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jswml.py
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# Joint stepwise maximum likelihood luminosity function and radial density
# estimation using the method of Cole (2011) but allowing for
# individual k-corections
#
# Revision history
#
# 1.0 21-may-13 Based on mlum.py and Shaun's rancat_jswml.f90
# 1.1 08-aug-14 Much simplified by separating out evolution fitting and
# Vdc_max calculation from LF fitting
import contextlib
import os
import matplotlib
from matplotlib.ticker import MaxNLocator
if not(os.environ.has_key('DISPLAY')):
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid import AxesGrid
import itertools
import lum
import math
import mpmath
import multiprocessing
import numpy as np
import pmap
import pickle
import pdb
import astropy.io.fits as fits
#import pyqt_fit.kde
import scipy.integrate
import scipy.interpolate
import scipy.optimize
import scipy.stats
import time
import util
# Allow customisation of printed array format,
# see http://stackoverflow.com/questions/2891790/pretty-printing-of-numpy-array
@contextlib.contextmanager
def printoptions(*args, **kwargs):
original = np.get_printoptions()
np.set_printoptions(*args, **kwargs)
yield
np.set_printoptions(**original)
# Avoid excessive space around markers in legend
matplotlib.rcParams['legend.handlelength'] = 0
# Treatment of numpy errors
np.seterr(all='warn')
# Global parameters
par = {'progName': 'jswml.py', 'version': 1.1, 'ev_model': 'z',
'clean_photom': True, 'use_wt': True, 'kc_use_poly': True}
cosmo = None
sel_dict = {}
chol_par_name = ('alpha', ' M*', ' phi*', ' beta', ' mu*', 'sigma')
methods = ('lfchi', 'denchi', 'post', 'min_slope', 'zero_slope')
mass_limits = (8, 8.5, 9, 9.5, 10, 10.5, 11, 11.5, 12)
mass_zlimits = (0.15, 8.5, 9, 9.5, 10, 10.5, 11, 11.5, 12)
mag_limits = (-23, -22, -21, -20, -19, -18, -17, -16, -15)
wmax = 5.0 # max incompleteness weighting
# Constants
lg2pi = math.log10(2 * math.pi)
ln10 = math.log(10)
J3 = 30000.0
# Jacknife regions are 4 deg segments starting at given RA
njack = 9
ra_jack = (129, 133, 137, 174, 178, 182, 211.5, 215.5, 219.5)
# Determined from GAMA-I. Early/late cut at n = 1.9
Q_all = 1.59
P_all = 0.14
Q_early = 1.31
P_early = 0.14
Q_late = 1.98
P_late = 0.13
# Determined from GAMA-II.
Q_clr = {'c': 0.78, 'b': 0.23, 'r': 0.83}
P_clr = {'c': 1.72, 'b': 3.55, 'r': 1.10}
Qdef, Pdef = 1.0, 1.0
# Factor by which to multiply apparent radius in arcsec to get
# absolute radius in kpc when distance measured in Mpc
radfac = math.pi/180.0/3.6
# Solar magnitudes from Blanton et al 2003 for ^{0.1}ugriz bands
Msun_ugriz = [6.80, 5.45, 4.76, 4.58, 4.51]
# FNugrizYJHK (z0=0) Solar magnitudes from Driver et al 2012
Msun_z0 = {'F': 16.02, 'N': 10.18, 'u': 6.38, 'g': 5.15, 'r': 4.71,
'i': 4.56, 'z': 4.54, 'Y': 4.52, 'J': 4.57, 'H': 4.71, 'K': 5.19}
# Imaging completeness from Blanton et al 2005, ApJ, 631, 208, Table 1
# Modified to remove decline at bright end and to prevent negative
# completeness values at faint end
sb_tab = (18, 19, 19.46, 19.79, 20.11, 20.44, 20.76, 21.09, 21.41,
21.74, 22.06, 22.39, 22.71, 23.04, 23.36, 23.69, 24.01,
24.34, 26.00)
comp_tab = (1.0, 1.0, 0.99, 0.97, 0.98, 0.98, 0.98, 0.97, 0.96, 0.96,
0.97, 0.94, 0.86, 0.84, 0.76, 0.63, 0.44, 0.33, 0.01)
# Polynomial fits to mass completeness limits from misc.mass_comp()
mass_comp_pfit = {'c': (50.96, -57.42, 23.57, 7.32),
'b': (44.40, -51.90, 22.22, 7.21),
'r': (25.88, -32.11, 15.62, 8.13)}
# Standard symbol and colour order for plots
sym_list = ('ko', 'bs', 'g^', 'r<', 'mv', 'y>', 'cp')
clr_list = 'bgrck'
# Plot labels
mag_petro_label = r'$^{0.1}M_{r_{\rm Petro}} -\ 5 \lg h$'
mag_sersic_label = r'$^{0.1}M_{r_{\rm Sersic}} -\ 5 \lg h$'
den_mag_label = r'$\phi(M)\ (h^3 {\rm Mpc}^{-3} {\rm mag}^{-1})$'
den_mass_label = r'$\phi(M)\ (h^3 {\rm Mpc}^{-3} {\rm dex}^{-1})$'
# Directory to save plots
plot_dir = os.environ['HOME'] + '/Documents/tex/papers/gama/jswml/'
#------------------------------------------------------------------------------
# Driver routines
#------------------------------------------------------------------------------
def apollo_jobs():
"""Submit several jobs on apollo."""
