Adaptive sparse generalized polynomial chaos expansion based on least angle regression

Description

The GPCE.lar function implements a polynomial chaos expansion of a given model or an external model. The strategy for the expansion of the model into a polynomial chaos basis is the adaptive sparse method based on the least angle regression. A statistical and a global sensitivity analysis of the model is then carried out.

Usage

  GPCE.lar(Model = NULL, PCSpace = "Uniform", 
           InputDim = 3, InputDistrib = c(),
           ParamDistrib = NULL, Q2tgt = 1 - 10^(-6), 
           Eps = 10^(-2) * (1 - Q2tgt), EpsForw = Eps, 
           EpsBack = Eps, EnrichStep = 50, 
           jmax= InputDim, pmaxi = 6, 
           DesignLength = 8, SeedSob =sample(1:1000, 1))
  
  
  
  

Arguments

Value

Author(s)

Munoz Zuniga Miguel

References

G. Blatman and B. Sudret, 2011, Adapive sparse polynomial chaos expansion based on least angle regression, Journal of Computational Physics, 230, 2345–2367.

See Also

tell.GPCE.lar

Examples

### CASE 1: model is a R function. 
### Model definition: y= 1 + Phi_1(x1)*Phi_1(x2)
Model <- function(x){
  PHerm = hermite.he.polynomials(5, normalized=FALSE)
  y=1+unlist(polynomial.values(PHerm[2],x[,1]))*unlist(polynomial.values(PHerm[2],x[,2]))
  return(y)
}

### Run the algorithm with the lar regression method
ResultObject=GPCE.lar(Model=Model, PCSpace="Gaussian", InputDim=3, InputDistrib=rep("Gaussian",3))
names(ResultObject)
###

### CASE 2: external model (for the example the function Model will be used externaly).

### initialized Output
Output=c()

### Get a first design
ResultObject=GPCE.lar(PCSpace="Gaussian",InputDim=3,InputDistrib=rep("Gaussian",3))
names(ResultObject)

### Calculate the model output for the given design and concatenate the model output results
### into the output vector 
Output=c(Output,Model(ResultObject$Design2Eval))

### Give the design and the calculated ouput to the tell function
ResultObject=tell(ResultObject,Output)
names(ResultObject)

### If the expansion has been calculated the function tell return the full expansion 
### paramaters, the moments analysis, the sensitivity analysis and the output distribution
### If not the function tell() return an enriched design. 
### In the later case the user calculate the output externally and give them
### to the tell function with the previous ResultObject for further calculation. 
### See GPCE.sparse documentation for an example.

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(GPC)
Loading required package: randtoolbox
Loading required package: rngWELL
This is randtoolbox. For overview, type 'help("randtoolbox")'.
Loading required package: orthopolynom
Loading required package: polynom
Loading required package: ks
Loading required package: KernSmooth
KernSmooth 2.23 loaded
Copyright M. P. Wand 1997-2009
Loading required package: misc3d
Loading required package: mvtnorm
Loading required package: rgl
Loading required package: lars
Loaded lars 1.2

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/GPC/GPCE.lar.Rd_%03d_medium.png", width=480, height=480)
> ### Name: GPCE.lar
> ### Title: Adaptive sparse generalized polynomial chaos expansion based on
> ###   least angle regression
> ### Aliases: GPCE.lar
> 
> ### ** Examples
> 
> ### CASE 1: model is a R function. 
> ### Model definition: y= 1 + Phi_1(x1)*Phi_1(x2)
> Model <- function(x){
+   PHerm = hermite.he.polynomials(5, normalized=FALSE)
+   y=1+unlist(polynomial.values(PHerm[2],x[,1]))*unlist(polynomial.values(PHerm[2],x[,2]))
+   return(y)
+ }
> 
> ### Run the algorithm with the lar regression method
> ResultObject=GPCE.lar(Model=Model, PCSpace="Gaussian", InputDim=3, InputDistrib=rep("Gaussian",3))
[1] "p is" "1"   
[1] "p is" "2"   
[1] "Entering PostProcessReg"
[1] "Entering EvalPCE"
> names(ResultObject)
[1] "TruncSet"     "Q2"           "Designs"      "CoeffPCE"     "Moments"     
[6] "Sensitivity"  "OutputDistib" "Args"         "Output"      
> ###
> 
> ### CASE 2: external model (for the example the function Model will be used externaly).
> 
> ### initialized Output
> Output=c()
> 
> ### Get a first design
> ResultObject=GPCE.lar(PCSpace="Gaussian",InputDim=3,InputDistrib=rep("Gaussian",3))
> names(ResultObject)
[1] "Designs"     "Design2Eval" "Args"        "p"           "SaveQmax"   
[6] "SaveAmax"   
> 
> ### Calculate the model output for the given design and concatenate the model output results
> ### into the output vector 
> Output=c(Output,Model(ResultObject$Design2Eval))
> 
> ### Give the design and the calculated ouput to the tell function
> ResultObject=tell(ResultObject,Output)
[1] "p is" "1"   
[1] "p is" "2"   
[1] "Entering PostProcessReg"
[1] "Entering EvalPCE"
> names(ResultObject)
[1] "TruncSet"     "Q2"           "Designs"      "CoeffPCE"     "Moments"     
[6] "Sensitivity"  "OutputDistib" "Args"         "Output"      
> 
> ### If the expansion has been calculated the function tell return the full expansion 
> ### paramaters, the moments analysis, the sensitivity analysis and the output distribution
> ### If not the function tell() return an enriched design. 
> ### In the later case the user calculate the output externally and give them
> ### to the tell function with the previous ResultObject for further calculation. 
> ### See GPCE.sparse documentation for an example.
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>