A quick start tutorial

A minimal example

We analyze a simulated data-set example_data.rds to show the basic workflow with pfar.

Data-set

In [1]:
dat = readRDS('../test/example_data.rds')
names(dat)
names(dat$X)
rbind(dim(dat$X[[1]]), dim(dat$X[[2]]), dim(dat$X[[3]]))
dat$loglik
  1. 'X'
  2. 'loglik'
  1. 'I10'
  2. 'I11'
  3. 'I12'
100300
100300
100300
-253747.479246202

The simulated data-set has 300 samples and 300 features. For this simulated data we know the model log-likelihood is -253747.5.

PFA model fit

We run a basic PFA using standard EM algorithm with uniform prior for sample distribution on edges, and random initialization of factors.

In [2]:
set.seed(999)
K = length(dat$X) + 1
X = do.call(rbind, dat$X)
control = list(logfile = 'example_data', verbose = F, alpha = NULL)
res = pfar::pfa(X, K = K, control = control)
saveRDS(res, 'example_result.rds')
In [3]:
print(res)
$F_init
           [,1]       [,2]       [,3]      [,4]       [,5]       [,6]
[1,] -13.348998  -6.135172 -0.2410379 11.148072 -27.134831  0.5598765
[2,]  -7.863766 -16.793477 -0.8523309 -3.953813 -19.079478 -0.2074457
[3,]  21.553799  -2.795115  0.6323632  9.772271  -8.718292 -7.3564686
[4,] -12.099822  -2.057069  2.1463089  5.418662 -11.954877 -4.2176940
           [,7]        [,8]       [,9]     [,10]      [,11]     [,12]     [,13]
[1,]   5.735254 -1.25255505 -10.073224  41.28228 -37.117860 0.7823492  5.613040
[2,]   8.767105 -0.04930917   2.801243  94.40522 -14.885702 0.7714685  6.803914
[3,] -52.307295  6.76842230 -14.100849 -10.18895  34.490508 0.2554594 -9.832734
[4,]  17.368005  0.82637636   5.976363 -12.98749  -1.903003 0.1782108 -2.472395
          [,14]      [,15]     [,16]     [,17]      [,18]      [,19]      [,20]
[1,] -17.314087 -1.2006322 -1.093316 39.707172 -0.6484892 -18.204571   1.424071
[2,]   2.841044 -1.0222291 -4.175962  8.051926  1.2533393 -10.710817  -2.779842
[3,]  72.385214 -0.3656819 20.736154 22.628640 -0.2693312  -5.838646 -22.065844
[4,] -19.034954 -0.9360468  2.383175 -9.988390  0.6711221 -10.380659  12.857708
         [,21]     [,22]     [,23]      [,24]      [,25]       [,26]      [,27]
[1,]  2.929561  7.841823 -72.13905   7.572319  1.6534863 10.81169415  1.9237456
[2,]  2.683675 -8.180446  45.26138 -57.463676 -0.9029282  4.69181826 -0.3714082
[3,]  3.131881 18.695659  60.24553  -2.302459 -2.0929239  2.78812234 -3.2250256
[4,] 44.725524 17.613733 -13.88307  38.544819 -2.6557854  0.01630739  4.3320699
        [,28]        [,29]       [,30]      [,31]     [,32]      [,33]
[1,] 16.50248   6.31669832 -11.0288759 -1.2770891 -15.29709  10.510806
[2,] 37.24271  -0.02830089  -8.6085011 -0.7748133 -21.64179  -2.301484
[3,] 20.44508 -47.08142972   0.1405926  0.6179233 -35.63414 -80.331685
[4,] 19.56172  -2.91586040 -23.6079005  3.7937406  27.82836 -85.257507
          [,34]      [,35]     [,36]      [,37]      [,38]      [,39]     [,40]
[1,] -0.3173273  7.1088891 -22.68315 0.57264089 -1.2799625  1.4469716 0.4164889
[2,] -0.4767600 10.2834031  12.67547 0.22529611 -0.6847221  1.4925852 1.3817822
[3,]  0.5728272 -1.5964410 -51.80986 0.02321989 -0.1352115 -0.4441614 0.1589391
[4,]  0.2889636 -0.8374573  19.10468 1.83568022  0.4391361  0.6690871 1.2329059
         [,41]       [,42]       [,43]      [,44]      [,45]        [,46]
[1,] 51.305246 -0.37943165  81.0715064 0.03659857  1.9694152  0.001568954
[2,] 51.280823  0.07157776 -92.7631572 0.04017713 -0.5460304 -1.089297582
[3,]  8.895741 -0.02720362  -0.1497575 0.05096505  1.5467576 -6.682089727
[4,]  3.146349  0.36087889  47.9619982 0.39974055 -0.2499945  3.609749818
          [,47]      [,48]      [,49]     [,50]       [,51]      [,52]
[1,] -4.2452099  0.9995401 -1.2426365 28.840178   0.1823778 -0.1688395
[2,]  3.5852012 -0.5178207 -0.1588095 26.836087 -10.6808494  0.3128267
[3,]  0.1651346  0.8559106  0.8361425 -8.803301  -4.3821510 -1.0652417
[4,] -0.7749267 -3.7026631  0.3106491 20.223351   5.4259939  2.4696126
          [,53]     [,54]     [,55]      [,56]      [,57]     [,58]      [,59]
[1,]  -2.564287 -3.049239 -2.626200 -1.6663045 -0.2676920 0.8502024 -10.034948
[2,]  -4.448601 -2.065220  5.569584 -0.7867428  0.6051425 1.5803933   5.386128
[3,]   6.017011 -1.209852 -1.947987 -3.9933715  1.8519133 1.9080995 -27.948103
[4,] -23.961868  3.299152 -4.999638  2.1845299  0.5507996 1.2123852  28.731797
         [,60]     [,61]     [,62]     [,63]      [,64]      [,65]     [,66]
[1,]  2.937819  6.815602  5.217984  17.28591  0.3806247  23.467148 -7.469575
[2,]  4.836168 -6.313231  2.329958  32.05255  2.8044896 -18.547281  4.050836
[3,] -4.027877  6.580486 -1.634543 -13.11690 -1.8008789 -42.096821 -7.629027
[4,]  2.321424  5.712193 -4.090386  12.24915  2.0670135   4.781562  3.939384
          [,67]     [,68]     [,69]      [,70]     [,71]       [,72]     [,73]
[1,] 0.96161420 -49.14527  3.519005 -0.2845107 40.952305 -29.7950299  2.814859
[2,] 0.88857515  93.75422 -3.961755  0.3094709  4.549892   0.5010759 -2.672563
[3,] 0.80295193 -38.95165  2.525233  0.1515185 47.682420  17.0047915 -6.506340
[4,] 0.03805528  15.84103  1.693943  0.1667022 39.964786   2.7073181  3.388306
          [,74]      [,75]       [,76]      [,77]      [,78]      [,79]
[1,] -0.6431580 -29.730941  0.10137963  -1.940551   7.543233  0.2388123
[2,] -0.5946237   7.118849  1.62840494   8.044427 -27.543384  0.9220701
[3,]  0.5849504 -96.223056 -3.85933137 -12.162317  13.333578 -0.6806710
[4,] -0.6097417 -14.334045  0.07384003  -7.656222   3.161408 -2.3939927
         [,80]     [,81]      [,82]     [,83]      [,84]     [,85]      [,86]
[1,]  8.650392 -36.45755 -1.4018759 -15.02501  0.8536503  21.74009 -0.9561480
[2,] 14.741939   7.77986 -4.5736108 -21.51473  0.8538885 -19.55070  0.1258712
[3,] -7.343168  13.13859  0.2847118 -20.07377 -0.1948219  14.84178 -0.4869168
[4,] 13.448893 -15.56777 -4.9864102 -24.14492  1.6309945 -19.99288 -0.5132478
          [,87]       [,88]      [,89]       [,90]      [,91]      [,92]
[1,]  49.458493 -12.1500118  4.7134814 -75.6527003  -8.822006 -45.665876
[2,]  22.914821  -3.3523416  0.2646867  -0.9352502 -18.522059  40.077296
[3,]   8.087877  -5.9657654 -0.1474845  33.7219630 -11.685642  -3.957804
[4,] -13.447784  -0.5519742 -1.1936334  -2.0517400 -75.765940  24.405976
          [,93]      [,94]      [,95]      [,96]      [,97]      [,98]
[1,]  13.814199  3.4297062  2.6003642   2.339364 -0.8437974 -0.3665396
[2,] -10.422209 -0.3414881  1.9776008 -21.360664 -3.3008659 -0.2736450
[3,] -12.718330 -0.5146143 -0.2103174 -16.495004  0.2820700 -0.5777662
[4,]  -7.210771  2.5689167  1.1472385  13.457509 -3.5847303  2.0713364
          [,99]     [,100]     [,101]     [,102]      [,103]     [,104]
[1,]  0.3368847 -1.2668700 -5.8915476  0.2259265   0.8177645  1.1087324
[2,] 19.1117597 -0.7968636 -0.1390304 -0.3491989 -10.5421456  4.3180236
[3,] -3.2240110 -0.1319639  2.9308950 -0.5476513  -7.3253471 -3.4956402
[4,] -4.0490343 -0.4570364  7.7109045 -0.6176941  -0.6965291 -0.6676457
        [,105]     [,106]     [,107]     [,108]     [,109]      [,110]
[1,] 4.1932606   2.154551  0.1071930  0.1509100   8.074045  1.36041361
[2,] 0.2201513  14.949757 -2.0093705 -0.7635891 -16.238237  0.24232214
[3,] 1.5474590  -8.252594 -0.3020748  0.6289739 -11.151716 -0.09360307
[4,] 3.7155598 -17.557084  0.1354761  0.2775487  -5.523109 -0.22873560
          [,111]     [,112]    [,113]     [,114]     [,115]    [,116]
[1,] -0.19648547  7.0500985 -1.220143 -1.2396751  1.6550994 0.7183490
[2,] -0.14734393  0.9711313 -2.742206 -0.8098564  1.4960106 0.9035872
[3,] -0.04393549 -5.5981705  1.016658 -2.1504776 -0.3103684 0.8004425
[4,] -0.64681620 -0.6067448 11.444425 -1.1334951  0.9043194 1.0832720
          [,117]    [,118]     [,119]     [,120]     [,121]     [,122]
[1,]  24.7252569 -4.902266 -11.791994   6.730668 -0.7233052 -3.5447634
[2,]   0.4021599  9.853904 -11.488905  12.298208 -2.9448013 -2.5814372
[3,] -58.3472183  1.509067 -13.900937 -15.936802 -8.4257698 -0.5263897
[4,] -20.6405615  9.305461  -2.200644   5.445051  7.2318619 -2.0768009
        [,123]     [,124]      [,125]      [,126]    [,127]    [,128]
[1,] -68.67766 -0.7404584  1.32009364  44.6045909 -1.089446  14.92927
[2,]  30.90809 -0.6579211  0.06201845  -0.4407469 -2.660409  27.75214
[3,] -70.12242 -0.1558405 -1.83490447  34.5513883  2.012280  14.48151
[4,] -47.34847 -0.4761025  2.63142055 -22.1591929 -2.120246 -14.28321
         [,129]     [,130]     [,131]     [,132]     [,133]    [,134]
[1,] -16.781393  0.6145901 -0.2143939 17.9788073 -1.0203267  4.351020
[2,]  -3.120577 -0.3797346 -0.5138562 -5.1325461  4.2509325 -8.303529
[3,]  -7.270716 -0.5894463 -0.2138536 -0.2605618  5.9675985 -5.115247
[4,] -13.083494  0.6667856 -0.7393831 -1.7756501  0.9884732  2.312402
         [,135]    [,136]     [,137]    [,138]       [,139]      [,140]
[1,]  -8.244828 12.377594   2.717242  13.08821 -0.265212716 -0.57897459
[2,]  11.002132  8.605466 -20.682311  55.63882 -0.797487693 -0.42633749
[3,] -17.812699 -2.267621  -9.825880 -33.63457 -0.723940233 -0.16568144
[4,] -19.580024 -9.298659  49.043804 -26.68136 -0.003767177  0.02962869
         [,141]    [,142]     [,143]     [,144]    [,145]     [,146]    [,147]
[1,]  0.5257832 -2.144575   6.105603  1.8135950 -7.743168 -27.457467  28.99450
[2,]  2.0272339  8.174273  63.924905  2.1568876 -3.593888  -6.610761  68.90983
[3,] -0.4799038  1.386036  74.791944 -0.1838934  4.564543  -5.916161  15.94686
[4,]  4.6828929  1.705606 -49.477089  3.8710105 13.172629 -31.042253 -63.35333
        [,148]      [,149]    [,150]     [,151]     [,152]   [,153]    [,154]
[1,] -1.517268 -1.31400847 -10.64780 -15.521435   1.526658 19.13285  5.346040
[2,] -0.112988  0.15201922  10.51398   4.656731 -66.931403 18.58389  2.416978
[3,] -1.265819 -0.72666006 -10.55274 -15.690948  46.660834 27.16045 -4.971443
[4,] -2.987775 -0.02030918 -13.34989  -3.173559 -67.237441 24.46403 -4.974347
        [,155]     [,156]    [,157]      [,158]       [,159]    [,160]
[1,]  2.035803  -6.415885 -8.829692  1.17418190  0.007293508  37.99177
[2,] -1.478969  -3.756303  8.790374 -0.06585956 -0.026473932 -14.95440
[3,] -5.149492   8.938089 16.428827 -1.79632823  0.209028321 -59.01635
[4,] -5.949733 -27.820230  8.745927 -0.49661759  0.179236203 -52.62035
          [,161]     [,162]    [,163]     [,164]    [,165]      [,166]
[1,]  0.09929574   3.880564  2.894051  0.1561344  46.46263 -2.61634846
[2,] -0.61278013 -10.824268 -4.125399 -0.3739111 -21.28410 -3.81026830
[3,]  1.23066644   3.018174  6.263258  0.1139255 -30.43268  0.41359232
[4,]  0.19528709 -42.905374 30.472715  0.3410982 -12.76187 -0.05089548
        [,167]     [,168]      [,169]     [,170]    [,171]     [,172]    [,173]
[1,]   5.07735 -0.4415129  0.06263033  7.3642860  4.732313  1.7408698 -38.34530
[2,] -29.65005 -0.2876143  0.06934697  3.7850145 -3.612198 -1.7138984 -55.90282
[3,]  80.34586 -0.3655313 -0.20382934 -1.2201482  2.689550  0.9920767 -32.19101
[4,] -32.79736 -0.8652638  1.12057089 -0.1929553 -1.365000  0.1927220 -42.78202
         [,174]     [,175]     [,176]     [,177]     [,178]    [,179]
[1,]  3.7383031 0.31258370  0.6347402  -8.343737  1.1146345 -4.672129
[2,] -0.3268397 0.49054626  1.3644301 -20.413601 -0.8247436 13.531154
[3,] 43.9949735 0.03262433  2.0318798  -1.609878 -0.2647686 -6.786325
[4,]  9.2905605 0.13947723 -1.0604721  -6.481981  0.4209331  6.849986
          [,180]    [,181]     [,182]    [,183]    [,184]    [,185]    [,186]
[1,] -15.1471326  1.215206  2.7370024  2.107834  4.573664 -35.08178 0.3577911
[2,]  12.4428467  1.343163  1.3110005 -1.137023 -5.481078  16.65493 2.4488976
[3,]   0.4758060 -1.565849 -1.9437721 -0.482244  2.199486  32.37581 1.9977334
[4,]  -0.7747972 -0.970846  0.6803685  1.113164 34.076748 -34.38905 1.2962291
          [,187]       [,188]      [,189]     [,190]    [,191]     [,192]
[1,]   0.8873579 -0.294400927  -6.6776713 -0.9819091  60.56014 -0.9151945
[2,]   9.8814347 -0.335839266   9.1474322  0.4521919 -10.39417  2.7585114
[3,] -13.7478853  0.007756409  -0.8540261 -0.1440629  37.87454 -1.8032514
[4,]   1.3508242 -0.105155658 -41.4744214 -1.2131766 -44.04116 -0.7185797
        [,193]     [,194]    [,195]    [,196]    [,197]     [,198]     [,199]
[1,] -4.108866 -2.4565727 -3.252201 -2.023826  3.032976   9.670344 -0.2898651
[2,]  3.732077 -4.3704270  3.490231 11.313819  5.488640 -38.926396 -1.3638446
[3,] -5.994188  2.5606942  7.054815 -6.104189 61.376312 -21.298171 -0.8058326
[4,] -2.381770 -0.8603968  2.755025 17.541870 16.221441  16.390867 -3.2124067
         [,200]     [,201]     [,202]      [,203]      [,204]        [,205]
[1,] 11.2288136 0.12159121 5.75585958  0.15077085  0.26965409 -2.499600e-01
[2,]  6.1710122 0.22792518 3.32319181 -0.09718763  0.18378886 -1.080401e+00
[3,]  0.9635929 0.05481598 0.09522514  0.98719000 -0.04195652  1.991442e+00
[4,] -0.7142684 0.13467102 2.28602848 -0.41731236  0.18680988 -7.766123e-05
        [,206]     [,207]     [,208]    [,209]     [,210]       [,211]
[1,] 0.8318784  0.1596014   67.86086  2.301634 -12.295150 -1.168839338
[2,] 3.2991157 -0.8989386  -72.50600 -3.849620  29.868424 -2.515768759
[3,] 5.1782668  1.4250454   18.39739 -5.728878   6.112689 -0.069669979
[4,] 7.6484912 -0.7234705 -101.56382 -4.513281  -6.264011  0.003537183
         [,212]    [,213]     [,214]     [,215]     [,216]     [,217]
[1,]  12.053206 10.029422  15.600101 -0.8987619  1.8502253  -3.854532
[2,]   1.368173 -1.013634 -12.250656  0.2324481 -0.8106771   9.217520
[3,]  -4.061305 -1.977501 -18.994119  0.7529249 -0.9833653  27.134161
[4,] -13.299733 13.978970   2.426743 -0.6490500 -1.0879298 -11.435804
          [,218]    [,219]     [,220]      [,221]     [,222]    [,223]
[1,]  0.07712361 0.7301310  5.1690833  0.09084376 -2.5336063  8.069897
[2,]  0.07093877 0.0433731 11.9672239  0.18797589  0.6502628 -4.856980
[3,] -0.07444057 0.6301796 -0.7305488 -0.02614767 -3.6845385 11.902138
[4,]  0.02566154 0.2085854 -2.7793164  0.26560011 -0.3407562 12.851965
         [,224]    [,225]      [,226]       [,227]    [,228]    [,229]
[1,] 0.06086713 29.269564 -12.2250059  0.140575641 14.546089  13.47702
[2,] 0.11579487 11.116149  39.9320906 -0.058228777  5.747561 -14.87454
[3,] 0.02792822 20.149404  28.7261792 -0.005357235 -3.222679  76.22386
[4,] 0.01932631 -5.425558  -0.4441624 -0.227455638 17.408164  39.80388
        [,230]     [,231]    [,232]      [,233]     [,234]     [,235]
[1,] 23.353430  -3.999691 -4.647498 -0.24234959 -0.9556609   2.420566
[2,] -2.600940 -10.101553 22.955998  0.10443657 -0.4158120 -26.120650
[3,] 11.737239  -2.348521 -4.515438 -0.05467059  1.0487462 -23.326187
[4,] -8.893813 -20.647810 25.152954  0.20134370  0.8776308 -59.689954
         [,236]      [,237]    [,238]      [,239]     [,240]     [,241]
[1,]  15.770862 -0.07964064 -1.587714 -0.11489238 -0.2276306 -10.355157
[2,]  -8.308193 -4.50237465  6.644429 -0.08762653 -1.2421405   2.656532
[3,] -44.372363 -7.41326384  4.704418  3.13823236  0.8570626  13.261889
[4,]   8.057141 -5.75169330 -3.020538  1.53142157 -0.6937480   3.360219
         [,242]      [,243]    [,244]    [,245]      [,246]     [,247]
[1,]  -3.165488  0.18023446 11.093354  1.618321 -0.01669725 -2.2392429
[2,]  14.534897  0.20651984 -7.776944  6.123576 -0.02695605 -1.1472225
[3,] -15.029727  0.18479130  7.313988 -3.286103 -0.10475574  0.6275386
[4,]  -1.163888 -0.07398812 -4.673323  2.100906  0.17451237 -2.0473055
         [,248]     [,249]      [,250]     [,251]     [,252]      [,253]
[1,]  -7.482765  4.3174827 -17.0103671  1.5955486  0.9033160  0.03999375
[2,] -10.469722 -9.5192126   4.3521495 -0.7881042  0.1697743 -0.29542519
[3,]   3.853312  0.3115897   0.3253829  0.2771575  2.5593542 -0.12389804
[4,]  15.056859  7.1950483 -11.0465083  0.3206301 -6.0788903 -0.01633137
         [,254]     [,255]      [,256]      [,257]     [,258]       [,259]
[1,] -0.8637981 -0.0564341  0.10781016  -0.9135963  -5.830103 -0.019961967
[2,]  0.4793273  0.2875093  0.09321535 -35.9406862 -35.153761  0.009556619
[3,] -5.2863976  1.3361763 -0.15480517  17.6201461  24.213999 -0.031953635
[4,]  3.8320998 -3.9897389 -0.02988476  26.9353049  37.857536 -0.015357842
         [,260]     [,261]      [,262]      [,263]     [,264]      [,265]
[1,]  4.3946840  4.2304021   3.2615779 0.066378825 -45.262078 -0.03275418
[2,]  3.6163046  0.9718617   6.2941726 0.104314803 -11.957298 -0.07791907
[3,] -0.9490384 -1.2975397   0.6039163 0.172325255   9.282745  0.14556054
[4,]  1.3145183 -0.3787254 -15.5577922 0.003380326  18.006886 -0.12986855
         [,266]     [,267]     [,268]     [,269]    [,270]   [,271]      [,272]
[1,]  45.425718 -11.724563  4.4381326  -7.517928  5.451095 24.75900  -9.4317498
[2,] -21.596237   3.548746  1.8195592 -10.181112  1.525206 28.91898  -0.6312319
[3,] -49.396201 -18.596712  7.7505596 -17.741561  3.205060 36.28934  -9.8503639
[4,]  -7.083812 -11.576075 -0.7698881   1.915056 -2.965325 13.52410 -10.7835391
         [,273]   [,274]    [,275]     [,276]    [,277]     [,278]    [,279]
[1,] -2.0013293 7.596320  29.89432 -20.896417 111.97365   4.830711 -7.788854
[2,]  0.5041564 7.132112 -47.16789  13.495311 116.36492 -56.252415 14.094680
[3,] -1.1562873 2.381221 -34.11078 -23.662607  56.08959  10.984132  4.100303
[4,]  4.3841369 7.046446 -19.75912  -6.454668  13.46645   5.161428 22.519123
          [,280]     [,281]    [,282]     [,283]    [,284]    [,285]
[1,]  0.02097962  22.685844 12.012258  7.4236646  1.704448 -6.628563
[2,]  0.04512516 -10.937256  8.891050 -0.2190126 -2.920129 24.722685
[3,] -0.07425092 -10.122969 15.980156  1.5896121 -1.500791 12.525410
[4,] -0.03098027   3.504565  2.947411  3.6553921  2.576781 -4.231330
          [,286]      [,287]     [,288]    [,289]    [,290]     [,291]
[1,]  -0.4390527 -0.15136410 -7.2928559 -2.327205 -2.254323 -0.2691634
[2,]  18.3252673 -0.07658125 -4.1779441  8.766922  2.482990  1.6667029
[3,] -14.5544346 -0.02350085 -0.2884566 -7.449817 -1.355799 -0.2085742
[4,] -29.7735367 -0.02141155  8.0580476 18.867898  3.394521  0.5736492
          [,292]    [,293]     [,294]     [,295]    [,296]     [,297]    [,298]
[1,] -0.95888307  3.673247  0.1643692 -31.165040 -3.974926 -0.1343968  8.427395
[2,] -2.31610934 -1.544033  0.3442958  -9.739480 -1.977845  0.9948401 40.449488
[3,]  0.04879839 16.595356 -1.1198810  -8.740222 -7.344459 -0.2303657 38.188185
[4,] -1.52883181  9.011060  0.1726146  -9.764585 12.288628 -0.3864735 10.604644
         [,299]      [,300]
[1,]  40.680611 -0.04417204
[2,]  -5.002198 -0.21129012
[3,] -32.613658 -0.24112202
[4,] -85.541503 -0.32085242

