require(Matrix)
## Loading required package: Matrix
## Warning: package 'Matrix' was built under R version 3.4.2
require(igraph)
## Loading required package: igraph
## Warning: package 'igraph' was built under R version 3.4.1
##
## Attaching package: 'igraph'
## The following objects are masked from 'package:stats':
##
## decompose, spectrum
## The following object is masked from 'package:base':
##
## union
states = read.csv("48states.csv", colClass = c("character", "character"))
g = graph.data.frame(states, directed=F)
g.degree = degree(g)
g.degree [g.degree == max(g.degree)]
## MISSOURI TENNESSEE
## 8 8
g.shortestpath.m = shortest.paths(g)
str(g.shortestpath.m)
## num [1:48, 1:48] 0 4 3 4 3 7 3 1 2 4 ...
## - attr(*, "dimnames")=List of 2
## ..$ : chr [1:48] "TEXAS" "WISCONSIN" "VIRGINIA" "WASHINGTON" ...
## ..$ : chr [1:48] "TEXAS" "WISCONSIN" "VIRGINIA" "WASHINGTON" ...
sorted.names = sort( rownames(g.shortestpath.m) )
gsm = g.shortestpath.m[, sorted.names]
gsm = gsm[sorted.names, ]
A = as_adjacency_matrix(g, type = c("both", "upper", "lower"), attr = NULL,
edges = FALSE, names = TRUE, sparse = igraph_opt("sparsematrices"))
rankMatrix(A)
## [1] 48
## attr(,"method")
## [1] "tolNorm2"
## attr(,"useGrad")
## [1] FALSE
## attr(,"tol")
## [1] 1.065814e-14
eigen(A)
## eigen() decomposition
## $values
## [1] 5.46905036 4.71349007 4.10283310 3.98769817 3.56553201
## [6] 3.29609990 2.92589988 2.47279120 2.21403386 1.98027335
## [11] 1.64326053 1.37137510 1.32589358 1.05103630 0.87007730
## [16] 0.72474178 0.49265884 0.25786926 0.13794547 0.06087911
## [21] -0.18440602 -0.30846880 -0.37586922 -0.69511879 -0.76035086
## [26] -0.82759766 -1.00000000 -1.04901188 -1.11963361 -1.21597743
## [31] -1.29093275 -1.39362399 -1.45885353 -1.51222782 -1.59093188
## [36] -1.64174682 -1.67854299 -1.74845653 -1.83665486 -1.93900022
## [41] -2.03895713 -2.13101810 -2.21289102 -2.25499195 -2.37505991
## [46] -2.39627221 -2.78120712 -2.84563603
##
## $vectors
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.1269362183 -0.037595880 0.191120477 0.017179147 0.14085327
## [2,] -0.1342561539 0.071741990 -0.239778162 0.127059399 0.02027220
## [3,] -0.1354063391 0.211752293 0.086709716 -0.111031700 -0.18431323
## [4,] -0.0338266747 -0.080078900 -0.010949302 -0.067103579 -0.12131413
## [5,] -0.2582273680 -0.119195635 -0.097785210 0.095623439 0.14619647
## [6,] -0.0058462038 0.027364688 -0.040557097 -0.200221510 0.21938914
## [7,] -0.2334173178 0.027787111 -0.247476898 0.182905195 0.11339213
## [8,] -0.2359207076 -0.083804838 0.195581899 0.037136383 0.20370474
## [9,] -0.3334726731 0.105698197 0.058235559 0.141495543 0.15033629
## [10,] -0.0582955868 -0.140444357 -0.001589589 -0.123980447 -0.20834424
## [11,] -0.1879761471 -0.107183098 -0.248112711 0.107153245 0.06329444
## [12,] -0.0312374324 0.048998675 0.099388387 0.009141556 -0.03555842
## [13,] -0.0214983987 0.076277237 -0.082433313 -0.377517079 0.29194375
## [14,] -0.1831862658 -0.295982537 0.043295372 -0.161989688 -0.14129937
## [15,] -0.0892716733 0.133319468 0.164494910 -0.016744545 -0.10958822
## [16,] -0.2048646256 -0.246091640 -0.098168091 -0.042349949 -0.03808803
## [17,] -0.2344864497 0.238516369 0.291341321 0.033186539 -0.06563561
## [18,] -0.0320928344 0.054511479 0.090408412 -0.001137113 -0.05484129
## [19,] -0.1720858750 -0.194330230 0.142128166 -0.079235812 0.04390342
## [20,] -0.0078784656 0.038151177 -0.058338963 -0.289781327 0.32467730
## [21,] -0.1381976245 0.130455228 -0.248376998 0.065730253 -0.06531480
## [22,] -0.2546395582 -0.265142754 0.077424414 -0.061291765 0.07187651
## [23,] -0.0636729692 0.141296550 -0.024125732 -0.214479862 -0.12652124
## [24,] -0.0025963189 0.014554770 -0.025626722 -0.131124543 0.16561797
## [25,] -0.1978881589 -0.076895257 0.056901330 0.053405145 0.16045684
## [26,] -0.0689963439 0.164487874 -0.095056328 -0.339631128 -0.04453663
## [27,] -0.0065734019 0.030814251 -0.045368949 -0.223348667 0.24034822
## [28,] -0.0862456542 0.123619846 0.206435714 0.012210082 -0.08595017
## [29,] -0.2375124487 0.274479950 -0.027411095 -0.036509914 -0.16411286
## [30,] -0.1030970866 -0.219091774 0.023876785 -0.172477505 -0.23869805
## [31,] -0.1156005468 0.210479995 -0.048543911 -0.208213126 -0.19131677
## [32,] -0.0217080078 