putting every 3rd row of a matrix in a new matrix - r

Question

I would like to create 3 matrices from a bigger matrix.
The new matrices should contain:
new matrix 1: the 1st, 4th, 7th.... element of the old matrix
new matrix 2: the 2nd, 5th, 8th.... element of the old matrix
new matrix 3: the 3rd, 6th, 9th.... element of the old matrix
So if my matrix looks like this:
m<-matrix(c(1:3),nrow=12, ncol=2)
[,1] [,2]
[1,] 1 1
[2,] 2 2
[3,] 3 3
[4,] 1 1
[5,] 2 2
[6,] 3 3
[7,] 1 1
[8,] 2 2
[9,] 3 3
[10,] 1 1
[11,] 2 2
[12,] 3 3
I tried it with a for loop like this
for(i in 1:4){
m1<-m[i+3,]
m2<-m[i+4,]
m3<-m[i+5,]
}
But this not only would not be able to give me the 1st/2nd/3rd rows, but also doesn't give me all rows.
There has to be a more elegant way to do it.

Answer 1

Take advantage of the cycling rule of indexing in R:
m[c(T, F, F),]
# [,1] [,2]
# [1,] 1 1
# [2,] 1 1
# [3,] 1 1
# [4,] 1 1
m[c(F, T, F),]
# [,1] [,2]
# [1,] 2 2
# [2,] 2 2
# [3,] 2 2
# [4,] 2 2
m[c(F, F, T),]
# [,1] [,2]
# [1,] 3 3
# [2,] 3 3
# [3,] 3 3
# [4,] 3 3
When we are indexing the matrix with vectors which have different length from the number of rows of the matrix, the vector here which has a smaller length will get cycled until their lengths match, so for instance, the first case, the actual indexing vector is extended to c(T, F, F, T, F, F, T, F, F) which will pick up the first, fourth and seventh row as expected. The same goes for case two and three.

Answer 2

We can use seq to do this. This will be faster for big datasets.
m[seq(1, nrow(m), by =3),]

Answer 3

Or we could do:
m[seq(nrow(m))%%3==1,] # 1th, 3th, 7th, ...
m[seq(nrow(m))%%3==2,] # 2th, 5th, 8th, ...
m[seq(nrow(m))%%3==0,] # 3th, 6th, 9th, ...
BENCHMARKING
library(microbenchmark)
m <- matrix(c(1:3),nrow=12, ncol=2)
func_Psidom <- function(m){m[c(T, F, F),]}
func_akrun <- function(m){ m[seq(1, nrow(m), by =3),]}
func_42 <- function(m){ m[c(TRUE,FALSE,FALSE), ]}
func_m0h3n <- function(m){m[seq(nrow(m))%%3==1,]}
r <- func_Psidom(m)
all(func_akrun(m)==r)
# [1] TRUE
all(func_42(m)==r)
# [1] TRUE
all(func_m0h3n(m)==r)
# [1] TRUE
microbenchmark(func_Psidom(m), func_akrun(m), func_42(m), func_m0h3n(m))
# Unit: microseconds
# expr min lq mean median uq max neval
# func_Psidom(m) 2.566 3.850 4.49990 4.2780 4.7050 14.543 100
# func_akrun(m) 38.923 39.779 43.58536 40.2065 41.0615 252.359 100
# func_42(m) 2.994 3.422 4.13628 4.2770 4.7050 13.688 100
# func_m0h3n(m) 18.820 20.103 22.37447 20.7445 21.3860 104.365 100
# ============================================================
m <- matrix(c(1:3),nrow=1200, ncol=2)
r <- func_Psidom(m)
all(func_akrun(m)==r)
# [1] TRUE
all(func_42(m)==r)
# [1] TRUE
all(func_m0h3n(m)==r)
# [1] TRUE
microbenchmark(func_Psidom(m), func_akrun(m), func_42(m), func_m0h3n(m))
# Unit: microseconds
# expr min lq mean median uq max neval
# func_Psidom(m) 12.832 13.6875 14.41458 14.542 14.543 22.242 100
# func_akrun(m) 56.033 57.3150 65.17700 57.743 58.599 289.998 100
# func_42(m) 12.832 13.4735 14.76962 14.115 14.543 56.032 100
# func_m0h3n(m) 76.990 78.2730 97.82522 78.702 79.557 1873.437 100
# ============================================================
m <- matrix(c(1:3),nrow=120000, ncol=2)
r <- func_Psidom(m)
all(func_akrun(m)==r)
# [1] TRUE
all(func_42(m)==r)
# [1] TRUE
all(func_m0h3n(m)==r)
# [1] TRUE
microbenchmark(func_Psidom(m), func_akrun(m), func_42(m), func_m0h3n(m))
# Unit: microseconds
# expr min lq mean median uq max neval
# func_Psidom(m) 963.665 978.6355 1168.161 1026.113 1076.798 3648.498 100
# func_akrun(m) 1674.117 1787.6785 2808.231 1890.760 2145.043 58450.377 100
# func_42(m) 960.672 976.2835 1244.467 1033.812 1115.507 3114.268 100
# func_m0h3n(m) 5817.920 6127.8070 7697.345 7455.895 8055.565 62414.963 100

Answer 4

Logical vectors get recycled to the length of the number of rows or columns when matrix indexing:
m[c(TRUE,FALSE,FALSE), ]
[,1] [,2]
[1,] 1 1
[2,] 1 1
[3,] 1 1
[4,] 1 1
m[c(TRUE,FALSE,FALSE)[c(2,1,3)], ] # the numeric vector permutes the logical values
[,1] [,2]
[1,] 2 2
[2,] 2 2
[3,] 2 2
[4,] 2 2
m[c(TRUE,FALSE,FALSE)[c(2,3,1)], ]
[,1] [,2]
[1,] 3 3
[2,] 3 3
[3,] 3 3
[4,] 3 3