{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Surface radiation field tools"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this tutorial we demonstrate usage of several tools for checking the implementation of a surface radiation field extension module."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The required atmosphere data files are needed and they can be found in the [Zenodo](https://zenodo.org/record/7094144)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(action='ignore')\n",
    "import numpy as np\n",
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/=============================================\\\n",
      "| X-PSI: X-ray Pulse Simulation and Inference |\n",
      "|---------------------------------------------|\n",
      "|                Version: 2.2.2               |\n",
      "|---------------------------------------------|\n",
      "|      https://xpsi-group.github.io/xpsi      |\n",
      "\\=============================================/\n",
      "\n",
      "Imported GetDist version: 1.4.7\n",
      "Imported nestcheck version: 0.2.1\n"
     ]
    }
   ],
   "source": [
    "import xpsi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "plt.rc('font', size=20.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate the specific intensity directly from local variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# keV (local comoving frame)\n",
    "E = np.logspace(-2.0, 0.5, 1000, base=10.0)\n",
    "\n",
    "# cos(angle to local surface normal in comoving frame)\n",
    "mu = np.ones(1000) * 0.5\n",
    "\n",
    "# log10(eff. temperature [K]) and log10(local eff. gravity [cm/s^2])\n",
    "local_vars = np.array([[6.11, 13.8]]*1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#xpsi.surface_radiation_field?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "#xpsi.surface_radiation_field.intensity?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Isotropic blackbody"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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prx6RFJSfn8/Xv/51Pv/8c3r16sWrr75Kq1atwi5Lkpx6LqRCX331Ffn5+bz99tvMmDGD2bNns3fvkTfctGzZ8ojxEj169NDgS5E0UDSz57nnnsvixYsZOHAgr732Gr169Qq7NElRChcZ6uDBg7z33nvFYWLOnDlHrRLapUsXhg4dWjxmol27dpo+WCRNtW/fntmzZzN69Ghmz57NkCFDePHFFxk2bFjYpUkK0mWROEiFyyIHDhzg3XffLQ4T77777lG3hXbv3p1hw4YxbNgwTj/9dC12JJKBDhw4wOWXX85zzz1H3bp1eeGFFzjnnHPCLkuSkO4WSbBkDBf79u1j7ty5xWFi3rx5R60U2rNnT4YPH14cJrTmgIhAMHvu9773Pf72t7+Rm5vLM888w+jRo8MuS5KMxlxkgD179jBnzpziMDF//nwOHfrvavFmRp8+fYrDxNChQ7XkuIiUKjs7m0ceeYR69eoxceJELrjgAp588kkuvvjisEuTFKFwkaJ27drF7Nmzi8PEggULOHz4cPH5rKws+vXrd0SY0EqhIlJZWVlZ3H///dSvX5/f//73XHrppWRlZXHhhReGXZqkAIWLFPHll1/yzjvvFIeJhQsXUlhYvGYb2dnZnHrqqQwbNozhw4czZMgQ3asuItViZtx1113Url2bCRMmcOmll1K7dm1dIpEKKVwkqe3btzNr1izefvtt3n77bd5//32ix8fk5OTQv3//4gGYgwcPplGjRiFWLCLpyMy44447OHDgAHfffTcXXnghU6ZMYdSoUWGXJklM4SLJzJ49mxtuuIEPP/zwiDBRq1atI8LEaaedptVCRaRGmBm/+93v2L9/Pw888ADnn38+r776KiNGjAi7NElSChdJpmnTpnzwwQfk5uYycODA4jAxaNAg6tWrF3Z5IpKhzIz77ruPgwcP8pe//IXRo0czc+ZM+vbtG3ZpkoQULpJM165defvttzn11FOpW7du2OWIiBQzMyZNmsTOnTt5+umnOffcc5kzZw7t27cPuzRJMpq7OcmYGaeffrqChYgkpaysLCZPnsyIESP47LPPGDVqFNu2bQu7LEkyChciIhKT2rVr88ILL9C7d29WrFjB17/+dfbt2xd2WZJEFC5ERCRmjRs35rXXXqNt27bMmzePK6+88ojb4yWzKVyIiEiVtGjRgtdee41GjRrx3HPPMWHChLBLkiShcCEiIlXWrVs3/vWvf5GVlcWdd97Jv/71r7BLkiSgcCEiItUyatQo/vSnPwFw1VVXkWwLOUrNU7gQEZFqu/HGG7nmmms4cOAAo0eP5rPPPgu7JAmRwoWIiFSbmfHggw8yZMgQNm/ezCWXXHLEYoqSWRQuREQkLnJzc3nmmWc4/vjjmTFjBrfffnvYJUlIFC5ERCRuTjzxRJ555hmys7O5++67mTJlStglSQgULkREJK5OP/10fv/73wNw5ZVXsmrVqpArkpqmcCEiInF38803861vfYudO3dy4YUXcvDgwbBLkhqkcCEiInFnZjz22GO0b9+e999/X+MvMozChYiIJETjxo35xz/+QXZ2Nn/84x954403wi5JaojChYiIJMygQYMYP348AFdccQVbt24NtyCpEQoXIiKSULfddhtDhw7ls88+4+qrr8bdwy5JEkzhQkREEio7O5snn3ySY445hpdffpm//OUvYZckCaZwISIiCdemTRsefvhhAG699VbWrVsXbkGSUAoXIiJSIy666CLGjh3Lnj17+O53v0thYWHYJUmCKFyIiEiNmTRpEs2aNWP69OnFPRmSfhQuRESkxjRr1oxJkyYB8NOf/pS1a9eGXJEkgsKFiIjUqLFjx3LRRRexd+9err76al0eSUMKFyIiUuP+/Oc/06xZM2bMmMHkyZPDLkfiTOFCRERq3HHHHcd9990HwC233MKWLVvCLUjiSuFCRERCcckll3DWWWexY8cObrnllrDLkThSuBARkVCYGQ899BB16tTh//7v/5g2bVrYJUmcKFyIiEhoOnbsyP/+7/8CcP3113PgwIGQK5J4ULgQEZFQ3XLLLXTv3p1Vq1Zx1113hV2OxIHChYiIhCo3N7d4vZE//OEPmvsiDShciIhI6IYMGcKll17KwYMHufnmm8MuR6pJ4UJERJLC3XffTf369XnhhRd48803wy5HqkHhQkREkkLLli355S9/CcCNN97IoUOHQq5IqkrhQkREksZNN91Ex44d+eijj3jooYfCLkeqSOFCRESSRp06dbjnnnsA+NWvfsXWrVtDrkiqQuFCRESSyje+8Q3OOeccdu7cyZ133hl2OVIFChciIpJUzIw//vGPZGVl8fDDD7Nq1aqwS5IYKVyIiEjS6dmzJ1deeSWHDx/mF7/4RdjlSIwqHS7M7Hwzy05kMSIiIkXuvPNO6tSpw7PPPsu8efPCLkdiEEvPxfPAejO708zaJKogERERgFatWnHTTTcB8NOf/hR3D7kiqaxYwsUkoB5wO7DazF4ys6+bmSWmNBERyXQ/+9nPaNq0KTNnzuTll18OuxyppEqHC3f/IdACuBrIB74GTCHozfiVmbVMTIkiIpKpGjduzK9+9SsgCBoFBQUhVySVEdOATnc/4O6T3X0Q0Bt4CGgAjAfWmtkLZjYq/mWKiEimuv7662nfvj3Lli3jqaeeCrscqYQq3y3i7kuiejPGAZ8D3wReMbO1ZnaLmdWPU50iIpKhcnNzi3svJkyYwOHDh0OuSCpSrVtRI+HhCuDHQEvAgA+ApsAfgI/NrG81axQRkQx32WWX0blzZ1atWsUTTzwRdjlSgSqFCzM72cweBjYDDwNdgL8C/dy9H0Fvxs+B44AH4lSriIhkqJycHO644w4Afv3rX/PVV1+FXJGUJ5Z5LuqZ2XfN7D2CAZ3XARuBG4GW7n6duy8CcPc97v4HgsCRF/+yRUQk01x88cV0796ddevW8fjjj4ddjpQjlp6LzcAjQF+COS9GunsPd5/o7rvKeM4moE71ShQREYHs7GzGjx8PwG9+8xsOHDgQbkFSpljCxW6Cu0LauPuF7j6jEs+ZBLSvQl0iIiJHueCCC+jduzcbN27k0UcfDbscKUMs4aKtu//a3T+r7BPcfZe7r69CXSIiIkfJysoq7r34wx/+oLEXSSqWcPGmmV1RXgMzu8zMplezJhERkTKNHj2aHj16sHHjRt05kqRiCRfDgXYVtGkLDKtqMSIiIhXJysoqXin197//vea9SELxXnK9LqD/lUVEJKEuvPBCOnbsyOrVq3n22WfDLkdKiDVclLoknQXaAucBn1S7KhERkXLk5OTws5/9DIC77rqLwsLCkCuSaOWGCzMrNLMCMytaKWZ80ePojaC3Yg3BbapPJ7ZkERERuOKKK2jZsiVLlizRiqlJpqKei5lRmwMbShwr2t4CngOuB36VqGKrysxuM7P5ZrbLzLZGlovvWaLNOjPzUrZXwqpbRETKVrt2bW699VYAfvvb3+Jeaue6hMAq+z+GmRUC4939zsSWFH9m9jpBj8p8gvVP7gQGAd3dfXukTTMgO+ppJwILgHHu/vfyXj8vL8/z8/MTUbqIiJRj3759tG3blm3btjFt2jRGjhwZdkkZw8wWuHups3DHMuaiPXB/fEqqWe5+jrs/HlnJdTFwOdAMGBzVZqu7f1a0EYwf2QVopJCISJKqV68eN954IwB/+tOfQq5GilQ6XLj7enffmYgizGysmU00s1mRSxduZk9W8JxWZvaYmW02s4ORyxr3mVmTSrxlQ4LPvqOM1zbgu8CT7r4v5g8kIiI15vvf/z5169bl1VdfZdmyZWGXI0BOWSfM7FcE4ywedPftkceV4e7+6xjruB3oA+whWAztpPIam1lHYA7QHJgCfAz0J1hEbZSZDXb3L8p5ifuBRcDcMs6fRdBT89fKfwQREQlD06ZNueqqq3jooYe45557NC14EihzzEVkjIUD3dx9ReRxZbi7Z1fc7Ij3GkEQKlYRTML1FvAPd7+sjPavA2cDP3b3iVHH7wFuAv7i7teX8dx7gIuBIe6+pow2zxJMd96/MvVrzIWISLhWrFjBSSedRG5uLuvXr+f4448Pu6S0V9UxFyOAkQR3iBQ9rswW82gad3/L3Vd6JUaXmlkHgmCxDniwxOk7gL3A5WZWv5Tn3gtcQrCia1nBojkwGlD0FRFJEV26dOEb3/gGBw8eZNKkSWGXk/HKvCzi7m+X9zhEReFlqrsf0Zvi7rvNbDZB+BgITCs6Z2b3E/RYDHf3j8t5/auAg2i+DhGRlHLzzTfz4osvMmnSJH7+859Tt27dsEvKWPGe/rsmdI3sV5RxfmVk36XogJk9CIwj6LXYYWYnRLYG0U+MDOS8Bnja3XfHt2wREUmkoUOHkpeXx7Zt27SgWcgqHS7MrJ2ZnRd9ucHMcsxsgpl9YGZzzOz8xJR5hMaRfVl3rhQdPybq2A8I7hCZBnwatd1S4rnDgc5U4pKImV1nZvlmlr9169ZKFS4iIoljZtx8880A3HvvvZoSPESx9FzcAfwfwSWDIrcD/wv0IrgM8YyZDYxfeVVikX3x+A13tzK28dFPjIz9MHd/r6I3cfdH3D3P3fOaNWsW308gIiJVMnbsWFq1asXy5ct58803wy4nY8USLgYB09z9MICZZRH0CHwMtCG4FXQvwd0aiVTUM9G4jPONSrQTEZEMkZOTw/e//30A/vznP4dcTeaKJVwcD6yPetwXOI5gHoyN7p5PMOfEqfErr1TLI/suZZzvHNmXNSZDRETS2DXXXENubi4vv/wya9euDbucjBRLuKjFkUuuD448nh51bCPBmhyJ9FZkf3ak96SYmTWM1LUfeDfBdYiISBJq3rw5F154Ie7Oww8/HHY5GSmWcLER6B31+Dxgm7tHz7XanGA9joRx99XAVKAdcEOJ0xOA+sAT7r43kXWIiEjy+uEPfwjAX//6V/bv3x9yNZmnzHkuSvEycJOZ/RE4QDBF9uMl2pzEkZdOKsXMxgBjIg9PiOwHmdnkyL+3uXv0nR0/IJj++wEzOwNYBgwgmMRrBfDLWGsQEZH00b9/f/Ly8sjPz+fpp59m3LhxYZeUUWLpufgDsBb4CfALgls57yg6aWZtgdOAmVWooy9wZWQ7J3KsQ9SxsdGNI70XecBkglBxM9AReAAYVMG6IiIikubMrLj3YuLEiVRiAmiJozLXFim1sVld4IzIw7ejJ5oysx7AmcDrFcyAmXa0toiISPI5cOAArVq14osvvmDOnDkMGjQo7JLSSlXXFjmKu+9395