Evaluating boolean expression over the columns of a matrix against the elements of a vector in R

I have a matrix of data, where I want to check whether or not the absolute value of each column falls within a certain range. Moreover, I would like to calculate the proportion of times it occurs across all columns. I know how to do this manually but I would like to write this generally outside of a loop so that any time the user gives me a matrix X and y of any size that it works. The only additional piece of information is that the number of columns of X will always be the same length of y. I also would like to do this in base R if possible. Here is my R code:

set.seed(42)

# Made up data
x <- matrix(rnorm(27), nrow = 9)

y <- c(.2, .5, 2)



> sum(abs(x[,1]) <= y[1] & abs(x[,2]) <= y[2] & abs(x[,3]) <= y[3]) / nrow(x)
[1] 0.2222222

So ideally I would want something like

sum(abs(x) <= y) / nrow(x)

>Solution :

sum(rowSums(t(t(abs(x)) <= y)) == ncol(x)) / nrow(x)
# [1] 0.2222222

Walk-through:

• Unfortunately, x > y recycles y across x, but column-wise, so it is effectively doing c(x[1,1] > y[1], x[2,1] > y[2], x[3,1] > y[3], x[4,1] > y[1], ...), which is not what we want. We can transpose x so that the get the correct recycling of y … and then transpose it again to get it back in the same shape as x (not strictly required).

  t(t(abs(x)) <= y)
  #        [,1]  [,2]  [,3]
  #  [1,] FALSE  TRUE FALSE
  #  [2,] FALSE FALSE  TRUE
  #  [3,] FALSE FALSE  TRUE
  #  [4,] FALSE FALSE  TRUE
  #  [5,] FALSE  TRUE  TRUE
  #  [6,]  TRUE  TRUE  TRUE
  #  [7,] FALSE FALSE  TRUE
  #  [8,]  TRUE  TRUE  TRUE
  #  [9,] FALSE FALSE  TRUE
  

• Now we want to know how many rows have as many TRUEs as x has columns, done with rowSums(.) == ncol(x). And the sum of all of these with sum(.).