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#' Simulate dynamic system
#'
#' Simulate the response of a system given the input
#'
#' @param model the system model to simulate
#' @param input a vector/matrix containing the input
#' @param sigma standard deviation of the innovations (Default= \code{0})
#' @param seed integer indicating the seed value of the random number generator
#'
#' @return
#' a vector containing the output
#'
#' @details
#' The routine is currently built only for SISO systems. Future Versions will
#' include support for MIMO systems. Current support
#'
#' @seealso
#' \code{\link{sim.idpoly}} for simulating polynomial models
#'
#' @export
sim <- function(model,input,sigma=0,seed=NULL) UseMethod("sim")
#' @export
sim.default <- function(model,input,sigma=0,seed=NULL){
print("The sim method is not developed for the current class of the object")
}
#' Simulate from a Polynomial Model
#'
#' Simulate the response of a system governed by a polynomial model
#' , given the input
#'
#' @param model an object of class \code{idpoly} containing the coefficients
#' @param input a vector/matrix containing the input
#' @param sigma standard deviation of the innovations (Default= \code{0})
#' @param seed integer indicating the seed value of the random number generator
#'
#' @return
#' a vector containing the output
#'
#' @details
#' The routine is currently built only for SISO systems. Future Versions will
#' include support for MIMO systems
#'
#' @seealso
#' \code{\link{idpoly}} for defining polynomial models
#'
#' @examples
#' # ARX Model
#' u <- rnorm(200,sd=1)
#' model <- idpoly(A=c(1,-1.5,0.7),B=c(0.8,-0.25),ioDelay=1)
#' y <- sim(model,u,sigma=0.1)
#'
#' @import polynom
#'
#' @export
sim.idpoly <- function(model,input,sigma=0,seed=NULL){
if(model$type=="arx"){
sim_arx(model,input,sigma,seed)
} else{
require(signal);require(polynom)
n <- length(input)[1]
if(!is.null(seed)) set.seed(seed)
ek <- rnorm(n,sd=sigma)
den1 <- as.numeric(polynomial(model$A)*polynomial(model$D))
filt1 <- Arma(b=model$C,a=den1)
vk <- signal::filter(filt1,ek)
B <- c(rep(0,model$ioDelay),model$B)
den2 <- as.numeric(polynomial(model$A)*polynomial(model$F1))
filt2 <- signal::Arma(b=B,a=den2)
ufk <- signal::filter(filt2,input)
yk <- as.numeric(ufk) + as.numeric(vk)
return(as.numeric(yk))
}
}
sim_arx <- function(model,input,sigma=0,seed=NULL){
na <- length(model$A) - 1; nk <- model$ioDelay;
nb <- length(model$B) - 1; nb1 <- nb+nk
n <- max(na,nb1)
coef <- matrix(c(model$A[-1],model$B),nrow=na+(nb+1))
if(class(input)=="idframe"){
uk <- input$input[,1,drop=T]
} else if(class(input) %in% c("matrix","data.frame")){
uk <- input[,1,drop=T]
} else if(is.numeric(input)){
uk <- input
}
y <- rep(0,length(input)+n)
u <- c(rep(0,n),uk)
if(!is.null(seed)) set.seed(seed)
ek <- rnorm(length(uk),sd=sigma)
# padLeftZeros <- function(x) c(rep(0,n),x)
# u <- apply(input,2,padLeftZeros)
for(i in n+1:length(uk)){
if(nk==0) v <- u[i-0:nb] else v <- u[i-nk:nb1]
reg <- matrix(c(-(y[i-1:na]),v),ncol=na+(nb+1))
y[i] <- reg%*%coef + ek[i-n]
}
return(y[n+1:length(uk)])
}
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