Ensemble sparse partial least squares regression.
Arguments
- x
Predictor matrix.
- y
Response vector.
- maxcomp
Maximum number of components included within each model. If not specified, will use
5by default.- cvfolds
Number of cross-validation folds used in each model for automatic parameter selection, default is
5.- alpha
Parameter (grid) controlling sparsity of the model. If not specified, default is
seq(0.2, 0.8, 0.2).- reptimes
Number of models to build with Monte-Carlo resampling or bootstrapping.
- method
Resampling method.
"mc"(Monte-Carlo resampling) or"boot"(bootstrapping). Default is"mc".- ratio
Sampling ratio used when
method = "mc".- parallel
Integer. Number of CPU cores to use. Default is
1(not parallelized).
Author
Nan Xiao <https://nanx.me>
Examples
data("logd1k")
x <- logd1k$x
y <- logd1k$y
set.seed(42)
fit <- enspls.fit(
x, y,
reptimes = 5, maxcomp = 3,
alpha = c(0.3, 0.6, 0.9)
)
print(fit)
#> Coefficients of the Models by Ensemble Sparse Partial Least Squares
#> ---
#> [,1] [,2] [,3] [,4]
#> BalabanJ -0.043615048 -0.070476160 -0.061234111 -0.0641194287
#> BertzCT -0.010797407 -0.010380918 -0.014190111 -0.0198473677
#> Chi0 0.034719388 0.031396910 0.031244743 0.0305194922
#> Chi0n 0.053961369 0.051389288 0.054495519 0.0524801055
#> Chi0v 0.053701577 0.051940514 0.053866466 0.0534589673
#> Chi1 0.051776232 0.049156542 0.049348357 0.0492213616
#> Chi1n 0.070459184 0.069096237 0.072714905 0.0727060040
#> Chi1v 0.044723121 0.043485995 0.047373453 0.0501593866
#> Chi2n 0.044969369 0.049246878 0.053608909 0.0505554796
#> Chi2v -0.007655968 -0.004618584 -0.001476135 0.0001540116
#> Chi3n 0.032584667 0.042587170 0.046107374 0.0415386369
#> Chi3v -0.028277116 -0.022984653 -0.021257238 -0.0203092032
#> Chi4n 0.025069486 0.035056020 0.037250699 0.0377062265
#> Chi4v -0.032725942 -0.028311655 -0.028345799 -0.0254204075
#> EState_VSA1 -0.145952322 -0.151990047 -0.160770607 -0.1525700022
#> EState_VSA10 -0.156900443 -0.168802906 -0.175239253 -0.1722320471
#> EState_VSA11 -0.127792171 -0.135963476 -0.143448807 -0.1529079518
#> EState_VSA2 -0.088764258 -0.081331379 -0.090132085 -0.0733057615
#> EState_VSA3 0.056790068 0.028421271 0.053648385 0.0386607294
#> EState_VSA4 0.063669587 0.074797750 0.074053361 0.0699041874
#> EState_VSA5 0.076840942 0.113331436 0.116703240 0.1013286787
#> EState_VSA6 -0.039520870 -0.054418432 -0.060441879 -0.0391363977
#> EState_VSA7 0.167588096 0.158416601 0.168272101 0.1618998057
#> EState_VSA8 0.009235939 0.004258386 -0.006701922 -0.0011150675
#> EState_VSA9 0.160639733 0.170068653 0.176254590 0.1714440988
#> ExactMolWt 0.050748220 0.048487236 0.047997890 0.0454753788
#> FractionCSP3 -0.002537413 0.016775756 0.014177552 0.0000000000
#> HallKierAlpha 0.019451372 0.000000000 0.000000000 0.0329693176
#> HeavyAtomCount 0.041665347 0.039779625 0.039215273 0.0389117918
#> HeavyAtomMolWt 0.049142955 0.047099309 0.045859934 0.0431088851
#> Ipc 0.057240507 0.060688810 0.069024848 0.0694421064
