Expected hessian for S-vine copula models
Arguments
- u
the data; should have approximately uniform margins..
- model
model inheriting from class svinecop_dist.
- cores
number of cores to use; if larger than one, computations are done in parallel on
coresbatches .
Value
Returns the observed Hessian matrix. Rows/columns correspond to to model parameters in the order: copula parameters of first tree, copula parameters of second tree, etc. Duplicated parameters in the copula model are omitted.
Examples
# load data set
data(returns)
# convert to uniform margins
u <- pseudo_obs(returns[1:100, 1:3])
# fit parametric S-vine copula model with Markov order 1
fit <- svinecop(u, p = 1, family_set = "parametric")
svinecop_loglik(u, fit)
#> [1] 91.58517
svinecop_scores(u, fit)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1.324510323 -1.1772603328 0.159468843 0.708184553 1.40300407
#> [2,] -0.478177991 -0.3150741740 -0.283158283 0.948042727 -1.26163819
#> [3,] -1.938624623 -0.2997446871 -0.341624271 -0.594614138 -1.80005022
#> [4,] 0.543175214 -1.3156656664 -0.348152377 -1.591077070 0.58739903
#> [5,] 0.920403816 -0.9818711575 -0.028612730 1.657918168 1.20468290
#> [6,] -1.288206254 0.0692231239 -0.176642303 0.904070129 -1.03063690
#> [7,] 0.736977483 -1.3576338530 -0.256673748 -2.029983362 1.24681250
#> [8,] -1.124436812 0.3871066986 0.071022356 0.960581105 -0.30654215
#> [9,] -1.157790468 0.2424144628 -0.098507860 -0.342325449 -0.97620491
#> [10,] -0.750484536 0.7981019455 0.257361977 -0.840721738 0.07389433
#> [11,] -1.075205402 0.4501013871 -0.102246680 -0.904690600 1.17200132
#> [12,] -0.001283765 -0.5932477287 -0.277817981 -0.060312296 1.28169073
#> [13,] -1.080445225 0.2894504217 -0.087425294 -0.885169334 -0.35322447
#> [14,] 1.611101066 0.2955975522 0.647740276 -0.411096211 -0.39762139
#> [15,] 0.635195992 -0.9058162849 -0.136895886 0.345149714 -1.10216477
#> [16,] 1.679200177 0.5658105214 0.543736139 -0.554924522 1.27813766
#> [17,] 0.278277783 -0.7529841555 -0.229720368 1.390818281 -0.96480854
#> [18,] -0.919851127 0.6376802351 0.095049936 -0.881600607 1.08917482
#> [19,] -0.943895183 -0.0821669323 -0.438456871 0.859149924 1.42315914
#> [20,] 1.790607306 2.0659033642 1.020337973 1.066983409 -1.70162701
#> [21,] -1.009836143 0.2733925409 -0.122119540 -0.336563970 -0.65180221
#> [22,] -1.041705460 0.1745261031 -0.309553152 -0.078198499 -0.78727276
#> [23,] 0.874416273 -1.3246084402 -0.169181725 -1.867255569 1.19878961
#> [24,] -1.065845516 0.5311880276 -0.036458029 1.324711896 -0.51158000
#> [25,] 0.826023174 -1.4829272786 -0.239337015 0.244208458 -1.32000610
#> [26,] 3.006604155 0.2780157345 0.340220396 -0.332842646 -0.93931990
#> [27,] 0.975667620 -1.1426619301 -0.057097538 0.740194144 -1.57296668
#> [28,] 0.220086455 -0.7696317140 -0.214633766 -1.213459664 0.78807666
#> [29,] 0.356559624 -0.8319720008 -0.256757449 1.093246959 1.28836891
#> [30,] 0.287740613 -1.0174927058 -0.374879504 -1.879622420 1.12382318
#> [31,] -1.031384588 0.2891953055 -0.212961943 0.233672359 -1.00198448
#> [32,] 2.613580786 0.3441633517 0.382028942 1.102047174 -0.55208982
#> [33,] -0.829782121 0.6560221992 0.137570158 -0.545364263 -0.37307585
