4. Einsum operation by DelayedTensor (original) (raw)
By using multiple arrays or DelayedArray objects as input and writing “,” on the right side of ->, multiplication will be performed.
Hadamard Product
Hadamard Product can also be implemented in einsum, multiplying by the product of each element.
einsum::einsum('i,i->i', arrA, arrA)## [1] 0.884184478 0.340358686 0.002033908DelayedTensor::einsum('i,i->i', darrA, darrA)## <3> HDF5Array object of type "double":
## [1] [2] [3]
## 0.884184478 0.340358686 0.002033908einsum::einsum('ij,ij->ij', arrC, arrC)## [,1] [,2] [,3] [,4]
## [1,] 0.095903242 0.24678554 0.059227497 0.8368940
## [2,] 0.882787494 0.81807979 0.002996237 0.2802761
## [3,] 0.005935327 0.08811278 0.761094754 0.2071186DelayedTensor::einsum('ij,ij->ij', darrC, darrC)## <3 x 4> HDF5Matrix object of type "double":
## [,1] [,2] [,3] [,4]
## [1,] 0.095903242 0.246785543 0.059227497 0.836893967
## [2,] 0.882787494 0.818079787 0.002996237 0.280276124
## [3,] 0.005935327 0.088112781 0.761094754 0.207118634einsum::einsum('ijk,ijk->ijk', arrE, arrE)## , , 1
##
## [,1] [,2] [,3] [,4]
## [1,] 0.2028159 0.0004338344 0.01546019 0.1336936
## [2,] 0.2380355 0.1002020960 0.26567733 0.5126514
## [3,] 0.1051715 0.5268546181 0.79519643 0.9216276
##
## , , 2
##
## [,1] [,2] [,3] [,4]
## [1,] 0.16408010 0.28529712 0.91606954 0.20772660
## [2,] 0.34232199 0.69825992 0.04006002 0.01233451
## [3,] 0.02332281 0.00782271 0.03883980 0.50818227
##
## , , 3
##
## [,1] [,2] [,3] [,4]
## [1,] 0.674755829 0.75037855 0.002103667 0.009575579
## [2,] 0.409741278 0.02674256 0.556983657 0.612811532
## [3,] 0.001260131 0.60885662 0.065592706 0.925295905
##
## , , 4
##
## [,1] [,2] [,3] [,4]
## [1,] 0.08261140 0.9146791 0.2101628 0.08021131
## [2,] 0.48018868 0.9121409 0.9838111 0.64812594
## [3,] 0.02002973 0.1031858 0.7083356 0.54029142
##
## , , 5
##
## [,1] [,2] [,3] [,4]
## [1,] 0.9278604 0.475383316 0.08161134 0.06594537
## [2,] 0.0454956 0.006059121 0.92710600 0.37007272
## [3,] 0.5927317 0.479415102 0.30768537 0.18924114DelayedTensor::einsum('ijk,ijk->ijk', darrE, darrE)## <3 x 4 x 5> HDF5Array object of type "double":
## ,,1
## [,1] [,2] [,3] [,4]
## [1,] 0.2028159394 0.0004338344 0.0154601912 0.1336935654
## [2,] 0.2380355177 0.1002020960 0.2656773349 0.5126514409
## [3,] 0.1051714751 0.5268546181 0.7951964262 0.9216276407
##
## ,,2
## [,1] [,2] [,3] [,4]
## [1,] 0.16408010 0.28529712 0.91606954 0.20772660
## [2,] 0.34232199 0.69825992 0.04006002 0.01233451
## [3,] 0.02332281 0.00782271 0.03883980 0.50818227
##
## ,,3
## [,1] [,2] [,3] [,4]
## [1,] 0.674755829 0.750378555 0.002103667 0.009575579
## [2,] 0.409741278 0.026742559 0.556983657 0.612811532
## [3,] 0.001260131 0.608856620 0.065592706 0.925295905
##
## ,,4
## [,1] [,2] [,3] [,4]
## [1,] 0.08261140 0.91467912 0.21016276 0.08021131
## [2,] 0.48018868 0.91214091 0.98381106 0.64812594
## [3,] 0.02002973 0.10318578 0.70833558 0.54029142
##
## ,,5
## [,1] [,2] [,3] [,4]
## [1,] 0.927860379 0.475383316 0.081611343 0.065945371
## [2,] 0.045495601 0.006059121 0.927106001 0.370072720
## [3,] 0.592731741 0.479415102 0.307685366 0.189241139Outer Product
The outer product can also be implemented in einsum, in which the subscripts in the input array are all different, and all of them are kept.
