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## Quickstart

### Installation

### Variables

Values can be assigned to variables with the operators `<-`

, `=`

or `->`

.

### Functions

R functions are invoked by their name, then followed by the parenthesis, and zero or more arguments.

### Packages

Additional functionality beyond those offered by the core R library are available with R packages. In order to install an additional package, the `install.packages`

function can be invoked.

There are two ways to invoke functions from add-on packages: using the package namespace or loading the package.

## Basic Data Types

There are several basic R data types that are of frequent occurrence in routine R calculations.

### Numeric

Decimal values are called numerics in R. It is the default computational data type. If a decimal value is assigned to a variable `x`

as follows, `x`

will be of **numeric** type.

`## [1] "numeric"`

Furthermore, even if an integer is assigned to a variable `x`

, it is still being saved as a numeric value.

`## [1] FALSE`

### Integer

In order to create an integer variable in R, the `as.integer`

function can be invoked.

`## [1] TRUE`

Integers can also be declared by appending an `L`

suffix.

`## [1] TRUE`

### Complex

Complex numbers are of `complex`

type

`## [1] "complex"`

Basic functions which support complex arithmetic are:

`## [1] 3`

`## [1] 4`

`## [1] 5`

`## [1] 0.9272952`

`## [1] 3-4i`

### Logical

A logical value is often created via comparison between variables.

`## [1] TRUE`

Standard logical operations are `&`

(and), `|`

(or), and `!`

(not).

`## [1] FALSE`

`## [1] TRUE`

`## [1] FALSE`

### Character

A character object is used to represent string values in R. Two character values can be concatenated with the `paste`

function.

`## [1] "[email protected]"`

However, it is often more convenient to create a readable string with the `sprintf`

function, which has a C language syntax.

`## [1] "Sam has 100 dollars"`

And to replace the first occurrence of the word “little” by another word “big” in the string, the `sub`

function can be applied.

`## [1] "Mary has a big lamb."`

More functions for string manipulation can be found in the R documentation.

## Basic Data Structures

### Vector

The basic data structure in R is the vector. They are usually created with the `c()`

function, short for combine:

`## [1] 1 2 3`

Vectors can contain only **similar data types**. If this is not the case, some conversion takes place.

`## [1] "FALSE" "1" "2"`

### Matrix

A matrix is a collection of **similar data types** arranged in a two-dimensional rectangular layout. They are usually created with the `matrix()`

function:

```
matrix(data = c(1,2,3,4,5,6), # the data elements
ncol = 3, # number of columns
nrow = 2, # number of rows
byrow = TRUE) # fill matrix by rows
```

```
## [,1] [,2] [,3]
## [1,] 1 2 3
## [2,] 4 5 6
```

#### Named Matrix

```
# Declaring a named matrix
matrix(data = c(1,2,3,4,5,6), # the data elements
ncol = 3, # number of columns
nrow = 2, # number of rows
byrow = TRUE, # fill matrix by rows
dimnames = list( # list containing names
c('r1','r2'), # rownames
c('c1','c2','c3') # colnames
))
```

```
## c1 c2 c3
## r1 1 2 3
## r2 4 5 6
```

```
# Generating a named matrix
M <- matrix(data = c(1,2,3,4,5,6), # the data elements
ncol = 3, # number of columns
nrow = 2, # number of rows
byrow = TRUE) # fill matrix by rows
rn <- c('r1','r2') # vector of rownames
cn <- c('c1','c2','c3') # vector of colnames
rownames(M) <- rn # assign rownames
colnames(M) <- cn # assign colnames
M
```

```
## c1 c2 c3
## r1 1 2 3
## r2 4 5 6
```

### Data Frame

A data frame is used for storing data tables. It is similar to a `matrix`

but `data.frame`

can contain **heterogeneous inputs** while a `matrix`

cannot. In `matrix`

only similar data types can be stored whereas in a `data.frame`

there can be different data types. They are usually created with the `data.frame()`

function. Beware `data.frame()`

’s default behaviour which turns strings into factors (a factor is a vector that can contain only predefined values, and is used to store categorical data). Use `stringsAsFactors = FALSE`

to suppress this behaviour:

```
v1 <- c(10,20,30) # numeric vector
v2 <- c('a','b','c') # character vector
v3 <- c(TRUE,TRUE,FALSE) # logical vector
data.frame(v1, v2, v3, stringsAsFactors = FALSE) # data.frame
```

```
## v1 v2 v3
## 1 10 a TRUE
## 2 20 b TRUE
## 3 30 c FALSE
```

