Compute initial mr.mash coefficients via group-lasso
Source:R/regularizedRegressionWrappers.R
computeCoefficientsGlasso.RdFit a group-lasso (one group per response) to obtain initial estimates of the
mr.mash coefficient matrix, optionally predicting on a new design.
Arguments
- X
Numeric design matrix (samples x variants).
- Y
Numeric response matrix (samples x conditions).
- standardize
Logical; standardize the columns of
Xbefore fitting.- numThreads
Integer; number of threads for the group-lasso fit.
- Xnew
Optional new design matrix for prediction;
NULLreturns in-sample coefficients.
Examples
data(eqtlRegionExample)
X <- eqtlRegionExample$X[, 1:30]
Y <- matrix(rnorm(nrow(X) * 3), nrow(X), 3)
computeCoefficientsGlasso(X = X, Y = Y, standardize = TRUE,
numThreads = 1L, Xnew = NULL)
#> $Bhat
#> [,1] [,2] [,3]
#> [1,] 0 0 0
#> [2,] 0 0 0
#> [3,] 0 0 0
#> [4,] 0 0 0
#> [5,] 0 0 0
#> [6,] 0 0 0
#> [7,] 0 0 0
#> [8,] 0 0 0
#> [9,] 0 0 0
#> [10,] 0 0 0
#> [11,] 0 0 0
#> [12,] 0 0 0
#> [13,] 0 0 0
#> [14,] 0 0 0
#> [15,] 0 0 0
#> [16,] 0 0 0
#> [17,] 0 0 0
#> [18,] 0 0 0
#> [19,] 0 0 0
#> [20,] 0 0 0
#> [21,] 0 0 0
#> [22,] 0 0 0
#> [23,] 0 0 0
#> [24,] 0 0 0
#> [25,] 0 0 0
#> [26,] 0 0 0
#> [27,] 0 0 0
#> [28,] 0 0 0
#> [29,] 0 0 0
#> [30,] 0 0 0
#>
#> $Ytrain
#> [,1] [,2] [,3]
#> [1,] -0.229860857 0.736062443 -0.7860695344
#> [2,] -0.537452763 0.664990339 -0.3002899838
#> [3,] -0.440710795 -0.680332955 1.8047594184
#> [4,] 1.782099088 0.285767969 -2.0674694352
#> [5,] -0.141434306 -2.381077981 -0.1152439716
#> [6,] 0.183724044 0.064484535 -3.3463982427
#> [7,] -0.966399123 -0.613208861 -0.0008497743
#> [8,] -2.189366752 2.287309076 0.0955797820
#> [9,] 0.112669559 1.762408887 -1.4361428512
#> [10,] -0.721204424 2.767010237 1.5306282762
#> [11,] -0.868276148 -0.934804682 -0.1216373536
#> [12,] 0.525638135 -1.453273122 -0.4778774073
#> [13,] 2.304728041 0.759859903 -0.1184103170
#> [14,] 1.125669987 -0.917739206 -0.5570462592
#> [15,] 1.374242019 -1.815927300 -0.6129907571
#> [16,] 2.757950213 -1.058514096 -1.2334755396
#> [17,] 1.318172793 -0.923125262 1.2048238196
#> [18,] 0.167542705 1.060363685 0.6180811423
#> [19,] 0.066829567 0.706132229 -1.3290076363
#> [20,] -0.799790767 -1.587851766 -0.7583258757
#> [21,] 1.636904015 0.343792196 1.2616125122
#> [22,] -1.165470418 -0.220187330 0.9506933445
#> [23,] 0.787955820 -0.142456618 1.5695419718
#> [24,] -0.681954235 1.239036904 0.8109116496
#> [25,] -1.289528922 1.033721908 0.3624077236
#> [26,] -0.357143496 -1.475380966 0.5258675803
#> [27,] 0.172217603 -0.695403382 -0.1840675633
#> [28,] 1.460697300 -0.830049408 -0.1397359423
#> [29,] -1.062454789 0.665697920 -1.0865690897
#> [30,] 0.269286521 2.057785691 -0.4849087543
#> [31,] 0.018172517 0.187159376 0.6763745948
#> [32,] -0.176545271 -0.136796902 -1.0359815127
#> [33,] 0.034868903 2.697362862 -1.5157669034
#> [34,] -0.095602092 -0.154570394 -0.9718434887
#> [35,] 0.146931385 -0.207160646 -0.3546173787
#> [36,] -0.285333727 0.777689346 -1.8861393581
#> [37,] 0.252990498 -0.113468303 1.5488365663
