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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
#
# Aaron LI
# Created: 2016-04-29
# Updated: 2016-05-02
#
# TODO:
# * to calculate the PEI error
#
"""
Calculate the power excess index (PEI), which is defined the area ratio of
the lower-left part with respect to the total rectangle, which is further
defined by the radial power spectrum and the scale of 0.035R500 and 0.35R500,
in the logarithmic space.
Reference:
Zhang, C., et al. 2016, ApJ
"""
import os
import glob
import argparse
import json
from collections import OrderedDict
import numpy as np
import scipy.interpolate
import scipy.integrate
import matplotlib.pyplot as plt
from matplotlib.backends.backend_agg import FigureCanvasAgg as FigureCanvas
from matplotlib.figure import Figure
from matplotlib.path import Path
import matplotlib.patches as patches
from make_r500_regions import get_r500
__version__ = "0.3.1"
__date__ = "2016-05-02"
plt.style.use("ggplot")
def calc_pei(data, r500, interp_np=101):
"""
Calculate the power excess index (PEI), which is defined the area ratio
of the lower-left part with respect to the total rectangle.
Arguments:
* data: 3-column power spectrum data (frequency, power, power_err)
* r500: R500 value in unit of the inverse of the above "frequency"
* interp_np: number of data points interpolated to calculate PEI
"""
freqs = data[:, 0]
psd1d = data[:, 1]
# frequency values corresponding to 0.35R500 and 0.035R500
pei_fmin = 1.0 / (0.350 * r500)
pei_fmax = 1.0 / (0.035 * r500)
# switch to the logarithmic scale
# XXX: how to deal with the errors
mask = (freqs > 0.0)
x = np.log10(freqs[mask])
y = np.log10(psd1d[mask])
pei_xmin = np.log10(pei_fmin)
pei_xmax = np.log10(pei_fmax)
# interpolate the power spectrum
f_interp = scipy.interpolate.interp1d(x, y, kind="linear",
assume_sorted=True)
x_interp = np.linspace(pei_xmin, pei_xmax, num=interp_np)
y_interp = f_interp(x_interp)
pei_ymin = np.min(y_interp)
pei_ymax = np.max(y_interp)
# calculate the PEI
area_total = (pei_xmax - pei_xmin) * (pei_ymax - pei_ymin)
area_below = scipy.integrate.trapz((y_interp-pei_ymin), x_interp)
pei_value = area_below / area_total
results = {
"area_total": area_total,
"area_below": area_below,
"pei_value": pei_value,
"pei_err": None,
}
data_interp_log10 = np.column_stack((x_interp, y_interp))
return (results, data_interp_log10)
def plot_pei(data, data_interp_log10, info={}, ax=None, fig=None):
"""
Make a plot to visualize the PEI rectangular.
