galsbi.sham_ot package

Submodules

galsbi.sham_ot.histograms module

class galsbi.sham_ot.histograms.HaloHistogram(z_min=None, z_max=None, min_mass=None, max_mass=6000000000000000.0, min_time_since_merger=0, max_time_since_merger=6, n_bins_mass=500, n_bins_z=500, n_bins_time=100)

Bases: object

Class to handle histograms of halos for optimal use in the SHAM-OT framework. The class saves the following histograms:

• 2D histogram of redshift vs halo mass for all halos, shape (n_z_bins, n_mass_bins)

• 2D histogram of redshift vs halo mass for central halos, shape (n_z_bins, n_mass_bins)

• 3D histogram of redshift vs halo mass vs time since last merger for subhalos, shape (n_z_bins, n_mass_bins, n_time_bins)

The indexing follows: hist[z_bin_index, mass_bin_index, time_bin_index], i.e. histogram[0] gives the 0th redshift bin as a histogram over log masses.

add_halo_catalog(halo_catalog, mass_field='m', redshift_field='z_true', is_central_field='is_halo', time_since_merger_field='delta_t', pinocchio_output_filename=None)

Adds a halo catalog to the histograms. The catalog should be a recarray or dictionary-like object containing the necessary fields: - Halo mass - Redshift - Is central halo - Time since last merger

Parameters:

• halo_catalog – A recarray or dictionary-like object containing halo data.

• mass_field – Field name for halo mass (default: ‘m’)

• redshift_field – Field name for redshift (default: ‘z_true’)

• is_central_field – Field name for central halo indicator (default: ‘is_halo’)

• time_since_merger_field – Field name for time since last merger (default: ‘delta_t’)

add_halo_histogram(halo_histogram)

Adds another HaloHistogram instance to the current one.

Parameters:

halo_histogram – Another HaloHistogram instance to add.

get_histogram(galaxy_type='blue', model='Berner+24', **kwargs)

Returns the histogram for red or blue galaxies for the specified SHAM model. Currently, the following models are supported:

• “Berner+24”: free parameters m_limit and quenching time, see arXiv:2310.15223

• “Peng+10”: quenching fractions based on mass, see arXiv:1003.4747

Parameters:

• galaxy_type – Type of galaxy (“blue” or “red”)

• model – Model name (default: “Berner+24”)

• m_limit – Mass limit for central halos in Berner+24 (default: 9e12)

• quenching_time – Quenching time for subhalos in Berner+24 (default: 2)

• mlim_sigma – Scatter in mass limit for extended Berner+24 (default: 0.3)

• initial_quenched_fraction – Initial quenched fraction for subhalos in extended Berner+24 (default: 0.1)

• quenching_time_sigma – Scatter in quenching time for extended Berner+24 (default: 0.5)

• M_mu – Characteristic mass for Peng+10 (default: 11.935)

• sigma – Mass scatter for Peng+10 (default: 0.51)

• b – Satellite quenching efficiency for Peng+10 (default: 0.41)

Returns:

Histogram for the specified galaxy type

get_mass_bins()

Returns the mass bin edges and log centers. :return: Array of mass bin edges and log centers.

get_time_bins()

Returns the time since last merger bin edges and centers. :return: Array of time since last merger bin edges and centers.

get_total_counts()

Returns the total counts of all histograms.

Returns:

Tuple of total counts for all, central, and subhalo histograms.

get_z_bins()

Returns the redshift bin edges and centers. :return: Array of redshift bin edges and centers.

property log_mass_bins

Returns the logarithmic mass bins for the histogram. If min_log_mass or max_log_mass is not set, it returns None.

property max_log_mass

Returns the maximum log mass of the histogram. If max_mass is not set, it returns None.

property min_log_mass

Returns the minimum log mass of the histogram. If min_mass is not set, it returns None.

save(filename)

Saves the class instance to a file using pickle.

