Source file ⇒ lec14.Rmd

Midterm

The Midterm will cover data wrangling and ggplot (I expect chapters 1-14 excluding chapter 13 and the relavent covered material on data camp) and the first 4 chapters of Intermediate R in Data Camp. It will consist of a 50 min written test. You will be able to use a cheat sheet for syntax. I will provide you with sample problems and a detailed description of the topics soon.

Today (Programming in R)

Conditionals and Control Flow (Chapter 1 Data Camp’s Intermediate R)
Loops (Chapter 2 Data Camp’s Intermediate R)

1. Conditionals and Control Flow

Computing in R consists of sequentially evaluating statements. Flow control structures allow us to control which statements are evaluated and in what order. In R the primary ones consist of

if/else statements and the ifelse function
for and while loops

Expressions, such as p <- .5 and sample(c(1, 0), size = 1, prob = c(p, 1-p)) can be grouped together using curly braces “{” and “}”. A group of expressions is called a block. For today’s lecture, the word statement will refer to either a single expression or a block.

The basic syntax for an if/else statement is

if ( condition ) {
  statement1
} else {
  statement2
}

You can also write this on a single line as:

if(condition) statement1 else statement2

First, condition is evaluated. If the first element of the result is TRUE then statement1 is evaluated. If the first element of the result is FALSE then statement2 is evaluated. Only the first element of the result is used. If the result is numeric, 0 is treated as FALSE and any other number as TRUE. If the result is not logical or numeric, or if it is NA, you will get an error.

For example,

a <- c(3==2,5==5,0)
a

## [1] 0 1 0

if(a){
  print("hi")
} else{
  print("bye")
}

## Warning in if (a) {: the condition has length > 1 and only the first
## element will be used

## [1] "bye"

However,

if("pizza"){
  print("hi")
} else{
  print("bye")
}

this will result in an error Error in if ("pizza") { : argument is not interpretable as logical

When we discussed Boolean algebra before, we met the operators & (AND) and | (OR).

Recall that these are both vectorized operators. For example:

x <- c(.2,3.3,.4)
(x < -1 | x > 1)

## [1] FALSE  TRUE FALSE

If/else statements, on the other hand, are based on a single,“global” condition. So we often see constructions using any or all to express something related to the whole vector, like

if(any(x<-1|x>1)) print("hi") else print("bye")

## [1] "hi"

if(all(x < -1|x > 1)) print("hi") else print("bye")

## [1] "bye"

The result of an if/else statement can be assigned. For example, these give the same result:

x <- c(.2,3.3,.4)

y <- if ( any(x <= 0) ) log(1+x) else log(x)
y

## [1] -1.6094379  1.1939225 -0.9162907

if ( any(x <= 0) ) y <- log(1+x) else y <- log(x)
y

## [1] -1.6094379  1.1939225 -0.9162907

Also,the else clause is optional. Another way to do the above is:

if( any(x <= 0) ) x <- 1+x
y <- log(x)
y

## [1] -1.6094379  1.1939225 -0.9162907

However this changes x as well.

If/else statements can be nested.

if (condition1 )
  statement1
else if (condition2)
  statement2
else if (condition3)
  statement3
else
  statement4

The conditions are evaluated, in order, until one evaluates to TRUE. The the associated statement/block is evaluated. The statement in the final else clause is evaluated if none of the conditions evaluates to TRUE.

A note about formatting if/else statements:

When the if statement is not in a block, the else (if present) must appear on the same line as statement1 or immediately following the closing brace. For example,

if (condition) {statement1}
else {statement2}

will be an error. For example

if(3==2){ print("hi")}
else {print("bye")}

gives an error Error: unexpected 'else' in "else"

I suggest using the format

if (condition) {
  statement1
} else {
  statement2
}

Some common uses of if/else clauses

With logical arguments to tell a function what to do

corplot <-  function(x,y,plotit=TRUE){
  df=data.frame(var1=x,var2=y)
  p <-  df %>% ggplot(aes(x=var1,y=var2)) + geom_point(size=3) +theme(text=element_text(size=25))
  if(plotit) print(p)
  cor(x,y)
}

corplot(runif(n=100,min=0,max=1),runif(n=100,min=0,max=1))

## [1] 0.1299759

To verify that the arguments of a function are as expected

m=matrix(c(1,2,3,4),nrow=2)
if( !is.matrix(m)){
  stop("m must be a matrix")
} else{
  print("hi")
}

## [1] "hi"

but

m=c(1,2,3)
if( !is.matrix(m)){
  stop("m must be a matrix")
  print("hi")
}

will throw an error Error: m must be a matrix

To handle common numerical errors

y <- 3
x <- 0
ratio <- if(x!=0) y/x else NA
ratio

## [1] NA

In general, to control which block of code is executed

normt <- function(n, dist){
  if ( dist == "normal" ){
    return( rnorm(n) )
  } else if (dist == "t"){
    return(rt(n, df = 1, ncp = 0))
  } else stop("distribution not implemented")
}
normt(10,"t")

##  [1]   2.59675807   1.02781113   0.68555543   0.00490631  -0.31825026
##  [6]  -0.78772245 -15.71949207  -0.03977380   0.37497647   0.20761216

These if/else constructions are useful for global tests, not tests applied to individual elements of a vector.

