STA 326 2.0 Programming and Data Analysis with R

# STA 326 2.0 Programming and Data Analysis with R
## Lesson 3: Functions in R
### Dr Thiyanga Talagala
### 2020-02-25

---

## Functions in R

👉🏻 Perform a specific task according to a set of instructions.

--
👉🏻  Some functions we have discussed so far,

> `c`, `matrix`, `array`, `list`, `data.frame`, `str`, `dim`, `length`, `nrow`, `plot`

👉🏻 In R, functions are **objects** of **class** *function*.

```r
class(length)
```

```
[1] "function"
```

👉🏻 There are basically two types of functions:

> 💻 Built-in functions 
  
      Already created or defined in the programming framework to make our work easier.
> 👨 User-defined functions
           
      Sometimes we need to create our own functions for a specific purpose.

---

## Basic components of a function

## Syntax

```r

name <- function(arg1, aug2, ...){

return(value)

}

```

]

## Example

```r
cal_sqrt <- function(x){

a <- x^2
b <- x^3
out <- c(a, b)
names(out) <- c("squared", "cubed")
out # or return(out)

}
```

## Evaluation

```r
cal_sqrt(2)
```

```
squared   cubed 
      4       8 
```

]
--

👉 Functions are created using the `function()`.
---

## Basic components of a function

### Syntax

```r

name <- function(arg1, aug2, ...){

return(value)

}

```

]

### Example

```r
*cal_sqrt <- function(x){

a <- x^2
b <- x^3
out <- c(a, b)
names(out) <- c("squared", "cubed")
out # or return(out)

}
```

]

- use verbs, where possible.
 
 - should be meaningful.
 
 - Use an underscore (_) to separate words.
 
 - avoid names of built-in functions.
 
 - start with lower case letters. Note that R is a case sensitive language.

---

## Basic components of a function

### Syntax

```r

name <- function(arg1, aug2, ...){

return(value)

}

```

]

### Example

```r
*cal_sqrt <- function(x){

a <- x^2
 b <- x^3
 out <- c(a, b)
 names(out) <- c("squared", "cubed")
 out # or return(out)

}
```

]

- value passed to the function to obtain the function's result.

---

## Basic components of a function

### Syntax

```r

name <- function(arg1, aug2, ...){

return(value)

}

```

]

### Example

```r
cal_sqrt <- function(x){

* a <- x^2
* b <- x^3
* out <- c(a, b)
* names(out) <- c("squared", "cubed")
* out # or return(out)

}
```

]

---

### Function body (Cont.)

- Place spaces around all operators such as =, +, -, <-, etc.

- Exception: Do not place spaces around the operators :, :: and :::

```r
1+2 # bad
1 + 2 # good 
```
--

- Place a space before left parentheses except evaluating the function (function call)

```r
if (a > 2) # good
if(a>2) # bad

# Function call ----
rnorm(2) # good
rnorm (2) # bad
```

- Use extra spacing to align multiple lines with <- or =

```r
# Bad ------
a = sum(c(1, 5, 8, 10))/2
sd = sd(c(1, 5, 8, 10))

# Good ------
a  = sum(c(1, 5, 8, 10))/2
sd = sd(c(1, 5, 8, 10))
```

---

### Function body (Cont.)

- Spacing inside parentheses or square brackets

```r
# Good ---
a[1, 2]
a[1, ]
if(x < 2)

# Bad ---
a[1,2]
a[1,]
if(x<2)
if( x<2 )

```

- {} do not go in one single line, always two lines

```r
# Good ---
if(y == 2){
print("even")
}

# Bad ---
if(y == 2){ print("even")}
```

---

## Built-in Functions

### How to call a built-in function in R

```r
function_name(arg1 = 1, arg2 = 3)

```

### Argument matching

The following calls to `mean` are all equivalent

```r
mydata <- c(rnorm(20), 100000)
mean(mydata) # matched by position
mean(x = mydata) # matched by name
mean(mydata, na.rm = FALSE)
mean(x = mydata, na.rm = FALSE) 
mean(na.rm = FALSE, x = mydata) 
mean(na.rm = FALSE, mydata)
```

```
[1] 4761.94
```

⚠️ Even though it works, do not change the order of the arguments too much.

