One other way to create a matrix is to use matrix() function.

nums <- c(col1, col2, col3)
nums

##  [1]   1   3   8   9   2  18  27  10   8  37 267  19

matrix(nums, ncol=2)

##      [,1] [,2]
## [1,]    1   27
## [2,]    3   10
## [3,]    8    8
## [4,]    9   37
## [5,]    2  267
## [6,]   18   19

rownames(my_matrix) <- c("row1", "row2", "row3", "row4")
my_matrix

##      col1 col2 col3
## row1    1    2    8
## row2    3   18   37
## row3    8   27  267
## row4    9   10   19

t(my_matrix)

##      row1 row2 row3 row4
## col1    1    3    8    9
## col2    2   18   27   10
## col3    8   37  267   19

To find out the dimension of a matrix:

ncol(my_matrix)

## [1] 3

nrow(my_matrix)

## [1] 4

dim(my_matrix)

## [1] 4 3

Calculations with numeric matrices.

my_matrix * 3

##      col1 col2 col3
## row1    3    6   24
## row2    9   54  111
## row3   24   81  801
## row4   27   30   57

log10(my_matrix)

##           col1     col2     col3
## row1 0.0000000 0.301030 0.903090
## row2 0.4771213 1.255273 1.568202
## row3 0.9030900 1.431364 2.426511
## row4 0.9542425 1.000000 1.278754

Total of each row.

rowSums(my_matrix)

## row1 row2 row3 row4 
##   11   58  302   38

Total of each column.

colSums(my_matrix)

## col1 col2 col3 
##   21   57  331

There is a data structure Array in R, that holds multi-dimensional (d > 2) data and is a generalized version of a matrix. Matrix is used much more commonly than Array, therefore we are not going to talk about Array here.

A data frame can be created using the function data.frame().

# creating a data frame using pre-defined vectors
patients_name=c("Patient1", "Patient2", "Patient3", "Patient4", "Patient5", "Patient6")
Family_history=c("Y", "N", "Y", "N", "Y", "Y")
patients_age=c(31, 40, 39, 50, 45, 65)
meta.data <- data.frame(patients_name=patients_name, disease_stage=disease_stage, Family_history=Family_history, patients_age=patients_age)
meta.data

##   patients_name disease_stage Family_history patients_age
## 1      Patient1        Stage1              Y           31
## 2      Patient2        Stage2              N           40
## 3      Patient3        Stage2              Y           39
## 4      Patient4        Stage3              N           50
## 5      Patient5        Stage1              Y           45
## 6      Patient6        Stage4              Y           65

is.data.frame(meta.data)

## [1] TRUE

is.data.frame(my_matrix)

## [1] FALSE

class(my_matrix)

## [1] "matrix" "array"

my_data <- as.data.frame(my_matrix)
class(my_data)

## [1] "data.frame"

A data frame can be transposed in the similar way as a matrix. However, the result of transposing a data frame might not be a data frame anymore.

my_data

##      col1 col2 col3
## row1    1    2    8
## row2    3   18   37
## row3    8   27  267
## row4    9   10   19

t(my_data)

##      row1 row2 row3 row4
## col1    1    3    8    9
## col2    2   18   27   10
## col3    8   37  267   19

A data frame can be extended.

# add a column that has the information on harmful mutations in BRCA1/BRCA2 genes for each patient.
meta.data

##   patients_name disease_stage Family_history patients_age
## 1      Patient1        Stage1              Y           31
## 2      Patient2        Stage2              N           40
## 3      Patient3        Stage2              Y           39
## 4      Patient4        Stage3              N           50
## 5      Patient5        Stage1              Y           45
## 6      Patient6        Stage4              Y           65

meta.data$BRCA <- c("YES", "NO", "YES", "YES", "YES", "NO")
meta.data

##   patients_name disease_stage Family_history patients_age BRCA
## 1      Patient1        Stage1              Y           31  YES
## 2      Patient2        Stage2              N           40   NO
## 3      Patient3        Stage2              Y           39  YES
## 4      Patient4        Stage3              N           50  YES
## 5      Patient5        Stage1              Y           45  YES
## 6      Patient6        Stage4              Y           65   NO

A data frame can also be extended using the functions cbind() and rbind(), for adding columns and rows respectively. When using cbind(), the number of values in the new column must match the number of rows in the data frame. When using rbind(), the two data frames must have the same variables/columns.

