Spherical density estimation
Usage
# S3 method for class 'spherical'
density(x, ...)
density_calc(
x,
FUN = exponential_kamb,
n = 128L,
sigma = 3,
weights = NULL,
upper.hem = FALSE,
r = 1
)Arguments
- x
object of class
"Vec3","Line","Ray", or"Plane", where the rows are the observations and the columns are the coordinates.- ...
arguments passed to
density_calc()- FUN
density estimation function if
kamb=TRUE; one ofexponential_kamb()(the default), kamb_count, andschmidt_count().- n
integer. Grid size.
128by default.- sigma
numeric. Radius for Kamb circle used for counting. 3 by default.
- weights
(optional) numeric vector of length of
nrow(x). The relative weight to be applied to each input measurement. The array will be normalized to sum to 1, so absolute value of theweightsdo not affect the result. Defaults toNULL- upper.hem
logical. Whether the projection is shown for upper hemisphere (
TRUE) or lower hemisphere (FALSE, the default).- r
numeric. radius of stereonet circle
Examples
set.seed(20250411)
test <- rfb(100, mu = Line(120, 10), k = 5, A = diag(c(-1, 0, 1)))
density(x = test, n = 100, sigma = 3, weights = runif(100))
#> $x
#> [1] -1.00000000 -0.97979798 -0.95959596 -0.93939394 -0.91919192 -0.89898990
#> [7] -0.87878788 -0.85858586 -0.83838384 -0.81818182 -0.79797980 -0.77777778
#> [13] -0.75757576 -0.73737374 -0.71717172 -0.69696970 -0.67676768 -0.65656566
#> [19] -0.63636364 -0.61616162 -0.59595960 -0.57575758 -0.55555556 -0.53535354
#> [25] -0.51515152 -0.49494949 -0.47474747 -0.45454545 -0.43434343 -0.41414141
#> [31] -0.39393939 -0.37373737 -0.35353535 -0.33333333 -0.31313131 -0.29292929
#> [37] -0.27272727 -0.25252525 -0.23232323 -0.21212121 -0.19191919 -0.17171717
#> [43] -0.15151515 -0.13131313 -0.11111111 -0.09090909 -0.07070707 -0.05050505
#> [49] -0.03030303 -0.01010101 0.01010101 0.03030303 0.05050505 0.07070707
#> [55] 0.09090909 0.11111111 0.13131313 0.15151515 0.17171717 0.19191919
#> [61] 0.21212121 0.23232323 0.25252525 0.27272727 0.29292929 0.31313131
#> [67] 0.33333333 0.35353535 0.37373737 0.39393939 0.41414141 0.43434343
#> [73] 0.45454545 0.47474747 0.49494949 0.51515152 0.53535354 0.55555556
#> [79] 0.57575758 0.59595960 0.61616162 0.63636364 0.65656566 0.67676768
#> [85] 0.69696970 0.71717172 0.73737374 0.75757576 0.77777778 0.79797980
#> [91] 0.81818182 0.83838384 0.85858586 0.87878788 0.89898990 0.91919192
#> [97] 0.93939394 0.95959596 0.97979798 1.00000000
#>
#> $y
#> [1] -1.00000000 -0.97979798 -0.95959596 -0.93939394 -0.91919192 -0.89898990
#> [7] -0.87878788 -0.85858586 -0.83838384 -0.81818182 -0.79797980 -0.77777778
#> [13] -0.75757576 -0.73737374 -0.71717172 -0.69696970 -0.67676768 -0.65656566
#> [19] -0.63636364 -0.61616162 -0.59595960 -0.57575758 -0.55555556 -0.53535354
#> [25] -0.51515152 -0.49494949 -0.47474747 -0.45454545 -0.43434343 -0.41414141
#> [31] -0.39393939 -0.37373737 -0.35353535 -0.33333333 -0.31313131 -0.29292929
#> [37] -0.27272727 -0.25252525 -0.23232323 -0.21212121 -0.19191919 -0.17171717
#> [43] -0.15151515 -0.13131313 -0.11111111 -0.09090909 -0.07070707 -0.05050505
#> [49] -0.03030303 -0.01010101 0.01010101 0.03030303 0.05050505 0.07070707
#> [55] 0.09090909 0.11111111 0.13131313 0.15151515 0.17171717 0.19191919
#> [61] 0.21212121 0.23232323 0.25252525 0.27272727 0.29292929 0.31313131
#> [67] 0.33333333 0.35353535 0.37373737 0.39393939 0.41414141 0.43434343
#> [73] 0.45454545 0.47474747 0.49494949 0.51515152 0.53535354 0.55555556
#> [79] 0.57575758 0.59595960 0.61616162 0.63636364 0.65656566 0.67676768
#> [85] 0.69696970 0.71717172 0.73737374 0.75757576 0.77777778 0.79797980
#> [91] 0.81818182 0.83838384 0.85858586 0.87878788 0.89898990 0.91919192
#> [97] 0.93939394 0.95959596 0.97979798 1.00000000
#>
#> $density
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7]
#> [1,] NA NA NA NA NA NA NA
#> [2,] NA NA NA NA NA NA NA
#> [3,] NA NA NA NA NA NA NA
#> [4,] NA NA NA NA NA NA NA
#> [5,] NA NA NA NA NA NA NA
#> [6,] NA NA NA NA NA NA NA
#> [7,] NA NA NA NA NA NA NA
#> [8,] NA NA NA NA NA NA NA
#> [9,] NA NA NA NA NA NA NA
#> [10,] NA NA NA NA NA NA NA
#> [11,] NA NA NA NA NA NA NA
#> [12,] NA NA NA NA NA NA NA
#> [13,] NA NA NA NA NA NA NA
#> [14,] NA NA NA NA NA NA NA
#> [15,] NA NA NA NA NA NA NA
#> [16,] NA NA NA NA NA NA NA
#> [17,] NA NA NA NA NA NA NA
#> [18,] NA NA NA NA NA NA NA
#> [19,] NA NA NA NA NA NA NA
#> [20,] NA NA NA NA NA NA NA
#> [21,] NA NA NA NA NA NA NA
#> [22,] NA NA NA NA NA NA NA
#> [23,] NA NA NA NA NA NA NA
#> [24,] NA NA NA NA NA NA NA
#> [25,] NA NA NA NA NA NA NA
#> [26,] NA NA NA NA NA NA NA
#> [27,] NA NA NA NA NA NA 0.08150490
#> [28,] NA NA NA NA NA NA 0.09360992
#> [29,] NA NA NA NA NA 0.1648084 0.10828434
#> [30,] NA NA NA NA NA 0.1844840 0.12452440
#> [31,] NA NA NA NA NA 0.2051838 0.14157355
#> [32,] NA NA NA NA 0.2966302 0.2262192 0.15895271
#> [33,] NA NA NA NA 0.3216438 0.2471880 0.17647371
#> [34,] NA NA NA 0.4271186 0.3461867 0.2679837 0.19423633
#> [35,] NA NA NA 0.4552971 0.3702140 0.2887875 0.21261007
#> [36,] NA NA NA 0.4826145 0.3939655 0.3100445 0.23220240
#> [37,] NA NA 0.6051840 0.5093480 0.4179370 0.3324263 0.25381540
#> [38,] NA NA 0.6351967 0.5360213 0.4428381 0.3567822 0.27839359
#> [39,] NA NA 0.6648596 0.5633590 0.4695401 0.3840827 0.30696578
#> [40,] NA NA 0.6948902 0.5922316 0.4990156 0.4153580 0.34058414
#> [41,] NA 0.8391121 0.7261374 0.6235949 0.5322764 0.4516355 0.38026370
#> [42,] NA 0.8733732 0.7595220 0.6584277 0.5703109 0.4938797 0.42692525
#> [43,] NA 0.9093672 0.7959758 0.6976719 0.6140267 0.5429373 0.48134459
#> [44,] NA 0.9479574 0.8363853 0.7421780 0.6642002 0.5994916 0.54411052
#> [45,] NA 0.9899551 0.8815404 0.7926603 0.7214361 0.6640267 0.61559378
#> [46,] NA 1.0360720 0.9320943 0.8496617 0.7861394 0.7368048 0.69592818
#> [47,] NA 1.0868818 0.9885321 0.9135314 0.8585001 0.8178567 0.78500503
#> [48,] NA 1.1427919 1.0511514 0.9844142 0.9384904 0.9069851 0.88248066
#> [49,] NA 1.2040227 1.1200525 1.0622509 1.0258738 1.0037808 0.98779642
#> [50,] NA 1.2705976 1.1951377 1.1467878 1.1202244 1.1076482 1.10020927
#> [51,] NA 1.3423381 1.2761172 1.2375934 1.2209519 1.2178393 1.21883060
#> [52,] NA 1.4188645 1.3625193 1.3340775 1.3273318 1.3334911 1.34266974
#> [53,] NA 1.4996004 1.4537016 1.4355121 1.4385340 1.4536629 1.47067855