einsum::einsum('i,j->ij', arrA, arrA)## [,1] [,2] [,3]
## [1,] 0.88418448 0.5485799 0.042406952
## [2,] 0.54857986 0.3403587 0.026310799
## [3,] 0.04240695 0.0263108 0.002033908DelayedTensor::einsum('i,j->ij', darrA, darrA)## <3 x 3> HDF5Matrix object of type "double":
## [,1] [,2] [,3]
## [1,] 0.884184478 0.548579864 0.042406952
## [2,] 0.548579864 0.340358686 0.026310799
## [3,] 0.042406952 0.026310799 0.002033908einsum::einsum('ij,klm->ijklm', arrC, arrE)## , , 1, 1, 1
##
## [,1] [,2] [,3] [,4]
## [1,] 0.13946579 0.2237231 0.10960055 0.4119896
## [2,] 0.42313517 0.4073323 0.02465126 0.2384208
## [3,] 0.03469552 0.1336812 0.39288949 0.2049560
##
## , , 2, 1, 1
##
## [,1] [,2] [,3] [,4]
## [1,] 0.15109063 0.2423710 0.11873604 0.4463300
## [2,] 0.45840460 0.4412845 0.02670601 0.2582938
## [3,] 0.03758748 0.1448239 0.42563786 0.2220396
##
## , , 3, 1, 1
##
## [,1] [,2] [,3] [,4]
## [1,] 0.10043050 0.1611049 0.07892429 0.2966772
## [2,] 0.30470324 0.2933235 0.01775158 0.1716888
## [3,] 0.02498454 0.0962650 0.28292306 0.1475906
##
## , , 1, 2, 1
##
## [,1] [,2] [,3] [,4]
## [1,] 0.006450281 0.010347176 0.005069016 0.019054484
## [2,] 0.019569965 0.018839085 0.001140119 0.011026940
## [3,] 0.001604665 0.006182746 0.018171105 0.009479197
##
## , , 2, 2, 1
##
## [,1] [,2] [,3] [,4]
## [1,] 0.09802911 0.15725275 0.07703713 0.2895834
## [2,] 0.29741748 0.28630981 0.01732712 0.1675836
## [3,] 0.02438713 0.09396321 0.27615809 0.1440615
##
## , , 3, 2, 1
##
## [,1] [,2] [,3] [,4]
## [1,] 0.22478226 0.3605830 0.17664733 0.6640192
## [2,] 0.68198289 0.6565128 0.03973136 0.3842717
## [3,] 0.05592007 0.2154591 0.63323478 0.3303353
##
## , , 1, 3, 1
##
## [,1] [,2] [,3] [,4]
## [1,] 0.038505616 0.06176853 0.030260014 0.11374771
## [2,] 0.116824926 0.11246186 0.006806056 0.06582646
## [3,] 0.009579211 0.03690854 0.108474284 0.05658705
##
## , , 2, 3, 1
##
## [,1] [,2] [,3] [,4]
## [1,] 0.15962242 0.2560573 0.12544084 0.4715334
## [2,] 0.48428982 0.4662030 0.02821404 0.2728791
## [3,] 0.03970997 0.1530019 0.44967280 0.2345778
##
## , , 3, 3, 1
##
## [,1] [,2] [,3] [,4]
## [1,] 0.27615560 0.4429932 0.21701957 0.8157788
## [2,] 0.83784811 0.8065570 0.04881185 0.4720959
## [3,] 0.06870044 0.2647017 0.77795876 0.4058325
##
## , , 1, 4, 1
##
## [,1] [,2] [,3] [,4]
## [1,] 0.1132327 0.1816415 0.08898503 0.3344956
## [2,] 0.3435448 0.3307144 0.02001443 0.1935746
## [3,] 0.0281694 0.1085362 0.31898820 0.1664044
##
## , , 2, 4, 1
##
## [,1] [,2] [,3] [,4]
## [1,] 0.22173167 0.3556894 0.17425000 0.6550076
## [2,] 0.67272749 0.6476031 0.03919216 0.3790567
## [3,] 0.05516116 0.2125350 0.62464095 0.3258522
##
## , , 3, 4, 1
##
## [,1] [,2] [,3] [,4]
## [1,] 0.29729965 0.4769113 