Test of the correlations functions using the spectral approach
The gstlearn Team
2026-06-19
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 objects are masked from 'package:base':
##
## encodeString, messageR 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"
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## [1] "Performing a single simulation"
##
##
## Table: Mono-variate statistics for the EXPONENTIAL covariance
##
## | | Number| min| max| median| mean| sd|
## |:-----------|------:|-------:|------:|------:|------:|------:|
## |EXPONENTIAL | 40000| -3.5265| 3.6768| 0.1534| 0.1406| 1.0186|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
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## [1] ">>> Simulation #2"
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## [1] ">>> Simulation #3"
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##
##
## Table: Mono-variate statistics for the EXPONENTIAL covariance
##
## | | Number| min| max| median| mean| sd|
## |:--------------|------:|-------:|------:|-------:|-------:|------:|
## |EXPONENTIAL.S1 | 40000| -3.6851| 3.8189| 0.0724| 0.0811| 1.0067|
## |EXPONENTIAL.S2 | 40000| -3.3703| 3.7813| -0.1042| -0.0919| 0.9353|
## |EXPONENTIAL.S3 | 40000| -3.6851| 3.8189| 0.0724| 0.0811| 1.0067|
## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#1 = 0.0670"
##
## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#2 = 0.0720"
##
## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#3 = 0.0566"
##
## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#4 = 0.0508"
##
## [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"
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## [1] "Computing simulation in slice xOy"
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## [1] "Performing a single simulation"
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##
## Table: Mono-variate statistics for the GAUSSIAN covariance
##
## | | Number| min| max| median| mean| sd|
## |:--------|------:|-------:|------:|------:|------:|------:|
## |GAUSSIAN | 40000| -3.2946| 3.3665| 0.0465| 0.0068| 1.0248|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
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## [1] ">>> Simulation #2"
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## [1] ">>> Simulation #3"
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##
##
## Table: Mono-variate statistics for the GAUSSIAN covariance
##
## | | Number| min| max| median| mean| sd|
## |:-----------|------:|-------:|------:|-------:|-------:|------:|
## |GAUSSIAN.S1 | 40000| -3.2276| 2.8831| 0.0947| 0.0714| 0.9957|
## |GAUSSIAN.S2 | 40000| -3.4055| 2.8449| -0.0331| -0.0465| 0.9961|
## |GAUSSIAN.S3 | 40000| -3.2403| 2.8936| 0.0967| 0.0794| 0.9948|
## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#1 = 0.0342"
##
## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#2 = 0.0493"
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## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#3 = 0.0161"
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## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#4 = 0.0300"
##
## [1] "-------------------------------------------"
## [1] " End of test #2"
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## [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"
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## [1] "Computing simulation in slice xOy"
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## [1] "Performing a single simulation"
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##
## Table: Mono-variate statistics for the MATERN covariance
##
## | | Number| min| max| median| mean| sd|
## |:------|------:|-------:|------:|-------:|-------:|------:|
## |MATERN | 40000| -3.2587| 3.4717| -0.1828| -0.1608| 0.9814|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
##
## [1] ">>> Simulation #2"
##
## [1] ">>> Simulation #3"
##
##
##
## Table: Mono-variate statistics for the MATERN covariance
##
## | | Number| min| max| median| mean| sd|
## |:---------|------:|-------:|------:|------:|------:|------:|
## |MATERN.S1 | 40000| -3.5475| 3.6345| 0.2251| 0.2077| 1.0209|
## |MATERN.S2 | 40000| -3.3392| 3.5550| 0.0372| 0.0649| 0.9586|
## |MATERN.S3 | 40000| -3.5407| 3.6381| 0.2214| 0.2024| 1.0198|
## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#1 = 0.1064"
