03 Functions

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.title[
# 03 Functions
]
.subtitle[
## Elements of R e R Markdown
]
.author[
### Claudio Zandonella
]

---

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# Defining Functions

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```r
name_function <- function(<argument-1>, 
                          <argument-2>, 
                          ...){
  
  <body-function>
    
  return(<result>)
}
```

```r
greetings <- function(name){
  
  res <- paste("Hello", name)
  
  return(res)
}

greetings("Claudio")
## [1] "Hello Claudio"
```

]

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### Arguments

- `function(x){...}`, argument `x` is require with not default value
- `function(x = 0){...}`, argument `x` is require with default value `0`
- `function(...){...}`, argument `...` allows arbitrary number of arguments

### Interactive

- `cat()` and `print()`, print objects in console
- `readline(prompt = "...")`, get user's response
- `menu(<choices>)`, user select answer from menu

]

---
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# Conditional Programming

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### If statement

```r
if (<test>) {
  <body>
}
```

```r
is_negative <- function(x){
  
  if (x < 0) {
    print(paste(x, "is negative"))
  }
}

is_negative(-2)
## [1] "-2 is negative"
```
]

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### If else statement

```r
if (<test>) {
  <body>
} else {
  <body>
}
```

```r
tell_sign <- function(x){
  
  if (x < 0) {
    print(paste(x, "is negative"))
  } else {
    print(paste(x, "is possitive"))
  }
}

is_negative(2)
```
]

---
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# Iterative Programming

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### For loop

```r
for (i in c(...)) {
    <body>
}
```

```r
call_friends <- function(friends){
  for( friend in friends){
    cat("Hello ", friend, "!\n", sep = "")
  }
}

call_friends(
  friends = c("Emy", "John", "Mat")
)
## Hello Emy!
## Hello John!
## Hello Mat!
```
]

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### While loop

```r
while (<test>) {
    <body>
}
```

```r
countdown <- function(count){
  
  while(count > 0){
    cat(count, "\n")
    count <- count - 1
  }
  cat("Start!\n")
}

countdown(count = 3)
## 3 
## 2 
## 1 
## Start!
```
]

---
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# Apply Family

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```r
apply(X = , MARGIN = , FUN = )
```

```r
(X <- matrix(1:12, ncol = 4))
##      [,1] [,2] [,3] [,4]
## [1,]    1    4    7   10
## [2,]    2    5    8   11
## [3,]    3    6    9   12

# By rows
apply(X, MARGIN = 1, FUN = sum)
## [1] 22 26 30

# By columns
apply(X, MARGIN = 2, FUN = sum)
## [1]  6 15 24 33

# Custom function
apply(X, MARGIN = 1, function(x){
        round(sd(x)/mean(x), 2) 
      })
## [1] 0.70 0.60 0.52
```
]

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### Other

- `tapply()`, apply a function to each group of values given by a combinations of factors
- `lapply()`, apply a function over all elements of a lists (return a list)
- `sapply()`, apply a function over all elements of a lists (return a vector or a list)
- `vapply()`, apply a function over all elements of a lists (return a vector)
- `replicate()`, repeatedly apply a function.
]

---
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# Probability Distributions

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### Normal Disribution

- `dnorm(x, mean = 0, sd = 1)`, get the density given the quantile 
- `pnorm(q, mean = 0, sd = 1)`, get the probability given the quantile
- `qnorm(p, mean = 0, sd = 1)`, get the quantile given the probability 
- `rnorm(n, mean = 0, sd = 1)`, sample `n` values

```r
dnorm(0, mean = 0, sd = 1)
## [1] 0.3989423
pnorm(0, mean = 0, sd = 1)
## [1] 0.5
qnorm(0, mean = 0, sd = 1)
## [1] -Inf
rnorm(0, mean = 0, sd = 1)
## numeric(0)
```
]

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### Other Distributions

<table class="table table-striped table-hover" style="margin-left: auto; margin-right: auto;">
 <thead>
  <tr>
   <th style="text-align:left;"> Discrete </th>
   <th style="text-align:left;"> Continuous </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> <code class="remark-inline-code">*binom()</code>, Binomial </td>
   <td style="text-align:left;"> <code class="remark-inline-code">*unif()</code>, Uniform </td>
  </tr>
  <tr>
   <td style="text-align:left;"> <code class="remark-inline-code">*pois()</code>, Poisson </td>
   <td style="text-align:left;"> <code class="remark-inline-code">*chisq()</code>, Chi-Square </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> <code class="remark-inline-code">*t()</code>, Student-t </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> <code class="remark-inline-code">*f()</code>, F </td>
  </tr>
  <tr>
   <td style="text-align:left;">  </td>
   <td style="text-align:left;"> <code class="remark-inline-code">*gamma()</code>, Gamma </td>
  </tr>
</tbody>
</table>

### Randomness

```r
# Random Number Generation
set.seed(seed = <value>)

# Smaple and permutations
sample(x = , size = , replace = , prob = )

```
]

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# Thanks!