A function to calculate the local spatial runs tests.
local.sp.runs.test.RdThis function calculates the local spatial runs tests for all localizations.
Usage
local.sp.runs.test(formula = NULL, data = NULL, fx = NULL,
distr = "asymptotic", listw = listw, alternative = "two.sided" , nsim = NULL,
control = list())Arguments
- formula
An (optional) formula with the factor included in
data- data
An (optional) data frame or a sf object containing the variable to testing for.
- fx
An (optional) factor of observations with the same length as the neighbors list in
listw- distr
a character string specifying the distribution "asymptotic" (default) or "bootstrap"
- listw
A neighbourhood list (an object type knn or nb) or a W matrix that indicates the order of the elements in each $m_i-environment$ (for example of inverse distance). To calculate the number of runs in each $m_i-environment$, an order must be established, for example from the nearest neighbour to the furthest one.
- alternative
a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".
- nsim
Default value is NULL to obtain the asymptotic version of the local test. For the bootstrap version nsim is the number of permutations to obtain the pseudo-value.
- control
Optional argument. See Control Argument section.
Value
The output is an object of the class localsrq local.SRQ A matrix with
runs.i | number of runs in the localization 'i'. |
E.i | expectation of local runs statistic in the localization 'i'. |
Sd.i | standard deviate of local runs statistic in the localization 'i'. |
z.value | standard value of local runs statistic (only for asymptotic version). |
p.value | p-value of local local runs statistic (only for asymptotic version). |
zseudo.value | standard value of local runs statistic (only for boots version). |
pseudo.value | p-value of local runs statistic (only for boots version). |
MeanNeig Mean of run.i MaxNeig Maximum of run.i listw the object listwalternative a character string describing the alternative hypothesis
Details
The object listw can be the class:
knn: Objects of the class knn that consider the neighbours in order of proximity.nb: If the neighbours are obtained from an sf object, the code internally will call the functionnb2nb_orderit will order them in order of proximity of the centroids.matrix: If a object of matrix class based in the inverse of the distance in introduced as argument, the functionnb2nb_orderwill also be called internally to transform the object the class matrix to a matrix of the class nb with ordered neighbours.
Control arguments
seedinit | Numerical value for the seed in boot version. Default value seedinit = 123 |
Author
| Fernando López | fernando.lopez@upct.es |
| Román Mínguez | roman.minguez@uclm.es |
| Antonio Páez | paezha@gmail.com |
| Manuel Ruiz | manuel.ruiz@upct.es |
@references
Ruiz, M., López, F., and Páez, A. (2021). A test for global and local homogeneity of categorical data based on spatial runs. Working paper.
Examples
# Case 1: Local spatial runs test based on knn
library(lwgeom)
N <- 100
cx <- runif(N)
cy <- runif(N)
x <- cbind(cx,cy)
listw <- spdep::knearneigh(cbind(cx,cy), k = 10)
p <- c(1/6,3/6,2/6)
rho <- 0.5
fx <- dgp.spq(p = p, listw = listw, rho = rho)
# Asymtotic version
lsrq <- local.sp.runs.test(fx = fx, listw = listw, alternative = "less")
print(lsrq)
#> runs.i E.i Std.i z.value p.value
#> 1 6 7.183838 1.59988 -0.7399544 0.229663845
#> 2 8 7.183838 1.59988 0.5101392 0.695023022
#> 3 4 7.183838 1.59988 -1.9900479 0.023292830
#> 4 8 7.183838 1.59988 0.5101392 0.695023022
#> 5 5 7.183838 1.59988 -1.3650011 0.086126348
#> 6 9 7.183838 1.59988 1.1351860 0.871851293
#> 7 7 7.183838 1.59988 -0.1149076 0.454259185
#> 8 7 7.183838 1.59988 -0.1149076 0.454259185
#> 9 4 7.183838 1.59988 -1.9900479 0.023292830
#> 10 6 7.183838 1.59988 -0.7399544 0.229663845
#> 11 6 7.183838 1.59988 -0.7399544 0.229663845
#> 12 5 7.183838 1.59988 -1.3650011 0.086126348
#> 13 9 7.183838 1.59988 1.1351860 0.871851293
#> 14 7 7.183838 1.59988 -0.1149076 0.454259185
#> 15 7 7.183838 1.59988 -0.1149076 0.454259185
#> 16 7 7.183838 1.59988 -0.1149076 0.454259185
#> 17 8 7.183838 1.59988 0.5101392 0.695023022
#> 18 5 7.183838 1.59988 -1.3650011 0.086126348
#> 19 7 7.183838 1.59988 -0.1149076 0.454259185
#> 20 5 7.183838 1.59988 -1.3650011 0.086126348
#> 21 5 7.183838 1.59988 -1.3650011 0.086126348
#> 22 7 7.183838 1.59988 -0.1149076 0.454259185
#> 23 7 7.183838 1.59988 -0.1149076 0.454259185
#> 24 9 7.183838 1.59988 1.1351860 0.871851293
#> 25 7 7.183838 1.59988 -0.1149076 0.454259185
#> 26 5 7.183838 1.59988 -1.3650011 0.086126348
#> 27 5 7.183838 1.59988 -1.3650011 0.086126348
#> 28 7 7.183838 1.59988 -0.1149076 0.454259185
#> 29 6 7.183838 1.59988 -0.7399544 0.229663845
#> 30 7 7.183838 1.59988 -0.1149076 0.454259185
#> 31 7 7.183838 1.59988 -0.1149076 0.454259185
#> 32 7 7.183838 1.59988 -0.1149076 0.454259185
#> 33 8 7.183838 1.59988 0.5101392 0.695023022
#> 34 6 7.183838 1.59988 -0.7399544 0.229663845
#> 35 6 7.183838 1.59988 -0.7399544 0.229663845
#> 36 8 7.183838 1.59988 0.5101392 0.695023022
#> 37 7 7.183838 1.59988 -0.1149076 0.454259185
#> 38 8 7.183838 1.59988 0.5101392 0.695023022
#> 39 7 7.183838 1.59988 -0.1149076 0.454259185
#> 40 6 7.183838 1.59988 -0.7399544 0.229663845
#> 41 6 7.183838 1.59988 -0.7399544 0.229663845
#> 42 8 7.183838 1.59988 0.5101392 0.695023022
#> 43 5 7.183838 1.59988 -1.3650011 0.086126348
#> 44 8 7.183838 1.59988 0.5101392 0.695023022
#> 45 4 7.183838 1.59988 -1.9900479 0.023292830
#> 46 7 7.183838 1.59988 -0.1149076 0.454259185
#> 47 11 7.183838 1.59988 2.3852795 0.991466925
#> 48 8 7.183838 1.59988 0.5101392 0.695023022
#> 49 5 7.183838 1.59988 -1.3650011 0.086126348
#> 50 4 7.183838 1.59988 -1.9900479 0.023292830
#> 51 7 7.183838 1.59988 -0.1149076 0.454259185
#> 52 7 7.183838 1.59988 -0.1149076 0.454259185
#> 53 7 7.183838 1.59988 -0.1149076 0.454259185
#> 54 8 7.183838 1.59988 0.5101392 0.695023022
#> 55 8 7.183838 1.59988 0.5101392 0.695023022
#> 56 6 7.183838 1.59988 -0.7399544 0.229663845
#> 57 6 7.183838 1.59988 -0.7399544 0.229663845
#> 58 5 7.183838 1.59988 -1.3650011 0.086126348
#> 59 9 7.183838 1.59988 1.1351860 0.871851293
#> 60 7 7.183838 1.59988 -0.1149076 0.454259185
#> 61 9 7.183838 1.59988 1.1351860 0.871851293
#> 62 7 7.183838 1.59988 -0.1149076 0.454259185
#> 63 5 7.183838 1.59988 -1.3650011 0.086126348
#> 64 9 7.183838 1.59988 1.1351860 0.871851293
#> 65 5 7.183838 1.59988 -1.3650011 0.086126348
#> 66 8 7.183838 1.59988 0.5101392 0.695023022
#> 67 6 7.183838 1.59988 -0.7399544 0.229663845
#> 68 7 7.183838 1.59988 -0.1149076 0.454259185
#> 69 5 7.183838 1.59988 -1.3650011 0.086126348
#> 70 5 7.183838 1.59988 -1.3650011 0.086126348
#> 71 9 7.183838 1.59988 1.1351860 0.871851293
#> 72 10 7.183838 1.59988 1.7602327 0.960815822
#> 73 7 7.183838 1.59988 -0.1149076 0.454259185
#> 74 10 7.183838 1.59988 1.7602327 0.960815822
#> 75 6 7.183838 1.59988 -0.7399544 0.229663845
#> 76 7 7.183838 1.59988 -0.1149076 0.454259185
#> 77 4 7.183838 1.59988 -1.9900479 0.023292830
#> 78 6 7.183838 1.59988 -0.7399544 0.229663845
#> 79 5 7.183838 1.59988 -1.3650011 0.086126348
#> 80 6 7.183838 1.59988 -0.7399544 0.229663845
#> 81 10 7.183838 1.59988 1.7602327 0.960815822
#> 82 4 7.183838 1.59988 -1.9900479 0.023292830
#> 83 3 7.183838 1.59988 -2.6150947 0.004460136
#> 84 8 7.183838 1.59988 0.5101392 0.695023022
#> 85 5 7.183838 1.59988 -1.3650011 0.086126348
#> 86 7 7.183838 1.59988 -0.1149076 0.454259185
#> 87 8 7.183838 1.59988 0.5101392 0.695023022
#> 88 9 7.183838 1.59988 1.1351860 0.871851293
#> 89 7 7.183838 1.59988 -0.1149076 0.454259185
#> 90 5 7.183838 1.59988 -1.3650011 0.086126348
#> 91 8 7.183838 1.59988 0.5101392 0.695023022
#> 92 5 7.183838 1.59988 -1.3650011 0.086126348
#> 93 8 7.183838 1.59988 0.5101392 0.695023022
#> 94 6 7.183838 1.59988 -0.7399544 0.229663845
#> 95 8 7.183838 1.59988 0.5101392 0.695023022
#> 96 3 7.183838 1.59988 -2.6150947 0.004460136
#> 97 7 7.183838 1.59988 -0.1149076 0.454259185
#> 98 6 7.183838 1.59988 -0.7399544 0.229663845
#> 99 5 7.183838 1.59988 -1.3650011 0.086126348
#> 100 6 7.183838 1.59988 -0.7399544 0.229663845
plot(lsrq, sig = 0.05)
# Asymtotic version
lsrq <- local.sp.runs.test(fx = fx, listw = listw, alternative = "two.sided",
distr ="bootstrap", nsim = 399)
print(lsrq)
#> SRQ EP.i SdP.i zseudo.value pseudo.value
#> 1 6 7.197995 1.600376 -0.74857115 0.454115727
#> 2 8 7.080201 1.631531 0.56376464 0.572914316
#> 3 4 7.250627 1.651052 -1.96882125 0.048973622
#> 4 8 7.170426 1.685298 0.49224174 0.622548457
#> 5 5 7.263158 1.573468 -1.43832514 0.150341823
#> 6 9 7.298246 1.459253 1.16618195 0.243540890
#> 7 7 7.130326 1.537817 -0.08474727 0.932462317
#> 8 7 7.150376 1.573155 -0.09558874 0.923847206
#> 9 4 7.160401 1.600671 -1.97442302 0.048333663
#> 10 6 7.115288 1.659976 -0.67187019 0.501666337
#> 11 6 7.135338 1.582482 -0.71744137 0.473101802
#> 12 5 7.223058 1.611164 -1.37978372 0.167653245
#> 13 9 7.243108 1.603560 1.09562016 0.273245033
#> 14 7 7.215539 1.584681 -0.13601399 0.891810220
#> 15 7 7.263158 1.648334 -0.15965080 0.873156160
#> 16 7 7.228070 1.554896 -0.14667870 0.883385629
#> 17 8 7.125313 1.552866 0.56327250 0.573249339
#> 18 5 7.210526 1.530523 -1.44429433 0.148656201
#> 19 7 7.135338 1.542278 -0.08775222 0.930073615
#> 20 5 7.055138 1.647891 -1.24713206 0.212349080
#> 21 5 7.200501 1.548187 -1.42134039 0.155217828
#> 22 7 7.406015 1.550025 -0.26194100 0.793366930
#> 23 7 7.293233 1.529190 -0.19175715 0.847932434
#> 24 9 7.303258 1.612066 1.05252601 0.292558284
#> 25 7 7.187970 1.555427 -0.12084781 0.903811577
#> 26 5 7.070175 1.636606 -1.26491965 0.205900134
#> 27 5 7.130326 1.566951 -1.35953600 0.173976802
#> 28 7 7.165414 1.632800 -0.10130665 0.919307037
#> 29 6 7.155388 1.647570 -0.70126817 0.483135672
#> 30 7 7.085213 1.672346 -0.05095419 0.959362022
#> 31 7 7.082707 1.649022 -0.05015505 0.959998834
#> 32 7 7.107769 1.622987 -0.06640192 0.947057840
#> 33 8 7.077694 1.553559 0.59367272 0.552731031
#> 34 6 7.150376 1.626552 -0.70724810 0.479412310
#> 35 6 7.290727 1.627555 -0.79304672 0.427750603
#> 36 8 7.017544 1.603135 0.61283415 0.539986006
#> 37 7 7.253133 1.639213 -0.15442340 0.877275906
#> 38 8 7.260652 1.654059 0.44699041 0.654881983
#> 39 7 7.358396 1.570575 -0.22819407 0.819495368
#> 40 6 7.215539 1.547785 -0.78534106 0.432253625
#> 41 6 7.243108 1.612933 -0.77071240 0.440877420
#> 42 8 7.165414 1.609553 0.51852073 0.604095002
#> 43 5 7.190476 1.639282 -1.33624116 0.181470462
#> 44 8 7.092732 1.598970 0.56740779 0.570437159
#> 45 4 7.140351 1.585218 -1.98102172 0.047588838
#> 46 7 7.177945 1.535481 -0.11588864 0.907740797
#> 47 11 7.135338 1.621690 2.38310741 0.017167184
#> 48 8 7.177945 1.577453 0.52112828 0.602277412
#> 49 5 7.190476 1.645402 -1.33127150 0.183099692
#> 50 4 7.240602 1.512845 -2.14205825 0.032188795
#> 51 7 7.335840 1.629654 -0.20608029 0.836728193
#> 52 7 7.268170 1.507357 -0.17790771 0.858795456
#> 53 7 7.348371 1.525805 -0.22831940 0.819397944
#> 54 8 7.253133 1.555856 0.48003623 0.631201633
#> 55 8 7.005013 1.569167 0.63408624 0.526024541
#> 56 6 7.195489 1.635621 -0.73090816 0.464835250
#> 57 6 7.270677 1.499386 -0.84746475 0.396736130
#> 58 5 7.092732 1.554349 -1.34637149 0.178182741
#> 59 9 7.177945 1.519030 1.19948597 0.230339036
#> 60 7 6.979950 1.644115 0.01219509 0.990269970
#> 61 9 7.218045 1.664007 1.07088175 0.284222602
#> 62 7 7.223058 1.606479 -0.13884881 0.889569623
#> 63 5 7.090226 1.629465 -1.28276817 0.199573307
#> 64 9 7.152882 1.534915 1.20340039 0.228821417
#> 65 5 7.253133 1.611387 -1.39825714 0.162035863
#> 66 8 7.240602 1.651025 0.45995566 0.645548051
#> 67 6 7.290727 1.688176 -0.76456877 0.444528369
#> 68 7 7.172932 1.544212 -0.11198739 0.910833401
#> 69 5 7.127820 1.530659 -1.39013279 0.164488558
#> 70 5 7.002506 1.757252 -1.13956715 0.254466678
#> 71 9 7.117794 1.643828 1.14501376 0.252203456
#> 72 10 7.213033 1.593716 1.74872290 0.080338929
#> 73 7 7.192982 1.596274 -0.12089556 0.903773763
#> 74 10 7.228070 1.556511 1.78086062 0.074935223
#> 75 6 7.305764 1.552026 -0.84132877 0.400163780
#> 76 7 7.037594 1.546950 -0.02430200 0.980611720
#> 77 4 7.105263 1.608379 -1.93067921 0.053522736
#> 78 6 7.263158 1.612894 -0.78316220 0.433531867
#> 79 5 7.320802 1.596901 -1.45331585 0.146136078
#> 80 6 7.265664 1.605455 -0.78835221 0.430490717
#> 81 10 7.235589 1.668399 1.65692467 0.097534707
#> 82 4 7.278195 1.580440 -2.07423001 0.038057955
#> 83 3 7.055138 1.543984 -2.62641169 0.008629038
#> 84 8 7.345865 1.596377 0.40976250 0.681980176
#> 85 5 7.105263 1.608379 -1.30893506 0.190556350
#> 86 7 7.225564 1.637883 -0.13771672 0.890464302
#> 87 8 7.220551 1.658382 0.47000556 0.638351043
#> 88 9 7.187970 1.635736 1.10777629 0.267958444
#> 89 7 7.162907 1.563088 -0.10422144 0.916993622
#> 90 5 7.102757 1.621764 -1.29658636 0.194773549
#> 91 8 7.208020 1.592803 0.49722409 0.619031036
#> 92 5 7.223058 1.598639 -1.39059356 0.164348711
#> 93 8 7.238095 1.677804 0.45410822 0.649750936
#> 94 6 7.095238 1.500738 -0.72979985 0.465512538
#> 95 8 7.218045 1.628908 0.48004847 0.631192927
#> 96 3 7.270677 1.695965 -2.51813898 0.011797676
#> 97 7 7.152882 1.630176 -0.09378265 0.925281810
#> 98 6 7.110276 1.579667 -0.70285447 0.482146450
#> 99 5 7.127820 1.662837 -1.27963178 0.200674669
#> 100 6 7.182957 1.663716 -0.71103337 0.477063560
plot(lsrq, sig = 0.1)
# \donttest{
# Case 2:Fastfood example. sf (points)
library(lwgeom)
data("FastFood.sf")
sf::sf_use_s2(FALSE)
x <- sf::st_coordinates(sf::st_centroid(FastFood.sf))
#> Warning: st_centroid assumes attributes are constant over geometries of x
#> Warning: bounding box has potentially an invalid value range for longlat data
#> Warning: st_centroid does not give correct centroids for longitude/latitude data
listw <- spdep::knearneigh(x, k = 10)
formula <- ~ Type
lsrq <- local.sp.runs.test(formula = formula, data = FastFood.sf, listw = listw)
print(lsrq)
#> runs.i E.i Std.i z.value p.value
#> 1 8 7.668307 1.490157 0.2225895 0.82385504
#> 2 9 7.668307 1.490157 0.8936597 0.37150400
#> 3 9 7.668307 1.490157 0.8936597 0.37150400
#> 4 8 7.668307 1.490157 0.2225895 0.82385504
#> 5 10 7.668307 1.490157 1.5647299 0.11764625
#> 6 8 7.668307 1.490157 0.2225895 0.82385504
#> 7 8 7.668307 1.490157 0.2225895 0.82385504
#> 8 7 7.668307 1.490157 -0.4484808 0.65380626
#> 9 7 7.668307 1.490157 -0.4484808 0.65380626
#> 10 7 7.668307 1.490157 -0.4484808 0.65380626
#> 11 7 7.668307 1.490157 -0.4484808 0.65380626
#> 12 8 7.668307 1.490157 0.2225895 0.82385504
#> 13 9 7.668307 1.490157 0.8936597 0.37150400
#> 14 7 7.668307 1.490157 -0.4484808 0.65380626
#> 15 10 7.668307 1.490157 1.5647299 0.11764625
#> 16 9 7.668307 1.490157 0.8936597 0.37150400
#> 17 7 7.668307 1.490157 -0.4484808 0.65380626
#> 18 9 7.668307 1.490157 0.8936597 0.37150400
#> 19 10 7.668307 1.490157 1.5647299 0.11764625
#> 20 9 7.668307 1.490157 0.8936597 0.37150400
#> 21 9 7.668307 1.490157 0.8936597 0.37150400
#> 22 10 7.668307 1.490157 1.5647299 0.11764625
#> 23 7 7.668307 1.490157 -0.4484808 0.65380626
#> 24 6 7.668307 1.490157 -1.1195510 0.26290515
#> 25 9 7.668307 1.490157 0.8936597 0.37150400
#> 26 9 7.668307 1.490157 0.8936597 0.37150400
#> 27 10 7.668307 1.490157 1.5647299 0.11764625
#> 28 8 7.668307 1.490157 0.2225895 0.82385504
#> 29 8 7.668307 1.490157 0.2225895 0.82385504
#> 30 10 7.668307 1.490157 1.5647299 0.11764625
#> 31 9 7.668307 1.490157 0.8936597 0.37150400
#> 32 8 7.668307 1.490157 0.2225895 0.82385504
#> 33 6 7.668307 1.490157 -1.1195510 0.26290515
#> 34 8 7.668307 1.490157 0.2225895 0.82385504
#> 35 8 7.668307 1.490157 0.2225895 0.82385504
#> 36 9 7.668307 1.490157 0.8936597 0.37150400
#> 37 8 7.668307 1.490157 0.2225895 0.82385504
#> 38 7 7.668307 1.490157 -0.4484808 0.65380626
#> 39 8 7.668307 1.490157 0.2225895 0.82385504
#> 40 9 7.668307 1.490157 0.8936597 0.37150400
#> 41 8 7.668307 1.490157 0.2225895 0.82385504
#> 42 9 7.668307 1.490157 0.8936597 0.37150400
#> 43 7 7.668307 1.490157 -0.4484808 0.65380626
#> 44 8 7.668307 1.490157 0.2225895 0.82385504
#> 45 8 7.668307 1.490157 0.2225895 0.82385504
#> 46 8 7.668307 1.490157 0.2225895 0.82385504
#> 47 7 7.668307 1.490157 -0.4484808 0.65380626
#> 48 6 7.668307 1.490157 -1.1195510 0.26290515
#> 49 6 7.668307 1.490157 -1.1195510 0.26290515
#> 50 8 7.668307 1.490157 0.2225895 0.82385504
#> 51 6 7.668307 1.490157 -1.1195510 0.26290515
#> 52 7 7.668307 1.490157 -0.4484808 0.65380626
#> 53 4 7.668307 1.490157 -2.4616914 0.01382836
#> 54 7 7.668307 1.490157 -0.4484808 0.65380626
#> 55 8 7.668307 1.490157 0.2225895 0.82385504
#> 56 8 7.668307 1.490157 0.2225895 0.82385504
#> 57 4 7.668307 1.490157 -2.4616914 0.01382836
#> 58 5 7.668307 1.490157 -1.7906212 0.07335410
#> 59 9 7.668307 1.490157 0.8936597 0.37150400
#> 60 11 7.668307 1.490157 2.2358001 0.02536487
#> 61 4 7.668307 1.490157 -2.4616914 0.01382836
#> 62 7 7.668307 1.490157 -0.4484808 0.65380626
#> 63 6 7.668307 1.490157 -1.1195510 0.26290515
#> 64 10 7.668307 1.490157 1.5647299 0.11764625
#> 65 9 7.668307 1.490157 0.8936597 0.37150400
#> 66 7 7.668307 1.490157 -0.4484808 0.65380626
#> 67 7 7.668307 1.490157 -0.4484808 0.65380626
#> 68 6 7.668307 1.490157 -1.1195510 0.26290515
#> 69 8 7.668307 1.490157 0.2225895 0.82385504
#> 70 10 7.668307 1.490157 1.5647299 0.11764625
#> 71 8 7.668307 1.490157 0.2225895 0.82385504
#> 72 8 7.668307 1.490157 0.2225895 0.82385504
#> 73 6 7.668307 1.490157 -1.1195510 0.26290515
#> 74 8 7.668307 1.490157 0.2225895 0.82385504
