Creating vector

Generally created using c()-

> c(1, 2, 3, 4, 5)
[1] 1 2 3 4 5

Using <- or = vector elements can be assigned -

> x <- c(1, 2, 3, 4, 5)
> print(x)
[1] 1 2 3 4 5

Advice: Do some research by yourself after a while to learn the difference in <- and =.

Data types in vector

The data types can be logical, integer, double, character, complex or raw. Data types in a vector can be found using the function typeof() -

> logi <- c(TRUE, FALSE, TRUE)
> typeof(logi)
[1] "logical"
> int <- c(1L, 2L, 5L, 9L)
> typeof(int)
[1] "integer"
> doub <- c(1, 2, 5, 9)
> typeof(doub)
[1] "double"
> char <- c("a", "cat", "Dhaka")
> typeof(char)
[1] "character"
> complx <- c(1+2i, -3i, 2-1i, 10 + 9i)
> typeof(complx)
[1] "complex"

There are functions called mode() and class(). Explore the vectors using these by yourself.

If multiple data types are used then order of importance in data type is: character > complex > double > integer > logical -

> typeof(c(1,"a"))
[1] "character"
> typeof(c(1,"a",3i))
[1] "character"
> typeof(c(1,3i))
[1] "complex"
> typeof(c(TRUE, 4))
[1] "double"
> typeof(c(10L, 4))
[1] "double"
> typeof(c(10L, FALSE))
[1] "integer"
> typeof(c(10L, 1 + 3i))
[1] "complex"

Changing data types

Using as.___() functions -

> int
[1] 1 2 5 9
> as.character(int)  # Changing to character
[1] "1" "2" "5" "9"
> as.double(int)   # Changing to double
[1] 1 2 5 9
> logi <- c(1,0,0,1)
> typeof(logi)
[1] "double"
> as.logical(logi)  # 1 is TRUE and 0 is FALSE in R
[1]  TRUE FALSE FALSE  TRUE
> doub <- c(1.8, 1, 5, pi)
> doub
[1] 1.800000 1.000000 5.000000 3.141593
> typeof(doub)
[1] "double"
> as.integer(doub)
[1] 1 1 5 3

Look how integers require less memory than doubles -

> int <- c(1L, 2L, 5L, 9L)
> doub <- c(1, 2, 5, 9)
> object.size(int)  # Returns memory allocation of int
64 bytes
> object.size(doub)  # Returns memory allocation of doub
80 bytes

Combining vectors

Using c():

> a <- c(1, 2, 3, 4, 5)
> b <- c(10, 11, 12, 13, 14)
> comb <- c(a,b)
> comb
 [1]  1  2  3  4  5 10 11 12 13 14

If combining multiple data types then the data type with most importance will be assiged -

> a <- c(1, 2, 3, 4, 5)
> d <- c("a", "b", "cat")
> comb <- c(a, d)
> comb
[1] "1"   "2"   "3"   "4"   "5"   "a"   "b"   "cat"
> typeof(comb)
[1] "character"

Length of vectors

Using the function length() -

> y <- c(10, 99, 12, 19, 100)
> length(y) # Returns the number of elements in y
[1] 5

Index

In R, array indexes starts at 1. And elements are selected by passing the index in []-

> y <- c(10, 99, 12, 19, 100)
> y[1] # Selects the 1st element in a
[1] 10
> y[4] # Selects the 4th element in a
[1] 19
> y[length(y)]   # Selects the last element in a
[1] 100

Deleting elements

Using - before the indexes -

> y[-1] # Removes the 1st element
[1]  99  12  19 100
> y[-4] # Removes the 4th element
[1]  10  99  12 100
> y[-c(1,4)] #Removed 1st and 4th element
[1]  99  12 100

Notice the original vector y is not changed -

> y
[1]  10  99  12  19 100

To change the original vector just assign the new vector to the old one -

> y <- y[-c(1,4)]
> y
[1]  99  12 100

Sequence

: method

Using : a sequence of integers can be created -

> 1:10  # Sequence of 1 to 10
 [1]  1  2  3  4  5  6  7  8  9 10
> 10:1  # Sequence of 10 to 1
 [1] 10  9  8  7  6  5  4  3  2  1
> -1:-10  # Sequence of -1 to -10
 [1]  -1  -2  -3  -4  -5  -6  -7  -8  -9 -10

seq() function

> seq(from=4, to=10)  # Sequence of integers from 4 to 10
[1]  4  5  6  7  8  9 10

Using the argument names is not necessary in all the cases -

> seq(4,10)
[1]  4  5  6  7  8  9 10

Passing only an integer will return the integers from 1 to that specific integer -

