library(MASS) #for the cats data

• If-statements

• For-loops

• Apply()

• Writing your own functions

New control flow constructs

• if(cond) expr
• if(cond) cons.expr else alt.expr
• for(var in seq) expr

New functions

• rev(): reverse version of an argument
• apply(): apply a function to margins of a matrix
• sapply(): apply a function to elements of a list, vector or matrix return
• lapply(): apply a function to elements of a list, list return
• print(): print an object to the console
• cat: outputs an object with less conversion than print()

Often, we want to run some code only if some condition is true.

For example:

a <- 2
if (a > 5){
  print("a is larger than 5.")
}

a <- 8
if (a > 5){
  print("a is larger than 5.")
} 

## [1] "a is larger than 5."

We can also specify something to be run if the condition is not true.

a <- 2
if (a > 5){
  print("a is larger than 5.")
} else {
  print("a is smaller than 5.")
}

## [1] "a is smaller than 5."

a <- 8
if (a > 5){
  print("a is larger than 5.")
} else {
  print("a is smaller than 5.")
}

## [1] "a is larger than 5."

For loops are used when we want to perform some repetitive calculations.

It is often tedious, or even impossible, to write this repetition out completely.

For-loops allow us to automate this!

for (i in 1:6){
  print(i)
}

## [1] 1
## [1] 2
## [1] 3
## [1] 4
## [1] 5
## [1] 6

for (some.var.name in 1:6){
  print(some.var.name)
}

## [1] 1
## [1] 2
## [1] 3
## [1] 4
## [1] 5
## [1] 6

for (i in 1:6){
  print(i < 5)
}

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

for (i in 1:nrow(cats)){
  if (cats$Bwt[i] > 2.5){
    cat(i, "is over 2.5. It is:", cats$Bwt[i], "\n")
  }
}

## 37 is over 2.5. It is: 2.6 
## 38 is over 2.5. It is: 2.6 
## 39 is over 2.5. It is: 2.6 
## 40 is over 2.5. It is: 2.7 
## 41 is over 2.5. It is: 2.7 
## 42 is over 2.5. It is: 2.7 
## 43 is over 2.5. It is: 2.9 
## 44 is over 2.5. It is: 2.9 
## 45 is over 2.5. It is: 2.9 
## 46 is over 2.5. It is: 3 
## 47 is over 2.5. It is: 3 
## 73 is over 2.5. It is: 2.6 
## 74 is over 2.5. It is: 2.6 
## 75 is over 2.5. It is: 2.6 
## 76 is over 2.5. It is: 2.6 
## 77 is over 2.5. It is: 2.6 
## 78 is over 2.5. It is: 2.6 
## 79 is over 2.5. It is: 2.7 
## 80 is over 2.5. It is: 2.7 
## 81 is over 2.5. It is: 2.7 
## 82 is over 2.5. It is: 2.7 
## 83 is over 2.5. It is: 2.7 
## 84 is over 2.5. It is: 2.7 
## 85 is over 2.5. It is: 2.7 
## 86 is over 2.5. It is: 2.7 
## 87 is over 2.5. It is: 2.7 
## 88 is over 2.5. It is: 2.8 
## 89 is over 2.5. It is: 2.8 
## 90 is over 2.5. It is: 2.8 
## 91 is over 2.5. It is: 2.8 
## 92 is over 2.5. It is: 2.8 
## 93 is over 2.5. It is: 2.8 
## 94 is over 2.5. It is: 2.8 
## 95 is over 2.5. It is: 2.9 
## 96 is over 2.5. It is: 2.9 
## 97 is over 2.5. It is: 2.9 
## 98 is over 2.5. It is: 2.9 
## 99 is over 2.5. It is: 2.9 
## 100 is over 2.5. It is: 3 
## 101 is over 2.5. It is: 3 
## 102 is over 2.5. It is: 3 
## 103 is over 2.5. It is: 3 
## 104 is over 2.5. It is: 3 
## 105 is over 2.5. It is: 3 
## 106 is over 2.5. It is: 3 
## 107 is over 2.5. It is: 3 
## 108 is over 2.5. It is: 3 
## 109 is over 2.5. It is: 3.1 
## 110 is over 2.5. It is: 3.1 
## 111 is over 2.5. It is: 3.1 
## 112 is over 2.5. It is: 3.1 
## 113 is over 2.5. It is: 3.1 
## 114 is over 2.5. It is: 3.1 
## 115 is over 2.5. It is: 3.2 
## 116 is over 2.5. It is: 3.2 
## 117 is over 2.5. It is: 3.2 
## 118 is over 2.5. It is: 3.2 
## 119 is over 2.5. It is: 3.2 
## 120 is over 2.5. It is: 3.2 
## 121 is over 2.5. It is: 3.3 
## 122 is over 2.5. It is: 3.3 
## 123 is over 2.5. It is: 3.3 
## 124 is over 2.5. It is: 3.3 
## 125 is over 2.5. It is: 3.3 
## 126 is over 2.5. It is: 3.4 
## 127 is over 2.5. It is: 3.4 
## 128 is over 2.5. It is: 3.4 
## 129 is over 2.5. It is: 3.4 
## 130 is over 2.5. It is: 3.4 
## 131 is over 2.5. It is: 3.5 
## 132 is over 2.5. It is: 3.5 
## 133 is over 2.5. It is: 3.5 
## 134 is over 2.5. It is: 3.5 
## 135 is over 2.5. It is: 3.5 
## 136 is over 2.5. It is: 3.6 
## 137 is over 2.5. It is: 3.6 
## 138 is over 2.5. It is: 3.6 
## 139 is over 2.5. It is: 3.6 
## 140 is over 2.5. It is: 3.7 
## 141 is over 2.5. It is: 3.8 
## 142 is over 2.5. It is: 3.8 
## 143 is over 2.5. It is: 3.9 
## 144 is over 2.5. It is: 3.9

