Description Usage Arguments Details Value Note Author(s) References See Also Examples
Function uses classify_curve
and then either findmaxbell
or findmaxtulip
to proceed. See [1] for definitions and details of algorithms.
1 | symextreme(x, y, concave = NULL, type = NULL)
|
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) |
type |
A character string inpute denoting the shape of the curve, either 'bell' or 'tulip' (default=NULL) |
This function is useful if we know that our curve has a symmetry around its extreme point but we cannot directly infer for the relevant shape.
A list with next memebers is returned:
maximum logical, if TRUE then curve has a maximum
minimum logical, if TRUE then curve has a minimum
results a named vector with components:
j1 the index of x-left
j2 the index of x-right
chi the estimation of extreme as x-abscissa
You can Use the 'type' input if you are sure for the shape of the curve.
Demetris T. Christopoulos
[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
classify_curve
, findmaxtulip
, findmaxbell
, findextreme
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | #
## Bell curve
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)
a=symextreme(x,y)
a
## $maximum
## [1] TRUE
##
## $minimum
## [1] FALSE
##
## $results
## j1 j2 chi
## 1.770000e+02 2.250000e+02 1.110223e-16
abline(v=a$results['chi'])
#
## Tulip curve
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)
a=symextreme(x,y)
a
## $maximum
## [1] TRUE
##
## $minimum
## [1] FALSE
##
## $results
## j1 j2 chi
## 1 1001 5
abline(v=a$results['chi'])
#
|
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