#> 75 8 7.668307 1.490157 0.2225895 0.82385504
#> 76 8 7.668307 1.490157 0.2225895 0.82385504
#> 77 10 7.668307 1.490157 1.5647299 0.11764625
#> 78 8 7.668307 1.490157 0.2225895 0.82385504
#> 79 9 7.668307 1.490157 0.8936597 0.37150400
#> 80 8 7.668307 1.490157 0.2225895 0.82385504
#> 81 8 7.668307 1.490157 0.2225895 0.82385504
#> 82 8 7.668307 1.490157 0.2225895 0.82385504
#> 83 9 7.668307 1.490157 0.8936597 0.37150400
#> 84 8 7.668307 1.490157 0.2225895 0.82385504
#> 85 9 7.668307 1.490157 0.8936597 0.37150400
#> 86 10 7.668307 1.490157 1.5647299 0.11764625
#> 87 7 7.668307 1.490157 -0.4484808 0.65380626
#> 88 9 7.668307 1.490157 0.8936597 0.37150400
#> 89 7 7.668307 1.490157 -0.4484808 0.65380626
#> 90 7 7.668307 1.490157 -0.4484808 0.65380626
#> 91 8 7.668307 1.490157 0.2225895 0.82385504
#> 92 11 7.668307 1.490157 2.2358001 0.02536487
#> 93 7 7.668307 1.490157 -0.4484808 0.65380626
#> 94 6 7.668307 1.490157 -1.1195510 0.26290515
#> 95 9 7.668307 1.490157 0.8936597 0.37150400
#> 96 8 7.668307 1.490157 0.2225895 0.82385504
#> 97 8 7.668307 1.490157 0.2225895 0.82385504
#> 98 9 7.668307 1.490157 0.8936597 0.37150400
#> 99 10 7.668307 1.490157 1.5647299 0.11764625
#> 100 10 7.668307 1.490157 1.5647299 0.11764625
#> 101 9 7.668307 1.490157 0.8936597 0.37150400
#> 102 7 7.668307 1.490157 -0.4484808 0.65380626
#> 103 10 7.668307 1.490157 1.5647299 0.11764625
#> 104 10 7.668307 1.490157 1.5647299 0.11764625
#> 105 9 7.668307 1.490157 0.8936597 0.37150400
#> 106 10 7.668307 1.490157 1.5647299 0.11764625
#> 107 7 7.668307 1.490157 -0.4484808 0.65380626
#> 108 8 7.668307 1.490157 0.2225895 0.82385504
#> 109 10 7.668307 1.490157 1.5647299 0.11764625
#> 110 7 7.668307 1.490157 -0.4484808 0.65380626
#> 111 11 7.668307 1.490157 2.2358001 0.02536487
#> 112 7 7.668307 1.490157 -0.4484808 0.65380626
#> 113 9 7.668307 1.490157 0.8936597 0.37150400
#> 114 10 7.668307 1.490157 1.5647299 0.11764625
#> 115 5 7.668307 1.490157 -1.7906212 0.07335410
#> 116 7 7.668307 1.490157 -0.4484808 0.65380626
#> 117 8 7.668307 1.490157 0.2225895 0.82385504
#> 118 9 7.668307 1.490157 0.8936597 0.37150400
#> 119 7 7.668307 1.490157 -0.4484808 0.65380626
#> 120 9 7.668307 1.490157 0.8936597 0.37150400
#> 121 9 7.668307 1.490157 0.8936597 0.37150400
#> 122 3 7.668307 1.490157 -3.1327617 0.00173170
#> 123 7 7.668307 1.490157 -0.4484808 0.65380626
#> 124 9 7.668307 1.490157 0.8936597 0.37150400
#> 125 9 7.668307 1.490157 0.8936597 0.37150400
#> 126 7 7.668307 1.490157 -0.4484808 0.65380626
#> 127 7 7.668307 1.490157 -0.4484808 0.65380626
#> 128 10 7.668307 1.490157 1.5647299 0.11764625
#> 129 9 7.668307 1.490157 0.8936597 0.37150400
#> 130 8 7.668307 1.490157 0.2225895 0.82385504
#> 131 6 7.668307 1.490157 -1.1195510 0.26290515
#> 132 9 7.668307 1.490157 0.8936597 0.37150400
#> 133 8 7.668307 1.490157 0.2225895 0.82385504
#> 134 9 7.668307 1.490157 0.8936597 0.37150400
#> 135 8 7.668307 1.490157 0.2225895 0.82385504
#> 136 7 7.668307 1.490157 -0.4484808 0.65380626
#> 137 5 7.668307 1.490157 -1.7906212 0.07335410
#> 138 9 7.668307 1.490157 0.8936597 0.37150400
#> 139 8 7.668307 1.490157 0.2225895 0.82385504
#> 140 8 7.668307 1.490157 0.2225895 0.82385504
#> 141 7 7.668307 1.490157 -0.4484808 0.65380626
#> 142 7 7.668307 1.490157 -0.4484808 0.65380626
#> 143 10 7.668307 1.490157 1.5647299 0.11764625
#> 144 8 7.668307 1.490157 0.2225895 0.82385504
#> 145 9 7.668307 1.490157 0.8936597 0.37150400
#> 146 7 7.668307 1.490157 -0.4484808 0.65380626
#> 147 9 7.668307 1.490157 0.8936597 0.37150400
#> 148 9 7.668307 1.490157 0.8936597 0.37150400
#> 149 9 7.668307 1.490157 0.8936597 0.37150400
#> 150 8 7.668307 1.490157 0.2225895 0.82385504
#> 151 9 7.668307 1.490157 0.8936597 0.37150400
#> 152 7 7.668307 1.490157 -0.4484808 0.65380626
#> 153 7 7.668307 1.490157 -0.4484808 0.65380626
#> 154 9 7.668307 1.490157 0.8936597 0.37150400
#> 155 9 7.668307 1.490157 0.8936597 0.37150400
#> 156 9 7.668307 1.490157 0.8936597 0.37150400
#> 157 10 7.668307 1.490157 1.5647299 0.11764625
#> 158 8 7.668307 1.490157 0.2225895 0.82385504
#> 159 8 7.668307 1.490157 0.2225895 0.82385504
#> 160 8 7.668307 1.490157 0.2225895 0.82385504
#> 161 8 7.668307 1.490157 0.2225895 0.82385504
#> 162 9 7.668307 1.490157 0.8936597 0.37150400
#> 163 8 7.668307 1.490157 0.2225895 0.82385504
#> 164 10 7.668307 1.490157 1.5647299 0.11764625
#> 165 8 7.668307 1.490157 0.2225895 0.82385504
#> 166 8 7.668307 1.490157 0.2225895 0.82385504
#> 167 10 7.668307 1.490157 1.5647299 0.11764625
#> 168 8 7.668307 1.490157 0.2225895 0.82385504
#> 169 6 7.668307 1.490157 -1.1195510 0.26290515
#> 170 9 7.668307 1.490157 0.8936597 0.37150400
#> 171 9 7.668307 1.490157 0.8936597 0.37150400
#> 172 9 7.668307 1.490157 0.8936597 0.37150400
#> 173 7 7.668307 1.490157 -0.4484808 0.65380626
#> 174 9 7.668307 1.490157 0.8936597 0.37150400
#> 175 7 7.668307 1.490157 -0.4484808 0.65380626
#> 176 10 7.668307 1.490157 1.5647299 0.11764625
#> 177 9 7.668307 1.490157 0.8936597 0.37150400
#> 178 7 7.668307 1.490157 -0.4484808 0.65380626
#> 179 7 7.668307 1.490157 -0.4484808 0.65380626
#> 180 10 7.668307 1.490157 1.5647299 0.11764625
#> 181 8 7.668307 1.490157 0.2225895 0.82385504
#> 182 11 7.668307 1.490157 2.2358001 0.02536487
#> 183 8 7.668307 1.490157 0.2225895 0.82385504
#> 184 8 7.668307 1.490157 0.2225895 0.82385504
#> 185 9 7.668307 1.490157 0.8936597 0.37150400
#> 186 4 7.668307 1.490157 -2.4616914 0.01382836
#> 187 8 7.668307 1.490157 0.2225895 0.82385504
#> 188 7 7.668307 1.490157 -0.4484808 0.65380626
#> 189 9 7.668307 1.490157 0.8936597 0.37150400
#> 190 8 7.668307 1.490157 0.2225895 0.82385504
#> 191 9 7.668307 1.490157 0.8936597 0.37150400
#> 192 8 7.668307 1.490157 0.2225895 0.82385504
#> 193 7 7.668307 1.490157 -0.4484808 0.65380626
#> 194 9 7.668307 1.490157 0.8936597 0.37150400
#> 195 10 7.668307 1.490157 1.5647299 0.11764625
#> 196 8 7.668307 1.490157 0.2225895 0.82385504
#> 197 8 7.668307 1.490157 0.2225895 0.82385504
#> 198 10 7.668307 1.490157 1.5647299 0.11764625
#> 199 7 7.668307 1.490157 -0.4484808 0.65380626
#> 200 10 7.668307 1.490157 1.5647299 0.11764625
#> 201 7 7.668307 1.490157 -0.4484808 0.65380626
#> 202 8 7.668307 1.490157 0.2225895 0.82385504
#> 203 7 7.668307 1.490157 -0.4484808 0.65380626
#> 204 9 7.668307 1.490157 0.8936597 0.37150400
#> 205 7 7.668307 1.490157 -0.4484808 0.65380626
#> 206 8 7.668307 1.490157 0.2225895 0.82385504
#> 207 7 7.668307 1.490157 -0.4484808 0.65380626
#> 208 8 7.668307 1.490157 0.2225895 0.82385504
#> 209 6 7.668307 1.490157 -1.1195510 0.26290515
#> 210 8 7.668307 1.490157 0.2225895 0.82385504
#> 211 9 7.668307 1.490157 0.8936597 0.37150400
#> 212 8 7.668307 1.490157 0.2225895 0.82385504
#> 213 10 7.668307 1.490157 1.5647299 0.11764625
#> 214 7 7.668307 1.490157 -0.4484808 0.65380626
#> 215 8 7.668307 1.490157 0.2225895 0.82385504
#> 216 7 7.668307 1.490157 -0.4484808 0.65380626
#> 217 8 7.668307 1.490157 0.2225895 0.82385504
#> 218 9 7.668307 1.490157 0.8936597 0.37150400
#> 219 7 7.668307 1.490157 -0.4484808 0.65380626
#> 220 8 7.668307 1.490157 0.2225895 0.82385504
#> 221 6 7.668307 1.490157 -1.1195510 0.26290515
#> 222 9 7.668307 1.490157 0.8936597 0.37150400
#> 223 7 7.668307 1.490157 -0.4484808 0.65380626
#> 224 4 7.668307 1.490157 -2.4616914 0.01382836
#> 225 11 7.668307 1.490157 2.2358001 0.02536487
#> 226 6 7.668307 1.490157 -1.1195510 0.26290515
#> 227 9 7.668307 1.490157 0.8936597 0.37150400
#> 228 6 7.668307 1.490157 -1.1195510 0.26290515
#> 229 6 7.668307 1.490157 -1.1195510 0.26290515
#> 230 7 7.668307 1.490157 -0.4484808 0.65380626
#> 231 7 7.668307 1.490157 -0.4484808 0.65380626
#> 232 7 7.668307 1.490157 -0.4484808 0.65380626
#> 233 6 7.668307 1.490157 -1.1195510 0.26290515
#> 234 7 7.668307 1.490157 -0.4484808 0.65380626
#> 235 8 7.668307 1.490157 0.2225895 0.82385504
#> 236 9 7.668307 1.490157 0.8936597 0.37150400
#> 237 6 7.668307 1.490157 -1.1195510 0.26290515
#> 238 10 7.668307 1.490157 1.5647299 0.11764625
#> 239 10 7.668307 1.490157 1.5647299 0.11764625
#> 240 10 7.668307 1.490157 1.5647299 0.11764625
#> 241 11 7.668307 1.490157 2.2358001 0.02536487
#> 242 11 7.668307 1.490157 2.2358001 0.02536487
#> 243 6 7.668307 1.490157 -1.1195510 0.26290515
#> 244 8 7.668307 1.490157 0.2225895 0.82385504
#> 245 7 7.668307 1.490157 -0.4484808 0.65380626
#> 246 7 7.668307 1.490157 -0.4484808 0.65380626
#> 247 9 7.668307 1.490157 0.8936597 0.37150400
#> 248 9 7.668307 1.490157 0.8936597 0.37150400
#> 249 7 7.668307 1.490157 -0.4484808 0.65380626
#> 250 9 7.668307 1.490157 0.8936597 0.37150400
#> 251 9 7.668307 1.490157 0.8936597 0.37150400
#> 252 6 7.668307 1.490157 -1.1195510 0.26290515
#> 253 7 7.668307 1.490157 -0.4484808 0.65380626
#> 254 10 7.668307 1.490157 1.5647299 0.11764625
#> 255 5 7.668307 1.490157 -1.7906212 0.07335410
#> 256 5 7.668307 1.490157 -1.7906212 0.07335410
#> 257 10 7.668307 1.490157 1.5647299 0.11764625
#> 258 8 7.668307 1.490157 0.2225895 0.82385504
#> 259 9 7.668307 1.490157 0.8936597 0.37150400
#> 260 7 7.668307 1.490157 -0.4484808 0.65380626
#> 261 10 7.668307 1.490157 1.5647299 0.11764625
#> 262 6 7.668307 1.490157 -1.1195510 0.26290515
#> 263 8 7.668307 1.490157 0.2225895 0.82385504
#> 264 6 7.668307 1.490157 -1.1195510 0.26290515
#> 265 7 7.668307 1.490157 -0.4484808 0.65380626
#> 266 7 7.668307 1.490157 -0.4484808 0.65380626
#> 267 7 7.668307 1.490157 -0.4484808 0.65380626
#> 268 9 7.668307 1.490157 0.8936597 0.37150400
#> 269 6 7.668307 1.490157 -1.1195510 0.26290515
#> 270 7 7.668307 1.490157 -0.4484808 0.65380626
#> 271 7 7.668307 1.490157 -0.4484808 0.65380626
#> 272 8 7.668307 1.490157 0.2225895 0.82385504
#> 273 8 7.668307 1.490157 0.2225895 0.82385504
#> 274 10 7.668307 1.490157 1.5647299 0.11764625
#> 275 5 7.668307 1.490157 -1.7906212 0.07335410
#> 276 7 7.668307 1.490157 -0.4484808 0.65380626
#> 277 10 7.668307 1.490157 1.5647299 0.11764625
#> 278 7 7.668307 1.490157 -0.4484808 0.65380626
#> 279 8 7.668307 1.490157 0.2225895 0.82385504
#> 280 7 7.668307 1.490157 -0.4484808 0.65380626
#> 281 7 7.668307 1.490157 -0.4484808 0.65380626
#> 282 8 7.668307 1.490157 0.2225895 0.82385504
#> 283 8 7.668307 1.490157 0.2225895 0.82385504
#> 284 9 7.668307 1.490157 0.8936597 0.37150400
#> 285 10 7.668307 1.490157 1.5647299 0.11764625
#> 286 8 7.668307 1.490157 0.2225895 0.82385504
#> 287 8 7.668307 1.490157 0.2225895 0.82385504
#> 288 9 7.668307 1.490157 0.8936597 0.37150400
#> 289 9 7.668307 1.490157 0.8936597 0.37150400
#> 290 10 7.668307 1.490157 1.5647299 0.11764625
#> 291 9 7.668307 1.490157 0.8936597 0.37150400
#> 292 9 7.668307 1.490157 0.8936597 0.37150400
#> 293 10 7.668307 1.490157 1.5647299 0.11764625
#> 294 8 7.668307 1.490157 0.2225895 0.82385504
#> 295 10 7.668307 1.490157 1.5647299 0.11764625
#> 296 8 7.668307 1.490157 0.2225895 0.82385504
#> 297 10 7.668307 1.490157 1.5647299 0.11764625
#> 298 8 7.668307 1.490157 0.2225895 0.82385504
#> 299 9 7.668307 1.490157 0.8936597 0.37150400
#> 300 9 7.668307 1.490157 0.8936597 0.37150400
#> 301 9 7.668307 1.490157 0.8936597 0.37150400
#> 302 7 7.668307 1.490157 -0.4484808 0.65380626
#> 303 7 7.668307 1.490157 -0.4484808 0.65380626
#> 304 9 7.668307 1.490157 0.8936597 0.37150400
#> 305 8 7.668307 1.490157 0.2225895 0.82385504
#> 306 10 7.668307 1.490157 1.5647299 0.11764625
#> 307 9 7.668307 1.490157 0.8936597 0.37150400
#> 308 6 7.668307 1.490157 -1.1195510 0.26290515
#> 309 8 7.668307 1.490157 0.2225895 0.82385504
#> 310 7 7.668307 1.490157 -0.4484808 0.65380626
#> 311 8 7.668307 1.490157 0.2225895 0.82385504
#> 312 8 7.668307 1.490157 0.2225895 0.82385504
#> 313 9 7.668307 1.490157 0.8936597 0.37150400
#> 314 4 7.668307 1.490157 -2.4616914 0.01382836
#> 315 6 7.668307 1.490157 -1.1195510 0.26290515
#> 316 7 7.668307 1.490157 -0.4484808 0.65380626
#> 317 8 7.668307 1.490157 0.2225895 0.82385504
#> 318 9 7.668307 1.490157 0.8936597 0.37150400
#> 319 8 7.668307 1.490157 0.2225895 0.82385504
#> 320 9 7.668307 1.490157 0.8936597 0.37150400
#> 321 7 7.668307 1.490157 -0.4484808 0.65380626
#> 322 9 7.668307 1.490157 0.8936597 0.37150400
#> 323 9 7.668307 1.490157 0.8936597 0.37150400
#> 324 9 7.668307 1.490157 0.8936597 0.37150400
#> 325 9 7.668307 1.490157 0.8936597 0.37150400
#> 326 5 7.668307 1.490157 -1.7906212 0.07335410
#> 327 6 7.668307 1.490157 -1.1195510 0.26290515
#> 328 8 7.668307 1.490157 0.2225895 0.82385504
#> 329 9 7.668307 1.490157 0.8936597 0.37150400
#> 330 10 7.668307 1.490157 1.5647299 0.11764625
#> 331 8 7.668307 1.490157 0.2225895 0.82385504
#> 332 8 7.668307 1.490157 0.2225895 0.82385504
#> 333 9 7.668307 1.490157 0.8936597 0.37150400
#> 334 8 7.668307 1.490157 0.2225895 0.82385504
#> 335 7 7.668307 1.490157 -0.4484808 0.65380626
#> 336 5 7.668307 1.490157 -1.7906212 0.07335410
#> 337 6 7.668307 1.490157 -1.1195510 0.26290515
#> 338 9 7.668307 1.490157 0.8936597 0.37150400
#> 339 8 7.668307 1.490157 0.2225895 0.82385504
#> 340 6 7.668307 1.490157 -1.1195510 0.26290515
#> 341 6 7.668307 1.490157 -1.1195510 0.26290515
#> 342 11 7.668307 1.490157 2.2358001 0.02536487
#> 343 9 7.668307 1.490157 0.8936597 0.37150400
#> 344 11 7.668307 1.490157 2.2358001 0.02536487
#> 345 9 7.668307 1.490157 0.8936597 0.37150400
#> 346 8 7.668307 1.490157 0.2225895 0.82385504
#> 347 9 7.668307 1.490157 0.8936597 0.37150400
#> 348 8 7.668307 1.490157 0.2225895 0.82385504
#> 349 11 7.668307 1.490157 2.2358001 0.02536487
#> 350 9 7.668307 1.490157 0.8936597 0.37150400
#> 351 9 7.668307 1.490157 0.8936597 0.37150400
#> 352 9 7.668307 1.490157 0.8936597 0.37150400
#> 353 7 7.668307 1.490157 -0.4484808 0.65380626
#> 354 9 7.668307 1.490157 0.8936597 0.37150400
#> 355 8 7.668307 1.490157 0.2225895 0.82385504
#> 356 11 7.668307 1.490157 2.2358001 0.02536487
#> 357 8 7.668307 1.490157 0.2225895 0.82385504
#> 358 9 7.668307 1.490157 0.8936597 0.37150400
#> 359 9 7.668307 1.490157 0.8936597 0.37150400
#> 360 9 7.668307 1.490157 0.8936597 0.37150400
#> 361 9 7.668307 1.490157 0.8936597 0.37150400
#> 362 8 7.668307 1.490157 0.2225895 0.82385504
#> 363 9 7.668307 1.490157 0.8936597 0.37150400
#> 364 6 7.668307 1.490157 -1.1195510 0.26290515
#> 365 10 7.668307 1.490157 1.5647299 0.11764625
#> 366 8 7.668307 1.490157 0.2225895 0.82385504
#> 367 10 7.668307 1.490157 1.5647299 0.11764625
#> 368 10 7.668307 1.490157 1.5647299 0.11764625
#> 369 7 7.668307 1.490157 -0.4484808 0.65380626
#> 370 8 7.668307 1.490157 0.2225895 0.82385504
#> 371 8 7.668307 1.490157 0.2225895 0.82385504
#> 372 9 7.668307 1.490157 0.8936597 0.37150400
#> 373 9 7.668307 1.490157 0.8936597 0.37150400
#> 374 10 7.668307 1.490157 1.5647299 0.11764625
#> 375 9 7.668307 1.490157 0.8936597 0.37150400
#> 376 8 7.668307 1.490157 0.2225895 0.82385504
#> 377 10 7.668307 1.490157 1.5647299 0.11764625
#> 378 8 7.668307 1.490157 0.2225895 0.82385504
#> 379 8 7.668307 1.490157 0.2225895 0.82385504
#> 380 8 7.668307 1.490157 0.2225895 0.82385504
#> 381 7 7.668307 1.490157 -0.4484808 0.65380626
#> 382 6 7.668307 1.490157 -1.1195510 0.26290515
#> 383 8 7.668307 1.490157 0.2225895 0.82385504
#> 384 10 7.668307 1.490157 1.5647299 0.11764625
#> 385 7 7.668307 1.490157 -0.4484808 0.65380626
#> 386 9 7.668307 1.490157 0.8936597 0.37150400
#> 387 8 7.668307 1.490157 0.2225895 0.82385504
#> 388 9 7.668307 1.490157 0.8936597 0.37150400
#> 389 8 7.668307 1.490157 0.2225895 0.82385504
#> 390 7 7.668307 1.490157 -0.4484808 0.65380626
#> 391 4 7.668307 1.490157 -2.4616914 0.01382836
#> 392 10 7.668307 1.490157 1.5647299 0.11764625
#> 393 6 7.668307 1.490157 -1.1195510 0.26290515
#> 394 8 7.668307 1.490157 0.2225895 0.82385504
#> 395 8 7.668307 1.490157 0.2225895 0.82385504
#> 396 7 7.668307 1.490157 -0.4484808 0.65380626
#> 397 8 7.668307 1.490157 0.2225895 0.82385504
#> 398 8 7.668307 1.490157 0.2225895 0.82385504
#> 399 9 7.668307 1.490157 0.8936597 0.37150400
#> 400 9 7.668307 1.490157 0.8936597 0.37150400
#> 401 9 7.668307 1.490157 0.8936597 0.37150400
#> 402 9 7.668307 1.490157 0.8936597 0.37150400
#> 403 9 7.668307 1.490157 0.8936597 0.37150400
#> 404 8 7.668307 1.490157 0.2225895 0.82385504
#> 405 5 7.668307 1.490157 -1.7906212 0.07335410
#> 406 7 7.668307 1.490157 -0.4484808 0.65380626
#> 407 8 7.668307 1.490157 0.2225895 0.82385504
#> 408 8 7.668307 1.490157 0.2225895 0.82385504
#> 409 8 7.668307 1.490157 0.2225895 0.82385504
#> 410 8 7.668307 1.490157 0.2225895 0.82385504
#> 411 8 7.668307 1.490157 0.2225895 0.82385504
#> 412 7 7.668307 1.490157 -0.4484808 0.65380626
#> 413 8 7.668307 1.490157 0.2225895 0.82385504
#> 414 10 7.668307 1.490157 1.5647299 0.11764625
#> 415 8 7.668307 1.490157 0.2225895 0.82385504
#> 416 9 7.668307 1.490157 0.8936597 0.37150400
#> 417 9 7.668307 1.490157 0.8936597 0.37150400
#> 418 8 7.668307 1.490157 0.2225895 0.82385504
#> 419 9 7.668307 1.490157 0.8936597 0.37150400
#> 420 8 7.668307 1.490157 0.2225895 0.82385504
#> 421 11 7.668307 1.490157 2.2358001 0.02536487
#> 422 7 7.668307 1.490157 -0.4484808 0.65380626
#> 423 6 7.668307 1.490157 -1.1195510 0.26290515
#> 424 8 7.668307 1.490157 0.2225895 0.82385504
#> 425 9 7.668307 1.490157 0.8936597 0.37150400
#> 426 5 7.668307 1.490157 -1.7906212 0.07335410
#> 427 9 7.668307 1.490157 0.8936597 0.37150400
#> 428 9 7.668307 1.490157 0.8936597 0.37150400
#> 429 11 7.668307 1.490157 2.2358001 0.02536487
#> 430 8 7.668307 1.490157 0.2225895 0.82385504
#> 431 7 7.668307 1.490157 -0.4484808 0.65380626
#> 432 7 7.668307 1.490157 -0.4484808 0.65380626
#> 433 7 7.668307 1.490157 -0.4484808 0.65380626
#> 434 9 7.668307 1.490157 0.8936597 0.37150400
#> 435 9 7.668307 1.490157 0.8936597 0.37150400
