You can ask Thierry to finish his ticket
https://trac.sagemath.org/ticket/15944
It was started 7 years ago and the description says "The doc is not
yet finished, but should be quite soon."
That would be a good start :)
Le 11/06/2021 à 22:55, Emmanuel Charpentier a écrit :
Very nice ! I wasn’t aware of it… Now a couple questions/remarks :
-
Is there a reason for this being implemented for ComplexBallField but
not for ComplexField (except CDF) ? What about ComplexIntervalField ?
-
I am not aware of anything comparing the abilities of the various
numerical tools available in Sagemath in the documentation. Did I miss it ?
At the very least, a tutorial illustrating them would be useful. A better
(but possibly quite heavier) text would be additions to the numerical
computing chapters of a new edition of *Computational mathematics with
Sagemath*, which is more and more in order…
What do you think ?
Le vendredi 11 juin 2021 à 21:27:05 UTC+2, vdelecroix a écrit :
Le 11/06/2021 à 20:22, Dima Pasechnik a écrit :
On Fri, 11 Jun 2021, 18:25 Emmanuel Charpentier, <
emanuel.c...@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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