19-functions.Rmd

```{r setup19, warning = FALSE, message = FALSE, include = FALSE}
knitr::opts_chunk$set(echo = TRUE, cache = TRUE)

library(nycflights13)
library(ggplot2)
library(dplyr)
library(forcats)
library(tidyr)
library(lubridate)
library(stringr)
library(e1071)
```

# Ch. 19: Functions

```{block2, type='rmdimportant'}
**Key questions:**  
  
* 19.3.1. #1
* 19.4.4. #2, 3
* 19.5.5. #2 (actually make a function that fixes this)
```

```{block2, type='rmdtip'}
**Functions and notes:**
```

* `function_name <- function(input1, input2) {}`
* `if () {}`
* `else if () {}`
* `else {}`
* `||` (or) , `&&` (and) -- used to combine multiple logical expressions
* `|` and `&` are vectorized operations not to be used with `if` statements
* `any` checks if any values in vector are `TRUE`
* `all` checks if all values in vector are `TRUE`
* `identical` strict check for if values are the same
* `dplyr::near` for more lenient comparison and typically better than `identical` as unaffected by floating point numbers and fine with different types
* `switch` evaluate selected code based on position or name (good for replacing long chain of `if` statements). e.g. 

```{r}
Operation_Times2 <- function(x, y, op){
   first_op <- switch(op,
     plus = x + y,
     minus = x - y,
     times = x * y,
     divide = x / y,
     stop("Unknown op!")
   )
   
   first_op * 2
  }

Operation_Times2(5, 7, "plus")
```

* `stop` stops expression and executes error action, note that `.call` default is `FALSE`
* `warning` generates a warning that corresponds with arguments, `suppressWarnings` may also be useful to no
* `stopifnot` test multiple args and will produce error message if any are not true -- compromise that prevents you from tedious work of putting multiple `if(){} else stop()` statements
* `...` useful catch-all if your function primarily wraps another function (note that misspelled arguments will not raise an error), e.g. 

```{r}
commas <- function(...) stringr::str_c(..., collapse = ", ")
commas(letters[1:10])
```

* `cut` can be used to discretize continuous variables (also saves long `if` statements)
* `return` allows you to return the function early, typically reserve use for when the function can return early with a simpler function
* `cat` function to print label in output
* `invisible` input does not get printed out

## 19.2: When should you write a function?

### 19.2.1

1.  Why is `TRUE` not a parameter to `rescale01()`? What would happen if `x` contained a single missing value, and `na.rm` was `FALSE`?
    
    * `TRUE` doesn't change between uses.
    * The output would be `NA`

1.  In the second variant of `rescale01()`, infinite values are left unchanged. Rewrite `rescale01()` so that `-Inf` is mapped to 0, and `Inf` is mapped to 1.

    ```{r}
    rescale01_inf <- function(x){
      
      rng <- range(x, na.rm = TRUE, finite = TRUE)
      x_scaled <- (x - rng[1]) / (rng[2] - rng[1])
      is_inf <- is.infinite(x)
      is_less0 <- x < 0
      x_scaled[is_inf & is_less0] <- 0
      x_scaled[is_inf & (!is_less0)] <- 1
      x_scaled
    }
    
    x <-  c(Inf, -Inf, 0, 3, -5)
    rescale01_inf(x)
    ```
    
1.  Practice turning the following code snippets into functions. Think about what each function does. What would you call it? How many arguments does it need? Can you rewrite it to be more expressive or less duplicative?

    ```{r, eval = FALSE}
    mean(is.na(x))
    
    x / sum(x, na.rm = TRUE)
    
    sd(x, na.rm = TRUE) / mean(x, na.rm = TRUE)
    ```

    * See solutions below:
    ```{r}
    x <- c(1, 4, 2, 0, NA, 3, NA)
    
    #mean(is.na(x))
    perc_na <- function(x) {
      is.na(x) %>% mean()
    }
    
    perc_na(x)
    
    #x / sum(x, na.rm = TRUE)
    prop_weighted <- function(x) {
      x / sum(x, na.rm = TRUE)
    }
    prop_weighted(x)
    
    #sd(x, na.rm = TRUE) / mean(x, na.rm = TRUE)
    CoefficientOfVariation <- function(x) {
      sd(x, na.rm = TRUE) / mean(x, na.rm = TRUE)
    }
    
    CoefficientOfVariation(x)
    
    ```


1.  Follow <http://nicercode.github.io/intro/writing-functions.html> to write your own functions to compute the variance and skew of a numeric vector.
    
