kzs.2d: Spatial Kolmogorov-Zurbenko Spline
In kzs: Kolmogorov-Zurbenko Spatial Smoothing and Applications
Description
Usage
Arguments
Details
Value
Note
Author(s)
See Also
Examples
Description
The kzs.2d function is a spatial extension of the kzs function for two input variables.
Usage
1
Arguments
y
a one-dimensional vector of real values representing the response variable to be smoothed.
x
a two-dimensional matrix of real values containing the input variables X = (X1, X2). Each column
represents an input variable.
smooth
a vector of size two that defines the width of the smoothing window along each input variable.
scale
a vector of size two in which each element will define a uniformly spaced scale along its respective
input variable.
k
an integer specifying the number of iterations kzs.2d will execute. By default, k = 1.
edges
a logical indicating whether or not to display the outcome data beyond the rectangular range of the two
input variables. By default, edges = TRUE.
plot
a logical indicating whether or not to produce a 3-dimensional plot of the kzs.2d outcome. By
default, this argument is set to TRUE.
Details
The details for this function are nearly identical to that of kzs, except now extended to
three dimensional space. The only difference is that the kzs.2d function averages all y that
are contained within a rectangular window made up of sides smooth[1] and smooth[2].
Value
a three column data frame of the form (x1, x2, yk):
x1
the x1 coordinates of a two-dimensional grid.
x2
the x2 coordinates of a two-dimensional grid.
yk
the smoothed response values resulting from k iterations of kzs.2d.
Note
Data set (Y, X1, X2) must be provided, usually as 3-dimensional observations that occur in time or
space; kzs.2d is designed for the general situation, including time series data. In many applications
where an input variable can be time, kzs.2d can resolve the problem of missing values in time series or
or irregularly observed values in Geographical Information Systems (GIS) data analysis. The name of this
function, kzs.2d, simply means that there are two input variables required for use.
The graphical output of kzs.2d is a result of the wireframe() function within the lattice package.
Author(s)
Derek Cyr cyr.derek@gmail.com and Igor Zurbenko igorg.zurbenko@gmail.com
See Also
kzs; For more on the parameter restrictions, see kzs.params
Examples
1
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# EXAMPLE - Estimating the Sinc function in the interval (-3pi, 3pi)
# Load the LATTICE package
# Gridded data for X = (x1, x2) input variables
x1 <- seq(-3*pi, 3*pi, length = 60)
x2 <- x1
df <- expand.grid(x1 = x1, x2 = x2)
# Apply the Sinc function to the (x1, x2) coordinates
df$z <- sin(sqrt(df$x1^2 + df$x2^2)) / sqrt(df$x1^2 + df$x2^2)
df$z[is.na(df$z)] <- 1
# Any point outside the circle of radius 3pi is set to 0. This provides
# a better picture of the outcome solely for the purposes of this example.
dst <- sqrt((df$x1 - 0)^2 + (df$x2 - 0)^2)
df$dist <- dst
df$z[df$dist > 3*pi] <- 0
# Add noise to distort the signal
ez <- rnorm(length(df$z), mean = 0, sd = 1) * 1/4
df$zn <- ez + df$z
### (1) 3D plot of the signal to be estimated by kzs.2d()
wireframe(z ~ x1 * x2, df, main = "Signal to be estimated", drape = TRUE,
colorkey = TRUE, scales = list(arrows = FALSE))
### (2) 3D plot of the signal buried in noise
wireframe(zn ~ x1 * x2, df, main = "Signal buried in noise", drape = TRUE,
colorkey = TRUE, scales = list(arrows = FALSE))
### (3) Execute kzs.2d()
# kzs.2d() may take time to run; k = 1 iteration is used here, but k = 2
# will provide a smoother outcome.
sw <- c(1, 1)
sc <- c(0.2, 0.2)
kzs.2d(y = df[,5], x = df[,1:2], smooth = sw, scale = sc, k = 1, edges = TRUE,
plot = TRUE)
Example output
Loading required package: lattice
x1 x2 yk
1 -9.92477796 -9.92477796 2.567973e-02
2 -9.72477796 -9.92477796 2.567973e-02
3 -9.52477796 -9.92477796 1.316873e-02
4 -9.32477796 -9.92477796 1.316873e-02
5 -9.12477796 -9.92477796 -4.744034e-02
6 -8.92477796 -9.92477796 -1.955955e-01
7 -8.72477796 -9.92477796 -2.693540e-01
8 -8.52477796 -9.92477796 -2.424179e-01
9 -8.32477796 -9.92477796 -2.090612e-01
10 -8.12477796 -9.92477796 -2.225288e-01
11 -7.92477796 -9.92477796 9.893776e-02
12 -7.72477796 -9.92477796 9.893776e-02
13 -7.52477796 -9.92477796 1.552823e-01
14 -7.32477796 -9.92477796 2.151326e-01
15 -7.12477796 -9.92477796 2.151326e-01
16 -6.92477796 -9.92477796 1.214875e-01
17 -6.72477796 -9.92477796 8.917226e-02
18 -6.52477796 -9.92477796 3.539644e-02
19 -6.32477796 -9.92477796 -1.816146e-01
20 -6.12477796 -9.92477796 -1.816146e-01
21 -5.92477796 -9.92477796 -3.378428e-01
22 -5.72477796 -9.92477796 -2.499233e-01
23 -5.52477796 -9.92477796 -2.499233e-01
24 -5.32477796 -9.92477796 6.093664e-03
25 -5.12477796 -9.92477796 -1.350104e-02
26 -4.92477796 -9.92477796 1.237590e-01
27 -4.72477796 -9.92477796 7.344731e-02
28 -4.52477796 -9.92477796 7.344731e-02
29 -4.32477796 -9.92477796 -1.923039e-02
30 -4.12477796 -9.92477796 1.482977e-02
31 -3.92477796 -9.92477796 1.482977e-02
32 -3.72477796 -9.92477796 1.449345e-01
33 -3.52477796 -9.92477796 1.071617e-02
34 -3.32477796 -9.92477796 4.444016e-02
35 -3.12477796 -9.92477796 -4.501629e-03
36 -2.92477796 -9.92477796 -4.501629e-03
37 -2.72477796 -9.92477796 -2.519598e-01
38 -2.52477796 -9.92477796 -1.759297e-01
39 -2.32477796 -9.92477796 -1.759297e-01
40 -2.12477796 -9.92477796 -8.150715e-02
41 -1.92477796 -9.92477796 -2.244468e-01
42 -1.72477796 -9.92477796 -2.169254e-01
43 -1.52477796 -9.92477796 -1.580118e-01
44 -1.32477796 -9.92477796 -1.580118e-01
45 -1.12477796 -9.92477796 -1.682121e-01
46 -0.92477796 -9.92477796 3.457007e-02
47 -0.72477796 -9.92477796 3.457007e-02
48 -0.52477796 -9.92477796 5.130201e-02
49 -0.32477796 -9.92477796 -4.519585e-02
50 -0.12477796 -9.92477796 -1.055067e-01
51 0.07522204 -9.92477796 -7.205982e-02
52 0.27522204 -9.92477796 -7.205982e-02
53 0.47522204 -9.92477796 -9.830700e-02
54 0.67522204 -9.92477796 9.471170e-02
55 0.87522204 -9.92477796 9.471170e-02
56 1.07522204 -9.92477796 3.805648e-02
57 1.27522204 -9.92477796 4.462729e-03
58 1.47522204 -9.92477796 1.116803e-02
59 1.67522204 -9.92477796 5.846550e-02
60 1.87522204 -9.92477796 5.846550e-02
61 2.07522204 -9.92477796 1.597113e-02
62 2.27522204 -9.92477796 3.275189e-02
63 2.47522204 -9.92477796 3.275189e-02
64 2.67522204 -9.92477796 -3.603330e-02
65 2.87522204 -9.92477796 -2.076724e-02
66 3.07522204 -9.92477796 5.298606e-02
67 3.27522204 -9.92477796 -8.805040e-02
68 3.47522204 -9.92477796 -8.805040e-02
69 3.67522204 -9.92477796 -1.427929e-01
70 3.87522204 -9.92477796 -6.582636e-02
71 4.07522204 -9.92477796 -6.582636e-02
72 4.27522204 -9.92477796 2.355925e-01
73 4.47522204 -9.92477796 1.230778e-01
74 4.67522204 -9.92477796 1.588784e-01
75 4.87522204 -9.92477796 -2.079322e-02
76 5.07522204 -9.92477796 -2.079322e-02
77 5.27522204 -9.92477796 -1.966219e-01
78 5.47522204 -9.92477796 -7.036866e-02
79 5.67522204 -9.92477796 -7.036866e-02
80 5.87522204 -9.92477796 3.350047e-03
81 6.07522204 -9.92477796 -2.167688e-02
82 6.27522204 -9.92477796 1.869184e-03
83 6.47522204 -9.92477796 2.708767e-02
84 6.67522204 -9.92477796 2.708767e-02
85 6.87522204 -9.92477796 2.385593e-02
86 7.07522204 -9.92477796 6.210974e-02
87 7.27522204 -9.92477796 6.210974e-02
88 7.47522204 -9.92477796 8.613539e-02
89 7.67522204 -9.92477796 7.728565e-02
90 7.87522204 -9.92477796 1.269221e-01
91 8.07522204 -9.92477796 5.451694e-02
92 8.27522204 -9.92477796 5.451694e-02
93 8.47522204 -9.92477796 -7.216864e-02
94 8.67522204 -9.92477796 -2.289121e-01
95 8.87522204 -9.92477796 -2.289121e-01
96 9.07522204 -9.92477796 -1.026135e-01
97 9.27522204 -9.92477796 -1.026135e-01
98 9.47522204 -9.92477796 -1.199049e-01
99 9.67522204 -9.92477796 1.796840e-01
100 9.87522204 -9.92477796 1.796840e-01
101 -9.92477796 -9.72477796 2.567973e-02
102 -9.72477796 -9.72477796 2.567973e-02
103 -9.52477796 -9.72477796 1.316873e-02
104 -9.32477796 -9.72477796 1.316873e-02
