rename "sbp_fit.py" to "fit_sbp.py"

1 files changed, 807 insertions, 0 deletions

diff --git a/fit_sbp.py b/fit_sbp.py
new file mode 100755
index 0000000..c22e0c8
--- /dev/null
+++ b/fit_sbp.py
@@ -0,0 +1,807 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+#
+# Aaron LI
+# Created: 2016-03-13
+# Updated: 2016-04-26
+#
+# Changelogs:
+# 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 commandline argument to select the sbp model
+# 2016-04-05:
+#   * Allow fix parameters
+# 2016-03-31:
+#   * Remove `ci_report()'
+#   * Add `make_results()' to orgnize 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:
+#   * Refactor 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 integrate basic information of config file to the output json
+#   * to output the ignored radius range in the same unit as input sbp data
+#
+
+"""
+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
+
+
+Sample config file:
+-------------------------------------------------
+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
+-------------------------------------------------
+"""
+
+__version__ = "0.6.2"
+__date__    = "2016-04-26"
+
+
+import os
+import sys
+import re
+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")
+
+
+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, func=None, params=lmfit.Parameters()):
+        self.name = name
+        self.func = func
+        self.params = params
+
+    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 plot(self, params, xdata, ax):
+        """
+        Plot the fitted model.
+        """
+        f_fitted = lambda x: self.func(x, params)
+        ydata = f_fitted(xdata)
+        ax.plot(xdata, ydata, 'k-')
+
+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(self.__class__, self).__init__(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(self.__class__, self).plot(params, xdata, ax)
+        ydata = self.sbeta(xdata, params)
+        # fitted paramters
+        ax.vlines(x=params["rc"].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["rc"].value, y=min(ydata),
+                s="beta: %.2f\nrc: %.2f" % (params["beta"].value,
+                    params["rc"].value))
+        ax.text(x=min(xdata), y=min(ydata),
+                s="bkg: %.3e" % params["bkg"].value,
+                verticalalignment="top")
+
+
+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(self.__class__, self).__init__(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(self.__class__, self).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 FitModelSBetaNorm(FitModel):
+    """
+    The single-beta model to be fitted.
+    Single-beta model, with a constant background.
+    Normalized the `s0' and `bkg' parameters by take the logarithm.
+    """
+    params = lmfit.Parameters()
+    params.add_many( # (name, value, vary, min, max, expr)
+                    ("log10_s0",   -8.0, True, -12.0, -6.0,  None),
+                    ("rc",   30.0, True, 1.0,   1.0e4, None),
+                    ("beta", 0.7,  True, 0.3,   1.1,   None),
+                    ("log10_bkg",  -9.0, True, -12.0, -7.0,  None))
+
+    @staticmethod
+    def sbeta(r, params):
+        parvals = params.valuesdict()
+        s0   = 10 ** parvals["log10_s0"]
+        rc   = parvals["rc"]
+        beta = parvals["beta"]
+        bkg  = 10 ** parvals["log10_bkg"]
+        return s0 * np.power((1 + (r/rc)**2), (0.5 - 3*beta)) + bkg
+
+    def __init__(self):
+        super(self.__class__, self).__init__(name="Single-beta",
+                func=self.sbeta, params=self.params)
+
+    def plot(self, params, xdata, ax):
+        """
+        Plot the fitted model, as well as the fitted parameters.
+        """
+        super(self.__class__, self).plot(params, xdata, ax)
+        ydata = self.sbeta(xdata, params)
+        # fitted paramters
+        ax.vlines(x=params["rc"].value, ymin=min(ydata), ymax=max(ydata),
+                linestyles="dashed")
+        ax.hlines(y=(10 ** params["bkg"].value), xmin=min(xdata),
+                xmax=max(xdata), linestyles="dashed")
+        ax.text(x=params["rc"].value, y=min(ydata),
+                s="beta: %.2f\nrc: %.2f" % (params["beta"].value,
+                    params["rc"].value))
+        ax.text(x=min(xdata), y=min(ydata),
+                s="bkg: %.3e" % (10 ** params["bkg"].value),
+                verticalalignment="top")
+
+
+class FitModelDBetaNorm(FitModel):
+    """
+    The double-beta model to be fitted.