0.067899758 -0.053519840 -0.229092867 0.06070853
## [33,] -0.1266371117 0.200078700 -0.139284127 -0.128638496 -0.16266212
## [34,] -0.0551935383 -0.125805661 0.023884271 -0.111207145 -0.15864067
## [35,] -0.1415520797 0.015845772 -0.279065375 0.136080784 0.04106613
## [36,] -0.1106762297 0.094787206 0.228891818 0.042138321 0.04154739
## [37,] -0.1096814151 -0.135439731 -0.134255585 -0.004765675 -0.05166695
## [38,] -0.0803082094 -0.048112344 -0.161213887 0.059801004 0.01477861
## [39,] -0.0809742399 0.027674606 0.169795412 0.034068250 0.09571926
## [40,] -0.1322777780 0.163165916 -0.152071194 0.005652420 -0.11469594
## [41,] -0.2210866450 0.164067046 -0.208850510 0.121958301 -0.01686227
## [42,] -0.2052397480 0.073252655 0.276629943 0.076536430 0.15888943
## [43,] -0.1267042007 -0.237006745 -0.043333571 -0.143608372 -0.22420519
## [44,] -0.0845934368 0.107334924 0.201338251 0.024243685 -0.04083453
## [45,] -0.0065734019 0.030814251 -0.045368949 -0.223348667 0.24034822
## [46,] -0.1404635674 -0.233447603 0.075705982 -0.147002579 -0.11859609
## [47,] -0.0282274455 0.079279722 -0.042093328 -0.196404999 -0.03094891
## [48,] -0.0004747294 0.003087897 -0.006246104 -0.032882264 0.04644972
## [,6] [,7] [,8] [,9] [,10]
## [1,] -0.15433668 0.038758775 -0.293507694 0.120178849 -0.143275371
## [2,] 0.01694524 0.184338924 -0.056227569 0.236909835 0.140575869
## [3,] 0.04006946 -0.133528566 0.108782578 -0.116138102 -0.098408554
## [4,] 0.08392612 0.098508725 -0.129072682 -0.198773911 0.110653949
## [5,] 0.02977982 -0.221290476 0.179044831 -0.155536557 0.151313884
## [6,] 0.10208301 0.120761438 0.058680015 -0.052201859 -0.084134168
## [7,] 0.07972409 0.008937100 -0.001401282 0.027433737 0.274619285
## [8,] -0.23919868 -0.025809991 -0.037673906 0.018941326 0.008109148
## [9,] -0.08386704 0.022720468 0.073271203 -0.292015812 0.241261140
## [10,] 0.09826935 0.211230394 -0.162414860 -0.211783340 0.250504572
## [11,] 0.25054231 -0.242523726 -0.106249402 0.012933933 -0.095694147
## [12,] 0.17798879 0.008820393 0.083862174 0.195012840 0.055165717
## [13,] 0.09821281 0.052621287 -0.013424752 0.030928690 0.072812396
## [14,] -0.02858334 0.060517228 0.090454156 0.135162051 -0.128800640
## [15,] 0.23165796 -0.044429880 0.199935346 0.098389473 0.006291263
## [16,] 0.15220564 -0.209432256 0.039493019 -0.092483240 -0.218156736
## [17,] 0.22996360 0.020424308 0.029461374 -0.075320379 0.001226677
## [18,] 0.16880256 -0.015620114 0.160127611 0.157959001 0.038899640
## [19,] -0.20836085 0.036727560 0.048275195 0.289270338 -0.151333179
## [20,] 0.15302117 0.183119342 0.087739197 -0.074571757 -0.108707118
## [21,] -0.07324914 0.247516264 -0.044333611 0.238644837 -0.102605141
## [22,] -0.16224479 -0.112155780 0.249804229 0.133196413 -0.069585274
## [23,] -0.08779489 -0.270436182 -0.079090516 0.035525224 0.099024296
## [24,] 0.08524184 0.117595247 0.070788981 -0.071933615 -0.130713928
## [25,] -0.13820294 -0.115019581 0.187822715 -0.133428235 0.167198583
## [26,] -0.12130606 -0.249679525 -0.154008998 0.131871679 0.161878247
## [27,] 0.10941770 0.122405444 0.050458235 -0.035948806 -0.036617054
## [28,] 0.32473215 -0.001273010 0.196026802 0.251337104 0.070740658
## [29,] -0.10582075 0.084475348 0.123606375 -0.241941621 -0.176862830
## [30,] 0.04824161 0.238780622 -0.067440959 -0.035397007 0.181523143
## [31,] -0.13593296 -0.180724809 -0.004915977 -0.073786387 -0.124555243
## [32,] -0.02891431 -0.145047523 -0.126523292 0.135276715 0.248385592
## [33,] -0.17319637 0.040386229 -0.011445625 0.027317260 -0.232284588
## [34,] 0.01337832 0.203753366 -0.048349464 -0.006415738 0.235269940
## [35,] 0.14064709 0.021593873 -0.152453774 0.269864177 0.025998673
## [36,] 0.13068497 0.051263418 -0.281291971 0.028443975 -0.050887494
## [37,] 0.23383146 -0.174321331 -0.158640892 -0.102208036 -0.257864287
## [38,] 0.18962437 -0.135087050 -0.168774488 0.081566085 -0.165411387
## [39,] -0.01973913 0.049035616 -0.377559179 0.033133192 -0.112292798
## [40,] -0.13456361 0.216578784 0.051349572 0.005692832 -0.217842011
## [41,] -0.09126884 0.261309997 0.059149631 -0.011416353 0.080365830
## [42,] -0.04141045 0.053451109 -0.358825352 -0.075264815 -0.028207569
## [43,] 0.17835954 0.076996271 -0.156754932 -0.228308830 -0.031379505