#> [54,] NA 1.5837782 1.5488615 1.5410486 1.5536485 1.5773705 1.60179272
#> [55,] NA 1.6704448 1.6470452 1.6497302 1.6717046 1.7036129 1.73496597
#> [56,] NA 1.7584687 1.7471519 1.7604988 1.7916808 1.8313876 1.86919354
#> [57,] NA 1.8465472 1.8479365 1.8721937 1.9125049 1.9596956 2.00352240
#> [58,] NA 1.9332161 1.9480095 1.9835456 2.0330443 2.0875319 2.13704674
#> [59,] NA 2.0168632 2.0458380 2.0931663 2.1520888 2.2138649 2.26888873
#> [60,] NA 2.0957482 2.1397495 2.1995375 2.2683271 2.3376067 2.39816618
#> [61,] NA NA 2.2279424 2.3010027 2.3803228 2.4575762 2.52394979
#> [62,] NA NA 2.3085052 2.3957659 2.4864930 2.5724617 2.64521438
#> [63,] NA NA 2.3794492 2.4819014 2.5850949 2.6807868 2.76078891
#> [64,] NA NA 2.4387536 2.5573774 2.6742247 2.7808851 2.86931090
#> [65,] NA NA NA 2.6200970 2.7518337 2.8708895 2.96919123
#> [66,] NA NA NA 2.6679586 2.8157646 2.9487411 3.05859494
#> [67,] NA NA NA 2.6989349 2.8638111 3.0122215 3.13544394
#> [68,] NA NA NA NA 2.8938016 3.0590125 3.19744680
#> [69,] NA NA NA NA 2.9037078 3.0867867 3.24216050
#> [70,] NA NA NA NA NA 3.0933274 3.26708750
#> [71,] NA NA NA NA NA 3.0766777 3.26980992
#> [72,] NA NA NA NA NA 3.0353125 3.24815873
#> [73,] NA NA NA NA NA NA 3.20041173
#> [74,] NA NA NA NA NA NA 3.12550771
#> [75,] NA NA NA NA NA NA NA
#> [76,] NA NA NA NA NA NA NA
#> [77,] NA NA NA NA NA NA NA
#> [78,] NA NA NA NA NA NA NA
#> [79,] NA NA NA NA NA NA NA
#> [80,] NA NA NA NA NA NA NA
#> [81,] NA NA NA NA NA NA NA
#> [82,] NA NA NA NA NA NA NA
#> [83,] NA NA NA NA NA NA NA
#> [84,] NA NA NA NA NA NA NA
#> [85,] NA NA NA NA NA NA NA
#> [86,] NA NA NA NA NA NA NA
#> [87,] NA NA NA NA NA NA NA
#> [88,] NA NA NA NA NA NA NA
#> [89,] NA NA NA NA NA NA NA
#> [90,] NA NA NA NA NA NA NA
#> [91,] NA NA NA NA NA NA NA
#> [92,] NA NA NA NA NA NA NA
#> [93,] NA NA NA NA NA NA NA
#> [94,] NA NA NA NA NA NA NA
#> [95,] NA NA NA NA NA NA NA
#> [96,] NA NA NA NA NA NA NA
#> [97,] NA NA NA NA NA NA NA
#> [98,] NA NA NA NA NA NA NA
#> [99,] NA NA NA NA NA NA NA
#> [100,] NA NA NA NA NA NA NA
#> [,8] [,9] [,10] [,11] [,12] [,13]
#> [1,] NA NA NA NA NA NA
#> [2,] NA NA NA NA NA NA
#> [3,] NA NA NA NA NA NA
#> [4,] NA NA NA NA NA NA
#> [5,] NA NA NA NA NA NA
#> [6,] NA NA NA NA NA NA
#> [7,] NA NA NA NA NA NA
#> [8,] NA NA NA NA NA NA
#> [9,] NA NA NA NA NA NA
#> [10,] NA NA NA NA NA NA
#> [11,] NA NA NA NA NA NA
#> [12,] NA NA NA NA NA NA
#> [13,] NA NA NA NA NA NA
#> [14,] NA NA NA NA NA NA
#> [15,] NA NA NA NA NA NA
#> [16,] NA NA NA NA NA NA
#> [17,] NA NA NA NA NA NA
#> [18,] NA NA NA NA NA NA
#> [19,] NA NA NA NA NA 0.001912355
#> [20,] NA NA NA NA 0.00000000 0.000000000
#> [21,] NA NA NA 0.00000000 0.00000000 0.000000000
#> [22,] NA NA NA 0.00000000 0.00000000 0.000000000
#> [23,] NA NA 0.000000000 0.00000000 0.00000000 0.000000000
#> [24,] NA 0.000000000 0.000000000 0.00000000 0.00000000 0.000000000
#> [25,] NA 0.000000000 0.000000000 0.00000000 0.00000000 0.000000000
#> [26,] 0.02749184 0.000000000 0.000000000 0.00000000 0.00000000 0.000000000
#> [27,] 0.03397194 0.000000000 0.000000000 0.00000000 0.00000000 0.000000000
#> [28,] 0.04364628 0.000000000 0.000000000 0.00000000 0.00000000 0.000000000
#> [29,] 0.05544447 0.007747508 0.000000000 0.00000000 0.00000000 0.000000000
#> [30,] 0.06852764 0.018043598 0.000000000 0.00000000 0.00000000 0.000000000
#> [31,] 0.08232193 0.029007761 0.000000000 0.00000000 0.00000000 0.000000000
#> [32,] 0.09653646 0.040505974 0.000000000 0.00000000 0.00000000 0.000000000
#> [33,] 0.11116576 0.052679223 0.002055826 0.00000000 0.00000000 0.000000000
#> [34,] 0.12647782 0.065924756 0.013392344 0.00000000 0.00000000 0.000000000
#> [35,] 0.14298852 0.080865414 0.026780848 0.00000000 0.00000000 0.000000000
#> [36,] 0.16142452 0.098308988 0.043080357 0.00000000 0.00000000 0.000000000
#> [37,] 0.18267658 0.119199951 0.063262597 0.01452222 0.00000000 0.000000000
#> [38,] 0.20774603 0.144566201 0.088359935 0.03853908 0.00000000 0.000000000
#> [39,] 0.23768725 0.175463414 0.119412589 0.06871153 0.02270671 0.000000000
#> [40,] 0.27354880 0.212919558 0.157417305 0.10599849 0.05796313 0.012982397
#> [41,] 0.31631620 0.257881846 0.203279283 0.15126162 0.10111622 0.052660963
#> [42,] 0.36685882 0.311168237 0.257768897 0.20522788 0.15285175 0.100647079
#> [43,] 0.42588326 0.373425334 0.321484462 0.26845771 0.21369890 0.157440471
#> [44,] 0.49389537 0.445094303 0.394822223 0.34131944 0.28400967 0.223381919
#> [45,] 0.57117264 0.526386265 0.477954589 0.42397056 0.36394369 0.298642215
#> [46,] 0.65774825 0.617268313 0.570817593 0.51634662 0.45345879 0.383215023
#> [47,] 0.75340773 0.717461005 0.673108375 0.61815829 0.55230788 0.476914048
#> [48,] 0.85769831 0.826447719 0.784293232 0.72889746 0.66004291 0.579375171
#> [49,] 0.96995050 0.943495679 0.903626356 0.84785259 0.77602638 0.690064223
#> [50,] 1.08931066 1.067687763 1.030178809 0.97413333 0.89945073 0.808290943
#> [51,] 1.21478213 1.197963388 1.162876581 1.10670374 1.02936549 0.933229295
#> [52,] 1.34527232 1.333166001 1.300545798 1.24442286 1.16471123 1.063943841
#> [53,] 1.47964168 1.472093913 1.441962388 1.38609042 1.30435910 1.199421283
#> [54,] 1.61675087 1.613550693 1.585902856 1.53049501 1.44715363 1.338605682
#> [55,] 1.75550172 1.756391031 1.731192385 1.67646138 1.59195618 1.480435399
#> [56,] 1.89486816 1.899558014 1.876746329 1.82289337 1.73768615 1.623879405
#> [57,] 2.03391392 2.042108229 2.021601394 1.96880877 1.88335660 1.767970483
#> [58,] 2.17179479 2.183221892 2.164933372 2.11336317 2.02810158 1.911832921
#> [59,] 2.30774450 2.322196376 2.306059222 2.25585999 2.17119250 2.054702556
#> [60,] 2.44104500 2.458422823 2.444422439 2.39574551 2.31204197 2.195937509
#> [61,] 2.57098296 2.591346974 2.579561943 2.53258797 2.45019386 2.335018466
#> [62,] 2.69679614 2.720416695 2.711066004 2.66604169 2.58529980 2.471537956
#> [63,] 2.81761386 2.845019847 2.838513835 2.79579771 2.71708244 2.605178507
#> [64,] 2.93239709 2.964417065 2.961408461 2.92152328 2.84528708 2.735679989
#> [65,] 3.03988371 3.077674673 3.079105146 3.04279360 2.96962339 2.862796673
#> [66,] 3.13854515 3.183603468 3.190740299 3.15901927 3.08969940 2.986244760
#> [67,] 3.22656065 3.280709503 3.295166262 3.26937383 3.20495081 3.105641415
#> [68,] 3.30181544 3.367163449 3.390898095 3.37272642 3.31456864 3.220436903
#> [69,] 3.36192915 3.440795584 3.476079261 3.46758541 3.41743022 3.329842426