dir = '/research/astro/gama/loveday/gama/jswml/auto'
# for ireal in range(26):
python_commands = ['import jswml',
'''jswml.ev_fit_samples("kcorrz00.fits",
"ev_z00_{}_petro_fit_{}.dat")''']
util.apollo_job(dir, python_commands)
def ev_fit_samples(infile='kcorrz01.fits', outroot='ev_{}_petro_fit_{}.dat',
colour='c', param='r_petro', method='lfchi', ev_model='z'):
"Determine ev parameters and density-corrected Vmax for specified sample."
par['ev_model'] = ev_model
par['clean_photom'] = True
clr_limits = ('a', 'z')
if (colour == 'b'): clr_limits = ('b', 'c')
if (colour == 'r'): clr_limits = ('r', 's')
sel_dict['colour'] = clr_limits
outfile = outroot.format(method, colour)
ev_fit(infile, outfile, Pbins=(0.0, 2.5, 25), Qbins=(0.0, 1.5, 30),
param=param, method=method)
del sel_dict['colour']
def ev_fit_test(infile='kcorrz01.fits', outroot='ev_test_Mlt{}.dat',
colour='c', param='r_petro', method='lfchi', ev_model='z',
Mmax=-12):
"""Determine ev parameters and density-corrected Vmax for specified sample
using small number of P, Q bins and no optimization."""
par['ev_model'] = ev_model
par['clean_photom'] = True
clr_limits = ('a', 'z')
if (colour == 'b'): clr_limits = ('b', 'c')
if (colour == 'r'): clr_limits = ('r', 's')
sel_dict['colour'] = clr_limits
# outfile = outroot.format(method, colour)
outfile = outroot.format(Mmax)
ev_fit(infile, outfile, Pbins=(0.0, 2.5, 25), Qbins=(0.0, 2.0, 20), opt=0,
param=param, method=method, Mmax=Mmax)
def ev_fit_mock(infile='kcorrz01.fits', outroot='ev_{:02d}.dat', ireal=0,
param='SDSS_R_OBS_APP', method='lfchi', ev_model='z'):
"""Evolution fitting for mocks."""
par['ev_model'] = ev_model
par['clean_photom'] = False
par['ireal'] = ireal
outfile = outroot.format(ireal)
print(ireal)
ev_fit(infile, outfile, Pbins=(-1.0, 2.0, 15), Qbins=(-1.0, 1.0, 10),
param=param, method=method)
def ev_sim_par(inroot='sim_z01_{}.fits', outroot='lf_kde_z01_{}_{}.dat'):
"""Evolution fitting for several simulations run in parallel."""
i = int(os.environ['SGE_TASK_ID']) - 1
infile = inroot.format(i)
for method in ('lfchi', 'post'):
outfile = outroot.format(method, i)
print infile, method
lf_PQ(inFile=infile, outFile=outfile,
param_list=(('r_petro',
(10, 19.8), (10, 19.8, 29), (-23, -15, 32), 0),),
zmin=0.002, zmax=0.65, nz=65, lf_zbins=((0, 20), (20, 64)),
Pbins=(0, 3.5, 35), Qbins=(0, 1.5, 30),
P_prior=(2, 1), Q_prior=(1, 1), method=method, err_type='j3',
use_mp=True, lf_est='kde')
def Vmax(infile='kcorrz01.fits', evroot='ev_{}_{}_fit_{}.dat',
outroot='Vmax_{}_{}.fits'):
"""Vmax calculation."""
par['clean_photom'] = False
magtype = 'petro'
for method in ('lfchi', 'post'):
for colour in 'cbr':
evfile = evroot.format(method, magtype, colour)
outfile = outroot.format(method, colour)
# Output Vmax values for ALL objects
# sel_dict['colour'] = ('a', 'z')
Vmax_out(infile, evfile, outfile)
def Vmax_z00(infile='kcorrz00.fits', evfile='ev_z00_lfchi_petro_fit_c.dat',
outfile='Vmax_z00.fits'):
"""Vmax calculation with k-correction to z=0.0."""
par['clean_photom'] = True
Vmax_out(infile, evfile, outfile)
def Vmax_noclean(infile='kcorrz01.fits', evroot='ev_lfchi_{}_fit_c.dat',
outroot='Vmax_{}_noclean.fits'):
"""Vmax calculation."""
par['clean_photom'] = False
for magtype in ('petro', 'sersic'):
evfile = evroot.format(magtype)
outfile = outroot.format(magtype)
Vmax_out(infile, evfile, outfile)
def Vmax_z_slices(infile='kcorrz01.fits', evroot='ev_lfchi_petro_fit_{}.dat',
outroot='Vmax_{}_z_{}_{}.fits'):
"""Vmax in redshift slices."""
for colour in 'cbr':
evfile = evroot.format(colour)
for zrange in ((0.002, 0.1), (0.1, 0.2), (0.2, 0.3), (0.3, 0.4),
(0.4, 0.5), (0.5, 0.6)):
# for zrange in ((0.002, 0.06), (0.002, 0.1), (0.1, 0.2), (0.2, 0.3),
# (0.3, 0.65)):
nz = int(math.ceil(100 * (zrange[1] - zrange[0])))
outfile = outroot.format(colour, zrange[0], zrange[1])
Vmax_out(infile, evfile, outfile, zmin=zrange[0], zmax=zrange[1],
nz=nz)
def Vmax_sim(inroot='sim_z01_{}.fits', evroot='lf_kde_z01_{}_{}.dat',
outroot='Vmax_{}_{}.fits'):
"""Vmax for simulations."""
