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mcgf_sim.R
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mcgf_sim.R
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#' Simulate Markov chain Gaussian field
#'
#' @param N Sample size.
#' @param base Base model, `sep` or `fs` for now.
#' @param lagrangian Lagrangian model, "none" or `lagr_tri` for now.
#' @param par_base Parameters for the base model (symmetric).
#' @param par_lagr Parameters for the Lagrangian model.
#' @param lambda Weight of the Lagrangian term, \eqn{\lambda\in[0, 1]}.
#' @param dists Distance matrices or arrays.
#' @param sd Standard deviation for each location.
#' @param lag Time lag.
#' @param scale_time Scale of time unit, default is 1. `lag` is divided by
#' `scale_time`.
#' @param horizon Forecast horizon, default is 1.
#' @param init Initial samples, default is 0.
#' @param mu_c,mu_p Means of current and past.
#' @param return_all Logical; if TRUE the joint covariance matrix, arrays of
#' distances and time lag are returned.
#'
#' @keywords internal
#'
#' @return Simulated Markov chain Gaussian field with user-specified covariance
#' structure. The simulation is done by kriging. The output data is in
#' space-wide format. `dists` must contain `h` for symmetric models, and `h1`
#' and `h2` for general stationary models. `horizon` controls forecasting
#' horizon. `sd`, `mu_c`, `mu_p`, and `init` must be vectors of appropriate
#' sizes.
.mcgf_sim <- function(N,
base,
lagrangian,
par_base,
par_lagr,
lambda,
dists,
sd,
lag,
scale_time = 1,
horizon = 1,
init = 0,
mu_c,
mu_p,
return_all = FALSE) {
lag_max <- lag + horizon - 1
n_var <- nrow(dists$h)
n_block_row <- lag_max + 1
n_rounds <- ceiling(N / horizon)
u <- (0:lag_max) / scale_time
dim_ar <- c(n_var, n_var, length(u))
h_ar <- array(dists$h, dim = dim_ar)
u_ar <- array(rep(u, each = n_var * n_var), dim = dim_ar)
if (lagrangian == "none") {
cov_ar <- cor_stat(
base = base,
lagrangian = lagrangian,
par_base = par_base,
h = h_ar,
u = u_ar,
base_fixed = FALSE
)
} else {
h1_ar <- array(dists$h1, dim = dim_ar)
h2_ar <- array(dists$h2, dim = dim_ar)
cov_ar <- cor_stat(
base = base,
lagrangian = lagrangian,
par_base = par_base,
par_lagr = par_lagr,
lambda = lambda,
h = h_ar,
h1 = h1_ar,
h2 = h2_ar,
u = u_ar,
base_fixed = FALSE
)
}
cov_ar <- cor2cov_ar(cov_ar, sd)
X_cov_par <- cov_par(cov = cov_ar, horizon = horizon)
new_cov_chol <- chol(X_cov_par$cov_curr)
X <- init
for (n in 1:n_rounds) {
X_past <- stats::embed(utils::tail(X, lag), lag)
X_new_mean <- mu_c + tcrossprod(X_cov_par$weights, X_past - mu_p)
# X_new <- mvnfast::rmvn(1, X_new_mean, X_cov_par$cov_curr)
X_new <- crossprod(new_cov_chol, stats::rnorm(length(X_new_mean)))
X_new <- matrix(X_new + X_new_mean, ncol = n_var, byrow = T)
X_new <- X_new[horizon:1, ]
X <- rbind(X, X_new)
}
rownames(X) <- 1:nrow(X)
colnames(X) <- colnames(dists$h)
if (return_all) {
cov_mat_joint <- cov_joint(cov = cov_ar)
par <- list(
cov_mat = cov_mat_joint,
dists = list(h = h_ar),
u = u_ar
)
if (lagrangian == "lagr_tri") {
par$dists <- list(h = h_ar, h1 = h1_ar, h2 = h2_ar)
}
return(list(X = X, par = par))
} else {
return(X = X)
}
}
#' Simulate Markov chain Gaussian field
#'
#' @inherit .mcgf_sim params details return
#'
#' @export
#' @examples
#' par_s <- list(nugget = 0.5, c = 0.01, gamma = 0.5)
#' par_t <- list(a = 1, alpha = 0.5)
#' par_base <- list(par_s = par_s, par_t = par_t)
#' par_lagr <- list(v1 = 5, v2 = 10)
#' h1 <- matrix(c(0, 5, -5, 0), nrow = 2)
#' h2 <- matrix(c(0, 8, -8, 0), nrow = 2)
#' h <- sqrt(h1^2 + h2^2)
#' dists <- list(h = h, h1 = h1, h2 = h2)
#'
#' set.seed(123)
#' X <- mcgf_sim(
#' N = 1000, base = "sep", lagrangian = "lagr_tri", lambda = 0.5,
#' par_base = par_base, par_lagr = par_lagr, dists = dists
#' )
#' plot.ts(X)
#'
#' @family simulations of Markov chain Gaussian fields
mcgf_sim <- function(N,
base = c("sep", "fs"),
lagrangian = c("none", "lagr_tri", "lagr_askey"),
par_base,
par_lagr,
lambda,
dists,
sd = 1,
lag = 1,
scale_time = 1,
horizon = 1,
init = 0,
mu_c = 0,
mu_p = 0,
return_all = FALSE) {
if (N < horizon) {
stop("`N` must be no less than `horizon`", call. = FALSE)
}
if (is.null(dists$h)) {
stop("missing 'h' in `dists`.", call. = FALSE)
}
if (lagrangian != "none") {
if (is.null(dists$h1)) {
stop("missing 'h1' in `dists`.", call. = FALSE)
}
if (is.null(dists$h2)) {
stop("missing 'h2' in `dists`.", call. = FALSE)
}
}
lag_max <- lag + horizon - 1
n_var <- nrow(dists$h)
n_block_row <- lag_max + 1
if (N < horizon + n_block_row) {
warning("'N' must be no less than ", horizon + n_block_row)
N <- horizon + n_block_row
}
if (length(init) == 1) {
init <- matrix(init, nrow = n_block_row, ncol = n_var)
} else {
if (NROW(init) != n_block_row || NCOL(init) != n_var) {
stop("dim of 'n_var' must be 1 or ", n_block_row, " x ", n_var, ".",
call. = FALSE
)
}
}
sd <- check_length(x = sd, length = n_var, name = "sd")
mu_c <- check_length(x = mu_c, length = n_var * horizon, name = "mu_c")
mu_p <- check_length(x = mu_p, length = n_var * lag, name = "mu_p")
res <- .mcgf_sim(
N = N,
base = base,
lagrangian = lagrangian,
par_base = par_base,
par_lagr = par_lagr,
lambda = lambda,
dists = dists,
sd = sd,
lag = lag,
scale_time = scale_time,
horizon = horizon,
init = init,
mu_c = mu_c,
mu_p = mu_p,
return_all = return_all
)
return(res)
}