#> [38,] -0.243102748 1.604393081 -1.4122495209
#> [39,] -0.522185493 -0.854770090 0.9477811346
#> [40,] -2.737308291 1.006132265 1.0236207332
#> [41,] 1.098522096 -1.250384901 -0.7874932054
#> [42,] -1.786034924 0.213276725 0.2291223270
#> [43,] -0.526051893 -0.728830070 -0.7142539765
#> [44,] -0.073735576 -2.335486663 0.3835721815
#> [45,] 0.713191770 0.427774634 -0.7089357276
#> [46,] -0.904437303 -0.227509182 0.0261034038
#> [47,] 0.706532555 -0.382543113 1.6639201790
#> [48,] -0.832611879 0.105804732 -0.4095778348
#> [49,] -0.678531278 1.236965641 -0.0061132059
#> [50,] -0.497896574 1.235497889 0.2848010284
#> [51,] -1.176033361 -0.778560328 0.8906084895
#> [52,] -1.126555621 -0.637430198 0.8812326622
#> [53,] 0.660617279 -1.082380562 -0.4146163234
#> [54,] -1.326897448 -1.411539296 0.2639895676
#> [55,] -2.617592708 0.369017829 0.5064654547
#> [56,] -1.201573910 -1.647816570 -0.4273110163
#> [57,] 0.951767610 0.011115514 1.5553357897
#> [58,] -1.213950738 -0.607016387 0.3933102925
#> [59,] -1.030468268 0.081123616 2.2140814458
#> [60,] -0.811979520 0.224634931 -1.7281035002
#> [61,] -0.005429719 -1.396470558 2.3707062904
#> [62,] 0.122830823 0.375165826 2.3099262222
#> [63,] -0.575588163 1.483826139 0.4497814099
#> [64,] 1.085626887 0.232826219 0.5820184807
#> [65,] -0.682018561 0.099942853 1.1081738819
#> [66,] -0.114918307 0.780471728 -1.2471531519
#> [67,] -0.181136534 0.070695634 -0.5030822170
#> [68,] 1.346329531 -0.231663356 0.2332340290
#> [69,] -0.019612271 -0.239032021 -0.8191103840
#> [70,] -0.671969372 0.794679464 -2.1996674696
#> [71,] -0.587516078 -0.271650337 -0.8029142326
#> [72,] -0.708010023 -1.364036108 0.3602135472
#> [73,] 0.079477713 -0.691222725 0.9734978288
#> [74,] 0.132397734 0.632474508 0.7969702293
#> [75,] -0.054494682 0.347827635 0.2268940028
#> [76,] 1.686746516 1.596420380 0.8921623340
#> [77,] 0.908834118 -0.267696206 2.1262300428
#> [78,] 0.673219280 0.286781465 0.9937875900
#> [79,] -0.272982365 -2.349098616 0.4761566594
#> [80,] 0.439844005 1.489689560 -1.5748424113
#> [81,] -1.881169744 0.938067211 -1.0759295362
#> [82,] -0.743109271 1.944237092 -2.3991916415
#> [83,] 1.025395179 0.564591699 -0.8090417745
#> [84,] 0.405310137 -1.131184423 -1.2081160615
#> [85,] 0.090637403 1.181631512 1.0987523905
#> [86,] 0.265306759 1.327721418 -0.8977027733
#> [87,] 0.687388460 -1.192242704 0.8004829228
#> [88,] -1.362092576 0.761135358 0.3182158073
#> [89,] 1.180537063 1.105962619 -0.2536723496
#> [90,] -1.779003015 0.756212831 1.7623970608
#> [91,] 1.006661965 -0.054560078 0.2672623842
#> [92,] -0.472337037 -1.142895552 1.7765462340
#> [93,] -0.882024146 0.509871369 0.6948144661
#> [94,] -0.870933305 -1.479390989 0.0776958487
#> [95,] 0.823440585 -1.285094395 0.0614350108
#> [96,] 1.149116104 1.241867544 1.1540302076
#> [97,] 1.450183909 0.893555471 -0.4756703181
#> [98,] -0.774728171 -1.137812114 1.3285541022
#> [99,] -0.467677715 -0.475624406 -0.9976809590
#> [100,] -1.772718659 -0.563764653 -2.2303646675
#> [101,] 0.159238487 -0.361839085 1.0609905975
