maxcurv: Maximum Curvature Point

In soilphysics: Soil Physical Analysis

Description

Function to determine the maximum curvature point of an univariate nonlinear function of x.

Usage

 maxcurv(x.range, fun, 
	method = c("general", "pd", "LRP", "spline"), 
	x0ini = NULL, 
	graph = TRUE, ...) 

Arguments

x.range	a numeric vector of length two, the range of x.
fun	a function of x; it must be a one-line-written function, with no curly braces '{}'.
method	a character indicating one of the following: "general" - for evaluating the general curvature function (k), "pd" - for evaluating perpendicular distances from a secant line, "LRP" - a NLS estimate of the maximum curvature point as the breaking point of Linear Response Plateau model, "spline" - a NLS estimate of the maximum curvature point as the breaking point of a piecewise linear spline. See details.
x0ini	an initial x-value for the maximum curvature point. Required only when "LRP" or "spline" are used.
graph	logical; if TRUE (default) a curve of fun is plotted.
...	further graphical arguments.

Details

The method "LRP" can be understood as an especial case of "spline". And both models are fitted via nls. The method "pd" is an adaptation of the method proposed by Lorentz et al. (2012). The "general" method should be preferred for finding global points. On the other hand, "pd", "LRP" and "spline" are suitable for finding local points of maximum curvature.

Value

A list of

fun	the function of x.
x0	the x critical value.
y0	the y critical value.
method	the method of determination (input).

Author(s)

Anderson Rodrigo da Silva <[e-mail]>

References

Lorentz, L.H.; Erichsen, R.; Lucio, A.D. (2012). Proposal method for plot size estimation in crops. Revista Ceres, 59:772–780.

See Also

function, curve

Examples

# Example 1: an exponential model
f <- function(x) exp(-x)
maxcurv(x.range = c(-2, 5), fun = f)

# Example 2: Gompertz Growth Model
Asym <- 8.5
b2 <- 2.3
b3 <- 0.6
g <- function(x) Asym * exp(-b2 * b3 ^ x)
maxcurv(x.range = c(-5, 20), fun = g)

# using "pd" method
maxcurv(x.range = c(-5, 20), fun = g, method = "pd")

# using "LRP" method
maxcurv(x.range = c(-5, 20), fun = g, method = "LRP", x0ini = 6.5)

# Example 3: Lessman & Atkins (1963) model for optimum plot size
a = 40.1
b = 0.72
cv <- function(x) a * x^-b
maxcurv(x.range = c(1, 50), fun = cv)

# using "spline" method
maxcurv(x.range = c(1, 50), fun = cv, method = "spline", x0ini = 6)

# End (not run)

Example output

Loading required package: rpanel
Loading required package: tcltk
Package `rpanel', version 1.1-4: type help(rpanel) for summary information
Loading required package: MASS
Loading required package: tkrplot
---
soilphysics version 3.1

Warning messages:
1: no DISPLAY variable so Tk is not available 
2: loading Rplot failed 

          Maximum curvature point 
 
f(x) = exp(-x) 
critical x:  0.3468694 
critical y:  0.7068977
method: general curvature 

          Maximum curvature point 
 
f(x) = Asym * exp(-b2 * b3^x) 
critical x:  -0.8741748 
critical y:  0.2334863
method: general curvature 

          Maximum curvature point 
 
f(x) = Asym * exp(-b2 * b3^x) 
critical x:  6.45229 
critical y:  7.806014
method: perpendicular distances 

          Maximum curvature point 
 
f(x) = Asym * exp(-b2 * b3^x) 
critical x:  7.37416 
critical y:  8.059748
method: Linear Response Plateau 

          Maximum curvature point 
 
f(x) = a * x^-b 
critical x:  6.841968 
critical y:  10.04186
method: general curvature 

          Maximum curvature point 
 
f(x) = a * x^-b 
critical x:  5.842235 
critical y:  11.25142
method: piecewise linear spline 

soilphysics documentation built on Jan. 13, 2021, 7:06 p.m.