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#!/usr/bin/env python3
#
# Copyright (c) Weitian LI <weitian@aaronly.me>
# MIT license
#
"""
Calculate the total power within the EoR window on the 2D power spectrum.
The adopted EoR window definition is from [thyagarajan2013],Eq.(26),Fig.(11).
.. [thyagarajan2013]
Thyagarajan et al. 2013, ApJ, 776, 6
"""
import argparse
from functools import lru_cache
import numpy as np
from astropy.io import fits
from astropy.cosmology import FlatLambdaCDM
import astropy.constants as ac
import matplotlib.pyplot as plt
from matplotlib.backends.backend_agg import FigureCanvasAgg as FigureCanvas
from matplotlib.figure import Figure
plt.style.use("ggplot")
# HI line frequency
freq21cm = 1420.405751 # [MHz]
# Adopted cosmology
H0 = 71.0 # [km/s/Mpc]
OmegaM0 = 0.27
cosmo = FlatLambdaCDM(H0=H0, Om0=OmegaM0)
@lru_cache()
def freq2z(freq):
z = freq21cm / freq - 1.0
return z
class PS2D:
"""
2D cylindrically averaged power spectrum; calculated by ``ps2d.py``.
Attributes
----------
ps2d : 2D `~numpy.ndarray`
Shape: [n_k_los, n_k_perp]
"""
def __init__(self, infile):
self.infile = infile
with fits.open(infile) as f:
self.header = f[0].header
self.ps2d = f[0].data[0, :, :] # errors ignored
self.freqc = self.header["Freq_C"]
self.freqmin = self.header["Freq_Min"]
self.freqmax = self.header["Freq_Max"]
self.bandwidth = self.freqmax - self.freqmin # [MHz]
self.zc = self.header["Z_C"]
self.pixelsize = self.header["PixSize"]
self.unit = self.header["BUNIT"]
@property
def k_perp(self):
dk = self.header["CDELT1P"]
nk = self.header["NAXIS1"]
return np.arange(nk) * dk
@property
def k_los(self):
dk = self.header["CDELT2P"]
nk = self.header["NAXIS2"]
return np.arange(nk) * dk
@property
def k_perp_min(self):
return self.k_perp[1] # ignore the first 0
@property
def k_perp_max(self):
return self.k_perp[-1]
@property
def k_los_min(self):
return self.k_los[1] # ignore the first 0
@property
def k_los_max(self):
return self.k_los[-1]
def sum_power(self, window):
"""
Sum the power within the defined window.
NOTE: The cylindrical average should be accounted for.
"""
k_perp = self.k_perp
k_los = self.k_los
dk_perp = k_perp[1] - k_perp[0]
dk_los = k_los[1] - k_los[0]
volume = np.zeros_like(self.ps2d)
volume[0, :] = 2*np.pi * k_perp * dk_perp * dk_los
for i in range(1, len(k_los)):
# The extra "2" to account for the average on +k_los and -k_los
volume[i, :] = 2*np.pi * k_perp * dk_perp * dk_los * 2
power = np.sum(self.ps2d * window * volume)
return power
def eor_window(self, fov, e,
k_perp_min=None, k_perp_max=None,
k_los_min=None, k_los_max=None):
"""
Determine the EoR window region.
Parameters
----------
fov : float
instrumental field of view (FoV)
Unit: [deg]
e : float
Thyagarajan proposed characteristic convolution width factor,
generally 0-3
Returns
-------
window : 2D bool `~numpy.ndarray`
2D array mask of the same size of the power spectrum indicating
the defined EoR window region.
header : fits.Header
FITS header with the keywords recording the EoR window variables
"""
if k_perp_min is None:
k_perp_min = self.k_perp_min
if k_perp_max is None:
k_perp_max = self.k_perp_max
if k_los_min is None:
k_los_min = self.k_los_min
if k_los_max is None:
k_los_max = self.k_los_max
window = np.ones_like(self.ps2d, dtype=bool)
k_perp = self.k_perp
k_los = self.k_los
k_wedge = self.wedge_edge(k_perp, fov=fov, e=e)
window[k_los < k_los_min, :] = False
window[k_los > k_los_max, :] = False
window[:, k_perp < k_perp_min] = False
window[:, k_perp > k_perp_max] = False
for i, k in enumerate(k_wedge):
window[k_los < k, i] = False
header = self.eor_window_header(fov=fov, e=e,
k_perp_min=k_perp_min,
k_perp_max=k_perp_max,
k_los_min=k_los_min,
k_los_max=k_los_max)
return (window, header)
def eor_window_header(self, fov, e, k_perp_min, k_perp_max,
k_los_min, k_los_max):
header = self.header.copy(strip=True)
header["FoV"] = (fov, "[deg] Field of view to determine EoR window")
header["e_ConvW"] = (e, "characteristic convolution width")
header["kper_min"] = (k_perp_min, "[Mpc^-1] minimum k_perp")
header["kper_max"] = (k_perp_max, "[Mpc^-1] maximum k_perp")
header["klos_min"] = (k_los_min, "[Mpc^-1] minimum k_los")
header["klos_max"] = (k_los_max, "[Mpc^-1] maximum k_los")
return header
def wedge_edge(self, k_perp, fov, e):
"""
The boundary/edge between the EoR window (top-left) and the
foreground wedge (bottom-right).
