fit_sbp.py

#!/usr/bin/env python3
#
# Copyright (c) 2016 Aaron LI
# MIT license
#
# Created: 2016-03-13
#
# Change logs:
# 2016-07-12:
#   * Remove "__version__" and "__date__"
#   * Use a default config to allow a minimal user config
# 2016-07-04:
#   * Remove unused classes "FitModelSBetaNorm" and "FitModelDBetaNorm"
#   * Fix minor typo
# 2016-05-06:
#   * Get rid of the argument `config_model` of function `make_sbpfit()`
#   * Add property `long_name` to models
#   * Add methods `reset()`, `get_model()`, `dump_params()`, `load_params()`
#   * Improve `SbpFit.load_data()`
#   * Split function `make_sbpfit()` out of `main()`
#   * Adjust errorbar styles
#   * Also plot r500 positions of interest with vertical lines
#   * Adjust plot appearance (e.g., text positions, secondary r500 axis)
#   * Simplify `super()` usage
#   * PEP8 fixes
# 2016-04-26:
#   * Reorder some methods of classes 'FitModelSBeta' and 'FitModelDBeta'
#   * Change the output file extension from ".txt" to ".json"
# 2016-04-21:
#   * Plot another X axis with unit "r500", with R500 values marked
#   * Adjust output image size/resolution
# 2016-04-20:
#   * Support "pix" and "kpc" units
#   * Allow ignore data w.r.t R500 value
#   * Major changes to the config syntax
#   * Add command line argument to select the sbp model
# 2016-04-05:
#   * Allow fix parameters
# 2016-03-31:
#   * Remove `ci_report()'
#   * Add `make_results()' to organize all results as s Python dictionary
#   * Report results as json string
# 2016-03-28:
#   * Add `main()', `make_model()'
#   * Use `configobj' to handle configurations
#   * Save fit results and plot
#   * Add `ci_report()'
# 2016-03-14:
#   * Re-factor classes `FitModelSBeta' and `FitModelDBeta'
#   * Add matplotlib plot support
#   * Add `ignore_data()' and `notice_data()' support
#   * Add classes `FitModelSBetaNorm' and `FitModelDBetaNorm'
#
# TODO:
#   * to allow fit the outer beta component, then fix it, and fit the inner one
#   * to output the ignored radius range in the same unit as input sbp data
#   * to estimate the uncertainties for model parameters using the
#     Monte Carlo method
#

"""
Fit the surface brightness profile (SBP) with the single-beta model:
  s(r) = s0 * [1.0 + (r/rc)^2] ^ (0.5-3*beta) + bkg
or the double-beta model:
  s(r) = s01 * [1.0 + (r/rc1)^2] ^ (0.5-3*beta1) +
         s02 * [1.0 + (r/rc2)^2] ^ (0.5-3*beta2) + bkg
"""


import sys
import argparse
import json
from collections import OrderedDict

import numpy as np
import lmfit
import matplotlib.pyplot as plt
from matplotlib.backends.backend_agg import FigureCanvasAgg as FigureCanvas
from matplotlib.figure import Figure
from configobj import ConfigObj

plt.style.use("ggplot")

config_default = """
## Configuration for `fit_sbp.py`

name     = <NAME>
obsid    = <OBSID>
r500_pix = <R500_PIX>
r500_kpc = <R500_KPC>

sbpfile  = sbprofile.txt
# unit of radius: pix (default) or kpc
unit     = pixel

# sbp model: "sbeta" or "dbeta"
model    = sbeta
#model    = dbeta

# output file to store the fitting results
outfile  = sbpfit.json
# output file to save the fitting plot
imgfile  = sbpfit.png

# data range to be ignored during fitting (same unit as the above "unit")
#ignore      = 0.0-20.0,
# specify the ignore range w.r.t R500 ("r500_pix" or "r500_kpc" required)
#ignore_r500 = 0.0-0.15,

[sbeta]
# model-related options (OVERRIDE the upper level options)
outfile     = sbpfit_sbeta.json
imgfile     = sbpfit_sbeta.png
#ignore      = 0.0-20.0,
#ignore_r500 = 0.0-0.15,
  [[params]]
  # model parameters
  # name = initial, lower, upper, variable (FIXED/False to fix the parameter)
  s0    = 1.0e-8,  0.0,  1.0e-6
  rc    = 30.0,    5.0,  1.0e4
  #rc    = 30.0,    5.0,  1.0e4,  FIXED
  beta  = 0.7,     0.3,  1.1
  bkg   = 1.0e-10, 0.0,  1.0e-8


