Introduction

This script evaluates the following class of gstlearn:

The class CorAniso implements a univariate stationary covariance on \(\mathbb{R}^d\),
The class CorMatern implements the multivariate stationary Matern’s stationary covariance on \(\mathbb{R}^d\),
The class CorGaussianMixture implements the multivariate stationary Matern’s or Cauchy covariance on \(\mathbb{R}^d\),
The class CorGneiting implements the multivariate stationary covariance on \(\mathbb{R}^d \times \mathbb{R}\).

For all these covariances, the variance is equal to one and a geometrical anisotropy is defined on \(\mathbb{R}^d\) by a rotation and \(d\) scaling or range positive coefficients.

Four covariances functions are defined:

the EXPONENTIAL covariance: \(C(\boldsymbol{h}) = \exp(-\|\boldsymbol{h}\|)\),
the GAUSSIAN covariance: \(C(\boldsymbol{h}) = \exp(-\|\boldsymbol{h}\|^2)\),
the MATERN covariance: \(C(\boldsymbol{h}; \nu) = \frac{2^{1-\nu}}{\Gamma(\nu)} \|\boldsymbol{h}\|^\nu K_\nu(\|\boldsymbol{h}\|) = \mathcal{M}_{\nu}(\|\boldsymbol{h}\|)\),
the CAUCHY covariance: \(C(\boldsymbol{h}; \nu) = (1 + \|\boldsymbol{h}\|^2)^{-\nu} = \mathcal{C}_{\nu}(\|\boldsymbol{h}\|)\),
the CAUCHY_GEN covariance: \(C(\boldsymbol{h}; \alpha, \nu) = (1 + \|\boldsymbol{h}\|^\alpha)^{-\nu}\),
the GNEITING_G covariance: \(C((\boldsymbol{h}, u); \alpha, \beta, \kappa) = (1 + |\frac{u}{a_t}|^\alpha)^{-\beta\frac{d}{2}} \exp(-\frac{\|\kappa\boldsymbol{h}\|^2}{(1 + |\frac{u}{a_t}|^\alpha)^{\beta}})\),
the GNEITING_M covariance: \(C_{ij}((\boldsymbol{h}, u); \alpha, \beta, \boldsymbol{\nu}, \boldsymbol{\kappa}) = \tau_{ij} \, (1 + |\frac{u}{a_t}|^\alpha)^{-\beta\frac{d}{2}} \mathcal{M}_{\nu_{ij}}(\kappa_{ij}\, \frac{\|\boldsymbol{h}\|}{(1 + |\frac{u}{a_t}|^\alpha)^{\beta/2}})\), with

\(\nu_{ij} = (\nu_i + \nu_j)/2\),
\(\kappa_{ij} = \sqrt{(\kappa_i^2 + \kappa_j^2)/2}\),
\(\tau_{ij} = \frac{\Gamma(\nu_{ij})}{\sqrt{\Gamma(\nu_{i})\Gamma(\nu_{j})}}\, \frac{\kappa_{i}^{\nu_{i}}\kappa_{j}^{\nu_{j}}}{\kappa_{ij}^{2\nu_{ij}}}\)

the GNEITING_C covariance: \(C((\boldsymbol{h}, u); \alpha, \beta, \boldsymbol{\nu}, \boldsymbol{\kappa}) = \tau_{ij} \, (1 + |\frac{u}{a_t}|^\alpha)^{-\beta\frac{d}{2}} \mathcal{C}_{\nu_{ij}}(\kappa_{ij}\, \frac{\|\boldsymbol{h}\|}{(1 + |\frac{u}{a_t}|^\alpha)^{\beta/2}})\),

\(\nu_{ij} = (\nu_i + \nu_j)/2\),
\(\kappa_{ij} = 1/\sqrt{(1/\kappa_i^2 + 1/\kappa_j^2)/2}\),
\(\tau_{ij} = \frac{\Gamma(\nu_{ij})}{\sqrt{\Gamma(\nu_{i})\Gamma(\nu_{j})}}\, \frac{\kappa_{ij}^{2\nu_{ij}}}{\kappa_{i}^{\nu_{i}}\kappa_{j}^{\nu_{j}}}\)

In all cases,

\(\boldsymbol{h} \in \mathbb{R}^d\) is the increment,
\(\|\boldsymbol{h}\|\) is the norm of the increments defined by the geometrical anisotropy,
\(\boldsymbol{\nu} > 0\) are the shape parameters defined for each variable, and
\(\boldsymbol{\kappa} > 0\) are the scale/range parameters defined for each variable.

For the Gneiting’s models, the covariance trace in time is defined by

\(\alpha \in (0,2]\),
\(\beta \in (0,1]\), and
\(a_t > 0\) a scale/range parameter of the time increment.

