[
https://issues.apache.org/jira/browse/MATH-327?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13011196#comment-13011196
]
Paul K. Feldman commented on MATH-327:
--------------------------------------
Another unit test:
A [7 x 168] =
0.003000302 -0.005529946 0.01538155 -0.001403205 -0.018213096
0.000076204 -0.000023713 0.000093626 0.000143789 -0.000092728
-0.00009325 -0.000471574 0.000256266 -0.000235424 -0.000559821
-0.000181869 0.000070384 0.000005498 0.000383238 0.000187495
0.000744314 -0.000299571 0.000655884 -0.000367504 -0.000296129
0.001865159 0.002139813 0.001156764 -0.000274115 0.00194246
-0.001067201 -0.000965123 -0.000838439 -0.000233388 -0.000400203
0.000097493 0.000236697 -0.000612503 0.000248345 0.000058795
0.000121681 0.000441167 0.000328212 0.000333702 0.000739353
0.000205686 0.00011173 0.001217128 0.000488424 0.000382149
0.000308471 -0.000490277 0.000345624 -0.000834169 0.000216899
0.000433887 -0.000369019 0.000646984 -0.000300974 0.000373483
0.000647662 -0.000253848 0.000223624 0.000634534 0.000747524
-0.000077809 -0.000353221 0.000240388 0.000414233 0.000207479
0.000041459 -0.000305439 -0.000105042 0.00019835 0.000413267
0.000026096 -0.00046518 -0.000128547 -0.000043406 0.00005626
0.00000624 -0.000126197 -0.000020413 -0.000151383 -0.000024204
-0.000030944 0.000022925 -0.000064255 0.000240003 0.000262614
0.000044858 -0.000320061 -0.000030874 0.000131975 0.000079968
-0.000113183 0.000073552 -0.000008934 0.00004173 0.000052111
-0.000061729 0.000044233 0.00031579 0.000136546 0.000069494
0.000086781 -0.000040722 0.000040594 0.000105801 0.000037761
0.000010309 -0.000152556 0.000021932 0.000034306 0.000012486
-0.000005934 -0.000046878 0.000023209 0.000008168 0.000008117
-0.000016579 -0.00000505 0.000004528 -0.00000555 -0.000000095
-0.00000136 -0.000005205 -0.000002595 0.000000285 -0.000001563
-0.000000953 -0.000000364 -0.000001132 -0.000000645 -0.000000775
-0.000000144 -0.000000641 -0.00000031 -0.000000023 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
0.002969656 -0.005304577 0.015172372 -0.001362703 -0.01832869
0.000054703 -0.000122829 -0.00003114 0.000041451 0.000025999
-0.000135931 -0.000186937 0.000239001 -0.000051824 -0.000383595
-0.00012191 -0.000021933 -0.000024977 0.000385048 0.000119015
0.000599602 -0.000358632 0.000726135 -0.000131523 -0.000116199
0.001494981 0.001850129 0.000724508 -0.000261562 0.001491656
-0.000748772 -0.000627043 -0.000597073 0.000000987 -0.000220861
-0.000078266 0.000303396 -0.000299759 0.000036112 0.000047285
0.000101568 0.000350496 0.000181929 0.000083279 0.00025771
0.000026141 -0.000010124 0.000382831 0.000080824 0.000021461
0.000143501 -0.000042618 0.000111455 -0.000339422 -0.000006761
0.000101824 -0.000082054 -0.000060832 -0.000124609 0.000138409
0.000029263 -0.000077077 0.000092533 -0.000011487 0.000023891
-0.000064685 0.000033676 0.000077876 0.000019453 0.000176876
-0.000211758 0.000035019 0.000043861 -0.000043324 0.000183336
-0.000029838 -0.000109527 0.000065992 -0.000221244 -0.000014366
-0.000032553 -0.000062429 0.00004144 0.000035076 0.000062257
0.000033082 0.000005334 0.000073079 -0.000159208 -0.000239372
-0.000056981 0.000281376 -0.000009754 -0.000031414 -0.000108677
0.000193121 -0.000082145 0.000036054 -0.000074536 -0.000005391
0.000091036 -0.00005061 -0.000360727 -0.000218139 -0.000109819
-0.000100537 0.000092986 -0.00010101 -0.000154437 -0.000115903
-0.000022312 0.000308967 -0.000020773 -0.000103365 -0.000013504
0.000011012 0.000171955 -0.000173067 -0.000026495 -0.000048153
0.000161432 0.000028197 -0.000036547 0.000067851 0.000013284
0.000040178 -0.000008893 0.000015076 -0.000015242 0.000013819
0.000003256 0.000000331 0.000014678 0.00000763 0.000002552
0.000004191 0.000004197 0.000000411 -0.000000075 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
0.002887098 -0.005162996 0.014815235 -0.001285135 -0.017864999
0.00000749 -0.000086847 -0.000083018 0.000105148 0.000081389
-0.000091836 -0.000139615 0.000144603 0.000009173 -0.000390802
-0.000178339 -0.000026705 0.000019374 0.000339385 0.000106817