#### Named Data Frame

```
# Declaring a named data.frame
v1 <- c(10,20,30) # numeric vector
v2 <- c('a','b','c') # character vector
v3 <- c(TRUE,TRUE,FALSE) # logical vector
data.frame('c1' = v1, # column named 'c1'
'c2' = v2, # column named 'c2'
'c3' = v3, # column named 'c3'
row.names = c('r1', 'r2', 'r3'), # vector of rownames
stringsAsFactors = FALSE) # suppress character conversion
```

```
## c1 c2 c3
## r1 10 a TRUE
## r2 20 b TRUE
## r3 30 c FALSE
```

```
# Generating a named data.frame
v1 <- c(10,20,30) # numeric vector
v2 <- c('a','b','c') # character vector
v3 <- c(TRUE,TRUE,FALSE) # logical vector
rn <- c('r1','r2','r3') # vector of rownames
cn <- c('c1','c2','c3') # vector of colnames
df <- data.frame(v1, v2, v3,stringsAsFactors = FALSE) # data.frame
rownames(df) <- rn # assign rownames
colnames(df) <- cn # assign colnames
df
```

```
## c1 c2 c3
## r1 10 a TRUE
## r2 20 b TRUE
## r3 30 c FALSE
```

### List

A `list`

is a generic structure which can be thought as an ordered set of objects. They are usually created with the `list()`

function:

```
## [[1]]
## [,1]
## [1,] 100
##
## [[2]]
## X1 X2 X3
## 1 1 2 3
##
## [[3]]
## [1] "a" "b" "c" "d"
```

#### Named List

```
# Declaring a named list
list('matrix' = matrix(100), # matrix
'data.frame' = data.frame(1,2,3), # data.frame
'vector' = c('a','b','c','d')) # vector
```

```
## $matrix
## [,1]
## [1,] 100
##
## $data.frame
## X1 X2 X3
## 1 1 2 3
##
## $vector
## [1] "a" "b" "c" "d"
```

```
# Generating a named list
M <- matrix(100) # matrix
df <- data.frame(1,2,3) # data.frame
v <- c('a','b','c','d') # vector
n <- c('matrix','data.frame','vector') # vector of names
l <- list(M, df, v) # list
names(l) <- n # assign names
l
```

```
## $matrix
## [,1]
## [1,] 100
##
## $data.frame
## X1 X2 X3
## 1 1 2 3
##
## $vector
## [1] "a" "b" "c" "d"
```

### Environment

Generally, an `environment`

is similar to a `list`

, with four important exceptions:

- Every name in an environment is unique.
- The names in an environment are not ordered (i.e., it doesn’t make sense to ask what the first element of an environment is).
- An environment has a parent (nested structure).
- Environments have
**reference**semantics.

To create an environment manually, use `new.env()`

.

`## `

## Basic Operations

### Subsetting

#### Vector

Values in a `vector`

are retrieved by using the single square bracket `[]`

operator.

```
## aaa bbb ccc ddd eee
## "a" "b" "c" "d" "e"
```

```
## ccc
## "c"
```

```
## aaa bbb ddd eee
## "a" "b" "d" "e"
```

`## `
## NA

```
## bbb ccc eee eee
## "b" "c" "e" "e"
```

```
## bbb ddd eee
## "b" "d" "e"
```

```
## ddd bbb
## "d" "b"
```

```
## ccc
## "c"
```

```
# the logical vector will be recycled if it is shorter than the vector to subset
i <- c(FALSE,TRUE) # -> c(FALSE,TRUE,FALSE,TRUE,FALSE)
s[i]
```

```
## bbb ddd
## "b" "d"
```

```
## ccc ddd eee
## "c" "d" "e"
```