cj2+4S55a6+/2ZFixERCQ51alTh2uvvRZA643UsFSc/ltERKRSrrvuOgCeffZZtm/fHnI1mSOmcGFmx5rZLWb2jJm9YWbTS9mmVfxKIiIiide+fXvOOussDh48yJNPPhl2ORmj0neLmNlJwAygGf+dYrs0GjUjIiJJ49prr+WNN97g0Ucf5Uc/+hHBGpWSSLH0XPyRYB6Luwnu5Kjl7lmlbNkJqVRERKQKRo8eTbNmzViyZAnz5s0Lu5yMEEu4GAq84u6/cPd17l6QqKJERETiJTc3l6uuugqARx+tcNFriYNYwoUBHyWqEBERkUS55pprAHj66afZtSuhE0kLsYWLBUDXRBUiIiKSKF26dGHYsGHs27ePf/7zn2GXk/ZiCRd3AueZ2fDElCIiIpI4Rbel6tJI4sWytkhrgiXVp5rZUwQ9GV+W1tDdn6h+aSIiIvHzrW99i2OPPZaFCxeycOFC+vXrF3ZJaSuWcDGZ4DZTAy6PbCVvO7XIMYULERFJKnXq1OHSSy9l4sSJTJ48WeEigSq9toiZXVnZF3X3v1e5ohSktUVERFLDggULyMvLo2nTpmzevJnc3NywS0pZ5a0tUumei0wLDCIikn769etHz549WbJkCa+++ipjxowJu6S0pLVFREQkY5gZV14ZdMT//e/6mzlRYg4XZtbMzK43s/vN7K8ljvePLMsuIiKSlC699FKysrJ45ZVX2LZtW9jlpKVYFy77LrAOeBD4ETAu6vTxwFzgO/EqTkREJN5OPPFEzjnnHA4dOsRTTz0VdjlpqdLhwszOAh4BVgDnAw9Fn3f3JcBSYEwc6xMREYk7XRpJrFh6Ln4GfAoMc/cXgS2ltPkQ6B6PwkRERBJl9OjRNG7cmAULFrB06dKwy0k7sYSLPOBldy9vUvaNwAnVK0lERCSx6tSpw0UXXQSo9yIRYgkXucDeCtocA2i1VBERSXpFl0aefPJJCgr0qyueYgkX64BTKmgzAFhe5WpERERqyKBBg+jYsSOffvopM2fODLuctBJLuJgCDDWzb5d20szGAb2B5+NRmIiISCKZGRdffDGAVkqNs1jCxR+ADcBTZvYvYBCAmf0w8vgRYCUwMe5VioiIJMB3vhPMnvD8889z8ODBkKtJH5UOF+6+AxgGvAN8GzibYKGyByKP5wBnuHtF4zJERESSQvfu3enduzc7duzg9ddfD7uctBHTJFruvsHdhwN9ge8DtxNMpnWquw9z901xr1BERCSBinovNKFW/FR6VVQpm1ZFFRFJXevXr6ddu3bUrVuXLVu20KBBg7BLSgnlrYoaywyda8zsxxW0ucHM1sRaoIiISFjatm3Laaedxv79+3nxxRfDLictxHJZpB3BPBblOQZoW8VaREREQlF0aUR3jcRHvJdcbwB8FefXFBERSahvf/vbZGdn8/rrr/PFF1+EXU7KKzdcmFmboi1y6JjoY1FbezMbBowFdFlERERSSvPmzTnjjDM4fPgwzz33XNjlpLyKei7WAWsjG8CNUY+jt1XAdKAj8GgiChUREUmkSy65BIBnn3025EpSX04F558AnGA+iysIVj1dVEq7AuALYJq7T41ngSIiIjVh9OjR5OTkMGPGDLZu3UqzZs3CLilllRsu3P2qon+b2RXAC+5+Z6KLEhERqWlNmjThzDPP5D//+Q///ve/ufbaa8MuKWXFMkNnloKFiIiks29/O1g+S+Muqifed4uIiIikrNGjR5Odnc20adN010g1xBQuzOxYM7vFzJ4xszfMbHop27REFSsiIpJITZs2ZeTIkRQUFGhCrWqoaEBnMTM7CZgBNCMY4FkWzScuIiIpa+zYsbzxxhs899xzjBs3LuxyUlIsPRd/BJoDdwMdgFqRcRglt+yEVCoiIlIDxowZQ1ZWFm+88QZffvll2OWkpFjCxVDgFXf/hbuvc/eCRBUlIiISlubNmzN8+HAOHTrESy+9FHY5KSmWcGHAR4kqREREJFmMHTsW0F0jVRVLuFgAdE1UISIiIsni/PPPx8x4/fXX2bVrV9jlpJxYwsWdwHlmNjwxpYiIiCSHE044gaFDh3Lw4EFee+21sMtJOZW+WwRoDUwBpprZUwQ9GV+W1tDdn6h+aSIiIuEZM2YMM2fOZMqUKVx00UVhl5NSzL1yd46aWSH/XWekSMknG+CZdsdIXl6e5+fnh12GiIjE0Zo1a+jYsSONGjVi69at5Obmhl1SUjGzBe6eV9q5WHoudLOviIhkjA4dOtCzZ0+WLFnC22+/zVlnnRV2SSmj0uHC3f+eyEJERESSzejRo1myZAlTpkxRuIiB1hYREREpw+jRowGYMmUKlR1GIAoXIiIiZTrllFNo0aIFGzduZOHChWGXkzLKDBdmtsbMVptZ+6jHldlW11z5IiIiiZOVlcU3v/lNIOi9kMopr+ciq8T5LIK7QSra1BsiIiJpI/rSiFROmQM63b1deY9FREQywYgRI2jYsCEffvgha9eupX379mGXlPTUyyAiIlKO2rVrc+655wLqvagshQsREZEK6NJIbBQuREREKnDeeeeRnZ3NrFmz+PLLL8MuJ+kpXIiIiFTgmGOOYfDgwRQUFDB16tSwy0l6ChciIiKV8LWvfQ2AV199NeRKkp/ChYiISCWcd955ALz22msUFhaGXE1yU7gQERGphB49etCmTRu2bNnCggULwi4nqSlciIiIVIKZFV8aeeWVV0KuJrlVOlyY2Rlm9piZtSjjfIvI+eHxKk5ERCSZFF0a0biL8sXSc/Ej4DR331zaycjxQZF2IiIiaWfkyJHUrl2b+fPn8/nnn4ddTtKKJVz0A+ZU0OYdIK/q5YiIiCSvevXqMWLECCAY2CmliyVcNAdK7bWI8nmknYiISFrSLakViyVc7ARaV9CmNbC36uWIiIgkt6JxF6+//jqHDh0KuZrkFEu4eA8YY2YnlHYyMtBzTKSdiIhIWurQoQMnnXQSu3btYs6cikYLZKZYwsVEoCEwy8y+aWa1AcystpmNBmYCDYAH4l+miIhI8tClkfJVOly4+1Tg10BH4AVgr5ltJbgM8v+ADsCv3f0/iShUREQkWYwaNQpA64yUIaZJtNz9DmAU8CqwHWgc2b8CnOPu4+NdoIiISLIZMmQIdevWZdGiRboltRQxz9Dp7lPd/Rvu3tzdcyP7b7r7G4koMB7M7DYzm29mu8xsq5m9ZGY9S7QZb2ZeYvssrJpFRCR51alTh2HDhgHwxhtJ++svNJky/fdwYBJwGjASOAy8aWbHlmi3HDgxautVgzWKiEgKOfvsswFdGilNTtgF1AR3Pyf6sZldTnBr7WDgpahTh91dvRUiIlKh6HBRWFhIVlam/L1esTJ/EmZWaGaHzaxL1OOCSmyHYy3CzMaa2UQzmxW5dOFm9mQFz2kVWctks5kdNLN1ZnafmTWpxFs2JPjsO0oc72Bmm8xsrZk9bWYdYv0sIiKSGbp3707Lli35/PPPWbx4cdjlJJXyei5mAg7sK/E4EW4H+gB7gI3ASeU1NrOOBFORNwemAB8D/YEbgVFmNtjdvyjnJe4HFgFzo47NA66KvFbzSE1zzKxHBa8lIiIZyMw4++yzefzxx5k6dSp9+vQJu6SkUWa4cPfh5T2Os5sIQsUqYBjwVgXtJxEEgB+7+8Sig2Z2T+S1fgtcX9oTI22GAEPcvaDouLu/VqLdu8Aa4Ergnhg/j4iIZIDocHHrrbeGXU7SKO+yyP8zswujHp9uZm0SUYS7v+XuK929wp6RyKWKs4F1wIMlTt9BMO/G5WZWv5Tn3gtcAox09zUV1LQHWAp0rtSHEBGRjHPmmWdiZsyaNYt9+/ZV/IQMUd7okzEceXniLYLLBmEbGdlPdffC6BPuvhuYDdQDBkafM7P7ge8QBIuPK3oTM6tD8Pk/jUfRIiKSfo477jj69evHwYMHmTlzZtjlJI3ywsWXQKOox5bYUiqta2S/oozzKyP7LkUHzOxBYBxBr8UOMzshsjWIavNHMxtmZu3NbADwHFAf+Htpb2Jm15lZvpnlb926tZofSUREUtU55wQ3JOqW1P8qb0DnMuASM5vPf/96b2dmp1f0ou6eyPjWOLLfWcb5ouPHRB37QWQ/rUTbCcD4yL9bAU8BxwFbgXeBge6+vrQ3cfdHgEcA8vLyEjXQVUREktzZZ5/NXXfdpXARpbxwMQH4N/DPqGNXRraKZFejpuoq6mEp/oXv7hX2urj7xQmrSERE0tagQYOoX78+S5cuZePGjbRq1SrskkJX3t0iU82sG3Am0JLgL/y3I1uYinomGpdxvlGJdiIiIgmTm5vL8OHDeeWVV5g+fTpXXHFF2CWFrtwZOiOXBP4GwdobwAx3v7MG6irP8si+Sxnni+7uKGtMhoiISFydccYZChdRYpn+ewTB7Z9hK5oD42wzy4q+Y8TMGhJM6b2fYMyEiIhIwo0cGdzIOH36dNwds2S5ByIclZ4I3d3fLmtwY01y99XAVKAdcEOJ0xMI7vB4wt331nBpIiKSoXr16kXTpk355JNPWLVqVdjlhK7MngszK+rXecHdd0c9rpC7PxFLEWY2hmBeDYATIvtBZjY58u9t7n5L1FN+QDD99wNmdgbBnS0DCHpXVgC/jOX9RUREqiMrK4sRI0bw3HPPMX36dDp3zuz5F8u7LDKZ4I6Ld4HdUY/LY5E2MYULoC9H34XSIbIBrAeKw4W7rzazPOBOYBRwHsHtsg8AE9x9e4zvLyIiUi1nnHFGcbj43ve+F3Y5oSovXFxNEBSK5rgYl6gi3H08/51vorLP+YQE1iQiIhKLonEXb731VsYvwV7eraiTSzwudaZKERERgc6dO9OyZUs2bdrEkiVL6N27d9glhSZzY5WIiEgcmdkRd41kskqHCzM7xcx+ZWbHl3H+hMj5vnGrTkREJIWcccYZgMJFLD0XNwPXAFvKOP858F3gJ9UtSkREJBWNGDECgLfffpvDhw+HXE14YgkXg4C33L3UO0Yix6cTTGIlIiKScdq0aUOnTp3YtWsXCxYsCLuc0MQSLk4ANlbQZjNwYtXLERERSW0adxFbuNgHNKugTTPgYNXLERERSW1F4WLatGkhVxKeWMLFImC0mTUo7aSZNQJGR9qJiIhkpKJxF3PmzOGrr74KuZpwxBIuHiHomXjDzI64edfM+hCs93FcpJ2IiEhGat68Od26dWP//v0ZO+4iloXL/kUwrfcA4H0z22xm881sM7AQ6E+wYNhTiSlVREQkNZx++ulAcNdIJoppEi13vwq4HviIYIDnKZH9UuA6d9d03CIikvGKwsXMmTNDriQc5a0tUip3fwR4xMzqAccAX7r7vngXJiIikqqKwsU777zD4cOHycmJ+ddtSqvy9N/uvs/dNytYiIiIHKlVq1Z06NCB3bt388EHH4RdTo2LOVyYWTMzu97M7jezv5Y43t/M6sa3RBERkdQzbNgwIDMvjcQULszsu8A64EHgRxy55PnxwFzgO/EqTkREJFVl8qDOWBYuO4vgNtMVwPnAQ9Hn3X0JwcDOMXGsT0REJCUV9VzMmjWLwsLCkKupWbH0XPwM+BQY5u4vUvoCZh8C3eNRmIiISCpr164drVq1Yvv27SxdujTscmpULOEiD3jZ3XeV02Yjwa2pIiIiGc3MMnbcRSzhIhfYW0GbY4CCKlcjIiKSRjJ1votYwsU6gkmzyjMAWF7lakRERNJI9KBOdw+5mpoTS7iYAgw1s2+XdtLMxgG9gefjUZiIiEiq69q1K82bN+fzzz9n5cqVYZdTY2IJF38ANgBPmdm/gEEAZvbDyONHgJXAxLhXKSIikoLMLCNvSY1l4bIdwDDgHeDbwNmAAQ9EHs8BznD3isZliIiIZIzoqcAzRUyTnbv7BmB4ZMn1QUBTYCfwrrtn5rqyIiIi5Rg8eDAAs2fPDrmSmlOllVTc/UOCOS1ERESkHL1796Z+/fqsXr2azz//nOOPPz7skhKuSguXmVktM+ttZkMj+1rxLkxERCQd5OTkMHDgQCBzei9iXVukqZk9CnwJvA/MiOy/NLNHzey4uFcoIiKS4jLt0kilL4uY2fHAbKADwTiL94DPCGbk7At8FxhhZoPd/fP4lyoiIpKaMi1cxNJzcRdBsLgPaOvuI9z9EncfAbQF7o+c/23cqxQREUlhAwYMwMxYuHAh+/fvD7uchIslXHwdmOXuPym5voi773L3mwh6Nr4RzwJFRERSXePGjenVqxeHDh1i/vz5YZeTcLGEi4YEc1yUZxbQoOrliIiIpKdMujQSS7j4GDixgjYnorVFREREjqJwUbr7gYsiE2gdxcz6AhcSjMkQERGRKEXhYu7cuRQWFoZcTWLFMonWWuAN4D0zewKYCXwOHE8wLfjlwGvAOjM7PfqJ7p5Za82KiIiU0LZtW1q0aMHmzZtZvnw53bp1C7ukhIklXMwAnGA9kWsIbj0tYpH9NyNbSdlVKU5ERCRdmBmDBw/m2WefZfbs2QoXEXcShAsRERGpguhwcc0114RdTsJUOly4+/gE1iEiIpL2MmVQZ5XWFhEREZHY9enTh3r16rFy5Uq2bNkSdjkJU+lwYWbZZlavlOMjzex+M/udmbWPb3kiIiLpo1atWvTv3x+AefPmhVxN4sTSc/FHYLuZNS46YGYXE9xB8iPgZwR3krSOb4kiIiLpY8CAAQC8++67IVeSOLGEi9OBt9x9Z9SxOwhWSL0C+ClwDPCTeBUnIiKSboqWX1e4CLQGVhU9MLMOQFdgors/6e5/JJjnYlR8SxQREUkfRT0X8+fPp6CgIORqEiOWcNEIiF6wbDDBran/iTq2FGgVh7pERETS0oknnkibNm3YvXs3y5YtC7uchIglXHwKRA/YPBPYDyyIOtYAOByHukRERNJWul8aiSVcvAt808y+bmZnAmOB6e5+KKpNB2BTPAsUERFJN0XhIl3vGIklXNwVaT8FeB3IBX5bdNLMGgHDgfT8SYmIiMRJut8xEssMnYvNbABwZeTQv9x9flST3sBU4Kk41iciIpJ2Tj75ZGrVqsXSpUvZvXs3DRs2DLukuIpphk53X+zut0S2+SXOvePu57v7m/EtUUREJL3UrVuXPn364O7Mnz+/4iekGE3/LSIiEoJ0HtSpcCEiIhKCdB7UqXAhIiISguhBne4ecjXxpXAhIiISgo4dO9K0aVO2bNnC+vXrwy4nrhQuREREQmBmaTvuQuFCREQkJOk634XChYiISEjSteei0pNoRTOz+gTLq2eXdt7dN1SjJhERkYxw6qmnArBo0SIOHTpErVq1Qq4oPmLquTCzy81sCcHqqBuAtaVsa+JdpIiISDo65phj6Ny5MwcPHmTJkiVhlxM3le65