Stat 585 - Data Types

class: center, middle, inverse, title-slide

.title[
# Stat 585 - Data Types
]
.author[
### Heike Hofmann
]

---

class: center, middle

# Data Types

---

## Basic Data Types

Name | Example
---- | -------
numeric | 2.93
integer | 2
character | "hello world"
logical | TRUE

Convert between data types with **cast operators** 
```
as.character, as.numeric, as.logical, as.integer, ...
```
e.g. `as.numeric("2.394")` or `as.character("3.14159")`

Test whether something has a data type with `is.XXX`, e.g. `is.character("fuzzy puppies")` or `is.logical("abcde")`

---

## Numeric values

Numeric objects have double precision, i.e. work with 53 bits

```r
pi <- as.numeric(gsub(" ","","3.14159 26535 89793 23846 26433"))
# maximum number of digits that can be shown is 22
print(pi, digits=22)
```

```
## [1] 3.141592653589793115998
```
first 15 digits are fine, anything beyond that is suspicious and most likely incorrect

Precision is machine dependent

---

## `.Machine$double.eps`

`.Machine$double.eps` is the machine's difference between two consecutive real valued numbers

```r
.Machine$double.eps
```

```
## [1] 2.220446e-16
```

```r
1 + .Machine$double.eps == 1
```

```
## [1] FALSE
```

```r
1 + .Machine$double.eps/2 == 1
```

```
## [1] TRUE
```

```r
1 + .Machine$double.eps == 1
```

```
## [1] FALSE
```

---

```r
.Machine
```

```
## $double.eps
## [1] 2.220446e-16
## 
## $double.neg.eps
## [1] 1.110223e-16
## 
## $double.xmin
## [1] 2.225074e-308
## 
## $double.xmax
## [1] 1.797693e+308
## 
## $double.base
## [1] 2
## 
## $double.digits
## [1] 53
## 
## $double.rounding
## [1] 5
## 
## $double.guard
## [1] 0
## 
## $double.ulp.digits
## [1] -52
## 
## $double.neg.ulp.digits
## [1] -53
## 
## $double.exponent
## [1] 11
## 
## $double.min.exp
## [1] -1022
## 
## $double.max.exp
## [1] 1024
## 
## $integer.max
## [1] 2147483647
## 
## $sizeof.long
## [1] 8
## 
## $sizeof.longlong
## [1] 8
## 
## $sizeof.longdouble
## [1] 16
## 
## $sizeof.pointer
## [1] 8
## 
## $longdouble.eps
## [1] 1.084202e-19
## 
## $longdouble.neg.eps
## [1] 5.421011e-20
## 
## $longdouble.digits
## [1] 64
## 
## $longdouble.rounding
## [1] 5
## 
## $longdouble.guard
## [1] 0
## 
## $longdouble.ulp.digits
## [1] -63
## 
## $longdouble.neg.ulp.digits
## [1] -64
## 
## $longdouble.exponent
## [1] 15
## 
## $longdouble.min.exp
## [1] -16382
## 
## $longdouble.max.exp
## [1] 16384
```

---

# ` 0.15 == 0.1 + 0.05`
# FALSE

---

## Checking for equality

Internal representation is not equal to decimal representation:

```r
i <- 0.1 + 0.05
i
```

```
## [1] 0.15
```

```r
if(i==0.15) cat("i equals 0.15") else cat("i does not equal 0.15")
```

```
## i does not equal 0.15
```

```r
print(i, digits=17)
```

```
## [1] 0.15000000000000002
```

```r
print(0.15, digits=17)
```

```
## [1] 0.14999999999999999
```
See also https://0.30000000000000004.com/ for an overview of other languages
---

## Checking for equality

Better practice:

```r
dplyr::near(i, 0.15)
```

```
## [1] TRUE
```

Default tolerance is specified as `.Machine$double.eps^0.5`,
i.e. floating point numbers are pairwise equal.

---

## Factors

Some data has names and a defined numerical ordering:

```r
# R constant
month.name
```

```
##  [1] "January"   "February"  "March"     "April"    
##  [5] "May"       "June"      "July"      "August"   
##  [9] "September" "October"   "November"  "December"
```

Factors are used to store both the numerical values and the associated labels:

```r
factor(month.name)
```

```
##  [1] January   February  March     April     May      
##  [6] June      July      August    September October  
## [11] November  December 
## 12 Levels: April August December February January ... September
```

By default, R uses alphabetical order for factors...

---

## Factors

```r
factor(month.name)
```

By default, R uses alphabetical order for factors...

Set level names to override the default ordering

```r
months <- factor(month.name, levels = month.name)
months
```

```
##  [1] January   February  March     April     May      
##  [6] June      July      August    September October  
## [11] November  December 
## 12 Levels: January February March April May June ... December
```

---

## Factors

You can access the labels of a factor using `levels()`

```r
levels(months)
```

```
##  [1] "January"   "February"  "March"     "April"    
##  [5] "May"       "June"      "July"      "August"   
##  [9] "September" "October"   "November"  "December"
```

You can access the order of the factor using `as.numeric()`:

```r
as.numeric(months)
```

```
##  [1]  1  2  3  4  5  6  7  8  9 10 11 12
```

---
class: inverse
## Your Turn

- Introduce an object consisting of the days of the week

- Make the object a factor; ensure that the days of the week are in chronological rather than alphabetical order

- Change the order of the levels to start with Sunday (in case your levels started with Sunday, change the order to start with Monday)

---

## Type Conversions

```r
# Get a numeric vector
x <- sample(1:10, 5)
x
```

```
## [1]  6  9 10  2  5
```

```r
# Create factor from numeric vector
fac_x <- factor(x)
fac_x
```

```
## [1] 6  9  10 2  5 
## Levels: 2 5 6 9 10
```

```r
# Convert factor to numeric
as.numeric(fac_x) # Huh?
```

```
## [1] 3 4 5 1 2
```
`as.numeric()` converts factors to their level numbers, not to their labels

---

## Type Conversions

```r
as.character(fac_x)
```

```
## [1] "6"  "9"  "10" "2"  "5"
```

```r
as.numeric(as.character(fac_x))
```

```
## [1]  6  9 10  2  5
```
`as.character()` extracts the labels; you can then use `as.numeric` to get the labels' numeric value.

---

## Type Conversions

implicit type conversions happen all the time:

```r
x <- c("4.5", 3, TRUE, "elephant")
# The logical value becomes a character
x
```

```
## [1] "4.5"      "3"        "TRUE"     "elephant"
```

Note that the cast from logical to  character doesn't survive intact

```r
as.numeric(x) 
```

```
## Warning: NAs introduced by coercion
```

```
## [1] 4.5 3.0  NA  NA
```

---

## Basic Data Structures

Data structures hold one or more basic data types and may have multiple dimensions:

| One type | Multiple Types
-- | -------- | --------------
1D | (Atomic) Vector | List
2D | Matrix | Data frame
nD | Array |

An individual value ("scalar" in other languages) is a length one vector in R

* **Vectors**: one-dimensional array of values of the same type; vectors have a length, but no dimension

* **Matrix**: two-dimensional array of values of the same type; matrices have a dimension given as (row, column), length returns the number of items (row x column)

* **Array**: any higher dimensional array (e.g. output of temperature data from netcdf data)

---

## Basic Data Structures