    * Re-do below to write measures for skew and variance (e.g. kurtosis, etc.)  
    
    ```{r}
    var_bry <- function(x){
      sum((x - mean(x)) ^ 2) / (length(x) - 1)
    }
    
    skewness_bry <- function(x) {
      mean((x - mean(x)) ^ 3) / var_bry(x) ^ (3 / 2)
    }
    
    
    ```
    
    Let's create some samples of distributions -- normal, t (with 7 degrees of freedom), unifrom, poisson (with lambda of 2).  
    
    Note that an example with a cauchy distribution and looking at difference in kurtosis between that and a normal distribution has been moved to the [Appendix] section [19.2.1.4].
    ```{r}
    nd <- rnorm(10000)
    td_df7 <- rt(10000, df = 7)
    ud <- runif(10000)
    pd_l2 <- rpois(10000, 2)
    ```
    
    
    Verify that these functions match with established functions
    ```{r}
    dplyr::near(skewness_bry(pd_l2), e1071::skewness(pd_l2, type = 3))
    
    dplyr::near(var_bry(pd_l2), var(pd_l2))
    
    ```
    
    Let's look at the distributions as well as their variance an skewness
    ```{r}
    distributions_df <- tibble(normal_dist = nd,
           t_7df_dist = td_df7,
           uniform_dist = ud,
           poisson_dist = pd_l2)
    
    distributions_df %>% 
      gather(normal_dist:poisson_dist, value = "sample", key = "dist_type") %>% 
      mutate(dist_type = factor(forcats::fct_inorder(dist_type))) %>% 
      ggplot(aes(x = sample))+
      geom_histogram()+
      facet_wrap(~ dist_type, scales = "free")
    
    tibble(dist_type = names(distributions_df),
    skewness = purrr::map_dbl(distributions_df, skewness_bry), 
    variance = purrr::map_dbl(distributions_df, var_bry))
    
    ```
    
    * excellent video explaining intuition behind skewness: https://www.youtube.com/watch?v=z3XaFUP1rAM  
    
1.  Write `both_na()`, a function that takes two vectors of the same length and returns the number of positions that have an `NA` in both vectors.
    
    ```{r, error = TRUE}
    both_na <- function(x, y) {
      if (length(x) == length(y)) {
      sum(is.na(x) & is.na(y))
      } else
      stop("Vectors are not equal length")
    }
    
    x <- c(4, NA, 7, NA, 3)
    y <- c(NA, NA, 5, NA, 0)
    z <- c(NA, 4)
    
    both_na(x, y)
    both_na(x, z)
    ```

1.  What do the following functions do? Why are they useful even though they are so short?
    
    ```{r}
    is_directory <- function(x) file.info(x)$isdir
    is_readable <- function(x) file.access(x, 4) == 0
    ```

    * first checks if what is being referred to is actually a directory
    * second checks if a specific file is readable
    

1.  Read the [complete lyrics](https://en.wikipedia.org/wiki/Little_Bunny_Foo_Foo) 
    to "Little Bunny Foo Foo". There's a lot of duplication in this song. Extend the initial piping example to recreate the complete song, and use functions to reduce the duplication.
    

## 19.3: Functions are for humans and computers

* Recommends snake_case over camelCase, but just choose one and be consistent
* When functions have a link, common prefix over suffix (i.e. input_select, input_text over, select_input, text_input) 
* ctrl + shift + r creates section breaks in R scripts like below  

`# test label --------------------------------------------------------------`

* (though these cannot be made in markdown documents)


### 19.3.1

1.  Read the source code for each of the following three functions, puzzle out what they do, and then brainstorm better names.
    
