RootsExtremaInflections (version 1.2.1)

findmaxtulip: Implementation of Tulip Extreme Finding Estimator (TEFE) algorithm for a planar curve

Description

For a curve that can be classified as 'tulip' a fast computation of its maximum is performed by applying Tulip Extreme Finding Estimator (TEFE) algorithm of [1].

Usage

findmaxtulip(x, y, concave = TRUE)

Arguments

x

A numeric vector for the independent variable without missing values

y

A numeric vector for the dependent variable without missing values

concave

Logical input, if TRUE then curve is supposed to have a maximum (default=TRUE)

Value

A named vector with next components is returned:

1. j1 the index of x vextor that is the left endpoint of final symmetrization interval

2. j1 the index of x vextor that is the right endpoint of final symmetrization interval

3. chi the estimation of extreme as x-abscissa

Details

If we want to compute minimum we just set concave=FALSE and proceed.

References

[1]Demetris T. Christopoulos (2019). New methods for computing extremes and roots of a planar curve: introducing Noisy Numerical Analysis (2019). ResearchGate. http://dx.doi.org/10.13140/RG.2.2.17158.32324

See Also

classify_curve, symextreme, findmaxbell, findextreme

Examples

# NOT RUN {
#
f=function(x){100-(x-5)^2}
x=seq(0,12,by=0.01);y=f(x)
plot(x,y,pch=19,cex=0.5)
cc=classify_curve(x,y)
cc$shapetype
## 1] "tulip"
a<-findmaxtulip(x,y)
a
## j1   j2  chi 
##  1 1001    5 
abline(v=a['chi'])
abline(v=x[a[1:2]],lty=2);abline(h=y[a[1:2]],lty=2)
points(x[a[1]:a[2]],y[a[1]:a[2]],pch=19,cex=0.5,col='blue')
#
## Same curve with noise from U(-1.5,1.5)
set.seed(2019-07-26);r=1.5;y=f(x)+runif(length(x),-r,r)
plot(x,y,pch=19,cex=0.5)
cc=classify_curve(x,y)
cc$shapetype
## 1] "tulip"
plot(x,y,pch=19,cex=0.5)
a<-findmaxtulip(x,y)
a
##    j1       j2      chi 
## 1.000 1002.000    5.005 
abline(v=a['chi'])
abline(v=x[a[1:2]],lty=2);abline(h=y[a[1:2]],lty=2)
points(x[a[1]:a[2]],y[a[1]:a[2]],pch=19,cex=0.5,col='blue')
#
# }