##
## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#2 = 0.0826"
##
## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#3 = 0.0405"
##
## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#4 = 0.0294"
##
## [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 | 40000| -3.0265| 2.3921| 0.1677| 0.1331| 0.9051|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
##
## [1] ">>> Simulation #2"
##
## [1] ">>> Simulation #3"
##
##
##
## Table: Mono-variate statistics for the CAUCHY covariance
##
## | | Number| min| max| median| mean| sd|
## |:---------|------:|-------:|------:|-------:|-------:|------:|
## |CAUCHY.S1 | 40000| -3.9045| 3.1264| -0.2841| -0.3331| 1.0257|
## |CAUCHY.S2 | 40000| -2.6804| 3.2965| 0.3245| 0.3031| 0.9496|
## |CAUCHY.S3 | 40000| -3.9180| 3.1168| -0.2845| -0.3331| 1.0238|
## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#1 = 0.0600"
##
## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#2 = 0.0730"
##
## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#3 = 0.0655"
##
## [1] "RMSE on vario CorAniso (ivar=1, jvar=1) in section xOy in dir#4 = 0.0732"
##
## [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 | 40000| -4.2943| 3.6633| -0.0233| -0.0266| 1.0175|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
##
## [1] ">>> Simulation #2"
##
## [1] ">>> Simulation #3"
##
##
##
## Table: Mono-variate statistics for the MATERN covariance
##
## | | Number| min| max| median| mean| sd|
## |:---------|------:|-------:|------:|-------:|-------:|------:|
## |MATERN.S1 | 40000| -3.6602| 3.7594| 0.0372| 0.0347| 1.0573|
## |MATERN.S2 | 40000| -3.7888| 3.3073| -0.0576| -0.0543| 0.9343|
## |MATERN.S3 | 40000| -3.6515| 3.7469| 0.0351| 0.0327| 1.0561|
## [1] "RMSE on vario CorMatern (ivar=1, jvar=1) in section xOy in dir#1 = 0.0580"
##
## [1] "RMSE on vario CorMatern (ivar=1, jvar=1) in section xOy in dir#2 = 0.1243"
##
## [1] "RMSE on vario CorMatern (ivar=1, jvar=1) in section xOy in dir#3 = 0.0535"
##
## [1] "RMSE on vario CorMatern (ivar=1, jvar=1) in section xOy in dir#4 = 0.0253"
##
## [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 | 40000| -4.3676| 3.6986| -0.0266| -0.0277| 1.0131|
## |MATERN.V2 | 40000| -3.9335| 3.5245| -0.0463| -0.0377| 0.9893|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
##
## [1] ">>> Simulation #2"
##
## [1] ">>> Simulation #3"
##
##
##
## Table: Mono-variate statistics for the MATERN covariance
##
## | | Number| min| max| median| mean| sd|
## |:------------|------:|-------:|------:|-------:|-------:|------:|
## |MATERN.V1.S1 | 40000| -3.7315| 3.9241| 0.0297| 0.0308| 1.0450|
## |MATERN.V2.S1 | 40000| -3.4231| 3.7255| 0.0688| 0.0650| 1.0541|
## |MATERN.V1.S2 | 40000| -3.8081| 3.2977| -0.0587| -0.0528| 0.9409|
## |MATERN.V2.S2 | 40000| -3.5115| 3.1140| -0.0734| -0.0716| 0.9169|
## |MATERN.V1.S3 | 40000| -3.7332| 3.9093| 0.0278| 0.0284| 1.0434|
## |MATERN.V2.S3 | 40000| -3.4225| 3.7192| 0.0686| 0.0635| 1.0533|
## [1] "RMSE on vario CorMatern (ivar=1, jvar=1) in section xOy in dir#1 = 0.0453"
##
## [1] "RMSE on vario CorMatern (ivar=1, jvar=1) in section xOy in dir#2 = 0.1173"
##
## [1] "RMSE on vario CorMatern (ivar=1, jvar=1) in section xOy in dir#3 = 0.0615"
##
## [1] "RMSE on vario CorMatern (ivar=1, jvar=1) in section xOy in dir#4 = 0.0349"
## [1] "RMSE on vario CorMatern (ivar=1, jvar=2) in section xOy in dir#1 = 0.0665"
##
## [1] "RMSE on vario CorMatern (ivar=1, jvar=2) in section xOy in dir#2 = 0.1350"
##
## [1] "RMSE on vario CorMatern (ivar=1, jvar=2) in section xOy in dir#3 = 0.0536"
##
## [1] "RMSE on vario CorMatern (ivar=1, jvar=2) in section xOy in dir#4 = 0.0303"
## [1] "RMSE on vario CorMatern (ivar=2, jvar=2) in section xOy in dir#1 = 0.0839"
##
## [1] "RMSE on vario CorMatern (ivar=2, jvar=2) in section xOy in dir#2 = 0.1560"
##
## [1] "RMSE on vario CorMatern (ivar=2, jvar=2) in section xOy in dir#3 = 0.0934"
##
## [1] "RMSE on vario CorMatern (ivar=2, jvar=2) in section xOy in dir#4 = 0.0212"
##
## [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 | 40000| -3.6871| 3.569| -0.037| -0.0095| 1.0103|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
##
## [1] ">>> Simulation #2"
