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#' Polynomial model with identifiable parameters
#'
#' Creates a polynomial model with identifiable coefficients
#'
#' @param A autoregressive coefficients
#' @param B,F1 coefficients of the numerator and denominator respectively
#' of the deterministic model between the input and output
#' @param C,D coefficients of the numerator and denominator respectively
#' of the stochastic model
#' @param ioDelay the delay in the input-output channel
#' @param Ts sampling interval
#' @param noiseVar variance of the white noise source (Default=\code{1})
#' @param intNoise Logical variable indicating presence or absence of integrator
#' in the noise channel (Default=\code{FALSE})
#' @param unit time unit (Default=\code{"seconds"})
#'
#' @details
#' Discrete-time polynomials are of the form
#' \deqn{
#' A(q^{-1}) y[k] = \frac{B(q^{-1})}{F1(q^{-1})} u[k] +
#' \frac{C(q^{-1})}{D(q^{-1})} e[k]
#' }
#'
#' @examples
#' # define output-error model
#' mod_oe <- idpoly(B=c(0.6,-0.2),F1=c(1,-0.5),ioDelay = 2,Ts=0.1,
#' noiseVar = 0.1)
#'
#' # define box-jenkins model with unit variance
#' B <- c(0.6,-0.2)
#' C <- c(1,-0.3)
#' D <- c(1,1.5,0.7)
#' F1 <- c(1,-0.5)
#' mod_bj <- idpoly(1,B,C,D,F1,ioDelay=1)
#'
#' @export
idpoly <- function(A=1,B=1,C=1,D=1,F1=1,ioDelay=0,Ts=1,
noiseVar=1,intNoise = F,unit = c("seconds","minutes",
"hours","days")[1]){
Bindex <- which.max(B!=0)
ioDelay <- ifelse(Bindex-1==0,ioDelay,Bindex-1)
B <- B[Bindex:length(B)]
out <- list(A= A,B=B,C=C,D=D,F1=F1,ioDelay = ioDelay,Ts=Ts,
noiseVar=noiseVar,unit=unit,intNoise = intNoise)
out$type <- typecheck(out)
class(out) <- "idpoly"
return(out)
}
typecheck <- function(x){
y <- lapply(x[1:5],checkUnity)
if(y$A){
out <- if(y$C && y$D) if(y$F1) "fir" else "oe" else "bj"
} else{
if(y$D && y$F1){
if(x$intNoise){
out <- if(y$C) "ari" else "arima"
} else{
out <- if(y$C) "ar" else "arma"
}
if(!y$B) out <- paste(out,"x",sep="")
} else{
out <- "polynomial"
}
}
out
}
checkUnity <- function(x){
out <- if(length(x)==1 && x==1) TRUE else FALSE
}
#' @export
print.idpoly <- function(x,se=NULL,dig=3){
main <- paste("Discrete-time",toupper(x$type),"model:")
if(x$type=="oe" || x$type=="bj"){
main <- paste(main,"y[k] = B(z)/F(z) u[k] +")
if(x$type=="bj"){
polyExp <- if(!checkUnity(x$C)) "C(z)/D(z)" else "1/D(z)"
if(x$intNoise==T) polyExp <- paste(polyExp,"1/(1-z^{-1})")
main <- paste(main,polyExp,"e[k] \n\n")
}
} else{
main <- paste(main,"A(z)y[k] =")
if(!checkUnity(x$B)) main <- paste(main,"B(z)u[k] +")
if(checkUnity(x$C)){
Cexp <- if(!x$intNoise) "" else "1/(1-z^{-1})"
}else{
Cexp <- "C(z)"
if(x$intNoise) Cexp <- paste(Cexp,"/(1-z^{-1})",sep="")
}
main <- paste(main,Cexp,"e[k] \n\n")
}
cat(main)
# Printing Standard error sequence
j=1
print_se <- function(se){
if(!is.null(se)){
cat(" (+/- ",round(se[j],dig),") ",sep = "")
j <<- j+1
}
}
if(length(x$A)>1){
cat("A(q^{-1}) = ")
for(i in seq_along(x$A)){
if(i-1==0){
cat(round(x$A[i],dig))
} else{
if(x$A[i]>0) cat(" + ") else cat("- ")
if(!(abs(x$A[i])==1)) cat(abs(round(x$A[i],dig)))
print_se(se)
cat("q^{-",i-1,"}",sep="")
}
cat("\t")
}
cat("\n")
}
cat("B(q^{-1}) = ")
for(i in seq_along(x$B)){
if(i+x$ioDelay-1==0){
cat(round(x$B[i],dig))
} else{
if(!((x$ioDelay!=0) && (i==1))){
if(x$B[i]>0) cat(" + ") else cat("- ")
} else{
if(x$B[i]<0) cat("-")
}
if(!(abs(x$B[i])==1)) cat(abs(round(x$B[i],dig)))
print_se(se)
cat("q^{-",i+x$ioDelay-1,"}",sep="")
}
cat("\t")
}
cat("\n")
if(length(x$C)>1){
cat("C(q^{-1}) = ")
for(i in seq_along(x$C)){
if(i-1==0){
cat(round(x$C[i],dig))
} else{
if(x$C[i]>0) cat(" + ") else cat("- ")
if(!(abs(x$C[i])==1)) cat(abs(round(x$C[i],dig)))
print_se(se)
cat("q^{-",i-1,"}",sep="")
}
cat("\t")
}
cat("\n")
}
if(length(x$D)>1){
cat("D(q^{-1}) = ")
for(i in seq_along(x$D)){
if(i-1==0){
cat(round(x$D[i],dig))
} else{
if(x$D[i]>0) cat(" + ") else cat("- ")
if(!(abs(x$D[i])==1)) cat(abs(round(x$D[i],dig)))
print_se(se)
cat("q^{-",i-1,"}",sep="")
}
cat("\t")
}
cat("\n")
}
if(length(x$F1)>1){
cat("F(q^{-1}) = ")
for(i in seq_along(x$F1)){
if(i-1==0){
cat(round(x$F1[i],dig))
} else{
if(x$F1[i]>0) cat(" + ") else cat("- ")
if(!(abs(x$F1[i])==1)) cat(abs(round(x$F1[i],dig)))
print_se(se)
cat("q^{-",i-1,"}",sep="")
}
cat("\t")
}
}
cat("\n")
}
params <- function(x){
c(x$A[-1],x$B,x$C[-1],x$D[-1],x$F1[-1])
}
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