#> [34,] -0.115778180 -0.5720084678 -0.360745667 1.555318331 -1.07103743
#> [35,] -0.148768043 -0.5308533396 -0.277914542 -0.715557201 -0.09809073
#> [36,] -0.011084526 -0.6080166667 -0.266071932 -1.011735354 0.30348742
#> [37,] 0.657446415 0.5303966882 0.366639034 0.558144150 4.47958471
#> [38,] 3.521224876 0.1933275730 0.271881039 0.903502308 2.20825950
#> [39,] -1.030211339 0.4369310536 -0.076344688 0.353770150 -1.07266474
#> [40,] 1.818178870 2.0036623463 1.057854966 -1.561721783 0.98520203
#> [41,] -1.734891825 0.7941737247 -0.048511320 -1.670939003 1.20632562
#> [42,] -0.948313820 0.0863239253 -0.195327875 0.944708042 -1.15716953
#> [43,] -0.845651122 0.7627167596 0.200488465 0.384271096 -1.09060806
#> [44,] -0.886173232 0.1524429857 -0.229968415 0.407293672 1.24370892
#> [45,] -0.378246649 -0.3307065317 -0.335304713 0.456287912 1.32225645
#> [46,] 1.619730040 -1.4793230793 0.408721556 -2.114408833 1.34436778
#> [47,] -0.363536058 -0.7478606610 -0.304565508 -1.266672332 0.15941535
#> [48,] -0.956016361 0.5415893044 0.036385199 0.002964888 8.12662400
#> [49,] -1.008916913 0.3206045170 -0.105003289 1.104688937 1.25924053
#> [50,] 1.014437289 -0.9181865513 0.196304120 0.257717264 -1.13094039
#> [51,] -0.297342767 -0.5435307221 -0.431234414 1.020628617 -1.91607477
#> [52,] -0.985162461 0.0984504440 -0.339637637 0.152055559 1.42470257
#> [53,] 0.547627263 -0.9162875608 -0.197410088 -1.116255333 1.33174936
#> [54,] -1.216026863 -0.0868405967 -0.239819226 0.952648713 -0.93677811
#> [55,] 0.627223976 -1.2707222393 -0.290804884 0.970188050 1.42254322
#> [56,] -0.068245278 -0.6235153421 -0.263422862 -1.197283167 0.86633708
#> [57,] -0.685701877 -0.1472562918 -0.373545621 -0.715820557 -0.13113521
#> [58,] -0.062005720 -0.7361068901 -0.419732772 -0.845044604 -0.10138515
#> [59,] -0.245886241 0.7200347495 0.322470694 1.147613716 -0.95791647
#> [60,] 0.305356609 -0.8169816734 -0.191397269 -0.581387596 -0.26724817
#> [61,] 1.132490067 -1.3533466355 -0.015419055 -0.815161116 -0.12425365
#> [62,] -1.038728153 0.2585242643 -0.117211841 0.541387608 -1.21809407
#> [63,] -1.124848293 0.5439578500 -0.057538625 0.263659886 -1.00824584
#> [64,] -0.196650123 -0.4566545860 -0.304676647 -0.857322294 0.11271062
#> [65,] -0.193423385 -0.4586387440 -0.306742427 -0.861944527 0.11824253
#> [66,] -0.189901249 -0.4611649643 -0.308856385 -0.867125368 0.12406205
#> [67,] 0.029812423 -0.6589038295 -0.335519667 1.549417569 -1.27458436
#> [68,] -0.990719755 0.3072086949 -0.130352963 -0.045303649 -0.80182567
#> [69,] 1.406706156 -0.3137420972 0.426171441 0.773864666 -1.32437201
#> [70,] -0.155680083 -0.5276578532 -0.353617746 -0.562336763 -0.27737432
#> [71,] -0.917340272 -0.0029257770 -0.379767796 -0.356046211 -0.55612962
#> [72,] -1.135976787 0.6504581494 0.018218257 -0.906016246 0.17276191
#> [73,] -1.827870051 1.0525348814 0.255533944 0.835728271 -1.72155887
#> [74,] -2.016564019 0.6753426494 -0.244054320 -1.793519246 0.79097722
#> [75,] -0.645948234 -0.3631602589 -0.289303648 0.329683431 -1.13892806
#> [76,] 0.812638536 -1.2247809479 -0.175703844 1.460880220 -2.17142176
#> [77,] -1.459642244 0.8111855214 0.054078062 0.729180684 -1.47545406