#> Kappa1 0.038204987 0.032402483 0.032511070 0.0348008587
#> Kappa2 0.073454618 0.061351458 0.062538464 0.0699833246
#> Kappa3 0.068769152 0.053787212 0.048842217 0.0663792137
#> LabuteASA 0.050468473 0.048957140 0.047963605 0.0492392904
#> MaxAbsEStateIndex -0.058201076 -0.046954270 -0.035764073 -0.0459235492
#> MaxEStateIndex -0.058201076 -0.046954270 -0.035764073 -0.0459235492
#> MinAbsEStateIndex 0.050724276 0.044527421 0.044215313 0.0353840523
#> MinEStateIndex 0.080735399 0.074187812 0.072888633 0.0724654251
#> MolMR 0.064441013 0.060992387 0.061907090 0.0617893424
#> MolWt 0.050700489 0.048453503 0.047956295 0.0454522770
#> NumValenceElectrons 0.041901095 0.039028411 0.040413395 0.0398859275
#> PEOE_VSA1 -0.123885717 -0.111986458 -0.128388290 -0.1335502496
#> PEOE_VSA10 0.060135647 0.072095820 0.042111810 0.0611046246
#> PEOE_VSA11 0.027518533 0.000000000 0.054256529 0.0593889088
#> PEOE_VSA12 -0.070409371 -0.085305819 -0.078339953 -0.0775848326
#> PEOE_VSA13 0.071124088 0.073838570 0.087264498 0.0780882742
#> PEOE_VSA14 -0.059283402 -0.052884362 -0.059018175 -0.0639531460
#> PEOE_VSA2 -0.135631007 -0.136699485 -0.158100226 -0.1453559333
#> PEOE_VSA3 -0.015399543 -0.030536558 -0.023616048 -0.0258053476
#> PEOE_VSA4 0.089159585 0.082572159 0.101865179 0.1083556038
#> PEOE_VSA5 0.000000000 0.000000000 0.000000000 0.0000000000
#> PEOE_VSA6 0.252455157 0.257218113 0.264862957 0.3016795122
#> PEOE_VSA7 0.131757300 0.126559513 0.126970928 0.1081498903
#> PEOE_VSA8 -0.251591255 -0.244659553 -0.247195649 -0.2892456024
#> PEOE_VSA9 0.093581834 0.074355909 0.075437882 0.0803304497
#> SMR_VSA1 -0.045809417 -0.040299095 -0.050701107 -0.0532047159
#> SMR_VSA10 0.025671513 0.036747988 0.020329048 0.0236814814
#> SMR_VSA2 0.000000000 0.000000000 0.000000000 0.0000000000
#> SMR_VSA3 -0.196156845 -0.207343129 -0.205718468 -0.1978050051
#> SMR_VSA4 0.086514311 0.092000949 0.090979644 0.1135589734
#> SMR_VSA5 0.144746921 0.144103173 0.158124866 0.1643202372
#> SMR_VSA6 -0.086355302 -0.087439103 -0.084443620 -0.0980728660
#> SMR_VSA7 0.021803034 0.011365422 -0.006054515 0.0030932243
#> SMR_VSA9 0.164334759 0.153864976 0.180528755 0.1579959854
#> SlogP_VSA1 -0.045042683 -0.031673412 -0.087011109 -0.0688301411
#> SlogP_VSA10 0.119767503 0.115394919 0.103222595 0.0843745870
#> SlogP_VSA11 0.114675123 0.110717941 0.114633271 0.0846142758
#> SlogP_VSA12 0.103280911 0.095740332 0.101496317 0.1105220578
#> SlogP_VSA2 -0.207711269 -0.202806412 -0.200423733 -0.2013781453
#> SlogP_VSA3 -0.153164458 -0.151392486 -0.134059624 -0.1516867090
#> SlogP_VSA4 0.080989430 0.078481646 0.076140508 0.0736978562
#> SlogP_VSA5 0.174022630 0.173399624 0.191735830 0.2059561988
#> SlogP_VSA6 0.136169116 0.133023697 0.110695001 0.1313060684
#> SlogP_VSA7 0.077780951 0.068859412 0.083787537 0.0846865586
#> SlogP_VSA8 0.000000000 0.000000000 0.067225424 0.0563976493
#> TPSA -0.220618737 -0.215277058 -0.233074352 -0.2170641606
