boot_pr_comp: Function to compute the confidence intervals for the...

In eigenprcomp: Computes confidence intervals for principal components

Description

The proportion explained by each eigenvalue and confidence intervals for each eigenvalue are computed via nonparametric bootstrap. When doing PCA, a natural question that arises when choosing the amount of components is whether the chosen set of eigenvalues conform a well defined set. If two eigenvalues are statistically equal, then the space spanned by them is not correctly defined, so consequently none of them should be included in the set of chosen eigenvalues. Ideally, the chosen set should include only eigenvalues that are statistically different between them, and also different respect to the other eigenvalues. On the other hand, it is usually important to compute a confidence interval for the proportion explained by the chosen set which is also addressed in this function.

Usage

boot_pr_comp(valores, size, alpha, plot = TRUE)

Arguments

valores	A matrix with the dataset should be specified.This dataset should have the observations as rows and the variables as columns.
size	The amount of boostrap replicates.
alpha	The alpha, which is by default 0,05.
plot	A boolean value indicating whether the plot of the eigenvalues CIs should be produced.

Value

proportions_quantiles	The upper and lower quantile for the explained proportion. Note that for k variables, only k-1 proportions are needed since k eigenvalues always explains the total variance
proportions_used	The boostrapped proportions used for the computation. It can be used to produce histograms
eigen_quantiles	The upper and lower quantile for the eigenvalues
eigen_used	The used eigenvalues for the eigenvalues

Author(s)

Francisco Juretig

Examples

boot_pr_comp(as.matrix(iris[,1:4]))

function(valores,size=1000,alpha=0.05,plot=TRUE){

if (is.matrix(valores)==FALSE){

return ("Oject is not a matrix")

  }else{

lengs               = length(valores[,1])
hlengs              = length(valores[1,])
store_bootstrap     = matrix(0,size,hlengs)
elements_aux        = NULL
indexes             = seq(1,lengs,1)
work_matrix         = matrix(0,lengs,hlengs)
empirical_quantiles1= matrix(0,hlengs-1,2)
store_eigen         = matrix(0,size,hlengs)
empirical_quantiles2= matrix(0,hlengs,2)

for (sim in 1:size){

resample_indexes= sample(indexes,length(indexes), replace=T)

for (ips in 1:length(resample_indexes)){
work_matrix[ips,] = valores[resample_indexes[ips],]
  }

cova           = (lengs-1)*cov(work_matrix)/(lengs)
auto_va        = unlist(eigen(cova)$values)
cum_eigen      = cumsum(auto_va)
total_var      = sum(auto_va)
percent        = (cum_eigen/total_var)

store_bootstrap[sim,] = percent 
store_eigen[sim,]     = auto_va
  }

store_bootstrap      = store_bootstrap[,-hlengs]

for (iter in 1:(hlengs-1)){
empirical_quantiles1[iter,2]    = quantile(store_bootstrap[,iter],1-alpha/2)
empirical_quantiles1[iter,1]    = quantile(store_bootstrap[,iter],alpha/2)
  }

for (iter in 1:(hlengs)){
empirical_quantiles2[iter,2]    = quantile(store_eigen[,iter],1-alpha/2)
empirical_quantiles2[iter,1]    = quantile(store_eigen[,iter],alpha/2)
  }

if (plot==TRUE){

plot(0:max( empirical_quantiles2[,2]),0:max( empirical_quantiles2[,2]),
xlim=c(0,max( empirical_quantiles2)),ylim=c(0,nrow( empirical_quantiles2)),
type="n",xlab="Values",ylab="Eigenvalues")

for (q in 1:nrow(empirical_quantiles2)){
segments( empirical_quantiles2[q,1],q, empirical_quantiles2[q,2],q,lwd=2)
abline(v= empirical_quantiles2[q,1],lty = 3)
  }

  }

colnames(empirical_quantiles1)        = c(paste(alpha/2*100,"%"),
paste((1-alpha/2)*100,"%"))
colnames(empirical_quantiles2)        = c(paste(alpha/2*100,"%"),
paste((1-alpha/2)*100,"%"))
lista  = list("proportions_quantiles" = empirical_quantiles1,
"proportions_used" = store_bootstrap,
"eigen_quantiles"= empirical_quantiles2,"eigen_used"=store_eigen)

return(lista)

  }
  }

Example output

$proportions_quantiles
         2.5 %    97.5 %
[1,] 0.9083078 0.9383528
[2,] 0.9723327 0.9826521
[3,] 0.9931681 0.9963351

