RootsExtremaInflections (version 1.2.1)

findmaxbell: Implementation of Bell Extreme Finding Estimator (BEFE) algorithm for a planar curve

Description

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

Usage

findmaxbell(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-left

2. j2 the index of x-right

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, findmaxtulip, findextreme

Examples

# NOT RUN {
#
f=function(x){1/(1+x^2)}
x=seq(-2,2.0,by=0.01);y=f(x)
plot(x,y,pch=19,cex=0.5)
cc=classify_curve(x,y)
cc$shapetype
## 1] "bell"
a1<-findmaxbell(x,y)
a1
## j1           j2          chi 
## 1.770000e+02 2.250000e+02 1.110223e-16 
abline(v=a1['chi'])
abline(v=x[a1[1:2]],lty=2);abline(h=y[a1[1:2]],lty=2)
points(x[a1[1]:a1[2]],y[a1[1]:a1[2]],pch=19,cex=0.5,col='blue')
#
## Same curve with noise from U(-0.05,0.05)
set.seed(2019-07-26);r=0.05;y=f(x)+runif(length(x),-r,r)
plot(x,y,pch=19,cex=0.5)
cc=classify_curve(x,y)
cc$shapetype
## 1] "bell"
a1<-findmaxbell(x,y)
a1
##     j1     j2    chi 
## 169.00 229.00  -0.02 
abline(v=a1['chi'])
abline(v=x[a1[1:2]],lty=2);abline(h=y[a1[1:2]],lty=2)
points(x[a1[1]:a1[2]],y[a1[1]:a1[2]],pch=19,cex=0.5,col='blue')
#
# }