#### Matrix

Values in a `matrix`

are retrieved by using the single square bracket `[]`

operator.

```
M <- matrix(1:12, nrow = 3, ncol = 4, byrow = TRUE)
rownames(M) <- c('r1','r2','r3')
colnames(M) <- c('c1','c2','c3','c4')
M # print the full matrix
```

```
## c1 c2 c3 c4
## r1 1 2 3 4
## r2 5 6 7 8
## r3 9 10 11 12
```

`## [1] 7`

```
## c1 c2 c3 c4
## 1 2 3 4
```

```
## r1 r2 r3
## 1 5 9
```

```
## c1 c2 c3 c4
## r2 5 6 7 8
## r3 9 10 11 12
```

```
## c2 c4
## r1 2 4
## r2 6 8
## r3 10 12
```

```
## c2 c4
## r1 2 4
## r3 10 12
```

```
## c1 c2 c3 c4
## r1 1 2 3 4
## r3 9 10 11 12
```

```
## c2 c4
## r1 2 4
## r2 6 8
## r3 10 12
```

```
## c2 c4
## 10 12
```

```
## c1 c2 c3 c4
## 1 2 3 4
```

```
# the logical vector will be recycled if it is shorter than the number of rows/columns to subset
i <- c(TRUE,FALSE) # -> c(TRUE,FALSE,TRUE)
M[i,]
```

```
## c1 c2 c3 c4
## r1 1 2 3 4
## r3 9 10 11 12
```

```
# select the column named 'c4' where 'c3' is less than twice 'c1'
i <- M[,'c3'] < 2*M[,'c1']
M[i,'c4']
```

```
## r2 r3
## 8 12
```

#### Data Frame

Elements of a `data.frame`

are retrieved by using the single square bracket `[]`

operator as seen with `matrix`

. Here, also the `$`

or `[[]]`

operators can be used to retrieve columns.

```
## age sex
## 1 48 M
## 2 18 F
## 3 51 M
```

`## [1] 48 18 51`

```
# retrieve the age of males ("M")
i <- df$sex == "M" # equivalent to df[["sex"]]=="M" or df[,"sex"]=="M"
df$age[i] # equivalent to df[["age"]][i] or df[i,"age"]
```

`## [1] 48 51`

#### List

A list is subsetted using the single square bracket `[]`

operator.

```
l <- list(
'data' = data.frame('age' = c(48,18,51), 'sex' = c('M','F','M')),
'letters' = c('a','b','c'),
'extra' = c(1:5)
)
l # print full list
```

```
## $data
## age sex
## 1 48 M
## 2 18 F
## 3 51 M
##
## $letters
## [1] "a" "b" "c"
##
## $extra
## [1] 1 2 3 4 5
```

```
## $data
## age sex
## 1 48 M
## 2 18 F
## 3 51 M
##
## $extra
## [1] 1 2 3 4 5
```

```
## $extra
## [1] 1 2 3 4 5
##
## $letters
## [1] "a" "b" "c"
```

```
## $data
## age sex
## 1 48 M
## 2 18 F
## 3 51 M
##
## $letters
## [1] "a" "b" "c"
```

Objects in a `list`

are retrieved by using the operator `[[]]`

or `$`

.

`## [1] "a" "b" "c"`

```
## age sex
## 1 48 M
## 2 18 F
## 3 51 M
```

#### Environment

An `environment`

is not subsettable, i.e. the `[]`

operator cannot be used. Objects in an `environment`

are retrieved by using the operator `[[]]`

, `$`

or the function `get()`

.

`## [1] 1`

`## [1] 1`

`## [1] 1`

Remember that an `environment`

is similar to a `list`

, but has a **reference** semantics.

```
x <- list() # using a list
x$a <- 1 # assign 1 to the element "a" in x
y <- x # COPY x to y
x$a <- 2 # assign 2 to the element "a" in x
y$a # what happens to the element "a" in y?
```

`## [1] 1`

```
x <- new.env() # using an environment
x$a <- 1 # assign 1 to the element "a" in x
y <- x # REFERENCE x to y
x$a <- 2 # assign 2 to the element "a" in x
y$a # what happens to the element "a" in y?
```

