4 an integrated user model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# User models in Sherpa - II"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the previous notebook - [User models in Sherpa](http://nbviewer.ipython.org/github/DougBurke/sherpa-standalone-notebooks/blob/master/user%20model.ipynb) - I showed how you could\n",
    "write a user model to fit the \n",
    "[Cumulative Distribution Function](http://en.wikipedia.org/wiki/Cumulative_distribution_function) (CDF) of a data set with a\n",
    "[Gamma distribution](http://en.wikipedia.org/wiki/Gamma_distribution). Rather than use the\n",
    "[load_user_model](http://cxc.harvard.edu/sherpa/ahelp/load_user_model.html) function, I showed\n",
    "how to write the model taking advantage of the Sherpa `Model` class, and the\n",
    "[add_model](http://cxc.harvard.edu/sherpa/ahelp/add_model.html) function to register the\n",
    "class with Sherpa.\n",
    "\n",
    "One question I got from a colleague was why I fit the CDF, rather than the\n",
    "[Probability Density Function](http://en.wikipedia.org/wiki/Probability_density_function) (PDF)\n",
    "of the data? Whilst I am not going to answer that question here, I do aim to show how\n",
    "to fit the PDF, since it:\n",
    "\n",
    " - lets me talk about writing models for \"integrated\" data sets\n",
    " - lets me fit the data using a Maximim Likelihood statistic, rather than the\n",
    "   \"least-squares\" approach I used previously."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Follow up"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I have a follow-up to this, which is available as\n",
    "[plotting in Sherpa when using the low-level API](http://nbviewer.ipython.org/github/DougBurke/sherpa-standalone-notebooks/blob/master/plotting%20using%20the%20lower-level%20routines.ipynb). This was written on May 5 2015.\n",
    "\n",
    "The notebook has since been updated to reflect changes in Sherpa."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Author and disclaimer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This was written by \n",
    "[Douglas Burke](http://hea-www.cfa.harvard.edu/~dburke/)\n",
    "on June 4 2015. This notebook, and others that may be of\n",
    "interest, can be found on GitHub at\n",
    "https://github.com/DougBurke/sherpa-standalone-notebooks.\n",
    "\n",
    "The information in this document is placed into the Publc Domain. It is not an official product of the Chandra\n",
    "X-ray Center, and I make no guarantee that it is not without bugs or embarassing typos. Please contact me via the GitHub repository\n",
    "if you have any questions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Last run"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When was this notebook last run?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2024-09-30 11:43'"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import datetime\n",
    "datetime.datetime.now().strftime(\"%Y-%m-%d %H:%M\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'4.17.0'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sherpa\n",
    "sherpa.__version__"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting up"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First of all I am going to load in the necessary modules, and set up the CDF model I wrote\n",
    "earlier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sherpa import utils\n",
    "from sherpa.models import model\n",
    "from sherpa.models.parameter import tinyval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sherpa import ui"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the imports out of the way, here are routines to calculate the CDF and PDF\n",
    "of a Gamma distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_gamma_cdf(x, k, theta):\n",
    "    \"\"\"Return the CDF of a gamma distribution.\n",
    "\n",
    "    The cumulative distribution function (CDF) of the gamma\n",
    "    distribution is defined in [1]_ as::\n",
    "\n",
    "       cdf(x;k,theta) = incomplete_gamma(k, x/theta)\n",
    "                        ----------------------------\n",
    "                                  gamma(k)\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    x : array\n",
    "       The values at which to evaluate the CDF.\n",
    "    k : number\n",
    "       The shape parameter, which must be greater than 0.\n",
    "    theta : number\n",
    "       The scale parameter, which must be greater than 0.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    cdf : array\n",
    "       The CDF evaluated at each element of x.\n",
    "\n",
    "    Notes\n",
    "    -----\n",
    "    The mean of the distribution is given by ``k * theta``,\n",
    "    and the rate is ``1 / theta``.\n",
    " \n",
    "    References\n",
    "    ----------\n",
    "\n",
    "    .. [1] http://en.wikipedia.org/wiki/Gamma_distribution\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    # Unfortunately igam does not accept a Numpy array as the\n",
    "    # second argument, so need to map over the input array.\n",
    "    #\n",
    "    tval = theta * 1.0\n",
    "    kval = k * 1.0\n",
    "    x = np.asarray(x)\n",
    "    out = np.zeros_like(x)\n",
    "    for i,xi in enumerate(x):\n",
    "        # igam is the \"regularized\" incomplete gamma (lower)\n",
    "        # form, so already has the normalization by gamma(a)\n",
    "        # included.\n",
    "        out[i] = utils.igam(kval, xi/tval)\n",
    "\n",
    "    return out\n",
    "\n",
    "def calc_gamma_pdf(x, k, theta):\n",
    "    \"\"\"Return the PDF of a gamma distribution.\n",
    "\n",
    "    The probability density function (PDF) of the gamma\n",
    "    distribution is defined in [1]_ as::\n",
    "\n",
    "       pdf(x;k,theta) = x^(k-1) e^(-x/theta)\n",
    "                        --------------------\n",
    "                          gamma(k) theta^k\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    x : array\n",
    "       The values at which to evaluate the PDF.\n",
    "    k : number\n",
    "       The shape parameter, which must be greater than 0.\n",
    "    theta : number\n",
    "       The scale parameter, which must be greater than 0.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    pdf : array\n",
    "       The PDF evaluated at each element of x.\n",
    "\n",
    "    Notes\n",
    "    -----\n",
    "    The mean of the distribution is given by ``k * theta``,\n",
    "    and the rate is ``1 / theta``.\n",
    " \n",
    "    References\n",
    "    ----------\n",
    "\n",
    "    .. [1] http://en.wikipedia.org/wiki/Gamma_distribution\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    tval = theta * 1.0\n",
    "    kval = k * 1.0\n",
    "    norm = utils.gamma(kval) * theta**kval\n",
    "    return x**(kval-1.0) * np.exp(-x / tval) / norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I am also going to need a routine that integrates the PDF over a range in x. This is just \n",
    "the difference in the CDF at the two points, so can be written as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_gamma_pdf_int(xlo, xhi, k, theta):\n",
