Component Density for a Parameterized MVN Mixture Model
cdensE.RdComputes component densities for points in a parameterized MVN mixture model.
Usage
cdensE(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensV(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensX(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensEII(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensVII(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensEEI(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensVEI(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensEVI(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensVVI(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensEEE(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensEEV(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensVEV(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensVVV(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensEVE(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensEVV(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensVEE(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensVVE(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensXII(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensXXI(data, logarithm = FALSE, parameters, warn = NULL, ...)
cdensXXX(data, logarithm = FALSE, parameters, warn = NULL, ...)Arguments
- data
A numeric vector, matrix, or data frame of observations. Categorical variables are not allowed. If a matrix or data frame, rows correspond to observations and columns correspond to variables.
- logarithm
A logical value indicating whether or not the logarithm of the component densities should be returned. The default is to return the component densities, obtained from the log component densities by exponentiation.
- parameters
The parameters of the model:
meanThe mean for each component. If there is more than one component, this is a matrix whose kth column is the mean of the kth component of the mixture model.
varianceA list of variance parameters for the model. The components of this list depend on the model specification. See the help file for
mclustVariancefor details.proMixing proportions for the components of the mixture. If the model includes a Poisson term for noise, there should be one more mixing proportion than the number of Gaussian components.
- warn
A logical value indicating whether or not a warning should be issued when computations fail. The default is
warn=FALSE.- ...
Catches unused arguments in indirect or list calls via
do.call.
Value
A numeric matrix whose [i,j]th
entry is the density of observation i in component j.
The densities are not scaled by mixing proportions.
Note
When one or more component densities are very large in magnitude, then it may be possible to compute the logarithm of the component densities but not the component densities themselves due to overflow.
Examples
# \donttest{
z2 <- unmap(hclass(hcVVV(faithful),2)) # initial value for 2 class case
model <- meVVV(data=faithful, z=z2)
cdensVVV(data=faithful, logarithm = TRUE, parameters = model$parameters)
#> [,1] [,2]
#> 1 -4.197962 -23.327906
#> 2 -23.342333 -2.639804
#> 3 -5.369492 -16.425216
#> 4 -15.294924 -3.232768
#> 5 -3.060038 -50.710265
#> 6 -13.290054 -7.761979
#> 7 -3.699704 -57.918268
#> 8 -5.334659 -26.752622
#> 9 -22.962876 -2.412796
#> 10 -3.034001 -44.933104
#> 11 -22.934312 -2.528941
#> 12 -3.676302 -32.771717
#> 13 -2.724501 -37.562422
#> 14 -27.479203 -3.332165
#> 15 -3.170498 -55.618395