#> 436 8 7.668307 1.490157 0.2225895 0.82385504
#> 437 10 7.668307 1.490157 1.5647299 0.11764625
#> 438 9 7.668307 1.490157 0.8936597 0.37150400
#> 439 10 7.668307 1.490157 1.5647299 0.11764625
#> 440 8 7.668307 1.490157 0.2225895 0.82385504
#> 441 10 7.668307 1.490157 1.5647299 0.11764625
#> 442 9 7.668307 1.490157 0.8936597 0.37150400
#> 443 7 7.668307 1.490157 -0.4484808 0.65380626
#> 444 8 7.668307 1.490157 0.2225895 0.82385504
#> 445 10 7.668307 1.490157 1.5647299 0.11764625
#> 446 8 7.668307 1.490157 0.2225895 0.82385504
#> 447 5 7.668307 1.490157 -1.7906212 0.07335410
#> 448 6 7.668307 1.490157 -1.1195510 0.26290515
#> 449 8 7.668307 1.490157 0.2225895 0.82385504
#> 450 8 7.668307 1.490157 0.2225895 0.82385504
#> 451 8 7.668307 1.490157 0.2225895 0.82385504
#> 452 8 7.668307 1.490157 0.2225895 0.82385504
#> 453 9 7.668307 1.490157 0.8936597 0.37150400
#> 454 10 7.668307 1.490157 1.5647299 0.11764625
#> 455 10 7.668307 1.490157 1.5647299 0.11764625
#> 456 8 7.668307 1.490157 0.2225895 0.82385504
#> 457 7 7.668307 1.490157 -0.4484808 0.65380626
#> 458 7 7.668307 1.490157 -0.4484808 0.65380626
#> 459 9 7.668307 1.490157 0.8936597 0.37150400
#> 460 9 7.668307 1.490157 0.8936597 0.37150400
#> 461 6 7.668307 1.490157 -1.1195510 0.26290515
#> 462 5 7.668307 1.490157 -1.7906212 0.07335410
#> 463 10 7.668307 1.490157 1.5647299 0.11764625
#> 464 8 7.668307 1.490157 0.2225895 0.82385504
#> 465 8 7.668307 1.490157 0.2225895 0.82385504
#> 466 7 7.668307 1.490157 -0.4484808 0.65380626
#> 467 6 7.668307 1.490157 -1.1195510 0.26290515
#> 468 9 7.668307 1.490157 0.8936597 0.37150400
#> 469 8 7.668307 1.490157 0.2225895 0.82385504
#> 470 8 7.668307 1.490157 0.2225895 0.82385504
#> 471 8 7.668307 1.490157 0.2225895 0.82385504
#> 472 7 7.668307 1.490157 -0.4484808 0.65380626
#> 473 10 7.668307 1.490157 1.5647299 0.11764625
#> 474 8 7.668307 1.490157 0.2225895 0.82385504
#> 475 9 7.668307 1.490157 0.8936597 0.37150400
#> 476 10 7.668307 1.490157 1.5647299 0.11764625
#> 477 7 7.668307 1.490157 -0.4484808 0.65380626
#> 478 4 7.668307 1.490157 -2.4616914 0.01382836
#> 479 6 7.668307 1.490157 -1.1195510 0.26290515
#> 480 8 7.668307 1.490157 0.2225895 0.82385504
#> 481 8 7.668307 1.490157 0.2225895 0.82385504
#> 482 8 7.668307 1.490157 0.2225895 0.82385504
#> 483 7 7.668307 1.490157 -0.4484808 0.65380626
#> 484 7 7.668307 1.490157 -0.4484808 0.65380626
#> 485 6 7.668307 1.490157 -1.1195510 0.26290515
#> 486 8 7.668307 1.490157 0.2225895 0.82385504
#> 487 9 7.668307 1.490157 0.8936597 0.37150400
#> 488 8 7.668307 1.490157 0.2225895 0.82385504
#> 489 10 7.668307 1.490157 1.5647299 0.11764625
#> 490 10 7.668307 1.490157 1.5647299 0.11764625
#> 491 8 7.668307 1.490157 0.2225895 0.82385504
#> 492 6 7.668307 1.490157 -1.1195510 0.26290515
#> 493 9 7.668307 1.490157 0.8936597 0.37150400
#> 494 6 7.668307 1.490157 -1.1195510 0.26290515
#> 495 7 7.668307 1.490157 -0.4484808 0.65380626
#> 496 9 7.668307 1.490157 0.8936597 0.37150400
#> 497 8 7.668307 1.490157 0.2225895 0.82385504
#> 498 6 7.668307 1.490157 -1.1195510 0.26290515
#> 499 7 7.668307 1.490157 -0.4484808 0.65380626
#> 500 8 7.668307 1.490157 0.2225895 0.82385504
#> 501 9 7.668307 1.490157 0.8936597 0.37150400
#> 502 10 7.668307 1.490157 1.5647299 0.11764625
#> 503 7 7.668307 1.490157 -0.4484808 0.65380626
#> 504 5 7.668307 1.490157 -1.7906212 0.07335410
#> 505 9 7.668307 1.490157 0.8936597 0.37150400
#> 506 7 7.668307 1.490157 -0.4484808 0.65380626
#> 507 6 7.668307 1.490157 -1.1195510 0.26290515
#> 508 10 7.668307 1.490157 1.5647299 0.11764625
#> 509 8 7.668307 1.490157 0.2225895 0.82385504
#> 510 7 7.668307 1.490157 -0.4484808 0.65380626
#> 511 8 7.668307 1.490157 0.2225895 0.82385504
#> 512 10 7.668307 1.490157 1.5647299 0.11764625
#> 513 9 7.668307 1.490157 0.8936597 0.37150400
#> 514 9 7.668307 1.490157 0.8936597 0.37150400
#> 515 10 7.668307 1.490157 1.5647299 0.11764625
#> 516 11 7.668307 1.490157 2.2358001 0.02536487
#> 517 7 7.668307 1.490157 -0.4484808 0.65380626
#> 518 7 7.668307 1.490157 -0.4484808 0.65380626
#> 519 9 7.668307 1.490157 0.8936597 0.37150400
#> 520 9 7.668307 1.490157 0.8936597 0.37150400
#> 521 7 7.668307 1.490157 -0.4484808 0.65380626
#> 522 6 7.668307 1.490157 -1.1195510 0.26290515
#> 523 10 7.668307 1.490157 1.5647299 0.11764625
#> 524 8 7.668307 1.490157 0.2225895 0.82385504
#> 525 10 7.668307 1.490157 1.5647299 0.11764625
#> 526 7 7.668307 1.490157 -0.4484808 0.65380626
#> 527 6 7.668307 1.490157 -1.1195510 0.26290515
#> 528 7 7.668307 1.490157 -0.4484808 0.65380626
#> 529 9 7.668307 1.490157 0.8936597 0.37150400
#> 530 6 7.668307 1.490157 -1.1195510 0.26290515
#> 531 9 7.668307 1.490157 0.8936597 0.37150400
#> 532 10 7.668307 1.490157 1.5647299 0.11764625
#> 533 10 7.668307 1.490157 1.5647299 0.11764625
#> 534 8 7.668307 1.490157 0.2225895 0.82385504
#> 535 10 7.668307 1.490157 1.5647299 0.11764625
#> 536 8 7.668307 1.490157 0.2225895 0.82385504
#> 537 9 7.668307 1.490157 0.8936597 0.37150400
#> 538 8 7.668307 1.490157 0.2225895 0.82385504
#> 539 8 7.668307 1.490157 0.2225895 0.82385504
#> 540 8 7.668307 1.490157 0.2225895 0.82385504
#> 541 9 7.668307 1.490157 0.8936597 0.37150400
#> 542 9 7.668307 1.490157 0.8936597 0.37150400
#> 543 8 7.668307 1.490157 0.2225895 0.82385504
#> 544 8 7.668307 1.490157 0.2225895 0.82385504
#> 545 8 7.668307 1.490157 0.2225895 0.82385504
#> 546 9 7.668307 1.490157 0.8936597 0.37150400
#> 547 9 7.668307 1.490157 0.8936597 0.37150400
#> 548 8 7.668307 1.490157 0.2225895 0.82385504
#> 549 7 7.668307 1.490157 -0.4484808 0.65380626
#> 550 10 7.668307 1.490157 1.5647299 0.11764625
#> 551 10 7.668307 1.490157 1.5647299 0.11764625
#> 552 9 7.668307 1.490157 0.8936597 0.37150400
#> 553 10 7.668307 1.490157 1.5647299 0.11764625
#> 554 9 7.668307 1.490157 0.8936597 0.37150400
#> 555 8 7.668307 1.490157 0.2225895 0.82385504
#> 556 8 7.668307 1.490157 0.2225895 0.82385504
#> 557 10 7.668307 1.490157 1.5647299 0.11764625
#> 558 7 7.668307 1.490157 -0.4484808 0.65380626
#> 559 9 7.668307 1.490157 0.8936597 0.37150400
#> 560 8 7.668307 1.490157 0.2225895 0.82385504
#> 561 9 7.668307 1.490157 0.8936597 0.37150400
#> 562 9 7.668307 1.490157 0.8936597 0.37150400
#> 563 8 7.668307 1.490157 0.2225895 0.82385504
#> 564 9 7.668307 1.490157 0.8936597 0.37150400
#> 565 6 7.668307 1.490157 -1.1195510 0.26290515
#> 566 10 7.668307 1.490157 1.5647299 0.11764625
#> 567 10 7.668307 1.490157 1.5647299 0.11764625
#> 568 10 7.668307 1.490157 1.5647299 0.11764625
#> 569 10 7.668307 1.490157 1.5647299 0.11764625
#> 570 8 7.668307 1.490157 0.2225895 0.82385504
#> 571 9 7.668307 1.490157 0.8936597 0.37150400
#> 572 6 7.668307 1.490157 -1.1195510 0.26290515
#> 573 9 7.668307 1.490157 0.8936597 0.37150400
#> 574 9 7.668307 1.490157 0.8936597 0.37150400
#> 575 9 7.668307 1.490157 0.8936597 0.37150400
#> 576 8 7.668307 1.490157 0.2225895 0.82385504
#> 577 10 7.668307 1.490157 1.5647299 0.11764625
#> 578 7 7.668307 1.490157 -0.4484808 0.65380626
#> 579 8 7.668307 1.490157 0.2225895 0.82385504
#> 580 7 7.668307 1.490157 -0.4484808 0.65380626
#> 581 8 7.668307 1.490157 0.2225895 0.82385504
#> 582 10 7.668307 1.490157 1.5647299 0.11764625
#> 583 7 7.668307 1.490157 -0.4484808 0.65380626
#> 584 9 7.668307 1.490157 0.8936597 0.37150400
#> 585 7 7.668307 1.490157 -0.4484808 0.65380626
#> 586 5 7.668307 1.490157 -1.7906212 0.07335410
#> 587 6 7.668307 1.490157 -1.1195510 0.26290515
#> 588 6 7.668307 1.490157 -1.1195510 0.26290515
#> 589 7 7.668307 1.490157 -0.4484808 0.65380626
#> 590 10 7.668307 1.490157 1.5647299 0.11764625
#> 591 7 7.668307 1.490157 -0.4484808 0.65380626
#> 592 8 7.668307 1.490157 0.2225895 0.82385504
#> 593 9 7.668307 1.490157 0.8936597 0.37150400
#> 594 9 7.668307 1.490157 0.8936597 0.37150400
#> 595 10 7.668307 1.490157 1.5647299 0.11764625
#> 596 9 7.668307 1.490157 0.8936597 0.37150400
#> 597 5 7.668307 1.490157 -1.7906212 0.07335410
#> 598 9 7.668307 1.490157 0.8936597 0.37150400
#> 599 10 7.668307 1.490157 1.5647299 0.11764625
#> 600 6 7.668307 1.490157 -1.1195510 0.26290515
#> 601 5 7.668307 1.490157 -1.7906212 0.07335410
#> 602 8 7.668307 1.490157 0.2225895 0.82385504
#> 603 9 7.668307 1.490157 0.8936597 0.37150400
#> 604 10 7.668307 1.490157 1.5647299 0.11764625
#> 605 8 7.668307 1.490157 0.2225895 0.82385504
#> 606 8 7.668307 1.490157 0.2225895 0.82385504
#> 607 4 7.668307 1.490157 -2.4616914 0.01382836
#> 608 9 7.668307 1.490157 0.8936597 0.37150400
#> 609 8 7.668307 1.490157 0.2225895 0.82385504
#> 610 9 7.668307 1.490157 0.8936597 0.37150400
#> 611 10 7.668307 1.490157 1.5647299 0.11764625
#> 612 7 7.668307 1.490157 -0.4484808 0.65380626
#> 613 8 7.668307 1.490157 0.2225895 0.82385504
#> 614 9 7.668307 1.490157 0.8936597 0.37150400
#> 615 7 7.668307 1.490157 -0.4484808 0.65380626
#> 616 6 7.668307 1.490157 -1.1195510 0.26290515
#> 617 4 7.668307 1.490157 -2.4616914 0.01382836
#> 618 6 7.668307 1.490157 -1.1195510 0.26290515
#> 619 6 7.668307 1.490157 -1.1195510 0.26290515
#> 620 8 7.668307 1.490157 0.2225895 0.82385504
#> 621 8 7.668307 1.490157 0.2225895 0.82385504
#> 622 7 7.668307 1.490157 -0.4484808 0.65380626
#> 623 5 7.668307 1.490157 -1.7906212 0.07335410
#> 624 6 7.668307 1.490157 -1.1195510 0.26290515
#> 625 9 7.668307 1.490157 0.8936597 0.37150400
#> 626 8 7.668307 1.490157 0.2225895 0.82385504
#> 627 7 7.668307 1.490157 -0.4484808 0.65380626
#> 628 9 7.668307 1.490157 0.8936597 0.37150400
#> 629 9 7.668307 1.490157 0.8936597 0.37150400
#> 630 7 7.668307 1.490157 -0.4484808 0.65380626
#> 631 8 7.668307 1.490157 0.2225895 0.82385504
#> 632 8 7.668307 1.490157 0.2225895 0.82385504
#> 633 9 7.668307 1.490157 0.8936597 0.37150400
#> 634 8 7.668307 1.490157 0.2225895 0.82385504
#> 635 8 7.668307 1.490157 0.2225895 0.82385504
#> 636 8 7.668307 1.490157 0.2225895 0.82385504
#> 637 10 7.668307 1.490157 1.5647299 0.11764625
#> 638 9 7.668307 1.490157 0.8936597 0.37150400
#> 639 7 7.668307 1.490157 -0.4484808 0.65380626
#> 640 9 7.668307 1.490157 0.8936597 0.37150400
#> 641 7 7.668307 1.490157 -0.4484808 0.65380626
#> 642 11 7.668307 1.490157 2.2358001 0.02536487
#> 643 8 7.668307 1.490157 0.2225895 0.82385504
#> 644 9 7.668307 1.490157 0.8936597 0.37150400
#> 645 7 7.668307 1.490157 -0.4484808 0.65380626
#> 646 10 7.668307 1.490157 1.5647299 0.11764625
#> 647 5 7.668307 1.490157 -1.7906212 0.07335410
#> 648 5 7.668307 1.490157 -1.7906212 0.07335410
#> 649 8 7.668307 1.490157 0.2225895 0.82385504
#> 650 9 7.668307 1.490157 0.8936597 0.37150400
#> 651 9 7.668307 1.490157 0.8936597 0.37150400
#> 652 6 7.668307 1.490157 -1.1195510 0.26290515
#> 653 7 7.668307 1.490157 -0.4484808 0.65380626
#> 654 8 7.668307 1.490157 0.2225895 0.82385504
#> 655 7 7.668307 1.490157 -0.4484808 0.65380626
#> 656 8 7.668307 1.490157 0.2225895 0.82385504
#> 657 8 7.668307 1.490157 0.2225895 0.82385504
#> 658 9 7.668307 1.490157 0.8936597 0.37150400
#> 659 7 7.668307 1.490157 -0.4484808 0.65380626
#> 660 9 7.668307 1.490157 0.8936597 0.37150400
#> 661 9 7.668307 1.490157 0.8936597 0.37150400
#> 662 7 7.668307 1.490157 -0.4484808 0.65380626
#> 663 9 7.668307 1.490157 0.8936597 0.37150400
#> 664 8 7.668307 1.490157 0.2225895 0.82385504
#> 665 8 7.668307 1.490157 0.2225895 0.82385504
#> 666 11 7.668307 1.490157 2.2358001 0.02536487
#> 667 8 7.668307 1.490157 0.2225895 0.82385504
#> 668 9 7.668307 1.490157 0.8936597 0.37150400
#> 669 9 7.668307 1.490157 0.8936597 0.37150400
#> 670 8 7.668307 1.490157 0.2225895 0.82385504
#> 671 9 7.668307 1.490157 0.8936597 0.37150400
#> 672 10 7.668307 1.490157 1.5647299 0.11764625
#> 673 10 7.668307 1.490157 1.5647299 0.11764625
#> 674 8 7.668307 1.490157 0.2225895 0.82385504
#> 675 9 7.668307 1.490157 0.8936597 0.37150400
#> 676 9 7.668307 1.490157 0.8936597 0.37150400
#> 677 9 7.668307 1.490157 0.8936597 0.37150400
#> 678 9 7.668307 1.490157 0.8936597 0.37150400
#> 679 9 7.668307 1.490157 0.8936597 0.37150400
#> 680 9 7.668307 1.490157 0.8936597 0.37150400
#> 681 6 7.668307 1.490157 -1.1195510 0.26290515
#> 682 6 7.668307 1.490157 -1.1195510 0.26290515
#> 683 7 7.668307 1.490157 -0.4484808 0.65380626
#> 684 8 7.668307 1.490157 0.2225895 0.82385504
#> 685 8 7.668307 1.490157 0.2225895 0.82385504
#> 686 7 7.668307 1.490157 -0.4484808 0.65380626
#> 687 8 7.668307 1.490157 0.2225895 0.82385504
#> 688 8 7.668307 1.490157 0.2225895 0.82385504
#> 689 8 7.668307 1.490157 0.2225895 0.82385504
#> 690 8 7.668307 1.490157 0.2225895 0.82385504
#> 691 7 7.668307 1.490157 -0.4484808 0.65380626
#> 692 6 7.668307 1.490157 -1.1195510 0.26290515
#> 693 10 7.668307 1.490157 1.5647299 0.11764625
#> 694 7 7.668307 1.490157 -0.4484808 0.65380626
#> 695 6 7.668307 1.490157 -1.1195510 0.26290515
#> 696 11 7.668307 1.490157 2.2358001 0.02536487
#> 697 8 7.668307 1.490157 0.2225895 0.82385504
#> 698 6 7.668307 1.490157 -1.1195510 0.26290515
#> 699 7 7.668307 1.490157 -0.4484808 0.65380626
#> 700 7 7.668307 1.490157 -0.4484808 0.65380626
#> 701 6 7.668307 1.490157 -1.1195510 0.26290515
#> 702 8 7.668307 1.490157 0.2225895 0.82385504
#> 703 8 7.668307 1.490157 0.2225895 0.82385504
#> 704 8 7.668307 1.490157 0.2225895 0.82385504
#> 705 8 7.668307 1.490157 0.2225895 0.82385504
#> 706 10 7.668307 1.490157 1.5647299 0.11764625
#> 707 9 7.668307 1.490157 0.8936597 0.37150400
#> 708 6 7.668307 1.490157 -1.1195510 0.26290515
#> 709 8 7.668307 1.490157 0.2225895 0.82385504
#> 710 10 7.668307 1.490157 1.5647299 0.11764625
#> 711 9 7.668307 1.490157 0.8936597 0.37150400
#> 712 9 7.668307 1.490157 0.8936597 0.37150400
#> 713 8 7.668307 1.490157 0.2225895 0.82385504
#> 714 8 7.668307 1.490157 0.2225895 0.82385504
#> 715 10 7.668307 1.490157 1.5647299 0.11764625
#> 716 7 7.668307 1.490157 -0.4484808 0.65380626
#> 717 7 7.668307 1.490157 -0.4484808 0.65380626
#> 718 9 7.668307 1.490157 0.8936597 0.37150400
#> 719 8 7.668307 1.490157 0.2225895 0.82385504
#> 720 8 7.668307 1.490157 0.2225895 0.82385504
#> 721 9 7.668307 1.490157 0.8936597 0.37150400
#> 722 9 7.668307 1.490157 0.8936597 0.37150400
#> 723 8 7.668307 1.490157 0.2225895 0.82385504
#> 724 8 7.668307 1.490157 0.2225895 0.82385504
#> 725 6 7.668307 1.490157 -1.1195510 0.26290515
#> 726 10 7.668307 1.490157 1.5647299 0.11764625
#> 727 8 7.668307 1.490157 0.2225895 0.82385504
#> 728 9 7.668307 1.490157 0.8936597 0.37150400
#> 729 7 7.668307 1.490157 -0.4484808 0.65380626
#> 730 9 7.668307 1.490157 0.8936597 0.37150400
#> 731 9 7.668307 1.490157 0.8936597 0.37150400
#> 732 7 7.668307 1.490157 -0.4484808 0.65380626
#> 733 10 7.668307 1.490157 1.5647299 0.11764625
#> 734 6 7.668307 1.490157 -1.1195510 0.26290515
#> 735 6 7.668307 1.490157 -1.1195510 0.26290515
#> 736 5 7.668307 1.490157 -1.7906212 0.07335410
#> 737 6 7.668307 1.490157 -1.1195510 0.26290515
#> 738 7 7.668307 1.490157 -0.4484808 0.65380626
#> 739 10 7.668307 1.490157 1.5647299 0.11764625
#> 740 9 7.668307 1.490157 0.8936597 0.37150400
#> 741 9 7.668307 1.490157 0.8936597 0.37150400
#> 742 7 7.668307 1.490157 -0.4484808 0.65380626
#> 743 8 7.668307 1.490157 0.2225895 0.82385504
#> 744 7 7.668307 1.490157 -0.4484808 0.65380626
#> 745 9 7.668307 1.490157 0.8936597 0.37150400
#> 746 9 7.668307 1.490157 0.8936597 0.37150400
#> 747 6 7.668307 1.490157 -1.1195510 0.26290515
#> 748 9 7.668307 1.490157 0.8936597 0.37150400
#> 749 9 7.668307 1.490157 0.8936597 0.37150400
#> 750 6 7.668307 1.490157 -1.1195510 0.26290515
#> 751 8 7.668307 1.490157 0.2225895 0.82385504
#> 752 8 7.668307 1.490157 0.2225895 0.82385504
#> 753 9 7.668307 1.490157 0.8936597 0.37150400
#> 754 9 7.668307 1.490157 0.8936597 0.37150400
#> 755 7 7.668307 1.490157 -0.4484808 0.65380626
#> 756 9 7.668307 1.490157 0.8936597 0.37150400
#> 757 11 7.668307 1.490157 2.2358001 0.02536487
#> 758 7 7.668307 1.490157 -0.4484808 0.65380626
#> 759 9 7.668307 1.490157 0.8936597 0.37150400
#> 760 7 7.668307 1.490157 -0.4484808 0.65380626
#> 761 9 7.668307 1.490157 0.8936597 0.37150400
#> 762 7 7.668307 1.490157 -0.4484808 0.65380626
#> 763 8 7.668307 1.490157 0.2225895 0.82385504
#> 764 8 7.668307 1.490157 0.2225895 0.82385504
#> 765 4 7.668307 1.490157 -2.4616914 0.01382836
#> 766 8 7.668307 1.490157 0.2225895 0.82385504
#> 767 9 7.668307 1.490157 0.8936597 0.37150400
#> 768 8 7.668307 1.490157 0.2225895 0.82385504
#> 769 11 7.668307 1.490157 2.2358001 0.02536487
#> 770 8 7.668307 1.490157 0.2225895 0.82385504
#> 771 10 7.668307 1.490157 1.5647299 0.11764625
#> 772 7 7.668307 1.490157 -0.4484808 0.65380626
#> 773 6 7.668307 1.490157 -1.1195510 0.26290515
#> 774 10 7.668307 1.490157 1.5647299 0.11764625
#> 775 7 7.668307 1.490157 -0.4484808 0.65380626
#> 776 9 7.668307 1.490157 0.8936597 0.37150400
#> 777 8 7.668307 1.490157 0.2225895 0.82385504
#> 778 6 7.668307 1.490157 -1.1195510 0.26290515
#> 779 8 7.668307 1.490157 0.2225895 0.82385504
#> 780 10 7.668307 1.490157 1.5647299 0.11764625
#> 781 10 7.668307 1.490157 1.5647299 0.11764625
#> 782 10 7.668307 1.490157 1.5647299 0.11764625
#> 783 9 7.668307 1.490157 0.8936597 0.37150400
#> 784 6 7.668307 1.490157 -1.1195510 0.26290515
#> 785 10 7.668307 1.490157 1.5647299 0.11764625
#> 786 7 7.668307 1.490157 -0.4484808 0.65380626
#> 787 8 7.668307 1.490157 0.2225895 0.82385504
#> 788 9 7.668307 1.490157 0.8936597 0.37150400
#> 789 10 7.668307 1.490157 1.5647299 0.11764625
#> 790 5 7.668307 1.490157 -1.7906212 0.07335410
#> 791 9 7.668307 1.490157 0.8936597 0.37150400
#> 792 8 7.668307 1.490157 0.2225895 0.82385504
#> 793 8 7.668307 1.490157 0.2225895 0.82385504
#> 794 8 7.668307 1.490157 0.2225895 0.82385504
