fn_exp_lin: Exponential-linear function
View source: R/99_growth_curves.R
| fn_exp_lin | R Documentation |
Exponential-linear function
Description
A piecewise function that models a response with an initial exponential growth phase followed by a linear phase. Commonly used to describe processes with rapid early increases that slow into a linear trend, while maintaining continuity.
Usage
fn_exp_lin(t, t1, t2, alpha, beta)
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 |
t2 |
The transition time between exponential and linear phases. Must be greater than |
alpha |
The exponential growth rate during the exponential phase. |
beta |
The slope of the linear phase after |
Details
f(t; t_1, t_2, \alpha, \beta) =
\begin{cases}
0 & \text{if } t < t_1 \\
e^{\alpha \cdot (t - t_1)} - 1 & \text{if } t_1 \leq t \leq t_2 \\
\beta \cdot (t - t_2) + \left(e^{\alpha \cdot (t_2 - t_1)} - 1\right) & \text{if } t > t_2
\end{cases}
The exponential segment starts from 0 at t1, and the linear segment
continues smoothly from the end of the exponential part. This ensures value
continuity at t2, but not necessarily smoothness in slope.
Value
A numeric vector of the same length as t, representing the function values.
Examples
library(flexFitR)
plot_fn(
fn = "fn_exp_lin",
params = c(t1 = 35, t2 = 55, alpha = 1 / 20, beta = -1 / 40),
interval = c(0, 108),
n_points = 2000,
auc_label_size = 3
)
