findipiterplot: A function to show implementation of BESE and BEDE methods by...

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

We apply the BESE and BEDE methods, we plot results showing the bisection like convergence to the true inflection point. One plot is created for BESE and another one for BEDE. If it is possible, then we compute 95% confidence intervals for the results. Parallel computing also available under user request.

Usage

1
findipiterplot(x, y, index, plots = TRUE, ci = FALSE, doparallel = FALSE)

Arguments

x

The numeric vector of x-abscissas, must be of length at least 4.

y

The numeric vector of the noisy or not y-ordinates

index

If data is convex/concave then index=0
If data is concave/convex then index=1

plots

When plots=TRUE the plot commands are executed (default value = TRUE)

ci

When ci=TRUE the 95% confidence intervals are computed, if sufficient results are available (default value = FALSE)

doparallel

If doparallel=TRUE then parallel computing is applied, based on the available workers of current machine (default value = FALSE)

Details

It applies iteratively when that is theoretically allowable the methods ESE, EDE, stores all useful results and according to the input computes 95% confidence intervals and plots the two sequences (BESE, BEDE). Useful for a graphical investigation of the inflection point.

Value

ans$first

The output of first run for ESE and EDE methods

ans$BESE

The vector of BESE iterations

ans$BEDE

The vector of BEDE iterations

ans$aesmout

Mean, Std Deviation and 95 % confidence interval for all BESE iterations, if possible

ans$aedmout

Mean, Std Deviation and 95 % confidence interval for all BEDE iterations, if possible

ans$xysl

A list of xy data frames containing the data used for every ESE iteration

ans$xydl

A list of xy data frames containing the data used for every EDE iteration

Note

Non direct methods have been removed in version 1.3 due to their limited functionality.

Author(s)

Demetris T. Christopoulos

References

[1]Demetris T. Christopoulos (2014). Developing methods for identifying the inflection point of a convex/concave curve. arXiv:1206.5478v2 [math.NA]. https://arxiv.org/pdf/1206.5478v2.pdf

[2]Demetris T. Christopoulos (2016). On the efficient identification of an inflection point.International Journal of Mathematics and Scientific Computing, (ISSN: 2231-5330), vol. 6(1). https://veltech.edu.in/wp-content/uploads/2016/04/Paper-04-2016.pdf

See Also

See also bese and bede.

Examples

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#
#Lets create some convex/concave data based on the Fisher-Pry model, without noise
f=function(x){5+5*tanh(x-5)};xa=0;xb=15;
set.seed(12345);x=sort(runif(5001,xa,xb));y=f(x);
#
t1=Sys.time();
a<-findipiterplot(x,y,0,TRUE,TRUE,FALSE);
t2=Sys.time();print(as.POSIXlt(t2, "GMT")-as.POSIXlt(t1, "GMT"),quote=F);
#Time difference of 2.692897 secs
#Lets see available results
ls(a)
# [1] "aedmout" "aesmout" "BEDE"    "BESE"    "first"   "xydl"    "xysl"  
a$first;#Show first solution
#       i1   i2  chi_S,D
# ESE 1128 2072 4.835633
# EDE 1091 2221 4.999979
a$BESE;#Show ESE iterations
#                       1        2        3        4        5        6        7        8
# ESE iterations 4.835633 5.054775 4.978086 5.011331 4.993876 5.003637 4.998145 4.999782
a$BEDE;#Show EDE iterations
#                       1        2        3        4        5        6        7        8        
# EDE iterations 4.999979 4.996327 4.997657 5.001511 4.996464 5.000629 4.999149 4.999885 
#        9       10
# 5.000082 4.999782
a$aesmout;#Statistics and 95%c c.i. for ESE
#                mean      sdev   95%(l)   95%(r)
# ESE method 4.984408 0.0640699 4.930844 5.037972
a$aedmout;#Statistics and 95%c c.i. for EDE
#                mean        sdev   95%(l) 95%(r)
# EDE method 4.999146 0.001753223 4.997892 5.0004
#
#Look how bisection based method (BESE) converges in 8 steps...
#
lapply(a$xysl,summary);
# [[1]]
# x                   y           
# Min.   : 0.006405   Min.   : 0.00046  
# 1st Qu.: 3.802278   1st Qu.: 0.83521  
# Median : 7.583006   Median : 9.94325  
# Mean   : 7.504537   Mean   : 6.68942  
# 3rd Qu.:11.240944   3rd Qu.: 9.99996  
# Max.   :14.994895   Max.   :10.00000  
# 
#...
#
# 
# [[8]]
# x               y        
# Min.   :4.978   Min.   :4.891  
# 1st Qu.:4.988   1st Qu.:4.938  
# Median :5.004   Median :5.018  
# Mean   :4.999   Mean   :4.997  
# 3rd Qu.:5.009   3rd Qu.:5.043  
# Max.   :5.018   Max.   :5.090  
# 
# and BEDE in 10 steps:
#
lapply(a$xydl,summary)
# [[1]]
# x                   y           
# Min.   : 0.006405   Min.   : 0.00046  
# 1st Qu.: 3.802278   1st Qu.: 0.83521  
# Median : 7.583006   Median : 9.94325  
# Mean   : 7.504537   Mean   : 6.68942  
# 3rd Qu.:11.240944   3rd Qu.: 9.99996  
# Max.   :14.994895   Max.   :10.00000  
# 
# ...
# 
# [[10]]
# x               y        
# Min.   :4.982   Min.   :4.911  
# 1st Qu.:4.993   1st Qu.:4.965  
# Median :5.004   Median :5.019  
# Mean   :5.001   Mean   :5.007  
# 3rd Qu.:5.009   3rd Qu.:5.045  
# Max.   :5.018   Max.   :5.090  
#
# See also the pdf plots 'ese_iterations.pdf' and 'ede_iterations.pdf'

