R/mvn.R
In jeksterslabds/jeksterslabRdata: Jekster's Lab Data Generation Utilities
Defines functions
mvnramsigma2
mvnram
mvn
Documented in
mvn
mvnram
mvnramsigma2
#' @author Ivan Jacob Agaloos Pesigan
#'
#' @title Generate Multivariate Normal Data
#' \eqn{
#' \mathbf{X} \sim \mathcal{N}_{k}
#' \left( \boldsymbol{\mu}, \boldsymbol{\Sigma} \right)
#' %(\#eq:dist-X-mvn)
#' }
#'
#' @description Generates an \eqn{n \times k} multivariate data matrix
#' or a list of \eqn{n \times k} multivariate data matrices of length `R`
#' from the multivariate normal distribution
#' \deqn{
#' \mathbf{X} \sim \mathcal{N}_{k}
#' \left( \boldsymbol{\mu}, \boldsymbol{\Sigma} \right) .
#' %(\#eq:dist-X-mvn)
#' }
#' This function is a wrapper around [`MASS::mvrnorm()`].
#'
#' @details The multivariate normal distribution has two parameters, namely
#' the \eqn{k \times 1} mean vector `mu` \eqn{\left( \boldsymbol{\mu} \right)}
#' and the \eqn{k \times k} variance-covariance matrix `Sigma`
#' \eqn{\left( \boldsymbol{\Sigma} \right)}.
#' If `mu` is not provided,
#' it is set to a vector of zeroes with the appropriate length.
#'
#' Options for explicit parallelism are provided when `R > 1`
#' especially when `R` is large. See `par` and suceeding arguments.
#'
#' @return If `R = NULL` or `R = 1`, returns an \eqn{n \times k}
#' multivariate normal data matrix or data frame .
#' If `R` is an integer greater than 1, (e.g., `R = 10`)
#' returns a list of length `R` of \eqn{n \times k}
#' multivariate normal data matrix or data frame.
#'
#' @references Venables, W. N., Ripley, B. D., & Venables, W. N. (2002).
#' *Modern applied statistics with S*. New York, N.Y: Springer.
#'
#' [Wikipedia: Multivariate normal distribution](https://en.wikipedia.org/wiki/Multivariate_normal_distribution)
#'
#' @seealso [`jeksterslabRdist::mvnpdf()`], [`jeksterslabRdist::mvnll()`],
#' and [`jeksterslabRdist::mvn2ll()`],
#' for more information on the multivariate normal distribution.
#'
#' @family multivariate data functions
#' @keywords multivariate, normal
#' @inheritParams jeksterslabRdist::mvnpdf
#' @inheritParams univ
#' @inherit jeksterslabRdist::mvnpdf details references
#' @importFrom MASS mvrnorm
#' @param tol Numeric.
#' Tolerance (relative to largest variance)
#' for numerical lack of positive-definiteness in `Sigma`.
#' @param empirical Logical.
#' If `TRUE`, `mu` and `Sigma` specify the empirical,
#' not population. mean and covariance matrix.
#' @param df Logical.
#' If `TRUE`, the function returns a data frame.
#' If `FALSE`, the function returns a matrix.
#' @param varnames Character string.
#' Optional column names with the same length as `mu`.
#' @examples
#' mu <- c(100, 100, 100)
#' Sigma <- matrix(
#' data = c(225, 112.50, 56.25, 112.5, 225, 112.5, 56.25, 112.50, 225),
#' ncol = 3
#' )
#' X <- mvn(n = 100, mu = mu, Sigma = Sigma)
#' Xstar <- mvn(n = 100, mu = mu, Sigma = Sigma, R = 100)
#' str(Xstar, list.len = 6)
#' @export
mvn <- function(n, # mvrnorm
mu = NULL,
Sigma,
tol = 1e-6,
empirical = FALSE,
df = FALSE,
varnames = NULL,
# iter
R = NULL,
# par_lapply
par = FALSE,
ncores = NULL,
mc = TRUE,
lb = FALSE,
cl_eval = FALSE,
cl_export = FALSE,
cl_expr,
cl_vars) {
# main function----------------------------------------------------------------
foo <- function(iter,
n,
mu,
Sigma,
tol,
empirical,
df) {
out <- mvrnorm(
n = n,
mu = mu,
Sigma = Sigma,
tol = tol,
empirical = empirical
)
if (df) {
out <- as.data.frame(out)
}
out
}
#------------------------------------------------------------------------------
# mu to a vector of zeros------------------------------------------------------
if (is.null(mu)) {
mu <- rep(
x = 0,
times = nrow(Sigma)
)
message(
paste0(
"mu = NULL. mu is set to a vector of zeroes of length ",
nrow(Sigma),
"."
