aboutsummaryrefslogtreecommitdiffstats
path: root/fg21sim/extragalactic/clusters/psformalism.py
blob: f17aae1f8f919aa9ba799fd01e59750e20f35411 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
# Copyright (c) 2017-2018 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 halo mass function to derive the mass
and redshift for each cluster.
"""

import logging
import random
from functools import lru_cache

import numpy as np
import hmf

from ...share import CONFIGS, COSMO
from ...utils.units import UnitConversions as AUC
from ...utils.io import write_dndlnm


logger = logging.getLogger(__name__)


class PSFormalism:
    """
    Press-Schechter (PS) formalism

    Calculate the halo mass distribution with respect to mass and redshift,
    determine the clusters number counts and generate their distribution
    (mass and z) within a sky patch of certain coverage.
    """
    def __init__(self, configs=CONFIGS):
        self.configs = configs
        self._set_configs()

    def _set_configs(self):
        """
        Load the required configurations and set them.
        """
        comp = "extragalactic/psformalism"
        self.model = self.configs.getn(comp+"/model")
        self.M_min = self.configs.getn(comp+"/M_min")
        self.M_max = self.configs.getn(comp+"/M_max")
        self.M_step = self.configs.getn(comp+"/M_step")
        self.z_min = self.configs.getn(comp+"/z_min")
        self.z_max = self.configs.getn(comp+"/z_max")
        self.z_step = self.configs.getn(comp+"/z_step")
        self.dndlnm_outfile = self.configs.get_path(comp+"/dndlnm_outfile")

        comp = "extragalactic/clusters"
        self.Mmin_cluster = self.configs.getn(comp+"/mass_min")  # [Msun]
        self.boost = self.configs.getn(comp+"/boost")

        self.clobber = self.configs.getn("output/clobber")

    @property
    def hmf_model(self):
        return {"PS": "PS",
                "SMT": "SMT",
                "JENKINS": "Jenkins"}[self.model.upper()]

    def hmf_massfunc(self, z=0.0):
        """
        Halo mass function as a `~hmf.MassFunction` instance.
        """
        if not hasattr(self, "_hmf_massfunc"):
            h = COSMO.h
            cosmo = COSMO._cosmo
            self._hmf_massfunc = hmf.MassFunction(
                Mmin=np.log10(self.M_min*h),
                Mmax=np.log10(self.M_max*h),
                dlog10m=self.M_step,
                hmf_model=self.hmf_model,
                cosmo_model=cosmo,
                n=COSMO.ns,
                sigma_8=COSMO.sigma8)
            logger.info("Initialized '%s' halo mass function." %
                        self.hmf_model)

        massfunc = self._hmf_massfunc
        massfunc.update(z=z)
        return massfunc

    @property
    @lru_cache()
    def z(self):
        """
        The redshift points where to calculate the dndlnm data.
        """
        return np.arange(self.z_min, self.z_max+self.z_step/2, self.z_step)

    @property
    @lru_cache()
    def mass(self):
        """
        The mass points where to calculate the dndlnm data.

        NOTE:
        The maximum mass end is exclusive, to be  consistent with hmf's
        mass function!
        """
        return 10 ** np.arange(np.log10(self.M_min),
                               np.log10(self.M_max),
                               self.M_step)

    @property
    def dndlnm(self):
        """
        The calculated halo mass distributions data.
        """
        if not hasattr(self, "_dndlnm"):
            self._dndlnm = self.calc_dndlnm()
        return self._dndlnm

    def calc_dndlnm(self):
        """
        Calculate the halo mass distributions expressed in ``dndlnm``,
        the differential mass distribution in terms of natural log of
        masses.
        Unit: [Mpc^-3] (the little "h" is folded into the values)

        NOTE
        ----
        dndlnm = d n(M,z) / d ln(M); [Mpc^-3]
        describes the number of halos per comoving volume (Mpc^3) at
        redshift z per unit logarithmic mass interval at mass M.
        """
        logger.info("Calculating dndlnm data ...")
        dndlnm = []
        h = COSMO.h
        for z_ in self.z:
            massfunc = self.hmf_massfunc(z_)
            dndlnm.append(massfunc.dndlnm * h**3)
        self._dndlnm = np.array(dndlnm)
        logger.info("Calculated dndlnm within redshift: %.1f - %.1f" %
                    (self.z_min, self.z_max))
        return self._dndlnm

    def write(self, outfile=None):
        """
        Write the calculate dndlnm data into file as NumPy ".npz" format.
        """
        if outfile is None:
            outfile = self.dndlnm_outfile
        write_dndlnm(outfile, dndlnm=self.dndlnm, z=self.z, mass=self.mass,
                     clobber=self.clobber)
        logger.info("Wrote dndlnm data into file: %s" % outfile)

    @property
    def Mmin_halo(self):
        return self.Mmin_cluster * COSMO.darkmatter_fraction