$proportions_used
             [,1]      [,2]      [,3]
   [1,] 0.9215936 0.9725221 0.9933997
   [2,] 0.9237067 0.9781605 0.9958286
   [3,] 0.9363677 0.9796772 0.9952248
   [4,] 0.9318408 0.9785907 0.9948977
   [5,] 0.9283152 0.9782674 0.9962053
   [6,] 0.9285544 0.9763430 0.9940601
   [7,] 0.9173178 0.9733782 0.9940065
   [8,] 0.9186419 0.9796296 0.9953409
   [9,] 0.9228076 0.9773456 0.9950044
  [10,] 0.9274159 0.9762168 0.9954941
  [11,] 0.9133982 0.9721645 0.9941713
  [12,] 0.9261818 0.9830938 0.9960672
  [13,] 0.9283694 0.9804640 0.9950547
  [14,] 0.9254052 0.9773487 0.9957123
  [15,] 0.9292127 0.9817383 0.9950005
  [16,] 0.9181727 0.9771468 0.9956652
  [17,] 0.9273074 0.9826490 0.9953977
  [18,] 0.9326426 0.9784970 0.9960010
  [19,] 0.9291142 0.9814283 0.9954570
  [20,] 0.9339807 0.9763369 0.9947395
  [21,] 0.9215452 0.9792076 0.9949113
  [22,] 0.9371671 0.9805552 0.9953198
  [23,] 0.9276382 0.9791163 0.9941589
  [24,] 0.9352371 0.9784765 0.9953017
  [25,] 0.9337106 0.9810797 0.9959584
  [26,] 0.9150830 0.9728523 0.9939543
  [27,] 0.9299915 0.9799410 0.9956171
  [28,] 0.9265507 0.9770434 0.9944977
  [29,] 0.9174276 0.9764371 0.9932040
  [30,] 0.9302251 0.9809786 0.9939008
  [31,] 0.9289621 0.9790270 0.9946771
  [32,] 0.9394592 0.9813081 0.9952334
  [33,] 0.9316479 0.9743650 0.9945082
  [34,] 0.9247639 0.9781051 0.9950821
  [35,] 0.9096137 0.9753658 0.9950545
  [36,] 0.9276011 0.9786044 0.9944957
  [37,] 0.9251996 0.9810937 0.9955657
  [38,] 0.9236140 0.9800212 0.9951059
  [39,] 0.9241019 0.9782615 0.9953919
  [40,] 0.9318722 0.9785701 0.9950154
  [41,] 0.9211314 0.9816743 0.9950084
  [42,] 0.9264564 0.9759629 0.9953453
  [43,] 0.9247263 0.9790869 0.9954510
  [44,] 0.9389301 0.9833366 0.9961660
  [45,] 0.9459343 0.9838443 0.9951498
  [46,] 0.9225332 0.9783895 0.9940907
  [47,] 0.9324387 0.9805423 0.9945940
  [48,] 0.9265799 0.9789452 0.9937611
  [49,] 0.9237737 0.9821632 0.9953022
  [50,] 0.9136941 0.9740769 0.9942077
  [51,] 0.9239504 0.9799580 0.9954663
  [52,] 0.9224643 0.9783044 0.9937731
  [53,] 0.9249791 0.9815761 0.9949139
  [54,] 0.9276840 0.9760867 0.9939049
  [55,] 0.9191269 0.9762557 0.9940802
  [56,] 0.9186783 0.9789542 0.9949963
  [57,] 0.9263165 0.9754104 0.9945717
  [58,] 0.9201095 0.9776593 0.9941384
  [59,] 0.9331211 0.9818473 0.9959987
  [60,] 0.9338275 0.9796381 0.9956144
  [61,] 0.9363712 0.9821007 0.9952129
  [62,] 0.9168660 0.9807480 0.9948080
  [63,] 0.9322591 0.9792734 0.9951441
  [64,] 0.9217332 0.9795169 0.9951085
  [65,] 0.9327245 0.9775076 0.9951336
  [66,] 0.9235006 0.9765512 0.9943334
  [67,] 0.9177409 0.9782462 0.9950466
  [68,] 0.9308980 0.9806635 0.9938574
  [69,] 0.9263351 0.9790568 0.9963455
  [70,] 0.9284301 0.9802555 0.9962544
  [71,] 0.9354072 0.9766929 0.9941084
  [72,] 0.9283305 0.9736862 0.9950429
  [73,] 0.9204434 0.9793005 0.9955181
  [74,] 0.9260689 0.9732625 0.9928511
  [75,] 0.9297671 0.9788035 0.9944649
  [76,] 0.9340690 0.9778519 0.9960909
  [77,] 0.9210552 0.9794100 0.9956967
  [78,] 0.9280877 0.9773282 0.9950268
  [79,] 0.9162935 0.9774523 0.9939953
  [80,] 0.9156167 0.9775904 0.9945347
  [81,] 0.9235528 0.9774583 0.9941419
  [82,] 0.9408092 0.9805066 0.9953324
  [83,] 0.9340481 0.9806135 0.9940724
  [84,] 0.9186575 0.9739844 0.9949813
  [85,] 0.9274819 0.9769682 0.9941924
  [86,] 0.9318580 0.9780646 0.9954229
  [87,] 0.9217233 0.9792849 0.9959296
  [88,] 0.9156163 0.9772415 0.9943309
  [89,] 0.9180432 0.9805535 0.9943702
  [90,] 0.9258194 0.9775676 0.9944011
  [91,] 0.9240406 0.9785334 0.9941064
  [92,] 0.9293238 0.9799344 0.9955234
  [93,] 0.9267767 0.9819092 0.9961225
  [94,] 0.9268908 0.9811490 0.9956730
  [95,] 0.9186815 0.9789227 0.9937615
  [96,] 0.9298665 0.9775899 0.9945509
  [97,] 0.9166103 0.9733730 0.9927506
  [98,] 0.9245670 0.9773107 0.9949811
  [99,] 0.9254964 0.9832126 0.9952328
 [100,] 0.9269799 0.9771512 0.9948487
 [101,] 0.9350906 0.9801150 0.9962719
 [102,] 0.9332412 0.9784995 0.9945267
 [103,] 0.9184286 0.9760263 0.9952723
 [104,] 0.9268043 0.9768654 0.9957914
 [105,] 0.9383478 0.9830610 0.9950360
 [106,] 0.9047408 0.9716905 0.9928113
 [107,] 0.9206166 0.9742794 0.9941336
 [108,] 0.9321411 0.9816485 0.9956612
 [109,] 0.9295302 0.9751920 0.9940013
 [110,] 0.9186198 0.9796376 0.9950596
 [111,] 0.9056301 0.9711703 0.9950367
 [112,] 0.9194265 0.9802294 0.9948779
 [113,] 0.9314188 0.9814618 0.9943887
 [114,] 0.9277716 0.9763698 0.9953969
 [115,] 0.9261825 0.9793016 0.9941411
 [116,] 0.9255803 0.9774387 0.9938321
 [117,] 0.9147196 0.9782477 0.9951467
 [118,] 0.9218630 0.9759998 0.9949280
 [119,] 0.9292267 0.9816314 0.9948744
 [120,] 0.9260899 0.9789763 0.9957659
 [121,] 0.9293613 0.9799354 0.9952444
 [122,] 0.9159828 0.9688112 0.9948136
 [123,] 0.9260102 0.9757532 0.9947447
 [124,] 0.9193469 0.9788215 0.9937441
 [125,] 0.9333037 0.9809669 0.9947750
 [126,] 0.9163874 0.9769961 0.9951208
 [127,] 0.9255079 0.9790156 0.9952664
 [128,] 0.9260744 0.9783546 0.9950369
 [129,] 0.9190083 0.9781080 0.9962087
 [130,] 0.9216204 0.9758152 0.9952037
 [131,] 0.9265880 0.9752330 0.9936721
 [132,] 0.9229992 0.9792844 0.9947409
 [133,] 0.9186771 0.9805473 0.9961175
 [134,] 0.9251788 0.9786010 0.9952651
 [135,] 0.9300001 0.9770501 0.9937674
 [136,] 0.9277385 0.9825462 0.9948869
 [137,] 0.9174265 0.9750337 0.9942672
 [138,] 0.9341387 0.9785296 0.9942122
 [139,] 0.9257301 0.9808799 0.9951621
 [140,] 0.9237824 0.9774200 0.9942743
 [141,] 0.9281985 0.9791231 0.9951634
 [142,] 0.9276764 0.9811959 0.9957834
 [143,] 0.9319716 0.9779098 0.9947718
 [144,] 0.9248545 0.9850411 0.9965502
 [145,] 0.9349930 0.9829236 0.9959814
 [146,] 0.9208561 0.9780261 0.9950859
 [147,] 0.9337374 0.9776274 0.9951756
 [148,] 0.9200826 0.9766921 0.9964063
 [149,] 0.9254122 0.9786063 0.9957273
 [150,] 0.9100244 0.9753865 0.9946436
 [151,] 0.9303462 0.9728389 0.9949430
 [152,] 0.9219570 0.9761657 0.9949641
 [153,] 0.9287874 0.9763897 0.9953032
 [154,] 0.9224787 0.9804294 0.9943442
 [155,] 0.9325488 0.9855059 0.9962128
 [156,] 0.9354961 0.9813271 0.9948602
 [157,] 0.9328587 0.9768571 0.9946925
 [158,] 0.9320529 0.9831057 0.9955935
 [159,] 0.9278058 0.9759305 0.9945889
 [160,] 0.9252912 0.9749328 0.9949543
 [161,] 0.9231712 0.9816026 0.9947356
 [162,] 0.9344255 0.9813413 0.9940977
 [163,] 0.9299518 0.9776193 0.9955400
 [164,] 0.9260039 0.9812477 0.9958168
 [165,] 0.9239946 0.9790907 0.9943925
 [166,] 0.9192395 0.9757472 0.9941542
 [167,] 0.9141298 0.9768803 0.9956577
 [168,] 0.9052578 0.9759082 0.9966853
 [169,] 0.9319721 0.9797980 0.9947024
 [170,] 0.9325302 0.9795377 0.9946103
 [171,] 0.9325745 0.9786473 0.9943907
 [172,] 0.9239120 0.9761800 0.9952295
 [173,] 0.9327936 0.9805871 0.9961278
 [174,] 0.9224875 0.9779524 0.9951265
 [175,] 0.9188093 0.9794238 0.9963614
 [176,] 0.9171322 0.9759364 0.9953343
 [177,] 0.9278223 0.9759555 0.9949469
 [178,] 0.9369393 0.9813255 0.9963132
 [179,] 0.9182878 0.9764175 0.9950174
 [180,] 0.9231167 0.9756577 0.9949831
 [181,] 0.9227484 0.9799009 0.9959648
 [182,] 0.9182805 0.9772330 0.9939324
 [183,] 0.9264919 0.9774920 0.9947268
 [184,] 0.9263454 0.9769871 0.9953023
 [185,] 0.9234254 0.9761749 0.9945993
 [186,] 0.9305998 0.9791665 0.9959868
 [187,] 0.9287022 0.9757768 0.9943727
 [188,] 0.9302296 0.9814566 0.9940287
 [189,] 0.9265165 0.9807055 0.9954170
 [190,] 0.9212980 0.9789500 0.9951403
 [191,] 0.9266098 0.9754041 0.9952207
 [192,] 0.9088831 0.9728154 0.9939210
 [193,] 0.9367362 0.9830815 0.9949377
 [194,] 0.9251168 0.9742882 0.9953939
 [195,] 0.9160979 0.9760737 0.9938173
 [196,] 0.9227888 0.9786482 0.9940885
 [197,] 0.9260291 0.9769663 0.9952850
 [198,] 0.9283809 0.9775791 0.9953947
 [199,] 0.9177323 0.9776765 0.9947084
 [200,] 0.9163928 0.9802012 0.9949654
 [201,] 0.9270686 0.9784874 0.9940059
 [202,] 0.9233699 0.9795972 0.9943985
 [203,] 0.9182928 0.9718397 0.9939330
 [204,] 0.9335898 0.9781597 0.9958063
 [205,] 0.9014482 0.9825130 0.9958630
 [206,] 0.9273607 0.9769486 0.9933698
 [207,] 0.9098689 0.9766982 0.9953206
 [208,] 0.9231685 0.9786039 0.9959693
 [209,] 0.9228757 0.9771618 0.9942295
 [210,] 0.9343610 0.9762919 0.9946515
 [211,] 0.9362157 0.9791328 0.9958645
 [212,] 0.9100075 0.9687488 0.9940574
 [213,] 0.9361099 0.9817895 0.9940068
 [214,] 0.9190148 0.9799545 0.9943930
 [215,] 0.9204076 0.9732976 0.9949898
 [216,] 0.9354423 0.9799140 0.9953654
 [217,] 0.9282859 0.9791247 0.9946160
 [218,] 0.9220593 0.9787142 0.9931687
 [219,] 0.9173398 0.9781234 0.9949539
 [220,] 0.9318359 0.9770398 0.9939757
 [221,] 0.9459894 0.9829464 0.9966084
 [222,] 0.9335678 0.9796749 0.9957776
 [223,] 0.9153784 0.9812341 0.9960710
 [224,] 0.9200097 0.9775060 0.9944151
 [225,] 0.9291174 0.9744653 0.9927873
 [226,] 0.9358007 0.9779137 0.9958021
 [227,] 0.9272449 0.9779898 0.9941514
 [228,] 0.9273677 0.9795200 0.9949987
 [229,] 0.9198674 0.9724753 0.9945713
 [230,] 0.9236116 0.9768888 0.9950768
 [231,] 0.9222967 0.9774459 0.9949588
 [232,] 0.9190472 0.9769564 0.9946793
 [233,] 0.9181474 0.9815662 0.9960806
 [234,] 0.9290179 0.9828811 0.9956021
 [235,] 0.9215082 0.9773503 0.9940065
 [236,] 0.9098742 0.9777132 0.9955664
 [237,] 0.9302037 0.9804884 0.9957326
 [238,] 0.9305051 0.9807159 0.9955667
 [239,] 0.9245169 0.9745716 0.9947813
 [240,] 0.9386246 0.9763471 0.9947884
 [241,] 0.9285107 0.9783688 0.9956338
 [242,] 0.9106843 0.9751796 0.9936599
 [243,] 0.9253956 0.9786420 0.9961206
 [244,] 0.9286632 0.9806307 0.9946174
 [245,] 0.9268797 0.9798151 0.9967169
 [246,] 0.9392338 0.9780566 0.9946311
 [247,] 0.9279484 0.9762318 0.9963627
 [248,] 0.9192520 0.9772745 0.9946042
 [249,] 0.9311826 0.9782091 0.9956429
 [250,] 0.9268728 0.9744624 0.9948243
 [251,] 0.9280244 0.9750491 0.9932523
 [252,] 0.9264000 0.9791773 0.9948617
 [253,] 0.9259116 0.9780954 0.9935630
 [254,] 0.9023792 0.9690053 0.9949903
 [255,] 0.9299743 0.9777868 0.9947390
 [256,] 0.9261723 0.9786567 0.9948128
 [257,] 0.9292465 0.9791240 0.9960020
 [258,] 0.9324390 0.9780869 0.9956330
 [259,] 0.9275917 0.9800992 0.9949210
 [260,] 0.9197677 0.9773158 0.9938319
 [261,] 0.9306826 0.9803369 0.9959076
 [262,] 0.9242601 0.9762426 0.9942136
 [263,] 0.9271513 0.9769372 0.9950521
 [264,] 0.9197973 0.9800529 0.9964859
 [265,] 0.9231072 0.9773996 0.9938925
 [266,] 0.9317950 0.9797832 0.9955112
 [267,] 0.9300604 0.9816550 0.9946388
 [268,] 0.9130427 0.9791332 0.9955790
 [269,] 0.9157323 0.9689071 0.9924665
 [270,] 0.9252361 0.9768022 0.9939756
 [271,] 0.9122613 0.9751049 0.9942454
 [272,] 0.9420363 0.9842226 0.9958428
 [273,] 0.9192215 0.9769707 0.9951372
 [274,] 0.9241678 0.9768441 0.9935809
 [275,] 0.9363264 0.9792892 0.9958247
 [276,] 0.9256483 0.9775762 0.9940861
 [277,] 0.9225858 0.9779930 0.9944978
 [278,] 0.9310745 0.9787771 0.9953412
 [279,] 0.9217194 0.9786337 0.9951502
 [280,] 0.9226798 0.9739784 0.9938773
 [281,] 0.9146752 0.9736774 0.9946684
 [282,] 0.9278815 0.9790253 0.9953274
 [283,] 0.9343617 0.9776825 0.9945815
 [284,] 0.9300841 0.9763705 0.9948208
 [285,] 0.9369288 0.9790879 0.9953315
 [286,] 0.9142092 0.9777287 0.9961784
 [287,] 0.9142108 0.9747459 0.9952269
 [288,] 0.9184249 0.9810397 0.9956338
 [289,] 0.9147492 0.9752907 0.9944658
 [290,] 0.9185991 0.9741624 0.9951504
 [291,] 0.9288601 0.9799632 0.9941309
 [292,] 0.9201110 0.9775793 0.9943755
 [293,] 0.9247449 0.9824766 0.9951879
 [294,] 0.9194683 0.9768094 0.9937785
 [295,] 0.9263122 0.9803329 0.9943319
 [296,] 0.9331469 0.9764392 0.9941982
 [297,] 0.9239779 0.9780062 0.9946409
 [298,] 0.9356726 0.9801100 0.9957427
 [299,] 0.9339145 0.9799522 0.9949177
 [300,] 0.9207244 0.9749684 0.9935782
 [301,] 0.9288915 0.9776864 0.9947166
 [302,] 0.9234813 0.9750234 0.9954095
 [303,] 0.9218472 0.9795531 0.9966713
 [304,] 0.9218464 0.9736346 0.9941539
 [305,] 0.9170509 0.9783725 0.9957683
 [306,] 0.9339369 0.9799860 0.9940999
 [307,] 0.9375388 0.9817208 0.9950898
 [308,] 0.9094122 0.9729218 0.9942666
 [309,] 0.9219849 0.9776352 0.9958005
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 [683,] 0.9310626 0.9841906 0.9953691
 [684,] 0.9142754 0.9759924 0.9946327
 [685,] 0.9257700 0.9785515 0.9940638
