\name{RFparameters}
\alias{RFparameters}
\title{Control Parameters}
\description{
  \code{RFparameters} sets and returns control parameters for the simulation
  of random fields
}
\usage{
   RFparameters(..., no.readonly=FALSE)
}
\arguments{
  \item{...}{arguments in \code{tag = value} form, or a list of tagged
    values.}
  \item{no.readonly}{If \command{RFparameters} is called without
    parameter then all parameters are returned in a list. If
    \code{no.readonly=TRUE} then only rewritable parameters are returned.
  }
}
\details{
  The possible parameters are
  %
  \cr\cr\bold{General options}\cr
  \describe{
  \item{\code{PracticalRange}}{logical or 2, 3, 11, 12, 13.
    If not \code{FALSE} the range of the covariance functions is
    adjusted so that cov(1) is about 0.05 (for \code{scale==1}).
    \itemize{
      \item \code{FALSE} : the practical range ajustment is not used.
      \item \code{TRUE} : \code{PracticalRange} is applicable only if the value
      is known exactly.
      \item \code{2} : \code{PracticalRange} is applicable if the value is
      known pretty well
      \item \code{3} : \code{PracticalRange} is applicable if the value is
      roughly known
      \item \code{11} : if the practical range is not known exactly it
      is approximated numerically.
       \item \code{12} : if the practical range is not known pretty well it
       is approximated numerically.
      \item \code{13} : if the practical range is even not known
      approximately it is approximated numerically.
    }
    Note that values beyond \code{FALSE}, \code{TRUE}, and \code{11},
    are only used for specialists' purposes.
    
    Default: \code{FALSE} [init].}

  \item{\code{PrintLevel}}{If \code{PrintLevel}\eqn{\le0}{<=0}
      there is not any output on the screen.  The
      higher the number the more tracing information is given. 
      Default: 1 [init, do].\cr
      1 : error messages\cr
      2 : messages about partial failures of the algorithm\cr
      >2 : additional informations
      
      Note that \code{PrintLevel} is also used in other packages
      as a default, for example in \link[SoPhy]{SoPhy}
      (\command{\link[SoPhy]{risk.index}} and
      \command{\link[SoPhy]{create.roots}}). The changing of
      \code{PrintLevel} here may cause some unexpected effects in these
      functions. See the documentation there.
    }
  }
  %
  \bold{General options for simulating}\cr
  \describe{
    \item{\code{pch}}{Character or empty string.
      The character is printed after each
      performed simulation if more than one simulation is performed at
      once. If \code{pch='!'} then a counter is shown instead of the character.
      Note that also '\eqn{\mbox{\textasciicircum}}{^}H's are printed if
      the counter (\code{pch='!'}) is shown, 
      which may have undesirable interactions with some few other R
      functions, e.g.  \command{\link[utils]{Sweave}}.
      Default: \code{'*'} [do]. 
    }
   \item{\code{Storing}}{Logical.
      If \code{TRUE} then intermediate results are kept
      after each simulation; if several simulation are performed with the same
      model parameters then
      \code{Storing=TRUE} accelerates the simulations, but needs additional
      memory. \cr
      Note that in subsequent calls of \command{\link{GaussRF}}
      intermediate changes of RFparameters with flag "[init]"
      do not have any influence on the algorithm.
      Hence, for studying the effects for
      divers values of technical parameters like
      \code{CE.force}, \code{CE.mmin}, etc. the parameter \code{Storing} must be
      \code{FALSE}.  See also last paragraphs in the Details.
      Default: \code{TRUE} [init, do].
    }
    \item{\code{stationary.only}}{Logical or NA. Used for the automatic
      choice of methods. See also \link{RFMethods}.
      \itemize{
	\item \code{TRUE}: the simulation of non-stationary random
	fields is refused. In particular, the intrinsic
	embedding method is excluded and
	the simulation of Brownian motion is rejected.
	\item \code{FALSE}: intrinsic embedding is always allowed,
	actually it's the first one considered in the automatic
	selection algorithm.
	\item \code{NA}: the simulation of the Brownian motion allowed,
	but intrinsic embedding is not used for stationary random fields.
      }
      Default: \code{NA} [init].}        
  }
  %