#> 16 -20.214896 -2.518439
#> 17 -21.915710 -4.216529
#> 18 -3.455892 -59.675676
#> 19 -26.760842 -3.595670
#> 20 -2.679311 -39.367492
#> 21 -24.676501 -2.687279
#> 22 -27.479203 -3.332165
#> 23 -4.858440 -20.080789
#> 24 -7.357413 -10.919858
#> 25 -3.707075 -47.408698
#> 26 -4.826034 -25.481836
#> 27 -20.944700 -2.269342
#> 28 -2.921123 -33.631614
#> 29 -3.238694 -28.304652
#> 30 -2.776193 -45.080634
#> 31 -3.466375 -39.469218
#> 32 -3.010859 -45.669805
#> 33 -6.449804 -15.147156
#> 34 -2.893828 -33.676595
#> 35 -3.472704 -26.585813
#> 36 -21.731435 -2.312102
#> 37 -25.554020 -2.900109
#> 38 -3.677658 -59.639204
#> 39 -21.329762 -3.062301
#> 40 -4.247178 -61.991292
#> 41 -2.677669 -42.761619
#> 42 -20.946033 -2.714943
#> 43 -2.993015 -51.386831
#> 44 -22.685815 -3.270025
#> 45 -3.960485 -47.302375
#> 46 -6.598464 -20.802812
#> 47 -6.211837 -25.551593
#> 48 -20.374670 -2.305713
#> 49 -3.012673 -52.862464
#> 50 -19.230203 -2.593682
#> 51 -4.415900 -57.463454
#> 52 -4.155687 -59.620152
#> 53 -22.934312 -2.528941
#> 54 -3.677658 -59.639204
#> 55 -24.193790 -2.917515
#> 56 -3.702828 -62.476248
#> 57 -4.178361 -23.158393
#> 58 -22.961895 -5.472180
#> 59 -3.220395 -49.108148
#> 60 -2.680246 -42.118651
#> 61 -16.621517 -2.671928
#> 62 -2.929064 -49.161225
#> 63 -26.881283 -3.164999
#> 64 -3.442207 -58.957948
#> 65 -21.320242 -3.337036
#> 66 -4.816504 -50.784915
#> 67 -2.736993 -36.607377
#> 68 -3.452079 -54.126106
#> 69 -17.334988 -3.949120
#> 70 -4.544447 -53.441400
#> 71 -3.052678 -34.577311
#> 72 -20.567346 -2.316439
#> 73 -2.869289 -47.303898
#> 74 -3.793379 -30.306906
#> 75 -18.780967 -3.237428
#> 76 -5.551980 -68.561758
#> 77 -18.770649 -2.736682
#> 78 -3.090617 -49.336764
#> 79 -3.201066 -28.392013
#> 80 -4.826034 -25.481836
#> 81 -3.011010 -34.787362
#> 82 -2.723047 -43.012954
#> 83 -4.062219 -33.036185
#> 84 -11.298804 -5.524240
#> 85 -3.345808 -32.488922
#> 86 -4.208793 -66.504258
#> 87 -3.076628 -30.077285
#> 88 -2.841868 -48.182626
#> 89 -22.581164 -3.203542
#> 90 -3.857276 -35.951643
#> 91 -16.678900 -2.737894
#> 92 -4.225630 -47.419501
#> 93 -24.413541 -2.615064
#> 94 -3.870686 -58.569039
#> 95 -20.629889 -4.070450
#> 96 -3.710463 -39.347779
#> 97 -3.145918 -54.839806
#> 98 -3.587831 -24.925274
#> 99 -23.891950 -2.520996
#> 100 -3.791269 -62.817662
#> 101 -13.314929 -4.015144
#> 102 -3.620549 -47.127765
#> 103 -22.563187 -2.807059
#> 104 -2.852246 -48.725153
#> 105 -2.924853 -34.554491
#> 106 -26.172906 -3.091087
#> 107 -3.211476 -56.013763
#> 108 -24.406371 -2.696018
#> 109 -3.729394 -62.392134
#> 110 -4.061563 -25.984956
#> 111 -4.136478 -54.869882
#> 112 -15.940531 -2.852310
#> 113 -4.281280 -65.752555
#> 114 -2.758530 -44.560136
#> 115 -23.139134 -3.748921
#> 116 -3.024552 -52.518067
#> 117 -20.025202 -3.417245
#> 118 -3.127196 -52.956969
#> 119 -21.540990 -3.130198
#> 120 -3.362336 -48.054637
#> 121 -16.003038 -5.076151
#> 122 -4.349739 -32.007303
#> 123 -2.792823 -38.748925
#> 124 -20.567346 -2.316439
#> 125 -3.595774 -54.494859
#> 126 -3.719606 -27.759651
#> 127 -26.996373 -3.552868
#> 128 -2.807859 -48.321385
#> 129 -17.801948 -2.616670
#> 130 -4.095762 -57.353351
#> 131 -27.507973 -3.569953
#> 132 -2.932976 -38.642050
#> 133 -13.219165 -6.598774
#> 134 -3.924297 -46.755621
#> 135 -27.188030 -3.355339
#> 136 -2.728314 -44.556354
#> 137 -23.709163 -2.491718
#> 138 -3.983323 -65.582239
#> 139 -21.075819 -2.254025
#> 140 -3.650663 -26.069747
#> 141 -2.704316 -39.618171
#> 142 -16.326223 -2.794102
#> 143 -2.847325 -49.422198