## [44,] 0.26193669 0.027080595 0.011346845 0.180427927 0.038502542
## [45,] 0.10941770 0.122405444 0.050458235 -0.035948806 -0.036617054
## [46,] -0.10241469 0.146150933 0.110297690 0.232975685 0.033871077
## [47,] -0.07221118 -0.227336293 -0.145431934 0.136706860 0.257180725
## [48,] 0.02586142 0.040191138 0.028627156 -0.032489844 -0.066008023
## [,11] [,12] [,13] [,14] [,15]
## [1,] -0.099643714 0.0786030590 0.2370736975 0.036692213 -0.042633056
## [2,] -0.098633485 -0.0064999438 0.0536957489 -0.241128573 -0.218745333
## [3,] -0.375033353 0.0997258651 -0.0302497029 -0.128345136 -0.158346501
## [4,] 0.089195340 0.0190103318 0.3001843694 -0.005352065 -0.274709457
## [5,] 0.095691459 -0.0769909062 -0.0971445877 0.038261855 -0.025641418
## [6,] -0.103819289 -0.3181593563 0.0822591603 -0.013989263 0.070083529
## [7,] -0.142555115 -0.0270085509 -0.0836957817 -0.123901657 -0.081112303
## [8,] -0.024560936 0.0600514551 0.2892976722 0.198297298 -0.076475454
## [9,] 0.017006868 0.0043081711 -0.0104030456 0.019535764 0.126085494
## [10,] -0.019075383 0.0051379051 0.1783576845 0.191515550 -0.114601223
## [11,] -0.101788822 0.0123431395 -0.0866681007 0.169721385 0.099128714
## [12,] 0.244525623 -0.1343661512 -0.0144036069 0.227319797 -0.270714179
## [13,] 0.101338864 0.1627843947 -0.0301120660 -0.011006893 0.100423671
## [14,] 0.035547280 -0.0104612744 -0.1211327029 -0.300407387 -0.001160090
## [15,] -0.206350645 0.1671324222 0.2770769979 -0.130231670 0.190226522
## [16,] 0.205948306 -0.0253112279 -0.0274459817 -0.234395234 0.010171534
## [17,] -0.048614118 0.0188998355 -0.1495438401 -0.094079021 0.099364083
## [18,] -0.046076065 0.1171084083 0.3543778446 -0.021786901 0.221766619
## [19,] -0.112286634 0.0558605404 0.0743453049 -0.014734192 -0.065860493
## [20,] -0.087266285 -0.0405380757 -0.0017131960 0.012387413 -0.081953763
## [21,] 0.127005817 -0.0117059955 0.1253423447 -0.012917658 -0.057811614
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## [24,] -0.184674719 -0.5585621371 0.1408921544 -0.016083743 0.042508180
## [25,] 0.100925410 -0.0348094333 0.1122835395 0.226884945 -0.081608837
## [26,] 0.130110372 -0.0669632747 0.0315346816 0.044822684 0.057526387
## [27,] 0.021876951 0.3291720956 -0.0976553822 0.027049760 -0.142160744
## [28,] 0.130635666 -0.0065328673 0.1927903106 0.107332846 0.002727578
## [29,] -0.012334739 0.0472626052 -0.1089745114 0.045839007 0.110269886
## [30,] -0.105035973 -0.0142405484 -0.1204985350 0.080599418 0.116131949
## [31,] -0.150962987 -0.0237719300 -0.0580703255 0.135338800 -0.263462159
## [32,] 0.183747454 -0.0094450194 0.0433047234 -0.108888997 0.326041691
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## [34,] -0.181151755 -0.0186561788 -0.1628573692 0.323183205 0.183282825
## [35,] -0.229997268 0.0247938150 0.0087165519 0.111823594 -0.123857648
## [36,] 0.119078201 -0.1217401490 -0.3097837498 -0.102269321 -0.038690660
## [37,] 0.065620891 0.0545709729 0.0817741120 0.060837618 0.155914672
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## [39,] -0.002821714 -0.0216139605 -0.0524609283 -0.102667791 0.012789940
## [40,] 0.246667125 0.0005100111 0.0516559070 0.072475266 0.184356379
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## [43,] 0.165646564 0.0209323905 0.2196548433 -0.197140765 -0.124417239
## [44,] 0.271183639 -0.1777335264 -0.2118879605 0.131588512 -0.238269840
## [45,] 0.021876951 0.3291720956 -0.0976553822 0.027049760 -0.142160744
## [46,] -0.173568174 -0.0164819758 -0.2737906895 0.067562310 0.157939499
## [47,] 0.070495704 -0.1087737843 0.0559948390 -0.148262079 0.125731416
## [48,] -0.112383104 -0.4073007730 0.1062620384 -0.015302747 0.048855636
## [,16] [,17] [,18] [,19] [,20]
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## [4,] -0.029275772 0.125935121 0.215556117 -0.2310458442 0.331326772
## [5,] 0.340588556 -0.093979374 0.038939005 -0.0313837807 0.173275821
## [6,] -0.017953074 0.022664822 0.372401038 0.4158130272 0.027376347
## [7,] 0.035031621 -0.299110229 0.165970726 -0.1451006657 -0.013715246
## [8,] -0.185746153 0.090816539 -0.055511539 0.0622958624 -0.116376646
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## [10,] 0.077517410 0.045403832 0.044656524 -0.0361971078 0.210516854
