In the previous tutorial we saw atomic vectors and list. In this tutorial we look at Matrix and Array in R.
Array
An array is a vector with additional attributes
dim
which stores the dimension of the array and
dimnames
which stores the names of the dimensions. Here’s an example:
1 2 3 4 5 6 7 8 9 10 11 12 | > array(1:8,dim=c(2,2,2)) , , 1 [,1] [,2] [1,] 1 3 [2,] 2 4 , , 2 [,1] [,2] [1,] 5 7 [2,] 6 8 |
This creates a 2,2,2 array. You can check if an object is an array by using the
is.array()
function
1 2 3 | > x=array(1:8,dim=c(2,2,2)) > is.array(x) [1] TRUE |
The array has an attribute called dim.
1 2 3 | > attributes(x) $dim [1] 2 2 2 |
You can also get the dimensions using the
dim
function
1 2 | > dim(x) [1] 2 2 2 |
we can assign names to the dimensions. In the example below we create a list with dimnames. The length of each element in the list should correspond to the dimension.
1 2 3 4 5 6 7 8 9 10 11 12 13 | > x=array(1:8,dim=c(2,2,2),dimnames=list(c('a','b'),c('e','f'),c('g','h'))) > x , , g e f a 1 3 b 2 4 , , h e f a 5 7 b 6 8 |
Matrix
A matrix is an 2 dimensional array. Lets create one
1 2 3 4 5 | > a=matrix(1:8,nrow=2,ncol=4) > a [,1] [,2] [,3] [,4] [1,] 1 3 5 7 [2,] 2 4 6 8 |
The data is filled column first. nrow specifies number of rows and ncol specifies number of columns. To fill in rows first use the ‘byrow’ specifier
1 2 3 4 5 | > a=matrix(1:8,nrow=2,ncol=4,byrow=TRUE) > a [,1] [,2] [,3] [,4] [1,] 1 2 3 4 [2,] 5 6 7 8 |
An element of a matrix can be accessed by specifying ‘row,column’
1 2 | > a[2,3] [1] 7 |
This retrieves the element at row 2 and column 3. You can also specify a single index
1 2 3 4 | > a[1] [1] 1 > a[2] [1] 5 |
This accesses the elements in column first order. To select a complete row or complete column
1 2 3 4 5 6 | # get first row > a[1,] [1] 1 2 3 4 # get first column > a[,1] [1] 1 5 |
Multiple rows or columns can also be accessed
1 2 3 4 5 6 7 8 | > a[,c(1,2)] [,1] [,2] [1,] 1 2 [2,] 5 6 > a[,1:3] [,1] [,2] [,3] [1,] 1 2 3 [2,] 5 6 7 |
You can assign names to the rows and columns. The names can be used to access the elements
1 2 3 4 5 6 7 | > dimnames(a)=list(c("a","b"),c("c","d","e","f")) > a c d e f a 1 2 3 4 b 5 6 7 8 > a["a","e"] [1] 3 |
You can check if an object is a matrix by using
is.matrix()
. Length of a matrix is given by
length()
. To find the number of rows and number of columns use the
nrow()
and
ncol()
functions respectively. To get all the dimensions use the
dim()
function.
1 2 3 4 5 6 7 8 9 | > a=matrix(1:8,nrow=2,ncol=4,byrow=TRUE) > length(a) [1] 8 > dim(a) [1] 2 4 > nrow(a) [1] 2 > ncol(a) [1] 4 |
To get all the names of the rows use the
rownames
function and to get all the column names use the
colnames
function.
1 2 3 4 5 6 | > a=matrix(1:8,nrow=2,ncol=4,byrow=TRUE) > dimnames(a)=list(c("a","b"),c("c","d","e","f")) > rownames(a) [1] "a" "b" > colnames(a) [1] "c" "d" "e" "f" |
We can combine two matrices row wise using
rbind()
and columnwise using
cbind()
. we Will explore this function in details in the subsequent tutorials, but for now, lets look at one example
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | # create two matrices with dimensions 2x2 > a=matrix(1:4,ncol=2,nrow=2) > a [,1] [,2] [1,] 1 3 [2,] 2 4 > b=matrix(5:8,ncol=2,nrow=2) > b [,1] [,2] [1,] 5 7 [2,] 6 8 # cbind combines the matrices by columns. #think of it as putting the matrix on the side of the other matrix. > cbind(a,b) [,1] [,2] [,3] [,4] [1,] 1 3 5 7 [2,] 2 4 6 8 #rbind combines the matrices by rows. #Think of it as putting the matrix on the bottom of the other matrix. > rbind(a,b) [,1] [,2] [1,] 1 3 [2,] 2 4 [3,] 5 7 [4,] 6 8 |
We can convert the matrix back to a vector by using the c() function
1 2 3 4 5 | > c(a) [1] 1 2 3 4 #as.vector also works > as.vector(a) [1] 1 2 3 4 |
A list can also be converted to a matrix.
1 2 3 4 5 6 7 8 9 10 11 | > l = list("a",c(1,2),TRUE,"b") > matrix(l,nrow=2,ncol=2) [,1] [,2] [1,] "a" TRUE [2,] Numeric,2 "b" # we create a 2x2 matrix. > m=matrix(l,nrow=2,ncol=2) # the 2,1 element is a vector > m[2,1] [[1]] [1] 1 2 |
So far we have been using cases where we provide all elements while creating a matrix. Lets look at two examples, where we provide less elements than is required by the ncol and nrow specification.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | # 6 elements and nrow*ncol = 6. all good. > a=matrix(1:6,nrow=3,ncol=2) > a [,1] [,2] [1,] 1 4 [2,] 2 5 [3,] 3 6 #3 elements and nrow*ncol = 6. # R recycles elements since number of elements is a multiple or #sub-multiple of number or rows. > a=matrix(1:3,nrow=3,ncol=2) > a [,1] [,2] [1,] 1 1 [2,] 2 2 [3,] 3 3 # 4 elements and nrow*ncol = 6. Not good. > a=matrix(1:4,nrow=3,ncol=2) Warning message: In matrix(1:4, nrow = 3, ncol = 2) : data length [4] is not a sub-multiple or multiple of the number of rows [3] |
