Groups of Data - Vectors, Matrices & Lists

In this notebook, we will learn how to handle groups of data — or, in R terminology, groups of objects.

R provides several ways for grouping objects:
- Vector: Collection of objects with the same data type
- Matrix: Table consisting of objects with the same data type
- List: Collection of objects with possibly different data types

Vector

A vector is a collection of objects with the same data type.

To create a vector, use the c() function:

amino_acids <- c("methionine", "leucine", "alanine", "valine", "glutamine", "threonine")

Accessing items in a vector can be done like so:

amino_acids[1] # Access the first element

[1] "methionine"

amino_acids[2] # Access the second element

[1] "leucine"

We can also combine two vectors into a single vector using the c() function:

addl_amino_acids <- c("glycine", "cysteine", "serine")
many_amino_acids <- c(amino_acids, addl_amino_acids)
many_amino_acids

[1] "methionine" "leucine"    "alanine"    "valine"     "glutamine"  "threonine"  "glycine"    "cysteine"   "serine"    

Matrix

A matrix is a table consisting of objects with the same data type.

To create a matrix, use the matrix() function:

amino_acids_matrix <- matrix(c("methionine", "leucine", "alanine", "valine", "glutamine", "threonine"), nrow=3, ncol=2)
amino_acids_matrix

     [,1]         [,2]       
[1,] "methionine" "valine"   
[2,] "leucine"    "glutamine"
[3,] "alanine"    "threonine"

We can add rows and columns using rbind() and cbind(), respectively:

amino_acids_matrix <-  rbind(amino_acids_matrix, c("proline", "arginine"))
amino_acids_matrix

     [,1]         [,2]       
[1,] "methionine" "valine"   
[2,] "leucine"    "glutamine"
[3,] "alanine"    "threonine"
[4,] "proline"    "arginine" 

amino_acids_matrix <-  cbind(amino_acids_matrix, c("histidine", "phenylalanine", "tryptophan", "selenocysteine"))
amino_acids_matrix

     [,1]         [,2]        [,3]            
[1,] "methionine" "valine"    "histidine"     
[2,] "leucine"    "glutamine" "phenylalanine" 
[3,] "alanine"    "threonine" "tryptophan"    
[4,] "proline"    "arginine"  "selenocysteine"

Accessing items in a matrix can be done like so:

amino_acids_matrix[1, 2] # Accesses the first row, second column

[1] "valine"

amino_acids_matrix[4, 3] # Accesses the fourth row, third column

[1] "selenocysteine"

We can also check if the items in a matrix satisfies a given condition: - any() checks if at least one of the items satisfies the condition - all() checks if all of the items satisfy the condition

numbers <- matrix(c(2, 4, 6, 8, 10, 12, 14, 16, 18), nrow=3, ncol=3)
any(numbers < 6)

[1] TRUE

any(numbers < 1)

[1] FALSE

all(numbers < 20)

[1] TRUE

all(numbers < 5)

[1] FALSE

It is possible to name the rows and columns (also called the dimensions) of a matrix using colnames() and rownames(), respectively.

This can greatly aid in making our matrix more descriptive, especially when we perform some analysis.

colnames(numbers) <- c("Treatment 1", "Treatment 2", "Treatment 3")
rownames(numbers) <- c("Patient 1", "Patient 2", "Patient 3")
numbers

          Treatment 1 Treatment 2 Treatment 3
Patient 1           2           8          14
Patient 2           4          10          16
Patient 3           6          12          18

Finally, we demonstrate some matrix operations:

numbers1 <- matrix(c(2, 4, 6, 8, 10, 12, 14, 16, 18), nrow=3, ncol=3)
numbers2 <- matrix(c(12, 14, 16, 18, 20, 22, 24, 26, 28), nrow=3, ncol=3)

numbers1 + numbers2

     [,1] [,2] [,3]
[1,]   14   26   38
[2,]   18   30   42
[3,]   22   34   46

numbers1 - numbers2

     [,1] [,2] [,3]
[1,]  -10  -10  -10
[2,]  -10  -10  -10
[3,]  -10  -10  -10

numbers1 * numbers2

     [,1] [,2] [,3]
[1,]   24  144  336
[2,]   56  200  416
[3,]   96  264  504

numbers1 / numbers2

          [,1]      [,2]      [,3]
[1,] 0.1666667 0.4444444 0.5833333
[2,] 0.2857143 0.5000000 0.6153846
[3,] 0.3750000 0.5454545 0.6428571

100 * numbers1 # Scalar multiplication

     [,1] [,2] [,3]
[1,]  200  800 1400
[2,]  400 1000 1600
[3,]  600 1200 1800

t(numbers1) # Matrix transpose

     [,1] [,2] [,3]
[1,]    2    4    6
[2,]    8   10   12
[3,]   14   16   18

List

A list is a collection of objects with possibly different data types.

To create a list, use the list() function:

assorted_list <- list("proline", "methionine", 1, 2)
assorted_list

[[1]]
[1] "proline"

[[2]]
[1] "methionine"

[[3]]
[1] 1

[[4]]
[1] 2

Accessing list items can be a bit tricky though.

Observe how assorted_list[1] does not return the item proline per se. It actually returns a list containing proline.

assorted_list[1]

[[1]]
[1] "proline"

If we want the item proline to be returned, we have to use double brackets:

assorted_list[[1]]

[1] "proline"

If we want a summary of the list elements, we can use the summary() function.

summary(assorted_list)

     Length Class  Mode     
[1,] 1      -none- character
[2,] 1      -none- character
[3,] 1      -none- numeric  
[4,] 1      -none- numeric  

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1. De La Salle University, Manila, Philippines, gonzales.markedward@gmail.com↩︎