\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 an absolute counter is shown instead of the character. If \code{pch='\%'} then a counter of percentages is shown instead of the character. Note that also '\eqn{\mbox{\textasciicircum}}{^}H's are printed in the last two cases, 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{FALSE} then the intermediate results are destroyed after the simulation of the random field(s). On the other hand, if \code{Storing=TRUE}, then several simulations for the same model parameters are performed faster, see the examples. Note that in subsequent calls of \command{\link{GaussRF}} intermediate changes of RFparameters with flag "[init]" do not have any influence on the algorithm, if \code{Storing=TRUE}. See alse \code{CE.several}, \code{TBMCE.several} and \code{local.several} for related parameters. Default: \code{FALSE} [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].} \item{\code{exactness}}{logical or NA. \itemize{ \item \code{TRUE}: add.MPP, hyperplanes and all turning bands methods are excluded. If the circulant embedding method is considered as badly behaved, then the matrix decomposition methods are preferred. \item \code{FALSE}: if the circulant embedding method is considered as badly behaved or the number of points to be simulated is large, the turning bands methods are rather preferred. \item \code{NA}: approximative non-exact methods are excluded, i.e. TBM2 if the Abel transform of the covariance function cannot be given explicitely. } Default: \code{NA} [init]. } \item{\code{skipchecks}}{logical. If \code{TRUE}, the check whether the given parameter values and the dimension are within the allowed range is skipped. Do not change the value of this variable except you really know what you do. Default: \code{FALSE} [init]. } \item{\code{direct.bestvariables}}{integer. When searching for an appropriate simuation method the matrix decomposition method (see \sQuote{direct method} below) is preferred if the number of variables is less than or equal to \code{direct.bestvariables} Default: \code{800} [init]} } % \bold{Options for simulating with the standard circulant embedding method}\cr \describe{ \item{\code{CE.force}}{Logical. Circulant embedding does not work if a certain circulant 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, integer if positive. \code{CE.mmin} determines the initial size of the circulant matrix. If \code{CE.mmin=0} the minimal starting size is determined automatically according to the dimensions of the grid. If \code{CE.mmin>0} then the absolute starting size is given. If \code{CE.mmin<0} then the automatically determined matrix size is multiplied by \eqn{|\code{CE.mmin}|}; here \code{CE.mmin} must be smaller than -1; the value -1 takes over the minimal starting size.\cr Note: in any cases, the initial size might be increased according to \code{CE.useprimes}.\cr Default: \code{0} [init].} \item{\code{CE.strategy}}{0 : if the circulant matrix has negative eigenvalues then the size in each direction is doubled; \cr 1 : the size is enhanced only in one direction, namely that one 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. In some cases \code{CE.strategy=0} works better, in other cases \code{CE.strategy=1}. Just try. \cr Default: \code{0} [init].} \item{\code{CE.maxmem}}{ maximal total size of the circulant matrix. The total amount of memory needed for the internal calculations is about 16 (=2 * sizeof(double)) times as large as \code{CE.maxmem} if \command{\link{RFparameters}}\code{()$Storing=FALSE} and 32 (=4 * sizeof(double)) time as large if \code{Storing=TRUE}. Note that \code{CE.maxmem} can be used to control the automatic choice of the simulation algorithm. Namely, in case of huge circulant matrices, other simulation methods (TBM) are faster and might be preferred be the user. \cr Default: \code{4096^2 = 16777216} [init]. } \item{\code{CE.tolIm}}{ 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}}{ Eigenvalues between \code{CE.tolRe} and 0 are considered as 0 and set 0. Default: \code{-1E-7} [init].} \item{\code{CE.trials}}{ A larger circulant 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 according to \code{CE.strategy}, 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.several}}{logical. If \code{FALSE} only half the memory is need, but only a single independent realisation can created. Default: \code{TRUE} [init]. } \item{\code{CE.useprimes}}{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{TRUE} [init].