#> 144 -4.045263 -58.391303
#> 145 -2.958232 -41.064783
#> 146 -19.435158 -2.621356
#> 147 -3.068862 -52.205973
#> 148 -23.376850 -2.685890
#> 149 -6.763224 -77.891170
#> 150 -23.754624 -2.623325
#> 151 -5.104238 -67.202584
#> 152 -2.943287 -31.692611
#> 153 -13.516733 -4.266377
#> 154 -2.956467 -51.358696
#> 155 -4.605864 -19.879599
#> 156 -4.048571 -30.189017
#> 157 -2.795904 -47.949919
#> 158 -6.048704 -43.036756
#> 159 -23.754624 -2.623325
#> 160 -4.868659 -37.175298
#> 161 -24.424929 -4.196397
#> 162 -3.473474 -39.792856
#> 163 -19.516176 -2.456391
#> 164 -3.285133 -27.903995
#> 165 -5.999115 -17.754059
#> 166 -3.425381 -49.479805
#> 167 -14.207790 -3.676640
#> 168 -4.424334 -69.131072
#> 169 -22.648320 -2.350947
#> 170 -5.022950 -58.257673
#> 171 -24.420125 -2.683646
#> 172 -18.892222 -2.315269
#> 173 -3.260305 -49.672861
#> 174 -6.086198 -14.806481
#> 175 -2.757288 -37.731271
#> 176 -2.681165 -42.607500
#> 177 -3.867798 -46.141116
#> 178 -19.239233 -4.027522
#> 179 -3.625995 -35.349204
#> 180 -3.163973 -35.561099
#> 181 -21.935642 -2.425455
#> 182 -3.260305 -49.672861
#> 183 -2.841467 -40.992268
#> 184 -4.038653 -28.833247
#> 185 -22.081202 -2.412819
#> 186 -2.849526 -44.792442
#> 187 -3.225392 -36.894643
#> 188 -27.188030 -3.355339
#> 189 -2.800981 -46.048960
#> 190 -18.619497 -2.376900
#> 191 -3.484011 -58.647539
#> 192 -21.874287 -2.752047
#> 193 -4.179506 -57.580043
#> 194 -3.189917 -37.341307
#> 195 -2.996970 -30.808798
#> 196 -2.704316 -39.618171
#> 197 -6.608032 -26.436920
#> 198 -2.869070 -42.356538
#> 199 -20.000070 -2.924230
#> 200 -3.351040 -52.911852
#> 201 -17.793378 -2.672037
#> 202 -2.722907 -43.533303
#> 203 -5.032900 -42.701164
#> 204 -22.946061 -2.429771
#> 205 -3.168950 -50.499176
#> 206 -27.737489 -3.448581
#> 207 -2.870129 -42.388558
#> 208 -3.912003 -31.230266
#> 209 -24.248577 -2.673448
#> 210 -2.852246 -48.725153
#> 211 -13.414135 -6.405328
#> 212 -3.242152 -54.626111
#> 213 -24.967565 -2.741435
#> 214 -3.377164 -26.866904
#> 215 -6.924280 -15.976850
#> 216 -2.891784 -37.973694
#> 217 -17.613974 -3.401969
#> 218 -5.470209 -65.202518
#> 219 -20.568685 -2.238339
#> 220 -2.888887 -35.527396
#> 221 -24.413541 -2.615064
#> 222 -2.742433 -41.035802
#> 223 -23.974824 -2.840374
#> 224 -3.366504 -45.814869
#> 225 -2.915115 -32.036623
#> 226 -2.753490 -35.545441
#> 227 -2.802601 -34.253551
#> 228 -2.722189 -39.554079
#> 229 -4.089498 -27.945174
#> 230 -2.958889 -49.009002
#> 231 -4.055045 -32.541083
#> 232 -16.953218 -3.397325
#> 233 -3.409814 -40.685358
#> 234 -20.879977 -2.964063
#> 235 -4.097194 -50.902135
#> 236 -22.330375 -2.393566
#> 237 -22.727043 -2.478507
#> 238 -2.805091 -39.753714
#> 239 -3.018993 -31.139851
#> 240 -14.374714 -3.799218
#> 241 -3.008801 -35.278518
#> 242 -21.777249 -4.372194
#> 243 -3.983323 -65.582239
#> 244 -9.754270 -7.750691
#> 245 -3.107232 -52.380234
#> 246 -3.616466 -29.739030
#> 247 -18.892222 -2.315269
#> 248 -2.724757 -44.058193
#> 249 -16.384450 -4.578577
#> 250 -3.320311 -41.221848
#> 251 -18.901661 -2.449105
#> 252 -2.815687 -47.100028
#> 253 -4.347960 -20.388537
#> 254 -3.867798 -46.141116
#> 255 -3.979570 -41.033588
#> 256 -3.437195 -28.390477
#> 257 -3.849179 -28.079956
#> 258 -2.815687 -47.100028
#> 259 -20.185417 -2.278720
#> 260 -2.679752 -40.358850
#> 261 -3.680269 -56.644036
#> 262 -2.956702 -50.248606
#> 263 -21.366355 -2.826749
#> 264 -2.841467 -40.992268
#> 265 -27.853767 -4.245748
#> 266 -16.147464 -2.829734
#> 267 -4.204452 -55.521276
#> 268 -2.817372 -36.347359