#> VSA_EState10 0.093743521 0.084141143 0.095789368 0.1014189884
#> VSA_EState8 0.089001823 0.076620959 0.083263325 0.0777088146
#> VSA_EState9 -0.089786907 -0.081994686 -0.094262874 -0.0921319769
#> [,5]
#> BalabanJ -0.073894883
#> BertzCT -0.007687107
#> Chi0 0.032319300
#> Chi0n 0.052919408
#> Chi0v 0.056854869
#> Chi1 0.048305879
#> Chi1n 0.069904194
#> Chi1v 0.051215760
#> Chi2n 0.048557618
#> Chi2v 0.005050211
#> Chi3n 0.038590608
#> Chi3v -0.016430846
#> Chi4n 0.028264216
#> Chi4v -0.022830716
#> EState_VSA1 -0.151918402
#> EState_VSA10 -0.163913222
#> EState_VSA11 -0.114487283
#> EState_VSA2 -0.074990673
#> EState_VSA3 0.027238867
#> EState_VSA4 0.081673528
#> EState_VSA5 0.119173308
#> EState_VSA6 -0.062270377
#> EState_VSA7 0.169929249
#> EState_VSA8 -0.008508467
#> EState_VSA9 0.169614152
#> ExactMolWt 0.053132588
#> FractionCSP3 0.000000000
#> HallKierAlpha 0.000000000
#> HeavyAtomCount 0.039291679
#> HeavyAtomMolWt 0.051773716
#> Ipc 0.040666065
#> Kappa1 0.035993825
#> Kappa2 0.066238470
#> Kappa3 0.056805777
#> LabuteASA 0.050833015
#> MaxAbsEStateIndex -0.039681288
#> MaxEStateIndex -0.039681288
#> MinAbsEStateIndex 0.058219064
#> MinEStateIndex 0.090836706
#> MolMR 0.065637066
#> MolWt 0.053101413
#> NumValenceElectrons 0.038876330
#> PEOE_VSA1 -0.131939533
#> PEOE_VSA10 0.063132746
#> PEOE_VSA11 0.000000000
#> PEOE_VSA12 -0.064913191
#> PEOE_VSA13 0.062907184
#> PEOE_VSA14 -0.053503851
#> PEOE_VSA2 -0.123394883
#> PEOE_VSA3 -0.021138001
#> PEOE_VSA4 0.044285049
#> PEOE_VSA5 0.000000000
#> PEOE_VSA6 0.269371381
#> PEOE_VSA7 0.118261626
#> PEOE_VSA8 -0.241824460
#> PEOE_VSA9 0.084102621
#> SMR_VSA1 -0.042033373
#> SMR_VSA10 0.054396319
#> SMR_VSA2 0.000000000
#> SMR_VSA3 -0.223644660
#> SMR_VSA4 0.086073286
#> SMR_VSA5 0.152844318
#> SMR_VSA6 -0.100483543
#> SMR_VSA7 0.017135164
#> SMR_VSA9 0.142266776
#> SlogP_VSA1 -0.055774803
#> SlogP_VSA10 0.082997064
#> SlogP_VSA11 0.088648633
#> SlogP_VSA12 0.112241959
#> SlogP_VSA2 -0.204690587
#> SlogP_VSA3 -0.156349706
#> SlogP_VSA4 0.077452104
#> SlogP_VSA5 0.198178112
#> SlogP_VSA6 0.127587128
#> SlogP_VSA7 0.000000000
#> SlogP_VSA8 0.000000000
#> TPSA -0.214509241
#> VSA_EState10 0.084382079
#> VSA_EState8 0.077845374
#> VSA_EState9 -0.085217775
predict(fit, newx = x)
#> [1] -0.21812478 0.12954374 -0.22836445 0.72266012 -0.65113402 -0.67093505
#> [7] 0.61382930 -0.45282799 0.04079630 -0.06416978 0.79365384 0.12145376
#> [13] 0.94735040 -0.31389461 0.71790961 0.86124578 0.11327756 -0.75816147
#> [19] -0.14327956 0.50469871 1.13848250 0.13954518 1.82076630 1.01476461
#> [25] 0.61597016 0.56588233 1.24949794 0.78184040 0.07023968 -0.32560716
#> [31] -0.24545686 0.91085846 0.13738773 -0.53752609 0.63554844 0.51586274
#> [37] 0.85954447 -0.34395002 -0.34058240 0.78555752 -0.37085733 0.90052950
#> [43] 0.61609279 -0.07109915 -0.02722697 0.10367080 0.33241944 0.22370098
#> [49] -0.18123400 -0.06948561 -0.04929142 -0.02625836 1.41948475 1.05831350