for method in ('post', 'lfchi'):
for i in xrange(10):
infile = inroot.format(i)
evfile = evroot.format(method, i)
outfile = outroot.format(method, i)
Vmax_out(infile, evfile, outfile)
def Vmax_mocks(infile='kcorrz01.fits', evroot='ev_{:02d}.dat',
outroot='Vmax_{:02d}.fits', param='SDSS_R_OBS_APP'):
"""Vmax for mocks."""
par['clean_photom'] = False
for ireal in (1, 2, 5, 6, 14, 20):
par['ireal'] = ireal
evfile = evroot.format(ireal)
outfile = outroot.format(ireal)
Vmax_out(infile, evfile, outfile, param=param)
def Vmax_pinch_test(infile='Vmax_lfchi_c.fits', nz=65, idebug=1,
param='r_petro',
plot_file='Vmax_pinch_test.png', plot_size=(5, 8)):
"""Vmax pinch test."""
global par
hdulist = fits.open(infile)
header = hdulist[1].header
par['H0'] = header['H0']
par['omega_l'] = header['OMEGA_L']
par['z0'] = header['Z0']
par['area'] = header['AREA'] * (math.pi/180.0)**2
par['ev_model'] = header['ev_model']
Q = header['Q']
P = header['P']
mlims = [0, 19.8]
mlims[0] = header['mlim_0']
mlims[1] = header['mlim_1']
zmin = header['zmin']
zmax = header['zmax']
ev_model = 'z'
hdulist.close()
print 'P, Q, nz, zmin, zmax =', P, Q, nz, zmin, zmax
par.update({'infile': infile, 'param': param, 'zmin': zmin, 'zmax': zmax,
'mlims': mlims, 'dmlim': 2, 'Mmin': -99, 'Mmax': 99, 'Mbin': 1,
'ev_model': ev_model, 'idebug': idebug})
# Volume out to galaxy redshifts
# First calculate volumes without evolution
samp = Sample(infile, par, sel_dict, 0, nqmin=2)
gala = samp.calc_limits(0)
zbin, zhist, V, V_int = z_binning(gala, nz, (zmin, zmax))
zstep = zbin[1] - zbin[0]
S_obs, S_vis = vis_calc(gala, nz, zmin, zstep, V, V_int)
converged, Npred, delta, den_var, Pz, Vmax_dc, niter = delta_solve(
0, 0, gala, nz, (zmin, zmax), zbin, zhist, V, V_int, S_vis)
V_raw = np.dot(V, S_obs)
V_dc = np.dot(delta * V, S_obs)
# Now volume with evolution
samp = Sample(infile, par, sel_dict, Q, nqmin=2)
gala = samp.calc_limits(Q)
zbin, zhist, V, V_int = z_binning(gala, nz, (zmin, zmax))
zstep = zbin[1] - zbin[0]
S_obs, S_vis = vis_calc(gala, nz, zmin, zstep, V, V_int)
converged, Npred, delta, den_var, Pz, Vmax_dec, niter = delta_solve(
P, Q, gala, nz, (zmin, zmax), zbin, zhist, V, V_int, S_vis)
V_dec = np.dot(delta * Pz * V, S_obs)
plt.clf()
fig, axes = plt.subplots(4, 1, sharex=True, sharey=True, num=1)
plt.subplots_adjust(hspace=0.0)
ax = axes[0]
ax.scatter(gala['appval_sel'], gala['zhi']/gala['z'], 0.1)
ax.semilogy(basey=10, nonposy='clip')
ax.set_ylabel('zmax/z')
ax = axes[1]
ax.scatter(gala['appval_sel'], samp.Vmax_raw/V_raw, 0.1)
ax.semilogy(basey=10, nonposy='clip')
ax.text(0.1, 0.1, 'Raw', transform=ax.transAxes)
ax = axes[2]
ax.scatter(gala['appval_sel'], samp.Vmax_dc/V_dc, 0.1)
ax.semilogy(basey=10, nonposy='clip')
ax.text(0.1, 0.1, 'DC', transform=ax.transAxes)
ax.set_ylabel('Vmax/V')
odd = samp.Vmax_dc/V_dc < 1
print (samp.Vmax_dc/V_dc)[odd]
# pdb.set_trace()
ax = axes[3]
ax.scatter(gala['appval_sel'], samp.Vmax_dec/V_dec, 0.1)
ax.semilogy(basey=10, nonposy='clip')
ax.text(0.1, 0.1, 'DEC', transform=ax.transAxes)
ax.set_xlim(19, 19.9)
ax.set_ylim(0.5, 5)
ax.set_xlabel('r_petro')
plt.draw()
if plot_file:
fig = plt.gcf()
fig.set_size_inches(plot_size)
plt.savefig(plot_dir + plot_file, bbox_inches='tight')
print 'plot saved to ', plot_dir + plot_file
def lf1(infile='Vmax_lfchi_c.fits', outroot='lf_{}_wt{}.dat',
param='z_sersic', Mmin=-25, Mmax=-12, nbin=26, clean_photom=1,
use_wt=1):
"""LF in specified band."""
par['clean_photom'] = clean_photom
par['use_wt'] = use_wt
outfile = outroot.format(param, use_wt)
lf_1d(infile, outfile, param, Mmin, Mmax, nbin)
def lfr(inroot='Vmax_{}_{}.fits', outroot='lf_{}_{}_{}.dat',
method='lfchi', param='r_petro', Mmin=-25, Mmax=-12, nbin=52,
clean_photom=True):
"""Petrosian r-band LF."""
