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
|
#
# 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
#
suppressMessages(library(fields))
options(echo=FALSE)
test.for.zero.flag<- 1
set.seed(123)
# Local Kriging - sparse matrix implementation (small example)
#source( "makeBigB.R")
# -----------------------------
# Define grid and observations
# -----------------------------
m<- 40
n<- 45
nx<- m
ny<- n
M<- 10
dx<- 1
dy<- 1
sigma2<-2.0
aRange<- 5.5
np<-4
set.seed( 123)
# locations random but avoid edges
s<- cbind( dx*runif( M, np, (m-(np+1))),
dy* runif( M, np, (n-(np+1)))
)
# random uniform is ok as we just checking agreement
set.seed( 222)
y<- matrix( runif(m*n),m,n)
yUnrolled<- c( y)
#look<- sparseB%*%yUnrolled
look2<- predVar<- rep( NA, M)
theShift<- 0:(2*np-1) - (np - 1)
for( k in 1:M){
#k<- 3
yTemp<- NULL
sTemp<- NULL
i0<- trunc(s[k,1])
j0<- trunc(s[k,2])
for( j in theShift + j0){
for( i in theShift + i0){
#cat( i,j, fill=TRUE)
sTemp<- rbind( sTemp, c(i,j))
yTemp<- c(yTemp,y[i,j])
}
}
Sigma11<- sigma2*exp(-rdist(sTemp, sTemp)/aRange)
Sigma11Inv<- solve(Sigma11)
Sigma21<- sigma2*exp(-rdist(rbind(s[k,]), sTemp)/aRange)
Btest<- Sigma21%*%Sigma11Inv
result<- Sigma21%*%Sigma11Inv%*%yTemp
look2[k]<- result
predVar[k]<- sigma2 - diag(Sigma21%*%Sigma11Inv%*%t(Sigma21 ) )
}
###################################
# test new function
###################################
sparseObj0<- offGridWeights( s, list( x= 1:m, y=1:n),
aRange=aRange, sigma2=sigma2,
Covariance="Exponential",
np=np)
look5<- sparseObj0$B%*%yUnrolled
test.for.zero( look2, look5 )
test.for.zero(predVar, sparseObj0$predictionVariance )
# check 15.4
mKrigObj<- mKrig( s, rnorm( nrow(s)),
sigma2=sigma2, tau=0,
aRange=aRange,
Covariance="Exponential")
sparseObj<- offGridWeights( s, list( x= 1:m, y=1:n),
mKrigObject = mKrigObj, np=np
)
look3<- sparseObj$B%*%yUnrolled
test.for.zero( look2, look3 )
test.for.zero(predVar, sparseObj$predictionVariance )
# cheating on mKrig object
fakeObj<- list( args = list( Covariance= "Exponential" ),
summary= c(aRange=aRange*2.5, sigma2=sigma2)
)
# fakeObj1<- list( args = list( Covariance= "Matern", smoothness=.5 ),
# summary= c(aRange=10*2.5, sigma2=sigma2)
# )
sparseObj1<- offGridWeights( s*2.5,
list( x = (1:m)*2.5,
y = (1:n)*2.5 ),
mKrigObject = fakeObj,
np = np
)
look4<- sparseObj1$B%*%yUnrolled
test.for.zero( look2, look4 , tag="sparse vs mKrig")
test.for.zero( sparseObj$predictionVariance,
predVar, tag="prediction Variance sparse vs mKrig" )
cat("all done with off grid weight tests part 1", fill=TRUE)
|