#> [55] 0.06012419 0.29274788 0.08855050 1.19392450 -0.03963956 -0.03859852
#> [61] 1.55698261 -0.48803906 1.02916294 1.73890966 1.87076311 1.37864665
#> [67] 0.35687448 1.29920486 0.83581663 0.56929089 0.03734973 -0.08841345
#> [73] 0.64824435 0.48630316 0.60329239 0.88549938 0.78232696 2.06775912
#> [79] 0.16023107 0.21624428 0.65925599 0.28744740 0.35358473 0.02157764
#> [85] 0.01210593 1.43460139 0.34611658 1.93062414 1.47011892 0.32332532
#> [91] -2.75216196 -0.09239403 1.93228703 1.18745000 0.92896916 0.07936765
#> [97] 0.57574740 3.06349960 1.57459052 0.69355876 2.03717644 2.32170182
#> [103] 2.37872621 0.55675433 0.73749034 0.30514075 2.52839101 0.81552872
#> [109] 1.86824783 2.05754038 1.89541525 0.95149315 2.16796051 1.50048941
#> [115] -0.74991974 1.47102994 0.78846108 0.66757694 2.02478816 2.05613690
#> [121] 2.15884081 0.96573182 1.45225310 2.03433230 0.69620378 0.67020676
#> [127] 0.60352076 0.56561324 0.67297570 0.92097974 1.72925411 0.41515221
#> [133] 0.69226657 1.00435210 3.18574778 1.65347736 2.00896410 0.88105080
#> [139] 1.87852077 1.50276630 2.01475491 1.50202430 2.34787066 2.29547931
#> [145] 1.73951951 1.87369573 0.10181703 1.60406984 2.63131115 1.67713625
#> [151] 2.37758761 1.16420952 0.09014479 0.79038294 0.60273235 2.97783189
#> [157] 1.55249758 1.27479322 -0.08177682 2.06224907 1.71203469 0.40430446
#> [163] 1.03784594 -0.05585030 2.90963566 2.25324795 3.27452491 1.81465273
#> [169] 0.06877732 3.14362520 0.96626930 0.09014479 2.25611724 1.53916617
#> [175] 0.96493001 0.55419333 0.61360396 3.08944475 0.87403643 0.72478628
#> [181] 1.04688102 1.16477997 2.57168201 0.42632452 2.01035298 0.76253155
#> [187] 3.09110582 1.90929431 2.15958110 0.78591758 2.46880186 2.84296075
#> [193] 1.28366233 2.85257488 2.68044169 3.39255631 2.26836661 2.24079808
#> [199] 2.49018036 1.93415899 2.83879092 2.11303966 1.51774075 3.03877760
#> [205] 2.59849402 0.65488715 2.72806244 1.17884939 0.17669859 2.15719871
#> [211] 0.15514763 2.42822603 2.42822603 1.25667525 0.31329578 1.14045628
#> [217] 0.95532579 1.63389965 2.17121808 1.29001363 1.76115996 1.25941899
#> [223] 1.42414047 2.83953430 2.67740439 2.95166975 1.68227772 3.40071089
#> [229] 1.62936448 0.85561182 3.01245972 0.92991875 0.77365439 1.96666960
#> [235] 3.00024939 3.28503639 0.61310141 1.94201300 2.40353511 1.19232925
#> [241] -0.09550114 1.23995297 2.63687470 1.19868790 1.04309578 1.62212216
#> [247] 2.92205143 2.95577383 2.18272258 2.64482555 0.48114460 2.04582163
#> [253] 1.87306332 -0.48062134 1.20106309 2.72936162 0.64610937 3.27270717
#> [259] 0.28593226 1.39754699 0.18411421 2.40169555 0.81423011 1.58414644
#> [265] 1.76375833 1.14836361 3.37076887 0.78232687 3.61412792 1.86824079
#> [271] 0.86233170 2.10578513 1.97974267 1.79262966 1.33904094 3.48216209
#> [277] 1.36733642 0.88696460 2.18699788 0.60802340 1.81861812 -0.33457214
#> [283] 1.15571465 0.56439084 2.53973482 1.20095316 2.89299092 0.71214121
#> [289] 1.78068714 2.27025387 2.06220738 1.08875116 3.34335307 1.80834886
