inflection (version 1.3.6)

check_curve: Checks a curve and decides for its convexity type

Description

Given a planar curve with discrete (xi,yi) points this function can find if it is convex, concave or for the sigmoid case if it is convex/concave or concave/convex.

Usage

check_curve(x, y)

Arguments

x

The numeric vector of x-abscissas

y

The numeric vector of y-abscissas

Value

A list with members:

1. ctype, the convexity type of the curve

2. index, the index that can be used from other functions to identify the inflection point

Details

It uses the function findipl which provides us with a consistent estimator for the surfaces left and right that are used here, see [1],[2] for more details.

References

[1]Demetris T. Christopoulos (2014). Developing methods for identifying the inflection point of a convex/concave curve. arXiv:1206.5478v2 [math.NA]. https://arxiv.org/pdf/1206.5478v2.pdf

[2]Demetris T. Christopoulos (2016). On the efficient identification of an inflection point.International Journal of Mathematics and Scientific Computing, (ISSN: 2231-5330), vol. 6(1). https://veltech.edu.in/wp-content/uploads/2016/04/Paper-04-2016.pdf

[3]Bardsley, W. G. & Childs, R. E. Sigmoid curves, non-linear double-reciprocal plots and allosterism Biochemical Journal, Portland Press Limited, 1975, 149, 313-328

See Also

findipl, ese, ede, bese, bede .

Examples

# NOT RUN {
## Lets create a really hard data set, an exxample of a "2:2 function" taken from [3]
## This function for x>0 has an inflectrion point at 
## x = -1/8+(1/24)*sqrt(381) = 0.6883008876 ~0.69
## We want to see ,if function 'check_curve()' will proper classify it,
## given that we used [0.2,4] as definition range.
f=function(x){(1/8*x+1/2*x^2)/(1+1/8*x+1/2*x^2)}
x=seq(0.2,4,0.05)
y=f(x)
plot(x,y,pch=19,cex=0.5)
cc=check_curve(x,y)
cc
## $ctype
## [1] "convex_concave"
## 
## $index
## [1] 0
##
## Yes it found it.
# }