$F
          [,1]      [,2]        [,3]      [,4]       [,5]      [,6]      [,7]
[1,] -3.242815 -2.493204  0.04062949 -1.211331 -2.3488412  3.214511 10.210627
[2,]  2.060717  1.843979  0.49832149  1.812487 -1.2130156 -1.391015 -9.784061
[3,] -3.061635 -1.644841  0.23507834 -2.142987 -0.1439008  1.394137 -2.128563
[4,] -2.079434 -1.858723 -0.62253235 -2.008433  5.6836311 -1.302952  6.294036
           [,8]        [,9]     [,10]     [,11]       [,12]      [,13]
[1,]  0.8620731  1.52653434  5.410035  4.905228  0.76875191 -5.4572507
[2,] -0.1661146 -0.07822668  5.525013 -3.943370  0.79094995  0.7255569
[3,]  1.5595450  0.93523594 -2.873673 -3.812005  0.03236466 -3.9855230
[4,]  2.2793363 -0.08027882 -7.959934 -1.181506 -0.24012048 -3.7624211
         [,14]       [,15]       [,16]      [,17]      [,18]     [,19]
[1,]  6.409822 -1.13925379  0.07888143 -5.9057305 -0.3452852  0.190220
[2,] -2.879983 -0.97606209  1.04130569 -1.1841752  0.7685904  2.910855
[3,]  9.448915 -0.04095424 -1.91971864 -4.0401172  0.2019555 -2.333689
[4,] -4.212832 -0.94424779 -2.85299528  0.7457504  0.8067978 -0.697907
          [,20]       [,21]       [,22]      [,23]     [,24]      [,25]
[1,] -0.8687538  -7.2268021  1.03005436   7.654811 -3.875883  0.5156335
[2,]  0.9696736  -0.7715845 -3.09254488   9.672506 -2.422286  0.3481297
[3,]  0.3624321  -9.1161278  0.22926552 -11.901094  8.258661 -0.4329527
[4,]  0.1465412 -13.8249657 -0.04975943  -7.159358  3.866243  1.5210444
           [,26]      [,27]      [,28]     [,29]      [,30]     [,31]
[1,]  4.40996437 0.45404279  -5.023784 -5.756136  6.6761352 0.2278618
[2,] -0.73429822 0.76760955   6.508089  1.235378 -2.5850484 0.2556589
[3,] -0.47559533 0.02377983  -4.195488 -1.627590  0.9045831 0.6401926
[4,]  0.04179114 0.91271974 -12.198009 -3.299079  1.9128047 1.2835663
          [,32]     [,33]       [,34]      [,35]     [,36]      [,37]
[1,]  12.706703 15.911937  0.76415473 -0.9669008 -1.024218 0.78568396
[2,]  -5.564820  2.092506 -0.19958373 -2.0813469  5.645705 0.76290921
[3,]  -1.373691  1.233328  0.04862926  2.0623679  2.548652 0.07606449
[4,] -14.330275  8.499869  0.77195964 -3.0105223 -5.977057 1.65638912
            [,38]      [,39]     [,40]      [,41]       [,42]      [,43]
[1,] -1.511009214 1.46473052 1.4143348  4.9265122 -0.45276531 -0.8269058
[2,] -0.304400027 0.81770698 0.8144092 -0.6867471  0.25409454  2.8795170
[3,] -0.003582537 0.08501988 0.0885864 -4.0401178  0.01425413 -9.4386942
[4,]  1.246989897 0.98596597 1.4373349  0.5657554  0.56029057 -6.9446722
           [,44]      [,45]       [,46]       [,47]      [,48]      [,49]
[1,] 0.042394682 -1.4922594  0.02488360 -0.82651614  0.2815030 -0.8982509
[2,] 0.032587974 -1.4048247 -1.06588761 -0.08063862 -0.6640826 -0.1161979
[3,] 0.006582757 -0.6874732 -0.03758478 -0.72095695  0.3120794  0.2524254
[4,] 0.798577863  0.2641817 -0.50047552  0.24823433 -1.4801754  0.4836135
          [,50]      [,51]      [,52]      [,53]       [,54]      [,55]
[1,] -11.341939  0.8223400 1.24264054  2.3729576 -1.22306470 -0.3345273
[2,]   4.227177 -0.3189339 1.53317953 -0.2990815  0.28692004  0.6589135
[3,]  -4.807059 -0.3599482 0.08300417 -5.6324302  0.04601024 -0.5784889
[4,]  -1.420138 -2.1287289 0.49990523 -1.6146634  1.51491200  1.4468544
          [,56]      [,57]      [,58]     [,59]      [,60]      [,61]     [,62]
[1,] -0.7684467 0.61571094  0.2312461 -4.607698  0.2423892 -0.3450542  1.595374
[2,] -1.2439136 0.42316301 -0.2488420  1.054553  0.2529523 -1.0046854  1.802692
[3,]  0.2091951 0.07737308  0.2821631 -4.046493 -0.9835248  1.1653470 -0.318675
[4,] -0.4492942 1.39672713  1.0264698  4.890577 -0.4575342 -1.3865845  1.082387
         [,63]     [,64]      [,65]     [,66]       [,67]      [,68]      [,69]
[1,] -5.878159 0.4989834  6.4008567  3.750200  0.59268965 -0.9647088  1.1866268
[2,]  2.792278 0.4957709 -1.3886392  1.095803  0.98815114 -5.5095519  1.0469209
[3,] -6.167290 0.1796037 -3.4334803 -2.079311 -0.00348317  6.0157565 -0.7255477
[4,] -8.176389 0.2530315 -0.6076329  1.054095 -0.21126225 11.5374430  0.3366046
          [,70]       [,71]      [,72]      [,73]       [,74]      [,75]
[1,] -0.4074720  -3.8719417 -5.8766088  0.1433292 -0.99287593   8.230192
[2,]  0.5844555   1.0684696 -0.5592688 -0.2588128  0.11235889   1.434499
[3,]  0.0142014 -10.1142451  2.6253635 -0.3486538  0.02505563 -10.735052
[4,] -0.1456895   0.6929432  7.3248151 -0.9226541 -0.21062226  -2.194577
          [,76]     [,77]      [,78]       [,79]     [,80]      [,81]
[1,] -0.9530021  2.999979 -7.0804895  1.15941199  2.876848   5.289841
[2,] -0.3338127 -1.836209  2.6293594 -0.08096839 -4.667244   7.164831
[3,] -0.5343701 -3.228965  0.5642104 -0.36844396  3.860055 -22.191558
[4,] -0.4040371  2.401051 -3.4866227 -0.56118567  9.864438 -12.660349
          [,82]     [,83]      [,84]      [,85]        [,86]      [,87]
[1,] -2.9415227  2.672670  0.5397926 -0.1098288 -0.303561956 -0.3263012
[2,] -1.5271570 -0.970330  0.8220913 -4.8117499 -0.602279787 -3.9229166
[3,] -0.7140312  2.885887 -0.1523134 -6.2870342  0.008453469 -0.1650553
[4,]  0.2046873  2.855976  1.8039403 -0.5413824 -0.691823678 -0.9617756
          [,88]      [,89]      [,90]      [,91]      [,92]      [,93]
[1,] -1.3967646 -0.5424484 11.3412911  0.2906619  0.2238028  3.2478469
[2,]  0.1692865  0.0573157 -5.5642913 -9.0004114 -2.5500294 -0.3797066
[3,] -2.0733914 -0.4207634  0.3001284 17.6319413  0.8780541 -1.4831216
[4,]  1.2859617 -0.6427348  5.4716403 22.5350360 -5.0239584  0.8976209
          [,94]      [,95]      [,96]      [,97]        [,98]      [,99]
[1,] -0.1978964  2.1728183  1.1441868 -0.7309290 -0.780838030  2.9728010
[2,]  1.3024889  1.2344920  0.4361876 -0.9808019 -0.007885716 -0.2172182
[3,] -0.3719396 -0.1126217  1.0259945  0.1743406 -0.648434468 -3.5233211
[4,]  2.1822470  1.0292256 -0.9594451 -1.4845383 -1.421494679 -0.7651191
          [,100]    [,101]     [,102]     [,103]      [,104]     [,105]
[1,] -1.40702990 -3.749603 -0.4047505 -0.4645597 -0.20768511 1.47474161
[2,] -0.56598798  1.816499 -0.1998493  0.2946658  0.05580552 0.04268908
[3,] -0.03075728  2.089415 -0.1176660 -0.9427109  0.66983631 0.04053243
[4,] -0.29246101  4.019595 -1.6758066 -0.3424670  0.46531810 1.51767413
        [,106]      [,107]     [,108]     [,109]      [,110]       [,111]
[1,] -2.863456 -0.79162205 -0.4914944  4.1111512  1.59459206 -0.149771776
[2,] -0.332302 -0.68476056 -0.3298033 -0.6116226 -0.30981583 -0.078560848
[3,] -1.114025 -0.03227373  0.1311356  5.1718710 -0.01088452 -0.006363212
[4,]  1.149516 -0.67457027  0.1256892  2.1243980 -0.27988797 -1.186959102
        [,112]     [,113]     [,114]    [,115]      [,116]    [,117]
[1,] -1.321654 -0.2133373 -0.4331437 0.5629292  0.58579562  5.799889
[2,]  1.046412  0.4588880  0.1790244 0.8973417  0.73442800 -5.687080
[3,] -1.065199  1.4771408 -0.6926515 0.1709746 -0.07650399  6.626141
[4,] -3.640843  0.2109068  0.2343528 1.4333662  0.76849226 -2.139475
          [,118]     [,119]     [,120]     [,121]      [,122]      [,123]
[1,]  0.33899142 -0.2261046 -4.1593754 -1.6084188 -3.83663210 -17.7909254
[2,] -0.02944385 -1.6093574  2.2918778 -0.2640301 -2.02432391   4.2934050
[3,]  1.52030252  2.1701597  0.1484212  0.6114063 -0.06468693 -14.5941724
[4,]  0.01379462 -2.3416737  1.4636602  0.2940407 -2.17625833  -0.8847549
          [,124]      [,125]     [,126]     [,127]    [,128]    [,129]
[1,] -0.83699634 -0.33967276   2.079967  1.1736839 -6.181660 0.5033104
[2,] -0.53087514  0.03716748   6.808901 -0.2160581  4.972068 1.2250061
[3,] -0.02227088  0.03706355 -11.394724  0.3691278 -5.516875 3.3891097
[4,] -0.45201081  1.54168911  -6.364825  0.2193487  2.376236 2.5337787
          [,130]      [,131]     [,132]     [,133]     [,134]    [,135]
[1,] -0.01221911 -0.08365531 -0.8300372 -0.3407993 -1.7511150 3.5829472
[2,]  0.49178823 -0.76983010 -0.2298082  1.2153991 -0.9758060 2.3390573
[3,] -0.11525568 -0.02869450  0.7991110 -0.3587648 -0.3786591 0.1597171
[4,]  1.52394996 -0.51521637  1.0634160  0.9703266  0.5665870 2.9859300
         [,136]     [,137]    [,138]      [,139]      [,140]     [,141]
[1,]  0.3559413 -0.3056161  8.132424 -0.38741018 -0.62400485 -0.7024832
[2,]  0.3235722  1.8289516 -5.732819  0.01492201 -0.28536969 -0.9475469
[3,] -1.1576011 -8.9804757 15.373939  0.07525858 -0.01638576  0.1759241
[4,]  0.2656573  5.1399930 -2.198700 -0.19200679  0.48518508 -0.2786833
         [,142]     [,143]    [,144]     [,145]    [,146]    [,147]      [,148]
[1,]  1.8475742   2.326873 0.4216147  0.5304004  6.558417  3.368625 -1.36530586
[2,]  0.3947523  -2.895541 0.4655084 -2.4483383 -5.388945 -1.139448 -0.32095948
[3,] -0.2082046 -16.213205 0.1093408  2.3317157 -1.981802 11.773711  0.01605486
[4,] -2.5790655   3.133749 0.7886303  2.3698231  1.559376  7.916367  0.10923161
          [,149]     [,150]     [,151]    [,152]    [,153]     [,154]
[1,] -1.14308572 -3.3461698 0.05356217 -4.257168 10.361978  1.0814730
[2,] -0.10044732  0.6244582 1.24573154  6.585718 -9.273142 -0.4936392
[3,]  0.01208226 -2.8322489 0.12964622 -2.667820  2.798881  0.2717948
[4,]  0.61945414 -2.5594891 0.78128692 -3.663848 12.870407  0.7780932
          [,155]     [,156]     [,157]      [,158]       [,159]     [,160]
[1,]  0.88733948  0.2438589 -1.3756727 -0.15123624  0.007165594  0.7789711
[2,]  0.02873978 -0.5730086  0.4482383 -0.08422916 -0.022830278 -2.4160454
[3,] -0.74031133 -0.7948108  2.3991650 -0.22560211  0.164285444  6.1615194
[4,]  0.28970491 -5.4017703  0.8158170 -0.57698517  0.335140182 -7.8187517
          [,161]     [,162]     [,163]      [,164]     [,165]     [,166]
[1,]  0.08530027 -8.9186338  0.3184046 -0.03864116 -7.2673075  0.2326652
[2,] -0.11146112  2.1540124 -2.3671741  0.29827561  0.9533112  0.2182800
[3,]  0.12110656 -0.5548934 -1.1791754  0.01057492 -9.0299348 -0.3386190
[4,]  0.38994401 11.8927435  1.8630498  0.00284960 -1.7490194  0.1317323
        [,167]      [,168]     [,169]     [,170]     [,171]     [,172]
[1,] 14.261085 -0.61863042  0.1566208  0.1995060 -0.2289082  0.2207371
[2,] -9.163436  0.07369333  0.2188737  0.7210744 -0.1362719  0.1582753
[3,]  3.920251 -0.02812365 -0.2684705 -0.5699861  0.2642365 -0.8692925
[4,] 11.839554 -0.12845859 -0.2842903  0.8893853 -0.1766651  0.3498077
         [,173]    [,174]      [,175]     [,176]    [,177]      [,178]
[1,]  0.9934405  1.959825  0.08587838  0.6749341 -6.700411 -0.07230658
[2,]  5.5802749  4.236923  0.10292187 -0.2755600  1.902616  0.12426031
[3,] -3.0933620 -6.916532 -0.02780063  0.2454761 -2.606116 -0.24945567
[4,] -4.9961949 -4.537168  0.02613026  0.3112352 -6.171488 -0.01894370
        [,179]    [,180]      [,181]     [,182]     [,183]    [,184]    [,185]
[1,] -1.772369 -6.873160 -0.15112994 -0.3930192 -0.2221555  7.476000  2.043880
[2,]  1.102884  2.543027  0.09234374 -0.1542219  0.5780532  5.844911 -5.821874
[3,]  2.199251 -4.448978  0.40533884 -0.1255436 -0.2983844 -4.643162  7.633857
[4,] -3.899607  1.133562  0.05336669 -0.2669143 -0.4559142  3.521693  1.684559
          [,186]    [,187]      [,188]      [,189]      [,190]    [,191]
[1,] -0.02850307 -1.321055 -0.28249499 -10.2993384  0.03508471 -4.415820
[2,]  0.36020497  1.968021 -0.28709354   4.4355778  0.34241338 -5.911835
[3,]  0.32984970 -3.362792  0.08588581   0.4625298  0.10667508 10.055877
[4,] -0.22773840 -5.023189  0.03254503  -0.3245112 -0.31914981 14.682197
         [,192]     [,193]      [,194]     [,195]     [,196]    [,197]
[1,]  0.7340764  0.1265590 -0.07085978 -1.1231125  1.9491098 -4.014937
[2,]  0.0433947  0.1377152 -0.72254583  0.2761309  0.1055906  7.910564
[3,] -1.0554555  0.2804423 -0.19717374  0.5481973 -2.4760208 -6.756667
[4,] -0.8853572 -0.6338381  1.98850288 -0.5848097 -0.7486702 -5.263169
        [,198]      [,199]     [,200]     [,201]      [,202]      [,203]
[1,]  2.354860  0.05282143 -0.9060678 0.10136015  1.11720158 -0.01909431
[2,] -2.089755 -0.05364621 -1.7122547 0.15860194  0.05021952  0.29699153
[3,]  1.353252 -0.33740960 -0.5531906 0.07424534  0.09751069  0.13125679
[4,]  7.569861 -0.01079388  2.0069724 0.03160369 -0.13205683  0.25719785
          [,204]     [,205]       [,206]     [,207]    [,208]      [,209]
[1,]  0.23526791 -0.6213941  0.002647635 -0.3545754 14.762590 -0.08550597
[2,]  0.29412231  0.3265245 -0.372861420  0.5570402  5.231395  0.05140447
[3,] -0.08731199 -0.7466842  0.374690777 -0.5895700  3.882495 -0.56936187
[4,]  0.08832298 -0.2549344  0.348970843 -0.2839768 -9.178391 -0.21969378
         [,210]      [,211]     [,212]     [,213]    [,214]       [,215]
[1,]  1.5966428  0.08398399  0.9789985 -2.4604386 0.5411292  0.119630594
[2,] -2.6079475  0.13126758 -0.2987695 -0.6778527 0.2411266 -0.009703821
[3,] -0.8816798 -0.40151339  2.4929700  1.9335052 2.1137827  0.060298228
[4,]  1.7467449 -0.41418021 -0.2520211 -0.6243231 0.1435629 -0.039401569
          [,216]      [,217]      [,218]     [,219]      [,220]       [,221]
[1,]  0.05693633 -13.5321093  0.10873081  0.1145316  0.54462797 -0.007420877
[2,]  0.04489213   9.0725667  0.07624519 -0.1118322 -0.51846716  0.291766714
[3,] -0.25301561   0.4750266 -0.08781194  0.2064027  0.01239457 -0.064563262
[4,] -0.18033792  -1.5287344 -0.02988009 -0.3493062 -0.20294615  0.196591192
          [,222]     [,223]      [,224]     [,225]     [,226]      [,227]
[1,] -0.38017311  0.1050410  0.00134853  3.7096640 -8.4074311  0.20376916
[2,]  0.03571231 -1.1824217  0.17698453  0.8278298  4.9840008 -0.16453280
[3,]  0.42939827  0.2936196  0.06098160 -2.4041720 -0.8546184 -0.02082086
[4,] -0.01343456 -0.7608597 -0.07542521 -1.5121077 -3.8543140 -0.26280106
         [,228]    [,229]     [,230]     [,231]     [,232]      [,233]
[1,] -1.8956131 -7.887358 -0.7692344 -0.1143308  9.1179740 -0.31010438
[2,]  0.9250455  5.636305  0.9607119  1.1262935 -1.0100450  0.15570320
[3,]  1.1822376  3.515950 -2.9293800 -1.1166495  4.8820787 -0.05598824
[4,]  1.0517618 -3.939604 -2.2402605 -1.0727200 -0.4536293  0.13463323
         [,234]     [,235]    [,236]     [,237]     [,238]     [,239]
[1,] -0.1450411  -1.308901 -3.174600  4.5779652 -0.3433661  0.3114397
[2,]  0.2453334 -18.562114  1.091667 -1.2152183  0.6081400 -0.0397243
[3,] -0.1136630   1.154520 -3.195981  2.0648143 -0.2962651  0.3259557
[4,] -0.4545036  -3.469757  9.257154 -0.3848772 -0.7136097 -0.1773252
         [,240]     [,241]     [,242]     [,243]     [,244]     [,245]
[1,]  0.2445558  0.5987702 -1.4212190  0.1537836 -0.2502668  0.4901663
[2,]  0.1010656 -0.2375459  1.3720944  0.1933433  0.1536213 -0.3806390
[3,] -0.1032439  0.4855381  0.4362237  0.1553750 -0.3349494 -0.8831721
[4,] -0.2611160 -1.4291370 -2.5881403 -0.4111485 -1.0951303  0.8217262
          [,246]      [,247]     [,248]      [,249]     [,250]     [,251]
[1,] -0.04876132  0.26131570 -0.5059924 -2.10243767 -1.8742121  0.2438199
[2,]  0.03690786  0.08188627  0.4982647 -1.24743218 -1.0966674 -0.1002299
[3,] -0.20646161 -0.27226149  1.8071604  1.66619794 -0.7847394  0.1771392
[4,]  0.26057403 -0.41350484 -0.1794002  0.04099559  3.4303663 -0.2477400
          [,252]      [,253]      [,254]       [,255]      [,256]    [,257]
[1,] -0.08098125  0.03360084  0.09657432 -0.426836378  0.04488469 -5.620561
[2,]  0.15518872 -0.33569061  0.64937492  0.274014703  0.09600554 -1.975804
[3,]  0.29236697 -0.09196286  0.43016214 -0.449153317 -0.19904441  5.047141
[4,] -0.80693099  0.30314876 -0.46180406  0.003133558  0.07116233 -1.691370
        [,258]      [,259]     [,260]     [,261]       [,262]      [,263]
[1,] -3.714665 -0.10753750 -0.6264489 -0.3624042 -3.529942479  0.07441298
[2,] -2.295206  0.02964672  0.5824442  0.1211806  0.061574304  0.08387336
[3,]  5.035433  0.05990144 -0.2701028 -0.5033018 -1.756310639  0.13798791
[4,]  5.972737 -0.15234580 -0.6292468  0.2372743  0.005290217 -0.02277273
        [,264]      [,265]   [,266]      [,267]     [,268]     [,269]
[1,]  3.826884 -0.13101816 5.893980  0.08524722 -0.8267392  1.8196489
[2,] -2.945259  0.04017926 1.747234  0.71971358 -0.8345374 -1.3214627
[3,]  2.004099  0.02245168 4.530074 -2.24562908  0.7902187 -0.1000606
[4,]  4.430546 -0.27452178 2.120533 -0.93538081  0.3604998 -2.9520107
         [,270]     [,271]     [,272]     [,273]     [,274]     [,275]
[1,]  0.3387843  4.0097538 -1.2080993 -0.2788930  0.8016583   4.955468
[2,]  0.1838479  1.2104177 -1.8503400 -0.1989671  1.7830385 -10.286437
[3,] -1.0006848  1.2174431  0.5409546 -0.5895468 -2.2653887   7.392615
[4,] -1.5203156 -0.2677372  0.9566367  0.1494004 -1.4513149   2.432416
        [,276]     [,277]     [,278]    [,279]      [,280]     [,281]   [,282]
[1,] -5.559777  1.9521058  -1.987959 -1.308821 -0.01360259 -1.2152245 2.057409
[2,]  8.596061 -3.9455266  11.495409  1.185306 -0.04305377 -0.1818016 0.276336
[3,] -2.501261  0.7556837 -17.956409 -1.653117 -0.10191013  0.6720834 2.893422
[4,] -4.892252  6.1540251  -8.189556 -0.437276 -0.02127297 -0.1328047 2.677418
         [,283]      [,284]      [,285]     [,286]       [,287]       [,288]
[1,] -0.1505588  0.15378220  0.29675716  0.5264735 -0.068824194 -0.331503798
[2,]  1.1406051 -0.01123832  0.42418891  1.6446962  0.003636188 -0.003843804
[3,] -1.1573368 -0.33185100 -0.09140048 -0.8672410  0.003299673  0.560253913
[4,] -1.4603676 -0.37421666  1.20663017 -0.5559216 -0.083286856  0.205362585
         [,289]      [,290]      [,291]     [,292]     [,293]      [,294]
[1,]  4.0453909  0.24217098  0.08672702  0.3513502 -0.1027956  0.23329403
[2,] -0.5963736 -0.12615537  0.32765976 -0.1511392  1.3747512  0.02192779
[3,] -3.9846017 -0.09575865  0.22076966  0.3849984  3.0178273 -0.35647209
[4,]  6.1317263  0.25985130 -0.09681628 -0.7771163  2.0049124 -0.42284559
          [,295]     [,296]      [,297]    [,298]    [,299]       [,300]
[1,]  0.08851597 -0.2832533  0.30663999  7.358585 -3.181171 -0.005312627
[2,] -1.04430414  0.4892782  0.01890647 -1.806531 -6.638342 -0.280658363
[3,] -1.47121669 -0.4532981 -0.14362920 11.495181 11.805503 -0.225160584
[4,] -4.98022262 -0.3004489  0.04565085  1.867721  1.679602 -0.217912470

