#' Vector of Expected Values \eqn{\mathbf{v}}
#'
#' Derives the vector of expected values \eqn{\mathbf{v}}
#' using the Reticular Action Model (RAM) notation.
#'
#' The vector of expected values \eqn{\mathbf{v}}
#' as a function of Reticular Action Model (RAM) matrices
#' is given by
#'
#' \deqn{
#' \mathbf{v}
#' =
#' \left(
#' \mathbf{I} - \mathbf{A}
#' \right)^{\mathsf{T}}
#' \mathbf{u} \\
#' =
#' \mathbf{E}
#' \mathbf{u}
#' }
#'
#' where
#'
#' - \eqn{\mathbf{A}_{t \times t}} represents asymmetric paths
#' (single-headed arrows),
#' such as regression coefficients and factor loadings,
#' - \eqn{\mathbf{I}_{t \times t}} represents an identity matrix, and
#' - \eqn{\mathbf{u}_{t \times 1}} vector of parameters
#' for the mean structure.
#'
#' @return \eqn{\mathbf{v} = \mathbf{E} \mathbf{u}}
#'
#' @author Ivan Jacob Agaloos Pesigan
#'
#' @family RAM matrices functions
#' @keywords ram
#'
#' @inherit ramR references
#' @inheritParams IminusA
#' @inheritParams CheckRAMMatrices
#' @export
v <- function(A,
u,
check = TRUE,
...) {
UseMethod("v")
}
#' @rdname v
#' @inheritParams IminusA
#' @inheritParams v
#' @examples
#' # Numeric -----------------------------------------------------------
#' # This is a numerical example for the model
#' # y = alpha + beta * x + e
#' # y = 0 + 1 * x + e
#' #--------------------------------------------------------------------
#'
#' A <- matrixR::ZeroMatrix(3)
#' A[1, ] <- c(0, 1, 1)
#' u <- c(0.00, 0.50, 0.00)
#' colnames(A) <- rownames(A) <- c("y", "x", "e")
#' v(A, u)
#' @export
v.default <- function(A,
u,
check = TRUE,
...) {
if (check) {
RAM <- CheckRAMMatrices(
A = A,
u = u
)
A <- RAM$A
u <- RAM$u
}
E <- E(
A = A,
check = FALSE
) # A is already checked
v <- as.matrix(E %*% u)
colnames(v) <- "v"
return(v)
}
#' @rdname v
#' @inheritParams IminusA
#' @inheritParams v
#' @examples
#' # Symbolic ----------------------------------------------------------
#' # This is a symbolic example for the model
#' # y = alpha + beta * x + e
#' # y = 0 + 1 * x + e
#' #--------------------------------------------------------------------
#'
#' A <- matrixR::ZeroMatrix(3)
#' A[1, ] <- c(0, "beta", 1)
#' u <- c("alpha", "mux", 0)
#' v(Ryacas::ysym(A), u)
#' v(Ryacas::ysym(A), u, format = "str")
#' v(Ryacas::ysym(A), u, format = "tex")
#' v(Ryacas::ysym(A), u, R = TRUE)
#'
#' # Assigning values to symbols
#'
#' alpha <- 0
#' beta <- 1
#' mux <- 0.50
#'
#' v(Ryacas::ysym(A), u)
#' v(Ryacas::ysym(A), u, format = "str")
#' v(Ryacas::ysym(A), u, format = "tex")
#' v(Ryacas::ysym(A), u, R = TRUE)
#' eval(v(Ryacas::ysym(A), u, R = TRUE))
#' @export
v.yac_symbol <- function(A,
u,
check = TRUE,
exe = TRUE,
R = FALSE,
format = "ysym",
simplify = FALSE,
...) {
if (check) {
u <- CheckRAMMatrices(
A = A,
u = u
)$u
} else {
u <- yacR::as.ysym.mat(u)
}
E <- E(
A = A,
check = FALSE,
exe = FALSE
)
expr <- paste0(
E,
"*",
u
)
if (exe) {
return(
yacR::Exe(
expr,
R = R,
format = format,
simplify = simplify
)
)
} else {
return(expr)
}
}
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