## [11,] 0.048639755 -0.135868884 0.057752284 -0.0722649824 0.167524947
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## [29,] -0.184356659 -0.106204106 0.095207349 -0.0893704916 0.103404388
## [30,] 0.041476285 -0.057927593 -0.076340744 0.0804508246 -0.262249182
## [31,] 0.104975322 -0.144582303 0.121744663 -0.0371976998 -0.214644952
## [32,] -0.144710482 0.096986903 0.128245413 -0.1452680778 0.144001918
## [33,] 0.242020004 0.004775827 0.149853992 -0.1600998847 -0.179825177
## [34,] 0.142714377 -0.062278148 -0.138628601 0.1412764123 0.134084463
## [35,] -0.006145550 0.248883933 0.116195334 -0.1056669255 -0.089614763
## [36,] 0.189507284 0.229708295 -0.003006369 -0.0233022951 0.057322500
## [37,] -0.222826628 -0.028111583 -0.188836374 0.1794841212 -0.077829861
## [38,] -0.248823000 0.172337242 -0.057737616 0.0112523687 0.001319388
## [39,] 0.353987284 -0.170732323 -0.044060413 0.0719044431 0.112458474
## [40,] 0.046554178 -0.009809241 -0.147044539 0.0776460419 0.299058674
## [41,] -0.177774031 -0.194540413 -0.150112299 0.1368865080 0.112259886
## [42,] 0.062472119 0.014995214 -0.040279784 0.0233757289 -0.190945645
## [43,] -0.098734785 0.016639218 0.010928772 0.0043253802 -0.190345976
## [44,] -0.148840419 0.016518403 0.006477177 0.0031952581 0.066146578
## [45,] 0.033158600 -0.029481549 -0.255448732 -0.1571432208 -0.004754105
## [46,] -0.015562624 -0.018158120 -0.004063834 -0.0247652757 0.059895270
## [47,] -0.129631843 0.044174594 -0.291868363 0.0805780092 0.203848834
## [48,] -0.005359378 -0.007695342 -0.362763583 -0.5662128808 -0.045960460
## [,21] [,22] [,23] [,24] [,25]
## [1,] 0.2208684340 0.10690302 -0.0567608955 -0.155898463 -0.074579510
## [2,] 0.1898046899 -0.22211101 0.1754099184 0.087867822 -0.235829896
## [3,] 0.2808638752 -0.05587835 -0.1674022699 -0.054751545 0.074018912
## [4,] -0.2787962425 -0.07958535 0.0279084092 0.319894237 0.166149094
## [5,] 0.0520892097 0.11095478 -0.0643586902 -0.043754704 0.072364435
## [6,] -0.0478331810 0.01395297 -0.0001071867 -0.024016761 0.133456083
## [7,] -0.0989230516 0.03892521 0.0645295180 -0.161341370 0.045281001
## [8,] 0.0914676161 0.05799847 0.1431359915 -0.123311586 -0.033412692
## [9,] -0.1265634291 0.06725144 -0.0103623344 0.138102034 0.090524393
## [10,] 0.0545418416 0.01449414 0.0704037353 -0.110304763 -0.117276487
## [11,] -0.0051836656 0.16303815 0.0342795235 -0.089469119 0.065430389
## [12,] 0.1802470852 -0.03223512 -0.2896552122 0.309137322 0.101932694
## [13,] 0.1853353149 -0.19391493 -0.0228618240 -0.070137157 0.309809532
## [14,] -0.1256251896 0.10716955 -0.2517133008 -0.017923935 0.037348054
## [15,] 0.0941576011 0.02557857 -0.0097242616 -0.061422279 0.132601719
## [16,] 0.2388284314 0.09181721 0.1550428935 0.166849340 -0.114027888
## [17,] 0.0733705996 0.19886519 0.1253007131 0.052873786 -0.004976271
## [18,] -0.3401693852 -0.18118989 0.0577320441 -0.055263294 -0.155497131
## [19,] -0.1015483111 0.02870859 0.1735511930 -0.199138324 -0.004286802
## [20,] -0.1405522589 0.13785758 0.0159622374 0.050803287 -0.232596797
## [21,] 0.1558267223 0.16072970 0.0287623700 0.080857412 0.160951232
## [22,] -0.0168191971 -0.16525633 0.0224517576 0.149096634 -0.089010287
## [23,] -0.1928507401 0.09047383 0.0432072719 -0.049798085 0.283260448
## [24,] -0.0359623294 0.05175330 0.0069398748 0.036028371 -0.178686184
## [25,] -0.0009446519 -0.23000177 -0.2417509076 -0.172822804 -0.053219967
## [26,] -0.0333347697 -0.04913203 0.1575154865 -0.006986629 0.149008983
## [27,] -0.0378105609 0.04284195 0.0050147111 0.011405613 -0.043862129
## [28,] -0.0314283182 0.03031286 -0.0119754366 0.099836833 -0.014369342
## [29,] -0.0150338247 -0.09208359 -0.1584579914 0.072905644 -0.337252118
## [30,] 0.0570007973 0.11728702 -0.2531948113 -0.278750797 0.025068562
## [31,] -0.0114366257 -0.20559727 0.0625956283 0.023499761 -0.129914121
## [32,] 0.2631643832 -0.12854571 -0.1748069035 0.006142532 -0.197707958
## [33,] -0.0375355580 0.17004049 0.1016097330 0.022295489 -0.070255911
## [34,] 0.2148677369 -0.05222812 0.2797174524 0.147591205 -0.092991259
## [35,] -0.0050779836 0.14876701 -0.2356485522 0.066328791 -0.113326538
## [36,] -0.2218555310 -0.19065963 0.1309069246 -0.243077379 -0.034582124
## [37,] 0.0546275776 -0.25428436 0.2819585060 -0.001869257 0.009623732
## [38,] -0.2405882843 -0.18647203 -0.2144082928 0.035978865 0.050335206
## [39,] -0.0387887502 -0.29418764 -0.3544232848 0.104440738 -0.061571454
## [40,] -0.0890997193 0.13363101 -0.1286074642 -0.185774201 0.210625167
## [41,] -0.0868268148 -0.27990760 0.0764254754 -0.046923408 0.086407770
## [42,] 0.0081399761 0.17450432 0.0590707737 0.326377123 0.155977543
## [43,] -0.0031301357 0.01005546 -0.0808936472 -0.112059731 -0.009055120
## [44,] -0.0018103297 -0.02036933 0.1208479147 -0.314723993 -0.063135270
## [45,] -0.0378105609 0.04284195 0.0050147111 0.011405613 -0.043862129
## [46,] -0.1511655434 -0.11567042 0.0776538960 0.286462141 0.162913909
## [47,] -0.2005296421 0.28269930 -0.0689491284 0.072853997 -0.308491100
## [48,] 0.1950171100 -0.16777483 -0.0184635360 -0.051830524 0.235004907
## [,26] [,27] [,28] [,29] [,30]
## [1,] -0.127166434 2.731135e-16 0.26359174 0.181976368 0.11436565
## [2,] -0.088739549 1.015117e-16 0.07560462 -0.032232181 -0.13898014
## [3,] -0.015547383 -1.467448e-16 -0.21577436 0.061910783 0.05873831
## [4,] -0.093074515 -1.330338e-16 -0.07201234 0.179951085 0.04546114
## [5,] -0.114359259 2.437475e-16 0.14059459 0.099344900 0.22366027
## [6,] 0.086523021 -1.810011e-16 0.12570137 0.130224023 -0.31930645
## [7,] -0.124905760 -1.124855e-16 -0.21934319 -0.110444882 -0.18685123
## [8,] 0.196662154 -4.120809e-16 -0.28275058 -0.095230236 -0.12657648
## [9,] -0.044553819 2.388999e-16 0.08002881 0.082750215 0.10707304
## [10,] 0.188131678 5.687204e-17 0.14269228 -0.312112389 0.02548184
## [11,] 0.089516659 -5.609270e-16 -0.16896008 0.047125885 -0.01931472
## [12,] 0.017756690 -1.171073e-16 -0.29880890 -0.144789663 -0.06144100
## [13,] 0.160135921 -3.936951e-16 0.10218335 0.074237929 -0.08866092
## [14,] 0.089955733 -2.375453e-16 0.07185781 -0.107852977 0.05731813
## [15,] -0.264309423 -2.138098e-16 -0.12016699 -0.334234233 -0.07822829
## [16,] 0.250433771 1.199660e-16 0.09980885 -0.026968192 0.01226232
## [17,] -0.089870376 2.733304e-17 0.21566856 0.014346740 -0.02147510
## [18,] 0.347154187 4.278574e-16 -0.12232562 0.303191345 0.09430460
## [19,] -0.099963598 -4.771598e-17 0.04193232 0.015298876 0.05797566
## [20,] -0.126565698 8.964093e-16 -0.11423107 -0.103925705 0.21699915
## [21,] -0.063161280 4.018948e-16 0.03720737 0.219864132 0.30107951
## [22,] 0.145137539 1.928977e-16 0.03757852 -0.244356030 -0.09706321
## [23,] 0.137450244 -2.676872e-16 0.08695401 0.080444357 0.04133720
## [24,] -0.105176472 -3.699221e-16 -0.11981451 -0.116115417 0.25993120
## [25,] -0.220984935 7.246944e-18 0.02340170 0.140663114 -0.08807204
## [26,] -0.088612459 -6.291678e-16 0.13886957 -0.240204897 0.02608926
## [27,] -0.018368497 -7.071068e-01 0.00587977 0.014006089 -0.05791495
## [28,] -0.022994568 -1.554468e-16 0.24848802 -0.005228987 -0.03644398
## [29,] 0.140468545 3.650444e-16 0.09964179 0.132796322 -0.18001404
## [30,] -0.037092085 -2.640402e-16 -0.05328392 0.017814319 0.05643042
## [31,] 0.089127988 3.231950e-16 -0.05574751 0.037329420 0.16695576
## [32,] 0.032864017 3.852128e-16 -0.26929096 0.102775121 0.29985762
## [33,] -0.247521062 2.463818e-16 -0.05121122 -0.076741839 -0.14916518
## [34,] 0.085572692 2.696332e-16 0.04276084 0.041053011 -0.05211534
## [35,] 0.196419524 1.493479e-16 0.01406534 0.131085293 -0.13472675
## [36,] 0.088239879 -3.161639e-16 -0.23349785 -0.051687982 -0.01580170
## [37,] -0.306405646 1.949212e-16 -0.11862103 0.125299610 -0.09874961
## [38,] 0.024733592 6.132436e-17 0.26073658 -0.271080454 0.20789126
## [39,] -0.176230024 4.727516e-16 0.11423177 -0.054105927 -0.13010028
## [40,] 0.127025056 -6.710082e-16 -0.16625005 -0.063862235 -0.13272900
## [41,] 0.065088158 -3.188850e-16 0.08876034 -0.204416310 0.18949518
## [42,] 0.184774109 -2.860682e-16 -0.14992437 -0.069709571 0.05963505
## [43,] -0.111103428 1.321714e-16 -0.06715047 0.110633106 -0.08076156
## [44,] 0.008299174 3.048275e-16 0.06496607 0.167340360 0.11115484
## [45,] -0.018368497 7.071068e-01 0.00587977 0.014006089 -0.05791495
## [46,] -0.221859353 1.236200e-16 -0.13426499 0.248333739 -0.01854118
## [47,] -0.098721646 6.055661e-16 0.04143650 0.050896488 -0.30204844
## [48,] 0.127086479 2.956172e-16 0.11421654 0.103708406 -0.21376318
## [,31] [,32] [,33] [,34] [,35]