## Loading required package: ggplot2

## Loading required package: ggpubr

## Loading required package: ggnewscale

## 
## Attaching package: 'gstlearn'

## The following object is masked from 'package:base':
## 
##     message

R functions

Auxiliary functions

Covariance models

Test of the models

## [1] " Begining of test #1:"
## 
## [1] " - Class CorAniso"
## 
## [1] " - Model EXPONENTIAL"
## 
## [1] " - Number of variables 1"
## 
## [1] "Creation of the model"
## [1] "Creating a EXPONENTIAL CovAniso model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 0.750000"
## [1] "Testing the covariance"

## [1] "Test in dir #1 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOy"
## 
## [1] "Performing a single simulation"

## 
## 
## Table: Mono-variate statistics for the EXPONENTIAL covariance
## 
## |                    | Number|     min|    max| median|   mean|     sd|
## |:-------------------|------:|-------:|------:|------:|------:|------:|
## |EXPONENTIAL.V1.simu |  40000| -3.8208| 3.5577| 0.0227| -0.005| 1.0899|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the EXPONENTIAL covariance
## 
## |                  | Number|     min|    max|  median|    mean|     sd|
## |:-----------------|------:|-------:|------:|-------:|-------:|------:|
## |EXPONENTIAL.V1.S1 |  40000| -3.7040| 3.2331| -0.3669| -0.3533| 0.9713|
## |EXPONENTIAL.V1.S2 |  40000| -3.3784| 4.1307| -0.0122|  0.0208| 0.9436|

## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#1 = 0.0542"
## 
## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#2 = 0.1175"
## 
## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#3 = 0.0262"
## 
## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#4 = 0.0358"
## 
## [1] "-------------------------------------------"
## [1] " End of test #1"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #2:"
## 
## [1] " - Class CorAniso"
## 
## [1] " - Model GAUSSIAN"
## 
## [1] " - Number of variables 1"
## 
## [1] "Creation of the model"
## [1] "Creating a GAUSSIAN CovAniso model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 0.750000"
## [1] "Testing the covariance"

## [1] "Test in dir #1 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOy"
## 
## [1] "Performing a single simulation"

## 
## 
## Table: Mono-variate statistics for the GAUSSIAN covariance
## 
## |                 | Number|    min|    max| median|   mean|     sd|
## |:----------------|------:|------:|------:|------:|------:|------:|
## |GAUSSIAN.V1.simu |  40000| -2.978| 3.3255| 0.1512| 0.1453| 0.9807|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the GAUSSIAN covariance
## 
## |               | Number|    min|    max| median|   mean|     sd|
## |:--------------|------:|------:|------:|------:|------:|------:|
## |GAUSSIAN.V1.S1 |  40000| -3.113| 2.7729| 0.0838| 0.0670| 0.9304|
## |GAUSSIAN.V1.S2 |  40000| -3.539| 3.2360| 0.0416| 0.0241| 0.9953|

## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#1 = 0.0224"
## 
## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#2 = 0.0837"
## 
## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#3 = 0.0541"
## 
## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#4 = 0.0706"
## 
## [1] "-------------------------------------------"
## [1] " End of test #2"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #3:"
## 
## [1] " - Class CorAniso"
## 
## [1] " - Model MATERN"
## 
## [1] " - Number of variables 1"
## 
## [1] "Creation of the model"
## [1] "Creating a MATERN CovAniso model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 0.750000"
## [1] "Testing the covariance"

## [1] "Test in dir #1 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOy"
## 
## [1] "Performing a single simulation"

## 
## 
## Table: Mono-variate statistics for the MATERN covariance
## 
## |               | Number|     min|    max| median|   mean|     sd|
## |:--------------|------:|-------:|------:|------:|------:|------:|
## |MATERN.V1.simu |  40000| -3.4472| 4.0174| 0.0563| 0.0528| 1.0359|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the MATERN covariance
## 
## |             | Number|     min|    max|  median|   mean|     sd|
## |:------------|------:|-------:|------:|-------:|------:|------:|
## |MATERN.V1.S1 |  40000| -3.4218| 3.8750| -0.0044| 0.0093| 0.9945|
## |MATERN.V1.S2 |  40000| -2.9123| 4.1179|  0.3677| 0.4080| 1.0136|

## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#1 = 0.0339"
## 
## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#2 = 0.0759"
## 
## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#3 = 0.0326"
## 
## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#4 = 0.0535"
## 
## [1] "-------------------------------------------"
## [1] " End of test #3"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #4:"
## 
## [1] " - Class CorAniso"
## 
## [1] " - Model CAUCHY"
## 
## [1] " - Number of variables 1"
## 
## [1] "Creation of the model"
## [1] "Creating a CAUCHY CovAniso model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 0.750000"
## [1] "Testing the covariance"

## [1] "Test in dir #1 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorAniso (Var-1, Var-1) in space: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOy"
## 
## [1] "Performing a single simulation"

## 
## 
## Table: Mono-variate statistics for the CAUCHY covariance
## 
## |               | Number|     min|    max|  median|    mean|    sd|
## |:--------------|------:|-------:|------:|-------:|-------:|-----:|
## |CAUCHY.V1.simu |  40000| -3.1883| 2.6597| -0.1184| -0.1289| 1.057|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the CAUCHY covariance
## 
## |             | Number|     min|    max|  median|    mean|     sd|
## |:------------|------:|-------:|------:|-------:|-------:|------:|
## |CAUCHY.V1.S1 |  40000| -2.8152| 3.3524|  0.3210|  0.3047| 0.9292|
## |CAUCHY.V1.S2 |  40000| -3.3313| 2.5612| -0.1455| -0.1347| 0.8178|

## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#1 = 0.1323"
## 
## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#2 = 0.1116"
## 
## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#3 = 0.0707"
## 
## [1] "RMSE on vario CovAniso (ivar=1, jvar=1) in section xOy in dir#4 = 0.0164"
## 
## [1] "-------------------------------------------"
## [1] " End of test #4"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #5:"
## 
## [1] " - Class CorMatern"
## 
## [1] " - Model MATERN"
## 
## [1] " - Number of variables 1"
## 
## [1] "Creation of the model"
## [1] "Testing the covariance"

## [1] "Test in dir #1 for CorMatern (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorMatern (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorMatern (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorMatern (Var-1, Var-1) in space: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOy"
## 
## [1] "Performing a single simulation"

## 
## 
## Table: Mono-variate statistics for the MATERN covariance
## 
## |               | Number|     min|    max| median|   mean|     sd|
## |:--------------|------:|-------:|------:|------:|------:|------:|
## |MATERN.V1.simu |  40000| -3.4472| 4.0174| 0.0563| 0.0528| 1.0359|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the MATERN covariance
## 
## |             | Number|     min|    max|  median|   mean|     sd|
## |:------------|------:|-------:|------:|-------:|------:|------:|
## |MATERN.V1.S1 |  40000| -3.4218| 3.8750| -0.0044| 0.0093| 0.9945|
## |MATERN.V1.S2 |  40000| -2.9123| 4.1179|  0.3677| 0.4080| 1.0136|

## [1] "RMSE on vario CovMatern (ivar=1, jvar=1) in section xOy in dir#1 = 0.1839"
## 
## [1] "RMSE on vario CovMatern (ivar=1, jvar=1) in section xOy in dir#2 = 0.1488"
## 
## [1] "RMSE on vario CovMatern (ivar=1, jvar=1) in section xOy in dir#3 = 0.2197"
## 
## [1] "RMSE on vario CovMatern (ivar=1, jvar=1) in section xOy in dir#4 = 0.1664"
## 
## [1] "-------------------------------------------"
## [1] " End of test #5"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #6:"
## 
## [1] " - Class CorMatern"
## 
## [1] " - Model MATERN"
## 
## [1] " - Number of variables 2"
## 
## [1] "Creation of the model"
## [1] "Testing the covariance"
## 
## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.75"
## [1] " - kappa[1] = 2.00"

## [1] "Test in dir #1 for CorMatern (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorMatern (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorMatern (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorMatern (Var-1, Var-1) in space: OK"
## 
## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 0.92"
## [1] " - nu[1]       = 0.62"
## [1] " - kappa[1] = 1.58"

## [1] "Test in dir #1 for CorMatern (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #2 for CorMatern (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #3 for CorMatern (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #4 for CorMatern (Var-1, Var-2) in space: OK"
## 
## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.50"
## [1] " - kappa[1] = 1.00"

## [1] "Test in dir #1 for CorMatern (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #2 for CorMatern (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #3 for CorMatern (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #4 for CorMatern (Var-2, Var-2) in space: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOy"
## 
## [1] "Performing a single simulation"
## 
## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.75"
## [1] " - kappa[1] = 2.00"

## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.50"
## [1] " - kappa[1] = 1.00"

## 
## 
## Table: Mono-variate statistics for the MATERN covariance
## 
## |               | Number|     min|    max|  median|    mean|     sd|
## |:--------------|------:|-------:|------:|-------:|-------:|------:|
## |MATERN.V1.simu |  40000| -3.7465| 5.4029| -0.0005|  0.0120| 1.0147|
## |MATERN.V2.simu |  40000| -3.7327| 4.7901| -0.1055| -0.1145| 0.9580|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the MATERN covariance
## 
## |             | Number|     min|    max|  median|    mean|     sd|
## |:------------|------:|-------:|------:|-------:|-------:|------:|
## |MATERN.V1.S1 |  40000| -3.3816| 3.9814|  0.1289|  0.1061| 1.0309|
## |MATERN.V2.S1 |  40000| -3.6748| 3.3949|  0.1724|  0.1418| 1.0237|
## |MATERN.V1.S2 |  40000| -3.6883| 3.6183| -0.0746| -0.0719| 1.0010|
## |MATERN.V2.S2 |  40000| -3.4307| 3.4111| -0.1066| -0.1220| 0.9913|

## [1] "RMSE on vario CovMatern (ivar=1, jvar=1) in section xOy in dir#1 = 0.0542"
## 
## [1] "RMSE on vario CovMatern (ivar=1, jvar=1) in section xOy in dir#2 = 0.0376"
## 
## [1] "RMSE on vario CovMatern (ivar=1, jvar=1) in section xOy in dir#3 = 0.0472"
## 
## [1] "RMSE on vario CovMatern (ivar=1, jvar=1) in section xOy in dir#4 = 0.0329"