0.000534724 -0.000295593 0.000630123 -0.00006547 -0.000158208
0.001252922 0.001515506 0.000467301 -0.000238628 0.001181597
-0.000586928 -0.000454072 -0.000436001 0.00011785 -0.000120203
-0.000050288 0.000131089 -0.00013403 -0.000094773 0.000109751
0.000052716 0.000224419 0.000031617 -0.000005773 0.000039057
-0.000067576 -0.000073733 -0.000022599 -0.00008645 -0.000176968
-0.000001081 0.000065436 -0.000057159 0.000019626 -0.000076696
-0.000085582 0.000027081 -0.000237917 0.000027559 -0.000027321
-0.000138684 -0.000010139 0.000026879 -0.000280673 -0.000163613
-0.00006582 0.00008998 -0.000072257 -0.000129705 0.000144026
-0.000195254 0.000131956 0.000008668 -0.00004325 -0.000036238
-0.000014767 0.000003249 0.000103041 -0.000106909 -0.000013922
-0.000025123 0.000014109 0.000077397 0.000074812 0.000097137
0.000008743 -0.000015867 0.000078784 -0.000160333 -0.000220779
-0.000096102 0.000276578 0.000044677 -0.000166 -0.000113381
0.000126259 -0.000094119 0.000046776 0.000006033 -0.000019026
0.000047752 -0.000077061 -0.000245975 -0.000149312 -0.000033577
-0.000036015 0.000006292 -0.000016404 -0.000042226 0.000005486
-0.000030862 -0.000047629 -0.000008657 0.000011517 -0.00001011
-0.000010266 0.000024103 0.000041587 -0.000072901 0.00008128
-0.000182947 -0.000016937 0.000031871 -0.000074912 0.000004791
-0.000132392 0.00002209 -0.000042783 0.000027412 -0.000036629
-0.000013631 0.000006481 -0.000035375 -0.00002774 -0.000009908
-0.000015946 -0.000012614 -0.000001499 0.000000198 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
0.002831307 -0.005036083 0.014495839 -0.001222631 -0.01743462
-0.000021877 -0.000089791 -0.00008631 0.000101769 0.000084557
-0.000093566 -0.000003847 0.000103268 0.000007839 -0.000342041
-0.000176391 -0.000013103 0.000043794 0.000266074 0.00011671
0.000488465 -0.00024847 0.000460824 -0.000028753 -0.00021999
0.001021342 0.001224627 0.000221835 -0.00029908 0.000917751
-0.000398617 -0.000299065 -0.000313377 0.000213555 -0.000069759
-0.000065952 0.000058733 -0.00002764 -0.000131624 0.000092763
0.000093374 0.000102217 -0.000039354 -0.000046958 -0.000102751
-0.000104948 -0.000110721 -0.000264731 -0.000183338 -0.000194462
-0.000097041 0.000096354 -0.000152521 0.000223908 -0.00014148
-0.00020514 0.000060268 -0.000291261 0.00009264 -0.000133008
-0.000194146 -0.000000404 0.000022513 -0.000420375 -0.000274199
-0.000004157 0.000118682 -0.000145176 -0.000187359 0.000118614
-0.000190098 0.000157552 -0.000000434 0.000005534 -0.000122158
-0.000035336 0.000091302 0.000070502 -0.000035075 0.000026897
-0.000026027 0.000068863 0.000030758 0.000118906 0.000052865
-0.000026329 -0.00000826 0.000101079 -0.000197935 -0.000140233
-0.000114663 0.000170086 0.000034608 -0.000173948 -0.000106214
0.000022543 -0.000095437 0.000028632 0.000052431 0.000005499
-0.000007454 -0.000044578 -0.000000059 0.000043577 0.000018142
0.000032244 -0.000026283 0.000068926 0.000042058 0.000008931
-0.000011774 -0.000111127 -0.000011769 0.000009934 0.000014911
-0.000079832 -0.000083897 0.000157805 0.000059901 -0.000004452
-0.000123879 -0.000055225 0.000008354 -0.000052262 -0.000087207
0.000107662 0.000039901 0.000035044 0.000016752 0.000021868
0.000026419 -0.000009502 0.000036966 0.000039395 0.000019642
0.000030458 0.000013378 0.000008617 -0.000000132 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
0.002756109 -0.004887643 0.014196414 -0.00116362 -0.01703753
0.000004375 -0.000097905 -0.000069192 0.000084888 0.000113941
-0.000104082 0.000006669 0.000086462 -0.000044821 -0.000238952
-0.000135702 0.000022235 0.000037076 0.000177186 0.000152045
0.000381545 -0.000224624 0.000260298 -0.000069067 -0.000207512
0.000794191 0.00090326 0.000111248 -0.00026504 0.00064074
-0.000259072 -0.000186556 -0.000222422 0.000225984 -0.000048346
-0.000070009 0.000011544 0.000062158 -0.000140825 0.000057386
0.000083756 0.000017278 -0.000134431 -0.000146456 -0.000251551
-0.000135834 -0.000087733 -0.000452141 -0.000243808 -0.000136996
-0.000212436 0.000144639 -0.000265376 0.000421396 -0.000148677
