Iteration

Day 17

Prof Emily Kurtz

Carleton College
Stat 220 - Spring 2026

Recap from last class: Standardizing a vector

Here’s a short function that standardizes an input vector

standardize <- function(x, na.rm = TRUE) {
  (x - mean(x, na.rm = na.rm)) / sd(x, na.rm = na.rm)
}

Now we can easily standardize all of our variables, right?

Cancer data

Set of digitized breast cancer image features
Row = an image of a tumor sample
Variables include the diagnosis (benign or malignant) and measurements

Rows: 569
Columns: 12
$ ID                <dbl> 842302, 842517, 84300903, 84348301, 84358402, 843786…
$ Class             <chr> "M", "M", "M", "M", "M", "M", "M", "M", "M", "M", "M…
$ Radius            <dbl> 17.990, 20.570, 19.690, 11.420, 20.290, 12.450, 18.2…
$ Texture           <dbl> 10.38, 17.77, 21.25, 20.38, 14.34, 15.70, 19.98, 20.…
$ Perimeter         <dbl> 122.80, 132.90, 130.00, 77.58, 135.10, 82.57, 119.60…
$ Area              <dbl> 1001.0, 1326.0, 1203.0, 386.1, 1297.0, 477.1, 1040.0…
$ Smoothness        <dbl> 0.11840, 0.08474, 0.10960, 0.14250, 0.10030, 0.12780…
$ Compactness       <dbl> 0.27760, 0.07864, 0.15990, 0.28390, 0.13280, 0.17000…
$ Concavity         <dbl> 0.30010, 0.08690, 0.19740, 0.24140, 0.19800, 0.15780…
$ Concave_Points    <dbl> 0.14710, 0.07017, 0.12790, 0.10520, 0.10430, 0.08089…
$ Symmetry          <dbl> 0.2419, 0.1812, 0.2069, 0.2597, 0.1809, 0.2087, 0.17…
$ Fractal_Dimension <dbl> 0.07871, 0.05667, 0.05999, 0.09744, 0.05883, 0.07613…

Standardizing cancer data

scaled_cancer <- unscaled_cancer %>%
  mutate(
    Radius = standardize(Radius),
    Texture = standardize(Texture),
    Perimeter = standardize(Perimeter),
    Area = standardize(Area),
    Smoothness = standardize(Smoothness),
    Compactness = standardize(Compactness),
    Concavity = standardize(Concavity),
    Concave_points = standardize(Concave_Points),
    Symmetry = standardize(Symmetry),
    Fractal_dimension = standardize(Fractal_Dimension)
  )

Sure, we have replaced the calculations with a function that will behave identically for all columns, but we are still repeating ourselves 10 times

Iteration

Programmatically repeat the code
We have two options for doing this:
- using a for loop, or similar (imperative programming)
- mapping with functional programming

for loops

for loops are the simplest and most common type of loop in R
Given a vector iterate through the elements and evaluate the code block for each

Goal: Standardize all of the numeric columns via for loops.

for loops

(1) Set up a object to store results

scaled_cancer <- unscaled_cancer %>%
  mutate(
    Radius = NA,
    Texture = NA,
    Perimeter = NA,
    Area = NA,
    Smoothness = NA,
    Compactness = NA,
    Concavity = NA,
    Concave_Points = NA,
    Symmetry = NA,
    Fractal_dimension = NA
  )