---

## Argument matching (cont.)

- some arguments have default values

```r
mean(mydata, trim=0)
```

```
[1] 4761.94
```

```r
mean(mydata) # Default value for trim is 0
```

```
[1] 4761.94
```

```r
mean(mydata, trim=0.1)
```

```
[1] 0.1449313
```

```r
mean(mydata, tr=0.1) # Partial Matching
```

```
[1] 0.1449313
```
---

background-image: url('helpmean.png')
background-position: center
background-size: contain

## ?mean

---

# Your turn

---

1. Calculate the mean of 1, 2, 3, 8, 10, 20, 56, NA.

---

# Basic maths functions

|  Operator | Description  |
|---|---|
|  abs(x) | absolute value of x   |
| log(x, base = y)  |  logarithm of x with base y; if base is not specified, returns the natural logarithm |
|exp(x)| exponential of x|
|sqrt(x)|square root of x|
|factorial(x)| factorial of x|

---
# Basic statistic functions

|  Operator | Description  |
|---|---|
|  mean(x) | mean of x   |
| median(x)  |  median of x |
|mode(x)| mode of x|
|var(x)|variance of x|
|sd(x)|standard deviation of x|
|scale(x)| z-score of x|
|quantile(x)| quantiles of x|
|summary(x)|summary of x: mean, minimum, maximum, etc.|

---

## Type conversion functions

|  Test | Convert  |
|---|---|
|  is.numeric() | as.numeric()   |
| is.character()  |  as.character() |
|is.vector()| as.vector()|
|is.matrix()|as.matrix()|
|is.data.frame()| as.data.frame()|
|is.factor()| as.factor()|
|is.logical()|as.logical()|
|is.na()||
]

## Example

```r
a <- c(1, 2, 3); a
```

```
[1] 1 2 3
```

```r
is.numeric(a)
```

```
[1] TRUE
```

```r
is.vector(a)
```

```
[1] TRUE
```

```r
b <- as.character(a); b
```

```
[1] "1" "2" "3"
```

```r
is.vector(b)
```

```
[1] TRUE
```

```r
is.character(b)
```

```
[1] TRUE
```
]

---

# Your turn

---

Remove missing values in the following vector

```
 [1]  0.61940020 -0.93808729  0.95518590 -0.22663938  0.29591186          NA
 [7]  0.36788089  0.71791098  0.71202022  0.22765782          NA          NA
[13] -0.74024324  0.02081516 -0.14979979 -0.22351308  0.98729725          NA
[19]          NA          NA          NA          NA          NA          NA
[25]          NA          NA          NA -1.50016003  0.18682734  0.20808590
[31]  0.70102264 -0.10633074 -1.18460046  0.06475501  0.11568817 -0.04333140
[37] -0.22020064  0.02764713  0.10165760 -0.18234246  1.32914659 -1.29704248
[43]  1.05317749 -0.70109051  0.09798707  0.10457263 -0.21449845
```
---

# Probability distribution functions

- Each probability distribution in R is associated with four functions.

- Naming convention for the four functions:

For each function there is a root name. For example, the **root name** for the normal distribution is `norm`. This root is prefixed by one of the letters `d`, `p`, `q`, `r`.
    
  - **d** prefix for the **distribution** function

- **p** prefix for the **cumulative probability**

- **q** prefix for the **quantile**

- **r** prefix for the **random** number generator

- Example: `dnorm`, `pnorm`, `qnorm`, `rnorm`
---

## Illustration with Standard normal distribution

The general formula for the probability density function of the normal distribution with mean `$\mu$` and variance `$\sigma$` is given by

$$
f_X(x) = \frac{1}{\sigma\sqrt{(2\pi)}} e^{-(x-\mu)^2/2\sigma^2}
$$

If we let the mean `$\mu=0$` and the standard deviation `$\sigma=1$`, we get the probability density function for the standard normal distribution.