)
)
}
#------------------------------------------------------------------------------
# optional column names------------------------------------------------------
if (!is.null(varnames)) {
names(mu) <- varnames
}
#------------------------------------------------------------------------------
# negotiate single rep of multiple rep
if (is.null(R)) {
single_rep <- TRUE
} else {
if (R == 1) {
single_rep <- TRUE
} else {
single_rep <- FALSE
}
}
#------------------------------------------------------------------------------
# execute----------------------------------------------------------------------
if (single_rep) {
# single rep-----------------------------------------------------------------
return(
foo(
n = n,
mu = mu,
Sigma = Sigma,
tol = tol,
empirical = empirical,
df = df
)
)
# ---------------------------------------------------------------------------
} else {
# multiple reps--------------------------------------------------------------
return(
par_lapply(
# iter
X = 1:R,
# foo
FUN = foo,
# foo
n = n,
mu = mu,
Sigma = Sigma,
tol = tol,
empirical = empirical,
df = df,
# par_lapply
par = par,
ncores = ncores,
mc = mc,
lb = lb,
cl_eval = cl_eval,
cl_export = cl_export,
cl_expr = cl_expr,
cl_vars = cl_vars,
rbind = NULL # always null
)
)
#----------------------------------------------------------------------------
}
}
#' @author Ivan Jacob Agaloos Pesigan
#'
#' @title Generate Multivariate Normal Data
#' \eqn{
#' \mathbf{X} \sim \mathcal{N}_{k}
#' \left( \boldsymbol{\mu}, \boldsymbol{\Sigma} \right)
#' %(\#eq:dist-X-mvn)
#' }
#' from the Reticular Action Model Matrices
#'
#' @description Generates an \eqn{n \times k} multivariate data matrix
#' or a list of \eqn{n \times k} multivariate data matrices of length `R`
#' from the multivariate normal distribution
#' \deqn{
#' \mathbf{X} \sim \mathcal{N}_{k}
#' \left( \boldsymbol{\mu}, \boldsymbol{\Sigma} \right) .
#' %(\#eq:dist-X-mvn)
#' }
#' The model-implied matrices used to generate data
#' is derived from the Reticular Action Model (RAM) Matrices.
#'
#' @details The multivariate normal distribution has two parameters,
#' namely the \eqn{k \times 1} mean vector
#' `mu` \eqn{\left( \boldsymbol{\mu} \right)}
#' and the \eqn{k \times k} variance-covariance matrix
#' `Sigma` \eqn{\left( \boldsymbol{\Sigma} \right)}.
#'
#' The mean vector `mu` can be supplied directly using the `mu` argument.
#' It can also be derived using `M`.
#' Note that the argument `mu` takes precedence over `M`.
#' If `mu` is not provided, it is computed using `M`
#' with the [`jeksterslabRsem::ram_mutheta()`] function.
#' If both `mu` and `M` are not provided,
#' `mu` is set to a vector of zeroes with the appropriate length.
#'
#' The variance-covariance matrix `Sigma` is derived
#' from the RAM matrices `A`, `S`, `F`, and `I`.
#'
#' `mu` and `Sigma` are then used by the [`mvn()`] function
#' to generate multivariate normal data.
#'
#' Options for explicit parallelism are provided when `R > 1`
#' especially when `R` is large. See `par` and suceeding arguments.