$L
                [,1]         [,2]          [,3]          [,4]
  [1,] 1.447834e-114 0.0033925704  9.966074e-01 4.240653e-103
  [2,] 1.848014e-113 0.0030248738  9.969751e-01 1.139683e-103
  [3,] 1.935297e-113 0.0047796558  9.952203e-01 2.004950e-104
  [4,] 8.950411e-114 0.0090585315  9.909415e-01 1.574055e-103
  [5,] 7.015401e-114 0.0042104006  9.957896e-01 8.308885e-104
  [6,] 6.752072e-113 0.0348980647  9.651019e-01 1.534170e-103
  [7,] 1.853206e-113 0.0301007310  9.698993e-01 1.428298e-102
  [8,] 5.777505e-116 0.0672603606  9.327396e-01 8.006641e-106
  [9,] 3.222532e-113 0.0647135298  9.352865e-01 2.932698e-105
 [10,] 3.644409e-115 0.0595185464  9.404815e-01 1.043648e-103
 [11,] 8.494094e-114 0.0705427521  9.294572e-01 8.506713e-106
 [12,] 5.195667e-115 0.0619895411  9.380105e-01 2.892309e-104
 [13,] 1.688591e-114 0.0757601874  9.242398e-01 6.040438e-106
 [14,] 2.943405e-114 0.0584654905  9.415345e-01 6.879883e-105
 [15,] 4.437704e-116 0.0897104050  9.102896e-01 7.470731e-108
 [16,] 4.710894e-113 0.1191694115  8.808306e-01 3.668578e-109
 [17,] 4.308560e-114 0.1166358313  8.833642e-01 6.958654e-110
 [18,] 8.832277e-125 0.1706728786  8.293271e-01 3.117261e-115
 [19,] 3.096954e-123 0.1505495818  8.494504e-01 1.928183e-112
 [20,] 8.315745e-118 0.1716539767  8.283460e-01 8.941291e-116
 [21,] 3.183082e-121 0.1497806352  8.502194e-01 1.909269e-113
 [22,] 9.449921e-122 0.2044629066  7.955371e-01 2.282988e-124
 [23,] 2.393419e-125 0.1936988195  8.063012e-01 9.042155e-121
 [24,] 3.240488e-127 0.2115720803  7.884279e-01 1.179954e-114
 [25,] 7.910128e-129 0.2269404141  7.730596e-01 1.707972e-128
 [26,] 1.066093e-127 0.2081710163  7.918290e-01 1.332812e-123
 [27,] 4.143878e-133 0.2451472320  7.548528e-01 1.028655e-126
 [28,] 1.034111e-129 0.2180923356  7.819077e-01 2.206751e-123
 [29,] 4.210881e-128 0.2456074042  7.543926e-01 5.481872e-132
 [30,] 1.895408e-132 0.2634495911  7.365504e-01 1.362824e-129
 [31,] 6.208966e-134 0.2424850171  7.575150e-01 4.006126e-134
 [32,] 3.932895e-135 0.2889378884  7.110621e-01 2.347909e-141
 [33,] 8.050174e-138 0.3086956810  6.913043e-01 6.701390e-150
 [34,] 1.149009e-146 0.3238939393  6.761061e-01 7.100173e-151
 [35,] 1.597108e-150 0.3220171055  6.779829e-01 2.816301e-146
 [36,] 4.599823e-152 0.3201766244  6.798234e-01 1.627574e-150
 [37,] 8.721889e-151 0.3320121372  6.679879e-01 1.951093e-154
 [38,] 1.651536e-138 0.3521200490  6.478800e-01 4.095410e-162
 [39,] 1.321336e-150 0.3569998991  6.430001e-01 8.373131e-159
 [40,] 2.668703e-160 0.3716289271  6.283711e-01 1.653154e-164
 [41,] 5.092162e-158 0.3631601840  6.368398e-01 3.608150e-164
 [42,] 2.751660e-158 0.3817916139  6.182084e-01 2.025534e-169
 [43,] 6.064615e-165 0.3892556249  6.107444e-01 3.308151e-167
 [44,] 1.505922e-168 0.4353630917  5.646369e-01 4.400370e-189
 [45,] 1.399380e-167 0.4286504183  5.713496e-01 8.834577e-182
 [46,] 8.159838e-175 0.4392152753  5.607847e-01 3.028791e-187
 [47,] 1.224365e-169 0.4206881462  5.793119e-01 6.370210e-185
 [48,] 1.207234e-175 0.4625104850  5.374895e-01 1.107109e-193
 [49,] 1.095827e-179 0.4716255155  5.283745e-01 2.843374e-193
 [50,] 7.838197e-191 0.4820831470  5.179169e-01 5.569465e-191
 [51,] 9.031237e-187 0.4711801444  5.288199e-01 3.029875e-190
 [52,] 3.253428e-177 0.4757082415  5.242918e-01 4.804533e-196
 [53,] 5.885835e-186 0.5007388436  4.992612e-01 2.297255e-174
 [54,] 9.540554e-170 0.5303630152  4.696370e-01 4.078233e-152
 [55,] 2.278609e-175 0.5221360414  4.778640e-01 2.338908e-161
 [56,] 1.760503e-172 0.5266956861  4.733043e-01 3.925817e-157
 [57,] 6.646891e-167 0.5339490302  4.660510e-01 2.352055e-151
 [58,] 1.431870e-152 0.5554404784  4.445595e-01 1.861802e-139
 [59,] 1.649384e-147 0.5630389328  4.369611e-01 1.836570e-133
 [60,] 7.064174e-148 0.5619089888  4.380910e-01 3.934829e-131
 [61,] 2.986155e-130 0.5898179873  4.101820e-01 2.272533e-115
 [62,] 5.412545e-117 0.6130537948  3.869462e-01 7.494335e-103
 [63,]  3.019111e-96 0.6504079101  3.495921e-01  3.433102e-86
 [64,] 8.163150e-116 0.6143332421  3.856668e-01 1.217505e-108
 [65,] 3.738169e-107 0.6297905927  3.702094e-01  1.026335e-94
 [66,] 7.593804e-105 0.6331784883  3.668215e-01  1.524328e-92
 [67,]  5.631632e-98 0.6466511235  3.533489e-01  4.124632e-85
 [68,]  4.743349e-90 0.6632487888  3.367512e-01  1.521377e-82
 [69,]  5.375876e-75 0.6928421648  3.071578e-01  1.919984e-63
 [70,]  4.675001e-69 0.7055344267  2.944656e-01  1.113712e-61
 [71,]  9.069614e-69 0.7058013255  2.941987e-01  4.454647e-62
 [72,]  2.118432e-63 0.7187380594  2.812619e-01  8.965974e-52
 [73,]  6.458006e-66 0.7132948076  2.867052e-01  5.421844e-58
 [74,]  1.175408e-47 0.7603093417  2.396907e-01  2.996760e-42
 [75,]  6.327437e-55 0.7408787716  2.591212e-01  2.922848e-47
 [76,]  7.671089e-48 0.7590461710  2.409538e-01  9.774733e-43
 [77,]  5.190500e-64 0.7176422459  2.823578e-01  7.754022e-58
 [78,]  5.105119e-40 0.7799806737  2.200193e-01  6.141391e-37
 [79,]  7.714129e-36 0.7919875150  2.080125e-01  7.514817e-34
 [80,]  1.189130e-41 0.7764427628  2.235572e-01  1.147695e-35
 [81,]  3.291122e-42 0.7750866717  2.249133e-01  1.162658e-38
 [82,]  2.183553e-26 0.8283241235  1.716759e-01  3.212195e-24
 [83,]  6.707151e-28 0.8225258922  1.774741e-01  1.220188e-20
 [84,]  1.831457e-26 0.8266886719  1.733113e-01  4.198369e-22
 [85,]  7.018819e-24 0.8381361398  1.618639e-01  2.443267e-20
 [86,]  5.399128e-18 0.8644814956  1.355185e-01  1.421007e-16
 [87,]  4.617971e-17 0.8676580059  1.323420e-01  2.549781e-14
 [88,]  1.619927e-20 0.8525885273  1.474115e-01  2.194069e-16
 [89,]  2.058699e-16 0.8673030264  1.326970e-01  1.187764e-14
 [90,]  3.645991e-09 0.9133826516  8.661725e-02  8.984886e-08
 [91,]  4.131128e-11 0.9067650439  9.323477e-02  1.811480e-07
 [92,]  4.355419e-07 0.9290078606  7.098498e-02  6.723082e-06
 [93,]  9.579354e-08 0.9238343225  7.616539e-02  1.873330e-07
 [94,]  1.340165e-08 0.9179204625  8.207879e-02  7.331341e-07
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 [96,]  7.238583e-04 0.9772268128  5.390061e-03  1.665927e-02
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 [98,]  1.580307e-03 0.9927304445  1.905221e-03  3.784027e-03
 [99,]  9.088926e-04 0.9921016927  6.039742e-03  9.496725e-04
[100,]  1.197022e-03 0.9807360330  8.121871e-04  1.725476e-02
[101,]  9.960420e-01 0.0039580033 8.128440e-114 5.547886e-119
[102,]  9.872385e-01 0.0127615204 4.475288e-113 8.497713e-119
[103,]  9.956722e-01 0.0043277855 4.030581e-114 3.816402e-119
[104,]  9.600761e-01 0.0399239261 7.415647e-114 6.882952e-119
[105,]  9.717706e-01 0.0282293957 4.956851e-114 4.004993e-119
[106,]  9.602405e-01 0.0397594953 1.089145e-113 4.888662e-118
[107,]  9.585310e-01 0.0414689618 2.990703e-113 2.368486e-119
[108,]  9.266448e-01 0.0733551612 3.411228e-115 4.190249e-122
[109,]  9.199823e-01 0.0800177357 9.621590e-115 4.718782e-120
[110,]  9.133350e-01 0.0866649598 6.472227e-113 3.132112e-118
[111,]  9.048473e-01 0.0951526699 2.296168e-117 6.623487e-123
[112,]  9.033719e-01 0.0966281332 1.404731e-113 1.242558e-118
[113,]  9.108068e-01 0.0891931637 2.544937e-114 1.680822e-118
[114,]  8.636376e-01 0.1363624301 6.147413e-118 2.787780e-125
[115,]  8.520168e-01 0.1479832322 8.128595e-119 1.031796e-127
[116,]  8.845979e-01 0.1154020995 1.661145e-115 1.237666e-121
[117,]  8.492227e-01 0.1507772964 2.396315e-120 3.617466e-125
[118,]  8.164046e-01 0.1835954173 8.414195e-121 9.671156e-131
[119,]  8.288533e-01 0.1711467099 3.935897e-124 7.926006e-136
[120,]  7.891811e-01 0.2108188993 2.497157e-123 5.879986e-133
[121,]  7.965179e-01 0.2034820687 2.626946e-122 5.831253e-135
[122,]  8.054847e-01 0.1945153461 1.172877e-129 1.940313e-134
[123,]  7.940760e-01 0.2059239751 1.501301e-121 2.494780e-130
[124,]  7.589434e-01 0.2410566318 9.087161e-133 5.718199e-138
[125,]  7.709917e-01 0.2290082816 4.256305e-127 4.510766e-140
[126,]  7.454405e-01 0.2545594740 9.446615e-132 1.452120e-136
[127,]  7.083625e-01 0.2916375195 2.555500e-135 1.376488e-151
[128,]  7.408905e-01 0.2591094612 4.740493e-133 4.484612e-141
[129,]  7.225233e-01 0.2774767200 1.704410e-136 3.151456e-151
[130,]  6.698174e-01 0.3301826143 1.314804e-152 2.524138e-163
[131,]  6.934967e-01 0.3065032635 3.777018e-142 1.312689e-154
[132,]  6.952997e-01 0.3047002923 5.701095e-141 3.289674e-152
[133,]  7.106859e-01 0.2893140542 5.639690e-137 3.066615e-145
[134,]  6.602352e-01 0.3397648138 6.649632e-149 1.757025e-165
[135,]  6.312569e-01 0.3687431149 2.267579e-158 1.431299e-174
[136,]  6.468822e-01 0.3531177717 2.469536e-142 7.273151e-163
[137,]  6.444642e-01 0.3555358408 2.320156e-152 1.289590e-176
[138,]  6.273871e-01 0.3726129083 7.246242e-160 6.070626e-175
[139,]  6.322022e-01 0.3677977627 8.371311e-162 3.087069e-178
[140,]  5.754880e-01 0.4245120450 4.371058e-170 1.500292e-186
[141,]  6.302655e-01 0.3697345068 1.128885e-156 3.982124e-173
[142,]  6.030715e-01 0.3969284540 2.362788e-166 3.150568e-183
[143,]  5.925326e-01 0.4074674364 9.639553e-164 8.851696e-181
[144,]  5.711025e-01 0.4288975152 1.314331e-177 1.565918e-194
[145,]  5.488755e-01 0.4511244960 2.388896e-172 5.936808e-196
[146,]  5.420813e-01 0.4579186779 8.386703e-188 2.450699e-200
[147,]  5.471827e-01 0.4528173027 1.615872e-178 3.483311e-196
[148,]  4.958513e-01 0.5041487081 6.255213e-181 7.137600e-227
[149,]  5.131299e-01 0.4868701112 2.365932e-190 3.253158e-216
[150,]  5.107143e-01 0.4892856817 4.159954e-185 7.216706e-208
[151,]  4.960394e-01 0.5039606040 4.827692e-190 1.748712e-216
[152,]  4.702883e-01 0.5297116644 1.024737e-204 1.198951e-232
[153,]  4.661209e-01 0.5338790943 5.981810e-197 3.897357e-218
[154,]  4.579597e-01 0.5420402602 1.395256e-205 4.587789e-236
[155,]  4.506330e-01 0.5493669625 5.247035e-198 3.113886e-228
[156,]  4.804182e-01 0.5195817977 3.912041e-190 6.978820e-221
[157,]  4.223672e-01 0.5776327549 4.506367e-203 2.070795e-201
[158,]  4.036985e-01 0.5963014655 3.324234e-186 3.867705e-184
[159,]  3.994003e-01 0.6005997431 4.918751e-182 1.250442e-180
[160,]  4.099851e-01 0.5900149395 1.116277e-191 8.298832e-190
[161,]  3.915175e-01 0.6084824967 7.951115e-175 3.262162e-173
[162,]  3.980261e-01 0.6019738859 1.489422e-180 1.773367e-178
[163,]  3.605330e-01 0.6394669810 5.279170e-149 1.147220e-147
[164,]  3.861208e-01 0.6138792250 3.645173e-170 1.045250e-168
[165,]  3.424271e-01 0.6575728988 7.740218e-135 2.347970e-133
[166,]  3.493407e-01 0.6506593486 3.115901e-140 1.103117e-138
[167,]  3.372573e-01 0.6627427420 8.733319e-131 5.072044e-130
[168,]  3.269472e-01 0.6730527670 4.706180e-123 9.863393e-122
[169,]  2.852902e-01 0.7147097999  5.804342e-95  2.617686e-93
[170,]  2.977406e-01 0.7022594304 7.711819e-103 8.993134e-102
[171,]  2.847338e-01 0.7152662384  8.798737e-95  6.254713e-93
[172,]  2.773918e-01 0.7226082481  1.371053e-89  8.559249e-89
[173,]  2.669930e-01 0.7330070391  1.096662e-83  4.901407e-83
[174,]  2.539894e-01 0.7460106217  4.263865e-76  2.342169e-74
[175,]  2.965559e-01 0.7034441395 2.075103e-102 5.860364e-101
[176,]  2.480090e-01 0.7519910102  1.306326e-72  4.126329e-71
[177,]  2.386947e-01 0.7613053018  6.345905e-68  6.951239e-66
[178,]  2.135205e-01 0.7864795291  9.356191e-55  3.994571e-54
[179,]  1.992398e-01 0.8007601550  1.309858e-48  1.304232e-47
[180,]  2.048468e-01 0.7951532337  6.711438e-51  3.740290e-50
[181,]  2.337575e-01 0.7662424951  5.117932e-65  9.486361e-63
[182,]  1.704388e-01 0.8295611847  1.672345e-36  1.018116e-34
[183,]  1.662416e-01 0.8337584059  1.777684e-34  2.126837e-34
[184,]  1.716877e-01 0.8283123209  6.684882e-37  1.964348e-35
[185,]  1.487646e-01 0.8512353765  2.679472e-28  1.871430e-27
[186,]  1.158911e-01 0.8841088856  1.116385e-18  1.286773e-17
[187,]  1.530849e-01 0.8469150551  3.536831e-30  9.860630e-30
[188,]  1.189126e-01 0.8810874030  2.434806e-19  2.325614e-18
[189,]  1.090136e-01 0.8909863647  7.346637e-17  1.162160e-15
[190,]  8.091907e-02 0.9190809265  2.783394e-11  1.192838e-10
[191,]  8.590429e-02 0.9140957051  3.778630e-12  1.382571e-11
[192,]  8.263083e-02 0.9173691647  2.770620e-11  2.918789e-10
[193,]  7.241690e-02 0.9275830848  2.869484e-09  1.040898e-08
[194,]  5.762323e-02 0.9423722123  1.427742e-06  3.127610e-06
[195,]  5.683933e-02 0.9431601420  2.959071e-07  2.303503e-07
[196,]  1.404951e-02 0.9742500153  7.494330e-03  4.206150e-03
[197,]  8.549754e-03 0.9885616791  7.655884e-04  2.122978e-03
[198,]  6.897805e-03 0.9799600862  3.741247e-03  9.400862e-03
[199,]  1.640602e-02 0.9786788340  2.503748e-03  2.411397e-03
[200,]  1.558843e-03 0.9948802231  1.994539e-03  1.566395e-03
[201,] 5.062493e-120 0.0012469319 5.761119e-105  9.987531e-01
[202,] 3.299582e-120 0.0023060672 2.036827e-104  9.976939e-01
[203,] 1.061672e-119 0.0045341805 1.001211e-103  9.954658e-01
[204,] 4.761096e-120 0.0023763670 3.932260e-104  9.976236e-01
[205,] 1.951430e-119 0.0009176536 5.323645e-105  9.990823e-01
[206,] 7.835889e-119 0.0068162948 2.950115e-104  9.931837e-01
[207,] 5.106650e-119 0.0068791217 2.527170e-104  9.931209e-01
[208,] 7.907269e-119 0.0041246074 2.237207e-104  9.958754e-01
[209,] 2.055470e-119 0.0158108198 3.202803e-103  9.841892e-01
[210,] 5.840485e-120 0.0259970368 5.555501e-103  9.740030e-01
[211,] 7.267499e-120 0.0426209571 1.808612e-103  9.573790e-01
[212,] 1.815480e-118 0.0613976590 1.515149e-105  9.386023e-01
[213,] 3.027851e-119 0.0670942907 8.943544e-104  9.329057e-01
[214,] 8.091858e-121 0.0862830503 7.427420e-106  9.137169e-01
[215,] 3.777329e-122 0.1181078151 9.378446e-111  8.818922e-01
[216,] 1.152252e-121 0.0893027689 2.018511e-106  9.106972e-01
[217,] 3.680789e-121 0.1352786947 7.710994e-109  8.647213e-01
[218,] 2.678395e-128 0.1418614537 7.773666e-107  8.581385e-01
[219,] 2.328327e-127 0.1423487606 1.860371e-109  8.576512e-01
[220,] 2.067794e-126 0.1547384414 2.576270e-109  8.452616e-01
[221,] 4.624019e-124 0.1146011602 4.217048e-106  8.853988e-01
[222,] 2.006182e-131 0.1678950726 3.913376e-116  8.321049e-01
[223,] 1.020020e-129 0.1799584425 2.128467e-120  8.200416e-01
[224,] 2.704012e-137 0.2167409550 2.101936e-123  7.832590e-01
[225,] 1.070145e-135 0.2180098077 2.093379e-123  7.819902e-01
[226,] 5.723467e-136 0.2305139992 1.732653e-122  7.694860e-01
[227,] 1.245808e-138 0.2236335584 4.585410e-126  7.763664e-01
[228,] 1.321132e-136 0.2510431929 8.881288e-137  7.489568e-01
[229,] 3.072135e-142 0.2638665825 4.056118e-135  7.361334e-01
[230,] 1.301166e-143 0.2647414646 7.065103e-134  7.352585e-01
[231,] 1.532301e-148 0.2787116014 2.493870e-139  7.212884e-01
[232,] 2.423367e-140 0.2636949498 3.932410e-134  7.363051e-01
[233,] 3.619508e-141 0.2647419379 4.338386e-136  7.352581e-01
[234,] 1.298734e-151 0.2966008960 8.721276e-146  7.033991e-01
[235,] 4.873423e-149 0.3066658932 4.304097e-147  6.933341e-01
[236,] 4.753471e-160 0.3126071454 1.780119e-149  6.873929e-01
[237,] 1.006280e-154 0.3017965158 3.006575e-145  6.982035e-01
[238,] 7.493079e-162 0.3574024432 2.631447e-162  6.425976e-01
[239,] 1.158428e-176 0.3880903967 3.336350e-161  6.119096e-01
[240,] 5.250920e-171 0.3600679815 1.177765e-161  6.399320e-01
[241,] 3.632512e-188 0.4073786472 1.929437e-179  5.926214e-01
[242,] 3.675624e-172 0.3846909227 1.607474e-176  6.153091e-01
[243,] 9.144428e-180 0.3928005305 1.171113e-167  6.071995e-01
[244,] 4.277285e-187 0.4164860825 1.334298e-181  5.835139e-01
[245,] 1.032857e-181 0.4288817309 3.527611e-191  5.711183e-01
[246,] 5.984955e-204 0.4436866004 1.561263e-193  5.563134e-01
[247,] 1.220116e-179 0.4160329749 2.006403e-181  5.839670e-01
[248,] 1.578434e-203 0.4665921735 6.491465e-185  5.334078e-01
[249,] 1.620327e-174 0.5062615011 1.232620e-162  4.937385e-01
[250,] 1.121718e-201 0.4438254603 6.009518e-183  5.561745e-01
[251,] 2.482711e-176 0.5032314263 4.441912e-164  4.967686e-01
[252,] 1.033430e-169 0.5140505756 6.761271e-150  4.859494e-01
[253,] 5.094496e-190 0.4842791057 1.594348e-179  5.157209e-01
[254,] 1.677967e-177 0.5015736757 2.845819e-160  4.984263e-01
[255,] 1.699275e-158 0.5305924827 7.586700e-145  4.694075e-01
[256,] 3.381984e-169 0.5146068982 4.039934e-156  4.853931e-01
[257,] 8.882695e-138 0.5620867276 2.958713e-125  4.379133e-01
[258,] 4.267338e-143 0.5536986794 6.326388e-131  4.463013e-01
[259,] 1.254657e-135 0.5662886907 3.305704e-117  4.337113e-01
[260,] 3.046872e-136 0.5658286763 5.910900e-123  4.341713e-01
[261,] 9.833567e-118 0.5965282133 4.097952e-110  4.034718e-01
[262,] 5.485249e-111 0.6088242580 7.766620e-104  3.911757e-01
[263,] 1.139999e-122 0.5864651251 1.774940e-114  4.135349e-01
[264,]  3.991599e-95 0.6398360475  6.569618e-85  3.601640e-01
[265,]  5.165614e-95 0.6396117049  2.723828e-83  3.603883e-01
[266,]  3.139238e-95 0.6380612204  2.741032e-85  3.619388e-01
[267,]  1.221542e-77 0.6759332723  1.344946e-68  3.240667e-01
[268,]  4.817795e-71 0.6904280679  1.134776e-64  3.095719e-01
[269,]  2.058798e-82 0.6653174037  1.111260e-71  3.346826e-01
[270,]  2.528225e-73 0.6855046139  7.972504e-69  3.144954e-01
[271,]  5.266887e-67 0.6987398231  2.439936e-59  3.012602e-01
[272,]  9.973931e-75 0.6813376007  4.467480e-68  3.186624e-01
[273,]  4.279294e-56 0.7264187281  2.591321e-51  2.735813e-01
[274,]  1.983826e-68 0.6961570553  9.183708e-64  3.038429e-01
[275,]  5.000724e-51 0.7383383039  3.419581e-45  2.616617e-01
[276,]  1.100362e-50 0.7389964507  1.839629e-49  2.610035e-01
[277,]  2.847888e-31 0.7961524788  1.102248e-30  2.038475e-01
[278,]  8.762937e-40 0.7737672116  5.077691e-35  2.262328e-01
[279,]  1.732587e-46 0.7529087106  2.653022e-40  2.470913e-01
[280,]  1.691004e-33 0.7896485783  3.049743e-31  2.103514e-01
[281,]  2.036241e-34 0.7927523068  1.291197e-29  2.072477e-01
[282,]  1.687186e-41 0.7676307396  7.695495e-39  2.323693e-01
[283,]  8.625400e-31 0.8025878310  5.495485e-28  1.974122e-01
[284,]  2.088441e-23 0.8330220254  4.109409e-20  1.669780e-01
[285,]  1.635463e-19 0.8478250603  3.295476e-17  1.521749e-01
[286,]  1.295982e-13 0.8798114023  3.086416e-12  1.201886e-01
[287,]  5.770715e-16 0.8668929676  1.105128e-13  1.331070e-01
[288,]  5.685203e-09 0.9075347802  5.845299e-09  9.246521e-02
[289,]  1.284144e-13 0.8825303775  1.146132e-10  1.174696e-01
[290,]  2.864516e-17 0.8592594710  3.343122e-15  1.407405e-01
[291,]  1.781848e-06 0.9312361429  6.462843e-07  6.876143e-02
[292,]  5.152109e-08 0.9231686922  6.151460e-06  7.682510e-02
[293,]  7.636996e-04 0.9550555749  3.122870e-04  4.386844e-02
[294,]  1.831942e-07 0.9229363466  2.711107e-06  7.706076e-02
[295,]  1.082812e-04 0.9512074644  6.033985e-04  4.808086e-02
[296,]  2.251432e-07 0.9270983627  4.883636e-05  7.285258e-02
[297,]  3.165321e-04 0.9785259373  2.961566e-03  1.819596e-02
[298,]  3.009536e-04 0.9655384122  6.152249e-04  3.354541e-02
[299,]  4.326891e-03 0.9813952730  4.163593e-03  1.011424e-02
[300,]  2.863136e-03 0.9950276056  4.467908e-04  1.662468e-03