par['clean_photom'] = clean_photom
for colour in 'cbr':
clr_limits = ('a', 'z')
if (colour == 'b'): clr_limits = ('b', 'c')
if (colour == 'r'): clr_limits = ('r', 's')
sel_dict['colour'] = clr_limits
infile = inroot.format(method, colour)
outfile = outroot.format(param, method, colour)
lf_1d(infile, outfile, param, Mmin, Mmax, nbin)
del sel_dict['colour']
def lfr_z00(infile='Vmax_z00.fits', outfile='lf_r_z00.dat',
param='r_petro', Mmin=-25, Mmax=-12, nbin=52,
clean_photom=True):
"""Petrosian r-band LF k-corrected to z=0.0."""
par['clean_photom'] = clean_photom
lf_1d(infile, outfile, param, Mmin, Mmax, nbin)
def lfr_mocks(inroot='Vmax_{:02d}.fits', outroot='lf_{:02d}.dat',
method='lfchi', param='SDSS_R_OBS_APP', Mmin=-25, Mmax=-12,
nbin=52):
"""Petrosian r-band LF for mocks."""
par['clean_photom'] = False
for ireal in (1, 2, 5, 6, 14, 20):
par['ireal'] = ireal
infile = inroot.format(ireal)
outfile = outroot.format(ireal)
lf_1d(infile, outfile, param, Mmin, Mmax, nbin)
def lfr_ev(inroot='Vmax_{}_z_{}_{}.fits', outroot='lf_{}_{}_z_{}_{}.dat',
param='r_petro', Mmin=-25, Mmax=-12, nbin=52):
"""Evolution of r-band LF."""
par['clean_photom'] = True
for colour in 'cbr':
clr_limits = ('a', 'z')
if (colour == 'b'): clr_limits = ('b', 'c')
if (colour == 'r'): clr_limits = ('r', 's')
sel_dict['colour'] = clr_limits
for zrange in ((0.002, 0.1), (0.1, 0.2), (0.2, 0.3), (0.3, 0.65)):
infile = inroot.format(colour, zrange[0], zrange[1])
outfile = outroot.format(param, colour, zrange[0], zrange[1])
lf_1d(infile, outfile, param, Mmin, Mmax, nbin)
del sel_dict['colour']
def lfr_zslices(inroot='Vmax_{}_z_{}_{}.fits', outroot='lfr_zslice_{}_{}.dat',
param='r_petro', Mmin=-25, Mmax=-12, nbin=52,
Vmax_type='Vmax_raw'):
"""r-band LF in redshift slices, without any evolution corrections."""
par['clean_photom'] = True
colour = 'c'
for zrange in ((0.002, 0.1), (0.1, 0.2), (0.2, 0.3), (0.3, 0.4),
(0.4, 0.5), (0.5, 0.6)):
infile = inroot.format(colour, zrange[0], zrange[1])
outfile = outroot.format(zrange[0], zrange[1])
lf_1d(infile, outfile, param, Mmin, Mmax, nbin, Vmax_type=Vmax_type,
Q=0)
def smf(inroot='Vmax_lfchi_{}.fits', outroot='smf_{}.dat',
param='logmstar_fluxscale', Mmin=6, Mmax=13, nbin=28,
schec_guess=(-1.0, 10.6, -2)):
"Stellar mass function."
global par
par['clean_photom'] = True
for colour in 'cbr':
par['colour'] = colour
clr_limits = ('a', 'z')
if (colour == 'b'): clr_limits = ('b', 'c')
if (colour == 'r'): clr_limits = ('r', 's')
sel_dict['colour'] = clr_limits
infile = inroot.format(colour)
outfile = outroot.format(colour)
lf_1d(infile, outfile, param, Mmin, Mmax, nbin,
schec_guess=schec_guess)
def smf_ev(inroot='Vmax_z_{}_{}.fits', outroot='smf_{}_{}_{}.dat',
param='logmstar_fluxscale', Mmin=6, Mmax=13, nbin=28,
schec_guess=(-1.0, 10.6, -2)):
"Evolution of stellar mass function."
global par
# par['use_wt'] = False
par['clean_photom'] = True
for colour in 'cbr':
par['colour'] = colour
clr_limits = ('a', 'z')
if (colour == 'b'): clr_limits = ('b', 'c')
if (colour == 'r'): clr_limits = ('r', 's')
sel_dict['colour'] = clr_limits
for zrange in ((0.002, 0.06), (0.002, 0.1), (0.1, 0.2), (0.2, 0.3),
(0.3, 0.65)):
infile = inroot.format(zrange[0], zrange[1])
outfile = outroot.format(colour, zrange[0], zrange[1])
lf_1d(infile, outfile, param, Mmin, Mmax, nbin,
schec_guess=schec_guess)
def lf_sim(inroot='Vmax_{}_{}.fits', outroot='lf_bin_{}_{}.fits',
param='r_petro', Mmin=-24, Mmax=-12, nbin=48):
"""Petrosian r-band LF for simulations."""
for method in ('post', 'lfchi'):
for i in xrange(10):
infile = inroot.format(method, i)
outfile = outroot.format(method, i)
lf_1d(infile, outfile, param, Mmin, Mmax, nbin)
def delta_lf_plots(infile='kcorrz01.fits',
param_list=(('r_petro', (14, 19.8), (14, 19.8, 27),
(-23, -18, 20), 0),),
zmin=0.002, zmax=0.65, nz=65, lf_zbins=((0, 20), (20, 64)),
idebug=1, Pbins=(0.0, 4.0, 20), Qbins=(0.0, 2.0, 20),
P_prior=(1,1), Q_prior=(1,1), method='lfchi', err_type='jack'):
"Delta and LF plots to demonstrate lfchi method."