[dbeta]
outfile     = sbpfit_dbeta.json
imgfile     = sbpfit_dbeta.png
#ignore      = 0.0-20.0,
#ignore_r500 = 0.0-0.15,
  [[params]]
  s01   = 1.0e-8,  0.0,  1.0e-6
  rc1   = 50.0,    10.0, 1.0e4
  beta1 = 0.7,     0.3,  1.1
  s02   = 1.0e-8,  0.0,  1.0e-6
  rc2   = 30.0,    2.0,  5.0e2
  beta2 = 0.7,     0.3,  1.1
  bkg   = 1.0e-10, 0.0,  1.0e-8
"""


class FitModel:
    """
    Meta-class of the fitting model.

    The supplied `func' should have the following syntax:
        y = f(x, params)
    where the `params' is `lmfit.Parameters' instance which contains all
    the model parameters to be fitted, and should be provided as well.
    """
    def __init__(self, name=None, long_name=None,
                 func=None, params=lmfit.Parameters()):
        self.name = name
        self.long_name = long_name
        self.func = func
        self.params = params.copy()

    def f(self, x):
        return self.func(x, self.params)

    def get_param(self, name=None):
        """
        Return the requested `Parameter' object or the whole
        `Parameters' object of no name supplied.
        """
        try:
            return self.params[name]
        except KeyError:
            return self.params

    def set_param(self, name, *args, **kwargs):
        """
        Set the properties of the specified parameter.
        """
        param = self.params[name]
        param.set(*args, **kwargs)

    def dump_params(self, serialize=True):
        """
        Dump the current values/settings for all model parameters,
        and these dumped results can be later loaded by `load_params()`.
        """
        if serialize:
            return self.params.dumps()
        else:
            return self.params.copy()

    def load_params(self, params):
        """
        Load the provided parameters values/settings.
        """
        if isinstance(params, lmfit.parameter.Parameters):
            self.params = params.copy()
        else:
            p = lmfit.parameter.Parameters()
            p.loads(params)
            self.params = p

    def plot(self, params, xdata, ax):
        """
        Plot the fitted model.
        """
        def f_fitted(x):
            return self.func(x, params)
        ydata = f_fitted(xdata)
        ax.plot(xdata, ydata, color="black", linestyle="solid")


class FitModelSBeta(FitModel):
    """
    The single-beta model to be fitted.
    Single-beta model, with a constant background.
    """
    params = lmfit.Parameters()
    params.add_many(  # (name, value, vary, min, max, expr)
                    ("s0",   1.0e-8, True, 0.0, 1.0e-6, None),
                    ("rc",   30.0,   True, 1.0, 1.0e4,  None),
                    ("beta", 0.7,    True, 0.3, 1.1,    None),
                    ("bkg",  1.0e-9, True, 0.0, 1.0e-7, None))

    def __init__(self):
        super().__init__(name="sbeta", long_name="Single-beta",
                         func=self.sbeta, params=self.params)

    @staticmethod
    def sbeta(r, params):
        parvals = params.valuesdict()
        s0 = parvals["s0"]
        rc = parvals["rc"]
        beta = parvals["beta"]
        bkg = parvals["bkg"]
        return s0 * np.power((1 + (r/rc)**2), (0.5 - 3*beta)) + bkg

    def plot(self, params, xdata, ax):
        """
        Plot the fitted model, as well as the fitted parameters.
        """
        super().plot(params, xdata, ax)
        xmin, xmax = ax.get_xlim()
        ymin, ymax = ax.get_ylim()
        ybkg = max(ymin, params["bkg"].value)
        # fitted paramters
        ax.vlines(x=params["rc"].value, ymin=ymin, ymax=ymax,
                  color="gray", linestyles="dashed")
        ax.hlines(y=params["bkg"].value, xmin=xmin, xmax=xmax,
                  color="gray", linestyles="dashed")
        ax.text(x=params["rc"].value/1.1, y=ymin*1.5,
                s="beta: %.2f\nrc: %.2f" % (params["beta"].value,
                                            params["rc"].value),
                horizontalalignment="right", verticalalignment="bottom")
        ax.text(x=xmin*1.1, y=ybkg*1.1,
                s="bkg: %.3e" % params["bkg"].value,
                verticalalignment="bottom")


class FitModelDBeta(FitModel):
    """
    The double-beta model to be fitted.
    Double-beta model, with a constant background.

