Posterior sample CMB T maps?

[drphilmarshall]

Hi @hke!

I think we are ready for a sample of posterior sample Planck temperature maps! @rogerblandford has checked that his treatment of the alm's matches healpy's, and is moving on to the potential reconstruction. Would you mind putting let's say 100 posterior sample maps, in the same format as the one on the Planck wiki at http://pla.esac.esa.int/pla/aio/product-action?MAP.MAP_ID=COM_CompMap_CMB-commrul_0256_R1.00.fits , on a website somewhere? Then I can download them, do the SH decomposition and give them to Roger. He's on a tight deadline: due to give a talk on this on Tuesday! Anything you can do for us on this timescale would be really great.

Thanks very much!

Phil

[hke]

Hi Phil,

I'm forwarding this email to Ingunn -- she should have the samples you need, I think.

Ingunn -- can you please find 100 Nside=256, Planck+ext samples, and put them on your webpage, so Phil can access them?

Thanks!

Hans Kristian

Den 28. aug. 2015 22:22, skrev Phil Marshall:

Hi @hke https://github.com/hke!

I think we are ready for a sample of posterior sample Planck temperature maps! @rogerblandford https://github.com/rogerblandford has checked that his treatment of the |alm|'s matches |healpy|'s, and is moving on to the potential reconstruction. Would you mind putting let's say 100 posterior sample maps, in the same format as the one on the Planck wiki at http://pla.esac.esa.int/pla/aio/product-action?MAP.MAP_ID=COM_CompMap_CMB-commrul_0256_R1.00.fits , on a website somewhere? Then I can download them, do the SH decomposition and give them to Roger. He's on a tight deadline: due to give a talk on this on Tuesday! Anything you can do for us on this timescale would be really great.

Thanks very much!

Phil

— Reply to this email directly or view it on GitHub https://github.com/rogerblandford/Music/issues/10.

[hke]

Hi Phil,

100 CMB samples from the Commander 32-band (Planck+WMAP+Haslam) runs can now be found here:

http://folk.uio.no/ingunnkw/planck/32band/commander_32band_Clsamples100.tar.gz

The maps are at Healpix nside=256, 1 degree resolution, and are in thermodynamic uK.

Thanks,

Ingunn

---

From: Hans Kristian Eriksen h.k.k.eriksen@astro.uio.no Sent: 28 August 2015 22:30 To: reply@reply.github.com; Ingunn Kathrine Wehus Subject: Re: [Music] Posterior sample CMB T maps? (#10)

Hi Phil,

I'm forwarding this email to Ingunn -- she should have the samples you need, I think.

Ingunn -- can you please find 100 Nside=256, Planck+ext samples, and put them on your webpage, so Phil can access them?

Thanks!

Hans Kristian

Den 28. aug. 2015 22:22, skrev Phil Marshall:

Hi @hke https://github.com/hke!

I think we are ready for a sample of posterior sample Planck temperature maps! @rogerblandford https://github.com/rogerblandford has checked that his treatment of the |alm|'s matches |healpy|'s, and is moving on to the potential reconstruction. Would you mind putting let's say 100 posterior sample maps, in the same format as the one on the Planck wiki at http://pla.esac.esa.int/pla/aio/product-action?MAP.MAP_ID=COM_CompMap_CMB-commrul_0256_R1.00.fits , on a website somewhere? Then I can download them, do the SH decomposition and give them to Roger. He's on a tight deadline: due to give a talk on this on Tuesday! Anything you can do for us on this timescale would be really great.

Thanks very much!

Phil

� Reply to this email directly or view it on GitHub https://github.com/rogerblandford/Music/issues/10.

[rogerblandford]

Many thanks, Hans-Kristian and Ingunn. Roger On Aug 28, 2015, at 2:15 PM, Hans Kristian Eriksen notifications@github.com<mailto:notifications@github.com> wrote:

Hi Phil,

100 CMB samples from the Commander 32-band (Planck+WMAP+Haslam) runs can now be found here:

http://folk.uio.no/ingunnkw/planck/32band/commander_32band_Clsamples100.tar.gz

The maps are at Healpix nside=256, 1 degree resolution, and are in thermodynamic uK.

Thanks,

Ingunn

---

From: Hans Kristian Eriksen h.k.k.eriksen@astro.uio.no<mailto:h.k.k.eriksen@astro.uio.no> Sent: 28 August 2015 22:30 To: reply@reply.github.commailto:reply@reply.github.com; Ingunn Kathrine Wehus Subject: Re: [Music] Posterior sample CMB T maps? (#10)

Hi Phil,

I'm forwarding this email to Ingunn -- she should have the samples you need, I think.

Ingunn -- can you please find 100 Nside=256, Planck+ext samples, and put them on your webpage, so Phil can access them?

Thanks!

Hans Kristian

Den 28. aug. 2015 22:22, skrev Phil Marshall:

Hi @hke https://github.com/hke!