 [686,] 0.9235354 0.9772326 0.9949922
 [687,] 0.9227014 0.9759518 0.9953629
 [688,] 0.9263017 0.9743111 0.9951576
 [689,] 0.9211781 0.9804953 0.9944122
 [690,] 0.9269893 0.9783638 0.9945421
 [691,] 0.9104307 0.9725119 0.9945755
 [692,] 0.9286024 0.9792577 0.9950346
 [693,] 0.9257849 0.9772260 0.9955080
 [694,] 0.9364333 0.9803325 0.9948754
 [695,] 0.9327743 0.9779775 0.9958602
 [696,] 0.9106332 0.9792858 0.9960288
 [697,] 0.9178447 0.9743026 0.9942032
 [698,] 0.9341757 0.9786582 0.9964457
 [699,] 0.9273553 0.9819619 0.9956085
 [700,] 0.9168925 0.9770620 0.9955939
 [701,] 0.9165447 0.9759949 0.9950320
 [702,] 0.9316887 0.9764988 0.9953288
 [703,] 0.9289114 0.9792766 0.9944989
 [704,] 0.9273459 0.9806662 0.9964427
 [705,] 0.9261068 0.9808017 0.9949419
 [706,] 0.9245330 0.9778337 0.9948429
 [707,] 0.9205155 0.9771169 0.9933281
 [708,] 0.9136947 0.9752233 0.9944223
 [709,] 0.9276657 0.9787076 0.9948439
 [710,] 0.9228565 0.9727207 0.9944468
 [711,] 0.9256337 0.9753788 0.9942186
 [712,] 0.9235211 0.9781075 0.9964336
 [713,] 0.9311543 0.9781508 0.9938618
 [714,] 0.9246337 0.9813388 0.9942186
 [715,] 0.9233772 0.9754109 0.9945103
 [716,] 0.9130579 0.9766165 0.9946548
 [717,] 0.9144608 0.9754102 0.9951126
 [718,] 0.9154017 0.9758222 0.9947161
 [719,] 0.9305260 0.9836106 0.9964160
 [720,] 0.9336118 0.9766625 0.9934651
 [721,] 0.9230023 0.9774356 0.9941999
 [722,] 0.9120445 0.9752504 0.9947686
 [723,] 0.9252146 0.9778411 0.9947762
 [724,] 0.9320805 0.9782497 0.9941329
 [725,] 0.9246497 0.9749252 0.9948198
 [726,] 0.9122360 0.9750937 0.9938513
 [727,] 0.9223946 0.9758133 0.9946138
 [728,] 0.9223818 0.9757089 0.9940961
 [729,] 0.9263858 0.9782908 0.9937283
 [730,] 0.9241847 0.9732317 0.9933522
 [731,] 0.9152233 0.9777750 0.9947112
 [732,] 0.9207253 0.9761817 0.9955366
 [733,] 0.9220078 0.9800114 0.9940899
 [734,] 0.9307536 0.9727751 0.9945989
 [735,] 0.9385469 0.9812412 0.9957605
 [736,] 0.9254379 0.9754925 0.9939919
 [737,] 0.9449075 0.9815772 0.9951655
 [738,] 0.9278402 0.9754147 0.9940286
 [739,] 0.9303797 0.9766393 0.9961076
 [740,] 0.9318372 0.9774540 0.9950781
 [741,] 0.9262849 0.9798947 0.9954967
 [742,] 0.9290433 0.9786330 0.9952393
 [743,] 0.9286474 0.9771696 0.9958441
 [744,] 0.9165352 0.9766370 0.9948997
 [745,] 0.9205223 0.9790419 0.9944659
 [746,] 0.9165469 0.9775060 0.9956773
 [747,] 0.9192032 0.9762007 0.9948741
 [748,] 0.9288569 0.9748238 0.9955736
 [749,] 0.9197657 0.9736641 0.9942331
 [750,] 0.9323070 0.9781091 0.9948678
 [751,] 0.9171650 0.9746888 0.9946464
 [752,] 0.9260044 0.9796595 0.9954102
 [753,] 0.9283446 0.9772055 0.9953839
 [754,] 0.9292158 0.9779380 0.9944413
 [755,] 0.9260647 0.9778667 0.9953203
 [756,] 0.9249820 0.9808946 0.9954204
 [757,] 0.9033754 0.9775636 0.9929372
 [758,] 0.9319053 0.9756321 0.9951115
 [759,] 0.9188007 0.9813716 0.9954273
 [760,] 0.9181429 0.9719133 0.9931822
 [761,] 0.9216541 0.9764042 0.9952359
 [762,] 0.9238668 0.9793794 0.9955347
 [763,] 0.9303667 0.9791629 0.9955494
 [764,] 0.9378500 0.9814811 0.9955384
 [765,] 0.9214266 0.9799904 0.9960896
 [766,] 0.9263533 0.9796364 0.9950111
 [767,] 0.9276856 0.9797606 0.9957026
 [768,] 0.9055838 0.9746629 0.9941053
 [769,] 0.9227959 0.9757949 0.9948353
 [770,] 0.9276566 0.9738396 0.9958666
 [771,] 0.9366070 0.9780150 0.9933155
 [772,] 0.9218551 0.9790109 0.9954825
 [773,] 0.9191019 0.9741770 0.9949011
 [774,] 0.9184512 0.9805150 0.9952688
 [775,] 0.9173473 0.9828045 0.9954860
 [776,] 0.9175586 0.9767618 0.9955280
 [777,] 0.9142537 0.9780281 0.9947747
 [778,] 0.9203706 0.9798874 0.9950172
 [779,] 0.9231961 0.9799081 0.9946286
 [780,] 0.9157563 0.9774162 0.9938066
 [781,] 0.9301694 0.9813308 0.9962081
 [782,] 0.9374275 0.9784145 0.9939454
 [783,] 0.9151683 0.9785811 0.9953208
 [784,] 0.9141365 0.9711325 0.9928229
 [785,] 0.9099946 0.9776434 0.9955465
 [786,] 0.9312110 0.9795122 0.9958009
 [787,] 0.9174055 0.9763556 0.9937487
 [788,] 0.9188546 0.9775357 0.9939026
 [789,] 0.9286823 0.9779615 0.9955361
 [790,] 0.9275269 0.9797913 0.9956506
 [791,] 0.9281195 0.9732412 0.9932413
 [792,] 0.9213455 0.9750619 0.9944268
 [793,] 0.9293646 0.9760838 0.9951544
 [794,] 0.9194800 0.9794056 0.9947939
 [795,] 0.9278301 0.9764971 0.9945656
 [796,] 0.9194834 0.9770356 0.9952377
 [797,] 0.9273981 0.9809764 0.9951529
 [798,] 0.9171793 0.9757373 0.9932430
 [799,] 0.9303812 0.9805490 0.9966095
 [800,] 0.9099436 0.9765602 0.9948806
 [801,] 0.9258139 0.9793821 0.9952119
 [802,] 0.9363032 0.9779813 0.9944499
 [803,] 0.9278824 0.9796445 0.9942439
 [804,] 0.9341161 0.9764554 0.9953056
 [805,] 0.9345336 0.9806664 0.9958818
 [806,] 0.9148715 0.9770731 0.9938024
 [807,] 0.9114670 0.9757165 0.9937025
 [808,] 0.9251058 0.9802235 0.9955804
 [809,] 0.9068066 0.9779185 0.9950628
 [810,] 0.9402699 0.9817559 0.9951107
 [811,] 0.9169173 0.9760539 0.9956473
 [812,] 0.9237549 0.9758917 0.9954480
 [813,] 0.9278769 0.9794457 0.9949683
 [814,] 0.9241577 0.9729210 0.9951624
 [815,] 0.9354078 0.9792191 0.9963348
 [816,] 0.9213529 0.9759545 0.9948762
 [817,] 0.9181799 0.9803105 0.9938903
 [818,] 0.9131811 0.9710686 0.9924104
 [819,] 0.9343061 0.9843861 0.9953888
 [820,] 0.9184873 0.9835137 0.9942709
 [821,] 0.9233299 0.9740012 0.9935641
 [822,] 0.9375262 0.9800330 0.9949917
 [823,] 0.9239245 0.9789699 0.9941716
 [824,] 0.9246783 0.9763099 0.9931338
 [825,] 0.9197845 0.9769701 0.9946289
 [826,] 0.9243104 0.9752184 0.9952225
 [827,] 0.9361875 0.9810494 0.9947398
 [828,] 0.9182860 0.9791210 0.9955021
 [829,] 0.9245324 0.9798126 0.9952871
 [830,] 0.9141704 0.9709489 0.9942395
 [831,] 0.9112234 0.9713891 0.9951490
 [832,] 0.9139241 0.9714996 0.9947817
 [833,] 0.9055334 0.9718347 0.9928178
 [834,] 0.9364448 0.9789792 0.9940704
 [835,] 0.9159265 0.9796598 0.9949076
 [836,] 0.9256014 0.9765225 0.9940025
 [837,] 0.9190341 0.9772159 0.9946582
 [838,] 0.9100037 0.9740686 0.9928295
 [839,] 0.9358228 0.9822824 0.9961413
 [840,] 0.9015340 0.9724765 0.9924903
 [841,] 0.9182964 0.9737027 0.9923372
 [842,] 0.9218973 0.9763639 0.9943793
 [843,] 0.9336199 0.9794674 0.9956074
 [844,] 0.9178651 0.9811637 0.9954317
 [845,] 0.9236200 0.9766673 0.9937843
 [846,] 0.9153051 0.9776743 0.9946257
 [847,] 0.9347115 0.9803971 0.9958395
 [848,] 0.9283530 0.9794970 0.9946738
 [849,] 0.9366510 0.9773896 0.9949215
 [850,] 0.9179765 0.9726789 0.9951098
 [851,] 0.9273219 0.9797011 0.9957389
 [852,] 0.9253115 0.9786061 0.9942074
 [853,] 0.9351426 0.9816215 0.9949764
 [854,] 0.9224209 0.9760652 0.9942299
 [855,] 0.9272080 0.9726320 0.9938256
 [856,] 0.9286726 0.9819686 0.9955866
 [857,] 0.9290352 0.9773624 0.9956371
 [858,] 0.9090152 0.9741906 0.9947274
 [859,] 0.9203492 0.9778382 0.9947290
 [860,] 0.9307044 0.9797175 0.9955313
 [861,] 0.9313991 0.9798010 0.9955825
 [862,] 0.9234654 0.9825763 0.9958790
 [863,] 0.9327962 0.9813718 0.9961641
 [864,] 0.9404008 0.9803799 0.9961620
 [865,] 0.9288817 0.9797359 0.9935542
 [866,] 0.9266586 0.9801382 0.9953196
 [867,] 0.9224196 0.9795331 0.9950083
 [868,] 0.9314544 0.9786038 0.9942057
 [869,] 0.9237157 0.9765978 0.9948863
 [870,] 0.9304886 0.9818500 0.9954318
 [871,] 0.9218368 0.9793503 0.9943727
 [872,] 0.9134756 0.9810578 0.9961642
 [873,] 0.9292442 0.9734523 0.9947742
 [874,] 0.9388160 0.9777406 0.9931439
 [875,] 0.9385784 0.9819755 0.9948658
 [876,] 0.9244875 0.9770347 0.9935591
 [877,] 0.9364967 0.9793369 0.9954319
 [878,] 0.9329568 0.9798294 0.9953114
 [879,] 0.9100355 0.9784706 0.9940724
 [880,] 0.9188419 0.9753002 0.9949633
 [881,] 0.9343350 0.9784296 0.9942429
 [882,] 0.9325813 0.9774131 0.9956349
 [883,] 0.9295796 0.9792014 0.9955363
 [884,] 0.9344807 0.9755667 0.9943232
 [885,] 0.9222574 0.9784477 0.9951762
 [886,] 0.9301259 0.9759562 0.9951501
 [887,] 0.9255533 0.9804709 0.9947469
 [888,] 0.9280456 0.9821630 0.9952498
 [889,] 0.9381563 0.9797891 0.9956153
 [890,] 0.9206589 0.9796485 0.9941258
 [891,] 0.9169349 0.9761976 0.9945962
 [892,] 0.9180580 0.9784116 0.9946057
 [893,] 0.9283039 0.9791680 0.9952372
 [894,] 0.9247094 0.9772460 0.9954227
 [895,] 0.9223762 0.9810607 0.9959110
 [896,] 0.9213203 0.9745868 0.9943251
 [897,] 0.9271951 0.9791948 0.9949492
 [898,] 0.9256259 0.9742539 0.9955797
 [899,] 0.9220405 0.9755439 0.9958330
 [900,] 0.9297531 0.9807702 0.9945273
 [901,] 0.9205318 0.9745753 0.9941173
 [902,] 0.9328480 0.9784574 0.9958401
 [903,] 0.9227917 0.9760506 0.9949385
 [904,] 0.9147283 0.9757831 0.9958563
 [905,] 0.9104554 0.9735733 0.9947922
 [906,] 0.9240237 0.9793343 0.9952492
 [907,] 0.9344064 0.9792544 0.9963500
 [908,] 0.9252197 0.9737469 0.9945273
 [909,] 0.9354083 0.9761810 0.9940611
 [910,] 0.9304477 0.9796704 0.9953861
 [911,] 0.9146526 0.9775712 0.9952189
 [912,] 0.9315626 0.9738338 0.9933336
 [913,] 0.9214984 0.9734686 0.9949932
 [914,] 0.9366225 0.9823733 0.9946039
 [915,] 0.9362454 0.9781654 0.9952739
 [916,] 0.9292932 0.9743475 0.9942088
 [917,] 0.9216233 0.9761033 0.9944404
 [918,] 0.9280516 0.9779959 0.9946100
 [919,] 0.9247055 0.9753586 0.9946077
 [920,] 0.9370009 0.9790555 0.9958656
 [921,] 0.9191108 0.9819954 0.9955812
 [922,] 0.9359253 0.9759776 0.9956258
 [923,] 0.9301181 0.9780528 0.9950642
 [924,] 0.9093256 0.9699284 0.9933534
 [925,] 0.9229975 0.9812554 0.9957680
 [926,] 0.9161416 0.9792875 0.9945019
 [927,] 0.9309593 0.9773117 0.9933895
 [928,] 0.9150096 0.9812539 0.9958849
 [929,] 0.9288611 0.9765116 0.9938973
 [930,] 0.9199567 0.9780348 0.9948132
 [931,] 0.9251630 0.9791889 0.9956903
 [932,] 0.9112702 0.9762200 0.9949273
 [933,] 0.9301348 0.9770903 0.9939602
 [934,] 0.9311300 0.9817367 0.9952620
 [935,] 0.9228058 0.9799578 0.9961180
 [936,] 0.9298554 0.9781651 0.9942128
 [937,] 0.9236923 0.9802424 0.9955993
 [938,] 0.9296984 0.9766271 0.9948385
 [939,] 0.9253046 0.9785988 0.9952592
 [940,] 0.9200933 0.9823978 0.9947177
 [941,] 0.9132869 0.9764151 0.9943725
 [942,] 0.9362986 0.9823422 0.9953472
 [943,] 0.9219265 0.9803517 0.9954803
 [944,] 0.9256528 0.9800784 0.9942111
 [945,] 0.9358741 0.9813044 0.9957687
 [946,] 0.9131786 0.9748704 0.9940403
 [947,] 0.9149681 0.9778669 0.9949631
 [948,] 0.9193912 0.9762874 0.9957170
 [949,] 0.9387380 0.9799366 0.9943283
 [950,] 0.9352172 0.9799815 0.9955838
 [951,] 0.9266074 0.9792968 0.9962267
 [952,] 0.9321202 0.9797474 0.9951455
 [953,] 0.9324886 0.9757276 0.9945709
 [954,] 0.9229457 0.9833672 0.9952457
 [955,] 0.9294339 0.9763743 0.9949136
 [956,] 0.9254964 0.9784564 0.9948942
 [957,] 0.9183795 0.9818050 0.9948361
 [958,] 0.9211979 0.9750787 0.9948420
 [959,] 0.9205162 0.9793003 0.9947054
 [960,] 0.9236946 0.9800312 0.9955507
 [961,] 0.9238015 0.9774186 0.9944742
 [962,] 0.9278614 0.9784305 0.9948682
 [963,] 0.9256279 0.9793104 0.9955302
 [964,] 0.9269468 0.9747009 0.9937722
 [965,] 0.9319718 0.9784181 0.9940883
 [966,] 0.9229306 0.9800074 0.9962292
 [967,] 0.9239756 0.9781732 0.9944818
 [968,] 0.9120900 0.9728255 0.9937193
 [969,] 0.9294066 0.9771137 0.9935433
 [970,] 0.9221625 0.9806830 0.9955096
 [971,] 0.9026066 0.9742508 0.9922875
 [972,] 0.9302212 0.9813386 0.9954690
 [973,] 0.9364559 0.9797281 0.9958561
 [974,] 0.9297623 0.9772062 0.9943919
 [975,] 0.9305863 0.9778654 0.9952995
 [976,] 0.9357661 0.9777372 0.9950007
 [977,] 0.9309466 0.9783849 0.9940928
 [978,] 0.9100606 0.9789887 0.9952612
 [979,] 0.9268950 0.9812717 0.9960160
 [980,] 0.9251374 0.9771424 0.9937096
 [981,] 0.9244903 0.9761115 0.9947938
 [982,] 0.9192818 0.9801523 0.9953325
 [983,] 0.9351016 0.9794826 0.9958025
 [984,] 0.9244688 0.9805465 0.9949029
 [985,] 0.9280909 0.9793938 0.9939273
 [986,] 0.9326900 0.9748480 0.9941812
 [987,] 0.9288755 0.9758863 0.9943870
 [988,] 0.9257148 0.9754758 0.9951444
 [989,] 0.9301101 0.9772230 0.9934291
 [990,] 0.9309045 0.9810184 0.9959628
 [991,] 0.9108774 0.9786484 0.9937845
 [992,] 0.9218116 0.9769884 0.9949162
 [993,] 0.9258126 0.9801541 0.9954443
 [994,] 0.9271305 0.9801144 0.9952318
 [995,] 0.9081526 0.9759854 0.9948548
 [996,] 0.9235967 0.9785597 0.9957822
 [997,] 0.9243217 0.9732614 0.9941965
 [998,] 0.9344517 0.9799745 0.9956550
 [999,] 0.9280058 0.9786595 0.9947993
[1000,] 0.9109437 0.9782425 0.9943734