#> 795 7 7.668307 1.490157 -0.4484808 0.65380626
#> 796 7 7.668307 1.490157 -0.4484808 0.65380626
#> 797 6 7.668307 1.490157 -1.1195510 0.26290515
#> 798 8 7.668307 1.490157 0.2225895 0.82385504
#> 799 8 7.668307 1.490157 0.2225895 0.82385504
#> 800 9 7.668307 1.490157 0.8936597 0.37150400
#> 801 8 7.668307 1.490157 0.2225895 0.82385504
#> 802 10 7.668307 1.490157 1.5647299 0.11764625
#> 803 7 7.668307 1.490157 -0.4484808 0.65380626
#> 804 9 7.668307 1.490157 0.8936597 0.37150400
#> 805 10 7.668307 1.490157 1.5647299 0.11764625
#> 806 8 7.668307 1.490157 0.2225895 0.82385504
#> 807 10 7.668307 1.490157 1.5647299 0.11764625
#> 808 8 7.668307 1.490157 0.2225895 0.82385504
#> 809 7 7.668307 1.490157 -0.4484808 0.65380626
#> 810 10 7.668307 1.490157 1.5647299 0.11764625
#> 811 10 7.668307 1.490157 1.5647299 0.11764625
#> 812 9 7.668307 1.490157 0.8936597 0.37150400
#> 813 9 7.668307 1.490157 0.8936597 0.37150400
#> 814 5 7.668307 1.490157 -1.7906212 0.07335410
#> 815 10 7.668307 1.490157 1.5647299 0.11764625
#> 816 10 7.668307 1.490157 1.5647299 0.11764625
#> 817 9 7.668307 1.490157 0.8936597 0.37150400
#> 818 10 7.668307 1.490157 1.5647299 0.11764625
#> 819 9 7.668307 1.490157 0.8936597 0.37150400
#> 820 7 7.668307 1.490157 -0.4484808 0.65380626
#> 821 8 7.668307 1.490157 0.2225895 0.82385504
#> 822 7 7.668307 1.490157 -0.4484808 0.65380626
#> 823 6 7.668307 1.490157 -1.1195510 0.26290515
#> 824 5 7.668307 1.490157 -1.7906212 0.07335410
#> 825 7 7.668307 1.490157 -0.4484808 0.65380626
#> 826 7 7.668307 1.490157 -0.4484808 0.65380626
#> 827 9 7.668307 1.490157 0.8936597 0.37150400
#> 828 6 7.668307 1.490157 -1.1195510 0.26290515
#> 829 8 7.668307 1.490157 0.2225895 0.82385504
#> 830 9 7.668307 1.490157 0.8936597 0.37150400
#> 831 9 7.668307 1.490157 0.8936597 0.37150400
#> 832 9 7.668307 1.490157 0.8936597 0.37150400
#> 833 7 7.668307 1.490157 -0.4484808 0.65380626
#> 834 8 7.668307 1.490157 0.2225895 0.82385504
#> 835 8 7.668307 1.490157 0.2225895 0.82385504
#> 836 8 7.668307 1.490157 0.2225895 0.82385504
#> 837 9 7.668307 1.490157 0.8936597 0.37150400
#> 838 8 7.668307 1.490157 0.2225895 0.82385504
#> 839 8 7.668307 1.490157 0.2225895 0.82385504
#> 840 7 7.668307 1.490157 -0.4484808 0.65380626
#> 841 9 7.668307 1.490157 0.8936597 0.37150400
#> 842 9 7.668307 1.490157 0.8936597 0.37150400
#> 843 7 7.668307 1.490157 -0.4484808 0.65380626
#> 844 10 7.668307 1.490157 1.5647299 0.11764625
#> 845 9 7.668307 1.490157 0.8936597 0.37150400
#> 846 9 7.668307 1.490157 0.8936597 0.37150400
#> 847 9 7.668307 1.490157 0.8936597 0.37150400
#> 848 8 7.668307 1.490157 0.2225895 0.82385504
#> 849 5 7.668307 1.490157 -1.7906212 0.07335410
#> 850 9 7.668307 1.490157 0.8936597 0.37150400
#> 851 10 7.668307 1.490157 1.5647299 0.11764625
#> 852 8 7.668307 1.490157 0.2225895 0.82385504
#> 853 7 7.668307 1.490157 -0.4484808 0.65380626
#> 854 10 7.668307 1.490157 1.5647299 0.11764625
#> 855 7 7.668307 1.490157 -0.4484808 0.65380626
#> 856 9 7.668307 1.490157 0.8936597 0.37150400
#> 857 9 7.668307 1.490157 0.8936597 0.37150400
#> 858 7 7.668307 1.490157 -0.4484808 0.65380626
#> 859 8 7.668307 1.490157 0.2225895 0.82385504
#> 860 10 7.668307 1.490157 1.5647299 0.11764625
#> 861 8 7.668307 1.490157 0.2225895 0.82385504
#> 862 7 7.668307 1.490157 -0.4484808 0.65380626
#> 863 7 7.668307 1.490157 -0.4484808 0.65380626
#> 864 7 7.668307 1.490157 -0.4484808 0.65380626
#> 865 7 7.668307 1.490157 -0.4484808 0.65380626
#> 866 9 7.668307 1.490157 0.8936597 0.37150400
#> 867 6 7.668307 1.490157 -1.1195510 0.26290515
#> 868 8 7.668307 1.490157 0.2225895 0.82385504
#> 869 9 7.668307 1.490157 0.8936597 0.37150400
#> 870 8 7.668307 1.490157 0.2225895 0.82385504
#> 871 8 7.668307 1.490157 0.2225895 0.82385504
#> 872 10 7.668307 1.490157 1.5647299 0.11764625
#> 873 6 7.668307 1.490157 -1.1195510 0.26290515
#> 874 7 7.668307 1.490157 -0.4484808 0.65380626
#> 875 8 7.668307 1.490157 0.2225895 0.82385504
#> 876 8 7.668307 1.490157 0.2225895 0.82385504
#> 877 7 7.668307 1.490157 -0.4484808 0.65380626
plot(lsrq, sf = FastFood.sf, sig = 0.05)
#> Warning: bounding box has potentially an invalid value range for longlat data
# }
# Case 3: With a sf object (poligons)
library(lwgeom)
fname <- system.file("shape/nc.shp", package="sf")
nc <- sf::st_read(fname)
#> Reading layer `nc' from data source
#> `/home/runner/work/_temp/Library/sf/shape/nc.shp' using driver `ESRI Shapefile'
#> Simple feature collection with 100 features and 14 fields
#> Geometry type: MULTIPOLYGON
#> Dimension: XY
#> Bounding box: xmin: -84.32385 ymin: 33.88199 xmax: -75.45698 ymax: 36.58965
#> Geodetic CRS: NAD27
listw <- spdep::poly2nb(as(nc,"Spatial"), queen = FALSE)
#> although coordinates are longitude/latitude, st_intersects assumes that they are planar
p <- c(1/6,3/6,2/6)
rho = 0.5
nc$fx <- dgp.spq(p = p, listw = listw, rho = rho)
plot(nc["fx"])
formula <- ~ fx
lsrq <- local.sp.runs.test(formula = formula, data = nc, listw = listw)
#> Warning: st_centroid assumes attributes are constant over geometries of x
#> Warning: st_centroid does not give correct centroids for longitude/latitude data
print(lsrq)
#> runs.i E.i Std.i z.value p.value
#> 1 3 2.855152 0.8722689 0.16605945 0.868110166
#> 2 3 2.855152 0.8722689 0.16605945 0.868110166
#> 3 5 4.091919 1.1317511 0.80236794 0.422340153
#> 4 3 2.236768 0.7064182 1.08042568 0.279952664
#> 5 3 3.473535 1.0106752 -0.46853368 0.639402990
#> 6 3 2.855152 0.8722689 0.16605945 0.868110166
#> 7 3 2.855152 0.8722689 0.16605945 0.868110166
#> 8 5 4.091919 1.1317511 0.80236794 0.422340153
#> 9 3 3.473535 1.0106752 -0.46853368 0.639402990
#> 10 4 2.855152 0.8722689 1.31249497 0.189353181
#> 11 2 3.473535 1.0106752 -1.45797128 0.144848459
#> 12 2 3.473535 1.0106752 -1.45797128 0.144848459
#> 13 5 4.091919 1.1317511 0.80236794 0.422340153
#> 14 3 3.473535 1.0106752 -0.46853368 0.639402990
#> 15 4 2.855152 0.8722689 1.31249497 0.189353181
#> 16 5 4.710303 1.2405813 0.23351712 0.815359874
#> 17 3 2.855152 0.8722689 0.16605945 0.868110166
#> 18 7 5.947071 1.4323964 0.73508234 0.462289347
#> 19 5 3.473535 1.0106752 1.51034151 0.130956304
#> 20 3 2.855152 0.8722689 0.16605945 0.868110166
#> 21 2 2.236768 0.7064182 -0.33516646 0.737499518
#> 22 4 4.091919 1.1317511 -0.08121856 0.935268142
#> 23 3 4.091919 1.1317511 -0.96480505 0.334642465
#> 24 4 4.091919 1.1317511 -0.08121856 0.935268142
#> 25 4 4.710303 1.2405813 -0.57255663 0.566944931
#> 26 3 4.091919 1.1317511 -0.96480505 0.334642465
#> 27 5 4.710303 1.2405813 0.23351712 0.815359874
#> 28 5 4.091919 1.1317511 0.80236794 0.422340153
#> 29 4 4.091919 1.1317511 -0.08121856 0.935268142
#> 30 5 4.091919 1.1317511 0.80236794 0.422340153
#> 31 1 4.091919 1.1317511 -2.73197805 0.006295534
#> 32 4 2.855152 0.8722689 1.31249497 0.189353181
#> 33 2 4.091919 1.1317511 -1.84839155 0.064545720
#> 34 6 4.710303 1.2405813 1.03959088 0.298530015
#> 35 4 3.473535 1.0106752 0.52090392 0.602433708
#> 36 4 4.710303 1.2405813 -0.57255663 0.566944931
#> 37 5 4.710303 1.2405813 0.23351712 0.815359874
#> 38 3 2.855152 0.8722689 0.16605945 0.868110166
#> 39 7 6.565455 1.5186493 0.28613944 0.774771326
#> 40 1 4.091919 1.1317511 -2.73197805 0.006295534
#> 41 3 3.473535 1.0106752 -0.46853368 0.639402990
#> 42 4 4.710303 1.2405813 -0.57255663 0.566944931
#> 43 5 4.710303 1.2405813 0.23351712 0.815359874
#> 44 5 4.091919 1.1317511 0.80236794 0.422340153
#> 45 2 2.236768 0.7064182 -0.33516646 0.737499518
#> 46 6 4.710303 1.2405813 1.03959088 0.298530015
#> 47 6 4.710303 1.2405813 1.03959088 0.298530015
#> 48 5 5.947071 1.4323964 -0.66117921 0.508497395
#> 49 1 4.710303 1.2405813 -2.99077790 0.002782678
#> 50 4 4.091919 1.1317511 -0.08121856 0.935268142
#> 51 5 5.328687 1.3401523 -0.24526083 0.806254475
#> 52 5 4.091919 1.1317511 0.80236794 0.422340153
#> 53 5 4.710303 1.2405813 0.23351712 0.815359874
#> 54 5 4.710303 1.2405813 0.23351712 0.815359874
#> 55 6 4.091919 1.1317511 1.68595444 0.091804576
#> 56 1 2.236768 0.7064182 -1.75075861 0.079987499
#> 57 3 4.710303 1.2405813 -1.37863039 0.168008742
#> 58 5 3.473535 1.0106752 1.51034151 0.130956304
#> 59 1 3.473535 1.0106752 -2.44740888 0.014388750
#> 60 2 2.855152 0.8722689 -0.98037608 0.326900515
#> 61 5 4.710303 1.2405813 0.23351712 0.815359874
#> 62 3 4.710303 1.2405813 -1.37863039 0.168008742
#> 63 7 5.328687 1.3401523 1.24710688 0.212358312
#> 64 2 3.473535 1.0106752 -1.45797128 0.144848459
#> 65 4 4.091919 1.1317511 -0.08121856 0.935268142
#> 66 5 3.473535 1.0106752 1.51034151 0.130956304
#> 67 5 5.947071 1.4323964 -0.66117921 0.508497395
#> 68 3 4.091919 1.1317511 -0.96480505 0.334642465
#> 69 6 4.091919 1.1317511 1.68595444 0.091804576
#> 70 2 4.710303 1.2405813 -2.18470415 0.028910546
#> 71 3 4.091919 1.1317511 -0.96480505 0.334642465
#> 72 4 3.473535 1.0106752 0.52090392 0.602433708
#> 73 4 2.855152 0.8722689 1.31249497 0.189353181
#> 74 3 4.710303 1.2405813 -1.37863039 0.168008742
#> 75 3 2.855152 0.8722689 0.16605945 0.868110166
#> 76 2 2.855152 0.8722689 -0.98037608 0.326900515
#> 77 3 2.236768 0.7064182 1.08042568 0.279952664
#> 78 3 4.091919 1.1317511 -0.96480505 0.334642465
#> 79 5 5.328687 1.3401523 -0.24526083 0.806254475
#> 80 3 2.236768 0.7064182 1.08042568 0.279952664
#> 81 3 2.855152 0.8722689 0.16605945 0.868110166
#> 82 5 4.710303 1.2405813 0.23351712 0.815359874
#> 83 3 4.091919 1.1317511 -0.96480505 0.334642465
#> 84 3 3.473535 1.0106752 -0.46853368 0.639402990
#> 85 1 3.473535 1.0106752 -2.44740888 0.014388750
#> 86 2 3.473535 1.0106752 -1.45797128 0.144848459
#> 87 4 3.473535 1.0106752 0.52090392 0.602433708
#> 88 3 4.710303 1.2405813 -1.37863039 0.168008742
#> 89 1 3.473535 1.0106752 -2.44740888 0.014388750
#> 90 1 2.236768 0.7064182 -1.75075861 0.079987499
#> 91 3 4.710303 1.2405813 -1.37863039 0.168008742
#> 92 3 2.855152 0.8722689 0.16605945 0.868110166
#> 93 4 3.473535 1.0106752 0.52090392 0.602433708
#> 94 5 4.091919 1.1317511 0.80236794 0.422340153
#> 95 1 2.855152 0.8722689 -2.12681160 0.033435740
#> 96 4 4.091919 1.1317511 -0.08121856 0.935268142
#> 97 6 5.328687 1.3401523 0.50092302 0.616425301
#> 98 3 3.473535 1.0106752 -0.46853368 0.639402990
#> 99 1 2.236768 0.7064182 -1.75075861 0.079987499
#> 100 1 2.855152 0.8722689 -2.12681160 0.033435740
plot(lsrq, sf = nc)
# Version boot
lsrq <- local.sp.runs.test(formula = formula, data = nc, listw = listw,
distr ="bootstrap", nsim = 399)
#> Warning: st_centroid assumes attributes are constant over geometries of x
#> Warning: st_centroid does not give correct centroids for longitude/latitude data
print(lsrq)
#> SRQ EP.i SdP.i zseudo.value pseudo.value
#> 1 3 2.919799 0.8166508 0.09820660 0.921768240
#> 2 3 2.849624 0.8491460 0.17709080 0.859437065
#> 3 5 4.072682 1.0877253 0.85252987 0.393920070
#> 4 3 2.182957 0.7257713 1.12575765 0.260268114
#> 5 3 3.436090 1.0076595 -0.43277539 0.665177955
#> 6 3 2.857143 0.8400424 0.17005945 0.864963386
#> 7 3 2.781955 0.8967138 0.24316020 0.807881296
#> 8 5 4.160401 1.0863871 0.77283591 0.439619498
#> 9 3 3.508772 1.0096510 -0.50390869 0.614325546
#> 10 4 2.819549 0.8550875 1.38050328 0.167431741
#> 11 2 3.388471 1.0282284 -1.35035285 0.176902828
#> 12 2 3.538847 1.0139081 -1.51773820 0.129080411
#> 13 5 4.085213 1.1464417 0.79793589 0.424907694
#> 14 3 3.353383 1.0360014 -0.34110328 0.733025835
#> 15 4 2.776942 0.8982785 1.36155735 0.173337622
#> 16 5 4.729323 1.1996303 0.22563342 0.821486543
#> 17 3 2.794486 0.8870196 0.23169025 0.816778603
#> 18 7 6.000000 1.3431382 0.74452505 0.456558893
#> 19 5 3.516291 0.9637189 1.53956650 0.123666057
#> 20 3 2.889724 0.8038036 0.13719234 0.890878769
#> 21 2 2.233083 0.6749713 -0.34532242 0.729851996
#> 22 4 4.045113 1.1421438 -0.03949834 0.968493078
#> 23 3 4.070175 1.1275837 -0.94908738 0.342576171
#> 24 4 4.032581 1.0896688 -0.02990033 0.976146544
#> 25 4 4.694236 1.2468017 -0.55681316 0.577655088
#> 26 3 4.100251 1.1386208 -0.96630122 0.333893475
#> 27 5 4.679198 1.2729672 0.25201120 0.801032404
#> 28 5 4.057644 1.1666149 0.80776943 0.419223324
#> 29 4 4.067669 1.1355084 -0.05959373 0.952479216
#> 30 5 3.984962 1.1882060 0.85426059 0.392960619
#> 31 1 4.082707 1.1007885 -2.80045323 0.005103090
#> 32 4 2.847118 0.8905904 1.29451455 0.195487745
#> 33 2 4.102757 1.1127256 -1.88973538 0.058793360
#> 34 6 4.701754 1.2045858 1.07775267 0.281144147
#> 35 4 3.416040 1.0501703 0.55606210 0.578168403
#> 36 4 4.741855 1.1950600 -0.62076769 0.534752485
#> 37 5 4.671679 1.2641063 0.25972563 0.795075424
#> 38 3 2.807018 0.8884241 0.21721885 0.828037798
#> 39 7 6.596491 1.5137851 0.26655617 0.789810905
#> 40 1 4.165414 1.1017149 -2.87316949 0.004063760
#> 41 3 3.446115 0.9881096 -0.45148363 0.651641022
#> 42 4 4.669173 1.2444155 -0.53774076 0.590756035
#> 43 5 4.644110 1.2635831 0.28165121 0.778210967
#> 44 5 4.057644 1.1360628 0.82949279 0.406825616
#> 45 2 2.288221 0.7261356 -0.39692385 0.691423615
#> 46 6 4.709273 1.2157630 1.06165991 0.288390105
#> 47 6 4.694236 1.2923205 1.01040291 0.312302294
#> 48 5 6.062657 1.3537901 -0.78494932 0.432483281
#> 49 1 4.864662 1.1911438 -3.24449643 0.001176585
#> 50 4 4.120301 1.1210924 -0.10730672 0.914545650
#> 51 5 5.250627 1.3080129 -0.19160863 0.848048782
#> 52 5 4.125313 1.1602009 0.75390969 0.450903451
#> 53 5 4.754386 1.2236466 0.20072301 0.840915168
#> 54 5 4.759398 1.2018644 0.20019022 0.841331812
#> 55 6 3.972431 1.1869228 1.70825675 0.087588712
#> 56 1 2.218045 0.7264391 -1.67673398 0.093594513
#> 57 3 4.804511 1.2943168 -1.39418053 0.163263097
#> 58 5 3.448622 1.0182959 1.52350460 0.127632511
#> 59 1 3.418546 1.0310540 -2.34570302 0.018991233
#> 60 2 2.882206 0.8528163 -1.03446138 0.300920524
#> 61 5 4.796992 1.1825324 0.17167184 0.863695522
#> 62 3 4.724311 1.2397055 -1.39090351 0.164254689
#> 63 7 5.290727 1.3638142 1.25330355 0.210095255
#> 64 2 3.431078 1.0246395 -1.39666463 0.162514444
#> 65 4 4.117794 1.0411914 -0.11313432 0.909924063
#> 66 5 3.458647 1.0261256 1.50210979 0.133068756
#> 67 5 5.944862 1.4586314 -0.64777310 0.517131718
#> 68 3 4.042607 1.0445788 -0.99811185 0.318225124
#> 69 6 4.157895 1.1016806 1.67208655 0.094507257
#> 70 2 4.674185 1.2457406 -2.14666318 0.031820106
#> 71 3 4.030075 1.1136872 -0.92492323 0.355005842
#> 72 4 3.471178 0.9815107 0.53878381 0.590036036
#> 73 4 2.889724 0.8784807 1.26385896 0.206280653
#> 74 3 4.739348 1.2729227 -1.36642103 0.171806851
#> 75 3 2.807018 0.8299367 0.23252673 0.816128929
#> 76 2 2.872180 0.8775268 -0.99390749 0.320267909
#> 77 3 2.225564 0.6976256 1.11010268 0.266954781
#> 78 3 4.112782 1.0912222 -1.01975745 0.307843507
#> 79 5 5.280702 1.3750847 -0.20413416 0.838248658
#> 80 3 2.190476 0.7255630 1.11571808 0.264542828
#> 81 3 2.909774 0.8721715 0.10344934 0.917606356
#> 82 5 4.749373 1.2490573 0.20065258 0.840970240
#> 83 3 4.067669 1.0694160 -0.99836656 0.318101643
#> 84 3 3.446115 1.0804237 -0.41290774 0.679674211
#> 85 1 3.466165 1.0858769 -2.27112790 0.023139236
#> 86 2 3.478697 0.9893515 -1.49461212 0.135015701
#> 87 4 3.438596 1.0373013 0.54121546 0.588359080
#> 88 3 4.659148 1.2274541 -1.35169854 0.176471773
#> 89 1 3.446115 1.0255425 -2.38519157 0.017070229
#> 90 1 2.243108 0.6971200 -1.78320494 0.074552948
#> 91 3 4.656642 1.2318633 -1.34482585 0.178681481
#> 92 3 2.817043 0.8848872 0.20675786 0.836198964
#> 93 4 3.453634 1.0405017 0.52509853 0.599514698
#> 94 5 4.135338 1.1415978 0.75741356 0.448802137
#> 95 1 2.892231 0.8511977 -2.22302133 0.026214362
#> 96 4 4.230576 1.1306455 -0.20393346 0.838405501
#> 97 6 5.360902 1.3617441 0.46932295 0.638838814
#> 98 3 3.556391 0.9543358 -0.58301385 0.559883979
#> 99 1 2.260652 0.6475548 -1.94678758 0.051560207
#> 100 1 2.859649 0.8389697 -2.21658664 0.026651351
plot(lsrq, sf = nc)
# Case 4: With isolated areas
library(lwgeom)
data(provinces_spain)
listw <- spdep::poly2nb(as(provinces_spain,"Spatial"), queen = FALSE)
#> although coordinates are longitude/latitude, st_intersects assumes that they are planar
provinces_spain$Male2Female <- factor(provinces_spain$Male2Female > 100)
levels(provinces_spain$Male2Female) = c("men","woman")
plot(provinces_spain["Male2Female"])
formula <- ~ Male2Female
lsrq <- local.sp.runs.test(formula = formula, data = provinces_spain, listw = listw)
#> Warning: st_centroid assumes attributes are constant over geometries of x
#> Warning: st_centroid does not give correct centroids for longitude/latitude data
print(lsrq)
#> runs.i E.i Std.i z.value p.value
#> 1 3 2.963265 1.2181954 0.03015501 0.97594343
#> 2 3 3.748571 1.4356803 -0.52140538 0.60208441
#> 3 3 2.177959 0.9361800 0.87807987 0.37990038
#> 4 3 1.785306 0.7491685 1.62138936 0.10493416
#> 5 4 3.355918 1.3328119 0.48325020 0.62891810
#> 6 3 3.355918 1.3328119 -0.26704320 0.78943590
#> 7 0 1.000000 NaN NaN NaN
#> 8 3 2.177959 0.9361800 0.87807987 0.37990038
#> 9 4 4.141224 1.5291733 -0.09235349 0.92641719
#> 10 2 2.570612 1.0881246 -0.52439971 0.60000056
#> 11 1 2.177959 0.9361800 -1.25826142 0.20829723
#> 12 3 2.177959 0.9361800 0.87807987 0.37990038
#> 13 5 3.355918 1.3328119 1.23354359 0.21737302
#> 14 1 3.355918 1.3328119 -1.76762999 0.07712278
#> 15 1 1.785306 0.7491685 -1.04823694 0.29452945
#> 16 5 3.748571 1.4356803 0.87166242 0.38339257
#> 17 2 1.785306 0.7491685 0.28657621 0.77443683
#> 18 5 3.355918 1.3328119 1.23354359 0.21737302
#> 19 5 3.355918 1.3328119 1.23354359 0.21737302
#> 20 1 2.177959 0.9361800 -1.25826142 0.20829723
#> 21 2 2.177959 0.9361800 -0.19009078 0.84923800
#> 22 1 2.570612 1.0881246 -1.44341209 0.14890442
#> 23 1 3.748571 1.4356803 -1.91447317 0.05555972
