R/log_partitions_functions.R

In YipengUva/RpESCA: R implementaion of pESCA models with various concave penalties

#' The log-partation function of Bernoulli distribution
#'
#' This function define the log-partation function
#' of Bernoulli distribution. The formula is
#' \code{log_part_B(Theta) = log(1 + exp(Theta))}.
#' Details can be found in \url{https://arxiv.org/abs/1902.06241}.
#'
#' @param Theta a matrix of natural parameter
#'
#' @return The value of the corresponding log-partation function
#'
#' @examples
#' \dontrun{log_part_B(matrix(0:9,2,5))}
log_part_B <- function(Theta) {
    
    log(1 + exp(Theta))
}

#' The first order gradient of log-partation function of Bernoulli distribution
#'
#' This function define first order gradient of the log-partation function
#' of Bernoulli distribution. The formula is
#' \code{log_part_B_g(Theta) = exp(Theta)/(1+exp(Theta))}.
#' Details can be found in \url{https://arxiv.org/abs/1902.06241}.
#'
#' @inheritParams log_part_B
#'
#' @return value of the first order gradient
#'
#' @examples
#' \dontrun{log_part_B_g(matrix(0:9,2,5))}
log_part_B_g <- function(Theta) {
    
    exp(Theta)/(1 + exp(Theta))
}

#' The log-partation function of Gaussian distribution
#'
#' This function define the log-partation function
#' of Gaussian distribution. The formula is
#' \code{log_part_G(Theta) = 0.5*(Theta^2)}.
#' Details can be found in \url{https://arxiv.org/abs/1902.06241}.
#'
#' @inheritParams log_part_B
#'
#' @return the value of the corresponding log-partation function
#'
#' @examples
#' \dontrun{log_part_G(matrix(0:9,2,5))}
log_part_G <- function(Theta) {
    
    0.5 * (Theta^2)
}

#' The first order gradient of log-partation function of Gaussian distribution
#'
#' This function define first order gradient of the log-partation function
#' of Gaussian distribution. The formula is
#' \code{log_part_G_g(Theta) = Theta}.
#' Details can be found in \url{https://arxiv.org/abs/1902.06241}.
#'
#' @inheritParams log_part_G
#'
#' @return value of the first order gradient
#'
#' @examples
#' \dontrun{log_part_G_g(matrix(0:9,2,5))}
log_part_G_g <- function(Theta) {
    
    Theta
}

#' The log-partation function of Possion distribution
#'
#' This function define the log-partation function
#' of Possion distribution. The formula is
#' \code{log_part_G(Theta) = exp(Theta)}.
#' Details can be found in \url{https://arxiv.org/abs/1902.06241}.
#'
#' @inheritParams log_part_B
#'
#' @return the value of the corresponding log-partation function
#'
#' @examples
#' \dontrun{log_part_P(matrix(0:9,2,5))}
log_part_P <- function(Theta) {
    
    exp(Theta)
}

#' The first order gradient of log-partation function of Possion distribution
#'
#' This function define first order gradient of the log-partation function
#' of Possion distribution. The formula is
#' \code{log_part_P_g(Theta) = exp(Theta)}.
#' Details can be found in \url{https://arxiv.org/abs/1902.06241}.
#'
#' @inheritParams log_part_P
#'
#' @return value of the first order gradient
#'
#' @examples
#' \dontrun{log_part_P_g(matrix(0:9,2,5))}
log_part_P_g <- function(Theta) {
    
    exp(Theta)
}