#> [102,] -0.334629805 -1.118899392 -0.6866584510
#> [103,] 0.282309522 -0.289070459 0.5477755020
#> [104,] -0.428610906 0.994053333 0.4920247668
#> [105,] 1.691745875 -0.977922513 0.0661302605
#> [106,] -0.027613550 1.001417677 -0.5933043912
#> [107,] -1.729908674 0.966693540 0.6094863653
#> [108,] 0.168621544 -0.072470571 -0.3800374915
#> [109,] 1.347726443 0.470998220 -0.5006633704
#> [110,] 1.528870085 0.031745612 -0.1976449331
#> [111,] 0.112928260 -0.003389207 -0.6294497240
#> [112,] -1.296715047 0.913391290 1.4232751547
#> [113,] 0.478314160 1.903170783 -1.5668221876
#> [114,] -1.732522697 0.001073557 0.4683435754
#> [115,] 2.544361175 -1.507577560 -1.1692382883
#> [116,] 0.010220525 -1.537754414 -0.4854110016
#> [117,] -1.068902341 0.213146106 1.2305034404
#> [118,] -1.330495470 0.415590895 0.3467242972
#> [119,] -0.004397303 0.969702324 -0.8057939316
#> [120,] 0.615727691 0.579170755 0.0883783247
#> [121,] 1.508060766 0.274287246 -0.9000928351
#> [122,] -0.775922374 -0.798784730 0.9982222745
#> [123,] 0.934268563 1.496289395 -0.3251110497
#> [124,] -0.787283497 -1.426337060 0.7590950192
#> [125,] -1.892829540 1.267131845 -1.6429523141
#> [126,] 0.022290854 0.636685344 0.7047725297
#> [127,] 0.091412171 -1.022498038 0.3113450960
#> [128,] -1.039636928 -0.144078504 -0.1572749202
#> [129,] 1.135480286 -0.487117712 3.1065543658
#> [130,] 0.127434724 -0.439882538 -0.9213661594
#> [131,] -0.095575658 0.921810476 0.2477788717
#> [132,] -0.897385195 1.266258711 0.5720525498
#> [133,] -0.575685952 0.091757792 -0.9734868579
#> [134,] 0.551929598 -1.162842557 1.3328957474
#> [135,] -0.188938886 -2.260731664 -0.1089672288
#> [136,] -0.734227223 -0.556427072 -0.0193803743
#> [137,] 0.029154134 -0.835438364 1.1603542126
#> [138,] 0.929780681 -0.961900987 1.4918116683
#> [139,] 0.671658269 1.173627424 0.9716645970
#> [140,] -1.028949559 -0.265134633 -0.4161220260
#> [141,] 1.590792523 -0.812855415 0.7198700439
#> [142,] 0.932394070 2.126166059 1.0941844303
#> [143,] 0.636574799 0.311118772 0.1517362570
#> [144,] -1.311974671 0.742908619 0.2820126129
#> [145,] -0.160489145 -0.920152557 -0.3751930635
#> [146,] -2.472189462 1.210788988 0.2336775421
#> [147,] -1.753636552 0.906411777 1.2912170758
#> [148,] -0.670855397 -0.780770106 0.3391002482
#> [149,] 1.087909367 -0.026142913 0.1303777704
#> [150,] 0.155762241 -1.961998301 0.1407764506
#> [151,] 0.197706364 0.172082291 -1.1159056852
#> [152,] -0.729124016 -0.541741841 2.1747890319
#> [153,] -0.053754649 -0.590791564 1.0257107543
#> [154,] -0.984079841 -0.047557631 0.7129470478
#> [155,] 0.223196900 1.006506083 0.1610820412
#> [156,] -1.086448286 0.313857372 -1.3631774496
#> [157,] -2.384853870 0.093507598 0.1045571996
#> [158,] -0.770370884 1.195999382 -0.2530674330
#> [159,] 0.008385502 0.056298739 0.8212878230
#> [160,] -0.398937753 -0.564899373 -0.2751599506
#> [161,] -0.822660608 -1.181371166 1.3550662433
#> [162,] -0.164125437 0.815931074 1.4942745037
#> [163,] -0.820736331 -1.372896174 -0.1870741160
#> [164,] 0.881897159 -0.902761121 -1.5963915477