> seq(7)  # Returns integers from 1 to 7
[1] 1 2 3 4 5 6 7
> seq(-5) # Returns integers from 1 to -10
[1]  1  0 -1 -2 -3 -4 -5

by

To get a sequence of integers with an increment of 3 use the by argument-

> seq(1, 10, by = 3)
[1]  1  4  7 10

More example -

> seq(1, 2, by = 0.1) # Sequence of double increment by 0.1
 [1] 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

longth.out

If we want specific number of values in an interval then length.out argument can be used -

> seq(0, 20, length.out = 5)  # Returns exactly 5 numbers between 0 and 20
[1]  0  5 10 15 20
> seq(0, 1, length.out = 10)  # Returns exactly 10 numbers between 0 and 1
 [1] 0.0000000 0.1111111 0.2222222 0.3333333 0.4444444 0.5555556 0.6666667
 [8] 0.7777778 0.8888889 1.0000000

Arguments can be written in short form unless they match other argument names -

> seq(0, 1, len = 10) 
 [1] 0.0000000 0.1111111 0.2222222 0.3333333 0.4444444 0.5555556 0.6666667
 [8] 0.7777778 0.8888889 1.0000000

Sequence of date

> start_date <- as.Date("2020-01-01")
> end_date <- as.Date("2021-12-31")
> months_seq <- seq(start_date, end_date, by="+1 months")
> format(months_seq, "%d %B %Y")
 [1] "01 January 2020"   "01 February 2020"  "01 March 2020"    
 [4] "01 April 2020"     "01 May 2020"       "01 June 2020"     
 [7] "01 July 2020"      "01 August 2020"    "01 September 2020"
[10] "01 October 2020"   "01 November 2020"  "01 December 2020" 
[13] "01 January 2021"   "01 February 2021"  "01 March 2021"    
[16] "01 April 2021"     "01 May 2021"       "01 June 2021"     
[19] "01 July 2021"      "01 August 2021"    "01 September 2021"
[22] "01 October 2021"   "01 November 2021"  "01 December 2021" 

Visit this link to learn in detail about dates in R.

Repeatation

rep() function

To get a vector with repeated values use the rep() function -

> rep(2, times = 10) # Returns 10 2s
 [1] 2 2 2 2 2 2 2 2 2 2

When passing a vector with length more than 1, the whole vector will repeat -

> rep(c(1,2, 99), times = 5) 
 [1]  1  2 99  1  2 99  1  2 99  1  2 99  1  2 99

Using the argument each we can get the elements repeated by each at a time -

> rep(c(1, 2, 99), each = 3)
[1]  1  1  1  2  2  2 99 99 99

Using both each and times-

> rep(c(1, 2, 99), each = 3, times = 2)
 [1]  1  1  1  2  2  2 99 99 99  1  1  1  2  2  2 99 99 99

gl() function

To create a sequence of factor type data `gl() function can be used -

> fac_seq <- gl(n = 2, k = 3)
> fac_seq
[1] 1 1 1 2 2 2
Levels: 1 2
> class(fac_seq)
[1] "factor"

We can specify the levels using the argument labels-

> fac_seq <- gl(n = 2, k = 3, labels = c("Control", "Treatment"))
> fac_seq
[1] Control   Control   Control   Treatment Treatment Treatment
Levels: Control Treatment

If we want the levels to be ordered then ordered argument can be used -

> gl(n = 2, k = 3, labels = c("January", "May"), ordered = T)
[1] January January January May     May     May    
Levels: January < May

To know more about factors visit here.

Names in vector

While creating vector we can specify names of elements -

> x <- c("1st"=98, "2nd"=93, "3rd"=89, "4th"=88)
> x
1st 2nd 3rd 4th 
 98  93  89  88 

We can access the names using names() function -

> names(x)
[1] "1st" "2nd" "3rd" "4th"

So we can replace the names too!

> names(x) <- c("First", "Second", "Third", "Fourth")
> x
 First Second  Third Fourth 
    98     93     89     88 