MLOrgMeAAmAW8AlaAVVERKRa8vLyWLlyJfn5+Zx88slhlxMXsVwWuQXYAQxx9/RcgF5ERKSG5eXl8dRTTzF//nyuvfbasMuJi1gui3QCnlOwEBERiZ+icRf5+fkhVxI/sYSL7cCBRBUiIiKSiU4++WSysrJYvHgxBw6kx6/ZWMLFy8BwM7NEFSMiIpJpGjRoQLdu3Th8+DAffPBB2OXERSzh4jagNvCwmTVIUD0iIiIZJy8vD0ifSyOxhItngX3ANcCnZrbQzKaXsk1LTKkiIiLpqWjcxfz580OuJD5iuVtkeNS/6wN9y2iXXku7iYiIJFi69VxUOly4u6YKFxERSYA+ffqQk5PDsmXL2LNnDw0apPboAwUGERGRkNWpU4devXpRWFjI+++/H3Y51ZYR4cLMbjOz+Wa2y8y2mtlLZtazRJsbzOzDSJtdZjbXzL4WVs0iIpJZ0mncRczhwswuNrM3zewLMztsZtvN7A0zuzgRBcbJcGAScBowkmDa8jfN7NioNhuBnwH9gDxgOvBvM+tds6WKiEgmSqdxF7GsLWLAE8B3ACNYY2QrcBxwBjDSzL7p7t9JRKHV4e7nRD82s8uBncBg4KVImyklnvZLM/s+MAj4sCbqFBGRzJWpPRffAy4FFgJnAnXc/USgTuTxAuAiM7s+1iLMbKyZTTSzWZFLEm5mT1bwnFZm9piZbTazg2a2zszuM7MmlXjLhgSffUcZr50d6YlpAMyJ9fOIiIjEqkePHtSpU4dVq1axY0epv55SRizh4mpgHXC6u0939wIAdy9w9+nAsMj571ahjtuBHxLc3rqposZm1pEgzIwD3gPuJVjq/UZgrpk1reAl7gcWAXNLvG4vM9sDHAQeBs5398WxfBAREZGqqFWrFn379gVgwYIF4RZTTbGEi+7AC+6+v7STkeP/BrpVoY6bgC5AI+D7lWg/CWgO/Njdx7j7z919JEHI6Ar8tqwnmtk9wBDggqKAFGU5QcAZCDwE/L3kwE8REZFESZdxF7GECycYa1GeKq074u5vuftKd69wAi4z6wCcTdBL8mCJ03cAe4HLzax+Kc+9F7gEGOnua0qp4yt3X+Xu+e5+G0Hvxk2xfh4REZGqOOWUUwBS/nbUWMLFMuBbZla3tJOR42OAj+JQV3lGRvZT3b0w+oS77wZmA/UIeh+i67ufYDDqSHf/uJLvlUWwnoqIiEjCnXzyyQAsXLgw5EqqJ5Zw8RjQBphpZmeYWQ4UD34cAbwFtI20S6Sukf2KMs6vjOy7FB0wswcJxmdcAuwwsxMiW4OoNr83s6Fm1i4y9uJ3BLew/iPun0BERKQU3bt3Jzc3l1WrVrFz586wy6myWMLFX4CngFOAqcB+M/scOAC8CfQHnnX3h+Ne5ZEaR/Zl/dSLjh8TdewHBHeITAM+jdpuiWpzAvAkwbiLacCpwLnu/lppb2Jm15lZvpnlb926tQofQ0RE5Ei1atWiV69eACm9/Hqlw4UHLiW4HXU6wS/xYyP76cCl7p4ME2kVjfsoHr/h7lbGNj6qzVXu3tbda7t7c3c/091fL+tN3P0Rd89z97xmzZol7tOIiEhG6devH5Dal0ZiWRUVAHd/iqAHIyxFPRONyzjfqEQ7ERGRlFE07iKVB3VWuufCzK6oaCrsyFiFK6pfVrmWR/ZdyjjfObIva0yGiIhI0kqHnotYxlxMJrgbpDzfBB6vajGV9FZkf7aZHVG/mTUkmNJ7P/BugusQERGJu169epGVlcWyZcvYv7/UqaWSXrxXRc0maqxDIrj7aoIBpe2AG0qcngDUB55w972JrENERCQR6tWrR7du3SgoKGDx4tScJDrmMRcV6EIZ63WUx8zG8N9ekRMi+0FmNjny723uHn1nxw8I1vx4wMzOIJiDYwAwguByyC9jrUFERCRZnHzyySxdupSFCxfSv3//sMuJWbnhwsxKzlkxxszaldI0m2AOjKHAK1Wooy9wZYljHSIbwHqibht199VmlgfcCYwCziO4tfQBYIK7b69CDSIiIkmhX79+PPnkkyk7qLOinourov7tBCGgbxltHZhHFabLjtwSOj7G53xCMDGWiIhIWkn1QZ0VhYv2kb0RrDp6H8GKoiUVADs0zkFERKT6ilZH/fDDDzl06BC1atUKt6AYlRsu3H190b/NbALwVvQxERERib/GjRvTsWNHVq9ezbJly+jdu9yZIJJOLDN0TnD3mYksRkRERAKpvIhZzLeimtlAM/urmS0ws9VmttDMHjWz0xJRoIiISCYqGneRioM6Y7oV1cx+A9zGf9fvKNIXuNrM7nb3X8SpNhERkYyVET0XZvZt4BfABuAagttE60b210SO/8zMLkxAnSIiIhmlKFwsWrSIwsLCkKuJTSyXRX4EfA6c6u6Pufs6dz8Y2T9GsET5Vo6eNVNERERidPzxx9OiRQv27NnDqlWrwi4nJrGEiz7Ac+6+rbSTkePPUvY8GCIiIhKDoltSP/jgg3ALiVEs4SIH2FdBm33Ef0pxERGRjFR0C2o6h4tVwNdLrkRaJHL8PGB1PAoTERHJdH369AGCybRSSSzh4imgGzDFzDpHnzCzjsBzQHfgn/ErT0REJHMVhYtU67mI5RLGPQSLhH0NONfMNhMsFnYC0JIgqLwTaSciIiLV1LlzZ+rUqcOGDRvYsWMHTZo0CbukSollhs6vgLMIljNfC7QiuEOkdeTxL4EzIu1ERESkmnJycujZsyeQWpdGYpqh090Pufvv3L0z0IggWDRy986R44cSUqWIiEiGSsVxF1W+s8Pd9wB74liLiIiIlJCKd4zEvLaIiIiI1JxUHNQZU7gws2Fm9rKZbTGzQ2ZWUMp2OFHFioiIZJqinoslS5Zw+HBq/Iqt9GURM/sa8G8gm2AdkeVAanxKERGRFNWkSRPatGnDhg0bWLlyJd26dQu7pArFMuZiPHAI+Jq7T01MOSIiIlJSnz592LBhAx9++GFKhItYLov0BP6lYCEiIlKzUm3cRSzhYg+wPVGFiIiISOlS7Y6RWMLFNGBQogoRERGR0qVzz8XPgI5mdruZWaIKEhERkSN17NiRevXqsWnTJr744ouwy6lQmQM6zeyxUg4vBSYAV5vZIuDLUtq4u383LtWJiIgI2dnZ9OrVi3nz5vHhhx8yYsSIsEsqV3l3i1xVzrl2ka00DihciIiIxFGfPn2YN28eH3zwQUqHi/Y1VoWIiIiUK5XGXZQZLtx9fU0WIiIiImVLpTtGKjWJlpm1IVhe3YH57v5JQqsSERGRI/Tq1QuAZcuWUVBQQHZ2dsgVla3Cu0XM7I/AGuAZ4FlgrZn9f4kuTERERP6rcePGtG7dmgMHDrB69eqwyylXueHCzL4D/AQw4GOC9UQM+ImZXZL48kRERKRIz549gWARs2RWUc/FdwkWJzvT3Xu4e3fgHKAQ3REiIiJSo9IlXPQG/u3ubxUdcPc3gSlA3wTWJSIiIiWkS7hoQnAppKSPgWPiXo2IiIiUqWhQZ6qHiyyCZdZLOkQw9kJERERqyEknnURWVhYrVqzg4MGDYZdTpsqsLeIJr0JEREQqVLduXTp16kRBQQEff/xx2OWUqTLhYryZFURvwK8ASh6PbIcTW7KIiEjmSoVxF5UJFxbjFstKqyIiIhKDVAgX5c7Q6e4KCiIiIkmkaFDn4sWLQ66kbAoPIiIiKSQVei4ULkRERFJIp06dyM3NZf369ezatSvsckqlcCEiIpJCcnJy6NatGwAfffRRyNWUTuFCREQkxST7ZFoKFyIiIimmaNxFsg7qVLgQERFJMck+qFPhQkREJMUoXIiIiEhctWnThoYNG7Jlyxa2bNkSdjlHUbgQERFJMWZW3HuxdOnSkKs5msKFiIhICkrmQZ0KFyIiIimoR48eQHLOdaFwISIikoKKJtJatmxZyJUcTeFCREQkBXXv3h1Qz4WIiIjEScuWLWnYsCHbtm1j69atYZdzBIULERGRFGRmSdt7oXAhIiKSohQuREREJK4ULkRERCSuknXpdYULERGRFFXUc5Fst6MqXIiIiKSotm3bUrduXT799FN27NgRdjnFFC5ERERSVFZWVlJOpqVwISIiksKScVCnwoWIiEgKS8ZBnQoXIiIiKUw9FyIiIhJXyXjHiMKFiIhICuvQoQO5ubls2LCB3bt3h10OoHAhIiKS0nJycujatSsAH3/8ccjVBBQuREREUlyyjbtQuBAREUlxyXbHSEaECzO7zczmm9kuM9tqZi+ZWc8SbU43sxfNbJOZuZldFVK5IiIiMVHPRTiGA5OA04CRwGHgTTM7NqpNA2AJcCOwv6YLFBERqapku2MkJ+wCaoK7nxP92MwuB3YCg4GXIm1eBV6NnJ9cwyWKiIhUWefOncnOzmbNmjXs37+funXrhlpPUvRcmNlYM5toZrMily7czJ6s4DmtzOwxM9tsZgfNbJ2Z3WdmTSrxlg0JPnvyrPIiIiJSRbm5uXTq1Al3Z8WKFWGXkxzhArgd+CHQF9hUUWMz6wgsAMYB7wH3AmsILmnMNbOmFbzE/cAiYG6VKxYREUkiJ510EgDLly8PuZLkCRc3AV2ARsD3K9F+EtAc+LG7j3H3n7v7SIKQ0RX4bVlPNLN7gCHABe5eUO3KRUREkkAyzXWRFOHC3d9y95Xu7hW1NbMOwNnAOuDBEqfvAPYCl5tZ/VKeey9wCTDS3ddUu3AREZEkoZ6L6hkZ2U9198LoE+6+G5gN1AMGRp8zs/uB7xAEi/BjnYiISByp56J6ukb2ZY1YWRnZdyk6YGYPEozPuATYYWYnRLYGUW0amFlfM+tL8HNpE3ncJu6fQEREJM6KwsXy5cupxIWAhErFcNE4st9Zxvmi48dEHfsBwR0i04BPo7ZbotrkAe9HtrrAhMi/7yztTczsOjPLN7P8rVu3xv4pRERE4qhp06Ycd9xx7N27l02bKrw3IqFSMVxUxCL74tjm7lbGNj6qzYwy2lxV2pu4+yPunufuec2aNUvoBxIREamMonEXYV8aScVwUdQz0biM841KtBMREckI0ZdGwpSK4aLoJ9aljPOdI/vwZxERERGpQeq5qLq3IvuzzeyI+s2sIcGU3vuBd2u6MBERkTCp56KK3H01MBVoB9xQ4vQEoD7whLvvreHSREREQpUsPRdJsXCZmY0BxkQenhDZD4paQGybu0ff2fEDYA7wgJmdASwDBgAjCC6H/DLBJYuIiCSd9u3bU6tWLT755BP27t1L/fpHzSdZI5Kl56IvcGVkK1rBtEPUsbHRjSO9F3nAZIJQcTPQEXgAGOTuX9RE0SIiIskkJyeHTp06AYS6gFlShAt3H1/O7aLm7u1Kec4n7j7O3U9091x3b+vuN7r79hA+goiISFJIhmnAkyJciIiISHwkwzTgChciIiJpRD0XIiIiElfquRAREZG4KgoXK1asoLCwsILWiaFwISIikkaaNGlC8+bN2bdvHxs3bgylBoULERGRNBP2uAuFCxERkTQT9rgLhQsREZE0o54LERERiSv1XIiIiEhcFYWLlStXhvL+ChciIiJppl27duTk5LBhwwb2799f4++vcCEiIpJmcnJy6NChAwCrVq2q8fdXuBAREUlDXbp0AcK5NKJwISIikoY6d+4MhLP0usKFiIhIGlLPhYiIiMRVUbhQz4WIiIjEhS6LiIiISFy1bNmSunXrsmXLFnbu3Fmj761wISIikoaysrLo1KkTUPPjLhQuRERE0lRYgzoVLkRERNJUWIM6FS5ERETSVFiDOhUuRERE0pQui4iIiEhcRfdcuHuNva/ChYiISJpq1qwZjRs3ZufOnWzbtq3G3lfhQkREJE2ZWSiDOhUuRERE0lgYgzoVLkRERNJYGIM6FS5ERETSWBiXRXJq7J1ERESkxo0aNYply5bRvn37GntPhQsREZE01qRJE5o0aVKj76nLIiIiIhJXChciIiISVwoXIiIiElcKFyIiIhJXChciIiISVwoXIiIiElcKFyIiIhJXChciIiISVwoXIiIiElcKFyIiIhJXChciIiISVwoXIiIiElcKFyIiIhJXChciIiISVwoXIiIiElcKFyIiIhJXChciIiISV+buYdeQ8sxsK7C+xOHGwM5ynlbR+eOAbdUsLWwVfcZUeL/qvGZVnhvLcyrTtrpt9D1Mjves7uvF+vx4fw8r007fw+R/z5Kv19bdm5Xa0t21JWADHqnm+fywP0Oifwap8H7Vec2qPDeW51SmbXXb6HuYHO9Z3deL9fnx/h5Wpp2+h8n/nrG8ni6LJM5L1TyfDmr6Mybi/arzmlV5bizPqUzbeLVJZWF8vni/Z3VfL9bnx/t7WJl2+h4m/3tW+vV0WSRJmVm+u+eFXYdkNn0PJRnoe5h61HORvB4JuwAR9D2U5KDvYYpRz4WIiIjElXouREREJK4ULtKQmd1mZvPNbJeZbTWzl8ysZ9h1SeYxs9PN7EUz22RmbmZXhV2TpDcz+4GZrTWzA2a2wMyGhl1TJlK4SE/DgUnAacBI4DDwppkdG2ZRkpEaAEuAG4H9Idciac7MLgLuB+4CTgbmAK+ZWZtQC8tAGnORAcysAcHEJ2PcPd1v95IkZWZ7gB+6++Swa5H0ZGbzgA/d/dqoYyuB59z9tvAqyzzquYgDMxtrZhPNbFbkUoSb2ZMVPKeVmT1mZpvN7KCZrTOz+8ysSQJKbEjwv/WOBLy2JJEU+C5KBkvk99PMcoFTgKklXmIqQS+u1KCcsAtIE7cDfYA9wEbgpPIam1lHgu665sAU4GOgP0HX8SgzG+zuX8SxvvuBRcDcOL6mJKdk/y5KZkvk9/M4IBv4vMTLfA6cGa8PIJWjnov4uAnoAjQCvl+J9pMI/s/yY3cf4+4/d/eRwL1AV+C30Y3N7DeRhF/eNry0NzKze4AhwAXuXlDlTyipImm/iyIk+PsZUfJav5VyTBJMYy7iLPIf1reAf7j7ZaWc7wCsBtYBHd29MOpcQ+BTgv8zNHf3vZHjxxGk8vJscPd9Jd7rXuBiYIS7f1zFjyQpKpm+i5HnasyFFIv39zNyWWQfcIm7PxvV9kGgp7sPS9ynkZJ0WaTmjYzsp0b/nwXA3Xeb2WzgbGAgMC1yfBsxrghoZvcTBIvhChZShhr5LopUUUzfT3f/yswWAGcBz0Y1Pwt4viYKlv/SZZGa1zWyX1HG+ZWRfZeqvkEkqY8DLgF2mNkJka1BVV9T0lJNfBcbmFlfM+tL8N+bNpHHujVQKlKV7+c9wFVmdo2ZdYv8kdUCeDhBNUoZFC5qXuPIfmcZ54uOH1ON9/gBwR0i0wi6Dou2W6rxmpJ+auK7mAe8H9nqAhMi/76zGq8pmSHm76e7/wv4H4KBo4