$P
              [,1]        [,2]          [,3]       [,4]
[1,]  2.840377e-03 0.000000000  0.000000e+00 0.00000000
[2,]  3.263836e-01 0.006383986  0.000000e+00 0.00000000
[3,] 5.880813e-114 0.315898028  9.685471e-03 0.00000000
[4,] 2.156421e-119 0.317826516 6.030310e-104 0.02098203

$alpha
NULL

$loglik
  [1] -282396.2 -261067.0 -257144.3 -255428.0 -254674.0 -254371.5 -254248.3
  [8] -254186.1 -254150.5 -254129.9 -254117.5 -254109.7 -254104.6 -254101.1
 [15] -254098.7 -254096.9 -254095.5 -254094.4 -254093.6 -254093.0 -254092.5
 [22] -254092.0 -254091.7 -254091.4 -254091.2 -254091.1 -254090.9 -254090.8
 [29] -254090.7 -254090.6 -254090.5 -254090.5 -254090.4 -254090.4 -254090.3
 [36] -254090.3 -254090.3 -254090.3 -254090.3 -254090.2 -254090.2 -254090.2
 [43] -254090.2 -254090.2 -254090.2 -254090.2 -254090.2 -254090.2 -254090.2
 [50] -254090.2 -254090.2 -254090.2 -254090.2 -254090.1 -254090.1 -254090.1
 [57] -254090.1 -254090.1 -254090.1 -254090.1 -254090.1 -254090.1 -254090.1
 [64] -254090.1 -254090.1 -254090.1 -254090.1 -254090.1 -254090.1 -254090.1
 [71] -254090.1 -254090.1 -254090.1 -254090.1 -254090.1 -254090.0 -254090.0
 [78] -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0
 [85] -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0
 [92] -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0
 [99] -254090.0 -254090.0 -254090.0 -254090.0

$BIC
[1] 521926

$niter
[1] 102

$status
[1] 0

$runtime
   user  system elapsed 
283.452  20.376  96.711 

The algorithm converged within 102 iterations. The fitted log-likelihood is -254090.0.

Search for best initial values

The previous run has used a random factor initialization. There are cases when we worry about convergence issue, ie, EM algorithm trapped on local optima, and the way out is to initialize the algorithm with different factors and adopt an initialization that gives the best log-likelihood.

Here we add init = c(20, 5) to the control list. It means we want to try 20 random initial factors and pick up the best one in likelihood after 5 iterations:

In [4]:
set.seed(999)
control = list(logfile = 'example_data', verbose = F, alpha = NULL, init = c(20,5))
res = pfar::pfa(X, K = K, control = control)
res
$F_init
          [,1]      [,2]        [,3]      [,4]       [,5]      [,6]       [,7]
[1,] -1.779343 -1.648705 -0.54478104 -1.739496  4.9511441 -1.423721   5.394134
[2,] -2.577555 -2.095564  0.08257832 -0.923324 -2.3667268  2.767845   8.539143
[3,] -3.023605 -1.656210  0.23060192 -2.066017 -0.1884845  1.353863  -1.993595
[4,]  2.085944  1.964491  0.51729482  1.870755 -1.1152618 -1.365222 -10.348029
           [,8]        [,9]     [,10]     [,11]       [,12]      [,13]
[1,]  2.0389172 -0.10411703 -6.868646 -0.821511 -0.15643893 -3.4024710
[2,]  0.7140160  1.37308833  5.399136  4.339226  0.76845140 -4.7144721
[3,]  1.5283138  0.83875048 -2.753111 -3.420314  0.04768409 -3.9941015
[4,] -0.1491795 -0.04432678  5.649249 -4.515974  0.79939268  0.7593258
         [,14]      [,15]       [,16]      [,17]      [,18]      [,19]
[1,] -4.114082 -0.9480789 -2.62226713  0.8886139  0.8016255 -0.5326564
[2,]  5.432922 -1.1240489 -0.07893925 -5.3639914 -0.2433817  0.5195113
[3,]  9.153406 -0.0632237 -1.93794887 -3.9074186  0.2141715 -2.2546693
[4,] -2.861580 -0.9751405  1.24502652 -1.3734872  0.7753580  2.9864834
          [,20]       [,21]       [,22]      [,23]     [,24]      [,25]
[1,]  0.1530494 -12.7521553 -0.04379439  -5.443037  3.638959  1.4422785
[2,] -0.6645321  -6.7172554  0.63558417   8.008657 -3.468454  0.5084303
[3,]  0.3913791  -9.1136820  0.16569721 -11.308577  8.196353 -0.4085334
[4,]  0.9890541  -0.5542702 -3.24013186   9.531922 -2.768149  0.3275535
          [,26]      [,27]      [,28]     [,29]      [,30]     [,31]      [,32]
[1,]  0.1785547 0.91178617 -10.873109 -3.068303  1.6419882 1.2302157 -13.262331
[2,]  4.0022659 0.56739340  -3.731067 -5.150840  5.7959216 0.2442433  11.200128
[3,] -0.3898492 0.05527327  -4.056597 -1.637438  0.9201581 0.6460683  -1.504107
[4,] -0.9139431 0.72274478   6.708776  1.402386 -2.7245509 0.2247884  -5.814909
         [,33]       [,34]     [,35]      [,36]     [,37]        [,38]
[1,]  8.493528  0.69726638 -2.793107 -5.5463512 1.5968198  1.120505417
[2,] 14.881545  0.67883389 -1.066539 -0.7904754 0.7881829 -1.393462199
[3,]  1.369374  0.04299614  2.104279  2.3130399 0.1004095 -0.008649157
[4,]  1.619289 -0.21330197 -2.200302  6.2515668 0.7468363 -0.311324760
         [,39]     [,40]      [,41]      [,42]      [,43]       [,44]
[1,] 0.9747461 1.3935712  0.6351459  0.5345756 -6.2363677 0.737447715
[2,] 1.4124211 1.3547306  4.8429789 -0.3854967 -0.8666196 0.043082778
[3,] 0.1007951 0.1050633 -3.7642462  0.0192171 -9.3586181 0.009281951
[4,] 0.8103193 0.8071638 -1.0538311  0.2553783  3.2403313 0.026022000
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[4,] -1.3971819 -1.08568373 -0.05440328 -0.7078497 -0.1193886  4.623623
          [,51]      [,52]      [,53]       [,54]      [,55]      [,56]
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[4,] -0.1910981 1.56255952 -0.5766839  0.26980861  0.6802437 -1.2573150
         [,57]      [,58]     [,59]      [,60]      [,61]      [,62]     [,63]
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[4,] 0.3866469 -0.2645805  1.021891  0.3212598 -0.9354468  1.7864713  2.859762
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[1,] 0.2530175 -1.2514119  0.9796685 -0.1116582  9.744508  0.3847999
[2,] 0.5038803  5.2862629  3.4235546  0.6250464 -1.771537  1.1700264
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[4,] 0.5072427 -0.9449814  1.1418851  0.9997203 -5.362710  1.0559882
           [,70]      [,71]     [,72]      [,73]       [,74]      [,75]
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[4,]  0.59565528  0.7093769 -0.452247 -0.2585190  0.11859215   1.568300
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[4,] -0.3469584 -1.893197  2.2949434 -0.0821510 -4.733388   7.655913
           [,82]      [,83]      [,84]      [,85]        [,86]      [,87]
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         [,88]       [,89]      [,90]      [,91]       [,92]      [,93]
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[2,] -1.245073 -0.49334842  9.6627685 -0.8994644 -0.02423174  2.9381636
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[4,]  0.196631  0.06487329 -5.5951653 -9.1627541 -2.70225428 -0.4748514
          [,94]       [,95]      [,96]      [,97]       [,98]       [,99]
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[4,]  1.3171884  1.23855412  0.3371006 -0.9659246  0.01828764 -0.08474006
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[4,] -0.3745116 -0.68929323 -0.3342143 -0.6504836 -0.31945255 -0.06863823
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[2,] -1.0619003 -0.3410646 -0.3745717 0.5954719  0.59794948  4.509296
[3,] -0.9923313  1.3099222 -0.6701193 0.1837141 -0.05884855  5.998686
[4,]  1.0513580  0.6206616  0.1915034 0.8971292  0.73677516 -5.246471
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[4,] -0.06563066 -1.5166441  2.270269 -0.3186689 -2.0118166   4.4636243
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[3,] -0.03478515  0.04475280 -11.130531  0.3741669 -5.099903 3.3452380
[4,] -0.52959527  0.01041518   7.108176 -0.1940708  4.893675 1.2652214
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[2,]  0.04797426 -0.14757219 -0.8014498 -0.1946376 -1.6406405 3.5664931
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[4,]  0.47695946 -0.77537988 -0.1696801  1.2250290 -0.9994147 2.2820173
         [,136]     [,137]    [,138]      [,139]      [,140]     [,141]
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[2,]  0.3852167 -0.2015313  6.501022 -0.35194450 -0.59022531 -0.7064026
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[4,]  0.2344372  1.7720988 -5.708958  0.02061829 -0.29063243 -0.9554731
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[2,]  1.7677185   1.936694 0.4468307  0.2130476  5.505012  3.003573
[3,] -0.1641572 -15.728460 0.1221881  2.1767536 -2.031860 11.660397
[4,]  0.3485765  -3.090814 0.4546928 -2.4170440 -5.531715 -1.235070
            [,148]      [,149]     [,150]     [,151]    [,152]    [,153]
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[2,] -1.2928954592 -1.04225292 -3.0061732 0.04004751 -2.745216  8.507963
[3,] -0.0006344918  0.02689282 -2.8036460 0.04421732 -2.767616  2.512105
[4,] -0.2926513479 -0.10903706  0.7050242 1.40461152  6.562276 -9.472032
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[4,] -0.5284731  0.02257257 -0.6345777  0.5542318 -0.07815602 -0.026738009
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[2,]  0.6215332  0.06694397 -7.826999  0.2094318 -0.004138903 -6.1601878
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[4,] -2.5701570 -0.11895033  1.977550 -2.6920789  0.302706627  0.7826809
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[2,]  0.2212872 12.346647 -0.54876770  0.1598152  0.2741587 -0.1945037
[3,] -0.3193088  3.634918 -0.01786128 -0.2553364 -0.5480248  0.2714130
[4,]  0.2209888 -9.504512  0.06607624  0.2202200  0.7034919 -0.1464751
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[1,]  0.3865805 -5.105255 -4.420669  0.02829847  0.2679759 -5.283990
[2,]  0.2351965  1.543205  2.050819  0.08835509  0.5767360 -5.599163
[3,] -0.8287647 -3.350893 -6.862284 -0.02490271  0.2292948 -2.515816
[4,]  0.1194419  6.216775  4.693494  0.10494522 -0.2795247  1.768616
            [,178]    [,179]    [,180]      [,181]     [,182]     [,183]
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[2,] -0.0438312702 -1.573166 -6.034951 -0.14162929 -0.3993569 -0.1442528
[3,] -0.2359328219  2.090008 -4.294345  0.38716949 -0.1268802 -0.2772726
[4,]  0.1166864548  1.253086  2.709626  0.10228510 -0.1164226  0.5877431
        [,184]    [,185]     [,186]     [,187]       [,188]     [,189]
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[3,] -4.351030  7.517607  0.3223809 -3.1940149  0.078243609  0.3758971
[4,]  5.932987 -6.029825  0.3620508  1.9159852 -0.289866090  4.3771679
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[4,]  0.35058084 -6.294771  0.06117796  0.21441225 -0.7518820  0.2377942
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[3,] -2.4657161 -6.215188  1.215413 -0.338609469 -0.5338004 0.07543457
[4,]  0.2507928  7.852107 -1.891885 -0.047316632 -1.7853419 0.16041107
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[4,]  0.05274529 0.299971297  0.29555600  0.3162371 -0.2994830  0.5708198
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[3,]  4.285441 -0.53061635 -0.7837003 -0.3988848  2.4721350  1.8461280
[4,]  4.713031  0.02482877 -2.7536131  0.1576993 -0.3685025 -0.6576425
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[3,] 2.0238066  0.06322667 -0.23180574   0.4964715 -0.08390705  0.20063593
[4,] 0.2911071 -0.01921089  0.01926741   9.6363738  0.07666438 -0.10993404
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[4,] -0.52427848  0.29365936  0.029018937 -1.15605785  0.18003104  0.8737349
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[3,] -0.903958 -0.0235565  1.0967534  3.413293 -2.904179 -1.0947824  4.6767512
[4,]  5.262425 -0.1655622  1.0575497  5.582925  1.014182  1.1996240 -0.9464489
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[4,]  0.15876365  0.24785672 -18.2957974  0.8974788 -1.1881349  0.6221749
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[4,] -0.03302154  0.09941356 -0.3711448  1.431691  0.1988567  0.1648486
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[4,] -0.3943831  0.03501004  0.07864066  0.5294075 -1.4223032 -1.0308739
         [,251]      [,252]        [,253]     [,254]      [,255]      [,256]
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[4,] -0.1069152  0.20419842 -0.3428492012  0.6949156  0.24719014  0.09659789
        [,257]    [,258]      [,259]     [,260]     [,261]      [,262]
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[4,] -2.142980 -2.343431  0.03214290  0.6165053  0.1242996 -0.04148507
          [,263]    [,264]      [,265]   [,266]     [,267]     [,268]
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[3,]  0.13639849  1.875104  0.02150507 4.582296 -2.1983197  0.7761626
[4,]  0.08523442 -2.893088  0.04367101 1.665810  0.7494496 -0.8699663
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[4,] -1.2363655  0.1403713  1.0967245 -1.8113807 -0.2198579  1.8398176
         [,275]    [,276]     [,277]      [,278]    [,279]      [,280]
[1,]   1.634522 -3.892629  5.0008037  -6.8946284 -0.371597 -0.02296905
[2,]   3.389565 -4.602419  1.2305113  -0.6294633 -1.112854 -0.01642999
[3,]   6.901726 -2.290929  0.9568969 -17.4031281 -1.630853 -0.10021831
[4,] -10.442210  8.952386 -3.9395012  11.8214882  1.267865 -0.04341289
          [,281]    [,282]      [,283]      [,284]     [,285]     [,286]
[1,] -0.03851694 2.5958794 -1.22830172 -0.32228583  1.2521146 -0.1473589
[2,] -1.15454514 1.9253520 -0.01857098  0.15212691  0.3149033  0.8480724
[3,]  0.63026100 2.9364902 -1.11126400 -0.31601859 -0.1144009 -0.6943409
[4,] -0.19694337 0.1488316  1.15139465 -0.02847456  0.3842912  1.4272011
           [,287]      [,288]     [,289]      [,290]      [,291]     [,292]
[1,] -0.076288035  0.21824599  5.4640108  0.25455504 -0.05780221 -0.7676852
[2,] -0.062870907 -0.27568239  3.5805106  0.22776609  0.10873047  0.2930633
[3,]  0.002637296  0.55562318 -3.8160784 -0.08101995  0.22090985  0.3629601
[4,]  0.005088722 -0.03081736 -0.6245035 -0.15580638  0.33039972 -0.1231762
          [,293]      [,294]      [,295]     [,296]      [,297]    [,298]
[1,] 2.059135108 -0.38278041 -4.26634915 -0.2707477  0.04494173  1.541416
[2,] 0.005256263  0.22342984  0.01118074 -0.1529523  0.28439098  6.520740
[3,] 3.020708986 -0.34663682 -1.42050244 -0.3923273 -0.13385456 11.216607
[4,] 1.327066139  0.01757447 -1.22442600  0.4725513  0.01265407 -1.878904
        [,299]     [,300]
[1,]  1.615199 -0.2229319
[2,] -3.222105 -0.0306271
[3,] 11.670904 -0.2259986
[4,] -7.208818 -0.2825762