Example output

Time difference of 1.87582 secs
[1] "BEDE"    "BESE"    "aedmout" "aesmout" "first"   "xydl"    "xysl"   
      i1   i2  chi_S,D
ESE 1128 2072 4.835633
EDE 1091 2221 4.999979
                      1        2        3        4        5        6        7
ESE iterations 4.835633 5.054775 4.978086 5.011331 4.993876 5.003637 4.998145
                      8
ESE iterations 4.999782
                      1        2        3        4        5        6        7
EDE iterations 4.999979 4.996327 4.997657 5.001511 4.996464 5.000629 4.999149
                      8        9       10
EDE iterations 4.999885 5.000082 4.999782
               mean      sdev   95%(l)   95%(r)
ESE method 4.984408 0.0640699 4.930844 5.037972
               mean        sdev   95%(l) 95%(r)
EDE method 4.999146 0.001753223 4.997892 5.0004
[[1]]
       x                   y           
 Min.   : 0.006405   Min.   : 0.00046  
 1st Qu.: 3.802278   1st Qu.: 0.83521  
 Median : 7.583006   Median : 9.94325  
 Mean   : 7.504537   Mean   : 6.68942  
 3rd Qu.:11.240944   3rd Qu.: 9.99996  
 Max.   :14.994895   Max.   :10.00000  

[[2]]
       x               y         
 Min.   :3.452   Min.   :0.4325  
 1st Qu.:4.576   1st Qu.:2.9982  
 Median :4.958   Median :4.7913  
 Mean   :4.910   Mean   :4.7112  
 3rd Qu.:5.287   3rd Qu.:6.3987  
 Max.   :6.219   Max.   :9.1975  

[[3]]
       x               y        
 Min.   :4.462   Min.   :2.543  
 1st Qu.:4.844   1st Qu.:4.227  
 Median :4.985   Median :4.925  
 Mean   :5.003   Mean   :5.004  
 3rd Qu.:5.104   3rd Qu.:5.520  
 Max.   :5.648   Max.   :7.850  

[[4]]
       x               y        
 Min.   :4.688   Min.   :3.491  
 1st Qu.:4.913   1st Qu.:4.565  
 Median :4.982   Median :4.911  
 Mean   :4.977   Mean   :4.889  
 3rd Qu.:5.052   3rd Qu.:5.259  
 Max.   :5.268   Max.   :6.308  

[[5]]
       x               y        
 Min.   :4.865   Min.   :4.330  
 1st Qu.:4.956   1st Qu.:4.781  
 Median :5.004   Median :5.018  
 Mean   :4.999   Mean   :4.996  
 3rd Qu.:5.045   3rd Qu.:5.223  
 Max.   :5.158   Max.   :5.781  

[[6]]
       x               y        
 Min.   :4.921   Min.   :4.605  
 1st Qu.:4.968   1st Qu.:4.838  
 Median :5.004   Median :5.018  
 Mean   :4.997   Mean   :4.987  
 3rd Qu.:5.023   3rd Qu.:5.115  
 Max.   :5.067   Max.   :5.334  