0.23363582 0.8782395
## [2,] 0.90199853 0.8683115 0.05254917 0.5082423
## [3,] 0.07396054 0.2849687 0.83752371 0.4369053
##
## , , 1, 1, 2
##
## [,1] [,2] [,3] [,4]
## [1,] 0.12544247 0.2012277 0.09858019 0.3705640
## [2,] 0.38058883 0.3663750 0.02217257 0.2144475
## [3,] 0.03120687 0.1202396 0.35338435 0.1843476
##
## , , 2, 1, 2
##
## [,1] [,2] [,3] [,4]
## [1,] 0.18118992 0.2906546 0.1423899 0.5352450
## [2,] 0.54972500 0.5291944 0.0320262 0.3097494
## [3,] 0.04507541 0.1736748 0.5104307 0.2662729
##
## , , 3, 1, 2
##
## [,1] [,2] [,3] [,4]
## [1,] 0.04729411 0.07586654 0.037166539 0.13970941
## [2,] 0.14348897 0.13813008 0.008359466 0.08085064
## [3,] 0.01176556 0.04533252 0.133232384 0.06950243
##
## , , 1, 2, 2
##
## [,1] [,2] [,3] [,4]
## [1,] 0.16541136 0.2653436 0.12999013 0.4886343
## [2,] 0.50185329 0.4831106 0.02923727 0.2827755
## [3,] 0.04115011 0.1585507 0.46598084 0.2430851
##
## , , 2, 2, 2
##
## [,1] [,2] [,3] [,4]
## [1,] 0.25877672 0.4151150 0.20336221 0.7644407
## [2,] 0.78512109 0.7557991 0.04574005 0.4423862
## [3,] 0.06437702 0.2480436 0.72900066 0.3802928
##
## , , 3, 2, 2
##
## [,1] [,2] [,3] [,4]
## [1,] 0.027390203 0.04393782 0.021524858 0.08091217
## [2,] 0.083101084 0.07999750 0.004841352 0.04682434
## [3,] 0.006813981 0.02625416 0.077161022 0.04025207
##
## , , 1, 3, 2
##
## [,1] [,2] [,3] [,4]
## [1,] 0.29640182 0.4754711 0.23293026 0.8755873
## [2,] 0.89927456 0.8656893 0.05239047 0.5067074
## [3,] 0.07373718 0.2841081 0.83499444 0.4355859
##
## , , 2, 3, 2
##
## [,1] [,2] [,3] [,4]
## [1,] 0.06198295 0.09942955 0.04870991 0.18310104
## [2,] 0.18805448 0.18103120 0.01095579 0.10596164
## [3,] 0.01541977 0.05941212 0.17461235 0.09108884
##
## , , 3, 3, 2
##
## [,1] [,2] [,3] [,4]
## [1,] 0.06103165 0.09790353 0.04796232 0.18029085
## [2,] 0.18516827 0.17825278 0.01078764 0.10433536
## [3,] 0.01518311 0.05850028 0.17193245 0.08969083
##
## , , 1, 4, 2
##
## [,1] [,2] [,3] [,4]
## [1,] 0.14114409 0.2264154 0.11091946 0.4169474
## [2,] 0.42822710 0.4122341 0.02494791 0.2412899
## [3,] 0.03511304 0.1352899 0.39761744 0.2074224
##
## , , 2, 4, 2
##
## [,1] [,2] [,3] [,4]
## [1,] 0.034393597 0.05517226 0.027028543 0.10160058
## [2,] 0.104349179 0.10045204 0.006079236 0.05879684
## [3,] 0.008556246 0.03296707 0.096890303 0.05054411
##
## , , 3, 4, 2
##
## [,1] [,2] [,3] [,4]
## [1,] 0.2207631 0.3541356 0.17348880 0.6521462
## [2,] 0.6697887 0.6447741 0.03902095 0.3774008
## [3,] 0.0549202 0.2116066 0.62191226 0.3244288
##
## , , 1, 1, 3
##
## [,1] [,2] [,3] [,4]
## [1,] 0.25438410 0.4080686 0.19991023 0.7514646
## [2,] 0.77179402 0.7429698 0.04496363 0.4348769
## [3,] 0.06328425 0.2438332 0.71662621 0.3738375
##
## , , 2, 1, 3
##
