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.- nthreads
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,
nthreads = 1L, Xnew = NULL)
#> $Bhat
#> [,1] [,2] [,3]
#> [1,] 0.0000000000 0.000000e+00 0.0000000000
#> [2,] 0.0000000000 0.000000e+00 0.0000000000
#> [3,] 0.0000000000 0.000000e+00 0.0000000000
#> [4,] 0.0000000000 0.000000e+00 0.0000000000
#> [5,] 0.0000000000 0.000000e+00 0.0000000000
#> [6,] 0.0000000000 0.000000e+00 0.0000000000
#> [7,] 0.0000000000 0.000000e+00 0.0000000000
#> [8,] 0.0000000000 0.000000e+00 0.0000000000
#> [9,] 0.0000000000 0.000000e+00 0.0000000000
#> [10,] 0.0000000000 0.000000e+00 0.0000000000
#> [11,] 0.0000000000 0.000000e+00 0.0000000000
#> [12,] 0.0000000000 0.000000e+00 0.0000000000
#> [13,] -0.0894393712 8.243836e-02 0.0793489887
#> [14,] 0.0000000000 0.000000e+00 0.0000000000
#> [15,] 0.0000000000 0.000000e+00 0.0000000000
#> [16,] 0.0000000000 0.000000e+00 0.0000000000
#> [17,] 0.0000000000 0.000000e+00 0.0000000000
#> [18,] 0.0000000000 0.000000e+00 0.0000000000
#> [19,] -0.0144305703 2.693492e-03 0.0215252198
#> [20,] 0.0000000000 0.000000e+00 0.0000000000
#> [21,] 0.0000000000 0.000000e+00 0.0000000000
#> [22,] 0.0000000000 0.000000e+00 0.0000000000
#> [23,] 0.0000000000 0.000000e+00 0.0000000000
#> [24,] 0.0000000000 0.000000e+00 0.0000000000
#> [25,] -0.0001056799 9.740764e-05 0.0000937573
#> [26,] 0.0000000000 0.000000e+00 0.0000000000
#> [27,] 0.0000000000 0.000000e+00 0.0000000000
#> [28,] -0.1970164581 3.305338e-01 -0.2550815055
#> [29,] 0.0000000000 0.000000e+00 0.0000000000
#> [30,] 0.0529182661 6.736030e-02 0.0618297597
#>
#> $Ytrain
#> [,1] [,2] [,3]
#> [1,] -0.5648993730 -0.275159951 0.186781092
#> [2,] -1.1813711662 1.355066243 -1.508871388
#> [3,] 0.8159310738 1.494274504 -1.030197432
#> [4,] -1.3728961736 -0.187074116 0.644253306
#> [5,] -0.9027611211 -1.596391548 -0.644182498
#> [6,] 1.0461022722 0.419502637 2.181352347
#> [7,] 1.9380119291 -0.961830383 -0.393869291
#> [8,] -1.3771933670 0.063341413 -1.968115779
#> [9,] 0.2590473503 -0.565057838 0.669443801
#> [10,] -0.2556865717 -0.238220109 2.135913713
#> [11,] 1.5790188512 -0.096328419 0.643648388
#> [12,] 0.1182570881 -1.028786726 -1.571727774
#> [13,] 0.6476339331 -0.557779801 0.354625911
#> [14,] -0.1144404702 0.630617837 -0.371989615
#> [15,] -0.3378921345 -0.451103214 2.988194770
#> [16,] -2.0254191035 0.682166587 -0.117547121
#> [17,] 0.1093093648 0.301611852 -0.125762474
#> [18,] 0.9938934908 1.015023927 1.866555624
#> [19,] 0.4173320545 0.880438626 -1.618940888
#> [20,] 0.2041291373 -2.083660546 -0.187030222
#> [21,] -0.2524749108 -1.733131893 -0.294732665
#> [22,] 0.4028898082 0.108477441 -1.775963822
#> [23,] -0.9337994445 -0.209333285 0.424554638
#> [24,] -0.9207734578 0.025848193 0.461637512
#> [25,] 1.0124566816 0.929895337 -1.703716705
#> [26,] 2.1802735961 0.834142906 -0.370774040
#> [27,] -0.7173189903 0.656411747 0.148050091
#> [28,] 0.2428474824 -0.756641918 2.067139258
#> [29,] 0.8945379546 -0.340430177 -0.462891298
#> [30,] 0.0075139018 1.051134172 -0.310830320
