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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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Response matrix #20

Closed drphilmarshall closed 8 years ago

drphilmarshall commented 8 years ago

First test: generate a phi field, and compute the corresponding T map and display it. Should be fun! :-)

LaurencePeanuts commented 8 years ago

Hi @drphilmarshall I've generated maps, but there is an issue that I'm struggling to understand... From the way healpy stores a_lm's it looks like the negative m's are thrown out...? To me it also looks like the way the get_alm function is build, all the negative m's are dependent on the positive m's... so there isn't really 2l+1 independent ms for each l... am I right or am I missing something?

Thanks! Laurence

drphilmarshall commented 8 years ago

No, that's right - the negative m's have to depend on the positive ones in such a way as to make the temperature maps everywhere real. As far as I know, my get_alm function does the right thing...

On Tue, Dec 8, 2015 at 3:18 PM, Laurence Perreault Levasseur < notifications@github.com> wrote:

Hi @drphimarshall

I've generated maps, but there is an issue that I'm struggling to understand... From the way healpy stores a_lm's it looks like the negative m's are thrown out...? To me it also looks like the way the get_alm function is build, all the negative m's are dependent on the positive m's... so there isn't really 2l+1 independent ms for each l... am I right or am I missing something?

Thanks! Laurence

— Reply to this email directly or view it on GitHub https://github.com/rogerblandford/Music/issues/20#issuecomment-163053249 .

rogerblandford commented 8 years ago

Yes. I reorganize them to give my a_y the coefficients of real spherical harmonics Y_y. Roger On Dec 8, 2015, at 5:09 PM, Phil Marshall notifications@github.com<mailto:notifications@github.com> wrote:

No, that's right - the negative m's have to depend on the positive ones in such a way as to make the temperature maps everywhere real. As far as I know, my get_alm function does the right thing...

On Tue, Dec 8, 2015 at 3:18 PM, Laurence Perreault Levasseur < notifications@github.commailto:notifications@github.com> wrote:

Hi @drphimarshall

I've generated maps, but there is an issue that I'm struggling to understand... From the way healpy stores a_lm's it looks like the negative m's are thrown out...? To me it also looks like the way the get_alm function is build, all the negative m's are dependent on the positive m's... so there isn't really 2l+1 independent ms for each l... am I right or am I missing something?

Thanks! Laurence

— Reply to this email directly or view it on GitHub https://github.com/rogerblandford/Music/issues/20#issuecomment-163053249 .

— Reply to this email directly or view it on GitHubhttps://github.com/rogerblandford/Music/issues/20#issuecomment-163074767.

LaurencePeanuts commented 8 years ago

Great! That right we need a real sky! that's a good sign for the R matrix and the ay that the python code generate since, now that I'm looking at it, for each l the ay have: ay for -m equal to (-1)^(m)*(ay for m)^\dagger . I guess I didn't have much intuition for real spherical harmonics... Looks like there is still some debugging to though... I can make T maps but haven't figured how to recover sensible a_lms from them (yet).

Best, Laurence

2015-12-08 17:29 GMT-08:00 Roger Blandford notifications@github.com:

Yes. I reorganize them to give my a_y the coefficients of real spherical harmonics Y_y. Roger On Dec 8, 2015, at 5:09 PM, Phil Marshall <notifications@github.com mailto:notifications@github.com> wrote:

No, that's right - the negative m's have to depend on the positive ones in such a way as to make the temperature maps everywhere real. As far as I know, my get_alm function does the right thing...

On Tue, Dec 8, 2015 at 3:18 PM, Laurence Perreault Levasseur < notifications@github.commailto:notifications@github.com> wrote:

Hi @drphimarshall

I've generated maps, but there is an issue that I'm struggling to understand... From the way healpy stores a_lm's it looks like the negative m's are thrown out...? To me it also looks like the way the get_alm function is build, all the negative m's are dependent on the positive m's... so there isn't really 2l+1 independent ms for each l... am I right or am I missing something?

Thanks! Laurence

— Reply to this email directly or view it on GitHub < https://github.com/rogerblandford/Music/issues/20#issuecomment-163053249> .

— Reply to this email directly or view it on GitHub< https://github.com/rogerblandford/Music/issues/20#issuecomment-163074767>.

— Reply to this email directly or view it on GitHub https://github.com/rogerblandford/Music/issues/20#issuecomment-163077567 .

drphilmarshall commented 8 years ago

Do you mean that when you use the healpy map2alm function you get a_lm's that are non-sensible? In what way?

On Wed, Dec 9, 2015 at 2:38 AM, Laurence Perreault Levasseur < notifications@github.com> wrote:

Great! That right we need a real sky! that's a good sign for the R matrix and the ay that the python code generate since, now that I'm looking at it, for each l the ay have: ay for -m equal to (-1)^(m)*(ay for m)^\dagger . I guess I didn't have much intuition for real spherical harmonics... Looks like there is still some debugging to though... I can make T maps but haven't figured how to recover sensible a_lms from them (yet).

Best, Laurence

2015-12-08 17:29 GMT-08:00 Roger Blandford notifications@github.com:

Yes. I reorganize them to give my a_y the coefficients of real spherical harmonics Y_y. Roger On Dec 8, 2015, at 5:09 PM, Phil Marshall <notifications@github.com mailto:notifications@github.com> wrote:

No, that's right - the negative m's have to depend on the positive ones in such a way as to make the temperature maps everywhere real. As far as I know, my get_alm function does the right thing...

On Tue, Dec 8, 2015 at 3:18 PM, Laurence Perreault Levasseur < notifications@github.commailto:notifications@github.com> wrote:

Hi @drphimarshall

I've generated maps, but there is an issue that I'm struggling to understand... From the way healpy stores a_lm's it looks like the negative m's are thrown out...? To me it also looks like the way the get_alm function is build, all the negative m's are dependent on the positive m's... so there isn't really 2l+1 independent ms for each l... am I right or am I missing something?

Thanks! Laurence

— Reply to this email directly or view it on GitHub < https://github.com/rogerblandford/Music/issues/20#issuecomment-163053249

.

— Reply to this email directly or view it on GitHub< https://github.com/rogerblandford/Music/issues/20#issuecomment-163074767 .

— Reply to this email directly or view it on GitHub < https://github.com/rogerblandford/Music/issues/20#issuecomment-163077567>

.

— Reply to this email directly or view it on GitHub https://github.com/rogerblandford/Music/issues/20#issuecomment-163184072 .

LaurencePeanuts commented 8 years ago

Yeah, they are pretty much zero. The monopole should be zero, but it returns dipole components between 1e-20 and 1e-37 while they should be around 1e-5. Same thing goes for pretty much all the multipoles. I'm sure I'm doing something stupid though...

drphilmarshall commented 8 years ago

Hey @LaurencePeanuts ! Show us a T-map :-)

drphilmarshall commented 8 years ago

Scratch that - you already did, in #8 :-)

LaurencePeanuts commented 8 years ago

Just for reference, the T-maps are in this notebook .