#> 24 4 2.963265 1.2181954 0.85104136 0.39474638
#> 25 5 2.963265 1.2181954 1.67192771 0.09453858
#> 26 1 2.963265 1.2181954 -1.61161769 0.10704516
#> 27 2 2.963265 1.2181954 -0.79073134 0.42910078
#> 28 1 2.570612 1.0881246 -1.44341209 0.14890442
#> 29 4 2.570612 1.0881246 1.31362503 0.18897242
#> 30 2 2.963265 1.2181954 -0.79073134 0.42910078
#> 31 1 2.570612 1.0881246 -1.44341209 0.14890442
#> 32 1 2.177959 0.9361800 -1.25826142 0.20829723
#> 33 3 2.570612 1.0881246 0.39461266 0.69312877
#> 34 0 1.000000 NaN NaN NaN
#> 35 1 2.177959 0.9361800 -1.25826142 0.20829723
#> 36 3 2.570612 1.0881246 0.39461266 0.69312877
#> 37 0 1.000000 NaN NaN NaN
#> 38 3 2.963265 1.2181954 0.03015501 0.97594343
#> 39 3 3.355918 1.3328119 -0.26704320 0.78943590
#> 40 1 2.963265 1.2181954 -1.61161769 0.10704516
#> 41 5 2.963265 1.2181954 1.67192771 0.09453858
#> 42 5 3.355918 1.3328119 1.23354359 0.21737302
#> 43 4 3.355918 1.3328119 0.48325020 0.62891810
#> 44 4 2.963265 1.2181954 0.85104136 0.39474638
#> 45 5 3.748571 1.4356803 0.87166242 0.38339257
#> 46 3 2.570612 1.0881246 0.39461266 0.69312877
#> 47 1 2.570612 1.0881246 -1.44341209 0.14890442
#> 48 8 4.141224 1.5291733 2.52343903 0.01162132
#> 49 5 2.963265 1.2181954 1.67192771 0.09453858
#> 50 1 2.177959 0.9361800 -1.25826142 0.20829723
plot(lsrq, sf = provinces_spain, sig = 0.1)
# Boots Version
lsrq <- local.sp.runs.test(formula = formula, data = provinces_spain, listw = listw,
distr ="bootstrap", nsim = 199)
#> Warning: st_centroid assumes attributes are constant over geometries of x
#> Warning: st_centroid does not give correct centroids for longitude/latitude data
print(lsrq)
#> SRQ EP.i SdP.i zseudo.value pseudo.value
#> 1 3 2.904523 1.2333455 0.07741334 0.93829473
#> 2 3 3.748744 1.3696516 -0.54666730 0.58460732
#> 3 3 2.120603 0.9241582 0.95156545 0.34131741
#> 4 3 1.768844 0.7432077 1.65654326 0.09761185
#> 5 4 3.296482 1.2900308 0.54534945 0.58551320
#> 6 3 3.487437 1.2667436 -0.38479546 0.70038896
#> 7 0 0.000000 0.0000000 NaN NaN
#> 8 3 2.266332 0.9125512 0.80397503 0.42141140
#> 9 4 4.160804 1.5256300 -0.10540172 0.91605705
#> 10 2 2.623116 1.1297932 -0.55153065 0.58126996
#> 11 1 2.261307 0.9385462 -1.34389390 0.17898270
#> 12 3 2.211055 1.0128859 0.77890782 0.43603401
#> 13 5 3.467337 1.3362424 1.14699493 0.25138372
#> 14 1 3.457286 1.2897947 -1.90517640 0.05675714
#> 15 1 1.723618 0.7170330 -1.00918379 0.31288650
#> 16 5 3.814070 1.4179951 0.83634255 0.40296222
#> 17 2 1.824121 0.7681942 0.22895174 0.81890643
#> 18 5 3.195980 1.2700051 1.42048252 0.15546725
#> 19 5 3.552764 1.4688620 0.98527719 0.32448793
#> 20 1 2.221106 0.9163811 -1.33253024 0.18268601
#> 21 2 2.100503 0.8989049 -0.11180550 0.91097763
#> 22 1 2.567839 1.0797357 -1.45205833 0.14648539
#> 23 1 3.839196 1.5189947 -1.86912834 0.06160496
#> 24 4 3.005025 1.1827783 0.84121840 0.40022559
#> 25 5 2.919598 1.2364693 1.68253426 0.09246529
#> 26 1 2.869347 1.1472475 -1.62941887 0.10322438
#> 27 2 3.030151 1.2427956 -0.82889798 0.40716214
#> 28 1 2.633166 1.1464066 -1.42459567 0.15427411
#> 29 4 2.452261 1.0132867 1.52744402 0.12665064
#> 30 2 3.035176 1.2406291 -0.83439597 0.40405789
#> 31 1 2.603015 1.0580098 -1.51512304 0.12974125
#> 32 1 2.110553 0.9308621 -1.19303683 0.23285495
#> 33 3 2.547739 1.0232067 0.44200386 0.65848641
#> 34 0 0.000000 0.0000000 NaN NaN
#> 35 1 2.125628 0.8985378 -1.25273320 0.21030282
#> 36 3 2.587940 1.1595259 0.35536964 0.72231269
#> 37 0 0.000000 0.0000000 NaN NaN
#> 38 3 2.864322 1.2499226 0.10854944 0.91355987
#> 39 3 3.417085 1.4431691 -0.28900663 0.77257630
#> 40 1 2.974874 1.1825208 -1.67005468 0.09490855
#> 41 5 2.934673 1.1852433 1.74253384 0.08141508
#> 42 5 3.351759 1.3768961 1.19707015 0.23127922
#> 43 4 3.452261 1.3013134 0.42091220 0.67381919
#> 44 4 2.974874 1.1739478 0.87322932 0.38253809
#> 45 5 3.944724 1.4536474 0.72595073 0.46786897
#> 46 3 2.648241 1.1750282 0.29936199 0.76466386
#> 47 1 2.497487 1.0292410 -1.45494340 0.14568493
#> 48 8 4.130653 1.5995628 2.41900273 0.01556312
#> 49 5 2.984925 1.2491508 1.61315625 0.10671056
#> 50 1 2.251256 0.9832876 -1.27252322 0.20318728
plot(lsrq, sf = provinces_spain, sig = 0.10)
# Case 5: SRQ test based on a distance matrix (inverse distance)
# \donttest{
library(lwgeom)
N <- 100
cx <- runif(N)
cy <- runif(N)
coor <- as.data.frame(cbind(cx,cy))
coor <- sf::st_as_sf(coor,coords = c("cx","cy"))
n = dim(coor)[1]
dis <- 1/matrix(as.numeric(sf::st_distance(coor,coor)), ncol = n, nrow = n)
diag(dis) <- 0
dis <- (dis < quantile(dis,.10))*dis
p <- c(1/6,3/6,2/6)
rho <- 0.5
fx <- dgp.spq(p = p, listw = dis, rho = rho)
lsrq <- local.sp.runs.test(fx = fx, listw = dis)
print(lsrq)
#> runs.i E.i Std.i z.value p.value
#> 1 2 2.855152 0.8722689 -0.98037608 0.32690051
#> 2 5 4.091919 1.1317511 0.80236794 0.42234015
#> 3 4 3.473535 1.0106752 0.52090392 0.60243371
#> 4 4 3.473535 1.0106752 0.52090392 0.60243371
#> 5 17 14.604444 2.3462098 1.02103210 0.30723923
#> 6 14 14.604444 2.3462098 -0.25762591 0.79669563
#> 7 19 22.643434 2.9150932 -1.24985177 0.21135370
#> 8 3 2.236768 0.7064182 1.08042568 0.27995266
#> 9 3 3.473535 1.0106752 -0.46853368 0.63940299
#> 10 0 1.000000 NaN NaN NaN
#> 11 17 22.025051 2.8765991 -1.74687204 0.08065954
#> 12 0 1.000000 NaN NaN NaN
#> 13 9 10.275758 1.9514092 -0.65376220 0.51326502
#> 14 0 1.000000 NaN NaN NaN
#> 15 0 1.000000 NaN NaN NaN
#> 16 0 1.000000 NaN NaN NaN
#> 17 6 5.328687 1.3401523 0.50092302 0.61642530
#> 18 4 3.473535 1.0106752 0.52090392 0.60243371
#> 19 16 17.696364 2.5846046 -0.65633392 0.51160930
#> 20 2 2.855152 0.8722689 -0.98037608 0.32690051
#> 21 4 3.473535 1.0106752 0.52090392 0.60243371
#> 22 3 2.236768 0.7064182 1.08042568 0.27995266
#> 23 30 23.261818 2.9528798 2.28190184 0.02249514
#> 24 8 7.183838 1.5998803 0.51013918 0.60995396
#> 25 9 10.275758 1.9514092 -0.65376220 0.51326502
#> 26 0 1.000000 NaN NaN NaN
#> 27 4 3.473535 1.0106752 0.52090392 0.60243371
#> 28 1 2.236768 0.7064182 -1.75075861 0.07998750
#> 29 0 1.000000 NaN NaN NaN
#> 30 25 24.498586 3.0264361 0.16567808 0.86841029
#> 31 2 2.236768 0.7064182 -0.33516646 0.73749952
#> 32 4 4.091919 1.1317511 -0.08121856 0.93526814
#> 33 4 2.855152 0.8722689 1.31249497 0.18935318
#> 34 9 9.038990 1.8199699 -0.02142338 0.98290793
#> 35 4 3.473535 1.0106752 0.52090392 0.60243371
#> 36 6 7.183838 1.5998803 -0.73995436 0.45932769
#> 37 9 8.420606 1.7500327 0.33107607 0.74058703
#> 38 3 2.855152 0.8722689 0.16605945 0.86811017
#> 39 0 1.000000 NaN NaN NaN
#> 40 4 3.473535 1.0106752 0.52090392 0.60243371
#> 41 1 1.618384 0.4857831 -1.27296272 0.20303127
#> 42 9 9.038990 1.8199699 -0.02142338 0.98290793
#> 43 9 6.565455 1.5186493 1.60309920 0.10891276
#> 44 12 9.038990 1.8199699 1.62695551 0.10374655
#> 45 3 2.236768 0.7064182 1.08042568 0.27995266
#> 46 3 2.855152 0.8722689 0.16605945 0.86811017
#> 47 8 6.565455 1.5186493 0.94461932 0.34485326
#> 48 9 7.183838 1.5998803 1.13518595 0.25629741
#> 49 11 10.275758 1.9514092 0.37113816 0.71053463
#> 50 8 7.802222 1.6768193 0.11794817 0.90610872
#> 51 5 3.473535 1.0106752 1.51034151 0.13095630
#> 52 5 6.565455 1.5186493 -1.03082032 0.30262509
#> 53 5 4.710303 1.2405813 0.23351712 0.81535987
#> 54 9 9.657374 1.8869954 -0.34837061 0.72756187
#> 55 7 7.802222 1.6768193 -0.47841899 0.63235202
#> 56 2 2.236768 0.7064182 -0.33516646 0.73749952
#> 57 5 4.091919 1.1317511 0.80236794 0.42234015
#> 58 0 1.000000 NaN NaN NaN
#> 59 0 1.000000 NaN NaN NaN
#> 60 5 5.328687 1.3401523 -0.24526083 0.80625447
#> 61 8 8.420606 1.7500327 -0.24034183 0.81006527
#> 62 9 7.802222 1.6768193 0.71431534 0.47503221
#> 63 0 1.000000 NaN NaN NaN
#> 64 14 11.512525 2.0733657 1.19972796 0.23024501
#> 65 10 10.894141 2.0134619 -0.44408161 0.65698359
#> 66 12 10.275758 1.9514092 0.88358834 0.37691847
#> 67 0 1.000000 NaN NaN NaN
#> 68 5 5.328687 1.3401523 -0.24526083 0.80625447
#> 69 0 1.000000 NaN NaN NaN
#> 70 4 3.473535 1.0106752 0.52090392 0.60243371
#> 71 8 9.657374 1.8869954 -0.87831360 0.37977356
#> 72 4 3.473535 1.0106752 0.52090392 0.60243371
#> 73 1 2.236768 0.7064182 -1.75075861 0.07998750
#> 74 1 2.855152 0.8722689 -2.12681160 0.03343574
#> 75 15 16.459596 2.4927161 -0.58554439 0.55818172
#> 76 5 6.565455 1.5186493 -1.03082032 0.30262509
#> 77 5 3.473535 1.0106752 1.51034151 0.13095630
#> 78 18 20.788283 2.7973712 -0.99675111 0.31888533
#> 79 8 5.947071 1.4323964 1.43321312 0.15179694
#> 80 4 2.855152 0.8722689 1.31249497 0.18935318
#> 81 9 7.802222 1.6768193 0.71431534 0.47503221
#> 82 14 12.749293 2.1874260 0.57177115 0.56747702
#> 83 0 1.000000 NaN NaN NaN
#> 84 5 4.091919 1.1317511 0.80236794 0.42234015
#> 85 16 17.696364 2.5846046 -0.65633392 0.51160930
#> 86 6 7.183838 1.5998803 -0.73995436 0.45932769
#> 87 5 4.091919 1.1317511 0.80236794 0.42234015
#> 88 0 1.000000 NaN NaN NaN
#> 89 0 1.000000 NaN NaN NaN
#> 90 4 3.473535 1.0106752 0.52090392 0.60243371
#> 91 1 1.618384 0.4857831 -1.27296272 0.20303127
#> 92 11 11.512525 2.0733657 -0.24719482 0.80475745
#> 93 18 17.696364 2.5846046 0.11747885 0.90648061
#> 94 7 6.565455 1.5186493 0.28613944 0.77477133
#> 95 6 6.565455 1.5186493 -0.37234044 0.70963939
#> 96 2 2.855152 0.8722689 -0.98037608 0.32690051
#> 97 14 15.841212 2.4451048 -0.75301970 0.45143807
#> 98 24 21.406667 2.8373687 0.91399235 0.36072086
#> 99 6 5.947071 1.4323964 0.03695157 0.97052362
#> 100 0 1.000000 NaN NaN NaN
plot(lsrq, coor = cbind(cx,cy), sig = 0.05)
lsrq <- local.sp.runs.test(fx = fx, listw = dis, data = )
print(lsrq)
#> runs.i E.i Std.i z.value p.value
#> 1 2 2.855152 0.8722689 -0.98037608 0.32690051
#> 2 5 4.091919 1.1317511 0.80236794 0.42234015
#> 3 4 3.473535 1.0106752 0.52090392 0.60243371
#> 4 4 3.473535 1.0106752 0.52090392 0.60243371
#> 5 17 14.604444 2.3462098 1.02103210 0.30723923
#> 6 14 14.604444 2.3462098 -0.25762591 0.79669563
#> 7 19 22.643434 2.9150932 -1.24985177 0.21135370
#> 8 3 2.236768 0.7064182 1.08042568 0.27995266
#> 9 3 3.473535 1.0106752 -0.46853368 0.63940299
#> 10 0 1.000000 NaN NaN NaN
#> 11 17 22.025051 2.8765991 -1.74687204 0.08065954
#> 12 0 1.000000 NaN NaN NaN
#> 13 9 10.275758 1.9514092 -0.65376220 0.51326502
#> 14 0 1.000000 NaN NaN NaN
#> 15 0 1.000000 NaN NaN NaN
#> 16 0 1.000000 NaN NaN NaN
#> 17 6 5.328687 1.3401523 0.50092302 0.61642530
#> 18 4 3.473535 1.0106752 0.52090392 0.60243371
#> 19 16 17.696364 2.5846046 -0.65633392 0.51160930
#> 20 2 2.855152 0.8722689 -0.98037608 0.32690051
#> 21 4 3.473535 1.0106752 0.52090392 0.60243371
#> 22 3 2.236768 0.7064182 1.08042568 0.27995266
#> 23 30 23.261818 2.9528798 2.28190184 0.02249514
#> 24 8 7.183838 1.5998803 0.51013918 0.60995396
#> 25 9 10.275758 1.9514092 -0.65376220 0.51326502
#> 26 0 1.000000 NaN NaN NaN
#> 27 4 3.473535 1.0106752 0.52090392 0.60243371
#> 28 1 2.236768 0.7064182 -1.75075861 0.07998750
#> 29 0 1.000000 NaN NaN NaN
#> 30 25 24.498586 3.0264361 0.16567808 0.86841029
#> 31 2 2.236768 0.7064182 -0.33516646 0.73749952
#> 32 4 4.091919 1.1317511 -0.08121856 0.93526814
#> 33 4 2.855152 0.8722689 1.31249497 0.18935318
#> 34 9 9.038990 1.8199699 -0.02142338 0.98290793
#> 35 4 3.473535 1.0106752 0.52090392 0.60243371
#> 36 6 7.183838 1.5998803 -0.73995436 0.45932769
#> 37 9 8.420606 1.7500327 0.33107607 0.74058703
#> 38 3 2.855152 0.8722689 0.16605945 0.86811017
#> 39 0 1.000000 NaN NaN NaN
#> 40 4 3.473535 1.0106752 0.52090392 0.60243371
#> 41 1 1.618384 0.4857831 -1.27296272 0.20303127
#> 42 9 9.038990 1.8199699 -0.02142338 0.98290793
#> 43 9 6.565455 1.5186493 1.60309920 0.10891276
#> 44 12 9.038990 1.8199699 1.62695551 0.10374655
#> 45 3 2.236768 0.7064182 1.08042568 0.27995266
#> 46 3 2.855152 0.8722689 0.16605945 0.86811017
#> 47 8 6.565455 1.5186493 0.94461932 0.34485326
#> 48 9 7.183838 1.5998803 1.13518595 0.25629741
#> 49 11 10.275758 1.9514092 0.37113816 0.71053463
#> 50 8 7.802222 1.6768193 0.11794817 0.90610872
#> 51 5 3.473535 1.0106752 1.51034151 0.13095630
#> 52 5 6.565455 1.5186493 -1.03082032 0.30262509
#> 53 5 4.710303 1.2405813 0.23351712 0.81535987
#> 54 9 9.657374 1.8869954 -0.34837061 0.72756187
#> 55 7 7.802222 1.6768193 -0.47841899 0.63235202
#> 56 2 2.236768 0.7064182 -0.33516646 0.73749952
#> 57 5 4.091919 1.1317511 0.80236794 0.42234015
#> 58 0 1.000000 NaN NaN NaN
#> 59 0 1.000000 NaN NaN NaN
#> 60 5 5.328687 1.3401523 -0.24526083 0.80625447
#> 61 8 8.420606 1.7500327 -0.24034183 0.81006527
#> 62 9 7.802222 1.6768193 0.71431534 0.47503221
#> 63 0 1.000000 NaN NaN NaN
#> 64 14 11.512525 2.0733657 1.19972796 0.23024501
#> 65 10 10.894141 2.0134619 -0.44408161 0.65698359
#> 66 12 10.275758 1.9514092 0.88358834 0.37691847
#> 67 0 1.000000 NaN NaN NaN
#> 68 5 5.328687 1.3401523 -0.24526083 0.80625447
#> 69 0 1.000000 NaN NaN NaN
#> 70 4 3.473535 1.0106752 0.52090392 0.60243371
#> 71 8 9.657374 1.8869954 -0.87831360 0.37977356
#> 72 4 3.473535 1.0106752 0.52090392 0.60243371
#> 73 1 2.236768 0.7064182 -1.75075861 0.07998750
#> 74 1 2.855152 0.8722689 -2.12681160 0.03343574
#> 75 15 16.459596 2.4927161 -0.58554439 0.55818172
#> 76 5 6.565455 1.5186493 -1.03082032 0.30262509
#> 77 5 3.473535 1.0106752 1.51034151 0.13095630
#> 78 18 20.788283 2.7973712 -0.99675111 0.31888533
#> 79 8 5.947071 1.4323964 1.43321312 0.15179694
#> 80 4 2.855152 0.8722689 1.31249497 0.18935318
#> 81 9 7.802222 1.6768193 0.71431534 0.47503221
#> 82 14 12.749293 2.1874260 0.57177115 0.56747702
#> 83 0 1.000000 NaN NaN NaN
#> 84 5 4.091919 1.1317511 0.80236794 0.42234015
#> 85 16 17.696364 2.5846046 -0.65633392 0.51160930
#> 86 6 7.183838 1.5998803 -0.73995436 0.45932769
#> 87 5 4.091919 1.1317511 0.80236794 0.42234015
#> 88 0 1.000000 NaN NaN NaN
#> 89 0 1.000000 NaN NaN NaN
#> 90 4 3.473535 1.0106752 0.52090392 0.60243371
#> 91 1 1.618384 0.4857831 -1.27296272 0.20303127
#> 92 11 11.512525 2.0733657 -0.24719482 0.80475745
#> 93 18 17.696364 2.5846046 0.11747885 0.90648061
#> 94 7 6.565455 1.5186493 0.28613944 0.77477133
#> 95 6 6.565455 1.5186493 -0.37234044 0.70963939
#> 96 2 2.855152 0.8722689 -0.98037608 0.32690051
#> 97 14 15.841212 2.4451048 -0.75301970 0.45143807
#> 98 24 21.406667 2.8373687 0.91399235 0.36072086
#> 99 6 5.947071 1.4323964 0.03695157 0.97052362
#> 100 0 1.000000 NaN NaN NaN
plot(lsrq, sf = coor)
# Version boots
lsrq <- local.sp.runs.test(fx = fx, listw = dis, data = coor,
distr ="bootstrap", nsim = 299)
print(lsrq)
#> SRQ EP.i SdP.i zseudo.value pseudo.value
#> 1 2 2.849498 0.8399174 -1.01140705 0.31182165
#> 2 5 4.086957 1.1952635 0.76388469 0.44493596
#> 3 4 3.484950 0.9910375 0.51970806 0.60326707
#> 4 4 3.501672 0.9945306 0.50106829 0.61632306
#> 5 17 14.759197 2.3030926 0.97295378 0.33057627
#> 6 14 14.585284 2.3804117 -0.24587523 0.80577882
#> 7 19 22.729097 2.9028202 -1.28464620 0.19891594
#> 8 3 2.277592 0.6901995 1.04666549 0.29525389
#> 9 3 3.464883 1.0139650 -0.45848026 0.64660744
#> 10 0 0.000000 0.0000000 NaN NaN
#> 11 17 22.053512 2.8947672 -1.74574027 0.08085609
#> 12 0 0.000000 0.0000000 NaN NaN
#> 13 9 10.451505 1.8245592 -0.79553737 0.42630098
#> 14 0 0.000000 0.0000000 NaN NaN
#> 15 0 0.000000 0.0000000 NaN NaN
#> 16 0 0.000000 0.0000000 NaN NaN
#> 17 6 5.334448 1.3368238 0.49786055 0.61858234
#> 18 4 3.498328 1.0012562 0.50104283 0.61634098
#> 19 16 17.652174 2.5526839 -0.64723013 0.51748301
#> 20 2 2.879599 0.8585643 -1.02449941 0.30559945
#> 21 4 3.468227 0.9735567 0.54621635 0.58491723
#> 22 3 2.230769 0.7306266 1.05283712 0.29241565
#> 23 30 23.301003 3.0294470 2.21129354 0.02701552
#> 24 8 7.207358 1.6355364 0.48463743 0.62793356
#> 25 9 10.274247 1.8676976 -0.68225579 0.49507723
#> 26 0 0.000000 0.0000000 NaN NaN
#> 27 4 3.444816 1.0196714 0.54447340 0.58611575
#> 28 1 2.180602 0.7558441 -1.56196496 0.11829624
#> 29 0 0.000000 0.0000000 NaN NaN
#> 30 25 24.665552 3.2966096 0.10145216 0.91919153
#> 31 2 2.297659 0.6915316 -0.43043421 0.66687982
#> 32 4 4.096990 1.1617322 -0.08348737 0.93346402
#> 33 4 2.953177 0.8381517 1.24896573 0.21167761
#> 34 9 8.859532 1.8153894 0.07737636 0.93832415
#> 35 4 3.474916 0.9806207 0.53546044 0.59233150
#> 36 6 7.270903 1.5337991 -0.82859807 0.40733188
#> 37 9 8.525084 1.7499395 0.27139018 0.78609095
#> 38 3 2.856187 0.8800855 0.16340765 0.87019748
#> 39 0 0.000000 0.0000000 NaN NaN
#> 40 4 3.484950 0.9600795 0.53646618 0.59163640
#> 41 1 1.591973 0.4922920 -1.20248386 0.22917612
#> 42 9 8.926421 1.7933334 0.04102896 0.96727281
#> 43 9 6.729097 1.4366451 1.58069866 0.11394695
#> 44 12 9.123746 1.6952573 1.69664757 0.08976331
#> 45 3 2.270903 0.7119706 1.02405484 0.30580937
#> 46 3 2.886288 0.8749569 0.12996340 0.89659538
#> 47 8 6.357860 1.3618841 1.20578577 0.22790010
#> 48 9 7.267559 1.4684550 1.17977157 0.23809108
#> 49 11 10.244147 1.8977002 0.39829940 0.69040950
#> 50 8 7.739130 1.6665402 0.15653362 0.87561242
#> 51 5 3.551839 1.0329252 1.40199939 0.16091543
#> 52 5 6.628763 1.5476684 -1.05239765 0.29261714
#> 53 5 4.655518 1.2281901 0.28047905 0.77910999
#> 54 9 9.822742 1.8075210 -0.45517728 0.64898171
#> 55 7 7.658863 1.6211728 -0.40641125 0.68444046
#> 56 2 2.301003 0.7256326 -0.41481510 0.67827726
#> 57 5 4.173913 1.1800303 0.70005571 0.48389252
#> 58 0 0.000000 0.0000000 NaN NaN
#> 59 0 0.000000 0.0000000 NaN NaN
#> 60 5 5.331104 1.3538669 -0.24456148 0.80679600
#> 61 8 8.394649 1.6193373 -0.24371009 0.80745536
#> 62 9 7.816054 1.5894819 0.74486313 0.45635447
#> 63 0 0.000000 0.0000000 NaN NaN
#> 64 14 11.688963 1.9559525 1.18154033 0.23738814
#> 65 10 11.100334 1.9772107 -0.55650843 0.57786333
#> 66 12 10.197324 2.0459141 0.88111009 0.37825824
#> 67 0 0.000000 0.0000000 NaN NaN