$F
          [,1]      [,2]        [,3]      [,4]      [,5]      [,6]      [,7]
[1,] -2.079379 -1.858700 -0.62254812 -2.008619  5.683756 -1.302857  6.293958
[2,] -3.240444 -2.491305  0.04080108 -1.210173 -2.348727  3.212495 10.202216
[3,] -3.062020 -1.645077  0.23505784 -2.143453 -0.143809  1.394338 -2.128206
[4,]  2.060501  1.843819  0.49831231  1.812534 -1.212826 -1.390965 -9.783532
           [,8]        [,9]     [,10]     [,11]      [,12]      [,13]     [,14]
[1,]  2.2793299 -0.08023177 -7.959624 -1.181567 -0.2401349 -3.7622834 -4.212661
[2,]  0.8615443  1.52586846  5.410483  4.901174  0.7687708 -5.4541163  6.406408
[3,]  1.5596396  0.93537643 -2.874079 -3.812242  0.0323003 -3.9855473  9.450337
[4,] -0.1660043 -0.07825065  5.524377 -3.943065  0.7909295  0.7250558 -2.880223
           [,15]       [,16]      [,17]      [,18]      [,19]      [,20]
[1,] -0.94425053 -2.85319101  0.7455762  0.8067992 -0.6977944  0.1466359
[2,] -1.13919089  0.07916122 -5.9038471 -0.3448257  0.1914822 -0.8679663
[3,] -0.04086799 -1.92008283 -4.0403686  0.2019000 -2.3341490  0.3624113
[4,] -0.97605385  1.04136990 -1.1840889  0.7685866  2.9106685  0.9695983
           [,21]       [,22]      [,23]     [,24]      [,25]       [,26]
[1,] -13.8247847 -0.04979895  -7.159364  3.866639  1.5210823  0.04183964
[2,]  -7.2240606  1.02836589   7.655521 -3.875245  0.5155647  4.40799351
[3,]  -9.1166200  0.22968224 -11.902869  8.259694 -0.4330351 -0.47543336
[4,]  -0.7720336 -3.09250186   9.672086 -2.422301  0.3481333 -0.73439568
          [,27]      [,28]     [,29]      [,30]     [,31]      [,32]     [,33]
[1,] 0.91273789 -12.198614 -3.299228  1.9128743 1.2835836 -14.330778  8.499914
[2,] 0.45430811  -5.018947 -5.753257  6.6722049 0.2278935  12.699582 15.906430
[3,] 0.02375847  -4.196162 -1.627932  0.9047582 0.6402336  -1.373244  1.233172
[4,] 0.76753698   6.507800  1.235364 -2.5848805 0.2556617  -5.564888  2.092564
           [,34]      [,35]     [,36]      [,37]        [,38]      [,39]
[1,]  0.77197684 -3.0106819 -5.977294 1.65641177  1.247013673 0.98598086
[2,]  0.76376404 -0.9676194 -1.021638 0.78567824 -1.510530163 1.46449142
[3,]  0.04865162  2.0625919  2.548534 0.07600542 -0.003564713 0.08495556
[4,] -0.19957431 -2.0811329  5.645582 0.76290802 -0.304374779 0.81769015
          [,40]      [,41]       [,42]      [,43]       [,44]      [,45]
[1,] 1.43734402  0.5659379  0.56029637 -6.9450329 0.798590109  0.2642128
[2,] 1.41409603  4.9244359 -0.45247948 -0.8250954 0.042384277 -1.4922297
[3,] 0.08851684 -4.0403504  0.01423001 -9.4400078 0.006575504 -0.6874025
[4,] 0.81441002 -0.6869143  0.25409742  2.8793840 0.032599107 -1.4048056
           [,46]       [,47]      [,48]      [,49]      [,50]      [,51]
[1,] -0.50047668  0.24823374 -1.4801982  0.4836263  -1.419972 -2.1288298
[2,]  0.02444091 -0.82626516  0.2811404 -0.8979323 -11.335458  0.8218316
[3,] -0.03747289 -0.72101811  0.3121630  0.2524579  -4.807765 -0.3599407
[4,] -1.06587944 -0.08061799 -0.6640870 -0.1161904   4.226890 -0.3189151
          [,52]      [,53]      [,54]      [,55]      [,56]     [,57]
[1,] 0.49991231 -1.6145165  1.5149293  1.4468566 -0.4492884 1.3967534
[2,] 1.24279177  2.3719797 -1.2224484 -0.3341234 -0.7686764 0.6156285
[3,] 0.08289187 -5.6329652  0.0459812 -0.5786308  0.2093301 0.0773588
[4,] 1.53313380 -0.2992093  0.2869338  0.6589280 -1.2438830 0.4231616
          [,58]     [,59]      [,60]      [,61]      [,62]     [,63]     [,64]
[1,]  1.0265038  4.890762 -0.4574150 -1.3865895  1.0824237 -8.176542 0.2530490
[2,]  0.2310469 -4.605563  0.2425841 -0.3455196  1.5955452 -5.874458 0.4990109
[3,]  0.2822078 -4.047068 -0.9835989  1.1654563 -0.3188345 -6.167962 0.1795701
[4,] -0.2488288  1.054614  0.2528118 -1.0045771  1.8026131  2.792002 0.4957507
          [,65]     [,66]        [,67]      [,68]      [,69]       [,70]
[1,] -0.6076742  1.054093 -0.211278942 11.5372296  0.3366083 -0.14569967
[2,]  6.3968658  3.749160  0.592865936 -0.9666373  1.1865760 -0.40706196
[3,] -3.4340694 -2.079538 -0.003565849  6.0162518 -0.7257132  0.01415294
[4,] -1.3882039  1.095746  0.988124686 -5.5089195  1.0468968  0.58444136
           [,71]      [,72]      [,73]       [,74]      [,75]      [,76]
[1,]   0.6929131  7.3252036 -0.9226676 -0.21063079  -2.194481 -0.4040209
[2,]  -3.8703221 -5.8742873  0.1431656 -0.99243001   8.227956 -0.9527167
[3,] -10.1151797  2.6258616 -0.3486209  0.02505105 -10.736041 -0.5343946
[4,]   1.0685111 -0.5593926 -0.2588334  0.11235709   1.434104 -0.3338298
         [,77]      [,78]      [,79]     [,80]      [,81]      [,82]      [,83]
[1,]  2.401112 -3.4868633 -0.5611881  9.864725 -12.660229  0.2047228  2.8564157
[2,]  2.998171 -7.0766654  1.1589038  2.873479   5.290702 -2.9408663  2.6713794
[3,] -3.229029  0.5639286 -0.3684701  3.860815 -22.193955 -0.7140244  2.8864540
[4,] -1.836254  2.6294204 -0.0809761 -4.666965   7.164168 -1.5271413 -0.9705487
          [,84]      [,85]        [,86]      [,87]      [,88]       [,89]
[1,]  1.8039628 -0.5414019 -0.691827291 -0.9617135  1.2860148 -0.64274232
[2,]  0.5399109 -0.1116761 -0.303670743 -0.3275458 -1.3961027 -0.54221271
[3,] -0.1524073 -6.2872263  0.008520707 -0.1648010 -2.0735997 -0.42082207
[4,]  0.8220929 -4.8116911 -0.602284674 -3.9229155  0.1692642  0.05731314
          [,90]      [,91]      [,92]      [,93]      [,94]      [,95]
[1,]  5.4720553 22.5353945 -5.0240990  0.8976141  2.1822696  1.0292333
[2,] 11.3344056  0.2865392  0.2223940  3.2463787 -0.1973388  2.1724444
[3,]  0.3007436 17.6342545  0.8784498 -1.4832261 -0.3721301 -0.1127422
[4,] -5.5642685 -8.9997356 -2.5499301 -0.3796945  1.3025161  1.2344737
          [,96]      [,97]        [,98]      [,99]     [,100]    [,101]
[1,] -0.9594629 -1.4845573 -1.421510820 -0.7650769 -0.2924585  4.019645
[2,]  1.1439501 -0.7310517 -0.780542630  2.9714650 -1.4066916 -3.747215
[3,]  1.0260472  0.1744509 -0.648490507 -3.5235047 -0.0307104  2.089479
[4,]  0.4361586 -0.9807903 -0.007899529 -0.2172927 -0.5659789  1.816463
         [,102]     [,103]      [,104]     [,105]     [,106]     [,107]
[1,] -1.6758354 -0.3424630  0.46530403 1.51770565  1.1494816 -0.6745677
[2,] -0.4046692 -0.4643007 -0.20761289 1.47411132 -2.8627174 -0.7915707
[3,] -0.1176528 -0.9428390  0.66983536 0.04050827 -1.1142932 -0.0322175
[4,] -0.1998624  0.2946698  0.05585304 0.04272457 -0.3321008 -0.6847587
         [,108]     [,109]     [,110]       [,111]    [,112]     [,113]
[1,]  0.1256967  2.1243324 -0.2798886 -1.186977559 -3.640917  0.2107443
[2,] -0.4914122  4.1091740  1.5938155 -0.149735808 -1.320616 -0.2131572
[3,]  0.1311824  5.1724024 -0.0108569 -0.006350232 -1.065411  1.4771873
[4,] -0.3298034 -0.6115055 -0.3098138 -0.078575428  1.046336  0.4589977
         [,114]    [,115]      [,116]    [,117]      [,118]     [,119]
[1,]  0.2343400 1.4333774  0.76849646 -2.139276  0.01382430 -2.3417185
[2,] -0.4329098 0.5630588  0.58585878  5.795180  0.33912186 -0.2265669
[3,] -0.6927580 0.1709062 -0.07657899  6.627256  1.52061852  2.1706030
[4,]  0.1790395 0.8973445  0.73442147 -5.687011 -0.02960262 -1.6093992
         [,120]     [,121]      [,122]     [,123]      [,124]      [,125]
[1,]  1.4637094  0.2940065 -2.17626884  -0.884519 -0.45201187  1.54174318
[2,] -4.1566311 -1.6078735 -3.83590282 -17.780466 -0.83687414 -0.33948303
[3,]  0.1482615  0.6114564 -0.06450526 -14.595260 -0.02222465  0.03706131
[4,]  2.2917834 -0.2639920 -2.02430761   4.292402 -0.53086936  0.03715965
         [,126]     [,127]    [,128]    [,129]      [,130]      [,131]
[1,]  -6.364862  0.2193561  2.376214 2.5337555  1.52397145 -0.51521394
[2,]   2.082292  1.1731547 -6.177091 0.5035693 -0.01200734 -0.08393809
[3,] -11.396020  0.3691828 -5.517957 3.3893092 -0.11531164 -0.02862661
[4,]   6.808334 -0.2160641  4.972010 1.2250595  0.49179073 -0.76982165
         [,132]     [,133]     [,134]    [,135]     [,136]     [,137]    [,138]
[1,]  1.0634838  0.9703122  0.5665215 2.9862023  0.2656437  5.1403031 -2.198956
[2,] -0.8298364 -0.3401150 -1.7508478 3.5823890  0.3559689 -0.3043139  8.125640
[3,]  0.7991334 -0.3588963 -0.3787061 0.1595422 -1.1577864 -8.9815198 15.375785
[4,] -0.2297657  1.2153696 -0.9757022 2.3389648  0.3235708  1.8286965 -5.732127
          [,139]      [,140]     [,141]     [,142]     [,143]    [,144]
[1,] -0.19201254  0.48519642 -0.2786684 -2.5791170   3.133383 0.7886495
[2,] -0.38725513 -0.62387331 -0.7025929  1.8469305   2.324374 0.4216722
[3,]  0.07525996 -0.01636605  0.1760149 -0.2082856 -16.214911 0.1093099
[4,]  0.01492591 -0.28535623 -0.9475275  0.3947479  -2.895100 0.4654901
         [,145]    [,146]    [,147]      [,148]      [,149]     [,150]
[1,]  2.3698737  1.559372  7.915748  0.10924893  0.61946442 -2.5595584
[2,]  0.5290716  6.553783  3.365892 -1.36489512 -1.14266465 -3.3443494
[3,]  2.3322274 -1.981390 11.774709  0.01608369  0.01208065 -2.8324588
[4,] -2.4482409 -5.388935 -1.138637 -0.32095092 -0.10043345  0.6243068
        [,151]    [,152]    [,153]     [,154]      [,155]     [,156]     [,157]
[1,] 0.7811789 -3.664219 12.870868  0.7781092  0.28973115 -5.4018277  0.8158602
[2,] 0.0537166 -4.252331 10.354007  1.0808203  0.88699260  0.2438760 -1.3749646
[3,] 0.1294912 -2.668351  2.799994  0.2718747 -0.74039241 -0.7948133  2.3993507
[4,] 1.2458892  6.585385 -9.272913 -0.4936209  0.02873219 -0.5731902  0.4482504
          [,158]       [,159]     [,160]      [,161]     [,162]     [,163]
[1,] -0.57699804  0.335145362 -7.8189362  0.38995783 11.8927641  1.8631338
[2,] -0.15121444  0.007150149  0.7775884  0.08522678 -8.9149181  0.3174526
[3,] -0.22561994  0.164300482  6.1623599  0.12112663 -0.5557032 -1.1787927
[4,] -0.08422933 -0.022823656 -2.4160025 -0.11145887  2.1546139 -2.3672790
           [,164]     [,165]     [,166]    [,167]      [,168]     [,169]
[1,]  0.002847604 -1.7488096  0.1317313 11.839824 -0.12846645 -0.2843076
[2,] -0.038494920 -7.2633103  0.2326381 14.250659 -0.61834444  0.1566451
[3,]  0.010550618 -9.0308118 -0.3386772  3.921041 -0.02812930 -0.2685209
[4,]  0.298266324  0.9529002  0.2182855 -9.162690  0.07368999  0.2188717
         [,170]     [,171]     [,172]     [,173]    [,174]      [,175]
[1,]  0.8893358 -0.1766681  0.3497966 -4.9962582 -4.537080  0.02613154
[2,]  0.1996601 -0.2288779  0.2207515  0.9953496  1.960787  0.08589252
[3,] -0.5700913  0.2642636 -0.8693808 -3.0937185 -6.917755 -0.02781657
[4,]  0.7211024 -0.1362630  0.1582602  5.5799145  4.236748  0.10291837
         [,176]    [,177]      [,178]    [,179]    [,180]      [,181]
[1,]  0.3112227 -6.171495 -0.01894459 -3.899677  1.133722  0.05337522
[2,]  0.6745264 -6.696444 -0.07222201 -1.771123 -6.868591 -0.15101493
[3,]  0.2455172 -2.606390 -0.24948616  2.199392 -4.449450  0.40536775
[4,] -0.2755342  1.902262  0.12425333  1.102800  2.542597  0.09233655
         [,182]     [,183]    [,184]    [,185]      [,186]    [,187]
[1,] -0.2669075 -0.4559516  3.521229  1.684367 -0.22774713 -5.023276
[2,] -0.3929275 -0.2218653  7.475125  2.040408 -0.02833401 -1.319406
[3,] -0.1255415 -0.2984617 -4.644261  7.634954  0.32982979 -3.363183
[4,] -0.1542237  0.5780569  5.845098 -5.821471  0.36020142  1.967773
          [,188]      [,189]      [,190]    [,191]      [,192]     [,193]
[1,]  0.03254878  -0.3244615 -0.31916095 14.682984 -0.88539157 -0.6338000
[2,] -0.28250081 -10.2932619  0.03521119 -4.414968  0.73380035  0.1265817
[3,]  0.08591816   0.4622446  0.10666421 10.057525 -1.05554439  0.2804675
[4,] -0.28708571   4.4354140  0.34240164 -5.912272  0.04337984  0.1376800
          [,194]     [,195]     [,196]    [,197]    [,198]      [,199]
[1,]  1.98857540 -0.5849043 -0.7486932 -5.263325  7.570257 -0.01079657
[2,] -0.07112064 -1.1225370  1.9483566 -4.010059  2.353568  0.05278586
[3,] -0.19715866  0.5482191 -2.4762750 -6.758120  1.353671 -0.33742753
[4,] -0.72251709  0.2761530  0.1055764  7.910364 -2.089944 -0.05365189
         [,200]     [,201]      [,202]      [,203]      [,204]     [,205]
[1,]  2.0069228 0.03160192 -0.13205574  0.25719500  0.08832129 -0.2549563
[2,] -0.9066009 0.10138394  1.11675665 -0.01897039  0.23529631 -0.6210105
[3,] -0.5532167 0.07423841  0.09750182  0.13123938 -0.08734587 -0.7467830
[4,] -1.7120558 0.15859969  0.05022449  0.29699349  0.29411555  0.3265183
           [,206]     [,207]    [,208]      [,209]     [,210]      [,211]
[1,]  0.348967113 -0.2839456 -9.179052 -0.21970769  1.7468265 -0.41419351
[2,]  0.002405623 -0.3541933 14.757867 -0.08536663  1.5949098  0.08395812
[3,]  0.374727935 -0.5896578  3.882068 -0.56939793 -0.8816562 -0.40158788
[4,] -0.372802864  0.5569996  5.231796  0.05136546 -2.6078461  0.13128536
         [,212]     [,213]    [,214]       [,215]      [,216]      [,217]
[1,] -0.2519822 -0.6242785 0.1435865 -0.039399685 -0.18034104  -1.5293105
[2,]  0.9785969 -2.4596274 0.5410564  0.119577636  0.05698361 -13.5239030
[3,]  2.4932847  1.9337801 2.1140390  0.060304506 -0.25301446   0.4736411
[4,] -0.2988279 -0.6778932 0.2410810 -0.009704426  0.04485995   9.0731218
          [,218]     [,219]      [,220]       [,221]      [,222]     [,223]
[1,] -0.02988142 -0.3493173 -0.20293747  0.196591131 -0.01347681 -0.7608548
[2,]  0.10871903  0.1144366  0.54421108 -0.007296075 -0.38003857  0.1045420
[3,] -0.08782626  0.2064237  0.01243081 -0.064595444  0.42940918  0.2937961
[4,]  0.07624227 -0.1118261 -0.51846369  0.291762031  0.03575014 -1.1824318
           [,224]     [,225]    [,226]      [,227]     [,228]    [,229]
[1,] -0.075429006 -1.5118052 -3.854208 -0.26280269  1.0516793 -3.939965
[2,]  0.001421691  3.7087456 -8.402187  0.20362008 -1.8945047 -7.881969
[3,]  0.060971988 -2.4043309 -0.854994 -0.02080657  1.1822634  3.515923
[4,]  0.176980457  0.8275283  4.983812 -0.16453369  0.9250927  5.636261
         [,230]     [,231]     [,232]      [,233]     [,234]     [,235]
[1,] -2.2402987 -1.0726653 -0.4532528  0.13463328 -0.4544935  -3.469524
[2,] -0.7684210 -0.1136234  9.1143612 -0.30991389 -0.1448021  -1.315694
[3,] -2.9296060 -1.1167469  4.8827137 -0.05600786 -0.1136723   1.156346
[4,]  0.9605697  1.1261191 -1.0103488  0.15570154  0.2452811 -18.561939
        [,236]     [,237]     [,238]      [,239]     [,240]     [,241]
[1,]  9.256882 -0.3847471 -0.7136205 -0.17733848 -0.2611219 -1.4291759
[2,] -3.173362  4.5758538 -0.3429140  0.31129534  0.2444883  0.5984306
[3,] -3.196605  2.0653738 -0.2963387  0.32598007 -0.1032691  0.4856699
[4,]  1.092119 -1.2154113  0.6080930 -0.03971586  0.1010662 -0.2375698
         [,242]     [,243]     [,244]     [,245]      [,246]      [,247]
[1,] -2.5881408 -0.4111574 -1.0951683  0.8217733  0.26057842 -0.41351167
[2,] -1.4199471  0.1538052 -0.2501078  0.4898319 -0.04872739  0.26125272
[3,]  0.4362167  0.1553756 -0.3349857 -0.8831941 -0.20648605 -0.27230633
[4,]  1.3719551  0.1933337  0.1536117 -0.3806564  0.03690936  0.08187983
         [,248]      [,249]     [,250]     [,251]      [,252]      [,253]
[1,] -0.1794440  0.04103958  3.4305628 -0.2477420 -0.80692477  0.30315882
[2,] -0.5058354 -2.10190012 -1.8740771  0.2436910 -0.08088637  0.03344578
[3,]  1.8072170  1.66652383 -0.7847028  0.1771691  0.29238539 -0.09194380
[4,]  0.4983873 -1.24749607 -1.0966066 -0.1002353  0.15517102 -0.33568030
          [,254]       [,255]      [,256]    [,257]    [,258]      [,259]
[1,] -0.46185583  0.003137974  0.07116313 -1.691283  5.972903 -0.15234893
[2,]  0.09676506 -0.426483578  0.04490750 -5.619089 -3.714062 -0.10747989
[3,]  0.43015859 -0.449200110 -0.19907114  5.047865  5.036192  0.05990592
[4,]  0.64938124  0.273974757  0.09600230 -1.975811 -2.295133  0.02964408
         [,260]     [,261]       [,262]      [,263]    [,264]      [,265]
[1,] -0.6292594  0.2372577  0.005267213 -0.02277421  4.430548 -0.27452670
[2,] -0.6259747 -0.3622081 -3.528541538  0.07441829  3.823584 -0.13094548
[3,] -0.2702032 -0.5033662 -1.756518401  0.13799346  2.004519  0.02245252
[4,]  0.5824394  0.1211875  0.061607725  0.08387188 -2.944922  0.04017425
       [,266]      [,267]     [,268]      [,269]     [,270]     [,271]
[1,] 2.120775 -0.93553847  0.3605565 -2.95206300 -1.5202647 -0.2677111
[2,] 5.892976  0.08541951 -0.8267109  1.81859536  0.3389082  4.0089266
[3,] 4.530707 -2.24591607  0.7903542 -0.09988427 -1.0007669  1.2173248
[4,] 1.746799  0.71976188 -0.8345355 -1.32156303  0.1837227  1.2103194
         [,272]     [,273]     [,274]     [,275]    [,276]     [,277]
[1,]  0.9567194  0.1494219 -1.4513051   2.432349 -4.892707  6.1537920
[2,] -1.2083172 -0.2788191  0.8020678   4.949095 -5.554425  1.9481638
[3,]  0.5412080 -0.5895605 -2.2657506   7.394292 -2.502538  0.7548296
[4,] -1.8503394 -0.1989938  1.7829544 -10.286079  8.596189 -3.9442765
         [,278]    [,279]      [,280]     [,281]    [,282]     [,283]
[1,]  -8.189883 -0.437340 -0.02127218 -0.1328459 2.6772987 -1.4603979
[2,]  -1.982364 -1.307912 -0.01361447 -1.2147628 2.0565078 -0.1500025
[3,] -17.958997 -1.653427 -0.10191558  0.6721365 2.8936022 -1.1575088
[4,]  11.494974  1.185342 -0.04305411 -0.1817856 0.2765123  1.1405383
          [,284]      [,285]     [,286]       [,287]       [,288]     [,289]
[1,] -0.37421677  1.20662764 -0.5558903 -0.083288209  0.205385316  6.1319898
[2,]  0.15376276  0.29689418  0.5273441 -0.068793932 -0.331384555  4.0439384
[3,] -0.33186306 -0.09144157 -0.8672674  0.003300142  0.560331156 -3.9849471
[4,] -0.01126842  0.42416731  1.6444213  0.003634927 -0.003849381 -0.5965251
          [,290]     [,291]     [,292]     [,293]      [,294]      [,295]
[1,]  0.25986742 -0.0968265 -0.7771251  2.0048424 -0.42285326 -4.98035828
[2,]  0.24203236  0.0868293  0.3511616 -0.1022964  0.23320929  0.08772802
[3,] -0.09575083  0.2207637  0.3850445  3.0179414 -0.35650689 -1.47117950
[4,] -0.12616087  0.3276536 -0.1511470  1.3748446  0.02192092 -1.04423380
         [,296]      [,297]    [,298]    [,299]       [,300]
[1,] -0.3005043  0.04565680  1.867738  1.679833 -0.217911697
[2,] -0.2829652  0.30653600  7.355011 -3.181493 -0.005424656
[3,] -0.4533766 -0.14364366 11.496291 11.807574 -0.225155595
[4,]  0.4892868  0.01889897 -1.806418 -6.638694 -0.280657440

