fn_quad_plat: Quadratic-plateau function

In flexFitR: Flexible Non-Linear Least Square Model Fitting

Quadratic-plateau function

Description

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.

Details

f(t; t_1, t_2, b, k) = \begin{cases} 0 & \text{if } t < t_1 \\ b (t - t_1) + \frac{k - b (t_2 - t_1)}{(t_2 - t_1)^2} (t - t_1)^2 & \text{if } t_1 \leq t \leq t_2 \\ k & \text{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.

Value

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

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
)

flexFitR documentation built on April 16, 2025, 5:09 p.m.