#> 68 5 5.374582 1.3855036 -0.27035797 0.78688487
#> 69 0 0.000000 0.0000000 NaN NaN
#> 70 4 3.481605 0.9773420 0.53041273 0.59582580
#> 71 8 9.802676 1.7507025 -1.02968699 0.30315697
#> 72 4 3.628763 0.9620180 0.38589450 0.69957481
#> 73 1 2.250836 0.7422695 -1.68515082 0.09195948
#> 74 1 2.846154 0.8687781 -2.12500039 0.03358658
#> 75 15 16.605351 2.3065645 -0.69599232 0.48643364
#> 76 5 6.575251 1.5228207 -1.03442965 0.30093535
#> 77 5 3.488294 1.0211012 1.48046601 0.13874893
#> 78 18 20.715719 2.7458548 -0.98902501 0.32265090
#> 79 8 5.913043 1.4257214 1.46378981 0.14325139
#> 80 4 2.926421 0.7823156 1.37230883 0.16996732
#> 81 9 7.896321 1.6525209 0.66787593 0.50421280
#> 82 14 12.528428 2.1616769 0.68075480 0.49602665
#> 83 0 0.000000 0.0000000 NaN NaN
#> 84 5 4.076923 1.0825504 0.85268726 0.39383276
#> 85 16 17.555184 2.7206885 -0.57161412 0.56758343
#> 86 6 7.237458 1.5262144 -0.81080233 0.41747920
#> 87 5 4.063545 1.2148309 0.77085199 0.44079467
#> 88 0 0.000000 0.0000000 NaN NaN
#> 89 0 0.000000 0.0000000 NaN NaN
#> 90 4 3.434783 1.0190769 0.55463666 0.57914321
#> 91 1 1.622074 0.4856820 -1.28082498 0.20025515
#> 92 11 11.628763 2.0380546 -0.30851114 0.75769343
#> 93 18 17.692308 2.6858393 0.11456095 0.90879313
#> 94 7 6.732441 1.5354812 0.17425061 0.86166851
#> 95 6 6.762542 1.4402419 -0.52945396 0.59649057
#> 96 2 2.859532 0.8901028 -0.96565449 0.33421710
#> 97 14 16.053512 2.4502731 -0.83807462 0.40198880
#> 98 24 21.254181 2.8735558 0.95554761 0.33930084
#> 99 6 6.127090 1.3844420 -0.09179893 0.92685779
#> 100 0 0.000000 0.0000000 NaN NaN
plot(lsrq, sf = coor)
# SRQ test based on inverse distance
library(lwgeom)
data("FastFood.sf")
sf::sf_use_s2(FALSE)
n = dim(FastFood.sf)[1]
dis <- 1000000/matrix(as.numeric(
sf::st_distance(FastFood.sf, FastFood.sf)),
ncol = n, nrow = n)
#> Warning: bounding box has potentially an invalid value range for longlat data
#> Warning: bounding box has potentially an invalid value range for longlat data
#> Warning: bounding box has potentially an invalid value range for longlat data
diag(dis) <- 0
dis <- (dis < quantile(dis,.01))*dis
formula <- ~ Type
lsrq <- local.sp.runs.test(formula = formula, data = FastFood.sf, listw = dis)
#> Warning: st_centroid assumes attributes are constant over geometries of x
#> Warning: bounding box has potentially an invalid value range for longlat data
#> Warning: st_centroid does not give correct centroids for longitude/latitude data
print(lsrq)
#> runs.i E.i Std.i z.value p.value
#> 1 8 5.667815 1.24677180 1.870579e+00 0.061403444
#> 2 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 3 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 4 8 6.334645 1.33284778 1.249471e+00 0.211492867
#> 5 6 7.001476 1.41369228 -7.084116e-01 0.478689660
#> 6 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 7 5 3.667323 0.94250012 1.413981e+00 0.157367469
#> 8 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 9 8 11.669291 1.88488922 -1.946688e+00 0.051572177
#> 10 16 22.338582 2.66558409 -2.377933e+00 0.017409967
#> 11 26 21.004920 2.58094570 1.935368e+00 0.052945152
#> 12 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 13 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 14 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 15 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 16 2 3.667323 0.94250012 -1.769042e+00 0.076886794
#> 17 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 18 7 7.001476 1.41369228 -1.044130e-03 0.999166905
#> 19 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 20 30 25.005904 2.82726846 1.766403e+00 0.077328250
#> 21 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 22 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 23 3 5.000984 1.15429461 -1.733512e+00 0.083004632
#> 24 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 25 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 26 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 27 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 28 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 29 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 30 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 31 8 5.667815 1.24677180 1.870579e+00 0.061403444
#> 32 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 33 9 7.001476 1.41369228 1.413691e+00 0.157452675
#> 34 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 35 12 9.668799 1.69902630 1.372081e+00 0.170038313
#> 36 27 25.672735 2.86626456 4.630644e-01 0.643318223
#> 37 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 38 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 39 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 40 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 41 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 42 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 43 8 5.667815 1.24677180 1.870579e+00 0.061403444
#> 44 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 45 8 8.335137 1.56288494 -2.144351e-01 0.830207752
#> 46 8 7.668307 1.49015700 2.225895e-01 0.823855039
#> 47 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 48 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 49 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 50 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 51 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 52 5 3.667323 0.94250012 1.413981e+00 0.157367469
#> 53 11 9.668799 1.69902630 7.835083e-01 0.433328678
#> 54 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 55 13 13.002952 1.99922042 -1.476654e-03 0.998821801
#> 56 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 57 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 58 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 59 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 60 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 61 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 62 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 63 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 64 5 5.667815 1.24677180 -5.356351e-01 0.592210772
#> 65 1 2.333661 0.66649415 -2.001010e+00 0.045391330
#> 66 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 67 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 68 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 69 9 7.001476 1.41369228 1.413691e+00 0.157452675
#> 70 8 7.001476 1.41369228 7.063234e-01 0.479987051
#> 71 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 72 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 73 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 74 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 75 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 76 18 15.670275 2.21020923 1.054074e+00 0.291848820
#> 77 12 11.669291 1.88488922 1.754529e-01 0.860723812
#> 78 28 29.006888 3.05378310 -3.297184e-01 0.741612777
#> 79 14 17.670767 2.35608263 -1.557996e+00 0.119234240
#> 80 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 81 23 22.338582 2.66558409 2.481326e-01 0.804031790
#> 82 18 19.004428 2.44850757 -4.102206e-01 0.681644134
#> 83 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 84 22 22.338582 2.66558409 -1.270197e-01 0.898924830
#> 85 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 86 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 87 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 88 8 5.667815 1.24677180 1.870579e+00 0.061403444
#> 89 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 90 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 91 1 2.333661 0.66649415 -2.001010e+00 0.045391330
#> 92 5 3.667323 0.94250012 1.413981e+00 0.157367469
#> 93 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 94 24 23.005412 2.70691089 3.674254e-01 0.713301756
#> 95 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 96 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 97 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 98 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 99 10 9.668799 1.69902630 1.949359e-01 0.845443130
#> 100 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 101 5 5.667815 1.24677180 -5.356351e-01 0.592210772
#> 102 10 7.668307 1.49015700 1.564730e+00 0.117646250
#> 103 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 104 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 105 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 106 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 107 9 8.335137 1.56288494 4.254072e-01 0.670539828
#> 108 17 16.337106 2.25988030 2.933317e-01 0.769268647
#> 109 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 110 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 111 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 112 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 113 8 5.667815 1.24677180 1.870579e+00 0.061403444
#> 114 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 115 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 116 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 117 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 118 14 14.336614 2.10735730 -1.597325e-01 0.873091777
#> 119 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 120 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 121 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 122 7 7.001476 1.41369228 -1.044130e-03 0.999166905
#> 123 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 124 15 14.336614 2.10735730 3.147955e-01 0.752916966
#> 125 7 5.000984 1.15429461 1.731807e+00 0.083307861
#> 126 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 127 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 128 16 13.669783 2.05400069 1.134477e+00 0.256594389
#> 129 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 130 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 131 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 132 8 9.001968 1.63237562 -6.138098e-01 0.539341040
#> 133 5 5.000984 1.15429461 -8.525138e-04 0.999319792
#> 134 5 5.000984 1.15429461 -8.525138e-04 0.999319792
#> 135 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 136 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 137 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 138 25 20.338090 2.53756790 1.837157e+00 0.066186734
#> 139 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 140 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 141 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 142 5 3.667323 0.94250012 1.413981e+00 0.157367469
#> 143 14 13.669783 2.05400069 1.607678e-01 0.872276289
#> 144 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 145 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 146 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 147 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 148 13 12.336121 1.94289607 3.416953e-01 0.732580185
#> 149 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 150 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 151 8 9.001968 1.63237562 -6.138098e-01 0.539341040
#> 152 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 153 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 154 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 155 13 13.002952 1.99922042 -1.476654e-03 0.998821801
#> 156 10 9.668799 1.69902630 1.949359e-01 0.845443130
#> 157 13 13.669783 2.05400069 -3.260870e-01 0.744358567
#> 158 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 159 6 4.334153 1.05373221 1.580901e+00 0.113900606
#> 160 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 161 28 29.006888 3.05378310 -3.297184e-01 0.741612777
#> 162 8 7.668307 1.49015700 2.225895e-01 0.823855039
#> 163 5 5.000984 1.15429461 -8.525138e-04 0.999319792
#> 164 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 165 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 166 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 167 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 168 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 169 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 170 8 6.334645 1.33284778 1.249471e+00 0.211492867
#> 171 10 8.335137 1.56288494 1.065250e+00 0.286762989
#> 172 4 7.001476 1.41369228 -2.123147e+00 0.033741562
#> 173 8 7.001476 1.41369228 7.063234e-01 0.479987051
#> 174 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 175 2 4.334153 1.05373221 -2.215130e+00 0.026751172
#> 176 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 177 14 12.336121 1.94289607 8.563909e-01 0.391781595
#> 178 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 179 23 19.004428 2.44850757 1.631840e+00 0.102713268
#> 180 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 181 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 182 23 25.005904 2.82726846 -7.094849e-01 0.478023611
#> 183 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 184 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 185 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 186 7 7.668307 1.49015700 -4.484808e-01 0.653806265
#> 187 12 13.002952 1.99922042 -5.016716e-01 0.615898528
#> 188 19 21.671751 2.62360628 -1.018351e+00 0.308511387
#> 189 9 7.001476 1.41369228 1.413691e+00 0.157452675
#> 190 6 7.668307 1.49015700 -1.119551e+00 0.262905149
#> 191 7 7.001476 1.41369228 -1.044130e-03 0.999166905
#> 192 7 5.667815 1.24677180 1.068508e+00 0.285291559
#> 193 15 15.670275 2.21020923 -3.032631e-01 0.761689381
#> 194 7 7.001476 1.41369228 -1.044130e-03 0.999166905
#> 195 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 196 28 24.339074 2.78772681 1.313230e+00 0.189105471
#> 197 14 12.336121 1.94289607 8.563909e-01 0.391781595
#> 198 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 199 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 200 8 7.001476 1.41369228 7.063234e-01 0.479987051
#> 201 5 5.667815 1.24677180 -5.356351e-01 0.592210772
#> 202 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 203 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 204 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 205 11 8.335137 1.56288494 1.705092e+00 0.088177272
#> 206 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 207 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 208 9 7.668307 1.49015700 8.936597e-01 0.371503999
#> 209 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 210 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 211 11 9.001968 1.63237562 1.224003e+00 0.220951271
#> 212 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 213 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 214 12 9.668799 1.69902630 1.372081e+00 0.170038313
#> 215 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 216 1 3.667323 0.94250012 -2.830050e+00 0.004654069
#> 217 7 5.000984 1.15429461 1.731807e+00 0.083307861
#> 218 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 219 8 6.334645 1.33284778 1.249471e+00 0.211492867
#> 220 22 21.671751 2.62360628 1.251137e-01 0.900433545
#> 221 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 222 14 13.669783 2.05400069 1.607678e-01 0.872276289
#> 223 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 224 24 18.337598 2.40273961 2.356644e+00 0.018440905
#> 225 7 5.667815 1.24677180 1.068508e+00 0.285291559
#> 226 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 227 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 228 26 23.672243 2.74761605 8.471915e-01 0.396888375
#> 229 1 2.333661 0.66649415 -2.001010e+00 0.045391330
#> 230 22 24.339074 2.78772681 -8.390613e-01 0.401434920
#> 231 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 232 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 233 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 234 4 5.667815 1.24677180 -1.337706e+00 0.180992136
#> 235 7 5.667815 1.24677180 1.068508e+00 0.285291559
#> 236 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 237 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 238 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 239 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 240 1 3.000492 0.81624798 -2.450839e+00 0.014252386
#> 241 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 242 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 243 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 244 18 20.338090 2.53756790 -9.213900e-01 0.356846869
#> 245 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 246 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 247 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 248 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 249 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 250 10 9.001968 1.63237562 6.113984e-01 0.540935839
#> 251 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 252 7 5.667815 1.24677180 1.068508e+00 0.285291559
#> 253 12 12.336121 1.94289607 -1.730002e-01 0.862651241
#> 254 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 255 19 19.004428 2.44850757 -1.808544e-03 0.998556991
#> 256 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 257 7 8.335137 1.56288494 -8.542775e-01 0.392951254
#> 258 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 259 9 9.001968 1.63237562 -1.205669e-03 0.999038016
#> 260 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 261 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 262 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 263 7 5.000984 1.15429461 1.731807e+00 0.083307861
#> 264 3 7.001476 1.41369228 -2.830514e+00 0.004647325