#> [295] 1.26597645 1.26006793 2.14407649 1.21207573 -2.75006981 3.17121785
#> [301] 2.52956041 0.61595411 3.22833031 3.14958916 3.82252458 3.07133976
#> [307] 1.13923521 1.03993387 3.44022105 1.73357169 3.91978792 2.90468063
#> [313] 2.70803946 0.82956052 4.01176722 1.94481665 1.67873024 3.08522677
#> [319] 2.73714144 3.38938308 1.78975322 1.85503315 2.68328479 1.50043339
#> [325] 1.52681426 1.94564739 2.24680402 1.37832637 1.31035711 0.92777893
#> [331] 1.34967920 2.23747659 1.66338801 2.54412817 1.93949832 3.84327323
#> [337] 2.34041959 1.62665557 1.20543992 1.64058558 3.19045356 2.85175173
#> [343] 3.27029989 -0.29061181 3.47756378 3.22449876 1.87360099 2.63433780
#> [349] 2.34452145 1.95996065 1.92284893 0.51518892 2.13868280 1.86215339
#> [355] 1.94798224 4.67569714 1.61282318 1.34482648 1.75862888 1.65518633
#> [361] 1.91067522 2.04404224 3.39635454 1.87228118 1.90006205 2.13868280
#> [367] 0.15782769 3.43364346 1.57178256 4.63798128 2.23237403 2.04628161
#> [373] 3.46524125 2.02383227 1.80821689 2.07126869 1.63056250 2.54983769
#> [379] 0.10987772 1.83567901 1.25431766 2.48009915 1.41915723 1.52965346
#> [385] 2.15499145 3.70594696 -0.28194095 3.32677095 1.87966418 2.10558633
#> [391] 3.99745324 1.55812086 1.99856187 3.89588884 3.77808186 3.42453266
#> [397] 1.81677761 2.19658826 1.77536759 1.51930238 2.05827236 3.10030703
#> [403] 2.92326945 2.10587800 2.29381554 0.91106401 1.79888417 2.67948613
#> [409] 3.04804372 3.50287327 2.86365029 2.10789329 3.58978806 1.72754828
#> [415] 1.96350768 1.82919623 3.86178071 1.35734911 1.98331961 3.55699494
#> [421] 2.33318865 0.33378792 1.81271763 1.87268863 0.07939267 1.59116606
#> [427] 4.67063598 5.25186747 5.80784312 2.14972593 2.28486539 2.09380743
#> [433] 4.78504057 1.62716609 3.70046592 1.86838471 2.20729621 1.61991796
#> [439] 1.77143505 1.61991796 2.38545261 2.21020362 3.74839551 3.40623513
#> [445] 1.88220243 2.74557869 2.45981970 2.48980577 2.28032701 2.49807785
#> [451] 4.23368979 2.52989391 2.59780943 2.45304004 3.75197506 2.48980577
#> [457] 2.49824529 2.55615346 3.33953104 1.93195431 2.52501761 2.94709171
#> [463] 3.38900481 2.74764906 2.33555991 1.96482182 4.66543938 2.92528097
#> [469] 3.12002394 2.29980988 3.19779522 2.83128396 4.53536185 3.38698261
#> [475] 1.76854000 3.11151338 2.79375543 -0.86677482 3.06584623 2.12109409
#> [481] 4.20163913 3.57745841 4.83825320 4.28016048 2.17954723 2.25650264
#> [487] 1.96389737 1.12702691 2.42451663 4.62654854 3.47534571 3.23082867
#> [493] 2.25615596 2.35024310 1.95823140 2.43676940 0.32568673 4.12169719
#> [499] 4.92582143 4.14635067 4.43675970 3.11677301 3.34475616 3.26580201
#> [505] 2.98354412 5.06105114 1.46841915 5.38613437 3.75547063 4.25938458
#> [511] -0.10976488 3.03492810 3.69930400 3.14044768 3.12086214 4.15293048
#> [517] 2.98127075 3.99768217 -0.35398504 2.97702915 5.20639521 3.67008569
#> [523] 4.35526891 4.34339153 4.60734460 1.02229384 4.23555332 3.49136278