#> [78,] -1.190479326 0.0948680542 -0.418008737 -1.466250277 1.67112735
#> [79,] -0.330680386 0.9509817750 0.722811218 -0.922431280 0.06648672
#> [80,] -1.111500126 0.0865130321 -0.178793934 -1.352304957 0.10908256
#> [81,] 1.099032474 -1.7494511600 -0.123849452 -2.518389674 1.76882187
#> [82,] -1.737901853 1.1120679119 0.412386714 0.891583283 -1.78137767
#> [83,] -0.146430817 0.6542669417 0.308185432 -1.356998498 0.40107306
#> [84,] 0.987770402 -0.9439871560 0.023951251 -0.319818340 -0.49368471
#> [85,] 0.995004575 -0.9503984866 0.024453652 -0.415172238 -0.39755711
#> [86,] -2.249076789 1.2941897161 0.748255605 1.647628679 -2.59112966
#> [87,] 1.157755537 -0.6931695543 0.261936216 -0.220681495 -0.68386527
#> [88,] 4.818629220 0.0008336461 0.003140566 -0.844235040 -1.00837354
#> [89,] 1.127226087 -0.7370259633 0.228062483 0.262920811 -1.02991678
#> [90,] 1.933674395 3.1467784811 2.031182794 8.961287117 0.21233968
#> [91,] 1.528129548 0.6207758895 0.698744203 0.558218918 -1.40883576
#> [92,] 1.204292700 0.5696953755 0.446530940 1.134208416 -0.78738036
#> [93,] 0.635857244 -1.0202279740 -0.048879717 0.669195608 1.07980444
#> [94,] -1.125051335 0.9350225764 0.306753324 -0.003928252 -0.81994428
#> [95,] 1.547272466 -0.1743515413 0.522363221 0.427828690 5.74506952
#> [96,] -1.511529341 -0.0053245851 -0.206254997 -0.928018188 -1.09799945
#> [97,] -0.533337324 0.7813785892 0.300614286 0.647704349 -1.23644379
#> [98,] 0.236984583 -0.7332241181 -0.251931052 0.927673366 -1.48052807
#> [99,] -1.093756101 0.2837869568 -0.250239302 -1.369743424 0.89960593
#> [,6] [,7] [,8] [,9] [,10]
#> [1,] 0.634433611 -0.309469402 -0.200467089 0.03015007 -0.572129108
#> [2,] 0.034305552 0.232360235 0.069624731 1.86207046 -0.562350438
#> [3,] -0.341793004 -0.905300979 -0.138032697 -0.52598946 -0.424589904
#> [4,] -0.302782318 2.154558976 -0.042198872 -0.33990518 -0.047328921
#> [5,] 0.584220019 1.209412557 -0.198543011 0.49518996 -0.069891379
#> [6,] 0.150511304 -1.108936615 0.032336636 1.26628216 -0.399961207
#> [7,] -0.036207630 0.722070441 -0.063041202 -0.37371490 -0.010386195
#> [8,] 0.314319959 0.800109212 -0.008843081 0.70734174 0.017977663
#> [9,] -0.260519635 -1.584175996 -0.042389527 -0.23693044 0.131877832
#> [10,] -0.239008374 -0.816085385 0.112008472 0.79699381 -0.081951944
#> [11,] 0.210967946 -0.563067327 0.186664027 -0.10776197 -1.068303173
#> [12,] 0.410592827 -1.700259796 -0.075664534 0.19408038 0.188461243
#> [13,] -0.260266208 -2.258645444 -0.008168221 0.17254825 0.132785313
#> [14,] -0.306142565 -0.022144550 0.102044490 -0.43586730 -0.008720380
#> [15,] -0.236826379 0.186971829 0.105560531 -0.15551162 -1.649077055
#> [16,] 0.324340930 0.312850852 0.465793947 2.19445683 0.999867969
#> [17,] 0.377149123 0.658853754 0.228642481 0.74877140 1.094979676
#> [18,] 0.206569118 0.739028525 0.258978001 0.60836012 0.872131352
#> [19,] 0.725552610 -0.134551168 0.203498151 -0.45124269 -0.865673189
#> [20,] -0.035439045 0.006993861 0.410035225 2.80218031 0.823937285
#> [21,] -0.255692910 0.648205545 -0.031532371 -0.18032427 -0.098616272
#> [22,] -0.331042139 0.524623031 -0.072552112 -0.05581049 -0.006219726
