Le 11/06/2021 à 20:22, Dima Pasechnik a écrit :
On Fri, 11 Jun 2021, 18:25 Emmanuel Charpentier, <
emanuel.charpent...@gmail.com> wrote:
OK. That was not an error of mine (nor my Sage installation), but a a
genuine problem. So no indication to file a ticket.
Note : Numerics with"standard" are not a problem :
sage: %time matrix([[CDF(u) for u in v] for v in pM]).eigenvectors_right()
CPU times: user 1.95 ms, sys: 15 µs, total: 1.96 ms
Wall time: 1.85 ms
[(-1.5855741097050124 - 1.9835895314317984*I,
[(0.9524479486112228, -0.2837102376875301 - 0.11002559239003057*I,
0.011400252227268036 - 0.010761481586469179*I)],
1),
(0.10840730449357763 + 1.6730496133213792*I,
[(0.8835538411020463, 0.2631022513327894 - 0.3627905504445216*I,
0.05890961187635257 + 0.12256626515553348*I)],
1),
(0.4060235736555931 + 2.708455679766778*I,
[(0.8864942697472706, 0.26813150779882816 - 0.24992379361655742*I,
-0.24416421274380526 - 0.14196949964794017*I)],
1)]
But if you need extended precision, there's a snag :
```
sage: C= ComplexField(200)
sage: %time foo = matrix([[C(u) for u in v] for v in
pM]).eigenvectors_right()
<timed exec>:1: UserWarning: Using generic algorithm for an inexact ring,
which may result in garbage from numerical precision issues.
in fact, arb has some linear algebra implemented, only that functionality
is not wrapped in Sage.
hmmm, 10 years ago it was indeed not in sage but
sage: sM = matrix(3, [-sqrt(2) - 1, 1/4*I*sqrt(759) - 1/4, -2*sqrt(3),
....: 1/2*I*sqrt(3) + 1/2, 1/8*sqrt(33) + 1/8, -1/5*sqrt(29) + 3/5,
....: 0, 1/4, 1/2*I*sqrt(23) + 1/2])
sage: sM.change_ring(ComplexBallField(256)).eigenvectors_right_approx()
<ipython-input-2-597c50ed1766>:1: FutureWarning: This
class/method/function is marked as experimental. It, its functionality
or its interface might change without a formal deprecation.
See https://trac.sagemath.org/30393 for details.
sM.change_ring(ComplexBallField(Integer(256))).eigenvectors_right_approx()
[([-1.585574109705012818320754555380077143033164486087030751802791286603000260637687
+/- 3.06e-79] -
[1.983589531431798407272840921819657822844388213332549281429493414447825431290207
+/- 3.05e-79]*I,
[([-0.7645889954375910796175588680760753644497544472611288268496784517551156034840851
+/- 3.49e-80] +
[0.5679443307838031693126382504352883182783867453515207101490113908352846374511589
+/- 4.71e-80]*I,
[0.2933600072059874975695356608056928703375239897336479003693686118090527352449637
+/- 2.62e-80] -
[0.08085193950422595460559726747128398322364244288273211664977438986727139956036997
+/- 1.86e-81]*I,
[-0.002734621817507568627793755191059520745414855464984622057215624183928681966128039
+/- 3.48e-83] +
[0.01543687404549433149004830726668865175938723340836903249472149019570000983681407
+/- 6.01e-82]*I)],
1),
([0.1084073044935780329693711992135459902927450863702466775904749191406132984593997
+/- 2.35e-80] +
[1.673049613321379085900796686139959744878064234423412272818114017801709044221350
+/- 4.95e-79]*I,
[([-0.2673371902772041016297440268511643741966917470300012123253823050737523650735768
+/- 3.44e-80] -
[0.02255276973433239605480951065284270406141140134762632616605864073042511737197782
+/- 6.64e-82]*I,
[-0.08886719147182478198522558738553193426651781904829084677832088009136722752956601
+/- 2.61e-81] +
[0.1030539596890842335569665014655476103537849006257746372204680855562700952313454
+/- 1.45e-80]*I,
[-0.01469578961696251938128853753478067963226607548513094281484268115068461631364436
+/- 3.99e-82] -
[0.03858858880485532751435734250502627274540851776921042689105965744221705829132246
+/- 3.42e-81]*I)],
1),
([0.4060235736555933190310210654841992389482805815876850469981213132923920738981516
+/- 2.51e-80] +
[2.708455679766779092170763267761045037964677499861201681854033953870245005022438
+/- 1.50e-79]*I,
[([0.2103718533466063742076462260260793168410401002165862474556218965077763660977134
+/- 3.27e-80] +
[0.05448236953479104093710977337474251123511802942923003190706717417804356762302697
+/- 3.17e-81]*I,
[0.07898952661654168047766696024137805415491440866540645841786257582178406891492673
+/- 1.47e-81] -
[0.04282993479195057509885682538044990967004220531263985306993932362186424999425426
+/- 2.1e-84]*I,
[-0.04921683614015854406786925932481355184588924524472501364264944877387240329246417
+/- 4.04e-82] -
[0.04869634593105051448079497440445424999631243725298577782757982000687160120825688
+/- 3.53e-81]*I)],
1)]
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