#> [529] 6.23164106 -0.73213442 6.65914329 3.98747765 5.24720195 3.52351064
#> [535] 6.83949436 0.07215180 -1.06854684 0.16100615 0.44678247 0.43315286
#> [541] -0.10079426 3.06433482 4.61374803 4.26642723 3.75676158 4.13011292
#> [547] 4.05504812 5.23447514 0.54320694 0.26358850 0.47923280 1.20245467
#> [553] -0.33440371 3.60480349 5.03799222 4.17442486 0.94032030 -0.84196436
#> [559] 1.17200396 2.84595264 0.82206120 0.37274485 2.62865316 1.54254898
#> [565] 0.34930257 3.35566735 2.61556407 0.72745670 3.65243665 2.46128995
#> [571] 2.04239169 3.09122324 1.93178301 0.72266765 3.19908188 1.71153471
#> [577] 3.23303968 2.44735657 -0.34046193 2.52795400 2.31663297 1.02046448
#> [583] 0.30053738 0.03439801 1.44552645 -0.28297008 -0.05359628 1.38017913
#> [589] 0.79243316 2.65741366 2.19443573 1.56331062 0.02061230 3.80736290
#> [595] 1.43335855 1.16154812 4.33192061 0.57137921 0.87993187 4.60455368
#> [601] 1.37004326 1.42974011 3.19568580 1.35103257 1.36075138 1.74941627
#> [607] 0.04450224 1.68423209 1.39919257 2.87960962 1.83390217 1.66876834
#> [613] 1.76391927 0.58754943 3.33107676 3.24056100 1.90729682 1.50235623
#> [619] 3.37939931 1.48313360 1.52958825 2.13012720 2.03571818 2.37949339
#> [625] 3.09800295 1.50962024 0.22642826 1.24724197 1.53492749 1.19980790
#> [631] 1.99926854 1.88464256 2.39671056 2.92585700 1.79840483 2.68684025
#> [637] 2.69582679 3.86711302 3.23477431 2.63882016 2.85708426 1.98060621
#> [643] 1.82458996 2.55023124 2.81165120 3.48882850 1.61761933 3.95978480
#> [649] 2.25949158 2.13363580 1.20988843 2.22934956 1.98518542 2.08235507
#> [655] 2.22223289 2.57025667 1.28315518 2.57460140 3.23886008 2.08637661
#> [661] 2.68321245 1.07853455 2.61303559 3.48569156 3.84252931 3.52689545
#> [667] 2.62372010 2.47400812 2.55102202 2.28441657 1.78789095 3.00505167
#> [673] 1.42512225 2.12897264 2.02097509 2.12943268 1.87190663 2.51703177
#> [679] 1.84668372 1.62795235 2.61682582 2.07902538 1.49666236 1.78954124
#> [685] 1.43065456 1.19936785 2.26893635 2.42806920 2.50375078 2.78842705
#> [691] 1.67792977 2.38307478 2.11808710 2.39554277 2.97456240 2.24011090
#> [697] 3.42408655 2.07366955 1.89735276 2.20297747 2.48659082 2.69900519
#> [703] 2.06677043 2.21659692 2.84902153 3.58248775 3.57745650 3.58951649
#> [709] 3.47544471 2.92680732 3.39805023 5.14890527 3.04034041 2.22302725
#> [715] 4.38766610 5.03225521 5.29484031 1.02325019 2.69245784 2.49343203
#> [721] 2.23769200 1.49479959 1.41587049 1.44922585 1.85351325 1.37985474
#> [727] 1.49030317 0.83513612 3.36371068 4.23638545 4.00612353 4.21052304
#> [733] 3.88632749 3.94353482 3.71756999 3.33760044 3.42221209 3.54601607
#> [739] 4.22028005 4.18488502 -0.16212599 4.04014889 3.46776328 2.95417121
#> [745] 3.76126857 3.46775817 0.51817085 2.89209189 2.80727717 3.62248373
#> [751] 3.86104976 -0.18241765 0.93921904 3.70525847 1.63443089 2.43718262
#> [757] 2.90832587 2.33495255 2.30508579 1.76630774 1.98572361 1.80773511