scaled_cancer

# A tibble: 569 × 13
        ID Class Radius Texture Perimeter Area  Smoothness Compactness Concavity
     <dbl> <chr> <lgl>  <lgl>   <lgl>     <lgl> <lgl>      <lgl>       <lgl>    
 1  8.42e5 M     NA     NA      NA        NA    NA         NA          NA       
 2  8.43e5 M     NA     NA      NA        NA    NA         NA          NA       
 3  8.43e7 M     NA     NA      NA        NA    NA         NA          NA       
 4  8.43e7 M     NA     NA      NA        NA    NA         NA          NA       
 5  8.44e7 M     NA     NA      NA        NA    NA         NA          NA       
 6  8.44e5 M     NA     NA      NA        NA    NA         NA          NA       
 7  8.44e5 M     NA     NA      NA        NA    NA         NA          NA       
 8  8.45e7 M     NA     NA      NA        NA    NA         NA          NA       
 9  8.45e5 M     NA     NA      NA        NA    NA         NA          NA       
10  8.45e7 M     NA     NA      NA        NA    NA         NA          NA       
# ℹ 559 more rows
# ℹ 4 more variables: Concave_Points <lgl>, Symmetry <lgl>,
#   Fractal_Dimension <dbl>, Fractal_dimension <lgl>

for loops

(2) Determine an index over which to iterate

Columns 3 to 12 are numeric, our index is 3:12

# A tibble: 569 × 13
        ID Class Radius Texture Perimeter Area  Smoothness Compactness Concavity
     <dbl> <chr> <lgl>  <lgl>   <lgl>     <lgl> <lgl>      <lgl>       <lgl>    
 1  8.42e5 M     NA     NA      NA        NA    NA         NA          NA       
 2  8.43e5 M     NA     NA      NA        NA    NA         NA          NA       
 3  8.43e7 M     NA     NA      NA        NA    NA         NA          NA       
 4  8.43e7 M     NA     NA      NA        NA    NA         NA          NA       
 5  8.44e7 M     NA     NA      NA        NA    NA         NA          NA       
 6  8.44e5 M     NA     NA      NA        NA    NA         NA          NA       
 7  8.44e5 M     NA     NA      NA        NA    NA         NA          NA       
 8  8.45e7 M     NA     NA      NA        NA    NA         NA          NA       
 9  8.45e5 M     NA     NA      NA        NA    NA         NA          NA       
10  8.45e7 M     NA     NA      NA        NA    NA         NA          NA       
# ℹ 559 more rows
# ℹ 4 more variables: Concave_Points <lgl>, Symmetry <lgl>,
#   Fractal_Dimension <dbl>, Fractal_dimension <lgl>

for loops

(3) Iterate through the index, standardize and save results
`i <- 3`

for (i in 3:12){
  scaled_cancer[, i] <- standardize(unscaled_cancer[[i]])
}

# A tibble: 569 × 13
        ID Class Radius Texture Perimeter Area  Smoothness Compactness Concavity
     <dbl> <chr>  <dbl> <lgl>   <lgl>     <lgl> <lgl>      <lgl>       <lgl>    
1   842302 M      1.10  NA      NA        NA    NA         NA          NA       
2   842517 M      1.83  NA      NA        NA    NA         NA          NA       
3 84300903 M      1.58  NA      NA        NA    NA         NA          NA       
4 84348301 M     -0.768 NA      NA        NA    NA         NA          NA       
5 84358402 M      1.75  NA      NA        NA    NA         NA          NA       
# ℹ 564 more rows
# ℹ 4 more variables: Concave_Points <lgl>, Symmetry <lgl>,
#   Fractal_Dimension <dbl>, Fractal_dimension <lgl>

for loops

(3) Iterate through the index, standardize and save results
`i <- 4`

for (i in 3:12){
  scaled_cancer[, i] <- standardize(unscaled_cancer[[i]])
}

# A tibble: 569 × 13
        ID Class Radius Texture Perimeter Area  Smoothness Compactness Concavity
     <dbl> <chr>  <dbl>   <dbl> <lgl>     <lgl> <lgl>      <lgl>       <lgl>    
1   842302 M      1.10   -2.07  NA        NA    NA         NA          NA       
2   842517 M      1.83   -0.353 NA        NA    NA         NA          NA       
3 84300903 M      1.58    0.456 NA        NA    NA         NA          NA       
4 84348301 M     -0.768   0.254 NA        NA    NA         NA          NA       
5 84358402 M      1.75   -1.15  NA        NA    NA         NA          NA       
# ℹ 564 more rows
# ℹ 4 more variables: Concave_Points <lgl>, Symmetry <lgl>,
#   Fractal_Dimension <dbl>, Fractal_dimension <lgl>