#'
#' @seealso
#' [`jeksterslabRsem::ram_Sigmatheta()`], and [`jeksterslabRsem::ram_mutheta()`]
#' for more information on the Reticular Action Model (RAM)
#' and [`mvn()`] for multivariate normal data generation.
#'
#' @family multivariate data functions
#' @keywords multivariate normal
#' @inheritParams mvn
#' @inheritParams jeksterslabRsem::ram_mutheta
#' @inheritParams jeksterslabRsem::ram_Sigmatheta
#' @inherit mvn return
#' @inherit jeksterslabRsem::ram_Sigmatheta references
#' @importFrom jeksterslabRsem ram_mutheta
#' @importFrom jeksterslabRsem ram_Sigmatheta
#' @examples
#' mu <- c(100, 100, 100)
#' A <- matrix(
#' data = c(0, sqrt(0.26), 0, 0, 0, sqrt(0.26), 0, 0, 0),
#' ncol = 3
#' )
#' S <- diag(c(225, 166.5, 116.5))
#' F <- I <- diag(3)
#' X <- mvnram(n = 100, mu = mu, A = A, S = S, F = F, I = I)
#' Xstar <- mvnram(n = 100, mu = mu, A = A, S = S, F = F, I = I, R = 100)
#' str(Xstar, list.len = 6)
#' @export
mvnram <- function(n,
mu = NULL,
M = NULL,
A,
S,
F,
I,
tol = 1e-6,
empirical = FALSE,
df = FALSE,
varnames = NULL,
R = NULL,
par = FALSE,
ncores = NULL,
mc = TRUE,
lb = FALSE,
cl_eval = FALSE,
cl_export = FALSE,
cl_expr,
cl_vars) {
# derive Sigma-----------------------------------------------------------------
Sigma <- ram_Sigmatheta(
A = A,
S = S,
F = F,
I = I
)
#------------------------------------------------------------------------------
# negotiate derivation of mu---------------------------------------------------
if (is.null(mu)) {
# mu is not provided
if (is.null(M)) {
message(
paste0(
"mu = NULL and M = NULL. mu is set to a vector of zeroes of length ",
nrow(Sigma),
"."
)
)
# both mu and M are not provided
# generate mu from zero
generate_mu_from_M <- FALSE
generate_mu_from_zero <- TRUE
} else {
message(
"mu = NULL. mu is computed using M."
)
# mu is not provided
# M is provided
# generate mu from M
generate_mu_from_M <- TRUE
generate_mu_from_zero <- FALSE
}
} else {
# mu is provided
# even if M is provided mu takes precedence
generate_mu_from_M <- FALSE
generate_mu_from_zero <- FALSE
}
# derive mu from M-------------------------------------------------------------
if (generate_mu_from_M) {
mu <- ram_mutheta(
A = A,
F = F,
I = I,
M = M
)
}
#------------------------------------------------------------------------------
# generate mu from zeros-------------------------------------------------------
if (generate_mu_from_zero) {
mu <- rep(
x = 0,
times = nrow(Sigma)
)
}
#------------------------------------------------------------------------------
# execute----------------------------------------------------------------------
mvn(
# mvrnorm
n = n,
mu = mu,
Sigma = Sigma,
tol = tol,
empirical = empirical,
df = df,
varnames = varnames,
# iter
R = R,
# par_lapply
par = par,
ncores = ncores,
mc = mc,
lb = lb,
cl_eval = cl_eval,
cl_export = cl_export,
cl_expr = cl_expr,
cl_vars = cl_vars
)
#------------------------------------------------------------------------------
}
#' @author Ivan Jacob Agaloos Pesigan
#'
#' @title Generate Multivariate Normal Data
#' \eqn{
#' \mathbf{X} \sim \mathcal{N}_{k}
#' \left( \boldsymbol{\mu}, \boldsymbol{\Sigma} \right)
#' %(\#eq:dist-X-mvn)
#' }
#' from the Reticular Action Model Matrices
#' \eqn{\mathrm{A}}, \eqn{\mathrm{F}}, \eqn{\mathrm{I}},
#' and the vector of variable variances \eqn{\sigma^2}
#'
#' @details The \eqn{\mathbf{S}} matrix is derived
#' from a vector of variances sigma2 \eqn{\left( \sigma^2 \right)}
#' and the proceeds to generating data using the [`mvnram()`] function.