    NOTE:
    the first beta component (s01, rc1, beta1) describes the main and
    outer SBP; while the second beta component (s02, rc2, beta2) accounts
    for the central brightness excess.
    """
    params = lmfit.Parameters()
    params.add("s01",   value=1.0e-8, min=0.0,  max=1.0e-6)
    params.add("rc1",   value=50.0,   min=10.0, max=1.0e4)
    params.add("beta1", value=0.7,    min=0.3,  max=1.1)
    # params.add("df_s0", value=1.0e-8, min=0.0,  max=1.0e-6)
    # params.add("s02",   expr="s01 + df_s0")
    params.add("s02",   value=1.0e-8, min=0.0,  max=1.0e-6)
    # params.add("df_rc", value=30.0,   min=0.0,  max=1.0e4)
    # params.add("rc2",   expr="rc1 - df_rc")
    params.add("rc2",   value=20.0,   min=1.0,  max=5.0e2)
    params.add("beta2", value=0.7,    min=0.3,  max=1.1)
    params.add("bkg",   value=1.0e-9, min=0.0,  max=1.0e-7)

    def __init__(self):
        super().__init__(name="dbeta", long_name="Double-beta",
                         func=self.dbeta, params=self.params)

    @classmethod
    def dbeta(self, r, params):
        return self.beta1(r, params) + self.beta2(r, params)

    @staticmethod
    def beta1(r, params):
        """
        This beta component describes the main/outer part of the SBP.
        """
        parvals = params.valuesdict()
        s01 = parvals["s01"]
        rc1 = parvals["rc1"]
        beta1 = parvals["beta1"]
        bkg = parvals["bkg"]
        return s01 * np.power((1 + (r/rc1)**2), (0.5 - 3*beta1)) + bkg

    @staticmethod
    def beta2(r, params):
        """
        This beta component describes the central/excess part of the SBP.
        """
        parvals = params.valuesdict()
        s02 = parvals["s02"]
        rc2 = parvals["rc2"]
        beta2 = parvals["beta2"]
        return s02 * np.power((1 + (r/rc2)**2), (0.5 - 3*beta2))

    def plot(self, params, xdata, ax):
        """
        Plot the fitted model, and each beta component,
        as well as the fitted parameters.
        """
        super().plot(params, xdata, ax)
        beta1_ydata = self.beta1(xdata, params)
        beta2_ydata = self.beta2(xdata, params)
        ax.plot(xdata, beta1_ydata, 'b-.')
        ax.plot(xdata, beta2_ydata, 'b-.')
        # fitted paramters
        ydata = beta1_ydata + beta2_ydata
        ax.vlines(x=params["rc1"].value, ymin=min(ydata), ymax=max(ydata),
                  linestyles="dashed")
        ax.vlines(x=params["rc2"].value, ymin=min(ydata), ymax=max(ydata),
                  linestyles="dashed")
        ax.hlines(y=params["bkg"].value, xmin=min(xdata), xmax=max(xdata),
                  linestyles="dashed")
        ax.text(x=params["rc1"].value, y=min(ydata),
                s="beta1: %.2f\nrc1: %.2f" % (params["beta1"].value,
                                              params["rc1"].value))
        ax.text(x=params["rc2"].value, y=min(ydata),
                s="beta2: %.2f\nrc2: %.2f" % (params["beta2"].value,
                                              params["rc2"].value))
        ax.text(x=min(xdata), y=min(ydata),
                s="bkg: %.3e" % params["bkg"].value,
                verticalalignment="top")


class SbpFit:
    """
    Class to handle the SBP fitting with single-/double-beta model.
    """
    # fitting model
    model = None
    # optimization method
    method = None
    # SBP data
    xdata = None
    ydata = None
    xerr = None
    yerr = None
    xunit = None
    # fitting source information
    name = None
    obsid = None
    r500_pix = None
    r500_kpc = None
    kpc_per_pix = None
    # mask to determine the effective data points used in fitting
    mask = None
    # residual function to which apply the optimization
    f_residual = None
    fitter = None
    fitted = None
    # calculated confidence intervals results
    ci = None
    # fitted results including the above `ci` if it is not None
    results = None