#> [31,] 0.7000826541 -0.544198740 -2.395454555
#> [32,] 0.8413997481 -0.048925856 0.810439399
#> [33,] 0.7743753128 0.771280722 -0.366914396
#> [34,] 0.0359297070 -0.727805985 -0.488149567
#> [35,] -0.9180594374 0.990997414 -0.281173743
#> [36,] 0.0183135871 0.114893604 -0.205802236
#> [37,] 0.6233860993 1.708536783 0.189504540
#> [38,] -1.7573350478 -0.473660624 0.602988804
#> [39,] 1.4262527525 -0.230813231 0.494646191
#> [40,] -1.1431535610 1.491703842 0.134734990
#> [41,] 0.1312868802 -1.310209183 0.101997126
#> [42,] 0.6594868643 -1.151083312 -0.933075809
#> [43,] 0.7076776865 2.363400574 0.640838415
#> [44,] -0.5278150976 -0.178808377 -1.228523222
#> [45,] -0.5771685342 1.525352112 0.661116037
#> [46,] 0.3950434208 -0.185428470 1.529810695
#> [47,] -1.6645460611 2.256405866 -0.078642895
#> [48,] 0.6349221457 -0.174607944 1.550064048
#> [49,] 0.4134075020 -0.590537814 0.957126551
#> [50,] -0.2552450660 -1.174308888 0.931524785
#> [51,] 0.0545814177 -0.606865912 0.369424155
#> [52,] 0.2658672454 1.369682975 0.548289751
#> [53,] -0.2517390841 -1.280047235 -0.449179354
#> [54,] 0.7075105259 -1.432454849 -0.824975003
#> [55,] -0.1867550521 -0.852946965 -0.220946470
#> [56,] -1.1414421272 -0.320851612 1.617018829
#> [57,] 1.3298091058 0.638278714 -1.465042414
#> [58,] -0.9013855479 -0.187606056 -0.511735298
#> [59,] 0.8305216569 0.658797146 1.505444685
#> [60,] -1.0041613100 1.815852804 -1.186033433
#> [61,] -0.9781732467 -1.398560540 0.518722124
#> [62,] -0.4310927298 0.630322307 -1.363170335
#> [63,] 0.4646819794 0.492518889 -0.576948309
#> [64,] 0.4883851650 0.504022299 -0.782477456
#> [65,] 0.2575918223 0.051340521 -0.635413748
#> [66,] -0.2946765507 -0.992824384 -0.297013931
#> [67,] -0.5533313473 -0.441381907 0.232714981
#> [68,] 0.2317840468 0.148260192 -0.397413506
#> [69,] -0.4417025360 -0.549394478 0.472069515
#> [70,] 0.1817377391 0.322315744 -0.358412913
#> [71,] -1.2661954151 1.016932714 -0.266355821
#> [72,] -0.6089459970 1.142393234 0.023637756
#> [73,] -0.4044447352 -0.803435546 0.027814473
#> [74,] 1.8012243097 -0.635255645 -0.478817905
#> [75,] 0.0153696397 -1.854700845 -0.991813722
#> [76,] -0.9330248330 -0.269385150 -0.652508339
#> [77,] 0.8645709053 0.690235859 0.153769000
#> [78,] -0.2036490956 -1.315493811 0.805138166
#> [79,] -0.7049285164 1.006408374 -0.496321311
#> [80,] 1.1861883477 -0.074685437 1.802612878
#> [81,] 0.5280311480 0.775828110 -0.385511897
#> [82,] -0.2689075494 -0.939276446 -0.810297982
#> [83,] 1.3874822151 -0.821581802 -0.914785196
#> [84,] -0.3236967795 1.052581703 -2.047630148
#> [85,] 0.0968136119 0.931915950 1.111750071
#> [86,] 2.4472961976 -0.614566132 0.931370656
#> [87,] -1.2828354085 -0.479406349 1.062461790
#> [88,] -0.6447165418 -0.007596127 0.998760654
#> [89,] 0.0666283706 1.032780512 0.341277086
#> [90,] 0.1002545723 0.064241481 1.668338039
#> [91,] -1.6475110835 0.051294569 1.694300410
#> [92,] 0.1631748979 0.562896278 1.185346233
#> [93,] 0.2855380184 -0.671450696 -1.050694967
#> [94,] 0.5154407876 0.182718923 2.602133379