## [1,] -0.141762811 0.103918920 0.210191184 -0.153130736 0.025104254
## [2,] -0.102362255 0.366476860 -0.012958516 -0.208060316 0.224704625
## [3,] 0.085976489 0.038582144 0.040415597 -0.075883211 -0.047972690
## [4,] -0.214721441 0.045615920 0.236311489 0.067142648 0.067701012
## [5,] 0.151260130 0.286498930 -0.033246153 -0.157871173 -0.064528887
## [6,] 0.148578211 0.150335130 0.092644667 0.154786200 -0.203840715
## [7,] -0.045340049 -0.073908874 -0.069966033 -0.130020320 -0.310352671
## [8,] -0.145269681 -0.027901139 0.091434246 0.193019398 -0.078669819
## [9,] 0.213021394 -0.187779542 0.031107495 -0.014078023 -0.058076830
## [10,] 0.273651514 0.042957846 -0.292027716 0.057361623 0.034323506
## [11,] -0.111261711 0.002857108 -0.001056778 0.387608054 0.370903641
## [12,] 0.316258203 0.054203513 0.085352875 -0.120065576 0.199516272
## [13,] 0.010975443 -0.026917547 -0.030197563 -0.067793679 0.118711708
## [14,] 0.031434024 -0.152707972 0.158819055 -0.044663859 -0.007394071
## [15,] 0.032721338 -0.066890443 0.288763839 0.075551516 -0.037865934
## [16,] -0.060972464 -0.128514736 0.189567683 0.005107489 0.038598615
## [17,] -0.043274516 0.022285713 -0.140473516 -0.056937069 0.127591038
## [18,] 0.179497435 0.087744078 0.070703146 -0.183747715 0.096867613
## [19,] 0.369834848 -0.105056178 -0.188080626 -0.029966534 0.138861006
## [20,] -0.090723679 -0.083009855 -0.050624307 -0.089174946 0.159232506
## [21,] 0.269609439 -0.071769895 -0.029353536 0.255633115 -0.067884491
## [22,] -0.093447295 0.137690421 -0.126988343 0.011966087 -0.174796343
## [23,] -0.043387653 -0.081276842 -0.170895789 -0.137403535 0.016650137
## [24,] -0.112056243 -0.099583241 -0.054333130 -0.077103374 0.046352478
## [25,] -0.097266530 -0.149616160 0.025837244 -0.021846106 0.236384652
## [26,] -0.098117537 -0.129182855 0.082111471 -0.101249796 0.297662454
## [27,] 0.034810378 0.045925092 0.032869737 0.062481843 -0.107275771
## [28,] -0.264440455 -0.055391809 -0.391909372 0.202316891 -0.116243839
## [29,] 0.018131010 0.013862385 -0.002327383 -0.002286040 0.191473015
## [30,] -0.131147571 0.329818692 0.005597738 0.201206155 0.136293811
## [31,] -0.075180044 0.058250186 -0.034027587 0.235827831 -0.221526975
## [32,] -0.043526311 0.007520335 -0.145817484 0.013194342 -0.227364944
## [33,] 0.134450073 0.076836312 0.100337370 -0.039802825 -0.105378590
## [34,] -0.010936115 -0.328772410 0.236832572 -0.196196042 -0.116569979
## [35,] -0.041736163 -0.315799160 -0.050592296 -0.093042677 -0.012069958
## [36,] 0.177128548 0.006980632 0.056944208 0.006065066 0.109189003
## [37,] 0.097186778 0.011292019 -0.221363130 -0.045866193 -0.043560903
## [38,] 0.043233156 0.216450086 0.187141614 -0.164458807 -0.198168623
## [39,] 0.021287307 -0.251592819 -0.124535644 0.153349687 -0.057811929
## [40,] -0.288008870 0.021759251 -0.162780491 -0.327734170 -0.032073845
## [41,] -0.050390440 -0.049253017 0.168816443 0.282064480 0.032817368
## [42,] -0.062846218 0.239726236 -0.085456127 -0.084833993 -0.042318415
## [43,] 0.003539426 -0.106529287 -0.052716135 -0.158896602 -0.142031204
## [44,] -0.143827616 -0.020147507 0.267392029 -0.020750387 -0.201172959
## [45,] 0.034810378 0.045925092 0.032869737 0.062481843 -0.107275771
## [46,] -0.128386154 0.085408581 -0.059074057 0.038125335 0.014837579
## [47,] 0.143331635 0.145619882 0.160812444 0.149090623 -0.054652024
## [48,] 0.086802541 0.071456320 0.037243718 0.050986613 -0.029135426
## [,36] [,37] [,38] [,39] [,40]
## [1,] -0.043845131 -0.033831445 0.164383465 0.145682409 0.281244048
## [2,] 0.204396537 0.027015341 -0.181766767 -0.053608619 -0.270393246
## [3,] -0.092797272 -0.014164134 -0.244892720 -0.013535116 0.188789030
## [4,] 0.085831433 0.029569550 -0.098934967 -0.137437060 0.013489470
## [5,] 0.028961498 0.021884627 0.147215092 -0.223195375 -0.145763960
## [6,] 0.147970209 -0.060812857 0.022145907 0.061498179 -0.006099202
## [7,] -0.057111001 0.034175824 -0.093820013 0.056489224 0.259653541
## [8,] -0.100428211 0.014135492 -0.138145912 -0.294039244 -0.142517360
## [9,] -0.054469875 -0.009969256 -0.058197022 -0.023515272 -0.257871763
## [10,] -0.076284248 -0.039661260 -0.066130031 0.379527200 -0.067526461
## [11,] 0.119763225 -0.006335031 -0.173265135 0.125915817 -0.006332030