To select elements in vectors like these we can use either indexes or names -

> x[1]
First 
   98 
> x["First"]
First 
   98 

To delete the names simply assign NULL to the names of the vector -

> names(x) <- NULL
> x
[1] 98 93 89 88

R class hierarchy

> x <- 1L
> print(c(class(x), mode(x), storage.mode(x), typeof(x)))
[1] "integer" "numeric" "integer" "integer"
> x <- 1
> print(c(class(x), mode(x), storage.mode(x), typeof(x)))
[1] "numeric" "numeric" "double"  "double" 
> x <- letters
> print(c(class(x), mode(x), storage.mode(x), typeof(x)))
[1] "character" "character" "character" "character"
> x <- TRUE
> print(c(class(x), mode(x), storage.mode(x), typeof(x)))
[1] "logical" "logical" "logical" "logical"
> x <- cars
> print(c(class(x), mode(x), storage.mode(x), typeof(x)))
[1] "data.frame" "list"       "list"       "list"      
> x <- cars[1]
> print(c(class(x), mode(x), storage.mode(x), typeof(x)))
[1] "data.frame" "list"       "list"       "list"      
> x <- cars[[1]]
> print(c(class(x), mode(x), storage.mode(x), typeof(x)))
[1] "numeric" "numeric" "double"  "double" 
> x <- matrix(cars)
> print(c(class(x), mode(x), storage.mode(x), typeof(x)))
[1] "matrix" "array"  "list"   "list"   "list"  
> x <- new.env()
> print(c(class(x), mode(x), storage.mode(x), typeof(x)))
[1] "environment" "environment" "environment" "environment"
> x <- expression(1 + 1)
> print(c(class(x), mode(x), storage.mode(x), typeof(x)))
[1] "expression" "expression" "expression" "expression"
> x <- quote(y <- 1 + 1)
> print(c(class(x), mode(x), storage.mode(x), typeof(x)))
[1] "<-"       "call"     "language" "language"
> x <- ls
> print(c(class(x), mode(x), storage.mode(x), typeof(x)))
[1] "function" "function" "function" "closure" 
---
title: "Vector"
author: 'MD AHSANUL ISLAM'
output: 
  html_document:
    toc: true
    toc_float: true
    theme: cerulean
    highlight: haddock
    code_download: true
---

```{r, include=FALSE}
knitr::opts_chunk$set(
  comment = "", prompt = TRUE, message = FALSE, warning = FALSE
)
```

---

# Creating vector
Generally created using `c()`-
```{r}
c(1, 2, 3, 4, 5)
```

Using `<-` or `=` vector elements can be assigned -
```{r}
x <- c(1, 2, 3, 4, 5)
print(x)
```

Advice: Do some research by yourself after a while to learn the difference in `<-` and `=`.

# Data types in vector

The data types can be logical, integer, double, character, complex or raw. Data types in a vector can be found using the function `typeof()` - 
```{r}
logi <- c(TRUE, FALSE, TRUE)
typeof(logi)
int <- c(1L, 2L, 5L, 9L)
typeof(int)
doub <- c(1, 2, 5, 9)
typeof(doub)
char <- c("a", "cat", "Dhaka")
typeof(char)
complx <- c(1+2i, -3i, 2-1i, 10 + 9i)
typeof(complx)
```

There are functions called `mode()` and `class()`. Explore the vectors using these by yourself.

If multiple data types are used then order of importance in data type is: character > complex > double > integer > logical -
```{r}
typeof(c(1,"a"))
typeof(c(1,"a",3i))
typeof(c(1,3i))
typeof(c(TRUE, 4))
typeof(c(10L, 4))
typeof(c(10L, FALSE))
typeof(c(10L, 1 + 3i))
```

# Changing data types
Using `as.___()` functions - 
```{r}
int
as.character(int)  # Changing to character
as.double(int)   # Changing to double
logi <- c(1,0,0,1)
typeof(logi)
as.logical(logi)  # 1 is TRUE and 0 is FALSE in R
doub <- c(1.8, 1, 5, pi)
doub
typeof(doub)
as.integer(doub)
```

Look how integers require less memory than doubles - 
```{r}
int <- c(1L, 2L, 5L, 9L)
doub <- c(1, 2, 5, 9)
object.size(int)  # Returns memory allocation of int
object.size(doub)  # Returns memory allocation of doub
```


# Combining vectors

Using `c()`:
```{r}
a <- c(1, 2, 3, 4, 5)
b <- c(10, 11, 12, 13, 14)
comb <- c(a,b)
comb
```

If combining multiple data types then the data type with most importance will be assiged - 
```{r}
a <- c(1, 2, 3, 4, 5)
d <- c("a", "b", "cat")
comb <- c(a, d)
comb
typeof(comb)
```

# Length of vectors
Using the function `length()` -
```{r}
y <- c(10, 99, 12, 19, 100)
length(y) # Returns the number of elements in y
```

# Index
In `R`, array indexes starts at 1. And elements are selected by passing the index in `[]`-
```{r}
y <- c(10, 99, 12, 19, 100)
y[1] # Selects the 1st element in a
y[4] # Selects the 4th element in a
y[length(y)]   # Selects the last element in a
```

# Deleting elements
Using `-` before the indexes - 
```{r}
y[-1] # Removes the 1st element
y[-4] # Removes the 4th element
y[-c(1,4)] #Removed 1st and 4th element
```
Notice the original vector `y` is not changed - 
```{r}
y
```

