Libsharp – spherical harmonic transforms revisited

Reinecke, M.; Seljebotn, Dag Sverre

doi:10.1051/0004-6361/201321494

Cited by 78 publications

(83 citation statements)

References 28 publications

(53 reference statements)

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“…The major bottleneck of the code performance is due to the need of calculating a single inverse spherical harmonic transform which is required to obtain the overpixelized map of the unlensed signal. This can certainly be alleviated further by using better algorithms and/or numerical implementations, e.g., capitalizing on hardware accelerators such as GPGPU (Hupca et al 2012;Szydlarski et al 2011;Fabbian et al 2012;Reinecke & Seljebotn 2013). We leave these code optimizations for future work.…”

Section: Discussionmentioning

confidence: 99%

High-precision simulations of the weak lensing effect on cosmic microwave background polarization

Fabbian

Stompor

2013

A&A

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We studied the accuracy, robustness, and self-consistency of pixel-domain simulations of the gravitational lensing effect on the primordial cosmic microwave background (CMB) anisotropies due to the large-scale structure of the Universe. In particular, we investigated the dependence of the precision of the results precision on some crucial parameters of these techniques and propose a semi-analytic framework to determine their values so that the required precision is a priori assured and the numerical workload simultaneously optimized. Our focus was on the B-mode signal, but we also discuss other CMB observables, such as the total intensity, T , and E-mode polarization, emphasizing differences and similarities between all these cases. Our semi-analytic considerations are backed up by extensive numerical results. Those are obtained using a code, nicknamed lenS 2 HAT -for lensing using scalable spherical harmonic transforms (S 2 HAT) -which we have developed in the course of this work. The code implements a version of the previously described pixel-domain approach and permits performing the simulations at very high resolutions and data volumes, thanks to its efficient parallelization provided by the S 2 HAT library -a parallel library for calculating of the spherical harmonic transforms. The code is made publicly available.

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Section: Discussionmentioning

confidence: 99%

High-precision simulations of the weak lensing effect on cosmic microwave background polarization

Fabbian

Stompor

2013

A&A

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“…Order of magnitude of the accuracy of the HEALPix spherical harmonic transform, averaged over the parameter N side . have been widely studied in the past (see, e.g., Reinecke 2011;Doroshkevich et al 2011;Reinecke & Seljebotn 2013), and that of the MW sampling were presented in McEwen & Wiaux (2011). We do not compile the entirety of these results here, but we have reproduced the essential results on our machine; Table 1 summarises the orders of accuracy of the HEALPix iterative spherical harmonic transform.…”

Section: Numerical Validationmentioning

confidence: 99%

“…Using the same setup as previously, we calculated the maximum error on the spherical harmonic coefficients when performing the transform back and forth, averaged over the values of N side , since the results were found to be sensitive only to the ratio L/N side . Even with several iterations, which multiplies the number of transforms and thus computation time, the spherical harmonic transform in HEALPix remains at least an order of magnitude less accurate than the MW and GLESP counterparts (which, being both theoretically exact, achieve comparable performances, see Reinecke 2011;Reinecke & Seljebotn 2013;Doroshkevich et al 2011;McEwen & Wiaux 2011). Since the wavelet transforms implemented in MRS and Needatool are also computed in harmonic space, their complexity and accuracy are dominated by that of the underlying spherical harmonic transforms.…”

Section: Numerical Validationmentioning

confidence: 99%

S2LET: A code to perform fast wavelet analysis on the sphere

Leistedt

McEwen

Vandergheynst

et al. 2013

A&A

101

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We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are constructed through a tiling of the harmonic line and can be used to probe spatially localised, scale-dependent features of signals on the sphere. The reconstruction of a signal from its wavelets coefficients is made exact here through the use of a sampling theorem on the sphere. Moreover, a multiresolution algorithm is presented to capture all information of each wavelet scale in the minimal number of samples on the sphere. In addition S2LET supports the HEALPix pixelisation scheme, in which case the transform is not exact but nevertheless achieves good numerical accuracy. The core routines of S2LET are written in C and have interfaces in Matlab, IDL and Java. Real signals can be written to and read from FITS files and plotted as Mollweide projections. The S2LET code is made publicly available, is extensively documented, and ships with several examples in the four languages supported. At present the code is restricted to axisymmetric wavelets but will be extended to directional, steerable wavelets in a future release.

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“…(31), (32) allow us to consider a spatially varying g nl , too. We focus on a scalar for simplicity.…”

Section: The Bayesian G Nl -Posteriormentioning

confidence: 99%

Fast and precise way to calculate the posterior for the local non-Gaussianity parameterfnlfrom cosmic microwave background observations

et al. 2013

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We present an approximate calculation of the full Bayesian posterior probability distribution for the local non-Gaussianity parameter f nl from observations of cosmic microwave background anisotropies within the framework of information field theory. The approximation that we introduce allows us to dispense with numerically expensive sampling techniques. We use a novel posterior validation method (DIP test) in cosmology to test the precision of our method. It transfers inaccuracies of the calculated posterior into deviations from a uniform distribution for a specially constructed test quantity. For this procedure we study toy cases that use one-and two-dimensional flat skies, as well as the full spherical sky. We find that we are able to calculate the posterior precisely under a flat-sky approximation, albeit not in the spherical case. We argue that this is most likely due to an insufficient precision of the used numerical implementation of the spherical harmonic transform, which might affect other non-Gaussianity estimators as well. Furthermore, we present how a nonlinear reconstruction of the primordial gravitational potential on the full spherical sky can be obtained in principle. Using the flat-sky approximation, we find deviations for the posterior of f nl from a Gaussian shape that become more significant for larger values of the underlying true f nl . We also perform a comparison to the well-known estimator of Komatsu et al. [Astrophys. J. 634, 14 (2005)] and finally derive the posterior for the local non-Gaussianity parameter g nl as an example of how to extend the introduced formalism to higher orders of non-Gaussianity.

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Libsharp – spherical harmonic transforms revisited

Cited by 78 publications

References 28 publications

High-precision simulations of the weak lensing effect on cosmic microwave background polarization

High-precision simulations of the weak lensing effect on cosmic microwave background polarization

S2LET: A code to perform fast wavelet analysis on the sphere

Fast and precise way to calculate the posterior for the local non-Gaussianity parameterfnlfrom cosmic microwave background observations

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