Quadratic-plateau function — fn_quad

Computes a value based on a quadratic-plateau growth curve.

Usage

fn_quad_plat(t, t1 = 45, t2 = 80, b = 1, k = 100)

Arguments

t: A numeric vector of input values (e.g., time).
t1: The onset time of the response. The function is 0 for all values less than t1.
t2: The time at which the plateau begins. Must be greater than t1.
b: The initial slope of the curve at t1.
k: The plateau height. The function transitions to this constant value at t2.

Value

A numeric vector of the same length as t, representing the function values.

Details

$f (t; t_{1}, t_{2}, b, k) = {\begin{cases} 0 & if t < t_{1} \\ b (t - t_{1}) + \frac{k - b (t_{2} - t_{1})}{(t_{2} - t_{1})^{2}} (t - t_{1})^{2} & if t_{1} \leq t \leq t_{2} \\ k & if t > t_{2} \end{cases}$

This function allows the user to specify the initial slope b. The curvature term is automatically calculated so that the function reaches the plateau value k exactly at t2. The transition to the plateau is continuous in value but not necessarily smooth in derivative.

Examples

library(flexFitR)
plot_fn(
  fn = "fn_quad_plat",
  params = c(t1 = 35, t2 = 80, b = 4, k = 100),
  interval = c(0, 108),
  n_points = 2000,
  auc_label_size = 3
)