$eigen_quantiles
          2.5 %     97.5 %
[1,] 3.62695705 4.72675151
[2,] 0.18451818 0.29638727
[3,] 0.05884472 0.09430172
[4,] 0.01710371 0.03001819

$eigen_used
            [,1]      [,2]       [,3]       [,4]
   [1,] 4.014121 0.2218257 0.09093496 0.02874845
   [2,] 4.155585 0.2449775 0.07948571 0.01876630
   [3,] 4.804333 0.2222130 0.07977203 0.02450071
   [4,] 4.177331 0.2095746 0.07310203 0.02287316
   [5,] 4.236471 0.2279627 0.08186134 0.01731773
   [6,] 3.892996 0.2003554 0.07427942 0.02490336
   [7,] 3.829744 0.2340487 0.08612179 0.02502236
   [8,] 3.927267 0.2607272 0.06716709 0.01991784
   [9,] 4.418752 0.2611489 0.08455670 0.02392102
  [10,] 4.111983 0.2163741 0.08547165 0.01997831
  [11,] 3.658886 0.2354057 0.08815504 0.02334845
  [12,] 4.599900 0.2826549 0.06443227 0.01953247
  [13,] 4.164754 0.2337013 0.06545532 0.02218513
  [14,] 4.212606 0.2364560 0.08359444 0.01951815
  [15,] 4.776854 0.2700214 0.06817757 0.02570114
  [16,] 3.995068 0.2566026 0.08057567 0.01886121
  [17,] 4.093209 0.2442821 0.05627385 0.02031475
  [18,] 4.552927 0.2238500 0.08544983 0.01952226
  [19,] 4.419830 0.2488597 0.06673511 0.02161127
  [20,] 4.461426 0.2023265 0.08790491 0.02512847
  [21,] 3.944597 0.2468193 0.06721852 0.02178155
  [22,] 4.295602 0.1988734 0.06767503 0.02145241
  [23,] 3.993713 0.2216257 0.06476242 0.02514720
  [24,] 4.553267 0.2105141 0.08191460 0.02287407
  [25,] 4.371849 0.2217932 0.06966548 0.01892363
  [26,] 3.947968 0.2492356 0.09104103 0.02608303
  [27,] 4.530425 0.2433276 0.07636565 0.02135124
  [28,] 3.998774 0.2179145 0.07532868 0.02374665
  [29,] 4.093676 0.2633078 0.07481622 0.03032439
  [30,] 4.619575 0.2520463 0.06417291 0.03028890
  [31,] 4.806643 0.2590466 0.08097687 0.02754157
  [32,] 4.261309 0.1898230 0.06316388 0.02162104
  [33,] 4.086304 0.1873613 0.08835046 0.02408747
  [34,] 3.750650 0.2163406 0.06885532 0.01994602
  [35,] 3.618009 0.2615304 0.07831235 0.01967089
  [36,] 4.129754 0.2270706 0.07074924 0.02450566
  [37,] 4.016144 0.2426274 0.06282083 0.01924860
  [38,] 4.313508 0.2634358 0.07044906 0.02285678
  [39,] 4.004943 0.2347211 0.07424090 0.01997113
  [40,] 4.567529 0.2288876 0.08060579 0.02443186
  [41,] 3.962458 0.2604391 0.05735960 0.02147254
  [42,] 4.542669 0.2427438 0.09503717 0.02282323
  [43,] 4.349550 0.2556912 0.07697016 0.02139674
  [44,] 4.212963 0.1992513 0.05756512 0.01720322
  [45,] 4.298738 0.1722793 0.05137721 0.02204148
  [46,] 4.208752 0.2548257 0.07163126 0.02695934
  [47,] 4.441224 0.2291181 0.06692869 0.02574883
  [48,] 3.936841 0.2224891 0.06294972 0.02650777
  [49,] 4.537286 0.2867908 0.06453486 0.02307402
  [50,] 4.127674 0.2727832 0.09094229 0.02616724
  [51,] 4.027512 0.2441377 0.06760082 0.01976257
  [52,] 4.170918 0.2524807 0.06994197 0.02815477
  [53,] 4.349901 0.2661589 0.06272360 0.02391858
  [54,] 4.071679 0.2124433 0.07820554 0.02675176
  [55,] 3.580024 0.2225183 0.06942678 0.02305791
  [56,] 4.099540 0.2689776 0.07158657 0.02232870
  [57,] 4.205174 0.2228705 0.08698566 0.02464293
  [58,] 4.238404 0.2650979 0.07590947 0.02700114
  [59,] 4.770428 0.2491045 0.07234669 0.02045621
  [60,] 4.345316 0.2131674 0.07434165 0.02040701
  [61,] 4.779716 0.2334267 0.06693138 0.02443588
  [62,] 4.222054 0.2941685 0.06474497 0.02390831
  [63,] 4.202462 0.2119326 0.07154224 0.02188959
  [64,] 3.970651 0.2489215 0.06716540 0.02107171
  [65,] 4.314780 0.2071662 0.08153776 0.02251199
  [66,] 4.277362 0.2457133 0.08236185 0.02624574
  [67,] 3.630858 0.2393773 0.06646719 0.01959728
  [68,] 4.111803 0.2198157 0.05827801 0.02713196
  [69,] 4.568995 0.2600412 0.08527368 0.01802531
  [70,] 4.241781 0.2367781 0.07309519 0.01711278
  [71,] 4.244636 0.1873439 0.07902680 0.02673468
  [72,] 4.107935 0.2007024 0.09450506 0.02193544
  [73,] 4.038582 0.2582443 0.07115700 0.01966500
  [74,] 4.086422 0.2082490 0.08643762 0.03154566
  [75,] 4.186488 0.2207975 0.07051908 0.02492315
  [76,] 4.285081 0.2008557 0.08367256 0.01793295
  [77,] 4.192585 0.2656276 0.07413614 0.01958817
  [78,] 4.429039 0.2349866 0.08446171 0.02373316
  [79,] 3.978666 0.2655594 0.07183169 0.02607337
  [80,] 4.027092 0.2725745 0.07452506 0.02403766
  [81,] 4.388727 0.2561593 0.07928024 0.02783782
  [82,] 4.726746 0.1994449 0.07448654 0.02345085
  [83,] 4.327285 0.2157293 0.06235280 0.02746174
  [84,] 3.632992 0.2187999 0.08303587 0.01984723
  [85,] 4.236660 0.2260495 0.07867869 0.02652846
  [86,] 4.348020 0.2155982 0.08099336 0.02135664
  [87,] 4.170116 0.2604236 0.07530475 0.01841573
  [88,] 4.115268 0.2769767 0.07680871 0.02547993
  [89,] 4.121341 0.2806255 0.06202699 0.02527359
  [90,] 3.931310 0.2197387 0.07147998 0.02377460
  [91,] 3.974402 0.2343797 0.06698152 0.02534885
  [92,] 4.081093 0.2222550 0.06845831 0.01965887
  [93,] 4.507112 0.2681211 0.06912224 0.01885714
  [94,] 4.508385 0.2639113 0.07064478 0.02104639
  [95,] 4.102617 0.2690232 0.06626674 0.02785963
  [96,] 4.360108 0.2237732 0.07952924 0.02555065
  [97,] 3.950020 0.2446121 0.08350546 0.03124037
  [98,] 4.149260 0.2367028 0.07930108 0.02252365
  [99,] 4.552064 0.2838778 0.05912130 0.02344770
 [100,] 4.190634 0.2268113 0.08000586 0.02328750
 [101,] 4.547646 0.2189685 0.07857617 0.01813076
 [102,] 4.118875 0.1997483 0.07073646 0.02415645
 [103,] 4.270871 0.2678403 0.08949743 0.02198489
 [104,] 4.004584 0.2163067 0.08177633 0.01818469
 [105,] 4.205025 0.2003736 0.05366369 0.02224526
 [106,] 3.496319 0.2587233 0.08161994 0.02778046
 [107,] 3.903709 0.2275474 0.08418814 0.02487550
 [108,] 4.827080 0.2563732 0.07256442 0.02246859
 [109,] 4.267242 0.2096220 0.08634901 0.02753839
 [110,] 3.973014 0.2639009 0.06669963 0.02136725
 [111,] 3.511070 0.2540949 0.09252854 0.01924248
 [112,] 4.331521 0.2864490 0.06901056 0.02413098
 [113,] 4.575744 0.2458445 0.06350523 0.02756656
 [114,] 3.943847 0.2065851 0.08088201 0.01956728
 [115,] 4.416164 0.2532790 0.07075686 0.02793611
 [116,] 3.833719 0.2147959 0.06790084 0.02554701
 [117,] 4.143355 0.2877595 0.07654683 0.02198353
 [118,] 3.760388 0.2208303 0.07721027 0.02068924
 [119,] 4.353979 0.2455472 0.06205161 0.02401626
 [120,] 4.642335 0.2651108 0.08416349 0.02122504
 [121,] 4.487672 0.2442106 0.07392359 0.02296385
 [122,] 3.710517 0.2140004 0.10533219 0.02100921
 [123,] 3.854542 0.2070565 0.07905268 0.02187532
 [124,] 4.222327 0.2731519 0.06853543 0.02873193
 [125,] 4.221057 0.2155668 0.06244983 0.02363117
 [126,] 4.147275 0.2742953 0.08202666 0.02208176
 [127,] 3.859021 0.2231069 0.06775982 0.01973720
 [128,] 4.049228 0.2285933 0.07294287 0.02170104
 [129,] 3.701103 0.2380107 0.07289667 0.01526866
 [130,] 4.198867 0.2469095 0.08833355 0.02185154
 [131,] 4.015854 0.2108284 0.07991553 0.02742519
 [132,] 3.969795 0.2420813 0.06647785 0.02261926
 [133,] 4.443837 0.2992791 0.07531637 0.01878056
 [134,] 4.244707 0.2451000 0.07645499 0.02172347
 [135,] 4.098565 0.2073524 0.07367383 0.02746759
 [136,] 4.441383 0.2623818 0.05907879 0.02447824
 [137,] 4.006833 0.2515977 0.08400142 0.02503805
 [138,] 4.345982 0.2065237 0.07296174 0.02692717
 [139,] 4.257653 0.2536472 0.06568700 0.02225079
 [140,] 4.188008 0.2431685 0.07640938 0.02595781
 [141,] 4.331234 0.2376283 0.07484875 0.02256878
 [142,] 4.461797 0.2574100 0.07016046 0.02028053
 [143,] 4.207633 0.2074002 0.07612790 0.02360410
 [144,] 4.287035 0.2789863 0.05334887 0.01599116
 [145,] 4.310079 0.2209479 0.06019331 0.01852449
 [146,] 4.413046 0.2739778 0.08175581 0.02355018
 [147,] 4.158403 0.1954639 0.07815102 0.02148562
 [148,] 3.796358 0.2335769 0.08134298 0.01482786
 [149,] 3.700305 0.2126991 0.06845913 0.01708478
 [150,] 3.583913 0.2574128 0.07583958 0.02109486
 [151,] 4.111633 0.1877949 0.09768817 0.02234938
 [152,] 3.928068 0.2309604 0.08009191 0.02145594
 [153,] 4.025526 0.2063165 0.08197438 0.02035687
 [154,] 4.141142 0.2601493 0.06246548 0.02538993
 [155,] 4.665852 0.2649621 0.05357018 0.01894874
 [156,] 4.446807 0.2178539 0.06432839 0.02443182
 [157,] 4.330760 0.2042608 0.08280014 0.02463994
 [158,] 4.392232 0.2405827 0.05884767 0.02076530
 [159,] 4.260189 0.2209733 0.08567364 0.02484590
 [160,] 3.838238 0.2059204 0.08305192 0.02093044
 [161,] 4.229340 0.2676928 0.06016648 0.02411808
 [162,] 4.446003 0.2232256 0.06069480 0.02808334
 [163,] 4.081210 0.2091947 0.07864731 0.01957315
 [164,] 4.141114 0.2470521 0.06515316 0.01870745
 [165,] 4.301554 0.2564935 0.07123579 0.02610521
 [166,] 3.985288 0.2449844 0.07980194 0.02534411
 [167,] 4.049533 0.2779806 0.08318272 0.01923605
 [168,] 3.953467 0.3085465 0.09073815 0.01447603
 [169,] 4.458967 0.2288205 0.07130896 0.02534622
 [170,] 3.869862 0.1950745 0.06254890 0.02236643
 [171,] 4.389479 0.2168574 0.07410151 0.02640218
 [172,] 4.052611 0.2292664 0.08355773 0.02092522
 [173,] 4.595826 0.2354762 0.07656840 0.01907792
 [174,] 4.092122 0.2460405 0.07618373 0.02161852
 [175,] 4.444818 0.2932277 0.08193699 0.01760220
 [176,] 3.967805 0.2544055 0.08392164 0.02018522
 [177,] 4.439710 0.2303218 0.09087528 0.02417961
 [178,] 4.959299 0.2349399 0.07933109 0.01951479
 [179,] 3.814234 0.2414498 0.07725721 0.02069585
 [180,] 3.879224 0.2207937 0.08121108 0.02108272
 [181,] 3.877297 0.2401491 0.06749919 0.01695534
 [182,] 3.756061 0.2411344 0.06830596 0.02481844
 [183,] 4.123228 0.2269691 0.07670095 0.02346769
 [184,] 4.251550 0.2324253 0.08405904 0.02156063
 [185,] 4.160801 0.2376803 0.08301748 0.02433461
 [186,] 4.459935 0.2327575 0.08061201 0.01923349
 [187,] 4.293318 0.2176223 0.08596759 0.02601444
 [188,] 4.679015 0.2576695 0.06323704 0.03003540
 [189,] 4.263687 0.2493691 0.06770007 0.02109045
 [190,] 4.417467 0.2764316 0.07762960 0.02330135
 [191,] 4.225237 0.2224962 0.09036156 0.02179315
 [192,] 3.704447 0.2605764 0.08602284 0.02477696
 [193,] 4.719894 0.2335179 0.05973920 0.02550744
 [194,] 3.937235 0.2092704 0.08982461 0.01960304
 [195,] 3.627186 0.2374675 0.07025366 0.02447990
 [196,] 4.127900 0.2498751 0.06906905 0.02644372
 [197,] 4.183670 0.2301272 0.08276128 0.02130160
 [198,] 4.143499 0.2195787 0.07951374 0.02055410
 [199,] 4.019009 0.2625126 0.07458774 0.02317331
 [200,] 3.790127 0.2639061 0.06106376 0.02082264
 [201,] 4.373745 0.2425847 0.07321376 0.02827895
 [202,] 4.006637 0.2439784 0.06422504 0.02430563
 [203,] 3.413653 0.1990549 0.08212926 0.02255346
 [204,] 4.049147 0.1933078 0.07653615 0.01818900
 [205,] 4.064983 0.3655528 0.06020038 0.01865541
 [206,] 4.020530 0.2149861 0.07119351 0.02874478
 [207,] 4.183048 0.3072425 0.08561498 0.02151297
 [208,] 4.383747 0.2632399 0.08246103 0.01914029
 [209,] 3.889629 0.2287986 0.07193515 0.02432080
 [210,] 3.991499 0.1791249 0.07843035 0.02284816
 [211,] 4.532341 0.2077670 0.08100037 0.02002065
 [212,] 3.919545 0.2530084 0.10900781 0.02559584
 [213,] 4.258876 0.2078214 0.05558300 0.02726653
 [214,] 3.723404 0.2468984 0.05849770 0.02271694
 [215,] 3.881607 0.2230515 0.09148196 0.02112942
 [216,] 4.808668 0.2286081 0.07942831 0.02382437
 [217,] 4.353868 0.2384454 0.07265754 0.02525212
 [218,] 4.082067 0.2508178 0.06399189 0.03024292
 [219,] 4.045970 0.2680891 0.07423179 0.02225586
 [220,] 4.279600 0.2076057 0.07778079 0.02766747
 [221,] 4.723371 0.1845277 0.06821530 0.01693435
 [222,] 4.219799 0.2084076 0.07278536 0.01908575
 [223,] 4.211619 0.3029993 0.06826389 0.01807732
 [224,] 4.160695 0.2600241 0.07647026 0.02525753
 [225,] 3.830129 0.1869394 0.07552903 0.02973334
 [226,] 4.355119 0.1959897 0.08325055 0.01953672
 [227,] 4.172523 0.2283477 0.07272596 0.02631824
 [228,] 4.155736 0.2337057 0.06936353 0.02241186
 [229,] 3.878875 0.2218357 0.09317392 0.02289167
 [230,] 3.609422 0.2082045 0.07107740 0.01923970
 [231,] 4.404387 0.2633627 0.08363238 0.02407381
 [232,] 3.835923 0.2417013 0.07397189 0.02220765
 [233,] 3.879324 0.2679552 0.06132540 0.01656032
 [234,] 4.736587 0.2746207 0.06485778 0.02242288
 [235,] 4.019183 0.2435567 0.07264625 0.02614100
 [236,] 4.172043 0.3110620 0.08186210 0.02032945
 [237,] 4.080022 0.2205568 0.06686347 0.01871746
 [238,] 4.356970 0.2351054 0.06953702 0.02075841
 [239,] 3.977118 0.2153272 0.08693883 0.02244987
 [240,] 4.223145 0.1697243 0.08297281 0.02344842
 [241,] 4.497578 0.2415061 0.08362917 0.02114918