## [,1] [,2] [,3] [,4]
## [1,] 0.19823097 0.3179909 0.15578174 0.5855852
## [2,] 0.60142703 0.5789655 0.03503829 0.3388815
## [3,] 0.04931479 0.1900091 0.55843705 0.2913161
##
## , , 3, 1, 3
##
## [,1] [,2] [,3] [,4]
## [1,] 0.010993210 0.01763469 0.008639121 0.03247455
## [2,] 0.033353081 0.03210744 0.001943104 0.01879321
## [3,] 0.002734829 0.01053725 0.030969004 0.01615539
##
## , , 1, 2, 3
##
## [,1] [,2] [,3] [,4]
## [1,] 0.26826058 0.4303285 0.21081519 0.7924565
## [2,] 0.81389484 0.7834983 0.04741637 0.4585992
## [3,] 0.06673636 0.2571341 0.75571766 0.3942301
##
## , , 2, 2, 3
##
## [,1] [,2] [,3] [,4]
## [1,] 0.05064285 0.08123840 0.039798176 0.14960176
## [2,] 0.15364894 0.14791060 0.008951371 0.08657541
## [3,] 0.01259864 0.04854237 0.142666118 0.07442367
##
## , , 3, 2, 3
##
## [,1] [,2] [,3] [,4]
## [1,] 0.24164297 0.3876300 0.18989748 0.7138266
## [2,] 0.73313778 0.7057572 0.04271158 0.4130956
## [3,] 0.06011458 0.2316205 0.68073312 0.3551134
##
## , , 1, 3, 3
##
## [,1] [,2] [,3] [,4]
## [1,] 0.014203820 0.02278497 0.011162211 0.04195887
## [2,] 0.043093980 0.04148455 0.002510595 0.02428184
## [3,] 0.003533547 0.01361470 0.040013624 0.02087364
##
## , , 2, 3, 3
##
## [,1] [,2] [,3] [,4]
## [1,] 0.23112018 0.3707499 0.18162805 0.6827417
## [2,] 0.70121196 0.6750238 0.04085162 0.3951066
## [3,] 0.05749678 0.2215341 0.65108935 0.3396494
##
## , , 3, 3, 3
##
## [,1] [,2] [,3] [,4]
## [1,] 0.07931301 0.12722944 0.06232890 0.2342950
## [2,] 0.24063337 0.23164643 0.01401896 0.1355879
## [3,] 0.01973105 0.07602339 0.22343291 0.1165567
##
## , , 1, 4, 3
##
## [,1] [,2] [,3] [,4]
## [1,] 0.030303945 0.04861188 0.02381465 0.08951952
## [2,] 0.091941295 0.08850756 0.00535637 0.05180547
## [3,] 0.007538846 0.02904705 0.08536933 0.04453404
##
## , , 2, 4, 3
##
## [,1] [,2] [,3] [,4]
## [1,] 0.24242651 0.3888869 0.19051324 0.7161412
## [2,] 0.73551503 0.7080457 0.04285007 0.4144351
## [3,] 0.06030951 0.2323715 0.68294044 0.3562649
##
## , , 3, 4, 3
##
## [,1] [,2] [,3] [,4]
## [1,] 0.29789071 0.4778594 0.23410032 0.8799855
## [2,] 0.90379182 0.8700379 0.05265364 0.5092527
## [3,] 0.07410758 0.2855353 0.83918881 0.4377739
##
## , , 1, 1, 4
##
## [,1] [,2] [,3] [,4]
## [1,] 0.08900956 0.14278410 0.06994903 0.2629391
## [2,] 0.27005242 0.25996676 0.01573287 0.1521644
## [3,] 0.02214330 0.08531776 0.25074908 0.1308066
##
## , , 2, 1, 4
##
## [,1] [,2] [,3] [,4]
## [1,] 0.21459649 0.3442436 0.16864274 0.6339298
## [2,] 0.65107954 0.6267636 0.03793098 0.3668589
## [3,] 0.05338611 0.2056958 0.60454039 0.3153665
##
## , , 3, 1, 4
##
## [,1] [,2] [,3] [,4]
## [1,] 0.04382825 0.07030681 0.034442859 0.12947107
## [2,] 0.13297365 0.12800748 0.007746858 0.07492566
