STA 517 3.0 Programming and Statistical Computing with R

# STA 517 3.0 Programming and Statistical Computing with R
## 🚦Writing Functions in R
### 
### Dr Thiyanga Talagala

---

# Today's menu

- User-written functions

]

]

---

## 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"
```

---

## Functions in R (cont.)

👉🏻 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.

---

## Syntax

```r

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

return(value)

}

```

]

### Example

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

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

}
```

### Evaluation

```r
cal_power(2)
```

```
squared   cubed 
      4       8 
```

]

👉 Functions are created using the `function()`

---

## Basic components of a function

**1. Function name**

---

### Syntax

```r

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

return(value)

}

```

]

### Example

```r
*cal_power <- 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

1. Function name

**2. Function arguments/ inputs**

---

### Syntax

```r

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

return(value)

}

```

]

### Example

```r
*cal_power <- 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

1. Function name

2. Function arguments/ inputs

**3. Function body**

---

### Syntax

```r

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

return(value)

}

```

]

### Example

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

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

}
```

]

---

## Function with single line

### Mathod 1

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

x^2

}
```

]

### Method 2

```r
cal_sqrt <- function(x) x^2
```

]

---

### 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
```

---

### Function body (Cont.)

- 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 )

```

---

### Function body (Cont.)

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

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

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

---

background-image: url('dengue.jpg')
background-position: center
background-size: contain

---

**Load the mozzie dataset**

```r
library(mozzie)
data(mozzie); head(mozzie, 2)
```

```
  ID Year Week Colombo Gampaha Kalutara Kandy Matale Nuwara Eliya Galle
1  1 2008   52      15       7        1    11      4            0     0
2  2 2009    1      44      23        5    16     21            2     0
  Hambantota Matara Jaffna Kilinochchi Mannar Vavuniya Mulative Batticalo
1          6     22      0           0      8        0        0         1
2          5     18      1           0      0        0        0         0
  Ampara Trincomalee Kurunagala Puttalam Anuradhapura Polonnaruwa Badulla
1      0           0          2        1            2           0       1
2      1           1         10        5            0           0       1
  Monaragala Ratnapura Kegalle
1          1         2      16
2          0         1      25
```

---

> Use Min-Max transformation to rescale all the districts variables onto 0-1 range.

> Min-Max transformation is `$\frac{x_i-min(x)}{max(x)-min(x)}$` where `$x=(x_1, x_2, ...x_n)$`.

---

** Min-Max transformation on `mozzie`**

```r
minmax.colombo <- (mozzie$Colombo - min(mozzie$Colombo, na.rm = TRUE)) /
  (max(mozzie$Colombo, na.rm=TRUE) - min(mozzie$Colombo, na.rm=TRUE))
head(minmax.colombo) # Colombo district
```

```
[1] 0.03157895 0.09263158 0.08210526 0.12000000 0.11157895 0.06105263
```

```r
minmax.gampaha <- (mozzie$Gampaha - min(mozzie$Gampaha, na.rm = TRUE)) /
  (max(mozzie$Gampaha, na.rm = TRUE) - min(mozzie$Gampaha, na.rm = TRUE)) 
head(minmax.gampaha) # Gampaha district
```

```
[1] 0.02734375 0.08984375 0.07421875 0.08984375 0.09375000 0.06640625
```

---

```r
minmax.kalutara <- (mozzie$Gampaha - min(mozzie$Kalutara, na.rm = TRUE)) /
  (max(mozzie$Kalutara, na.rm = TRUE) - min(mozzie$Kalutara, na.rm = TRUE))
head(minmax.kalutara) # Kalutara district
```

```
[1] 0.09333333 0.30666667 0.25333333 0.30666667 0.32000000 0.22666667
```

---
## Copying-and-pasting

> You could easily make errors.

> A mistake copied becomes a mistake repeated.

## When should you write a function?

- Whenever you need to copy and paste a block of codes many times

- A function is a reusable block of programming code designed to do a specific task.

- If you don't find a suitable built-in function to serve your purpose, you can write your own function

- To share your work with others

---

# Writing a function

### Step 1: Function name

```r
rescale_minmax

```
--

### Step 2: Assign your function to the name

```r
rescale_minmax <- 
```
--

### Step 3: Tell R that you are writing a function

```r_
rescale_minmax <- function(x) # Arguments/inputs should be defined inside ()

```
---

### Step 4: Curly braces define the start and the end of your work

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

# Task

# output

}

```

---
## Step 5: Function inputs, task and outputs

**Find all the inputs that correspond to a given function output?**

```r
# Colombo district
(mozzie$Colombo - min(mozzie$Colombo, na.rm = TRUE)) /
  (max(mozzie$Colombo, na.rm=TRUE) - min(mozzie$Colombo, na.rm=TRUE))
```

--
**Re-write the code with general names**

```r
x <- mozzie$Colombo
(x - min(x, na.rm = TRUE)) / (max(x, na.rm=TRUE) - min(x, na.rm=TRUE))
```

---
**Remove duplication/ Make your code efficient and readable**

```r
rng <- range(x, na.rm = TRUE)
rng
```

```
[1]   0 475
```

```r
rng <- range(x, na.rm = TRUE)
(x - rng[1]) / (rng[2] - rng[1])
```

---

# Step 6: Complete your function

**Type A**