#> [95,] 1.2145157020 0.717038417 1.345045872
#> [96,] -0.0381417823 2.291532047 -0.121661865
#> [97,] 0.2609549087 -1.280849138 0.922352881
#> [98,] -0.5126725537 -0.221144455 -2.126821023
#> [99,] -0.1636170721 0.920032128 0.566329686
#> [100,] -0.1658268264 -1.049744622 0.721490844
#> [101,] -2.1072470241 -1.415102698 0.580719569
#> [102,] 1.5913157488 0.000383019 0.526773106
#> [103,] -2.3302515144 0.648702272 -0.058447633
#> [104,] -0.0674735652 0.161569390 -0.796318966
#> [105,] -0.5153121831 0.609824625 -1.213146926
#> [106,] 1.0191569875 0.303677153 -0.942369362
#> [107,] -0.0727532656 1.043836118 1.557026745
#> [108,] -0.0215156419 0.547636947 -0.977356609
#> [109,] 0.3896660954 0.826245808 1.052569574
#> [110,] -0.7654523959 -0.020385808 0.028418015
#> [111,] 1.8273792360 -1.667375524 -0.136636992
#> [112,] 0.9659499503 -0.687587455 -0.576662721
#> [113,] 0.2905381139 -1.787020731 -1.094889030
#> [114,] 0.8753388724 0.649349545 -1.047091330
#> [115,] -0.5131765747 -1.275135716 -1.397142757
#> [116,] -0.5551745355 -0.273538810 1.191278706
#> [117,] 1.1125824622 0.454285187 0.941843101
#> [118,] -0.3962923049 -1.979684345 -0.655233112
#> [119,] -0.2504082961 -1.079765144 -1.805238372
#> [120,] 1.2872671011 -0.582096086 0.032620365
#> [121,] 0.7649435845 -0.514614262 -0.296060787
#> [122,] -0.2705775385 1.002530655 1.029281991
#> [123,] 1.5119790696 0.773756507 -0.979808329
#> [124,] -0.3315274764 0.603177576 0.222849965
#> [125,] -0.9560675327 0.661010337 -1.679521360
#> [126,] -0.5730826248 0.545670957 0.011096985
#> [127,] 0.9550782370 -0.587763157 -0.425093783
#> [128,] -2.3760758485 0.777356694 0.033674937
#> [129,] 0.5398045855 -0.950021033 -0.685209011
#> [130,] 0.3566523091 -2.804330599 1.802142138
#> [131,] 1.5621241826 -0.120056084 0.043332903
#> [132,] -1.7381220211 0.028014389 0.203827190
#> [133,] 0.6309620270 0.800610191 -0.748972957
#> [134,] 1.0207109829 0.128355899 0.174973537
#> [135,] -0.0758701958 -0.424130780 -1.205668312
#> [136,] -1.0205286904 0.987683962 -0.209059968
#> [137,] 1.2715664242 -1.196318372 1.085565730
#> [138,] 0.4991721699 -0.155896962 -0.035621976
#> [139,] -0.3046727898 -0.181290643 0.377157236
#> [140,] 0.6275918167 -1.363446171 0.322679493
#> [141,] -0.3289455162 0.539490964 0.126806876
#> [142,] -0.5405600991 1.928177370 1.614590917
#> [143,] 1.0855274156 -0.469636051 -1.511971620
#> [144,] -0.0312411298 -0.174670348 1.721614200
#> [145,] 1.3735473288 1.493510333 1.082913764
#> [146,] 0.6618467058 1.507611788 1.545626206
#> [147,] 0.5717022241 0.815596954 -0.126807505
#> [148,] 0.7446960955 0.772824796 0.800371575
#> [149,] 0.8909515494 -0.054847867 -0.005410086
#> [150,] -1.4108425774 1.237598998 -0.131678580
#> [151,] -0.2526536168 -1.230776270 0.747535270
#> [152,] 0.6841519109 -1.514518633 -0.430328290
#> [153,] -0.6365803176 -2.163832893 0.715346474
#> [154,] -1.5563124658 -0.436717494 0.931046040
#> [155,] 1.6460209940 -0.076586114 -0.215626381
#> [156,] -0.1442327894 -1.047364818 0.744229721
#> [157,] 1.0089391381 1.832011869 -1.105724497