## [3,] 0.01090335 0.04201041 0.123468700 0.06440908
##
## , , 1, 2, 4
##
## [,1] [,2] [,3] [,4]
## [1,] 0.2961768 0.4751101 0.2327534 0.8749225
## [2,] 0.8985918 0.8650321 0.0523507 0.5063227
## [3,] 0.0736812 0.2838924 0.8343605 0.4352552
##
## , , 2, 2, 4
##
## [,1] [,2] [,3] [,4]
## [1,] 0.2957656 0.4744504 0.23243025 0.8737077
## [2,] 0.8973442 0.8638310 0.05227801 0.5056197
## [3,] 0.0735789 0.2834983 0.83320205 0.4346509
##
## , , 3, 2, 4
##
## [,1] [,2] [,3] [,4]
## [1,] 0.09947789 0.15957681 0.07817567 0.2938632
## [2,] 0.30181305 0.29054123 0.01758320 0.1700603
## [3,] 0.02474755 0.09535191 0.28023947 0.1461906
##
## , , 1, 3, 4
##
## [,1] [,2] [,3] [,4]
## [1,] 0.14196933 0.2277392 0.11156798 0.4193852
## [2,] 0.43073083 0.4146443 0.02509377 0.2427006
## [3,] 0.03531833 0.1360809 0.39994221 0.2086351
##
## , , 2, 3, 4
##
## [,1] [,2] [,3] [,4]
## [1,] 0.30716554 0.4927376 0.24138904 0.9073839
## [2,] 0.93193138 0.8971265 0.05429301 0.5251083
## [3,] 0.07641492 0.2944254 0.86531696 0.4514040
##
## , , 3, 3, 4
##
## [,1] [,2] [,3] [,4]
## [1,] 0.26063706 0.4180992 0.20482418 0.7699362
## [2,] 0.79076532 0.7612326 0.04606888 0.4455666
## [3,] 0.06483983 0.2498268 0.73424144 0.3830268
##
## , , 1, 4, 4
##
## [,1] [,2] [,3] [,4]
## [1,] 0.08770704 0.14069467 0.06892543 0.2590914
## [2,] 0.26610062 0.25616255 0.01550265 0.1499377
## [3,] 0.02181927 0.08406927 0.24707976 0.1288924
##
## , , 2, 4, 4
##
## [,1] [,2] [,3] [,4]
## [1,] 0.24931382 0.3999351 0.19592569 0.7364867
## [2,] 0.75641092 0.7281612 0.04406744 0.4262091
## [3,] 0.06202289 0.2389732 0.70234269 0.3663864
##
## , , 3, 4, 4
##
## [,1] [,2] [,3] [,4]
## [1,] 0.22763062 0.3651522 0.17888574 0.6724334
## [2,] 0.69062472 0.6648319 0.04023482 0.3891411
## [3,] 0.05662867 0.2181893 0.64125889 0.3345212
##
## , , 1, 1, 5
##
## [,1] [,2] [,3] [,4]
## [1,] 0.29830323 0.4785212 0.23442450 0.8812041
## [2,] 0.90504339 0.8712427 0.05272655 0.5099580
## [3,] 0.07421021 0.2859307 0.84035092 0.4383802
##
## , , 2, 1, 5
##
## [,1] [,2] [,3] [,4]
## [1,] 0.06605434 0.10596064 0.05190945 0.19512815
## [2,] 0.20040695 0.19292235 0.01167543 0.11292179
## [3,] 0.01643263 0.06331464 0.18608187 0.09707207
##
## , , 3, 1, 5
##
## [,1] [,2] [,3] [,4]
## [1,] 0.23842168 0.3824626 0.1873660 0.7043107
## [2,] 0.72336448 0.6963489 0.0421422 0.4075887
## [3,] 0.05931321 0.2285328 0.6716584 0.3503795
##
## , , 1, 2, 5
##
## [,1] [,2] [,3] [,4]
## [1,] 0.21352003 0.3425168 0.16779679 0.6307499
## [2,] 0.64781359 0.6236197 0.03774071 0.3650186
## [3,] 0.05311832 0.2046640 0.60150790 0.3137845
##
## , , 2, 2, 5
##
## [,1] [,2] [,3] [,4]
## [1,] 0.024105795 0.03866915 0.018943774 0.07120984
## [2,] 0.073136285 0.07040486 