1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
|
#
# 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
"stationary.cov" <- function(x1, x2=NULL, Covariance = "Exponential", Distance = "rdist",
Dist.args = NULL, aRange = 1, V = NULL, C = NA, marginal = FALSE,
derivative = 0, distMat = NA, onlyUpper = FALSE,
theta=NULL, ...) {
# get covariance function arguments from call
# theta argument has been deopreciated.
if( !is.null( theta)){
aRange<- theta
}
cov.args <- list(...)
# 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)
#
# separate out a single scalar transformation and a
# more complicated scaling and rotation.
# this is done partly to have the use of great circle distance make sense
# by applying the scaling _after_ finding the distance.
#
if (length(aRange) > 1) {
stop("aRange as a vector matrix has been depreciated use the V argument")
}
#
# following now treats V as a full matrix for scaling and rotation.
#
# try to catch incorrect conbination of great circle distance and V
if (Distance == "rdist.earth" & !is.null(V)) {
stop("V not supported with great circle distance")
}
# use V the anisotropic scaling and rotation from covariance arguments
# if exists
if( !is.null(cov.args$V) ){
V<- cov.args$V
}
if (!is.null(V)) {
if (aRange != 1) {
stop("can't specify both aRange and V!")
}
x1 <- x1 %*% t(solve(V))
x2 <- x2 %*% t(solve(V))
}
#
# locations are now scaled and rotated correctly
# now apply covariance function to pairwise distance matrix, or multiply
# by C vector or just find marginal variance
# this if block finds the cross covariance matrix
if (is.na(C[1]) && !marginal) {
#
# if distMat is supplied, evaluate covariance for upper triangular part only
#
if(is.na(distMat[1])) {
# distMat not supplied so must compute it along with covariance matrix
# note overall scaling by aRange (which is just aRange under isotropic case)
if(is.null(x2))
distMat <- do.call(Distance, c(list(x1), Dist.args))
else
distMat <- do.call(Distance, c(list(x1=x1, x2=x2), Dist.args))
}
#
# now convert distance matrix to covariance matrix
#
# print("**** in stationary.cov" )
# cat("aRange", aRange, fill=TRUE)
#
if(inherits(distMat, "dist")) {
#
# distMat is in compact form, so evaluate covariance over all distMat and convert to matrix form
diagVal = do.call(Covariance, c(list(d=0), cov.args))
if(onlyUpper)
return(compactToMat(do.call(Covariance, c(list(d=distMat*(1/aRange)), cov.args)), diagVal))
else
# if onlyUpper==FALSE, also set lower triangle of covariance matrix
return(compactToMat(do.call(Covariance, c(list(d=distMat*(1/aRange)), cov.args)), diagVal, lower.tri=TRUE))
}
else {
# distMat is a full matrix
# print(Covariance)
# print( aRange)
tmp<- do.call(Covariance, c(list(d = distMat/aRange), cov.args))
return( tmp)
}
}
# or multiply cross covariance by C
# as coded below this is not particularly efficient of memory
else if(!is.na(C[1])) {
if(onlyUpper) {
#the onlyUpper option is not compatible with the C option
onlyUpper = FALSE
}
if(is.null(x2))
bigD <- do.call(Distance, c(list(x1, x1), Dist.args))
else
bigD <- do.call(Distance, c(list(x1=x1, x2=x2), Dist.args))
if (derivative == 0) {
return(do.call(Covariance, c(list(d = bigD*(1/aRange)), cov.args)) %*% C)
}
else {
# find partial derivatives
tempW <- do.call(Covariance, c(list(d = bigD*(1/aRange)),
cov.args, derivative = derivative))
# loop over dimensions and knock out each partial accumulate these in
# in temp
temp <- matrix(NA, ncol = d, nrow = n1)
for (kd in 1:d) {
# Be careful if the distance (tempD) is close to zero.
# Note that the x1 and x2 are in transformed ( V inverse) scale
sM <- ifelse(bigD == 0, 0, tempW * outer(x1[, kd], x2[, kd], "-")/(aRange * bigD))
# accumlate the new partial
temp[, kd] <- sM %*% C
}
# transform back to original coordinates.
if (!is.null(V)) {
temp <- temp %*% t(solve(V))
}
return(temp)
}
}
# or find marginal variance and return a vector.
else if (marginal) {
tau2 <- do.call(Covariance, c(list(d = 0), cov.args))
return(rep(tau2, nrow(x1)))
}
# should not get here based on sequence of conditional if statements above.
}
|