} \item{\code{CE.dependent}}{Logical. If \code{FALSE} then independent random fields are created. If \code{TRUE} then at least 4 non-overlapping rectangles are taken out of the the expanded grid defined by the circulant matrix. These simulations are dependent. See below for an example. See \code{CE.trials} for some more information on the circulant matrix. Default: \code{FALSE} [init].} } \bold{Options for simulating with the local ce methods (cutoff, intrinsic)}\cr \describe{ \item{\code{local.force}}{see CE.force above. Default: \code{FALSE} [init]. } \item{\code{local.mmin}}{see CE.mmin above. Difference: if \code{local.mmin=0} the automatic determination of the initial size of the circulant matrix takes into account an expansion factor. This expansion factor is intended to make the circulant matrix positive definite and is either theoretically or numerically known, or guessed. If the usual strategy of circulant embedding (doubling the grid sizes) should be taken over then \code{local.mmin} must be set to \code{-1}. Default: \code{0} [init].} \item{\code{local.maxmem}}{see \code{CE.maxmem} above. Default: \code{20000000} [init].} \item{\code{local.tolIm}}{see \code{CE.tolIm} above. Default: \code{1E-7} [init].} \item{\code{local.tolRe}}{see \code{CE.tolRe} above. Default: \code{-1E-9} [init].} \item{\code{local.several}}{see \code{CE.several} above. Default: \code{1} [init].} \item{\code{local.useprimes}}{see \code{CE.useprimes} above. Default: \code{TRUE} [init].} \item{\code{local.dependent}}{see \code{CE.dependent} above. Default: \code{FALSE} [init].} } % \bold{Options for simulating by simple matrix decomposition}\cr \describe{ \item{\code{direct.maxvariables}}{ 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 to avoid great losses of time during the automatic search of a simulation method (\code{method=NULL} in \command{\link{GaussRF}}). Default: \code{4096} [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].} } % \bold{Options for simulating nugget effects}\cr Simulating a nugget effect seems trivial. It gets complicated and best methods (including \code{direct} and \code{circulant embedding}!) fail if zonal anisotropies are considered, where sets of points have to be identified that belong to the same subspace of eigenvalue 0 of the anisotropy matrix. \describe{ \item{\code{nugget.tol}}{ points at a distance less than or equal to \code{nugget.tol} are considered as being identical. This strategy applies to the simulation method and the covariance function itself. Hence, the covariance function is only positive definite if \code{nugget.tol=0.0}. However, if the anisotropy matrix does not have full rank and \code{nugget.tol=0.0} then, the simulations are likely to be odd. The value of \code{nugget.tol} should be of order \eqn{10^{-15}}{1e-15}. Default: \code{0.0} [init]. } } \bold{Options for simulating with a turning bands method}\cr Currently, there are 3 variants of the turning bands method implemented: \describe{ \item{\code{spectral}}{The spectral turning bands method is implemented for 2 (and 1) dimensions only.} \item{\code{TBM2}}{It is based on the two dimensional turning bands operator and is applicable for 1 and 2 dimensions. As an additional dimension the time dimension can be added. } \item{\code{TBM3}}{It is based on the three dimensional turning bands operator and is applicable for 1,2,3 dimensions. As an additional dimension the time dimension can be added. } } The following parameters are used. \describe{ \item{\code{spectral.grid}}{Logical. 