#> [165,] 0.900527307 1.046102272 0.4195026370
#> [166,] -1.062235277 1.938011929 -0.9618303830
#> [167,] -0.879443591 -1.377193367 0.0633414132
#> [168,] -0.647609787 0.259047350 -0.5650578378
#> [169,] -0.401275505 -0.255686572 -0.2382201086
#> [170,] 1.231251975 1.579018851 -0.0963284195
#> [171,] -0.924896335 0.118257088 -1.0287867255
#> [172,] -1.543024607 0.647633933 -0.5577798012
#> [173,] 0.385904222 -0.114440470 0.6306178368
#> [174,] -0.730252723 -0.337892135 -0.4511032136
#> [175,] -0.076751128 -2.025419104 0.6821665871
#> [176,] -0.648789025 0.109309365 0.3016118517
#> [177,] -0.527459758 0.993893491 1.0150239267
#> [178,] 1.005247271 0.417332055 0.8804386257
#> [179,] -1.169248359 0.204129137 -2.0836605460
#> [180,] -1.565484270 -0.252474911 -1.7331318928
#> [181,] -0.962117718 0.402889808 0.1084774407
#> [182,] -0.155882836 -0.933799444 -0.2093332848
#> [183,] 0.272277292 -0.920773458 0.0258481932
#> [184,] -1.244211159 1.012456682 0.9298953373
#> [185,] -1.807924570 2.180273596 0.8341429062
#> [186,] 0.322649526 -0.717318990 0.6564117467
#> [187,] -1.191569111 0.242847482 -0.7566419179
#> [188,] 1.340588128 0.894537955 -0.3404301772
#> [189,] -0.544418473 0.007513902 1.0511341721
#> [190,] -0.296879325 0.700082654 -0.5441987400
#> [191,] -0.695099975 0.841399748 -0.0489258559
#> [192,] 0.241000538 0.774375313 0.7712807223
#> [193,] 0.254911625 0.035929707 -0.7278059852
#> [194,] 0.438360349 -0.918059437 0.9909974139
#> [195,] 0.737312704 0.018313587 0.1148936038
#> [196,] -0.481764871 0.623386099 1.7085367835
#> [197,] -0.549338390 -1.757335048 -0.4736606243
#> [198,] 0.255677306 1.426252753 -0.2308132306
#> [199,] -1.103186251 -1.143153561 1.4917038424
#> [200,] -2.193412671 0.131286880 -1.3102091829
#> [201,] 1.128767719 0.659486864 -1.1510833125
#> [202,] -0.429824440 0.707677687 2.3634005737
#> [203,] -0.810883652 -0.527815098 -0.1788083769
#> [204,] -0.864916368 -0.577168534 1.5253521119
#> [205,] 1.082645233 0.395043421 -0.1854284698
#> [206,] 1.045596246 -1.664546061 2.2564058662
#> [207,] -1.365866582 0.634922146 -0.1746079438
#> [208,] 1.069897749 0.413407502 -0.5905378142
#> [209,] -0.877445622 -0.255245066 -1.1743088876
#> [210,] -0.693829232 0.054581418 -0.6068659124
#> [211,] -0.608464507 0.265867245 1.3696829754
#> [212,] 0.006859659 -0.251739084 -1.2800472351
#> [213,] -0.411825032 0.707510526 -1.4324548494
#> [214,] -0.662841226 -0.186755052 -0.8529469648
#> [215,] 0.503105954 -1.141442127 -0.3208516121
#> [216,] 0.339495603 1.329809106 0.6382787142
#> [217,] -0.285821138 -0.901385548 -0.1876060556
#> [218,] -0.115318138 0.830521657 0.6587971455
#> [219,] -0.128708677 -1.004161310 1.8158528039
#> [220,] 0.341507407 -0.978173247 -1.3985605396
#> [221,] -0.134605045 -0.431092730 0.6303223070
#> [222,] -1.032460144 0.464681979 0.4925188893
#> [223,] -0.293014829 0.488385165 0.5040222990
#> [224,] 0.646749017 0.257591822 0.0513405209
#> [225,] 1.388175822 -0.294676551 -0.9928243838
#> [226,] 0.071442202 -0.553331347 -0.4413819070
#> [227,] -1.375018206 0.231784047 0.1482601920