  \bold{Options for simulating with the circulant embedding method}\cr
  \describe{
    \item{\code{CE.force}}{Logical.  Circulant embedding does not work if a
      certain matrix has negative eigenvalues.  Sometimes it is convenient
      to replace all the negative eigenvalues by zero
      (\code{CE.force==TRUE}) after \code{CE.trials} number of trials. 
      Default: \code{FALSE} [init].
    }
    \item{\code{CE.mmin}}{Scalar or vector. 
      Circulant embedding usually uses the smallest matrix
      possible; by \code{CE.mmin} the minimum number of rows and columns
      of the matrix are given.  If \code{CE.mmin>=0} then the minimum
      absolute size is given.\cr
      If \code{CE.mmin<0} then the follow holds.
      If \code{CE.userfft==FALSE} then the matrix
      has \code{-CE.mmin} times the size of the size of the smallest
      matrix.  If \code{CE.userfft==TRUE} then the matrix
      has \code{max(-CE.mmin/2,1)} times the size of the size of the smallest
      matrix.  Default: \code{0} [init].}    
    \item{\code{CE.strategy}}{0 : if matrix has negative eigenvalues then the
      size in each direction is doubled; \cr 1 : the size is enhanced only in
      one direction, namely that where the covariance function has the
      largest value at the end point of the grid - note that
      the default value of \code{CE.trials} is probably too small
      in that case. \cr Default: \code{0}
      [init].}
    \item{\code{CE.maxmem}}{maximum edge length of the ciculant matrix;
      the total amount of memory needed for internal calculation
      is about 16 (=2 * sizeof(double))
      times as large if \command{\link{RFparameters}}\code{()$Storing=FALSE}
      and 32 (=4 * sizeof(double)) time as large if \code{Storing=TUE}
      \cr Default: \code{20000000} [init].
    }
    \item{\code{CE.tolIm}}{Circulant embedding.
      If the modulus of the imaginary part is less than
      \code{CE.tolIm} then the eigenvalue is considered as real. 
      Default: \code{1E-3} [init].}
    \item{\code{CE.tolRe}}{Circulant embedding.
      Threshold above which eigenvalues are considered as
      non-negative.  Default: \code{-1E-7} [init].}
    \item{\code{CE.trials}}{Circulant embedding.
      A larger embedding matrix is likely to make more eigenvalues
      non-negative. If at least one of the thresholds \code{CE.tolRe} and
      \code{CE.tolIm} are missed then the matrix size is doubled,
      and the matrix is checked again.  This procedure is repeated
      up to \code{CE.trials-1} times.  If there are still negative
      eigenvalues, the simulation method fails if \code{CE.force==FALSE}. 
      Default: \code{3} [init].
    }
    \item{\code{CE.userfft}}{Logical.  If \code{FALSE}
      the columns of the circulant matrix
      have length \eqn{2^k} for some \eqn{k}.  Otherwise the algorithm
      tries to find a nicely factorizable number close to the size of the
      given matrix.  Default: \code{FALSE}  [init].}
  }
  %
  \bold{Options for simulating with the local circulant embedding methods}\cr
  \describe{
    \item{\code{cutoff.a}}{Cut-off embedding.
      The key parameter in the local covariance functions. If
      \code{cutoff.a==0} then the simulation method will assign
      an appropriate value to it for each local covariance function;
      If \code{cutoff.a>0} then the simulation method will use this
      value for every local covariance function.
      Default: \code{0} [init].
    }
    \item{\code{intrinsic.r}}{Intrinsic embedding.
      The key parameter in the local covariance functions. If
      \code{intrinsic.r==0} then the simulation method will assign
      an appropriate value to it for each local covariance function;
      If \code{intrinsic.r>0} then the simulation method will use this
      value for every local covariance function.
      Default: \code{0} [init].
    }
  }                                                                           
  \bold{Options for simulating by simple matrix decomposition}\cr
  \describe{
    \item{\code{direct.checkprecision}}{Gaussian
      random vectors can be generated
      by means of the square root of the covariance matrix. 
      By default Cholesky decomposition is used.  If
      \code{direct.checkprecision==TRUE} then the precision is checked. 
      Default: \code{FALSE} [init].}
    \item{\code{direct.maxvariables}}{Decomposition of the covariance matrix.
      If the number of variables to generate is
      greater than \code{direct.maxvariables}, then any matrix decomposition
      method is rejected.  It is important that this option is set
      conveniently if \code{method==NULL} in  \link{GaussRF}. 
      Default: \code{1800} [init]}
    \item{\code{direct.method}}{Decomposition of the covariance matrix.
      If \code{direct.method==1}, Cholesky
      decomposition will not be attempted, but singular value
      decomposition
      used instead.
      Default: \code{0} [init].}
    \item{\code{direct.requiredprecision}}{Decomposition of the covariance
      matrix. 
      If \code{direct.checkprecision==TRUE} and
      the \code{direct.requiredprecision} is not reached then Cholesky
      decomposition fails, and singular value decomposition is used. 
      Default: \code{1e-11} [init].
    }
  }
%