## [1] "RMSE on vario CovMatern (ivar=1, jvar=2) in section xOy in dir#1 = 0.0509"
## 
## [1] "RMSE on vario CovMatern (ivar=1, jvar=2) in section xOy in dir#2 = 0.0360"
## 
## [1] "RMSE on vario CovMatern (ivar=1, jvar=2) in section xOy in dir#3 = 0.0528"
## 
## [1] "RMSE on vario CovMatern (ivar=1, jvar=2) in section xOy in dir#4 = 0.0303"

## [1] "RMSE on vario CovMatern (ivar=2, jvar=2) in section xOy in dir#1 = 0.0517"
## 
## [1] "RMSE on vario CovMatern (ivar=2, jvar=2) in section xOy in dir#2 = 0.0363"
## 
## [1] "RMSE on vario CovMatern (ivar=2, jvar=2) in section xOy in dir#3 = 0.0575"
## 
## [1] "RMSE on vario CovMatern (ivar=2, jvar=2) in section xOy in dir#4 = 0.0291"
## 
## [1] "-------------------------------------------"
## [1] " End of test #6"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #7:"
## 
## [1] " - Class CorGaussianMixture"
## 
## [1] " - Model GAUSSIAN"
## 
## [1] " - Number of variables 1"
## 
## [1] "Creation of the model"
## [1] "Testing the covariance"

## [1] "Test in dir #1 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOy"
## 
## [1] "Performing a single simulation"

## 
## 
## Table: Mono-variate statistics for the GAUSSIAN covariance
## 
## |                 | Number|     min|    max| median|   mean|     sd|
## |:----------------|------:|-------:|------:|------:|------:|------:|
## |GAUSSIAN.V1.simu |  40000| -3.8028| 3.7957| 0.0219| 0.0148| 1.0107|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the GAUSSIAN covariance
## 
## |               | Number|     min|    max|  median|    mean|     sd|
## |:--------------|------:|-------:|------:|-------:|-------:|------:|
## |GAUSSIAN.V1.S1 |  40000| -4.0302| 3.3128| -0.0079| -0.0391| 1.0454|
## |GAUSSIAN.V1.S2 |  40000| -3.5535| 3.7315|  0.0318|  0.0231| 0.9905|

## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#1 = 0.0570"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#2 = 0.0528"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#3 = 0.0384"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#4 = 0.0556"
## 
## [1] "-------------------------------------------"
## [1] " End of test #7"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #8:"
## 
## [1] " - Class CorGaussianMixture"
## 
## [1] " - Model MATERN"
## 
## [1] " - Number of variables 1"
## 
## [1] "Creation of the model"
## [1] "Testing the covariance"

## [1] "Test in dir #1 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOy"
## 
## [1] "Performing a single simulation"

## 
## 
## Table: Mono-variate statistics for the MATERN covariance
## 
## |               | Number|     min|    max|  median|    mean|     sd|
## |:--------------|------:|-------:|------:|-------:|-------:|------:|
## |MATERN.V1.simu |  40000| -4.0469| 3.5239| -0.0712| -0.0802| 0.9527|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the MATERN covariance
## 
## |             | Number|     min|    max|  median|    mean|     sd|
## |:------------|------:|-------:|------:|-------:|-------:|------:|
## |MATERN.V1.S1 |  40000| -3.8361| 3.7075| -0.0643| -0.0633| 0.9754|
## |MATERN.V1.S2 |  40000| -3.6909| 3.6477|  0.0076|  0.0261| 1.0391|

## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#1 = 0.0159"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#2 = 0.0426"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#3 = 0.0579"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#4 = 0.0418"
## 
## [1] "-------------------------------------------"
## [1] " End of test #8"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #9:"
## 
## [1] " - Class CorGaussianMixture"
## 
## [1] " - Model MATERN"
## 
## [1] " - Number of variables 2"
## 
## [1] "Creation of the model"
## [1] "Testing the covariance"
## 
## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.75"
## [1] " - kappa[1] = 2.00"

## [1] "Test in dir #1 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 0.92"
## [1] " - nu[1]       = 0.62"
## [1] " - kappa[1] = 1.58"

## [1] "Test in dir #1 for CorGaussianMixture (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #2 for CorGaussianMixture (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #3 for CorGaussianMixture (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #4 for CorGaussianMixture (Var-1, Var-2) in space: OK"
## 
## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.50"
## [1] " - kappa[1] = 1.00"

## [1] "Test in dir #1 for CorGaussianMixture (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #2 for CorGaussianMixture (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #3 for CorGaussianMixture (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #4 for CorGaussianMixture (Var-2, Var-2) in space: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOy"
## 
## [1] "Performing a single simulation"
## 
## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.75"
## [1] " - kappa[1] = 2.00"

## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.50"
## [1] " - kappa[1] = 1.00"

