self start for the exponential-linear growth equation
Self starter for an exponential-linear growth equation
explin(t, cm, rm, tb) SSexplin(t, cm, rm, tb)
t |
input vector (time) |
cm |
parameter related to the maximum growth during the linear phase |
rm |
parameter related to the maximum growth during the exponential phase |
tb |
time at which switch happens |
J. GOUDRIAAN, J. L. MONTEITH, A Mathematical Function for Crop Growth Based on Light Interception and Leaf Area Expansion, Annals of Botany, Volume 66, Issue 6, December 1990, Pages 695–701, doi: 10.1093/oxfordjournals.aob.a088084
The equation is:
(cm/rm) * log(1 + exp(rm * (t - tb)))
This function is described in Archontoulis and Miguez (2015) - (doi:10.2134/agronj2012.0506).
a numeric vector of the same length as x containing parameter estimates for equation specified
explin: vector of the same length as x using a explin function
require(ggplot2) set.seed(12345) x <- seq(1,100, by = 5) y <- explin(x, 20, 0.14, 30) + rnorm(length(x), 0, 5) y <- abs(y) dat <- data.frame(x = x, y = y) fit <- nls(y ~ SSexplin(x, cm, rm, tb), data = dat) ## plot ggplot(data = dat, aes(x = x, y = y)) + geom_point() + geom_line(aes(y = fitted(fit)))
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