Parameters:

filename – Name of the file to save the instance to.

galsbi.sham_ot.histograms.load_halo_histogram(filename)

Loads a HaloHistogram instance from a file.

Parameters:

filename – Name of the file to load the instance from.

Returns:

Loaded HaloHistogram instance.

galsbi.sham_ot.histograms.read_pinocchio_config_details(pinocchio_output_filename)

Reads the Pinocchio output file to extract details about the simulation, such as particle mass, minimum number of particles, and redshift range. :param pinocchio_output_filename: Path to the Pinocchio output file. :return: Tuple containing particle mass, minimum number of particles,

minimum redshift, and maximum redshift.

galsbi.sham_ot.histograms.rebin_halo_histogram(halo_hist, new_n_bins_mass=None, new_n_bins_z=None, new_n_bins_time=None)

Rebins a HaloHistogram to a new number of bins by combining neighboring bins. The new number of bins must be a divisor of the current number of bins.

Parameters:

• halo_hist – HaloHistogram instance to rebin

• new_n_bins_mass – New number of mass bins (must divide current n_bins_mass)

• new_n_bins_z – New number of redshift bins (must divide current n_bins_z)

• new_n_bins_time – New number of time bins (must divide current n_bins_time)

Returns:

New HaloHistogram instance with rebinned histograms

galsbi.sham_ot.sham_ot module

galsbi.sham_ot.sham_ot.compute_faintest_absmag(luminosity_function, z0, z1, n_halos, pixarea, initial_guess=-20, grid_size=100)

Compute the faintest absolute magnitude for a given number of halos in a given redshift range. This is done by computing the integral of the luminosity function over the redshift range and from the maximum absolute magnitude to the faintest absolute magnitude.

Parameters:

• luminosity_function – luminosity function instance

• z0 – lower redshift limit

• z1 – upper redshift limit

• n_halos – number of halos in the redshift range

• pixarea – sky area in square radians of the simulation

• initial_guess – initial guess for the faintest absolute magnitude

• grid_size – number of points in the redshift grid for integration

Returns:

faintest absolute magnitude

galsbi.sham_ot.sham_ot.compute_n_halos_given_faintest_absmag(luminosity_function, z0, z1, faintest_absmag, pixarea, grid_size=100)

Compute the number of halos given the faintest absolute magnitude in a given redshift range. This is done by computing the integral of the luminosity function over the redshift range and from the maximum absolute magnitude to the faintest absolute magnitude.

Parameters:

• luminosity_function – luminosity function instance

• z0 – lower redshift limit

• z1 – upper redshift limit

• faintest_absmag – faintest absolute magnitude

• pixarea – sky area in square radians of the simulation

• grid_size – number of points in the redshift grid for integration

Returns:

number of halos in the redshift range

galsbi.sham_ot.sham_ot.find_ot_solution(logmasses, halo_histogram, luminosity_function, z0, z1, pixarea, magnitude_bins=100, m_max=-5, faintest_mag_initial_guess=-20, epsilon=None, mu_0=9.94, alpha=-1.7, regularizer='sinkhorn')

Finds the OT solution for the given mass distribution and luminosity function. Returns an interpolator predicting the absolute magnitude given the log halo mass.

Parameters:

• logmasses – log-masses of the halos at which the histogram is evaluated

• halo_histogram – histogram of the halos at the given redshift

• luminosity_function – luminosity function instance

• z0 – lower redshift limit

• z1 – upper redshift limit

• pixarea – sky area in square radians of the simulation

• magnitude_bins – number of bins in the absolute magnitude histogram

• m_max – maximum absolute magnitude to consider (default: -5)

• faintest_mag_initial_guess – initial guess for faintest magnitude

• epsilon – regularization parameter for OT (None for unregularized)

• mu_0 – halo mass scale parameter for cost matrix modification (Fischbacher+25)

• alpha – exponent for cost matrix scaling (Fischbacher+25)

• regularizer – regularizer type for OT

Returns:

OT solution interpolator, faintest magnitude

galsbi.sham_ot.sham_ot.generate_galaxy_histogram(luminosity_function, faintest_absmag, brightest_absmag=-27, nbins=100, redshift=0)

Generate a histogram of galaxies in absolute magnitude space based on the given luminosity function and redshift.

