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rogerblandford / Music

Speculative project to map the entire universe over time with low spatial resolution using CMB, 21 cm and local surveys
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CMB T map alm's: units, imaginary parts #9

Closed drphilmarshall closed 9 years ago

drphilmarshall commented 9 years ago

Hi @hke,

Roger's playing around with transforming the alm's from healpy.map2alm into 3D potential, which you can see we've extracted here:

https://github.com/drphilmarshall/Music/blob/master/Planck_Demo.ipynb

Looks like the units are microkelvin, is that correct? Or are they delta T / T? It's also a bit odd how the imaginary parts of the alm coefficients are all exactly zero: is that something you get to choose? Or a bug somewhere? I double checked the map2alm outputs, they really do seem to be integer zero...

Thanks!

Phil

hke commented 9 years ago

Hi Phil and Roger,

Roger's playing around with transforming the |alm|'s from |healpy.map2alm| into 3D potential, which you can see we've extracted here:

https://github.com/drphilmarshall/Music/blob/master/Planck_Demo.ipynb

Looks like the units are microkelvin, is that correct? Or are they delta T / T? It's also a bit odd how the imaginary parts of the |alm| coefficients are all exactly zero: is that something you get to choose? Or a bug somewhere? I double checked the |map2alm| outputs, they really do seem to be integer zero...

The units are indeed thermodynamic microkelvin, yes, not dT/T. However, the imaginary parts should not be all zero, no. Only the elements with m=0 should be zero, while all others should have equal variance in the real and imaginary part, both given by C_l/2. So if you're actually seeing zeros everywhere (not just for m=0), then you do have a bug, yes :-)

Hans Kristian

rogerblandford commented 9 years ago

Many thanks, Hans Kristian. This is what we were expecting. Will try to locate bug. Best, Roger

On Aug 27, 2015, at 11:21 AM, Hans Kristian Eriksen notifications@github.com<mailto:notifications@github.com> wrote:

Hi Phil and Roger,

Roger's playing around with transforming the |alm|'s from |healpy.map2alm| into 3D potential, which you can see we've extracted here:

https://github.com/drphilmarshall/Music/blob/master/Planck_Demo.ipynb

Looks like the units are microkelvin, is that correct? Or are they delta T / T? It's also a bit odd how the imaginary parts of the |alm| coefficients are all exactly zero: is that something you get to choose? Or a bug somewhere? I double checked the |map2alm| outputs, they really do seem to be integer zero...

The units are indeed thermodynamic microkelvin, yes, not dT/T. However, the imaginary parts should not be all zero, no. Only the elements with m=0 should be zero, while all others should have equal variance in the real and imaginary part, both given by C_l/2. So if you're actually seeing zeros everywhere (not just for m=0), then you do have a bug, yes :-)

Hans Kristian

— Reply to this email directly or view it on GitHubhttps://github.com/rogerblandford/Music/issues/9#issuecomment-135513338.

drphilmarshall commented 9 years ago

Yes, thanks Hans Kristian! I'll point the healpy developers at this issue thread, if it's my misuse of their code they have probably seen it before, and if its a genuine bug they'll want to know about it!

On Thu, Aug 27, 2015 at 11:30 AM, Roger Blandford notifications@github.com wrote:

Many thanks, Hans Kristian. This is what we were expecting. Will try to locate bug. Best, Roger

On Aug 27, 2015, at 11:21 AM, Hans Kristian Eriksen < notifications@github.commailto:notifications@github.com> wrote:

Hi Phil and Roger,

Roger's playing around with transforming the |alm|'s from |healpy.map2alm| into 3D potential, which you can see we've extracted here:

https://github.com/drphilmarshall/Music/blob/master/Planck_Demo.ipynb

Looks like the units are microkelvin, is that correct? Or are they delta T / T? It's also a bit odd how the imaginary parts of the |alm| coefficients are all exactly zero: is that something you get to choose? Or a bug somewhere? I double checked the |map2alm| outputs, they really do seem to be integer zero...

The units are indeed thermodynamic microkelvin, yes, not dT/T. However, the imaginary parts should not be all zero, no. Only the elements with m=0 should be zero, while all others should have equal variance in the real and imaginary part, both given by C_l/2. So if you're actually seeing zeros everywhere (not just for m=0), then you do have a bug, yes :-)

Hans Kristian

— Reply to this email directly or view it on GitHub< https://github.com/rogerblandford/Music/issues/9#issuecomment-135513338>.

— Reply to this email directly or view it on GitHub https://github.com/rogerblandford/Music/issues/9#issuecomment-135515659.

drphilmarshall commented 9 years ago

OK, well, that was embarrassing - I have now implemented a get_alm function that interprets the healpy alm array correctly, and now the imaginary parts look good. 

        elif m >= 0:
            index = hp.Alm.getidx(self.lmax, l, m)
            prefactor = 1.0
            value = self.alm[index]
        else:
            index = hp.Alm.getidx(self.lmax, l, -m)
            prefactor = -1.0**m
            value = np.conjugate(self.alm[index])

        return prefactor * value

I'm thinking this could be a nice addition to healpy actually, for others who are trying to use the spherical harmonic components that healpy produces. I'll suggest it, so that reading my issue won't be a total waste of their time!

Roger: look out for an email with new alms in it.