Description Usage Arguments Details Value Author(s) Examples
Provide a summary of a multi-fidelity cokriging model. In particular, it provides the parameter estimations and the results of the cross-validation procedure.
1 2 |
object |
an object of class S3 ( |
CrossValidation |
a Boolean. If |
... |
no other argument for this method. |
"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
).
A list with following items (see "MuFicokm"
):
CovNames |
a list of character strings giving the covariance structures used for the cokriging model. The element i of the list corresponds to the covariance structure of the Gaussian process δ_i(x) with δ_1(x) = Z_1(x). (see |
Cov.val |
a list of vectors giving the values of the hyper-parameters of the cokriging model. The element i of the list corresponds to the hyper-parameters of the Gaussian process δ_i(x) with δ_1(x) = Z_1(x). (see |
Var.val |
a list of numerics giving the values of the variance parameters of the cokriging model. The element i of the list corresponds to the variance of the Gaussian process δ_i(x) with δ_1(x) = Z_1(x). (see |
Rho.val |
a list of vectors giving the values of the trends γ_i of the adjustment parameters ρ_i of the cokriging model. The element i of the list corresponds to the adjustment parameter between Z_i and δ_i(x). (see |
Trend.val |
a list of vectors giving the values of the trend parameters of the Gaussian processes δ_i(x) and Z_1(x). |
Loic Le Gratiet
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 | #--- 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
|
Loading required package: DiceKriging
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) : -30.15302
N = 1, M = 5 machine precision = 2.22045e-16
At X0, 0 variables are exactly at the bounds
At iterate 0 f= 30.153 |proj g|= 0.34507
At iterate 1 f = 30.096 |proj g|= 0.33244
At iterate 2 f = 30.039 |proj g|= 1.2483
At iterate 3 f = 30.034 |proj g|= 0.18578
At iterate 4 f = 30.033 |proj g|= 0.007017
At iterate 5 f = 30.033 |proj g|= 4.2326e-05
At iterate 6 f = 30.033 |proj g|= 9.5387e-09
iterations 6
function evaluations 8
segments explored during Cauchy searches 6
BFGS updates skipped 0
active bounds at final generalized Cauchy point 0
norm of the final projected gradient 9.5387e-09
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|= 1.7011e-09
At iterate 1 f = 3.814 |proj g|= 1.701e-09
iterations 1
function evaluations 2
segments explored during Cauchy searches 1
BFGS updates skipped 0
active bounds at final generalized Cauchy point 0
norm of the final projected gradient 1.70105e-09
final function value 3.814
F = 3.814
final value 3.813998
converged
Level 1: parameter estimation
Covariance type: matern5_2
Variance estimation: 142.5592
Trend estimation: 1.856447
Correlation length estimation: 0.3014264
Level 2 : parameter estimation
Covariance type: matern5_2
Variance estimation: 0.3942074
Trend estimation: 2.473242
Adjustment estimation: 0.3601547
Correlation length estimation: 0.01307602
Leave One Cross Validation
RMSE:0.9018081
Std RMSE:0.7447739
Q2:0.9299403
[1] "CovNames" "Cov.Val" "Var.Val" "Rho.Val" "Trend.Val"
[[1]]
[1] 0.3014264
[[2]]
[1] 0.01307602
[[1]]
[1] 142.5592
[[2]]
[1] 0.3942074
[[1]]
[1] 1.856447
[[2]]
[1] 2.473242
[[1]]
[1] 0.3601547
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