for loops

(3) Iterate through the index, standardize and save results
`i <- 5`

for (i in 3:12){
  scaled_cancer[, i] <- standardize(unscaled_cancer[[i]])
}

# A tibble: 569 × 13
        ID Class Radius Texture Perimeter Area  Smoothness Compactness Concavity
     <dbl> <chr>  <dbl>   <dbl>     <dbl> <lgl> <lgl>      <lgl>       <lgl>    
1   842302 M      1.10   -2.07      1.27  NA    NA         NA          NA       
2   842517 M      1.83   -0.353     1.68  NA    NA         NA          NA       
3 84300903 M      1.58    0.456     1.57  NA    NA         NA          NA       
4 84348301 M     -0.768   0.254    -0.592 NA    NA         NA          NA       
5 84358402 M      1.75   -1.15      1.78  NA    NA         NA          NA       
# ℹ 564 more rows
# ℹ 4 more variables: Concave_Points <lgl>, Symmetry <lgl>,
#   Fractal_Dimension <dbl>, Fractal_dimension <lgl>

for loops

(3) Iterate through the index, standardize and save results
`i <- 6`

for (i in 3:12){
  scaled_cancer[, i] <- standardize(unscaled_cancer[[i]])
}

# A tibble: 569 × 13
       ID Class Radius Texture Perimeter   Area Smoothness Compactness Concavity
    <dbl> <chr>  <dbl>   <dbl>     <dbl>  <dbl> <lgl>      <lgl>       <lgl>    
1  8.42e5 M      1.10   -2.07      1.27   0.984 NA         NA          NA       
2  8.43e5 M      1.83   -0.353     1.68   1.91  NA         NA          NA       
3  8.43e7 M      1.58    0.456     1.57   1.56  NA         NA          NA       
4  8.43e7 M     -0.768   0.254    -0.592 -0.764 NA         NA          NA       
5  8.44e7 M      1.75   -1.15      1.78   1.82  NA         NA          NA       
# ℹ 564 more rows
# ℹ 4 more variables: Concave_Points <lgl>, Symmetry <lgl>,
#   Fractal_Dimension <dbl>, Fractal_dimension <lgl>

Putting it all together:

# Preallocate storage
scaled_cancer <- unscaled_cancer %>%
  mutate(
    Radius = NA,
    Texture = NA,
    Perimeter = NA,
    Area = NA,
    Smoothness = NA,
    Compactness = NA,
    Concavity = NA,
    Concave_Points = NA,
    Symmetry = NA,
    Fractal_dimension = NA
  )

# Iterate over numeric columns and save
for (i in 3:12){
  scaled_cancer[, i] <- standardize(unscaled_cancer[[i]])
}

scaled_cancer

# A tibble: 569 × 13
       ID Class Radius Texture Perimeter   Area Smoothness Compactness Concavity
    <dbl> <chr>  <dbl>   <dbl>     <dbl>  <dbl>      <dbl>       <dbl>     <dbl>
 1 8.42e5 M      1.10   -2.07     1.27    0.984      1.57       3.28      2.65  
 2 8.43e5 M      1.83   -0.353    1.68    1.91      -0.826     -0.487    -0.0238
 3 8.43e7 M      1.58    0.456    1.57    1.56       0.941      1.05      1.36  
 4 8.43e7 M     -0.768   0.254   -0.592  -0.764      3.28       3.40      1.91  
 5 8.44e7 M      1.75   -1.15     1.78    1.82       0.280      0.539     1.37  
 6 8.44e5 M     -0.476  -0.835   -0.387  -0.505      2.24       1.24      0.866 
 7 8.44e5 M      1.17    0.161    1.14    1.09      -0.123      0.0882    0.300 
 8 8.45e7 M     -0.118   0.358   -0.0728 -0.219      1.60       1.14      0.0610
 9 8.45e5 M     -0.320   0.588   -0.184  -0.384      2.20       1.68      1.22  
10 8.45e7 M     -0.473   1.10    -0.329  -0.509      1.58       2.56      1.74  
# ℹ 559 more rows
# ℹ 4 more variables: Concave_Points <dbl>, Symmetry <dbl>,
#   Fractal_Dimension <dbl>, Fractal_dimension <lgl>

