cor_stat: Calculate general stationary correlation.

In mcgf: Markov Chain Gaussian Fields Simulation and Parameter Estimation

Calculate general stationary correlation.

Description

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.

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.

Value

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

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
)

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
)

mcgf documentation built on June 29, 2024, 9:09 a.m.