 [242,] 4.008352 0.2838746 0.08134030 0.02790580
 [243,] 4.104365 0.2361614 0.07752206 0.01720604
 [244,] 3.899433 0.2182102 0.05872994 0.02260129
 [245,] 4.008694 0.2289422 0.07309922 0.01419901
 [246,] 4.300233 0.1777484 0.07588541 0.02458128
 [247,] 4.221259 0.2196426 0.09157607 0.01654594
 [248,] 4.124883 0.2603597 0.07776188 0.02421225
 [249,] 4.039307 0.2039927 0.07562463 0.01890030
 [250,] 3.876671 0.1990450 0.08516408 0.02164747
 [251,] 4.108692 0.2081950 0.08059218 0.02987443
 [252,] 4.689380 0.2671557 0.07939318 0.02600980
 [253,] 4.240342 0.2389832 0.07083621 0.02947911
 [254,] 3.411395 0.2518762 0.09823475 0.01893898
 [255,] 3.811606 0.1959649 0.06948057 0.02156271
 [256,] 4.519320 0.2561011 0.07883477 0.02531125
 [257,] 4.021922 0.2158775 0.07305078 0.01730378
 [258,] 4.453619 0.2180282 0.08380596 0.02085799
 [259,] 4.057283 0.2296680 0.06483022 0.02221567
 [260,] 3.931404 0.2459802 0.07059580 0.02636446
 [261,] 4.177283 0.2228688 0.06988736 0.01836845
 [262,] 3.891708 0.2188785 0.07566912 0.02436422
 [263,] 3.972078 0.2132914 0.07760750 0.02119757
 [264,] 4.250815 0.2784693 0.07594477 0.01624037
 [265,] 4.034714 0.2373011 0.07208701 0.02669460
 [266,] 4.144836 0.2134627 0.06996144 0.01996738
 [267,] 4.050160 0.2246806 0.05654106 0.02334644
 [268,] 4.027372 0.2915209 0.07254137 0.01950066
 [269,] 3.720311 0.2160313 0.09571403 0.03060595
 [270,] 3.983355 0.2220041 0.07393542 0.02593642
 [271,] 3.850506 0.2652528 0.08078875 0.02428933
 [272,] 4.860504 0.2176633 0.05995539 0.02144944
 [273,] 3.875744 0.2434896 0.07659608 0.02050327
 [274,] 4.105255 0.2339940 0.07434666 0.02851441
 [275,] 4.591263 0.2106677 0.08108118 0.02047369
 [276,] 4.310762 0.2418294 0.07688660 0.02754128
 [277,] 4.249625 0.2552172 0.07602476 0.02534429
 [278,] 4.595490 0.2354451 0.08175544 0.02299418
 [279,] 4.051774 0.2501889 0.07260490 0.02131900
 [280,] 3.933176 0.2186741 0.08482455 0.02609979
 [281,] 4.377939 0.2824039 0.10047004 0.02551864
 [282,] 4.633095 0.2553709 0.08139973 0.02333126
 [283,] 4.489408 0.2081472 0.08119587 0.02603475
 [284,] 4.370907 0.2175218 0.08670677 0.02433938
 [285,] 4.484727 0.2018000 0.07775168 0.02234655
 [286,] 3.885887 0.2699924 0.07842112 0.01624406
 [287,] 4.195224 0.2777896 0.09398520 0.02190349
 [288,] 4.184585 0.2852893 0.06649481 0.01989333
 [289,] 3.948911 0.2613536 0.08277738 0.02389084
 [290,] 3.888925 0.2352294 0.08885348 0.02053091
 [291,] 4.265214 0.2346592 0.06505653 0.02695007
 [292,] 4.018689 0.2509993 0.07335922 0.02456559
 [293,] 4.281580 0.2672986 0.05885324 0.02228018
 [294,] 4.132154 0.2576947 0.07626004 0.02796007
 [295,] 4.067919 0.2372330 0.06147680 0.02489150
 [296,] 3.946770 0.1831058 0.07511214 0.02453900
 [297,] 3.985567 0.2330506 0.07175337 0.02311662
 [298,] 4.492159 0.2133439 0.07505250 0.02043906
 [299,] 4.089071 0.2015723 0.06552566 0.02225226
 [300,] 4.263510 0.2511827 0.08617449 0.02973686
 [301,] 4.325081 0.2271977 0.07929530 0.02460054
 [302,] 4.098259 0.2287356 0.09046982 0.02037201
 [303,] 4.168700 0.2609527 0.07741067 0.01505279
 [304,] 4.111026 0.2309523 0.09150695 0.02607112
 [305,] 4.250267 0.2842075 0.08062476 0.01961269
 [306,] 4.079766 0.2011587 0.06165478 0.02577359
 [307,] 4.726977 0.2227613 0.06740507 0.02475696
 [308,] 3.462187 0.2417847 0.08126086 0.02182756
 [309,] 4.155810 0.2508418 0.08187906 0.01892921
 [310,] 3.995825 0.2271975 0.08660014 0.02553631
 [311,] 4.502320 0.2857891 0.06709512 0.01991696
 [312,] 4.657695 0.2701187 0.08403000 0.01774640
 [313,] 4.106598 0.2791599 0.08287705 0.01777840
 [314,] 4.416740 0.2178032 0.07332868 0.02245701
 [315,] 4.461696 0.2551338 0.07528223 0.02220012
 [316,] 4.474576 0.2116879 0.09134374 0.02306673
 [317,] 3.972646 0.2191965 0.06802902 0.02322539
 [318,] 3.833744 0.2216265 0.07353919 0.02550924
 [319,] 4.313936 0.2158603 0.08602482 0.01693209
 [320,] 4.177331 0.2466502 0.06683537 0.03119269
 [321,] 4.051305 0.2625660 0.07525796 0.02050289
 [322,] 3.806066 0.2220702 0.08244407 0.02465049
 [323,] 3.838277 0.2237202 0.07856781 0.01889340
 [324,] 4.782230 0.2189716 0.06787292 0.02996079
 [325,] 4.124418 0.1796964 0.08136449 0.02053696
 [326,] 4.305764 0.2396876 0.08140814 0.02302252
 [327,] 3.765151 0.2932929 0.06226025 0.03001790
 [328,] 4.262405 0.2618507 0.08142736 0.02528656
 [329,] 4.155472 0.2259292 0.08809677 0.01995787
 [330,] 4.152332 0.2835422 0.08014290 0.01731167
 [331,] 4.255991 0.2833612 0.07070238 0.02319134
 [332,] 4.200520 0.2230896 0.07778673 0.02571421
 [333,] 4.158723 0.2642345 0.08209945 0.02830223
 [334,] 4.011996 0.2252793 0.08181310 0.03026569
 [335,] 4.305358 0.2202074 0.07539911 0.02258923
 [336,] 3.976022 0.2540485 0.07581182 0.02209610
 [337,] 4.548244 0.2475926 0.08089127 0.02364544
 [338,] 3.653102 0.2890100 0.07774419 0.01982774
 [339,] 4.696420 0.2231788 0.06847001 0.02109018
 [340,] 4.084219 0.2057976 0.07288537 0.02112568
 [341,] 4.454443 0.2483434 0.06482676 0.02868135
 [342,] 4.244555 0.2295548 0.07012654 0.02619344
 [343,] 4.377997 0.2622384 0.07188630 0.02239273
 [344,] 4.648088 0.2369318 0.07778553 0.02162951
 [345,] 4.323677 0.2460707 0.08319041 0.01977115
 [346,] 4.186298 0.2301393 0.07769108 0.02895555
 [347,] 4.405027 0.2021532 0.05863867 0.02635713
 [348,] 4.112238 0.2023249 0.07465147 0.02255946
 [349,] 3.916362 0.2558297 0.08358950 0.02545916
 [350,] 4.276893 0.2117320 0.05564382 0.02434603
 [351,] 4.230599 0.2513912 0.08483704 0.02626429
 [352,] 4.300695 0.2526941 0.07040540 0.01922991
 [353,] 3.962619 0.2538110 0.07445629 0.02147876
 [354,] 4.402425 0.2319107 0.08221416 0.02386174
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 [361,] 3.670365 0.2270622 0.08195146 0.02187687
 [362,] 4.358798 0.2155190 0.07585957 0.01938580
 [363,] 4.411682 0.2405254 0.07354690 0.02264873
 [364,] 4.001941 0.2132191 0.07857266 0.02798396
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 [381,] 3.707016 0.1909943 0.06832805 0.02461146
 [382,] 3.720270 0.2198854 0.06925668 0.02077227
 [383,] 3.939218 0.2054397 0.07610220 0.02437247
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 [385,] 4.210826 0.2125905 0.07646962 0.01828520
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 [387,] 4.071793 0.2266262 0.08511655 0.02153152
 [388,] 4.240527 0.2600632 0.07031366 0.02182229
 [389,] 4.475814 0.1841470 0.07798698 0.02866781
 [390,] 4.044184 0.2125006 0.07145987 0.01651954
 [391,] 4.193573 0.2024599 0.07748797 0.02388632
 [392,] 4.166935 0.2754785 0.07765570 0.02403526
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 [396,] 4.012239 0.2349793 0.07079125 0.02447170
 [397,] 4.342046 0.2631909 0.08811302 0.02303764
 [398,] 4.515011 0.1877496 0.08244649 0.02480061
 [399,] 4.224218 0.2147067 0.06594125 0.02324019
 [400,] 3.895940 0.2739768 0.08198761 0.01701944
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 [403,] 4.502500 0.2005611 0.07657018 0.02234560
 [404,] 4.145040 0.2693090 0.06400130 0.02663024
 [405,] 4.403229 0.2419145 0.06420828 0.02425660
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 [410,] 4.108284 0.2162320 0.09166037 0.02234051
 [411,] 4.272971 0.2522502 0.06921478 0.02277894
 [412,] 4.261977 0.2547488 0.07211564 0.02288280
 [413,] 3.880073 0.2095210 0.07732805 0.02028969
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 [415,] 4.252898 0.2057176 0.08465302 0.02100951
 [416,] 4.214957 0.2627692 0.07742360 0.01599253
 [417,] 4.142164 0.2713395 0.08129767 0.02022869
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 [419,] 4.310024 0.2315165 0.06495955 0.02495020
 [420,] 3.757197 0.2153490 0.07801644 0.02020648
 [421,] 3.756041 0.2224783 0.05834006 0.02409125
 [422,] 4.447937 0.2607714 0.06455196 0.02123126
 [423,] 4.551593 0.2339616 0.06178438 0.02165631
 [424,] 4.677534 0.2684793 0.07707952 0.02369414
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 [426,] 4.531917 0.1949828 0.06650930 0.02636619
 [427,] 4.299477 0.2551803 0.06854648 0.02289285
 [428,] 3.809129 0.2158215 0.08013629 0.02213094
 [429,] 4.482098 0.2526061 0.08376816 0.02124238
 [430,] 3.428589 0.1957170 0.07810259 0.02371804
 [431,] 4.066258 0.1767987 0.07830867 0.02204567
 [432,] 3.991035 0.2683848 0.06225340 0.02702893
 [433,] 4.280216 0.2247522 0.07958720 0.02297180
 [434,] 4.044286 0.3073923 0.08045507 0.02102509
 [435,] 4.204243 0.2657973 0.06981862 0.01880445
 [436,] 4.084272 0.2867125 0.06489557 0.02127842
 [437,] 3.688229 0.2492302 0.07197542 0.02355075
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 [439,] 4.245369 0.1901094 0.07327028 0.02444047
 [440,] 4.683886 0.3064086 0.07847560 0.02233332
 [441,] 3.508821 0.2488777 0.08419832 0.02195884
 [442,] 4.272617 0.1937148 0.07189661 0.02757160
 [443,] 4.147811 0.2276890 0.08122587 0.02212738
 [444,] 4.593322 0.2524364 0.08727418 0.01969000
 [445,] 4.436179 0.2496175 0.07621258 0.02558562
 [446,] 4.377180 0.2052471 0.08251128 0.02925823
 [447,] 3.798461 0.2502362 0.07471278 0.02396592
 [448,] 4.218488 0.2386991 0.08229443 0.02283015
 [449,] 4.111721 0.2343792 0.07898011 0.02301178
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 [451,] 3.519297 0.2509363 0.09673185 0.01980377
 [452,] 3.900064 0.2044088 0.07202644 0.02126168
 [453,] 4.241971 0.2298150 0.07338022 0.02022130
 [454,] 3.961136 0.2722850 0.09381688 0.02742472
 [455,] 4.128294 0.2434188 0.06973802 0.01910090
 [456,] 4.387637 0.2593767 0.09186769 0.02824573
 [457,] 4.220710 0.2828772 0.07329702 0.02190380
 [458,] 4.241205 0.2408178 0.07597680 0.02686918
 [459,] 3.741796 0.2667295 0.07881169 0.02014356
 [460,] 4.282329 0.2851086 0.05755660 0.02250006
 [461,] 3.990408 0.2290225 0.07623480 0.02277106
 [462,] 4.406163 0.1879772 0.07118638 0.02700655
 [463,] 4.350922 0.2697616 0.07079363 0.02410589
 [464,] 4.316150 0.2429232 0.09442358 0.02339881
 [465,] 4.001031 0.2650771 0.06018627 0.01930006
 [466,] 4.545400 0.2062302 0.06625706 0.02457381
 [467,] 3.741211 0.2103365 0.08370993 0.02407208
 [468,] 3.840038 0.2185842 0.07904689 0.02993632
 [469,] 4.221483 0.2738331 0.07777784 0.02655277
 [470,] 4.347200 0.2686685 0.06700952 0.01899138
 [471,] 4.093699 0.2368766 0.06396106 0.02159510
 [472,] 4.067342 0.2410521 0.06238562 0.01710415
 [473,] 4.407270 0.2502236 0.06104069 0.01872212
 [474,] 3.469179 0.2205367 0.08266537 0.02526206
 [475,] 3.936363 0.2498023 0.07880435 0.02412783
 [476,] 4.753010 0.2545007 0.06541827 0.02112669
 [477,] 4.596798 0.2169276 0.07594230 0.02502973
 [478,] 4.087889 0.1767491 0.07158101 0.02406253
 [479,] 4.168574 0.1963235 0.07039456 0.02196167
 [480,] 4.526909 0.2280676 0.07878096 0.02070395
 [481,] 4.363787 0.2791818 0.06819011 0.02260722
 [482,] 4.202819 0.2421700 0.05946736 0.02087393
 [483,] 4.056382 0.2913321 0.07738336 0.02004268
 [484,] 3.989428 0.2750680 0.08569169 0.02342263
 [485,] 3.958492 0.2447427 0.07223982 0.02153238
 [486,] 4.136042 0.2598170 0.06871625 0.02646147
 [487,] 4.454789 0.2591634 0.07936422 0.01880152
 [488,] 4.094542 0.2292919 0.06301710 0.02334237
 [489,] 4.512945 0.2435483 0.07772624 0.02309318
 [490,] 3.814567 0.2030028 0.07701847 0.02159638
 [491,] 4.423078 0.2252475 0.08471253 0.02182985
 [492,] 4.284415 0.2102268 0.07666894 0.02737126
 [493,] 3.849704 0.2085496 0.07058068 0.02123862
 [494,] 3.994448 0.2623840 0.07620421 0.02411842
 [495,] 4.105418 0.1853504 0.07208421 0.02059075
 [496,] 4.236636 0.2036055 0.06800775 0.02306676
 [497,] 4.331010 0.2385862 0.07455193 0.02193091
 [498,] 3.650597 0.2918403 0.06538626 0.03138826
 [499,] 4.071634 0.2213150 0.06797837 0.02306648
 [500,] 3.847630 0.2160880 0.08819806 0.02605778
 [501,] 4.088703 0.2672333 0.07411969 0.02318899
 [502,] 4.338077 0.2227084 0.06476155 0.02181372
 [503,] 4.271251 0.1880193 0.07695177 0.01913131
 [504,] 4.085915 0.2557539 0.06839749 0.02155064
 [505,] 4.160292 0.2470968 0.06650035 0.02508532
 [506,] 4.201243 0.2187447 0.07743338 0.02128468
 [507,] 3.965332 0.2162869 0.08001139 0.02642102
 [508,] 4.084620 0.2474915 0.08032695 0.02084619
 [509,] 3.888195 0.2164840 0.08169870 0.02534899
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 [511,] 3.987112 0.2139475 0.07822967 0.01840529