    "    \"\"\"Return the PDF of a gamma distribution integrated over a bin.\n",
    "\n",
    "    The probability density function (PDF) of the gamma\n",
    "    distribution is defined in [1]_ as::\n",
    "\n",
    "       pdf(x;k,theta) = x^(k-1) e^(-x/theta)\n",
    "                        --------------------\n",
    "                          gamma(k) theta^k\n",
    "\n",
    "    Integrating this gives::\n",
    "\n",
    "      - theta^k igamma(k, x/theta) + c\n",
    "      ----------------------------\n",
    "            gamma(k) theta^k\n",
    "\n",
    "    where igamma is the incomplete gamma function. Note that this is\n",
    "    the \"upper\" form (so int_x^infinity), and sherpa.utils.igam\n",
    "    calculates the lower-form (which is 1-upper), which is also\n",
    "    a normalized form, so we get to::\n",
    "\n",
    "       sherpa.utils.igam(k,xhi/theta) - sherpa.utils.igam(k,xlo/theta)\n",
    "\n",
    "    which shouldn't be surprising as it's just::\n",
    "\n",
    "       cdf(xhi;k,theta) - cdf(xlo;k,theta)\n",
    "\n",
    "    This means that this is just::\n",
    "\n",
    "       calc_gamma_cdf(xhi,k,t) - calc_gamma_cdf(xlo,k,t)\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    xlo, xhi : array\n",
    "       The bin edges over which to integrate the PDF.\n",
    "    k : number\n",
    "       The shape parameter, which must be greater than 0.\n",
    "    theta : number\n",
    "       The scale parameter, which must be greater than 0.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    pdf : array\n",
    "       The PDF integrated over xlo to xhi.\n",
    "\n",
    "    References\n",
    "    ----------\n",
    "\n",
    "    .. [1] http://en.wikipedia.org/wiki/Gamma_distribution\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    return calc_gamma_cdf(xhi, k, theta) - calc_gamma_cdf(xlo, k, theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these, I can write the `GammaCDF` class, which is essentially the same as in the\n",
    "previous version, *except* that I have now used a finite, but *small*, lower limit on the\n",
    "`k` and `theta` parameter values, rather than allow them to go down to `0`. The lower limit\n",
    "is given by `sherpa.models.parameter.tinyval`, which is:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1754943508222875e-38"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tinyval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "class GammaCDF(model.ArithmeticModel):\n",
    "    \"\"\"A Gamma CDF.\n",
    "\n",
    "    The cumulative distribution function (CDF) for the Gamma\n",
    "    distribution, as defined by [1]_, is::\n",
    "\n",
    "       cdf(x;k,theta) = incomplete_gamma(k, x/theta)\n",
    "                        ----------------------------\n",
    "                                  gamma(k)\n",
    "\n",
    "    The model parameters are:\n",
    "\n",
    "    k\n",
    "       The shape parameter, which must be greater than 0.\n",
    "\n",
    "    theta\n",
    "       The scale parameter, which must be greater than 0.\n",
    "\n",
    "    Notes\n",
    "    -----\n",
    "    The mean of the distribution is given by ``k * theta``,\n",
    "    and the rate is ``1 / theta``.\n",
    "    \n",
    "    References\n",
    "    ----------\n",
    "\n",
    "    .. [1] http://en.wikipedia.org/wiki/Gamma_distribution\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    ndim = 1\n",
    "    \n",
    "    def __init__(self, name='gammacdf'):\n",
    "        self.k = model.Parameter(name, 'k', 5, min=tinyval, hard_min=0)\n",
    "        self.theta = model.Parameter(name, 'theta', 2, min=tinyval, hard_min=0)\n",
    "\n",
    "        model.ArithmeticModel.__init__(self, name, (self.k, self.theta))\n",
    "\n",
    "    @model.modelCacher1d\n",
    "    def calc(self, pars, x, *args, **kwargs):\n",
    "        (k, theta) = pars\n",
    "        if len(args) == 1:\n",
    "            x = (x + args[0]) / 2.0\n",
    "\n",
    "        return calc_gamma_cdf(x, k, theta)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above model expects either one or two `x` arrays - the independent variable value - which are the location at which to evaluate the model (one array), or the low and high edges of each bin, over which the model should be evaluated. In the CDF case I just use the mid-point of the bin; that is I do not \"integrate\" the model. However, for the PDF case, where the data is \"integrated\" - i.e. it represents the number of events within the range, we can integrate up the data. The overall form of the `GammaPDF` class is very similar to `GammaCDF`, but\n",
    "\n",
    " - an extra parameter is needed (the number of events),\n",
    " - the handling of the model evaluation is slightly different,\n",
    " - and a `guess` routine is added so that the normalisation can be set based on the data,\n",
    "\n",
    "as shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "class GammaPDF(model.ArithmeticModel):\n",
    "    \"\"\"A Gamma PDF.\n",
    "\n",
    "    The probability density function (PDF) for the Gamma\n",
    "    distribution, as defined by [1]_, is::\n",
    "\n",
    "       pdf(x;k,theta) = x^(k-1) e^(-x/theta)\n",
    "                        --------------------\n",
    "                          gamma(k) theta^k\n",
    "\n",
    "    The model parameters are:\n",
    "\n",
    "    k\n",
    "       The shape parameter, which must be greater than 0.\n",
    "\n",
    "    theta\n",
    "       The scale parameter, which must be greater than 0.\n",
    "\n",
    "    norm\n",
    "       Normalization. The soft minimum is set to 0, but the\n",
    "       hard_min is left at the default value, so the minimum\n",
    "       can be made negative if the user wants.\n",
    "\n",
    "    Notes\n",
    "    -----\n",
    "    The mean of the distribution is given by ``k * theta``,\n",
    "    and the rate is ``1 / theta``.\n",
    "\n",
    "    References\n",
    "    ----------\n",
    "\n",
    "    .. [1] http://en.wikipedia.org/wiki/Gamma_distribution\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    ndim = 1\n",
    "    \n",
    "    def __init__(self, name='gammapdf'):\n",
    "        self.k = model.Parameter(name, 'k', 5, min=tinyval, hard_min=0)\n",
    "        self.theta = model.Parameter(name, 'theta', 2, min=tinyval, hard_min=0)\n",
    "        self.norm = model.Parameter(name, 'norm', 1, min=0) # allow -ve if they realy want it\n",
    "        \n",
    "        model.ArithmeticModel.__init__(self, name, (self.k, self.theta, self.norm))\n",
    "\n",
    "    @model.modelCacher1d\n",
    "    def calc(self, pars, x, *args, **kwargs):\n",
    "        (k, theta, norm) = pars\n",
    "        if len(args) == 0:\n",
    "            return norm * calc_gamma_pdf(x, k, theta)\n",
    "        elif len(args) == 1:\n",
    "            # note: this could be a 2D dataset\n",
    "            return norm * calc_gamma_pdf_int(x, args[0], k, theta)\n",
    "        else:\n",
    "            raise ValueError(\"Expected x or xlo/xhi grid.\")\n",
