\name{RMstp}
\alias{RMstp}
\alias{RMstp}
\title{Single temporal process}
\description{
 \command{\link{RMstp}} is a univariate covariance model which depends on
 a submodel \eqn{\phi}{phi} wich is a normal mixture model.
 The covariance is given by
 \deqn{ 
 C(x,y) = |S_x|^{1/4} |S_y|^{1/4} |A|^{-1/2}
 \phi(Q(x,y)^{1/2})
 }
 where
 \deqn{
 Q(x,y) = c^2 - m^2 + h^t (S_x + 2(m + c)M) A^{-1} (A_y + 2
 (m-c)M)h,
 }
 \deqn{
 c = -z^t h + \xi_2(x) - \xi_2(y),
 }
 \deqn{
 A = S_x + S_y + 4 M h h^t M 
 }
 \deqn{
 m = h^t M h
 }
 \deqn{
 h = S(x) - S(y)
 }
}
\usage{
RMstp(xi2, phi, S, z, M, var, scale, Aniso, proj) 
}
\arguments{
 \item{xi2}{arbitrary univariate function on \eqn{R^d}}
 \item{phi}{an \command{\link{RMmodel}} that is a normal mixture model}
 \item{S}{arbitrary d-variate function on \eqn{R^d}}
 \item{z}{arbitrary vector, \eqn{z \in R^d}}
 \item{M}{an arbitrary \eqn{d \times d}{d x d} matrix}
 \item{var,scale,Aniso,proj}{optional parameters; same meaning for any \command{\link{RMmodel}}. If not passed, the above covariance function remains unmodified.}
}
\details{
 See Schlather (2008) formula (13).
 The model allows for mimicking cyclonic behaviour.
}
\value{
 \command{\link{RMstp}} returns an object of class \code{\link[=RMmodel-class]{RMmodel}}
}
\references{
 \itemize{
 \item Schlather, M. (2008)
 On some covariance models based on normal scale mixtures.
 \emph{Submitted}
 }
}
\author{Martin Schlather, \email{schlather@math.uni-mannheim.de}
}
\seealso{
 \command{\link{RMmodel}},
 \command{\link{RFsimulate}},
 \command{\link{RFfit}}.
}

\keyword{spatial}
\keyword{models}
\examples{
RFoptions(seed=0)
model <- RMstp(xi2 = RMrotat(phi= -2 * pi, speed=1),
               phi = RMwhittle(nu = 1),
               M=matrix(nc=3, rep(0, 9)),
               S=RMetaxxa(E=rep(1, 3), alpha = -2 * pi,
                          A=t(matrix(nc=3, c(2, 0, 0, 1, 1 , 0, 0, 0, 0))))
              )
x <- seq(0, 10, if (interactive()) 0.7 else 5) 
plot(RFsimulate(model, x=x, y=x, z=x))
\dontshow{RFoptions(seed=NA)}
}