{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Adding two Gaussians\n",
    "======================"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--------------------- Parameter summary ------------------------\n",
      "      A_GF(1) =            0, free: F, restricted: F, related: F\n",
      "     mu_GF(1) =            0, free: F, restricted: F, related: F\n",
      "    sig_GF(1) =            0, free: F, restricted: F, related: F\n",
      "    off_GF(1) =            0, free: F, restricted: F, related: F\n",
      "    lin_GF(1) =            0, free: F, restricted: F, related: F\n",
      "      A_GF(2) =            0, free: F, restricted: F, related: F\n",
      "     mu_GF(2) =            0, free: F, restricted: F, related: F\n",
      "    sig_GF(2) =            0, free: F, restricted: F, related: F\n",
      "    off_GF(2) =            0, free: F, restricted: F, related: F\n",
      "    lin_GF(2) =            0, free: F, restricted: F, related: F\n",
      "----------------------------------------------------------------\n",
      "--------------------- Parameter summary ------------------------\n",
      "      A_GF(1) =      1.02055, free: T, restricted: F, related: F\n",
      "     mu_GF(1) =    0.0202002, free: T, restricted: F, related: F\n",
      "    sig_GF(1) =      1.01276, free: T, restricted: F, related: F\n",
      "    off_GF(1) =            0, free: F, restricted: F, related: F\n",
      "    lin_GF(1) =            0, free: F, restricted: F, related: F\n",
      "      A_GF(2) =      1.97874, free: T, restricted: F, related: F\n",
      "     mu_GF(2) =      3.00805, free: T, restricted: F, related: F\n",
      "    sig_GF(2) =     0.982554, free: T, restricted: F, related: F\n",
      "    off_GF(2) =            0, free: F, restricted: F, related: F\n",
      "    lin_GF(2) =            0, free: F, restricted: F, related: F\n",
      "----------------------------------------------------------------\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import print_function, division\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "# ... and now the funcFit package\n",
    "from PyAstronomy import funcFit2 as fuf2\n",
    "import scipy.optimize as sco\n",
    "\n",
    "np.random.seed(1234)\n",
    "\n",
    "# Instantiate Gaussian model objects\n",
    "gf1 = fuf2.GaussFit()\n",
    "gf2 = fuf2.GaussFit()\n",
    "# Sum the models (refers to their 'evaluate' methods)\n",
    "# Any of +-*/ and ** can be used\n",
    "gf = gf1 + gf2\n",
    "\n",
    "gf.parameterSummary()\n",
    "\n",
    "gf[\"A_GF(1)\"] = 1\n",
    "gf[\"A_GF(2)\"] = 2\n",
    "gf[\"mu_GF(1)\"] = 0.0\n",
    "gf[\"mu_GF(2)\"] = 3.0\n",
    "gf[\"sig_GF(1)\"] = 1.0\n",
    "gf[\"sig_GF(2)\"] = 1.0\n",
    "\n",
    "# Evaluate model and add noise\n",
    "x = np.linspace(-4., 6., 200)\n",
    "y = gf.evaluate(x) + np.random.normal(0, 0.02, len(x))\n",
    "\n",
    "# Re-fit model\n",
    "# Use filename-like pattern matching to thaw parameters\n",
    "gf.thaw([\"A_*\", \"sig_*\", \"mu_*\"])\n",
    "fuf2.fitfmin_l_bfgs_b(gf, gf.chisqr, x, y, yerr=0.02)\n",
    "\n",
    "gf.parameterSummary()\n",
    "\n",
    "plt.errorbar(x, y, yerr=0.02, fmt=\"b+\", alpha=0.5)\n",
    "plt.plot(x, gf.evaluate(x), 'r--', lw=2)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}