## 
## 
## Table: Mono-variate statistics for the MATERN covariance
## 
## |               | Number|     min|    max|  median|    mean|     sd|
## |:--------------|------:|-------:|------:|-------:|-------:|------:|
## |MATERN.V1.simu |  40000| -3.3341| 3.9293| -0.0398| -0.0342| 0.9883|
## |MATERN.V2.simu |  40000| -3.2664| 3.6578| -0.0410| -0.0457| 0.9284|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the MATERN covariance
## 
## |             | Number|     min|    max|  median|    mean|     sd|
## |:------------|------:|-------:|------:|-------:|-------:|------:|
## |MATERN.V1.S1 |  40000| -3.9276| 4.1286|  0.0439|  0.0177| 0.9853|
## |MATERN.V2.S1 |  40000| -3.3708| 4.5189|  0.2839|  0.2637| 0.9842|
## |MATERN.V1.S2 |  40000| -4.1792| 3.6839| -0.1308| -0.1231| 0.9819|
## |MATERN.V2.S2 |  40000| -3.6304| 3.0847| -0.1846| -0.1775| 0.8829|

## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#1 = 0.0462"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#2 = 0.0483"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#3 = 0.0189"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#4 = 0.0342"

## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=2) in section xOy in dir#1 = 0.0245"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=2) in section xOy in dir#2 = 0.0250"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=2) in section xOy in dir#3 = 0.0180"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=2) in section xOy in dir#4 = 0.0237"

## [1] "RMSE on vario GaussianMixture (ivar=2, jvar=2) in section xOy in dir#1 = 0.0625"
## 
## [1] "RMSE on vario GaussianMixture (ivar=2, jvar=2) in section xOy in dir#2 = 0.0667"
## 
## [1] "RMSE on vario GaussianMixture (ivar=2, jvar=2) in section xOy in dir#3 = 0.0396"
## 
## [1] "RMSE on vario GaussianMixture (ivar=2, jvar=2) in section xOy in dir#4 = 0.0253"
## 
## [1] "-------------------------------------------"
## [1] " End of test #9"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #10:"
## 
## [1] " - Class CorGaussianMixture"
## 
## [1] " - Model CAUCHY"
## 
## [1] " - Number of variables 1"
## 
## [1] "Creation of the model"
## [1] "Testing the covariance"

## [1] "Test in dir #1 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOy"
## 
## [1] "Performing a single simulation"

## 
## 
## Table: Mono-variate statistics for the CAUCHY covariance
## 
## |               | Number|     min|    max| median|   mean|     sd|
## |:--------------|------:|-------:|------:|------:|------:|------:|
## |CAUCHY.V1.simu |  40000| -3.4901| 4.2409| 0.2626| 0.2539| 0.9904|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the CAUCHY covariance
## 
## |             | Number|     min|    max|  median|    mean|     sd|
## |:------------|------:|-------:|------:|-------:|-------:|------:|
## |CAUCHY.V1.S1 |  40000| -4.0454| 3.7882|  0.0432|  0.0361| 1.0282|
## |CAUCHY.V1.S2 |  40000| -4.2616| 3.1227| -0.3615| -0.3534| 1.0166|

## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#1 = 0.0458"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#2 = 0.0533"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#3 = 0.0335"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#4 = 0.0904"
## 
## [1] "-------------------------------------------"
## [1] " End of test #10"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #11:"
## 
## [1] " - Class CorGaussianMixture"
## 
## [1] " - Model CAUCHY"
## 
## [1] " - Number of variables 2"
## 
## [1] "Creation of the model"
## [1] "Testing the covariance"
## 
## [1] "Creating a CAUCHY GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.75"
## [1] " - kappa[1] = 2.00"

## [1] "Test in dir #1 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorGaussianMixture (Var-1, Var-1) in space: OK"
## 
## [1] "Creating a CAUCHY GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 0.78"
## [1] " - nu[1]       = 0.62"
## [1] " - kappa[1] = 1.26"

## [1] "Test in dir #1 for CorGaussianMixture (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #2 for CorGaussianMixture (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #3 for CorGaussianMixture (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #4 for CorGaussianMixture (Var-1, Var-2) in space: OK"
## 
## [1] "Creating a CAUCHY GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.50"
## [1] " - kappa[1] = 1.00"

## [1] "Test in dir #1 for CorGaussianMixture (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #2 for CorGaussianMixture (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #3 for CorGaussianMixture (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #4 for CorGaussianMixture (Var-2, Var-2) in space: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOy"
## 
## [1] "Performing a single simulation"
## 
## [1] "Creating a CAUCHY GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.75"
## [1] " - kappa[1] = 2.00"

## [1] "Creating a CAUCHY GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.50"
## [1] " - kappa[1] = 1.00"

## 
## 
## Table: Mono-variate statistics for the CAUCHY covariance
## 
## |               | Number|     min|    max| median|   mean|     sd|
## |:--------------|------:|-------:|------:|------:|------:|------:|
## |CAUCHY.V1.simu |  40000| -3.0850| 3.9531| 0.0309| 0.0242| 0.9900|
## |CAUCHY.V2.simu |  40000| -2.5333| 3.2763| 0.2241| 0.2373| 0.9223|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the CAUCHY covariance
## 
## |             | Number|     min|    max| median|   mean|     sd|
## |:------------|------:|-------:|------:|------:|------:|------:|
## |CAUCHY.V1.S1 |  40000| -3.1840| 3.2165| 0.0763| 0.0638| 0.9417|
## |CAUCHY.V2.S1 |  40000| -2.3401| 2.7882| 0.1990| 0.1937| 0.9082|
## |CAUCHY.V1.S2 |  40000| -3.0323| 4.2058| 0.0959| 0.1115| 1.0051|
## |CAUCHY.V2.S2 |  40000| -2.0670| 3.5834| 0.4327| 0.5367| 0.9845|

## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#1 = 0.0603"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#2 = 0.0473"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#3 = 0.0595"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=1) in section xOy in dir#4 = 0.0526"

## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=2) in section xOy in dir#1 = 0.0413"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=2) in section xOy in dir#2 = 0.0303"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=2) in section xOy in dir#3 = 0.0334"
## 
## [1] "RMSE on vario GaussianMixture (ivar=1, jvar=2) in section xOy in dir#4 = 0.0249"

## [1] "RMSE on vario GaussianMixture (ivar=2, jvar=2) in section xOy in dir#1 = 0.0424"
## 
## [1] "RMSE on vario GaussianMixture (ivar=2, jvar=2) in section xOy in dir#2 = 0.0543"
## 
## [1] "RMSE on vario GaussianMixture (ivar=2, jvar=2) in section xOy in dir#3 = 0.0363"
## 
## [1] "RMSE on vario GaussianMixture (ivar=2, jvar=2) in section xOy in dir#4 = 0.0303"
## 
## [1] "-------------------------------------------"
## [1] " End of test #11"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #12:"
## 
## [1] " - Class CorGneiting"
## 
## [1] " - Model GNEITING_G"
## 
## [1] " - Number of variables 1"
## 
## [1] "Creation of the model"
## [1] "Creating a GAUSSIAN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 1.00"
## [1] " - kappa[1] = 2.00"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_G Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"
## [1] "Testing the covariance"

## [1] "Test in dir #1 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-1, Var-1) in space: OK"

## [1] "Test in dir #1 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOt"
## 
## [1] "Performing a single simulation"

## 
## 
## Table: Mono-variate statistics for the GNEITING_G covariance
## 
## |                   | Number|     min|    max| median|   mean|     sd|
## |:------------------|------:|-------:|------:|------:|------:|------:|
## |GNEITING_G.V1.simu |  40000| -3.4416| 3.4779| -0.014| -0.027| 0.9729|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the GNEITING_G covariance
## 
## |                 | Number|     min|    max|  median|    mean|     sd|
## |:----------------|------:|-------:|------:|-------:|-------:|------:|
## |GNEITING_G.V1.S1 |  40000| -3.7845| 3.3920| -0.0401| -0.0379| 1.0367|
## |GNEITING_G.V1.S2 |  40000| -3.6836| 3.6397|  0.0662|  0.0376| 1.0477|

## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#1 = 0.1058"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#2 = 0.1229"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#3 = 0.0809"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#4 = 0.1014"
## 
## [1] "-------------------------------------------"
## [1] " End of test #12"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #13:"
## 
## [1] " - Class CorGneiting"
## 
## [1] " - Model GNEITING_M"
## 
## [1] " - Number of variables 1"
## 
## [1] "Creation of the model"
## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.75"
## [1] " - kappa[1] = 2.00"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_M Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"
## [1] "Testing the covariance"

## [1] "Test in dir #1 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-1, Var-1) in space: OK"

## [1] "Test in dir #1 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOt"
## 
## [1] "Performing a single simulation"

## 
## 
## Table: Mono-variate statistics for the GNEITING_M covariance
## 
## |                   | Number|     min|   max|  median|    mean|     sd|
## |:------------------|------:|-------:|-----:|-------:|-------:|------:|
## |GNEITING_M.V1.simu |  40000| -3.9421| 3.338| -0.0452| -0.0534| 0.9799|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the GNEITING_M covariance
## 
## |                 | Number|     min|    max|  median|    mean|     sd|
## |:----------------|------:|-------:|------:|-------:|-------:|------:|
## |GNEITING_M.V1.S1 |  40000| -4.5821| 3.3619| -0.0523| -0.1095| 0.9815|
## |GNEITING_M.V1.S2 |  40000| -3.4529| 3.4247|  0.1999|  0.1705| 1.0156|

## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#1 = 0.0181"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#2 = 0.0468"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#3 = 0.0405"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#4 = 0.0411"
## 
## [1] "-------------------------------------------"
## [1] " End of test #13"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #14:"
## 
## [1] " - Class CorGneiting"
## 
## [1] " - Model GNEITING_M"
## 
## [1] " - Number of variables 2"
## 
## [1] "Creation of the model"
## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :2"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.75"
## [1] " - kappa[1] = 2.00"
## [1] " - variance[2] = 1.00"
## [1] " - nu[2]       = 0.50"
## [1] " - kappa[2] = 1.00"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_M Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :2"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"
## [1] "Testing the covariance"
## 
## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.75"
## [1] " - kappa[1] = 2.00"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_M Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"

## [1] "Test in dir #1 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-1, Var-1) in space: OK"

## [1] "Test in dir #1 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 0.92"
## [1] " - nu[1]       = 0.62"
## [1] " - kappa[1] = 1.58"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_M Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"

