Flatsky module

flatsky.cl2map(flatskymapparams, cl, el=None)

cl2map module - creates a flat sky map based on the flatskymap parameters and the input power spectra. Look into make_gaussian_realisation for a more general code.

Parameters:

  • flatskymyapparams (list) – [nx, ny, dx, dy] where ny, nx = flatskymap.shape; and dy, dx are the pixel resolution in arcminutes. for example: [100, 100, 0.5, 0.5] is a 50’ x 50’ flatskymap that has dimensions 100 x 100 with dx = dy = 0.5 arcminutes.

  • cl (array) – 1d vector of Cl power spectra: temp / pol. power spectra

  • el (array (optional)) – Multipole over which the signal / noise spectra are defined. Default is None and el will be np.arange( len(cl_signal) )

Returns:

flatskymap – flatskymap with the given underlying power spectrum cl.

Return type:

array

See also

make_gaussian_realisation

flatsky.cl_to_cl2d(el, cl, flatskymapparams, left=0.0, right=0.0)

Interpolating a 1d power spectrum (cl) defined on multipoles (el) to 2D assuming azimuthal symmetry (i.e:) isotropy.

Parameters:

  • el (array) – Multipoles over which the power spectrium is defined.

  • cl (array) – 1d power spectrum that needs to be interpolated on the 2D grid.

  • flatskymyapparams (list) – [nx, ny, dx, dy] where ny, nx = flatskymap.shape; and dy, dx are the pixel resolution in arcminutes. for example: [100, 100, 0.5, 0.5] is a 50’ x 50’ flatskymap that has dimensions 100 x 100 with dx = dy = 0.5 arcminutes.

  • left (float) – value to be used for interpolation outside of the range (lower side). default is zero.

  • right (float) – value to be used for interpolation outside of the range (higher side). default is zero.

Returns:

cl2d – interpolated power spectrum on the 2D grid.

Return type:

array, shape is (ny, nx).

flatsky.convert_eb_qu(map1, map2, flatskymapparams, eb_to_qu=1)

Convert EB/QU into each other.

Parameters:

  • map1 (array) – flatsky map of E or Q.

  • map2 (array) – flatsky map of B or U.

  • flatskymyapparams (list) – [nx, ny, dx, dy] where ny, nx = flatskymap.shape; and dy, dx are the pixel resolution in arcminutes. for example: [100, 100, 0.5, 0.5] is a 50’ x 50’ flatskymap that has dimensions 100 x 100 with dx = dy = 0.5 arcminutes.

  • eb_to_qu (bool) – Either EB–>QU or QU–>EB. Default is EB–>QU.

Returns:

  • map1_mod (array) – flatsky map of E or Q.

  • map2_mod (array) – flatsky map of B or U.

flatsky.get_lpf_hpf(flatskymapparams, lmin_lmax, filter_type=0)

Get 2D Fourier filters. Supports low-pass (LPF), high-pass (HPF), and band-pass (BPF) filters.

Parameters:

  • flatskymyapparams (list) – [nx, ny, dx, dy] where ny, nx = flatskymap.shape; and dy, dx are the pixel resolution in arcminutes. for example: [100, 100, 0.5, 0.5] is a 50’ x 50’ flatskymap that has dimensions 100 x 100 with dx = dy = 0.5 arcminutes.

  • lmin_lmax (list) – Contains lmin and lmax values for the filters. For low-pass (LPF), lmax = lmin_lmax[0]. For high-pass (HPF), lmin = lmin_lmax[0]. For band-pass (BPF), lmin, lmax = lmin_lmax.

  • filter_type (int) – 0: LPF 1: HPF 2: BPF Default is LPF.

Returns:

fft_filter – Requested 2D Fourier filter.

Return type:

array

flatsky.get_lxly(flatskymapparams)

return lx, ly modes (kx, ky Fourier modes) for a flatsky map grid.

Parameters:

flatskymyapparams (list) – [nx, ny, dx, dy] where ny, nx = flatskymap.shape; and dy, dx are the pixel resolution in arcminutes. for example: [100, 100, 0.5, 0.5] is a 50’ x 50’ flatskymap that has dimensions 100 x 100 with dx = dy = 0.5 arcminutes.

Returns:

lx, ly

Return type:

array, shape is (ny, nx).

flatsky.get_lxly_az_angle(lx, ly)

azimuthal angle from lx, ly

Parameters:

  • lx (array) – lx modes

  • ly (array) – ly modes

Returns:

phi – azimuthal angle

Return type:

array

flatsky.make_gaussian_realisation(mapparams, el, cl, cl2=None, cl12=None, cltwod=None, tf=None, bl=None, qu_or_eb='qu')

Make gaussian realisation of flat sky map or 2maps based on the flatskymap parameters and the input power spectra. Look into cl2map for a simple version.