 [512,] 4.184168 0.1919282 0.09447281 0.01901398
 [513,] 4.382839 0.2010120 0.08444880 0.02324811
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 [515,] 3.913990 0.2567739 0.08216134 0.02821995
 [516,] 4.349153 0.2455925 0.07044742 0.02169583
 [517,] 4.243672 0.2039628 0.07721389 0.01818495
 [518,] 4.194623 0.2468005 0.08613968 0.01976414
 [519,] 4.318807 0.2747094 0.06379166 0.02594197
 [520,] 3.773799 0.2207410 0.07571981 0.02876077
 [521,] 4.004271 0.1698561 0.06608344 0.02266928
 [522,] 3.829651 0.2638484 0.09136375 0.03024043
 [523,] 4.317712 0.2084623 0.08689856 0.02693113
 [524,] 4.521285 0.2553238 0.07315878 0.02203139
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 [526,] 4.430158 0.1972067 0.07641771 0.01888907
 [527,] 4.361975 0.2521615 0.08921627 0.02355609
 [528,] 4.253441 0.2598961 0.08850956 0.02741054
 [529,] 3.986356 0.2271656 0.07823385 0.02079449
 [530,] 4.208461 0.2596796 0.06667867 0.03264258
 [531,] 4.333865 0.2652941 0.07369775 0.02408810
 [532,] 4.360887 0.2632500 0.06631103 0.02410040
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 [534,] 3.913268 0.2075487 0.07035226 0.02105751
 [535,] 3.934252 0.2190136 0.07202174 0.02207970
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 [537,] 3.885061 0.2283494 0.07260182 0.02349649
 [538,] 3.992724 0.2280534 0.07296906 0.01741377
 [539,] 4.186864 0.2320638 0.06074805 0.02706640
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 [541,] 3.898799 0.2049922 0.06474984 0.02388024
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 [543,] 4.073263 0.2719221 0.06132159 0.02356726
 [544,] 4.130619 0.1547701 0.07240553 0.01794130
 [545,] 4.094519 0.2184613 0.06680571 0.02230513
 [546,] 3.853401 0.2129348 0.08518237 0.02370498
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 [548,] 4.344854 0.2502436 0.07501423 0.02098494
 [549,] 4.292500 0.2185696 0.08353725 0.02699666
 [550,] 4.370598 0.1925157 0.07577606 0.02004190
 [551,] 4.040314 0.2873689 0.07957537 0.01754326
 [552,] 4.471715 0.2304898 0.07401154 0.02703032
 [553,] 4.047226 0.2295809 0.05938936 0.02233771
 [554,] 4.379102 0.2290799 0.08006405 0.01880064
 [555,] 3.837937 0.2340416 0.07181914 0.02155522
 [556,] 3.967014 0.2200143 0.07545446 0.02054888
 [557,] 4.459385 0.2449228 0.09224035 0.01668323
 [558,] 4.248381 0.2786208 0.08140245 0.02731085
 [559,] 3.788316 0.2656269 0.09633465 0.01665163
 [560,] 3.847079 0.2017139 0.07762600 0.02175490
 [561,] 4.215834 0.2343248 0.08342360 0.01962450
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 [563,] 4.113348 0.2643302 0.07607600 0.02445927
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 [565,] 4.001714 0.2278133 0.08079718 0.02256041
 [566,] 4.720305 0.2357131 0.07847245 0.02151187
 [567,] 4.194938 0.2631536 0.06223135 0.02413064
 [568,] 3.895106 0.2244350 0.08724732 0.02144447
 [569,] 3.969344 0.2944552 0.08473682 0.02149153
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 [571,] 3.940917 0.2161369 0.07584055 0.02384110
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 [573,] 3.913144 0.1875237 0.08571206 0.02139122
 [574,] 4.001597 0.2729035 0.07102862 0.02725964
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 [576,] 3.823068 0.2749203 0.07393174 0.02538410
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 [578,] 4.236223 0.2413589 0.07727504 0.02124605
 [579,] 3.984625 0.2661934 0.07207185 0.02215196
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 [581,] 3.692361 0.2291646 0.09036651 0.02120379
 [582,] 4.189857 0.2491672 0.06367250 0.01913651
 [583,] 4.170683 0.2665605 0.07760357 0.02650832
 [584,] 4.579705 0.2861201 0.07711200 0.02284826
 [585,] 4.036295 0.2427565 0.09060403 0.02188597
 [586,] 4.233250 0.1973018 0.06909379 0.02180948
 [587,] 3.796134 0.2046788 0.08560617 0.01846969
 [588,] 4.170967 0.1924623 0.07578699 0.02009189
 [589,] 3.970755 0.2371266 0.08279860 0.01991587
 [590,] 4.294960 0.2291912 0.07245211 0.02118080
 [591,] 4.043407 0.2355596 0.09688675 0.02607352
 [592,] 4.025111 0.2532320 0.08700509 0.02418869
 [593,] 4.755582 0.2476491 0.09390546 0.02387901
 [594,] 4.433832 0.2230037 0.05799213 0.02345179
 [595,] 4.123601 0.2561759 0.06863027 0.02130719
 [596,] 3.985333 0.2926064 0.07538632 0.02488977
 [597,] 4.279534 0.2457952 0.07500975 0.02641636
 [598,] 4.072195 0.2525169 0.07300908 0.02127591
 [599,] 4.084829 0.2160403 0.08054172 0.01826403
 [600,] 4.723068 0.2396282 0.06961819 0.02154572
 [601,] 4.206720 0.2434444 0.07942222 0.01914372
 [602,] 4.096448 0.2096832 0.07943195 0.01759177
 [603,] 4.201234 0.2562660 0.07284794 0.01876269
 [604,] 4.131626 0.2245583 0.07501958 0.02024148
 [605,] 4.195917 0.2355923 0.07435833 0.02321878
 [606,] 4.414815 0.2237809 0.08421906 0.02809986
 [607,] 3.973185 0.2400278 0.06748871 0.01854555
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 [609,] 3.971129 0.2422161 0.08211534 0.02311694
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 [611,] 3.722612 0.2461201 0.06155449 0.02293848
 [612,] 4.145617 0.2406640 0.06748049 0.02559162
 [613,] 4.104006 0.2585748 0.07728525 0.02623229
 [614,] 4.472580 0.2433058 0.07598080 0.02575867
 [615,] 4.627380 0.2560245 0.08108561 0.02580570
 [616,] 4.338638 0.2931667 0.08017329 0.02143279
 [617,] 4.375289 0.2421450 0.07868314 0.01963662
 [618,] 3.930168 0.2246917 0.08499318 0.01930925
 [619,] 4.818578 0.3280215 0.07079592 0.02840150
 [620,] 4.068931 0.2315521 0.07489536 0.02019181
 [621,] 3.908860 0.2530957 0.06414568 0.02114713
 [622,] 4.377582 0.2449782 0.07204469 0.02384552
 [623,] 3.789907 0.2930555 0.07381559 0.02157838
 [624,] 4.231545 0.2508826 0.06222611 0.02422528
 [625,] 4.275309 0.2432417 0.07220602 0.02234995
 [626,] 3.859739 0.2035901 0.08565162 0.02032989
 [627,] 4.263633 0.1870368 0.08228503 0.01896900
 [628,] 4.346259 0.2713263 0.06837078 0.02190612
 [629,] 4.291765 0.2489994 0.06963447 0.02671122
 [630,] 4.346867 0.2280241 0.08304233 0.02542763
 [631,] 4.209782 0.2829443 0.09360987 0.02733251
 [632,] 4.068102 0.2447036 0.06766154 0.02184203
 [633,] 4.456582 0.2823869 0.06999709 0.02124424
 [634,] 3.879802 0.2324188 0.07128407 0.02047330
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 [636,] 4.025425 0.2512244 0.08415978 0.03085813
 [637,] 3.887291 0.1739952 0.06755064 0.02252493
 [638,] 4.489171 0.2887946 0.08440109 0.02664401
 [639,] 3.702380 0.2079264 0.08293299 0.02715122
 [640,] 4.011482 0.2235691 0.07161081 0.02239059
 [641,] 4.221983 0.2568162 0.07211046 0.01805541
 [642,] 4.006805 0.1966076 0.07718048 0.02070211
 [643,] 4.454366 0.2574514 0.08563351 0.01698546
 [644,] 4.285553 0.2365661 0.07630219 0.02121386
 [645,] 4.139755 0.2389696 0.07210448 0.01749501
 [646,] 4.215373 0.2697061 0.06468601 0.02395851
 [647,] 4.528316 0.2549756 0.08565679 0.02570467
 [648,] 4.770051 0.2235835 0.08060124 0.02381220
 [649,] 3.996386 0.2531782 0.07088098 0.02253069
 [650,] 4.357572 0.1930180 0.06710602 0.02498978
 [651,] 4.016139 0.1943402 0.08651856 0.01964380
 [652,] 4.156165 0.2431842 0.06096447 0.02209826
 [653,] 4.194136 0.2324903 0.07166754 0.02026884
 [654,] 4.192862 0.2078711 0.06431013 0.01731145
 [655,] 4.444095 0.2369810 0.07176183 0.02576497
 [656,] 4.073273 0.2097403 0.06839918 0.02689556
 [657,] 3.950831 0.2233306 0.07918744 0.02007037
 [658,] 3.885804 0.2102348 0.09089113 0.02879373
 [659,] 4.010395 0.2597444 0.07745413 0.02148466
 [660,] 3.570911 0.2400483 0.08969278 0.02144119
 [661,] 3.645190 0.2228431 0.07135699 0.01480527
 [662,] 3.796557 0.2239165 0.08928012 0.01741880
 [663,] 3.983983 0.2467327 0.07873290 0.02208080
 [664,] 3.807119 0.2206531 0.07752991 0.01930736
 [665,] 4.566044 0.2642540 0.09398019 0.01770526
 [666,] 4.193389 0.2928209 0.07116820 0.02374119
 [667,] 4.212405 0.2357616 0.06788869 0.01857187
 [668,] 3.916676 0.2861822 0.08706301 0.02623801
 [669,] 4.080987 0.2380486 0.08098067 0.02149836
 [670,] 4.432268 0.2719528 0.07103574 0.02138507
 [671,] 4.188085 0.2536091 0.07161766 0.02409323
 [672,] 3.934956 0.2809156 0.06579407 0.02497696
 [673,] 4.044545 0.2304934 0.07002086 0.02390076
 [674,] 4.152861 0.2707658 0.07911272 0.02544728
 [675,] 4.429747 0.2602874 0.06512307 0.02352212
 [676,] 3.964844 0.2403775 0.07616342 0.02182458
 [677,] 3.607850 0.1801691 0.07352862 0.01899665
 [678,] 4.537320 0.1955673 0.08254052 0.02078604
 [679,] 4.465585 0.2354958 0.07638254 0.02320838
 [680,] 4.091476 0.3193310 0.08495334 0.02248688
 [681,] 4.481712 0.2263838 0.06739741 0.01923712
 [682,] 4.080470 0.2384781 0.06822779 0.02440938
 [683,] 4.635940 0.2645343 0.05566008 0.02305807
 [684,] 3.762142 0.2539589 0.07670266 0.02208589
 [685,] 3.865204 0.2203693 0.06476584 0.02478418
 [686,] 3.996169 0.2323497 0.07684615 0.02166899
 [687,] 4.119754 0.2377568 0.08666834 0.02070409
 [688,] 4.263692 0.2209835 0.09595470 0.02228914
 [689,] 4.265704 0.2746804 0.06444498 0.02587537
 [690,] 4.463411 0.2473662 0.07789757 0.02627951
 [691,] 3.954890 0.2696794 0.09584350 0.02356404
 [692,] 3.998301 0.2181077 0.06793094 0.02137956
 [693,] 4.131092 0.2295437 0.08157873 0.02004459
 [694,] 4.961354 0.2325844 0.07705027 0.02715081
 [695,] 4.429655 0.2146657 0.08492340 0.01965940
 [696,] 4.373500 0.3297180 0.08041190 0.01907234
 [697,] 3.956545 0.2433723 0.08578532 0.02498841
 [698,] 4.271601 0.2034004 0.08133473 0.01625239
 [699,] 4.184996 0.2464304 0.06158445 0.01981825
 [700,] 3.987555 0.2616765 0.08059492 0.01916214
 [701,] 4.241768 0.2751353 0.08810381 0.02299179
 [702,] 3.963644 0.1906336 0.08010770 0.01987258
 [703,] 4.313281 0.2338643 0.07068243 0.02554387
 [704,] 4.583906 0.2635643 0.07798367 0.01758397
 [705,] 4.163658 0.2459012 0.06357248 0.02274073
 [706,] 4.118974 0.2374649 0.07577937 0.02297567
 [707,] 3.892630 0.2393533 0.06855282 0.02821399
 [708,] 3.877687 0.2611252 0.08147989 0.02367159
 [709,] 4.737513 0.2606668 0.08240666 0.02633195
 [710,] 4.047292 0.2186852 0.09528196 0.02435428
 [711,] 4.156016 0.2233513 0.08458909 0.02595804
 [712,] 4.723844 0.2792111 0.09373856 0.01824252
 [713,] 4.351380 0.2196198 0.07341915 0.02868429
 [714,] 4.109859 0.2520457 0.05724871 0.02569753
 [715,] 3.835084 0.2161126 0.07932618 0.02280034
 [716,] 3.986379 0.2774947 0.07875437 0.02333700
 [717,] 3.888697 0.2591841 0.08378310 0.02078357
 [718,] 4.193136 0.2767652 0.08654629 0.02420374
 [719,] 4.436202 0.2530765 0.06104845 0.01708652
 [720,] 4.354735 0.2008056 0.07837392 0.03048155
 [721,] 4.182748 0.2466737 0.07597053 0.02628423
 [722,] 3.999616 0.2771789 0.08559361 0.02294154
 [723,] 4.240388 0.2411945 0.07761604 0.02394135
 [724,] 4.412576 0.2185701 0.07519301 0.02777561
 [725,] 4.102859 0.2230823 0.08827646 0.02298564
 [726,] 4.056833 0.2795363 0.08341752 0.02734418
 [727,] 3.971396 0.2299960 0.08094593 0.02319043
 [728,] 4.114805 0.2378960 0.08202617 0.02633778
 [729,] 4.593819 0.2573899 0.07655233 0.03110048
 [730,] 3.816969 0.2025687 0.08309930 0.02745617
 [731,] 4.336360 0.2963720 0.08024429 0.02505861
 [732,] 4.230733 0.2548222 0.08893559 0.02050948
 [733,] 4.217212 0.2653056 0.06439431 0.02703228
 [734,] 4.158828 0.1877617 0.09751411 0.02413337
 [735,] 4.076150 0.1854232 0.06305820 0.01841217
 [736,] 4.328116 0.2340970 0.08651865 0.02809871
 [737,] 4.374768 0.1697744 0.06291175 0.02238294
 [738,] 4.347961 0.2229393 0.08722665 0.02798259
 [739,] 4.163291 0.2070037 0.08711731 0.01741782
 [740,] 4.231819 0.2071624 0.08003769 0.02235227
 [741,] 4.185395 0.2422347 0.07049718 0.02034808
 [742,] 4.141714 0.2210728 0.07403186 0.02122334
 [743,] 4.189181 0.2188863 0.08424143 0.01874767
 [744,] 4.325695 0.2836579 0.08619280 0.02407137
 [745,] 4.182282 0.2658766 0.07007714 0.02514361
 [746,] 3.940574 0.2620858 0.07812529 0.01858486
 [747,] 3.474008 0.2154147 0.07057357 0.01937259
 [748,] 3.927180 0.1943467 0.08772954 0.01871461
 [749,] 3.816977 0.2236751 0.08536020 0.02393242
 [750,] 4.239636 0.2082835 0.07620954 0.02333858
 [751,] 3.872462 0.2428776 0.08426526 0.02260395
 [752,] 4.282561 0.2481426 0.07284382 0.02122661
 [753,] 4.324827 0.2276257 0.08468643 0.02150493
 [754,] 4.312432 0.2261162 0.07659112 0.02579743
 [755,] 4.029156 0.2253820 0.07593800 0.02036041
