Last week: Plotting tools

plot(): generic plotting function
points(): add points to an existing plot
lines(), abline(): add lines to an existing plot
text(), legend(): add text to an existing plot
rect(), polygon(): add shapes to an existing plot
hist(), image(): histogram and heatmap
heat.colors(), topo.colors(), etc: create a color vector
density(): estimate density, which can be plotted
contour(): draw contours, or add to existing plot
curve(): draw a curve, or add to existing plot

Part I

Function basics

Why do we need functions?

Data structures tie related values into one object
Functions tie related commands into one object
In both cases: easier to understand, easier to work with, easier to build into larger things

Remember those commands you typed over and over?

From our lectures on text manipulation and regexes:

# Get King's word counts
king.lines = readLines("https://www.stat.cmu.edu/~arinaldo/Teaching/36350/F22/data/king.txt")
king.text = paste(king.lines, collapse=" ")
king.words = strsplit(king.text, split="[[:space:]]|[[:punct:]]")[[1]]
king.words = king.words[king.words != ""]
king.wordtab = table(king.words)

# Now retype for other speeches, etc.

Creating your own function

Call function() to create your own function. Document your function with comments

# get.wordtab.king: get a word table from King's "I Have A Dream" speech
# Input: none
# Output: word table, i.e., vector with counts as entries and associated
#   words as names

get.wordtab.king = function() {
  lines = readLines("https://www.stat.cmu.edu/~arinaldo/Teaching/36350/F22/data/king.txt")
  text = paste(lines, collapse=" ")
  words = strsplit(text, split="[[:space:]]|[[:punct:]]")[[1]]
  words = words[words != ""]
  wordtab = table(words)
  return(wordtab)
}

Much better: create a word table function that takes a URL of web

# get.wordtab.from.url: get a word table from text on the web
# Input:
# - str.url: string, specifying URL of a web page 
# Output: word table, i.e., vector with counts as entries and associated
#   words as names

get.wordtab.from.url = function(str.url) {
  lines = readLines(str.url)
  text = paste(lines, collapse=" ")
  words = strsplit(text, split="[[:space:]]|[[:punct:]]")[[1]]
  words = words[words != ""]
  wordtab = table(words)
  return(wordtab)
}

Function structure

The structure of a function has three basic parts:

Inputs (or arguments)
Body (code that is executed)
Output (or return value)

R doesn’t let your function have multiple outputs, but you can return a list

Using your created function

Our created functions can be used just like the built-in ones

# Using our function
king.wordtab.new = get.wordtab.from.url(
  "https://www.stat.cmu.edu/~arinaldo/Teaching/36350/F22/data/king.txt")
all(king.wordtab.new == king.wordtab)

## [1] TRUE

# Revealing our function's definition
get.wordtab.from.url

## function(str.url) {
##   lines = readLines(str.url)
##   text = paste(lines, collapse=" ")
##   words = strsplit(text, split="[[:space:]]|[[:punct:]]")[[1]]
##   words = words[words != ""]
##   wordtab = table(words)
##   return(wordtab)
## }
## <environment: 0x7f88e5c41500>

Default return value

With no explicit return() statement, the default is just to return whatever is on the last line. So the following is equivalent to what we had before

get.wordtab.from.url = function(str.url) {
  lines = readLines(str.url)
  text = paste(lines, collapse=" ")
  words = strsplit(text, split="[[:space:]]|[[:punct:]]")[[1]]
  words = words[words != ""]
  table(words)
}

Multiple inputs

Our function can take more than one input

# get.wordtab.from.url: get a word table from text on the web
# Inputs:
# - str.url: string, specifying URL of a web page 
# - split: string, specifying what to split on
# Output: word table, i.e., vector with counts as entries and associated
#   words as names

get.wordtab.from.url = function(str.url, split) {
  lines = readLines(str.url)
  text = paste(lines, collapse=" ")
  words = strsplit(text, split=split)[[1]]
  words = words[words != ""]
  table(words)
}

Default inputs

Our function can also specify default values for the inputs (if the user doesn’t specify an input in the function call, then the default value is used)

# get.wordtab.from.url: get a word table from text on the web
# Inputs:
# - str.url: string, specifying URL of a web page 
# - split: string, specifying what to split on. Default is the regex pattern
#   "[[:space:]]|[[:punct:]]"
# - tolower: Boolean, TRUE if words should be converted to lower case before
#   the word table is computed. Default is TRUE
# Output: word table, i.e., vector with counts as entries and associated
#   words as names

get.wordtab.from.url = function(str.url, split="[[:space:]]|[[:punct:]]", 
                                tolower=TRUE) {
  lines = readLines(str.url)
  text = paste(lines, collapse=" ")
  words = strsplit(text, split=split)[[1]]
  words = words[words != ""]
    