#' **The first element in sigma2 should be the variance of an exogenous variable.**
#'
#' @family multivariate data functions
#' @keywords multivariate normal
#' @inheritParams mvnram
#' @inheritParams jeksterslabRsem::ram_S
#' @inherit mvnram description return
#' @importFrom jeksterslabRsem ram_S
#' @examples
#' mu <- c(100, 100, 100)
#' A <- matrix(
#' data = c(0, sqrt(0.26), 0, 0, 0, sqrt(0.26), 0, 0, 0),
#' ncol = 3
#' )
#' sigma2 <- c(225, 225, 225)
#' F <- I <- diag(3)
#' X <- mvnramsigma2(n = 100, mu = mu, A = A, sigma2 = sigma2, F = F, I = I)
#' str(X)
#' Xstar <- mvnramsigma2(n = 100, mu = mu, A = A, sigma2 = sigma2, F = F, I = I, R = 100)
#' str(Xstar, list.len = 6)
#' @export
mvnramsigma2 <- function(n,
mu = NULL,
M = NULL,
A,
sigma2,
F,
I,
tol = 1e-6,
empirical = FALSE,
df = FALSE,
varnames = NULL,
R = NULL,
par = FALSE,
ncores = NULL,
mc = TRUE,
lb = FALSE,
cl_eval = FALSE,
cl_export = FALSE,
cl_expr,
cl_vars) {
S <- ram_S(
A = A,
sigma2 = sigma2,
F = F,
I = I,
SigmaMatrix = FALSE
)
mvnram(
n = n,
A = A,
S = S,
F = F,
I = I,
M = M,
mu = mu,
tol = tol,
empirical = empirical,
df = df,
varnames = varnames,
R = R,
par = par,
ncores = ncores,
mc = mc,
lb = lb,
cl_eval = cl_eval,
cl_export = cl_export,
cl_expr = cl_expr,
cl_vars = cl_vars
)
}
jeksterslabds/jeksterslabRdata documentation built on July 24, 2020, 5:49 a.m.
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Defines functions mvnramsigma2 mvnram mvn
Documented in mvn mvnram mvnramsigma2
#' @author Ivan Jacob Agaloos Pesigan
#'
#' @title Generate Multivariate Normal Data
#' \eqn{
#' \mathbf{X} \sim \mathcal{N}_{k}
#' \left( \boldsymbol{\mu}, \boldsymbol{\Sigma} \right)
#' %(\#eq:dist-X-mvn)
#' }
#'
#' @description Generates an \eqn{n \times k} multivariate data matrix
#' or a list of \eqn{n \times k} multivariate data matrices of length `R`
#' from the multivariate normal distribution
#' \deqn{
#' \mathbf{X} \sim \mathcal{N}_{k}
#' \left( \boldsymbol{\mu}, \boldsymbol{\Sigma} \right) .
#' %(\#eq:dist-X-mvn)
#' }
#' This function is a wrapper around [`MASS::mvrnorm()`].
#'
#' @details The multivariate normal distribution has two parameters, namely
#' the \eqn{k \times 1} mean vector `mu` \eqn{\left( \boldsymbol{\mu} \right)}
#' and the \eqn{k \times k} variance-covariance matrix `Sigma`
#' \eqn{\left( \boldsymbol{\Sigma} \right)}.
#' If `mu` is not provided,
#' it is set to a vector of zeroes with the appropriate length.
#'
#' Options for explicit parallelism are provided when `R > 1`
#' especially when `R` is large. See `par` and suceeding arguments.
#'
#' @return If `R = NULL` or `R = 1`, returns an \eqn{n \times k}
#' multivariate normal data matrix or data frame .
#' If `R` is an integer greater than 1, (e.g., `R = 10`)
#' returns a list of length `R` of \eqn{n \times k}
#' multivariate normal data matrix or data frame.
#'
#' @references Venables, W. N., Ripley, B. D., & Venables, W. N. (2002).