sIxpud5+7rE1KhlEmXRZKPRfZVHgzj7lZxK5EKxeO7OCPqdUTiqdTvp7tPIhgIKiFSz0XNK0rbjcs436hEO5FE0XdRkpm+nylM4aLmLY/sy7qO3TmyL+s6o0i86LsoyUzfzxSmcFHz3orszzazI37+kdurBhOswfBuTRcmGUffRUlm+n6mMIWLGubuqwmmo20H3FDi9ASgPvBE0bwCIomi76IkM30/U5sm0YoDMxsDjIk8PAE4B1gDzIoc2+but0S1Lzml7TJgADCCoIvvNE25LFWh76IkM30/M4fCRRyY2XjgjnKarHf3diWe05rgdrxRQFOCW0X/DUxw9+0JKVTSnr6Lksz0/cwcChciIiISVxpzISIiInGlcCEiIiJxpXAhIiIicaVwISIiInGlcCEiIiJxpXAhIiIicaVwISIiInGlcCEiIiJxpXAhIhnHzMabmUdtD5c4PzlyvF1IJR7FzF4uUfNVYdckUpacsAsQkeozs8pMtTvC3WckupYU83dgHZCf6DeKrOy5DmgN9HD3j8ppW5dgmut6QCt33wL8M1JnX2B0ousVqQ6FC5H0MqGcc+tqqogUMrmmApe7F5rZYwRra1wD/KSc5hcCjYHnIsECd/8nQKTHQuFCkprChUgacffxYdcg5fobcDtwuZn93N2/KqPdNZH9IzVTlkh8acyFSAaKGnMw3MzGmtl7ZrbPzLab2dNm1rKM5x1rZr8zs2Vmtt/MdprZNDM7u5S2VxWNDTCzUWY2I9Leo9o0NrP7zGyjmR0ws4/N7Cdm1iHy3MlRbZ+OHDu9jNrGRs5PjMOPqFRm1sfMNpnZLjM7K+p4pX4u7v4J8B/gOOD8Mt7jJGAIsBZ4M1GfRSSRFC5EMtsPgCcJLpk8CCwBLgLeNLPa0Q3NrC2wAPg5sBV4GPgX0A34j5ldW8Z7jAVeBnZHnvNM5PXqANOBG4EtwP3ADOCXwJ9KeZ1Jkf33ynif6yL7hPy1b2ZnADMBA0539zcix2P9uTwa2V9D6YqO/9W1bLWkKF0WEUkjZja+jFMH3P33pRwfBZzq7oujXuOfwCUE1/WfiWr7d6AtcIm7Px3V/hiCUPCAmb3o7p+XeI/zgPPc/T8ljt8K9AOeBr5T9IvUzH4LLCxZqLvPNLOlwAVmdqO7b4uqoT1wJjAn+rPEi5ldBjwGrALOdff1Uadj/bm8DGwGzjCz9u6+Nuo5ucAVwOHI+4mkJPVciKSXO8rYfl5G+wdK+WVc9Jd1/6IDZtYHGAY8H/0LFMDdv4y8Rx3gglLeY0opwQLgSqAQuC36L/TIpYP7yqj3IaB25LnRriPoUfhLGc+rMjP7GfAEMA8YHB0sqvJzcfcCguBgwHdLvN1ooBnwkrt/Fu/PIlJT1HMhkkbc3WJ8Smm3YH4S2TeJOjYosm9cRu9Is8i+Wynn3it5wMwaAR2BT9x9XSnPeae0Ygl+yf+eIEz8KfJatYCrgB0c2dMSD/cCY4Dngcvc/UCJ81X9ufwV+AUwzszuiAQOgKJLKBrIKSlN4UIks31ZyrHDkX121LGmkf1Zka0sDUo5Vtpf4I0i+5KXUCjvuLvvNrMngevNbIS7v0Xw1/4JwH2l/PKvrqLBoy+X8dpV+rm4+3ozewM4h+Cy0UuRCbvOBNYDU6tTtEjYdFlERCpjZ2R/o7tbOdu4Up5b2qDEXZH98WW8X1nHIbg0Av8d2JnIgZxjCMZZ/K2MAavV+bkU1Vv0ut8luFTyN3cvjOeHEKlpChciUhnvRvZD4/Fi7r4LWAO0LGOK7SHlPPdDYDZwvpkNIPhrf6a7L4tHbSV8QtB7sRz4i5ndUOJ8dX4uLxL06pxnZq0JLu0UjccQSWkKFyJSIXfPB2YB3zKzq0trY2a9zKx5DC/7BMF/g35nZsVjRSK/aP+nguc+BOQSjIUwgts/E8LdPyUYtLkY+LOZ3Rx1rso/F3c/DEwmuPz0D6AV8Kq7b4r7hxCpYRpzIZJGyrkVFeDf7r6oGi//HYJ5Kf5mZj8muHviS4Jfir2BngQDHLdU8vX+QHDZ4WKgq5lNJZjy+kKC+STGENxNUppnCQZbtgS2Af8v1g8TC3ffamYjgNeBP5pZHXf/beR0dX4ujwI/4789HxrIKWlB4UIkvdxRzrl1wKKqvrC7bzSzU4AfEdxaeSnBX92fAR8BEwn+uq/s6+2P/MK+k2CirZsIZqW8i6A3YAz/HZtR8rlfmdk/CHo4Jrv7wap9qspz9+2RibReA34TCRj/W52fi7uvMbNpBJd2NkZeWyTlmSaAE5FkExk8+QhwvbuXOneFmc0gGA/R1d1Xxvj64wmCWMqtFBtZuOxxYJy7Tw63GpHSacyFiITGzFqUcqw18L8Et8S+XMbz+hOMg3g91mBRwluR9UgSNmYjXszs5ci6LI+HXYtIRXRZRETC9HxkEqwFBOMU2gFfB+oRzNx5xOBGM/s+wTiLcQTjMcq7DFSeGSUelzaZWLL5J0fWuSikOkQqpMsiIhIaM/sBcDnQmWAw5x7gfeDP7n7UIE0zW0cwUHINMN7d/1lz1YpIZSlciIiISFxpzIWIiIjElcKFiIiIxJXChYiIiMSVwoWIiIjElcKFiIiIxJXChYiIiMTV/w+9U6eRjIYD5QAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,8))\n",
    "\n",
    "BB_I = xpsi.surface_radiation_field.intensity(E, mu, local_vars, atmos_extension=\"BB\", # NB: isotropic blackbody\n",
    "                                              region_extension='elsewhere', numTHREADS=2)\n",
    "\n",
    "plt.plot(E, BB_I, 'k-', lw=2.0)\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.set_yscale('log')\n",
    "ax.set_xscale('log')\n",
    "ax.set_ylabel('Photon specific intensity')\n",
    "_ = ax.set_xlabel('Energy [keV]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Polarized non-isotropic burst blackbody"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Note: This block only works for X-PSI versions above 2.2.0.\n",
    "\n",
    "plt.figure(figsize=(8,8))\n",
    "\n",
    "BB_Q = xpsi.surface_radiation_field.intensity(E, mu, local_vars, atmos_extension=\"Pol_BB_Burst\", stokesQ=1,\n",
    "                                              region_extension='hot', numTHREADS=2)\n",
    "\n",
    "plt.plot(E, BB_Q, 'k-', lw=2.0)\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.set_xscale('log')\n",
    "ax.set_ylabel('Stokes Q intensity')\n",
    "_ = ax.set_xlabel('Energy [keV]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numerical atmosphere"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's check out a numerical atmosphere (this code you typically find in a custom photosphere class). The numerical atmospheres loaded here were generated by the NSX atmosphere code ([Ho & Lai (2001)](https://ui.adsabs.harvard.edu/abs/2001MNRAS.327.1081H/abstract); [Ho & Heinke (2009)](https://ui.adsabs.harvard.edu/link_gateway/2009Natur.462...71H/doi:10.1038/nature08525)), courtesy of W.C.G. Ho for NICER modeling efforts. One of these atmospheres (fully-ionized hydrogen; Ho & Lai 2001) was used in [Riley et al. (2019)](https://ui.adsabs.harvard.edu/abs/2019ApJ...887L..21R/abstract); also see [Bogdanov et al. (2021)](https://ui.adsabs.harvard.edu/abs/2021ApJ...914L..15B/abstract) and [Riley et al. (2021)](https://ui.adsabs.harvard.edu/abs/2021ApJ...918L..27R/abstract). For this tutorial we need the data files `nsx_H_v171019.out` and `nsx_He_v170925.out` that can be found in [Zenodo](https://zenodo.org/record/7094145). The repository includes also a fully-ionized hydrogen data file with an extended surface gravity grid (`nsx_H_v200804.out`), which was used in [Riley et al. (2021)](https://ui.adsabs.harvard.edu/abs/2021ApJ...918L..27R/abstract), but not in this tutorial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def preload(path, size):\n",
    "    NSX = np.loadtxt(path, dtype=np.double)\n",
    "    logT = np.zeros(size[0])\n",
    "    logg = np.zeros(size[1])\n",
    "    _mu = np.zeros(size[2]) # use underscore to bypass errors with the other mu array\n",
    "    logE = np.zeros(size[3])\n",
    "\n",
    "    reorder_buf = np.zeros(size)\n",
    "\n",
    "    index = 0\n",
    "    for i in range(reorder_buf.shape[0]):\n",
    "        for j in range(reorder_buf.shape[1]):\n",
    "            for k in range(reorder_buf.shape[3]):\n",
    "                for l in range(reorder_buf.shape[2]):\n",
    "                    logT[i] = NSX[index,3]\n",
    "                    logg[j] = NSX[index,4]\n",
    "                    logE[k] = NSX[index,0]\n",
    "                    _mu[reorder_buf.shape[2] - l - 1] = NSX[index,1]\n",
    "                    reorder_buf[i,j,reorder_buf.shape[2] - l - 1,k] = 10.0**(NSX[index,2])\n",
    "                    index += 1\n",
    "\n",
    "    buf = np.zeros(np.prod(reorder_buf.shape))\n",
    "\n",
    "    bufdex = 0\n",
    "    for i in range(reorder_buf.shape[0]):\n",
    "        for j in range(reorder_buf.shape[1]):\n",
    "            for k in range(reorder_buf.shape[2]):\n",
    "                for l in range(reorder_buf.shape[3]):\n",
    "                    buf[bufdex] = reorder_buf[i,j,k,l]; bufdex += 1\n",
    "\n",
    "    atmosphere = (logT, logg, _mu, logE, buf)\n",
    "    \n",
    "    return atmosphere"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "H_fully = preload('../../examples/examples_modeling_tutorial/model_data/nsx_H_v171019.out',\n",
    "                    size=(35, 11, 67, 166))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "He_fully = preload('../../examples/examples_modeling_tutorial/model_data/nsx_He_v170925.out',\n",
    "                      size=(29, 11, 67, 166))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,8))\n",
    "\n",
    "plt.plot(E, BB_I, 'k--', lw=1.0)\n",
    "\n",
    "hot_I = xpsi.surface_radiation_field.intensity(E, mu, local_vars,\n",
    "                                               atmosphere=H_fully,\n",