#> 269 -24.104705 -3.678010
#> 270 -4.123883 -49.898080
#> 271 -27.361985 -3.380903
#> 272 -3.541020 -45.116720
#> attr(,"logarithm")
#> [1] TRUE
#> attr(,"modelName")
#> [1] "VVV"
#> attr(,"returnCode")
#> [1] 0
data(cross)
z2 <- unmap(cross[,1])
model <- meEEV(data = cross[,-1], z = z2)
EEVdensities <- cdensEEV( data = cross[,-1], parameters = model$parameters)
cbind(cross[,-1],map(EEVdensities))# }
#> X1 X2 map(EEVdensities)
#> 1 1.262954285 -14.370462129 1
#> 2 -0.326233361 4.418706353 1
#> 3 1.329799263 3.794430288 1
#> 4 1.272429321 16.865135087 1
#> 5 0.414641434 9.310628915 1
#> 6 -1.539950042 0.736292793 2
#> 7 -0.928567035 -0.742713858 2
#> 8 -0.294720447 5.454660878 1
#> 9 -0.005767173 -7.986781308 1
#> 10 2.404653389 0.948792512 2
#> 11 0.763593461 3.175870260 1
#> 12 -0.799009249 4.953540226 1
#> 13 -1.147657009 -10.208978717 1
#> 14 -0.289461574 13.161163849 1
#> 15 -0.299215118 6.319050396 1
#> 16 -0.411510833 22.564000336 1
#> 17 0.252223448 -17.010244293 1
#> 18 -0.891921127 -5.308315112 1
#> 19 0.435683299 -15.430520672 1
#> 20 -1.237538422 -3.788981080 1
#> 21 -0.224267885 2.791272389 1
#> 22 0.377395646 15.323135274 1
#> 23 0.133336361 -3.990463239 1
#> 24 0.804189510 -10.787373750 1
#> 25 -0.057106774 -2.766428228 1
#> 26 0.503607972 5.589487825 1
#> 27 1.085769362 1.637119723 1
#> 28 -0.690953840 11.865608381 1
#> 29 -1.284599354 -2.690183821 1
#> 30 0.046726172 -14.833995679 1
#> 31 -0.235706556 8.563486227 1
#> 32 -0.542888255 -10.018106578 1
#> 33 -0.433310317 5.552698281 1
#> 34 -0.649471647 4.621443448 1
#> 35 0.726750747 3.325131934 1
#> 36 1.151911754 15.515047175 1
#> 37 0.992160365 -1.855301100 1
#> 38 -0.429513109 -11.827756259 1
#> 39 1.238304101 0.571266866 2
#> 40 -0.279346282 -2.087797060 1
#> 41 1.757903090 5.715542948 1
#> 42 0.560746091 14.711798569 1
#> 43 -0.452783973 -16.274948214 1
#> 44 -0.832043296 -1.924973563 1
#> 45 -1.166570547 0.633295272 2
#> 46 -1.065590580 4.947369026 1
#> 47 -1.563782051 -6.271411914 1
#> 48 1.156536997 3.515093481 1
#> 49 0.832047129 3.432701332 1
#> 50 -0.227328691 -0.111354928 2
#> 51 0.266137362 -1.119914878 1
#> 52 -0.376702719 13.200701339 1
#> 53 2.441364629 6.065358088 1
#> 54 -0.795339117 17.607827369 1
#> 55 -0.054877474 -2.421369111 1
#> 56 0.250141323 -11.200963665 1
#> 57 0.618243294 -3.561326303 1
#> 58 -0.172623503 0.876569891 1
#> 59 -2.223900274 -2.145482551 2
#> 60 -1.263614385 -3.706451609 1
#> 61 0.358728896 -14.194962440 1
#> 62 -0.011045478 -7.175484858 1
#> 63 -0.940649163 -9.866131045 1
#> 64 -0.115825322 2.774778738 1
#> 65 -0.814968709 3.103156113 1
#> 66 0.242263481 13.856832788 1
#> 67 -1.425098395 -2.965627731 1
#> 68 0.365941123 8.535504157 1
#> 69 0.248412649 -4.313300281 1
#> 70 0.065288182 -13.633981155 1
#> 71 0.019156392 3.910829903 1
#> 72 0.257338377 -4.675830003 1
#> 73 -0.649010078 -7.511031297 1
#> 74 -0.119168762 -6.809828484 1
#> 75 0.664135700 9.805531457 1
#> 76 1.100969102 14.151896257 1
#> 77 0.143771481 9.066279291 1
#> 78 -0.117753598 -2.458421938 1
#> 79 -0.912068367 -11.787115875 1
#> 80 -1.437586241 2.003164478 1
#> 81 -0.797089525 10.020898654 1
#> 82 1.254083106 7.536549576 1
#> 83 0.772142186 2.830650915 1
#> 84 -0.219515627 1.999962649 1
#> 85 -0.424810283 -7.592538509 1
#> 86 -0.418980099 3.994247931 1
#> 87 0.996986861 0.502173998 2
#> 88 -0.275778029 0.611751506 1
#> 89 1.256018817 -1.817655681 1
#> 90 0.646674390 -10.422137286 1
#> 91 1.299312303 -5.334689431 1
#> 92 -0.873262112 6.894588456 1