empty.cats <- matrix(NA, nrow = nrow(cats), ncol = ncol(cats))

for (i in 1:ncol(cats)){
  empty.cats[, i] <- rep(i, nrow(cats))
}

head(empty.cats)

##      [,1] [,2] [,3]
## [1,]    1    2    3
## [2,]    1    2    3
## [3,]    1    2    3
## [4,]    1    2    3
## [5,]    1    2    3
## [6,]    1    2    3

for (i in 1:3){
  for (j in 1:3){
    print(paste(i, "x", j, "=", i*j))
  }
}

## [1] "1 x 1 = 1"
## [1] "1 x 2 = 2"
## [1] "1 x 3 = 3"
## [1] "2 x 1 = 2"
## [1] "2 x 2 = 4"
## [1] "2 x 3 = 6"
## [1] "3 x 1 = 3"
## [1] "3 x 2 = 6"
## [1] "3 x 3 = 9"

my.list <- list(A = c(4, 2, 1:3), B = "Hello.", C = TRUE)

for (list.item in my.list){
  cat("One element is", list.item, "\n")
}

## One element is 4 2 1 2 3 
## One element is Hello. 
## One element is TRUE

But if we want to change the item, we have to be able to access it, so we are better off using 1:length(list), or 1:ncol(data.frame)/1:nrow(data.frame).

my.list <- list(A = c(4, 2, 1:3), B = "Hello.", C = c(TRUE, TRUE, FALSE))

for (iter in 1:length(my.list)){
  my.list[[iter]] <- rev(my.list[[iter]])
}
my.list

## $A
## [1] 3 2 1 2 4
## 
## $B
## [1] "Hello."
## 
## $C
## [1] FALSE  TRUE  TRUE

The apply family is a group of very useful functions that allow you to easily execute a function of your choice over a list of objects, such as a list, a data.frame, or matrix.

We will look at three examples:

• apply

• sapply

• lapply

apply is used for matrices (and sometimes dataframes). It can take a function that takes a vector as input, and apply it to each row or column.