#> [70,] 3.40432039 3.499123759 3.548474047 3.55206059 3.51203918 3.432757900
#> [71,] 3.42631220 3.539421537 3.605495318 3.62385267 3.59648295 3.527706153
#> [72,] 3.42528083 3.558832539 3.644276238 3.68028005 3.66841751 3.612782735
#> [73,] 3.39884612 3.554534239 3.661793325 3.71835326 3.72509157 3.685633207
#> [74,] 3.34509625 3.523949566 3.655044814 3.73490570 3.76342182 3.743471673
#> [75,] 3.26283173 3.464997577 3.621282409 3.72678523 3.78012957 3.783154477
#> [76,] NA 3.376365550 3.558285980 3.69110411 3.77194352 3.801320345
#> [77,] NA 3.257775441 3.464660431 3.62553479 3.73586539 3.794602138
#> [78,] NA NA 3.340123377 3.52862734 3.66948332 3.759905472
#> [79,] NA NA NA 3.40011278 3.57130539 3.694736653
#> [80,] NA NA NA 3.24114839 3.44107327 3.597548435
#> [81,] NA NA NA NA 3.28000841 3.468059933
#> [82,] NA NA NA NA NA 3.307500227
#> [83,] NA NA NA NA NA NA
#> [84,] NA NA NA NA NA NA
#> [85,] NA NA NA NA NA NA
#> [86,] NA NA NA NA NA NA
#> [87,] NA NA NA NA NA NA
#> [88,] NA NA NA NA NA NA
#> [89,] NA NA NA NA NA NA
#> [90,] NA NA NA NA NA NA
#> [91,] NA NA NA NA NA NA
#> [92,] NA NA NA NA NA NA
#> [93,] NA NA NA NA NA NA
#> [94,] NA NA NA NA NA NA
#> [95,] NA NA NA NA NA NA
#> [96,] NA NA NA NA NA NA
#> [97,] NA NA NA NA NA NA
#> [98,] NA NA NA NA NA NA
#> [99,] NA NA NA NA NA NA
#> [100,] NA NA NA NA NA NA
#> [,14] [,15] [,16] [,17] [,18] [,19]
#> [1,] NA NA NA NA NA NA
#> [2,] NA NA NA NA NA NA
#> [3,] NA NA NA NA NA NA
#> [4,] NA NA NA NA NA NA
#> [5,] NA NA NA NA NA NA
#> [6,] NA NA NA NA NA NA
#> [7,] NA NA NA NA NA NA
#> [8,] NA NA NA NA NA NA
#> [9,] NA NA NA NA NA NA
#> [10,] NA NA NA NA NA NA
#> [11,] NA NA NA NA NA NA
#> [12,] NA NA NA NA NA NA
#> [13,] NA NA NA NA NA 0.28510633
#> [14,] NA NA NA NA 0.21810836 0.19458386
#> [15,] NA NA NA 0.15889750 0.13759846 0.12045377
#> [16,] NA NA 0.10735870 0.08767361 0.07251365 0.06186980
#> [17,] NA 0.063683478 0.04478177 0.03082310 0.02180192 0.01765772
#> [18,] 0.028321453 0.009224942 0.00000000 0.00000000 0.00000000 0.00000000
#> [19,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [20,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [21,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [22,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [23,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [24,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [25,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [26,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [27,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [28,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [29,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [30,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [31,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [32,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [33,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [34,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [35,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [36,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [37,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [38,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [39,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [40,] 0.000000000 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [41,] 0.006154516 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [42,] 0.049181296 0.000000000 0.00000000 0.00000000 0.00000000 0.00000000
#> [43,] 0.100601453 0.044531620 0.00000000 0.00000000 0.00000000 0.00000000
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#> [45,] 0.229790536 0.159692350 0.09084898 0.02562955 0.00000000 0.00000000
#> [46,] 0.307776648 0.229966626 0.15282779 0.07924191 0.01164991 0.00000000
#> [47,] 0.394584452 0.308677590 0.22279991 0.14037144 0.06430534 0.00000000
#> [48,] 0.489946339 0.395656126 0.30068778 0.20901842 0.12405512 0.04841659
#> [49,] 0.593448970 0.490615608 0.38632706 0.28512808 0.19093519 0.10678667
#> [50,] 0.704542095 0.593156305 0.47946764 0.36858924 0.26495510 0.17203507
#> [51,] 0.822552083 0.702772661 0.57977559 0.45923233 0.34609330 0.24426517
#> [52,] 0.946700215 0.818863718 0.68683653 0.55682682 0.43429034 0.32356781
#> [53,] 1.076125307 0.940746607 0.80016042 0.66107832 0.52943983 0.41000798
#> [54,] 1.209909788 1.067672659 0.91918765 0.77162542 0.63137706 0.50360711
#> [55,] 1.347107912 1.198845454 1.04329626 0.88803606 0.73986558 0.60432110
#> [56,] 1.486774535 1.333439940 1.17181005 1.00980408 0.85458220 0.71201469
#> [57,] 1.627992726 1.470621770 1.30400748 1.13634638 0.97510177 0.82643393
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#> [59,] 1.911701638 1.749474894 1.57640204 1.40103434 1.23126350 1.07368463
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#> [62,] 2.329959816 2.167733446 1.99322083 1.81510062 1.64152049 1.47939873
#> [63,] 2.465298994 2.304569975 2.13130800 1.95417449 1.78133866 1.61977059
#> [64,] 2.597967185 2.439256976 2.26782789 2.09232034 1.92091682 1.76063237
#> [65,] 2.727678566 2.571395200 2.40220920 2.22875192 2.05922657 1.90070107
#> [66,] 2.854166508 2.700650600 2.53397723 2.36279455 2.19534847 2.03878251
#> [67,] 2.977139371 2.826732249 2.66275772 2.49391689 2.32853274 2.17386016
#> [68,] 3.096225306 2.949356793 2.78826636 2.62174951 2.45824910 2.30517744
#> [69,] 3.210906479 3.068197457 2.91027965 2.74608319 2.58421675 2.43230206
#> [70,] 3.320444635 3.182817011 3.02858385 2.86684109 2.70640565 2.55516110
#> [71,] 3.423802299 3.292586358 3.14290075 2.98402052 2.82500196 2.67403638
#> [72,] 3.519566935 3.396593594 3.25279230 3.09760324 2.94033308 2.78951246
#> [73,] 3.605888848 3.493552303 3.35755014 3.20743718 3.05275209 2.90237325
#> [74,] 3.680446827 3.581722020 3.45608094 3.31309779 3.16248629 3.01344882
#> [75,] 3.740457608 3.658857463 3.54680322 3.41374262 3.26946100 3.12341979
#> [76,] 3.782745087 3.722205223 3.62757536 3.50797839 3.37311583 3.23259446
#> [77,] 3.803881773 3.768565972 3.69567642 3.59376383 3.47223700 3.34068059
#> [78,] 3.800407573 3.794435795 3.74786005 3.66837319 3.56483310 3.44658039
#> [79,] 3.769119642 3.796231434 3.78049614 3.72844298 3.64808283 3.54824091
#> [80,] 3.707412882 3.770591374 3.78980437 3.77011748 3.71837960 3.64259217
#> [81,] 3.613635965 3.714729291 3.77216948 3.78929604 3.77148861 3.72559957