  \bold{Options for simulating with a turning bands method}\cr
  \describe{
    \item{\code{spectral.grid}}{Logical.  Spectral turning bands is implemented
      for 2 dimensions only.  The angle of the lines is random if
      \code{spectral.grid==FALSE}, 
      and \eqn{k\pi/}{k*pi/}\code{spectral.lines}
      for \eqn{k}{k} in \code{1:spectral.lines},
      otherwise.  Default: \code{TRUE} [do].}
    \item{\code{spectral.lines}}{Spectral turning bands.
      Number of lines used (in total for all additive components of the
      covariance function).  Default: \code{500} [do].}
    %\item{\code{TBM.method}}{Set at init time; setting ignored and stored
    %setting used if other parameters are identical to former parameters!
    %-- use DeleteKey, to make sure that the current setting is used.
    % [init]}
    \item{\code{TBM.method}}{character.
      Currently either \code{'circulant embedding'} or \code{'direct'}.
      The preferred method to simulate on the line. If \code{'direct'}
      then the method is overwritten if the number of points on the grid
      is larger than \code{direct.maxvariables}.
      Default: \code{"circulant embedding"} [init].
    }
    \item{\code{TBM2.every}}{If \code{TBM2.every>0} then every
      \code{TBM2.every}th iteration is announced.
      Default: \code{0} [do].}
    \item{\code{TBM2.lines}}{Ordinary 2-dimensional turning bands method. 
      Number of lines used. 
      Default: \code{60} [do].}
    \item{\code{TBM2.linesimufactor}}{Either \code{TBM2.linesimufactor} or
      \code{TBM2.linesimustep} must be greater than zero.  The parameter
      that is zero is ignored.  The grid on the line is
      \code{TBM2.linesimufactor}-times
      finer than the smallest distance. 
      See also \code{TBM2.linesimustep}. 
      Default: \code{2.0} [init].}
    \item{\code{TBM2.linesimustep}}{
      If \code{TBM2.linesimustep} is positive the grid on the line has lag
      \code{TBM2.linesimustep}. 
      See also \code{TBM2.linesimufactor}. 
      Default: \code{0.0} [init].}
    \item{\code{TBM2.num}}{
      Logical. If \code{TRUE} then the covariance function on the line
      for the two-dimensional simulation is approximated numerically.
      If \code{FALSE} only those models are allowed for the
      2-dimensional simulation that have an analytic representation on
      the line.
      Default: \code{TRUE} [init].}
    \item{\code{TBM3D2.every}}{If \code{TBM3D2.every>0} then every
      \code{TBM3D2.every}th iteration is announced.
      Default: \code{0} [do].}
    \item{\code{TBM3D2.lines}}{Ordinary 3-dimensional turning bands method,
      simulation of a \emph{2-dimensional} field. 
      Number of lines used. 
      Default: \code{500} [do].}
    \item{\code{TBM3D2.linesimufactor}}{Either \code{TBM3D2.linesimufactor} or
      \code{TBM2.linesimustep} must be greater than zero.  The parameter
      that is zero is ignored.  The grid on the line is
      \code{TBM3D2.linesimufactor}-times
      smaller than the smallest distance. See also \code{TBM3D2.linesimustep}. 
      Default: \code{2.0} [init].}
    \item{\code{TBM3D2.linesimustep}}{The grid on the line has lag
      \code{TBM3D2.linesimustep}.  See also \code{TBM3D2.linesimufactor}. 
      Default: \code{0.0} [init].}
    \item{\code{TBM3D3.every}}{If \code{TBM3D3.every>0} then every
      \code{TBM3D3.every}th iteration is announced.
      Default: \code{0} [do].}
    \item{\code{TBM3D3.lines}}{Ordinary 3-dimensional turning bands method,
      simulation of a \emph{3-dimensional field}. 
      Number of lines used. 
      Default: \code{500} [do].}
    \item{\code{TBM3D3.linesimufactor}}{Either \code{TBM3D3.linesimufactor} or
      \code{TBM2.linesimustep} must be greater than zero.  The parameter
      that is zero is ignored.  The grid on the line is
      \code{TBM3D3.linesimufactor}-times smaller than the smallest
      distance.  See also \code{TBM3D3.linesimustep}.
      Default: \code{2.0} [init].}
    \item{\code{TBM3D3.linesimustep}}{The grid on the line has lag
      \code{TBM3D3.linesimustep}.  See also \code{TBM3D3.linesimufactor}. 
      Default: \code{0.0} [init].}
    \item{\code{TBMCE.force}}{Ordinary TBM methods. This
      parameter corresponds to \code{CE.force} and is used when
      simulating with circulant embedding on line. 
      Default: \code{FALSE} [init].}
    \item{\code{TBMCE.mmin}}{Ordinary TBM methods.  This parameter corresponds to
      \code{CE.mmin}.  Default: \code{0} [init].}
    \item{\code{TBMCE.strategy}}{Ordinary TBM methods.  This parameter
      corresponds to \code{CE.strategy}.  Default: \code{0} [init].}
    \item{\code{TBMCE.maxmem}}{Ordinary TBM methods.  This parameter
      corresponds to \code{CE.maxmem}.  Default: \code{10000000} [init].}
    \item{\code{TBMCE.tolIm}}{Ordinary TBM methods.  This parameter corresponds
      to \code{CE.tolIm}.  Default: \code{1E-3} [init].}
    \item{\code{TBMCE.tolRe}}{Ordinary TBM methods.  This parameter corresponds
      to \code{CE.tolRe}. Default: \code{-1E-7} [init].}
    \item{\code{TBMCE.trials}}{Ordinary TBM methods.  This parameter corresponds
      to \code{CE.trials}.  Default: \code{3} [init].}
    \item{\code{TBMCE.userfft}}{Ordinary TBM methods.  This parameter corresponds
      to \code{CE.userfft}.  Default: \code{TRUE} [init].}
  }
  %