  # Convert to lower case, if we're asked to
  if (tolower) words = tolower(words)
  
  table(words)
}

Examples of function calls

# Inputs can be called by name, or without names
king.wordtab1 = get.wordtab.from.url(
  str.url="https://www.stat.cmu.edu/~arinaldo/Teaching/36350/F22/data/king.txt",
  split="[[:space:]]|[[:punct:]]", tolower=TRUE)
king.wordtab2 = get.wordtab.from.url(
  "https://www.stat.cmu.edu/~arinaldo/Teaching/36350/F22/data/king.txt",
  "[[:space:]]|[[:punct:]]", TRUE)
all(king.wordtab2 == king.wordtab1)

## [1] TRUE

# Inputs can be called by partial names (if uniquely identifying)
king.wordtab3 = get.wordtab.from.url(
  str="https://www.stat.cmu.edu/~arinaldo/Teaching/36350/F22/data/king.txt",
  spl="[[:space:]]|[[:punct:]]", tolower=TRUE)
all(king.wordtab3 == king.wordtab1)

## [1] TRUE

# When inputs aren't specified, default values are used
king.wordtab4 = get.wordtab.from.url(
  str.url="https://www.stat.cmu.edu/~arinaldo/Teaching/36350/F22/data/king.txt",
  split="[[:space:]]|[[:punct:]]")
all(king.wordtab4 == king.wordtab1)

## [1] TRUE

# Named inputs can go in any order
king.wordtab5 = get.wordtab.from.url(
  tolower=TRUE, split="[[:space:]]|[[:punct:]]",
  str.url="https://www.stat.cmu.edu/~arinaldo/Teaching/36350/F22/data/king.txt")
all(king.wordtab5 == king.wordtab1)

## [1] TRUE

The dangers of using inputs without names

While named inputs can go in any order, unnamed inputs must go in the proper order (as they are specified in the function’s definition). E.g., the following code would throw an error:

king.wordtab6 = get.wordtab.from.url("[[:space:]]|[[:punct:]]",
  "https://www.stat.cmu.edu/~arinaldo/Teaching/36350/F22/data/king.txt",
  tolower=FALSE)

## Warning in file(con, "r"): cannot open file '[[:space:]]|[[:punct:]]': No such file
## or directory

## Error in file(con, "r"): cannot open the connection

because our function would try to open up “[[:space:]]|[[:punct:]]” as the URL of a web page

When calling a function with multiple arguments, use input names for safety, unless you’re absolutely certain of the right order for (some) inputs

Part II

Return values and side effects

Returning more than one thing

When creating a function in R, though you cannot return more than one output, you can return a list. This (by definition) can contain an arbitrary number of arbitrary objects

# get.wordtab.from.url: get a word table from text on the web
# Inputs:
# - str.url: string, specifying URL of a web page 
# - split: string, specifying what to split on. Default is the regex pattern
#   "[[:space:]]|[[:punct:]]"
# - tolower: Boolean, TRUE if words should be converted to lower case before
#   the word table is computed. Default is TRUE
# - keep.nums: Boolean, TRUE if words containing numbers should be kept in the
#   word table. Default is FALSE
# Output: list, containing word table, and then some basic numeric summaries

get.wordtab.from.url = function(str.url, split="[[:space:]]|[[:punct:]]",
                                tolower=TRUE, keep.nums=FALSE) {
  lines = readLines(str.url)
  text = paste(lines, collapse=" ")
  words = strsplit(text, split=split)[[1]]
  words = words[words != ""]
    
  # Convert to lower case, if we're asked to
  if (tolower) words = tolower(words)
  
  # Get rid of words with numbers, if we're asked to
  if (!keep.nums) 
    words = grep("[0-9]", words, inv=TRUE, val=TRUE)
  
  # Compute the word table
  wordtab = table(words)
  
  return(list(wordtab=wordtab,
              number.unique.words=length(wordtab),
              number.total.words=sum(wordtab),
              longest.word=words[which.max(nchar(words))]))
}

# King's "I Have A Dream" speech 
king.wordtab = get.wordtab.from.url(
  "https://www.stat.cmu.edu/~arinaldo/Teaching/36350/F22/data/king.txt")
lapply(king.wordtab, head)

## $wordtab
## words
##       a    able   again     ago   ahead alabama 
##      37       8       2       1       1       3 
## 
## $number.unique.words
## [1] 528
## 
## $number.total.words
## [1] 1631
## 
## $longest.word
## [1] "discrimination"

# Lincoln's Gettysburg address
lincoln.wordtab = get.wordtab.from.url(
  "https://www.stat.cmu.edu/~arinaldo/Teaching/36350/F22/data/lincoln.txt")
lapply(lincoln.wordtab, head)

## $wordtab
## words
##        a    above      add advanced      ago      all 
##        7        1        1        1        1        1 
## 
## $number.unique.words
## [1] 138
## 
## $number.total.words
## [1] 272
## 
## $longest.word
## [1] "proposition"

Side effects

A side effect of a function is something that happens as a result of the function’s body, but is not returned. Examples:

Printing something out to the console
Plotting something on the display
Saving an R data file, or a PDF, etc.