$L
                [,1]          [,2]          [,3]         [,4]
  [1,] 1.173392e-140 1.945412e-158  9.965816e-01 0.0034183507
  [2,] 3.149551e-141 2.486287e-157  9.969523e-01 0.0030477223
  [3,] 5.528302e-142 2.602837e-157  9.951836e-01 0.0048163817
  [4,] 4.342502e-141 1.201572e-157  9.908740e-01 0.0091260203
  [5,] 2.294392e-141 9.430228e-158  9.957573e-01 0.0042427238
  [6,] 4.201006e-141 9.023143e-157  9.649802e-01 0.0350197845
  [7,] 3.925956e-140 2.475502e-157  9.697712e-01 0.0302287864
  [8,] 2.169193e-143 7.630602e-160  9.326488e-01 0.0673511683
  [9,] 7.960512e-143 4.285524e-157  9.351955e-01 0.0648045309
 [10,] 2.844758e-141 4.824077e-159  9.403878e-01 0.0596122441
 [11,] 2.304978e-143 1.128062e-157  9.293673e-01 0.0706326884
 [12,] 7.871436e-142 6.880171e-159  9.379170e-01 0.0620829714
 [13,] 1.635472e-143 2.238498e-158  9.241494e-01 0.0758505990
 [14,] 1.869949e-142 3.906052e-158  9.414410e-01 0.0585590486
 [15,] 2.013219e-145 5.865572e-160  9.102028e-01 0.0897971686
 [16,] 9.860402e-147 6.254783e-157  8.807416e-01 0.1192584126
 [17,] 1.868314e-147 5.711856e-158  8.832769e-01 0.1167231012
 [18,] 8.315049e-153 1.159346e-168  8.292472e-01 0.1707528283
 [19,] 5.157676e-150 4.062941e-167  8.493666e-01 0.1506334285
 [20,] 2.381236e-153 1.099191e-161  8.282619e-01 0.1717381323
 [21,] 5.101846e-151 4.188472e-165  8.501370e-01 0.1498630265
 [22,] 6.024154e-162 1.245982e-165  7.954577e-01 0.2045422620
 [23,] 2.395103e-158 3.148025e-169  8.062202e-01 0.1937797584
 [24,] 3.146563e-152 4.262310e-171  7.883475e-01 0.2116524652
 [25,] 4.495461e-166 1.041454e-172  7.729835e-01 0.2270164787
 [26,] 3.524270e-161 1.403026e-171  7.917507e-01 0.2082492566
 [27,] 2.712162e-164 5.446921e-177  7.547733e-01 0.2452267155
 [28,] 5.836169e-161 1.358678e-173  7.818289e-01 0.2181711499
 [29,] 1.439915e-169 5.562451e-172  7.543177e-01 0.2456823446
 [30,] 3.590537e-167 2.499431e-176  7.364751e-01 0.2635249101
 [31,] 1.049855e-171 8.161750e-178  7.574421e-01 0.2425578729
 [32,] 6.131639e-179 5.200425e-179  7.109897e-01 0.2890102529
 [33,] 1.740350e-187 1.066666e-181  6.912343e-01 0.3087657376
 [34,] 1.846667e-188 1.519632e-190  6.760390e-01 0.3239609981
 [35,] 7.329719e-184 2.101021e-194  6.779114e-01 0.3220886001
 [36,] 4.232626e-188 6.047714e-196  6.797561e-01 0.3202439002
 [37,] 5.059048e-192 1.150882e-194  6.679192e-01 0.3320807688
 [38,] 1.056249e-199 2.202737e-182  6.478102e-01 0.3521898293
 [39,] 2.168712e-196 1.754412e-194  6.429339e-01 0.3570660622
 [40,] 4.272099e-202 3.530347e-204  6.283070e-01 0.3716929728
 [41,] 9.307304e-202 6.742274e-202  6.367739e-01 0.3632261272
 [42,] 5.223034e-207 3.662579e-202  6.181454e-01 0.3818546424
 [43,] 8.538169e-205 8.055327e-209  6.106798e-01 0.3893201883
 [44,] 3.530179e-223 2.021512e-212  5.645793e-01 0.4354206787
 [45,] 2.268455e-219 1.873417e-211  5.712877e-01 0.4287122513
 [46,] 6.042820e-218 1.093770e-218  5.607248e-01 0.4392751679
 [47,] 1.629941e-222 1.634458e-213  5.792495e-01 0.4207504815
 [48,] 1.835173e-198 1.800875e-219  5.374294e-01 0.4625706225
 [49,] 2.779989e-193 2.718100e-213  5.283154e-01 0.4716845506
 [50,] 5.430951e-191 1.607320e-205  5.178622e-01 0.4821378010
 [51,] 2.958290e-190 5.236210e-214  5.287607e-01 0.4712393369
 [52,] 4.706409e-196 6.638827e-210  5.242336e-01 0.4757663825
 [53,] 2.257287e-174 7.927531e-191  4.992040e-01 0.5007959697
 [54,] 4.001831e-152 9.487702e-170  4.695843e-01 0.5304156601
 [55,] 2.302441e-161 2.268867e-175  4.778094e-01 0.5221906091
 [56,] 3.848539e-157 1.747720e-172  4.732523e-01 0.5267477014
 [57,] 2.311045e-151 6.609750e-167  4.659986e-01 0.5340014251
 [58,] 1.835077e-139 1.426991e-152  4.445087e-01 0.5554913378
 [59,] 1.809005e-133 1.643337e-147  4.369113e-01 0.5630886576
 [60,] 3.886758e-131 7.064944e-148  4.380384e-01 0.5619616244
 [61,] 2.240458e-115 2.977365e-130  4.101348e-01 0.5898651922
 [62,] 7.389162e-103 5.396679e-117  3.869024e-01 0.6130975543
 [63,]  3.397337e-86  3.013920e-96  3.495520e-01 0.6504480367
 [64,] 1.209264e-108 8.163993e-116  3.856206e-01 0.6143793874
 [65,]  1.015365e-94 3.737250e-107  3.701653e-01 0.6298346683
 [66,]  1.514079e-92 7.616666e-105  3.667750e-01 0.6332249923
 [67,]  4.105524e-85  5.662482e-98  3.533022e-01 0.6466977549
 [68,]  1.507441e-82  4.734419e-90  3.367133e-01 0.6632867480
 [69,]  1.908799e-63  5.394670e-75  3.071179e-01 0.6928821401
 [70,]  1.110839e-61  4.695326e-69  2.944260e-01 0.7055739689
 [71,]  4.436233e-62  9.088722e-69  2.941611e-01 0.7058389145
 [72,]  8.933038e-52  2.129773e-63  2.812227e-01 0.7187772719
 [73,]  5.398805e-58  6.477355e-66  2.866679e-01 0.7133320868
 [74,]  2.988431e-42  1.178764e-47  2.396591e-01 0.7603409315
 [75,]  2.917544e-47  6.361564e-55  2.590848e-01 0.7409152022
 [76,]  9.750500e-43  7.691160e-48  2.409220e-01 0.7590779621
 [77,]  7.740834e-58  5.212753e-64  2.823195e-01 0.7176805147
 [78,]  6.146376e-37  5.127445e-40  2.199871e-01 0.7800128948
 [79,]  7.524560e-34  7.743275e-36  2.079818e-01 0.7920182458
 [80,]  1.149330e-35  1.197809e-41  2.235214e-01 0.7764786296
 [81,]  1.163993e-38  3.308322e-42  2.248801e-01 0.7751199169
 [82,]  3.214933e-24  2.190886e-26  1.716501e-01 0.8283498980
 [83,]  1.218822e-20  6.746241e-28  1.774439e-01 0.8225560692
 [84,]  4.197920e-22  1.839561e-26  1.732832e-01 0.8267168080
 [85,]  2.443781e-20  7.049312e-24  1.618375e-01 0.8381625176
 [86,]  1.421775e-16  5.412970e-18  1.354976e-01 0.8645023606
 [87,]  2.551397e-14  4.637041e-17  1.323178e-01 0.8676821983
 [88,]  2.193684e-16  1.627002e-20  1.473860e-01 0.8526140234
 [89,]  1.190165e-14  2.068912e-16  1.326706e-01 0.8673294363
 [90,]  8.995207e-08  3.659447e-09  8.659579e-02 0.9134041177
 [91,]  1.809891e-07  4.145290e-11  9.321570e-02 0.9067841202
 [92,]  6.724434e-06  4.366358e-07  7.096607e-02 0.9290267729
 [93,]  1.875728e-07  9.606614e-08  7.614621e-02 0.9238535016
 [94,]  7.338084e-07  1.345095e-08  8.205688e-02 0.9179423679
 [95,]  9.726068e-04  8.134415e-04  2.062988e-02 0.9775840726
 [96,]  1.659178e-02  7.231258e-04  5.373428e-03 0.9773116615
 [97,]  1.973119e-02  5.685890e-04  5.154685e-03 0.9745455344
 [98,]  3.748785e-03  1.569140e-03  1.888297e-03 0.9927937779
 [99,]  9.411757e-04  9.023709e-04  5.985129e-03 0.9921713248
[100,]  1.716394e-02  1.194348e-03  8.088769e-04 0.9808328315
[101,] 1.580961e-158  9.962148e-01 1.038533e-157 0.0037851838
[102,] 2.471873e-158  9.876558e-01 5.786187e-157 0.0123442282
[103,] 1.090725e-158  9.958595e-01 5.169374e-158 0.0041404726
[104,] 2.085052e-158  9.604953e-01 1.009051e-157 0.0395047092
[105,] 1.204179e-158  9.722467e-01 6.693165e-158 0.0277532762
[106,] 1.462101e-157  9.606641e-01 1.477574e-157 0.0393358851
[107,] 7.236945e-159  9.589459e-01 4.032974e-157 0.0410541375
[108,] 1.340781e-161  9.270322e-01 4.770024e-159 0.0729677825
[109,] 1.472497e-159  9.203642e-01 1.338417e-158 0.0796358202
[110,] 9.632710e-158  9.137123e-01 8.862448e-157 0.0862876559
[111,] 2.129845e-162  9.052251e-01 3.283387e-161 0.0947749470
[112,] 3.849539e-158  9.037467e-01 1.940378e-157 0.0962532847
[113,] 5.188877e-158  9.111869e-01 3.531719e-158 0.0888130588
[114,] 9.109164e-165  8.639981e-01 8.811558e-162 0.1360019392
[115,] 3.415665e-167  8.523682e-01 1.169292e-162 0.1476317772
[116,] 3.938969e-161  8.849663e-01 2.336972e-159 0.1150337086
[117,] 1.180244e-164  8.495743e-01 3.479801e-164 0.1504256520
[118,] 3.244623e-170  8.167431e-01 1.224154e-164 0.1832569225
[119,] 2.742792e-175  8.291955e-01 5.825830e-168 0.1708044810
[120,] 1.988432e-172  7.895078e-01 3.671281e-167 0.2104922367
[121,] 1.990644e-174  7.968482e-01 3.848718e-166 0.2031518103
[122,] 6.630466e-174  8.058223e-01 1.778080e-173 0.1941777479
[123,] 8.345195e-170  7.944036e-01 2.191337e-165 0.2055964151
[124,] 1.968451e-177  7.592600e-01 1.380454e-176 0.2407399978
[125,] 1.567742e-179  7.713130e-01 6.345692e-171 0.2286870472
[126,] 4.968506e-176  7.457498e-01 1.427185e-175 0.2542501980
[127,] 4.908552e-191  7.086551e-01 3.887160e-179 0.2913448816
[128,] 1.557274e-180  7.411980e-01 7.190440e-177 0.2588019896
[129,] 1.128983e-190  7.228248e-01 2.611904e-180 0.2771751677
[130,] 9.250418e-203  6.700980e-01 2.087813e-196 0.3299020279
[131,] 4.714191e-194  6.937855e-01 5.850549e-186 0.3062145135
[132,] 1.174106e-191  6.955890e-01 8.805725e-185 0.3044110397
[133,] 1.076346e-184  7.109828e-01 8.631719e-181 0.2890172180
[134,] 6.437719e-205  6.605078e-01 1.040805e-192 0.3394921986
[135,] 5.325876e-214  6.315195e-01 3.606975e-202 0.3684804772
[136,] 2.644987e-202  6.471522e-01 3.804576e-186 0.3528478445
[137,] 4.851000e-216  6.447338e-01 3.659038e-196 0.3552661524
[138,] 2.262328e-214  6.276497e-01 1.156379e-203 0.3723502624
[139,] 1.161395e-217  6.324675e-01 1.344725e-205 0.3675324734
[140,] 5.643974e-226  5.757295e-01 7.033415e-214 0.4242704785
[141,] 1.478743e-212  6.305294e-01 1.793627e-200 0.3694705557
[142,] 1.188554e-222  6.033256e-01 3.807991e-210 0.3966744121
[143,] 3.302119e-220  5.927791e-01 1.537970e-207 0.4072208705
[144,] 5.989998e-234  5.713439e-01 2.147060e-221 0.4286561452
[145,] 2.251946e-235  5.491042e-01 3.832654e-216 0.4508957926
[146,] 9.359165e-240  5.423085e-01 1.381878e-231 0.4576914832
[147,] 1.324886e-235  5.474128e-01 2.621540e-222 0.4525872468
[148,] 2.799568e-266  4.960573e-01 1.007087e-224 0.5039426540
[149,] 1.267685e-255  5.133464e-01 3.879153e-234 0.4866535516
