#!/usr/bin/env python3
# -*- coding: utf-8 -*-
#
# Aaron LI
# Created: 2016-04-29
# Updated: 2016-05-01
#
# 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 rectangulr, 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
"""

__version__ = "0.2.1"
__date__    = "2016-05-01"


import sys
import os
import glob
import argparse
import json
from collections import OrderedDict

import numpy as np
import scipy as sp
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

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 rectangulr.

    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]
    psd1d_err = data[:, 2]
    # frequency values corresponding to 0.35R500 and 0.035R500
    f1 = 1.0 / (0.350 * r500)
    f2 = 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])
    x1 = np.log10(f1)
    x2 = np.log10(f2)
    # interpolate the power spectrum
    # FIXME: include a pair surrounding data points for interpolation
    f_interp = sp.interpolate.interp1d(x, y, kind="cubic", assume_sorted=True)
    y1       = f_interp(x1)
    y2       = f_interp(x2)
    if interp_np % 2 == 0:
        # Simpson's rule requires an even number of intervals
        interp_np += 1
    x_interp = np.linspace(x1, x2, num=interp_np)
    y_interp = f_interp(x_interp)
    # calculate the PEI
    area_total = abs(x1 - x2) * abs(y1 - y2)
    area_below = sp.integrate.simps((y_interp-y2), 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, ax=None, fig=None):
    """
    Make a plot to visualize the PEI rectangular.
    """
    if ax is None:
        fig, ax = plt.subplots(1, 1)
    freqs     = data[:, 0]
    psd1d     = data[:, 1]
    psd1d_err = data[:, 2]
    #
    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("Radially Averaged Power Spectral Density")
    ax.set_xlabel(r"k (pixel$^{-1}$)")
    ax.set_ylabel("Power")
    # plot the interpolated data points and the PEI rectangle
    # credit: http://matplotlib.org/users/path_tutorial.html
    x_interp = 10 ** data_interp_log10[:, 0]
    y_interp = 10 ** data_interp_log10[:, 1]
    ax.plot(x_interp, y_interp, linestyle="--", marker="D", markersize=2,
            color="green", alpha=0.9)
    vertices = [
        (x_interp[0],  y_interp[-1]),  # left, bottom
        (x_interp[0],  y_interp[0]),   # left, top
        (x_interp[-1], y_interp[0]),   # right, top
        (x_interp[-1], y_interp[-1]),  # right, bottom
        (x_interp[0],  y_interp[-1]),  # 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))
    canvas = FigureCanvas(fig)
    ax = fig.add_subplot(111)
    plot_pei(psd_data, data_interp_log10, 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: #