#> [82,] 3.487415858 3.626801166 3.72451131 3.78196919 3.80281783 3.79244563
#> [83,] 3.329898462 3.506236124 3.64466739 3.74461287 3.80778597 3.83783928
#> [84,] NA 3.353977572 3.53173561 3.67459471 3.78225226 3.85643063
#> [85,] NA NA 3.38632324 3.57053744 3.72295752 3.84329016
#> [86,] NA NA NA 3.43258643 3.62791999 3.79439773
#> [87,] NA NA NA NA 3.49673378 3.70708289
#> [88,] NA NA NA NA NA 3.58036714
#> [89,] NA NA NA NA NA NA
#> [90,] NA NA NA NA NA NA
#> [91,] NA NA NA NA NA NA
#> [92,] NA NA NA NA NA NA
#> [93,] NA NA NA NA NA NA
#> [94,] NA NA NA NA NA NA
#> [95,] NA NA NA NA NA NA
#> [96,] NA NA NA NA NA NA
#> [97,] NA NA NA NA NA NA
#> [98,] NA NA NA NA NA NA
#> [99,] NA NA NA NA NA NA
#> [100,] NA NA NA NA NA NA
#> [,20] [,21] [,22] [,23] [,24] [,25]
#> [1,] NA NA NA NA NA NA
#> [2,] NA NA NA NA NA NA
#> [3,] NA NA NA NA NA NA
#> [4,] NA NA NA NA NA NA
#> [5,] NA NA NA NA NA NA
#> [6,] NA NA NA NA NA NA
#> [7,] NA NA NA NA NA NA
#> [8,] NA NA NA NA NA NA
#> [9,] NA NA NA NA 0.611323251 0.58324125
#> [10,] NA NA NA 0.50639309 0.478297344 0.45497033
#> [11,] NA 0.4445498623 0.413688214 0.38676076 0.364142287 0.34613256
#> [12,] 0.360334350 0.3316900812 0.306795011 0.28591056 0.269238147 0.25692547
#> [13,] 0.259024926 0.2366772158 0.218221414 0.20376340 0.193360212 0.18701101
#> [14,] 0.174936893 0.1592422477 0.147524715 0.13975888 0.135855832 0.13564570
#> [15,] 0.107481351 0.0986484137 0.093867331 0.09297681 0.095718575 0.10171983
#> [16,] 0.055680436 0.0538239620 0.056094267 0.06216978 0.071588180 0.08373725
#> [17,] 0.018266250 0.0234104187 0.032741531 0.04574390 0.061715647 0.07977512
#> [18,] 0.000000000 0.0057631144 0.022015718 0.04172894 0.063933538 0.08746169
#> [19,] 0.000000000 0.0000000000 0.021782676 0.04777351 0.075664321 0.10400161
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#> [24,] 0.003312179 0.0439787453 0.086962101 0.13015993 0.171292957 0.20805853
#> [25,] 0.010228241 0.0518135668 0.095135653 0.13800085 0.178086979 0.21310372
#> [26,] 0.013509190 0.0547065041 0.097066068 0.13836319 0.176295936 0.20864666
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#> [28,] 0.005403416 0.0423081974 0.079391997 0.11453715 0.145645101 0.17078523
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#> [48,] 0.000000000 0.0000000000 0.000000000 0.00000000 0.000000000 0.00000000
#> [49,] 0.034745294 0.0000000000 0.000000000 0.00000000 0.000000000 0.00000000
#> [50,] 0.092218069 0.0268332517 0.000000000 0.00000000 0.000000000 0.00000000
#> [51,] 0.156471319 0.0842649788 0.028149447 0.00000000 0.000000000 0.00000000
#> [52,] 0.227719481 0.1485275536 0.086618642 0.04165360 0.012538173 0.00000000
#> [53,] 0.306175504 0.2199536368 0.152094752 0.10229281 0.069410920 0.05169842
#> [54,] 0.392028957 0.2988774422 0.225029502 0.17021391 0.133255372 0.11231114
#> [55,] 0.485417382 0.3856017117 0.305870297 0.24598583 0.204737568 0.18019762
#> [56,] 0.586391478 0.4803555464 0.395012896 0.33015630 0.284540532 0.25615834
#> [57,] 0.694875943 0.5832448632 0.492743125 0.42318670 0.373294439 0.34098341
#> [58,] 0.810629313 0.6941991226 0.599171341 0.52537554 0.471490567 0.43535875
#> [59,] 0.933207489 0.8129198242 0.714165764 0.63677692 0.579385689 0.53975746
#> [60,] 1.061936653 0.9388377229 0.837292745 0.75712314 0.696906742 0.65432682
#> [61,] 1.195901600 1.0710864186 0.967773213 0.88576213 0.823567912 0.77878436
#> [62,] 1.333954965 1.2084996549 1.104464583 1.02162090 0.958413262 0.91233784
#> [63,] 1.474751272 1.3496381486 1.245876036 1.16320528 1.099997307 1.05364381
#> [64,] 1.616807274 1.4928491184 1.390222349 1.30864326 1.246413405 1.20081717
#> [65,] 1.758586890 1.6363580882 1.535517543 1.45577525 1.395375564 1.35149973
#> [66,] 1.898605530 1.7783884037 1.679704895 1.60228944 1.544353747 1.50299017
#> [67,] 2.035545208 1.9172997240 1.820814937 1.74589469 1.690756425 1.65243080
#> [68,] 2.168368941 2.0517330531 1.957138491 1.88451788 1.832147876 1.79703968
#> [69,] 2.296421055 2.1807471539 2.087398176 2.01650836 1.966482153 1.93436984
#> [70,] 2.419499288 2.3039297938 2.210899600 2.14082859 2.092331498 2.06257247
#> [71,] 2.537885338 2.4214674225 2.327642921 2.25720905 2.209084684 2.18063739
#> [72,] 2.652322674 2.5341586737 2.438376723 2.36624596 2.317090625 2.28858322
#> [73,] 2.763934130 2.6433604882 2.544579216 2.46942290 2.417724656 2.38757095
#> [74,] 2.874076899 2.7508606488 2.648356605 2.56904232 2.513359128 2.47991846
#> [75,] 2.984139052 2.8586770138 2.752254921 2.66805887 2.607226264 2.56899957
#> [76,] 3.095289254 2.9687916056 2.858989674 2.76981514 2.703169493 2.65901966
#> [77,] 3.208199628 3.0828366249 2.971107110 2.87768981 2.805289597 2.75466995
#> [78,] 3.322769656 3.2017587369 3.090601103 2.99467951 2.917503693 2.86067526
#> [79,] 3.437885455 3.3254964588 3.218519861 3.12294715 3.043047611 2.98126293
#> [80,] 3.551251882 3.4527114973 3.354605095 3.26337963 3.183964465 3.11959488
#> [81,] 3.659333078 3.5806165048 3.497011075 3.41520605 3.340632098 3.27721609
#> [82,] 3.757428824 3.7049371418 3.642149975 3.57572911 3.511387366 3.45358126
#> [83,] 3.839899411 3.8200345946 3.784701462 3.74021778 3.692303322 3.64572213
#> [84,] 3.900531882 3.9191963028 3.917808365 3.90199574 3.877164858 3.84811025
#> [85,] 3.933018810 3.9950800315 4.033457996 4.05273906 4.057669153 4.05275326
#> [86,] 3.931501828 4.0402737931 4.123023928 4.18297109 4.223851793 4.24953737
#> [87,] 3.891120881 4.0479167079 4.177920986 4.28271718 4.364712076 4.42680075
#> [88,] 3.808510449 4.0123184040 4.190312132 4.34226248 4.468987736 4.57209601
#> [89,] 3.682196452 3.9295193943 4.153803496 4.35294743 4.526015320 4.67308190
#> [90,] NA 3.7977506233 4.064073334 4.30793896 4.526610581 4.71847804
#> [91,] NA NA NA 4.20292813 4.463911784 4.69902152
#> [92,] NA NA NA NA 4.334141610 4.60837481
#> [93,] NA NA NA NA NA NA
#> [94,] NA NA NA NA NA NA
#> [95,] NA NA NA NA NA NA
#> [96,] NA NA NA NA NA NA
#> [97,] NA NA NA NA NA NA
#> [98,] NA NA NA NA NA NA
#> [99,] NA NA NA NA NA NA
#> [100,] NA NA NA NA NA NA
#> [,26] [,27] [,28] [,29] [,30] [,31]
#> [1,] NA NA NA NA NA NA
#> [2,] NA NA NA NA NA NA
#> [3,] NA NA NA NA NA NA
#> [4,] NA NA NA NA NA NA
#> [5,] NA NA NA NA NA NA
#> [6,] NA NA NA 0.98346905 0.98034257 0.985436068
#> [7,] NA 0.840150233 0.82341411 0.81393393 0.81203249 0.817847335
