---
title: "Transforming Data"
author: "JJB + Course"
date: "9/07/2018"
output:
   html_document:
     toc: true
     toc_float: true
---


# Functions

## Example: Add

```{r}
add = function(x, y) {
  return(x + y)
}

add(1, 3)
```

## Example: Hello World!

```{r}
message("Hello World!")

say_hello_world = function() { 
  message("Hello World!")
}

say_hello_world()
```


## Example: Generic Code to Specific Routine

Generic _R_ script values

```{r}
set.seed(1115)

sample(6, size = 1)

sample(6, size = 1)

sample(6, size = 1)
```

Adding a name to the routine...

```{r}
roll_die = function(num_sides) {
    roll = sample(num_sides, size = 1)
    return(roll)
}

set.seed(1115)
roll_die(6)
```

What happens if we forget to specify a `num_sides` value? E.g. what is `roll_die()`?

Making the function receive default settings...

```{r}
roll_die_default = function(num_sides = 6) {
    roll = sample(num_sides, size = 1)
    return(roll)
}

set.seed(1115)
roll_die_default()

set.seed(1115)
roll_die_default(6)
```

Generalizing to _n_ rolls:

```{r}
roll_n_die = function(num_rolls, num_sides = 6) {
    rolls = sample(num_sides, size = num_rolls,
                   replace = TRUE)
    return(rolls)
}

set.seed(1115)
roll_n_die(3, 6)
```

## Exercise: Transforming a Workflow

Clean up the following code by implementing a function that:

1. Generates data from a normal distribution
2. Applies the mean normalization 

```{r}
set.seed(325)

x = rnorm(10)
y = rnorm(10)

x_nmu = (x - mean(x)) / (max(x) - min(x))
x_nmu
y_nmu = (y - mean(y)) / (max(y) - min(y))
y_nmu
```

# Classes and Objects

## Example: Vector Types

```{r view-vectors}
# Vector of numeric elements
w = c(9.5, -3.14, 88.9999, 12.0)
     # ^     ^      ^        ^  decimals

# Vector of integer elements
x = c(1L, 2L, 3L, 4L)

# Vector of logical elements
y = c(TRUE, FALSE, FALSE, TRUE)

# Vector of character elements
z = c("a", "b", "c", "d")
```

## Example: Creating a Data Frame by Hand

```{r viewing-heights}
subject_heights = data.frame(
  id     = c(1, 2, 3, 55),
  sex    = c("M", "F", "F", "M"),
  height = c(6.1, 5.5, 5.2, 5.9)
)
```

## Example: Determine Class and Structure


```{r looking-into-data}
class(subject_heights)
str(subject_heights)
```

# Vectors 

## Example: Vectorization and Elements

```{r vectorized-addition}
x = c(1, 2, 3, 4)
y = c(5, 6, 7, 8)
z = x + y
z
```

## Example: Vectorized Binary Operators

```{r example-of-ops}
x = c(1, 2, 3, 4)
y = c(5, 6, 7, 8)
x + y             # Addition
x - y             # Subtraction
x * y             # Multiplication       
x / y             # Division
x ^ y             # Exponentiation
x %/% y           # Integer Division
x %% y            # Modulus
```


### Aside: Modulus

```{r mod-ex}
12 %% 7                 # a = n*q + r => 12 = 1*7 + 5

outer(9:1, 2:9, `%%`)   # Compute the cross between X & Y
```


## Example: Recycling

```{r recycle-process}
a = c(1, 2, 3, 4)
length(a)

b = c(5, 6, 7)
length(b)

a + b
```

## Example: Recycling - Round 2

```{r expansion-shorter}
c(1, 2, 3, 4) + c(-1, 1) 
```

## Exercise: Determining Scalars

Explain what happens if we have a vector and add a single value

```{r whats-a-scalar}
a = 2 
x = c(1, 2, 3, 4) 
x + a
```


```{r calculate-1p-conf}
p_hat = 0.85

z_value = 1.96
n = 92

p_hat + z_value * sqrt(p_hat*(1-p_hat) / n)

p_hat - z_value * sqrt(p_hat*(1-p_hat) / n)

p_hat + z_value * c(-1, 1) * sqrt(p_hat*(1-p_hat) / n)

```

```{r}
a = 2

b = c(1, -49)

a

b

d = 1:50

d

 ```




## Example: Everything is a Vector

```{r etia}
a = 2
length(a)

a_vec = c(2)
length(a_vec)
```

```{r eq-check}
identical(a, a_vec)
```


# Subsets

## Example: Positional Indexes

```{r ex-vector}
ex_vec = c(5, 3, -2, 42)
```


## Example: Retrieving a Single Value

```{r retrieve-first}
ex_vec = c(5, 3, -2, 42)

# Retrieve first element
ex_vec[1]

# Retrieve second element
ex_vec[4]

# Retrieve the nth element
last_pos = length(ex_vec)
ex_vec[last_pos]
```

## Example: Retrieve Multiple Values

```{r retrieve-seq}
ex_vec = c(5, 3, -2, 42)

ex_vec[c(2, 3)]

ex_vec[2:3]
```

## Example: Retrieve Multiple Values by Removing Indices

```{r neg-seq}
ex_vec = c(5, 3, -2, 42)

ex_vec[-c(1, 4)]
```

## Exercise: Positional Index Methods

Using all sequence methods, create sequences for the following vectors. Are all approaches the same?

```{r}
int_vec = c(8L, -2L, 5L, 0L)
empty_vec = numeric(0)
```

```{r}
int_vec

class(int_vec)
```

```{r}
empty_vec
```


```{r}
# sequence generation for integer

seq(1, length(int_vec))

seq_len(length(int_vec))

seq_along(int_vec)
```

```{r}
1:length(empty_vec)

length(empty_vec)

1:0

c(1, 0)
```

```{r}
seq_along(empty_vec)

```