For loops vs. functionals

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1. Read the documentation for apply(). In the 2nd case, what two for-loops does it generalize.

For an object with two-dimensions, such as a matrix or data frame, apply() replaces looping over the rows or columns of a matrix or data-frame. The apply() function is used like apply(X, MARGIN, FUN, ...), where X is a matrix or array, FUN is a function to apply, and … are additional arguments passed to FUN.

When MARGIN = 1, then the function is applied to each row. For example, the following example calculates the row means of a matrix.

X <- matrix(rnorm(15), nrow = 5)
X

            [,1]       [,2]        [,3]
[1,]  1.27367038  0.3025072 -0.55797988
[2,] -0.15047721  0.6893436  1.91526339
[3,]  0.91338311  0.2370009  0.18501749
[4,] -0.09615776 -0.7576654  0.01170414
[5,]  0.64507221  0.9404452 -0.03963321

apply(X, 1, mean)

[1]  0.3393992  0.8180432  0.4451338 -0.2807063  0.5152947

That is equivalent to this for-loop.

X_row_means <- vector("numeric", length = nrow(X))
for (i in seq_len(nrow(X))) {
  X_row_means[[i]] <- mean(X[i, ])
}
X_row_means

[1]  0.3393992  0.8180432  0.4451338 -0.2807063  0.5152947

X <- matrix(rnorm(15), nrow = 5)
X

           [,1]       [,2]       [,3]
[1,] -0.1387458  1.5879591 -1.1505933
[2,] -0.9116576  0.7854943 -1.3605260
[3,] -1.1144945 -0.3911062 -1.0232832
[4,] -1.0380229  1.2678207  1.3070090
[5,] -0.2940543  0.1393491 -0.4864869

When MARGIN = 2, apply() is equivalent to a for-loop looping over columns.

apply(X, 2, mean)

[1] -0.6993950  0.6779034 -0.5427761

X_col_means <- vector("numeric", length = ncol(X))
for (i in seq_len(ncol(X))) {
  X_col_means[[i]] <- mean(X[, i])
}
X_col_means

[1] -0.6993950  0.6779034 -0.5427761

2. Adapt col_summary() so that it only applies to numeric columns. You might want to start with an is_numeric() function that returns a logical vector that has a TRUE corresponding to each numeric column.

The original col_summary() function is

col_summary <- function(df, fun) {
  out <- vector("double", length(df))
  for (i in seq_along(df)) {
    out[i] <- fun(df[[i]])
  }
  out
}

The adapted version adds extra logic to only apply the function to numeric columns.

col_summary2 <- function(df, fun) {
  # create an empty vector which will store whether each
  # column is numeric
  numeric_cols <- vector("logical", length(df))
  # test whether each column is numeric
  for (i in seq_along(df)) {
    numeric_cols[[i]] <- is.numeric(df[[i]])
  }
  # find the indexes of the numeric columns
  idxs <- which(numeric_cols)
  # find the number of numeric columns
  n <- sum(numeric_cols)
  # create a vector to hold the results
  out <- vector("double", n)
  # apply the function only to numeric vectors
  for (i in seq_along(idxs)) {
    out[[i]] <- fun(df[[idxs[[i]]]])
  }
  # name the vector
  names(out) <- names(df)[idxs]
  out
}

Let’s test that col_summary2() works by creating a small data frame with some numeric and non-numeric columns.

df <- tibble(
  X1 = c(1, 2, 3),
  X2 = c("A", "B", "C"),
  X3 = c(0, -1, 5),
  X4 = c(TRUE, FALSE, TRUE)
)
col_summary2(df, mean)

      X1       X3 
2.000000 1.333333 

As expected, it only calculates the mean of the numeric columns, X1 and X3. Let’s test that it works with another function.

col_summary2(df, median)

X1 X3 
 2  0