## [1] "Test in dir #1 for CorGneiting (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-1, Var-2) in space: OK"

## [1] "Test in dir #1 for CorGneiting (Var-1, Var-2) in space x time: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-1, Var-2) in space x time: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-1, Var-2) in space x time: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-1, Var-2) in space x time: OK"
## 
## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.50"
## [1] " - kappa[1] = 1.00"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_M Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"

## [1] "Test in dir #1 for CorGneiting (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-2, Var-2) in space: OK"

## [1] "Test in dir #1 for CorGneiting (Var-2, Var-2) in space x time: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-2, Var-2) in space x time: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-2, Var-2) in space x time: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-2, Var-2) in space x time: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOt"
## 
## [1] "Performing a single simulation"
## 
## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.75"
## [1] " - kappa[1] = 2.00"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_M Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"

## [1] "Creating a MATERN GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.50"
## [1] " - kappa[1] = 1.00"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_M Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"

## 
## 
## Table: Mono-variate statistics for the GNEITING_M covariance
## 
## |                   | Number|     min|    max|  median|    mean|     sd|
## |:------------------|------:|-------:|------:|-------:|-------:|------:|
## |GNEITING_M.V1.simu |  40000| -4.5066| 3.2087|  0.0344| -0.0134| 0.9854|
## |GNEITING_M.V2.simu |  40000| -4.3797| 2.9840| -0.0257| -0.0657| 0.9214|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the GNEITING_M covariance
## 
## |                 | Number|     min|    max|  median|    mean|     sd|
## |:----------------|------:|-------:|------:|-------:|-------:|------:|
## |GNEITING_M.V1.S1 |  40000| -3.6068| 3.3077| -0.0717| -0.1000| 1.0011|
## |GNEITING_M.V2.S1 |  40000| -3.5011| 3.1670| -0.0649| -0.0909| 0.9104|
## |GNEITING_M.V1.S2 |  40000| -4.7484| 2.8812| -0.3033| -0.3493| 1.0535|
## |GNEITING_M.V2.S2 |  40000| -4.4014| 2.8933| -0.2251| -0.2744| 1.0034|

## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#1 = 0.0684"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#2 = 0.0748"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#3 = 0.0796"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#4 = 0.1111"

## [1] "RMSE on vario CovGneiting (ivar=1, jvar=2) in section xOt in dir#1 = 0.0447"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=2) in section xOt in dir#2 = 0.0602"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=2) in section xOt in dir#3 = 0.0585"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=2) in section xOt in dir#4 = 0.0871"

## [1] "RMSE on vario CovGneiting (ivar=2, jvar=2) in section xOt in dir#1 = 0.0665"
## 
## [1] "RMSE on vario CovGneiting (ivar=2, jvar=2) in section xOt in dir#2 = 0.0561"
## 
## [1] "RMSE on vario CovGneiting (ivar=2, jvar=2) in section xOt in dir#3 = 0.0300"
## 
## [1] "RMSE on vario CovGneiting (ivar=2, jvar=2) in section xOt in dir#4 = 0.0163"
## 
## [1] "-------------------------------------------"
## [1] " End of test #14"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #15:"
## 
## [1] " - Class CorGneiting"
## 
## [1] " - Model GNEITING_C"
## 
## [1] " - Number of variables 1"
## 
## [1] "Creation of the model"
## [1] "Creating a CAUCHY GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.75"
## [1] " - kappa[1] = 2.00"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_C Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"
## [1] "Testing the covariance"

## [1] "Test in dir #1 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-1, Var-1) in space: OK"

## [1] "Test in dir #1 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOt"
## 
## [1] "Performing a single simulation"

## 
## 
## Table: Mono-variate statistics for the GNEITING_C covariance
## 
## |                   | Number|    min|    max| median|   mean|     sd|
## |:------------------|------:|------:|------:|------:|------:|------:|
## |GNEITING_C.V1.simu |  40000| -3.449| 4.2834| 0.0984| 0.0859| 1.0207|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the GNEITING_C covariance
## 
## |                 | Number|     min|    max| median|   mean|     sd|
## |:----------------|------:|-------:|------:|------:|------:|------:|
## |GNEITING_C.V1.S1 |  40000| -3.2153| 3.9169| 0.0419| 0.0834| 1.0088|
## |GNEITING_C.V1.S2 |  40000| -3.2986| 3.3912| 0.1095| 0.1480| 0.9957|

## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#1 = 0.0255"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#2 = 0.0575"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#3 = 0.0351"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#4 = 0.0246"
## 
## [1] "-------------------------------------------"
## [1] " End of test #15"
## 
## [1] "-------------------------------------------"
## [1] " Begining of test #16:"
## 
## [1] " - Class CorGneiting"
## 
## [1] " - Model GNEITING_C"
## 
## [1] " - Number of variables 2"
## 
## [1] "Creation of the model"
## [1] "Creating a CAUCHY GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :2"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.75"
## [1] " - kappa[1] = 2.00"
## [1] " - variance[2] = 1.00"
## [1] " - nu[2]       = 0.50"
## [1] " - kappa[2] = 1.00"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_C Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :2"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"
## [1] "Testing the covariance"
## 
## [1] "Creating a CAUCHY GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.75"
## [1] " - kappa[1] = 2.00"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_C Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"