Your turn

Load the palmerpenguins package.

Write a for loop that calculates the mean of the numeric variables in the penguins data set and stores the means in a named vector. Don’t forget to create an object to store your results before you run the loop!

Rows: 344
Columns: 8
$ species           <fct> Adelie, Adelie, Adelie, Adelie, Adelie, Adelie, Adel…
$ island            <fct> Torgersen, Torgersen, Torgersen, Torgersen, Torgerse…
$ bill_length_mm    <dbl> 39.1, 39.5, 40.3, NA, 36.7, 39.3, 38.9, 39.2, 34.1, …
$ bill_depth_mm     <dbl> 18.7, 17.4, 18.0, NA, 19.3, 20.6, 17.8, 19.6, 18.1, …
$ flipper_length_mm <int> 181, 186, 195, NA, 193, 190, 181, 195, 193, 190, 186…
$ body_mass_g       <int> 3750, 3800, 3250, NA, 3450, 3650, 3625, 4675, 3475, …
$ sex               <fct> male, female, female, NA, female, male, female, male…
$ year              <int> 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007, 2007…

Preallocate storage to increase speed

add_to_vector <- function(n) {
  output <- NULL 
  for (i in 1:n) {
    output <- c(output, i)
  }
  output
}

add_to_vector(10000)

0.15 sec elapsed

add_to_vector2 <- function(n) {
  output <- vector("integer", n)  
  for (i in 1:n) {
   output[i] <- i
  }
  output
}

add_to_vector2(10000)

0.07 sec elapsed

The difference is noticable for larger n

add_to_vector <- function(n) {
  output <- NULL 
  for (i in 1:n) {
    output <- c(output, i)
  }
  output
}

add_to_vector(100000)

6.38 sec elapsed

add_to_vector2 <- function(n) {
  output <- vector("integer", n)  
  for (i in 1:n) {
   output[i] <- i
  }
  output
}

add_to_vector2(100000)

0.438 sec elapsed

Preallocating output

Here are a few useful ways to preallocate storage for a vector of length n:

output <- double(n)    # numeric vector
output <- integer(n)   # integer vector
output <- character(n) # character vector
output <- rep(NA, n)   # vector of NAs

You can make tibbles of NAs by combining vectors via tibble()

output_tbl <- tibble(
  a = double(n),
  b = integer(n),
  c = character(n),
  d = rep(NA, n)
)

Create index vector

Useful ways to create index vector to iterate over:

1:n - manual creation if you already have n stored
seq_along(df) - construct an index “along” the columns of your data frame/tibble

e.g. seq_along(unscaled_cancer)
⚠️ Use this instead of 1:nrow(df)or 1:length(x)
x - pass in a vector, there’s no reason it needs to be an “index”

e.g. colnames(unscaled_cancer)

Your turn:

Revisit the {palmerpenguins} penguins data.

Write a for loop that calculates the summary() of a numeric variable and the table() of a factor variable.

Store the results in a list (it will have length 8).