#> [228,] -0.595028947 -0.441702536 -0.5493944785
#> [229,] -0.771314572 0.181737739 0.3223157438
#> [230,] -0.158618853 -1.266195415 1.0169327140
#> [231,] -0.672731220 -0.608945997 1.1423932343
#> [232,] 0.507259968 -0.404444735 -0.8034355459
#> [233,] -1.250269879 1.801224310 -0.6352556446
#> [234,] -0.522447163 0.015369640 -1.8547008454
#> [235,] -0.861754234 -0.933024833 -0.2693851502
#> [236,] 0.272337710 0.864570905 0.6902358592
#> [237,] 0.210314512 -0.203649096 -1.3154938106
#> [238,] -0.498271738 -0.704928516 1.0064083744
#> [239,] 0.236939770 1.186188348 -0.0746854368
#> [240,] 1.693154510 0.528031148 0.7758281095
#> [241,] 0.132992597 -0.268907549 -0.9392764456
#> [242,] -0.946212624 1.387482215 -0.8215818020
#> [243,] -0.634225008 -0.323696779 1.0525817034
#> [244,] -1.232221167 0.096813612 0.9319159504
#> [245,] -0.858620554 2.447296198 -0.6145661324
#> [246,] -0.443947957 -1.282835409 -0.4794063487
#> [247,] 1.435180292 -0.644716542 -0.0075961268
#> [248,] -0.745074957 0.066628371 1.0327805117
#> [249,] -0.496692723 0.100254572 0.0642414811
#> [250,] 0.114887212 -1.647511084 0.0512945693
#> [251,] -1.043135565 0.163174898 0.5628962783
#> [252,] 0.444952663 0.285538018 -0.6714506965
#> [253,] 1.374296146 0.515440788 0.1827189233
#> [254,] -0.336951511 1.214515702 0.7170384173
#> [255,] -1.112584607 -0.038141782 2.2915320474
#> [256,] -0.895677357 0.260954909 -1.2808491379
#> [257,] 0.524475860 -0.512672554 -0.2211444553
#> [258,] 0.852342959 -0.163617072 0.9200321278
#> [259,] 0.735483458 -0.165826826 -1.0497446222
#> [260,] -0.532589316 -2.107247024 -1.4151026981
#> [261,] -0.298994661 1.591315749 0.0003830190
#> [262,] 0.244734758 -2.330251514 0.6487022722
#> [263,] 0.833367098 -0.067473565 0.1615693902
#> [264,] 0.340399973 -0.515312183 0.6098246254
#> [265,] 1.158354680 1.019156988 0.3036771531
#> [266,] -1.045374858 -0.072753266 1.0438361183
#> [267,] -0.493037867 -0.021515642 0.5476369472
#> [268,] -0.604332596 0.389666095 0.8262458078
#> [269,] -1.658051083 -0.765452396 -0.0203858075
#> [270,] 0.024488172 1.827379236 -1.6673755243
#> [271,] -0.304880053 0.965949950 -0.6875874546
#> [272,] -2.307557248 0.290538114 -1.7870207307
#> [273,] 0.533108571 0.875338872 0.6493495452
#> [274,] -0.332300982 -0.513176575 -1.2751357161
#> [275,] 0.522823286 -0.555174535 -0.2735388101
#> [276,] -0.316339006 1.112582462 0.4542851870
#> [277,] -1.253982507 -0.396292305 -1.9796843449
#> [278,] -0.729588732 -0.250408296 -1.0797651444
#> [279,] -0.887950278 1.287267101 -0.5820960863
#> [280,] 1.042720420 0.764943584 -0.5146142619
#> [281,] 0.600101672 -0.270577539 1.0025306550
#> [282,] 0.534321169 1.511979070 0.7737565074
#> [283,] 1.336036394 -0.331527476 0.6031775760
#> [284,] -1.103243925 -0.956067533 0.6610103367
#> [285,] 2.118993421 -0.573082625 0.5456709565
#> [286,] 0.458892518 0.955078237 -0.5877631574
#> [287,] -0.766828396 -2.376075849 0.7773566941
#> [288,] 0.618576392 0.539804586 -0.9500210330
#> [289,] 0.936150806 0.356652309 -2.8043305994
#> [290,] 0.907113635 1.562124183 -0.1200560836