 [756,] 4.380610 0.2647958 0.06879241 0.02168847
 [757,] 4.109997 0.3375265 0.06994413 0.03213275
 [758,] 3.899267 0.1829610 0.08150560 0.02045424
 [759,] 4.182849 0.2848545 0.06398875 0.02081737
 [760,] 3.689427 0.2160691 0.08546579 0.02739648
 [761,] 3.992228 0.2371551 0.08157106 0.02063616
 [762,] 4.226577 0.2539635 0.07390856 0.02042810
 [763,] 4.740436 0.2486281 0.08349335 0.02267679
 [764,] 4.484151 0.2086141 0.06721199 0.02133250
 [765,] 4.110875 0.2612779 0.07182542 0.01744589
 [766,] 3.876523 0.2229745 0.06433855 0.02087722
 [767,] 4.601153 0.2582826 0.07906951 0.02131413
 [768,] 4.262370 0.3251390 0.09151082 0.02774490
 [769,] 3.895150 0.2237100 0.08037019 0.02180044
 [770,] 4.256211 0.2118939 0.10106294 0.01896438
 [771,] 4.026653 0.1780210 0.06577988 0.02873785
 [772,] 3.999627 0.2479804 0.07146474 0.01960001
 [773,] 3.937498 0.2359457 0.08878356 0.02184399
 [774,] 4.416645 0.2984521 0.07094812 0.02275126
 [775,] 4.258236 0.3038455 0.05886644 0.02095359
 [776,] 4.054671 0.2616177 0.08292781 0.01976146
 [777,] 3.806793 0.2655457 0.06972975 0.02175738
 [778,] 4.236415 0.2739524 0.06964177 0.02293555
 [779,] 4.379960 0.2690613 0.06983910 0.02548359
 [780,] 4.057244 0.2731833 0.07261741 0.02743959
 [781,] 4.427193 0.2435058 0.07080903 0.01804785
 [782,] 3.879994 0.1696443 0.06428235 0.02505980
 [783,] 4.001476 0.2772659 0.07319260 0.02045918
 [784,] 3.479319 0.2169341 0.08255637 0.02731686
 [785,] 3.994919 0.2969814 0.07859549 0.01955086
 [786,] 4.542809 0.2356319 0.07946277 0.02048460
 [787,] 3.790099 0.2435416 0.07185682 0.02582604
 [788,] 4.311546 0.2753494 0.07679862 0.02861077
 [789,] 4.143562 0.2198720 0.07841386 0.01991693
 [790,] 3.996685 0.2252054 0.06833739 0.01874148
 [791,] 3.927491 0.1909402 0.08463335 0.02860073
 [792,] 3.883780 0.2264328 0.08162959 0.02349270
 [793,] 4.359099 0.2191319 0.08944932 0.02272764
 [794,] 4.133957 0.2694238 0.06918560 0.02340639
 [795,] 4.270195 0.2239822 0.08315739 0.02501109
 [796,] 4.105217 0.2569533 0.08126683 0.02126235
 [797,] 4.049475 0.2339489 0.06190168 0.02116490
 [798,] 3.660463 0.2337050 0.06986532 0.02696719
 [799,] 4.742458 0.2557218 0.08186518 0.01728269
 [800,] 3.888632 0.2846851 0.07829192 0.02187778
 [801,] 4.189313 0.2423964 0.07162977 0.02166635
 [802,] 4.147506 0.1846200 0.07295027 0.02458495
 [803,] 4.001312 0.2232140 0.06295736 0.02482196
 [804,] 3.990665 0.1808793 0.08053047 0.02005502
 [805,] 4.125479 0.2036522 0.06716814 0.01817954
 [806,] 3.874359 0.2634153 0.07084627 0.02624613
 [807,] 3.955202 0.2788028 0.07804799 0.02732746
 [808,] 4.349373 0.2591353 0.07220047 0.02077857
 [809,] 3.943617 0.3092590 0.07455877 0.02147141
 [810,] 4.145949 0.1829250 0.05888538 0.02155862
 [811,] 3.891224 0.2509646 0.08315076 0.01847186
 [812,] 4.236887 0.2391303 0.08969682 0.02087816
 [813,] 4.225390 0.2348356 0.07068723 0.02291353
 [814,] 3.585705 0.1892000 0.08629609 0.01876974
 [815,] 4.403605 0.2062500 0.08057538 0.01725438
 [816,] 4.382015 0.2596891 0.08999266 0.02436910
 [817,] 4.372209 0.2958549 0.06466449 0.02909327
 [818,] 3.533922 0.2240189 0.08259071 0.02937086
 [819,] 4.090517 0.2192571 0.04817138 0.02018827
 [820,] 4.052504 0.2869060 0.04746258 0.02527766
 [821,] 3.717708 0.2040233 0.07876831 0.02591374
 [822,] 4.702359 0.2132020 0.07502849 0.02512004
 [823,] 4.326919 0.2577886 0.07119235 0.02729569
 [824,] 4.157994 0.2321716 0.07565182 0.03087519
 [825,] 3.696699 0.2298341 0.07097235 0.02158715
 [826,] 3.998556 0.2202271 0.08653753 0.02066749
 [827,] 4.098236 0.1963866 0.05993080 0.02302706
 [828,] 4.182824 0.2771057 0.07461653 0.02048808
 [829,] 4.424241 0.2645369 0.07405102 0.02255324
 [830,] 3.635927 0.2258247 0.09263375 0.02291120
 [831,] 3.553681 0.2346405 0.09266132 0.01891833
 [832,] 3.951594 0.2489431 0.10066648 0.02256259
 [833,] 3.786088 0.2772098 0.08773131 0.03002936
 [834,] 4.403257 0.2000012 0.07096009 0.02788180
 [835,] 4.086382 0.2843444 0.06802735 0.02271977
 [836,] 4.033756 0.2219133 0.07617760 0.02613717
 [837,] 4.273327 0.2705339 0.08110326 0.02483847
 [838,] 3.469193 0.2442335 0.07152163 0.02733613
 [839,] 4.475439 0.2221864 0.06627792 0.01845387
 [840,] 3.608184 0.2839314 0.08010060 0.03005575
 [841,] 3.955984 0.2386882 0.08027646 0.03301122
 [842,] 3.797506 0.2243604 0.07420955 0.02315303
 [843,] 4.722879 0.2319277 0.08164720 0.02222050
 [844,] 4.240827 0.2924592 0.06592270 0.02110716
 [845,] 3.688350 0.2118373 0.06835405 0.02482173
 [846,] 4.090402 0.2787215 0.07575405 0.02401716
 [847,] 4.805716 0.2348876 0.07939500 0.02139094
 [848,] 4.276048 0.2355720 0.06990536 0.02453285
 [849,] 4.262367 0.1853872 0.07978153 0.02311025
 [850,] 4.120493 0.2455411 0.10068506 0.02195033
 [851,] 4.149425 0.2343776 0.07176334 0.01906668
 [852,] 3.960707 0.2281225 0.06678002 0.02479461
 [853,] 4.335981 0.2155091 0.06192252 0.02329311
 [854,] 4.289008 0.2494317 0.08446102 0.02682920
 [855,] 3.936171 0.1928334 0.08997093 0.02621127
 [856,] 4.704068 0.2699636 0.06898057 0.02235533
 [857,] 4.212430 0.2191249 0.08286116 0.01978217
 [858,] 3.968019 0.2845027 0.08964717 0.02301573
 [859,] 4.057207 0.2534308 0.07446037 0.02323627
 [860,] 4.586395 0.2415302 0.07792868 0.02202104
 [861,] 4.528601 0.2353373 0.07673187 0.02147860
 [862,] 4.455945 0.2852247 0.06418872 0.01988471
 [863,] 4.347291 0.2263864 0.06893955 0.01787710
 [864,] 4.372266 0.1858774 0.07337689 0.01784412
 [865,] 4.369598 0.2392257 0.06500319 0.03032204
 [866,] 4.115175 0.2374966 0.06741848 0.02078513
 [867,] 4.406181 0.2728176 0.07392128 0.02384434
 [868,] 4.266494 0.2159662 0.07146428 0.02654037
 [869,] 4.370769 0.2502234 0.08653634 0.02419666
 [870,] 4.854574 0.2679640 0.07085932 0.02383350
 [871,] 4.404602 0.2748034 0.07177789 0.02688787
 [872,] 4.249973 0.3144284 0.07028295 0.01784612
 [873,] 4.224799 0.2009915 0.09693983 0.02375911
 [874,] 4.439439 0.1840650 0.07283837 0.03242106
 [875,] 4.690082 0.2168559 0.06441288 0.02565548
 [876,] 3.836297 0.2180523 0.06857039 0.02672767
 [877,] 4.594749 0.2101872 0.07896719 0.02241271
 [878,] 4.588508 0.2305306 0.07614417 0.02305972
 [879,] 3.750283 0.2820230 0.06429545 0.02442790
 [880,] 4.068753 0.2500049 0.08707083 0.02230317
 [881,] 4.121486 0.1945073 0.06975492 0.02539538
 [882,] 4.384702 0.2107849 0.08567317 0.02052339
 [883,] 3.889924 0.2076474 0.06835513 0.01867881
 [884,] 4.065393 0.1787418 0.08159879 0.02469670
 [885,] 3.991092 0.2431648 0.07239291 0.02087523
 [886,] 3.871421 0.1907575 0.07988996 0.02018640
 [887,] 4.298798 0.2550689 0.06630583 0.02439834
 [888,] 4.559801 0.2658973 0.06429957 0.02333946
 [889,] 4.642910 0.2060396 0.07832347 0.02169991
 [890,] 4.273373 0.2738088 0.06719847 0.02726587
 [891,] 4.156491 0.2686396 0.08340152 0.02449549
 [892,] 4.135386 0.2718620 0.07294651 0.02429846
 [893,] 4.279915 0.2345069 0.07408656 0.02195890
 [894,] 3.911005 0.2222004 0.07687739 0.01935952
 [895,] 4.346238 0.2765215 0.06997448 0.01926761
 [896,] 3.995816 0.2310198 0.08560606 0.02461240
 [897,] 4.375702 0.2454015 0.07434960 0.02383618
 [898,] 4.307348 0.2262874 0.09923838 0.02056982
 [899,] 4.186182 0.2429121 0.09211524 0.01891870
 [900,] 4.587760 0.2517381 0.06788277 0.02700452
 [901,] 3.970345 0.2330951 0.08428632 0.02537285
 [902,] 4.647743 0.2272406 0.08660582 0.02072607
 [903,] 4.216520 0.2433561 0.08630495 0.02312747
 [904,] 3.991130 0.2663937 0.08758302 0.01807963
 [905,] 3.939817 0.2731304 0.09182095 0.02253553
 [906,] 4.036889 0.2416421 0.06952929 0.02075517
 [907,] 4.685533 0.2248881 0.08572503 0.01830280
 [908,] 4.198501 0.2202087 0.09429860 0.02483403
 [909,] 4.097057 0.1785831 0.07831439 0.02601218
 [910,] 4.387845 0.2321262 0.07411299 0.02175828
 [911,] 4.116090 0.2831442 0.07941757 0.02151569
 [912,] 4.190063 0.1901312 0.08770791 0.02998459
 [913,] 4.053614 0.2286139 0.09468544 0.02202445
 [914,] 4.302475 0.2101613 0.05618263 0.02478746
 [915,] 4.419800 0.1978945 0.08076538 0.02231084
 [916,] 3.944370 0.1912324 0.08430115 0.02458049
 [917,] 4.103549 0.2425736 0.08164634 0.02475424
 [918,] 4.003802 0.2154694 0.07167657 0.02325375
 [919,] 4.028198 0.2206548 0.08385304 0.02348990
 [920,] 4.304295 0.1931861 0.07722058 0.01899198
 [921,] 4.381344 0.2997668 0.06476283 0.02106419
 [922,] 4.334740 0.1855024 0.09100084 0.02025896
 [923,] 4.523925 0.2331456 0.08274057 0.02400682
 [924,] 3.888117 0.2591270 0.10016111 0.02841966
 [925,] 4.140910 0.2613666 0.06510896 0.01898636
 [926,] 4.095025 0.2822531 0.06800665 0.02457552
 [927,] 4.471822 0.2226513 0.07722901 0.03175347
 [928,] 4.132450 0.2991787 0.06607805 0.01858488
 [929,] 4.094719 0.2100590 0.07664180 0.02690267
 [930,] 3.968725 0.2505510 0.07238277 0.02237592
 [931,] 4.268252 0.2492490 0.07612965 0.01988264
 [932,] 4.231183 0.3015731 0.08686103 0.02355357
 [933,] 4.054686 0.2046908 0.07353999 0.02632891
 [934,] 4.786044 0.2601203 0.06952081 0.02435328
 [935,] 4.249978 0.2632130 0.07442567 0.01787872
 [936,] 4.441979 0.2307787 0.07666076 0.02764592
 [937,] 4.434788 0.2715058 0.07373083 0.02112839
 [938,] 3.967740 0.2002808 0.07772190 0.02202826
 [939,] 4.639137 0.2671976 0.08352915 0.02376852
 [940,] 4.152366 0.2811793 0.05559945 0.02383914
 [941,] 4.181864 0.2890590 0.08222539 0.02576776
 [942,] 4.335474 0.2132023 0.06021891 0.02154434
 [943,] 4.058896 0.2572243 0.06660544 0.01989867
 [944,] 4.256658 0.2502787 0.06498967 0.02662068
 [945,] 4.588296 0.2227304 0.07091389 0.02074479
 [946,] 4.046259 0.2733541 0.08494109 0.02640708
 [947,] 4.118800 0.2831441 0.07696010 0.02267377
 [948,] 4.130468 0.2556125 0.08728943 0.01924192
 [949,] 4.451994 0.1953858 0.06825316 0.02689807
 [950,] 4.916602 0.2353336 0.08202410 0.02321662
 [951,] 4.696307 0.2670447 0.08580561 0.01912413
 [952,] 4.421731 0.2259308 0.07304431 0.02302850
 [953,] 4.070655 0.1887539 0.08225829 0.02369980
 [954,] 4.493708 0.2941846 0.05783497 0.02314802
 [955,] 4.435809 0.2240273 0.08848072 0.02427533
 [956,] 4.239569 0.2426022 0.07529953 0.02338881
 [957,] 4.257666 0.2940446 0.06041303 0.02394010
 [958,] 3.922767 0.2294421 0.08415868 0.02196453
 [959,] 4.180625 0.2669743 0.06996385 0.02404609
 [960,] 4.366167 0.2662950 0.07335837 0.02103100
 [961,] 4.035621 0.2342260 0.07450713 0.02413947
 [962,] 4.171314 0.2273395 0.07389771 0.02307078
 [963,] 4.351481 0.2523674 0.07625104 0.02101317
 [964,] 3.948570 0.2034211 0.08123933 0.02652876
 [965,] 4.335931 0.2160882 0.07290419 0.02750383
 [966,] 4.405045 0.2724213 0.07742490 0.01799766
 [967,] 3.931064 0.2305843 0.06938529 0.02347720
 [968,] 3.814160 0.2539825 0.08737315 0.02626460
 [969,] 3.865164 0.1984016 0.06832634 0.02685192
 [970,] 4.167760 0.2644865 0.06700970 0.02029449
 [971,] 3.630513 0.2881710 0.07254820 0.03102168
 [972,] 3.841252 0.2110838 0.05835012 0.01871034
 [973,] 4.404949 0.2035457 0.07586407 0.01949212
 [974,] 4.396228 0.2243307 0.08125964 0.02651710
 [975,] 4.514115 0.2293425 0.08457013 0.02280119
 [976,] 3.863457 0.1732843 0.07127497 0.02064052
 [977,] 4.470745 0.2278160 0.07543510 0.02836837
 [978,] 3.942854 0.2986321 0.07050106 0.02053073
 [979,] 4.499996 0.2639942 0.07158241 0.01934189
 [980,] 4.279122 0.2405436 0.07662956 0.02909570
 [981,] 4.060468 0.2267262 0.08205470 0.02286632
 [982,] 4.423022 0.2928719 0.07303776 0.02245727
 [983,] 4.206544 0.1996476 0.07341453 0.01888254
 [984,] 3.869540 0.2347236 0.06009160 0.02133484
 [985,] 4.367671 0.2414356 0.06839577 0.02857875
 [986,] 4.018440 0.1816354 0.08329595 0.02506999
 [987,] 4.143246 0.2096917 0.08252218 0.02503675
 [988,] 4.232941 0.2275382 0.08993687 0.02220287
 [989,] 4.419365 0.2238542 0.07700252 0.03122118
 [990,] 4.083620 0.2198357 0.06555678 0.01771009
 [991,] 3.777667 0.2810658 0.06277355 0.02577740
 [992,] 3.998002 0.2393079 0.07775492 0.02204900
 [993,] 3.932904 0.2308459 0.06495352 0.01935282
 [994,] 4.296648 0.2455460 0.07005929 0.02209757
 [995,] 4.141908 0.3093720 0.08606012 0.02346604
 [996,] 4.085976 0.2431552 0.07619191 0.01865958
 [997,] 4.081344 0.2160935 0.09243889 0.02562543
 [998,] 4.125323 0.2009691 0.06922495 0.01918178
 [999,] 4.398971 0.2401103 0.07650688 0.02465242
[1000,] 3.992960 0.2949924 0.07070691 0.02466306