[150,] 2.754869e-247  5.109259e-01 6.747899e-229 0.4890741226
[151,] 6.748352e-256  4.962461e-01 7.859861e-234 0.5037538510
[152,] 9.398659e-249  4.704855e-01 1.703475e-248 0.5295145174
[153,] 9.951775e-244  4.663186e-01 9.775463e-241 0.5336813821
[154,] 4.514363e-236  4.581513e-01 6.167167e-238 0.5418487186
[155,] 3.043917e-228  4.508220e-01 3.260345e-230 0.5491780243
[156,] 4.291143e-259  4.806190e-01 6.337625e-234 0.5193809943
[157,] 2.062324e-201  4.225438e-01 4.481658e-203 0.5774561746
[158,] 3.824562e-184  4.038709e-01 3.282315e-186 0.5961290736
[159,] 1.238505e-180  3.995701e-01 4.864830e-182 0.6004298627
[160,] 8.195499e-190  4.101606e-01 1.100777e-191 0.5898393912
[161,] 3.251185e-173  3.916810e-01 7.915123e-175 0.6083189857
[162,] 1.774035e-178  3.981904e-01 1.488397e-180 0.6018096156
[163,] 1.141578e-147  3.606847e-01 5.247425e-149 0.6393152908
[164,] 1.037897e-168  3.862840e-01 3.615028e-170 0.6137160261
[165,] 2.328655e-133  3.425733e-01 7.668482e-135 0.6574266868
[166,] 1.096058e-138  3.494886e-01 3.092711e-140 0.6505113898
[167,] 5.058558e-130  3.373982e-01 8.700753e-131 0.6626018019
[168,] 9.807758e-122  3.270856e-01 4.675471e-123 0.6729144013
[169,]  2.608179e-93  2.854103e-01  5.779381e-95 0.7145896760
[170,] 8.977093e-102  2.978646e-01 7.691977e-103 0.7021353829
[171,]  6.217969e-93  2.848552e-01  8.740671e-95 0.7151447946
[172,]  8.556706e-89  2.775064e-01  1.369734e-89 0.7224936260
[173,]  4.884138e-83  2.671058e-01  1.091890e-83 0.7328942452
[174,]  2.329371e-74  2.540982e-01  4.238457e-76 0.7459018444
[175,] 5.823041e-101  2.966825e-01 2.060008e-102 0.7033174942
[176,]  4.109827e-71  2.481142e-01  1.300518e-72 0.7518858248
[177,]  6.898536e-66  2.387990e-01  6.295445e-68 0.7612009973
[178,]  3.987053e-54  2.136100e-01  9.333895e-55 0.7863899853
[179,]  1.298529e-47  1.993260e-01  1.303381e-48 0.8006739635
[180,]  3.726578e-50  2.049345e-01  6.683388e-51 0.7950654720
[181,]  9.421897e-63  2.338590e-01  5.082913e-65 0.7661410266
[182,]  1.010860e-34  1.705163e-01  1.660281e-36 0.8294836775
[183,]  2.122485e-34  1.663121e-01  1.773249e-34 0.8336879157
[184,]  1.952133e-35  1.717646e-01  6.642991e-37 0.8282353825
[185,]  1.865698e-27  1.488289e-01  2.671188e-28 0.8511710879
[186,]  1.284381e-17  1.159402e-01  1.114490e-18 0.8840597870
[187,]  9.827012e-30  1.531518e-01  3.523434e-30 0.8468481616
[188,]  2.315053e-18  1.189673e-01  2.424034e-19 0.8810327220
[189,]  1.156258e-15  1.090655e-01  7.310541e-17 0.8909345448
[190,]  1.188679e-10  8.095910e-02  2.773455e-11 0.9190409000
[191,]  1.378494e-11  8.594473e-02  3.767148e-12 0.9140552730
[192,]  2.908645e-10  8.267010e-02  2.761939e-11 0.9173298952
[193,]  1.038275e-08  7.245046e-02  2.862640e-09 0.9275495269
[194,]  3.121959e-06  5.764797e-02  1.425431e-06 0.9423474844
[195,]  2.299924e-07  5.686548e-02  2.954287e-07 0.9431339907
[196,]  4.193447e-03  1.404311e-02  7.472010e-03 0.9742914334
[197,]  2.107454e-03  8.504624e-03  7.603314e-04 0.9886275908
[198,]  9.360564e-03  6.886834e-03  3.727169e-03 0.9800254334
[199,]  2.401462e-03  1.637804e-02  2.493993e-03 0.9787265040
[200,]  1.550016e-03  1.545511e-03  1.973938e-03 0.9949305357
[201,]  9.987521e-01 1.505235e-159 1.582123e-142 0.0012479298
[202,]  9.976917e-01 9.814273e-160 5.595014e-142 0.0023083020
[203,]  9.954610e-01 3.156764e-159 2.751130e-141 0.0045390170
[204,]  9.976213e-01 1.415876e-159 1.080349e-141 0.0023787078
[205,]  9.990816e-01 5.801783e-159 1.461984e-142 0.0009183621
[206,]  9.931761e-01 2.329363e-158 8.102468e-142 0.0068238681
[207,]  9.931137e-01 1.518125e-158 6.939571e-142 0.0068863330
[208,]  9.958713e-01 2.351159e-158 6.144132e-142 0.0041287408
[209,]  9.841725e-01 6.109229e-159 8.797489e-141 0.0158275326
[210,]  9.739799e-01 1.735105e-159 1.526000e-140 0.0260200592
[211,]  9.573577e-01 2.158180e-159 4.963093e-141 0.0426423073
[212,]  9.385854e-01 5.396128e-158 4.149844e-143 0.0614145981
[213,]  9.328886e-01 8.991024e-159 2.451210e-141 0.0671113667
[214,]  9.136996e-01 2.404077e-160 2.032747e-143 0.0863004477
[215,]  8.818764e-01 1.124653e-161 2.561474e-148 0.1181235826
[216,]  9.106803e-01 3.422600e-161 5.524200e-144 0.0893197244
[217,]  8.647050e-01 1.095642e-160 2.105558e-146 0.1352949675
[218,]  8.581207e-01 7.958592e-168 2.125919e-144 0.1418792706
[219,]  8.576343e-01 6.928603e-167 5.080654e-147 0.1423656768
[220,]  8.452448e-01 6.158438e-166 7.030755e-147 0.1547552305
[221,]  8.853818e-01 1.374670e-163 1.153574e-143 0.1146182291
[222,]  8.320867e-01 5.974067e-171 1.066174e-153 0.1679132714
[223,]  8.200256e-01 3.050694e-169 5.793113e-158 0.1799743640
[224,]  7.832419e-01 8.096356e-177 5.711291e-161 0.2167581106
[225,]  7.819730e-01 3.205547e-175 5.684665e-161 0.2180270283
[226,]  7.694692e-01 1.716667e-175 4.706678e-160 0.2305308401
[227,]  7.763497e-01 3.736679e-178 1.245196e-163 0.2236502565
[228,]  7.489402e-01 3.981422e-176 2.403646e-174 0.2510598216
[229,]  7.361174e-01 9.269789e-182 1.097992e-172 0.2638826107
[230,]  7.352419e-01 3.919535e-183 1.913214e-171 0.2647581277
[231,]  7.212715e-01 4.629804e-188 6.737267e-177 0.2787285149
[232,]  7.362883e-01 7.316239e-180 1.062802e-171 0.2637116745
[233,]  7.352411e-01 1.090435e-180 1.173276e-173 0.2647589175
[234,]  7.033820e-01 3.935317e-191 2.353680e-183 0.2966180470
[235,]  6.933180e-01 1.480917e-188 1.160784e-184 0.3066820432
[236,]  6.873758e-01 1.443515e-199 4.800065e-187 0.3126241567
[237,]  6.981858e-01 3.049113e-194 8.104810e-183 0.3018141603
[238,]  6.425808e-01 2.298442e-201 7.058675e-200 0.3574191837
[239,]  6.118918e-01 3.556691e-216 8.932589e-199 0.3881081585
[240,]  6.399140e-01 1.608841e-210 3.159395e-199 0.3600860237
[241,]  5.926031e-01 1.122711e-227 5.148598e-217 0.4073969462
[242,]  6.152928e-01 1.133180e-211 4.308058e-214 0.3847072051
[243,]  6.071814e-01 2.810704e-219 3.134519e-205 0.3928185663
[244,]  5.834963e-01 1.323747e-226 3.559602e-219 0.4165036684
[245,]  5.711016e-01 3.220660e-221 1.884419e-218 0.4288984200
[246,]  5.562949e-01 4.298564e-221 3.695450e-205 0.4437050885
[247,]  5.839494e-01 3.778002e-219 5.349302e-219 0.4160505862
[248,]  5.333898e-01 1.645512e-203 6.657973e-185 0.4666101968
[249,]  4.937214e-01 1.680190e-174 1.260363e-162 0.5062785904
[250,]  5.561560e-01 7.779887e-221 8.106455e-198 0.4438440176
[251,]  4.967509e-01 2.576651e-176 4.548530e-164 0.5032490814
[252,]  4.859308e-01 1.073462e-169 6.907923e-150 0.5140691551
[253,]  5.157038e-01 5.292343e-190 1.635585e-179 0.4842961534
[254,]  4.984091e-01 1.740501e-177 2.904142e-160 0.5015909307
[255,]  4.693887e-01 1.763130e-158 7.764737e-145 0.5306113162
[256,]  4.853751e-01 3.509813e-169 4.136055e-156 0.5146249134
[257,]  4.378957e-01 9.168868e-138 3.016796e-125 0.5621043195
[258,]  4.462835e-01 4.410477e-143 6.458260e-131 0.5537164968
[259,]  4.336936e-01 1.295055e-135 3.363379e-117 0.5663063835
[260,]  4.341535e-01 3.146812e-136 6.028734e-123 0.5658464539
[261,]  4.034540e-01 1.012644e-117 4.178044e-110 0.5965459544
[262,]  3.911572e-01 5.648621e-111 7.927965e-104 0.6088427841
[263,]  4.135171e-01 1.174669e-122 1.809247e-114 0.5864829009
[264,]  3.601457e-01  4.098775e-95  6.682760e-85 0.6398542723
[265,]  3.603699e-01  5.304651e-95  2.767391e-83 0.6396300934
[266,]  3.619215e-01  3.219656e-95  2.781278e-85 0.6380785480
[267,]  3.240472e-01  1.252251e-77  1.366782e-68 0.6759527808
[268,]  3.095532e-01  4.928875e-71  1.152376e-64 0.6904468213
[269,]  3.346643e-01  2.109524e-82  1.127312e-71 0.6653357399
[270,]  3.144772e-01  2.586330e-73  8.104528e-69 0.6855227875
[271,]  3.012416e-01  5.381695e-67  2.473149e-59 0.6987584252
[272,]  3.186445e-01  1.020039e-74  4.533519e-68 0.6813554943
[273,]  2.735620e-01  4.367133e-56  2.627423e-51 0.7264380107
[274,]  3.038237e-01  2.029387e-68  9.336990e-64 0.6961762603
[275,]  2.616443e-01  5.090055e-51  3.455768e-45 0.7383556676
[276,]  2.609864e-01  1.119992e-50  1.864770e-49 0.7390135515
[277,]  2.038302e-01  2.886827e-31  1.113239e-30 0.7961697867
[278,]  2.262143e-01  8.904481e-40  5.130321e-35 0.7737856570
[279,]  2.470729e-01  1.762936e-46  2.682511e-40 0.7529271454
[280,]  2.103328e-01  1.716126e-33  3.078668e-31 0.7896672365
[281,]  2.072278e-01  2.068577e-34  1.304537e-29 0.7927721697
[282,]  2.323514e-01  1.714635e-41  7.787477e-39 0.7676486153
[283,]  1.973936e-01  8.746001e-31  5.546589e-28 0.8026063510
[284,]  1.669596e-01  2.113011e-23  4.140396e-20 0.8330404460
[285,]  1.521572e-01  1.652310e-19  3.317394e-17 0.8478427808
[286,]  1.201699e-01  1.307114e-13  3.103981e-12 0.8798301432
[287,]  1.330888e-01  5.824862e-16  1.111157e-13 0.8669112225
[288,]  9.244682e-02  5.722278e-09  5.870598e-09 0.9075531651
[289,]  1.174511e-01  1.294888e-13  1.151623e-10 0.8825489259
[290,]  1.407217e-01  2.893318e-17  3.364227e-15 0.8592782572
[291,]  6.874198e-02  1.791322e-06  6.483862e-07 0.9312555788
[292,]  7.680548e-02  5.182351e-08  6.170363e-06 0.9231882930
[293,]  4.382307e-02  7.661222e-04  3.125660e-04 0.9550982437
[294,]  7.704172e-02  1.842131e-07  2.719610e-06 0.9229553758
[295,]  4.804447e-02  1.086421e-04  6.040760e-04 0.9512428091
[296,]  7.283257e-02  2.264097e-07  4.894218e-05 0.9271182641
[297,]  1.811347e-02  3.161193e-04  2.950520e-03 0.9786198903
[298,]  3.347264e-02  3.014305e-04  6.148735e-04 0.9656110563
[299,]  1.006591e-02  4.318718e-03  4.146362e-03 0.9814690127
[300,]  1.644536e-03  2.838708e-03  4.420837e-04 0.9950746720

