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From "Paul K. Feldman (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (MATH-327) Maximal number of iterations (540) exceeded
Date Fri, 25 Mar 2011 13:55:05 GMT

    [ 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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