Data Structure: List & Matrix

A list is a generic vector containing other objects.

For example, the following variable x is a list containing copies of three vectors n, s, b, and a numeric value 3.

n = c(2, 3, 5) 
s = c("aa", "bb", "cc", "dd", "ee") 
b = c(TRUE, FALSE, TRUE, FALSE, FALSE) 
x = list(n, s, b, 3)   # x contains copies of n, s, b

List Slicing We retrieve a list slice with the single square bracket “[]” operator. The following is a slice containing the second member of x, which is a copy of s.

x[3]

With an index vector, we can retrieve a slice with multiple members. Here a slice containing the second and fourth members of x

x[c(2, 4)] 

Member Reference In order to reference a list member directly, we have to use the double square bracket “[[]]” operator. The following object x[[2]] is the second member of x. In other words, x[[2]] is a copy of s, but is not a slice containing s or its copy.

x[[2]]

We can modify its content directly.

 x[[2]][1] = "ta" 
 x[[2]] 
 

Named List Members

We can assign names to list members, and reference them by names instead of numeric indexes.

For example, in the following, v is a list of two members, named “bob” and “john”.

v = list(bob=c(2, 3, 5), john=c("aa", "bb"))
v

List Slicing We retrieve a list slice with the single square bracket “[]” operator. Here is a list slice containing a member of v named “bob”.

 v["bob"] 

With an index vector, we can retrieve a slice with multiple members. Here is a list slice with both members of v. Notice how they are reversed from their original positions in v.

v[c("john", "bob")] 

Member Reference In order to reference a list member directly, we have to use the double square bracket “[[]]” operator. The following references a member of v by name.

 v[["bob"]] 

A named list member can also be referenced directly with the “$” operator in lieu of the double square bracket operator.

v$bob 

Matrix

A matrix is a collection of data elements arranged in a two-dimensional rectangular layout. The data elements must be of the same basic type

A = matrix(c(2, 4, 3, 1, 5, 7), # the data elements 
           nrow=2,              # number of rows 
           ncol=3,              # number of columns
           byrow = TRUE)        # fill matrix by rows 
 
A                      # print the matrix 

An element at the mth row, nth column of A can be accessed by the expression A[m, n].

A[2, 3]      # element at 2nd row, 3rd column 

The entire mth row A can be extracted as A[m, ].

A[2, ] # 2nd row

Similarly, the entire nth column A can be extracted as A[ ,n].

A[ ,3]       # the 3rd column 

We can also extract more than one rows or columns at a time.

A[ ,c(1,3)]  # the 1st and 3rd columns 

Matrix Construction

There are various ways to construct a matrix. When we construct a matrix directly with data elements, the matrix content is filled along the column orientation by default. For example, in the following code snippet, the content of B is filled along the columns consecutively.

B = matrix(c(2, 4, 3, 1, 5, 7), 
           nrow=3, 
           ncol=2) 
 
B             # B has 3 rows and 2 columns 

Transpose We construct the transpose of a matrix by interchanging its columns and rows with the function t .

t(B)          # transpose of B 

Combining Matrices The columns of two matrices having the same number of rows can be combined into a larger matrix. For example, suppose we have another matrix C also with 3 rows.

C = matrix(c(7, 4, 2),nrow=3,ncol=1) 
 
C             # C has 3 rows 

Then we can combine the columns of B and C with cbind.

cbind(B, C) 

Similarly, we can combine the rows of two matrices if they have the same number of columns with the rbind function.

D = matrix(c(6, 2),nrow=1,ncol=2) 
 
D             # D has 2 columns 

rbind(B, D)