However, there is a vectorized function called ifelse

args(ifelse)

## function (test, yes, no) 
## NULL

Here test is an R object that can be coerced to logical. yes and no are R objects of the same size as test

y=2
x=c(-1,0,2)
x!=0

## [1]  TRUE FALSE  TRUE

y/x

## [1]  -2 Inf   1

NA

## [1] NA

ifelse(x!=0, y/x,NA)

## [1] -2 NA  1

For each element of test, the corresponding element of yes is returned if the element is TRUE, and the corresponding element of no is returned if it is FALSE.

Task for you

The modulo operator in R is %%. For example

15 %% 2

## [1] 1

15 %% 3

## [1] 0

Assign true to the boolean variable leapYear if the integer variable year is a leap year. The rule for determining leap years is that one of the following conditions must hold: 1) the year is divisible by 4 but not divisible by 100, or 2) the year is divisible by 400.

year <-  2016
if((year%%4==0 & year%%100 != 0) | (year%% 400 ==0)  ) leapyear <- TRUE  else leapyear <- FALSE
leapyear

## [1] TRUE

Can you do this if year is a vector 2000:2016?

year <- 2000:2016
leapyear <- ifelse((year%%4 & year%%100 !=0) | (year%% 400 ==0), TRUE,FALSE)
leapyear

##  [1]  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE
## [12]  TRUE FALSE  TRUE  TRUE  TRUE FALSE

2. Loops

Looping is the repeated evaluation of a statement or block of statements.

Much of what is handled using loops in other languages can be more efficiently handled in R using vectorized calculations or one of the apply mechanisms.

However, certain algorithms, such as those requiring recursion, can only be handled by loops.

There are two main looping constructs in R: for and while.

for loops

A for loop repeats a statement or block of statements a predefined number of times.

The syntax in R is

for ( name in vector ){
  statement
}

For each element in vector, the variable name is set to the value of that element and statement is evaluated.

vector often contains integers, but can be any valid type.

Examples:

for( word in c("my","name","is","adam")){
  print(word)
}

## [1] "my"
## [1] "name"
## [1] "is"
## [1] "adam"

xseq <- seq(-2.5, 2.5, length = 100) 
yseq <- xseq^2
df <- data.frame(xseq,yseq) 
p <- df %>% ggplot(aes(x=xseq, y=yseq)) + geom_line(stat="identity", col="red")

for(i in -2:2){
 p <- p + geom_point(x=i,y=2,col="blue",size=3)
}
p

while loops

A while loop repeats a statement or block of statements for as many times as a particular condition is TRUE.

The syntax in R is

while (condition){
  statement
}

condition is evaluated, and if it is TRUE, statement is evaluated. This process continues until condition evaluates to FALSE.

Task for you

The expression,

sample(c(1, 0), size = 1, prob = c(p, 1-p))

simulates a random coin flip, where the coin has probability p of coming up heads, represented by a 1. For p=.5 simulate flipping a coin until 20 of heads are obtained. Produce the vector of 0 and 1.

p=.5
count=0
flips=c()
while(count<20){
  flip= sample(c(1, 0), size = 1, prob = c(p, 1-p))
  flips=c(flips,flip)
  count=count + flip
}
flips

##  [1] 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 1 1

The break statement causes a loop to exit. This is particularly useful with while loops, which, if we’re not careful, might loop indefinitely (or until we kill R).

Here is an example:

# Simulate steps for random walk to cross threshold = 10
max.iter <- 10000
x <- 0
steps <- 0
mywalk=c()
while(x < 10){
  x <- x + sample(c(-1, 1), 1)
  steps <- steps + 1
  mywalk=c(mywalk,x)
  if(steps == max.iter){
    warning("Maximum iteration reached")
    break }
}
mywalk %>% head(100)

##  [1]  1  0  1  0  1  2  3  2  1  2  1  2  3  4  5  6  5  6  7  8  9 10

Lec14

Stat 133

Midterm

Today (Programming in R)

1. Conditionals and Control Flow

Some common uses of if/else clauses

Task for you

2. Loops

for loops

while loops

Task for you