#' *Modern applied statistics with S*. New York, N.Y: Springer.
#'
#' [Wikipedia: Multivariate normal distribution](https://en.wikipedia.org/wiki/Multivariate_normal_distribution)
#'
#' @seealso [`jeksterslabRdist::mvnpdf()`], [`jeksterslabRdist::mvnll()`],
#' and [`jeksterslabRdist::mvn2ll()`],
#' for more information on the multivariate normal distribution.
#'
#' @family multivariate data functions
#' @keywords multivariate, normal
#' @inheritParams jeksterslabRdist::mvnpdf
#' @inheritParams univ
#' @inherit jeksterslabRdist::mvnpdf details references
#' @importFrom MASS mvrnorm
#' @param tol Numeric.
#' Tolerance (relative to largest variance)
#' for numerical lack of positive-definiteness in `Sigma`.
#' @param empirical Logical.
#' If `TRUE`, `mu` and `Sigma` specify the empirical,
#' not population. mean and covariance matrix.
#' @param df Logical.
#' If `TRUE`, the function returns a data frame.
#' If `FALSE`, the function returns a matrix.
#' @param varnames Character string.
#' Optional column names with the same length as `mu`.
#' @examples
#' mu <- c(100, 100, 100)
#' Sigma <- matrix(
#' data = c(225, 112.50, 56.25, 112.5, 225, 112.5, 56.25, 112.50, 225),
#' ncol = 3
#' )
#' X <- mvn(n = 100, mu = mu, Sigma = Sigma)
#' Xstar <- mvn(n = 100, mu = mu, Sigma = Sigma, R = 100)
#' str(Xstar, list.len = 6)
#' @export
mvn <- function(n, # mvrnorm
mu = NULL,
Sigma,
tol = 1e-6,
empirical = FALSE,
df = FALSE,
varnames = NULL,
# iter
R = NULL,
# par_lapply
par = FALSE,
ncores = NULL,
mc = TRUE,
lb = FALSE,
cl_eval = FALSE,
cl_export = FALSE,
cl_expr,
cl_vars) {
# main function----------------------------------------------------------------
foo <- function(iter,
n,
mu,
Sigma,
tol,
empirical,
df) {
out <- mvrnorm(
n = n,
mu = mu,
Sigma = Sigma,
tol = tol,
empirical = empirical
)
if (df) {
out <- as.data.frame(out)
}
out
}
#------------------------------------------------------------------------------
# mu to a vector of zeros------------------------------------------------------
if (is.null(mu)) {
mu <- rep(
x = 0,
times = nrow(Sigma)
)
message(
paste0(
"mu = NULL. mu is set to a vector of zeroes of length ",
nrow(Sigma),
"."
)
)
}
#------------------------------------------------------------------------------
# optional column names------------------------------------------------------
if (!is.null(varnames)) {
names(mu) <- varnames
}
#------------------------------------------------------------------------------
# negotiate single rep of multiple rep
if (is.null(R)) {
single_rep <- TRUE
} else {
if (R == 1) {
single_rep <- TRUE
} else {
single_rep <- FALSE
}
}
#------------------------------------------------------------------------------
# execute----------------------------------------------------------------------
if (single_rep) {
# single rep-----------------------------------------------------------------
return(
foo(
n = n,
mu = mu,
Sigma = Sigma,
tol = tol,
empirical = empirical,
df = df
)
)
# ---------------------------------------------------------------------------
} else {
# multiple reps--------------------------------------------------------------
return(
par_lapply(
# iter
X = 1:R,
# foo
FUN = foo,
# foo
n = n,
mu = mu,
Sigma = Sigma,
tol = tol,
empirical = empirical,
df = df,
# par_lapply
par = par,
ncores = ncores,
mc = mc,
lb = lb,
cl_eval = cl_eval,
cl_export = cl_export,
cl_expr = cl_expr,
cl_vars = cl_vars,
rbind = NULL # always null
)
)
#----------------------------------------------------------------------------
}
}
#' @author Ivan Jacob Agaloos Pesigan
#'
#' @title Generate Multivariate Normal Data
#' \eqn{
#' \mathbf{X} \sim \mathcal{N}_{k}
#' \left( \boldsymbol{\mu}, \boldsymbol{\Sigma} \right)
#' %(\#eq:dist-X-mvn)
#' }
#' from the Reticular Action Model Matrices
#'
#' @description Generates an \eqn{n \times k} multivariate data matrix
#' or a list of \eqn{n \times k} multivariate data matrices of length `R`
#' from the multivariate normal distribution
#' \deqn{
#' \mathbf{X} \sim \mathcal{N}_{k}
#' \left( \boldsymbol{\mu}, \boldsymbol{\Sigma} \right) .