##
## [1] ">>> Simulation #3"
##
##
##
## Table: Mono-variate statistics for the GAUSSIAN covariance
##
## | | Number| min| max| median| mean| sd|
## |:-----------|------:|-------:|------:|-------:|-------:|------:|
## |GAUSSIAN.S1 | 40000| -3.5445| 3.8243| -0.0607| -0.0709| 0.9957|
## |GAUSSIAN.S2 | 40000| -3.5364| 4.2514| 0.0466| 0.0198| 0.9939|
## |GAUSSIAN.S3 | 40000| -3.6894| 3.7950| 0.0699| 0.0580| 1.0395|
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#1 = 0.0202"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#2 = 0.0318"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#3 = 0.0688"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#4 = 0.0321"
##
## [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 | 40000| -3.6402| 3.9536| -0.0953| -0.0831| 1.0461|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
##
## [1] ">>> Simulation #2"
##
## [1] ">>> Simulation #3"
##
##
##
## Table: Mono-variate statistics for the MATERN covariance
##
## | | Number| min| max| median| mean| sd|
## |:---------|------:|-------:|------:|------:|------:|------:|
## |MATERN.S1 | 40000| -3.8092| 3.5508| 0.055| 0.0470| 0.9708|
## |MATERN.S2 | 40000| -3.3309| 3.2958| 0.034| 0.0158| 0.9493|
## |MATERN.S3 | 40000| -3.7741| 3.5488| 0.058| 0.0471| 0.9718|
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#1 = 0.0609"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#2 = 0.0554"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#3 = 0.0498"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#4 = 0.0966"
##
## [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 | 40000| -3.5801| 3.6364| 0.0023| 0.0038| 1.0024|
## |MATERN.V2 | 40000| -3.3768| 3.6633| -0.0125| -0.0041| 0.9426|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
##
## [1] ">>> Simulation #2"
##
## [1] ">>> Simulation #3"
##
##
##
## Table: Mono-variate statistics for the MATERN covariance
##
## | | Number| min| max| median| mean| sd|
## |:------------|------:|-------:|------:|-------:|-------:|------:|
## |MATERN.V1.S1 | 40000| -3.4219| 3.7114| 0.0252| 0.0198| 0.9701|
## |MATERN.V2.S1 | 40000| -3.6719| 3.9318| 0.1824| 0.1764| 0.9911|
## |MATERN.V1.S2 | 40000| -3.7777| 3.9847| -0.0310| -0.0425| 0.9745|
## |MATERN.V2.S2 | 40000| -3.9024| 4.4872| -0.2162| -0.2093| 1.0193|
## |MATERN.V1.S3 | 40000| -3.4907| 3.4895| 0.0308| 0.0186| 0.9584|
## |MATERN.V2.S3 | 40000| -3.6096| 3.8360| 0.1794| 0.1743| 0.9708|
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#1 = 0.0865"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#2 = 0.0791"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#3 = 0.0409"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#4 = 0.0175"
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=2) in section xOy in dir#1 = 0.0970"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=2) in section xOy in dir#2 = 0.0836"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=2) in section xOy in dir#3 = 0.0442"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=2) in section xOy in dir#4 = 0.0253"
## [1] "RMSE on vario CorGaussianMixture (ivar=2, jvar=2) in section xOy in dir#1 = 0.1422"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=2, jvar=2) in section xOy in dir#2 = 0.0787"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=2, jvar=2) in section xOy in dir#3 = 0.0430"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=2, jvar=2) in section xOy in dir#4 = 0.0680"
##
## [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 | 40000| -3.8273| 3.0178| -0.1194| -0.1037| 0.9575|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
##
## [1] ">>> Simulation #2"
##
## [1] ">>> Simulation #3"
##
##
##
## Table: Mono-variate statistics for the CAUCHY covariance
##
## | | Number| min| max| median| mean| sd|
## |:---------|------:|-------:|------:|------:|------:|------:|
## |CAUCHY.S1 | 40000| -3.1053| 4.3256| 0.2165| 0.2246| 1.0252|
## |CAUCHY.S2 | 40000| -3.3522| 4.0414| 0.1145| 0.1047| 1.0214|
## |CAUCHY.S3 | 40000| -3.1049| 4.3161| 0.2166| 0.2246| 1.0255|
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#1 = 0.0634"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#2 = 0.0644"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#3 = 0.0288"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#4 = 0.0593"
