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Fix rotate_alm test #703

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Fix rotate_alm test #703

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@zonca zonca commented Jun 10, 2021

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zonca commented Jun 10, 2021 •
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the rotate_alm comparison with Fortran had a bug, it was comparing the Fortran to Fortran instead of healpy to Fortran.

the Alms are actually quite different between healpy and Fortran:

(Pdb) orig
[0j, (31+0j), 0j, (52+0j), (52+21j), 0j, (73+0j), (73+21j), (73+42j), 0j, 0j, (41+0j), 0j, (62+0j), (62+21j), 0j, (83+0j), (83+21j), (83+42j), 0j]
(Pdb) ref
array([   0.00000000 +0.j        ,  -64.00566224 +0.j        ,
         -3.19617408 +2.0021959j ,   87.82013608 +0.j        ,
         -6.57242310+50.11280794j,    0.79259236 -0.9284526j ,
        -49.67325547 +0.j        ,  -51.28126239-61.62891293j,
         -9.32823219+79.07879935j,   -0.15720457 +0.32469296j,
          0.00000000 +0.j        ,  -85.55208091 +0.j        ,
         -3.57384286 +2.93255811j,  107.54117225 +0.j        ,
         -2.77944942+57.10153224j,    0.79421285 -1.10982745j,
        -60.71533037 +0.j        ,  -61.09151238-65.99438789j,
         -4.86354653+86.52772532j,   -0.14716538 +0.36047478j])
(Pdb) mine
array([   0.00000000 +0.j        ,  -64.00565796 +0.j        ,
          6.01334854 +5.73849263j,   87.82013608 +0.j        ,
         -6.58093829+50.1084887j ,   -3.75913914 -2.13645466j,
        -49.67325547 +0.j        ,  -51.28126266-61.62891268j,
         -8.92714885+79.1993621j ,    1.63993991 +0.47239151j,
          0.00000000 +0.j        ,  -85.55207525 +0.j        ,
          8.23166716 +6.11553975j,  107.54117225 +0.j        ,
         -2.78936165+57.09751076j,   -4.40081795 -2.03054971j,
        -60.71533037 +0.j        ,  -61.09151267-65.9943876j ,
         -4.42280461+86.63057763j,    1.80108316 +0.39800113j])

E       Mismatched elements: 14 / 20 (70%)
E       Max absolute difference: 12.227078099911715
E       Max relative difference: 1.1956782734781954
E        x: array([   0.000000 +0.j      ,  -64.005662 +0.j      ,
E                -3.196174 +2.002196j,   87.820136 +0.j      ,
E                -6.572423+50.112808j,    0.792592 -0.928453j,...
E        y: array([   0.000000 +0.j      ,  -64.005658 +0.j      ,
E                 6.013349 +5.738493j,   87.820136 +0.j      ,
E                -6.580938+50.108489j,   -3.759139 -2.136455j,...

@zonca zonca force-pushed the fix_rotate_alm_test branch from 27724ca to b665391 Compare January 15, 2022 04:44
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zonca commented Jan 21, 2022

@keskitalo you contributed this unit test back in #399
would you like to take a look at it?
Anyway I think it is just an issue in the test, the routines should be fine.

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keskitalo commented Jan 21, 2022 •
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Thanks for finding the error, @zonca !

The initialization of the a_lm array in the test does indeed have an error. Instead of

for i in range(3):
    for ell in range(lmax + 1):
        for m in range(ell):
            ind = hp.Alm.getidx(lmax, ell, m)
            alm[i, ind] = (i + 1) * 10 + ell + 1j * m

It should be (changed loop ranges for both ell and m):

for i in range(3):
    for ell in range(2, lmax + 1):
        for m in range(ell + 1):
            ind = hp.Alm.getidx(lmax, ell, m)
            alm[i, ind] = (i + 1) * 10 + ell + 1j * m

Unfortunately, at least on my test system, I now see small but genuine discrepancies:

#   refererence                                              Healpy 
0  0j                                                               0j
1 (-64.0056622444+0j)                              (-64.0056622444+0j)
2 (-3.19617408364+2.00219590117j)       (-3.19617407425+2.00219591617j)
3 (87.8201360825+0j)                                (87.8201360825+0j)
4 (-6.57242309702+50.1128079361j)      (-6.5724228618+50.1128079669j)
5 (0.792592362074-0.928452597766j)  (0.792592353357-0.928452605206j)
6 (-49.6732554742+0j)                              (-49.6732554742+0j)
7 (-51.2812623888-61.6289129316j)       (-51.2812626781-61.6289126909j)
8 (-9.3282321943+79.0787993482j)       (-9.32823145193+79.0787994357j)
9 (-0.157204566965+0.3246929587j)    (-0.157204562393+0.324692960914j)
10 0j                                                              0j
11 (-85.5520809077+0j)                            (-85.5520809077+0j)
12 (-3.57384285749+2.93255811219j)    (-3.57384284372+2.93255812897j)
13 (107.541172254+0j)                                (107.541172254+0j)
14 (-2.77944941833+57.1015322415j)     (-2.77944915031+57.1015322546j)
15 (0.794212854046-1.10982745343j)    (0.794212843627-1.10982746089j)
16 (-60.7153303746+0j)                             (-60.7153303746+0j)
17 (-61.0915123767-65.9943878923j)     (-61.0915126865-65.9943876056j)
18 (-4.86354653261+86.5277253196j)   (-4.86354572031+86.5277253653j)
19 (-0.147165377786+0.360474777237j)(-0.14716537271+0.36047477931j)

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@zonca @keskitalo