#' %(\#eq:dist-X-mvn)
#' }
#' The model-implied matrices used to generate data
#' is derived from the Reticular Action Model (RAM) Matrices.
#'
#' @details The multivariate normal distribution has two parameters,
#' namely the \eqn{k \times 1} mean vector
#' `mu` \eqn{\left( \boldsymbol{\mu} \right)}
#' and the \eqn{k \times k} variance-covariance matrix
#' `Sigma` \eqn{\left( \boldsymbol{\Sigma} \right)}.
#'
#' The mean vector `mu` can be supplied directly using the `mu` argument.
#' It can also be derived using `M`.
#' Note that the argument `mu` takes precedence over `M`.
#' If `mu` is not provided, it is computed using `M`
#' with the [`jeksterslabRsem::ram_mutheta()`] function.
#' If both `mu` and `M` are not provided,
#' `mu` is set to a vector of zeroes with the appropriate length.
#'
#' The variance-covariance matrix `Sigma` is derived
#' from the RAM matrices `A`, `S`, `F`, and `I`.
#'
#' `mu` and `Sigma` are then used by the [`mvn()`] function
#' to generate multivariate normal data.
#'
#' Options for explicit parallelism are provided when `R > 1`
#' especially when `R` is large. See `par` and suceeding arguments.
#'
#' @seealso
#' [`jeksterslabRsem::ram_Sigmatheta()`], and [`jeksterslabRsem::ram_mutheta()`]
#' for more information on the Reticular Action Model (RAM)
#' and [`mvn()`] for multivariate normal data generation.
#'
#' @family multivariate data functions
#' @keywords multivariate normal
#' @inheritParams mvn
#' @inheritParams jeksterslabRsem::ram_mutheta
#' @inheritParams jeksterslabRsem::ram_Sigmatheta
#' @inherit mvn return
#' @inherit jeksterslabRsem::ram_Sigmatheta references
#' @importFrom jeksterslabRsem ram_mutheta
#' @importFrom jeksterslabRsem ram_Sigmatheta
#' @examples
#' mu <- c(100, 100, 100)
#' A <- matrix(
#' data = c(0, sqrt(0.26), 0, 0, 0, sqrt(0.26), 0, 0, 0),
#' ncol = 3
#' )
#' S <- diag(c(225, 166.5, 116.5))
#' F <- I <- diag(3)
#' X <- mvnram(n = 100, mu = mu, A = A, S = S, F = F, I = I)
#' Xstar <- mvnram(n = 100, mu = mu, A = A, S = S, F = F, I = I, R = 100)
#' str(Xstar, list.len = 6)
#' @export
mvnram <- function(n,
mu = NULL,
M = NULL,
A,
S,
F,
I,
tol = 1e-6,
empirical = FALSE,
df = FALSE,
varnames = NULL,
R = NULL,
par = FALSE,
ncores = NULL,
mc = TRUE,
lb = FALSE,
cl_eval = FALSE,
cl_export = FALSE,
cl_expr,
cl_vars) {
# derive Sigma-----------------------------------------------------------------
Sigma <- ram_Sigmatheta(
A = A,
S = S,
F = F,
I = I
)
#------------------------------------------------------------------------------
# negotiate derivation of mu---------------------------------------------------
if (is.null(mu)) {
# mu is not provided
if (is.null(M)) {
message(
paste0(
"mu = NULL and M = NULL. mu is set to a vector of zeroes of length ",
nrow(Sigma),
"."