    @staticmethod
    def delta(x, logeven=False):
        """
        Calculate the delta values for each element of a vector,
        assuming they are evenly or log-evenly distributed,
        by extrapolating.
        """
        x = np.asarray(x)
        if logeven:
            ratio = x[1] / x[0]
            x_left = x[0] / ratio
            x_right = x[-1] * ratio
        else:
            step = x[1] - x[0]
            x_left = x[0] - step
            x_right = x[-1] + step
        x2 = np.concatenate([[x_left], x, [x_right]])
        dx = (x2[2:] - x2[:-2]) / 2
        return dx

    @property
    def number_grid(self):
        """
        The halo number per unit solid angle [sr] distribution w.r.t.
        mass and redshift.
        Unit: [/sr]
        """
        if not hasattr(self, "_number_grid"):
            dz = self.delta(self.z)
            dM = self.delta(self.mass, logeven=True)
            dlnM = dM / self.mass
            dlnMgrid, dzgrid = np.meshgrid(dlnM, dz)
            __, zgrid = np.meshgrid(self.mass, self.z)
            dVcgrid = COSMO.dVc(zgrid)  # [Mpc^3/sr]
            self._number_grid = self.dndlnm * dlnMgrid * (dVcgrid*dzgrid)

        return self._number_grid

    def calc_cluster_counts(self, coverage):
        """
        Calculate the total number of clusters (>= minimum mass) within
        the FoV coverage according to the halo number density distribution.

        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.
        """
        logger.info("Calculating the total number of clusters within "
                    "sky patch of coverage %.1f [deg^2]" % coverage)
        logger.info("Minimum cluster mass: %.2e [Msun]" % self.Mmin_cluster)
        logger.info("Minimum halo mass: %.2e [Msun]" % self.Mmin_halo)
        coverage *= AUC.deg2rad**2  # [deg^2] -> [rad^2] = [sr]
        midx = (self.mass >= self.Mmin_halo)
        numgrid = self.number_grid
        counts = np.sum(numgrid[:, midx]) * coverage * self.boost
        counts = int(np.round(counts))
        logger.info("Total number of clusters: %d" % counts)
        return counts

    def sample_z_m(self, counts):
        """
        Randomly generate the requested number of pairs of (z, M) following
        the halo number distribution.

        NOTE
        ----
        First derive the cluster (M>=Mmin) number distribution w.r.t.
        redshifts, from which the redshift for each cluster is sampled
        using the acceptance-rejection algorithm.  Then for each cluster
        at redshift z, the corresponding halo mass distribution is used
        to generate the cluster mass using the same algorithm.

        NOTE
        ----
        Sampling masses in logarithmic scale improve the speed very
        significantly (~30x)!

        Parameters
        ----------
        counts : int, optional
            The number of (z, mass) pairs to be sampled.

        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.
        """
        logger.info("Sampling (z, mass) pairs for %d clusters ..." % counts)

        z = self.z
        zmin = z.min()
        zmax = z.max()
        log10mass = np.log10(self.mass)
        log10Mmin = np.log10(self.Mmin_halo)
        log10Mmax = log10mass.max()
        midx = (log10mass >= log10Mmin)
        log10mass = log10mass[midx]
        Ngrid = self.number_grid[:, midx]

        logger.info("Sampling redshifts ...")
        z_list = []
        zi_list = []
        Nzdist = Ngrid.sum(axis=1)
        NMax = Nzdist.max()
        i = 0
        while i < counts:
            zc = random.uniform(zmin, zmax)
            zi = (z < zc).sum()
            Nzc = Nzdist[zi]
            r = random.random()
            if r < Nzc/NMax:
                z_list.append(zc)
                zi_list.append(zi)
                i += 1

        logger.info("Sampling masses ...")
        mass_list = []
        NMax_list = Ngrid.max(axis=1)
        i = 0
        while i < counts:
            zi = zi_list[i]
            NMax = NMax_list[zi]
            Nmassdist = Ngrid[zi, :]
            log10Mc = random.uniform(log10Mmin, log10Mmax)
            Mi = (log10mass < log10Mc).sum()
            NMc = Nmassdist[Mi]
            r = random.random()
            if r < NMc/NMax:
                mass_list.append(10**log10Mc)
                i += 1

        logger.info("Sampled %d pairs of (z, mass) for each cluster" % counts)
        z = np.array(z_list)
        mass = np.array(mass_list) / COSMO.darkmatter_fraction
        comment = [
            "halo mass function model: %s" % self.hmf_model,
            "cluster minimum mass: %.2e [Msun]" % self.Mmin_cluster,
            "dark matter fraction: %.2f" % COSMO.darkmatter_fraction,
            "cluster counts: %d" % counts,
            "boost factor for cluster counts: %s" % self.boost,
            "",
            "z - redshift",
            "mass - [Msun] cluster total mass",
        ]
        return (z, mass, comment)