Parameters:

• luminosity_function – luminosity function instance

• faintest_absmag – faintest absolute magnitude

• brightest_absmag – brightest absolute magnitude

• nbins – number of bins in the histogram

• redshift – redshift of the galaxies

Returns:

absolute magnitudes, histogram

galsbi.sham_ot.sham_ot.get_interpolated_ot_solution(ot_solution, x1, x2)

Returns a deterministic interpolator for unregularized OT solution. To ensure a smooth interpolator, all constant segments in the OT solution are removed.

Parameters:

• ot_solution – OT solution matrix (n x m)

• x1 – x values of the source distribution (n)

• x2 – x values of the target distribution (m)

Returns:

interpolator

galsbi.sham_ot.sham_ot.get_regularized_ot_solution(ot_solution, x1, x2)

Returns a callable for regularized OT solution that samples from probability distributions. For each query logmass, it interpolates between nearby probability distributions and samples. Vectorized implementation for efficient processing of large arrays.

Parameters:

• ot_solution – OT solution matrix (n x m)

• x1 – x values of the source distribution (logmasses) (n)

• x2 – x values of the target distribution (absolute magnitudes) (m)

Returns:

callable that takes logmass and returns sampled absolute magnitude

galsbi.sham_ot.sham_ot.sample_catalog_from_simulation(halo_catalog, ot_solution)

Sample a galaxy catalog from a halo catalog using the OT solution.

Parameters:

• halo_catalog – Halo catalog (masked for redshift)

• ot_solution – OT solution interpolator

• zmin – lower redshift limit

• zmax – upper redshift limit

Returns:

abs. magnitudes, redshifts, ra, dec, is_halo, logmasses, time_since_merger

galsbi.sham_ot.sham_ot.select_type(halo_catalog, is_blue, model='Berner+24', **kwargs)

Select galaxies based on the SHAM model and type (blue/red). Depending on the model, different additional arguments are needed.

• For the Berner+24 model: m_limit (mass limit in Msun/h) and quenching_time

  (time after which a galaxy is considered red in Gyr).

• For the Berner+24_ext model: m_limit, quenching_time,

  mlim_sigma (transition width for the mass limit), initial_quenched_fraction (baseline quenched fraction at low mass for subhalos), quenching_time_sigma (transition width for the quenched fraction).

Parameters:

• halo_catalog – Halo catalog

• is_blue – flag to select blue galaxies

• model – SHAM model to use for selecting galaxies

• Mlimit – mass limit for the SHAM model (in Msun/h)

• quenching_time – time after which a galaxy is considered red (in Gyr)

• M_mu – mass limit for the Peng model (in log Msun/h)

• sigma – transition width from star-forming to quenched (only for Peng model

• b – baseline quenched fraction at low mass for subhalos (only for Peng model)

Returns:

boolean mask for selected galaxies

galsbi.sham_ot.sham_ot.select_type_berner(halo_catalog, is_blue, m_limit=8000000000000.0, quenching_time=2)

Select galaxies based on the Berner SHAM model. See arXiv:2310.15223 for details.

Parameters:

• halo_catalog – Halo catalog

• is_blue – flag to select blue galaxies (True) or red galaxies (False)

• Mlimit – mass limit for the SHAM model (in Msun/h)

• quenching_time – time after which a galaxy is considered red (in Gyr)

Returns:

boolean mask for selected galaxies

galsbi.sham_ot.sham_ot.select_type_berner_ext(halo_catalog, is_blue, m_limit=8000000000000.0, quenching_time=2, mlim_sigma=0.2, initial_quenched_fraction=0.0, quenching_time_sigma=0.2)

Select galaxies based on the extended Berner SHAM model.

