Class
NumCosmoMathSphereMap
Description [src]
final class NumCosmoMath.SphereMap : GObject.Object
{
/* No available fields */
}Maps on the sphere in the HEALPix pixelization.
An independent implementation of the HEALPix pixelization of the sphere, written from
its definition in Górski et al. (2005) and
not derived from the HEALPix code. For a resolution parameter nside, a power of two,
the sphere is divided into $12\,\mathrm{nside}^2$ pixels of equal area on
$4\,\mathrm{nside} - 1$ rings of constant latitude. Pixels are numbered in RING or
NESTED order (NcmSphereMapOrder), with the same indices, centres and pixel lookups as
HEALPix; the tests compare them with healpy.
The object holds a map of values on those pixels, reads and writes it in the HEALPix
FITS format, and computes its spherical harmonic coefficients $a_{\ell m}$ and power
spectrum $C_\ell$ up to NcmSphereMap:lmax, and a map from given $a_{\ell m}$.
Functions
ncm_sphere_map_clear
If smap is not NULL, decreases the reference count of smap.
When its reference count drops to 0, the object is finalized
(i.e. its memory is freed).
Set smap to NULL.
Instance methods
ncm_sphere_map_add_to_ang
Adds s to the pixel of smap, in its current ordering, that contains the direction
(theta, phi), see ncm_sphere_map_ang2pix_ring().
ncm_sphere_map_add_to_vec
Adds s to the pixel of smap, in its current ordering, that contains the direction
of vec.
ncm_sphere_map_alm2map
Replaces the map of smap by the synthesis of its current $a_{\ell m}$,
$\sum_{\ell m} a_{\ell m} Y_{\ell m}$ at the pixel centres, in RING order. Any
$\ell_\mathrm{max}$ works: an $m$ above a ring’s Nyquist frequency folds onto it as in
healpy’s alm2map, which the result matches to $10^{-13}$ of the largest pixel.
ncm_sphere_map_ang2pix_nest
Gets the NESTED index of the pixel that contains the direction (theta, phi).
ncm_sphere_map_ang2pix_ring
Gets the RING index of the pixel that contains the direction (theta, phi).
ncm_sphere_map_calc_Ctheta
Computes the angular two-point correlation function
$$C(\theta) = \sum_{\ell=0}^{\ell_\mathrm{max}} \frac{2\ell + 1}{4\pi} C_\ell P_\ell(\cos\theta)$$
from the current $C_\ell$ (ncm_sphere_map_prepare_alm(), ncm_sphere_map_update_Cl() or
ncm_sphere_map_set_Cls()), as a spline on $\theta \in [0, \pi]$ with knots added until
it reproduces the sum to reltol.
ncm_sphere_map_compute_cross_Cl
Computes the cross-spectrum between two maps: $$C_\ell^\mathrm{cross} = \frac{1}{2\ell+1} \sum_{m=-\ell}^\ell \mathrm{Re}(a_{lm}^{(1)} \bar{a}_{lm}^{(2)})$$.
ncm_sphere_map_free
Decreases the reference count of smap. When its reference count
drops to 0, the object is finalized (i.e. its memory is freed).
ncm_sphere_map_get_Cl
Gets $C_\ell$ as computed by the last ncm_sphere_map_prepare_alm() or
ncm_sphere_map_update_Cl(), or set by ncm_sphere_map_set_Cls().
ncm_sphere_map_get_alm
Gets $a_{\ell m}$, as computed by ncm_sphere_map_prepare_alm() or set by
ncm_sphere_map_set_alm(). The coefficients of negative $m$ follow from the real map,
$a_{\ell, -m} = (-1)^m a_{\ell m}^*$.
ncm_sphere_map_get_middle_size
Get the number of pixels of the middle of smap. That is
the number of pixels of the middle rings.
ncm_sphere_map_get_ring_first_index
Get the RING-order index of the first pixel of the ring r_i of smap, see ncm_sphere_map_get_ring_size().
ncm_sphere_map_get_ring_size
Get the number of pixels of the ring r_i of smap, counting rings from the north pole,
$0 \le$ r_i $<$ ncm_sphere_map_get_nrings().
ncm_sphere_map_load_fits
Loads a full-sky map in the HEALPix FITS format: a binary table in the first extension
with the map in one column, any number of pixels per row, and the keys NSIDE, ORDERING
(RING if missing, with a warning) and COORDSYS (celestial if missing, with a warning).
