Spectral simulation of random functions on \(R^2\)
gstlearn Core Team
2026-03-19
Initialization
Using the API defined by gstlearn.
nsim = 20
ns = 5000
# target grid in 2d
ndim = 2
dx = c(0.5, 0.5, 0.5)[1:ndim]
nx = c(100, 100, 100)[1:ndim]
grid = DbGrid_create(nx = nx, dx = dx)2d univariate (CorAniso)
idx = 3
type = c("EXPONENTIAL", "GAUSSIAN", "MATERN")[idx]
nvar = 1
# parameters for the space trace
nu = c(NA, NA, 3/4)[idx]
# space anisotropy
timeRange = 2.0
ranges = c(5,10)[1:ndim]
angles = c(30, 0)[1:ndim]
# covariance model
ctxt = CovContext(nvar = nvar, space = SpaceRN_create(ndim))
mod = CorAniso_create(ctxt = ctxt, type = ECov_fromKey(type),
params = nu,
ranges = ranges, angles = angles,
flagRange = FALSE)
err = draw_model(model = mod, prefix = type)
# simulation using "gstlearn API"
model = ModelGeneric(ctxt = ctxt)
err = model$setCov(mod)
err = simuSpectral(dbin = NULL, dbout = grid, model = model, nbsimu = nsim, ns = ns,
verbose = flag.verbose,
namconv = NamingConvention(type))
# QC
res = QC_section (model = model$getCov(), grid = grid, prefix = type, nsimu = nsim, isec = 1,
flag.histo = TRUE, flag.map = TRUE, flag.vario = TRUE,
verbose = flag.verbose)
knitr::kable(res$tab , digits = 3, caption = sprintf("Statistics for %s", res$prefix))| Number | Minimum | Maximum | Mean | St. Dev. | |
|---|---|---|---|---|---|
| MATERN.S1 | 10000 | -2.509 | 2.836 | -0.003 | 0.913 |
| MATERN.S2 | 10000 | -2.752 | 2.891 | -0.020 | 0.793 |
| MATERN.S3 | 10000 | -2.513 | 2.849 | 0.000 | 0.916 |
| MATERN.S4 | 10000 | -2.752 | 2.891 | -0.020 | 0.793 |
| MATERN.S5 | 10000 | -2.496 | 2.821 | -0.001 | 0.907 |
| MATERN.S6 | 10000 | -2.752 | 2.891 | -0.020 | 0.793 |
| MATERN.S7 | 10000 | -2.765 | 3.366 | 0.473 | 1.058 |
| MATERN.S8 | 10000 | -2.714 | 2.619 | 0.017 | 0.824 |
| MATERN.S9 | 10000 | -2.765 | 3.366 | 0.473 | 1.058 |
| MATERN.S10 | 10000 | -2.715 | 2.605 | 0.023 | 0.823 |
| MATERN.S11 | 10000 | -2.819 | 3.405 | 0.472 | 1.077 |
| MATERN.S12 | 10000 | -2.738 | 2.616 | 0.016 | 0.829 |
| MATERN.S13 | 10000 | -2.729 | 3.250 | 0.466 | 1.051 |
| MATERN.S14 | 10000 | -2.334 | 2.467 | 0.227 | 0.862 |
| MATERN.S15 | 10000 | -3.453 | 2.022 | -0.497 | 0.912 |
| MATERN.S16 | 10000 | -2.334 | 2.467 | 0.227 | 0.862 |
| MATERN.S17 | 10000 | -3.463 | 2.032 | -0.498 | 0.916 |
| MATERN.S18 | 10000 | -2.334 | 2.467 | 0.227 | 0.862 |
| MATERN.S19 | 10000 | -3.438 | 2.072 | -0.493 | 0.910 |
| MATERN.S20 | 10000 | -2.334 | 2.467 | 0.227 | 0.862 |
Factorized covariance in 2d
type = "Fac2d_exp_gauss"
ctxt1d = CovContext(nvar = 1, space = SpaceRN_create(1))
ctxt2d = CovContext(nvar = 1, space = SpaceRN_create(2))
mod = CorFactorized_create(ctxt = ctxt2d)
# first factor: exponential covariance along Ox
err = mod$addFactor(