#> [8,] 0.70336345 0.682778210 0.66872336 0.66154604 0.66144183 0.668450648
#> [9,] 0.56051551 0.543604516 0.53284794 0.52846618 0.53055199 0.539058883
#> [10,] 0.43680089 0.424089129 0.41704359 0.41577075 0.42026135 0.430378045
#> [11,] 0.33296455 0.324800102 0.32171850 0.32370299 0.33062944 0.342259719
#> [12,] 0.24906043 0.245658924 0.24665259 0.25188054 0.26108736 0.273927611
#> [13,] 0.18464333 0.186101362 0.19114134 0.19943591 0.21058706 0.224144946
#> [14,] 0.13886466 0.145152371 0.15406266 0.16508627 0.17768205 0.191311083
#> [15,] 0.11048965 0.121433252 0.13388378 0.14714694 0.16055148 0.173497323
#> [16,] 0.09786810 0.113132150 0.12863745 0.14351640 0.15699425 0.168448202
#> [17,] 0.09889677 0.117974121 0.13590203 0.15166607 0.16442613 0.173582102
#> [18,] 0.11100892 0.133224333 0.15281737 0.16866603 0.17991095 0.186022631
#> [19,] 0.13121798 0.155748466 0.17615878 0.19126767 0.20024629 0.202681562
#> [20,] 0.15622767 0.182140264 0.20247672 0.21604958 0.22210925 0.220398486
#> [21,] 0.18260590 0.208910317 0.22829423 0.23961701 0.24225161 0.236126042
#> [22,] 0.20700483 0.232715877 0.25033991 0.25883151 0.25772038 0.247136663
#> [23,] 0.22639874 0.250601586 0.26578511 0.27103904 0.26607218 0.251219905
#> [24,] 0.23830684 0.260217278 0.27245158 0.27426320 0.26554924 0.246839680
#> [25,] 0.24096948 0.259982004 0.26895979 0.26733568 0.25519099 0.233227467
#> [26,] 0.23345387 0.249172054 0.25479784 0.24994601 0.23486601 0.210398670
#> [27,] 0.21567657 0.227923050 0.23030398 0.22260650 0.20522232 0.179092177
#> [28,] 0.18834330 0.197149501 0.19656861 0.18654049 0.16756649 0.140644958
#> [29,] 0.15281842 0.158396949 0.15527338 0.14351339 0.12369166 0.096822232
#> [30,] 0.11094531 0.113650060 0.10849212 0.09563164 0.07567995 0.049627998
#> [31,] 0.06484367 0.065123607 0.05848072 0.04513683 0.02570523 0.001120519
#> [32,] 0.01670956 0.015062319 0.00748159 0.00000000 0.00000000 0.000000000
#> [33,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [34,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [35,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [36,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [37,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [38,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [39,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [40,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [41,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [42,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [43,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [44,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [45,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [46,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [47,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [48,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [49,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [50,] 0.00000000 0.000000000 0.00000000 0.00000000 0.00000000 0.000000000
#> [51,] 0.00000000 0.000000000 0.00000000 0.00000000 0.01114006 0.032802721
#> [52,] 0.00000000 0.001962879 0.01648282 0.03592666 0.05784416 0.079933771
#> [53,] 0.04697674 0.052788932 0.06651985 0.08550035 0.10710938 0.128883762
#> [54,] 0.10507580 0.108946772 0.12115664 0.13888550 0.15936832 0.180008000
#> [55,] 0.16994527 0.171249098 0.18121144 0.19688850 0.21540150 0.234051093
#> [56,] 0.24248468 0.240675946 0.24772668 0.26059686 0.27632559 0.292144713
#> [57,] 0.32363335 0.318303281 0.32190073 0.33131563 0.34353540 0.355755896
#> [58,] 0.41427058 0.405199074 0.40498166 0.41046046 0.41859789 0.426583321
#> [59,] 0.51509542 0.502292981 0.49812863 0.49941270 0.50310288 0.506405622
#> [60,] 0.62649675 0.610230747 0.60225225 0.59934757 0.59848141 0.596892548
#> [61,] 0.74842824 0.729228644 0.71784970 0.71105194 0.70580863 0.699395842
#> [62,] 0.88030468 0.858945993 0.84485412 0.83475213 0.82561218 0.814741241
#> [63,] 1.02093652 0.998394500 0.98251866 0.96997339 0.95770907 0.943045417
#> [64,] 1.16851738 1.145901566 1.12935436 1.11545239 1.10109374 1.083581572
#> [65,] 1.32067526 1.299140805 1.28313766 1.26912047 1.25389683 1.234714702
#> [66,] 1.47459217 1.455237005 1.44099717 1.42816957 1.41342882 1.393922408
#> [67,] 1.62718975 1.610945335 1.59958183 1.58920548 1.57631525 1.557909905
#> [68,] 1.77537052 1.762896291 1.75530399 1.74848391 1.73872119 1.722819174
#> [69,] 1.91629743 1.907889754 1.90464209 1.90221583 1.89665353 1.884522682
#> [70,] 2.04768762 2.043214334 2.04447974 2.04691984 2.04632004 2.038982618
#> [71,] 2.16809239 2.166962728 2.17245126 2.17979190 2.18451638 2.182648024
#> [72,] 2.27713295 2.278310739 2.28726003 2.29905764 2.30900617 2.312855319
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#> [72,] 1.95839402 1.846692076 1.723583692 1.59172419 1.45400899 1.313406596
#> [73,] 2.11241776 2.003470081 1.881981459 1.75056315 1.61210905 1.469627369
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#> [75,] 2.38994291 2.291751694 2.179264636 2.05485097 1.92124869 1.781399109
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#> [79,] 2.84165098 2.774610070 2.693088558 2.59850331 2.49275882 2.378112828
#> [80,] 2.95408875 2.893543501 2.819183018 2.73216229 2.63413283 2.527120016
#> [81,] 3.07790151 3.022221917 2.953580151 2.87289241 2.78157059 2.681412116
#> [82,] 3.21924607 3.166429705 3.101604132 3.02548477 2.93927246 2.844556190
#> [83,] 3.38336778 3.331224076 3.268024801 3.19433452 3.11118422 3.019986847
#> [84,] 3.57383826 3.520200892 3.456361857 3.38279287 3.30040512 3.210477499
#> [85,] 3.79187273 3.734819033 3.668226783 3.59253692 3.50859564 3.417595095
#> [86,] 4.03581710 3.973871781 3.902787807 3.82303787 3.73545871 3.641204156
#> [87,] 4.30087838 4.233181077 4.156434178 4.07120236 3.97836603 3.879086530
#> [88,] 4.57914052 4.505561898 4.422691124 4.33124112 4.23218459 4.126731243
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#> [81,] 1.22158761 1.177628783 1.12314334 1.057788055 0.9818251764 0.896194121
#> [82,] 1.32129140 1.262666113 1.19321011 1.112978151 1.0226690463 0.923659970
#> [83,] 1.40229266 1.328844849 1.24463445 1.150143330 1.0465088711 0.935517388
#> [84,] 1.46055146 1.372674094 1.27451569 1.166989298 1.0516441916 0.930617914
#> [85,] 1.49321565 1.391881245 1.28117632 1.162419495 1.0375146329 0.908864919
