# R/lyapunov.R In maotai: Tools for Matrix Algebra, Optimization and Inference

#### Documented in lyapunov

#' Solve Lyapunov Equation
#'
#' The Lyapunov equation is of form
#' \deqn{AX + XA^\top = Q}
#' where \eqn{A} and \eqn{Q} are square matrices of same size. Above form is also known as \emph{continuous} form.
#' This is a wrapper of \code{armadillo}'s \code{sylvester} function.
#'
#' @param A a \eqn{(p\times p)} matrix as above.
#' @param Q a \eqn{(p\times p)} matrix as above.
#'
#' @return a solution matrix \eqn{X} of size \eqn{(p\times p)}.
#'
#' @examples
#' ## simulated example
#' #  generate square matrices
#' A = matrix(rnorm(25),nrow=5)
#' X = matrix(rnorm(25),nrow=5)
#' Q = A%*%X + X%*%t(A)
#'
#' #  solve using 'lyapunov' function
#' solX = lyapunov(A,Q)
#' \dontrun{
#' pm1 = "* Experiment with Lyapunov Solver"
#' pm2 = paste("* Absolute Error  : ",norm(solX-X,"f"),sep="")
#' pm3 = paste("* Relative Error  : ",norm(solX-X,"f")/norm(X,"f"),sep="")
#' cat(paste(pm1,"\n",pm2,"\n",pm3,sep=""))
#' }
#'
#' @references
#'
#'
#' @export
lyapunov <- function(A, Q){
###################################################################
# check square matrix
if (!check_sqmat(A)){
stop("* lyapunov : an input 'A' should be a square matrix.")
}
if (!check_sqmat(Q)){
stop("* lyapunov : an input 'Q' should be a square matrix.")
}

###################################################################
B = t(A)
C = -Q

###################################################################
# pass and return
return(solve_lyapunov(A,B,C))
}


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maotai documentation built on Oct. 25, 2021, 9:06 a.m.