inflection (version 1.3.6)

bese: Bisection Extremum Surface Estimator Method

Description

It iterates in a way similar to the well known bisection method in root finding, with the only exception that our \([a_{n},b_{n}]\) intervals contain the inflection point now and the rule for choosing them follows definitions and Lemmas of [1], [2]. It uses parallel computing under user request.

Usage

bese(x, y, index, doparallel = FALSE)

Arguments

x

The numeric vector of x-abscissas, must be of length at least 4.

y

The numeric vector of the noisy or not y-ordinates, must be of length at least 4.

index

If data is convex/concave then index=0 If data is concave/convex then index=1

doparallel

If doparallel=TRUE then parallel computing is applied, based on the available workers of current machine (default value = FALSE)

Value

It returns a list of two elements:

iplast

the last estimation found

iters

a matrix with 4 columns ("n", "a", "b", "ESE") that give the number of x-y pairs used at each iteration, the [a,b] range where we searched and the ESE estimated inflection point.

Details

This function is suitable for making a `fine tuning' while searching for inflection point. For very large data sets it is better using first EDE method, see ede. Then we apply BESE at a smaller range.

References

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

[2]Demetris T. Christopoulos, 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, 2016

See Also

See also the simple version ese and iterations plot using findipiterplot.

Examples

# NOT RUN {
#Fisher-pry model with noise and 50k cases:
N=5*10^4+1;
set.seed(2017-05-11);x=seq(0,15,length.out = N);y=5+5*tanh(x-5)+runif(N,-0.25,0.25);
#We first run BEDE to find a smaller neighborhood for inflection point
iters=bede(x,y,0)$iters;
iters;
#Now we find last interval
ab=apply(iters[dim(iters)[1],c('a','b')],2,function(xx,x){which(x==xx)},x);ab;
#Apply BESE to that
eseit=bese(x[ab[1]:ab[2]],y[ab[1]:ab[2]],0)
eseit$iplast
eseit$iters
#Or apply directly to data with doparallel=TRUE
#
#t1=Sys.time();
#eseit=bese(x,y,0,doparallel = TRUE);#...Bisection ESE (BESE)
#t2=Sys.time();print(as.POSIXlt(t2, "GMT")-as.POSIXlt(t1, "GMT"),quote=F);
# Time difference of 56.14608 secs
#eseit$iplast#...last estimation for inflection point
# [1] 5.0241
#eseit$iters#...all iterations done...
#       n      a       b     ESE
# 1 50001 0.0000 15.0000 4.81740
# 2  9375 4.4721  5.6505 5.06130
# 3  3929 4.7007  5.2758 4.98825
# 4  1918 4.8654  5.1828 5.02410
#Better accuracy, slightly more time, provided that there exist multi cores.
#plot(eseit$iters$ESE,type='b');abline(h=5,col='blue',lwd=3)
#
# }