lensit.ffs_covs.ell_mat

class lensit.ffs_covs.ell_mat.ell_mat(lib_dir, shape, lsides, cache=1)

Library helping with flat-sky patch discretization and harmonic mode structure.

This handles Fourier mode structure on the flat sky, at the given resolution and size of specified rectangular box.

Parameters:

• lib_dir – various things might be cached there (unlens cache is set to 0, in which case only a hashdict is put there at instantiation)
• shape (2-tuple) – pair of int defining the number of pixels on each side of the box
• lsides (2-tuple) – physical size (in radians) of the box sides
• cache (optional) – if non-zero, a bunch of matrices might be cached to speed up some calculations.

alm2rfftmap(alm, filt_func=<function ell_mat.<lambda>>)

Returns a ffs_alm array from a rfftmap.

Pseudo-inverse to fftmap2alm

bin_inell(rfftmap)

Bin in a rfftmap according to multipole \(\ell\)

Input must have the same shape then self.rshape

degrade(LDshape, lib_dir=None)

Returns an ell_mat instance on the same physical flat-sky patch but a degraded sampling resolution

get_Nell()

Mode number counts on the flat-sky patch.

Goes roughly like \(2\ell + 1\)

get_cossin_2iphi_mat()

Returns:\(\cos(2i\phi), \sin(2i\phi)\) as rfft arrays

get_e2iphi_mat(cache_only=False)

Returns the matrix containing the phase \(e^{2 i \phi}\)

get_ellmat(ellmax=None)

Returns the matrix containing the multipole ell assigned to 2d-frequency \(k = (k_x,k_y)\)

get_phasemat(ellmax=None)

Returns the rfft array containing the phase \(\phi\) where 2d-frequencies are \(k = |k| e^{i \phi}\)

get_pixwinmat()

Pixel window function rfft array \(\sin(k_x l_{\rm cell, x} / 2) \sin (k_y l_{\rm cell, y} / 2 )\)

get_unique_ells(return_index=False, return_inverse=False, return_counts=False)

Returns list of multipoles \(\ell\) present in the flat-sky patch

static k2ell(k)

Mapping of 2d-frequency \(k\) to multipole \(\ell\)

\(\ell = \rm{int}\left(|k| - \frac 12 \right)\)

map2cl(m, m2=None)

Returns s pseudo-\(C_\ell\) estimate from a map.

Returns a cross-\(C_\ell\) if m2 is set. Must have compatible shape.

rfft2_reals()

Pure reals modes in 2d rfft according to patch specifics

rfftmap2alm(rfftmap, filt_func=<function ell_mat.<lambda>>)

Turns a rfft map to ffs_alm array.

This performs the filtering defined by the instance together with the normalization

class lensit.ffs_covs.ell_mat.ffs_alm(ellmat, filt_func=<function ffs_alm.<lambda>>, kxfilt_func=None, kyfilt_func=None)

Library to facilitate operations on flat-sky alms in the ffs scheme.

Methods includes alm2map and map2alm, among other things. The instance contains info on the sky patch size and discretization.

Parameters:

• ellmat – lensit.ffs_covs.ell_mat.ell_mat instance carrying flat-sky patch definitions
• filt_func (callable, optional) – mutlipole filtering. Set this to discard multipoles in map2alm Defaults to lambda ell : ell > 0
• kxfilt_func (callable, optional) – filtering on x-component of the 2d-frequencies
• kyfilt_func (callable, optional) – filtering on y-component of the 2d-frequencies

EBlms2QUalms(EBlms)

Turns EB alms list into QU alms.

QUlms2EBalms(QUlms)

Turns QU alms list into EB alms.

TEBlms2TQUalms(TEBlms)

Turns TEB alms list into TQU alms.

TQUlms2TEBalms(TQUlms)

Turns TQU alms list into TEB alms.

alm2Pk_minimal(alm)

Power spectrum estimation on the grid, with minimal binning (only exact same frequencies).

Many bins will have only number count 4 or something.

Returns:list with integer array of squared frequencies, integer array number counts, and Pk estimates. (only non zero counts frequencies)

alm2cl(alm, alm2=None, ellmax=None)

Returns power spectrum of alm array

alm2map(alm, lib_almout=None)

Returns position-space map from alm array

almxfl(alm, fl, inplace=False)

Multiply :flat-sky math:a_{ell lm} array with isotropic function \(f_\ell\)

bicubic_prefilter(alm)

Refilter the map for use in bicubic spline prefiltering.

Mostly useful for lensing of maps.

bin_realpart_inell(alm, ellmax=None)

Bin real part of a rfftmap according to multipole \(\ell\)

Input must have the same shape then self.rshape

get_Nell()

Mode number counts on the flat-sky patch.

Analog of \(2\ell + 1\) on the flat-sky. instance mode filtering is included (i.e. set to zero for mods filtered out)

map2alm(m, lib_almin=None)

Computes alm array of input position-space map

map2cl(m1, m2=None, ellmax=None)

Returns power spectrum of alm array

udgrade(lib_alm, alm)

Degrades or upgrades a alm vector from this ffs_alm instance to another instance.

class lensit.ffs_covs.ell_mat.ffs_alm_pyFFTW(ellmat, filt_func=<function ffs_alm_pyFFTW.<lambda>>, num_threads=1, flags_init=('FFTW_MEASURE', ))

Same as ffs_alm but with pyfftw fft-engine threaded fftw library (up to 10 times faster than numpy’s).

alm2map(alm, lib_almout=None)

Returns position-space map from alm array