#> 93 0.008370960 0.350353050 1
#> 94 -0.880871723 0.131821312 2
#> 95 0.596259017 -1.676852712 1
#> 96 0.119717641 12.605317446 1
#> 97 -0.282173877 0.166370131 2
#> 98 1.455988401 2.242764105 1
#> 99 0.229019591 1.342986621 1
#> 100 0.996543929 -8.669098624 1
#> 101 0.781859185 -0.598200967 2
#> 102 -0.776776622 11.582298370 1
#> 103 -0.615989908 4.123127335 1
#> 104 0.046580303 -13.068254611 1
#> 105 -1.130385778 0.696080492 2
#> 106 0.576718782 5.039057457 1
#> 107 -1.280749432 -0.674519130 2
#> 108 1.625447303 7.044279280 1
#> 109 -0.500696596 -1.554017076 1
#> 110 1.678297208 -9.461644006 1
#> 111 -0.412519887 6.565061509 1
#> 112 -0.972286836 2.363987184 1
#> 113 0.025382868 4.892920732 1
#> 114 0.027475337 9.369542685 1
#> 115 -1.680182722 1.777555383 1
#> 116 1.053750863 -14.666204586 1
#> 117 -1.119599105 1.089362091 1
#> 118 0.335617210 -14.736797569 1
#> 119 0.494795767 -4.779387954 1
#> 120 0.138052709 8.583118128 1
#> 121 -0.118792026 -15.485855959 1
#> 122 0.197684262 0.956885579 1
#> 123 -1.068692711 -5.478016469 1
#> 124 -0.803213217 -2.710772844 1
#> 125 -1.113765136 8.785822722 1
#> 126 1.580091684 4.104078024 1
#> 127 1.497818761 11.649672607 1
#> 128 0.262645459 -10.198819855 1
#> 129 -1.232901200 -7.825143157 1
#> 130 -0.003723534 -6.794732627 1
#> 131 1.511672283 -1.166718152 2
#> 132 -0.475698284 -9.016212019 1
#> 133 0.797916438 -7.378814513 1
#> 134 -0.974002561 -8.770972218 1
#> 135 0.689372698 5.438784678 1
#> 136 -0.955839103 4.939088294 1
#> 137 -1.231707058 8.247893912 1
#> 138 -0.956891881 23.954097300 1
#> 139 -0.869782874 -1.622313589 1
#> 140 -0.910680682 6.165132895 1
#> 141 0.741276305 29.397730670 1
#> 142 0.068511533 5.045404136 1
#> 143 -0.323750755 -0.621155677 1
#> 144 -1.086503047 -8.751986424 1
#> 145 -1.015928947 -4.919279272 1
#> 146 -0.767790185 -15.198230952 1
#> 147 -1.119720061 -14.151354291 1
#> 148 -0.448174237 -3.644884426 1
#> 149 0.471736374 2.873577762 1
#> 150 -1.180490683 0.363849135 2
#> 151 1.470256997 -3.510086065 1
#> 152 -1.311420592 -16.373000071 1
#> 153 -0.096524923 5.932626392 1
#> 154 2.369719908 4.136595054 1
#> 155 0.890626476 14.549637031 1
#> 156 -0.252183161 -16.705714453 1
#> 157 -0.865763755 -2.581414949 1
#> 158 0.582586000 15.752896998 1
#> 159 -0.012529347 1.047722514 1
#> 160 -0.374854762 12.458278424 1
#> 161 0.317885735 5.167988214 1
#> 162 -0.488805635 1.228417308 1
#> 163 2.658658027 8.227943901 1
#> 164 1.680278205 -16.207436862 1
#> 165 0.779584009 -3.058925752 1
#> 166 0.713240520 5.456381150 1
#> 167 -0.542881937 12.070172795 1
#> 168 0.885778374 6.905585591 1
#> 169 -0.348594685 1.743531002 1
#> 170 -1.008054578 10.265100215 1
#> 171 1.883182542 0.124783240 2
#> 172 -0.928971079 -9.947753191 1
#> 173 -0.294196454 -0.226463752 2
#> 174 -0.614950271 -1.473060039 1
#> 175 -0.947075792 3.330537731 1
#> 176 0.598975150 -3.427420825 1
#> 177 -1.523614882 5.876571324 1
#> 178 -0.206189002 18.552076255 1
#> 179 -0.574295414 -16.169804432 1
#> 180 -1.390166037 5.256694120 1
#> 181 -0.070417383 -6.504778115 1
#> 182 -0.430879530 -5.662481985 1
#> 183 -0.592225373 -16.345854493 1
#> 184 0.981116160 -2.333601885 1
#> 185 0.532409357 3.011690461 1
#> 186 -0.090456124 -12.844508514 1
#> 187 0.156490492 17.447654098 1
#> 188 -0.737311691 -6.835771919 1
#> 189 -0.201341206 -20.508985274 1
#> 190 1.102176595 -1.026456898 2
#> 191 -0.016748256 21.166709991 1
#> 192 0.161788634 14.366887229 1
#> 193 2.024761390 11.497009599 1
#> 194 -0.703694254 7.100737723 1
#> 195 0.960792384 4.153188441 1