    ```{r}
    f1 <- function(string, prefix) {
      substr(string, 1, nchar(prefix)) == prefix
    }
    f2 <- function(x) {
      if (length(x) <= 1) return(NULL)
      x[-length(x)]
    }
    f3 <- function(x, y) {
      rep(y, length.out = length(x))
    }
    ```
    
    * `f1`: `check_prefix`
    * `f2`: `return_not_last`
    * `f3`: `repeat_for_length`
    
    
1.  Take a function that you've written recently and spend 5 minutes brainstorming a better name for it and its arguments.
    
    * done seperately

1.  Compare and contrast `rnorm()` and `MASS::mvrnorm()`. How could you make them more consistent? 
    
    * uses mu = and Sigma = instead of mean = and sd = , and has extra parameters like tol, empirical, EISPACK
    * Similar in that both are pulling samples from gaussian distribution
    * `mvrnorm` is multivariate though, could change name to `rnorm_mv`
    
    
1.  Make a case for why `norm_r()`, `norm_d()` etc would be better than `rnorm()`, `dnorm()`. Make a case for the opposite.
    
    * `norm_*` would show the commonality of them being from the same distribution. One could argue the important commonality though may be more related to it being either a random sample or a density distribution, in which case the `r*` or `d*` coming first may make more sense. To me, the fact that the help pages has all of the 'normal distribution' functions on the same page suggests the former may make more sense. However, I actually like having it be set-up the way it is, because I am more likely to forget the name of the distribution type I want over the fact that I want a random sample, so it's easier to type `r` and then do ctrl + space and have autocomplete help me find the specific distribution I want, e.g. `rnorm`, `runif`, `rpois`, `rbinom`...
    
## 19.4: Conditional execution

Function example that uses `if` statement:
```{r}
has_name <- function(x) {
  nms <- names(x) 
  if (is.null(nms)) { 
    rep(FALSE, length(x))
  } else {
    !is.na(nms) & nms != ""
  }
}
```

* note that if all names are blank, it returns the one-unit vector value `NULL`, hence the need for the `if` statement here...^[`NULL` types are not vectors but only single length elements of a different type. `is.null` is not vectorized in the way that `is.na`. E.g. it's job is to return `TRUE` if given a `NULL`. For example, a list of `NULL`s is a `list` type (not a `NULL` type) therefore the following: `is.null(list(NULL, NULL))` would be `FALSE` -- to return a list of `TRUE` values you would need to run `map(list(NULL, NULL), is.null)`.]

### 19.4.4.

1.  What's the difference between `if` and `ifelse()`? Carefully read the help and construct three examples that illustrate the key differences.
    
    * `ifelse` is vectorized, `if` is not
        + Typically use `if` in functions when giving conditional options for how to evaluate
        + Typically use `ifelse` when changing specific values in a vector
    * If you supply `if` with a vector of length > 1, it will use the first value
        
    ```{r, error = TRUE}
    x <- c(3, 4, 6)
    y <- c("5", "c", "9")
    
    # Use `ifelse` simple transformations of values
    ifelse(x < 5, 0, x)
    
    # Use `if` for single condition tests
    cutoff_make0 <- function(x, cutoff = 0){
      if(is.numeric(x)){
        ifelse(x < cutoff, 0, x)
      } else stop("The input provided is not a numeric vector")
    }
    
    cutoff_make0(x, cutoff = 4)
    cutoff_make0(y, cutoff = 4)
    ```
    
1.  Write a greeting function that says "good morning", "good afternoon", or "good evening", depending on the time of day. (Hint: use a time argument that defaults to `lubridate::now()`. That will make it easier to test your function.)

