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
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
|
R version 4.4.0 (2024-04-24) -- "Puppy Cup"
Copyright (C) 2024 The R Foundation for Statistical Computing
Platform: aarch64-apple-darwin20
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> #
> # fields is a package for analysis of spatial data written for
> # the R software environment.
> # Copyright (C) 2022 Colorado School of Mines
> # 1500 Illinois St., Golden, CO 80401
> # Contact: Douglas Nychka, douglasnychka@gmail.edu,
> #
> # 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
> ##END HEADER
>
>
> # test of sreg and related functions
>
> suppressMessages(library(fields))
> #options(echo=FALSE)
>
> test.for.zero.flag<- 1
>
>
>
> # simple covariance function for implementation
> exp_cov <- function(dist){
+ sigma2<-1
+ covariance <- sigma2* exp(-dist / 10) # 10 is arbitrary
+ return(covariance)
+ }
>
> # -----------------------------
> # Define grid and observations
> # -----------------------------
>
> m<- 10
> n<- 11
> nx<- m
> ny<- n
> M<- 15
> dx<- 1
> dy<- 1
> sigma2<-2.0
> np<-3
>
>
> # first a case where all obs in same grid box.
> # addition of "dx" also tests that this works when grid is not just integers
> # set dx=1 for the most basic case
> dx<- .5
> s0<- rbind(
+ c(5.1,6.2),
+ c(5.1,6.5),
+ c( 5.85,6.45)
+ )
> s0<- s0*dx
>
> test0<- offGridWeights( s0, list( x= (1:m)*dx, y=(1:n)*dx),
+ aRange=10*dx, sigma2=sigma2,
+ Covariance="Exponential",
+ np=2,
+ debug=TRUE)
[1] 2
Found 1 grid box(es) containing more than 1 obs location
> # explicit nearest neighbors in this case
> sTmp<- cbind( rep(4:7,4), rep(5:8,each=4) )
> sGrid<- sTmp*dx
>
> # check that same grid being used by function
> test.for.zero(sGrid, cbind(test0$gridX[,1], test0$gridY[,1]) )
PASSED test at tolerance 1e-08
>
> S21 <- 2.0* exp( -rdist( s0, sGrid)/(10*dx))
> S11 <- 2.0* exp( -rdist( sGrid , sGrid)/(10*dx) )
> S22 <- 2.0* exp( -rdist( s0, s0)/(10*dx))
> # local weights applied for prediction
> Btest<- S21%*% solve( S11)
> # find indices for neigborhood
> sIndex<- sTmp[,1] + (sTmp[,2]-1)*m
> # Kriging weights
> Bfull<- spam2full(test0$B[,sIndex])
> test.for.zero( Bfull, Btest)
PASSED test at tolerance 1e-08
> # standard error matrix
> # note that transpsoe also taken so SEtest%*%t( SEtest) = cov matrix
> SEtest<- t(chol(S22 - S21%*% solve( S11)%*%t(S21) ))
> SEfull <- spam2full(test0$SE)
> test.for.zero( SEfull, SEtest)
PASSED test at tolerance 1e-08
>
>
> # now test several observation locations
>
> dx<- .45
> s<- rbind(
+ c(5.1,6.2),
+ c(7.1,7.2),
+ c(5.1,6.5),
+ c(8.5,4.4),
+ c( 5.85,6.45),
+ c(7.3,7.4)
+ )
> s<- s * dx
> # Note s0 from above is s[c(1,3,5),]
> ind1<- c(1,3,5)
>
> sTmp<- cbind( rep(4:7,4), rep(5:8,each=4) )
> sGrid<- sTmp*dx
> sIndex<- sTmp[,1] + (sTmp[,2]-1)*m
>
> S21<- 2.0* exp( -rdist( s[ind1,], sGrid)/(10*dx) )
> S11<- 2.0* exp( -rdist( sGrid , sGrid)/(10*dx) )
> S22<- 2.0* exp( -rdist( s[ind1,], s[ind1,])/(10*dx) )
>
> sparseObj<- offGridWeights( s, list( x= (1:m)*dx, y=(1:n)*dx),
+ aRange=(10*dx), sigma2=sigma2,
+ Covariance="Exponential",
+ np=2,
+ debug=TRUE)
[1] 2
Found 2 grid box(es) containing more than 1 obs location
>
> test.for.zero( sparseObj$Sigma21Star[ind1,], S21 )
PASSED test at tolerance 1e-08
> test.for.zero( sparseObj$Sigma11Inv, solve(S11) )
PASSED test at tolerance 1e-08
>
> Btest<- S21%*% solve( S11)
> look2<- spam2full( sparseObj$B)
> test.for.zero( Btest,look2[ind1, sIndex] )
PASSED test at tolerance 1e-08
>
>
> SEfull<- spam2full( sparseObj$SE)
> SE2full<- (SEfull)%*%t(SEfull)
> test.for.zero(diag( SE2full), sparseObj$predictionVariance )
PASSED test at tolerance 1e-08
>
> SEtest<- t(chol(S22 - S21%*%solve( S11)%*%t( S21) ))
> test.for.zero(SEtest, SEfull[ind1, ind1] )
PASSED test at tolerance 1e-08
>
> # check that debug FALSE also works
>
> sparseObj1<- offGridWeights( s, list( x= (1:m)*dx, y=(1:n)*dx),
+ aRange=(10*dx), sigma2=sigma2,
+ Covariance="Exponential",
+ np=2,
+ debug=FALSE)
[1] 2
Found 2 grid box(es) containing more than 1 obs location
>
> test.for.zero( sparseObj$B, sparseObj1$B)
PASSED test at tolerance 1e-08
> test.for.zero( sparseObj$SE, sparseObj1$SE)
PASSED test at tolerance 1e-08
>
> cat("all done with off grid weight tests part 2", fill=TRUE)
all done with off grid weight tests part 2
>
>
> proc.time()
user system elapsed
0.283 0.023 0.414
|