    "            \n",
    "    def guess(self, dep, *args, **kwargs):\n",
    "        \"\"\"Set the norm parameter based on the data.\n",
    "        \n",
    "        The norm parameter is set to be the sum of the dependent axis\n",
    "        and frozen. The ``k`` and ``theta`` parameters are not changed.\n",
    "        \n",
    "        Notes\n",
    "        -----\n",
    "        The mean of the values equals k * theta and the mode is\n",
    "        (k-1) * theta - when k > 1 - so these could be used to set\n",
    "        k and theta, but I am not convinced it is worth the effort.\n",
    "        \n",
    "        \"\"\"\n",
    "        norm = dep.sum()\n",
    "        self.norm.val = dep.sum()\n",
    "        self.norm.frozen = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These models can now be added to Sherpa:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "ui.add_model(GammaCDF)\n",
    "ui.add_model(GammaPDF)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's set up the same data as used in the previous notebook:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.default_rng(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "k_orig = 1.1\n",
    "theta_orig = 2.6\n",
    "ysim = stats.gamma.rvs(a=k_orig, scale=theta_orig, size=1000, random_state=rng)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Repeating the CDF fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First I am going to repeat the CDF fit:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "xcdf = ysim.copy()\n",
    "xcdf.sort()\n",
    "ycdf = np.arange(1, xcdf.size+1) * 1.0 / xcdf.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset               = cdf\n",
      "Method                = levmar\n",
      "Statistic             = leastsq\n",
      "Initial fit statistic = 238.936\n",
      "Final fit statistic   = 0.0284038 at function evaluation 26\n",
      "Data points           = 1000\n",
      "Degrees of freedom    = 998\n",
      "Change in statistic   = 238.907\n",
      "   cdf.k          1.12593      +/- 0.33594     \n",
      "   cdf.theta      2.53022      +/- 0.997753    \n"
     ]
    }
   ],
   "source": [
    "ui.load_arrays('cdf', xcdf, ycdf)\n",
    "ui.set_model('cdf', gammacdf.cdf)\n",
    "ui.set_stat('leastsq')\n",
    "ui.fit('cdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitting with the PDF model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now I can try the PDF model, which requires binning `ysim` up. I am going to arbitrarily\n",
    "choose 31 equal-width bins and ensure that it's not actually the PDF that we fit, but the\n",
    "PDF times the number of events (so that I can use a Maximum-Likelihood statistic for the fit):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "(ypdf, edges) = np.histogram(ysim, bins=31, density=False)\n",
    "xlo = edges[:-1]\n",
    "xhi = edges[1:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time the data is labelled as an \"integrated\" data set - that is, it is of type\n",
    "`ui.Data1DInt` rather than `ui.Data1D`, which is the default. This means that the columns refer to the low and high edges of the independent axis, and then the dependent axis values. Since I have integer values, I can use the \"Cash\" statistic - from\n",
    "[Parameter estimation in astronomy through application of\n",
    "the likelihood ratio](http://adsabs.harvard.edu/abs/1979ApJ...228..939C) - which is a Maximum-Likelihood statistic where the data values are assumed to follow a Poisson distribution. I have\n",
    "seen cases where the default optimiser - the Levenberg-Marquardt method - does not work well\n",
    "with the Cash statistic (normally when the normalisation of the model is very-far away from the data, which is not an issue for the \"pdf\" data set, but is for the \"check\" data set I try later), so I chose the Nelder-Mead Simplex algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "ui.load_arrays('pdf', xlo, xhi, ypdf, ui.Data1DInt)\n",
    "ui.set_stat('cash')\n",
    "ui.set_method('neldermead')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When plotted, data bars are added. These values are *not* used in the fit, and are only to help visualize the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: The displayed errorbars have been supplied with the data or calculated using chi2xspecvar; the errors are not used in fits with cash\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.plot_data('pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here I create an instance of the `GammaPDF` class - using the `gammapdf` function created by\n",
    "the `add_model` call - called `pdf`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>/*\n",
       "Copyright (C) 2020  Smithsonian Astrophysical Observatory\n",
       "\n",
       "\n",
       " This program is free software; you can redistribute it and/or modify\n",
       " it under the terms of the GNU General Public License as published by\n",
       " the Free Software Foundation; either version 3 of the License, or\n",
       " (at your option) any later version.\n",
       "\n",
       " This program is distributed in the hope that it will be useful,\n",
       " but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
       " MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
       " GNU General Public License for more details.\n",
       "\n",
       " You should have received a copy of the GNU General Public License along\n",
       " with this program; if not, write to the Free Software Foundation, Inc.,\n",
       " 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.\n",
       "\n",
       "*/\n",
       "\n",
       ":root {\n",
       "  --sherpa-border-color: var(--jp-border-color2, #e0e0e0);\n",
       "  --sherpa-background-color: var(--jp-layout-color0, white);\n",
       "  --sherpa-background-color-row-even: var(--jp-layout-color1, white);\n",
       "  --sherpa-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
       "\n",
       "  /* https://medium.com/ge-design/iot-cool-gray-is-a-great-background-color-for-data-visualization-ebf18c318418 */\n",
       "  --sherpa-background-color-dark1: #EBEFF2;\n",
       "  --sherpa-background-color-dark2: #D8E0E5;\n",
       "}\n",
       "\n",
       "div.sherpa-text-fallback {\n",
       "    display: none;\n",
       "}\n",
       "\n",
       "div.sherpa {\n",
       "    display: block;\n",
       "}\n",
       "\n",
       "div.sherpa details summary {\n",
       "    display: list-item;  /* needed for notebook, not lab */\n",
       "    font-size: larger;\n",
       "}\n",
       "\n",
       "div.sherpa details div.datavals {\n",
       "    display: grid;\n",
       "    grid-template-columns: 1fr 3fr;\n",
       "    column-gap: 0.5em;\n",
       "}\n",
       "\n",
       "div.sherpa div.dataname {\n",
       "    font-weight: bold;\n",
       "    border-right: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa div.dataval { }\n",
       "\n",
       "div.sherpa div.datavals div:nth-child(4n + 1) ,\n",
       "div.sherpa div.datavals div:nth-child(4n + 2) {\n",