-0.000262259 0.000043509 -0.000298101 0.000123116 -0.000182754
-0.000189525 0.000046441 -0.000032655 -0.000384988 -0.000406727
0.000091405 0.000189811 -0.000144187 -0.000117633 0.000105068
-0.000075964 0.000148894 0.00004975 0.000094222 -0.000219824
-0.000073299 0.000100216 0.000046446 -0.00002118 0.000072675
0.00004038 0.000129741 -0.000046565 0.00011456 -0.000035221
-0.0000787 0.000024227 0.000092911 -0.000123184 -0.000023855
-0.000078062 0.000047717 0.000046576 -0.000088641 -0.00002932
-0.000090071 -0.000041614 0.000003208 0.000036034 0.000008077
0.000009485 -0.000014586 0.000140279 0.000173089 0.000056949
0.000011312 -0.000016935 0.0000546 0.000071702 0.000054964
0.000038482 -0.000020307 0.000019496 -0.000076559 0.000037942
-0.000004126 -0.000097085 0.000158935 0.000084689 -0.000032025
0.000027741 -0.000001712 0.000047726 0.000067935 0.000062807
0.000042019 -0.000107553 0.000003783 -0.000068377 0.000033799
-0.000008086 -0.000014471 -0.000014571 -0.000012693 -0.000021009
-0.000043842 -0.000001391 -0.00002082 0.000000039 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
0.002713439 -0.004752147 0.013965534 -0.001108472 -0.01672038
0.000009941 -0.000112401 -0.00006527 0.000078248 0.000152419
-0.000116667 0.000033126 0.000064384 -0.00007936 -0.000147899
-0.000068426 0.000033315 0.00002579 0.000120293 0.000215288
0.000323611 -0.000171217 0.000157969 -0.00005578 -0.00015296
0.000572407 0.000688925 0.000060766 -0.00020446 0.00048807
-0.00014862 -0.00009754 -0.000180141 0.000210196 -0.000036916
-0.000060428 0.00000925 0.000081098 -0.000136197 0.000013623
0.000080662 -0.000003224 -0.000165756 -0.00019215 -0.000308542
-0.000137013 -0.000061222 -0.000510196 -0.000248039 -0.000057964
-0.000224912 0.000125232 -0.000278473 0.000514189 -0.000154484
-0.000254711 -0.000009644 -0.000268256 0.000156188 -0.000188104
-0.000139626 0.000072911 -0.00008888 -0.000233338 -0.00046348
0.000144267 0.000185848 -0.000069423 -0.000046224 0.000076921
0.000062911 0.000085604 0.000134094 0.000122251 -0.000171917
-0.000080133 0.000124002 -0.000011948 -0.00006699 0.000122377
0.000084481 0.000108265 -0.000117191 0.000053756 -0.000096093
-0.000050405 0.000012092 0.000013554 -0.000033783 0.00004524
0.000030117 -0.000098499 0.000016659 0.000051857 0.000022419
-0.000134127 0.000007665 -0.000040693 -0.000026113 -0.000036273
0.000006864 0.000076699 0.000169231 0.000164427 0.000030649
0.000033798 -0.00002345 -0.00001429 0.000047296 0.00007971
0.000069608 0.000062877 0.000017838 -0.000017769 0.00002631
0.000071317 -0.000130968 0.000042289 0.000067647 -0.000064236
0.000128106 0.000063577 0.000000735 0.000037498 0.000047856
-0.000035523 0.000035664 0.000029723 0.000045477 -0.000025745
-0.000041613 0.000047659 -0.000017681 -0.000030828 0.00001873
0.000035826 -0.000004717 0.000033014 0.000000109 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
0.002654198 -0.004617799 0.013738668 -0.00106814 -0.016441538
0.000020623 -0.000085095 -0.00006464 0.000053609 0.000186066
-0.000107783 0.000031834 0.000022983 -0.000074228 -0.000068779
-0.000039889 0.000029619 0.000041417 0.000044411 0.000255179
0.000198631 -0.000132924 0.000082586 -0.00006463 -0.000063918
0.000359364 0.000438507 0.00003992 -0.000101309 0.000328214
-0.000061309 0.000003358 -0.000096576 0.000163887 -0.000022349
-0.000050092 -0.000012869 0.000115162 -0.000111409 -0.000009761
0.000077735 0.000014956 -0.000206665 -0.000207496 -0.000314351
-0.000161785 -0.000017807 -0.000524724 -0.000276115 0.000019489
-0.000205149 0.00009544 -0.000241665 0.000578938 -0.000166919
-0.00022578 -0.000108395 -0.000231887 0.000217214 -0.000205621
-0.000083071 0.000108178 -0.000157203 0.000010994 -0.000467108
0.000166157 0.000150765 -0.000021731 0.00002444 0.000040855
0.000246309 -0.000001378 0.000270913 0.000055249 -0.000110662
-0.000061757 0.000080507 -0.000087269 -0.000080525 0.000103341
0.000076934 0.000031422 -0.000094885 0.000004692 -0.000073083
0.000050076 -0.000016419 -0.000076807 0.00008026 0.000072597
0.000083693 -0.00015694 0.00000627 0.00009672 0.000092051