#> 196 1.790485054 -3.942622204 1
#> 197 -1.064165163 -13.570263083 1
#> 198 0.017636546 -20.006515182 1
#> 199 -0.389908629 -10.608051982 1
#> 200 -0.490832752 -16.044842013 1
#> 201 -1.045717652 -8.891272253 1
#> 202 -0.896211264 6.556398195 1
#> 203 1.269387164 -7.962164231 1
#> 204 0.593840949 -13.845972754 1
#> 205 0.775634319 -8.750041223 1
#> 206 1.557370376 -15.463225713 1
#> 207 -0.365401797 7.233817853 1
#> 208 0.816556449 -13.516084530 1
#> 209 -0.060634778 -1.309491640 1
#> 210 -0.501378318 5.215127511 1
#> 211 0.926062725 10.813730185 1
#> 212 0.036937691 17.045197079 1
#> 213 -1.066200174 -15.842037091 1
#> 214 -0.238456353 8.320921224 1
#> 215 1.495223444 -5.008879512 1
#> 216 1.172158547 -1.625257244 1
#> 217 -1.457707210 13.026962568 1
#> 218 0.095056227 -5.464183076 1
#> 219 0.847664964 6.114261873 1
#> 220 -1.624364530 -0.842018763 2
#> 221 1.408563357 -4.410776626 1
#> 222 -0.541760362 12.695934450 1
#> 223 0.278664724 -2.021164108 1
#> 224 -0.193972745 -1.912459406 1
#> 225 1.576158181 6.267406264 1
#> 226 -1.475547635 8.236642547 1
#> 227 -0.144608207 -8.310368843 1
#> 228 -1.075010191 10.321859366 1
#> 229 0.406542732 -5.722785388 1
#> 230 2.229262202 -7.977989776 1
#> 231 -1.514497008 -20.998230162 1
#> 232 -0.061707422 -1.309417242 1
#> 233 -0.147270790 2.852676214 1
#> 234 1.541593069 -6.367229890 1
#> 235 -0.981855669 11.179400023 1
#> 236 0.496578173 5.581369757 1
#> 237 1.696947881 0.899127608 2
#> 238 -0.260736309 16.269331389 1
#> 239 -0.705928586 -13.521869810 1
#> 240 -0.161178506 2.570764187 1
#> 241 0.501321828 7.611362679 1
#> 242 -1.013539670 -8.958083738 1
#> 243 1.614752235 -2.311687121 1
#> 244 0.005641985 -0.502704390 1
#> 245 -2.904899060 -4.005047159 1
#> 246 -1.107164819 0.627255927 2
#> 247 1.547566933 -1.392045354 2
#> 248 -0.976830350 -7.481371135 1
#> 249 -0.101503448 6.853899171 1
#> 250 0.042650250 -5.188562393 1
#> 251 -0.797552249 -0.626368228 2
#> 252 10.322980923 0.481335326 2
#> 253 0.781313160 1.695271084 1
#> 254 -2.655045308 -1.761226294 2
#> 255 4.610996449 0.198013015 2
#> 256 2.549822711 0.397349099 2
#> 257 3.460893446 0.029225495 2
#> 258 9.043239051 2.560273389 2
#> 259 -2.573692121 1.257127712 2
#> 260 -2.136059016 -0.534537686 2
#> 261 -1.833069305 -0.625227429 2
#> 262 9.652248051 0.913848687 2
#> 263 17.552500071 1.007199535 2
#> 264 8.680086602 0.719291823 2
#> 265 9.345641296 -0.604711661 2
#> 266 15.919862434 0.539054406 2
#> 267 -5.144851323 -0.076830886 2
#> 268 -13.232546008 1.849919560 2
#> 269 -9.993298001 -0.854907551 2
#> 270 2.289630502 0.032637295 2
#> 271 0.210102128 -1.025059481 1
#> 272 -24.443327651 -0.982249076 2
#> 273 10.667603263 0.004101957 2
#> 274 -1.977796778 -0.233427178 2
#> 275 -0.510054846 -0.498888219 2
#> 276 3.659080585 1.549712963 2
#> 277 -11.784869547 0.087496917 2
#> 278 -6.360221582 1.318701131 2
#> 279 9.305025029 -0.981224119 2
#> 280 17.754848707 -0.245622588 2
#> 281 6.187725661 -1.403933837 2
#> 282 6.644182950 1.440893147 2
#> 283 -15.374432086 -0.981359991 2
#> 284 9.473578117 1.474244904 2
#> 285 10.109151981 -0.991197245 2
#> 286 -3.191328052 -0.094497345 2
#> 287 1.694149680 -2.875141684 1
#> 288 8.314200246 -0.246866101 2
#> 289 19.374307588 0.014744490 2
#> 290 -9.987654084 -1.919087703 2
#> 291 9.265573999 -0.287813744 2
#> 292 12.394392748 -0.346637445 2
#> 293 8.233299467 -1.839588585 2
#> 294 2.642610883 0.898588941 2
#> 295 -1.365647622 -1.212855011 2
#> 296 1.484022958 -0.218964232 2
#> 297 7.817196875 0.564268161 2
