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:
> 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
> x=array(1:8,dim=c(2,2,2)) > is.array(x) [1] TRUE
The array has an attribute called dim.
> attributes(x) $dim [1] 2 2 2
You can also get the dimensions using the
dim
function
> 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.
> 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
> 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
> 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’
> a[2,3] [1] 7
This retrieves the element at row 2 and column 3. You can also specify a single index
> a[1] [1] 1 > a[2] [1] 5
This accesses the elements in column first order. To select a complete row or complete column
# 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
> 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
> 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.
> 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.
> 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
# 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
> 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.
> 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.
# 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]