    "                                               region_extension='hot',\n",
    "                                               atmos_extension=\"Num4D\",\n",
    "                                               numTHREADS=2)\n",
    "\n",
    "plt.plot(E, hot_I, 'b-', lw=2.0)\n",
    "\n",
    "elsewhere_I = xpsi.surface_radiation_field.intensity(E, mu, local_vars,\n",
    "                                                     atmosphere=H_fully,\n",
    "                                                     region_extension='elsewhere',\n",
    "                                                     atmos_extension=\"Num4D\",\n",
    "                                                     numTHREADS=2)\n",
    "\n",
    "plt.plot(E, elsewhere_I, 'r-', lw=1.0)\n",
    "\n",
    "He_fully_I = xpsi.surface_radiation_field.intensity(E, mu, local_vars,\n",
    "                                                     atmosphere=He_fully,\n",
    "                                                     region_extension='hot',\n",
    "                                                     atmos_extension=\"Num4D\",\n",
    "                                                     numTHREADS=2)\n",
    "\n",
    "plt.plot(E, He_fully_I, 'k-.', lw=1.0)\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.set_yscale('log')\n",
    "ax.set_ylim([9.0e25,4.0e29])\n",
    "ax.set_xscale('log')\n",
    "ax.set_ylabel('Photon specific intensity')\n",
    "_ = ax.set_xlabel('Energy [keV]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This behaviour is typical for an isotropic blackbody radiation field with temperature $T$ in comparison to a radiation field emergent from a (non-magnetic, fully-ionized) geometrically-thin H/He atmosphere with effective temperature $T$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the angular dependence:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1152x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# keV (local comoving frame)\n",
    "E = np.ones(1000) * 0.2\n",
    "\n",
    "# cos(angle to local surface normal in comoving frame)\n",
    "mu = np.linspace(0.01,1.0,1000)\n",
    "\n",
    "fig = plt.figure(figsize=(16,8))\n",
    "\n",
    "# Hydrogen\n",
    "\n",
    "ax = fig.add_subplot(121, projection='polar')\n",
    "\n",
    "ax.set_theta_direction(1)\n",
    "ax.set_thetamin(-90.0)\n",
    "ax.set_thetamax(90.0)\n",
    "\n",
    "# log10(eff. temperature [K]) and log10(local eff. gravity [cm/s^2])\n",
    "local_vars = np.array([[6.0, 13.8]]*1000)\n",
    "\n",
    "H_fully_I = xpsi.surface_radiation_field.intensity(E, mu, local_vars,\n",
    "                                                   atmosphere=H_fully,\n",
    "                                                   region_extension='hot',\n",
    "                                                   atmos_extension=\"Num4D\",\n",
    "                                                   numTHREADS=2)\n",
    "\n",
    "ax.plot(np.arccos(mu), np.log10(H_fully_I/np.max(H_fully_I)), 'k-', lw=1.0)\n",
    "ax.plot(-np.arccos(mu), np.log10(H_fully_I/np.max(H_fully_I)), 'k-', lw=1.0)\n",
    "\n",
    "# log10(eff. temperature [K]) and log10(local eff. gravity [cm/s^2])\n",
    "local_vars = np.array([[5.5, 13.8]]*1000)\n",
    "\n",
    "H_fully_I = xpsi.surface_radiation_field.intensity(E, mu, local_vars,\n",
    "                                                   atmosphere=H_fully,\n",
    "                                                   region_extension='hot',\n",
    "                                                   atmos_extension=\"Num4D\",\n",
    "                                                   numTHREADS=2)\n",
    "\n",
    "\n",
    "ax.plot(np.arccos(mu), np.log10(H_fully_I/np.max(H_fully_I)), 'r-', lw=1.0)\n",
    "ax.plot(-np.arccos(mu), np.log10(H_fully_I/np.max(H_fully_I)), 'r-', lw=1.0)\n",
    "\n",
    "# log10(eff. temperature [K]) and log10(local eff. gravity [cm/s^2])\n",
    "local_vars = np.array([[6.5, 13.8]]*1000)\n",
    "\n",
    "H_fully_I = xpsi.surface_radiation_field.intensity(E, mu, local_vars,\n",
    "                                                   atmosphere=H_fully,\n",
    "                                                   region_extension='hot',\n",
    "                                                   atmos_extension=\"Num4D\",\n",
    "                                                   numTHREADS=2)\n",
    "\n",
    "\n",
    "ax.plot(np.arccos(mu), np.log10(H_fully_I/np.max(H_fully_I)), 'b-', lw=1.0)\n",
    "ax.plot(-np.arccos(mu), np.log10(H_fully_I/np.max(H_fully_I)), 'b-', lw=1.0)\n",
    "\n",
    "ax.set_rmax(0.05)\n",
    "ax.set_rmin(-1)\n",
    "ax.set_theta_zero_location(\"N\")\n",
    "ax.set_rticks([-1.0,-0.5, 0.0])\n",
    "ax.set_xlabel('log10$(I_E/I_E(\\mu=1))$')\n",
    "ax.xaxis.set_label_coords(0.5, 0.15)\n",
    "_ = ax.set_title('H (fully-ionized)', pad=-50)\n",
    "\n",
    "# Helium\n",
    "\n",
    "ax = fig.add_subplot(122, projection='polar')\n",
    "\n",
    "ax.set_theta_direction(1)\n",
    "ax.set_thetamin(-90.0)\n",
    "ax.set_thetamax(90.0)\n",
    "\n",
    "# log10(eff. temperature [K]) and log10(local eff. gravity [cm/s^2])\n",
    "local_vars = np.array([[6.0, 13.8]]*1000)\n",
    "\n",
    "He_fully_I = xpsi.surface_radiation_field.intensity(E, mu, local_vars,\n",
    "                                                     atmosphere=He_fully,\n",
    "                                                     region_extension='hot',\n",
    "                                                     atmos_extension=\"Num4D\",\n",
    "                                                     numTHREADS=2)\n",
    "\n",
    "ax.plot(np.arccos(mu), np.log10(He_fully_I/np.max(He_fully_I)), 'k-', lw=1.0)\n",
    "ax.plot(-np.arccos(mu), np.log10(He_fully_I/np.max(He_fully_I)), 'k-', lw=1.0)\n",
    "\n",
    "# log10(eff. temperature [K]) and log10(local eff. gravity [cm/s^2])\n",
    "local_vars = np.array([[5.5, 13.8]]*1000)\n",
    "\n",
    "He_fully_I = xpsi.surface_radiation_field.intensity(E, mu, local_vars,\n",
    "                                                     atmosphere=He_fully,\n",
    "                                                     region_extension='hot',\n",
    "                                                     atmos_extension=\"Num4D\",\n",
    "                                                     numTHREADS=2)\n",
    "\n",
    "ax.plot(np.arccos(mu), np.log10(He_fully_I/np.max(He_fully_I)), 'r-', lw=1.0)\n",
    "ax.plot(-np.arccos(mu), np.log10(He_fully_I/np.max(He_fully_I)), 'r-', lw=1.0)\n",
    "\n",
    "# log10(eff. temperature [K]) and log10(local eff. gravity [cm/s^2])\n",
    "local_vars = np.array([[6.5, 13.8]]*1000)\n",
    "\n",
    "He_fully_I = xpsi.surface_radiation_field.intensity(E, mu, local_vars,\n",
    "                                                     atmosphere=He_fully,\n",
    "                                                     region_extension='hot',\n",
    "                                                     atmos_extension=\"Num4D\",\n",
    "                                                     numTHREADS=2)\n",
    "\n",
    "ax.plot(np.arccos(mu), np.log10(He_fully_I/np.max(He_fully_I)), 'b-', lw=1.0)\n",
    "ax.plot(-np.arccos(mu), np.log10(He_fully_I/np.max(He_fully_I)), 'b-', lw=1.0)\n",