#> [291,] 1.088480614 -1.738122021 0.0280143885
#> [292,] 0.617859314 0.630962027 0.8006101906
#> [293,] 0.922803012 1.020710983 0.1283558988
#> [294,] -0.892552416 -0.075870196 -0.4241307804
#> [295,] 1.149479699 -1.020528690 0.9876839616
#> [296,] -1.955181559 1.271566424 -1.1963183725
#> [297,] 0.351270243 0.499172170 -0.1558969624
#> [298,] -1.791015615 -0.304672790 -0.1812906429
#> [299,] -0.178799399 0.627591817 -1.3634461709
#> [300,] -0.745618295 -0.328945516 0.5394909642
#> [301,] 0.555980878 -0.540560099 1.9281773697
#> [302,] 0.361917371 1.085527416 -0.4696360510
#> [303,] 0.868925785 -0.031241130 -0.1746703475
#> [304,] -2.033371491 1.373547329 1.4935103328
#> [305,] 1.099807240 0.661846706 1.5076117878
#> [306,] -1.864778836 0.571702224 0.8155969540
#> [307,] -0.905722333 0.744696096 0.7728247958
#> [308,] -0.186394422 0.890951549 -0.0548478672
#> [309,] -0.674276997 -1.410842577 1.2375989978
#> [310,] 0.476845924 -0.252653617 -1.2307762704
#> [311,] -0.201583247 0.684151911 -1.5145186326
#> [312,] -0.440396523 -0.636580318 -2.1638328931
#> [313,] -0.083558660 -1.556312466 -0.4367174944
#> [314,] -0.786005089 1.646020994 -0.0765861139
#> [315,] 2.568258267 -0.144232789 -1.0473648178
#> [316,] 0.200995346 1.008939138 1.8320118687
#> [317,] 1.226795638 2.073742997 -0.9855732265
#> [318,] 0.054245596 -0.669452616 0.6528441822
#> [319,] 0.489910410 0.153152448 0.0663422208
#> [320,] 0.780057063 -0.481721641 -0.3145372654
#> [321,] 1.436856735 -0.670373613 0.6896058849
#> [322,] -0.620496928 -3.530779804 -1.5472378081
#> [323,] 2.092561352 -0.608134760 1.4607107928
#> [324,] -0.641878348 -0.880455882 -1.6033719662
#> [325,] -0.412166631 -0.171832652 -0.2392480638
#> [326,] -0.852685303 -0.689871246 1.0215157404
#> [327,] 0.603253060 -0.315381208 0.2174279791
#> [328,] 0.259664249 -1.118581410 -1.2522204520
#> [329,] 1.518280001 -0.722535759 -0.9034761032
#> [330,] -0.582501123 -0.834295556 -0.3100302176
#> [331,] 1.208351684 0.397450719 0.5744148019
#> [332,] -0.564608318 -0.727414926 -0.6044012621
#> [333,] -0.432516341 -0.904802618 0.2879846005
#> [334,] 0.746956269 -0.962609011 -0.2998393561
#> [335,] 1.040915104 0.476323202 0.3208598625
#> [336,] -0.082706106 -1.539430352 2.1894245297
#> [337,] 1.404697502 0.280570876 1.0792347428
#> [338,] -0.964155061 -0.057125889 1.3281760621
#> [339,] 0.155952853 0.591304566 -1.1511251709
#> [340,] 0.867509810 0.096934576 -0.0461214107
#> [341,] 1.696567314 -0.749738305 1.1072958003
#> [342,] 0.720907645 -0.394334832 -0.4574386151
#> [343,] -1.362580554 0.879682026 -1.5089389003
#> [344,] -0.771025337 0.567761206 0.6480234734
#> [345,] -1.006695690 -0.216661196 0.3619194843
#> [346,] -2.623503268 -0.312230900 -1.7495771242
#> [347,] 0.736612191 -0.045424521 -2.2042270721
#> [348,] -0.864466757 0.714101172 -0.0061030445
#> [349,] 0.549497324 -1.803940324 -1.2669727739
#> [350,] -0.040278433 0.914138747 -1.3951330243
#> [351,] -1.596487364 0.472867115 0.6782194532
#> [352,] -1.499188488 0.221950369 0.1447485739
