Rotate a Matrix in R by 90 degrees clockwise

Question

I have a matrix in R like this:

|1|2|3|
|1|2|3|
|1|2|3|

Is there an easy way to rotate the entire matrix by 90 degrees clockwise to get these results?

|1|1|1|
|2|2|2|
|3|3|3|

and again rotating 90 degrees:

|3|2|1|
|3|2|1|
|3|2|1|

?

Solution 1

t does not rotate the entries, it flips along the diagonal:

x <- matrix(1:9, 3)
x
##      [,1] [,2] [,3]
## [1,]    1    4    7
## [2,]    2    5    8
## [3,]    3    6    9

t(x)
##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    4    5    6
## [3,]    7    8    9

90 degree clockwise rotation of R matrix:

You need to also reverse the columns prior to the transpose:

rotate <- function(x) t(apply(x, 2, rev))
rotate(x)
##      [,1] [,2] [,3]
## [1,]    3    2    1
## [2,]    6    5    4
## [3,]    9    8    7

rotate(rotate(x))
##      [,1] [,2] [,3]
## [1,]    9    6    3
## [2,]    8    5    2
## [3,]    7    4    1

rotate(rotate(rotate(x)))
##      [,1] [,2] [,3]
## [1,]    7    8    9
## [2,]    4    5    6
## [3,]    1    2    3

rotate(rotate(rotate(rotate(x))))
##      [,1] [,2] [,3]
## [1,]    1    4    7
## [2,]    2    5    8
## [3,]    3    6    9

90 degree counter clockwise rotation of R matrix:

Doing the transpose prior to the reverse is the same as rotate counter clockwise:

foo = matrix(1:9, 3)
foo
## [,1] [,2] [,3]
## [1,]    1    4    7
## [2,]    2    5    8
## [3,]    3    6    9

foo <- apply(t(foo),2,rev)
foo

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

Solution 2

m <- matrix(rep(1:3,each=3),3)

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

t(m[nrow(m):1,])

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

m[nrow(m):1,ncol(m):1]

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

t(m)[ncol(m):1,]

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

Solution 3

An easy way to rotate a matrix by 180° is this:

m <- matrix(1:8,ncol=4)
#      [,1] [,2] [,3] [,4]
# [1,]    1    3    5    7
# [2,]    2    4    6    8


rot <- function(x) "[<-"(x, , rev(x))

rot(m)
#      [,1] [,2] [,3] [,4]
# [1,]    8    6    4    2
# [2,]    7    5    3    1

rot(rot(m))
#      [,1] [,2] [,3] [,4]
# [1,]    1    3    5    7
# [2,]    2    4    6    8

Solution 4

R methods to rotate a matrix 90 degrees and -90 degrees

#first reverse, then transpose, it's the same as rotate 90 degrees
rotate_clockwise         <- function(x) { t(     apply(x, 2, rev))}
#first transpose, then reverse, it's the same as rotate -90 degrees:
rotate_counter_clockwise <- function(x) { apply(     t(x),2, rev)}

#or if you want a library to help make things easier to read:
#install.packages("pracma")
library(pracma)
rotate_one_eighty <- function(x) { rot90(x, 2) }
rotate_two_seventy <- function(x) { rot90(x, -1) }

foo = matrix(1:9, 3)
foo

foo = rotate_clockwise(foo)
foo

foo = rotate_counter_clockwise(foo)
foo

foo = rotate_one_eighty(foo)
foo

Prints:

     [,1] [,2] [,3]
[1,]    1    4    7          #original matrix
[2,]    2    5    8
[3,]    3    6    9
     [,1] [,2] [,3]
[1,]    3    2    1
[2,]    6    5    4          #rotated 90 degrees
[3,]    9    8    7
     [,1] [,2] [,3]
[1,]    1    4    7
[2,]    2    5    8          #rotated -90 degrees
[3,]    3    6    9
     [,1] [,2] [,3]
[1,]    9    6    3
[2,]    8    5    2          #rotated 180 degrees
[3,]    7    4    1

Notice that rotating a matrix clockwise, then counterclockwise returns the numbers to their original position, then rotating by 180 is like rotating by 90 twice.

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