global par
par = {'zmin': zmin, 'zmax': zmax, 'idebug': idebug}
samp = read_gama(infile, param_list)
qty = samp.qty_list[0]
lf_bins = np.linspace(qty.absMin, qty.absMax, qty.nabs+1)
costfn = Cost(samp, nz, (zmin, zmax), lf_bins, lf_zbins, method,
P_prior, Q_prior, Qbins[0], Qbins[1], err_type)
c = costfn((0.0, 0.0))
fig = plt.gcf()
fig.set_size_inches(3, 6)
plt.savefig(plot_dir + 'delta_lf_0_0.pdf', bbox_inches='tight')
c = costfn((1.7, 0.7))
fig = plt.gcf()
fig.set_size_inches(3, 6)
plt.savefig(plot_dir + 'delta_lf_1.7_0.7.pdf', bbox_inches='tight')
def ran_gen_sample(infile='kcorrz01.fits', Q=Qdef, P=Pdef,
outfile='ranz.dat', param='lum', limits=(-25, -10),
colour='c', zmin=0.002, zmax=0.65, nz=65, nfac=30):
"""Generate random distribution for single specified sample."""
clr_limits = ('a', 'z')
if (colour == 'b'):
clr_limits = ('b', 'c')
if (colour == 'r'):
clr_limits = ('r', 's')
sel_dict['colour'] = clr_limits
Mmin = -25
Mmax = -10
if param == 'lum':
Mmin = limits[0]
Mmax = limits[1]
if param == 'mass':
M_h_corr = 2*math.log10(1.0/0.7)
sel_dict['logmstar'] = (limits[0] + M_h_corr, limits[1] + M_h_corr)
par.update({'zmin': zmin, 'zmax': zmax, 'nz': nz,
'Mmin': Mmin, 'Mmax': Mmax, 'Mbin': 1,
'param': 'r_petro', 'dmlim': 2, 'mlims': (0, 19.8),
'idebug': 1})
ran_gen(infile, outfile, nfac=nfac, Q=Q, P=P, vol=0)
# -----------------------------------------------------------------------------
# Main procedures
# -----------------------------------------------------------------------------
def ev_fit(infile, outfile, mlims=(0, 19.8), param='r_petro',
Mmin=-24, Mmax=-12, Mbin=48, dmlim=2,
zmin=0.002, zmax=0.65, nz=65,
lf_zbins=((0, 20), (20, 65)),
Pbins=(-0.5, 4.0, 45), Qbins=(0.0, 1.5, 30),
P_prior=(2, 1), Q_prior=(1, 1),
idebug=1, method='lfchi', err_type='jack', use_mp=False, opt=True,
lf_est='kde'):
"""Fit evolution parameters and radial overdensities.
Searches over both Q and P values,
rather than trying to estimate P from Cole eqn (25).
Elements of P_prior and Q_prior are mean and variance."""
global par
par.update({'infile': infile, 'mlims': mlims,
'param': param, 'dmlim': dmlim,
'zmin': zmin, 'zmax': zmax,
'Mmin': Mmin, 'Mmax': Mmax, 'Mbin': Mbin,
'idebug': idebug, 'method': method, 'lf_est': lf_est})
print '\n************************\njswml.py version ', par['version']
print method
print sel_dict
assert method in methods
lf_bins = np.linspace(Mmin, Mmax, Mbin+1)
samp = Sample(infile, par, sel_dict)
costfn = Cost(samp, nz, (zmin, zmax), lf_bins, lf_zbins, method,
P_prior, Q_prior, Qbins[0], Qbins[1], err_type)
out = {'par': par}
if par['idebug'] > 0:
print 'Q, P chi^2 grid using', method
# Calculate chi^2 on (P,Q) grid to get likelihood contours and to find
# starting point for minimization
Qmin = Qbins[0]
Qmax = Qbins[1]
nQ = Qbins[2]
Qstep = float(Qmax - Qmin)/nQ
Pmin = Pbins[0]
Pmax = Pbins[1]
nP = Pbins[2]
Pstep = float(Pmax - Pmin)/nP
Qa = np.linspace(Qmin, Qmax, nQ, endpoint=False) + 0.5*Qstep
Pa = np.linspace(Pmin, Pmax, nP, endpoint=False) + 0.5*Pstep
plt.clf()
if use_mp:
chi2grid = np.array(pmap.parallel_map(lambda Q: [costfn((P, Q))
for P in Pa], Qa))
else:
chi2grid = np.array(map(lambda Q: [costfn((P, Q)) for P in Pa], Qa))
extent = (Pmin, Pmax, Qmin, Qmax)
cmap = matplotlib.cm.jet
ax = plt.subplot(313)
im = ax.imshow(chi2grid, cmap=cmap, aspect='auto', origin='lower',
extent=extent, interpolation='nearest')
cb = plt.colorbar(im, ax=ax)
(j, i) = np.unravel_index(np.argmin(chi2grid), chi2grid.shape)
P_maxl = Pmin + (i+0.5)*Pstep
Q_maxl = Qmin + (j+0.5)*Qstep
ax.plot(P_maxl, Q_maxl, '+')
ax.set_xlabel('P')
ax.set_ylabel('Q')
plt.draw()
if opt:
if par['idebug'] > 0:
print 'Simplex optimization ...'