#> [763] 0.60768891 1.24569432 2.61209995 3.52387960 2.64435353 2.06969196
#> [769] 2.21997924 1.72627403 3.35042252 2.10889268 2.09549945 2.88778738
#> [775] 2.88468560 3.59390191 2.45624807 3.37754538 2.62880307 2.61171299
#> [781] 1.29638245 3.40204416 2.60158561 1.20316935 1.71267140 3.08726162
#> [787] 3.25355282 2.28729865 1.03321808 1.13218134 2.38850702 1.18475727
#> [793] 2.57776595 2.13003670 1.10652215 1.84150657 2.62334347 3.01581911
#> [799] 2.90756502 1.25945797 2.70314847 2.11654158 1.83729565 2.19720590
#> [805] 2.69223950 0.25382039 3.37072235 2.72318454 2.79339183 2.82372254
#> [811] 3.28577166 3.25679310 3.57511360 2.54612189 3.60093209 2.25260092
#> [817] 2.30215625 1.83709314 3.41978388 4.01353323 3.41660117 4.37468597
#> [823] 0.29674498 3.57935835 3.70495425 3.98561637 3.45428191 3.66086337
#> [829] 3.27497089 3.14702539 4.23455078 1.76968264 3.18460459 2.81532365
#> [835] 3.90984128 3.90256934 4.00893968 3.04089864 3.46683945 3.50718720
#> [841] 3.40930517 4.95646668 3.27164935 1.58848984 2.90261349 4.09175507
#> [847] 3.81362927 3.88564651 2.81371095 4.53622110 3.78021124 4.15543848
#> [853] 4.32904620 3.95981489 3.99602330 3.83388189 2.76998912 4.58693927
#> [859] 4.42723853 3.97654608 4.21212374 4.68451308 1.81950652 4.10562453
#> [865] 4.57932529 5.15001640 5.57831159 5.57807989 5.09739506 5.01455994
#> [871] 0.10896540 0.12535700 0.06271390 0.36057485 0.43108839 0.93320995
#> [877] 0.16181753 -1.01411812 -0.10253743 0.30790409 -0.49951206 1.59514054
#> [883] 2.08502953 2.40905181 2.82254816 4.84046308 3.74823508 1.30450749
#> [889] 1.01459294 1.50277127 1.62491853 1.71717767 0.36370044 2.26131572
#> [895] 1.88923418 0.29393852 0.33754865 0.59342459 1.60689411 1.22826065
#> [901] 1.60922010 1.66156897 1.88934216 1.51557287 2.25085324 1.27091542
#> [907] 0.54446153 2.84840128 2.53119334 0.45189876 0.39820538 0.89873987
#> [913] 0.61200794 0.67950270 0.81035050 -0.27761592 -0.18237907 -0.14164102
#> [919] 0.03506333 0.30686449 0.56680784 0.91550647 -0.60697486 -0.40537849
#> [925] -0.36208492 -0.31864564 -0.05437869 2.73532574 1.93536313 0.62171751
#> [931] 0.98490465 3.80736290 0.53687998 1.69084326 4.65621160 4.28264442
#> [937] 0.46110121 -0.34046193 1.50065578 2.04239169 1.72653109 2.44735657
#> [943] 4.72436140 4.17442486 1.07618295 1.35734911 0.19316557 2.31663297
#> [949] 0.80594103 2.14192424 1.93178301 2.78284665 1.03068374 1.01076709
#> [955] 0.21041549 1.05094298 0.05928069 1.90677231 0.52526021 1.56331062
#> [961] 1.12259152 1.32515959 1.17843465 2.06983829 2.14192424 0.93414463
#> [967] 2.20041325 3.58129049 2.97850838 3.03047152 0.69043958 0.59915148
#> [973] 3.27879775 0.80955659 0.18395801 2.54807064 2.73532574 1.15388766
#> [979] 1.99028693 0.33342454 0.50063027 0.36747631 1.17422988 4.80446578
#> [985] 0.82812425 0.14862912 0.26265082 0.21386016 2.53847394 -0.03859852
#> [991] 4.17015248 2.85175173 0.34930257 2.71290613 2.21749003 1.15036197
#> [997] 0.58697193 1.29162488 0.21005844 0.75058928