)
)
# both mu and M are not provided
# generate mu from zero
generate_mu_from_M <- FALSE
generate_mu_from_zero <- TRUE
} else {
message(
"mu = NULL. mu is computed using M."
)
# mu is not provided
# M is provided
# generate mu from M
generate_mu_from_M <- TRUE
generate_mu_from_zero <- FALSE
}
} else {
# mu is provided
# even if M is provided mu takes precedence
generate_mu_from_M <- FALSE
generate_mu_from_zero <- FALSE
}
# derive mu from M-------------------------------------------------------------
if (generate_mu_from_M) {
mu <- ram_mutheta(
A = A,
F = F,
I = I,
M = M
)
}
#------------------------------------------------------------------------------
# generate mu from zeros-------------------------------------------------------
if (generate_mu_from_zero) {
mu <- rep(
x = 0,
times = nrow(Sigma)
)
}
#------------------------------------------------------------------------------
# execute----------------------------------------------------------------------
mvn(
# mvrnorm
n = n,
mu = mu,
Sigma = Sigma,
tol = tol,
empirical = empirical,
df = df,
varnames = varnames,
# iter
R = R,
# par_lapply
par = par,
ncores = ncores,
mc = mc,
lb = lb,
cl_eval = cl_eval,
cl_export = cl_export,
cl_expr = cl_expr,
cl_vars = cl_vars
)
#------------------------------------------------------------------------------
}
#' @author Ivan Jacob Agaloos Pesigan
#'
#' @title Generate Multivariate Normal Data
#' \eqn{
#' \mathbf{X} \sim \mathcal{N}_{k}
#' \left( \boldsymbol{\mu}, \boldsymbol{\Sigma} \right)
#' %(\#eq:dist-X-mvn)
#' }
#' from the Reticular Action Model Matrices
#' \eqn{\mathrm{A}}, \eqn{\mathrm{F}}, \eqn{\mathrm{I}},
#' and the vector of variable variances \eqn{\sigma^2}
#'
#' @details The \eqn{\mathbf{S}} matrix is derived
#' from a vector of variances sigma2 \eqn{\left( \sigma^2 \right)}
#' and the proceeds to generating data using the [`mvnram()`] function.
#' **The first element in sigma2 should be the variance of an exogenous variable.**
#'
#' @family multivariate data functions
#' @keywords multivariate normal
#' @inheritParams mvnram
#' @inheritParams jeksterslabRsem::ram_S
#' @inherit mvnram description return
#' @importFrom jeksterslabRsem ram_S
#' @examples
#' mu <- c(100, 100, 100)
#' A <- matrix(
#' data = c(0, sqrt(0.26), 0, 0, 0, sqrt(0.26), 0, 0, 0),
#' ncol = 3
#' )
#' sigma2 <- c(225, 225, 225)
#' F <- I <- diag(3)
#' X <- mvnramsigma2(n = 100, mu = mu, A = A, sigma2 = sigma2, F = F, I = I)
#' str(X)
#' Xstar <- mvnramsigma2(n = 100, mu = mu, A = A, sigma2 = sigma2, F = F, I = I, R = 100)
#' str(Xstar, list.len = 6)
#' @export
mvnramsigma2 <- function(n,
mu = NULL,
M = NULL,
A,
sigma2,
F,
I,
tol = 1e-6,
empirical = FALSE,
df = FALSE,
varnames = NULL,
R = NULL,
par = FALSE,
ncores = NULL,
mc = TRUE,
lb = FALSE,
cl_eval = FALSE,
cl_export = FALSE,
cl_expr,
cl_vars) {
S <- ram_S(
A = A,
sigma2 = sigma2,
F = F,
I = I,
SigmaMatrix = FALSE
)
mvnram(
n = n,
A = A,
S = S,
F = F,
I = I,
M = M,
mu = mu,
tol = tol,
empirical = empirical,
df = df,
varnames = varnames,
R = R,
par = par,
ncores = ncores,
mc = mc,
lb = lb,
cl_eval = cl_eval,
cl_export = cl_export,
cl_expr = cl_expr,
cl_vars = cl_vars
)
}
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