Parameters:

• halo_catalog – Halo catalog

• is_blue – flag to select blue galaxies (True) or red galaxies (False)

• m_limit – mass limit for the SHAM model (in Msun/h)

• quenching_time – time after which a galaxy is considered red (in Gyr)

• mlim_sigma – transition width for the mass limit

• initial_quenched_fraction – baseline quenched fraction at low mass for subhalos

• quenching_time_sigma – transition width for the quenched fraction

Returns:

boolean mask for selected galaxies

galsbi.sham_ot.sham_ot.select_type_peng(halo_catalog, is_blue, M_mu=11.935, sigma=0.51, b=0.41)

” Select galaxies based on the Peng SHAM model. See arXiv:1003.4747 for details

Parameters:

• halo_catalog – Halo catalog

• is_blue – flag to select blue galaxies (True) or red galaxies (False)

• M_mu – mass limit for the SHAM model (in log Msun/h)

• sigma – transition width from star-forming to quenched

• b – baseline quenched fraction at low mass for subhalos

Returns:

boolean mask for selected galaxies

galsbi.sham_ot.sham_ot.solve_ot(masses_histogram, absmags_histogram, logmasses=None, absmags=None, epsilon=None, mu_0=9.94, alpha=-1.7, regularizer='sinkhorn', norm='sqeuclidean')

Solve the Optimal Transport problem between two histograms. This function assumes that the histograms are already consistently normalized. If unregularized OT is used (epsilon=None), it is not necessary to define the logmasses and absmags. This makes only a difference if the regularized OT is used.

Parameters:

• masses_histogram – Histogram of the halo masses

• absmags_histogram – Histogram of the galaxy absolute magnitudes

• logmasses – log-masses of the halos

• absmags – absolute magnitudes of the galaxies

• epsilon – Regularization parameter

• mu_0 – halo mass scale parameter for cost matrix modification (Fischbacher+25)

• alpha – exponent for cost matrix scaling (Fischbacher+25)

• regularizer – Regularizer to use

• norm – Norm to use

Returns:

cost matrix, ot solution

galsbi.sham_ot.sham_ot.z_density(lumfunction, z, m_max)

galsbi.sham_ot.utils module

galsbi.sham_ot.utils.adapted_err_function(x, mu, sigma, min_val=-1, max_val=1)

Adapted error function that adapts mean, width, and limits of the classical error function.

The error function erf(x/sqrt(2)) is the probability that a normally distributed random variable with mean 0 and standard deviation 1 is less than x. The adapted error function has additinional parameters mu and sigma to adapt the mean and standard deviation of the distribution.

The range of the error function is normally [-1, 1], but can be adapted to a different range by setting min_val and max_val. If min_val and max_val are not set, the range is [-1, 1].

Parameters:

• x – input value

• mu – x coordinate of the center of the error function

• sigma – width of the error function

• min_val – minimum value of the error function

• max_val – maximum value of the error function

Returns:

adapted error function value

galsbi.sham_ot.utils.determine_skyarea_of_pinocchio_sim(pinocchio_output_filename)

Determines the sky area of a Pinocchio simulation from the output log file.

Parameters:

pinocchio_output_filename – Filename of the Pinocchio output log file

Returns:

Sky area in square radians

galsbi.sham_ot.utils.opening_to_skyarea(opening_degrees)

For a given lightcone opening angle in degrees, return the corresponding sky area in radians^2. Opening = 90 degrees corresponds to half-sky, i.e. area = 2 * np.pi. Opening = 180 degrees corresponds to full-sky, i.e. area = 4 * np.pi.

Parameters:

opening_degrees – Opening angle in degrees

Returns:

Sky area in square radians

Module contents