    "\n",
    "ax.set_rmax(0.05)\n",
    "ax.set_rmin(-1)\n",
    "ax.set_theta_zero_location(\"N\")\n",
    "ax.set_rticks([-1.0,-0.5, 0.0])\n",
    "ax.set_xlabel('log10$(I_E/I_E(\\mu=1))$')\n",
    "ax.xaxis.set_label_coords(0.5, 0.15)\n",
    "_ = ax.set_title('He (fully-ionized)', pad=-50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate the specific intensity indirectly via global variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calculate intensities by specifying spacetime coordinates at the surface and values for some set of global variables that control the radiation field."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#xpsi.surface_radiation_field.intensity_from_globals?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating parameter:\n",
      "    > Named \"frequency\" with fixed value 2.053e+02.\n",
      "    > Spin frequency [Hz].\n",
      "Creating parameter:\n",
      "    > Named \"mass\" with bounds [1.000e-03, 3.000e+00].\n",
      "    > Gravitational mass [solar masses].\n",
      "Creating parameter:\n",
      "    > Named \"radius\" with bounds [1.000e+00, 2.000e+01].\n",
      "    > Coordinate equatorial radius [km].\n",
      "Creating parameter:\n",
      "    > Named \"distance\" with bounds [1.000e-02, 3.000e+01].\n",
      "    > Earth distance [kpc].\n",
      "Creating parameter:\n",
      "    > Named \"cos_inclination\" with bounds [-1.000e+00, 1.000e+00].\n",
      "    > Cosine of Earth inclination to rotation axis.\n"
     ]
    }
   ],
   "source": [
    "# unimportant here; just use strict bounds\n",
    "bounds = dict(mass = (None, None), \n",
    "              radius = (None, None),\n",
    "              distance = (None, None),\n",
    "              cos_inclination = (None, None))\n",
    "\n",
    "spacetime = xpsi.Spacetime(bounds, dict(frequency = 1.0/(4.87e-3))) # J0030 spin"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# keV (local comoving frame)\n",
    "E = np.logspace(-2.0, 0.5, 1000, base=10.0)\n",
    "\n",
    "# cos(angle to local surface normal in comoving frame)\n",
    "mu = np.ones(1000) * 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "colatitude = np.ones(1000) * 1.0 # radians\n",
    "azimuth = np.zeros(1000)\n",
    "phase = np.zeros(1000)\n",
    "\n",
    "#The general format of the default global variables:\n",
    "#np.array([self['p__super_colatitude'],\n",
    "#self['p__phase_shift'] * 2.0 * math.pi,\n",
    "#self['p__super_radius'],\n",
    "#self['p__cede_colatitude'],\n",
    "#self['p__phase_shift'] * 2.0 * math.pi - self['p__cede_azimuth'],\n",
    "#self['p__cede_radius'],\n",
    "#self['s__super_colatitude'],\n",
    "#(self['s__phase_shift'] + 0.5) * 2.0 * math.pi,\n",
    "#self['s__super_radius'],\n",
    "#self['s__cede_colatitude'],\n",
    "#(self['s__phase_shift'] + 0.5) * 2.0 * math.pi - self['s__cede_azimuth'],\n",
    "#self['s__cede_radius'],\n",
    "#self['p__super_temperature'],\n",
    "#self['p__cede_temperature'],\n",
    "#self['s__super_temperature'],\n",
    "#self['s__cede_temperature']])\n",
    "\n",
    "#For a star with uniform temperature:\n",
    "global_vars = np.array([0.0,\n",
    "                        0.0,\n",
    "                        np.pi,\n",
    "                        0.0,\n",
    "                        0.0,\n",
    "                        0.0,\n",
    "                        0.0,\n",
    "                        0.0,\n",
    "                        0.0,\n",
    "                        0.0,\n",
    "                        0.0,\n",
    "                        0.0,\n",
    "                        6.11,\n",
    "                        0.0,\n",
    "                        0.0,\n",
    "                        0.0]) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Spin frequency [Hz] = 2.053e+02,\n",
       " Gravitational mass [solar masses],\n",
       " Coordinate equatorial radius [km],\n",
       " Earth distance [kpc],\n",
       " Cosine of Earth inclination to rotation axis]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spacetime.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "spacetime['radius'] = 12.0\n",
    "spacetime['mass'] = 1.4\n",
    "# we do not need the observer coordinates (typically handled\n",
    "# by xpsi.Spacetime instances) to compute effective gravity so\n",
    "# no need to set values\n",
    "\n",
    "# the first 5 arguments are 1D arrays that specific a point sequence in the\n",
    "# joint space of surface spacetime coordinates, energy, and angle\n",
    "# if you have a set of such points that does not conform readily\n",
    "# to a 1D array, write a custom wrapper to handle the structure\n",
    "# in your point set\n",
    "I_E = xpsi.surface_radiation_field.intensity_from_globals(E,\n",
    "                                                          mu,\n",
    "                                                          colatitude,\n",
    "                                                          azimuth,\n",
    "                                                          phase,\n",
    "                                                          global_vars,       # -> eff. temp.\n",
    "                                                          spacetime.R,       # -> eff. grav.\n",
    "                                                          spacetime.zeta,    # -> eff. grav.\n",
    "                                                          spacetime.epsilon, # -> eff. grav.\n",
    "                                                          atmosphere=H_fully,\n",
    "                                                          atmos_extension=\"Num4D\",\n",
    "                                                          numTHREADS=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that only the `hot` region extension is invoked here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the spectrum and also the spectrum generated by declaring the effective gravity directly above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,8))\n",
    "\n",
    "plt.plot(E, hot_I, 'k-', lw=1.0)\n",
    "plt.plot(E, I_E, 'r-', lw=1.0)\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.set_yscale('log')\n",
    "ax.set_xscale('log')\n",
    "ax.set_ylabel('Photon specific intensity')\n",
    "_ = ax.set_xlabel('Energy [keV]')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing the pulse profiles from blackbody emission and numerical atmospheres"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First some plotting methods for figures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Defining the spacetime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating parameter:\n",
      "    > Named \"frequency\" with fixed value 3.000e+02.\n",
      "    > Spin frequency [Hz].\n",
      "Creating parameter:\n",
      "    > Named \"mass\" with bounds [1.000e+00, 3.000e+00].\n",
      "    > Gravitational mass [solar masses].\n",
      "Creating parameter:\n",
      "    > Named \"radius\" with bounds [1.000e+00, 2.000e+01].\n",
      "    > Coordinate equatorial radius [km].\n",
      "Creating parameter:\n",
      "    > Named \"distance\" with bounds [1.000e-02, 3.000e+01].\n",
      "    > Earth distance [kpc].\n",
      "Creating parameter:\n",