##
## [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 | 40000| -3.0690| 3.5484| -0.0158| -0.0030| 0.9292|
## |CAUCHY.V2 | 40000| -2.2295| 2.9123| 0.0323| 0.0763| 0.7615|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
##
## [1] ">>> Simulation #2"
##
## [1] ">>> Simulation #3"
##
##
##
## Table: Mono-variate statistics for the CAUCHY covariance
##
## | | Number| min| max| median| mean| sd|
## |:------------|------:|-------:|------:|-------:|-------:|------:|
## |CAUCHY.V1.S1 | 40000| -4.0932| 2.5034| -0.4682| -0.4825| 1.0107|
## |CAUCHY.V2.S1 | 40000| -3.8857| 2.3825| -1.0378| -1.0488| 0.9745|
## |CAUCHY.V1.S2 | 40000| -3.9565| 3.1529| -0.1223| -0.1278| 1.0936|
## |CAUCHY.V2.S2 | 40000| -3.9990| 2.8338| -0.2536| -0.2995| 1.2008|
## |CAUCHY.V1.S3 | 40000| -3.9734| 2.5081| -0.4625| -0.4777| 1.0056|
## |CAUCHY.V2.S3 | 40000| -3.8595| 2.3185| -1.0233| -1.0317| 0.9628|
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#1 = 0.0554"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#2 = 0.0994"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#3 = 0.0609"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=1) in section xOy in dir#4 = 0.0638"
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=2) in section xOy in dir#1 = 0.0608"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=2) in section xOy in dir#2 = 0.1439"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=2) in section xOy in dir#3 = 0.0834"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=1, jvar=2) in section xOy in dir#4 = 0.0523"
## [1] "RMSE on vario CorGaussianMixture (ivar=2, jvar=2) in section xOy in dir#1 = 0.0755"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=2, jvar=2) in section xOy in dir#2 = 0.1763"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=2, jvar=2) in section xOy in dir#3 = 0.0923"
##
## [1] "RMSE on vario CorGaussianMixture (ivar=2, jvar=2) in section xOy in dir#4 = 0.0615"
##
## [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 | 40000| -3.8438| 3.5949| 0.0853| 0.0549| 0.9787|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
##
## [1] ">>> Simulation #2"
##
## [1] ">>> Simulation #3"
##
##
##
## Table: Mono-variate statistics for the GNEITING_G covariance
##
## | | Number| min| max| median| mean| sd|
## |:-------------|------:|-------:|------:|-------:|-------:|------:|
## |GNEITING_G.S1 | 40000| -3.4214| 3.5357| -0.0092| -0.0099| 0.9998|
## |GNEITING_G.S2 | 40000| -4.5572| 3.2524| -0.1080| -0.0954| 0.9968|
## |GNEITING_G.S3 | 40000| -4.0711| 4.5462| -0.0298| -0.0701| 1.0115|
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#1 = 0.0383"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#2 = 0.0296"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#3 = 0.0230"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#4 = 0.0208"
##
## [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 | 40000| -4.0502| 3.8218| -0.0273| -0.0134| 0.9611|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
##
## [1] ">>> Simulation #2"
##
## [1] ">>> Simulation #3"
##
##
##
## Table: Mono-variate statistics for the GNEITING_M covariance
##
## | | Number| min| max| median| mean| sd|
## |:-------------|------:|-------:|------:|-------:|-------:|------:|
## |GNEITING_M.S1 | 40000| -4.3843| 3.9347| -0.0073| -0.0122| 1.0504|
## |GNEITING_M.S2 | 40000| -3.2397| 3.2566| -0.0420| -0.0325| 1.0096|
## |GNEITING_M.S3 | 40000| -4.4176| 3.9704| -0.0062| -0.0122| 1.0511|
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#1 = 0.0720"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#2 = 0.1136"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#3 = 0.0330"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#4 = 0.1020"