Parameters:

  • flatskymyapparams (list) – [nx, ny, dx, dy] where ny, nx = flatskymap.shape; and dy, dx are the pixel resolution in arcminutes. for example: [100, 100, 0.5, 0.5] is a 50’ x 50’ flatskymap that has dimensions 100 x 100 with dx = dy = 0.5 arcminutes.

  • el (array) – Multipoles over which the power spectrum is defined.

  • cl (array) – 1d vector of Cl auto-power spectra for map1.

  • cl2 (array (optional)) – 1d vector of Cl2 auto-power spectra for map2. Default is None. Used to generate correlated maps.

  • cl12 (array (optional)) – 1d vector of Cl2 cross-power spectra of map1 and map2. Default is None. Used to generate correlated maps.

  • cltwod (array) – 2D version of cl. Default is None. Computed using 1d vector assuming azimuthal symmetry.

  • tf (array) – 2D filtering. Default is None. Used to removed filtered modes.

  • bl (array) – 1d beam window function. Default is None. Used for smoothing the maps.

  • qu_or_eb (array) – Generates TQU or TEB maps if cl, cl2, cl12 are supplied. Default is ‘QU’.

Returns:

sim_map_arr – sim_map1: T-map. if cl2 and cl12 are provided: sim_map2: Q or E map. sim_map3: U or B map.

Return type:

array.

See also

cl2map

flatsky.map2cl(flatskymapparams, flatskymap1, flatskymap2=None, binsize=None)

map2cl module - get the auto-/cross-power spectra of map/maps

Parameters:

  • flatskymyapparams (list) – [nx, ny, dx, dy] where ny, nx = flatskymap.shape; and dy, dx are the pixel resolution in arcminutes. for example: [100, 100, 0.5, 0.5] is a 50’ x 50’ flatskymap that has dimensions 100 x 100 with dx = dy = 0.5 arcminutes.

  • flatskymap1 (array) – flatskymap1 with dimensions (ny, nx).

  • flatskymap2 (array (Optional)) – flatskymap2 with dimensions (ny, nx). Default is None. If None, compute the auto-spectrum of flatskymap1. If not None, compute the cross-spectrum between flatskymap1 and flatskymap2.

  • binsize (int) – el bins. computed automatically based on the fft grid spacing if None.

Returns:

  • el (array) – Multipoles over which the power spectrum is defined.

  • cl (array) – auto/cross power spectrum.

flatsky.radial_profile(z, xy=None, bin_size=1.0, minbin=0.0, maxbin=10.0, to_arcmins=1, get_errors=1)

get the radial profile of an image (both real and fourier space). Can be used to compute radial profile of stacked profiles or 2D power spectrum.

Parameters:

  • z (array) – image to get the radial profile.

  • xy (array) – x and y grid. Same shape as the image z. Default is None. If None, x, y = np.indices(image.shape)

  • bin_size (float) – radial binning factor. default is 1.

  • minbin (float) – minimum bin for radial profile default is 0.

  • maxbin (float) – minimum bin for radial profile default is 10.

  • to_arcmins (bool) – If set, then xy are assumed to be in degrees and multipled by 60 to convert to arcmins.

  • get_errors (bool) – obtain scatter in each bin. This is not the error due to variance. Just the sample variance. Default is True.

Returns:

radprf – Array with three elements cotaining radprf[:,0] = radial bins radprf[:,1] = radial binned values if get_errors: radprf[:,2] = radial bin errors.

Return type:

array.

flatsky.wiener_filter(flatskymyapparams, cl_signal, cl_noise, el=None)

Get 2D Wiener filter.

\[W(\ell) = \frac{ C_{\ell}^{\rm signal} } {C_{\ell}^{\rm signal} + C_{\ell}^{\rm noise}}\]
Parameters:

  • flatskymyapparams (list) – [nx, ny, dx, dy] where ny, nx = flatskymap.shape; and dy, dx are the pixel resolution in arcminutes. for example: [100, 100, 0.5, 0.5] is a 50’ x 50’ flatskymap that has dimensions 100 x 100 with dx = dy = 0.5 arcminutes.

  • cl_signal (array) – Power spectrum of the signal component.

  • cl_noise (array) – Power spectrum of the noise component.

  • el (array (optional)) – Multipole over which the signal / noise spectra are defined. Default is None and el will be np.arange( len(cl_signal) )

Returns:

wiener_filter – 2D Wiener filter.

Return type:

array