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#
# fields is a package for analysis of spatial data written for
# the R software environment.
# Copyright (C) 2024 Colorado School of Mines
# 1500 Illinois St., Golden, CO 80401
# Contact: Douglas Nychka, douglasnychka@gmail.com,
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with the R software environment if not, write to the Free Software
# Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
# or see http://www.r-project.org/Licenses/GPL-2
##END HEADER
"Paciorek.cov" <- function(x1,
x2 = NULL,
Distance = "rdist",
Dist.args = NULL,
aRangeObj = 1,
rhoObj = NULL,
C = NA,
marginal = FALSE,
smoothness = .5)
{
# get covariance function arguments from call
if (class(aRangeObj)[1] == "numeric") {
class(aRangeObj) <- "constant"
}
# coerce x1 and x2 to matrices
if (is.data.frame(x1))
x1 <- as.matrix(x1)
if (!is.matrix(x1))
x1 <- matrix(c(x1), ncol = 1)
if (is.null(x2))
x2 = x1
if (is.data.frame(x2))
x2 <- as.matrix(x2)
if (!is.matrix(x2) & !is.null(x2))
x2 <- matrix(c(x2), ncol = 1)
d <- ncol(x1)
n1 <- nrow(x1)
n2 <- nrow(x2)
#
if (!marginal) {
aRangex1 <- c(predict(aRangeObj, x1))
aRangex2 <- c(predict(aRangeObj, x2))
# this is (Sigma_i + Sigma_j )/2
aRange2Matrix <- (outer(aRangex1 ^ 2, aRangex2 ^ 2, '+') / 2)
distMat <- do.call(Distance, c(list(x1 = x1,
x2 = x2), Dist.args))
dimX<- ncol( x1) # adjust for dimension.
# detS1= (determinant Sigma_i) ^1/4
detS1<- (aRangex1)^(2*dimX/4)
detS2<- (aRangex2)^(2*dimX/4)
# detS12 = (determinant (Sigma_i + Sigma_j)/2 ) ^1/2
detS12 <- aRange2Matrix^(dimX/2)
normCov <-outer(detS1, detS2, "*")/detS12
covMat <- normCov * Matern(
distMat / sqrt(aRange2Matrix),
smoothness = smoothness)
if (!is.null(rhoObj)) {
cat( "sigma Obj used", fill=TRUE)
sigmax1 <- c(sqrt(predict(rhoObj, x1)))
sigmax2 <- c(sqrt(predict(rhoObj, x2)))
covMat <- t(t(sigmax1 * covMat) * sigmax2)
}
# else assume that rho is constant and 1.0
if (is.na(C[1])) {
# distMat is a full matrix
return(covMat)
}
# or multiply cross covariance by C
# as coded below this is not particularly efficient of memory
else{
return(covMat %*% C)
}
}
else{
if (!is.null(rhoObj)) {
marginalVariance <- predict(rhoObj, x1)
}
else{
marginalVariance <- rep(1, ncol(x1))
}
return(marginalVariance)
}
}
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