To change the original vector just assign the new vector to the old one - 
```{r}
y <- y[-c(1,4)]
y
```

# Sequence

## `:` method

Using `:` a sequence of integers can be created - 
```{r}
1:10  # Sequence of 1 to 10
10:1  # Sequence of 10 to 1
-1:-10  # Sequence of -1 to -10
```

## seq() function
```{r}
seq(from=4, to=10)  # Sequence of integers from 4 to 10
```
Using the argument names is not necessary in all the cases - 
```{r}
seq(4,10)
```
Passing only an integer will return the integers from 1 to that specific integer - 
```{r}
seq(7)  # Returns integers from 1 to 7
seq(-5) # Returns integers from 1 to -10
```

### `by`
To get a sequence of integers with an increment of 3 use the `by` argument-
```{r}
seq(1, 10, by = 3)
```
More example -
```{r}
seq(1, 2, by = 0.1) # Sequence of double increment by 0.1
```

### `longth.out`

If we want specific number of values in an interval then `length.out` argument can be used -
```{r}
seq(0, 20, length.out = 5)  # Returns exactly 5 numbers between 0 and 20
seq(0, 1, length.out = 10)  # Returns exactly 10 numbers between 0 and 1
```
Arguments can be written in short form unless they match other argument names - 
```{r}
seq(0, 1, len = 10) 
```

## Sequence of date

```{r}
start_date <- as.Date("2020-01-01")
end_date <- as.Date("2021-12-31")
months_seq <- seq(start_date, end_date, by="+1 months")
format(months_seq, "%d %B %Y")
```

Visit this [link](https://rstudio-pubs-static.s3.amazonaws.com/667330_36c1f23cad5c416a8d81bdee3e77513d.html#sequence-of-dates) to learn in detail about dates in R.

# Repeatation

## rep() function
To get a vector with repeated values use the `rep()` function - 
```{r}
rep(2, times = 10) # Returns 10 2s
```
When passing a vector with length more than 1, the whole vector will repeat - 
```{r}
rep(c(1,2, 99), times = 5) 
```
Using the argument `each` we can get the elements repeated by each at a time - 
```{r}
rep(c(1, 2, 99), each = 3)
```
Using both `each` and `times`-
```{r}
rep(c(1, 2, 99), each = 3, times = 2)
```

## gl() function
To create a sequence of factor type data `gl() function can be used - 
```{r}
fac_seq <- gl(n = 2, k = 3)
fac_seq
class(fac_seq)
```
We can specify the levels using the argument `labels`-
```{r}
fac_seq <- gl(n = 2, k = 3, labels = c("Control", "Treatment"))
fac_seq
```
If we want the levels to be ordered then `ordered` argument can be used -
```{r}
gl(n = 2, k = 3, labels = c("January", "May"), ordered = T)
```
To know more about factors visit [here](https://rpubs.com/MdAhsanul/factor).

# Names in vector

While creating vector we can specify names of elements - 
```{r}
x <- c("1st"=98, "2nd"=93, "3rd"=89, "4th"=88)
x
```
We can access the names using `names()` function - 
```{r}
names(x)
```
So we can replace the names too!
```{r}
names(x) <- c("First", "Second", "Third", "Fourth")
x
```
To select elements in vectors like these we can use either indexes or names -
```{r}
x[1]
x["First"]
```
To delete the names simply assign NULL to the names of the vector - 
```{r}
names(x) <- NULL
x
```

# R class hierarchy

```{r}
x <- 1L
print(c(class(x), mode(x), storage.mode(x), typeof(x)))

x <- 1
print(c(class(x), mode(x), storage.mode(x), typeof(x)))

x <- letters
print(c(class(x), mode(x), storage.mode(x), typeof(x)))

x <- TRUE
print(c(class(x), mode(x), storage.mode(x), typeof(x)))

x <- cars
print(c(class(x), mode(x), storage.mode(x), typeof(x)))

x <- cars[1]
print(c(class(x), mode(x), storage.mode(x), typeof(x)))

x <- cars[[1]]
print(c(class(x), mode(x), storage.mode(x), typeof(x)))

x <- matrix(cars)
print(c(class(x), mode(x), storage.mode(x), typeof(x)))

x <- new.env()
print(c(class(x), mode(x), storage.mode(x), typeof(x)))

x <- expression(1 + 1)
print(c(class(x), mode(x), storage.mode(x), typeof(x)))

x <- quote(y <- 1 + 1)
print(c(class(x), mode(x), storage.mode(x), typeof(x)))

x <- ls
print(c(class(x), mode(x), storage.mode(x), typeof(x)))
```