  \bold{Options for simulating with Poisson point processes}\cr
  \describe{
    \item{\code{add.MPP.realisations}}{Random coins.
      Number of superposed
      realisations (to approximate the normal distribution; total number
      for all (additive) components with same anisotropy);
      Default: \code{100} [do].}
    \item{\code{MPP.approxzero}}{Marked point processes. Functions that
      do not have 
      compact support are set to zero outside the ball outside which the
      function has absolute values less than \code{MPP.approxzero}. 
      Default: \code{0.001} [init].}
    \item{\code{MPP.radius}}{Marked point processes.
      In order avoid edge effects, the simulation area is enlarged by
      a constant \eqn{r}{r} so that all marks have their
      (supposed) support in the ball with radius \eqn{r}{r} centred at
      the origin; see also \code{MPP.approxzero}.
      If \code{MPP.radius>0} the true radius \eqn{r}{r} is replaced by
      \code{MPP.radius}.
      Default: \code{0.0} [init].}
  }
%

  \bold{Options for simulating hyperplane tessellations}\cr
  \describe{
    \item{\code{hyper.superpos}}{integer.
      number of superposed hyperplane tessellations.
      Default: \code{300} [do].
    }
    \item{\code{hyper.maxlines}}{integer.
      estimated number of maximal lines.
      Default: \code{1000} [init].
    }
    \item{\code{hyper.mar.distr}}{integer.
      code for the marginal distribution used in the
      simulation:
      \itemize{
	\item{0}{uniform distribution}
	\item{1}{Frechet distribution with form parameter
	  \code{hyper.mar.param}}
	\item{2}{Bernoulli distribution (Binomial with \eqn{n=1}) with
	  parameter \code{hyper.mar.param}}
      }
      The parameter should not be changed yet.
      Default: \code{0} [do].
    }
    \item{code{hyper.mar.param}}{Parameter used for the marginal
      distribution.
      Default: \code{0} [do].
    }
  }
  