#> [86,] 1.49893312 1.385672111 1.26436362 1.136674987 1.0047790805 0.871237378
#> [87,] 1.47799863 1.354822078 1.22528279 1.091311832 0.9552438963 0.819679828
#> [88,] 1.43230030 1.301573381 1.16644831 1.029014351 0.8916501846 0.756878670
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#> [90,] 1.28046044 1.142345248 1.00417564 0.868018268 0.7360123614 0.610247029
#> [91,] 1.18308866 1.045052832 0.90912196 0.777204918 0.6512026973 NA
#> [92,] 1.07754403 0.941855093 0.81029907 0.684564035 NA NA
#> [93,] 0.96805405 0.836729995 NA NA NA NA
#> [94,] 0.85830558 NA NA NA NA NA
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#> [,80] [,81] [,82] [,83] [,84] [,85] [,86]
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#> [11,] 3.67619221 NA NA NA NA NA NA
#> [12,] 3.33633484 3.4518781 NA NA NA NA NA
#> [13,] 2.98630041 3.1256603 3.2667912 NA NA NA NA
#> [14,] 2.64146952 2.7959459 2.9583179 3.1243876 NA NA NA
#> [15,] 2.31441456 2.4760247 2.6510084 2.8358940 3.0253432 NA NA
#> [16,] 2.01438950 2.1762978 2.3561546 2.5513733 2.7574547 2.9678535 NA
#> [17,] 1.74724849 1.9040087 2.0822507 2.2803348 2.4947677 2.7199382 2.9480644
#> [18,] 1.51569907 1.6633343 1.8349063 2.0297020 2.2452993 2.4772007 2.7186275
#> [19,] 1.31978107 1.4557389 1.6170530 1.8038536 2.0147686 2.2464887 2.4934362
#> [20,] 1.15746697 1.2804872 1.4293471 1.6048933 1.8067156 2.0326769 2.2784902
#> [21,] 1.02529582 1.1352246 1.2706756 1.4330595 1.6227919 1.8388202 2.0781444
#> [22,] 0.91897394 1.0165520 1.1386879 1.2871934 1.4631444 1.6664329 1.8952649
#> [23,] 0.83389673 0.9205423 1.0302935 1.1652018 1.3268243 1.5158230 1.7314711
#> [24,] 0.76556528 0.8431653 0.9420869 1.0644690 1.2121696 1.3864282 1.5874067
#> [25,] 0.70988702 0.7806065 0.8706773 0.9821891 1.1171287 1.2771154 1.4629976
#> [26,] 0.66336242 0.7294767 0.8129174 0.9156077 1.0395059 1.1864190 1.3576701
#> [27,] 0.62316932 0.6869221 0.7660374 0.8621750 0.9771276 1.1127115 1.2705142
#> [28,] 0.58716311 0.6506512 0.7276960 0.8196199 0.9279351 1.0543086 1.2003924
#> [29,] 0.55381447 0.6188990 0.6959708 0.7859636 0.8900191 1.0095196 1.1460001
#> [30,] 0.52210814 0.5903509 0.6693068 0.7594922 0.8616142 0.9766610 1.1058925
#> [31,] 0.49142424 0.5640478 0.6464452 0.7387088 0.8410723 0.9540491 1.0784917
#> [32,] 0.46142103 0.5392906 0.6263499 0.7222811 0.8268318 0.9399877 1.0620917
#> [33,] 0.43193268 0.5155569 0.6081439 0.7089995 0.8173954 0.9327651 1.0548696
#> [34,] 0.40289073 0.4924384 0.5910657 0.6977513 0.8113236 0.9306654 1.0549142
#> [35,] 0.37427229 0.4696031 0.5744457 0.6875150 0.8072466 0.9319984 1.0602717
#> [36,] 0.34607342 0.4467781 0.5577032 0.6773720 0.8038925 0.9351445 1.0690063
#> [37,] 0.31830297 0.4237508 0.5403571 0.6665302 0.8001261 0.9386093 1.0792722
#> [38,] 0.29098986 0.4003805 0.5220442 0.6543526 0.7949901 0.9410802 1.0893850
#> [39,] 0.26419653 0.3766124 0.5025388 0.6403840 0.7877422 0.9414765 1.0978881
#> [40,] 0.23803197 0.3524901 0.4817653 0.6243686 0.7778806 0.9389861 1.1036033
#> [41,] 0.21265926 0.3281593 0.4598017 0.6062550 0.7651544 0.9330848 1.1056625
#> [42,] 0.18829480 0.3038625 0.4368707 0.5861862 0.7495558 0.9235344 1.1035168
#> [43,] 0.16519848 0.2799232 0.4133185 0.5644761 0.7312961 0.9103629 1.0969240
#> [44,] 0.14365608 0.2567212 0.3895847 0.5415734 0.7107675 0.8938266 1.0859165
#> [45,] 0.12395642 0.2346634 0.3661651 0.5180189 0.6884959 0.8743617 1.0707558
#> [46,] 0.10636677 0.2141516 0.3435727 0.4943991 0.6650881 0.8525289 1.0518769
#> [47,] 0.09111014 0.1955535 0.3223004 0.4713008 0.6411811 0.8289567 1.0298305
#> [48,] 0.07834746 0.1791775 0.3027890 0.4492724 0.6173945 0.8042888 1.0052266
#> [49,] 0.06816710 0.1652564 0.2854031 0.4287913 0.5942916 0.7791387 0.9786840
#> [50,] 0.06058266 0.1539383 0.2704157 0.4102420 0.5723500 0.7540531 0.9507883
#> [51,] 0.05553897 0.1452870 0.2580022 0.3939032 0.5519425 0.7294865 0.9220604
#> [52,] 0.05292484 0.1392889 0.2482418 0.3799443 0.5333271 0.7057855 0.8929339
#> [53,] 0.05259041 0.1358657 0.2411257 0.3684284 0.5166463 0.6831823 0.8637431
#> [54,] 0.05436627 0.1348896 0.2365691 0.3593219 0.5019322 0.6617959 0.8347191
#> [55,] 0.05808162 0.1361991 0.2344252 0.3525062 0.4891172 0.6416400 0.8059927
#> [56,] 0.06357915 0.1396133 0.2344994 0.3477927 0.4780479 0.6226353 0.7776037
#> [57,] 0.07072524 0.1449437 0.2365632 0.3449377 0.4685018 0.6046257 0.7495149
#> [58,] 0.07941516 0.1520027 0.2403661 0.3436588 0.4602056 0.5873983 0.7216306
#> [59,] 0.08957426 0.1606105 0.2456481 0.3436513 0.4528561 0.5707051 0.6938176
#> [60,] 0.10115680 0.1706006 0.2521518 0.3446066 0.4461418 0.5542883 0.6659304
#> [61,] 0.11414502 0.1818271 0.2596367 0.3462316 0.4397676 0.5379058 0.6378367
#> [62,] 0.12855068 0.1941740 0.2678951 0.3482710 0.4334804 0.5213591 0.6094440
#> [63,] 0.14442081 0.2075680 0.2767713 0.3505305 0.4270944 0.5045194 0.5807242
#> [64,] 0.16184792 0.2219950 0.2861822 0.3528996 0.4205155 0.4873500 0.5517344
#> [65,] 0.18098332 0.2375167 0.2961358 0.3553713 0.4137594 0.4699235 0.5226296
#> [66,] 0.20205024 0.2542850 0.3067459 0.3580553 0.4069627 0.4524281 0.4936664
#> [67,] 0.22535167 0.2725486 0.3182366 0.3611787 0.4003793 0.4351617 0.4651929
#> [68,] 0.25126695 0.2926468 0.3309316 0.3650719 0.3943632 0.4185097 0.4376248
#> [69,] 0.28023103 0.3149842 0.3452255 0.3701359 0.3893314 0.4029070 0.4114081
#> [70,] 0.31269170 0.3399844 0.3615337 0.3767894 0.3857109 0.3887858 0.3869688
#> [71,] 0.34904276 0.3680205 0.3802218 0.3853991 0.3838710 0.3765122 0.3646572
#> [72,] 0.38953521 0.3993273 0.4015209 0.3961987 0.3840487 0.3663199 0.3446916
#> [73,] 0.43417353 0.4339030 0.4254352 0.4092064 0.3862765 0.3582500 0.3271107
#> [74,] 0.48260920 0.4714126 0.4516584 0.4241529 0.3903243 0.3521066 0.3117434
#> [75,] 0.53404829 0.5111104 0.4795106 0.4404349 0.3956676 0.3474395 0.2982034
#> [76,] 0.58719213 0.5517983 0.5079140 0.4571055 0.4014918 0.3435588 0.2859122
#> [77,] 0.64023004 0.5918360 0.5354182 0.4729124 0.4067386 0.3395867 0.2741525
#> [78,] 0.69089880 0.6292144 0.5602831 0.4863849 0.4101941 0.3345417 0.2621444
#> [79,] 0.73661535 0.6616934 0.5806164 0.4959662 0.4106096 0.3274455 0.2491368
#> [80,] 0.77467804 0.6869957 0.5945540 0.5001752 0.4068421 0.3174393 0.2344998
#> [81,] 0.80251813 0.7030363 0.6004615 0.4977770 0.3979923 0.3038914 0.2178042
#> [82,] 0.81797091 0.7081558 0.5971274 0.4879349 0.3835189 0.2864781 0.1988769