#> [158,] 2.0737429968 -0.985573226 -1.214497001
#> [159,] -0.6694526157 0.652844182 -0.256308904
#> [160,] 0.1531524480 0.066342221 -0.854188197
#> [161,] -0.4817216409 -0.314537265 -2.193237439
#> [162,] -0.6703736133 0.689605885 -0.443207797
#> [163,] -3.5307798035 -1.547237808 1.296267815
#> [164,] -0.6081347598 1.460710793 0.230126136
#> [165,] -0.8804558820 -1.603371966 0.968714071
#> [166,] -0.1718326523 -0.239248064 1.533481251
#> [167,] -0.6898712464 1.021515740 -1.920781371
#> [168,] -0.3153812077 0.217427979 0.750566373
#> [169,] -1.1185814100 -1.252220452 0.160205505
#> [170,] -0.7225357586 -0.903476103 0.867465505
#> [171,] -0.8342955561 -0.310030218 -0.111173569
#> [172,] 0.3974507194 0.574414802 -0.098467070
#> [173,] -0.7274149257 -0.604401262 1.162337680
#> [174,] -0.9048026176 0.287984600 1.520034631
#> [175,] -0.9626090113 -0.299839356 0.689087617
#> [176,] 0.4763232020 0.320859862 0.723676509
#> [177,] -1.5394303524 2.189424530 0.438994425
#> [178,] 0.2805708761 1.079234743 -1.993935828
#> [179,] -0.0571258886 1.328176062 0.435496987
#> [180,] 0.5913045659 -1.151125171 -0.060590231
#> [181,] 0.0969345759 -0.046121411 -0.581146240
#> [182,] -0.7497383051 1.107295800 -1.103530910
#> [183,] -0.3943348323 -0.457438615 -1.326415954
#> [184,] 0.8796820260 -1.508938900 -1.427077791
#> [185,] 0.5677612062 0.648023473 0.875414945
#> [186,] -0.2166611960 0.361919484 0.952310847
#> [187,] -0.3122309000 -1.749577124 1.076024968
#> [188,] -0.0454245212 -2.204227072 -1.368370417
#> [189,] 0.7141011721 -0.006103045 1.237886574
#> [190,] -1.8039403243 -1.266972774 0.521799928
#> [191,] 0.9141387470 -1.395133024 -0.881970221
#> [192,] 0.4728671149 0.678219453 -0.487653872
#> [193,] 0.2219503685 0.144748574 -0.586407019
#> [194,] 0.4814792470 -0.796086962 0.808145259
#> [195,] 0.0423028845 1.584637028 -0.934756708
#> [196,] 0.4035920028 -1.167794046 -0.071436172
#> [197,] -0.0418616897 -1.253903536 -1.013775785
#> [198,] 0.6596879530 -2.570634121 1.124149599
#> [199,] 0.7821882961 -1.213675935 0.584083065
#> [200,] 0.2676156695 0.108820729 0.587319955
#> [201,] -0.7900241975 1.497416912 -1.235100416
#> [202,] -0.3194755506 -0.321215285 1.552528495
#> [203,] 0.1538230721 -1.195589355 -0.577495494
#> [204,] -0.8667664705 0.715907924 1.020534161
#> [205,] -0.3928615665 0.649430521 0.524647088
#> [206,] -0.3236534326 -0.441936558 -0.903382933
#> [207,] -0.0980536005 -0.668284561 -0.461169261
#> [208,] 0.0949426568 0.977406639 0.917772721
#> [209,] 2.5475832859 0.484419928 1.281964224
#> [210,] -0.7085321826 0.550636629 -0.055552817
#> [211,] 1.2101953827 -0.164134952 -0.922900862
#> [212,] 1.7548094551 1.198214762 0.080063075
#> [213,] 0.5527795478 0.838613201 1.446332619
#> [214,] 0.5229929546 -0.636154284 -0.580921492
#> [215,] 0.8182072550 -0.789715065 0.169006970
#> [216,] 0.2732084585 -0.121611909 1.582256149
#> [217,] -1.3908366138 -0.123227243 -1.778297238
#> [218,] 1.8006783945 -0.010937075 -0.475237196
#> [219,] 0.2545862458 -0.314593216 -1.252496863