I think we are ready for a sample of posterior sample Planck temperature maps! @rogerblandford https://github.com/rogerblandford has checked that his treatment of the |alm|'s matches |healpy|'s, and is moving on to the potential reconstruction. Would you mind putting let's say 100 posterior sample maps, in the same format as the one on the Planck wiki at http://pla.esac.esa.int/pla/aio/product-action?MAP.MAP_ID=COM_CompMap_CMB-commrul_0256_R1.00.fits , on a website somewhere? Then I can download them, do the SH decomposition and give them to Roger. He's on a tight deadline: due to give a talk on this on Tuesday! Anything you can do for us on this timescale would be really great.

Thanks very much!

Phil

� Reply to this email directly or view it on GitHub https://github.com/rogerblandford/Music/issues/10.

— Reply to this email directly or view it on GitHubhttps://github.com/rogerblandford/Music/issues/10#issuecomment-135889224.

[drphilmarshall]

Excellent! Thanks @hke. I have decomposed them all for Roger, and am taking a look at them in this new notebook. I think I can see differences between them, but man, Planck is good data.

[ingunnkw]

If you only look at l<10 the maps should look very similar. We use Planck data from 93% of the sky. The remaining 7% in the Galactic plane is filled with a constrained realization.

[drphilmarshall]

Interesting! At some point we'll have to learn more about that, and make some decisions about whether or not to mask that 7%. My guess is that it won't matter much, and using the whole map is fine. Thanks very much for the maps, Ingunn! :-)

On Fri, Aug 28, 2015 at 4:14 PM, Ingunn Kathrine Wehus < notifications@github.com> wrote:

If you only look at l<10 the maps should look very similar. We use Planck data from 93% of the sky. The remaining 7% in the Galactic plane is filled with a constrained realization.

— Reply to this email directly or view it on GitHub https://github.com/rogerblandford/Music/issues/10#issuecomment-135908458 .

[rogerblandford]

For the moment I see no advantage in masking the zoa. Trying to improve what I know is already a very careful procedure will take us even further from our area of competence! If you can produce the other 99 files without the headers, I think I can see what to do next, but it would be great if you could compute the means variances and covariances. Hope Kids’ night went well. Roger On Aug 28, 2015, at 10:08 PM, Phil Marshall notifications@github.com<mailto:notifications@github.com> wrote:

Interesting! At some point we'll have to learn more about that, and make some decisions about whether or not to mask that 7%. My guess is that it won't matter much, and using the whole map is fine. Thanks very much for the maps, Ingunn! :-)

On Fri, Aug 28, 2015 at 4:14 PM, Ingunn Kathrine Wehus < notifications@github.commailto:notifications@github.com> wrote:

If you only look at l<10 the maps should look very similar. We use Planck data from 93% of the sky. The remaining 7% in the Galactic plane is filled with a constrained realization.

— Reply to this email directly or view it on GitHub https://github.com/rogerblandford/Music/issues/10#issuecomment-135908458 .

— Reply to this email directly or view it on GitHubhttps://github.com/rogerblandford/Music/issues/10#issuecomment-135942400.

[drphilmarshall]

Alright, check out the Planck samples notebook here - I plotted up the alm coefficients from Ingunn's sample maps to look for correlations, there's some interesting patterns. A Laplace approximation actually looks like it'll work well, which is good because we've been a bit nervous about trying to invert the response matrix that connects the 3D potential Fourier coefficients with the temperature map alm's. The first thing we'll try is an inversion that included the Gaussian uncertainties on the alm's, which should be a bit more stable, numerically, I think.

Roger, I've written out the mean alm array, and its covariance matrix for you to play around with. Please see my notes at https://github.com/drphilmarshall/Music/blob/master/PlanckSamples_Demo.ipynb: I'm only writing out the positive m's, and I think our response (R) matrix needs to work under the same restriction, producing only a minimal set of Fourier coefficients... That way we will enforce a real potential. I'll email you the means and covariance files.

[drphilmarshall]

Iterating on the covariance matrix: separating real and imaginary parts (in order to preserve the covariance of these measurements) gives a pretty ill-conditioned covariance matrix. Ignoring the imaginary parts of the m=0 coefficients improves matters to some extent, but doesn't solve the problem. Hopefully multiplying by the response matrix and inverting by SVD will be stable.

My notes are in https://github.com/rogerblandford/Music/blob/master/PlanckSamples_Demo.ipynb and the "edited, separated" mean alm's and covariance matrix can be downloaded from:

https://github.com/rogerblandford/Music/blob/master/data/commander_32band_Clsamples100_mean_edited_separated.txt

https://github.com/rogerblandford/Music/blob/master/data/commander_32band_Clsamples100_cov_edited_separated.txt

[drphilmarshall]

Roger, there's a pseudo-inverse of C in https://github.com/rogerblandford/Music/blob/master/data/commander_32band_Clsamples100_inverse_cov_edited_separated.txt for you to play with. Singular values less than 1e-15 were reset to zero. Good luck!