CorAniso_create(ctxt = ctxt1d, type = ECov_fromKey("EXPONENTIAL"),
params = NULL, ranges = 5.0, flagRange = FALSE),
proj = matToGst(matrix(c(1,0), 2, 1))
)
# Second factor: gaussian covariance along Oy
err = mod$addFactor(
CorAniso_create(ctxt = ctxt1d, type = ECov_fromKey("GAUSSIAN"),
params = NULL, ranges = 5.0, flagRange = FALSE),
proj = matToGst(matrix(c(0,1), 2, 1))
)
err = draw_model(model = mod, prefix = type)
# simulation using "gstlearn API"
model = ModelGeneric(ctxt = ctxt)
err = model$setCov(mod)
err = simuSpectral(dbin = NULL, dbout = grid, model = model, nbsimu = nsim, ns = ns,
verbose = flag.verbose,
namconv = NamingConvention(type))
# QC
res = QC_section (model = model$getCov(), grid = grid, prefix = type, nsimu = nsim, isec = 1,
flag.histo = TRUE, flag.map = TRUE, flag.vario = TRUE,
verbose = flag.verbose)
knitr::kable(res$tab , digits = 3, caption = sprintf("Statistics for %s", res$prefix))| Number | Minimum | Maximum | Mean | St. Dev. | |
|---|---|---|---|---|---|
| Fac2d_exp_gauss.S1 | 10000 | -2.686 | 3.220 | 0.212 | 0.968 |
| Fac2d_exp_gauss.S2 | 10000 | -3.240 | 2.992 | -0.119 | 1.090 |
| Fac2d_exp_gauss.S3 | 10000 | -2.686 | 3.220 | 0.212 | 0.968 |
| Fac2d_exp_gauss.S4 | 10000 | -2.722 | 3.012 | 0.120 | 0.923 |
| Fac2d_exp_gauss.S5 | 10000 | -2.687 | 3.223 | 0.212 | 0.969 |
| Fac2d_exp_gauss.S6 | 10000 | -2.722 | 3.012 | 0.120 | 0.923 |
| Fac2d_exp_gauss.S7 | 10000 | -3.413 | 3.277 | 0.152 | 0.939 |
| Fac2d_exp_gauss.S8 | 10000 | -2.721 | 3.011 | 0.120 | 0.923 |
| Fac2d_exp_gauss.S9 | 10000 | -3.413 | 3.277 | 0.152 | 0.939 |
| Fac2d_exp_gauss.S10 | 10000 | -2.934 | 3.450 | -0.037 | 0.956 |
| Fac2d_exp_gauss.S11 | 10000 | -3.358 | 3.277 | 0.152 | 0.936 |
| Fac2d_exp_gauss.S12 | 10000 | -2.917 | 3.493 | -0.038 | 0.957 |
| Fac2d_exp_gauss.S13 | 10000 | -2.728 | 4.224 | 0.291 | 0.949 |
| Fac2d_exp_gauss.S14 | 10000 | -3.115 | 2.410 | -0.179 | 0.887 |
| Fac2d_exp_gauss.S15 | 10000 | -2.728 | 4.224 | 0.291 | 0.949 |
| Fac2d_exp_gauss.S16 | 10000 | -3.115 | 2.410 | -0.179 | 0.887 |
| Fac2d_exp_gauss.S17 | 10000 | -3.087 | 3.699 | -0.036 | 0.951 |
| Fac2d_exp_gauss.S18 | 10000 | -3.115 | 2.410 | -0.179 | 0.887 |
| Fac2d_exp_gauss.S19 | 10000 | -3.088 | 3.698 | -0.036 | 0.951 |
| Fac2d_exp_gauss.S20 | 10000 | -3.104 | 2.415 | -0.179 | 0.886 |
2d trivariate matern
type = "MATERN"
nsim = 13
ctxt = CovContext(nvar = 3, space = SpaceRN_create(2))
mod = CorGaussianMixture_create(ctxt = ctxt, type = ECov_fromKey(type),
params = c(3/4, 1.0, 1/2), kappas = c(1,1, 1/2),
ranges = c(2,4), angles = c(30,0),
flagRange = FALSE)
err = draw_model(model = mod, prefix = type)
# simulation using "gstlearn API"
model = ModelGeneric(ctxt = ctxt)
err = model$setCov(mod)
err = grid$deleteColumns(names = paste(type, "*", sep = "."))