105 -9.12477796 -9.72477796 -4.744034e-02
106 -8.92477796 -9.72477796 -1.955955e-01
107 -8.72477796 -9.72477796 -2.693540e-01
108 -8.52477796 -9.72477796 -2.424179e-01
109 -8.32477796 -9.72477796 -2.090612e-01
110 -8.12477796 -9.72477796 -2.225288e-01
111 -7.92477796 -9.72477796 9.893776e-02
112 -7.72477796 -9.72477796 9.893776e-02
113 -7.52477796 -9.72477796 1.552823e-01
114 -7.32477796 -9.72477796 2.151326e-01
115 -7.12477796 -9.72477796 2.151326e-01
116 -6.92477796 -9.72477796 1.214875e-01
117 -6.72477796 -9.72477796 8.917226e-02
118 -6.52477796 -9.72477796 3.539644e-02
119 -6.32477796 -9.72477796 -1.816146e-01
120 -6.12477796 -9.72477796 -1.816146e-01
121 -5.92477796 -9.72477796 -3.378428e-01
122 -5.72477796 -9.72477796 -2.499233e-01
123 -5.52477796 -9.72477796 -2.499233e-01
124 -5.32477796 -9.72477796 6.093664e-03
125 -5.12477796 -9.72477796 -1.350104e-02
126 -4.92477796 -9.72477796 1.237590e-01
127 -4.72477796 -9.72477796 7.344731e-02
128 -4.52477796 -9.72477796 7.344731e-02
129 -4.32477796 -9.72477796 -1.923039e-02
130 -4.12477796 -9.72477796 1.482977e-02
131 -3.92477796 -9.72477796 1.482977e-02
132 -3.72477796 -9.72477796 1.449345e-01
133 -3.52477796 -9.72477796 1.071617e-02
134 -3.32477796 -9.72477796 4.444016e-02
135 -3.12477796 -9.72477796 -4.501629e-03
136 -2.92477796 -9.72477796 -4.501629e-03
137 -2.72477796 -9.72477796 -2.519598e-01
138 -2.52477796 -9.72477796 -1.759297e-01
139 -2.32477796 -9.72477796 -1.759297e-01
140 -2.12477796 -9.72477796 -8.150715e-02
141 -1.92477796 -9.72477796 -2.244468e-01
142 -1.72477796 -9.72477796 -2.169254e-01
143 -1.52477796 -9.72477796 -1.580118e-01
144 -1.32477796 -9.72477796 -1.580118e-01
145 -1.12477796 -9.72477796 -1.682121e-01
146 -0.92477796 -9.72477796 3.457007e-02
147 -0.72477796 -9.72477796 3.457007e-02
148 -0.52477796 -9.72477796 5.130201e-02
149 -0.32477796 -9.72477796 -4.519585e-02
150 -0.12477796 -9.72477796 -1.055067e-01
151 0.07522204 -9.72477796 -7.205982e-02
152 0.27522204 -9.72477796 -7.205982e-02
153 0.47522204 -9.72477796 -9.830700e-02
154 0.67522204 -9.72477796 9.471170e-02
155 0.87522204 -9.72477796 9.471170e-02
156 1.07522204 -9.72477796 3.805648e-02
157 1.27522204 -9.72477796 4.462729e-03
158 1.47522204 -9.72477796 1.116803e-02
159 1.67522204 -9.72477796 5.846550e-02
160 1.87522204 -9.72477796 5.846550e-02
161 2.07522204 -9.72477796 1.597113e-02
162 2.27522204 -9.72477796 3.275189e-02
163 2.47522204 -9.72477796 3.275189e-02
164 2.67522204 -9.72477796 -3.603330e-02
165 2.87522204 -9.72477796 -2.076724e-02
166 3.07522204 -9.72477796 5.298606e-02
167 3.27522204 -9.72477796 -8.805040e-02
168 3.47522204 -9.72477796 -8.805040e-02
169 3.67522204 -9.72477796 -1.427929e-01
170 3.87522204 -9.72477796 -6.582636e-02
171 4.07522204 -9.72477796 -6.582636e-02
172 4.27522204 -9.72477796 2.355925e-01
173 4.47522204 -9.72477796 1.230778e-01
174 4.67522204 -9.72477796 1.588784e-01
175 4.87522204 -9.72477796 -2.079322e-02
176 5.07522204 -9.72477796 -2.079322e-02
177 5.27522204 -9.72477796 -1.966219e-01
178 5.47522204 -9.72477796 -7.036866e-02
179 5.67522204 -9.72477796 -7.036866e-02
180 5.87522204 -9.72477796 3.350047e-03
181 6.07522204 -9.72477796 -2.167688e-02
182 6.27522204 -9.72477796 1.869184e-03
183 6.47522204 -9.72477796 2.708767e-02
184 6.67522204 -9.72477796 2.708767e-02
185 6.87522204 -9.72477796 2.385593e-02
186 7.07522204 -9.72477796 6.210974e-02
187 7.27522204 -9.72477796 6.210974e-02
188 7.47522204 -9.72477796 8.613539e-02
189 7.67522204 -9.72477796 7.728565e-02
190 7.87522204 -9.72477796 1.269221e-01
191 8.07522204 -9.72477796 5.451694e-02
192 8.27522204 -9.72477796 5.451694e-02
193 8.47522204 -9.72477796 -7.216864e-02
194 8.67522204 -9.72477796 -2.289121e-01
195 8.87522204 -9.72477796 -2.289121e-01
196 9.07522204 -9.72477796 -1.026135e-01
197 9.27522204 -9.72477796 -1.026135e-01
198 9.47522204 -9.72477796 -1.199049e-01
199 9.67522204 -9.72477796 1.796840e-01
200 9.87522204 -9.72477796 1.796840e-01
201 -9.92477796 -9.52477796 9.736955e-02
202 -9.72477796 -9.52477796 9.736955e-02
203 -9.52477796 -9.52477796 1.293472e-01
204 -9.32477796 -9.52477796 1.293472e-01
205 -9.12477796 -9.52477796 7.568873e-02
206 -8.92477796 -9.52477796 3.403676e-02
207 -8.72477796 -9.52477796 1.292583e-02
208 -8.52477796 -9.52477796 -3.262339e-02
209 -8.32477796 -9.52477796 -2.021159e-02
210 -8.12477796 -9.52477796 -1.640609e-02
211 -7.92477796 -9.52477796 6.204918e-02
212 -7.72477796 -9.52477796 6.204918e-02
213 -7.52477796 -9.52477796 1.367257e-01
214 -7.32477796 -9.52477796 1.591578e-01
215 -7.12477796 -9.52477796 1.591578e-01
216 -6.92477796 -9.52477796 1.854816e-01
217 -6.72477796 -9.52477796 1.910899e-01
218 -6.52477796 -9.52477796 1.718843e-01
219 -6.32477796 -9.52477796 7.205885e-02
220 -6.12477796 -9.52477796 7.205885e-02
221 -5.92477796 -9.52477796 -2.552557e-02
222 -5.72477796 -9.52477796 -2.078004e-02
223 -5.52477796 -9.52477796 -2.078004e-02
224 -5.32477796 -9.52477796 5.657101e-02
225 -5.12477796 -9.52477796 4.054721e-02
226 -4.92477796 -9.52477796 7.717473e-02
227 -4.72477796 -9.52477796 2.751613e-02
228 -4.52477796 -9.52477796 2.751613e-02
229 -4.32477796 -9.52477796 2.496433e-02
230 -4.12477796 -9.52477796 5.566382e-02
231 -3.92477796 -9.52477796 5.566382e-02
232 -3.72477796 -9.52477796 9.887982e-02
233 -3.52477796 -9.52477796 -3.165407e-02
234 -3.32477796 -9.52477796 -4.528595e-02
235 -3.12477796 -9.52477796 -1.147578e-01
236 -2.92477796 -9.52477796 -1.147578e-01
237 -2.72477796 -9.52477796 -2.264047e-01
238 -2.52477796 -9.52477796 -6.525021e-02
239 -2.32477796 -9.52477796 -6.525021e-02
240 -2.12477796 -9.52477796 -5.233583e-02
241 -1.92477796 -9.52477796 -1.459463e-01
242 -1.72477796 -9.52477796 -1.505561e-01
243 -1.52477796 -9.52477796 -1.510324e-01
244 -1.32477796 -9.52477796 -1.510324e-01
245 -1.12477796 -9.52477796 -8.567618e-02
246 -0.92477796 -9.52477796 6.772757e-02
247 -0.72477796 -9.52477796 6.772757e-02
248 -0.52477796 -9.52477796 1.097028e-01
249 -0.32477796 -9.52477796 1.467449e-03
250 -0.12477796 -9.52477796 -3.503356e-02
251 0.07522204 -9.52477796 -3.330220e-02
252 0.27522204 -9.52477796 -3.330220e-02
253 0.47522204 -9.52477796 -4.942032e-03
254 0.67522204 -9.52477796 1.770146e-01
255 0.87522204 -9.52477796 1.770146e-01
256 1.07522204 -9.52477796 1.515466e-01
257 1.27522204 -9.52477796 1.090462e-01
258 1.47522204 -9.52477796 5.546649e-02
259 1.67522204 -9.52477796 6.661485e-02
260 1.87522204 -9.52477796 6.661485e-02
261 2.07522204 -9.52477796 5.028429e-03
262 2.27522204 -9.52477796 4.538195e-03
263 2.47522204 -9.52477796 4.538195e-03
264 2.67522204 -9.52477796 -6.204143e-02
265 2.87522204 -9.52477796 -1.684004e-02
266 3.07522204 -9.52477796 5.172515e-02
267 3.27522204 -9.52477796 -3.546349e-02
268 3.47522204 -9.52477796 -3.546349e-02
269 3.67522204 -9.52477796 -5.788479e-02
270 3.87522204 -9.52477796 -4.903710e-02
271 4.07522204 -9.52477796 -4.903710e-02
272 4.27522204 -9.52477796 1.317217e-01
273 4.47522204 -9.52477796 5.507174e-02
274 4.67522204 -9.52477796 7.707119e-02
275 4.87522204 -9.52477796 -1.830043e-02
276 5.07522204 -9.52477796 -1.830043e-02
277 5.27522204 -9.52477796 -1.256319e-01
278 5.47522204 -9.52477796 5.918672e-03
279 5.67522204 -9.52477796 5.918672e-03
280 5.87522204 -9.52477796 6.240185e-02
281 6.07522204 -9.52477796 5.227379e-02
282 6.27522204 -9.52477796 9.010166e-02
283 6.47522204 -9.52477796 4.802916e-02
284 6.67522204 -9.52477796 4.802916e-02
285 6.87522204 -9.52477796 3.265935e-02
286 7.07522204 -9.52477796 -1.639605e-02
287 7.27522204 -9.52477796 -1.639605e-02
288 7.47522204 -9.52477796 5.672861e-02
289 7.67522204 -9.52477796 7.231155e-02
290 7.87522204 -9.52477796 1.022379e-01
291 8.07522204 -9.52477796 1.437844e-01
292 8.27522204 -9.52477796 1.437844e-01
293 8.47522204 -9.52477796 7.545739e-02
294 8.67522204 -9.52477796 -4.294358e-02
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1689 7.67522204 -6.72477796 -5.412265e-02
1690 7.87522204 -6.72477796 -9.331134e-02
1691 8.07522204 -6.72477796 -4.406551e-02
1692 8.27522204 -6.72477796 -4.406551e-02