    def __init__(self, model, method="lbfgsb",
                 xdata=None, ydata=None, xerr=None, yerr=None, xunit="pix",
                 name=None, obsid=None, r500_pix=None, r500_kpc=None):
        self.method = method
        self.model = model
        self.load_data(xdata=xdata, ydata=ydata, xerr=xerr, yerr=yerr,
                       xunit=xunit, keep_mask=False)
        self.set_source(name=name, obsid=obsid,
                        r500_pix=r500_pix, r500_kpc=r500_kpc)

    def set_source(self, name, obsid=None, r500_pix=None, r500_kpc=None):
        self.name = name
        try:
            self.obsid = int(obsid)
        except TypeError:
            self.obsid = None
        try:
            self.r500_pix = float(r500_pix)
        except TypeError:
            self.r500_pix = None
        try:
            self.r500_kpc = float(r500_kpc)
        except TypeError:
            self.r500_kpc = None
        try:
            self.kpc_per_pix = self.r500_kpc / self.r500_pix
        except (TypeError, ZeroDivisionError):
            self.kpc_per_pix = -1

    def load_data(self, xdata, ydata=None, xerr=None, yerr=None, xunit="pix",
                  keep_mask=False):
        if xdata.ndim == 2 and xdata.shape[1] == 4:
            # 4-column data
            self.xdata = xdata[:, 0]
            self.xerr = xdata[:, 1]
            self.ydata = xdata[:, 2]
            self.yerr = xdata[:, 3]
        else:
            self.xdata = xdata
            self.ydata = ydata
            self.xerr = xerr
            self.yerr = yerr
        #
        if not keep_mask:
            if xdata is not None:
                self.mask = np.ones(xdata.shape, dtype=np.bool)
            else:
                self.mask = None
        #
        if xunit.lower() in ["pix", "pixel"]:
            self.xunit = "pix"
        elif xunit.lower() == "kpc":
            self.xunit = "kpc"
        else:
            raise ValueError("invalid xunit: %s" % xunit)

    def reset(self, keep_source=True):
        """
        Reset the SbpFit properties but excluding the model, data, and mask.
        """
        self.f_residual = None
        self.fitter = None
        self.fitted = None
        self.ci = None
        self.results = None
        if not keep_source:
            self.name = None
            self.obsid = None
            self.r500_pix = None
            self.r500_kpc = None
            self.kpc_per_pix = None

    def ignore_data(self, xmin=None, xmax=None, unit=None):
        """
        Ignore the data points within range [xmin, xmax].
        If xmin is None, then xmin=min(xdata);
        if xmax is None, then xmax=max(xdata).

        if unit is None, then assume the same unit as `self.xunit'.
        """
        if unit is None:
            unit = self.xunit
        if xmin is not None:
            xmin = self.convert_unit(xmin, unit=unit)
        else:
            xmin = np.min(self.xdata)
        if xmax is not None:
            xmax = self.convert_unit(xmax, unit=unit)
        else:
            xmax = np.max(self.xdata)
        ignore_idx = np.logical_and(self.xdata >= xmin, self.xdata <= xmax)
        self.mask[ignore_idx] = False
        # reset `f_residual'
        self.f_residual = None

    def notice_data(self, xmin=None, xmax=None, unit=None):
        """
        Notice the data points within range [xmin, xmax].
        If xmin is None, then xmin=min(xdata);
        if xmax is None, then xmax=max(xdata).

        if unit is None, then assume the same unit as `self.xunit'.
        """
        if unit is None:
            unit = self.xunit
        if xmin is not None:
            xmin = self.convert_unit(xmin, unit=unit)
        else:
            xmin = np.min(self.xdata)
        if xmax is not None:
            xmax = self.convert_unit(xmax, unit=unit)
        else:
            xmax = np.max(self.xdata)
        notice_idx = np.logical_and(self.xdata >= xmin, self.xdata <= xmax)
        self.mask[notice_idx] = True
        # reset `f_residual'
        self.f_residual = None