#> [220,] 0.0172895176 0.609468553 -0.424469979
#> [221,] -0.0984869628 0.403637776 0.054408113
#> [222,] -0.4526063276 -0.622529772 -0.336802675
#> [223,] -0.1499796352 0.822818073 0.064177979
#> [224,] 0.3903772136 1.233910003 1.342969572
#> [225,] 1.0163816341 -0.523038407 -1.593621510
#> [226,] -0.4023670043 -0.593454855 -0.638553874
#> [227,] 0.3022305729 -0.224540640 0.237107075
#> [228,] 2.6586836295 0.304888795 0.330937472
#> [229,] -1.3336066942 0.077198254 -0.104119690
#> [230,] -0.2782831253 -0.531876021 0.459986636
#> [231,] -0.5915824819 -0.487298815 -1.566795984
#> [232,] 0.1565346145 -0.127285560 -0.889943823
#> [233,] -0.6248571422 1.212755345 -0.134192503
#> [234,] -0.5234342255 0.154557366 0.667031846
#> [235,] 0.7643458733 -0.649855701 0.617631573
#> [236,] 0.7173741792 -2.478795844 0.163371556
#> [237,] 1.5445238749 -1.473032599 0.439136974
#> [238,] 1.4056291914 -1.268054009 0.056923397
#> [239,] 1.8256605147 0.444041371 0.508358608
#> [240,] 0.4857006669 1.031915256 0.640826575
#> [241,] 0.0228126213 -0.692726623 0.579968792
#> [242,] -0.3327512997 0.070492696 -0.193790976
#> [243,] 0.2397178479 0.347482158 1.968775292
#> [244,] -0.4415577957 -0.602198487 -2.159026547
#> [245,] 1.9448919790 -0.063771915 0.288359076
#> [246,] 0.3765897835 0.379337948 -1.068399363
#> [247,] -0.1655935728 0.454600249 -0.652642624
#> [248,] 0.6062224106 -0.034762305 -0.273290691
#> [249,] -1.8862266235 -0.659748218 0.422091090
#> [250,] -1.4655857336 -1.719221859 1.387241303
#> [251,] -0.4261460027 -0.351578737 -0.716658224
#> [252,] 0.4949256173 0.724996517 0.604079751
#> [253,] -1.4728454198 0.317448688 -1.100170463
#> [254,] 0.6332118806 -1.072661845 -2.194562589
#> [255,] 1.8082913720 -0.683216985 -0.572536731
#> [256,] -1.4949849887 -1.264747417 0.484270898
#> [257,] -0.7860695344 1.283567962 0.891624634
#> [258,] -0.3002899838 -1.307636127 -0.024255911
#> [259,] 1.8047594184 0.332640413 -0.670115103
#> [260,] -2.0674694352 1.289228504 -1.291555438
#> [261,] -0.1152439716 0.622357799 0.020860710
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#> [264,] 0.0955797820 0.713143818 0.487505993
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#> [266,] 1.5306282762 0.825038744 -2.016142927
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#> [271,] -0.6129907571 2.056609905 -0.555498946
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#> [273,] 1.2048238196 -0.607486131 0.523891502
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#> [277,] 1.2616125122 -0.447085402 0.537462776
#> [278,] 0.9506933445 0.765853775 0.437087345
#> [279,] 1.5695419718 0.055011330 -0.118266718
#> [280,] 0.8109116496 -0.840006600 0.101810696
#> [281,] 0.3624077236 -0.647407367 -0.293184401
#> [282,] 0.5258675803 -1.435170051 0.340830635
#> [283,] -0.1840675633 0.792031333 -0.803883683
#> [284,] -0.1397359423 0.244143060 0.471028790
#> [285,] -1.0865690897 0.553637036 0.016771011
#> [286,] -0.4849087543 -1.789636593 -0.626930164
#> [287,] 0.6763745948 0.161274339 1.783658393