# Use simplex method to optimize ev parameters (P,Q)
res = scipy.optimize.fmin(costfn, (P_maxl, Q_maxl), xtol=0.1, ftol=0.1,
full_output=True)
Popt = res[0][0]
Qopt = res[0][1]
else:
c = costfn((P_maxl, Q_maxl))
Popt = P_maxl
Qopt = Q_maxl
out['Pbins'] = Pbins
out['Qbins'] = Qbins
out['chi2grid'] = chi2grid
out['Pa'] = Pa
out['Qa'] = Qa
out['P'] = Popt
out['P_err'] = 0
out['Q'] = Qopt
out['Q_err'] = 0
out['zbin'] = costfn.zbin
out['delta'] = costfn.delta
out['delta_err'] = costfn.delta_err
out['den_var'] = costfn.den_var
out['lf_bins'] = lf_bins
out['phi'] = costfn.phi
out['phi_err'] = costfn.phi_err
out['Mbin'] = costfn.Mbin
out['Mhist'] = costfn.Mhist
out['whist'] = costfn.whist
out['ev_fit_chisq'] = costfn.chisq
out['ev_fit_nu'] = costfn.nu
fout = open(outfile, 'w')
pickle.dump(out, fout)
fout.close()
def Vmax_out(infile, evfile, outfile, param='r_petro',
zmin=0.002, zmax=0.65, nz=65, mlims=(0, 19.8), idebug=1):
"""Output file of density-corrected Vmax."""
global par
dat = pickle.load(open(evfile, 'r'))
P = dat['P']
Q = dat['Q']
try:
ev_model = dat['par']['ev_model']
except:
ev_model = 'z'
print 'P, Q, nz, zmin, zmax =', P, Q, nz, zmin, zmax
par.update({'infile': infile, 'param': param, 'zmin': zmin, 'zmax': zmax,
'mlims': mlims, 'dmlim': 2, 'Mmin': -99, 'Mmax': 99, 'Mbin': 1,
'ev_model': ev_model, 'idebug': idebug})
# First calculate Vmax values without evolution
samp = Sample(infile, par, sel_dict, 0, nqmin=2)
gala = samp.calc_limits(0)
zbin, zhist, V, V_int = z_binning(gala, nz, (zmin, zmax))
zstep = zbin[1] - zbin[0]
S_obs, S_vis = vis_calc(gala, nz, zmin, zstep, V, V_int)
Vmax_raw = np.dot(V, S_vis)
converged, Npred, delta, den_var, Pz, Vmax_dc, niter = delta_solve(
0, 0, gala, nz, (zmin, zmax), zbin, zhist, V, V_int, S_vis)
# Vmax_dc = np.dot(delta * V, S)
# Now include evolution
samp = Sample(infile, par, sel_dict, Q, nqmin=2)
gala = samp.calc_limits(Q)
S_obs, S_vis = vis_calc(gala, nz, zmin, zstep, V, V_int)
converged, Npred, delta, den_var, Pz, Vmax_dec, niter = delta_solve(
P, Q, gala, nz, (zmin, zmax), zbin, zhist, V, V_int, S_vis)
# Vmax_ec = np.dot(Pz * V, S)
# Output a new file of selected objects
header = samp.header
header['H0'] = (par['H0'], 'Hubble parameter (km/s/Mpc)')
header['mlim_0'] = (mlims[0], 'Petrosian r-band mag bright limit')
header['mlim_1'] = (mlims[1], 'Petrosian r-band mag faint limit')
header['ev_model'] = (ev_model, 'ev z-dependence, z1z = z/(1+z)')
header['Q'] = (Q, 'Luminosity evolution')
header['P'] = (P, 'Density evolution')
header['zmin'] = zmin
header['zmax'] = zmax
for ik in xrange(5):
header['kc_{}'.format(ik)] = (samp.kmean[ik],
'Mean kcorr coeff {}'.format(ik))
hdu = fits.BinTableHDU(data=samp.tbdata, header=header)
hdu.writeto(outfile, clobber=True)
# Add Vmax columns
hdulist = fits.open(outfile)
cols = hdulist[1].data.columns
c1 = fits.Column(name='Vmax_raw', format='E', unit='(Mpc/h)^3',
array=Vmax_raw)
c2 = fits.Column(name='Vmax_dc', format='E', unit='(Mpc/h)^3',
array=Vmax_dc)
# c3 = fits.Column(name='Vmax_ec', format='E', unit='(Mpc/h)^3',
# array=Vmax_ec)
c4 = fits.Column(name='Vmax_dec', format='E', unit='(Mpc/h)^3',
array=Vmax_dec)
# pdb.set_trace()
hdu = fits.BinTableHDU.from_columns(cols + c1 + c2 + c4, header=header)
hdu.writeto(outfile, clobber=True)
def lf_1d(infile, outfile, param, Mmin=-24, Mmax=-12, nbin=48, dmlim=2,
Vmax_type='Vmax_dec', Q='read', schec_guess=(-1.0, -20.0, -2),
saund_guess=(-1.0, -20.0, 0.4, -2), idebug=1, lf_est='bin'):
"""Univariate LF using density-corrected Vmax."""