## [12,] 0.015414504 -0.035646000 0.110315118 -0.011830029 0.060182508
## [13,] -0.092883453 -0.002427860 -0.022317731 -0.069531939 0.007925255
## [14,] 0.311404818 0.096472020 -0.283416823 0.202430070 0.061821713
## [15,] 0.012771875 0.012177372 0.225105353 0.071924342 -0.272534672
## [16,] -0.009343961 -0.013385332 0.022467738 -0.049298602 -0.096448981
## [17,] -0.001906742 -0.036859025 -0.009474814 0.023063412 0.114872354
## [18,] -0.134800361 -0.063017802 -0.114750769 0.083312904 0.050853308
## [19,] 0.202405624 0.031755416 0.054162720 -0.143377772 -0.162583087
## [20,] -0.213648796 0.632261078 0.016127554 0.018456463 -0.001292040
## [21,] -0.073566783 0.010439035 -0.018422743 -0.028680935 0.087746295
## [22,] -0.314906720 -0.063576672 0.040454905 0.012997185 0.210560540
## [23,] -0.004188593 -0.019173724 -0.169286930 -0.096182925 -0.029808686
## [24,] 0.063602629 -0.527756223 -0.032530978 -0.061875455 0.005193140
## [25,] 0.268520884 0.022356180 0.004960339 0.287344518 0.173075041
## [26,] -0.163123402 -0.141679495 0.093637520 -0.002381537 0.019564698
## [27,] 0.116033924 -0.235140231 0.002252238 0.018005530 -0.002256963
## [28,] 0.208536189 0.093600719 -0.024468622 -0.224941393 0.173930096
## [29,] -0.106107432 -0.051130911 0.033563794 -0.120540758 -0.010877655
## [30,] -0.140250033 -0.040251118 0.017319909 -0.261277289 -0.016910864
## [31,] 0.251780518 0.118761396 0.348276873 0.146595264 -0.167713310
## [32,] 0.149225256 0.044587003 -0.097393873 0.014122006 -0.023026601
## [33,] -0.047143166 0.026802155 -0.321968637 -0.036604571 0.157528757
## [34,] 0.244287256 0.087227200 -0.041872977 -0.171243372 0.092984840
## [35,] -0.155213415 -0.072594163 0.308375283 0.017502118 -0.042762304
## [36,] 0.161866890 0.035584297 0.218090369 -0.239337942 0.214535025
## [37,] -0.065253169 -0.016004588 -0.009385422 0.099499575 0.025357954
## [38,] 0.061339152 0.056557254 -0.071906121 -0.132260837 0.012241556
## [39,] -0.137167723 -0.018642119 -0.239211866 -0.091068828 -0.272148235
## [40,] 0.168414243 0.018621405 0.105892724 0.072237927 -0.234168322
## [41,] -0.049676166 -0.017367108 0.121678763 0.053150123 0.219655030
## [42,] 0.107172915 0.029538747 0.035777715 0.260917538 0.031916413
## [43,] -0.064629235 -0.009972501 0.239113521 -0.127102756 0.041370376
## [44,] -0.233842902 -0.033767375 -0.168412566 0.246669073 -0.290623992
## [45,] 0.116033924 -0.235140231 0.002252238 0.018005530 -0.002256963
## [46,] -0.184523545 -0.066502226 0.122023203 0.196265061 -0.095860300
## [47,] 0.011016765 0.069266153 0.098969165 0.045976224 0.017158631
## [48,] -0.038740827 0.314413289 0.018605540 0.033689212 -0.002678256
## [,41] [,42] [,43] [,44] [,45]
## [1,] 0.174638599 0.086475669 -0.128844507 -0.066787468 -0.1843365161
## [2,] 0.042921951 -0.065172035 -0.008706158 0.022217078 -0.0820102678
## [3,] -0.255840269 -0.251605622 0.028329069 -0.267404453 0.1529234772
## [4,] -0.042423702 0.237827234 -0.021868689 -0.087856472 0.0869758000
## [5,] -0.128645278 -0.038463324 -0.010234596 0.097329556 -0.0244278280
## [6,] 0.110327377 0.025438955 0.279132222 -0.127645951 -0.0480987316
## [7,] -0.049263044 0.074828765 -0.076949310 -0.095252760 -0.0341359262
## [8,] -0.034443512 -0.109947371 -0.080731941 -0.075208101 -0.2382728679
## [9,] 0.099056832 0.052445245 -0.092568793 -0.174000407 -0.0715978172
## [10,] 0.104477458 -0.081742706 -0.163976394 -0.128921211 -0.0671039415
## [11,] -0.008442478 -0.124256733 0.123284612 0.244249571 -0.1688774714
## [12,] 0.047429364 0.081435826 0.049046648 -0.004587643 -0.1098595039
## [13,] -0.161476099 -0.040994424 -0.485690580 0.230403525 0.0955577025
## [14,] -0.128820080 0.163084454 -0.159639288 0.037256317 -0.1992566016
## [15,] 0.198333572 0.122311299 -0.097172616 0.194827907 0.0279455548
## [16,] 0.213511290 -0.093842420 -0.079754815 -0.374946851 0.2297491410
## [17,] -0.044700659 0.134086638 0.220137704 -0.022991886 -0.2697181001
## [18,] -0.090938159 0.018405815 0.107682369 -0.036565081 -0.0569922882
## [19,] -0.081009274 -0.012777777 0.175621052 0.017109475 0.3403501942
## [20,] 0.021937711 0.005253277 0.061345508 -0.029077001 -0.0121573489
## [21,] -0.133807182 0.048068627 -0.062290284 0.020155019 -0.1990730286
## [22,] -0.047030736 0.240717358 0.119862969 