#> [288,] -1.0359815127 0.533788317 -1.149703884
#> [289,] -1.5157669034 -0.005928497 0.185744062
#> [290,] -0.9718434887 -0.626845466 -1.846564284
#> [291,] -0.3546173787 -0.298363488 1.009208962
#> [292,] -1.8861393581 2.283375408 -0.759471876
#> [293,] 1.5488365663 -0.494235935 -0.678358975
#> [294,] -1.4122495209 1.159904323 -0.597473303
#> [295,] 0.9477811346 0.693075900 1.597880739
#> [296,] 1.0236207332 -0.693613889 0.343042685
#> [297,] -0.7874932054 0.618855463 -0.719649837
#> [298,] 0.2291223270 -1.877933997 -0.818672727
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#> [302,] 0.0261034038 0.481820993 0.655864735
#> [303,] 1.6639201790 0.264475398 0.046623620
#> [304,] -0.4095778348 0.106864518 1.076735993
#> [305,] -0.0061132059 1.165607902 0.373963064
#> [306,] 0.2848010284 -0.924390774 -1.096174311
#> [307,] 0.8906084895 0.424323130 -0.179480213
#> [308,] 0.8812326622 1.282003202 -1.025062986
#> [309,] -0.4146163234 -0.779394914 -1.106749284
#> [310,] 0.2639895676 -0.798184475 0.414912363
#> [311,] 0.5064654547 -0.684990595 0.449915074
#> [312,] -0.4273110163 0.949833372 -2.775801968
#> [313,] 1.5553357897 -1.770895435 -0.210119131
#> [314,] 0.3933102925 0.359633843 2.078364022
#> [315,] 2.2140814458 -0.460179937 0.129955120
#> [316,] -1.7281035002 -0.701202063 1.785993271
#> [317,] 2.3707062904 -0.999680164 -0.859496280
#> [318,] 2.3099262222 -0.197502160 -2.275333347
#> [319,] 0.4497814099 -0.403499090 1.918183731
#> [320,] 0.5820184807 1.091751876 0.446583451
#> [321,] 1.1081738819 1.601957528 -1.681142384
#> [322,] -1.2471531519 0.539437114 -0.663323728
#> [323,] -0.5030822170 -1.420060266 0.631026520
#> [324,] 0.2332340290 0.088309669 -0.099813531
#> [325,] -0.8191103840 0.569597151 3.015539081
#> [326,] -2.1996674696 -1.827919515 1.739748839
#> [327,] -0.8029142326 0.706047935 0.252898255
#> [328,] 0.3602135472 -0.334342893 -2.358591366
#> [329,] 0.9734978288 1.632755611 -0.462339868
#> [330,] 0.7969702293 -0.663153823 0.492883954
#> [331,] 0.2268940028 -0.700266866 -1.160546831
#> [332,] 0.8921623340 -0.857115164 0.236551060
#> [333,] 2.1262300428 -0.714147684 0.297990413
#> [334,] 0.9937875900 -3.400786228 -0.935385059
#> [335,] 0.4761566594 0.721382917 0.126442139
#> [336,] -1.5748424113 0.836597346 -0.531750926
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#> [338,] -2.3991916415 0.808709510 0.237519906
#> [339,] -0.8090417745 1.733010208 -1.322025550
#> [340,] -1.2081160615 0.898214719 -0.789171134
#> [341,] 1.0987523905 -0.393681743 0.365707650
#> [342,] -0.8977027733 1.252987886 0.381200400
#> [343,] 0.8004829228 1.176215742 -0.983482479
#> [344,] 0.3182158073 -0.328906280 0.102663822
#> [345,] -0.2536723496 2.315428379 -1.128036192
#> [346,] 1.7623970608 -0.616806132 -0.513300294
#> [347,] 0.2672623842 2.850764698 -0.100042226
#> [348,] 1.7765462340 0.385176664 1.009999156
#> [349,] 0.6948144661 0.908171254 0.587421431
#> [350,] 0.0776958487 0.288906255 -0.890785182
#> [351,] 0.0614350108 -0.194258437 2.668797012
#> [352,] 1.1540302076 -1.115458525 0.315991023