    def convert_unit(self, x, unit):
        """
        Convert the value x in given unit to be the unit `self.xunit'
        """
        if unit == self.xunit:
            return x
        elif (unit == "pix") and (self.xunit == "kpc"):
            return (x / self.r500_pix * self.r500_kpc)
        elif (unit == "kpc") and (self.xunit == "pix"):
            return (x / self.r500_kpc * self.r500_pix)
        elif (unit == "r500") and (self.xunit == "pix"):
            return (x * self.r500_pix)
        elif (unit == "r500") and (self.xunit == "kpc"):
            return (x * self.r500_kpc)
        else:
            raise ValueError("invalid units: %s vs. %s" % (unit, self.xunit))

    def convert_to_r500(self, x, unit=None):
        """
        Convert the value x in given unit to be in unit "r500".
        """
        if unit is None:
            unit = self.xunit
        if unit == "r500":
            return x
        elif unit == "pix":
            return (x / self.r500_pix)
        elif unit == "kpc":
            return (x / self.r500_kpc)
        else:
            raise ValueError("invalid unit: %s" % unit)

    def set_residual(self):
        def f_residual(params):
            if self.yerr is None:
                return self.model.func(self.xdata[self.mask], params) - \
                        self.ydata
            else:
                return (self.model.func(self.xdata[self.mask], params) -
                        self.ydata[self.mask]) / self.yerr[self.mask]
        self.f_residual = f_residual

    def fit(self, method=None):
        if method is None:
            method = self.method
        if not hasattr(self, "f_residual") or self.f_residual is None:
            self.set_residual()
        self.fitter = lmfit.Minimizer(self.f_residual, self.model.params)
        self.fitted = self.fitter.minimize(method=method)
        self.model.load_params(self.fitted.params)

    def calc_ci(self, sigmas=[0.68, 0.90]):
        # `conf_interval' requires the fitted results have valid `stderr',
        # so we need to re-fit the model with method `leastsq'.
        fitted = self.fitter.minimize(method="leastsq",
                                      params=self.fitted.params)
        self.ci, self.trace = lmfit.conf_interval(self.fitter, fitted,
                                                  sigmas=sigmas, trace=True)

    def get_model(self):
        """
        Return the model associated with this `SbpFit`.
        If this `SbpFit` instance has been fitted, then the `model` is
        updated with the fitted parameters, i.e., a fitted model.
        """
        return self.model

    def dump_params(self):
        """
        Dump the current values/settings for all model parameters,
        and these dumped results can be later loaded by `load_params()`.
        """
        return self.model.dump_params()

    def load_params(self, params):
        """
        Load the provided parameters values/settings, and update the model.
        """
        self.model.load_params(params)

    def make_results(self):
        """
        Make the `self.results' dictionary which contains all the fitting
        results as well as the confidence intervals.
        """
        fitted = self.fitted
        self.results = OrderedDict()
        # fitting results
        self.results.update([
            ("nfev",   fitted.nfev),
            ("ndata",  fitted.ndata),
            ("nvarys", fitted.nvarys),  # number of variable parameters
            ("nfree",  fitted.nfree),  # degree of freedom
            ("chisqr", fitted.chisqr),
            ("redchi", fitted.redchi),
            ("aic",    fitted.aic),
            ("bic",    fitted.bic),
        ])
        params = fitted.params
        pnames = list(params.keys())
        pvalues = OrderedDict()
        for pn in pnames:
            par = params.get(pn)
            pvalues[pn] = [par.value, par.min, par.max, par.vary]
        self.results["params"] = pvalues
        # confidence intervals
        if hasattr(self, "ci") and self.ci is not None:
            ci = self.ci
            ci_values = OrderedDict()
            ci_sigmas = ["ci%02d" % (v[0]*100) for v in ci.get(pnames[0])]
            ci_names = sorted(list(set(ci_sigmas)))
            ci_idx = {k: [] for k in ci_names}
            for cn, idx in zip(ci_sigmas, range(len(ci_sigmas))):
                ci_idx[cn].append(idx)
            # parameters ci
            for pn in pnames:
                ci_pv = OrderedDict()
                pv = [v[1] for v in ci.get(pn)]
                # best
                pv_best = pv[ci_idx["ci00"][0]]
                ci_pv["best"] = pv_best
                # ci of each sigma
                pv2 = [v-pv_best for v in pv]
                for cn in ci_names[1:]:
                    ci_pv[cn] = [pv2[idx] for idx in ci_idx[cn]]
                ci_values[pn] = ci_pv
            self.results["ci"] = ci_values