-0.000114397 0.000057658 -0.000030369 -0.000037034 -0.000059939
-0.000030038 0.000095397 0.000100554 0.000056162 0.000021134
0.00002121 0.00001418 -0.000050626 0.00000043 0.000054517
0.000023516 0.000065812 0.00000895 0.000094756 -0.000010199
0.000131197 -0.00010293 -0.000061066 0.000003383 0.00000012
0.000065144 0.000028177 -0.000085212 -0.00000508 0.000002609
-0.000083369 0.0000428 -0.000049929 0.000005855 -0.000043563
0.000045236 -0.000031818 0.000035129 0.000036617 -0.000019773
0.000008113 0.000001782 -0.000039179 -0.000000243 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
b [7 x 1] =
-0.1
-0.066666667
-0.033333333
0.000000001
0.008333333
0.016666667
0.025
The SVD solve in ACM 2.2 throws the MaxIterationsExceededError.
In R, the solve works:
pinv <- with(svd(A), v %*% diag(1/d) %*% t(u))
x <- pinv %*% b
> Maximal number of iterations (540) exceeded
> --------------------------------------------
>
> Key: MATH-327
> URL: https://issues.apache.org/jira/browse/MATH-327
> Project: Commons Math
> Issue Type: Bug
> Environment: Windows 7 (32-bit) JDK 1.6_16
> Reporter: Mansoor Ahmed Khan
> Priority: Critical
> Fix For: 3.0
>
>
> I have a matrix of size 49x19 and when I apply SVD on this matrix it raises
> the following exception. The problem which I am facing is that SVD works for
> some matrix and doesn't work for others. I have no clue what is the possible
> reason.
> Exception::
> CorrespondenceAnalysis:
> org.apache.commons.math.MaxIterationsExceededException: Maximal number of
> iterations (540) exceeded
> [org.apache.commons.math.linear.EigenDecompositionImpl.processGeneralBlock(EigenDecompositionImpl.java:881),
>
> org.apache.commons.math.linear.EigenDecompositionImpl.findEigenvalues(EigenDecompositionImpl.java:651),
>
> org.apache.commons.math.linear.EigenDecompositionImpl.decompose(EigenDecompositionImpl.java:243),
>
> org.apache.commons.math.linear.EigenDecompositionImpl.<init>(EigenDecompositionImpl.java:202),
>
> org.apache.commons.math.linear.SingularValueDecompositionImpl.<init>(SingularValueDecompositionImpl.java:114),
> RealMatrix m = [[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000,
> 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096,
> 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143,
> 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000,
> 0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000,
> 1.00000000, 0.94999999, 0.95833331, 1.00000000, 1.00000000, 0.99107143,
> 0.94583333, 1.00000000, 0.95000000, 0.98333333, 0.92106681, 0.97368419,
> 1.00000000, 0.95357142, 0.95238096, 1.00000000, 0.93333334,
> 0.96428573],[1.00000000, 1.00000000, 0.94999999, 0.95833331, 1.00000000,
> 1.00000000, 0.99107143, 0.94583333, 1.00000000, 0.95000000, 0.98333333,
> 0.92106681, 0.97368419, 1.00000000, 0.95357142, 0.95238096, 1.00000000,
> 0.93333334, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096,
> 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143,
> 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000,
> 0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000,
> 1.00000000, 0.94999999, 0.95833331, 1.00000000, 1.00000000, 0.99107143,
> 0.94583333, 1.00000000, 0.95000000, 0.98333333, 0.92106681, 0.97368419,
> 1.00000000, 0.95357142, 0.95238096, 1.00000000, 0.93333334,
> 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000,
> 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096,
> 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 0.94999999,
> 0.95833331, 1.00000000, 1.00000000, 0.99107143, 0.94583333, 1.00000000,
> 0.95000000, 0.98333333, 0.92106681, 0.97368419, 1.00000000, 0.95357142,
> 0.95238096, 1.00000000, 0.93333334, 0.96428573],[1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000,
> 0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000,
> 1.00000000, 0.99107143, 0.95238096, 1.00000000, 1.00000000,
> 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000,
> 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096,
