Piecewise linear transformation without for loop or nested ifelse - r

Question

I'm trying to perform a piecewise linear transformation of my data. Here's an example table describing a transformation:
dat <- data.frame(x.low = 0:2, x.high = 1:3, y.low=c(0, 2, 3), y.high=c(2, 3, 10))
dat
# x.low x.high y.low y.high
# 1 0 1 0 2
# 2 1 2 2 3
# 3 2 3 3 10
If I defined x <- c(1.75, 2.5), I would expect transformed values 2.75 and 6.5 (my elements would be matched by rows 2 and 3 of dat, respectively).
I know how to solve this problem with a for loop, iterating through the rows of dat and transforming the corresponding values:
pw.lin.trans <- function(x, m) {
out <- rep(NA, length(x))
for (i in seq(nrow(m))) {
matching <- x >= m$x.low[i] & x <= m$x.high[i]
out[matching] <- m$y.low[i] + (x[matching] - m$x.low[i]) /
(m$x.high[i] - m$x.low[i]) * (m$y.high[i] - m$y.low[i])
}
out
}
pw.lin.trans(x, dat)
# [1] 2.75 6.50
While this works, it strikes me there should be a better approach that matches x values to rows of dat and then performs all the interpolations in a single computation. Could somebody point me to a non-for-loop solution for this problem?

Answer 1

Try approx:
(xp <- unique(c(dat$x.low, dat$x.high)))
## [1] 0 1 2 3
(yp <- unique(c(dat$y.low, dat$y.high)))
## [1] 0 2 3 10
x <- c(1.75, 2.5)
approx(xp, yp, x)
## $x
## [1] 1.75 2.50
##
## $y
## [1] 2.75 6.50
or approxfun (which returns a new function):
f <- approxfun(xp, yp)
f(x)
## [1] 2.75 6.50
Some benchmarks:
set.seed(123L)
x <- runif(10000, min(xp), max(yp))
library(microbenchmark)
microbenchmark(
pw.lin.trans(x, dat),
approx(xp, yp, x)$y,
f(x)
)
## Unit: microseconds
## expr min lq median uq max neval
## pw.lin.trans(x, dat) 3364.241 3395.244 3614.0375 3641.7365 6170.268 100
## approx(xp, yp, x)$y 359.080 379.669 424.0895 453.6800 522.756 100
## f(x) 202.899 209.168 217.8715 232.3555 293.499 100