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Normalization of alms #23
Description
I am trying to read alms I created with healpy from disk and transform them in the format expected by libsharp.
However it seems there is a different normalization between the alm I create with healpy and with libsharp.
Investigating this issue I even find some strange behavior, could you please take a look at this notebook and check if you find any mistake/algorithmic errors?
https://nbviewer.jupyter.org/gist/zonca/a481471543cd6f658dea5bd48d0f94e9
Activity
mreineck commentedon Jun 11, 2019
If I understand correctly, you are requesting real-valued a_lm from libsharp:
libsharp_order = libsharp.packed_real_order(lmax, ms=local_m_indices)I don't understand how the
analysiscall can return complex-valueda_lmin such a case. (Disclaimer: I don't know the current Python interface oflibsharpat all.)In any case: for real-valued
a_lmall entries withm!=0are scaled by a factorsqrt(2), so this is probably the discrepancy you are seeing.mreineck commentedon Jun 11, 2019
Sorry, I misread the notebook... the libsharp
a_lmare not complex-valued after all.For a description of the normalization, see e.g.
https://commander.readthedocs.io/en/latest/library_guide/sphere.html
zonca commentedon Jun 11, 2019
thanks, now normalization is clear.
What about that signal at
m=1which only appears in libsharp and not in HEALPix?mreineck commentedon Jun 11, 2019
I can't try this myself at the moment, but I think you are interpreting the storage scheme of the real package a_lm incorrectly.
They are storing only the values that can be different from zero, i.e. the imaginary value for (l=0, m) is left out, leading to a data set that has minimal size, but can be quite complicated to interpret.
mreineck commentedon Jun 11, 2019
To be explicit, the storage order for a given m is
Re(alm(0,m)), Re(alm(1,m)), Im(alm(1,m)), Re(alm(2,m))...
dagss commentedon Jun 11, 2019
@zonca what Martin says is correct, but this discussion seems a bit on the head for me.
The real-packed storage is very convenient for some things, but very different from what Healpix-the-software is using.
If you want the Healpix storage scheme then libsharp certainly supports that directly. Perhaps support is needed for that in the Python wrapper though I cannot remember.
zonca commentedon Jun 11, 2019
I didn't know
libsharpsupported the HEALPix storage scheme, I see there is a triangular and a rectangular order available in Python. Is one of them the same as HEALPix?mreineck commentedon Jun 11, 2019
Yes, triangular.