#> [83,] 0.81952691 0.7013223 0.5839165 0.4703205 0.3633113 0.2652285 0.1778261
#> [84,] 0.80652152 0.6822672 0.5608576 0.4451619 0.3377095 0.2405265 0.1550374
#> [85,] 0.77922828 0.6515292 0.5286492 0.4132238 0.3074717 0.2130791 NA
#> [86,] 0.73883667 0.6103984 0.4885850 0.3757285 0.2737042 NA NA
#> [87,] 0.68731781 0.5607743 0.4424182 0.3342405 NA NA NA
#> [88,] 0.62720617 0.5049676 0.3921976 NA NA NA NA
#> [89,] 0.56134487 0.4454943 NA NA NA NA NA
#> [90,] 0.49265056 NA NA NA NA NA NA
#> [91,] NA NA NA NA NA NA NA
#> [92,] NA NA NA NA NA NA NA
#> [93,] NA NA NA NA NA NA NA
#> [94,] NA NA NA NA NA NA NA
#> [95,] NA NA NA NA NA NA NA
#> [96,] NA NA NA NA NA NA NA
#> [97,] NA NA NA NA NA NA NA
#> [98,] NA NA NA NA NA NA NA
#> [99,] NA NA NA NA NA NA NA
#> [100,] NA NA NA NA NA NA NA
#> [,87] [,88] [,89] [,90] [,91] [,92]
#> [1,] NA NA NA NA NA NA
#> [2,] NA NA NA NA NA NA
#> [3,] NA NA NA NA NA NA
#> [4,] NA NA NA NA NA NA
#> [5,] NA NA NA NA NA NA
#> [6,] NA NA NA NA NA NA
#> [7,] NA NA NA NA NA NA
#> [8,] NA NA NA NA NA NA
#> [9,] NA NA NA NA NA NA
#> [10,] NA NA NA NA NA NA
#> [11,] NA NA NA NA NA NA
#> [12,] NA NA NA NA NA NA
#> [13,] NA NA NA NA NA NA
#> [14,] NA NA NA NA NA NA
#> [15,] NA NA NA NA NA NA
#> [16,] NA NA NA NA NA NA
#> [17,] NA NA NA NA NA NA
#> [18,] 2.9605726 NA NA NA NA NA
#> [19,] 2.7476436 2.99893803 NA NA NA NA
#> [20,] 2.5374480 2.80041345 3.05616202 NA NA NA
#> [21,] 2.3354279 2.60281718 2.87007462 3.12509864 NA NA
#> [22,] 2.1456895 2.41127490 2.68304746 2.94979581 NA NA
#> [23,] 1.9711371 2.22985021 2.50007168 2.77178840 3.033009361 NA
#> [24,] 1.8136620 2.06163940 2.32530556 2.59605179 2.862972309 3.113566306
#> [25,] 1.6743441 1.90890061 2.16212189 2.42691093 2.693690041 2.950887100
#> [26,] 1.5536327 1.77318461 2.01317601 2.26803820 2.529668929 2.787703875
#> [27,] 1.4514910 1.65544598 1.88047161 2.12246458 2.374854376 2.628673609
#> [28,] 1.3674975 1.55612503 1.76541160 1.99258928 2.232592704 2.477951610
#> [29,] 1.3009074 1.47520049 1.66883059 1.88018202 2.105595519 2.339113996
#> [30,] 1.2506858 1.41221980 1.59101295 1.78637909 1.995905482 2.215088031
#> [31,] 1.2155246 1.36631806 1.53170470 1.71167895 1.904867426 2.108092532
#> [32,] 1.1938575 1.33623736 1.49012933 1.65594590 1.833111437 2.019593678
#> [33,] 1.1838840 1.32035695 1.46501682 1.61842986 1.780555120 1.950282568
#> [34,] 1.1836100 1.31674097 1.45465235 1.59780833 1.746430822 1.900080096
#> [35,] 1.1909067 1.32320648 1.45694739 1.59225347 1.729340825 1.868172540
#> [36,] 1.2035857 1.33740966 1.46953155 1.59952320 1.727340118 1.853078233
#> [37,] 1.2194860 1.35694464 1.48986002 1.61707153 1.738042892 1.852742502
#> [38,] 1.2365618 1.37944683 1.51532873 1.64217107 1.758746163 1.864655269
#> [39,] 1.2529650 1.40269165 1.54338812 1.67203853 1.786562129 1.885983690
#> [40,] 1.2671129 1.42468024 1.57164676 1.70395449 1.818550349 1.913711262
#> [41,] 1.2777357 1.44370557 1.59795753 1.73536942 1.851841432 1.944774921
#> [42,] 1.2839002 1.45839483 1.62048133 1.76399006 1.883745464 1.976192619
#> [43,] 1.2850103 1.46772703 1.63772621 1.78784278 1.911840484 2.005175491
#> [44,] 1.2807852 1.47102749 1.64856240 1.80531304 1.934038584 2.029220609
#> [45,] 1.2712216 1.46794266 1.65221580 1.81516223 1.948629279 2.046182152
#> [46,] 1.2565434 1.45840048 1.64824411 1.81652464 1.954301468 2.054320494
#> [47,] 1.2371459 1.44256161 1.63650051 1.80888869 1.950146401 2.052329903
#> [48,] 1.2135393 1.42076692 1.61708968 1.79206626 1.935644660 2.039346415
#> [49,] 1.1862958 1.39348545 1.59032048 1.76615411 1.910640296 2.014937961
#> [50,] 1.1560037 1.36126648 1.55665883 1.73149086 1.875305127 1.979079060
#> [51,] 1.1232297 1.32469767 1.51668334 1.68861214 1.830095904 1.932112612
#> [52,] 1.0884908 1.28437071 1.47104531 1.63820605 1.775706798 1.874701404
#> [53,] 1.0522350 1.24085458 1.42043405 1.58107051 1.713019408 1.807772107
#> [54,] 1.0148308 1.19467656 1.36554818 1.51807389 1.643052384 1.732454693
#> [55,] 0.9765635 1.14631041 1.30707295 1.45011971 1.566912639 1.650020284
#> [56,] 0.9376394 1.09617117 1.24566383 1.37811655 1.485750035 1.561820458
#> [57,] 0.8981938 1.04461615 1.18193611 1.30295366 1.400717206 1.469230844
#> [58,] 0.8583061 0.99195135 1.11646055 1.22548289 1.312935890 1.373601474
#> [59,] 0.8180170 0.93844256 1.04976432 1.14650686 1.223470655 1.276215750
#> [60,] 0.7773499 0.88433034 0.98233678 1.06677319 1.133310302 1.178259152
#> [61,] 0.7363342 0.82984730 0.91463861 0.98697376 1.043356604 1.080797968
#> [62,] 0.6950286 0.77523601 0.84711271 0.90774772 0.954419386 0.984767512
#> [63,] 0.6535418 0.72076552 0.78019499 0.82968644 0.867216455 0.890968587
#> [64,] 0.6120501 0.66674379 0.71432262 0.75333840 0.782376566 0.800070457
#> [65,] 0.5708064 0.61352394 0.64993785 0.67921215 0.700443608 0.712618382
#> [66,] 0.5301405 0.56150203 0.58748543 0.60777577 0.621880422 0.629043817
#> [67,] 0.4904470 0.51110509 0.52740303 0.53945208 0.547071216 0.549675731
#> [68,] 0.4521612 0.46276945 0.47010450 0.47460963 0.476322255 0.474751974
#> [69,] 0.4157244 0.41691060 0.41595773 0.41355063 0.409861297 0.404430249
#> [70,] 0.3815393 0.37388774 0.36525966 0.35649803 0.347836927 0.338798732
#> [71,] 0.3499232 0.33396754 0.31821242 0.30358431 0.290319372 0.277886745
#> [72,] 0.3210639 0.29729257 0.27490476 0.25484518 0.237304446 0.221675994
#> [73,] 0.2949848 0.26386023 0.23530297 0.21022058 0.188721877 0.170112714
#> [74,] 0.2715282 0.23351682 0.19925435 0.16956468 0.144448520 0.123120705
#> [75,] 0.2503595 0.20596993 0.16650433 0.13266473 0.104325996 0.080614876
#> [76,] 0.2309964 0.18081917 0.13672641 0.09926753 0.068181397 0.042514679
#> [77,] 0.2128591 0.15760229 0.10956141 0.06911038 0.035849168 0.008756904
#> [78,] 0.1953376 0.13585078 0.08466113 0.04195299 0.007192331 NA
#> [79,] 0.1778658 0.11514735 0.06173077 0.01760711 NA NA
#> [80,] 0.1599917 0.09517744 0.04056522 0.00000000 NA NA
#> [81,] 0.1414345 0.07576867 0.02107685 NA NA NA
#> [82,] 0.1221207 0.05691579 NA NA NA NA
#> [83,] 0.1021997 NA NA NA NA NA
#> [84,] NA NA NA NA NA NA
#> [85,] NA NA NA NA NA NA
#> [86,] NA NA NA NA NA NA
#> [87,] NA NA NA NA NA NA
#> [88,] NA NA NA NA NA NA
#> [89,] NA NA NA NA NA NA
#> [90,] NA NA NA NA NA NA
#> [91,] NA NA NA NA NA NA
#> [92,] NA NA NA NA NA NA
#> [93,] NA NA NA NA NA NA
