R/eulermaruyama.R

In BayesForge: Bayesian Inference using 'numpyro' and 'XLA'

#' @title Euler-Maruyama method
#'
#' @description
#' Euler-Maruyama methode is a method for the approximate numerical solution of a stochastic differential equation (SDE).
#' It simulates the solution to an SDE by iteratively applying the Euler method to each time step, incorporating a random perturbation to account for the diffusion term.
#'
#' @param t A numeric vector representing the discretized time steps.
#' @param sde_fn A function that takes the current state and time as input and returns the drift and diffusion coefficients.
#' @param init_dist The initial distribution of the system.
#' @param shape A numeric vector specifying the shape of the output tensor.  Defaults to `NULL`.
#' @param event Integer representing the number of batch dimensions to reinterpret as event dimensions (used in model building).
#' @param mask A logical vector. Optional boolean array to mask observations.
#' @param create_obj Logical. If TRUE, returns the raw BI distribution object instead of creating a sample site. This is essential for building complex distributions like `MixtureSameFamily`.
#' @param validate_args A logical value indicating whether to validate the arguments. Defaults to `TRUE`.
#' @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 \code{sample=FALSE}, a BI Euler-Maruyama distribution object (for model building).
#'
#'  - When \code{sample=TRUE}, a JAX array of samples drawn from the Euler-Maruyama distribution (for direct sampling).
#'
#'  - When \code{create_obj=TRUE}, the raw BI distribution object (for advanced use cases).
#'
#' @examples
#' \donttest{
#' library(BayesForge)
#' m=importBF(platform='cpu')
#'ornstein_uhlenbeck_sde <- function(x, t) {
#'  # This function models dX = -theta * X dt + sigma dW
#'  theta <- 1.0
#'  sigma <- 0.5
#'
#'  drift <- -theta * x
#'  diffusion <- sigma
#'
#'  # Return a list of two elements: drift and diffusion
#'  # reticulate will convert this to a Python tuple
#'  return(list(drift, diffusion))
#'}
#'bf.dist.euler_maruyama(
#'t=c(0.0, 0.1, 0.2),
#'sde_fn = ornstein_uhlenbeck_sde,
#'init_dist=bf.dist.normal(0.0, 1.0, create_obj=TRUE),
#'sample = TRUE)
#' }
#' @export
bf.dist.euler_maruyama=function(t, sde_fn, init_dist, 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(reticulate::tuple, as.list(as.integer(shape)))
     event=as.integer(event)
     reticulate::py_run_string("def is_none(x): return x is None")
     if (!.BF_env$.py$is_none(seed)){seed=as.integer(seed);}

     .BF_env$.bf_instance$dist$euler_maruyama(
       t = .BF_env$jnp$array(t),
       sde_fn = sde_fn,
       init_dist = init_dist,
       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)
}