1693 8.47522204 -6.72477796 5.041663e-02
1694 8.67522204 -6.72477796 1.333885e-01
1695 8.87522204 -6.72477796 1.333885e-01
1696 9.07522204 -6.72477796 1.123339e-01
1697 9.27522204 -6.72477796 1.123339e-01
1698 9.47522204 -6.72477796 5.534694e-02
1699 9.67522204 -6.72477796 8.311656e-03
1700 9.87522204 -6.72477796 8.311656e-03
1701 -9.92477796 -6.52477796 6.190463e-02
1702 -9.72477796 -6.52477796 6.190463e-02
1703 -9.52477796 -6.52477796 1.224040e-01
1704 -9.32477796 -6.52477796 1.224040e-01
1705 -9.12477796 -6.52477796 3.129226e-02
1706 -8.92477796 -6.52477796 1.695695e-02
1707 -8.72477796 -6.52477796 1.974393e-03
1708 -8.52477796 -6.52477796 1.586873e-02
1709 -8.32477796 -6.52477796 -1.362207e-03
1710 -8.12477796 -6.52477796 4.849410e-02
1711 -7.92477796 -6.52477796 3.929106e-02
1712 -7.72477796 -6.52477796 3.929106e-02
1713 -7.52477796 -6.52477796 -1.230471e-01
1714 -7.32477796 -6.52477796 -9.513741e-02
1715 -7.12477796 -6.52477796 -9.513741e-02
1716 -6.92477796 -6.52477796 -1.467206e-02
1717 -6.72477796 -6.52477796 4.142271e-03
1718 -6.52477796 -6.52477796 9.299907e-02
1719 -6.32477796 -6.52477796 1.483005e-01
1720 -6.12477796 -6.52477796 1.483005e-01
1721 -5.92477796 -6.52477796 9.270751e-02
1722 -5.72477796 -6.52477796 8.394957e-02
1723 -5.52477796 -6.52477796 8.394957e-02
1724 -5.32477796 -6.52477796 3.647348e-02
1725 -5.12477796 -6.52477796 7.000066e-02
1726 -4.92477796 -6.52477796 8.634792e-02
1727 -4.72477796 -6.52477796 1.123853e-01
1728 -4.52477796 -6.52477796 1.123853e-01
1729 -4.32477796 -6.52477796 1.138964e-01
1730 -4.12477796 -6.52477796 1.152051e-01
1731 -3.92477796 -6.52477796 1.152051e-01
1732 -3.72477796 -6.52477796 9.702583e-02
1733 -3.52477796 -6.52477796 1.378654e-01
1734 -3.32477796 -6.52477796 1.642594e-01
1735 -3.12477796 -6.52477796 1.511084e-01
1736 -2.92477796 -6.52477796 1.511084e-01
1737 -2.72477796 -6.52477796 2.069998e-01
1738 -2.52477796 -6.52477796 1.825136e-01
1739 -2.32477796 -6.52477796 1.825136e-01
1740 -2.12477796 -6.52477796 1.594725e-01
1741 -1.92477796 -6.52477796 1.090311e-01
1742 -1.72477796 -6.52477796 7.018817e-02
1743 -1.52477796 -6.52477796 -2.904203e-02
1744 -1.32477796 -6.52477796 -2.904203e-02
1745 -1.12477796 -6.52477796 -2.163315e-02
1746 -0.92477796 -6.52477796 -1.319681e-02
1747 -0.72477796 -6.52477796 -1.319681e-02
1748 -0.52477796 -6.52477796 -4.464871e-03
1749 -0.32477796 -6.52477796 2.928542e-02
1750 -0.12477796 -6.52477796 9.661017e-03
1751 0.07522204 -6.52477796 -5.634191e-02
1752 0.27522204 -6.52477796 -5.634191e-02
1753 0.47522204 -6.52477796 -1.240126e-02
1754 0.67522204 -6.52477796 -7.742126e-02
1755 0.87522204 -6.52477796 -7.742126e-02
1756 1.07522204 -6.52477796 1.362943e-01
1757 1.27522204 -6.52477796 1.511945e-01
1758 1.47522204 -6.52477796 1.858417e-01
1759 1.67522204 -6.52477796 2.010376e-01
1760 1.87522204 -6.52477796 2.010376e-01
1761 2.07522204 -6.52477796 1.408629e-02
1762 2.27522204 -6.52477796 3.433022e-03
1763 2.47522204 -6.52477796 3.433022e-03
1764 2.67522204 -6.52477796 5.514081e-02
1765 2.87522204 -6.52477796 4.093919e-02
1766 3.07522204 -6.52477796 9.948563e-02
1767 3.27522204 -6.52477796 5.109390e-02
1768 3.47522204 -6.52477796 5.109390e-02
1769 3.67522204 -6.52477796 2.310924e-02
1770 3.87522204 -6.52477796 1.113964e-01
1771 4.07522204 -6.52477796 1.113964e-01
1772 4.27522204 -6.52477796 1.186890e-01
1773 4.47522204 -6.52477796 1.264930e-01
1774 4.67522204 -6.52477796 1.512462e-01
1775 4.87522204 -6.52477796 7.338339e-02
1776 5.07522204 -6.52477796 7.338339e-02
1777 5.27522204 -6.52477796 6.156714e-02
1778 5.47522204 -6.52477796 -2.961346e-02
1779 5.67522204 -6.52477796 -2.961346e-02
1780 5.87522204 -6.52477796 -5.598543e-02
1781 6.07522204 -6.52477796 -4.274435e-02
1782 6.27522204 -6.52477796 -5.872215e-02
1783 6.47522204 -6.52477796 2.439489e-02
1784 6.67522204 -6.52477796 2.439489e-02
1785 6.87522204 -6.52477796 6.596794e-02
1786 7.07522204 -6.52477796 4.033484e-02
1787 7.27522204 -6.52477796 4.033484e-02
1788 7.47522204 -6.52477796 -2.683559e-02
1789 7.67522204 -6.52477796 -5.712082e-02
1790 7.87522204 -6.52477796 -1.012314e-01
1791 8.07522204 -6.52477796 -6.666086e-02
1792 8.27522204 -6.52477796 -6.666086e-02
1793 8.47522204 -6.52477796 4.715668e-03
1794 8.67522204 -6.52477796 6.677095e-02
1795 8.87522204 -6.52477796 6.677095e-02
1796 9.07522204 -6.52477796 5.358870e-02
1797 9.27522204 -6.52477796 5.358870e-02
1798 9.47522204 -6.52477796 1.121684e-02
1799 9.67522204 -6.52477796 -1.575564e-02
1800 9.87522204 -6.52477796 -1.575564e-02
1801 -9.92477796 -6.32477796 3.856016e-02
1802 -9.72477796 -6.32477796 3.856016e-02
1803 -9.52477796 -6.32477796 9.996218e-02
1804 -9.32477796 -6.32477796 9.996218e-02
1805 -9.12477796 -6.32477796 5.679209e-02
1806 -8.92477796 -6.32477796 8.029520e-02
1807 -8.72477796 -6.32477796 9.420688e-02
1808 -8.52477796 -6.32477796 4.992288e-02
1809 -8.32477796 -6.32477796 7.148338e-02
1810 -8.12477796 -6.32477796 1.051605e-01
1811 -7.92477796 -6.32477796 4.205250e-02
1812 -7.72477796 -6.32477796 4.205250e-02
1813 -7.52477796 -6.32477796 -9.899902e-03
1814 -7.32477796 -6.32477796 -7.292448e-02
1815 -7.12477796 -6.32477796 -7.292448e-02
1816 -6.92477796 -6.32477796 7.531951e-02
1817 -6.72477796 -6.32477796 1.006281e-01
1818 -6.52477796 -6.32477796 1.766191e-01
1819 -6.32477796 -6.32477796 2.405426e-01
1820 -6.12477796 -6.32477796 2.405426e-01
1821 -5.92477796 -6.32477796 1.470725e-01
1822 -5.72477796 -6.32477796 2.781996e-02
1823 -5.52477796 -6.32477796 2.781996e-02
1824 -5.32477796 -6.32477796 1.254248e-02
1825 -5.12477796 -6.32477796 -9.813803e-03
1826 -4.92477796 -6.32477796 -5.501913e-02
1827 -4.72477796 -6.32477796 4.482348e-02
1828 -4.52477796 -6.32477796 4.482348e-02
1829 -4.32477796 -6.32477796 5.692356e-02
1830 -4.12477796 -6.32477796 1.116939e-01
1831 -3.92477796 -6.32477796 1.116939e-01
1832 -3.72477796 -6.32477796 7.997278e-02
1833 -3.52477796 -6.32477796 9.773298e-02
1834 -3.32477796 -6.32477796 8.720082e-02
1835 -3.12477796 -6.32477796 7.474345e-02
1836 -2.92477796 -6.32477796 7.474345e-02
1837 -2.72477796 -6.32477796 1.672598e-01
1838 -2.52477796 -6.32477796 1.528405e-01
1839 -2.32477796 -6.32477796 1.528405e-01
1840 -2.12477796 -6.32477796 1.342024e-01
1841 -1.92477796 -6.32477796 1.035203e-01
1842 -1.72477796 -6.32477796 3.779047e-02
1843 -1.52477796 -6.32477796 -1.745219e-02
1844 -1.32477796 -6.32477796 -1.745219e-02
1845 -1.12477796 -6.32477796 3.313826e-02
1846 -0.92477796 -6.32477796 3.313803e-04
1847 -0.72477796 -6.32477796 3.313803e-04
1848 -0.52477796 -6.32477796 -1.731378e-02
1849 -0.32477796 -6.32477796 -1.223687e-02
1850 -0.12477796 -6.32477796 -6.495362e-02
1851 0.07522204 -6.32477796 -6.361879e-02
1852 0.27522204 -6.32477796 -6.361879e-02
1853 0.47522204 -6.32477796 -8.584839e-02
1854 0.67522204 -6.32477796 -1.290034e-01
1855 0.87522204 -6.32477796 -1.290034e-01
1856 1.07522204 -6.32477796 -6.365422e-02
1857 1.27522204 -6.32477796 -3.326727e-03
1858 1.47522204 -6.32477796 5.476324e-02
1859 1.67522204 -6.32477796 1.315929e-01
1860 1.87522204 -6.32477796 1.315929e-01
1861 2.07522204 -6.32477796 -4.566737e-03
1862 2.27522204 -6.32477796 -2.302149e-02
1863 2.47522204 -6.32477796 -2.302149e-02
1864 2.67522204 -6.32477796 3.765585e-02
1865 2.87522204 -6.32477796 7.361243e-03
1866 3.07522204 -6.32477796 1.082729e-01
1867 3.27522204 -6.32477796 1.446230e-01
1868 3.47522204 -6.32477796 1.446230e-01
1869 3.67522204 -6.32477796 4.318860e-02
1870 3.87522204 -6.32477796 1.787954e-01
1871 4.07522204 -6.32477796 1.787954e-01
1872 4.27522204 -6.32477796 1.740898e-01
1873 4.47522204 -6.32477796 1.173416e-01
1874 4.67522204 -6.32477796 1.625399e-01
1875 4.87522204 -6.32477796 3.399953e-02
1876 5.07522204 -6.32477796 3.399953e-02
1877 5.27522204 -6.32477796 -4.112620e-02
1878 5.47522204 -6.32477796 -4.412747e-02
1879 5.67522204 -6.32477796 -4.412747e-02
1880 5.87522204 -6.32477796 -3.140453e-03
1881 6.07522204 -6.32477796 3.779418e-02
1882 6.27522204 -6.32477796 5.310961e-02
