lumfunc 0.2.6

Galaxian Luminosity Function Constructor package using the 1/Vmax estimator and Schechter model.

Luminosity Function Constructor and Modeller

This package allows the user to construct and model Galaxian Luminosity Functions using the estimator and Schechter function.

Installation

Use the package manager pip to install lumfunc.

pip install lumfunc

Keep the package up to date to access all commands.

pip install --upgrade lumfunc

Usage

Import the module in your Python code.

import lumfunc as lf

Load the catalogued data from survey. Usually stored in .fits or .csv files.

import numpy as np
import pandas as pd

# test data (photometric galaxian survey)
data_table = pd.read_csv('test_catalogue.csv')
RA_list = np.array(data_table['RA'])
Dec_list = np.array(data_table['Dec'])
r_app_mag_list = np.array(data_table['r_mag'])
r_app_mag_err_list = np.array(data_table['r_mag_err'])
z_photo_list = np.array(data_table['z_photo'])

get_maggy( ): Convert the measurements of flux in magnitudes to maggies for use with kcorrect_python:

Return maggies from magnitudes.

r_maggies_list = lf.get_maggy(r_app_mag_list) 
print(r_maggies_list[0:4])
# returns 
# [1.83315843e-08 2.27614539e-08 1.33659552e-08 1.13031632e-07]

# rudimentarily:
lf.get_maggy(np.array([19.342, 19.107, 19.685, 17.367]))
# returns
# array([1.83315843e-08, 2.27614539e-08, 1.33659552e-08, 1.13031632e-07])

get_maggy_inv_var( ): Convert the magnitude errors to maggy inverse variances for use with kcorrect_python

Return maggy inverse variances from maggies and magnitude errors.

r_maggy_inv_var_list = lf.get_maggy_inv_var(r_maggies_list, r_app_mag_err_list)
print(r_maggy_inv_var_list[0:4])
# returns 
# [2.19244475e+20 5.68838063e+20 4.12409497e+20 9.22674759e+19]

# rudimentarily:
lf.get_maggy_inv_var(np.array([1.83315843e-08, 2.27614539e-08, 1.33659552e-08, 1.13031632e-07]),
                     np.array([0.004, 0.002, 0.004, 0.001]))
# returns
# array([2.19244474e+20, 5.68838064e+20, 4.12409494e+20, 9.22674766e+19])

get_rest_mag( ): Convert the measured apparent magnitudes into rest-frame magnitudes using the catalogue data and output from kcorrect_python functions

Load maggy ratios output file from kcorrect_python.

maggy_ratios_table = pd.read_csv('test_maggy_ratios.csv', delimiter=' ')
r_maggy_ratio_list = np.array(maggy_ratios_table['maggy_ratio'])

Return rest-frame magnitudes from the apparent magnitudes, redshifts and maggy ratios.

r_rest_mag_list = lf.get_rest_mag(z_photo_list, r_app_mag_list, r_maggy_ratio_list)
print(r_rest_mag_list[0:4])
# returns 
# [-22.89979359 -21.51881811 -23.02717126 -20.79614551]

# rudimentarily:
lf.get_rest_mag(np.array([0.42, 0.24, 0.46, 0.09]),
                np.array([19.342, 19.107, 19.685, 17.367]),
                np.array([0.67165941, 0.81335927, 0.54066526, 0.91925443]))
# returns
# array([-22.8997936 , -21.51881811, -23.02717126, -20.79614551])

get_volume( ): Convert the survey area in square degrees and respective redshift of each data point into comoving volumes. So, estimate from values

Return comoving volume from the survey area and redshifts.

survey_area = 100.0 #sq. degrees
V_list = lf.get_volume(survey_area, z_photo_list)
print(V_list[:4])
# returns 
# [43208407.50293904 9274338.02683353 54988309.45363603 546254.32632565]

# rudimentarily:
lf.get_volume(100.0, np.array([0.42, 0.24, 0.46, 0.09]))
# returns
# array([43208407.50293904, 9274338.02683353, 54988309.45363603, 546254.32632565])

get_binned_phi( ): Bin and weigh galaxy counts per magnitude by

Return M, M errors and phi from the rest-frame magnitudes, values and number of bins.

n_bins = 10
M_list, M_err_list, phi_list = lf.get_binned_phi(r_rest_mag_list, V_list, n_bins)
print(M_list)
# returns
# [-27.75116273 -26.26581137 -24.78046    -23.29510864 -21.80975727
#  -20.32440591 -18.83905454 -17.35370318 -15.86835182 -14.38300045]
print(M_err_list)
# returns
# [0.74267568 0.74267568 0.74267568 0.74267568 0.74267568 
#  0.74267568 0.74267568 0.74267568 0.74267568 0.74267568]
print(phi_list)
# returns 
# [5.12016808e-10 0.00000000e+00 6.87358202e-08 3.55674570e-06 1.18791217e-05 
#  2.44735150e-05 5.43431411e-05 1.30067824e-04 1.04554476e-04 1.74886746e-03]