##
## [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 | 40000| -3.4077| 3.9103| -0.0797| -0.0574| 0.999|
## |GNEITING_M.V2 | 40000| -3.4113| 3.6434| -0.0584| -0.0420| 0.929|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
##
## [1] ">>> Simulation #2"
##
## [1] ">>> Simulation #3"
##
##
##
## Table: Mono-variate statistics for the GNEITING_M covariance
##
## | | Number| min| max| median| mean| sd|
## |:----------------|------:|-------:|------:|-------:|-------:|------:|
## |GNEITING_M.V1.S1 | 40000| -3.3747| 3.9455| 0.0165| 0.0523| 1.0010|
## |GNEITING_M.V2.S1 | 40000| -3.1653| 4.4624| 0.0186| 0.0512| 1.1117|
## |GNEITING_M.V1.S2 | 40000| -3.8160| 3.3330| -0.1048| -0.1048| 0.9453|
## |GNEITING_M.V2.S2 | 40000| -3.6629| 3.7265| -0.1353| -0.1059| 1.0308|
## |GNEITING_M.V1.S3 | 40000| -3.3713| 3.9695| 0.0288| 0.0526| 0.9959|
## |GNEITING_M.V2.S3 | 40000| -3.1335| 4.4163| 0.0346| 0.0519| 1.1014|
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#1 = 0.1017"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#2 = 0.0340"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#3 = 0.0308"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#4 = 0.0699"
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=2) in section xOt in dir#1 = 0.1035"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=2) in section xOt in dir#2 = 0.0279"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=2) in section xOt in dir#3 = 0.0248"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=2) in section xOt in dir#4 = 0.0578"
## [1] "RMSE on vario CorGneiting (ivar=2, jvar=2) in section xOt in dir#1 = 0.1418"
##
## [1] "RMSE on vario CorGneiting (ivar=2, jvar=2) in section xOt in dir#2 = 0.0427"
##
## [1] "RMSE on vario CorGneiting (ivar=2, jvar=2) in section xOt in dir#3 = 0.0189"
##
## [1] "RMSE on vario CorGneiting (ivar=2, jvar=2) in section xOt in dir#4 = 0.0469"
##
## [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 | 40000| -3.6667| 3.2427| -0.1693| -0.1665| 0.9843|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
##
## [1] ">>> Simulation #2"
##
## [1] ">>> Simulation #3"
##
##
##
## Table: Mono-variate statistics for the GNEITING_C covariance
##
## | | Number| min| max| median| mean| sd|
## |:-------------|------:|-------:|------:|------:|------:|------:|
## |GNEITING_C.S1 | 40000| -2.7863| 3.8441| 0.0630| 0.1075| 0.9416|
## |GNEITING_C.S2 | 40000| -2.9006| 3.2533| 0.0257| 0.0393| 0.9737|
## |GNEITING_C.S3 | 40000| -2.7654| 3.8123| 0.0663| 0.1075| 0.9429|
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#1 = 0.0941"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#2 = 0.0736"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#3 = 0.0940"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#4 = 0.0522"
##
## [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 | 40000| -4.2564| 2.9379| 0.0148| -0.0279| 1.0055|
## |GNEITING_C.V2 | 40000| -2.9447| 2.9704| 0.0874| 0.0924| 0.8735|
##
## [1] "Average variogram on various simulations"
##
## [1] ">>> Simulation #1"
##
## [1] ">>> Simulation #2"
##
## [1] ">>> Simulation #3"
##
##
##
## Table: Mono-variate statistics for the GNEITING_C covariance
##
## | | Number| min| max| median| mean| sd|
## |:----------------|------:|-------:|------:|-------:|-------:|------:|
## |GNEITING_C.V1.S1 | 40000| -3.7203| 3.7509| -0.1975| -0.1502| 1.1048|
## |GNEITING_C.V2.S1 | 40000| -3.2792| 3.4418| -0.2490| -0.1885| 1.0364|
## |GNEITING_C.V1.S2 | 40000| -4.3230| 2.9830| -0.2227| -0.2619| 0.9424|
## |GNEITING_C.V2.S2 | 40000| -2.9229| 2.7047| -0.3702| -0.3535| 0.8854|
## |GNEITING_C.V1.S3 | 40000| -3.9212| 3.8457| -0.1953| -0.1512| 1.0942|
## |GNEITING_C.V2.S3 | 40000| -3.2183| 3.4514| -0.2434| -0.1898| 1.0271|
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#1 = 0.0678"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#2 = 0.1294"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#3 = 0.0176"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=1) in section xOt in dir#4 = 0.0492"
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=2) in section xOt in dir#1 = 0.0422"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=2) in section xOt in dir#2 = 0.1015"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=2) in section xOt in dir#3 = 0.0144"
##
## [1] "RMSE on vario CorGneiting (ivar=1, jvar=2) in section xOt in dir#4 = 0.0297"
## [1] "RMSE on vario CorGneiting (ivar=2, jvar=2) in section xOt in dir#1 = 0.0210"
##
## [1] "RMSE on vario CorGneiting (ivar=2, jvar=2) in section xOt in dir#2 = 0.0607"
##
## [1] "RMSE on vario CorGneiting (ivar=2, jvar=2) in section xOt in dir#3 = 0.0377"
##
## [1] "RMSE on vario CorGneiting (ivar=2, jvar=2) in section xOt in dir#4 = 0.0504"
##
## [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.