RootsExtremaInflections (version 1.2.5)

findextreme: Implementation of Integration Extreme Finding Estimator (IEFE) for extreme points identification

Description

Given a noisy or not planar curve as a set of discrete \(\left\{(x_i,y_i),i=1,2,\ldots n\right\}\) points we use Integration Extreme Finding Estimator (IEFE) algorithm as it is described at [1] in ordfer to find the extreme point of it.

Usage

findextreme(x, y, parallel = FALSE, silent = TRUE, tryfast = FALSE)

Value

A named vector with next components is returned:

1. x1 the left endpoint of the final interval of BESE or BEDE iterations

2. x2 the right endpoint of the final interval of BESE or BEDE iterations

3. chi the estimation of extreme as x-abscissa

4. ychi the estimation of extreme as y-abscissa taken from the interpolation polynomial of 2nd degree for the data points (x1,y1), (x2,y2), (chi,ychi)

Arguments

x

A numeric vector for the independent variable without missing values

y

A numeric vector for the dependent variable without missing values

parallel

Logical input, if TRUE then parallel processing will be used (default=FALSE)

silent

Logical input, if TRUE then no details will be printed out during code execution (default=TRUE)

tryfast

Logical input, if TRUE then instead 'BEDE' will be used from IEFE algorithm instead of BESE (default=FALSE)

Author

Demetris T. Christopoulos

Details

The parallel=TRUE option must be used if length(x)>20000. The tryfast=TRUE can be used for big data sets, but BEDE is not so accuracy as BESE, so use it with caution.

References

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

See Also

symextreme, findmaxtulip, findmaxbell

Examples

## Legendre polynomial 5th order
## True extreme point p=0.2852315165, y=0.3466277
f=function(x){(63/8)*x^5-(35/4)*x^3+(15/8)*x} 
x=seq(0,0.7,0.001);y=f(x)
plot(x,y,pch=19,cex=0.5)
a=findextreme(x,y)
a
##        x1        x2       chi    yvalue 
## 0.2840000 0.2860000 0.2850000 0.3466274 
sol=a['chi']
abline(h=0)
abline(v=sol)
abline(v=a[1:2],lty=2)
abline(h=f(sol),lty=2)
points(sol,f(sol),pch=17,cex=2)
#
## The same function 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)
a=findextreme(x,y)
a
##        x1        x2       chi    yvalue 
## 0.2890000 0.2910000 0.2900000 0.3895484 
sol=a['chi']
abline(h=0)
abline(v=sol)
abline(v=a[1:2],lty=2)
abline(h=f(sol),lty=2)
points(sol,f(sol),pch=17,cex=2)
#