#> [23,] -0.031895183 -0.443957063 -0.076303990 -0.20376456 0.258021019
#> [24,] 0.413858345 -0.379302102 -0.113377982 0.12563427 0.179324519
#> [25,] -0.369408683 -1.527014171 0.072008481 -0.50897150 0.245673120
#> [26,] -0.258294309 1.465971485 0.172578285 0.80889534 0.594391671
#> [27,] -0.193476855 0.910689926 0.176488273 -0.52442484 1.072379298
#> [28,] -0.022982498 0.783963175 -0.148891469 -0.34215719 -0.623199730
#> [29,] 0.573516096 -1.040630677 -0.071165670 -0.05487143 -0.021692613
#> [30,] -0.082794249 0.702022204 -0.041356854 0.88723049 0.096363117
#> [31,] -0.251761392 -0.166403719 -0.070405845 0.02979584 0.112085024
#> [32,] 0.288203203 0.289598043 -0.191002675 0.72744152 -0.631400853
#> [33,] -0.259683405 -0.129148946 0.045384289 0.45832589 -1.283756571
#> [34,] 0.597531907 0.727748495 0.087415288 -0.29119252 0.338849911
#> [35,] -0.253333480 0.477228414 -0.061492653 -0.45110233 -0.089411698
#> [36,] -0.194982606 -0.186042134 -0.081950581 -0.20642850 -0.133050612
#> [37,] 0.432326870 0.323507639 -0.169398128 -0.20198480 0.324190059
#> [38,] 0.507688204 0.212060613 -0.280035694 1.52502285 -0.953311884
#> [39,] -0.182879769 0.253569296 -0.061917061 0.02725205 -0.747397996
#> [40,] -0.084358085 0.291966175 -0.094187924 -0.51554867 0.206514906
#> [41,] 0.019443670 0.065799134 0.193675985 -1.12311075 1.553239471
#> [42,] 0.080412557 0.308202935 0.008842171 0.59512155 0.376426563
#> [43,] -0.189991749 0.212060613 -0.082771412 0.52378618 0.292609327
#> [44,] 0.461012378 -0.331033841 0.142275623 0.03815067 -0.624436227
#> [45,] 0.506034733 -1.851216971 0.051217773 0.06162644 -0.062016085
#> [46,] 0.015773546 0.847477770 -0.103618068 1.27830212 0.303856268
#> [47,] -0.180683865 1.209412557 -0.181919333 1.17876528 -1.030626836
#> [48,] 0.006732624 2.314868671 -0.079521266 -0.20581736 0.175913519
#> [49,] 0.538669489 -2.404552076 -0.001441958 -0.32013733 0.127441159
#> [50,] -0.167574332 0.425031971 0.112509221 -0.84400023 -0.640749486
#> [51,] -0.119521775 0.754631127 -0.019410209 -0.28982051 -0.486160686
#> [52,] 0.541496942 0.382338286 0.191989879 0.17564238 0.104555615
#> [53,] 0.231321562 0.018709301 -0.108319270 1.31465385 0.432353600
#> [54,] 0.179068497 -0.156558601 0.069350105 0.82277290 -0.241255414
#> [55,] 0.776735779 0.306867211 -0.038778570 -0.23300820 0.121382446
#> [56,] 0.027895522 0.228545126 -0.131348459 2.58837448 0.063394118
#> [57,] -0.334370610 0.490512310 -0.043617610 -0.17889134 0.222966319
#> [58,] -0.375486471 -0.597707966 -0.042204152 -0.13447345 0.106819219
#> [59,] 0.213095854 -0.008677463 -0.166965527 -0.33036154 0.022458003
#> [60,] -0.262242262 0.190653183 -0.048929310 -0.60140416 0.680145053
#> [61,] -0.374019800 0.508738554 0.025720297 -0.25342122 -0.738880834
#> [62,] -0.090430585 0.555068515 -0.037558047 -0.07022847 -0.018152922
#> [63,] -0.227977446 0.191476239 -0.074528862 0.13872260 0.104079459
#> [64,] -0.251829065 0.249538306 -0.051007401 -0.28928131 0.170234915
#> [65,] -0.253225509 0.198703867 -0.050266350 -0.13331269 0.073603090
#> [66,] -0.254606970 0.212699228 -0.049581642 -0.12988040 0.078249391
#> [67,] 0.510310406 0.066853255 0.118700448 -0.07129437 -0.012824412
#> [68,] -0.240764520 0.455057476 -0.041609940 -0.11057807 0.242526253
#> [69,] -0.085668891 0.276620308 0.297151167 -0.45005429 0.014766813
#> [70,] -0.332492289 0.126756214 -0.037841999 -0.28828306 -0.397614699
#> [71,] -0.366388107 -0.287777227 -0.064821595 -0.20025743 0.144126779
#> [72,] -0.233448808 0.355435259 0.067532031 -0.12154503 -0.402454935
#> [73,] -0.181139515 0.316824957 -0.216292545 0.20747955 -1.353808320
#> [74,] -0.252172513 -2.718863600 0.063863190 0.58548818 -1.803586907
#> [75,] -0.154641250 0.649654304 0.007021581 0.64309790 0.749890230
#> [76,] 0.161587146 0.657473413 0.202794256 -0.51164475 -0.520845454
#> [77,] -0.169476407 -1.383113814 -0.160914663 0.47518195 0.784690768
#> [78,] 0.494968723 -0.348827375 0.189842169 0.28696763 -1.042796089
#> [79,] -0.328895196 -0.290903192 0.059859633 -5.77006458 -1.629555000
#> [80,] -0.189195913 0.590403907 -0.037867294 -0.08632497 -0.392259291
#> [81,] 0.368412137 1.756609085 -0.093968609 -0.28156801 0.112369550
#> [82,] -0.164409685 -2.512416224 -0.232893957 -3.86090275 0.333622972
#> [83,] -0.114345596 1.357056269 0.257013265 0.42176580 -1.792061229
#> [84,] -0.308586663 -0.103306439 0.054995698 -0.18961013 1.016825999
#> [85,] -0.310787603 0.205883966 0.042228258 -0.16983537 -1.225796375
#> [86,] 0.276115249 -1.063011702 -0.353863915 1.50516226 1.270388701
#> [87,] -0.252502358 0.534080754 0.037975264 -0.60062747 2.350606678
#> [88,] -0.322404389 -1.891070226 0.363419180 4.98129563 2.057781941
#> [89,] -0.191208862 -1.369974010 0.148493834 -0.66518621 2.063619014
#> [90,] 0.294550091 0.383313887 -0.332009271 -0.53563281 -2.979634879
#> [91,] -0.241566646 -0.626457640 -0.184451158 -7.65307541 1.026471752
#> [92,] 0.248176884 0.179552524 -0.190586059 0.44001884 -2.247792480
#> [93,] 0.450407184 -1.505034680 -0.336629901 -0.71403325 1.220950115
#> [94,] -0.303867033 -0.212128294 -0.071805531 -0.83171785 1.378769410
#> [95,] 0.447957916 -1.369974010 0.517869026 -0.22160155 1.672190419
#> [96,] -0.340250074 2.409437745 -0.099840586 -0.42806985 -0.723860749
#> [97,] -0.110065539 -0.777534730 -0.113168049 0.60628306 0.341063790
#> [98,] -0.056902024 0.216819889 0.120429869 -0.45711558 0.650645017
#> [99,] -0.070260092 0.241647205 0.079779472 0.18260868 0.584661395
#> [,11]
#> [1,] 0.0020229876
#> [2,] 0.0021096275
#> [3,] 0.0032358925
#> [4,] 0.0049212003
#> [5,] 0.0065876226
#> [6,] 0.0038495170
#> [7,] 0.0089671211
#> [8,] 0.0106720928
#> [9,] 0.0124244555
#> [10,] -0.0083144940
#> [11,] -0.0011137445
#> [12,] 0.0056370349
#> [13,] 0.0126885457
#> [14,] -0.0347093958
#> [15,] -0.0073454420
#> [16,] -0.0297275541
#> [17,] -0.0212301479
#> [18,] 0.0048227807
#> [19,] 0.0001024713
#> [20,] -0.0430780737
#> [21,] -0.0574253383
#> [22,] 0.0091544047
#> [23,] 0.0103590417
#> [24,] 0.0112536991
#> [25,] 0.0099598664
#> [26,] -0.0186982359
#> [27,] -0.0044009666
#> [28,] 0.0002133138
#> [29,] 0.0073859582
#> [30,] 0.0123655897
#> [31,] 0.0121577960
#> [32,] -0.0128880096
#> [33,] -0.0012383362
#> [34,] 0.0062105007
#> [35,] 0.0086544253
#> [36,] 0.0078653468
#> [37,] 0.0092100978
#> [38,] -0.0144105484
#> [39,] -0.0130449830
#> [40,] -0.0334801938
#> [41,] 0.0060492631
#> [42,] -0.0064050775