#> 298 -9.702310440 -0.525434376 2
#> 299 -11.000987714 0.744374225 2
#> 300 -6.403002264 0.128981753 2
#> 301 -12.816284997 1.488274257 2
#> 302 -15.024099707 -0.662681951 2
#> 303 12.413125191 -1.160655001 2
#> 304 -8.277071250 0.358774234 2
#> 305 -4.540410394 -0.194846384 2
#> 306 -10.212586314 -0.295282008 2
#> 307 4.614957495 0.496640424 2
#> 308 4.751899044 0.484912788 2
#> 309 10.694225916 0.018784501 2
#> 310 -4.158327218 0.634774565 2
#> 311 11.169623593 0.754444088 2
#> 312 1.233193967 0.833589035 2
#> 313 -11.696807150 0.965761296 2
#> 314 10.362680483 1.293879968 2
#> 315 13.621027301 -0.136551021 2
#> 316 7.219240884 -0.440138688 2
#> 317 -3.874832476 -1.227283914 2
#> 318 -12.102308462 -0.237653070 2
#> 319 0.336978632 -0.926858157 1
#> 320 -12.111496103 0.411235356 2
#> 321 -16.326038843 -0.198864577 2
#> 322 6.336301786 -0.557449639 2
#> 323 -2.691176974 -0.977157122 2
#> 324 -3.590021666 0.060735249 2
#> 325 -5.789855969 -0.597229480 2
#> 326 11.840445493 -1.258948697 2
#> 327 -14.264710933 -1.410047202 2
#> 328 -4.000467824 1.101304079 2
#> 329 5.095647701 -0.677242026 2
#> 330 2.612931070 -0.762173508 2
#> 331 -5.539898991 -0.291748602 2
#> 332 -0.558070369 -0.575188529 2
#> 333 -1.733492295 -0.443941868 2
#> 334 15.148385537 -0.312570444 2
#> 335 0.923164615 -0.603004426 2
#> 336 -5.893517821 -1.093934720 2
#> 337 10.679176797 0.714706191 2
#> 338 -11.451327046 -0.108812263 2
#> 339 4.842581221 -1.443797935 2
#> 340 11.077653524 0.806123264 2
#> 341 -10.491362671 -1.739835078 2
#> 342 2.917885035 -0.401320309 2
#> 343 8.557806375 -0.287582489 2
#> 344 10.056902417 -0.938407400 2
#> 345 13.715721419 0.287667139 2
#> 346 17.262435687 -1.505401124 2
#> 347 1.801595752 1.519297013 2
#> 348 -7.624714453 0.367409356 2
#> 349 -6.811807858 1.699862409 2
#> 350 6.255941547 0.644196977 2
#> 351 -14.156260870 -1.687801029 2
#> 352 4.502104199 0.647645994 2
#> 353 -10.394267936 0.448794227 2
#> 354 -8.326811055 1.026302158 2
#> 355 3.077141028 1.074978223 2
#> 356 -5.306651663 0.458309613 2
#> 357 -7.455945433 0.631586758 2
#> 358 -5.973571888 -0.580466398 2
#> 359 12.747967674 1.584192142 2
#> 360 -12.343521084 -1.763992940 2
#> 361 0.979746508 -1.880621970 1
#> 362 -4.201400270 -1.291719044 2
#> 363 26.655690270 0.909670446 2
#> 364 -1.420444621 -1.107755682 2
#> 365 16.374827460 -0.384123875 2
#> 366 7.773682959 0.082734834 2
#> 367 -14.097988979 -0.483882474 2
#> 368 4.639103719 -2.084741125 2
#> 369 6.265975609 1.167586964 2
#> 370 0.228789905 -0.076825771 2
#> 371 -17.566049711 0.530421395 2
#> 372 20.208228628 0.004908796 2
#> 373 -1.689634579 -0.530231430 2
#> 374 -12.611260707 0.102202410 2
#> 375 11.235226552 0.815459636 2
#> 376 -2.223704074 -1.506521863 2
#> 377 2.210035640 -1.157180172 2
#> 378 -7.008512017 1.301554937 2
#> 379 -16.117975627 -0.905640775 2
#> 380 -1.507714704 0.015563481 2
#> 381 6.758819432 -1.428005197 2
#> 382 -0.153210630 0.687979702 1
#> 383 0.248210766 0.594196501 1
#> 384 1.999315324 -0.270315244 2
#> 385 3.587686423 1.554076076 2
#> 386 -2.353665715 -0.510742458 2
#> 387 -2.728598617 -0.291842736 2
#> 388 -6.602146063 1.101438165 2
#> 389 -12.436692423 0.458665215 2
#> 390 -12.975186359 0.851908039 2
#> 391 -7.076791478 1.466199919 2
#> 392 -6.682340156 0.243863295 2
#> 393 -3.518822223 0.649421934 2
#> 394 -10.941795563 -0.641118156 2
#> 395 -8.013650322 0.464459771 2
#> 396 13.484453680 -0.309200447 2
#> 397 3.346551999 1.276020709 2
#> 398 2.349954751 -0.047611220 2
