DETE | R Documentation |
DETE
is used to calculate the first-order derivative of the explicit Troscianko equation at a given x-value.
DETE(P, x)
P |
the parameters of the explicit Troscianko equation. |
x |
the x-value used in the explicit Troscianko equation. |
The first-order derivative of the explicit Troscianko equation at a given x-value is:
h(x) = \left\{\alpha_{1}+\frac{2\,\alpha_{2}}{a}\,x-\frac{x}{a}\,\left[1-\left(\frac{x}{a}\right)^2\right]^{-1}\right\}\,\exp\left\{\alpha_{0}+\alpha_{1}\left(\frac{x}{a}\right)+\alpha_{2}\left(\frac{x}{a}\right)^2\right\}\,\sqrt{ 1-\left(\frac{x}{a}\right)^2 },
where P
has four parameters: a
, \alpha_{0}
, \alpha_{1}
, and \alpha_{2}
.
The argument P
in the DETE
function has the same parameters, as those in the
ETE
function.
Peijian Shi pjshi@njfu.edu.cn, Johan Gielis johan.gielis@uantwerpen.be, Brady K. Quinn Brady.Quinn@dfo-mpo.gc.ca.
Shi, P., Chen, L., Quinn, B.K., Yu, K., Miao, Q., Guo, X., Lian, M., Gielis, J., Niklas, K.J. (2023)
A simple way to calculate the volume and surface area of avian eggs.
Annals of the New York Academy of Sciences 1524, 118-
131. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/nyas.15000")}
ETE
, fitETE
, SurfaceAreaETE
Par5 <- c(2.25, -0.38, -0.29, -0.16)
xx2 <- seq(-2.25, 2.25, by=0.001)
h1 <- DETE(P=Par5, x=xx2)
h2 <- -DETE(P=Par5, x=xx2)
ind <- which(is.na(h1) | is.na(h2))
xx2 <- xx2[-ind]
h1 <- h1[-ind]
h2 <- h2[-ind]
dev.new()
plot(xx2, h1, type="l", col=4, cex.lab=1.5, cex.axis=1.5,
xlim=c(-2.25, 2.25), ylim=c(-30, 30), xlab=expression(italic(x)),
ylab=expression(paste(italic(h), "(", italic(x), ")", sep="")))
lines(xx2, h2, col=2)
graphics.off()
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