"""
if ax is None:
fig, ax = plt.subplots(1, 1)
# prepare data
freqs = data[:, 0]
psd1d = data[:, 1]
psd1d_err = data[:, 2]
x_interp = 10 ** data_interp_log10[:, 0]
y_interp = 10 ** data_interp_log10[:, 1]
pei_xmin = np.min(x_interp)
pei_xmax = np.max(x_interp)
pei_ymin = np.min(y_interp)
pei_ymax = np.max(y_interp)
#
mask = (freqs > 0.0)
xmin = np.min(freqs[mask]) / 1.2
xmax = np.max(freqs[mask])
ymin = np.min(psd1d[mask]) / 3.0
ymax = np.max(psd1d[mask] + psd1d_err[mask]) * 1.2
#
ax.plot(freqs, psd1d, color="black", linestyle="none",
marker="o", markersize=5, alpha=0.7)
ax.errorbar(freqs, psd1d, yerr=psd1d_err, fmt="none",
ecolor="blue", alpha=0.7)
ax.set_xscale("log")
ax.set_yscale("log")
ax.set_xlim(xmin, xmax)
ax.set_ylim(ymin, ymax)
ax.set_title("Power Spectral Density & PEI (%s; %d)" %
(info.get("name"), info.get("obsid")))
ax.set_xlabel(r"k (pixel$^{-1}$)")
ax.set_ylabel("Power")
ax.text(x=xmax/1.1, y=ymax/1.2,
s="PEI = %.2f / %.2f = %.2f" % (info.get("area_below"),
info.get("area_total"),
info.get("pei")),
horizontalalignment="right", verticalalignment="top")
# plot the interpolated data points and the PEI rectangle
# credit: http://matplotlib.org/users/path_tutorial.html
ax.plot(x_interp, y_interp, linestyle="--", marker="D", markersize=2,
color="green", alpha=0.9)
vertices = [
(pei_xmin, pei_ymin), # left, bottom
(pei_xmin, pei_ymax), # left, top
(pei_xmax, pei_ymax), # right, top
(pei_xmax, pei_ymin), # right, bottom
(pei_xmin, pei_ymin), # ignored
]
codes = [
Path.MOVETO,
Path.LINETO,
Path.LINETO,
Path.LINETO,
Path.CLOSEPOLY,
]
path = Path(vertices, codes)
patch = patches.PathPatch(path, fill=False, color="green", linewidth=2,
alpha=0.9)
ax.add_patch(patch)
fig.tight_layout()
return (fig, ax)
def main():
# default arguments
default_infile = "psd.txt"
default_outfile = "pei.json"
default_infojson = "../*_INFO.json"
parser = argparse.ArgumentParser(
description="Calculate the power excess index (PEI)",
epilog="Version: %s (%s)" % (__version__, __date__))
parser.add_argument("-V", "--version", action="version",
version="%(prog)s " + "%s (%s)" % (__version__,
__date__))
parser.add_argument("-j", "--json", dest="json", required=False,
help="the *_INFO.json file " +
"(default: find %s)" % default_infojson)
parser.add_argument("-i", "--infile", dest="infile",
required=False, default=default_infile,
help="input data of the radial power spectrum " +
"(default: %s)" % default_infile)
parser.add_argument("-o", "--outfile", dest="outfile",
required=False, default=default_outfile,
help="output json file to save the results " +
"(default: %s)" % default_outfile)
parser.add_argument("-p", "--png", dest="png", default=None,
help="make PEI plot and save " +
"(default: same basename as outfile)")
args = parser.parse_args()
if args.png is None:
args.png = os.path.splitext(args.outfile)[0] + ".png"
info_json = glob.glob(default_infojson)[0]
if args.json:
info_json = args.json
json_str = open(info_json).read().rstrip().rstrip(",")
info = json.loads(json_str)
name = info["Source Name"]
obsid = int(info["Obs. ID"])
r500 = get_r500(info)
r500_kpc = r500["r500_kpc"]
r500_pix = r500["r500_pix"]
kpc_per_pix = r500["kpc_per_pix"]
psd_data = np.loadtxt(args.infile)
pei, data_interp_log10 = calc_pei(psd_data, r500=r500_pix)
pei_data = OrderedDict([
("name", name),
("obsid", obsid),
("r500_kpc", r500_kpc),
("r500_pix", r500_pix),
("kpc_per_pix", kpc_per_pix),
("area_total", pei["area_total"]),
("area_below", pei["area_below"]),
("pei", pei["pei_value"]),
("pei_err", pei["pei_err"]),
])
pei_data_json = json.dumps(pei_data, indent=2)
print(pei_data_json)
open(args.outfile, "w").write(pei_data_json+"\n")
# Make and save a plot
fig = Figure(figsize=(10, 8))
FigureCanvas(fig)
ax = fig.add_subplot(111)
plot_pei(psd_data, data_interp_log10, info=pei_data, ax=ax, fig=fig)
fig.savefig(args.png, format="png", dpi=150)
if __name__ == "__main__":
main()
# vim: set ts=4 sw=4 tw=0 fenc=utf-8 ft=python: #
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