    ```{r}
    greeting <- function(when) {
      
      time <- hour(when)
      
      if (time < 12 && time > 4) {
        greating <- "good morning"
      } else if (time < 17 && time >= 12) {
        greeting <- "good afternoon"
      } else greeting <- "good evening"
      
      when_char <- as.character(when)
      mid <- ", it is: "
      cat(greeting, mid, when_char, sep = "")
    }
    
    greeting(now())
    ```

1.  Implement a `fizzbuzz` function. It takes a single number as input. If the number is divisible by three, it returns "fizz". If it's divisible by five it returns "buzz". If it's divisible by three and five, it returns "fizzbuzz". Otherwise, it returns the number. Make sure you first write working code before you create the function.
    
    ```{r, error = TRUE}
    fizzbuzz <- function(x){
      if(is.numeric(x) && length(x) == 1){
        y <- ""
        if (x %% 5 == 0) y <- str_c(y, "fizz")
        if (x %% 3 == 0) y <- str_c(y, "buzz")
        if (str_length(y) == 0) {
          print(x)
        } else print(y)
      } else stop("Input is not a numeric vector with length 1")
    }
    
    fizzbuzz(4)
    fizzbuzz(10)
    fizzbuzz(6)
    fizzbuzz(30)
    fizzbuzz(c(34, 21))
    ```
    
    
1.  How could you use `cut()` to simplify this set of nested if-else statements?

    ```{r, eval = FALSE}
    if (temp <= 0) {
      "freezing"
    } else if (temp <= 10) {
      "cold"
    } else if (temp <= 20) {
      "cool"
    } else if (temp <= 30) {
      "warm"
    } else {
      "hot"
    }
    ```
    
    * Below is example of fix
    
    ```{r}
    temp <- seq(-10, 50, 5)
    cut(temp, 
        breaks = c(-Inf, 0, 10, 20, 30, Inf),  #need to include negative and positive infiniity
        labels = c("freezing", "cold", "cool", "warm", "hot"),
        right = TRUE,
        oredered_result = TRUE)
    ```
    
    How would you change the call to `cut()` if I'd used `<` instead of `<=`? What is the other chief advantage of `cut()` for this problem? (Hint: what happens if you have many values in `temp`?)
    
    * See below change to `right` argument
    ```{r}
    cut(temp, 
        breaks = c(-Inf, 0, 10, 20, 30, Inf),  #need to include negative and positive infiniity
        labels = c("freezing", "cold", "cool", "warm", "hot"),
        right = FALSE,
        oredered_result = TRUE)
    ```

1.  What happens if you use `switch()` with numeric values?

    * It will return the index of the argument.
      + In example below, I input '3' into `switch` value so it does the `times` argument

    ```{r}
    math_operation <- function(x, y, op){
       switch(op,
         plus = x + y,
         minus = x - y,
         times = x * y,
         divide = x / y,
         stop("Unknown op!")
       )
      }
    
    math_operation(5, 4, 3)
    ```

1.  What does this `switch()` call do? What happens if `x` is "e"?

    ```{r, eval = FALSE}
    
    x <- "e"
    
    switch(x, 
      a = ,
      b = "ab",
      c = ,
      d = "cd"
    )
    ```
    
    Experiment, then carefully read the documentation. 
    
    * If `x` is 'e' nothing will be outputted. If `x` is 'c' or 'd' then 'cd' is outputted. If 'a' or 'b' then 'ab' is outputeed.  If blank it will continue down list until reaching an argument to output.
    
## 19.5: Function arguments

*Common non-descriptive short argument names: *  

* `x`, `y`, `z`: vectors.
* `w`: a vector of weights.
* `df`: a data frame.
* `i`, `j`: numeric indices (typically rows and columns).
* `n`: length, or number of rows.
* `p`: number of columns.

### 19.5.5.

1.  What does `commas(letters, collapse = "-")` do? Why?

    * `commas` function is below
    ```{r, error = TRUE}
    commas <- function(...) stringr::str_c(..., collapse = ", ")
    
    commas(letters[1:10])
    
    commas(letters[1:10], collapse = "-")
    ```
    
    * The above fails because are essentially specifying two different values for the `collapse` argument
    * Takes in vector of mulitple strings and outputs one-unit character string with items concatenated together and seperated by columns
    * Is able to do this via use of `...` that turns this into a wrapper on `stringr::str_c` with the `collapse` value specified

1.  It'd be nice if you could supply multiple characters to the `pad` argument, e.g. `rule("Title", pad = "-+")`. Why doesn't this currently work? How could you fix it?
    