"""
Hz = cosmo.H(self.zc).value # [km/s/Mpc]
Dc = cosmo.comoving_distance(self.zc).value # [Mpc]
c = ac.c.to("km/s").value # [km/s]
coef = Hz * Dc / (c * (1+self.zc))
term1 = np.sin(np.deg2rad(fov)) * k_perp # [Mpc^-1]
term2 = ((2*np.pi * e * freq21cm / self.bandwidth) /
((1 + self.zc) * Dc)) # [Mpc^-1]
k_los = coef * (term1 + term2)
return k_los
def plot(self, ax, fov, e,
k_perp_min=None, k_perp_max=None,
k_los_min=None, k_los_max=None,
colormap="jet"):
"""
Plot the 2D power spectrum with EoR window marked on.
"""
if k_perp_min is None:
k_perp_min = self.k_perp_min
if k_perp_max is None:
k_perp_max = self.k_perp_max
if k_los_min is None:
k_los_min = self.k_los_min
if k_los_max is None:
k_los_max = self.k_los_max
x = self.k_perp
y = self.k_los
y_wedge = self.wedge_edge(x, fov=fov, e=e)
title = "EoR Window (fov=%.1f[deg], e=%.1f)" % (fov, e)
# data
mappable = ax.pcolormesh(x[1:], y[1:],
np.log10(self.ps2d[1:, 1:]),
cmap=colormap)
# EoR window
ax.axvline(x=k_perp_min, color="black", linewidth=2, linestyle="--")
ax.axvline(x=k_perp_max, color="black", linewidth=2, linestyle="--")
ax.axhline(y=k_los_min, color="black", linewidth=2, linestyle="--")
ax.axhline(y=k_los_max, color="black", linewidth=2, linestyle="--")
ax.plot(x, y_wedge, color="black", linewidth=2, linestyle="--")
#
ax.set(xscale="log", yscale="log",
xlim=(x[1], x[-1]), ylim=(y[1], y[-1]),
xlabel=r"k$_{\perp}$ [Mpc$^{-1}$]",
ylabel=r"k$_{||}$ [Mpc$^{-1}$]",
title=title)
cb = ax.figure.colorbar(mappable, ax=ax, pad=0.01, aspect=30)
cb.ax.set_xlabel(r"[%s$^2$ Mpc$^3$]" % self.unit)
return ax
def main():
parser = argparse.ArgumentParser(
description="Determine EoR window region and calculate total power")
parser.add_argument("-F", "--fov", dest="fov",
type=float, required=True,
help="instrumental FoV to determine the EoR window")
parser.add_argument("-e", "--conv-width", dest="conv_width",
type=float, default=3.0,
help="characteristic convolution width (default: 3.0)")
parser.add_argument("-p", "--k-perp-min", dest="k_perp_min", type=float,
help="minimum k wavenumber perpendicular to LoS; " +
"unit: [Mpc^-1]")
parser.add_argument("-P", "--k-perp-max", dest="k_perp_max", type=float,
help="maximum k wavenumber perpendicular to LoS")
parser.add_argument("-l", "--k-los-min", dest="k_los_min", type=float,
help="minimum k wavenumber along LoS")
parser.add_argument("-L", "--k-los-max", dest="k_los_max", type=float,
help="maximum k wavenumber along LoS")
parser.add_argument("--save-window", dest="save_window",
help="save the determined EoR window into FITS " +
"file with the provided filename")
parser.add_argument("--plot", dest="plot",
help="plot the 2D power spectrum with the " +
"determined EoR window marked, and save into " +
"the specified file")
parser.add_argument("infile", help="2D power spectrum FITS file")
args = parser.parse_args()
ps2d = PS2D(args.infile)
window, header = ps2d.eor_window(fov=args.fov, e=args.conv_width,
k_perp_min=args.k_perp_min,
k_perp_max=args.k_perp_max,
k_los_min=args.k_los_min,
k_los_max=args.k_los_max)
power = ps2d.sum_power(window)
print("Total power within EoR window: %g [%s]" % (power, ps2d.unit))
if args.save_window:
hdu = fits.PrimaryHDU(data=window.astype(np.int16), header=header)
hdu.writeto(args.save_window)
print("Saved EoR window into file: %s" % args.save_window)
if args.plot:
fig = Figure(figsize=(8, 8), dpi=150)
FigureCanvas(fig)
ax = fig.add_subplot(1, 1, 1)
ps2d.plot(ax=ax, fov=args.fov, e=args.conv_width,
k_perp_min=args.k_perp_min, k_perp_max=args.k_perp_max,
k_los_min=args.k_los_min, k_los_max=args.k_los_max)
fig.tight_layout()
fig.savefig(args.plot)
print("Plotted 2D PSD with EoR window and saved to: %s" % args.plot)
if __name__ == "__main__":
main()
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