# get.wordtab.from.url: get a word table from text on the web
# Inputs:
# - str.url: string, specifying URL of a web page 
# - split: string, specifying what to split on. Default is the regex pattern
#   "[[:space:]]|[[:punct:]]"
# - tolower: Boolean, TRUE if words should be converted to lower case before
#   the word table is computed. Default is TRUE
# - keep.nums: Boolean, TRUE if words containing numbers should be kept in the
#   word table. Default is FALSE
# - hist: Boolean, TRUE if a histogram of word lengths should be plotted as a
#   side effect. Default is FALSE
# Output: list, containing word table, and then some basic numeric summaries

get.wordtab.from.url = function(str.url, split="[[:space:]]|[[:punct:]]",
                                tolower=TRUE, keep.nums=FALSE, hist=FALSE) {
  lines = readLines(str.url)
  text = paste(lines, collapse=" ")
  words = strsplit(text, split=split)[[1]]
  words = words[words != ""]
    
  # Convert to lower case, if we're asked to
  if (tolower) words = tolower(words)
    
  # Get rid of words with numbers, if we're asked to
  if (!keep.nums) 
    words = grep("[0-9]", words, inv=TRUE, val=TRUE)
  
  # Plot the histogram of the word lengths, if we're asked to
  if (hist) 
    hist(nchar(words), col="lightblue", breaks=0:max(nchar(words)),
         xlab="Word length")
  
  # Compute the word table
  wordtab = table(words)
  
  return(list(wordtab=wordtab,
              number.unique.words=length(wordtab),
              number.total.words=sum(wordtab),
              longest.word=words[which.max(nchar(words))]))
}

# King's speech
king.wordtab = get.wordtab.from.url(
  str.url="https://www.stat.cmu.edu/~arinaldo/Teaching/36350/F22/data/king.txt",
  hist=TRUE)

lapply(king.wordtab, head)

## $wordtab
## words
##       a    able   again     ago   ahead alabama 
##      37       8       2       1       1       3 
## 
## $number.unique.words
## [1] 528
## 
## $number.total.words
## [1] 1631
## 
## $longest.word
## [1] "discrimination"

# Lincoln's speech
lincoln.wordtab = get.wordtab.from.url(
  str.url="https://www.stat.cmu.edu/~arinaldo/Teaching/36350/F22/data/lincoln.txt",
  hist=TRUE)

lapply(lincoln.wordtab, head)

## $wordtab
## words
##        a    above      add advanced      ago      all 
##        7        1        1        1        1        1 
## 
## $number.unique.words
## [1] 138
## 
## $number.total.words
## [1] 272
## 
## $longest.word
## [1] "proposition"

Part III

Environments and design

Environment: what the function can see and do

Each function has its own environment
Names here override names in the global environment
Internal environment starts with the named arguments
Assignments inside the function only change the internal environment
Names undefined in the function are looked for in the global environment

Environment examples

x = 7
y = c("A","C","G","T","U")
adder = function(y) { x = x+y; x }
adder(1)

## [1] 8

## [1] 7

## [1] "A" "C" "G" "T" "U"

circle.area = function(r) { pi*r^2 }
circle.area(1:3)

## [1]  3.141593 12.566371 28.274334

true.pi = pi
pi = 3 # Valid in 1800s Indiana
circle.area(1:3)

## [1]  3 12 27

pi = true.pi # Restore sanity
circle.area(1:3)

## [1]  3.141593 12.566371 28.274334

Relying on variables outside of the function’s environment

Generally OK for built-in constants like pi, letters, month.names, etc.
Generally not OK for user-defined variables outside of the function
For the latter, pass these as input arguments to your function

Bad side effects

Not all side effects are desirable. One particularly bad side effect is if the function’s body changes the value of some variable outside of the function’s environment

Not easy to do (we won’t even tell you how)
But can be done and should be avoided at all costs!

Top-down function design

Start with the big-picture view of the task
Break the task into a few big parts
Figure out how to fit the parts together
Repeat this for each part

Start off with a code sketch

You can write top-level code, right away, for your function’s design:

# Not actual code
big.job = function(lots.of.arguments) {
  first.result = first.step(some.of.the.args)
  second.result = second.step(first.result, more.of.the.args)
  final.result = third.step(second.result, rest.of.the.args)
  return(final.result)
}

After you write down your design, go ahead and write the sub-functions (here first.step(), second.step(), third.step()). The process may be iterative, in that you may write these sub-functions, then go back and change the design a bit, etc.

With practice, this design strategy should become natural

Summary

Function: formal encapsulation of a block of code; generally makes your code easier to understand, to work with, and to modify
Functions are absolutely critical for writing (good) code for medium or large projects
A function’s structure consists of three main parts: inputs, body, and output
R allows the function designer to specify default values for any of the inputs
R doesn’t allow the designer to return multiple outputs, but can return a list
Side effects are things that happen as a result of a function call, but that aren’t returned as an output
Top-down design means breaking a big task into small parts, implementing each of these parts, and then putting them together

Functions

Statistical Computing, 36-350

Tuesday October 25, 2022