err = simuSpectral(dbin = NULL, dbout = grid, model = model, nbsimu = nsim, ns = ns,
verbose = flag.verbose,
namconv = NamingConvention(type))
res = QC_section (model = model$getCov(), grid = grid, prefix = type, nsimu = nsim, isec = 1,
flag.histo = TRUE, flag.map = TRUE, flag.vario = TRUE,
verbose = flag.verbose)
knitr::kable(res$tab , digits = 3, caption = sprintf("Statistics for %s", res$prefix))| Number | Minimum | Maximum | Mean | St. Dev. | |
|---|---|---|---|---|---|
| MATERN.V1.S1 | 10000 | -4.337 | 3.497 | -0.135 | 1.093 |
| MATERN.V1.S2 | 10000 | -3.716 | 3.569 | 0.207 | 1.057 |
| MATERN.V1.S3 | 10000 | -4.266 | 3.518 | -0.139 | 1.090 |
| MATERN.V1.S4 | 10000 | -3.744 | 3.559 | 0.208 | 1.056 |
| MATERN.V1.S5 | 10000 | -4.262 | 3.511 | -0.139 | 1.090 |
| MATERN.V1.S6 | 10000 | -3.504 | 3.223 | -0.085 | 0.935 |
| MATERN.V1.S7 | 10000 | -4.227 | 3.498 | -0.139 | 1.088 |
| MATERN.V1.S8 | 10000 | -3.500 | 3.228 | -0.085 | 0.935 |
| MATERN.V1.S9 | 10000 | -4.228 | 3.534 | -0.139 | 1.088 |
| MATERN.V1.S10 | 10000 | -3.485 | 3.223 | -0.087 | 0.935 |
| MATERN.V1.S11 | 10000 | -4.247 | 3.537 | -0.139 | 1.090 |
| MATERN.V1.S12 | 10000 | -3.441 | 3.180 | -0.090 | 0.934 |
| MATERN.V1.S13 | 10000 | -3.187 | 3.408 | -0.142 | 1.084 |
| MATERN.V2.S1 | 10000 | -4.039 | 3.242 | -0.140 | 1.125 |
| MATERN.V2.S2 | 10000 | -3.769 | 3.299 | 0.233 | 1.033 |
| MATERN.V2.S3 | 10000 | -3.963 | 3.256 | -0.146 | 1.122 |
| MATERN.V2.S4 | 10000 | -3.791 | 3.283 | 0.234 | 1.033 |
| MATERN.V2.S5 | 10000 | -3.958 | 3.249 | -0.146 | 1.122 |
| MATERN.V2.S6 | 10000 | -3.379 | 3.197 | -0.056 | 0.919 |
| MATERN.V2.S7 | 10000 | -3.921 | 3.237 | -0.145 | 1.119 |
| MATERN.V2.S8 | 10000 | -3.375 | 3.202 | -0.056 | 0.919 |
| MATERN.V2.S9 | 10000 | -3.918 | 3.272 | -0.146 | 1.118 |
| MATERN.V2.S10 | 10000 | -3.361 | 3.197 | -0.057 | 0.919 |
| MATERN.V2.S11 | 10000 | -3.940 | 3.278 | -0.146 | 1.120 |
| MATERN.V2.S12 | 10000 | -3.304 | 3.125 | -0.061 | 0.918 |
| MATERN.V2.S13 | 10000 | -3.071 | 3.191 | -0.165 | 1.112 |
| MATERN.V3.S1 | 10000 | -4.112 | 3.972 | -0.026 | 1.131 |
| MATERN.V3.S2 | 10000 | -3.513 | 3.575 | 0.267 | 0.954 |
| MATERN.V3.S3 | 10000 | -4.031 | 3.980 | -0.033 | 1.125 |
| MATERN.V3.S4 | 10000 | -3.531 | 3.569 | 0.268 | 0.955 |
| MATERN.V3.S5 | 10000 | -4.036 | 3.975 | -0.033 | 1.125 |
| MATERN.V3.S6 | 10000 | -2.571 | 3.411 | 0.483 | 0.927 |
| MATERN.V3.S7 | 10000 | -4.046 | 3.967 | -0.032 | 1.123 |
| MATERN.V3.S8 | 10000 | -2.568 | 3.415 | 0.483 | 0.927 |
| MATERN.V3.S9 | 10000 | -4.028 | 3.998 | -0.032 | 1.123 |