+    Double-beta model, with a constant background.
+    Normalized the `s01', `s02' and `bkg' parameters by take the logarithm.
+
+    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("log10_s01",   value=-8.0, min=-12.0, max=-6.0)
+    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("log10_s02",   value=-8.0, min=-12.0, max=-6.0)
+    #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("log10_bkg",   value=-9.0, min=-12.0, max=-7.0)
+
+    @staticmethod
+    def beta1(r, params):
+        """
+        This beta component describes the main/outer part of the SBP.
+        """
+        parvals = params.valuesdict()
+        s01   = 10 ** parvals["log10_s01"]
+        rc1   = parvals["rc1"]
+        beta1 = parvals["beta1"]
+        bkg   = 10 ** parvals["log10_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   = 10 ** parvals["log10_s02"]
+        rc2   = parvals["rc2"]
+        beta2 = parvals["beta2"]
+        return s02 * np.power((1 + (r/rc2)**2), (0.5 - 3*beta2))
+
+    @classmethod
+    def dbeta(self, r, params):
+        return self.beta1(r, params) + self.beta2(r, params)
+
+    def __init__(self):
+        super(self.__class__, self).__init__(name="Double-beta",
+                func=self.dbeta, params=self.params)
+
+    def plot(self, params, xdata, ax):
+        """
+        Plot the fitted model, and each beta component,
+        as well as the fitted parameters.
+        """
+        super(self.__class__, self).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["log10_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=(10 ** 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" % (10 ** params["bkg"].value),
+                verticalalignment="top")
+
+
+class SbpFit:
+    """
+    Class to handle the SBP fitting with single-/double-beta model.
+    """
+    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)
+        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, xerr, yerr, xunit="pix"):
+        self.xdata = xdata
+        self.ydata = ydata
+        self.xerr  = xerr
+        self.yerr  = yerr
+        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 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.fitted_model = lambda x: self.model.func(x, 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 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 varible paramters
+                nfree  = fitted.nfree,  # degree of freem
+                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")
+        # 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")
+            eb[-1][0].set_linestyle("-.")
+        # fitted model
+        xmax = self.xdata[-1] + self.xerr[-1]
+        xpred = np.power(10, np.linspace(0, np.log10(xmax), 2*len(self.xdata)))
+        ypred = self.fitted_model(xpred)
+        ymin = min(min(self.ydata), min(ypred))
+        ymax = max(max(self.ydata), max(ypred))
+        self.model.plot(params=self.fitted.params, xdata=xpred, ax=ax)
+        ax.set_xscale("log")
+        ax.set_yscale("log")
+        ax.set_xlim(1.0, xmax)
+        ax.set_ylim(ymin/1.2, ymax*1.2)
+        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, y=ymax,
+                s="redchi: %.2f / %.2f = %.2f" % (self.fitted.chisqr,
+                    self.fitted.nfree, self.fitted.chisqr/self.fitted.nfree),
+                horizontalalignment="right", verticalalignment="top")
+        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())
+                ax2_ticks = ax.get_xticks()
+                ax2.set_xticks(ax2_ticks)
+                ax2.set_xbound(ax.get_xbound())
+                ax2.set_xticklabels([ "%.2g" % self.convert_to_r500(x)
+                                    for x in ax2_ticks ])
+                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 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 main():
+    # parser for command line options and arguments
+    parser = argparse.ArgumentParser(
+            description="Fit surface brightness profile with " + \
+                        "single-/double-beta model",
+            epilog="Version: %s (%s)" % (__version__, __date__))
+    parser.add_argument("-V", "--version", action="version",
+            version="%(prog)s " + "%s (%s)" % (__version__, __date__))
+    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(args.config)
+
+    # 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)
+
+    # SBP fitting model
+    model = make_model(config, modelname=modelname)
+
+    # 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
+    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")
+
+    # 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))
+    canvas = FigureCanvas(fig)
+    ax = fig.add_subplot(111)
+    sbpfit.plot(ax=ax, fig=fig, r500_axis=True)
+    fig.savefig(imgfile, dpi=150)
+
+
+if __name__ == "__main__":
+    main()
+
+#  vim: set ts=4 sw=4 tw=0 fenc=utf-8 ft=python: #