#> 265 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 266 9 9.668799 1.69902630 -3.936365e-01 0.693849424
#> 267 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 268 8 8.335137 1.56288494 -2.144351e-01 0.830207752
#> 269 9 9.668799 1.69902630 -3.936365e-01 0.693849424
#> 270 16 14.336614 2.10735730 7.893234e-01 0.429922996
#> 271 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 272 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 273 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 274 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 275 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 276 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 277 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 278 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 279 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 280 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 281 21 28.340058 3.01721207 -2.432728e+00 0.014985534
#> 282 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 283 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 284 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 285 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 286 19 20.338090 2.53756790 -5.273118e-01 0.597977057
#> 287 5 5.000984 1.15429461 -8.525138e-04 0.999319792
#> 288 11 11.002460 1.82503944 -1.347987e-03 0.998924462
#> 289 5 7.001476 1.41369228 -1.415779e+00 0.156840170
#> 290 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 291 6 7.668307 1.49015700 -1.119551e+00 0.262905149
#> 292 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 293 8 7.668307 1.49015700 2.225895e-01 0.823855039
#> 294 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 295 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 296 20 19.671259 2.49343546 1.318426e-01 0.895108767
#> 297 12 9.668799 1.69902630 1.372081e+00 0.170038313
#> 298 29 28.340058 3.01721207 2.187259e-01 0.826863602
#> 299 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 300 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 301 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 302 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 303 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 304 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 305 8 7.001476 1.41369228 7.063234e-01 0.479987051
#> 306 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 307 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 308 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 309 19 20.338090 2.53756790 -5.273118e-01 0.597977057
#> 310 8 5.667815 1.24677180 1.870579e+00 0.061403444
#> 311 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 312 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 313 18 15.670275 2.21020923 1.054074e+00 0.291848820
#> 314 21 17.670767 2.35608263 1.413038e+00 0.157644698
#> 315 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 316 1 3.000492 0.81624798 -2.450839e+00 0.014252386
#> 317 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 318 5 5.000984 1.15429461 -8.525138e-04 0.999319792
#> 319 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 320 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 321 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 322 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 323 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 324 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 325 5 3.667323 0.94250012 1.413981e+00 0.157367469
#> 326 5 3.667323 0.94250012 1.413981e+00 0.157367469
#> 327 7 5.000984 1.15429461 1.731807e+00 0.083307861
#> 328 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 329 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 330 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 331 14 13.002952 1.99922042 4.987183e-01 0.617977839
#> 332 8 6.334645 1.33284778 1.249471e+00 0.211492867
#> 333 2 3.667323 0.94250012 -1.769042e+00 0.076886794
#> 334 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 335 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 336 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 337 26 27.673227 2.98019220 -5.614494e-01 0.574491241
#> 338 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 339 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 340 7 7.668307 1.49015700 -4.484808e-01 0.653806265
#> 341 19 22.338582 2.66558409 -1.252477e+00 0.210396262
#> 342 6 7.001476 1.41369228 -7.084116e-01 0.478689660
#> 343 4 5.667815 1.24677180 -1.337706e+00 0.180992136
#> 344 17 18.337598 2.40273961 -5.566968e-01 0.577734574
#> 345 5 6.334645 1.33284778 -1.001349e+00 0.316658251
#> 346 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 347 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 348 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 349 21 18.337598 2.40273961 1.108069e+00 0.267831809
#> 350 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 351 5 5.000984 1.15429461 -8.525138e-04 0.999319792
#> 352 17 12.336121 1.94289607 2.400478e+00 0.016373692
#> 353 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 354 21 21.671751 2.62360628 -2.560411e-01 0.797919132
#> 355 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 356 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 357 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 358 6 7.001476 1.41369228 -7.084116e-01 0.478689660
#> 359 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 360 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 361 8 5.667815 1.24677180 1.870579e+00 0.061403444
#> 362 5 3.667323 0.94250012 1.413981e+00 0.157367469
#> 363 6 4.334153 1.05373221 1.580901e+00 0.113900606
#> 364 22 20.338090 2.53756790 6.549225e-01 0.512517627
#> 365 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 366 8 5.667815 1.24677180 1.870579e+00 0.061403444
#> 367 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 368 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 369 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 370 2 3.667323 0.94250012 -1.769042e+00 0.076886794
#> 371 20 22.338582 2.66558409 -8.773243e-01 0.380310534
#> 372 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 373 9 10.335629 1.76315909 -7.575207e-01 0.448737987
#> 374 16 13.002952 1.99922042 1.499108e+00 0.133845550
#> 375 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 376 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 377 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 378 19 20.338090 2.53756790 -5.273118e-01 0.597977057
#> 379 8 7.001476 1.41369228 7.063234e-01 0.479987051
#> 380 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 381 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 382 13 12.336121 1.94289607 3.416953e-01 0.732580185
#> 383 5 5.000984 1.15429461 -8.525138e-04 0.999319792
#> 384 6 4.334153 1.05373221 1.580901e+00 0.113900606
#> 385 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 386 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 387 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 388 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 389 6 7.001476 1.41369228 -7.084116e-01 0.478689660
#> 390 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 391 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 392 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 393 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 394 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 395 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 396 9 8.335137 1.56288494 4.254072e-01 0.670539828
#> 397 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 398 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 399 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 400 9 7.001476 1.41369228 1.413691e+00 0.157452675
#> 401 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 402 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 403 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 404 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 405 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 406 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 407 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 408 7 7.001476 1.41369228 -1.044130e-03 0.999166905
#> 409 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 410 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 411 26 28.340058 3.01721207 -7.755695e-01 0.438003209
#> 412 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 413 13 12.336121 1.94289607 3.416953e-01 0.732580185
#> 414 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 415 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 416 20 19.671259 2.49343546 1.318426e-01 0.895108767
#> 417 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 418 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 419 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 420 5 5.000984 1.15429461 -8.525138e-04 0.999319792
#> 421 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 422 9 11.669291 1.88488922 -1.416153e+00 0.156730824
#> 423 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 424 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 425 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 426 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 427 30 27.673227 2.98019220 7.807459e-01 0.434951931
#> 428 1 4.334153 1.05373221 -3.164137e+00 0.001555434
#> 429 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 430 5 3.667323 0.94250012 1.413981e+00 0.157367469
#> 431 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 432 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 433 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 434 10 8.335137 1.56288494 1.065250e+00 0.286762989
#> 435 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 436 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 437 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 438 11 9.001968 1.63237562 1.224003e+00 0.220951271
#> 439 4 6.334645 1.33284778 -1.751622e+00 0.079838838
#> 440 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 441 1 2.333661 0.66649415 -2.001010e+00 0.045391330
#> 442 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 443 19 18.337598 2.40273961 2.756863e-01 0.782789004
#> 444 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 445 1 2.333661 0.66649415 -2.001010e+00 0.045391330
#> 446 6 4.334153 1.05373221 1.580901e+00 0.113900606
#> 447 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 448 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 449 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 450 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 451 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 452 10 13.669783 2.05400069 -1.786651e+00 0.073993879
#> 453 6 7.001476 1.41369228 -7.084116e-01 0.478689660
#> 454 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 455 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 456 26 21.671751 2.62360628 1.649733e+00 0.098997620
#> 457 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 458 11 10.335629 1.76315909 3.768069e-01 0.706317098
#> 459 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 460 5 3.667323 0.94250012 1.413981e+00 0.157367469
#> 461 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 462 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 463 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 464 9 10.335629 1.76315909 -7.575207e-01 0.448737987
#> 465 27 23.005412 2.70691089 1.475700e+00 0.140024514
#> 466 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 467 2 3.667323 0.94250012 -1.769042e+00 0.076886794
#> 468 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 469 10 9.668799 1.69902630 1.949359e-01 0.845443130
#> 470 7 7.001476 1.41369228 -1.044130e-03 0.999166905
#> 471 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 472 10 9.001968 1.63237562 6.113984e-01 0.540935839
#> 473 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 474 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 475 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 476 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 477 8 7.001476 1.41369228 7.063234e-01 0.479987051
#> 478 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 479 6 8.335137 1.56288494 -1.494120e+00 0.135144294
#> 480 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 481 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 482 7 7.001476 1.41369228 -1.044130e-03 0.999166905
#> 483 7 7.668307 1.49015700 -4.484808e-01 0.653806265
#> 484 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 485 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 486 12 11.002460 1.82503944 5.465854e-01 0.584663619
#> 487 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 488 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 489 7 5.000984 1.15429461 1.731807e+00 0.083307861
#> 490 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 491 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 492 30 29.673719 3.08992122 1.055952e-01 0.915903505
#> 493 8 6.334645 1.33284778 1.249471e+00 0.211492867
#> 494 7 8.335137 1.56288494 -8.542775e-01 0.392951254
#> 495 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 496 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 497 5 5.667815 1.24677180 -5.356351e-01 0.592210772
#> 498 7 7.001476 1.41369228 -1.044130e-03 0.999166905
#> 499 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 500 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 501 19 17.003936 2.30848272 8.646648e-01 0.387222785
#> 502 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 503 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 504 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 505 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 506 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 507 5 3.667323 0.94250012 1.413981e+00 0.157367469
#> 508 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 509 5 6.334645 1.33284778 -1.001349e+00 0.316658251
#> 510 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 511 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 512 8 7.668307 1.49015700 2.225895e-01 0.823855039
#> 513 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 514 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 515 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 516 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 517 25 28.340058 3.01721207 -1.107001e+00 0.268293366
#> 518 8 7.668307 1.49015700 2.225895e-01 0.823855039
#> 519 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 520 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 521 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 522 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 523 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 524 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 525 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 526 8 7.001476 1.41369228 7.063234e-01 0.479987051
#> 527 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 528 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 529 5 6.334645 1.33284778 -1.001349e+00 0.316658251
#> 530 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 531 19 20.338090 2.53756790 -5.273118e-01 0.597977057
#> 532 10 8.335137 1.56288494 1.065250e+00 0.286762989
#> 533 8 9.001968 1.63237562 -6.138098e-01 0.539341040
#> 534 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 535 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 536 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 537 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 538 19 21.671751 2.62360628 -1.018351e+00 0.308511387
#> 539 7 7.668307 1.49015700 -4.484808e-01 0.653806265
#> 540 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 541 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 542 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 543 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 544 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 545 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 546 7 5.667815 1.24677180 1.068508e+00 0.285291559
#> 547 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 548 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 549 5 5.000984 1.15429461 -8.525138e-04 0.999319792
#> 550 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 551 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 552 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 553 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 554 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 555 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 556 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 557 5 6.334645 1.33284778 -1.001349e+00 0.316658251
#> 558 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 559 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 560 27 24.339074 2.78772681 9.545148e-01 0.339823146
#> 561 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 562 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 563 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 564 25 23.005412 2.70691089 7.368502e-01 0.461213477
#> 565 10 8.335137 1.56288494 1.065250e+00 0.286762989
#> 566 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 567 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 568 20 19.671259 2.49343546 1.318426e-01 0.895108767
#> 569 7 5.667815 1.24677180 1.068508e+00 0.285291559
#> 570 8 5.667815 1.24677180 1.870579e+00 0.061403444
