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#' @title Gaussian State Space Distribution
#'
#' @description Samples from a Gaussian state space model.
#'
#' @param num_steps An integer representing the number of steps.
#' @param transition_matrix A numeric vector, matrix, or array representing the state space transition matrix \eqn{A}.
#' @param covariance_matrix A numeric vector, matrix, or array representing the covariance of the innovation noise \eqn{\epsilon}. Defaults to `reticulate::py_none()`.
#' @param precision_matrix A numeric vector, matrix, or array representing the precision matrix of the innovation noise \eqn{\epsilon}. Defaults to `reticulate::py_none()`.
#' @param scale_tril A numeric vector, matrix, or array representing the scale matrix of the innovation noise \eqn{\epsilon}. Defaults to `reticulate::py_none()`.
#' @param shape A numeric vector specifying the shape. When `sample=FALSE` (model building), this is used with `.expand(shape)` to set the distribution's batch shape. When `sample=TRUE` (direct sampling), this is used as `sample_shape` to draw a raw JAX array of the given shape.
#' @param event An integer representing the number of batch dimensions to reinterpret as event dimensions (used in model building).
#' @param mask A logical vector, matrix, or array representing an optional boolean array to mask observations. Defaults to `reticulate::py_none()`.
#' @param create_obj A logical value. If `TRUE`, returns the raw BI distribution object instead of creating a sample site. Defaults to `FALSE`.
#' @param validate_args Logical: Whether to validate parameter values. Defaults to `reticulate::py_none()`.
#' @param sample A logical value that controls the function's behavior. If `TRUE`,
#' the function will directly draw samples from the distribution. If `FALSE`,
#' it will create a random variable within a model. Defaults to `FALSE`.
#' @param seed An integer used to set the random seed for reproducibility when
#' `sample = TRUE`. This argument has no effect when `sample = FALSE`, as
#' randomness is handled by the model's inference engine. Defaults to 0.
#' @param obs A numeric vector or array of observed values. If provided, the
#' random variable is conditioned on these values. If `NULL`, the variable is
#' treated as a latent (unobserved) variable. Defaults to `NULL`.
#' @param name A character string representing the name of the random variable
#' within a model. This is used to uniquely identify the variable. Defaults to 'x'.
#' @param to_jax Boolean. Indicates whether to return a JAX array or not.
#'
#' @return When `sample=FALSE`:
#' - When `sample=FALSE`, a BI Gaussian State Space distribution object (for model building).
#'
#' - When `sample=TRUE`, a JAX array of samples drawn from the Gaussian State Space distribution (for direct sampling).
#'
#' - When `create_obj=TRUE`, the raw BI distribution object (for advanced use cases).
#'
#' @seealso This is a wrapper of \url{https://num.pyro.ai/en/stable/distributions.html#gaussianstatespace}
#'
#' @examples
#' \donttest{
#' library(BayesForge)
#' m=importBF(platform='cpu')
#' bf.dist.gaussian_state_space(
#' num_steps = 1,
#' transition_matrix = matrix(c(0.5), nrow = 1, byrow = TRUE),
#' covariance_matrix = matrix(c(1.0), nrow = 1, byrow = TRUE),
#' sample = TRUE)
#'}
#' @export
bf.dist.gaussian_state_space=function(num_steps, transition_matrix, covariance_matrix=py_none(), precision_matrix=py_none(), scale_tril=py_none(), validate_args=py_none(), name='x', obs=py_none(), mask=py_none(), sample=FALSE, seed = py_none(), shape=c(), event=0, create_obj=FALSE, to_jax = TRUE) {
shape=do.call(tuple, as.list(as.integer(shape)))
if (!.BF_env$.py$is_none(seed)){seed=as.integer(seed);}
num_steps=as.integer(num_steps);
if(!.BF_env$.py$is_none(transition_matrix)){transition_matrix = .BF_env$jnp$array(transition_matrix)}
if(!.BF_env$.py$is_none(covariance_matrix)){covariance_matrix = .BF_env$jnp$array(covariance_matrix)}
if(!.BF_env$.py$is_none(precision_matrix)){precision_matrix = .BF_env$jnp$array(precision_matrix)}
if(!.BF_env$.py$is_none(scale_tril)){scale_tril = .BF_env$jnp$array(scale_tril)}
.BF_env$.bf_instance$dist$gaussian_state_space(
num_steps,
transition_matrix = transition_matrix,
covariance_matrix= covariance_matrix,
precision_matrix= precision_matrix,
scale_tril= scale_tril,
validate_args= validate_args, name= name, obs= obs, mask= mask, sample= sample, seed= seed, shape= shape, event= event, create_obj= create_obj, to_jax = to_jax)
}
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