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# fields is a package for analysis of spatial data written for
# the R software environment .
# Copyright (C) 2018
# University Corporation for Atmospheric Research (UCAR)
# Contact: Douglas Nychka, nychka@ucar.edu,
# National Center for Atmospheric Research,
# PO Box 3000, Boulder, CO 80307-3000
#
# 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.
# test of vgram
suppressMessages(library(fields))
options(echo=FALSE)
data( ozone2)
y<- ozone2$y[16,]
x<- ozone2$lon.lat
vgram( x, y, lon.lat=TRUE)-> out
# compute "by hand"
outer( y, y ,"-")-> hold
hold<- .5*hold^2
rdist.earth( x,x)-> hold2
col( hold2)> row( hold2)-> upper
hold<- hold[upper]
hold2<- hold2[upper]
order( hold2)-> od
hold2<- hold2[od]
hold<- hold[od]
ind<- is.na(hold)
hold<- hold[!ind]
hold2<- hold2[!ind]
test.for.zero( hold, out$vgram, tag="vgram single time")
# multiple times including NAs at some times
y<- t(ozone2$y[16:18,])
x<- ozone2$lon.lat[,]
out<- vgram( x, y, lon.lat=TRUE)
N<- nrow( y)
hold<- cbind(c(outer( y[,1], y[,1],"-")),
c(outer( y[,2], y[,2],"-") ),
c(outer(y[,3], y[,3],"-")) )
hold<- .5*hold^2
hold<- rowMeans( hold, na.rm=TRUE)
hold<- matrix( hold, N,N)
rdist.earth( x,x)-> hold2
col( hold2)> row( hold2)-> upper
hold<- hold[upper]
hold2<- hold2[upper]
order( hold2)-> od
hold2<- hold2[od]
hold<- hold[od]
ind<- is.na(hold)
hold<- hold[!ind]
hold2<- hold2[!ind]
test.for.zero( hold, out$vgram, tag="vgram more than one time point")
# test covariogram versus correlogram
y<- ozone2$y[16,]
x<- ozone2$lon.lat
sigma2 = var(y, na.rm=TRUE)
lookCov = vgram(x, y, lon.lat=TRUE, type="covariogram")
lookCor = vgram(x, y, lon.lat=TRUE, type="correlogram")
test.for.zero(lookCov$vgram*(1/sigma2), lookCor$vgram, tag="correlogram versus covariogram")
# test cross-covariogram versus cross-correlogram
sigma2 = var(y, na.rm=TRUE)
lookCov = crossCoVGram(x, x, y, y, lon.lat=TRUE, type="cross-covariogram")
lookCor = crossCoVGram(x, x, y, y, lon.lat=TRUE, type="cross-correlogram")
test.for.zero(lookCov$vgram*(1/sigma2), lookCor$vgram, tag="correlogram versus covariogram")
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