# add a column that has the information on the racial information for each patient.
cbind(meta.data, Race=c("AJ", "AS", "AA", "NE", "NE", "AS"))

##   patients_name disease_stage Family_history patients_age BRCA Race
## 1      Patient1        Stage1              Y           31  YES   AJ
## 2      Patient2        Stage2              N           40   NO   AS
## 3      Patient3        Stage2              Y           39  YES   AA
## 4      Patient4        Stage3              N           50  YES   NE
## 5      Patient5        Stage1              Y           45  YES   NE
## 6      Patient6        Stage4              Y           65   NO   AS

# rbind can be used to add more rows to a data frame.
rbind(meta.data, data.frame(patients_name="Patient7", disease_stage="S4", Family_history="Y", patients_age=48, BRCA="YES"))

##   patients_name disease_stage Family_history patients_age BRCA
## 1      Patient1        Stage1              Y           31  YES
## 2      Patient2        Stage2              N           40   NO
## 3      Patient3        Stage2              Y           39  YES
## 4      Patient4        Stage3              N           50  YES
## 5      Patient5        Stage1              Y           45  YES
## 6      Patient6        Stage4              Y           65   NO
## 7      Patient7            S4              Y           48  YES

One may use the function merge to merge two data frames horizontally, based on one or more common key variables.

expression.data <- data.frame(patients_name=c("Patient3", "Patient4", "Patient5", "Patient1", "Patient2", "Patient6"), EGFR=c(10, 472, 103784, 1782, 187, 18289), TP53=c(16493, 72, 8193, 1849, 173894, 1482))
expression.data

##   patients_name   EGFR   TP53
## 1      Patient3     10  16493
## 2      Patient4    472     72
## 3      Patient5 103784   8193
## 4      Patient1   1782   1849
## 5      Patient2    187 173894
## 6      Patient6  18289   1482

md2 <- merge(meta.data, expression.data, by="patients_name")
md2

##   patients_name disease_stage Family_history patients_age BRCA   EGFR   TP53
## 1      Patient1        Stage1              Y           31  YES   1782   1849
## 2      Patient2        Stage2              N           40   NO    187 173894
## 3      Patient3        Stage2              Y           39  YES     10  16493
## 4      Patient4        Stage3              N           50  YES    472     72
## 5      Patient5        Stage1              Y           45  YES 103784   8193
## 6      Patient6        Stage4              Y           65   NO  18289   1482

A list is constructed using the function list().

my_list <- list(1:5, "a", c(TRUE, FALSE, FALSE), c(3.2, 103.0, 82.3))
my_list

## [[1]]
## [1] 1 2 3 4 5
## 
## [[2]]
## [1] "a"
## 
## [[3]]
## [1]  TRUE FALSE FALSE
## 
## [[4]]
## [1]   3.2 103.0  82.3

str(my_list)

## List of 4
##  $ : int [1:5] 1 2 3 4 5
##  $ : chr "a"
##  $ : logi [1:3] TRUE FALSE FALSE
##  $ : num [1:3] 3.2 103 82.3

One could construct a list by giving names to elements.

my_list <- list(Ranking=1:5, ID="a", Test=c(TRUE, FALSE, FALSE), Score=c(3.2, 103.0, 82.3))

# display the names of elements in the list using the function *names*, or *str*. Compare the output of *str* with the above results to see the difference.
names(my_list)

## [1] "Ranking" "ID"      "Test"    "Score"

str(my_list)

## List of 4
##  $ Ranking: int [1:5] 1 2 3 4 5
##  $ ID     : chr "a"
##  $ Test   : logi [1:3] TRUE FALSE FALSE
##  $ Score  : num [1:3] 3.2 103 82.3

# number of elements in the list
length(my_list)

## [1] 4

First, we are going to talk about subsetting data using [, which is the most commonly used operator. We will start by looking at vectors and talk about four ways to subset a vector.

• Positive integers return elements at the specified positions

# first to recall what are stored in gene_names
gene_names

## [1] "ESR1"  "p53"   "PI3K"  "BRCA1" "EGFR"

# obtain the first and the third elements
gene_names[c(1,3)]

## [1] "ESR1" "PI3K"

R uses 1 based indexing, meaning the first element is at the position 1, not at position 0.

• Negative integers omit elements at the specified positions

gene_names[-c(1,3)]

## [1] "p53"   "BRCA1" "EGFR"

One may not mixed positive and negative integers in one single subset operation.