       "    background: var(--sherpa-background-color-row-odd);\n",
       "}\n",
       "\n",
       "div.sherpa table.model tbody {\n",
       "    border-bottom: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa table.model tr.block {\n",
       "    border-top: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa table.model th.model-odd ,\n",
       "div.sherpa table.model th.model-even {\n",
       "    border-right: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa table.model th.model-odd {\n",
       "    background: var(--sherpa-background-color-dark1);\n",
       "}\n",
       "\n",
       "div.sherpa table.model th.model-even {\n",
       "    background: var(--sherpa-background-color-dark2);\n",
       "}\n",
       "\n",
       "div.sherpa .failed {\n",
       "    background: orange;\n",
       "    font-size: large;\n",
       "    padding: 1em;\n",
       "}\n",
       "</style><div class=\"sherpa-text-fallback\">&lt;GammaPDF model instance &#x27;gammapdf.pdf&#x27;&gt;</div><div hidden class=\"sherpa\"><details open><summary>Model</summary><table class=\"model\"><caption>Expression: gammapdf.pdf</caption><thead><tr><th>Component</th><th>Parameter</th><th>Thawed</th><th>Value</th><th>Min</th><th>Max</th><th>Units</th></tr></thead><tbody><tr><th class=\"model-odd\" scope=\"rowgroup\" rowspan=3>gammapdf.pdf</th><td>k</td><td><input disabled type=\"checkbox\" checked></input></td><td>5.0</td><td>TINY</td><td>MAX</td><td></td></tr><tr><td>theta</td><td><input disabled type=\"checkbox\" checked></input></td><td>2.0</td><td>TINY</td><td>MAX</td><td></td></tr><tr><td>norm</td><td><input disabled type=\"checkbox\" checked></input></td><td>1.0</td><td>0.0</td><td>MAX</td><td></td></tr></tbody></table></details></div>"
      ],
      "text/plain": [
       "<GammaPDF model instance 'gammapdf.pdf'>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ui.set_source('pdf', gammapdf.pdf)\n",
    "pdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As I went to the effort of writing a `guess` method for this class, let's see what it does:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>/*\n",
       "Copyright (C) 2020  Smithsonian Astrophysical Observatory\n",
       "\n",
       "\n",
       " This program is free software; you can redistribute it and/or modify\n",
       " it under the terms of the GNU General Public License as published by\n",
       " the Free Software Foundation; either version 3 of the License, or\n",
       " (at your option) any later version.\n",
       "\n",
       " This program is distributed in the hope that it will be useful,\n",
       " but WITHOUT ANY WARRANTY; without even the implied warranty of\n",
       " MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the\n",
       " GNU General Public License for more details.\n",
       "\n",
       " You should have received a copy of the GNU General Public License along\n",
       " with this program; if not, write to the Free Software Foundation, Inc.,\n",
       " 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.\n",
       "\n",
       "*/\n",
       "\n",
       ":root {\n",
       "  --sherpa-border-color: var(--jp-border-color2, #e0e0e0);\n",
       "  --sherpa-background-color: var(--jp-layout-color0, white);\n",
       "  --sherpa-background-color-row-even: var(--jp-layout-color1, white);\n",
       "  --sherpa-background-color-row-odd: var(--jp-layout-color2, #eeeeee);\n",
       "\n",
       "  /* https://medium.com/ge-design/iot-cool-gray-is-a-great-background-color-for-data-visualization-ebf18c318418 */\n",
       "  --sherpa-background-color-dark1: #EBEFF2;\n",
       "  --sherpa-background-color-dark2: #D8E0E5;\n",
       "}\n",
       "\n",
       "div.sherpa-text-fallback {\n",
       "    display: none;\n",
       "}\n",
       "\n",
       "div.sherpa {\n",
       "    display: block;\n",
       "}\n",
       "\n",
       "div.sherpa details summary {\n",
       "    display: list-item;  /* needed for notebook, not lab */\n",
       "    font-size: larger;\n",
       "}\n",
       "\n",
       "div.sherpa details div.datavals {\n",
       "    display: grid;\n",
       "    grid-template-columns: 1fr 3fr;\n",
       "    column-gap: 0.5em;\n",
       "}\n",
       "\n",
       "div.sherpa div.dataname {\n",
       "    font-weight: bold;\n",
       "    border-right: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa div.dataval { }\n",
       "\n",
       "div.sherpa div.datavals div:nth-child(4n + 1) ,\n",
       "div.sherpa div.datavals div:nth-child(4n + 2) {\n",
       "    background: var(--sherpa-background-color-row-odd);\n",
       "}\n",
       "\n",
       "div.sherpa table.model tbody {\n",
       "    border-bottom: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa table.model tr.block {\n",
       "    border-top: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa table.model th.model-odd ,\n",
       "div.sherpa table.model th.model-even {\n",
       "    border-right: 1px solid var(--sherpa-border-color);\n",
       "}\n",
       "\n",
       "div.sherpa table.model th.model-odd {\n",
       "    background: var(--sherpa-background-color-dark1);\n",
       "}\n",
       "\n",
       "div.sherpa table.model th.model-even {\n",
       "    background: var(--sherpa-background-color-dark2);\n",
       "}\n",
       "\n",
       "div.sherpa .failed {\n",
       "    background: orange;\n",
       "    font-size: large;\n",
       "    padding: 1em;\n",
       "}\n",
       "</style><div class=\"sherpa-text-fallback\">&lt;GammaPDF model instance &#x27;gammapdf.pdf&#x27;&gt;</div><div hidden class=\"sherpa\"><details open><summary>Model</summary><table class=\"model\"><caption>Expression: gammapdf.pdf</caption><thead><tr><th>Component</th><th>Parameter</th><th>Thawed</th><th>Value</th><th>Min</th><th>Max</th><th>Units</th></tr></thead><tbody><tr><th class=\"model-odd\" scope=\"rowgroup\" rowspan=3>gammapdf.pdf</th><td>k</td><td><input disabled type=\"checkbox\" checked></input></td><td>5.0</td><td>TINY</td><td>MAX</td><td></td></tr><tr><td>theta</td><td><input disabled type=\"checkbox\" checked></input></td><td>2.0</td><td>TINY</td><td>MAX</td><td></td></tr><tr><td>norm</td><td><input disabled type=\"checkbox\"></input></td><td>1000.0</td><td>0.0</td><td>MAX</td><td></td></tr></tbody></table></details></div>"
      ],
      "text/plain": [
       "<GammaPDF model instance 'gammapdf.pdf'>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ui.guess('pdf', pdf)\n",
    "pdf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `norm` parameter is now set to the sum of the data - in this 1000 - and has been frozen,\n",
    "so that it is not varied during the fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset               = pdf\n",
      "Method                = neldermead\n",
      "Statistic             = cash\n",
      "Initial fit statistic = -139.551\n",
      "Final fit statistic   = -6922.65 at function evaluation 221\n",
      "Data points           = 31\n",
      "Degrees of freedom    = 29\n",
      "Change in statistic   = 6783.1\n",
      "   pdf.k          1.11627     \n",