0.203257393 -0.0654176813
## [23,] 0.435094960 0.129307956 -0.013434578 0.226647936 0.0007791075
## [24,] -0.085414404 -0.018469727 -0.193344116 0.086514069 0.0308370156
## [25,] 0.054470343 -0.067926175 0.028773383 -0.022784312 0.1682973101
## [26,] -0.204098319 -0.040179742 0.287176174 -0.241675530 -0.0974015232
## [27,] 0.045916537 0.011415184 0.132075775 -0.061851619 -0.0247107772
## [28,] -0.012914563 -0.161534425 -0.141116732 -0.112373944 0.1074145443
## [29,] 0.095162050 0.057685069 -0.092832713 0.212056368 -0.0157858278
## [30,] -0.005665475 0.296538787 0.064443207 -0.119369692 0.2291019426
## [31,] -0.162242581 0.092785173 -0.079386940 -0.007545437 -0.1064231545
## [32,] 0.309243000 0.074017002 0.182974873 0.002543627 -0.0198761104
## [33,] 0.260487245 -0.092934544 -0.033563306 0.087390577 0.2122461344
## [34,] -0.146958533 0.064900601 0.107917953 0.170905609 -0.0172330667
## [35,] 0.060209821 0.113376281 0.017630132 -0.061423262 0.2225127560
## [36,] 0.181033903 -0.028401342 -0.200167693 -0.136776978 -0.0924284905
## [37,] -0.104424447 0.383969577 -0.109154401 -0.063627554 0.0517804022
## [38,] 0.025825508 -0.175075530 -0.014352421 -0.052859947 -0.0443844327
## [39,] -0.110730912 0.003078414 0.114422858 -0.004095152 -0.0428839037
## [40,] -0.126136295 0.039686070 0.021605701 -0.180055469 -0.0854137511
## [41,] 0.035344386 -0.097390885 0.140875241 0.086421670 0.2054754982
## [42,] -0.129896921 -0.064634482 0.075806883 0.212798982 0.3786168471
## [43,] -0.017977350 -0.425071436 0.212369418 0.327036849 -0.1394687945
## [44,] -0.083791877 -0.012006795 0.032581845 0.122719041 0.1535083592
## [45,] 0.045916537 0.011415184 0.132075775 -0.061851619 -0.0247107772
## [46,] 0.200830165 -0.353100437 -0.139277484 -0.137099869 -0.1210684352
## [47,] -0.264958803 -0.076557405 -0.206389046 0.005536147 0.0490507736
## [48,] 0.041891221 0.008667091 0.087371730 -0.038365578 -0.0129836790
## [,46] [,47] [,48]
## [1,] -0.030848335 -0.126766284 0.1007814759
## [2,] -0.018453210 -0.100900566 0.0960549006
## [3,] -0.148642320 -0.162440681 0.0938082324
## [4,] 0.006845561 0.011134134 -0.0093233898
## [5,] -0.298386254 0.027624094 -0.3158573581
## [6,] -0.106188735 0.035521380 0.0207724730
## [7,] 0.225354164 0.350138263 0.0607705280
## [8,] -0.094049193 0.110358157 -0.3079094291
## [9,] 0.007629335 -0.369241788 0.3788546259
## [10,] -0.081101869 0.030051818 -0.0656968616
## [11,] 0.018212194 -0.165041747 0.1834181509
## [12,] 0.107739983 -0.012002600 -0.0689488832
## [13,] 0.214315476 -0.091176877 -0.0551474253
## [14,] -0.274675004 -0.005723569 -0.1393900941
## [15,] -0.056555925 0.093830593 0.0773181781
## [16,] 0.273700340 0.155016030 -0.0001809073
## [17,] 0.374044115 -0.051103162 -0.3704530068
## [18,] 0.104875201 -0.026056556 -0.0725731171
## [19,] 0.154959825 0.057319530 0.0578178206
## [20,] -0.027325139 0.012013812 0.0072858703
## [21,] 0.067876736 0.296734133 0.1812933094
## [22,] 0.050684913 -0.204311204 0.2927710111
## [23,] 0.025529481 0.061753287 -0.0524860522
## [24,] 0.067466777 -0.019629249 -0.0112493425
## [25,] 0.139433741 0.156612119 -0.0168183314
## [26,] -0.236713818 0.159550944 0.1206335047
## [27,] -0.055057524 0.020935924 0.0124456799
## [28,] -0.194753606 -0.021361913 0.1291984983
## [29,] -0.209019087 0.434925604 0.1256666421
## [30,] 0.136591263 0.001886812 0.0647991506
## [31,] 0.222188876 -0.087625142 -0.0469898470
## [32,] -0.033215481 0.004623796 -0.0166537076
## [33,] 0.036420715 -0.250085484 -0.1539063257
## [34,] -0.013792710 -0.035583126 0.0392457598
## [35,] -0.189844551 -0.185171103 -0.1991281445
## [36,] -0.135057180 -0.067785700 0.1195317553
## [37,] -0.216394410 -0.022661111 -0.1126547489
## [38,] 0.161929336 0.134069109 0.0451093328
## [39,] 0.109502388 0.005426871 -0.0994873521
## [40,] 0.068393345 -0.108046011 0.0573577756
## [41,] -0.059167437 -0.181075919 -0.3162729785
## [42,] -0.096492013 0.179458733 0.0627915620
## [43,] 0.064698042 -0.061018150 0.0922278354
## [44,] -0.063420721 0.054743631 0.0670049278
## [45,] -0.055057524 0.020935924 0.0124456799
## [46,] -0.022438305 0.067025413 -0.1107814369
## [47,] 0.101991676 -0.081233801 -0.0180956891
## [48,] -0.028154888 0.007057816 0.0039531909
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