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|

?

Yeah but does `t` work 360 degrees around? or only 90 degrees to the right? — Johannes, May 11 '13 at 10:39

score 112 · Accepted Answer · edited Mar 19 '17 at 03:27

112

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

edited Mar 19 '17 at 03:27

Eric Leschinski

146,994
96
417
335

answered May 11 '13 at 12:25

Matthew Lundberg

42,009
6
90
112

nice and very intuitive. Thanks! – Johannes May 11 '13 at 14:05
14

apply is perhaps not optimal; from R-help archives: `rotate = function(mat) t(mat[nrow(mat):1,,drop=FALSE]) ` – baptiste May 11 '13 at 14:16
1

Is there a forumla for anti-clockwise rotation other than 2 repeat operations? This is quite an intensive process for large matrices. – geotheory Feb 11 '14 at 13:52
1

@geotheory Simply reverse the order of operations: `apply(t(x), 2, rev)` – Matthew Lundberg Feb 11 '14 at 14:17
Thanks. Or apparently `apply(x, 1, rev)`, which I don't understand as how can a reordering function possibly change change matrix dimensions (albeit not in this case)?! If you don't know I'll post as a question. – geotheory Feb 12 '14 at 08:11
1

Have posted it up: http://stackoverflow.com/questions/21729310/unexpected-apply-function-behaviour-in-r – geotheory Feb 12 '14 at 13:31
@baptiste Is there anything about changing the columns at the same time in docs? – Léo Léopold Hertz 준영 Nov 25 '16 at 21:19

Roland · Answer 2 · 2013-05-11T13:12:18.370

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

score 10 · Answer 3 · answered Feb 12 '14 at 14:30

10

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

answered Feb 12 '14 at 14:30

Sven Hohenstein

80,497
17
145
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1

A nice property of this function is that it preserves the sparseness if you're using `Matrix` classes. However, your code doesn't work (anymore?) in R 3.2.1, it complains about a missing `value` argument. Instead, this variation works: `rotate <- function(x) {x[] <- rev(x); x}`. – Ken Williams Sep 04 '15 at 14:51
I should mention though, that even though this preserves sparseness, it does have to temporarily instantiate a non-sparse vector whose size is the product of the matrix dimensions. – Ken Williams Sep 04 '15 at 14:54
@KenWilliams I cannot reproduce the problem. It still works on my machine with R 3.2.1. – Sven Hohenstein Sep 04 '15 at 18:04
1

Oh - it looks like it only fails when `m` is a `Matrix` object. It indeed worked fine when `m` was a vanilla `matrix`. – Ken Williams Sep 04 '15 at 19:08
@SvenHohenstein can you please explain the `"[<-"` part – pogibas Nov 07 '17 at 23:03
2

@PoGibas The function `[<-` is used for index replacement. In the code `x[i] <- y`, the object `x` will be altered. If you use `"[<-"(x, i, y)` instead, the modified object will be returned and `x` will not be changed. – Sven Hohenstein Nov 08 '17 at 05:18

Eric Leschinski · Answer 4 · 2017-03-19T04:14:04.343

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.

score 0 · Answer 5 · answered Aug 17 '17 at 15:15

0

Or combined in a single function (based on Eric Leschinski):

rotate  <- function(x, clockwise=T) {
  if (clockwise) { t( apply(x, 2, rev))
  } else {apply( t(x),2, rev)} 
}

answered Aug 17 '17 at 15:15

bud.dugong

689
7
16

Rotate a Matrix in R by 90 degrees clockwise

5 Answers5

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

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