      "   pdf.theta      2.55127     \n"
     ]
    }
   ],
   "source": [
    "ui.fit('pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fit is in the right area of parameter space (the input `k` and `theta` values are\n",
    "1.1 and 2.6), and the fit looks reasonable (note that, as of Sherpa 4.12.2, the model is plotted as a \"histogram\" for `Data1DInt` data, and from 4.16.1 the residuals also use a \"histogram\" style here):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: The displayed errorbars have been supplied with the data or calculated using chi2xspecvar; the errors are not used in fits with cash\n",
      "WARNING: The displayed errorbars have been supplied with the data or calculated using chi2xspecvar; the errors are not used in fits with cash\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.plot_fit_resid('pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the Y values cover more than one order of magnitude, let's use a log scale to check (the residual plot refuses to use a logarithmic scale for the Y axis):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: The displayed errorbars have been supplied with the data or calculated using chi2xspecvar; the errors are not used in fits with cash\n",
      "WARNING: The displayed errorbars have been supplied with the data or calculated using chi2xspecvar; the errors are not used in fits with cash\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkIAAAGwCAYAAABFFQqPAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAAA9hAAAPYQGoP6dpAAA8WklEQVR4nO3deXTU9b3/8dckkJAgGaCBLBIIuDYsSRtImlYr1FRELoqoh24awYun3tBWYtVgBQq14lK5udZpub/bKqXH66VWxQWLSlS4tyJLMG6AFY0SDQkgNQNJyJDk+/sDM2aZTGbNd2a+z8c5c8h81/fwzWTe81neX5thGIYAAAAsKM7sAAAAAMxCIgQAACyLRAgAAFgWiRAAALAsEiEAAGBZJEIAAMCySIQAAIBlDTI7gEjW0dGhuro6DRs2TDabzexwAACADwzD0PHjx5WZmam4OO9tPiRCXtTV1SkrK8vsMAAAQABqa2s1ZswYr9uQCHkxbNgwSaf/I1NSUkyOBgAA+MLpdCorK8v9Oe4NiZAXnd1hKSkpJEIAAEQZX4a1MFgaAABYFokQAACwLBIhAABgWSRCAADAskiEAACAZZEIRaBDjS167YOjOtTYYnYoAADENKbPe+BwOORwONTe3h6eExiGdKrZ46rHdnysVZv2SZLibNLKyyfq6nwPRR0HJ0tUuwYAICg2wzAMs4OIVE6nU3a7XY2NjaGtI+Rqku7ODO4YWd+QFm4mGQIAoAd/Pr/pGotWta97bFWiWw0AAN/RNWaGwcnSHXW9Ftc7W3TxA1vV0aWNLt5m05Zbvq30lKTTC1zN0m/O/vLnLnzqVqNLDQAAN7rGvAhb15gXG3Yd1B1PvqN2w1C8zaa7503S/Gljv9wg2G41utQAADHOn89vWoQizPxpY/Xtc0fpo6PNyk5NVoY9qfsGg5NPJzO1rwd2gs4utYShwQcLAECUIxGKQBn2pN4JUCeb7XSLTo/xQf12q3XtUgMAAJIYLB2dbLbTLTpdHumpqVo+b5pctiS1aIhctiQtmzdV6ampX2yTbHbUAABEHFqEYki/3WoAAKAbEqEY47VbrZOr97T7emeLO4Fyz1DriRlnAIAYQyJkRR7GCqV/8fCKGWcAgBjDGCGr6JxtFow+ijgCABCtaBGyij5mm73+4WdasG5Xr83XXV+gwgkjTz9hxhkAIEaRCFlJ52yzLsZlxKnVNqTXtPuxGalSQv+DrZtdbcpZ/oIk6eVbLtKEUWeENGQAAMKJrjGLy7AnaeXlE93P42zS3fMm+Tzj7ImqT9w/F6/Zqg27DoY8RgAAwiXmW4Rqa2t17bXX6vDhwxo0aJCWLVuma665xuywIsq1Rdkqzknze9r9ocYWrXjmXffzDkO648l39O1zRzF1HwAQFWI+ERo0aJAqKiqUl5en+vp65efn67LLLtPQodxioiufpt1L3abef3zoMyUaJ7uvN6SDh44qI2nkl8uYdg8AiFAxnwhlZGQoIyNDkpSenq7U1FQdO3aMRChQXQZNf0PSviEetvmfHs+Zdg8AiFARP0Zo27ZtmjNnjjIzM2Wz2bRx48Ze2zgcDmVnZ2vIkCEqLCzUzp07PR6rqqpK7e3tysrKCnPUMSbYqfdMuwcARKiIbxFqampSbm6uFi5cqHnz5vVav2HDBpWVlWnt2rUqLCxURUWFZs6cqffee0+jR492b3fs2DFdd911+q//+q+BDD829DH1vlO9s0UfH23RuNSk7lWpmXYPAIhwNsMwjP43iww2m01PPfWU5s6d615WWFioadOm6aGHHpIkdXR0KCsrSz/5yU9UXl4uSWptbdV3v/tdLVq0SNdee22fx29tbVVra6v7udPpVFZWlhobG5WSkhKeFxXLXE3S3Zmnf76jrtfUfQAAwsHpdMput/v0+R3xXWPeuFwuVVVVqbi42L0sLi5OxcXF2r59uyTJMAxdf/31+s53vuM1CZKk1atXy263ux90oQEAENuiOhE6evSo2tvblZaW1m15Wlqa6uvrJUl///vftWHDBm3cuFF5eXnKy8vT22+/7fF4S5cuVWNjo/tRW1sb9tcAAADME/FjhIJ1wQUXqKOjw6dtExMTlZiYGOaILKrHHe+bXW3Kv2uLJOn5n16o8al9dJsx9R4AEEZRnQilpqYqPj5eDQ0N3ZY3NDQoPb3fe6n3yeFwyOFwqL29PdgQ0anHoOlkdZl6//+87MfUewBAGEV111hCQoLy8/NVWVnpXtbR0aHKykoVFRUFfNzS0lLt3btXu3b1vhkp/MAd7wEAES7iW4ROnDihAwcOuJ/X1NSourpaI0eO1NixY1VWVqaSkhJNnTpVBQUFqqioUFNTkxYsWGBi1JAUtjvec6NXAECoRHwitHv3bs2YMcP9vKysTJJUUlKidevWaf78+Tpy5IiWL1+u+vp65eXlafPmzb0GUPuDrrEQCsMd73ve6HX1vMmaP21syEIGAFhHVNURGmj+1CGAf/68/SMte/r0DVvjbOqdzPRRg+hQY4u+dc/LvZKo/yufwY1eAQCSLFRHCNHrqvwx7p+3lF3kc4tOzdGmbkmQJLUbhj46yjgiAID/Ir5rDLEpOWGQPrpntm8bd5l6P8EuDbWd7NUiNN5unG5F6sS0ewCAD0iEPGCMUITpMmg6XdK7nko9PdTjOdPuAQA+YIyQF4wRMpFhSA9fenr6fKC4vxkAWJI/n9+0CCEy9XPH+z71c8d7pt4DALpisDQiV+fUe78eyV4P2XPq/YZdB8P9KgAAEYxECJZxqLFFK5551/28w5DuePIdHWpsMTEqAICZSIQ8cDgcysnJ0bRp08wOBSHE1HsAQE+MEfKgtLRUpaWl7sFWiFI97njP1HsAQE8kQohdPQZNM/UeANATXWOILdzxHgDgB1qEEFsCnXYv9Tv1HgAQe0iEPKCydJTzcMd7AAA8oWvMg9LSUu3du1e7du0yOxQAABBGJEIAAMCy6BoDPHEFMMaIafcAEHVIhABPAhk0zbR7AIg6dI0BnYKdes+0ewCIOrQIAZ28TL1/bMfHWrVpnyQpziatvHyirs7POr2SafcAELVoEfKAe41ZmIc73h9qidMvnq9Ri4aoRUPUZAzR7c98qEMtcT7d8R4AELlIhDxg+jy64matABC7SISAfoxPHaq4HuOf4202ZafSEgQA0Y5ECOhHhj1JKy+f6H4eZ5PunjdJGfYkE6MCAIQCg6UBH1yVP0bLnn5XkrSl7CJNGHWG5w0DqT8kUYMIAExCIgT4Kd0+pO+Vgc4eowYRAJiCrjEgWMHWH5I81iBqdrUpu3yTsss3qdnVFtzxAQAe0SIE+CA5YZA+ume255Ve6g/1ixpEAGAqEiEPHA6HHA6H2tvbzQ4F0aKz/hAAIKrQNeYBdYQQaeobT5odAgDEJBIhIMwCHevzRNUn7p+L12zVhl0HwxEeAFgaXWNApOgy9b7e2aJ7nqmSu1KRIf3qyd26aHyy0lO61C9i2j0ABIVECBhA9Y0n+65B1GXQdLqkdxM9bPNQj+d9TLtvdrUpZ/kLkqS9q2YqOYG3OgB4QtcYEGZeu7iCnXrvYdo9AMB3fE0EwuhQY4tWPPOu+3mHId3x5Dv69rmjTt+iw8vU+8d2fKxVm/ZJOn1bj5WXT9TV+VmnVzLtHgBCghYhIIx8unN959T7Ho8rCs9Vi4aoRUP0bNlMXV10fpf1vt/wlRlnANA3EiEgjEJ153qvt/XwgBlnAOAbEiEgjMy4c31f3XGHGlvCdk4AiFaMEQLCzOc71/fg9bYeXnjrjgtnAgYA0YhECBhA/nZx+cTVfaD1BLs01HayWzIUb7NpvN2QXE1fLqQGEQCQCAFRr8fssWBrEAGAlTBGyAOHw6GcnBxNmzbN7FAAz4KtPyRRgwgAJNkMwzD638yanE6n7Ha7GhsblZKSYnY4QHeG0Wci0+xqU/5dWyRJVXcWd68s3bUG0R11p6fjm4gq2ABCzZ/Pb/7iANGqs/6QR21q0RfjkRKGSiQXAOARXWMAAMCy+JoIxKBAp94DgNWQCAFW1mPqvdexRV2Faep9feNJn+ssAUAokAgBVtZj6n2ypH2dpY5+42W/EE6973k7kNXzJmv+tLFBHxcAfMEYIcBqwjT1vtnVpuzyTcou36RmV5tPh+F2IADMRosQYDU22+nWHA9T7/vtGus69T4EuB0IALORCAFW1OfU+y+n3de3xGvCGeGtMTQ+dajibOp1O5Ds1OSwnhcAOtE1BsCt53idDbsOhvV8GfYkrbx8ovt5nE26e94kWoMADBgSIQCSzBuvc1X+GPfPW8ouYqA0gAFFIgRAkvfxOv6qbzwZUAzp9iH9bwQAIUQiBEDSl+N1uvI6XsfVLLma3I+nd/xDSTqpJJ3UnDUv6K/b93dbL1fT6fujAUAEYbA0AElfjtdZ9vTp7rF+x+v0mD32fUnf79qg88IXj65CWH8IAELBEi1CV155pUaMGKGrr77a7FCAiNbveJ1gaxB5qD8EAGayRIvQz372My1cuFB/+tOfzA4FiBoex+v0UYOo3tmiix/Y2msa/JZbvq30lKSQ1x8CgFCxRIvQ9OnTNWzYMLPDAGJDZw2iLo/01FSVX56vFg1Ri4ao1TZEy+ZNVXpq6hfb9F0XqPMGsR/dM7vve5sBQJhEfCK0bds2zZkzR5mZmbLZbNq4cWOvbRwOh7KzszVkyBAVFhZq586dAx8oYHFMgwcQjSI+EWpqalJubq4cDofH9Rs2bFBZWZlWrFihPXv2KDc3VzNnztThw4f9Pldra6ucTme3BwD/MQ0eQLSI+HboWbNmadasWX2uX7NmjRYtWqQFCxZIktauXatNmzbp4YcfVnl5uV/nWr16tVauXBlUvAD64QpwsPTgZGabAQi5iE+EvHG5XKqqqtLSpUvdy+Li4lRcXKzt27f7fbylS5eqrKzM/dzpdCorKysksQL4QqCDpiNk6n2zq005y0/XBdi7aqZf45qC2RdAeET1u/Do0aNqb29XWlpat+VpaWnav3+/+3lxcbHefPNNNTU1acyYMXr88cdVVFTU63iJiYlKTEwMe9xApOocuBxyndPua18P/BidU+893iwWAAIT1YmQr7Zs2eLX9g6HQw6HQ+3t7WGKCLCYPqbd+4Sp9wDCKKoTodTUVMXHx6uhoaHb8oaGBqWnpwd83NLSUpWWlsrpdMputwcbJgDpy2n3ABBBIn7WmDcJCQnKz89XZWWle1lHR4cqKys9dn0BCB8z6gE1u9qUXb5J2eWb1OxqG5BzAogtEd8idOLECR04cMD9vKamRtXV1Ro5cqTGjh2rsrIylZSUaOrUqSooKFBFRYWamprcs8gAAAD6EvGJ0O7duzVjxgz3885ZXSUlJVq3bp3mz5+vI0eOaPny5aqvr1deXp42b97cawC1PxgjBACANUR8IjR9+nQZhuF1m8WLF2vx4sUhOydjhIAI1bMGkatNSTr5xc9N8vgnLYz1h+obT2rCqDMGfF8AoRPxiRAAuPWYPZYsaV9nEevf9LFPiOsPPVH1ifvn4jVbtXreZJ9vJxLMvgDCI6oHSwOwgM4aRIHqrD8UAocaW7TimXfdzzsM6Y4n39Ghxpaw7gsgfGgR8oAxQkAE8VKDqNnVpvy7TtcJq7qzuPtstTDUH6o52qSOHj317Yahj442K8OeFLZ9AYQPLUIelJaWau/evdq1a5fZoQCQvqxB5OHRoiFq0RDVt8T3WJcc8jDGpw5VXI8etnibTdmp/Z8rmH0BhA+JEICo1XPMzYZdB8N6vgx7klZePtH9PM4m3T1vkk8tOsHsCyB8SIQARCWzxtxclT/