| rootexinf {RootsExtremaInflections} | R Documentation |
Function to Find the Root, Extreme and Inflection of a Planar Curve
Description
It takes as input the x, y numeric vectors, the indices for the range to be searched plus some other
options and finds the root, extreme and inflection for that interval, while it plots data,
Taylor polynomial and and the computed |a_0|, |a_1|, |a_2| coefficients.
Usage
rootexinf(x, y, i1, i2, nt, alpha = 5, xlb = "x", ylb = "y", xnd = 3, ynd = 3,
plots = TRUE, plotpdf = FALSE, doparallel=FALSE)
Arguments
x |
A numeric vector for the independent variable |
y |
A numeric vector for the dependent variable |
i1 |
The first index for choosing a specific interval |
i2 |
The second index for choosing a specific interval |
nt |
The degree of the Taylor polynomial that will be fitted to the data |
alpha |
The level of statistical significance for the confidence intervals of coefficients |
xlb |
A label for the x-variable (default value = "x") |
ylb |
A label for the y-variable (default value = "y") |
xnd |
The number of digits for plotting the x-axis (default value = 3) |
ynd |
The number of digits for plotting the y-axis (default value = 3) |
plots |
If plots=TRUE then a plot is created on default monitor (default value = TRUE) |
plotpdf |
If plotpdf=TRUE then a pdf plot is created and stored on working directory (default value = FALSE) |
doparallel |
If doparallel=TRUE then parallel computing is applied, based on the available workers of current machine (default value = FALSE) |
Details
The points x_i that make the relevant |a_0|, |a_1|, |a_2| minimum are the estimations
for the function's root, etreme and inflection point at the interval [x_{i1},x_{i2}].
Value
It returns an environment with four components:
an0 |
a matrix with 3 columns: lower, upper bound of confidence interval and middle value for each coefficient a_n at the best choice in root searching |
an1 |
a matrix with 3 columns: lower, upper bound of confidence interval and middle value for each coefficient a_n at the best choice in extreme searching |
an2 |
a matrix with 3 columns: lower, upper bound of confidence interval and middle value for each coefficient a_n at the best choice in inflection searching |
frexinf |
a 3 x 3 matrix: for each row (root, extreme, inflection) the position i and the value of the estimated root, extreme and inflection |
Warnings
When you are using RStudio it is necessary to leave enough space for the plot window in order for the plots to appear normally.
The data should come from a function at least C^{(2)} in order to find the root, extreme and inflection point, provided those points exist.
Author(s)
Demetris T. Christopoulos
References
Demetris T. Christopoulos (2014). Roots, extrema and inflection points by using a proper Taylor regression procedure. SSRN. https://dx.doi.org/10.2139/ssrn.2521403
Examples
#Load data:
#Let's create some data:
f=function(x){3*cos(x-5)+1.5};xa=1.;xb=5;
set.seed(12345);x=sort(runif(5001,xa,xb));
r=0.1;y=f(x)+2*r*(runif(length(x))-0.5);plot(x,y);abline(h=0)
#a<-rootexinf(x,y,1,length(x),5,plotpdf = TRUE,doparallel = TRUE);a$an0;a$an1;a$an2;a$frexinf;
# Available workers are 12
# Time difference of 13.02153 secs
# File 'root_extreme_inflection_plot.pdf' has been created
# 2.5 % 97.5 % an0
# a0 -0.004165735 0.001838624 -0.001163555
# a1 2.588990973 2.600915136 2.594953055
# a2 0.731456294 0.741262772 0.736359533
# a3 -0.435591038 -0.423837041 -0.429714040
# a4 -0.052926049 -0.050039975 -0.051483012
# a5 0.017915715 0.020538155 0.019226935
# 2.5 % 97.5 % an1
# a0 -1.507117843 -1.500375848 -1.5037468451
# a1 -0.008343275 0.007916087 -0.0002135941
# a2 1.519432687 1.534103788 1.5267682378
# a3 -0.017663080 0.007780728 -0.0049411760
# a4 -0.159461025 -0.144303367 -0.1518821962
# a5 0.017915715 0.020538155 0.0192269354
# 2.5 % 97.5 % an2
# a0 1.503394727 1.509925166 1.5066599466
# a1 2.985374546 2.995259021 2.9903167834
# a2 -0.009041165 0.005898692 -0.0015712367
# a3 -0.489107253 -0.480579585 -0.4848434187
# a4 -0.003885327 0.002364758 -0.0007602842
# a5 0.017915715 0.020538155 0.0192269354
# index value
# root 2364 2.903791
# extreme 1057 1.859431
# inflection 3038 3.431413
# You have to compare with the exact values
# root=2.905604898
# extreme=1.858407346
# inflection=3.429203673