> 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143,
> 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000,
> 0.94999999, 0.95833331, 1.00000000, 1.00000000, 0.99107143, 0.94583333,
> 1.00000000, 0.95000000, 0.98333333, 0.92106681, 0.97368419, 1.00000000,
> 0.95357142, 0.95238096, 1.00000000, 0.93333334, 0.96428573],[1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000,
> 1.00000000, 0.99107143, 0.95238096, 1.00000000, 1.00000000,
> 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000,
> 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096,
> 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143,
> 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000,
> 0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000,
> 1.00000000, 0.99107143, 0.95238096, 1.00000000, 1.00000000,
> 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000,
> 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096,
> 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 0.94999999,
> 0.95833331, 1.00000000, 1.00000000, 0.99107143, 0.94583333, 1.00000000,
> 0.95000000, 0.98333333, 0.92106681, 0.97368419, 1.00000000, 0.95357142,
> 0.95238096, 1.00000000, 0.93333334, 0.96428573],[1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000,
> 0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000,
> 1.00000000, 0.99107143, 0.95238096, 1.00000000, 1.00000000,
> 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000,
> 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096,
> 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 0.94999999,
> 0.95833331, 1.00000000, 1.00000000, 0.99107143, 0.94583333, 1.00000000,
> 0.95000000, 0.98333333, 0.92106681, 0.97368419, 1.00000000, 0.95357142,
> 0.95238096, 1.00000000, 0.93333334, 0.96428573],[1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000,
> 0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000,
> 1.00000000, 0.99107143, 0.95238096, 1.00000000, 1.00000000,
> 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000,
> 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096,
> 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143,
> 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000,
> 0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000,
> 1.00000000, 0.99107143, 0.95238096, 1.00000000, 1.00000000,
> 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000,
> 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096,
> 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143,
> 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143, 1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000, 1.00000000,
> 0.99107143, 0.95238096, 1.00000000, 1.00000000, 0.96428573],[1.00000000,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.99107143,
> 1.00000000, 1.00000000, 1.00000000, 1.00000000, 0.94450431, 1.00000000,
> 1.00000000, 0.99107143, 0.95238096, 1.00000000, 1.00000000,
> 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096, 1.00000000,
> 1.00000000, 0.96428573],[1.00000000, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 1.00000000, 0.99107143, 1.00000000, 1.00000000, 1.00000000,
> 1.00000000, 0.94450431, 1.00000000, 1.00000000, 0.99107143, 0.95238096,
> 1.00000000, 1.00000000, 0.96428573],[1.00000000, 1.00000000, 0.94999999,
> 0.95833331, 1.00000000, 1.00000000, 0.99107143, 0.94583333, 1.00000000,
> 0.95000000, 0.98333333, 0.92106681, 0.97368419, 1.00000000, 0.95357142,
> 0.95238096, 1.00000000, 0.93333334, 0.96428573],[1.00000000, 1.00000000,
> 0.94999999, 0.95833331, 1.00000000, 1.00000000, 0.99107143, 0.94583333,
> 1.00000000, 0.95000000, 0.98333333, 0.92106681, 0.97368419, 1.00000000,
> 0.95357142, 0.95238096, 1.00000000, 0.93333334, 0.96428573]]
> RealMatrix rcp = MatrixUtils.createRealMatrix(CP);
> SingularValueDecomposition svd = new SingularValueDecompositionImpl(rcp);
>
> RealMatrix U = svd.getU();
> RealMatrix S = svd.getS();
> RealMatrix Vt = svd.getVT();
> double[] singularValues = svd.getSingularValues();
--
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