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. The preferred method to simulate on the line for \code{TBM2} and \code{TBM3}; currently either \code{'circulant embedding'} or \code{'direct'}. If \code{'direct'} then the method is overwritten if the number of points on the grid is larger than \code{direct.maxvariables}. If the circulant embedding method is used, then the \code{TBMCE} parameters below determine the behaviour of the circulant embedding algorithm. Default: \code{"circulant embedding"} [init]. } \item{\code{TBM.center}}{Scalar or vector. If not \code{NA}, the \code{TBM.center} is used as the center of the turning bands for \code{TBM2} and \code{TBM3}. Otherwise the center is determined automatically such that the line length is minimal. See also \code{TBM.points} and the examples below. Default: \code{NA} [init]. } \item{\code{TBM.points}}{integer. If greater than 0, \code{TBM.points} gives the number of points simulated on the TBM line, hence must be greater than the minimal number of points given by the size of the simulated field and the two paramters \code{TBMx.linesimufactor} and \code{TBMx.linesimustep}. If \code{TBM.points} is not positive the number of points is determined automatically. The use of \code{TBM.center} and \code{TBM.points} is highlighted in an example below. Default: \code{0} [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}}{ Number of lines used. Default: \code{60} [do].} \item{\code{TBM2.linesimufactor}}{ \code{TBM2.linesimufactor} or \code{TBM2.linesimustep} must be non-negative; if \code{TBM2.linesimustep} is positive then \code{TBM2.linesimufactor} is ignored. If both parameters are naught then \code{TBM.points} is used (and must be positive). 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 is approximated numerically. If \code{FALSE} only those models are allowed that have an analytic representation on the line. Default: \code{TRUE} [init].} \item{\code{TBM2.layers}}{ Logical. If \code{TRUE} then the turning layers are used whenever a time component is given. If \code{FALSE} the turning layers are used only when the traditional TBM is not applicable. If negative then turning layers may never be used. If greater than 1 then only turning layers may be used. Default: \code{FALSE} [init].} \item{\code{TBM3.every}}{If \code{TBM3.every>0} then every \code{TBM3.every}th iteration is announced. Default: \code{0} [do].} \item{\code{TBM3.lines}}{ Number of lines used. Default: \code{500} [do].} \item{\code{TBM3.linesimufactor}}{See \code{TBM2.linesimufactor} for the meaning. Default: \code{2.0} [init].} \item{\code{TBM3.layers}}{See \code{TBM2.layers} for the meaning. Default: \code{FALSE} [init].} \item{\code{TBM3.linesimus}}{See \code{TBM2.linesimustep} for the meaning. Default: \code{0.0} [init].} \item{\code{TBMCE.force}}{see \code{TBM.method} and \code{CE.force} Default: \code{FALSE} [init].} \item{\code{TBMCE.mmin}}{see \code{TBM.method} and \code{CE.mmin}. Default: \code{0} [init].} \item{\code{TBMCE.strategy}}{see \code{TBM.method} and \code{CE.strategy}. Default: \code{0} [init].} \item{\code{TBMCE.maxmem}}{see \code{TBM.method} and \code{CE.maxmem}. Default: \code{10000000} [init].} \item{\code{TBMCE.tolIm}}{see \code{TBM.method} and \code{CE.tolIm}. Default: \code{1E-3} [init].} \item{\code{TBMCE.tolRe}}{see \code{TBM.method} and \code{CE.tolRe}. Default: \code{-1E-7} [init].} \item{\code{TBMCE.trials}}{see \code{TBM.method} and \code{CE.trials}. Default: \code{3} [init].} \item{\code{TBMCE.useprimes}}{see \code{TBM.method} and \code{CE.useprimes}. Default: \code{TRUE} [init].} \item{\code{TBMCE.dependent}}{see \code{TBM.method} and \code{CE.dependent}. Default: \code{FALSE} [init].} } % \bold{Options for simulating with Poisson point processes}\cr \describe{ \item{\code{add.MPP.realisations}}{ 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}}{Functions that do not have compact support are set to zero outside the ball outside for which the function has absolute values less than \code{MPP.approxzero}. Default: \code{0.001} [init].} \item{\code{MPP.radius}}{ 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. Maximum number of allowed lines. Default: \code{1000} [init]. } \item{\code{hyper.mar.distr}}{integer. code for the marginal distribution used in the simulation: \describe{ \item{\code{0}}{uniform distribution} \item{\code{1}}{Frechet distribution with form parameter \code{hyper.mar.param}} \item{\code{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. The parameter should not be changed yet. 