llama.files.healpix.psf module

Functions for working with point sources, applying point spread functions (PSFs) thereto, and making those PSFs compatible with other HEALPix skymaps.

class llama.files.healpix.psf.Psf

Bases: abc.ABC

A point spread function that can be applied to a HEALPix skymap.

calculate()

Calculate a Point Spread Function (PSF) over a bunch of NUNIQ HEALPix pixels.

Returns:densities – An array of densities for this skymap. See Psf.indices for the corresponding pixel indices.
Return type:array
dangle

Return the angular distances of the important pixels in this PSF from the center of the PSF in units of [degrees]; the indices of these pixels are given by the indices property in NUNIQ ordering. Omitted pixels are too far from the center of the PSF to be important.

dec

The declination of the point having a spread function applied to it [degrees].

indices

Return the indices of the important pixels in this PSF in NUNIQ ordering; all other pixels will be assumed to be zero. Indices are sorted in ascending order and are guaranteed to be unique.

max_nside

Get the maximum HEALPix NSIDE scale, i.e. the scale at which 1.2*self.max_scale (the maximum relevant radius of the PSF, times a conservative factor to account for the fact that pixels are not perfectly square) will be smaller than the average width of a pixel. At this scale, the pixel containing the point-source and its 8 neighbors will completely contain all of the relevant PSF pixels at self.min_nside resolution returned by self.indices.

max_scale

The angular size of a circle in which nearly all of the probability will be contained [deg].

max_scale_indices

Get the 9 large pixel indices in NUNIQ ordering at the NSIDE scale defined by self.max_nside that will completely contain the PSF.

min_nside

Get the minimum HEALPix NSIDE required to provide adequate resolution for this PSF. Just find the NSIDE that will give pixel spaces smaller than self.min_scale.

min_scale

The rough scale [deg] of the smallest feature in this PSF. A discrete grid on which the PSF is being calculated should have pixel distances no greater than this.

pix_area

The area per-pixel in [deg**2] of the returned indices (note that they are at the same resolution, so this is a scalar).

ra

The right ascension of the point having a spread function applied to it [degrees].

skymap_product(indices, values, density=True)

Take the pixelwise product of self.calculate with another HEALPix NUNIQ-ordered skymap. Will cleverly downselect and resize the other skymap’s pixels to efficiently use memory and CPU resources.

Parameters:
  • indices (array) – Indices of other skymap’s HEALPix pixels in NUNIQ ordering.
  • values (array) – Corresponding values of the other skymap’s pixels.
  • density (bool, optional) – Whether the other skymap’s pixel values are some sort of density. If True (the default), the pixel values will not be modified during rescaling (since they don’t depend on pixel area). Otherwise, THE PIXEL VALUES WILL BE CONVERTED TO DENSITIES.
Returns:

  • product_indices (array) – The HEALPix NUNIQ indices of the pixels of the product of the two skymaps.
  • product_values (array) – The pixel values of the product of the two skymaps corresponding to the product_indices.

Examples

The product between a PSF and a lower-resolution density value of 1 should be the same as the original PSF:

>>> import numpy as np
>>> identity_inds = np.arange(4, 16)  # NSIDE = 1
>>> identity_values = np.ones_like(identity_inds)
>>> psf = PsfGaussian(30, 10, 1)  # use a Gaussian PSF as an example
>>> inds, values = psf.skymap_product(identity_inds, identity_values,
...                                   density=True)
>>> np.all(psf.indices == inds)
True
>>> np.all(psf.calculate() == values)
True
class llama.files.healpix.psf.PsfGaussian

Bases: llama.files.healpix.psf.GaussTuple, llama.files.healpix.psf.Psf

A Point Spread Function (PSF) for a Gaussian distribution.

ra : float
Right Ascension of the center of the distribution [degrees]
dec : float
Declination of the center of the distribution [degrees]
sigma : float
Standard deviation of the distribution [degrees]
calculate()

Return a 2-D Gaussian PDF function to be used as a PSF (point spread function) on the sphere. Note that this Gaussian PDF does not take account of curvature and is accurate only for small angular spreads. Angles must be in degrees.

max_scale

The angular size of a circle in which nearly all of the probability will be contained [deg].

min_scale

The rough scale [deg] of the smallest feature in this PSF. A discrete grid on which the PSF is being calculated should have pixel distances no greater than this.

llama.files.healpix.psf.resolutions()

Get an array mapping from HEALPix NSIDE values to corresponding resolutions in square degrees.