1883 6.47522204 -6.32477796 1.429498e-01
1884 6.67522204 -6.32477796 1.429498e-01
1885 6.87522204 -6.32477796 9.178984e-02
1886 7.07522204 -6.32477796 1.093678e-01
1887 7.27522204 -6.32477796 1.093678e-01
1888 7.47522204 -6.32477796 -5.097843e-03
1889 7.67522204 -6.32477796 -5.116092e-02
1890 7.87522204 -6.32477796 -3.726716e-02
1891 8.07522204 -6.32477796 -1.296815e-01
1892 8.27522204 -6.32477796 -1.296815e-01
1893 8.47522204 -6.32477796 -8.943758e-02
1894 8.67522204 -6.32477796 -2.296716e-02
1895 8.87522204 -6.32477796 -2.296716e-02
1896 9.07522204 -6.32477796 -2.500353e-02
1897 9.27522204 -6.32477796 -2.500353e-02
1898 9.47522204 -6.32477796 -2.997956e-02
1899 9.67522204 -6.32477796 -7.002023e-02
1900 9.87522204 -6.32477796 -7.002023e-02
1901 -9.92477796 -6.12477796 3.856016e-02
1902 -9.72477796 -6.12477796 3.856016e-02
1903 -9.52477796 -6.12477796 9.996218e-02
1904 -9.32477796 -6.12477796 9.996218e-02
1905 -9.12477796 -6.12477796 5.679209e-02
1906 -8.92477796 -6.12477796 8.029520e-02
1907 -8.72477796 -6.12477796 9.420688e-02
1908 -8.52477796 -6.12477796 4.992288e-02
1909 -8.32477796 -6.12477796 7.148338e-02
1910 -8.12477796 -6.12477796 1.051605e-01
1911 -7.92477796 -6.12477796 4.205250e-02
1912 -7.72477796 -6.12477796 4.205250e-02
1913 -7.52477796 -6.12477796 -9.899902e-03
1914 -7.32477796 -6.12477796 -7.292448e-02
1915 -7.12477796 -6.12477796 -7.292448e-02
1916 -6.92477796 -6.12477796 7.531951e-02
1917 -6.72477796 -6.12477796 1.006281e-01
1918 -6.52477796 -6.12477796 1.766191e-01
1919 -6.32477796 -6.12477796 2.405426e-01
1920 -6.12477796 -6.12477796 2.405426e-01
1921 -5.92477796 -6.12477796 1.470725e-01
1922 -5.72477796 -6.12477796 2.781996e-02
1923 -5.52477796 -6.12477796 2.781996e-02
1924 -5.32477796 -6.12477796 1.254248e-02
1925 -5.12477796 -6.12477796 -9.813803e-03
1926 -4.92477796 -6.12477796 -5.501913e-02
1927 -4.72477796 -6.12477796 4.482348e-02
1928 -4.52477796 -6.12477796 4.482348e-02
1929 -4.32477796 -6.12477796 5.692356e-02
1930 -4.12477796 -6.12477796 1.116939e-01
1931 -3.92477796 -6.12477796 1.116939e-01
1932 -3.72477796 -6.12477796 7.997278e-02
1933 -3.52477796 -6.12477796 9.773298e-02
1934 -3.32477796 -6.12477796 8.720082e-02
1935 -3.12477796 -6.12477796 7.474345e-02
1936 -2.92477796 -6.12477796 7.474345e-02
1937 -2.72477796 -6.12477796 1.672598e-01
1938 -2.52477796 -6.12477796 1.528405e-01
1939 -2.32477796 -6.12477796 1.528405e-01
1940 -2.12477796 -6.12477796 1.342024e-01
1941 -1.92477796 -6.12477796 1.035203e-01
1942 -1.72477796 -6.12477796 3.779047e-02
1943 -1.52477796 -6.12477796 -1.745219e-02
1944 -1.32477796 -6.12477796 -1.745219e-02
1945 -1.12477796 -6.12477796 3.313826e-02
1946 -0.92477796 -6.12477796 3.313803e-04
1947 -0.72477796 -6.12477796 3.313803e-04
1948 -0.52477796 -6.12477796 -1.731378e-02
1949 -0.32477796 -6.12477796 -1.223687e-02
1950 -0.12477796 -6.12477796 -6.495362e-02
1951 0.07522204 -6.12477796 -6.361879e-02
1952 0.27522204 -6.12477796 -6.361879e-02
1953 0.47522204 -6.12477796 -8.584839e-02
1954 0.67522204 -6.12477796 -1.290034e-01
1955 0.87522204 -6.12477796 -1.290034e-01
1956 1.07522204 -6.12477796 -6.365422e-02
1957 1.27522204 -6.12477796 -3.326727e-03
1958 1.47522204 -6.12477796 5.476324e-02
1959 1.67522204 -6.12477796 1.315929e-01
1960 1.87522204 -6.12477796 1.315929e-01
1961 2.07522204 -6.12477796 -4.566737e-03
1962 2.27522204 -6.12477796 -2.302149e-02
1963 2.47522204 -6.12477796 -2.302149e-02
1964 2.67522204 -6.12477796 3.765585e-02
1965 2.87522204 -6.12477796 7.361243e-03
1966 3.07522204 -6.12477796 1.082729e-01
1967 3.27522204 -6.12477796 1.446230e-01
1968 3.47522204 -6.12477796 1.446230e-01
1969 3.67522204 -6.12477796 4.318860e-02
1970 3.87522204 -6.12477796 1.787954e-01
1971 4.07522204 -6.12477796 1.787954e-01
1972 4.27522204 -6.12477796 1.740898e-01
1973 4.47522204 -6.12477796 1.173416e-01
1974 4.67522204 -6.12477796 1.625399e-01
1975 4.87522204 -6.12477796 3.399953e-02
1976 5.07522204 -6.12477796 3.399953e-02
1977 5.27522204 -6.12477796 -4.112620e-02
1978 5.47522204 -6.12477796 -4.412747e-02
1979 5.67522204 -6.12477796 -4.412747e-02
1980 5.87522204 -6.12477796 -3.140453e-03
1981 6.07522204 -6.12477796 3.779418e-02
1982 6.27522204 -6.12477796 5.310961e-02
1983 6.47522204 -6.12477796 1.429498e-01
1984 6.67522204 -6.12477796 1.429498e-01
1985 6.87522204 -6.12477796 9.178984e-02
1986 7.07522204 -6.12477796 1.093678e-01
1987 7.27522204 -6.12477796 1.093678e-01
1988 7.47522204 -6.12477796 -5.097843e-03
1989 7.67522204 -6.12477796 -5.116092e-02
1990 7.87522204 -6.12477796 -3.726716e-02
1991 8.07522204 -6.12477796 -1.296815e-01
1992 8.27522204 -6.12477796 -1.296815e-01
1993 8.47522204 -6.12477796 -8.943758e-02
1994 8.67522204 -6.12477796 -2.296716e-02
1995 8.87522204 -6.12477796 -2.296716e-02
1996 9.07522204 -6.12477796 -2.500353e-02
1997 9.27522204 -6.12477796 -2.500353e-02
1998 9.47522204 -6.12477796 -2.997956e-02
1999 9.67522204 -6.12477796 -7.002023e-02
2000 9.87522204 -6.12477796 -7.002023e-02
2001 -9.92477796 -5.92477796 -1.655773e-01
2002 -9.72477796 -5.92477796 -1.655773e-01
2003 -9.52477796 -5.92477796 -2.374095e-02
2004 -9.32477796 -5.92477796 -2.374095e-02
2005 -9.12477796 -5.92477796 -5.485687e-02
2006 -8.92477796 -5.92477796 -2.810241e-02
2007 -8.72477796 -5.92477796 1.772254e-02
2008 -8.52477796 -5.92477796 -7.501054e-02
2009 -8.32477796 -5.92477796 -7.995914e-02
2010 -8.12477796 -5.92477796 -6.758262e-02
2011 -7.92477796 -5.92477796 -4.243526e-02
2012 -7.72477796 -5.92477796 -4.243526e-02
2013 -7.52477796 -5.92477796 -2.159365e-02
2014 -7.32477796 -5.92477796 -4.232854e-02
2015 -7.12477796 -5.92477796 -4.232854e-02
2016 -6.92477796 -5.92477796 1.466512e-02
2017 -6.72477796 -5.92477796 6.005992e-02
2018 -6.52477796 -5.92477796 1.126062e-01
2019 -6.32477796 -5.92477796 2.123137e-01
2020 -6.12477796 -5.92477796 2.123137e-01
2021 -5.92477796 -5.92477796 1.612754e-01
2022 -5.72477796 -5.92477796 6.972918e-02
2023 -5.52477796 -5.92477796 6.972918e-02
2024 -5.32477796 -5.92477796 7.525090e-02
2025 -5.12477796 -5.92477796 1.598559e-02
2026 -4.92477796 -5.92477796 -2.717567e-02
2027 -4.72477796 -5.92477796 1.221826e-02
2028 -4.52477796 -5.92477796 1.221826e-02
2029 -4.32477796 -5.92477796 -1.517536e-02
2030 -4.12477796 -5.92477796 1.286953e-01
2031 -3.92477796 -5.92477796 1.286953e-01
2032 -3.72477796 -5.92477796 1.308961e-01
2033 -3.52477796 -5.92477796 1.699216e-01
2034 -3.32477796 -5.92477796 2.010632e-01
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9769 3.67522204 9.47522204 -5.041994e-02
9770 3.87522204 9.47522204 -4.161702e-02
9771 4.07522204 9.47522204 -4.161702e-02
9772 4.27522204 9.47522204 -8.483321e-02
9773 4.47522204 9.47522204 -3.421688e-02
9774 4.67522204 9.47522204 -2.974687e-02
9775 4.87522204 9.47522204 -7.866729e-03
9776 5.07522204 9.47522204 -7.866729e-03
9777 5.27522204 9.47522204 4.849629e-03
9778 5.47522204 9.47522204 -3.418813e-02
9779 5.67522204 9.47522204 -3.418813e-02
9780 5.87522204 9.47522204 3.656083e-02
9781 6.07522204 9.47522204 4.714649e-02
9782 6.27522204 9.47522204 1.029078e-01
9783 6.47522204 9.47522204 1.438952e-01
9784 6.67522204 9.47522204 1.438952e-01
9785 6.87522204 9.47522204 1.004535e-01
9786 7.07522204 9.47522204 1.394372e-01
9787 7.27522204 9.47522204 1.394372e-01
9788 7.47522204 9.47522204 1.039964e-01
9789 7.67522204 9.47522204 9.622495e-02
9790 7.87522204 9.47522204 9.530794e-02
9791 8.07522204 9.47522204 -3.390610e-02
9792 8.27522204 9.47522204 -3.390610e-02
9793 8.47522204 9.47522204 -4.120251e-02
9794 8.67522204 9.47522204 -5.891205e-02
9795 8.87522204 9.47522204 -5.891205e-02
9796 9.07522204 9.47522204 2.007650e-02
9797 9.27522204 9.47522204 2.007650e-02
9798 9.47522204 9.47522204 3.248008e-02
9799 9.67522204 9.47522204 4.517819e-02
9800 9.87522204 9.47522204 4.517819e-02
9801 -9.92477796 9.67522204 -9.960981e-02
9802 -9.72477796 9.67522204 -9.960981e-02
9803 -9.52477796 9.67522204 -8.231289e-02
9804 -9.32477796 9.67522204 -8.231289e-02
9805 -9.12477796 9.67522204 -5.804480e-02
9806 -8.92477796 9.67522204 -2.874439e-02