#> 571 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 572 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 573 16 16.337106 2.25988030 -1.491696e-01 0.881419775
#> 574 8 6.334645 1.33284778 1.249471e+00 0.211492867
#> 575 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 576 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 577 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 578 8 5.667815 1.24677180 1.870579e+00 0.061403444
#> 579 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 580 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 581 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 582 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 583 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 584 9 7.668307 1.49015700 8.936597e-01 0.371503999
#> 585 17 16.337106 2.25988030 2.933317e-01 0.769268647
#> 586 8 9.001968 1.63237562 -6.138098e-01 0.539341040
#> 587 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 588 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 589 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 590 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 591 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 592 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 593 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 594 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 595 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 596 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 597 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 598 21 22.338582 2.66558409 -5.021720e-01 0.615546559
#> 599 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 600 5 3.667323 0.94250012 1.413981e+00 0.157367469
#> 601 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 602 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 603 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 604 20 19.671259 2.49343546 1.318426e-01 0.895108767
#> 605 18 20.338090 2.53756790 -9.213900e-01 0.356846869
#> 606 8 7.001476 1.41369228 7.063234e-01 0.479987051
#> 607 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 608 5 5.667815 1.24677180 -5.356351e-01 0.592210772
#> 609 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 610 5 5.667815 1.24677180 -5.356351e-01 0.592210772
#> 611 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 612 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 613 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 614 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 615 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 616 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 617 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 618 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 619 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 620 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 621 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 622 6 4.334153 1.05373221 1.580901e+00 0.113900606
#> 623 17 15.670275 2.21020923 6.016286e-01 0.547421370
#> 624 7 5.667815 1.24677180 1.068508e+00 0.285291559
#> 625 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 626 9 9.001968 1.63237562 -1.205669e-03 0.999038016
#> 627 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 628 17 19.004428 2.44850757 -8.186326e-01 0.412996035
#> 629 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 630 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 631 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 632 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 633 14 13.002952 1.99922042 4.987183e-01 0.617977839
#> 634 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 635 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 636 15 19.671259 2.49343546 -1.873423e+00 0.061010020
#> 637 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 638 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 639 7 7.001476 1.41369228 -1.044130e-03 0.999166905
#> 640 22 20.338090 2.53756790 6.549225e-01 0.512517627
#> 641 6 4.334153 1.05373221 1.580901e+00 0.113900606
#> 642 2 3.667323 0.94250012 -1.769042e+00 0.076886794
#> 643 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 644 5 6.334645 1.33284778 -1.001349e+00 0.316658251
#> 645 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 646 1 2.333661 0.66649415 -2.001010e+00 0.045391330
#> 647 8 7.668307 1.49015700 2.225895e-01 0.823855039
#> 648 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 649 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 650 11 9.001968 1.63237562 1.224003e+00 0.220951271
#> 651 10 12.336121 1.94289607 -1.202391e+00 0.229211928
#> 652 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 653 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 654 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 655 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 656 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 657 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 658 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 659 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 660 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 661 27 23.005412 2.70691089 1.475700e+00 0.140024514
#> 662 6 9.001968 1.63237562 -1.839018e+00 0.065912542
#> 663 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 664 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 665 5 5.667815 1.24677180 -5.356351e-01 0.592210772
#> 666 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 667 1 2.333661 0.66649415 -2.001010e+00 0.045391330
#> 668 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 669 3 5.000984 1.15429461 -1.733512e+00 0.083004632
#> 670 10 11.002460 1.82503944 -5.492814e-01 0.582812384
#> 671 9 6.334645 1.33284778 1.999744e+00 0.045527894
#> 672 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 673 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 674 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 675 5 5.000984 1.15429461 -8.525138e-04 0.999319792
#> 676 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 677 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 678 12 11.002460 1.82503944 5.465854e-01 0.584663619
#> 679 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 680 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 681 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 682 5 5.000984 1.15429461 -8.525138e-04 0.999319792
#> 683 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 684 2 3.667323 0.94250012 -1.769042e+00 0.076886794
#> 685 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 686 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 687 5 3.667323 0.94250012 1.413981e+00 0.157367469
#> 688 9 9.001968 1.63237562 -1.205669e-03 0.999038016
#> 689 7 5.667815 1.24677180 1.068508e+00 0.285291559
#> 690 6 8.335137 1.56288494 -1.494120e+00 0.135144294
#> 691 5 3.667323 0.94250012 1.413981e+00 0.157367469
#> 692 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 693 2 5.000984 1.15429461 -2.599842e+00 0.009326659
#> 694 4 5.667815 1.24677180 -1.337706e+00 0.180992136
#> 695 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 696 13 11.669291 1.88488922 7.059880e-01 0.480195591
#> 697 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 698 9 7.668307 1.49015700 8.936597e-01 0.371503999
#> 699 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 700 8 7.001476 1.41369228 7.063234e-01 0.479987051
#> 701 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 702 19 15.670275 2.21020923 1.506520e+00 0.131933652
#> 703 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 704 9 8.335137 1.56288494 4.254072e-01 0.670539828
#> 705 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 706 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 707 17 16.337106 2.25988030 2.933317e-01 0.769268647
#> 708 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 709 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 710 10 9.668799 1.69902630 1.949359e-01 0.845443130
#> 711 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 712 5 7.001476 1.41369228 -1.415779e+00 0.156840170
#> 713 1 3.000492 0.81624798 -2.450839e+00 0.014252386
#> 714 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 715 2 4.334153 1.05373221 -2.215130e+00 0.026751172
#> 716 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 717 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 718 2 3.667323 0.94250012 -1.769042e+00 0.076886794
#> 719 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 720 8 9.001968 1.63237562 -6.138098e-01 0.539341040
#> 721 5 5.667815 1.24677180 -5.356351e-01 0.592210772
#> 722 3 5.000984 1.15429461 -1.733512e+00 0.083004632
#> 723 13 13.669783 2.05400069 -3.260870e-01 0.744358567
#> 724 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 725 10 7.668307 1.49015700 1.564730e+00 0.117646250
#> 726 9 7.001476 1.41369228 1.413691e+00 0.157452675
#> 727 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 728 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 729 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 730 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 731 4 5.667815 1.24677180 -1.337706e+00 0.180992136
#> 732 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 733 15 17.670767 2.35608263 -1.133562e+00 0.256978117
#> 734 1 2.333661 0.66649415 -2.001010e+00 0.045391330
#> 735 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 736 8 8.335137 1.56288494 -2.144351e-01 0.830207752
#> 737 22 21.004920 2.58094570 3.855485e-01 0.699831081
#> 738 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 739 10 7.668307 1.49015700 1.564730e+00 0.117646250
#> 740 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 741 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 742 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 743 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 744 16 14.336614 2.10735730 7.893234e-01 0.429922996
#> 745 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 746 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 747 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 748 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 749 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 750 4 6.334645 1.33284778 -1.751622e+00 0.079838838
#> 751 10 10.335629 1.76315909 -1.903569e-01 0.849029488
#> 752 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 753 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 754 25 21.671751 2.62360628 1.268578e+00 0.204591635
#> 755 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 756 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 757 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 758 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 759 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 760 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 761 10 9.668799 1.69902630 1.949359e-01 0.845443130
#> 762 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 763 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 764 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 765 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 766 4 4.334153 1.05373221 -3.171141e-01 0.751157001
#> 767 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 768 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 769 8 7.001476 1.41369228 7.063234e-01 0.479987051
#> 770 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 771 2 3.667323 0.94250012 -1.769042e+00 0.076886794
#> 772 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 773 7 7.668307 1.49015700 -4.484808e-01 0.653806265
#> 774 13 11.669291 1.88488922 7.059880e-01 0.480195591
#> 775 20 20.338090 2.53756790 -1.332337e-01 0.894008552
#> 776 27 29.006888 3.05378310 -6.571810e-01 0.511064513
#> 777 1 3.667323 0.94250012 -2.830050e+00 0.004654069
#> 778 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 779 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 780 18 12.336121 1.94289607 2.915173e+00 0.003554912
#> 781 1 2.333661 0.66649415 -2.001010e+00 0.045391330
#> 782 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 783 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 784 4 5.667815 1.24677180 -1.337706e+00 0.180992136
#> 785 5 5.667815 1.24677180 -5.356351e-01 0.592210772
#> 786 11 10.335629 1.76315909 3.768069e-01 0.706317098
#> 787 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 788 4 5.667815 1.24677180 -1.337706e+00 0.180992136
#> 789 10 9.668799 1.69902630 1.949359e-01 0.845443130
#> 790 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 791 6 6.334645 1.33284778 -2.510755e-01 0.801755749
#> 792 6 4.334153 1.05373221 1.580901e+00 0.113900606
#> 793 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 794 7 8.335137 1.56288494 -8.542775e-01 0.392951254
#> 795 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 796 11 9.668799 1.69902630 7.835083e-01 0.433328678
#> 797 8 7.668307 1.49015700 2.225895e-01 0.823855039
#> 798 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 799 19 18.337598 2.40273961 2.756863e-01 0.782789004
#> 800 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 801 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 802 5 5.667815 1.24677180 -5.356351e-01 0.592210772
#> 803 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 804 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 805 5 3.667323 0.94250012 1.413981e+00 0.157367469
#> 806 5 6.334645 1.33284778 -1.001349e+00 0.316658251
#> 807 11 7.668307 1.49015700 2.235800e+00 0.025364865
#> 808 8 5.667815 1.24677180 1.870579e+00 0.061403444
#> 809 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 810 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 811 13 13.669783 2.05400069 -3.260870e-01 0.744358567
#> 812 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 813 30 29.006888 3.05378310 3.252070e-01 0.745024412
#> 814 0 1.000000 0.01095397 -9.129110e+01 0.000000000
#> 815 6 9.001968 1.63237562 -1.839018e+00 0.065912542
#> 816 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 817 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 818 9 9.001968 1.63237562 -1.205669e-03 0.999038016
#> 819 1 1.666831 0.47134650 -1.414736e+00 0.157146034
#> 820 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 821 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 822 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 823 7 5.667815 1.24677180 1.068508e+00 0.285291559
#> 824 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 825 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 826 5 5.000984 1.15429461 -8.525138e-04 0.999319792
#> 827 13 11.669291 1.88488922 7.059880e-01 0.480195591
#> 828 8 6.334645 1.33284778 1.249471e+00 0.211492867
#> 829 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 830 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 831 4 3.667323 0.94250012 3.529732e-01 0.724108520
#> 832 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 833 5 4.334153 1.05373221 6.318936e-01 0.527456416
#> 834 5 5.000984 1.15429461 -8.525138e-04 0.999319792
#> 835 19 16.337106 2.25988030 1.178334e+00 0.238663359
#> 836 6 4.334153 1.05373221 1.580901e+00 0.113900606
#> 837 7 8.335137 1.56288494 -8.542775e-01 0.392951254
#> 838 8 6.334645 1.33284778 1.249471e+00 0.211492867
#> 839 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 840 27 29.673719 3.08992122 -8.653033e-01 0.386872338
#> 841 8 5.667815 1.24677180 1.870579e+00 0.061403444
#> 842 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 843 2 4.334153 1.05373221 -2.215130e+00 0.026751172
#> 844 6 5.000984 1.15429461 8.654774e-01 0.386776793
#> 845 6 5.667815 1.24677180 2.664363e-01 0.789903208
#> 846 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 847 18 16.337106 2.25988030 7.358330e-01 0.461832345
#> 848 10 7.668307 1.49015700 1.564730e+00 0.117646250
#> 849 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 850 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 851 21 20.338090 2.53756790 2.608444e-01 0.794212491
#> 852 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 853 1 3.000492 0.81624798 -2.450839e+00 0.014252386
#> 854 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 855 8 7.001476 1.41369228 7.063234e-01 0.479987051
#> 856 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 857 7 6.334645 1.33284778 4.991977e-01 0.617640087
#> 858 27 23.005412 2.70691089 1.475700e+00 0.140024514
#> 859 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 860 3 2.333661 0.66649415 9.997667e-01 0.317423430
#> 861 9 8.335137 1.56288494 4.254072e-01 0.670539828
#> 862 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 863 2 2.333661 0.66649415 -5.006216e-01 0.616637476
#> 864 2 1.666831 0.47134650 7.068459e-01 0.479662271
#> 865 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 866 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 867 1 2.333661 0.66649415 -2.001010e+00 0.045391330
#> 868 5 5.000984 1.15429461 -8.525138e-04 0.999319792
#> 869 2 3.000492 0.81624798 -1.225721e+00 0.220303808
#> 870 3 3.667323 0.94250012 -7.080346e-01 0.478923767
#> 871 4 5.000984 1.15429461 -8.671825e-01 0.385842041
#> 872 4 3.000492 0.81624798 1.224515e+00 0.220757976
#> 873 3 4.334153 1.05373221 -1.266122e+00 0.205469460
#> 874 23 21.004920 2.58094570 7.730034e-01 0.439520382
#> 875 5 7.001476 1.41369228 -1.415779e+00 0.156840170
#> 876 3 3.000492 0.81624798 -6.027899e-04 0.999519043
#> 877 7 7.668307 1.49015700 -4.484808e-01 0.653806265
plot(lsrq, sf = FastFood.sf)
#> Warning: bounding box has potentially an invalid value range for longlat data
# }