0.004260817 0.04120955
## [3,] 0.005996905 0.02310597 0.067908506 0.03542537
##
## , , 3, 2, 5
##
## [,1] [,2] [,3] [,4]
## [1,] 0.21442356 0.3439662 0.16850684 0.6334190
## [2,] 0.65055488 0.6262586 0.03790041 0.3665632
## [3,] 0.05334309 0.2055300 0.60405324 0.3151124
##
## , , 1, 3, 5
##
## [,1] [,2] [,3] [,4]
## [1,] 0.08846916 0.14191723 0.06952435 0.2613428
## [2,] 0.26841288 0.25838845 0.01563736 0.1512406
## [3,] 0.02200886 0.08479978 0.24922673 0.1300124
##
## , , 2, 3, 5
##
## [,1] [,2] [,3] [,4]
## [1,] 0.29818194 0.4783266 0.23432919 0.8808459
## [2,] 0.90467540 0.8708884 0.05270512 0.5097506
## [3,] 0.07418003 0.2858144 0.84000923 0.4382019
##
## , , 3, 3, 5
##
## [,1] [,2] [,3] [,4]
## [1,] 0.17177900 0.2755582 0.13499420 0.5074446
## [2,] 0.52117252 0.5017083 0.03036278 0.2936611
## [3,] 0.04273422 0.1646542 0.48391912 0.2524428
##
## , , 1, 4, 5
##
## [,1] [,2] [,3] [,4]
## [1,] 0.07952594 0.12757102 0.06249623 0.2349240
## [2,] 0.24127940 0.23226832 0.01405660 0.1359519
## [3,] 0.01978402 0.07622749 0.22403276 0.1168697
##
## , , 2, 4, 5
##
## [,1] [,2] [,3] [,4]
## [1,] 0.18839101 0.3022062 0.14804891 0.5565174
## [2,] 0.57157289 0.5502263 0.03329903 0.3220599
## [3,] 0.04686686 0.1805772 0.53071688 0.2768555
##
## , , 3, 4, 5
##
## [,1] [,2] [,3] [,4]
## [1,] 0.1347176 0.2161064 0.1058692 0.3979633
## [2,] 0.4087294 0.3934645 0.0238120 0.2303037
## [3,] 0.0335143 0.1291300 0.3795134 0.1979782DelayedTensor::einsum('ij,klm->ijklm', darrC, darrE)## <3 x 4 x 3 x 4 x 5> HDF5Array object of type "double":
## ,,1,1,1
## [,1] [,2] [,3] [,4]
## [1,] 0.13946579 0.22372314 0.10960055 0.41198961
## [2,] 0.42313517 0.40733232 0.02465126 0.23842077
## [3,] 0.03469552 0.13368125 0.39288949 0.20495600
##
## ,,2,1,1
## [,1] [,2] [,3] [,4]
## [1,] 0.15109063 0.24237105 0.11873604 0.44633002
## [2,] 0.45840460 0.44128454 0.02670601 0.25829377
## [3,] 0.03758748 0.14482393 0.42563786 0.22203962
##
## ,,3,1,1
## [,1] [,2] [,3] [,4]
## [1,] 0.10043050 0.16110493 0.07892429 0.29667722
## [2,] 0.30470324 0.29332347 0.01775158 0.17168883
## [3,] 0.02498454 0.09626500 0.28292306 0.14759056
##
## ...
##
## ,,1,4,5
## [,1] [,2] [,3] [,4]
## [1,] 0.07952594 0.12757102 0.06249623 0.23492399
## [2,] 0.24127940 0.23226832 0.01405660 0.13595188
## [3,] 0.01978402 0.07622749 0.22403276 0.11686965
##
## ,,2,4,5
## [,1] [,2] [,3] [,4]
## [1,] 0.18839101 0.30220622 0.14804891 0.55651741
## [2,] 0.57157289 0.55022633 0.03329903 0.32205985
## [3,] 0.04686686 0.18057723 0.53071688 0.27685548
##
## ,,3,4,5
## [,1] [,2] [,3] [,4]
## [1,] 0.1347176 0.2161064 0.1058692 0.3979633
## [2,] 0.4087294 0.3934645 0.0238120 0.2303037
## [3,] 0.0335143 0.1291300 0.3795134 0.1979782