`across()`

R has lots of alternatives to `for` loops

The basic data type in R is a vector
In R, an “integer” is the same as a vector of integers of length 1
In more general-purpose programming languages, single items are stored differently than arrays of those items
This means that R is highly optimized for vectorized operations

`across()`

.cols: columns to apply function to
.fns function to apply

across(.cols, 
       .fns)

unscaled_cancer |>
  summarize(across(Radius:Fractal_Dimension, mean))

# A tibble: 1 × 10
  Radius Texture Perimeter  Area Smoothness Compactness Concavity Concave_Points
   <dbl>   <dbl>     <dbl> <dbl>      <dbl>       <dbl>     <dbl>          <dbl>
1   14.1    19.3      92.0  655.     0.0964       0.104    0.0888         0.0489
# ℹ 2 more variables: Symmetry <dbl>, Fractal_Dimension <dbl>

unscaled_cancer |>
  summarize(across(Radius:Fractal_Dimension, list(mean = mean, 
                                                  sd = sd)))

# A tibble: 1 × 20
  Radius_mean Radius_sd Texture_mean Texture_sd Perimeter_mean Perimeter_sd
        <dbl>     <dbl>        <dbl>      <dbl>          <dbl>        <dbl>
1        14.1      3.52         19.3       4.30           92.0         24.3
# ℹ 14 more variables: Area_mean <dbl>, Area_sd <dbl>, Smoothness_mean <dbl>,
#   Smoothness_sd <dbl>, Compactness_mean <dbl>, Compactness_sd <dbl>,
#   Concavity_mean <dbl>, Concavity_sd <dbl>, Concave_Points_mean <dbl>,
#   Concave_Points_sd <dbl>, Symmetry_mean <dbl>, Symmetry_sd <dbl>,
#   Fractal_Dimension_mean <dbl>, Fractal_Dimension_sd <dbl>

unscaled_cancer |>
  mutate(across(Radius:Fractal_Dimension, standardize))

# A tibble: 569 × 12
       ID Class Radius Texture Perimeter   Area Smoothness Compactness Concavity
    <dbl> <chr>  <dbl>   <dbl>     <dbl>  <dbl>      <dbl>       <dbl>     <dbl>
 1 8.42e5 M      1.10   -2.07     1.27    0.984      1.57       3.28      2.65  
 2 8.43e5 M      1.83   -0.353    1.68    1.91      -0.826     -0.487    -0.0238
 3 8.43e7 M      1.58    0.456    1.57    1.56       0.941      1.05      1.36  
 4 8.43e7 M     -0.768   0.254   -0.592  -0.764      3.28       3.40      1.91  
 5 8.44e7 M      1.75   -1.15     1.78    1.82       0.280      0.539     1.37  
 6 8.44e5 M     -0.476  -0.835   -0.387  -0.505      2.24       1.24      0.866 
 7 8.44e5 M      1.17    0.161    1.14    1.09      -0.123      0.0882    0.300 
 8 8.45e7 M     -0.118   0.358   -0.0728 -0.219      1.60       1.14      0.0610
 9 8.45e5 M     -0.320   0.588   -0.184  -0.384      2.20       1.68      1.22  
10 8.45e7 M     -0.473   1.10    -0.329  -0.509      1.58       2.56      1.74  
# ℹ 559 more rows
# ℹ 3 more variables: Concave_Points <dbl>, Symmetry <dbl>,
#   Fractal_Dimension <dbl>

Helper functions for `across()`

where(is.numeric) selects all numeric columns.
where(is.character) selects all string columns.
where(is.Date) selects all date columns.
where(is.logical) selects all logical columns.