function (valores, size = 1000, alpha = 0.05, plot = TRUE) 
{
    if (is.matrix(valores) == FALSE) {
        return("Oject is not a matrix")
    }
    else {
        lengs = length(valores[, 1])
        hlengs = length(valores[1, ])
        store_bootstrap = matrix(0, size, hlengs)
        elements_aux = NULL
        indexes = seq(1, lengs, 1)
        work_matrix = matrix(0, lengs, hlengs)
        empirical_quantiles1 = matrix(0, hlengs - 1, 2)
        store_eigen = matrix(0, size, hlengs)
        empirical_quantiles2 = matrix(0, hlengs, 2)
        for (sim in 1:size) {
            resample_indexes = sample(indexes, length(indexes), 
                replace = T)
            for (ips in 1:length(resample_indexes)) {
                work_matrix[ips, ] = valores[resample_indexes[ips], 
                  ]
            }
            cova = (lengs - 1) * cov(work_matrix)/(lengs)
            auto_va = unlist(eigen(cova)$values)
            cum_eigen = cumsum(auto_va)
            total_var = sum(auto_va)
            percent = (cum_eigen/total_var)
            store_bootstrap[sim, ] = percent
            store_eigen[sim, ] = auto_va
        }
        store_bootstrap = store_bootstrap[, -hlengs]
        for (iter in 1:(hlengs - 1)) {
            empirical_quantiles1[iter, 2] = quantile(store_bootstrap[, 
                iter], 1 - alpha/2)
            empirical_quantiles1[iter, 1] = quantile(store_bootstrap[, 
                iter], alpha/2)
        }
        for (iter in 1:(hlengs)) {
            empirical_quantiles2[iter, 2] = quantile(store_eigen[, 
                iter], 1 - alpha/2)
            empirical_quantiles2[iter, 1] = quantile(store_eigen[, 
                iter], alpha/2)
        }
        if (plot == TRUE) {
            plot(0:max(empirical_quantiles2[, 2]), 0:max(empirical_quantiles2[, 
                2]), xlim = c(0, max(empirical_quantiles2)), 
                ylim = c(0, nrow(empirical_quantiles2)), type = "n", 
                xlab = "Values", ylab = "Eigenvalues")
            for (q in 1:nrow(empirical_quantiles2)) {
                segments(empirical_quantiles2[q, 1], q, empirical_quantiles2[q, 
                  2], q, lwd = 2)
                abline(v = empirical_quantiles2[q, 1], lty = 3)
            }
        }
        colnames(empirical_quantiles1) = c(paste(alpha/2 * 100, 
            "%"), paste((1 - alpha/2) * 100, "%"))
        colnames(empirical_quantiles2) = c(paste(alpha/2 * 100, 
            "%"), paste((1 - alpha/2) * 100, "%"))
        lista = list(proportions_quantiles = empirical_quantiles1, 
            proportions_used = store_bootstrap, eigen_quantiles = empirical_quantiles2, 
            eigen_used = store_eigen)
        return(lista)
    }
}

eigenprcomp documentation built on May 2, 2019, 4:48 a.m.