2,] FALSE FALSE  TRUE  TRUE
[3,] FALSE FALSE FALSE  TRUE
[4,] FALSE FALSE FALSE FALSE

lower.tri(mat)

      [,1]  [,2]  [,3]  [,4]
[1,] FALSE FALSE FALSE FALSE
[2,]  TRUE FALSE FALSE FALSE
[3,]  TRUE  TRUE FALSE FALSE
[4,]  TRUE  TRUE  TRUE FALSE

Extract and change elements

Row and column indices

ageMat <- matrix(sample(16:35, 6, replace=TRUE), nrow=2, ncol=3)
ageMat[2, 2]

[1] 20

ageMat[2, 2] <- 24
ageMat[2, 2]

[1] 24

ageMat[2,  ]

[1] 24 24 16

ageMat[ , 1]

[1] 32 24

ageMat[ ,  ]

     [,1] [,2] [,3]
[1,]   32   19   19
[2,]   24   24   16

ageMat[ , 1, drop=FALSE]

     [,1]
[1,]   32
[2,]   24

ageMat[ , 2:3]

     [,1] [,2]
[1,]   19   19
[2,]   24   16

ageMat[ , c(1, 3)]

     [,1] [,2]
[1,]   32   19
[2,]   24   16

Index vector

idxVec <- c(1, 3, 4)
ageMat[idxVec]

[1] 32 19 24

Index matrix

ageMatNew   <- ageMat
(replaceMat <- matrix(c(11, 21, 12, 22), nrow=2, ncol=2))

     [,1] [,2]
[1,]   11   12
[2,]   21   22

ageMatNew[ , c(1, 3)] <- replaceMat
ageMatNew

     [,1] [,2] [,3]
[1,]   11   19   12
[2,]   21   24   22

Logical index matrix

(idxMatLog <- ageMat >= 25)

      [,1]  [,2]  [,3]
[1,]  TRUE FALSE FALSE
[2,] FALSE FALSE FALSE

ageMat[idxMatLog]

[1] 32

(idxMatNum <- which(idxMatLog, arr.ind=TRUE))

     row col
[1,]   1   1

ageMat[idxMatNum]

[1] 32

(idxMat <- arrayInd(idxVec, dim(ageMat)))

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

Also see help(Extract)

Sort matrices

age    <- c(19, 19, 31, 19, 24)
weight <- c(95, 76, 94, 76, 76)
height <- c(197, 178, 189, 184, 173)
mat    <- cbind(age, weight, height)
(rowOrder1 <- order(mat[ , "age"]))

[1] 1 2 4 5 3

mat[rowOrder1, ]

     age weight height
[1,]  19     95    197
[2,]  19     76    178
[3,]  19     76    184
[4,]  24     76    173
[5,]  31     94    189

rowOrder2 <- order(mat[ , "age"], partial=mat[ , "weight"])
mat[rowOrder2, ]

     age weight height
[1,]  19     76    178
[2,]  19     76    184
[3,]  19     95    197
[4,]  24     76    173
[5,]  31     94    189

rowOrder3 <- order(mat[ , "weight"], -mat[ , "height"])
mat[rowOrder3, ]

     age weight height
[1,]  19     76    184
[2,]  19     76    178
[3,]  24     76    173
[4,]  31     94    189
[5,]  19     95    197

Arrays

Create arrays

(myArr1 <- array(1:12, c(2, 3, 2),
                 dimnames=list(row=c("f", "m"), column=c("CG", "WL", "T"),
                               layer=c("high", "low"))))

, , layer = high

   column
row CG WL T
  f  1  3 5
  m  2  4 6

, , layer = low

   column
row CG WL  T
  f  7  9 11
  m  8 10 12

Extract and change elements

myArr1[1, 3, 2]

[1] 11

myArr1[2, 1, 2] <- 19
myArr2 <- myArr1*2
myArr2[ , , "high"]

   column
row CG WL  T
  f  2  6 10
  m  4  8 12

Transpose arrays

Switch rows and columns

aperm(myArr1, c(2, 1, 3))

, , layer = high

      row
column f m
    CG 1 2
    WL 3 4
    T  5 6

, , layer = low

      row
column  f  m
    CG  7 19
    WL  9 10
    T  11 12

Switch rows and layers

aperm(myArr1, c(3, 2, 1))

, , row = f

      column
layer  CG WL  T
  high  1  3  5
  low   7  9 11

, , row = m

      column
layer  CG WL  T
  high  2  4  6
  low  19 10 12

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