## [1] "Test in dir #1 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-1, Var-1) in space: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-1, Var-1) in space: OK"

## [1] "Test in dir #1 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-1, Var-1) in space x time: OK"
## 
## [1] "Creating a CAUCHY GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 0.78"
## [1] " - nu[1]       = 0.62"
## [1] " - kappa[1] = 1.26"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_C Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"

## [1] "Test in dir #1 for CorGneiting (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-1, Var-2) in space: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-1, Var-2) in space: OK"

## [1] "Test in dir #1 for CorGneiting (Var-1, Var-2) in space x time: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-1, Var-2) in space x time: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-1, Var-2) in space x time: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-1, Var-2) in space x time: OK"
## 
## [1] "Creating a CAUCHY GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.50"
## [1] " - kappa[1] = 1.00"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_C Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"

## [1] "Test in dir #1 for CorGneiting (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-2, Var-2) in space: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-2, Var-2) in space: OK"

## [1] "Test in dir #1 for CorGneiting (Var-2, Var-2) in space x time: OK"
## 
## [1] "Test in dir #2 for CorGneiting (Var-2, Var-2) in space x time: OK"
## 
## [1] "Test in dir #3 for CorGneiting (Var-2, Var-2) in space x time: OK"
## 
## [1] "Test in dir #4 for CorGneiting (Var-2, Var-2) in space x time: OK"
## 
## [1] "Defining the 2d slice"
## 
## [1] "Computing simulation in slice xOt"
## 
## [1] "Performing a single simulation"
## 
## [1] "Creating a CAUCHY GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.75"
## [1] " - kappa[1] = 2.00"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_C Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"

## [1] "Creating a CAUCHY GaussianMixture model:"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - variance[1] = 1.00"
## [1] " - nu[1]       = 0.50"
## [1] " - kappa[1] = 1.00"
## [1] "Creating a CAUCHY_GEN CovAniso model:"
## [1] " - dimension of the space :1"
## [1] " - number of variables    :1"
## [1] " - variance               :1"
## [1] " - param[1] = 2.000000"
## [1] " - param[2] = 1.000000"
## [1] "Creating a space-time GNEITING_C Gneiting model:"
## [1] " - dimension of the model :3"
## [1] " - dimension of the space :2"
## [1] " - number of variables    :1"
## [1] " - alpha                  :2"
## [1] " - beta                   :1"
## [1] " - a_t                    :1"

## 
## 
## Table: Mono-variate statistics for the GNEITING_C covariance
## 
## |                   | Number|     min|    max| median|   mean|     sd|
## |:------------------|------:|-------:|------:|------:|------:|------:|
## |GNEITING_C.V1.simu |  40000| -3.3794| 3.2065| 0.0704| 0.0439| 0.9987|
## |GNEITING_C.V2.simu |  40000| -3.0400| 3.0430| 0.0319| 0.0325| 0.9523|
## 
## [1] "Average variogram on various simulations"
## 
## [1] ">>> Simulation #1"
## 
## [1] ">>> Simulation #2"
## 
## 
## 
## Table: Mono-variate statistics for the GNEITING_C covariance
## 
## |                 | Number|     min|    max|  median|    mean|     sd|
## |:----------------|------:|-------:|------:|-------:|-------:|------:|
## |GNEITING_C.V1.S1 |  40000| -3.4795| 3.6312|  0.0337|  0.0116| 1.0572|
## |GNEITING_C.V2.S1 |  40000| -3.3723| 3.2335|  0.0678|  0.0434| 1.0886|
## |GNEITING_C.V1.S2 |  40000| -3.9741| 3.2471| -0.5086| -0.5352| 1.0648|
## |GNEITING_C.V2.S2 |  40000| -3.2454| 2.3347| -0.5096| -0.5092| 0.8949|

## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#1 = 0.1091"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#2 = 0.1038"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#3 = 0.0942"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=1) in section xOt in dir#4 = 0.0834"

## [1] "RMSE on vario CovGneiting (ivar=1, jvar=2) in section xOt in dir#1 = 0.1097"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=2) in section xOt in dir#2 = 0.0728"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=2) in section xOt in dir#3 = 0.0770"
## 
## [1] "RMSE on vario CovGneiting (ivar=1, jvar=2) in section xOt in dir#4 = 0.0950"

## [1] "RMSE on vario CovGneiting (ivar=2, jvar=2) in section xOt in dir#1 = 0.0938"
## 
## [1] "RMSE on vario CovGneiting (ivar=2, jvar=2) in section xOt in dir#2 = 0.0329"
## 
## [1] "RMSE on vario CovGneiting (ivar=2, jvar=2) in section xOt in dir#3 = 0.0352"
## 
## [1] "RMSE on vario CovGneiting (ivar=2, jvar=2) in section xOt in dir#4 = 0.0620"
## 
## [1] "-------------------------------------------"
## [1] " End of test #16"
## 
## [1] "-------------------------------------------"

References

Allard, D., Benoit, L., and Obakrim, S. (2025). Modeling and simulating spatio-temporal, multivariate and nonstationary Gaussian Random Fields: a Gaussian mixtures perspective.

Test of the correlations functions using the spectral approach

The gstlearn Team

2026-01-23