The nside, ordering and coordinate system of smap are set from the file. A PIXTYPE other
than HEALPIX, a partial-sky map (INDXSCHM = EXPLICIT) or a column whose size does not
match NSIDE abort.
ncm_sphere_map_load_from_fits_catalog
Adds the objects of a catalog, a binary table in the first extension of fits_file, to
the pixels of smap that contain them: each object adds its signal, or one when S is
NULL. The map is not cleared first, see ncm_sphere_map_clear_pixels().
ncm_sphere_map_pix2ang_nest
Gets the centre of the pixel nest_index. The polar angle is measured from the north pole.
ncm_sphere_map_pix2ang_ring
Gets the centre of the pixel ring_index, see ncm_sphere_map_pix2ang_nest().
ncm_sphere_map_prepare_alm
Calculates the $a_{\ell m}$ of the map of smap up to $\ell_\mathrm{max}$, set by
ncm_sphere_map_set_lmax(), and from them the $C_\ell$ (ncm_sphere_map_get_Cl()). The
map is put in RING order first, and stays in it.
ncm_sphere_map_save_fits
Saves smap in the HEALPix FITS format read by ncm_sphere_map_load_fits() and healpy:
a binary table with one double-precision value per row, in the current ordering, and
the keys PIXTYPE, ORDERING, NSIDE, FIRSTPIX, LASTPIX, INDXSCHM and COORDSYS. The values
are written in double precision, so a save and load returns the map unchanged.
ncm_sphere_map_set_Cls
Sets the $C_\ell$ of smap used by ncm_sphere_map_get_Cl() and
ncm_sphere_map_calc_Ctheta(); the map and the $a_{\ell m}$ are not changed.
ncm_sphere_map_set_alm
Sets $a_{\ell m}$. The $C_\ell$ are not updated, see ncm_sphere_map_update_Cl().
ncm_sphere_map_set_coordsys
Sets the coordinate system of smap. It labels the map, for instance in the files of
ncm_sphere_map_save_fits(); the pixel values are not transformed.
ncm_sphere_map_set_iter
Sets the number of iterations to use in the spherical harmonic transform. Iterations improve the accuracy of the transform for undersampled maps (when lmax < 3 * nside). iter=0 uses only the direct transform; healpy’s map2alm defaults to 3 iterations.
ncm_sphere_map_set_lmax
Prepare the object to calculate $a_{\ell{}m}$ and/or $C_\ell$,
up to $\ell=$lmax.
ncm_sphere_map_set_map
Sets the pixels of smap to map, in the current ordering; map must hold
ncm_sphere_map_get_npix() values.
ncm_sphere_map_set_nside
Sets the nside parameter of smap, which must be a power of two, or zero to release
the pixels. A change allocates a new map, with every pixel zero.
ncm_sphere_map_update_Cl
Recomputes the $C_\ell$ from the current $a_{\ell m}$, for instance after ncm_sphere_map_set_alm().
ncm_sphere_map_vec2pix_nest
Gets the NESTED index of the pixel that contains the direction of vec, any non-zero vector.
ncm_sphere_map_vec2pix_ring
Gets the RING index of the pixel that contains the direction of vec, any non-zero vector.
Properties
NumCosmoMath.SphereMap:coordsys
The coordinate system the map is given in, see ncm_sphere_map_set_coordsys().
NumCosmoMath.SphereMap:iter
The number of refinement iterations of the map to $a_{\ell m}$ transform, see ncm_sphere_map_set_iter().
NumCosmoMath.SphereMap:lmax
The largest $\ell$ of the harmonic transforms, see ncm_sphere_map_set_lmax().
NumCosmoMath.SphereMap:nside
The HEALPix resolution parameter, a power of two, or zero for no pixels.
Signals
Signals inherited from GObject (1)
GObject::notify
The notify signal is emitted on an object when one of its properties has its value set through g_object_set_property(), g_object_set(), et al.