9807 -8.72477796 9.67522204 -5.122587e-03
9808 -8.52477796 9.67522204 9.070944e-02
9809 -8.32477796 9.67522204 5.033603e-02
9810 -8.12477796 9.67522204 7.028424e-02
9811 -7.92477796 9.67522204 4.117983e-02
9812 -7.72477796 9.67522204 4.117983e-02
9813 -7.52477796 9.67522204 -1.363228e-01
9814 -7.32477796 9.67522204 -1.728220e-01
9815 -7.12477796 9.67522204 -1.728220e-01
9816 -6.92477796 9.67522204 -1.375841e-01
9817 -6.72477796 9.67522204 -1.716369e-01
9818 -6.52477796 9.67522204 -1.255066e-01
9819 -6.32477796 9.67522204 -1.388467e-01
9820 -6.12477796 9.67522204 -1.388467e-01
9821 -5.92477796 9.67522204 -1.739546e-02
9822 -5.72477796 9.67522204 1.031234e-01
9823 -5.52477796 9.67522204 1.031234e-01
9824 -5.32477796 9.67522204 1.709674e-01
9825 -5.12477796 9.67522204 8.692991e-02
9826 -4.92477796 9.67522204 -3.139711e-02
9827 -4.72477796 9.67522204 -8.815527e-02
9828 -4.52477796 9.67522204 -8.815527e-02
9829 -4.32477796 9.67522204 -2.835852e-02
9830 -4.12477796 9.67522204 -1.575607e-01
9831 -3.92477796 9.67522204 -1.575607e-01
9832 -3.72477796 9.67522204 -1.205344e-01
9833 -3.52477796 9.67522204 1.279321e-02
9834 -3.32477796 9.67522204 -3.714919e-02
9835 -3.12477796 9.67522204 6.488542e-02
9836 -2.92477796 9.67522204 6.488542e-02
9837 -2.72477796 9.67522204 -3.096206e-04
9838 -2.52477796 9.67522204 -1.931577e-01
9839 -2.32477796 9.67522204 -1.931577e-01
9840 -2.12477796 9.67522204 -3.834666e-02
9841 -1.92477796 9.67522204 -8.320347e-02
9842 -1.72477796 9.67522204 -5.526467e-02
9843 -1.52477796 9.67522204 2.790785e-02
9844 -1.32477796 9.67522204 2.790785e-02
9845 -1.12477796 9.67522204 7.154067e-02
9846 -0.92477796 9.67522204 5.394615e-02
9847 -0.72477796 9.67522204 5.394615e-02
9848 -0.52477796 9.67522204 1.931115e-01
9849 -0.32477796 9.67522204 2.429306e-01
9850 -0.12477796 9.67522204 2.076919e-01
9851 0.07522204 9.67522204 3.866815e-01
9852 0.27522204 9.67522204 3.866815e-01
9853 0.47522204 9.67522204 1.736802e-01
9854 0.67522204 9.67522204 1.360002e-01
9855 0.87522204 9.67522204 1.360002e-01
9856 1.07522204 9.67522204 8.487772e-02
9857 1.27522204 9.67522204 6.066086e-02
9858 1.47522204 9.67522204 1.268007e-01
9859 1.67522204 9.67522204 1.025949e-01
9860 1.87522204 9.67522204 1.025949e-01
9861 2.07522204 9.67522204 -6.316486e-02
9862 2.27522204 9.67522204 1.540000e-01
9863 2.47522204 9.67522204 1.540000e-01
9864 2.67522204 9.67522204 1.615894e-01
9865 2.87522204 9.67522204 1.912132e-01
9866 3.07522204 9.67522204 3.830294e-01
9867 3.27522204 9.67522204 5.267256e-02
9868 3.47522204 9.67522204 5.267256e-02
9869 3.67522204 9.67522204 -7.906129e-02
9870 3.87522204 9.67522204 -1.820522e-01
9871 4.07522204 9.67522204 -1.820522e-01
9872 4.27522204 9.67522204 -8.576450e-02
9873 4.47522204 9.67522204 1.180351e-02
9874 4.67522204 9.67522204 7.097235e-02
9875 4.87522204 9.67522204 1.387907e-01
9876 5.07522204 9.67522204 1.387907e-01
9877 5.27522204 9.67522204 1.382417e-01
9878 5.47522204 9.67522204 1.300254e-01
9879 5.67522204 9.67522204 1.300254e-01
9880 5.87522204 9.67522204 1.940662e-01
9881 6.07522204 9.67522204 1.961015e-01
9882 6.27522204 9.67522204 2.829184e-01
9883 6.47522204 9.67522204 2.875313e-01
9884 6.67522204 9.67522204 2.875313e-01
9885 6.87522204 9.67522204 2.422030e-01
9886 7.07522204 9.67522204 3.303211e-01
9887 7.27522204 9.67522204 3.303211e-01
9888 7.47522204 9.67522204 2.928042e-01
9889 7.67522204 9.67522204 2.601441e-01
9890 7.87522204 9.67522204 2.699573e-01
9891 8.07522204 9.67522204 2.423586e-01
9892 8.27522204 9.67522204 2.423586e-01
9893 8.47522204 9.67522204 1.443136e-01
9894 8.67522204 9.67522204 1.419417e-01
9895 8.87522204 9.67522204 1.419417e-01
9896 9.07522204 9.67522204 9.817543e-03
9897 9.27522204 9.67522204 9.817543e-03
9898 9.47522204 9.67522204 7.122067e-02
9899 9.67522204 9.67522204 -1.260700e-02
9900 9.87522204 9.67522204 -1.260700e-02
9901 -9.92477796 9.87522204 -9.960981e-02
9902 -9.72477796 9.87522204 -9.960981e-02
9903 -9.52477796 9.87522204 -8.231289e-02
9904 -9.32477796 9.87522204 -8.231289e-02
9905 -9.12477796 9.87522204 -5.804480e-02
9906 -8.92477796 9.87522204 -2.874439e-02
9907 -8.72477796 9.87522204 -5.122587e-03
9908 -8.52477796 9.87522204 9.070944e-02
9909 -8.32477796 9.87522204 5.033603e-02
9910 -8.12477796 9.87522204 7.028424e-02
9911 -7.92477796 9.87522204 4.117983e-02
9912 -7.72477796 9.87522204 4.117983e-02
9913 -7.52477796 9.87522204 -1.363228e-01
9914 -7.32477796 9.87522204 -1.728220e-01
9915 -7.12477796 9.87522204 -1.728220e-01
9916 -6.92477796 9.87522204 -1.375841e-01
9917 -6.72477796 9.87522204 -1.716369e-01
9918 -6.52477796 9.87522204 -1.255066e-01
9919 -6.32477796 9.87522204 -1.388467e-01
9920 -6.12477796 9.87522204 -1.388467e-01
9921 -5.92477796 9.87522204 -1.739546e-02
9922 -5.72477796 9.87522204 1.031234e-01
9923 -5.52477796 9.87522204 1.031234e-01
9924 -5.32477796 9.87522204 1.709674e-01
9925 -5.12477796 9.87522204 8.692991e-02
9926 -4.92477796 9.87522204 -3.139711e-02
9927 -4.72477796 9.87522204 -8.815527e-02
9928 -4.52477796 9.87522204 -8.815527e-02
9929 -4.32477796 9.87522204 -2.835852e-02
9930 -4.12477796 9.87522204 -1.575607e-01
9931 -3.92477796 9.87522204 -1.575607e-01
9932 -3.72477796 9.87522204 -1.205344e-01
9933 -3.52477796 9.87522204 1.279321e-02
9934 -3.32477796 9.87522204 -3.714919e-02
9935 -3.12477796 9.87522204 6.488542e-02
9936 -2.92477796 9.87522204 6.488542e-02
9937 -2.72477796 9.87522204 -3.096206e-04
9938 -2.52477796 9.87522204 -1.931577e-01
9939 -2.32477796 9.87522204 -1.931577e-01
9940 -2.12477796 9.87522204 -3.834666e-02
9941 -1.92477796 9.87522204 -8.320347e-02
9942 -1.72477796 9.87522204 -5.526467e-02
9943 -1.52477796 9.87522204 2.790785e-02
9944 -1.32477796 9.87522204 2.790785e-02
9945 -1.12477796 9.87522204 7.154067e-02
9946 -0.92477796 9.87522204 5.394615e-02
9947 -0.72477796 9.87522204 5.394615e-02
9948 -0.52477796 9.87522204 1.931115e-01
9949 -0.32477796 9.87522204 2.429306e-01
9950 -0.12477796 9.87522204 2.076919e-01
9951 0.07522204 9.87522204 3.866815e-01
9952 0.27522204 9.87522204 3.866815e-01
9953 0.47522204 9.87522204 1.736802e-01
9954 0.67522204 9.87522204 1.360002e-01
9955 0.87522204 9.87522204 1.360002e-01
9956 1.07522204 9.87522204 8.487772e-02
9957 1.27522204 9.87522204 6.066086e-02
9958 1.47522204 9.87522204 1.268007e-01
9959 1.67522204 9.87522204 1.025949e-01
9960 1.87522204 9.87522204 1.025949e-01
9961 2.07522204 9.87522204 -6.316486e-02
9962 2.27522204 9.87522204 1.540000e-01
9963 2.47522204 9.87522204 1.540000e-01
9964 2.67522204 9.87522204 1.615894e-01
9965 2.87522204 9.87522204 1.912132e-01
9966 3.07522204 9.87522204 3.830294e-01
9967 3.27522204 9.87522204 5.267256e-02
9968 3.47522204 9.87522204 5.267256e-02
9969 3.67522204 9.87522204 -7.906129e-02
9970 3.87522204 9.87522204 -1.820522e-01
9971 4.07522204 9.87522204 -1.820522e-01
9972 4.27522204 9.87522204 -8.576450e-02
9973 4.47522204 9.87522204 1.180351e-02
9974 4.67522204 9.87522204 7.097235e-02
9975 4.87522204 9.87522204 1.387907e-01
9976 5.07522204 9.87522204 1.387907e-01
9977 5.27522204 9.87522204 1.382417e-01
9978 5.47522204 9.87522204 1.300254e-01
9979 5.67522204 9.87522204 1.300254e-01
9980 5.87522204 9.87522204 1.940662e-01
9981 6.07522204 9.87522204 1.961015e-01
9982 6.27522204 9.87522204 2.829184e-01
9983 6.47522204 9.87522204 2.875313e-01
9984 6.67522204 9.87522204 2.875313e-01
9985 6.87522204 9.87522204 2.422030e-01
9986 7.07522204 9.87522204 3.303211e-01
9987 7.27522204 9.87522204 3.303211e-01
9988 7.47522204 9.87522204 2.928042e-01
9989 7.67522204 9.87522204 2.601441e-01
9990 7.87522204 9.87522204 2.699573e-01
9991 8.07522204 9.87522204 2.423586e-01
9992 8.27522204 9.87522204 2.423586e-01
9993 8.47522204 9.87522204 1.443136e-01
9994 8.67522204 9.87522204 1.419417e-01
9995 8.87522204 9.87522204 1.419417e-01
9996 9.07522204 9.87522204 9.817543e-03
9997 9.27522204 9.87522204 9.817543e-03
9998 9.47522204 9.87522204 7.122067e-02
9999 9.67522204 9.87522204 -1.260700e-02
10000 9.87522204 9.87522204 -1.260700e-02
kzs documentation built on May 2, 2019, 4:20 a.m.