#> [94,] NA NA NA NA NA NA
#> [95,] NA NA NA NA NA NA
#> [96,] NA NA NA NA NA NA
#> [97,] NA NA NA NA NA NA
#> [98,] NA NA NA NA NA NA
#> [99,] NA NA NA NA NA NA
#> [100,] NA NA NA NA NA NA
#> [,93] [,94] [,95] [,96] [,97] [,98] [,99]
#> [1,] NA NA NA NA NA NA NA
#> [2,] NA NA NA NA NA NA NA
#> [3,] NA NA NA NA NA NA NA
#> [4,] NA NA NA NA NA NA NA
#> [5,] NA NA NA NA NA NA NA
#> [6,] NA NA NA NA NA NA NA
#> [7,] NA NA NA NA NA NA NA
#> [8,] NA NA NA NA NA NA NA
#> [9,] NA NA NA NA NA NA NA
#> [10,] NA NA NA NA NA NA NA
#> [11,] NA NA NA NA NA NA NA
#> [12,] NA NA NA NA NA NA NA
#> [13,] NA NA NA NA NA NA NA
#> [14,] NA NA NA NA NA NA NA
#> [15,] NA NA NA NA NA NA NA
#> [16,] NA NA NA NA NA NA NA
#> [17,] NA NA NA NA NA NA NA
#> [18,] NA NA NA NA NA NA NA
#> [19,] NA NA NA NA NA NA NA
#> [20,] NA NA NA NA NA NA NA
#> [21,] NA NA NA NA NA NA NA
#> [22,] NA NA NA NA NA NA NA
#> [23,] NA NA NA NA NA NA NA
#> [24,] NA NA NA NA NA NA NA
#> [25,] NA NA NA NA NA NA NA
#> [26,] 3.0302198 NA NA NA NA NA NA
#> [27,] 2.8730502 3.0961138 NA NA NA NA NA
#> [28,] 2.7190759 2.9449671 NA NA NA NA NA
#> [29,] 2.5725760 2.7961252 2.9991069 NA NA NA NA
#> [30,] 2.4372580 2.6538946 2.8553359 NA NA NA NA
#> [31,] 2.3161645 2.5220138 2.7172092 NA NA NA NA
#> [32,] 2.2115982 2.4035459 2.5884035 2.7583518 NA NA NA
#> [33,] 2.1250696 2.3007952 2.4719199 2.6319656 NA NA NA
#> [34,] 2.0572734 2.2152530 2.3699981 2.5165216 2.6494031 NA NA
#> [35,] 2.0080985 2.1475759 2.2840640 2.4141494 2.5338898 NA NA
#> [36,] 1.9766708 2.0976008 2.2147119 2.3261841 2.4296865 NA NA
#> [37,] 1.9614295 2.0643948 2.1617255 2.2531551 2.3380360 2.4154016 NA
#> [38,] 1.9602303 2.0463382 2.1241330 2.1948121 2.2594221 2.3187177 NA
#> [39,] 1.9704717 2.0412349 2.1002964 2.1501858 2.1936007 2.2330659 NA
#> [40,] 1.9892331 2.0464434 2.0880261 2.1176810 2.1396651 2.1582641 NA
#> [41,] 2.0134199 2.0590206 2.0847161 2.0951947 2.0961411 2.0935390 2.0928882
#> [42,] 2.0399045 2.0758705 2.0874912 2.0802529 2.0611060 2.0376209 2.0170064
#> [43,] 2.0656586 2.0938893 2.0933580 2.0701582 2.0323235 1.9888593 1.9485815
#> [44,] 2.0878697 2.1101019 2.0993519 2.0621401 2.0073878 1.9453515 1.8863054
#> [45,] 2.1040394 2.1217815 2.1026744 2.0534996 1.9838668 1.9050765 1.8286729
#> [46,] 2.1120589 2.1265507 2.1008127 2.0417414 1.9594386 1.8660260 1.7740989
#> [47,] 2.1102629 2.1224590 2.0916379 2.0246869 1.9320111 1.8263239 1.7210314
#> [48,] 2.0974598 2.1080358 2.0734778 2.0005622 1.8998207 1.7843282 1.6680486
#> [49,] 2.0729400 2.0823173 2.0451621 1.9680590 1.8615041 1.7387087 1.6139388
#> [50,] 2.0364635 2.0448486 2.0060391 1.9263649 1.8161394 1.6884971 1.5577545
#> [51,] 1.9882290 1.9956618 1.9559642 1.8751631 1.7632581 1.6331083 1.4988420
#> [52,] 1.9288263 1.9352327 1.8952633 1.8146044 1.7028264 1.5723327 1.4368447
#> [53,] 1.8591769 1.8644200 1.8246739 1.7452539 1.6352007 1.5063036 1.3716824
#> [54,] 1.7804649 1.7843910 1.7452694 1.6680185 1.5610628 1.4354430 1.3035129
#> [55,] 1.6940629 1.6965385 1.6583722 1.5840604 1.4813399 1.3603936 1.2326786
#> [56,] 1.6014577 1.6023960 1.5654618 1.4947053 1.3971184 1.2819440 1.1596478
#> [57,] 1.5041785 1.5035543 1.4680849 1.4013511 1.3095577 1.2009538 1.0849551
#> [58,] 1.4037332 1.4015855 1.3677727 1.3053843 1.2198120 1.1182855 1.0091493
#> [59,] 1.3015535 1.2979785 1.2659705 1.2081093 1.1289646 1.0347499 0.9327516
#> [60,] 1.1989528 1.1940887 1.1639835 1.1106952 1.0379806 0.9510672 0.8562288
#> [61,] 1.0970964 1.0911032 1.0629407 1.0141418 0.9476780 0.8678466 NA
#> [62,] 0.9969855 0.9900220 0.9637765 0.9192644 0.8587189 0.7855844 NA
#> [63,] 0.8994516 0.8916540 0.8672299 0.8266986 0.7716179 0.7046761 NA
#> [64,] 0.8051621 0.7966258 0.7738584 0.7369177 0.6867653 0.6254422 NA
#> [65,] 0.7146325 0.7054009 0.6840630 0.6502638 0.6044593 NA NA
#> [66,] 0.6282446 0.6183049 0.5981201 0.5669833 0.5249429 NA NA
#> [67,] 0.5462671 0.5355550 0.5162175 0.4872656 0.4484403 NA NA
#> [68,] 0.4688772 0.4572902 0.4384893 0.4112784 NA NA NA
#> [69,] 0.3961819 0.3835990 0.3650468 0.3391971 NA NA NA
#> [70,] 0.3282372 0.3145446 0.2960036 NA NA NA NA
#> [71,] 0.2650654 0.2501837 0.2314933 NA NA NA NA
#> [72,] 0.2066697 0.1905813 0.1716788 NA NA NA NA
#> [73,] 0.1530466 0.1358184 NA NA NA NA NA
#> [74,] 0.1041952 0.0859959 NA NA NA NA NA
#> [75,] 0.0601247 NA NA NA NA NA NA
#> [76,] NA NA NA NA NA NA NA
#> [77,] NA NA NA NA NA NA NA
#> [78,] NA NA NA NA NA NA NA
#> [79,] NA NA NA NA NA NA NA
#> [80,] NA NA NA NA NA NA NA
#> [81,] NA NA NA NA NA NA NA
#> [82,] NA NA NA NA NA NA NA
#> [83,] NA NA NA NA NA NA NA
#> [84,] NA NA NA NA NA NA NA
#> [85,] NA NA NA NA NA NA NA
#> [86,] NA NA NA NA NA NA NA
#> [87,] NA NA NA NA NA NA NA
#> [88,] NA NA NA NA NA NA NA
#> [89,] NA NA NA NA NA NA NA
#> [90,] NA NA NA NA NA NA NA
#> [91,] NA NA NA NA NA NA NA
#> [92,] NA NA NA NA NA NA NA
#> [93,] NA NA NA NA NA NA NA
#> [94,] NA NA NA NA NA NA NA
#> [95,] NA NA NA NA NA NA NA
#> [96,] NA NA NA NA NA NA NA
#> [97,] NA NA NA NA NA NA NA
#> [98,] NA NA NA NA NA NA NA
#> [99,] NA NA NA NA NA NA NA
#> [100,] NA NA NA NA NA NA NA
#> [,100]
#> [1,] NA
#> [2,] NA
#> [3,] NA
#> [4,] NA
#> [5,] NA
#> [6,] NA
#> [7,] NA
#> [8,] NA
#> [9,] NA
#> [10,] NA
#> [11,] NA
#> [12,] NA
#> [13,] NA
#> [14,] NA
#> [15,] NA
#> [16,] NA
#> [17,] NA
#> [18,] NA
#> [19,] NA
#> [20,] NA
#> [21,] NA
#> [22,] NA
#> [23,] NA
#> [24,] NA
#> [25,] NA
#> [26,] NA
#> [27,] NA
#> [28,] NA
#> [29,] NA
#> [30,] NA
#> [31,] NA
#> [32,] NA
#> [33,] NA
#> [34,] NA
#> [35,] NA
#> [36,] NA
#> [37,] NA
#> [38,] NA
#> [39,] NA
#> [40,] NA
#> [41,] NA
#> [42,] NA
#> [43,] NA
#> [44,] NA
#> [45,] NA
#> [46,] NA
#> [47,] NA
#> [48,] NA
#> [49,] NA
#> [50,] NA
#> [51,] NA
#> [52,] NA
#> [53,] NA
#> [54,] NA
#> [55,] NA
#> [56,] NA
#> [57,] NA
#> [58,] NA
#> [59,] NA
#> [60,] NA
#> [61,] NA
#> [62,] NA
#> [63,] NA
#> [64,] NA
#> [65,] NA
#> [66,] NA
#> [67,] NA
#> [68,] NA
#> [69,] NA
#> [70,] NA
#> [71,] NA
#> [72,] NA
#> [73,] NA
#> [74,] NA
#> [75,] NA
#> [76,] NA
#> [77,] NA
#> [78,] NA
#> [79,] NA
#> [80,] NA
#> [81,] NA
#> [82,] NA
#> [83,] NA
#> [84,] NA
#> [85,] NA
#> [86,] NA
#> [87,] NA
#> [88,] NA
#> [89,] NA
#> [90,] NA
#> [91,] NA
#> [92,] NA
#> [93,] NA
#> [94,] NA
#> [95,] NA
#> [96,] NA
#> [97,] NA
#> [98,] NA
#> [99,] NA
#> [100,] NA
#>
#> attr(,"class")
#> [1] "list" "sph_density"