    def report(self, outfile=sys.stdout):
        if not hasattr(self, "results") or self.results is None:
            self.make_results()
        jd = json.dumps(self.results, indent=2)
        print(jd, file=outfile)

    def plot(self, ax=None, fig=None, r500_axis=True):
        """
        Arguments:
          * r500_axis: whether to add a second X axis in unit "r500"
        """
        if ax is None:
            fig, ax = plt.subplots(1, 1)
        # noticed data points
        eb = ax.errorbar(self.xdata[self.mask], self.ydata[self.mask],
                         xerr=self.xerr[self.mask],
                         yerr=self.yerr[self.mask],
                         fmt="none", elinewidth=2, capthick=2)
        # ignored data points
        ignore_mask = np.logical_not(self.mask)
        if np.sum(ignore_mask) > 0:
            eb = ax.errorbar(self.xdata[ignore_mask], self.ydata[ignore_mask],
                             xerr=self.xerr[ignore_mask],
                             yerr=self.yerr[ignore_mask],
                             fmt="none", elinewidth=1, capthick=1)
            # eb[-1][0].set_linestyle("dashdot")
            # eb[-1][1].set_linestyle("dashdot")
        # fitted model
        xmin = 1.0
        xmax = self.xdata[-1] + self.xerr[-1]
        xpred = np.power(10, np.linspace(0, np.log10(xmax), 3*len(self.xdata)))
        ypred = self.model.f(xpred)
        ymin = min(min(self.ydata), min(ypred)) / 1.2
        ymax = max(max(self.ydata), max(ypred)) * 1.2
        ax.set_xscale("log")
        ax.set_yscale("log")
        ax.set_xlim(xmin, xmax)
        ax.set_ylim(ymin, ymax)
        self.model.plot(params=self.fitted.params, xdata=xpred, ax=ax)
        name = self.name
        if self.obsid is not None:
            name += "; %s" % self.obsid
        ax.set_title("Fitted Surface Brightness Profile (%s)" % name)
        ax.set_xlabel("Radius (%s)" % self.xunit)
        ax.set_ylabel(r"Surface Brightness (photons/cm$^2$/pixel$^2$/s)")
        ax.text(x=xmax/1.2, y=ymax/1.2,
                s=r"reduced $\chi^2$: %.2f / %.2f = %.2f" % (
                    self.fitted.chisqr, self.fitted.nfree,
                    self.fitted.chisqr/self.fitted.nfree),
                horizontalalignment="right", verticalalignment="top")
        try:
            # also mark r500 positions of interest with vertical lines
            r500_vlines = [0.05, 0.10, 0.2]
            vlines_x = [self.convert_unit(x, unit="r500")
                        for x in r500_vlines]
            ax.vlines(x=vlines_x, ymin=ymin, ymax=ymax,
                      color="blue", linestyles="dotted")
        except ValueError:
            # cannot convert values from unit "r500"
            pass
        plot_ret = [fig, ax]
        if r500_axis:
            # Add a second X-axis with labels in unit "r500"
            # Credit: https://stackoverflow.com/a/28192477/4856091
            try:
                ax.title.set_position([0.5, 1.1])  # raise title position
                ax2 = ax.twiny()
                # NOTE: the ORDER of the following lines MATTERS
                ax2.set_xscale(ax.get_xscale())
                # convert main `ax` ticks to be in unit `r500` {{{
                # ax2_ticks = ax.get_xticks()
                # ax2.set_xticks(ax2_ticks)
                # ax2.set_xticklabels(["%.2g" % self.convert_to_r500(x)
                #                      for x in ax2_ticks])
                # ax2.set_xlim(ax.get_xlim())
                # }}}
                # set new `ax2` to have specified ticks {{{
                r500_ticks = [0.01, 0.05, 0.1, 0.15, 0.2, 0.5, 1.0]
                ax2_ticks = np.array([self.convert_unit(x, unit="r500")
                                      for x in r500_ticks])
                ax2.set_xticks(ax2_ticks)
                ax2.set_xticklabels(["%.2f" % x for x in r500_ticks])
                ax2.set_xlim(ax.get_xlim())
                # }}}
                ax2.set_xlabel("Radius (r500; r500 = %s pix = %s kpc)" % (
                               self.r500_pix, self.r500_kpc))
                ax2.grid(False)
                plot_ret.append(ax2)
            except ValueError:
                # cannot convert X values to unit "r500"
                pass
        # automatically adjust layout
        fig.tight_layout()
        return plot_ret