| MATERN.V3.S10 | 10000 | -2.556 | 3.411 | 0.482 | 0.927 |
| MATERN.V3.S11 | 10000 | -4.057 | 4.000 | -0.032 | 1.124 |
| MATERN.V3.S12 | 10000 | -2.545 | 3.348 | 0.476 | 0.925 |
| MATERN.V3.S13 | 10000 | -3.162 | 3.577 | -0.079 | 1.144 |
1d gneiting
nsim = 17
# TEST of separability
type = c("GNEITING_G", "GNEITING_M", "GNEITING_C")[3]
ndim = 1
nvar = 1
sep = 1/2
# parameters for the time trace
alpha = 2.0
beta = 1.0
# parameters for the space trace
nu = c(1/2, 3/4, 1)[1:nvar]
rr = c(1, 2, 1)[1:nvar]
# space-time anisotropy
timeRange = 2.0
ranges = c(5,10)[1:ndim]
angles = c(30, 0)[1:ndim]
ctxt = CovContext(nvar = nvar, space = SpaceRN_create(ndim = ndim))
mod = CorGneiting_create(ctxt = ctxt, type = ECov_fromKey(type),
alpha = alpha, beta = beta, timeRange = timeRange,
params = nu, kappas = rr,
ranges = ranges, angles = angles,
flagRange = FALSE,
separability = sep)
err = draw_model(model = mod, prefix = type, flag.st = TRUE)
# simulation using "gstlearn API"
model = ModelGeneric(ctxt = ctxt)
err = model$setCov(mod)
# creation of a 2D x Time grid: section xOt
nx = c(100, 100)
dx = c(0.5, 0.5)
grid = DbGrid_create(nx = nx, dx = dx)
err = simuSpectral(dbin = NULL, dbout = grid, model = model, nbsimu = nsim, ns = ns,
verbose = flag.verbose,
namconv = NamingConvention(type))
res = QC_section (model = model$getCov(),
grid = grid, prefix = type, nsimu = nsim, isec = 2,
flag.histo = TRUE, flag.map = TRUE, flag.vario = TRUE,
verbose = flag.verbose, flag.st = TRUE)
# printing the statistics
knitr::kable(res$tab , digits = 3, caption = sprintf("Statistics for %s", res$prefix))| Number | Minimum | Maximum | Mean | St. Dev. | |
|---|---|---|---|---|---|
| GNEITING_C.S1 | 10000 | -3.388 | 2.979 | 0.292 | 0.925 |
| GNEITING_C.S2 | 10000 | -1.774 | 2.887 | 0.503 | 0.876 |
| GNEITING_C.S3 | 10000 | -3.395 | 2.973 | 0.288 | 0.924 |
| GNEITING_C.S4 | 10000 | -2.167 | 3.028 | 0.511 | 0.857 |
| GNEITING_C.S5 | 10000 | -3.392 | 2.972 | 0.288 | 0.925 |
| GNEITING_C.S6 | 10000 | -1.673 | 3.019 | 0.499 | 0.880 |
| GNEITING_C.S7 | 10000 | -3.193 | 2.454 | -0.531 | 0.888 |
| GNEITING_C.S8 | 10000 | -1.672 | 3.016 | 0.499 | 0.879 |
| GNEITING_C.S9 | 10000 | -3.184 | 2.449 | -0.535 | 0.888 |
| GNEITING_C.S10 | 10000 | -2.337 | 2.991 | 0.515 | 0.889 |
| GNEITING_C.S11 | 10000 | -2.986 | 2.178 | -0.506 | 0.919 |
| GNEITING_C.S12 | 10000 | -3.065 | 3.772 | 0.437 | 0.968 |
| GNEITING_C.S13 | 10000 | -3.005 | 2.214 | -0.505 | 0.930 |
| GNEITING_C.S14 | 10000 | -3.065 | 3.772 | 0.437 | 0.968 |
| GNEITING_C.S15 | 10000 | -3.009 | 2.219 | -0.505 | 0.930 |
