Calculate general stationary correlation.

Calculate general stationary correlation.

Usage

cor_stat(
  base = c("sep", "fs"),
  lagrangian = c("none", "lagr_tri", "lagr_askey"),
  par_base,
  par_lagr,
  lambda,
  h,
  h1,
  h2,
  u,
  base_fixed = FALSE
)

Arguments

base

Base model, sep or fs for now. Or correlation matrix/array.

lagrangian

Lagrangian model, none, lagr_tri, or lagr_askey.

par_base

Parameters for the base model (symmetric), used only when base_fixed = FALSE.

par_lagr

Parameters for the Lagrangian model. Used only when lagrangian is not none.

lambda

Weight of the Lagrangian term, \(\lambda\in[0, 1]\).

h

Euclidean distance matrix or array, used only when base_fixed = FALSE.

h1

Horizontal distance matrix or array, same dimension as h. Used only when lagrangian is not none.

h2

Vertical distance matrix or array, same dimension as h. Used only when lagrangian is not none.

u

Time lag, same dimension as h.

base_fixed

Logical; if TRUE, base is the correlation.

Value

Correlations for the general stationary model. Same dimension of base if base_fixed = FALSE.

Details

The general station model, a convex combination of a base model and a Lagrangian model, has the form $$C(\mathbf{h}, u)=(1-\lambda)C_{\text{Base}}(\mathbf{h}, u)+ \lambda C_{\text{Lagr}}(\mathbf{h}, u),$$ where \(\lambda\) is the weight of the Lagrangian term.

If base_fixed = TRUE, the correlation is of the form $$C(\mathbf{h}, u)=(1-\lambda)C_{\text{Base}}+ \lambda C_{\text{Lagr}}(\mathbf{h}, u),$$ where base is a correlation matrix/array and par_base and h are not used.

When lagrangian = "none", lambda must be 0.

See also

Other correlation functions: cor_cauchy(), cor_exp(), cor_fs(), cor_lagr_askey(), cor_lagr_exp(), cor_lagr_tri(), cor_sep(), cor_stat_rs()

Examples

par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5)
par_t <- list(a = 1, alpha = 0.5)
par_base <- list(par_s = par_s, par_t = par_t)
par_lagr <- list(v1 = 5, v2 = 10)
h1 <- matrix(c(0, 5, -5, 0), nrow = 2)
h2 <- matrix(c(0, 8, -8, 0), nrow = 2)
h <- sqrt(h1^2 + h2^2)
u <- matrix(0.1, nrow = 2, ncol = 2)
cor_stat(
    base = "sep", lagrangian = "lagr_tri", par_base = par_base,
    par_lagr = par_lagr, lambda = 0.8, h = h, h1 = h1, h2 = h2, u = u
)
#>           [,1]      [,2]
#> [1,] 0.9418182 0.5067249
#> [2,] 0.5867249 0.9418182

h1 <- array(c(0, 5, -5, 0), dim = c(2, 2, 3))
h2 <- array(c(0, 8, -8, 0), dim = c(2, 2, 3))
h <- sqrt(h1^2 + h2^2)
u <- array(rep(c(0.1, 0.2, 0.3), each = 4), dim = c(2, 2, 3))
fit_base <- cor_fs(
    nugget = 0.5, c = 0.01, gamma = 0.5, a = 1, alpha = 0.5,
    beta = 0.0, h = h, u = u
)
par_lagr <- list(v1 = 5, v2 = 10)
cor_stat(
    base = fit_base, lagrangian = "lagr_askey", par_lagr = par_lagr,
    h1 = h1, h2 = h2, u = u, lambda = 0.8, base_fixed = TRUE
)
#> , , 1
#> 
#>           [,1]      [,2]
#> [1,] 0.9225746 0.3899184
#> [2,] 0.4807108 0.9225746
#> 
#> , , 2
#> 
#>           [,1]      [,2]
#> [1,] 0.8497186 0.3405980
#> [2,] 0.5219630 0.8497186
#> 
#> , , 3
#> 
#>           [,1]      [,2]
#> [1,] 0.7807752 0.2944717
#> [2,] 0.5659495 0.7807752
#>