#> [43,] 0.0018569603
#> [44,] 0.0007467146
#> [45,] 0.0078929652
#> [46,] -0.0011634636
#> [47,] 0.0002925624
#> [48,] 0.0048277347
#> [49,] 0.0127360106
#> [50,] -0.0549645655
#> [51,] -0.0584754958
#> [52,] 0.0039357381
#> [53,] 0.0063977500
#> [54,] 0.0044448569
#> [55,] 0.0076704384
#> [56,] 0.0072484662
#> [57,] 0.0106129817
#> [58,] 0.0119115349
#> [59,] 0.0044288745
#> [60,] 0.0057698231
#> [61,] 0.0006943297
#> [62,] 0.0049121379
#> [63,] 0.0079548928
#> [64,] 0.0093431037
#> [65,] 0.0118907471
#> [66,] 0.0119901454
#> [67,] 0.0090907356
#> [68,] 0.0100439755
#> [69,] -0.0372823040
#> [70,] -0.0387077073
#> [71,] 0.0109195618
#> [72,] 0.0008706626
#> [73,] -0.0017467923
#> [74,] 0.0112328778
#> [75,] 0.0004984660
#> [76,] 0.0023482064
#> [77,] 0.0042985162
#> [78,] 0.0004894755
#> [79,] -0.0042625476
#> [80,] -0.0494843743
#> [81,] 0.0118052311
#> [82,] -0.0045119934
#> [83,] 0.0081255813
#> [84,] 0.0057865261
#> [85,] 0.0014376033
#> [86,] -0.0138554571
#> [87,] 0.0548157180
#> [88,] 0.0190526608
#> [89,] 0.0203916015
#> [90,] 0.0792719955
#> [91,] -0.0237114258
#> [92,] 0.0105995616
#> [93,] 0.0074101771
#> [94,] 0.0102696508
#> [95,] 0.0127464651
#> [96,] -0.0325279365
#> [97,] -0.0002019262
#> [98,] 0.0041231255
#> [99,] 0.0063340794
svinecop_hessian(u, fit)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] -1.508237948 0.245724962 -0.2123577392 0.0000000000 0.0000000000
#> [2,] 0.245724962 -0.358897440 -0.1894400011 0.0000000000 0.0000000000
#> [3,] -0.212357739 -0.189440001 -0.1439332397 0.0000000000 0.0000000000
#> [4,] 0.000000000 0.000000000 0.0000000000 -1.8369438255 0.4395037908
#> [5,] 0.000000000 0.000000000 0.0000000000 0.4395037908 -2.3393593241
#> [6,] 0.000000000 0.000000000 0.0000000000 -0.2396825205 -0.1228487433
#> [7,] 0.000000000 0.000000000 0.0000000000 0.0000000000 0.0000000000
#> [8,] 0.011211794 -0.005040945 -0.0023483398 -0.0097926406 -0.0083970476
#> [9,] -0.139805986 -0.021389998 -0.0121725193 0.0083447729 0.0011727996
#> [10,] 0.080825052 0.174039773 0.0286059701 0.0063901012 -0.0119390093
#> [11,] 0.002723707 -0.007959479 0.0004966099 -0.0005300762 -0.0001169792
#> [,6] [,7] [,8] [,9] [,10]
#> [1,] 0.0000000000 0.000000 0.0000000000 0.000000000 0.000000000
#> [2,] 0.0000000000 0.000000 0.0000000000 0.000000000 0.000000000
#> [3,] 0.0000000000 0.000000 0.0000000000 0.000000000 0.000000000
#> [4,] -0.2396825205 0.000000 0.0000000000 0.000000000 0.000000000
#> [5,] -0.1228487433 0.000000 0.0000000000 0.000000000 0.000000000
#> [6,] -0.0934740926 0.000000 0.0000000000 0.000000000 0.000000000
#> [7,] 0.0000000000 -1.006142 0.0000000000 0.000000000 0.000000000
#> [8,] -0.0046245355 0.000000 -0.0253265518 0.000000000 0.000000000
#> [9,] 0.0002681383 0.000000 -0.0170660253 -1.970633166 0.000000000
#> [10,] -0.0008670125 0.000000 0.0078621008 0.171049470 -0.777495105
#> [11,] -0.0001959336 0.000000 -0.0002101406 0.009046144 -0.007247017
#> [,11]
#> [1,] 0.0000000000
#> [2,] 0.0000000000
#> [3,] 0.0000000000
#> [4,] 0.0000000000
#> [5,] 0.0000000000
#> [6,] 0.0000000000
#> [7,] 0.0000000000
#> [8,] 0.0000000000
#> [9,] 0.0000000000
#> [10,] -0.0072470169
#> [11,] -0.0005494059