MARGIN is 1 for rows, 2 for columns.

apply(cats[, -1], MARGIN = 2, mean)

##       Bwt       Hwt 
##  2.723611 10.630556

But we’ve seen this done easier:

colMeans(cats[, -1])

##       Bwt       Hwt 
##  2.723611 10.630556

However, the power of apply() is that it can use any function we throw at it.

rand.mat <- matrix(rnorm(21), nrow = 3, ncol = 7)
rand.mat

##            [,1]       [,2]      [,3]       [,4]       [,5]        [,6]
## [1,] -0.5495413  1.6040110 0.2065810 -0.4313313  0.8031660  0.04598861
## [2,] -0.4558570 -0.0929378 0.7613544  1.1739431 -0.5310347  0.45647626
## [3,] -0.9278759  0.5931129 1.7889414  1.0087794  0.3678748 -0.96723643
##             [,7]
## [1,]  0.38257922
## [2,]  0.02234608
## [3,] -0.75743886

apply(rand.mat, MARGIN = 1, FUN = max)

## [1] 1.604011 1.173943 1.788941

apply(rand.mat, MARGIN = 2, FUN = max)

## [1] -0.4558570  1.6040110  1.7889414  1.1739431  0.8031660  0.4564763  0.3825792

rand.mat

##            [,1]       [,2]      [,3]       [,4]       [,5]        [,6]
## [1,] -0.5495413  1.6040110 0.2065810 -0.4313313  0.8031660  0.04598861
## [2,] -0.4558570 -0.0929378 0.7613544  1.1739431 -0.5310347  0.45647626
## [3,] -0.9278759  0.5931129 1.7889414  1.0087794  0.3678748 -0.96723643
##             [,7]
## [1,]  0.38257922
## [2,]  0.02234608
## [3,] -0.75743886

apply(rand.mat, MARGIN = 1, FUN = sum)

## [1] 2.061453 1.334290 1.106157

apply(rand.mat, MARGIN = 2, FUN = var)

## [1] 0.0624526 0.7287026 0.6445955 0.7796840 0.4629347 0.5370138 0.3395789

sapply() is used on list-objects and it returns a vector or a matrix, depending on the output of the function.

my.list <- list(A = c(4, 2, 1:3), B = "Hello.", C = TRUE)
sapply(my.list, class)

##           A           B           C 
##   "numeric" "character"   "logical"

my.list <- list(A = c(4, 2, 1:3), B = "Hello.", C = TRUE)
sapply(my.list, range)

##      A   B        C  
## [1,] "1" "Hello." "1"
## [2,] "4" "Hello." "1"

Why is each element a character string?

Any data.frame is also a list, where each column is one list-element.

class(cats)

## [1] "data.frame"

is.list(cats)

## [1] TRUE

print.default(cats[1:10, ])

## $Sex
##  [1] F F F F F F F F F F
## Levels: F M
## 
## $Bwt
##  [1] 2.0 2.0 2.0 2.1 2.1 2.1 2.1 2.1 2.1 2.1
## 
## $Hwt
##  [1] 7.0 7.4 9.5 7.2 7.3 7.6 8.1 8.2 8.3 8.5
## 
## attr(,"class")
## [1] "data.frame"

This means we can use sapply on data frames as well, which is often useful.

sapply(cats, class)

##       Sex       Bwt       Hwt 
##  "factor" "numeric" "numeric"

lapply() is exactly the same as sapply(), but it returns a list of the same length as input list object, each element of which is the result of applying FUN to the corresponding element of list.

lapply(cats, class)

## $Sex
## [1] "factor"
## 
## $Bwt
## [1] "numeric"
## 
## $Hwt
## [1] "numeric"

Functions are reusable pieces of code that take an input, do some computation on the input, and return output.

We have been using a lot of functions: code of the form something() is usually a function.

mean(1:6)

## [1] 3.5

We can make our own functions as follows:

squared <- function (x){
  x.square <- x * x
  return(x.square)
}

squared(4)

## [1] 16

x, the input, is called the (formal) argument of the function. x.square is called the return value.