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]. } } \bold{General comments on the options} \cr 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: \cr * \code{covmaxchar}: max. name length for variogram/covariance models \cr * \code{covnr}: number of currently implemented variogram/covariance models \cr * \code{distrmaxchar}: max. name length for a distribution \cr * \code{distrnr}: number of currently implemented distributions \cr * \code{maxdim}: maximum number of dimensions for a random field \cr * \code{maxmodels}: maximum number of elementary models in definition of a complex covariance model \cr * \code{methodmaxchar}: max. name length for methods \cr * \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()) ############################################################ ## ## ## use of TBM.points and TBM.center ## ## ## ############################################################ ## The following example shows that the same realisation ## can be obtained on different grid geometries (or point ## configurations) using TBM3 (or TBM2) % library(RandomFields, lib="~/TMP") x1 <- seq(-150,150,1) y1 <- seq(-15, 15, 1) x2 <- seq(-50, 50, 1) model <- "exponential" param <- c(0, 1, 0, 10) meth <- "TBM3" ###### simulation of a random field on long thing stripe runif(1) rs <- get(".Random.seed", envir=.GlobalEnv, inherits = FALSE) DeleteAllRegisters() z1 <- GaussRF(x1, y1, model=model, param=param, grid=TRUE, register=1, method=meth, TBM.center=0, Storing=TRUE) % str(GetRegisterInfo(1)) get(getOption("device"))(height=1.55, width=12) par(mar=c(2.2, 2.2, 0.1, 0.1)) image(x1, y1, z1, col=rainbow(100)) polygon(range(x2)[c(1,2,2,1)], range(y1)[c(1,1,2,2)], border="red", lwd=3) ###### definition of a random field on a square of shorter diagonal assign(".Random.seed", rs, envir=.GlobalEnv) z2 <- GaussRF(x2, x2, model=model, param=param, grid=TRUE, register=2, method=meth, TBM.center=0, TBM.points=length(GetRegisterInfo(1)$method[[1]]$mem$l)) % str(GetRegisterInfo(2)) get(getOption("device"))(height=4.3, width=4.3) par(mar=c(2.2, 2.2, 0.1, 0.1)) image(x2, x2, z2, zlim=range(z1), col=rainbow(100)) polygon(range(x2)[c(1,2,2,1)], range(y1)[c(1,1,2,2)], border="red", lwd=3) ############################################################ ## ## ## use of exactness ## ## ## ############################################################ % library(RandomFields, lib="~/TMP") x <- seq(0, 1, 1/30) model <- list(list(model="stable", var=1, scale=1, kappa=1.0), "+", list(model="gencauchy", var=1, scale=1, kappa=c(1, 2)), ) for (exactness in c(NA, FALSE, TRUE)) { readline(paste("\n\nexactness: ", exactness, "; press return")) DeleteRegister() z <- GaussRF(x, x, grid=TRUE, gridtriple=FALSE, model=model, exactness=exactness, stationary.only=NA, Print=4, n=1, TBM2.linesimustep=1, Storing=TRUE) str(lapply(GetRegisterInfo()$method, function(x) x[c("name", "covnr")])) } ############################################################# ## The following gives a tiny example on the advantage of ## ## local.dependent=TRUE (and CE.dependent=TRUE) if in a ## ## study most of the time is spent with simulating the ## ## Gaussian random fields. Here, the covariance at a pair ## ## of points is estimated. ## ############################################################# # In the example below, local.dependent speeds up the simulation # by about factor 27 at the price of an increased variance of # factor 1.5 x <- seq(0, 1, len=10) y <- seq(0, 1, len=10) grid.size <- c(length(x), length(y)) model <- list(list(model="exp", var=1.1, aniso=c(2,1,0.5,1))) CovarianceFct(matrix(c(1, -1), ncol=2), model=model) ## true value RFparameters(Storing=TRUE) m <- if (interactive()) 1000 else 2 # determine number of non-overlapping realisations on the torus DeleteRegister() InitGaussRF(x, y, model=model, grid=TRUE, method="cu") blocks <- GetRegisterInfo()$method[[1]]$mem$new$method[[1]]$mem$simupos (n <- prod(blocks) * 1) ## n any multiple of prod(blocks) to avoid ## dependencies between the m estimated covariance if ## if local.dep=TRUE; or put RFparameters(Storing=FALSE), ## but this is slower %str(GetRegisterInfo()) # using local.dependent=TRUE... c1 <- numeric(m) DeleteRegister() unix.time( for (i in 1:m) { cat("\n", i) z <- GaussRF(x, y, model=model, grid=TRUE, method="cu", n=n, local.dependent=TRUE, pch="") c1[i] <- cov(z[1,length(y),], z[length(x), 1 , ]) }) # about 35 0.3 35 0 0 var(c1) # about 0.013 # using local.dependent=FALSE... c2 <- numeric(m) DeleteRegister() unix.time( for (i in 1:m) { cat("\n", i) z <- GaussRF(x, y, model=model, grid=TRUE, method="cu", n=n, local.dependent=FALSE, pch="") c2[i] <- cov(z[1,length(y),], z[length(x), 1 , ]) }) # about 950 3 950 0 0 var(c2) # about 0.0087 } \keyword{spatial}