$P
              [,1]          [,2]        [,3]       [,4]
[1,]  2.097639e-02  0.000000e+00 0.000000000 0.00000000
[2,] 6.456086e-159  2.999597e-03 0.000000000 0.00000000
[3,] 1.658903e-141 7.846496e-158 0.009648433 0.00000000
[4,]  3.177566e-01  3.261808e-01 0.315885684 0.00655256

$alpha
NULL

$loglik
  [1] -261341.2 -254907.6 -254233.6 -254164.3 -254141.1 -254127.6 -254118.2
  [8] -254111.3 -254106.2 -254102.4 -254099.6 -254097.5 -254096.1 -254095.0
 [15] -254094.1 -254093.5 -254093.0 -254092.6 -254092.3 -254092.0 -254091.8
 [22] -254091.6 -254091.5 -254091.3 -254091.2 -254091.1 -254091.0 -254090.9
 [29] -254090.9 -254090.8 -254090.7 -254090.7 -254090.6 -254090.6 -254090.5
 [36] -254090.5 -254090.4 -254090.4 -254090.4 -254090.4 -254090.3 -254090.3
 [43] -254090.3 -254090.3 -254090.2 -254090.2 -254090.2 -254090.2 -254090.2
 [50] -254090.2 -254090.1 -254090.1 -254090.1 -254090.1 -254090.1 -254090.1
 [57] -254090.1 -254090.1 -254090.1 -254090.1 -254090.1 -254090.0 -254090.0
 [64] -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0
 [71] -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0
 [78] -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0
 [85] -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0
 [92] -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0
 [99] -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0
[106] -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0
[113] -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0
[120] -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0
[127] -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0 -254090.0
[134] -254090.0 -254090.0 -254090.0

$BIC
[1] 521926

$niter
[1] 136

$status
[1] 0

$runtime
   user  system elapsed 
376.620  28.784 126.927 

In this example we obtain identical result, indicating convergence is perhaps not an issue for this model fit.