Function summary for Multi-Fidelity Cokriging models

Description

Provide a summary of a multi-fidelity cokriging model. In particular, it provides the parameter estimations and the results of the cross-validation procedure.

Usage

## S3 method for class 'MuFicokm'
summary(object, CrossValidation = FALSE, ...)

Arguments

Details

"summary.MuFicokm" return the parameter estimations for each level and the result of the Leave-One-Out Cross-Validation (RMSE=Root Mean Squared Error ; Std RMSE=Standardized RMSE ; Q2=explained variance).

Value

A list with following items (see "MuFicokm"):

Author(s)

Loic Le Gratiet

Examples

#--- test functions (see [Le GRATIET, L. 2012])
	Funcf <- function(x){return(0.5*(6*x-2)^2*sin(12*x-4)+sin(10*cos(5*x)))}
	Funcc <- function(x){return((6*x-2)^2*sin(12*x-4)+10*(x-0.5)-5)}
#--- Data
	Dc <- seq(0,1,0.1)
	indDf <- c(1,3,7,11)
	DNest <- NestedDesign(Dc, nlevel=2 , indices = list(indDf) )
	zc <- Funcc(DNest$PX)
	Df <- ExtractNestDesign(DNest,2)
	zf <- Funcf(Df)
#--- Multi-fidelity cokriging creation without parameter estimations
		mymodel <- MuFicokm(
				formula = list(~1,~1), 
				MuFidesign = DNest, 
				response = list(zc,zf), 
				nlevel = 2)

		sum <- summary(object = mymodel, CrossValidation = TRUE)
		names(sum)
#--- Saving parameters
	#--covariance parameters
		sum$Cov.Val
	#--variance parameters
		sum$Var.Val
	#--trend parameters
		sum$Trend.Val
	#-- adjustment parameters
		sum$Rho.Val

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(MuFiCokriging)
Loading required package: DiceKriging
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/MuFiCokriging/summary.MuFicokm.Rd_%03d_medium.png", width=480, height=480)
> ### Name: summary.MuFicokm
> ### Title: Function summary for Multi-Fidelity Cokriging models
> ### Aliases: summary.MuFicokm
> 
> ### ** Examples
> 
> #--- test functions (see [Le GRATIET, L. 2012])
> 	Funcf <- function(x){return(0.5*(6*x-2)^2*sin(12*x-4)+sin(10*cos(5*x)))}
> 	Funcc <- function(x){return((6*x-2)^2*sin(12*x-4)+10*(x-0.5)-5)}
> #--- Data
> 	Dc <- seq(0,1,0.1)
> 	indDf <- c(1,3,7,11)
> 	DNest <- NestedDesign(Dc, nlevel=2 , indices = list(indDf) )
> 	zc <- Funcc(DNest$PX)
> 	Df <- ExtractNestDesign(DNest,2)
> 	zf <- Funcf(Df)
> #--- Multi-fidelity cokriging creation without parameter estimations
> 		mymodel <- MuFicokm(
+ 				formula = list(~1,~1), 
+ 				MuFidesign = DNest, 
+ 				response = list(zc,zf), 
+ 				nlevel = 2)

optimisation start
------------------
* estimation method   : MLE 
* optimisation method : BFGS 
* analytical gradient : used
* trend model : ~1
* covariance model : 
  - type :  matern5_2 
  - nugget : NO
  - parameters lower bounds :  1e-10 
  - parameters upper bounds :  2 
  - best initial criterion value(s) :  -30.12058 

N = 1, M = 5 machine precision = 2.22045e-16
At X0, 0 variables are exactly at the bounds
At iterate     0  f=       30.121  |proj g|=      0.33827
At iterate     1  f =       30.079  |proj g|=       0.32754
At iterate     2  f =       30.036  |proj g|=        0.8379
At iterate     3  f =       30.034  |proj g|=       0.10589
At iterate     4  f =       30.033  |proj g|=     0.0027327
At iterate     5  f =       30.033  |proj g|=    9.3487e-06

iterations 5
function evaluations 7
segments explored during Cauchy searches 5
BFGS updates skipped 0
active bounds at final generalized Cauchy point 0
norm of the final projected gradient 9.34872e-06
final function value 30.0335

F = 30.0335
final  value 30.033468 
converged

optimisation start
------------------
* estimation method   : MLE 
* optimisation method : BFGS 
* analytical gradient : used
* trend model : ~1
* covariance model : 
  - type :  matern5_2 
  - nugget : NO
  - parameters lower bounds :  1e-10 
  - parameters upper bounds :  2 
  - best initial criterion value(s) :  -3.813998 

N = 1, M = 5 machine precision = 2.22045e-16
At X0, 0 variables are exactly at the bounds
At iterate     0  f=        3.814  |proj g|=   3.5182e-21
Derivative >= 0, backtracking line search impossible.final  value 3.813998 
stopped after 0 iterations
> 
> 		sum <- summary(object = mymodel, CrossValidation = TRUE)
Level 1: parameter estimation 
 
 Covariance type: matern5_2 
 Variance estimation: 142.5591 
 Trend estimation: 1.856445 
 Correlation length estimation: 0.3014263 
 
Level  2 : parameter estimation 
 
 Covariance type: matern5_2 
 Variance estimation: 0.3942074 
 Trend estimation: 2.473242 
 Adjustment estimation: 0.3601547 
 Correlation length estimation: 0.007034777 
 
Leave One Cross Validation 

RMSE:0.9018081
Std RMSE:0.7447738
Q2:0.9299403

> 		names(sum)
[1] "CovNames"  "Cov.Val"   "Var.Val"   "Rho.Val"   "Trend.Val"
> #--- Saving parameters
> 	#--covariance parameters
> 		sum$Cov.Val
[[1]]
[1] 0.3014263

[[2]]
[1] 0.007034777

> 	#--variance parameters
> 		sum$Var.Val
[[1]]
[1] 142.5591

[[2]]
[1] 0.3942074

> 	#--trend parameters
> 		sum$Trend.Val
[[1]]
[1] 1.856445

[[2]]
[1] 2.473242

> 	#-- adjustment parameters
> 		sum$Rho.Val
[[1]]
[1] 0.3601547

> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>