| GNEITING_C.S16 | 10000 | -3.051 | 3.816 | 0.452 | 0.972 |
| GNEITING_C.S17 | 10000 | -3.011 | 2.221 | -0.505 | 0.930 |
nsim = 17
# TEST of separability
type = c("GNEITING_G", "GNEITING_M", "GNEITING_C")[2]
ndim = 1
nvar = 2
sep = 0
# parameters for the time trace
alpha = 2.0
beta = 1.0
# parameters for the space trace
nu = c(1/2, 3/4, 1)[1:nvar]
rr = c(1, 2, 1)[1:nvar]
# space-time anisotropy
timeRange = 2.0
ranges = c(5,10)[1:ndim]
angles = c(30, 0)[1:ndim]
ctxt = CovContext(nvar = nvar, space = SpaceRN_create(ndim = ndim))
mod = CorGneiting_create(ctxt = ctxt, type = ECov_fromKey(type),
alpha = alpha, beta = beta, timeRange = timeRange,
params = nu, kappas = rr,
ranges = ranges, angles = angles,
flagRange = FALSE,
separability = sep)
err = draw_model(model = mod, prefix = type, flag.st = TRUE)
# simulation using "gstlearn API"
model = ModelGeneric(ctxt = ctxt)
err = model$setCov(mod)
# creation of a 2D x Time grid: section xOt
nx = c(100, 100)
dx = c(0.5, 0.5)
grid = DbGrid_create(nx = nx, dx = dx)
err = simuSpectral(dbin = NULL, dbout = grid, model = model, nbsimu = nsim, ns = ns,
verbose = flag.verbose,
namconv = NamingConvention(type))
res = QC_section (model = model$getCov(),
grid = grid, prefix = type, nsimu = nsim, isec = 2,
flag.histo = TRUE, flag.map = TRUE, flag.vario = TRUE,
verbose = flag.verbose, flag.st = TRUE)
# printing the statistics
knitr::kable(res$tab , digits = 3, caption = sprintf("Statistics for %s", res$prefix))| Number | Minimum | Maximum | Mean | St. Dev. | |
|---|---|---|---|---|---|
| GNEITING_M.V1.S1 | 10000 | -2.853 | 2.972 | 0.104 | 0.916 |
| GNEITING_M.V1.S2 | 10000 | -2.870 | 2.960 | 0.002 | 0.973 |
| GNEITING_M.V1.S3 | 10000 | -2.883 | 2.989 | 0.108 | 0.917 |
| GNEITING_M.V1.S4 | 10000 | -2.891 | 2.944 | 0.005 | 0.972 |
| GNEITING_M.V1.S5 | 10000 | -2.876 | 2.990 | 0.108 | 0.917 |
| GNEITING_M.V1.S6 | 10000 | -2.886 | 2.954 | 0.008 | 0.975 |
| GNEITING_M.V1.S7 | 10000 | -3.282 | 3.199 | 0.201 | 0.933 |
| GNEITING_M.V1.S8 | 10000 | -2.887 | 2.952 | 0.008 | 0.975 |
| GNEITING_M.V1.S9 | 10000 | -3.280 | 3.201 | 0.201 | 0.933 |
| GNEITING_M.V1.S10 | 10000 | -2.889 | 2.939 | 0.009 | 0.976 |
| GNEITING_M.V1.S11 | 10000 | -3.347 | 3.304 | 0.202 | 0.936 |
| GNEITING_M.V1.S12 | 10000 | -3.636 | 2.469 | -0.199 | 0.876 |
| GNEITING_M.V1.S13 | 10000 | -3.325 | 3.223 | 0.200 | 0.934 |
| GNEITING_M.V1.S14 | 10000 | -3.627 | 2.477 | -0.199 | 0.875 |
| GNEITING_M.V1.S15 | 10000 | -3.326 | 3.219 | 0.201 | 0.934 |
| GNEITING_M.V1.S16 | 10000 | -3.632 | 2.521 | -0.195 | 0.879 |
| GNEITING_M.V1.S17 | 10000 | -3.326 | 3.217 | 0.201 | 0.934 |