global par
par.update({'infile': infile, 'param': param, 'dmlim': dmlim,
'idebug': idebug, 'lf_est': lf_est})
out = {'infile': infile, 'param': param, 'Mmin': Mmin, 'Mmax': Mmax,
'nbin': nbin, 'Vmax_type': Vmax_type, 'lf_est': lf_est}
print '\n************************\njswml.py version ', par['version']
print sel_dict
gala = read_vmax(infile, sel_dict, param, Vmax_type, Q=Q)
lf_bins = np.linspace(Mmin, Mmax, nbin+1)
# Find completeness limits in magnitude (Loveday+2012 sec 3.3)
Mbright = par['mlims'][0] - dmodk(par['zmax'], par['kc_mean'], par['Q'])
Mfaint = par['mlims'][1] - dmodk(par['zmin'], par['kc_mean'], par['Q'])
print 'Mag completeness limits:', Mbright, Mfaint
if param in ('logmstar', 'logmstar_fluxscale'):
# 95 percentile completeness in stellar mass
pfit = mass_comp_pfit[par['colour']]
Mmin = np.polyval(pfit, par['zmin'])
comp = (lf_bins[:-1] > Mmin)
print 'mass completeness limit:', Mmin
out['Mmin'] = Mmin
else:
comp = (lf_bins[1:] < Mfaint) * (lf_bins[:-1] > Mbright)
out['Mbright'] = Mbright
out['Mfaint'] = Mfaint
lf = lf1d(gala, gala['Vmax'], lf_bins)
schec = util.schec_fit(lf['Mbin'][comp], lf['phi'][comp],
lf['phi_err'][comp],
schec_guess, sigma=lf['kde_bandwidth'], loud=1)
saund = util.saund_fit(lf['Mbin'][comp], lf['phi'][comp],
lf['phi_err'][comp], saund_guess)
out['par'] = par
out['comp'] = comp
out['alpha'] = schec['alpha']
out['alpha_err'] = schec['alpha_err']
out['Mstar'] = schec['Mstar']
out['Mstar_err'] = schec['Mstar_err']
out['lpstar'] = schec['lpstar']
out['lpstar_err'] = schec['lpstar_err']
out['lf_chi2'] = schec['chi2']
out['lf_nu2'] = schec['nu']
out['kde_bandwidth'] = lf['kde_bandwidth']
plt.clf()
plt.semilogy(basey=10, nonposy='clip')
plt.errorbar(lf['Mbin'][comp], lf['phi'][comp], lf['phi_err'][comp],
fmt='o')
util.schec_plot(schec['alpha'], schec['Mstar'], 10**schec['lpstar'],
lf['Mbin'][0], lf['Mbin'][-1], lineStyle='--')
util.saund_plot(saund['alpha'], saund['Mstar'], saund['sigma'],
10**saund['lpstar'],
lf['Mbin'][0], lf['Mbin'][-1], lineStyle=':')
plt.xlabel(plot_label(param)[1])
plt.ylabel(r'$\Phi({})$'.format(plot_label(param)[1]))
plt.ylim(2e-7, 1)
plt.draw()
out['Mbin'] = lf['Mbin']
out['Mhist'] = lf['Mhist']
out['phi'] = lf['phi']
out['phi_err'] = lf['phi_err']
fout = open(outfile, 'w')
pickle.dump(out, fout)
fout.close()
def lfnd(inFile, outFile, param_list, zmin=0.002, zmax=0.65, nz=65,
idebug=1, lf_est='bin'):
"""Multivariate distribution function given evolution parameters."""
global par, plot
par = {'progName': 'jswml.py', 'version': '1.0', 'inFile': inFile,
'zmin': zmin, 'zmax': zmax, 'idebug': idebug, 'lf_est': lf_est}
# Default log radius and sb limits
# par['rad_min'] = -0.6
# par['rad_max'] = 1.6
# par['mu_min'] = 15
# par['mu_max'] = 26
par['rad_min'] = -99
par['rad_max'] = 99
par['mu_min'] = -99
par['mu_max'] = 99
print '\n************************\njswml.py version ', par['version']
print param_list, sel_dict
samp = read_gama(inFile, param_list)
qty = samp.qty_list[0]
lf_bins = np.linspace(qty.absMin, qty.absMax, qty.nabs+1)
Q = qty.Q
print 'Q =', Q
out = {'par': par, 'qty_list': samp.qty_list}
gala = samp.calc_limits()
zbin, zhist, V, V_int = z_binning(gala, nz, (zmin, zmax))
zstep = zbin[1] - zbin[0]
S_obs, S_vis = vis_calc(gala, nz, zmin, zstep, V, V_int)
converged, Npred, delta, den_var, Pz, Vdc_max, niter = delta_solve(
P, Q, gala, nz, (zmin, zmax), zbin, zhist, V, V_int, S_vis)
# Jacknife errors on delta
delta_jack = np.zeros((njack, nz))
for jack in range(njack):
idx = (gala['ra'] < ra_jack[jack]) + (gala['ra'] >= ra_jack[jack] + 4.0)
zhist, bin_edges = np.histogram(
gala['z'][idx], nz, (zmin, zmax), weights=gala['weight'][idx])
xx, xx, delta_jack[jack, :], xx, xx, xx, xx = delta_solve(
P, Q, gala[idx], nz, (zmin, zmax), zbin, zhist,
V, V_int, S[:, idx])
delta_err = np.sqrt((njack-1) * np.var(delta_jack, axis=0))
delta_poiss_err = delta/np.sqrt(zhist)
plt.clf()
ax = plt.subplot(211)
ax.step(zbin, delta, where='mid')
ax.errorbar(zbin, delta, delta_err, fmt='none')
ax.errorbar(zbin, delta, delta_poiss_err, fmt='none')