If there is no return(), the last line is automatically returned, so we can also just write:

squared <- function(x){
  x * x
}

squared(-2)

## [1] 4

We can also combine this with apply()

rand.mat

##            [,1]       [,2]      [,3]       [,4]       [,5]        [,6]
## [1,] -0.5495413  1.6040110 0.2065810 -0.4313313  0.8031660  0.04598861
## [2,] -0.4558570 -0.0929378 0.7613544  1.1739431 -0.5310347  0.45647626
## [3,] -0.9278759  0.5931129 1.7889414  1.0087794  0.3678748 -0.96723643
##             [,7]
## [1,]  0.38257922
## [2,]  0.02234608
## [3,] -0.75743886

apply(rand.mat, 2, squared)

##           [,1]        [,2]      [,3]      [,4]      [,5]        [,6]
## [1,] 0.3019956 2.572851154 0.0426757 0.1860467 0.6450756 0.002114953
## [2,] 0.2078056 0.008637434 0.5796606 1.3781424 0.2819978 0.208370575
## [3,] 0.8609536 0.351782879 3.2003112 1.0176358 0.1353319 0.935546313
##              [,7]
## [1,] 0.1463668596
## [2,] 0.0004993472
## [3,] 0.5737136215

areDivisible <- function(x, y){
  if (x > y){
    larger  <- x
    smaller <- y
  } else {
    larger  <- y
    smaller <- x
  }
  remainder <- larger %% smaller 
  remainder == 0
}

areDivisible(3, 10)

## [1] FALSE

areDivisible(3, 9)

## [1] TRUE

areDivisible(9, 3)

## [1] TRUE

• Default options for some arguments are provided in many functions.

• They allow us to provide an additional option, but if no choice is provided, we can choose for the user of the function.

areDivisible <- function(x, y, printInput = TRUE){
  if (printInput){
    cat("Testing if", x, "and", y, "are divisible: \n")
  }
  ((x %% y) == 0) | ((y %% x) == 0)
}

areDivisible(3, 10)

## Testing if 3 and 10 are divisible:

## [1] FALSE

areDivisible(3, 9, printInput = TRUE)

## Testing if 3 and 9 are divisible:

## [1] TRUE

areDivisible(9, 3, printInput = FALSE)

## [1] TRUE

• Your first self-written for-loop, or function, will probably not work.

• Don’t panic! Just go line-by-line, keeping track of what is currently inside each variable.

rand.vec <- rnorm(10)

# Add ten to each element.
for (i in 1:rand.vec){
  i <- i + 10
}

## Warning in 1:rand.vec: numerical expression has 10 elements: only the first used

rand.vec

##  [1] -0.86272069 -0.11600941  2.01116949  0.09772563 -0.69188855 -1.02612582
##  [7]  0.60817253 -1.09196830  2.19492100  1.37205518

# Add ten to each element.
for (i in 1:rand.vec){
    i <- i + 10
}

1:rand.vec

## Warning in 1:rand.vec: numerical expression has 10 elements: only the first used

## [1] 1 0

1:length(rand.vec)

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

Let’s try again:

# Add ten to each element.
for (i in 1:length(rand.vec)){
  i <- i + 10
}

rand.vec

##  [1] -0.86272069 -0.11600941  2.01116949  0.09772563 -0.69188855 -1.02612582
##  [7]  0.60817253 -1.09196830  2.19492100  1.37205518

Still, no luck.

# Add ten to each element.
for (i in 1:length(rand.vec)){
  i <- i + 10
}

i <- 1
i

## [1] 1

# Add ten to each element.
for (i in 1:length(rand.vec)){
  i <- i + 10
}

i <- i + 10
i

## [1] 11

i <- 2
i

## [1] 2

# Add ten to each element.
for (i in 1:length(rand.vec)){
  rand.vec[i] <- rand.vec[i] + 10
}

rand.vec

##  [1]  9.137279  9.883991 12.011169 10.097726  9.308111  8.973874 10.608173
##  [8]  8.908032 12.194921 11.372055

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