  \bold{Options specific to simulating max-stable random fields}
  \describe{
    \item{\code{maxstable.maxGauss}}{Max-stable random fields.
      The simulation of the max-stable process based on random fields uses
      a stopping rule that necessarily needs a finite upper endpoint
      of the marginal distribution of the random field.
      In the case of extremal Gaussian random fields,
      see \command{\link{MaxStableRF}}, the upper endpoint is
      approximated by \code{maxstable.maxGauss}.
      Default: \code{3.0} [init].
    }
  }

  The following refers to the simulation of Gaussian random fields
  (\command{\link{InitGaussRF}}, \command{\link{GaussRF}}), but most
  parts also apply
  for the simulation of max-stable random fields
  (\command{\link{InitMaxStableRF}}, \command{\link{MaxStableRF}}).
  
  Some of the global parameters determine the basic settings of a
  simulation, e.g. \code{direct.method} (which chooses a square
  root of a positive definite matrix).  The values of
  such parameters are read by
  \command{\link{InitGaussRF}} and stored in an internal register.
  Changing
  such a parameter between calling \command{\link{InitGaussRF}} and calling
  \command{\link{DoSimulateRF}} or between subsequent calls of
  \command{\link{GaussRF}} will not have any effect.  These parameters have
  the flag "[init]".
  
  Parameters like \code{TBM2.lines} (which determines the number of
  i.i.d. processes to be simulated on the line)
  are only relevant when generating
  random numbers.  These parameters are read by \code{DoSimulateRF}
  (or by the second part of \command{\link{GaussRF}}), and
  are marked by "[do]".
  
  \code{Storing} has an influence on both, \command{\link{InitGaussRF}} and
  \command{\link{DoSimulateRF}}.  \command{\link{InitGaussRF}} may reserve
  more memory if \code{Storing==TRUE}.  \command{\link{DoSimulateRF}} will
  free the register
  if \code{Storing==FALSE}, whatever the value of \code{Storing} was
  when \command{\link{InitGaussRF}} was called. 

  The distinction between [init] and [do] is also relevant if 
  \command{\link{GaussRF}} is used and called a second time
  with the same parameters for the random field and if
  \code{RFparameters()$Storing==TRUE}.  
  Then \command{\link{GaussRF}} realises that the second call has the
  same random field parameters, and
  takes over the stored intermediate results (that have been calculated
  with the \code{RFparameters()} at that time).  To prevent the use of
  stored intermediate results or to take into account intermediate
  changes of RFparameters
  set \code{RFparameters(Storing==FALSE)} or use
  \command{\link{DeleteRegister}()} between calls of \code{GaussRF}.

  A programme that checks whether the parameters are well
  adapted to a specific simulation problem is given as an example of
  \command{\link{EmpiricalVariogram}()}.

  For further details on the implemented methods, see \link{RFMethods}.
}
\value{
  If any parameter has been given
  \code{RFparameters} returns an invisible list of
  the given parameters in full name.

  Otherwise the complete list of parameters is returned. Further the
  values of the following internal readonly variables are returned
  
  \item{\code{covmaxchar}}{max. name length for variogram/covariance
  models}
  \item{\code{covnr}}{number of currently implemented
    variogram/covariance models}
  \item{\code{distrmaxchar}}{max. name length for a distribution}
  \item{\code{distrnr}}{number of currently implemented
    distributions} 
  \item{\code{maxdim}}{maximum number of dimensions for a
    random field}
  \item{\code{maxmodels}}{maximum number of elementary models in
    definition of a complex covariance model.}
  \item{\code{methodmaxchar}}{max. name length for methods}
  \item{\code{methodnr}}{number of currently implemented simulation methods}
}
\references{
  Schlather, M. (1999) \emph{An introduction to positive definite
    functions and to unconditional simulation of random fields.}
  Technical report ST 99-10, Dept. of Maths and Statistics,
  Lancaster University. 
}
\author{Martin Schlather, \email{schlath@hsu-hh.de}
  \url{http://www.unibw-hamburg.de/WWEB/math/schlath/schlather.html}}

\seealso{\command{\link{GaussRF}},
  \command{\link{GetPracticalRange}}, 
  \command{\link{MaxStableRF}},
  \code{\link{RandomFields}},
  and \command{\link{RFMethods}}.}

\examples{
 RFparameters(Storing=TRUE)
 str(RFparameters())
}
\keyword{spatial}