mapply gives us a way to call a non-vectorized function in a vectorized way.

From the R Documentation:

mapply is a multivariate version of sapply. mapply applies FUN to
the first elements of each ... argument, the second elements,
the third elements, and so on. Arguments are recycled if necessary.

mapply(FUN, ..., MoreArgs = NULL, SIMPLIFY = TRUE,
USE.NAMES = TRUE)

Example

list(rep(1, 4), rep(2, 3), rep(3, 2), rep(4, 1))
## []
##  1 1 1 1
##
## []
##  2 2 2
##
## []
##  3 3
##
## []
##  4

We see that we are repeatedly calling the same function (rep) where the first argument varies from 1 to 4, and the second argument varies from 4 to 1. Instead, we can use mapply:

mapply(rep, 1:4, 4:1)
## []
##  1 1 1 1
##
## []
##  2 2 2
##
## []
##  3 3
##
## []
##  4

Example

noise <- function(n, mean, std) {
rnorm(n, mean, std)
}
noise(5, 1, 2)
##  0.84136 0.04806 1.89196 2.76464 4.95360

The noise function is not vectorized. mapply gives us a way to make a vectorized call to noise:

mapply(noise, 1:5, 1:5, 2)
## []
##  1.625
##
## []
##   2.928 -1.840
##
## []
##  2.459 4.195 1.939
##
## []
##  5.195 3.731 5.249 2.959
##
## []
##  8.291 1.949 5.751 4.250 4.868
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