#> [353,] -0.4756703181 -0.715266669 2.499661934
#> [354,] 1.3285541022 2.026225224 -0.902657057
#> [355,] -0.9976809590 -1.578549683 0.407887222
#> [356,] -2.2303646675 1.641302951 -1.582300001
#> [357,] 1.0609905975 0.225927315 1.457819279
#> [358,] -0.6866584510 0.157850640 0.366612028
#> [359,] 0.5477755020 -2.511592774 -0.584414349
#> [360,] 0.4920247668 1.020332019 1.081107108
#> [361,] 0.0661302605 0.293742474 -1.048948282
#> [362,] -0.5933043912 1.695435064 0.699272997
#> [363,] 0.6094863653 -0.109083421 0.197389984
#> [364,] -0.3800374915 -0.146883676 0.530172111
#> [365,] -0.5006633704 1.027543524 -0.517293351
#> [366,] -0.1976449331 -0.406734679 0.986472914
#> [367,] -0.6294497240 -0.072202266 0.500735209
#> [368,] 1.4232751547 -0.431343976 0.462747101
#> [369,] -1.5668221876 -0.466420724 -0.337794384
#> [370,] 0.4683435754 -0.875344583 -0.368959062
#> [371,] -1.1692382883 1.111693814 -0.401980445
#> [372,] -0.4854110016 -0.805143020 -0.962680249
#> [373,] 1.2305034404 -0.047059697 0.610529245
#> [374,] 0.3467242972 -0.500451215 0.368213105
#> [375,] -0.8057939316 -1.672337413 2.300231548
#> [376,] 0.0883783247 2.022565700 -1.528976820
#> [377,] -0.9000928351 -0.593281069 -1.109278924
#> [378,] 0.9982222745 0.002044998 0.343093530
#> [379,] -0.3251110497 2.044686128 -0.305663620
#> [380,] 0.7590950192 0.182865973 0.810675359
#> [381,] -1.6429523141 0.146336404 -0.314867802
#> [382,] 0.7047725297 0.182217923 -0.091273390
#> [383,] 0.3113450960 0.040010733 1.268692215
#> [384,] -0.1572749202 -0.759377836 -1.981726863
#> [385,] 3.1065543658 0.306378462 -1.871377231
#> [386,] -0.9213661594 0.080588260 1.341884069
#> [387,] 0.2477788717 -0.174348767 -1.471472761
#> [388,] 0.5720525498 -0.681816234 -0.811863963
#> [389,] -0.9734868579 0.053572445 -1.052007520
#> [390,] 1.3328957474 0.219378674 -0.663438220
#> [391,] -0.1089672288 0.873483380 0.039329732
#> [392,] -0.0193803743 -0.860642513 -0.127311799
#> [393,] 1.1603542126 -1.120265731 -1.699605989
#> [394,] 1.4918116683 -0.810345467 1.684978210
#> [395,] 0.9716645970 -0.204542459 2.128882905
#> [396,] -0.4161220260 0.803664462 -0.355070224
#> [397,] 0.7198700439 1.080288950 -0.034430639
#> [398,] 1.0941844303 0.036373748 1.528421742
#> [399,] 0.1517362570 -0.995698944 0.640007637
#> [400,] 0.2820126129 -0.317064432 -0.203856028
#> [401,] -0.3751930635 1.303225736 0.075928415
#> [402,] 0.2336775421 -0.178675429 -0.196532365
#> [403,] 1.2912170758 -0.241240719 0.640007956
#> [404,] 0.3391002482 -1.500992853 -0.822398271
#> [405,] 0.1303777704 0.548866568 0.443080404
#> [406,] 0.1407764506 -1.340568525 -0.728155313
#> [407,] -1.1159056852 0.734290143 0.112594737
#> [408,] 2.1747890319 1.285559837 1.531846847
#> [409,] 1.0257107543 1.502803510 1.010304901
#> [410,] 0.7129470478 1.392671248 1.555300921
#> [411,] 0.1610820412 0.788054776 -0.200081800
#> [412,] -1.3631774496 0.161893209 -1.340139178
#> [413,] 0.1045571996 -0.774869490 0.398424302
#> [414,] -0.2530674330 0.635436993 0.971762834
#> [415,] 0.8212878230 0.052080931 0.195869353
#>