Piecewise Linear Function: An Introduction

Definition and meaning

Wikipedia defines a piecewise linear function as:

“a function defined on a (possibly unbounded) interval of real numbers, such that there is a collection of intervals on each of which the function is an affine function”

Example

# piecewise linear functions using if statements

# piecewise linear function defined using if for cases.
pw.function <- function(t) {
  if(t < 0.5) {
    0.7 * t/0.5
  } else {
    0.7 + 0.3*(t-0.5)/0.5
  }
}

pw.function <- Vectorize(pw.function)

tibble(t = seq(0.05:0.99, by = 0.05)) %>% 
  mutate(pfun_out = pw.function(t)) %>%
  ggplot() +
  geom_line(aes(x = t, y = pfun_out), group = "combined_grp")

Application

In segmentation and curve fitting. For a larger discourse refer to segmented package in cran.