`## [1] 2`

### Arithmetics

Arithmetic operations of **vectors** and **matrices** are performed element-by-element, **data.frames** are treated as **matrices** when containing one data type only. If two vectors are of unequal length, the shorter one will be recycled in order to match the longer vector. For example, the following vectors `u`

and `v`

have different lengths, and their sum is computed by recycling values of the shorter vector `u`

.

```
u <- c(10, 20, 30)
v <- c(1, 2, 3, 4, 5, 6, 7, 8, 9)
M <- matrix(c(1, 2, 3, 4, 5, 6, 7, 8, 9), ncol = 3, nrow = 3, byrow = TRUE)
# vector + vector
u + v
```

`## [1] 11 22 33 14 25 36 17 28 39`

`## [1] 11 21 31`

`## [1] 20 40 60`

```
## [,1] [,2] [,3]
## [1,] 2 3 4
## [2,] 5 6 7
## [3,] 8 9 10
```

```
## [,1] [,2] [,3]
## [1,] 11 12 13
## [2,] 24 25 26
## [3,] 37 38 39
```

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

```
## [,1] [,2] [,3]
## [1,] 10 20 30
## [2,] 80 100 120
## [3,] 210 240 270
```

```
## [,1]
## [1,] 140
## [2,] 320
## [3,] 500
```

## Control Structures

In order to control the execution of the expressions flow in R, we make use of the control structures.

### if

This task is carried out only if this condition is returned as `TRUE`

.

`## [1] "executing if"`

### if-else

The if-else combination is probably the most commonly used control structure in R (or perhaps any language). This structure allows you to test a condition and act on it depending on whether it’s true or false.

`## [1] "executing else"`

You can have a series of tests by following the initial if with any number of else `if`

s.

```
if(1>2){
print('executing if')
} else if(1<2) {
print('executing else-if')
} else {
print('executing else')
}
```

`## [1] "executing else-if"`

### for

In R, for loops take an interator variable and assign it successive values from a sequence or vector. For loops are most commonly used for iterating over the elements of an object (list, vector, etc.).

```
## [1] 1
## [1] 2
## [1] 3
## [1] 4
## [1] 5
```

### while

While loops begin by testing a condition. If it is true, then they execute the loop body. Once the loop body is executed, the condition is tested again, and so forth, until the condition is false, after which the loop exits. While loops can potentially result in infinite loops if not written properly. Use with care!

```
## [1] 2
## [1] 3
## [1] 4
## [1] 5
```

### repeat

`repeat`

initiates an infinite loop right from the start. These are not commonly used in statistical or data analysis applications but they do have their uses. The only way to exit a repeat loop is to call `break`

.

```
## [1] 5
## [1] 6
## [1] 7
## [1] 8
## [1] 9
```

### break

We use break statement inside a loop (repeat, for, while) to stop the iterations and flow the control outside of the loop. While in a nested looping situation, where there is a loop inside another loop, this statement exits from the innermost loop that is being evaluated.

`## [1] 1`

### next

`next`

jumps to the next cycle without completing a particular iteration. In fact, it jumps to the evaluation of the condition holding the current loop. Next statement enables to skip the current iteration of a loop without terminating it.

```
## [1] 1
## [1] 3
## [1] 4
```

### Loop Functions

https://bookdown.org/rdpeng/rprogdatascience/loop-functions.html

R has some functions which implement looping in a compact form to make your life easier.

`lapply()`

: Loop over a list and evaluate a function on each element

`sapply()`

: Same as lapply but try to simplify the result

`apply()`

: Apply a function over the margins of an array

#### lapply

The `lapply()`

function does the following simple series of operations:

- it loops over a list, iterating over each element in that list
- it applies a function to each element of the list (a function that you specify)
- returns a list

Here’s an example of applying the `mean()`

function to all elements of a list. If the original list has names, the the names will be preserved in the output.

```
## $a
## [1] 5.5
##
## $b
## [1] 50.5
```

You can use `lapply()`

to evaluate a function multiple times each with a different argument. Below, is an example where I call the `runif()`

function (to generate uniformly distributed random variables) four times, each time generating a different number of random numbers.

```
## [[1]]
## [1] 0.2875775
##
## [[2]]
## [1] 0.7883051 0.4089769
##
## [[3]]
## [1] 0.8830174 0.9404673 0.0455565
##
## [[4]]
## [1] 0.5281055 0.8924190 0.5514350 0.4566147
```

When you pass a function to `lapply()`

, `lapply()`

takes elements of the list and passes them as the first argument of the function you are applying. In the above example, the first argument of `runif()`

is `n`

, and so the elements of the sequence `1:4`

all got passed to the n argument of `runif()`

.