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Description Usage Arguments Details Value Note Author(s) See Also Examples
Description
The kzs.2d function is a spatial extension of the kzs function for two input variables.
Usage
1 |
Arguments
y |
a one-dimensional vector of real values representing the response variable to be smoothed. |
x |
a two-dimensional matrix of real values containing the input variables X = (X1, X2). Each column represents an input variable. |
smooth |
a vector of size two that defines the width of the smoothing window along each input variable. |
scale |
a vector of size two in which each element will define a uniformly spaced scale along its respective input variable. |
k |
an integer specifying the number of iterations |
edges |
a logical indicating whether or not to display the outcome data beyond the rectangular range of the two
input variables. By default, |
plot |
a logical indicating whether or not to produce a 3-dimensional plot of the |
Details
The details for this function are nearly identical to that of kzs, except now extended to
three dimensional space. The only difference is that the kzs.2d function averages all y that
are contained within a rectangular window made up of sides smooth[1] and smooth[2].
Value
a three column data frame of the form (x1, x2, yk):
x1 |
the |
x2 |
the |
yk |
the smoothed response values resulting from |
Note
Data set (Y, X1, X2) must be provided, usually as 3-dimensional observations that occur in time or
space; kzs.2d is designed for the general situation, including time series data. In many applications
where an input variable can be time, kzs.2d can resolve the problem of missing values in time series or
or irregularly observed values in Geographical Information Systems (GIS) data analysis. The name of this
function, kzs.2d, simply means that there are two input variables required for use.
The graphical output of kzs.2d is a result of the wireframe() function within the lattice package.
Author(s)
Derek Cyr cyr.derek@gmail.com and Igor Zurbenko igorg.zurbenko@gmail.com
See Also
kzs; For more on the parameter restrictions, see kzs.params
Examples
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 | # EXAMPLE - Estimating the Sinc function in the interval (-3pi, 3pi)
# Load the LATTICE package
# Gridded data for X = (x1, x2) input variables
x1 <- seq(-3*pi, 3*pi, length = 60)
x2 <- x1
df <- expand.grid(x1 = x1, x2 = x2)
# Apply the Sinc function to the (x1, x2) coordinates
df$z <- sin(sqrt(df$x1^2 + df$x2^2)) / sqrt(df$x1^2 + df$x2^2)
df$z[is.na(df$z)] <- 1
# Any point outside the circle of radius 3pi is set to 0. This provides
# a better picture of the outcome solely for the purposes of this example.
dst <- sqrt((df$x1 - 0)^2 + (df$x2 - 0)^2)
df$dist <- dst
df$z[df$dist > 3*pi] <- 0
# Add noise to distort the signal
ez <- rnorm(length(df$z), mean = 0, sd = 1) * 1/4
df$zn <- ez + df$z
### (1) 3D plot of the signal to be estimated by kzs.2d()
wireframe(z ~ x1 * x2, df, main = "Signal to be estimated", drape = TRUE,
colorkey = TRUE, scales = list(arrows = FALSE))
### (2) 3D plot of the signal buried in noise
wireframe(zn ~ x1 * x2, df, main = "Signal buried in noise", drape = TRUE,
colorkey = TRUE, scales = list(arrows = FALSE))
### (3) Execute kzs.2d()
# kzs.2d() may take time to run; k = 1 iteration is used here, but k = 2
# will provide a smoother outcome.
sw <- c(1, 1)
sc <- c(0.2, 0.2)
kzs.2d(y = df[,5], x = df[,1:2], smooth = sw, scale = sc, k = 1, edges = TRUE,
plot = TRUE)
|
Example output
Loading required package: lattice
x1 x2 yk
1 -9.92477796 -9.92477796 2.567973e-02
2 -9.72477796 -9.92477796 2.567973e-02
3 -9.52477796 -9.92477796 1.316873e-02
4 -9.32477796 -9.92477796 1.316873e-02
5 -9.12477796 -9.92477796 -4.744034e-02
6 -8.92477796 -9.92477796 -1.955955e-01
7 -8.72477796 -9.92477796 -2.693540e-01
8 -8.52477796 -9.92477796 -2.424179e-01
9 -8.32477796 -9.92477796 -2.090612e-01
10 -8.12477796 -9.92477796 -2.225288e-01
11 -7.92477796 -9.92477796 9.893776e-02
12 -7.72477796 -9.92477796 9.893776e-02
13 -7.52477796 -9.92477796 1.552823e-01
14 -7.32477796 -9.92477796 2.151326e-01
15 -7.12477796 -9.92477796 2.151326e-01
16 -6.92477796 -9.92477796 1.214875e-01
17 -6.72477796 -9.92477796 8.917226e-02
18 -6.52477796 -9.92477796 3.539644e-02
19 -6.32477796 -9.92477796 -1.816146e-01
20 -6.12477796 -9.92477796 -1.816146e-01
21 -5.92477796 -9.92477796 -3.378428e-01
22 -5.72477796 -9.92477796 -2.499233e-01
23 -5.52477796 -9.92477796 -2.499233e-01
24 -5.32477796 -9.92477796 6.093664e-03
25 -5.12477796 -9.92477796 -1.350104e-02
26 -4.92477796 -9.92477796 1.237590e-01
27 -4.72477796 -9.92477796 7.344731e-02
28 -4.52477796 -9.92477796 7.344731e-02
29 -4.32477796 -9.92477796 -1.923039e-02
30 -4.12477796 -9.92477796 1.482977e-02
31 -3.92477796 -9.92477796 1.482977e-02
32 -3.72477796 -9.92477796 1.449345e-01
33 -3.52477796 -9.92477796 1.071617e-02
34 -3.32477796 -9.92477796 4.444016e-02
35 -3.12477796 -9.92477796 -4.501629e-03
36 -2.92477796 -9.92477796 -4.501629e-03
37 -2.72477796 -9.92477796 -2.519598e-01
38 -2.52477796 -9.92477796 -1.759297e-01
39 -2.32477796 -9.92477796 -1.759297e-01
40 -2.12477796 -9.92477796 -8.150715e-02
41 -1.92477796 -9.92477796 -2.244468e-01
42 -1.72477796 -9.92477796 -2.169254e-01
43 -1.52477796 -9.92477796 -1.580118e-01
44 -1.32477796 -9.92477796 -1.580118e-01
45 -1.12477796 -9.92477796 -1.682121e-01
46 -0.92477796 -9.92477796 3.457007e-02
47 -0.72477796 -9.92477796 3.457007e-02
48 -0.52477796 -9.92477796 5.130201e-02
49 -0.32477796 -9.92477796 -4.519585e-02
50 -0.12477796 -9.92477796 -1.055067e-01
51 0.07522204 -9.92477796 -7.205982e-02
52 0.27522204 -9.92477796 -7.205982e-02
53 0.47522204 -9.92477796 -9.830700e-02
54 0.67522204 -9.92477796 9.471170e-02
55 0.87522204 -9.92477796 9.471170e-02
56 1.07522204 -9.92477796 3.805648e-02
57 1.27522204 -9.92477796 4.462729e-03
58 1.47522204 -9.92477796 1.116803e-02
59 1.67522204 -9.92477796 5.846550e-02
60 1.87522204 -9.92477796 5.846550e-02
61 2.07522204 -9.92477796 1.597113e-02
62 2.27522204 -9.92477796 3.275189e-02
63 2.47522204 -9.92477796 3.275189e-02
64 2.67522204 -9.92477796 -3.603330e-02
65 2.87522204 -9.92477796 -2.076724e-02
66 3.07522204 -9.92477796 5.298606e-02
67 3.27522204 -9.92477796 -8.805040e-02
68 3.47522204 -9.92477796 -8.805040e-02
69 3.67522204 -9.92477796 -1.427929e-01
70 3.87522204 -9.92477796 -6.582636e-02
71 4.07522204 -9.92477796 -6.582636e-02
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1817 -6.72477796 -6.32477796 1.006281e-01
1818 -6.52477796 -6.32477796 1.766191e-01
1819 -6.32477796 -6.32477796 2.405426e-01
1820 -6.12477796 -6.32477796 2.405426e-01
1821 -5.92477796 -6.32477796 1.470725e-01
1822 -5.72477796 -6.32477796 2.781996e-02
1823 -5.52477796 -6.32477796 2.781996e-02
1824 -5.32477796 -6.32477796 1.254248e-02
1825 -5.12477796 -6.32477796 -9.813803e-03
1826 -4.92477796 -6.32477796 -5.501913e-02
1827 -4.72477796 -6.32477796 4.482348e-02
1828 -4.52477796 -6.32477796 4.482348e-02
1829 -4.32477796 -6.32477796 5.692356e-02
1830 -4.12477796 -6.32477796 1.116939e-01
1831 -3.92477796 -6.32477796 1.116939e-01
1832 -3.72477796 -6.32477796 7.997278e-02
1833 -3.52477796 -6.32477796 9.773298e-02
1834 -3.32477796 -6.32477796 8.720082e-02
1835 -3.12477796 -6.32477796 7.474345e-02
1836 -2.92477796 -6.32477796 7.474345e-02
1837 -2.72477796 -6.32477796 1.672598e-01
1838 -2.52477796 -6.32477796 1.528405e-01
1839 -2.32477796 -6.32477796 1.528405e-01
1840 -2.12477796 -6.32477796 1.342024e-01
1841 -1.92477796 -6.32477796 1.035203e-01
1842 -1.72477796 -6.32477796 3.779047e-02
1843 -1.52477796 -6.32477796 -1.745219e-02
1844 -1.32477796 -6.32477796 -1.745219e-02
1845 -1.12477796 -6.32477796 3.313826e-02
1846 -0.92477796 -6.32477796 3.313803e-04
1847 -0.72477796 -6.32477796 3.313803e-04
1848 -0.52477796 -6.32477796 -1.731378e-02
1849 -0.32477796 -6.32477796 -1.223687e-02
1850 -0.12477796 -6.32477796 -6.495362e-02
1851 0.07522204 -6.32477796 -6.361879e-02
1852 0.27522204 -6.32477796 -6.361879e-02
1853 0.47522204 -6.32477796 -8.584839e-02
1854 0.67522204 -6.32477796 -1.290034e-01
1855 0.87522204 -6.32477796 -1.290034e-01