      "    > Named \"cos_inclination\" with bounds [-1.000e+00, 1.000e+00].\n",
      "    > Cosine of Earth inclination to rotation axis.\n"
     ]
    }
   ],
   "source": [
    "bounds = dict(distance = (None, None),                   # Default bounds for (Earth) distance\n",
    "                mass = (1.0, 3.0),                       # Default bounds for mass \n",
    "                radius = (None, None),                   # Default bounds for equatorial radius\n",
    "                cos_inclination = (None, None))          # Default bounds for (Earth) inclination to rotation axis\n",
    "\n",
    "values = dict(frequency=300.0 )                          # Fixed spin frequency\n",
    "\n",
    "spacetime = xpsi.Spacetime(bounds=bounds, values=values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constructing the hot regions with blackbody emission"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating parameter:\n",
      "    > Named \"super_colatitude\" with bounds [0.000e+00, 3.142e+00].\n",
      "    > The colatitude of the centre of the superseding region [radians].\n",
      "Creating parameter:\n",
      "    > Named \"super_radius\" with bounds [0.000e+00, 1.571e+00].\n",
      "    > The angular radius of the (circular) superseding region [radians].\n",
      "Creating parameter:\n",
      "    > Named \"phase_shift\" with bounds [0.000e+00, 1.000e-01].\n",
      "    > The phase of the hot region, a periodic parameter [cycles].\n",
      "Creating parameter:\n",
      "    > Named \"super_temperature\" with bounds [3.000e+00, 7.600e+00].\n",
      "    > log10(superseding region effective temperature [K]).\n",
      "Creating parameter:\n",
      "    > Named \"super_colatitude\" with bounds [0.000e+00, 3.142e+00].\n",
      "    > The colatitude of the centre of the superseding region [radians].\n",
      "Creating parameter:\n",
      "    > Named \"super_radius\" with bounds [0.000e+00, 1.571e+00].\n",
      "    > The angular radius of the (circular) superseding region [radians].\n",
      "Creating parameter:\n",
      "    > Named \"phase_shift\" with bounds [0.000e+00, 1.000e-01].\n",
      "    > The phase of the hot region, a periodic parameter [cycles].\n",
      "Creating parameter:\n",
      "    > Named \"super_temperature\" with bounds [3.000e+00, 7.600e+00].\n",
      "    > log10(superseding region effective temperature [K]).\n"
     ]
    }
   ],
   "source": [
    "bounds_hotregion = dict(super_colatitude = (None, None),\n",
    "              super_radius = (None, None),\n",
    "              phase_shift = (0.0, 0.1),\n",
    "              super_temperature = (None, None))\n",
    "\n",
    "# a simple circular, simply-connected spot\n",
    "primary_BB = xpsi.HotRegion(bounds=bounds_hotregion,\n",
    "                            values={}, # no initial values and no derived/fixed\n",
    "                            symmetry=True,\n",
    "                            omit=False,\n",
    "                            cede=False,\n",
    "                            concentric=False,\n",
    "                            sqrt_num_cells=32,\n",
    "                            min_sqrt_num_cells=10,\n",
    "                            max_sqrt_num_cells=64,\n",
    "                            num_leaves=100,\n",
    "                            num_rays=200,\n",
    "                            do_fast=False,\n",
    "                            atm_ext=\"BB\",#default blackbody, other options: \"Num4D\" or \"user\"                         \n",
    "                            prefix='p') # unique prefix needed because >1 instance\n",
    "\n",
    "# overlap of an omission region and\n",
    "# and a radiating super region\n",
    "secondary_BB = xpsi.HotRegion(bounds=bounds_hotregion,\n",
    "                              values={}, # no fixed/derived variables\n",
    "                              symmetry=True,\n",
    "                              omit=False,\n",
    "                              cede=False,\n",
    "                              concentric=False,\n",
    "                              sqrt_num_cells=32,\n",
    "                              min_sqrt_num_cells=10,\n",
    "                              max_sqrt_num_cells=100,\n",
    "                              num_leaves=100,\n",
    "                              num_rays=200,\n",
    "                              do_fast=False,\n",
    "                              is_secondary=True,\n",
    "                              atm_ext=\"BB\",#default blackbody, other options: \"Num4D\" or \"user\"               \n",
    "                              prefix='s')\n",
    "\n",
    "from xpsi import HotRegions\n",
    "hot_BB = HotRegions((primary_BB, secondary_BB))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constructing the photosphere for the hot regions with blackbody emission"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating parameter:\n",
      "    > Named \"mode_frequency\" with fixed value 3.000e+02.\n",
      "    > Coordinate frequency of the mode of radiative asymmetry in the\n",
      "photosphere that is assumed to generate the pulsed signal [Hz].\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Free parameters\n",
       "---------------\n",
       "p__phase_shift: The phase of the hot region, a periodic parameter [cycles].\n",
       "p__super_colatitude: The colatitude of the centre of the superseding region [radians].\n",
       "p__super_radius: The angular radius of the (circular) superseding region [radians].\n",
       "p__super_temperature: log10(superseding region effective temperature [K]).\n",
       "s__phase_shift: The phase of the hot region, a periodic parameter [cycles].\n",
       "s__super_colatitude: The colatitude of the centre of the superseding region [radians].\n",
       "s__super_radius: The angular radius of the (circular) superseding region [radians].\n",
       "s__super_temperature: log10(superseding region effective temperature [K]).\n",
       "\n",
       "Derived/fixed parameters\n",
       "------------------------\n",
       "mode_frequency: Coordinate frequency of the mode of radiative asymmetry in the\n",
       "photosphere that is assumed to generate the pulsed signal [Hz]."
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class CustomPhotosphere_BB(xpsi.Photosphere):\n",
    "    \"\"\" Implement method for imaging.\"\"\"\n",
    "    @property\n",
    "    def global_variables(self):\n",
    "\n",
    "        return np.array([self['p__super_colatitude'],\n",
    "                          self['p__phase_shift'] * 2.0 * math.pi,\n",
    "                          self['p__super_radius'],\n",
    "                          0.0, #self['p__cede_colatitude'],\n",
    "                          0.0, #self['p__phase_shift'] * 2.0 * math.pi - self['p__cede_azimuth'],\n",
    "                          0.0, #self['p__cede_radius'],\n",
    "                          self['s__super_colatitude'],\n",
    "                          (self['s__phase_shift'] + 0.5) * 2.0 * math.pi,\n",
    "                          self['s__super_radius'],\n",
    "                          0.0, #self['s__cede_colatitude'],\n",
    "                          0.0, #(self['s__phase_shift'] + 0.5) * 2.0 * math.pi - self['s__cede_azimuth'],\n",