# OR a rudimentarily example:
lf.get_binned_phi(
    np.array([-23, -21, -19, -22, -23, -23, -22, -23, -22, -22, -19, -21]),
    np.array([
        8e+08, 2e+08, 2e+07, 3e+08, 6e+08, 6e+08, 4e+08, 7e+08, 5e+08, 6e+08,
        7e+06, 1e+08
    ]), 4)
# returns 
# (array([-22.5, -21.5, -20.5, -19.5]),
#  array([0.5, 0.5, 0.5, 0.5]),
#  array([1.06411667e-08, 1.02900000e-08, 0.00000000e+00, 1.32300000e-07]))

get_patch_centers( ): To get spatial variances of the phi values, first divide uniformly and randomly simulated data points over the survey area into equally distributed and equally sized patches

Return patch centers as (RA, Dec) from the RA, Dec and number of patches.

n_patches = 10
centers_array = lf.get_patch_centers(RA_list,
                                     Dec_list,
                                     n_patches,
                                     survey='kids',
                                     max_iterations=int(100),
                                     tolerance=1.0e-1)
print(centers_array)
# returns
# [[ 1.38832190e+02 -1.00733144e+00]
#  [ 2.17105380e+02  1.08365630e+00]
#  [ 1.80666296e+02 -2.73070692e-01]
#  [ 1.34335764e+02  1.31532218e-01]
#  [ 1.38831715e+02  2.15292944e+00]
#  [ 1.29005160e+02  1.01211250e+00]
#  [ 2.13883209e+02 -1.52070351e-02]
#  [ 1.32326750e+02  2.01815821e+00]
#  [ 2.21141020e+02  4.73369162e-01]
#  [ 1.38831187e+02  5.23810834e-01]]

get_patch_labels( ): Then use the patch centers to label the survey data points by equally distributed and equally sized patches:

Return patch labels for each data point from RA, Dec, number of patches and patch center guesses.

labels = lf.get_patch_labels(RA_list,
                             Dec_list,
                             n_patches,
                             centers_array,
                             survey='kids',
                             numba_installed=True,
                             plot_savename='test_patches.png')
# displays plot

get_binned_phi_error( ): Using the patch labels, lastly compute the spatial variances of

Return error on phi from rest-frame magnitude, maximum observed volume, labels, number of patches and number of bins.

phi_err_list = lf.get_binned_phi_error(r_rest_mag_list, V_list, labels, 10, 10)
print(phi_err_list)
# returns
# [3.03839559e-06 7.40731159e-06 9.37491641e-06 1.52090965e-05
#  3.56343615e-05 5.44297508e-05 4.18036097e-05 1.39310857e-04
#  2.08627224e-04 3.58080092e-03]

get_plot( ): Instead, perform get_binned_phi() , get_patches_centers() , get_patches() and get_binned_phi_error() functions using only one function and visualise the luminsoity function

Plot the weighted luminosity function, binned by magnitude.

M_list, M_err_list, phi_list, phi_err_list = lf.get_plot(
    r_rest_mag_list,
    V_list,
    10,
    RA_list,
    Dec_list,
    10,
    centers_array,
    survey='kids',
    numba_installed=True,
    plot_savename='test_LF.png')

# displays plot

filter_plot_by_colour( )

Plots the 1/Vmax weighted luminosity function from data, binned by magnitude and filtered by galaxy colours. The galaxy colours are filtered by red and blue with the help of the input colour dichotomy line parameters. The colour dichotomy line parameters can be inferred from a CMD plot.

SchechterMagModel( )

Single Schechter luminosity function in terms of magnitude from 3 free parameters of the model.

DoubleSchechterMagModel( )

Double Schechter luminosity function in terms of magnitude from 5 free parameters of the model.

get_gof( )

Returns reduced chi squared estimate of goodness of fit.

get_schechter_phi( )

Least square fits single Schechter function model on data. Returns best fit phi, reduced chi squared estimate and the 3 Schechter parameters with their errors.

get_double_schechter_phi( )

Least square fits double Schechter function model on data. Returns best fit phi, reduced chi squared estimate and the 5 Schechter parameters with their errors.

Dependencies

Contributing

Pull requests are welcome. For major changes, please open an issue first to discuss what you would like to change.

Please make sure to update tests as appropriate.

License

MIT