G/fOWsov8GuwczL4AwoMxQh4wRgiIfH6Nuek57d5X/Uy9T7cP6XNdf4LZF0DokAh5QB0hIPJ1jrnpmgz1OeYm0EHTIZ56DyDy0DUGICr1O+Ym2Gn3Ukin3gOITLQIAYhaV+WP0bKnT48T2lJ2UfdKzV6m3fcrDFPvAUQmEiEAMcHjmJvOafcA0Ae/u8ZKSkq0bdu2cMQCAAAwoPxOhBobG1VcXKxzzjlHd999tz799NNwxGUqh8OhnJwcTZs2zexQAABAGPmdCG3cuFGffvqpbrrpJm3YsEHZ2dmaNWuW/vrXv+rUqVPhiHHAUVkaAABrCGjW2KhRo1RWVqY333xTO3bs0Nlnn61rr71WmZmZWrJkid5///1QxwkAIdPsalN2+SZll29Ss6vN+8auZsnV1O2RpJNK0sley90Pw/B+THjk13UBQiSowdKHDh3SSy+9pJdeeknx8fG67LLL9PbbbysnJ0f33XeflixZEqo4AcAcPWaPJUva1zku+zd97EP9ISBq+J0InTp1Ss8884weeeQRvfjii5oyZYpuvvlm/eAHP1BKSook6amnntLChQtJhABEp84aRLWvB7Z/Z/2hHjPWkhMG6aN7ZocgQACh4ncilJGRoY6ODn3/+9/Xzp07lZeX12ubGTNmaPjw4SEIDwBMEGgNIuoPAVHH70To3//933XNNddoyJC+75MzfPhw1dTUBBUYAJiKGkSAJfg9WPraa6/1mgTFAqbPAwBgDdxrzAOmzwMAYA3cYgMAwsEV4M1aBycz2wwYQCRCAKJWRM/CCnTQNFPvgQFF1xgAhErntPtgdE69BzAgaBECYGn1jSc1YdQZoTlYoNPuJabe9xDS6wJ4QYsQAMt5ouoT98/Fa7Zqw66DoTt457R7vx/JoYshSoX1ugB9IBECYCmHGlu04pl33c87DOmOJ9/RocYWE6MC1wVmIRHygDpCQOyqOdqkjh73RG03DH10lHE5ZuK6wCwkQh5QRwiIXeNThyqux4SseJtN2al0TZmJ6wKzkAgBsJQMe5JWXj7R/TzOJt09b5Iy7EkmRtWDq1lyNfn3MIz+jxvBouK6ICYxawyA5VyVP0bLnj49HmVL2UWRNzspkNljMVB/KOKvC2ISLUIALC3dHiH3Tgy2BlGM1R+KmOuCmEeLEABEgkBrEFF/CAgKiRAARIrOGkQABgxdYwAAwLJIhAAAgGXRNQYAscIV4GDpwclRPdsMCAaJEADEikAHTcfA1HsgUHSNAUA0C3bavRRzU+8Bf9Ai5IHD4ZDD4VB7e7vZoQCAml1tyln+giRp76qZSk7o8qc70Gn3ElPvg+T1usTQOYMRDfFGXkQRoLS0VKWlpXI6nbLb7WaHAwDeMe0eCBhdYwAAwLJIhAAAgGWRCAEAAMtijBAAILAaRNQfQgwgEQIABDZ7jPpDiAF0jQGAVQVbg4j6Q4gBtAgBgFUFWoOI+kOIISRCAGBl1CCCxdE1BgAALItECAAAWBaJEAAAsCzGCAEAAhdI/SGJGkSIGCRCACwnOWGQPrpnttlhxIZAZ495qEHEdYEZ6BoDAPgn2PpDEjWIEDFivkXoueee0y233KKOjg7dfvvt+td//VezQwKA6BZo/SGJGkSIODGdCLW1tamsrEyvvPKK7Ha78vPzdeWVV+orX/mK2aEBQHSj/hBiREx3je3cuVMTJ07UmWeeqTPOOEOzZs3Siy++aHZYABCw+saTZocAD8y4LtH2uxCp8UZ0IrRt2zbNmTNHmZmZstls2rhxY69tHA6HsrOzNWTIEBUWFmrnzp3udXV1dTrzzDPdz88880x9+umnAxE6AITME1WfuH8uXrNVG3YdNDEadDLjukTb70I0xBvRiVBTU5Nyc3PlcDg8rt+wYYPKysq0YsUK7dmzR7m5uZo5c6YOHz4c0PlaW1vldDq7PQDATIcaW7TimXfdzzsM6Y4n39GhxhYTowoRV7PkavL/YRhmR27KdYm234VoiTeixwjNmjVLs2bN6nP9mjVrtGjRIi1YsECStHbtWm3atEkPP/ywysvLlZmZ2a0F6NNPP1VBQUGfx1u9erVWrlwZuhcAAEGqOdqkjh6f++2GoY+ONivDntTv/s2uNuUsf0GStHfVTCUn+PZnP9D9/No3hFPvB/p1BnNdzDhnMOc1K96BEtEtQt64XC5VVVWpuLjYvSwuLk7FxcXavn27JKmgoEDvvPOOPv30U504cUJ/+9vfNHPmzD6PuXTpUjU2NroftbW1YX8dAODN+NShiutRdzDeZlN2arI5AQUrRqbem3Fdou13IVrijegWIW+OHj2q9vZ2paWldVuelpam/fv3S5IGDRqkBx54QDNmzFBHR4duu+02rzPGEhMTlZiYGNa4AcAfGfYkrbx8opY9fbqLIc4m3T1vUkR9o/ZLjEy9N+O6RNvvQrTEG7UtQr66/PLL9Y9//EMHDhzQjTfe6NM+DodDOTk5mjZtWpijA4D+XZU/xv3zlrKLNH/aWBOjCYHOqfd+PyKrJcGM6xJtvwvREG/UJkKpqamKj49XQ0NDt+UNDQ1KT08P6tilpaXau3evdu3aFdRxACDU0u1DzA4BHphxXaLtdyFS443aRCghIUH5+fmqrKx0L+vo6FBlZaWKiopMjAwAAESLiB4jdOLECR04cMD9vKamRtXV1Ro5cqTGjh2rsrIylZSUaOrUqSooKFBFRYWamprcs8gAAAC8iehEaPfu3ZoxY4b7eVlZmSSppKRE69at0/z583XkyBEtX75c9fX1ysvL0+bNm3sNoPaXw+GQw+FQe3t7UMcBAISJq8dga1ebkvRF5WJXkzx+vA1O7jblHpAiPBGaPn26jH4KZy1evFiLFy8O6XlLS0tVWloqp9Mpu90e0mMDAEKgx+yxZEn7Ooeg/KaPfTzUHwKidowQAMBigq1BFAH1hxB5IrpFCAAANy81iJpdbcq/a4skqerO4u7VjyOo/hAiD4mQB4wRAoAI1VmDqJc2teiLvrGEoZIftwSBtdE15gF1hAAAsAYSIQAAYFkkQgAAwLLoRPWAMUIAEKMCqT8kUYMohpEIeUAdIQCIUYHUH5KoQRTD6BoDAMS2YOsPSdQgimG0CAEAYlug9YckahBZAIkQACD2UX8IfaBrDAAAWBaJkAcOh0M5OTmaNm2a2aEAAIAwog3QA2aNAQB6CWTqPdPuIx6JEAAAvghk6j3T7iMeXWMAAPQl2Kn3TLuPeLQIAQDQl0Cn3jPtPmqQCAEA4A1T72MaXWMeMGsMAABrIBHyoLS0VHv37tWuXbvMDgUAAIQRiRAAALAsOjQBAAinQOoPSdQgGiAkQgAAhFMg9YckahANELrGAAAItWDrD0nUIBogtAgBABBqgdYfkqhBNMBIhAAACAfqD0UFusYAAIBlkQh5QEFFAACsgUTIAwoqAgBgDXRMAgAQqQKpQUT9Ib+QCAEAEKkCqUFE/SG/0DUGAEAkCbYGEfWH/EKLEAAAkSTQGkTUHwoIiRAAAJGGGkQDhq4xAABgWSRCAADAsmhTAwAg1vScdi8x9b4PJEIAAMQaD4OmmXrvGV1jAADEgmCn3UuWnHpPi5AHDodDDodD7e3tZocCAIBvvEy7l5h63xcSIQ9KS0tVWloqp9Mpu91udjgAAPimz2n3ElPvPaNrDAAAWBaJEAAAsCwSIQAAYFl0EAIAgC/1rEEU4/WHSIQAAMCXeswei/X6Q3SNAQBgdcHWIIri+kO0CAEAYHVeahDFev0hEiEAAOClBlFs1x+iawwAAFgWiRAAALAsEiEAAGBZsdXRBwAAzNGz/pDkWw0iydQ6RCRCAAAgeB5mj/lUg0iS7qjzcrPY8LJE19iVV16pESNG6OqrrzY7FAAAYkew9YcigCVahH72s59p4cKF+tOf/mR2KAAAxA4v9YekfmoQdTU4OVwR9ssSidD06dP16quvmh0GAACxp8/6Q1I01CAyvWts27ZtmjNnjjIzM2Wz2bRx48Ze2zgcDmVnZ2vIkCEqLCzUzp07Bz5QAAAQc0xPhJqampSbmyuHw+Fx/YYNG1RWVqYVK1Zoz549ys3N1cyZM3X48GH3Nnl5eZo0aVKvR11d3UC9DAAAEIVMb6OaNWuWZs2a1ef6NWvWaNGiRVqwYIEkae3atdq0aZMefvhhlZeXS5Kqq6tDEktra6taW1vdz51OZ0iOCwAAIpPpLULeuFwuVVVVqbi42L0sLi5OxcXF2r59e8jPt3r1atntdvcjKysr5OcAAACRI6IToaNHj6q9vV1paWndlqelpam+vt7n4xQXF+uaa67R888/rzFjxvSZRC1dulSNjY3uR21tbVDxAwCAyGZ619hA2LJli0/bJSYmKjExMczRAACASBHRLUKpqamKj49XQ0NDt+UNDQ1KT08P23kdDodycnI0bdq0sJ0DAACYL6JbhBISEpSfn6/KykrNnTtXktTR0aHKykotXrw4bOctLS1VaWmpGhsbNXz4cAZNAzBVs6tNHa2nC9Y5nU61+VGLJdB9zThnMKLpdZr1fxtt8Qaj83PbMIz+NzZMdvz4ceONN94w3njjDUOSsWbNGuONN94wPv74Y8MwDON//ud/jMTERGPdunXG3r17jRtvvNEYPny4UV9fH/bYamtrDUk8ePDgwYMHjyh81NbW9vtZbzMMX9Kl8Hn11Vc1Y8aMXstLSkq0bt06SdJDDz2k+++/X/X19crLy9ODDz6owsLCsMfW0dGhuro6DRs2TLYQ3xXX6XQqKytLtbW1SklJCemxER5cs+jDNYs+XLPoFGnXzTAMHT9+XJmZmYqL8z4KyPREyKqcTqfsdrsaGxsj4pcG/eOaRR+uWfThmkWnaL5uET1YGgAAIJxIhAAAgGWRCJkkMTFRK1asoG5RFOGaRR+uWfThmkWnaL5ujBECAACWRYsQAACwrIguqGi2cE6fBwAA4eHP9HkSIS/q6uq4Az0AAFGqtrZWY8aM8boNiZAXw4YNk6SIKRAFAAD611ngsfNz3BsSIS86u8NSUlJIhAAAiDK+DGthsDQAALAsEiEAAGBZJEIISrOrTdnlm5RdvknNrjazwwEAwC8kQgAAwLJIhAAAgGWRCCHq0B0HAAgVEiEAAGBZJEIAAMCySIQAAIBlkQgBAADLIhECAACWRSIEAAAsi0QIAABYFolQhAmmRg71dQAA8A+JEAAAsKxBgexUVlbm87Zr1qwJ5BQAAABhF1Ai9MYbb/i0nc1mC+TwQNg0u9qUs/wFSdLeVTOVnBDQWwAAECMC+hR45ZVXQh0HAADAgAvZGKEDBw7ohRdeUEtLiyTJMIxQHRoAACAsgk6EPvvsM1188cU699xzddlll+nQoUOSpBtuuEG33HJL0AECAACES9CJ0JIlSzR48GAdPHhQycnJ7uXz58/X5s2bgz08AABA2AQ9UvTFF1/UCy+8oDFjxnRbfs455+jjjz8O9vAAAABhE3SLUFNTU7eWoE7Hjh1TYmJisIf3atu2bZozZ44yMzNls9m0cePGbusNw9Dy5cuVkZGhpKQkFRcX6/333w9rTAAAIHoEnQhdeOGFWr9+vfu5zWZTR0eH7rvvPs2YMSPYw3vV1NSk3NxcORwOj+vvu+8+Pfjgg1q7dq127NihoUOHaubMmTp58mRY4wIAANEh6K6x++67TxdffLF2794tl8ul2267Te+++66OHTumv//976GIsU+zZs3SrFmzPK4zDEMVFRW68847dcUVV0iS1q9fr7S0NG3cuFHf+973whobAACIfEG3CE2aNEn/+Mc/dMEFF+iKK65QU1OT5s2bpzfeeENnnXVWKGIMSE1Njerr61VcXOxeZrfbVVhYqO3bt3vcp7W1VU6ns9sDAADErpCU1bXb7frFL34RikOFTH19vSQpLS2t2/K0tDT3up5Wr16tlStXhj02AAAQGQJKhN566y2ft50yZUogpzDF0qVLu91Hzel0Kisry8SIAABAOAWUCOXl5clms8kwjG73E+usJt11WXt7e5AhBiY9PV2S1NDQoIyMDPfyhoYG5eXledwnMTEx7DPdAHTH/d8AmCmgMUI1NTX68MMPVVNToyeeeELjx4/X7373O1VXV6u6ulq/+93vdNZZZ+mJJ54Idbw+Gz9+vNLT01VZWele5nQ6tWPHDhUVFZkWFwAAiBwBffUaN26c++drrrlGDz74oC677DL3silTpigrK0vLli3T3Llzgw6yLydOnNCBAwfcz2tqalRdXa2RI0dq7Nixuvnmm3XXXXfpnHPO0fjx47Vs2TJlZmaGNSYAABA9gm6DfvvttzV+/Phey8ePH6+9e/cGe3ivdu/e3a1WUef4npKSEq1bt0633XabmpqadOONN+rzzz/XBRdcoM2bN2vIkCFhjQsAAESHoBOhr371q1q9erX+8Ic/KCEhQZLkcrm0evVqffWrXw06QG+mT5/u9S73NptNq1at0qpVq8IaB8LDMAy1nOo9xqzZ1ebx566SBsd3G6sGAIAnQSdCa9eu1Zw5czRmzBj3DLG33npLNptNzz77bNABwpoMw9DVa7er6uN/et1u6l2VnpePG6HHf1xEMgQA8CroRKigoEAffvihHn30Ue3fv1/S6TvP/+AHP9DQoUODDhDW1HKqvd8kyJvdH/9TLafamYEEAPAqJJ8SQ4cO1Y033hiKQyFCmdlNtfvOYiUnxHc7T2dL0O47L+6W7DS72jX1ri0BnwsAYC0hSYQ++OADVVRUaN++fZKkiRMn6qc//ampt9iA7/qr42J2N1VyQnyfLTvJCYNo9QEABCzoe4298MILysnJ0c6dOzVlyhRNmTJFr7/+uiZOnKiXXnopFDHCZKHqpoJ/ml1tyi7fpOzyTX22toVjXwCwkqC/SpeXl2vJkiW65557ei2//fbb9d3vfjfYUyCC0E2FQAXTvSrFxkxAqmgDkSfod+G+ffv0l7/8pdfyhQsXqqKiItjDI8LQTYVABNu9KjETEEB4BP2pNWrUKFVXV+ucc87ptry6ulqjR48O9vBAwJpd1CCKFMF2r0rMBAQQHkH/RVm0aJFuvPFGffjhh/rmN78pSfr73/+ue++9t9ud3IGB1l+3HDWIzOFP9+rp9XSxAgifoBOhZcuWadiwYXrggQe0dOlSSVJmZqZ++ctf6qc//WnQAQL+SBocr6njRmg3NYgiVrR3rzLOB4gtQb+DbTablixZoiVLluj48eOSpGHDhgUdGBAIm82mx39c1OcsNQZ3AwC6CulXGRIgRAKbzebTt/RoaH0AAIRXwJ8C3/nOd3za7uWXXw70FIhhdC8gVvVVJkBisD4QiQL+9Hn11Vc1btw4zZ49W4MHDw5lTAAQlXwtEyAxWN8TviDBDAH/lt1777165JFH9Pjjj+uHP/yhFi5cqEmTJoUyNgCIKpQJAKJPwO+0W2+9Vbfeequ2b9+uhx9+WN/61rd03nnnaeHChfrBD36glJSUUMYJIMLF2rf5QCphd61d1bNMQOf2DNYHIkvQf6mKiopUVFSk//iP/9Djjz8uh8Ohn//856qrqyMZAhCVQlEJ21uZgNPrGawPRIKQvQv37NmjrVu3at++fZo0aRLjhoAwY1Bu+ATbxTV13AglDY7vf0OL4r5ziCRBJUJ1dXVat26d1q1bJ6fTqR/96EfasWOHcnJyQhUfAA8YlDtw/K2ELfFB7Q33nUOkCTgRuuyyy/TKK6/okksu0f3336/Zs2dr0CCaeRGbwjn+JdCxKAzKHRjRXgk70jCgHJEm4N+izZs3KyMjQwcPHtTKlSu1cuVKj9vt2bMn4ODgWTDNynxTjSyh+HYc7YNykxMG6aN7ZpsdBkzAfef8F22TEqIh3oAjWrFiRSjjgI+C/eCkSTmyhGIsyleGJni9nrRaIFJFe2tbpLUUdxroL7zBjleUzP2SbolEyOFw6P7771d9fb1yc3P129/+VgUFBWaHFZBgPzhpUo5ckTAWJRq+vXUVbfEiOg10UhJNX3hDMV5RMvf9G/N/NTZs2KCysjKtXbtWhYWFqqio0MyZM/Xee+9p9OjRpsQUTPbsrU5JNHWHoLdo/3aM/tENGH3MSErC9YU30C8O3vYLxZgvs8X8X9Y1a9Zo0aJFWrBggSRp7dq12rRpkx5++GGVl5ebElPLqXb3L5U33rJniQ9OmCPYQoNAJOkvOQhHUuJPQhLoF15P7zlfu6n82S+YIqJdmVluIqY/KV0ul6qqqrR06VL3sri4OBUXF2v79u29tm9tbVVra6v7udPp7PZvqDS72tTR2tzn+rjEZEnyus3XsobrVEuTnCe//JbR9RfS6Tyuth5vns7jOZ1OtfV48/S1XzD7mnHO/oQr3kBF2+s0DEPX/nGnqms/93jezt/dry97ts/Yep6z/9cSO9cl0HPGkv5e51t3XChJajvZLOdJ3/dtdrXrG795TZL0+s+/2esDue94fP9btPXW6Urqsr7F1a4ZD+6UJL3y04Je6y66/1VJUsPRf/Za16nnus71nedsO9mkto4vX2dbl33bTraorSO+y7ovY/36smc8vl5f3qOB7tcz1v7i7er4SY+LA+bP53ZsvtO+cPToUbW3tystLa3b8rS0NO3fv7/X9qtXr/Y4+y0rKytsMfZkG5yosWVPSJI+cVwr41Srx+1qJQ2/pe99MzMz+tw3oyKw/YLZ14xzejIQ8QYq2l+nr7+7Pc/pj0i4Lt3W3Rvy0/V7zmjQ9bocXHNVRP8u+LPfBC/nPCs7q899A91PMuc9Guh+/V3PcL1fghXSROiTTz5RZmam4uLiQnnYAbN06VKVlZW5nzudTmVlZam2tnbAbhfS9VtNXd0hn7/V9Ldvs6tNBb8+3Ty58xe9m1O9nTPQfc04Z3/CFW+gou11dt3X27fjDz6q7fUtVwps4GikXZdwMeOc4RLo71//x/1yX2/GlP7Zz4h9289rvHcc7vbUMAxd98edeqOP1lNfzvm1rOFaf0NB3++ZHufsPG9fY1B9eY8Gul+klWbp/Pz2RUjfaTk5OaqurtaECRNCediApaamKj4+Xg0NDd2WNzQ0KD09vdf2iYmJSkxM7LU8JSVlwBKhQV36X1NShvn1R8LbvoNcbe6mzZSUlF7rvJ0z0H3NOGd/whVvoKLtdXbdNy11RK9xD516rgtG13MOGjJUg7r8ER4U9+U5Bw1J0qAQzazz9n8ULt7OacbsuP7O6e0D19t1GRTXHvD/7TDDUMG5Z2p3P2N2Oo/vL2/7TR03QmlfGeHX79LGJcV9jqfrHDez51dzvI6bCSS5sPexPND3aLje25EipK/GMIxQHi5oCQkJys/PV2VlpebOnStJ6ujoUGVlpRYvXmxucAD85m3moz+zdiJ92n3Pga7BTNMONKHxdk7DkK5Zu117D/U/DqO/SR/+sNlsevzHRf0mF94G5Qa6XyBJic1m6zeOaJjYEuuzHSP7fz8EysrKVFJSoqlTp6qgoEAVFRVqampyzyJD9In1NyW6Sxocr6njRvTbCtCXaKydFUjCl5OR8kXC1315KBKaUCYz7mMGeGPacCYXA5WUmPU3jL+dnoX0it9xxx0aOXJkKA8ZtPnz5+vIkSNavny56uvrlZeXp82bN/caQA0gMgXaChBttbOCTfj2HnJq4grvZTlCndB4S74GuhhooB/yJAcIaSLUdZp6JFm8eDFdYYAH/nbBmFUPKNhWgGh4nYEmfP50U/XFU0ITqmQmGrp+YG38dgIWFkgXTDSKltcZaMK36acXeK1WH2xC428yQysLogmJECyFP9DBd8FIgY/vGEix9Dr7+731JYHqPI6vCQ3vFVgFiRAQg7x9iIVi5k2k1QzxxCqvE0BwSIQAC4qVab39scrr9IaWHcC7kL37m5ubdfDgQblcrm7Lp0yZEqpTAAMmlHVcrIIPXADRKOhE6MiRI1qwYIH+9re/eVzf3s5dpxF9QlW4LxgkFv3j/whAsIJOhG6++WZ9/vnn2rFjh6ZPn66nnnpKDQ0Nuuuuu/TAAw+EIkaEWCinEvv6QRQN05fDVbgv0qsYA4CVBf0X+eWXX9bTTz+tqVOnKi4uTuPGjdN3v/tdpaSkaPXq1Zo9m29rkcaMqcTRMH3ZKoX7QEsSgC8FfZv4pqYmjR49WpI0YsQIHTlyRJI0efJk7dmzJ9jDI0Q6WzuC4e9UYjPOGazOwbWeHp16rzN/ejUAIDBBtwidd955eu+995Sdna3c3Fz953/+p7Kzs7V27VplZGSEIkaEgBlTiZm+DACIdEEnQj/72c906NAhSdKKFSt06aWX6tFHH1VCQoLWrVsX7OERQmZMJWb6MgAgkgX96fOjH/3I/XN+fr4+/vhj7d+/X2PHjlVqamqwhwcAAAiboMcIrVq1Ss3Nze7nycnJ+vrXv66hQ4dq1apVwR4eAAAgbIJOhFauXKkTJ070Wt7c3KyVK1cGe3gAA6hzNtVH98ymuxKAJQSdCBmG4XEw65tvvqmRI0cGe3gAAICwCfgr34gRI2Sz2WSz2XTuued2S4ba29t14sQJ/fjHPw5JkAAAAOEQcCJUUVEhwzC0cOFCrVy5Una73b0uISFB2dnZKioqCkmQAAAA4RBwIlRSUiJJGj9+vL75zW9q8ODBIQsKAABgIAQ9GvKiiy5y/3zy5Mled59PSUkJ9hQAAABhEfRg6ebmZi1evFijR4/W0KFDNWLEiG4PAACASBV0InTrrbfq5Zdf1u9//3slJibqD3/4g1auXKnMzEytX78+FDECUaPZ1a5mV1uvx5fre67rffsRAMDACbpr7Nlnn9X69es1ffp0LViwQBdeeKHOPvtsjRs3To8++qh++MMfhiJOICr0dxf6zvurAQAiQ9AtQseOHdOECRMknR4PdOzYMUnSBRdcoG3btgV7+D79+te/1je/+U0lJydr+PDhHrc5ePCgZs+ereTkZI0ePVq33nqr2traPG4LBCppcLymjguuG3jquBFKGsxd7AFgoAXdIjRhwgTV1NRo7NixOv/88/WXv/xFBQUFevbZZ/tMUELB5XLpmmuuUVFRkf74xz/2Wt/e3q7Zs2crPT1dr732mg4dOqTrrrtOgwcP1t133x22uGA9NptNj/+4SC2nPHdzNbva3C1Bu++82GPF5qTB8R4LkwIAwivoRGjBggV68803ddFFF6m8vFxz5szRQw89pFOnTmnNmjWhiNGjztt39HWH+xdffFF79+7Vli1blJaWpry8PP3qV7/S7bffrl/+8pdKSEjotU9ra6taW1vdz51OZ1hiR+yx2Ww+3ZIiOWEQt64AgAgS9F/kJUuWuH8uLi7W/v37VVVVpbPPPltTpkwJ9vAB2759uyZPnqy0tDT3spkzZ+qmm27Su+++q6997Wu99lm9ejX3RwMAwEJC/tV03LhxGjduXKgP67f6+vpuSZAk9/P6+nqP+yxdulRlZWXu506nU1lZWeELElGj82akAIDYEtRg6Y6ODj388MP6l3/5F02aNEmTJ0/W5ZdfrvXr18swDL+PV15e7r5/WV+P/fv3BxOyV4mJiUpJSen2AAAAsSvgFiHDMHT55Zfr+eefV25uriZPnizDMLRv3z5df/31evLJJ7Vx40a/jnnLLbfo+uuv97pN5wy1/qSnp2vnzp3dljU0NLjXAQAABJwIrVu3Ttu2bVNlZaVmzJjRbd3LL7+suXPnav369bruuut8PuaoUaM0atSoQEPqpqioSL/+9a91+PBhjR49WpL00ksvKSUlRTk5OSE5BwAAiG4Bd4099thjuuOOO3olQZL0ne98R+Xl5Xr00UeDCs6bgwcPqrq6WgcPHlR7e7uqq6tVXV2tEydOSJIuueQS5eTk6Nprr9Wbb76pF154QXfeeadKS0uVmJgYtrgAAED0CLhF6K233tJ9993X5/pZs2bpwQcfDPTw/Vq+fLn+9Kc/uZ93zgJ75ZVXNH36dMXHx+u5557TTTfdpKKiIg0dOlQlJSVatWpV2GIyGwN6AQDwT8CJ0LFjx3rNyuoqLS1N//znPwM9fL/WrVvXZw2hTuPGjdPzzz8fthgAAEB0C7hrrL29XYMG9Z1HxcfHczsLAAAQ0YKaNXb99df3Od6ma4VmAACASBRwIlRSUtLvNv7MGAMAABhoASdCjzzySCjjAAAAGHDc/THCMPMLAICBQyIEU1gp4bPSawWAaBPUvcYAAACiGYkQAACwLBIhAABgWSRCAADAskiEAACAZZEIAQAAy2L6PJjeDQCwLFqEAACAZZEIAQAAyyIRAgAAlkUiBAAALIvB0l4YhiFJcjqdJkcCAAB81fm53fk57g2JkBfHjx+XJGVlZZkcCQAA8Nfx48dlt9u9bmMzfEmXLKqjo0N1dXUaNmyYbDZbSI/tdDqVlZWl2tpapaSkhPTYCA+uWfThmkUfrll0irTrZhiGjh8/rszMTMXFeR8FRIuQF3FxcRozZkxYz5GSkhIRvzTwHdcs+nDNog/XLDpF0nXrryWoE4OlAQCAZZEIAQAAyyIRMkliYqJWrFihxMREs0OBj7hm0YdrFn24ZtEpmq8bg6UBAIBl0SIEAAAsi0QIAABYFokQAACwLBIhAABgWSRCJnA4HMrOztaQIUNUWFionTt3mh0SvPjlL38pm83W7XH++eebHRa62LZtm+bMmaPMzEzZbDZt3Lix23rDMLR8+XJlZGQoKSlJxcXFev/9980JFpL6v2bXX399r/fdpZdeak6wkCStXr1a06ZN07BhwzR69GjNnTtX7733XrdtTp48qdLSUn3lK1/RGWecoauuukoNDQ0mRewbEqEBtmHDBpWVlWnFihXas2ePcnNzNXPmTB0+fNjs0ODFxIkTdejQIffj//7v/8wOCV00NTUpNzdXDofD4/r77rtPDz74oNauXasdO3Zo6NChmjlzpk6ePDnAkaJTf9dMki699NJu77vHHntsACNET1u3blVpaalef/11vfTSSzp16pQuueQSNTU1ubdZsmSJnn32WT3++OPaunWr6urqNG/ePBOj9oGBAVVQUGCUlpa6n7e3txuZmZnG6tWrTYwK3qxYscLIzc01Owz4SJLx1FNPuZ93dHQY6enpxv333+9e9vnnnxuJiYnGY489ZkKE6KnnNTMMwygpKTGuuOIKU+KBbw4fPmxIMrZu3WoYxun31eDBg43HH3/cvc2+ffsMScb27dvNCrNftAgNIJfLpaqqKhUXF7uXxcXFqbi4WNu3bzcxMvTn/fffV2ZmpiZMmKAf/vCHOnjwoNkhwUc1NTWqr6/v9r6z2+0qLCzkfRfhXn31VY0ePVrnnXeebrrpJn322Wdmh4QuGhsbJUkjR46UJFVVVenUqVPd3mvnn3++xo4dG9HvNRKhAXT06FG1t7crLS2t2/K0tDTV19ebFBX6U1hYqHXr1mnz5s36/e9/r5qaGl144YU6fvy42aHBB53vLd530eXSSy/V+vXrVVlZqXvvvVdbt27VrFmz1N7ebnZokNTR0aGbb75Z3/rWtzRp0iRJp99rCQkJGj58eLdtI/29xt3ngX7MmjXL/fOUKVNUWFiocePG6S9/+YtuuOEGEyMDYtf3vvc998+TJ0/WlClTdNZZZ+nVV1/VxRdfbGJkkKTS0lK98847MTFekhahAZSamqr4+PheI+gbGhqUnp5uUlTw1/Dhw3XuuefqwIEDZocCH3S+t3jfRbcJEyYoNTWV910EWLx4sZ577jm98sorGjNmjHt5enq6XC6XPv/8827bR/p7jURoACUkJCg/P1+VlZXuZR0dHaqsrFRRUZGJkcEfJ06c0AcffKCMjAyzQ4EPxo8fr/T09G7vO6fTqR07dvC+iyKffPKJPvvsM953JjIMQ4sXL9ZTTz2ll19+WePHj++2Pj8/X4MHD+72Xnvvvfd08ODBiH6v0TU2wMrKylRSUqKpU6eqoKBAFRUVampq0oIFC8wODX34+c9/rjlz5mjcuHGqq6vTihUrFB8fr+9///tmh4YvnDhxoltLQU1NjaqrqzVy5EiNHTtWN998s+666y6dc845Gj9+vJYtW6bMzEzNnTvXvKAtzts1GzlypFauXKmrrrpK6enp+uCDD3Tbbbfp7LPP1syZM02M2tpKS0v13//933r66ac1bNgw97gfu92upKQk2e123XDDDSorK9PIkSOVkpKin/zkJyoqKtI3vvENk6P3wuxpa1b029/+1hg7dqyRkJBgFBQUGK+//rrZIcGL+fPnGxkZGUZCQoJx5plnGvPnzzcOHDhgdljo4pVXXjEk9XqUlJQYhnF6Cv2yZcuMtLQ0IzEx0bj44ouN9957z9ygLc7bNWtubjYuueQSY9SoUcbgwYONcePGGYsWLTLq6+vNDtvSPF0vScYjjzzi3qalpcX4t3/7N2PEiBFGcnKyceWVVxqHDh0yL2gf2AzDMAY+/QIAADAfY4QAAIBlkQgBAADLIhECAACWRSIEAAAsi0QIAABYFokQAACwLBIhAABgWSRCAADAskiEAACAZZEIAQAAyyIRAgAAlkUiBMBSjhw5ovT0dN19993uZa+99poSEhJUWVlpYmQAzMBNVwFYzvPPP6+5c+fqtdde03nnnae8vDxdccUVWrNmjdmhARhgJEIALKm0tFRbtmzR1KlT9fbbb2vXrl1KTEw0OywAA4xECIAltbS0aNKkSaqtrVVVVZUmT55sdkgATMAYIQCW9MEHH6iurk4dHR366KOPzA4HgEloEQJgOS6XSwUFBcrLy9N5552niooKvf322xo9erTZoQEYYCRCACzn1ltv1V//+le9+eabOuOMM3TRRRfJbrfrueeeMzs0AAOMrjEAlvLqq6+qoqJCf/7zn5WSkqK4uDj9+c9/1v/+7//q97//vdnhARhgtAgBAADLokUIAABYFokQAACwLBIhAABgWSRCAADAskiEAACAZZEIAQAAyyIRAgAAlkUiBAAALItECAAAWBaJEAAAsCwSIQAAYFn/HyQcN/iegfiTAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.plot_fit_resid('pdf', ylog=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One