def make_model(config, modelname):
    """
    Make the model with parameters been set according to the `config`.
    """
    if modelname == "sbeta":
        # single-beta model
        model = FitModelSBeta()
    elif modelname == "dbeta":
        # double-beta model
        model = FitModelDBeta()
    else:
        raise ValueError("Invalid model: %s" % modelname)
    # set initial values and bounds for the model parameters
    params = config[modelname]["params"]
    for p, value in params.items():
        variable = True
        if len(value) == 4 and value[3].upper() in ["FIXED", "FALSE"]:
            variable = False
        model.set_param(name=p, value=float(value[0]),
                        min=float(value[1]), max=float(value[2]),
                        vary=variable)
    return model


def make_sbpfit(config, model):
    """
    Make the `SbpFit` instance according the the `config`.
    """
    # sbp data and fit object
    sbpdata = np.loadtxt(config["sbpfile"])
    sbpfit = SbpFit(model=model, xdata=sbpdata[:, 0], xerr=sbpdata[:, 1],
                    ydata=sbpdata[:, 2], yerr=sbpdata[:, 3],
                    xunit=config.get("unit", "pix"))
    sbpfit.set_source(name=config["name"], obsid=config.get("obsid"),
                      r500_pix=config.get("r500_pix"),
                      r500_kpc=config.get("r500_kpc"))
    # apply data range ignorance
    if "ignore" in config.keys():
        for ig in config.as_list("ignore"):
            xmin, xmax = map(float, ig.split("-"))
            sbpfit.ignore_data(xmin=xmin, xmax=xmax)
    if "ignore_r500" in config.keys():
        for ig in config.as_list("ignore_r500"):
            xmin, xmax = map(float, ig.split("-"))
            sbpfit.ignore_data(xmin=xmin, xmax=xmax, unit="r500")
    # apply additional data range ignorance specified within model section
    config_model = config.get(model.name)
    if "ignore" in config_model.keys():
        for ig in config_model.as_list("ignore"):
            xmin, xmax = map(float, ig.split("-"))
            sbpfit.ignore_data(xmin=xmin, xmax=xmax)
    if "ignore_r500" in config_model.keys():
        for ig in config_model.as_list("ignore_r500"):
            xmin, xmax = map(float, ig.split("-"))
            sbpfit.ignore_data(xmin=xmin, xmax=xmax, unit="r500")
    #
    return sbpfit


def main():
    # parser for command line options and arguments
    parser = argparse.ArgumentParser(
            description="Fit surface brightness profile with " +
                        "single-/double-beta model")
    parser.add_argument("config", help="Config file for SBP fitting")
    # exclusive argument group for model selection
    grp_model = parser.add_mutually_exclusive_group(required=False)
    grp_model.add_argument("-s", "--sbeta", dest="sbeta",
                           action="store_true",
                           help="single-beta model for SBP")
    grp_model.add_argument("-d", "--dbeta", dest="dbeta",
                           action="store_true",
                           help="double-beta model for SBP")
    #
    args = parser.parse_args()

    config = ConfigObj(config_default.splitlines())
    config_user = ConfigObj(open(args.config))
    config.merge(config_user)

    # determine the model name
    if args.sbeta:
        modelname = "sbeta"
    elif args.dbeta:
        modelname = "dbeta"
    else:
        modelname = config["model"]

    config_model = config[modelname]
    # determine the "outfile" and "imgfile"
    outfile = config.get("outfile")
    outfile = config_model.get("outfile", outfile)
    imgfile = config.get("imgfile")
    imgfile = config_model.get("imgfile", imgfile)

    model = make_model(config, modelname=modelname)
    sbpfit = make_sbpfit(config, model=model)

    # fit and calculate confidence intervals
    sbpfit.fit()
    sbpfit.calc_ci()
    sbpfit.report()
    with open(outfile, "w") as ofile:
        sbpfit.report(outfile=ofile)

    # make and save a plot
    fig = Figure(figsize=(10, 8))
    FigureCanvas(fig)
    ax = fig.add_subplot(1, 1, 1)
    sbpfit.plot(ax=ax, fig=fig, r500_axis=True)
    fig.savefig(imgfile, dpi=150)


if __name__ == "__main__":
    main()

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