ax.errorbar(zbin, delta, np.sqrt(den_var), fmt='none')
ax.plot([zmin, zmax], [1.0, 1.0], ':')
ax.set_ylim(0.3, 1.7)
ax.set_xlabel('Redshift z')
ax.set_ylabel(r'$\Delta(z)$')
if samp.nq > 1:
lf_bins = []
lf_range = []
absStep = 1.0
for qty in samp.qty_list:
absStep *= qty.absStep
lf_bins.append(qty.nabs)
lf_range.append((qty.absMin, qty.absMax))
Mhist, whist, phi, phi_err, edges = lfnd(gala, Vdc_max, lf_bins,
lf_range, absStep)
Mbin = edges[0][:-1] + 0.5 * samp.qty_list[0].absStep
phi_proj = (np.sum(phi, axis=tuple(range(1, samp.nq))) *
absStep/samp.qty_list[0].absStep)
Mhist_proj = np.sum(Mhist, axis=tuple(range(1, samp.nq)))
else:
lf = LF1d(gala, Vdc_max, lf_bins)
(Mbin, Mhist, whist, phi, phi_err) = (
lf.Mbin, lf.Mhist, lf.whist, lf.phi, lf.phi_err)
phi_proj = phi
edges = lf_bins
# pdb.set_trace()
schec = util.schec_fit(lf.Mbin, lf.phi, lf.phi_err,
(-1.0, -20.0, -2), sigma=lf.kde_bandwidth)
out['alpha'] = schec['alpha']
out['alpha_err'] = schec['alpha_err']
out['Mstar'] = schec['Mstar']
out['Mstar_err'] = schec['Mstar_err']
out['lpstar'] = schec['lpstar']
out['lpstar_err'] = schec['lpstar_err']
out['lf_chi2'] = schec['chi2']
out['lf_nu2'] = schec['nu']
out['kde_bandwidth'] = lf.kde_bandwidth
ax = plt.subplot(2, 1, 2)
ax.semilogy(basey=10, nonposy='clip')
ax.plot(Mbin, phi_proj)
fit = Mhist > 0
ax.set_xlabel(samp.qty_list[0].name)
ax.set_ylabel(r'$\Phi({})$'.format(samp.qty_list[0].name))
ax.set_ylim(2e-7, 1)
plt.draw()
out['P'] = P
out['P_err'] = 0
out['Q'] = samp.qty_list[0].Q
out['Q_err'] = 0
out['zbin'] = zbin
out['delta'] = delta
out['delta_err'] = delta_err
out['den_var'] = den_var
out['phi'] = phi
out['phi_err'] = phi_err
out['edges'] = edges
out['Mbin'] = Mbin
out['Mhist'] = Mhist
out['whist'] = whist
out['ev_fit_chisq'] = 0
out['ev_fit_nu'] = 1
fout = open(outFile, 'w')
pickle.dump(out, fout)
fout.close()
def ran_gen(gala, outfile, nfac, Q=Qdef, P=Pdef, vol=0):
"""Generate random distribution nfac times larger than input catalogue."""
def vol_ev(z):
"""Volume element multiplied by density evolution."""
pz = cosmo.dV(z) * den_evol(z, P)
return pz
global par
nz = par['nz']
zmin = par['zmin']
zmax = par['zmax']
print par
print sel_dict
# f = open(evfile, 'r')
# dat = pickle.load(f)
# f.close()
# P = dat['P']
# Q = dat['Q']
# print 'P, Q =', P, Q
# samp = Sample(infile, par, sel_dict)
# gala = samp.calc_limits(Q)
zbin, zhist, V, V_int = z_binning(gala, nz, (zmin, zmax))
zstep = zbin[1] - zbin[0]
S_obs, S_vis = vis_calc(gala, nz, zmin, zstep, V, V_int)
converged, Npred, delta, den_var, Pz, Vdc_max, niter = delta_solve(
P, Q, gala, nz, (zmin, zmax), zbin, zhist, V, V_int, S_vis)
V_max = np.dot(Pz * V, S_vis)
ndupe = np.round(nfac * V_max / Vdc_max).astype(np.int32)
ngal = len(gala['z'])
nran = np.sum(ndupe)
galhist, zbins = np.histogram(gala['z'], nz, (zmin, zmax))
ranhist = np.zeros(nz)
zcen = zbins[:-1] + 0.5 * (zbins[1]-zbins[0])
zstep = (zmax - zmin)/nz
info = par.copy()
info.update({'P': P, 'Q': Q, 'nfac': nfac,
'ngal': ngal, 'nran': nran,'sel_dict': sel_dict,
'galhist': list(galhist), 'zbins': list(zbins), 'zcen': list(zcen)})
fout = open(outfile, 'w')
print >> fout, info
for i in xrange(ngal):
if vol:
z = util.ran_fun(vol_ev, zmin, zmax, ndupe[i])
else:
# Avoid tail of randoms beyond highest z galaxy
# zhi = min(zmaxg, gala['zhi'][i])
z = util.ran_fun(vol_ev, gala['zlo'][i], gala['zhi'][i], ndupe[i])
for j in xrange(len(z)):
print >> fout, z[j], V_max[i], gala['weight'][i]
jz = int((z[j] - zmin)/zstep)
ranhist[jz] += 1
fout.close()
print nran, ' redshifts output'
plt.clf()
plt.step(zcen, galhist, where='mid')
plt.plot(zcen, ranhist*float(ngal)/nran)
plt.xlabel('Redshift')
plt.ylabel('Frequency')
plt.draw()
def vol_limit(Mmin, Mmax, zmin, zmax, infile='kcorrz01.fits', Q=0):
"""Form volume-limited sample between specified absolute magnitiude
and redshift limits."""
global par
par['clean_photom'] = 0
par['nz'] = 1
par['param'] = 'r_petro'
par['Mbin'] = 1
par['Mmin'] = Mmin
par['Mmax'] = Mmax
par['zmin'] = zmin
par['zmax'] = zmax