| GNEITING_M.V2.S1 | 10000 | -3.468 | 3.038 | 0.071 | 0.972 |
| GNEITING_M.V2.S2 | 10000 | -2.993 | 3.057 | -0.034 | 0.989 |
| GNEITING_M.V2.S3 | 10000 | -3.447 | 3.041 | 0.076 | 0.972 |
| GNEITING_M.V2.S4 | 10000 | -2.959 | 3.046 | -0.032 | 0.987 |
| GNEITING_M.V2.S5 | 10000 | -3.442 | 3.039 | 0.076 | 0.971 |
| GNEITING_M.V2.S6 | 10000 | -2.951 | 3.048 | -0.028 | 0.991 |
| GNEITING_M.V2.S7 | 10000 | -3.473 | 3.729 | 0.131 | 0.944 |
| GNEITING_M.V2.S8 | 10000 | -2.956 | 3.051 | -0.028 | 0.991 |
| GNEITING_M.V2.S9 | 10000 | -3.458 | 3.729 | 0.131 | 0.943 |
| GNEITING_M.V2.S10 | 10000 | -2.979 | 3.074 | -0.028 | 0.992 |
| GNEITING_M.V2.S11 | 10000 | -3.516 | 3.831 | 0.132 | 0.948 |
| GNEITING_M.V2.S12 | 10000 | -4.034 | 2.859 | -0.224 | 0.990 |
| GNEITING_M.V2.S13 | 10000 | -3.482 | 3.739 | 0.130 | 0.945 |
| GNEITING_M.V2.S14 | 10000 | -4.025 | 2.866 | -0.224 | 0.989 |
| GNEITING_M.V2.S15 | 10000 | -3.481 | 3.734 | 0.130 | 0.944 |
| GNEITING_M.V2.S16 | 10000 | -4.031 | 2.901 | -0.221 | 0.994 |
| GNEITING_M.V2.S17 | 10000 | -3.481 | 3.731 | 0.130 | 0.944 |
2d gneiting
nsim = 13
# TEST of separability
type = c("GNEITING_G", "GNEITING_M", "GNEITING_C")[3]
ndim = 2
nvar = 2
sep = 1/2
# parameters for the time trace
alpha = 2.0
beta = 1.0
# parameters for the space trace
nu = c(1/2, 3/4, 1)[1:nvar]
rr = c(1, 2, 1)[1:nvar]
# space-time anisotropy
timeRange = 2.0
ranges = c(5,10)[1:ndim]
angles = c(30, 0)[1:ndim]
ctxt = CovContext(nvar = nvar, space = SpaceRN_create(ndim = ndim))
mod = CorGneiting_create(ctxt = ctxt, type = ECov_fromKey(type),
alpha = alpha, beta = beta, timeRange = timeRange,
params = nu, kappas = rr,
ranges = ranges, angles = angles,
flagRange = FALSE,
separability = sep)
err = draw_model(model = mod, prefix = type, flag.st = TRUE)
# simulation using "gstlearn API"
model = ModelGeneric(ctxt = ctxt)
err = model$setCov(mod)
# creation of a 2D x Time grid: section xOt
res = list()
for (isec in 1:3) {
print(sprintf(">>>>> simulation of section %d", isec))
nx = c(100, 100, 100)
dx = c(0.5, 0.5, 0.5)
nx[isec] <- 1
grid = DbGrid_create(nx = nx, dx = dx)
err = simuSpectral(dbin = NULL, dbout = grid, model = model, nbsimu = nsim, ns = ns,
verbose = flag.verbose,
namconv = NamingConvention(type))
res[[1+length(res)]] = QC_section (model = model$getCov(),
grid = grid, prefix = type, nsimu = nsim, isec = isec,
flag.histo = TRUE, flag.map = TRUE, flag.vario = TRUE,
verbose = flag.verbose, flag.st = TRUE)
}## [1] ">>>>> simulation of section 1"
## [1] ">>>>> simulation of section 2"
## [1] ">>>>> simulation of section 3"