```r
rescale_minmax <- function(x){
  rng <- range(x, na.rm = TRUE)
  (x - rng[1]) / (rng[2] - rng[1])
}
```

**Type B**

```r
rescale_minmax <- function(x){
  rng <- range(x, na.rm = TRUE)
  out.rescaled <- (x - rng[1]) / (rng[2] - rng[1])
  out.rescaled
}
```

]

**Type C**

```r
rescale_minmax <- function(x){
  rng <- range(x, na.rm = TRUE)
  out.rescaled <- (x - rng[1]) / (rng[2] - rng[1])
  return(out.rescaled)
}
```

> In this situation Type A is the best.

]

---

# Step 7: Check your function with a few different inputs

```r
rescale_minmax <- function(x){
  rng <- range(x, na.rm = TRUE)
  (x - rng[1]) / (rng[2] - rng[1])
}
```

```r
rescale_minmax(c(1, 200, 250, 80, NA))
```

```
[1] 0.0000000 0.7991968 1.0000000 0.3172691        NA
```

---

## Back to our original example

```r
minmax.colombo <- rescale_minmax(mozzie$Colombo)
head(minmax.colombo)
```

```
[1] 0.03157895 0.09263158 0.08210526 0.12000000 0.11157895 0.06105263
```

```r
minmax.gampaha <- rescale_minmax(mozzie$Gampaha)
head(minmax.gampaha)
```

```
[1] 0.02734375 0.08984375 0.07421875 0.08984375 0.09375000 0.06640625
```

```r
minmax.kalutara <- rescale_minmax(mozzie$Kalutara)
head(minmax.kalutara)
```

```
[1] 0.01333333 0.06666667 0.14666667 0.16000000 0.25333333 0.13333333
```

---

# Move forward: When the requirements changes

```r
new.data.col <- c(400, 500, 350, 250, 60, 70, Inf)
rescale_minmax(new.data.col)
```

```
[1]   0   0   0   0   0   0 NaN
```

## Fix the code

```r
rescale_minmax <- function(x){
*  rng <- range(x, na.rm = TRUE, finite=TRUE)
  (x - rng[1]) / (rng[2] - rng[1])
}
```

---

```r
new.data.col <- c(400, 500, 350, 250, 60, 70, Inf)
rescale_minmax(new.data.col)
```

```
[1] 0.77272727 1.00000000 0.65909091 0.43181818 0.00000000 0.02272727        Inf
```
---

# Your turn

---

Rewrite `rescale_minmax` so that `-Inf` is set to 0, and `Inf` is mapped to 1.

---

# Your turn

---

R for Data Science - Exercise 19.2.1, Question 3

---

# Your turn

---

R for Data Science - Exercise 19.2.1, Question 4

---

background-image: url('laptop.jpg')
background-position: center
background-size: cover

- Descriptive names for variables.

- Comment your code.
]

---

# Your turn

---

Write your own function to calculate parameter estimates of simple linear regression model.

Help:
`$$\hat{\beta}=(X^TX)^{-1}X^TY$$`

![](slr2.png)

---

Write a function to calculate confidence intervals for mean.
`$$\bar{x} \pm t_{\alpha/2, (n-1)}\frac{s}{\sqrt(n)}$$`

---

## Function arguments

```r
cal_mean_ci <- function(x, conf){
  len.x <- length(x)
  se <- sd(x) / sqrt(len.x)
  alpha <- 1-conf
  mean(x) + se * qt(c(alpha / 2, 1 - alpha / 2), df = len.x-1)
  
}

data <- c(165, 170, 175, 180, 185)
cal_mean_ci(data, 0.95)
```

```
[1] 165.1838 184.8162
```

---

## Function with default values

```r
cal_mean_ci <- function(x, conf = 0.95){
  len.x <- length(x)
  se <- sd(x) / sqrt(len.x)
  alpha <- 1-conf
  mean(x) + se * qt(c(alpha / 2, 1 - alpha / 2), df = len.x-1)
  
}

cal_mean_ci(data)
```

```
[1] 165.1838 184.8162
```

```r
cal_mean_ci(data, 0.99)
```

```
[1] 158.7221 191.2779
```

---
class: inverse, center, middle

## In-class questions

---

## Problem 1

Write a function to calculate the correlation coefficient

`$$r=\frac{\sum_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum_{i=1}^n(x_i-\bar{x})^2\sum_{i=1}^n(y_i-\bar{y})^2}}$$`

Do not use the function `cor` inside your function.

---

## Problem 2

Write a function to generate 100 random numbers from a normal distribution and plot the distribution of the random numbers. Your function should display the generated random numbers and the corresponding plot.

---

## Problem 3

Write a function to compute z-score value of a A/L Mathematics student given the marks of the student. Assume

mean(Mathematics) = 60, sd(Mathematics) = 10,

mean(Chemistry) = 45, sd(Chemistry) = 20,

mean(Physics) = 55, sd(Physics) = 5.

---
background-image: url('PAGE-05.jpeg')
background-position: center
background-size: contain

---

## Local variables vs Global variables

in-class discussion using R Demo

---

## Problem 4

Write a function to calculate the median.

help:

```r
5%%2
```

```
[1] 1
```

```r
4%%2
```

```
[1] 0
```

Note: Do not use the built-in function `median` inside your function.

---
class: inverse, center, middle

# Next week: control structures

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## Thank you!

Slides available at: hellor.netlify.app