`across()` on unscaled cancer data

unscaled_cancer %>%
  mutate(across(where(is.numeric), standardize))

# A tibble: 569 × 12
       ID Class Radius Texture Perimeter   Area Smoothness Compactness Concavity
    <dbl> <chr>  <dbl>   <dbl>     <dbl>  <dbl>      <dbl>       <dbl>     <dbl>
 1 -0.236 M      1.10   -2.07     1.27    0.984      1.57       3.28      2.65  
 2 -0.236 M      1.83   -0.353    1.68    1.91      -0.826     -0.487    -0.0238
 3  0.431 M      1.58    0.456    1.57    1.56       0.941      1.05      1.36  
 4  0.432 M     -0.768   0.254   -0.592  -0.764      3.28       3.40      1.91  
 5  0.432 M      1.75   -1.15     1.78    1.82       0.280      0.539     1.37  
 6 -0.236 M     -0.476  -0.835   -0.387  -0.505      2.24       1.24      0.866 
 7 -0.236 M      1.17    0.161    1.14    1.09      -0.123      0.0882    0.300 
 8  0.433 M     -0.118   0.358   -0.0728 -0.219      1.60       1.14      0.0610
 9 -0.236 M     -0.320   0.588   -0.184  -0.384      2.20       1.68      1.22  
10  0.433 M     -0.473   1.10    -0.329  -0.509      1.58       2.56      1.74  
# ℹ 559 more rows
# ℹ 3 more variables: Concave_Points <dbl>, Symmetry <dbl>,
#   Fractal_Dimension <dbl>

`across()` with a new function

Let’s say we want the range of each quantitative variable (max(x) - min(x)). We could name a new function, or we could do it directly in across()

unscaled_cancer %>%
  summarize(across(where(is.numeric), function(x) max(x) - min(x)))

# A tibble: 1 × 11
         ID Radius Texture Perimeter  Area Smoothness Compactness Concavity
      <dbl>  <dbl>   <dbl>     <dbl> <dbl>      <dbl>       <dbl>     <dbl>
1 911311832   21.1    29.6      145. 2358.      0.111       0.326     0.427
# ℹ 3 more variables: Concave_Points <dbl>, Symmetry <dbl>,
#   Fractal_Dimension <dbl>

Or we can use shorthand - \(x)

unscaled_cancer %>%
  summarize(across(where(is.numeric), \(x) max(x) - min(x)))

# A tibble: 1 × 11
         ID Radius Texture Perimeter  Area Smoothness Compactness Concavity
      <dbl>  <dbl>   <dbl>     <dbl> <dbl>      <dbl>       <dbl>     <dbl>
1 911311832   21.1    29.6      145. 2358.      0.111       0.326     0.427
# ℹ 3 more variables: Concave_Points <dbl>, Symmetry <dbl>,
#   Fractal_Dimension <dbl>

Your turn

Use summarize and across to find the range of any quantitative variables, and the number of levels of any factor variables in the penguins dataset.

countdown(4)

The good news: we can use across to do lots of for-loop-type tasks in our {dplyr} pipelines.

The bad news: across() only works with {dplyr} functions like mutate or summarize

The good news: there’s a more general-purpose solution in the {tidyverse} (which we’ll see next time!)

Iteration

Recap from last class: Standardizing a vector

Cancer data

Standardizing cancer data

Iteration

for loops

for loops

(1) Set up a object to store results

for loops

(2) Determine an index over which to iterate

for loops

(3) Iterate through the index, standardize and save results i <- 3

for loops

(3) Iterate through the index, standardize and save results i <- 4

for loops

(3) Iterate through the index, standardize and save results i <- 5

for loops

(3) Iterate through the index, standardize and save results i <- 6

Putting it all together:

Your turn

Preallocate storage to increase speed

The difference is noticable for larger n

Preallocating output

Create index vector

Your turn:

across()

R has lots of alternatives to for loops

across()

across() on unscaled cancer data

Helper functions for across()

across() on unscaled cancer data

across() with a new function

Your turn

(3) Iterate through the index, standardize and save results
`i <- 3`

(3) Iterate through the index, standardize and save results
`i <- 4`

(3) Iterate through the index, standardize and save results
`i <- 5`

(3) Iterate through the index, standardize and save results
`i <- 6`

`across()`

R has lots of alternatives to `for` loops

`across()`

`across()` on unscaled cancer data

Helper functions for `across()`

`across()` on unscaled cancer data

`across()` with a new function