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# Copyright (c) 2017 Weitian LI <weitian@aaronly.me>
# MIT license
"""
Press-Schechter (PS) formalism
First determine the number of clusters within a sky patch (i.e., sky
coverage) according to the cluster distribution predicted by the PS
formalism; then sampling from the PS mass function to derive the mass
and redshift for each cluster.
"""
import logging
import random
import numpy as np
import pandas as pd
from ...share import CONFIGS, COSMO
from ...utils.interpolate import bilinear
from ...utils.units import UnitConversions as AUC
logger = logging.getLogger(__name__)
class PSFormalism:
"""
Press-Schechter (PS) formalism
Simulate the clusters number and their distribution (mass and z)
within a sky patch of certain coverage.
"""
def __init__(self, configs=CONFIGS):
self.configs = configs
self._set_configs()
self._load_data()
def _set_configs(self):
"""
Load the required configurations and set them.
"""
comp = "extragalactic/clusters"
self.datafile = self.configs.get_path(comp+"/ps_data")
self.f_darkmatter = self.configs.getn(comp+"/f_darkmatter")
self.Mmin_cluster = self.configs.getn(comp+"/mass_min") # [Msun]
self.Mmin_halo = self.Mmin_cluster * self.f_darkmatter
def _load_data(self, filepath=None):
"""
Load dndM data and reformat into a 2D density grid together with
redshifts and masses vectors.
Data File Description
---------------------
z1 mass1 density1
z1 mass2 density2
z1 .. density3
z2 mass1 density4
z2 mass2 density5
z2 .. density6
...
where,
* Redshifts: 0.0 -> 3.02, even-spacing, step 0.02
* Mass: unit 1e12 -> 9.12e15 [Msun], log-even (dark matter)
* Density: [number]/dVc/dM
with,
- dVc: differential comvoing volume, [Mpc^3]/[sr]/[unit redshift]
"""
if filepath is None:
filepath = self.datafile
data = np.loadtxt(filepath)
redshifts = data[:, 0]
masses = data[:, 1]
densities = data[:, 2]
redshifts = np.array(list(set(redshifts)))
redshifts.sort()
masses = np.array(list(set(masses)))
masses.sort()
densities = densities.reshape((len(redshifts), len(masses)))
logger.info("Loaded PS data from file: %s" % filepath)
logger.info("Number of redshift bins: %d" % len(redshifts))
logger.info("Number of mass bins: %d" % len(masses))
self.redshifts = redshifts
self.masses = masses
self.densities = densities
@staticmethod
def delta(x, logeven=False):
"""
Calculate the delta values for each element of a vector,
assuming they are evenly or log-evenly distributed,
with extrapolating.
"""
x = np.asarray(x)
if logeven:
x = np.log(x)
step = x[1] - x[0]
x1 = np.concatenate([[x[0]-step], x[:-1]])
x2 = np.concatenate([x[1:], [x[-1]+step]])
dx = (x2 - x1) * 0.5
if logeven:
dx = np.exp(dx)
return dx
@property
def number_grid(self):
"""
Calculate the number distribution w.r.t. redshift, mass, and
unit coverage [sr] from the density distribution.
"""
dz = self.delta(self.redshifts)
dM = self.delta(self.masses)
dMgrip, dzgrip = np.meshgrid(dM, dz)
Mgrip, zgrip = np.meshgrid(self.masses, self.redshifts)
dVcgrip = COSMO.differential_comoving_volume(zgrip).value # [Mpc^3/sr]
numgrid = self.densities * dVcgrip * dzgrip * dMgrip
return numgrid
def calc_cluster_counts(self, coverage):
"""
Calculate the total number of clusters (>= minimum mass) within
the FoV coverage according to the number density distribution
(e.g., predicted by the Press-Schechter mass function)
Parameters
----------
coverage : float
The coverage of the sky patch within which to determine the
total number of clusters.
Unit: [deg^2]
Returns
-------
counts : int
The total number of clusters within the sky patch.
Attributes
----------
counts
"""
logger.info("Determine the total number of clusters within "
"sky patch of coverage %.1f [deg^2]" % coverage)
coverage *= AUC.deg2rad**2 # [deg^2] -> [rad^2] = [sr]
midx = (self.masses >= self.Mmin_halo)
numgrid = self.number_grid
counts = np.sum(numgrid[:, midx]) * coverage
self.counts = int(np.round(counts))
logger.info("Total number of clusters: %d" % self.counts)
return self.counts
def sample_z_m(self, counts=None):
"""
Randomly generate the requested number of pairs of (z, M) following
the specified number distribution.
Parameters
----------
counts : int, optional
The number of (z, mass) pairs to be sampled.
If not specified, then default to ``self.counts``
Returns
-------
df : `~pandas.DataFrame`
A Pandas data frame with 2 columns, i.e., ``z`` and ``mass``.
comment : list[str]
Comments to the above data frame.
Attributes
----------
clusters : df
clusters_comment : comment
"""
if counts is None:
counts = self.counts
logger.info("Sampling (z, mass) pairs for %d clusters ..." % counts)
redshifts = self.redshifts
masses = self.masses
zmin = redshifts.min()
zmax = redshifts.max()
Mmax = masses.max()
midx = (masses >= self.Mmin_halo)
numgrid = self.number_grid
numgrid2 = numgrid[:, midx]
NM = numgrid2.max()
z_list = []
M_list = []
i = 0
while i < counts:
z = random.uniform(zmin, zmax)
M = random.uniform(self.mass_min, Mmax)
r = random.random()
zi1 = (self.redshifts < z).sum()
zi2 = zi1 - 1
if zi2 < 0:
zi2 += 1
zi1 += 1
Mi1 = (self.masses < M).sum()
Mi2 = Mi1 - 1
if Mi2 < 0:
Mi2 += 1
Mi1 += 1
N = bilinear(
z, np.log(M),
p11=(redshifts[zi1], np.log(masses[Mi1]), numgrid[zi1, Mi1]),
p12=(redshifts[zi1], np.log(masses[Mi2]), numgrid[zi1, Mi2]),
p21=(redshifts[zi2], np.log(masses[Mi1]), numgrid[zi2, Mi1]),
p22=(redshifts[zi2], np.log(masses[Mi2]), numgrid[zi2, Mi2]))
if r < N/NM:
z_list.append(z)
M_list.append(M)
i += 1
logger.info("Sampled %d (z, mass) pairs for each cluster" % counts)
df = pd.DataFrame(np.column_stack([z_list, M_list]),
columns=["z", "mass"])
df["mass"] /= self.f_darkmatter
comment = [
"cluster number counts : %d" % counts,
"z : redshift",
"mass : cluster total mass [Msun]",
]
self.clusters = df
self.clusters_comment = comment
return (df, comment)
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