Functions that you pass to `lapply()`

may have other arguments. For example, the `runif()`

function has a `min`

and `max`

argument too. Here is where the `...`

argument to `lapply()`

comes into play. Any arguments that you place in the `...`

argument will get passed down to the function being applied to the elements of the list.

Here, the `min = 0`

and `max = 10`

arguments are passed down to `runif()`

every time it gets called.

```
## [[1]]
## [1] 9.568333
##
## [[2]]
## [1] 4.533342 6.775706
##
## [[3]]
## [1] 5.726334 1.029247 8.998250
##
## [[4]]
## [1] 2.4608773 0.4205953 3.2792072 9.5450365
```

#### sapply

The `sapply()`

function behaves similarly to `lapply()`

; the only real difference is in the return value. `sapply()`

will try to simplify the result of `lapply()`

if possible. Essentially, `sapply()`

calls `lapply()`

on its input and then applies the following algorithm:

- if the result is a list where every element is length 1, then a vector is returned
- if the result is a list where every element is a vector of the same length (> 1), a matrix is returned
- if it can’t figure things out, a list is returned

```
## a b
## 5.5 50.5
```

#### apply

The `apply()`

function is used to a evaluate a function over the margins of an array. It is most often used to apply a function to the rows or columns of a `matrix`

or `data.frame`

.

Here we create a 20 by 10 matrix of Normal random numbers.

Compute the mean of each column: `MARGIN = 2`

.

```
## [1] -0.10796846 0.15666451 0.17238484 -0.02491125 0.02062309 -0.21667563
## [7] -0.22015146 0.20890536 0.02170259 0.02202638
```

Compute the mean of each row: `MARGIN = 1`

.

```
## [1] 0.406234477 -0.015545859 0.131356598 0.076696478 -0.299281746
## [6] 0.647064814 0.125209819 -0.234601007 0.232658077 -0.628908133
## [11] 0.092009303 0.003069751 -0.717961239 0.186628459 -0.248612490
## [16] -0.377757063 0.092656464 -0.172082143 0.391801315 0.374564059
```

## User-Defined Functions

Abstracting code into many small functions is key for writing nice R code. Functions are defined by code with a specific format:

where

`functionName`

: the name of the function (case sensitive)`arg1`

,`arg2`

,`arg3`

,`...`

: input values`arg3=NULL`

: default value. If`arg3`

is not provided when calling the function,`NULL`

will be used instead`return()`

: the output value

Define a function to compute the sum of the first `n`

integer numbers.

Compute the sum of the first 10 integers

`## [1] 55`

Define a function to compute the `p`

norm of a vector `x`

. By default, compute the Euclidean norm (`p = 2`

).

Compute the Euclidean norm of the vector `c(1,1)`

`## [1] 1.414214`

Compute the 3-norm of the vector `c(1,1)`

`## [1] 1.259921`

Compute the \(\infty\)-norm of the vector `c(1,1)`

`## [1] 1`

### Scope of functions

If you use an R function, the function first creates a temporary local environment. This local environment is nested within the global environment, which means that, from that local environment, you also can access any object from the global environment (not considered a good practice). As soon as the function ends, the local environment is destroyed along with all the objects in it.

```
# define function
test1 <- function(){
teststring <- 'This object is destroyed as soon as the function ends!'
return(invisible())
}
# run function
test1()
# try to access teststring
teststring
```

`## Error in eval(expr, envir, enclos): object 'teststring' not found`

If R sees any object name, it first searches the local environment. If it finds the object there, it uses that one else it searches in the global environment for that object.

```
# global i
i <- 1
# define function
test2 <- function(){
# there is no i in the local environment -> search in parent environment
i <- i*10
# return
return(i)
}
# run function
test2()
```

`## [1] 10`

`## [1] 1`

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