#> [353,] -1.332920192 0.481479247 -0.7960869624
#> [354,] -0.281465325 0.042302885 1.5846370277
#> [355,] -0.139310484 0.403592003 -1.1677940456
#> [356,] 0.209504570 -0.041861690 -1.2539035365
#> [357,] 1.454832720 0.659687953 -2.5706341209
#> [358,] 0.011930290 0.782188296 -1.2136759346
#> [359,] -0.730550275 0.267615669 0.1088207290
#> [360,] -1.079674745 -0.790024198 1.4974169115
#> [361,] 1.250711954 -0.319475551 -0.3212152852
#> [362,] 0.992491904 0.153823072 -1.1955893553
#> [363,] -0.102873472 -0.866766471 0.7159079245
#> [364,] 0.136161473 -0.392861567 0.6494305207
#> [365,] -0.771906165 -0.323653433 -0.4419365576
#> [366,] -0.562850899 -0.098053601 -0.6682845606
#> [367,] 1.385426536 0.094942657 0.9774066386
#> [368,] -0.977437812 2.547583286 0.4844199278
#> [369,] -0.180106165 -0.708532183 0.5506366288
#> [370,] -1.377822357 1.210195383 -0.1641349518
#> [371,] 0.015993257 1.754809455 1.1982147621
#> [372,] -1.848024615 0.552779548 0.8386132012
#> [373,] -3.137910315 0.522992955 -0.6361542841
#> [374,] 0.858074173 0.818207255 -0.7897150646
#> [375,] 0.039007595 0.273208458 -0.1216119091
#> [376,] -1.098745466 -1.390836614 -0.1232272429
#> [377,] -0.847854616 1.800678394 -0.0109370753
#> [378,] 1.074084498 0.254586246 -0.3145932163
#> [379,] -0.251709648 0.017289518 0.6094685535
#> [380,] 0.818886380 -0.098486963 0.4036377755
#> [381,] 1.072581583 -0.452606328 -0.6225297715
#> [382,] 1.937523530 -0.149979635 0.8228180725
#> [383,] -0.039354737 0.390377214 1.2339100033
#> [384,] 0.076465783 1.016381634 -0.5230384066
#> [385,] 2.509003429 -0.402367004 -0.5934548550
#> [386,] 0.433321462 0.302230573 -0.2245406399
#> [387,] 0.320799132 2.658683630 0.3048887946
#> [388,] 0.212163097 -1.333606694 0.0771982544
#> [389,] 0.593143451 -0.278283125 -0.5318760213
#> [390,] -0.686204544 -0.591582482 -0.4872988149
#> [391,] -0.253592593 0.156534615 -0.1272855602
#> [392,] 0.262010474 -0.624857142 1.2127553454
#> [393,] 0.589298973 -0.523434226 0.1545573659
#> [394,] -0.519715992 0.764345873 -0.6498557007
#> [395,] 0.503939434 0.717374179 -2.4787958438
#> [396,] -0.068619144 1.544523875 -1.4730325986
#> [397,] -0.315533334 1.405629191 -1.2680540094
#> [398,] 1.272148668 1.825660515 0.4440413708
#> [399,] -0.334600992 0.485700667 1.0319152564
#> [400,] 0.233210701 0.022812621 -0.6927266227
#> [401,] -2.119800432 -0.332751300 0.0704926965
#> [402,] 1.022877563 0.239717848 0.3474821580
#> [403,] -1.021305514 -0.441557796 -0.6021984874
#> [404,] 0.819142764 1.944891979 -0.0637719147
#> [405,] -0.419969491 0.376589784 0.3793379483
#> [406,] 0.970678236 -0.165593573 0.4546002489
#> [407,] -0.040297017 0.606222411 -0.0347623054
#> [408,] -0.047176951 -1.886226623 -0.6597482177
#> [409,] 0.392437352 -1.465585734 -1.7192218587
#> [410,] 1.906362782 -0.426146003 -0.3515787374
#> [411,] -0.229573607 0.494925617 0.7249965169
#> [412,] -1.441022106 -1.472845420 0.3174486876
#> [413,] -0.329235950 0.633211881 -1.0726618446
#> [414,] 0.292670135 1.808291372 -0.6832169846
#> [415,] -0.133047942 -1.494984989 -1.2647474172
#>