[[7]]
       x               y        
 Min.   :4.967   Min.   :4.835  
 1st Qu.:4.982   1st Qu.:4.911  
 Median :5.004   Median :5.019  
 Mean   :5.001   Mean   :5.007  
 3rd Qu.:5.018   3rd Qu.:5.090  
 Max.   :5.040   Max.   :5.201  

[[8]]
       x               y        
 Min.   :4.978   Min.   :4.891  
 1st Qu.:4.988   1st Qu.:4.938  
 Median :5.004   Median :5.018  
 Mean   :4.999   Mean   :4.997  
 3rd Qu.:5.009   3rd Qu.:5.043  
 Max.   :5.018   Max.   :5.090  

[[1]]
       x                   y           
 Min.   : 0.006405   Min.   : 0.00046  
 1st Qu.: 3.802278   1st Qu.: 0.83521  
 Median : 7.583006   Median : 9.94325  
 Mean   : 7.504537   Mean   : 6.68942  
 3rd Qu.:11.240944   3rd Qu.: 9.99996  
 Max.   :14.994895   Max.   :10.00000  

[[2]]
       x               y        
 Min.   :3.334   Min.   :0.345  
 1st Qu.:4.602   1st Qu.:3.110  
 Median :4.978   Median :4.891  
 Mean   :4.996   Mean   :4.973  
 3rd Qu.:5.391   3rd Qu.:6.860  
 Max.   :6.666   Max.   :9.655  

[[3]]
       x               y        
 Min.   :4.192   Min.   :1.659  
 1st Qu.:4.800   1st Qu.:4.014  
 Median :4.978   Median :4.891  
 Mean   :4.991   Mean   :4.950  
 3rd Qu.:5.166   3rd Qu.:5.824  
 Max.   :5.800   Max.   :8.321  

[[4]]
       x               y        
 Min.   :4.562   Min.   :2.940  
 1st Qu.:4.898   1st Qu.:4.494  
 Median :4.985   Median :4.925  
 Mean   :4.987   Mean   :4.935  
 3rd Qu.:5.078   3rd Qu.:5.390  
 Max.   :5.433   Max.   :7.040  

[[5]]
       x               y        
 Min.   :4.752   Min.   :3.787  
 1st Qu.:4.931   1st Qu.:4.655  
 Median :4.990   Median :4.951  
 Mean   :4.992   Mean   :4.958  
 3rd Qu.:5.052   3rd Qu.:5.259  
 Max.   :5.251   Max.   :6.228  

[[6]]
       x               y        
 Min.   :4.854   Min.   :4.275  
 1st Qu.:4.957   1st Qu.:4.787  
 Median :5.004   Median :5.018  
 Mean   :4.998   Mean   :4.988  
 3rd Qu.:5.040   3rd Qu.:5.201  
 Max.   :5.139   Max.   :5.690  

[[7]]
       x               y        
 Min.   :4.919   Min.   :4.597  
 1st Qu.:4.968   1st Qu.:4.838  
 Median :5.004   Median :5.018  
 Mean   :5.000   Mean   :4.998  
 3rd Qu.:5.025   3rd Qu.:5.126  
 Max.   :5.082   Max.   :5.409  

[[8]]
       x               y        
 Min.   :4.951   Min.   :4.757  
 1st Qu.:4.978   1st Qu.:4.891  
 Median :5.004   Median :5.018  
 Mean   :4.999   Mean   :4.996  
 3rd Qu.:5.018   3rd Qu.:5.091  
 Max.   :5.047   Max.   :5.234  

[[9]]
       x               y        
 Min.   :4.971   Min.   :4.854  
 1st Qu.:4.985   1st Qu.:4.925  
 Median :5.004   Median :5.019  
 Mean   :5.002   Mean   :5.009  
 3rd Qu.:5.013   3rd Qu.:5.067  
 Max.   :5.029   Max.   :5.144  

[[10]]
       x               y        
 Min.   :4.982   Min.   :4.911  
 1st Qu.:4.993   1st Qu.:4.965  
 Median :5.004   Median :5.019  
 Mean   :5.001   Mean   :5.007  
 3rd Qu.:5.009   3rd Qu.:5.045  
 Max.   :5.018   Max.   :5.090  

inflection documentation built on June 28, 2019, 5:03 p.m.