    * current `rule` function is below
    ```{r}
    rule <- function(..., pad = "-") {
      title <- paste0(...)
      width <- getOption("width") - nchar(title) - 5
      cat(title, " ", stringr::str_dup(pad, width), "\n", sep = "")
    }
    
    # Note that `cat` is used instead of `paste` because paste would output it as a character vector, whereas `cat` is focused on just ouptut, could also have used `print`, though print does more conversion than cat does (apparently)
    
    rule("Tis the season"," to be jolly")
    ```
    
    * doesn't work because pad ends-up being too many characters in this situation
    ```{r}
    rule("Tis the season"," to be jolly", pad="+-")
    ```
    
    * instead would need to make the number of times `pad` is duplicated dependent on its length, see below for fix
    
    ```{r}
    rule_pad_fix <- function(..., pad = "-") {
      title <- paste0(...)
      width <- getOption("width") - nchar(title) - 5
      width_fix <- width %/% stringr::str_length(pad)
      cat(title, " ", stringr::str_dup(pad, width_fix), "\n", sep = "")
    }
    
    rule_pad_fix("Tis the season"," to be jolly", pad="+-")
    ```
    
1.  What does the `trim` argument to `mean()` do? When might you use it?

    * `trim` specifies proportion of data to take off from both ends, good with outliers
    ```{r}
    mean(c(-1000, 1:100, 100000), trim = .025) 
    ```

1.  The default value for the `method` argument to `cor()` is 
    `c("pearson", "kendall", "spearman")`. What does that mean? What value is used by default?
  
    * is showing that you can choose from any of these, will default to use `pearson` (value in first position)
    
## 19.6: Return values

```{r}
show_missings <- function(df) {
  n <- sum(is.na(df))
  cat("Missing values: ", n, "\n", sep = "")
  invisible(df)
}

x <- show_missings(mtcars)

str(x)
```

* can still use in pipes
```{r}
mtcars %>% 
  show_missings() %>% 
  mutate(mpg = ifelse(mpg < 20, NA, mpg)) %>% 
  show_missings() 
```

## Appendix

### 19.2.1.4

*Function for Standard Error:* 

```{r}
x <- c(5, -2, 8, 6, 9)
sd(x, na.rm = TRUE) / sqrt(sum(!is.na(x)))

sample_se <- function(x) {
  sd(x, na.rm = TRUE) / sqrt(sum(!is.na(x)) - 1)
}    
#sqrt(var(x)/sum(!is.na(x)))

sample_se(x)
```

*Function for kurtosis:*
```{r}
kurtosis_type3 <- function(x){
  sum((x - mean(x)) ^ 4) / length(x) / sd(x) ^ 4 - 3
}
```

Notice differences between cauchy and normal distribution

```{r}
set.seed(1235)
norm_exp <- rnorm(10000)

set.seed(1235)
cauchy_exp <- rcauchy(10000)
```

```{r, fig.align = "default", fig.show='hold', out.width = "50%"}
hist(norm_exp)
hist(cauchy_exp)
```

kurtosis
```{r}
kurtosis_type3(norm_exp)
kurtosis_type3(cauchy_exp)
```

### 19.2.3.5

```{r, error = TRUE}
position_both_na <- function(x, y) {
  if (length(x) == length(y)) {
  (c(1:length(x)))[(is.na(x) & is.na(y))]
  } else
  stop("Vectors are not equal length")
}

x <- c(4, NA, 7, NA, 3)
y <- c(NA, NA, 5, NA, 0)
z <- c(NA, 4)
both_na(x, y)
both_na(x, z)

```

* specifies position where both are `NA`
* second example shows returning of 'stop' argument