point of fitting the PDF was to see what the errors on the parameters are (note that due to some oddity of the IPython notebook the \"lower\" and \"upper\" bound messages, which are displayed as the fit runs, and should appear before the table, are in fact displayed last here):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pdf.theta lower bound:\t-0.139882\n",
      "pdf.k lower bound:\t-0.053818\n",
      "pdf.theta upper bound:\t0.152128\n",
      "pdf.k upper bound:\t0.055068\n",
      "Dataset               = pdf\n",
      "Confidence Method     = confidence\n",
      "Iterative Fit Method  = None\n",
      "Fitting Method        = neldermead\n",
      "Statistic             = cash\n",
      "confidence 1-sigma (68.2689%) bounds:\n",
      "   Param            Best-Fit  Lower Bound  Upper Bound\n",
      "   -----            --------  -----------  -----------\n",
      "   pdf.k             1.11627    -0.053818     0.055068\n",
      "   pdf.theta         2.55127    -0.139882     0.152128\n"
     ]
    }
   ],
   "source": [
    "ui.conf('pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As well as the individual errors, let's look at how they are correlated (the contours\n",
    "give the one, two, and three sigma ranges, and the cross is the best-fit location). I have\n",
    "increased the number of points used in this plot since the evaluation is quick (as there\n",
    "are no free parameters beyond ``k`` and ``theta``).\n",
    "\n",
    "I'll repeat this plot later on, adding on the actual values and the results from the CDF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.reg_proj(pdf.k, pdf.theta, id='pdf', nloop=[41,41])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Trying out the \"non-integrated\" case"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `GammaPDF` model was written to work with both integrated and non-integrated data, so let's see what happens when the latter is used. In this case, I use the same y values but place them at the mid-point of each bin:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset               = check\n",
      "Method                = neldermead\n",
      "Statistic             = cash\n",
      "Initial fit statistic = 11348.9\n",
      "Final fit statistic   = -6922.62 at function evaluation 613\n",
      "Data points           = 31\n",
      "Degrees of freedom    = 28\n",
      "Change in statistic   = 18271.6\n",
      "   pdf2.k         1.13434     \n",
      "   pdf2.theta     2.52724     \n",
      "   pdf2.norm      664.083     \n"
     ]
    }
   ],
   "source": [
    "ui.load_arrays('check', (xlo+xhi)/2, ypdf)\n",
    "ui.set_source('check', gammapdf.pdf2)\n",
    "ui.fit('check')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, the results aren't too different - apart from the fact that the normalisation is lower than the \"expected\" value of 1000 (as I'm approximating a binned distribution with an un-binned one I wanted to see what happened to the `norm` parameter, which is why I did not fix it).\n",
    "\n",
    "The fit looks reasonable (but again, remember that the error bars should not be taken too seriously):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING: The displayed errorbars have been supplied with the data or calculated using chi2xspecvar; the errors are not used in fits with cash\n",
      "WARNING: The displayed errorbars have been supplied with the data or calculated using chi2xspecvar; the errors are not used in fits with cash\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ui.plot_fit_resid('check')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How about the errors?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pdf2.theta lower bound:\t-0.145103\n",
      "pdf2.norm lower bound:\t-20.8802\n",
      "pdf2.k lower bound:\t-0.0613981\n",
      "pdf2.theta upper bound:\t0.159716\n",
      "pdf2.norm upper bound:\t21.3042\n",
      "pdf2.k upper bound:\t0.0626481\n",
      "Dataset               = check\n",
      "Confidence Method     = confidence\n",
      "Iterative Fit Method  = None\n",
      "Fitting Method        = neldermead\n",
      "Statistic             = cash\n",
      "confidence 1-sigma (68.2689%) bounds:\n",
      "   Param            Best-Fit  Lower Bound  Upper Bound\n",
      "   -----            --------  -----------  -----------\n",
      "   pdf2.k            1.13434   -0.0613981    0.0626481\n",
      "   pdf2.theta        2.52724    -0.145103     0.159716\n",
      "   pdf2.norm         664.083     -20.8802      21.3042\n"
     ]
    }
   ],
   "source": [
    "ui.conf('check')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I could try fixing the normalization - to 1000 - and fitting again, but this is enough of\n",
    "a digression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing the answers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The point of this notebook is to give examples of how to write a user model in Sherpa, not\n",
    "what the best way to fit a Gamma distribution is, but let's just compare the results. I start\n",
    "with the region-projection plot shown earlier (Sherpa has cached the results for us so we do not need to recalculate it). Then I add on horizontal and vertical lines to show the true\n",
    "values (i.e. the `k_orig` and `theta_orig` values), and then two green points:\n",
    "\n",
    " - the filled circle shows the fit to the CDF\n",
    " - the filled triangle shows the fit to the \"unbinned\" PDF (i.e. the \"check\" data set)\n",
    "\n",
    "As can be seen, all values are within the one-sigma contour of the PDF fit, but the\n",
    "CDF result - which has no error associated with it - is actually closer to the expected value. Now, this is only one data set, so if you really want to investigate this you would have to run a large number of simulations. However, that would be the topic for another post!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rplot = ui.get_reg_proj()\n",
    "rplot.contour()\n",
    "plt.xlabel('$k$')\n",
    "plt.ylabel('$\\\\theta$')\n",
    "\n",
    "xr = plt.xlim()\n",
    "yr = plt.ylim()\n",
    "plt.vlines(k_orig, yr[0], yr[1], linestyles='dotted')\n",
    "plt.hlines(theta_orig, xr[0], xr[1], linestyles='dotted')\n",
    "\n",
    "plt.plot(cdf.k.val, cdf.theta.val, 'go')\n",
    "plt.plot(pdf2.k.val, pdf2.theta.val, 'g^');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}