# The following command will produce an error.
gene_names[c(-1, 2)]

## Error in gene_names[c(-1, 2)]: only 0's may be mixed with negative subscripts

• Logical vectors select elements where the corresponding logical value is TRUE, This is very useful because one may write the expression that creates the logical vector.

gene_names[c(TRUE, FALSE, TRUE, FALSE, FALSE)]

## [1] "ESR1" "PI3K"

Recall that we have created one vector called gene_expression. Let’s assume that gene_expression stores the expression values correspond to the genes in gene_names. Then we may subset the genes based on expression values.

gene_expression

##  ESR1   p53  PI3K BRCA1  EGFR 
##     0   100    50   200    80

gene_names[gene_expression > 50]

## [1] "p53"   "BRCA1" "EGFR"

If the logical vector is shorter in length than the data vector that we want to subset, then it will be recycled to be the same length as the data vector.

gene_names[c(TRUE, FALSE)]

## [1] "ESR1" "PI3K" "EGFR"

If the logical vector has “NA” in it, the corresponding value will be “NA” in the output. “NA” in R is a sysmbol for missing value.

gene_names[c(TRUE, NA, FALSE, TRUE, NA)]

## [1] "ESR1"  NA      "BRCA1" NA

• Character vectors return elements with matching names, when the vector is named.

gene_expression

##  ESR1   p53  PI3K BRCA1  EGFR 
##     0   100    50   200    80

gene_expression[c("ESR1", "p53")]

## ESR1  p53 
##    0  100

• Nothing returns the original vector, This is more useful for matrices, data frames than for vectors.

gene_names[]

## [1] "ESR1"  "p53"   "PI3K"  "BRCA1" "EGFR"

Subsetting a list works in the same way as subsetting an atomic vector. Using [ will always return a list.

my_list[1]

## $Ranking
## [1] 1 2 3 4 5

Subsetting a matrix can be done by simply generalizing the one dimension subsetting: one may supply a one dimension index for each dimension of the matrix. Blank/Nothing subsetting is now useful in keeping all rows or all columns.

my_matrix[c(TRUE, FALSE), ]

##      col1 col2 col3
## row1    1    2    8
## row3    8   27  267

Subsetting a data frame can be done similarly as subsetting a matrix. In addition, one may supply only one 1-dimensional index to subset a data frame. In this case, R will treat the data frame as a list with each column is an element in the list.

# recall a data frame created from above: *meta.data*
meta.data

##   patients_name disease_stage Family_history patients_age BRCA
## 1      Patient1        Stage1              Y           31  YES
## 2      Patient2        Stage2              N           40   NO
## 3      Patient3        Stage2              Y           39  YES
## 4      Patient4        Stage3              N           50  YES
## 5      Patient5        Stage1              Y           45  YES
## 6      Patient6        Stage4              Y           65   NO

# subset the data frame similarly to a matrix
meta.data[c(TRUE, FALSE, FALSE, TRUE),]

##   patients_name disease_stage Family_history patients_age BRCA
## 1      Patient1        Stage1              Y           31  YES
## 4      Patient4        Stage3              N           50  YES
## 5      Patient5        Stage1              Y           45  YES

# subset the data frame using one vector
meta.data[c("patients_age", "disease_stage")]

##   patients_age disease_stage
## 1           31        Stage1
## 2           40        Stage2
## 3           39        Stage2
## 4           50        Stage3
## 5           45        Stage1
## 6           65        Stage4

[[ is similar to [, except that it returns the content of the element.

# recall my_list
my_list

## $Ranking
## [1] 1 2 3 4 5
## 
## $ID
## [1] "a"
## 
## $Test
## [1]  TRUE FALSE FALSE
## 
## $Score
## [1]   3.2 103.0  82.3

# comparing [[ with [ in subsetting a list
my_list[[1]]

## [1] 1 2 3 4 5

my_list[1]

## $Ranking
## [1] 1 2 3 4 5

[[ is very useful when working with a list. Because when [ is applied to a list, it always returns a list. While [[ returns the contents of the list. [[ can only extrac/return one element, so it only accept one integer/string as input.

Because data frames are implemented as lists of columns, one may use [[ to extract a column from data frames.

meta.data[["disease_stage"]]

## [1] Stage1 Stage2 Stage2 Stage3 Stage1 Stage4
## Levels: Stage2 Stage1 Stage3 Stage4

$ is a shorthand for [[ combined with character subsetting.

# subsetting a list using $ 
my_list$Score

## [1]   3.2 103.0  82.3

# subsetting a data frame using
meta.data$disease_stage

## [1] Stage1 Stage2 Stage2 Stage3 Stage1 Stage4
## Levels: Stage2 Stage1 Stage3 Stage4

Simplifying vs. preserving subsetting

We have seen some examples of simplying vs. preserving subsetting, for example:

# simplifying subsetting
my_list[[1]]

## [1] 1 2 3 4 5

# preserving subsetting
my_list[1]

## $Ranking
## [1] 1 2 3 4 5

Basically, simplying subsetting returns the simplest possible data structure that can represent the output. While preserving subsetting keeps the structure of the output as the same as the input. In the above example, [[ simplifies the output to a vector, while [ keeps the output as a list.

Because the syntax of carrying out simplifying and preserving subsetting differs depending on the data structure, the table below provides the information for the most basic data structure.

Please play around with the data structures that we have created to understand the behaviours of simplifying and preserving subsetting