1856 1.07522204 -6.32477796 -6.365422e-02
1857 1.27522204 -6.32477796 -3.326727e-03
1858 1.47522204 -6.32477796 5.476324e-02
1859 1.67522204 -6.32477796 1.315929e-01
1860 1.87522204 -6.32477796 1.315929e-01
1861 2.07522204 -6.32477796 -4.566737e-03
1862 2.27522204 -6.32477796 -2.302149e-02
1863 2.47522204 -6.32477796 -2.302149e-02
1864 2.67522204 -6.32477796 3.765585e-02
1865 2.87522204 -6.32477796 7.361243e-03
1866 3.07522204 -6.32477796 1.082729e-01
1867 3.27522204 -6.32477796 1.446230e-01
1868 3.47522204 -6.32477796 1.446230e-01
1869 3.67522204 -6.32477796 4.318860e-02
1870 3.87522204 -6.32477796 1.787954e-01
1871 4.07522204 -6.32477796 1.787954e-01
1872 4.27522204 -6.32477796 1.740898e-01
1873 4.47522204 -6.32477796 1.173416e-01
1874 4.67522204 -6.32477796 1.625399e-01
1875 4.87522204 -6.32477796 3.399953e-02
1876 5.07522204 -6.32477796 3.399953e-02
1877 5.27522204 -6.32477796 -4.112620e-02
1878 5.47522204 -6.32477796 -4.412747e-02
1879 5.67522204 -6.32477796 -4.412747e-02
1880 5.87522204 -6.32477796 -3.140453e-03
1881 6.07522204 -6.32477796 3.779418e-02
1882 6.27522204 -6.32477796 5.310961e-02
1883 6.47522204 -6.32477796 1.429498e-01
1884 6.67522204 -6.32477796 1.429498e-01
1885 6.87522204 -6.32477796 9.178984e-02
1886 7.07522204 -6.32477796 1.093678e-01
1887 7.27522204 -6.32477796 1.093678e-01
1888 7.47522204 -6.32477796 -5.097843e-03
1889 7.67522204 -6.32477796 -5.116092e-02
1890 7.87522204 -6.32477796 -3.726716e-02
1891 8.07522204 -6.32477796 -1.296815e-01
1892 8.27522204 -6.32477796 -1.296815e-01
1893 8.47522204 -6.32477796 -8.943758e-02
1894 8.67522204 -6.32477796 -2.296716e-02
1895 8.87522204 -6.32477796 -2.296716e-02
1896 9.07522204 -6.32477796 -2.500353e-02
1897 9.27522204 -6.32477796 -2.500353e-02
1898 9.47522204 -6.32477796 -2.997956e-02
1899 9.67522204 -6.32477796 -7.002023e-02
1900 9.87522204 -6.32477796 -7.002023e-02
1901 -9.92477796 -6.12477796 3.856016e-02
1902 -9.72477796 -6.12477796 3.856016e-02
1903 -9.52477796 -6.12477796 9.996218e-02
1904 -9.32477796 -6.12477796 9.996218e-02
1905 -9.12477796 -6.12477796 5.679209e-02
1906 -8.92477796 -6.12477796 8.029520e-02
1907 -8.72477796 -6.12477796 9.420688e-02
1908 -8.52477796 -6.12477796 4.992288e-02
1909 -8.32477796 -6.12477796 7.148338e-02
1910 -8.12477796 -6.12477796 1.051605e-01
1911 -7.92477796 -6.12477796 4.205250e-02
1912 -7.72477796 -6.12477796 4.205250e-02
1913 -7.52477796 -6.12477796 -9.899902e-03
1914 -7.32477796 -6.12477796 -7.292448e-02
1915 -7.12477796 -6.12477796 -7.292448e-02
1916 -6.92477796 -6.12477796 7.531951e-02
1917 -6.72477796 -6.12477796 1.006281e-01
1918 -6.52477796 -6.12477796 1.766191e-01
1919 -6.32477796 -6.12477796 2.405426e-01
1920 -6.12477796 -6.12477796 2.405426e-01
1921 -5.92477796 -6.12477796 1.470725e-01
1922 -5.72477796 -6.12477796 2.781996e-02
1923 -5.52477796 -6.12477796 2.781996e-02
1924 -5.32477796 -6.12477796 1.254248e-02
1925 -5.12477796 -6.12477796 -9.813803e-03
1926 -4.92477796 -6.12477796 -5.501913e-02
1927 -4.72477796 -6.12477796 4.482348e-02
1928 -4.52477796 -6.12477796 4.482348e-02
1929 -4.32477796 -6.12477796 5.692356e-02
1930 -4.12477796 -6.12477796 1.116939e-01
1931 -3.92477796 -6.12477796 1.116939e-01
1932 -3.72477796 -6.12477796 7.997278e-02
1933 -3.52477796 -6.12477796 9.773298e-02
1934 -3.32477796 -6.12477796 8.720082e-02
1935 -3.12477796 -6.12477796 7.474345e-02
1936 -2.92477796 -6.12477796 7.474345e-02
1937 -2.72477796 -6.12477796 1.672598e-01
1938 -2.52477796 -6.12477796 1.528405e-01
1939 -2.32477796 -6.12477796 1.528405e-01
1940 -2.12477796 -6.12477796 1.342024e-01
1941 -1.92477796 -6.12477796 1.035203e-01
1942 -1.72477796 -6.12477796 3.779047e-02
1943 -1.52477796 -6.12477796 -1.745219e-02
1944 -1.32477796 -6.12477796 -1.745219e-02
1945 -1.12477796 -6.12477796 3.313826e-02
1946 -0.92477796 -6.12477796 3.313803e-04
1947 -0.72477796 -6.12477796 3.313803e-04
1948 -0.52477796 -6.12477796 -1.731378e-02
1949 -0.32477796 -6.12477796 -1.223687e-02
1950 -0.12477796 -6.12477796 -6.495362e-02
1951 0.07522204 -6.12477796 -6.361879e-02
1952 0.27522204 -6.12477796 -6.361879e-02
1953 0.47522204 -6.12477796 -8.584839e-02
1954 0.67522204 -6.12477796 -1.290034e-01
1955 0.87522204 -6.12477796 -1.290034e-01
1956 1.07522204 -6.12477796 -6.365422e-02
1957 1.27522204 -6.12477796 -3.326727e-03
1958 1.47522204 -6.12477796 5.476324e-02
1959 1.67522204 -6.12477796 1.315929e-01
1960 1.87522204 -6.12477796 1.315929e-01
1961 2.07522204 -6.12477796 -4.566737e-03
1962 2.27522204 -6.12477796 -2.302149e-02
1963 2.47522204 -6.12477796 -2.302149e-02
1964 2.67522204 -6.12477796 3.765585e-02
1965 2.87522204 -6.12477796 7.361243e-03
1966 3.07522204 -6.12477796 1.082729e-01
1967 3.27522204 -6.12477796 1.446230e-01
1968 3.47522204 -6.12477796 1.446230e-01
1969 3.67522204 -6.12477796 4.318860e-02
1970 3.87522204 -6.12477796 1.787954e-01
1971 4.07522204 -6.12477796 1.787954e-01
1972 4.27522204 -6.12477796 1.740898e-01
1973 4.47522204 -6.12477796 1.173416e-01
1974 4.67522204 -6.12477796 1.625399e-01
1975 4.87522204 -6.12477796 3.399953e-02
1976 5.07522204 -6.12477796 3.399953e-02
1977 5.27522204 -6.12477796 -4.112620e-02
1978 5.47522204 -6.12477796 -4.412747e-02
1979 5.67522204 -6.12477796 -4.412747e-02
1980 5.87522204 -6.12477796 -3.140453e-03
1981 6.07522204 -6.12477796 3.779418e-02
1982 6.27522204 -6.12477796 5.310961e-02
1983 6.47522204 -6.12477796 1.429498e-01
1984 6.67522204 -6.12477796 1.429498e-01
1985 6.87522204 -6.12477796 9.178984e-02
1986 7.07522204 -6.12477796 1.093678e-01
1987 7.27522204 -6.12477796 1.093678e-01
1988 7.47522204 -6.12477796 -5.097843e-03
1989 7.67522204 -6.12477796 -5.116092e-02
1990 7.87522204 -6.12477796 -3.726716e-02
1991 8.07522204 -6.12477796 -1.296815e-01
1992 8.27522204 -6.12477796 -1.296815e-01
1993 8.47522204 -6.12477796 -8.943758e-02
1994 8.67522204 -6.12477796 -2.296716e-02
1995 8.87522204 -6.12477796 -2.296716e-02
1996 9.07522204 -6.12477796 -2.500353e-02
1997 9.27522204 -6.12477796 -2.500353e-02
1998 9.47522204 -6.12477796 -2.997956e-02
1999 9.67522204 -6.12477796 -7.002023e-02
2000 9.87522204 -6.12477796 -7.002023e-02
2001 -9.92477796 -5.92477796 -1.655773e-01
2002 -9.72477796 -5.92477796 -1.655773e-01
2003 -9.52477796 -5.92477796 -2.374095e-02
2004 -9.32477796 -5.92477796 -2.374095e-02
2005 -9.12477796 -5.92477796 -5.485687e-02
2006 -8.92477796 -5.92477796 -2.810241e-02
2007 -8.72477796 -5.92477796 1.772254e-02
2008 -8.52477796 -5.92477796 -7.501054e-02
2009 -8.32477796 -5.92477796 -7.995914e-02
2010 -8.12477796 -5.92477796 -6.758262e-02
2011 -7.92477796 -5.92477796 -4.243526e-02
2012 -7.72477796 -5.92477796 -4.243526e-02
2013 -7.52477796 -5.92477796 -2.159365e-02
2014 -7.32477796 -5.92477796 -4.232854e-02
2015 -7.12477796 -5.92477796 -4.232854e-02
2016 -6.92477796 -5.92477796 1.466512e-02
2017 -6.72477796 -5.92477796 6.005992e-02
2018 -6.52477796 -5.92477796 1.126062e-01
2019 -6.32477796 -5.92477796 2.123137e-01
2020 -6.12477796 -5.92477796 2.123137e-01
2021 -5.92477796 -5.92477796 1.612754e-01
2022 -5.72477796 -5.92477796 6.972918e-02
2023 -5.52477796 -5.92477796 6.972918e-02
2024 -5.32477796 -5.92477796 7.525090e-02
2025 -5.12477796 -5.92477796 1.598559e-02
2026 -4.92477796 -5.92477796 -2.717567e-02
2027 -4.72477796 -5.92477796 1.221826e-02
2028 -4.52477796 -5.92477796 1.221826e-02
2029 -4.32477796 -5.92477796 -1.517536e-02
2030 -4.12477796 -5.92477796 1.286953e-01
2031 -3.92477796 -5.92477796 1.286953e-01
2032 -3.72477796 -5.92477796 1.308961e-01
2033 -3.52477796 -5.92477796 1.699216e-01
2034 -3.32477796 -5.92477796 2.010632e-01
2035 -3.12477796 -5.92477796 1.356299e-01
2036 -2.92477796 -5.92477796 1.356299e-01
2037 -2.72477796 -5.92477796 1.874277e-01
2038 -2.52477796 -5.92477796 1.086013e-01
2039 -2.32477796 -5.92477796 1.086013e-01
2040 -2.12477796 -5.92477796 6.924601e-02
2041 -1.92477796 -5.92477796 2.184085e-02
2042 -1.72477796 -5.92477796 -3.813996e-02
2043 -1.52477796 -5.92477796 -1.275345e-01
2044 -1.32477796 -5.92477796 -1.275345e-01
2045 -1.12477796 -5.92477796 -6.920059e-02
2046 -0.92477796 -5.92477796 -4.568172e-02
2047 -0.72477796 -5.92477796 -4.568172e-02
2048 -0.52477796 -5.92477796 -1.439655e-02
2049 -0.32477796 -5.92477796 -8.626495e-03