#> 399 -0.220894711 0.030101166 2
#> 400 -8.259203192 -0.003580270 2
#> 401 -5.326957960 -2.034572643 2
#> 402 -3.338937501 -0.992819963 2
#> 403 0.791318315 1.963858056 1
#> 404 -0.312537103 0.706528773 1
#> 405 16.257368421 0.039674980 2
#> 406 -3.062124587 -0.158518590 2
#> 407 -6.740669300 -0.162257551 2
#> 408 -14.752231548 0.438821912 2
#> 409 -9.010689082 0.780699292 2
#> 410 23.361946541 -0.981205622 2
#> 411 2.728789336 -0.141585732 2
#> 412 8.178726494 -1.256248953 2
#> 413 1.870649530 -0.429033676 2
#> 414 1.602126018 0.508776266 2
#> 415 -1.491884984 -1.446889743 2
#> 416 5.013932580 1.019512829 2
#> 417 12.999009631 1.178546976 2
#> 418 8.112213546 -0.010258765 2
#> 419 -1.998315400 0.268624871 2
#> 420 0.955721841 1.342028872 1
#> 421 -13.042987501 -0.583606443 2
#> 422 10.246965512 -0.937000891 2
#> 423 16.324422397 -1.152157056 2
#> 424 -13.599348594 -0.975183431 2
#> 425 -0.162781728 -0.711413598 1
#> 426 -7.921692885 0.371912476 2
#> 427 -10.777293894 -0.943514417 2
#> 428 9.618830620 -0.274367308 2
#> 429 10.500631726 0.154468494 2
#> 430 18.269626463 -1.288653202 2
#> 431 4.501554668 1.419102319 2
#> 432 -16.404748009 1.307827762 2
#> 433 4.402449548 -1.804975774 2
#> 434 -6.245004574 -0.484069527 2
#> 435 -1.791580607 -0.373211780 2
#> 436 2.177586688 0.169085902 2
#> 437 0.633172530 -1.172983603 1
#> 438 7.147314594 -0.376196737 2
#> 439 -5.898408265 0.783127640 2
#> 440 -6.097185874 0.991171304 2
#> 441 1.654366629 0.229284475 2
#> 442 7.899374403 0.336850949 2
#> 443 -3.530078214 -0.647231999 2
#> 444 -6.020534746 -0.443206682 2
#> 445 -9.091199188 1.161751761 2
#> 446 -6.757475362 0.065051010 2
#> 447 -2.551976970 -0.682467580 2
#> 448 -10.492226833 1.634341658 2
#> 449 6.221024872 -0.584849244 2
#> 450 -18.508838677 1.129936001 2
#> 451 -1.387570525 0.581201043 2
#> 452 -13.004048795 0.379293067 2
#> 453 10.945357773 -0.310740876 2
#> 454 -4.600540233 0.886390001 2
#> 455 10.156848815 -1.641864750 2
#> 456 -3.776789414 -0.988563742 2
#> 457 -1.914657611 -0.244003429 2
#> 458 -9.185947020 0.156056926 2
#> 459 -27.741272559 0.102051958 2
#> 460 14.815290267 -0.287458172 2
#> 461 -12.700926056 -0.293194886 2
#> 462 23.086238678 0.469477058 2
#> 463 2.930343425 -0.662588512 2
#> 464 -5.089840368 -2.190372666 2
#> 465 6.290088088 0.003854672 2
#> 466 7.926435876 0.862942829 2
#> 467 -2.049794739 0.980223359 2
#> 468 1.226706740 -0.291724771 2
#> 469 16.590674096 -0.061013476 2
#> 470 -12.648525462 1.511868401 2
#> 471 -0.441747634 -0.643609065 1
#> 472 7.147390560 -0.130950479 2
#> 473 -12.726211639 0.485211453 2
#> 474 -16.109346268 -0.645182435 2
#> 475 12.189575992 -0.463956220 2
#> 476 -6.729900347 0.567249697 2
#> 477 -9.337072301 -0.723407834 2
#> 478 -0.325549223 0.455884554 1
#> 479 -4.989155458 -1.197934626 2
#> 480 -5.029800765 -2.018180550 2
#> 481 -12.778860448 0.619723405 2
#> 482 -8.171638687 -0.132857466 2
#> 483 7.628697851 -0.434960740 2
#> 484 4.495167897 -0.521754179 2
#> 485 -5.740429658 0.992288426 2
#> 486 21.739546330 -1.085422408 2
#> 487 13.328173125 0.959832414 2
#> 488 -6.650835828 -1.039010541 2
#> 489 -0.879886196 -0.137841967 2
#> 490 -29.127471591 -0.214708418 2
#> 491 8.613572923 0.573718585 2
#> 492 5.034007572 -1.776449315 2
#> 493 -4.479306416 -0.256392295 2
#> 494 -1.745822786 -0.138550636 2
#> 495 0.777014412 0.557684974 2
#> 496 9.157567844 1.122346289 2
#> 497 -8.729262206 -0.982147207 2
#> 498 9.597171614 0.326905556 2
#> 499 6.799582393 0.447826608 2
#> 500 -6.329270648 1.183724120 2