apply(), lapply(), sapply(), and tapply() in R

In R, the functions apply(), lapply(), sapply(), and tapply() are all used for applying functions over data structures, but they differ in terms of their input types and outputs. Here’s a breakdown of each function:

1. apply()

• Purpose: Apply a function to the margins (rows or columns) of a matrix or an array.
• Usage: apply(X, MARGIN, FUN, ...)
  • X: The matrix or array you want to apply the function to.
  • MARGIN: The margin over which the function is applied:
    • 1 for rows.
    • 2 for columns.
  • FUN: The function to apply.
  • ...: Additional arguments for the function.
• Example:

  mat <- matrix(1:9, nrow = 3)
  apply(mat, 1, sum)  # Sum of each row
  apply(mat, 2, mean) # Mean of each column
  

2. lapply()

• Purpose: Apply a function to each element of a list (or vector) and return a list.
• Usage: lapply(X, FUN, ...)
  • X: A list or vector.
  • FUN: The function to apply.
  • ...: Additional arguments for the function.
• Example:

  my_list <- list(a = 1:3, b = 4:6)
  lapply(my_list, sum)  # Apply sum function to each element
  

• Note: lapply() always returns a list, even if the result is a simple object (e.g., a numeric value).

3. sapply()

• Purpose: Similar to lapply(), but attempts to simplify the result into a vector, matrix, or array.
• Usage: sapply(X, FUN, ...)
  • X: A list or vector.
  • FUN: The function to apply.
  • ...: Additional arguments for the function.
• Example:

  my_list <- list(a = 1:3, b = 4:6)
  sapply(my_list, sum)  # Apply sum and simplify result to a vector
  

• Note: sapply() tries to simplify the output to the most compact structure (e.g., a vector, matrix), depending on the results of applying the function.

4. tapply()

• Purpose: Apply a function to subsets of a vector, where the subsets are defined by a factor or grouping variable.
• Usage: tapply(X, INDEX, FUN, ...)
  • X: The vector to which the function is applied.
  • INDEX: A factor (or a list of factors) that defines the groups or subsets.
  • FUN: The function to apply to each subset.
  • ...: Additional arguments for the function.
• Example:

  data <- c(1, 2, 3, 4, 5, 6)
  group <- factor(c("A", "A", "B", "B", "C", "C"))
  tapply(data, group, sum)  # Apply sum function by groups A, B, and C
  

Summary of Differences:

• apply(): Applies a function to rows or columns of a matrix or array.
• lapply(): Applies a function to each element of a list and returns a list.
• sapply(): Applies a function to each element of a list and attempts to simplify the result to a vector or matrix.
• tapply(): Applies a function to subsets of a vector, defined by a factor or grouping variable.

Each of these functions is useful in different contexts depending on the data structure you’re working with and the type of result you expect.