2050 -0.12477796 -5.92477796 -5.498119e-02
2051 0.07522204 -5.92477796 -6.022021e-02
2052 0.27522204 -5.92477796 -6.022021e-02
2053 0.47522204 -5.92477796 -1.324981e-01
2054 0.67522204 -5.92477796 -1.975846e-01
2055 0.87522204 -5.92477796 -1.975846e-01
2056 1.07522204 -5.92477796 -1.925526e-01
2057 1.27522204 -5.92477796 -1.530931e-01
2058 1.47522204 -5.92477796 -9.057659e-02
2059 1.67522204 -5.92477796 8.016925e-02
2060 1.87522204 -5.92477796 8.016925e-02
2061 2.07522204 -5.92477796 3.295623e-02
2062 2.27522204 -5.92477796 7.292037e-02
2063 2.47522204 -5.92477796 7.292037e-02
2064 2.67522204 -5.92477796 3.870607e-02
2065 2.87522204 -5.92477796 1.371999e-02
2066 3.07522204 -5.92477796 8.231938e-02
2067 3.27522204 -5.92477796 8.686277e-02
2068 3.47522204 -5.92477796 8.686277e-02
2069 3.67522204 -5.92477796 2.458182e-03
2070 3.87522204 -5.92477796 1.230289e-01
2071 4.07522204 -5.92477796 1.230289e-01
2072 4.27522204 -5.92477796 1.512384e-01
2073 4.47522204 -5.92477796 1.550356e-01
2074 4.67522204 -5.92477796 2.167792e-01
2075 4.87522204 -5.92477796 1.143301e-01
2076 5.07522204 -5.92477796 1.143301e-01
2077 5.27522204 -5.92477796 -1.515243e-04
2078 5.47522204 -5.92477796 -1.762916e-02
2079 5.67522204 -5.92477796 -1.762916e-02
2080 5.87522204 -5.92477796 -2.886058e-03
2081 6.07522204 -5.92477796 1.449807e-02
2082 6.27522204 -5.92477796 7.266682e-02
2083 6.47522204 -5.92477796 1.250815e-01
2084 6.67522204 -5.92477796 1.250815e-01
2085 6.87522204 -5.92477796 3.884999e-02
2086 7.07522204 -5.92477796 1.002456e-01
2087 7.27522204 -5.92477796 1.002456e-01
2088 7.47522204 -5.92477796 -5.689061e-02
2089 7.67522204 -5.92477796 -6.503824e-02
2090 7.87522204 -5.92477796 -1.293810e-02
2091 8.07522204 -5.92477796 -2.802113e-02
2092 8.27522204 -5.92477796 -2.802113e-02
2093 8.47522204 -5.92477796 3.367171e-02
2094 8.67522204 -5.92477796 3.989518e-02
2095 8.87522204 -5.92477796 3.989518e-02
2096 9.07522204 -5.92477796 -6.291163e-02
2097 9.27522204 -5.92477796 -6.291163e-02
2098 9.47522204 -5.92477796 -8.682154e-02
2099 9.67522204 -5.92477796 -1.028323e-01
2100 9.87522204 -5.92477796 -1.028323e-01
2101 -9.92477796 -5.72477796 -6.047129e-02
2102 -9.72477796 -5.72477796 -6.047129e-02
2103 -9.52477796 -5.72477796 -7.269172e-02
2104 -9.32477796 -5.72477796 -7.269172e-02
2105 -9.12477796 -5.72477796 -1.026702e-01
2106 -8.92477796 -5.72477796 -5.269837e-02
2107 -8.72477796 -5.72477796 -5.010739e-02
2108 -8.52477796 -5.72477796 -9.554343e-02
2109 -8.32477796 -5.72477796 -1.335193e-01
2110 -8.12477796 -5.72477796 -1.238166e-01
2111 -7.92477796 -5.72477796 -9.569495e-02
2112 -7.72477796 -5.72477796 -9.569495e-02
2113 -7.52477796 -5.72477796 -2.874145e-02
2114 -7.32477796 -5.72477796 7.004864e-02
2115 -7.12477796 -5.72477796 7.004864e-02
2116 -6.92477796 -5.72477796 9.104052e-02
2117 -6.72477796 -5.72477796 1.281152e-01
2118 -6.52477796 -5.72477796 1.776068e-01
2119 -6.32477796 -5.72477796 2.207995e-01
2120 -6.12477796 -5.72477796 2.207995e-01
2121 -5.92477796 -5.72477796 2.281199e-01
2122 -5.72477796 -5.72477796 1.177051e-01
2123 -5.52477796 -5.72477796 1.177051e-01
2124 -5.32477796 -5.72477796 1.043857e-01
2125 -5.12477796 -5.72477796 1.029471e-01
2126 -4.92477796 -5.72477796 4.842306e-02
2127 -4.72477796 -5.72477796 1.272905e-01
2128 -4.52477796 -5.72477796 1.272905e-01
2129 -4.32477796 -5.72477796 1.770922e-02
2130 -4.12477796 -5.72477796 8.086817e-02
2131 -3.92477796 -5.72477796 8.086817e-02
2132 -3.72477796 -5.72477796 1.305894e-02
2133 -3.52477796 -5.72477796 3.628003e-02
2134 -3.32477796 -5.72477796 1.117736e-01
2135 -3.12477796 -5.72477796 -1.353009e-03
2136 -2.92477796 -5.72477796 -1.353009e-03
2137 -2.72477796 -5.72477796 5.414875e-02
2138 -2.52477796 -5.72477796 4.687739e-02
2139 -2.32477796 -5.72477796 4.687739e-02
2140 -2.12477796 -5.72477796 5.319078e-02
2141 -1.92477796 -5.72477796 1.882360e-02
2142 -1.72477796 -5.72477796 -1.082676e-02
2143 -1.52477796 -5.72477796 -8.105981e-02
2144 -1.32477796 -5.72477796 -8.105981e-02
2145 -1.12477796 -5.72477796 -4.768338e-03
2146 -0.92477796 -5.72477796 -6.171347e-02
2147 -0.72477796 -5.72477796 -6.171347e-02
2148 -0.52477796 -5.72477796 -2.417303e-02
2149 -0.32477796 -5.72477796 -4.775054e-02
2150 -0.12477796 -5.72477796 -1.291817e-01
2151 0.07522204 -5.72477796 -1.197079e-01
2152 0.27522204 -5.72477796 -1.197079e-01
2153 0.47522204 -5.72477796 -2.438559e-01
2154 0.67522204 -5.72477796 -2.672399e-01
2155 0.87522204 -5.72477796 -2.672399e-01
2156 1.07522204 -5.72477796 -2.726892e-01
2157 1.27522204 -5.72477796 -2.110925e-01
2158 1.47522204 -5.72477796 -1.526591e-01
2159 1.67522204 -5.72477796 -3.905721e-02
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9909 -8.32477796 9.87522204 5.033603e-02
9910 -8.12477796 9.87522204 7.028424e-02
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9913 -7.52477796 9.87522204 -1.363228e-01
9914 -7.32477796 9.87522204 -1.728220e-01
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9920 -6.12477796 9.87522204 -1.388467e-01
9921 -5.92477796 9.87522204 -1.739546e-02
9922 -5.72477796 9.87522204 1.031234e-01
9923 -5.52477796 9.87522204 1.031234e-01
9924 -5.32477796 9.87522204 1.709674e-01
9925 -5.12477796 9.87522204 8.692991e-02
9926 -4.92477796 9.87522204 -3.139711e-02
9927 -4.72477796 9.87522204 -8.815527e-02
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9929 -4.32477796 9.87522204 -2.835852e-02
9930 -4.12477796 9.87522204 -1.575607e-01
9931 -3.92477796 9.87522204 -1.575607e-01
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9933 -3.52477796 9.87522204 1.279321e-02
9934 -3.32477796 9.87522204 -3.714919e-02
9935 -3.12477796 9.87522204 6.488542e-02
9936 -2.92477796 9.87522204 6.488542e-02
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9939 -2.32477796 9.87522204 -1.931577e-01
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9946 -0.92477796 9.87522204 5.394615e-02
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9948 -0.52477796 9.87522204 1.931115e-01
9949 -0.32477796 9.87522204 2.429306e-01
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9951 0.07522204 9.87522204 3.866815e-01
9952 0.27522204 9.87522204 3.866815e-01
9953 0.47522204 9.87522204 1.736802e-01
9954 0.67522204 9.87522204 1.360002e-01
9955 0.87522204 9.87522204 1.360002e-01
9956 1.07522204 9.87522204 8.487772e-02
9957 1.27522204 9.87522204 6.066086e-02
9958 1.47522204 9.87522204 1.268007e-01
9959 1.67522204 9.87522204 1.025949e-01
9960 1.87522204 9.87522204 1.025949e-01
9961 2.07522204 9.87522204 -6.316486e-02
9962 2.27522204 9.87522204 1.540000e-01
9963 2.47522204 9.87522204 1.540000e-01
9964 2.67522204 9.87522204 1.615894e-01
9965 2.87522204 9.87522204 1.912132e-01
9966 3.07522204 9.87522204 3.830294e-01
9967 3.27522204 9.87522204 5.267256e-02
9968 3.47522204 9.87522204 5.267256e-02
9969 3.67522204 9.87522204 -7.906129e-02
9970 3.87522204 9.87522204 -1.820522e-01
9971 4.07522204 9.87522204 -1.820522e-01
9972 4.27522204 9.87522204 -8.576450e-02
9973 4.47522204 9.87522204 1.180351e-02
9974 4.67522204 9.87522204 7.097235e-02
9975 4.87522204 9.87522204 1.387907e-01
9976 5.07522204 9.87522204 1.387907e-01
9977 5.27522204 9.87522204 1.382417e-01
9978 5.47522204 9.87522204 1.300254e-01
9979 5.67522204 9.87522204 1.300254e-01
9980 5.87522204 9.87522204 1.940662e-01
9981 6.07522204 9.87522204 1.961015e-01
9982 6.27522204 9.87522204 2.829184e-01
9983 6.47522204 9.87522204 2.875313e-01
9984 6.67522204 9.87522204 2.875313e-01
9985 6.87522204 9.87522204 2.422030e-01
9986 7.07522204 9.87522204 3.303211e-01
9987 7.27522204 9.87522204 3.303211e-01
9988 7.47522204 9.87522204 2.928042e-01
9989 7.67522204 9.87522204 2.601441e-01
9990 7.87522204 9.87522204 2.699573e-01
9991 8.07522204 9.87522204 2.423586e-01
9992 8.27522204 9.87522204 2.423586e-01
9993 8.47522204 9.87522204 1.443136e-01
9994 8.67522204 9.87522204 1.419417e-01
9995 8.87522204 9.87522204 1.419417e-01
9996 9.07522204 9.87522204 9.817543e-03
9997 9.27522204 9.87522204 9.817543e-03
9998 9.47522204 9.87522204 7.122067e-02
9999 9.67522204 9.87522204 -1.260700e-02
10000 9.87522204 9.87522204 -1.260700e-02
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