    "                          0.0, #self['s__cede_radius'],\n",
    "                          self['p__super_temperature'],\n",
    "                          0.0, #self['p__cede_temperature'],\n",
    "                          self['s__super_temperature'],\n",
    "                          0.0]) #self['s__cede_temperature']])  \n",
    "\n",
    "photosphere_BB = CustomPhotosphere_BB(hot = hot_BB, elsewhere = None,\n",
    "                                      values=dict(mode_frequency = spacetime['frequency']))\n",
    "photosphere_BB"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constructing the star with the blackbody photosphere"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Gravitational mass [solar masses],\n",
       " Coordinate equatorial radius [km],\n",
       " Earth distance [kpc],\n",
       " Cosine of Earth inclination to rotation axis,\n",
       " The phase of the hot region, a periodic parameter [cycles],\n",
       " The colatitude of the centre of the superseding region [radians],\n",
       " The angular radius of the (circular) superseding region [radians],\n",
       " log10(superseding region effective temperature [K]),\n",
       " The phase of the hot region, a periodic parameter [cycles],\n",
       " The colatitude of the centre of the superseding region [radians],\n",
       " The angular radius of the (circular) superseding region [radians],\n",
       " log10(superseding region effective temperature [K])]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "star_BB = xpsi.Star(spacetime = spacetime, photospheres = photosphere_BB)\n",
    "star_BB.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Gravitational mass [solar masses] = 1.400e+00,\n",
       " Coordinate equatorial radius [km] = 1.200e+01,\n",
       " Earth distance [kpc] = 2.000e-01,\n",
       " Cosine of Earth inclination to rotation axis = 3.153e-01,\n",
       " The phase of the hot region, a periodic parameter [cycles] = 0.000e+00,\n",
       " The colatitude of the centre of the superseding region [radians] = 1.000e+00,\n",
       " The angular radius of the (circular) superseding region [radians] = 7.500e-02,\n",
       " log10(superseding region effective temperature [K]) = 6.000e+00,\n",
       " The phase of the hot region, a periodic parameter [cycles] = 2.500e-02,\n",
       " The colatitude of the centre of the superseding region [radians] = 2.142e+00,\n",
       " The angular radius of the (circular) superseding region [radians] = 2.000e-01,\n",
       " log10(superseding region effective temperature [K]) = 6.000e+00]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Star_params = [1.4,          # Mass\n",
    "               12.0,         # Radius\n",
    "               0.2,          # Distance\n",
    "               np.cos(1.25), # Cos(inclination)\n",
    "               0.0,          # phase of primary region\n",
    "               1.0,          # Colatitute of primary region\n",
    "               0.075,        # Angular radius of primary region\n",
    "               6.0,          # Temperature of primary region\n",
    "               0.025,        # phase of secondary region\n",
    "               np.pi - 1.0,  # Colatitute of secondary region\n",
    "               0.2,          # Angular radius of secondary region\n",
    "               6.0,]         # Temperature of secondary region\n",
    "star_BB(Star_params)\n",
    "star_BB.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constructing the hot regions with emission from a numerical atmosphere"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating parameter:\n",
      "    > Named \"super_colatitude\" with bounds [0.000e+00, 3.142e+00].\n",
      "    > The colatitude of the centre of the superseding region [radians].\n",
      "Creating parameter:\n",
      "    > Named \"super_radius\" with bounds [0.000e+00, 1.571e+00].\n",
      "    > The angular radius of the (circular) superseding region [radians].\n",
      "Creating parameter:\n",
      "    > Named \"phase_shift\" with bounds [0.000e+00, 1.000e-01].\n",
      "    > The phase of the hot region, a periodic parameter [cycles].\n",
      "Creating parameter:\n",
      "    > Named \"super_temperature\" with bounds [3.000e+00, 7.600e+00].\n",
      "    > log10(superseding region effective temperature [K]).\n",
      "Creating parameter:\n",
      "    > Named \"super_colatitude\" with bounds [0.000e+00, 3.142e+00].\n",
      "    > The colatitude of the centre of the superseding region [radians].\n",
      "Creating parameter:\n",
      "    > Named \"super_radius\" with bounds [0.000e+00, 1.571e+00].\n",
      "    > The angular radius of the (circular) superseding region [radians].\n",
      "Creating parameter:\n",
      "    > Named \"phase_shift\" with bounds [0.000e+00, 1.000e-01].\n",
      "    > The phase of the hot region, a periodic parameter [cycles].\n",
      "Creating parameter:\n",
      "    > Named \"super_temperature\" with bounds [3.000e+00, 7.600e+00].\n",
      "    > log10(superseding region effective temperature [K]).\n"
     ]
    }
   ],
   "source": [
    "# a simple circular, simply-connected spot\n",
    "primary_num4D = xpsi.HotRegion(bounds=bounds_hotregion,\n",
    "                            values={}, # no initial values and no derived/fixed\n",
    "                            symmetry=True,\n",
    "                            omit=False,\n",
    "                            cede=False,\n",
    "                            concentric=False,\n",
    "                            sqrt_num_cells=32,\n",
    "                            min_sqrt_num_cells=10,\n",
    "                            max_sqrt_num_cells=64,\n",
    "                            num_leaves=100,\n",
    "                            num_rays=200,\n",
    "                            do_fast=False,\n",
    "                            atm_ext=\"Num4D\",#default blackbody, other options: \"Num4D\" or \"user\"                         \n",
    "                            prefix='p') # unique prefix needed because >1 instance\n",
    "\n",
    "# overlap of an omission region and\n",
    "# and a radiating super region\n",
    "secondary_num4D = xpsi.HotRegion(bounds=bounds_hotregion,\n",
    "                              values={}, # no fixed/derived variables\n",
    "                              symmetry=True,\n",
    "                              omit=False,\n",
    "                              cede=False,\n",
    "                              concentric=False,\n",
    "                              sqrt_num_cells=32,\n",
    "                              min_sqrt_num_cells=10,\n",
    "                              max_sqrt_num_cells=100,\n",
    "                              num_leaves=100,\n",
    "                              num_rays=200,\n",
    "                              do_fast=False,\n",
    "                              is_secondary=True,\n",
    "                              atm_ext=\"Num4D\",#default blackbody, other options: \"Num4D\" or \"user\"               \n",
    "                              prefix='s')\n",
    "\n",
    "hot_Num4D = HotRegions((primary_num4D, secondary_num4D))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constructing the photosphere for the hot regions with emission from a numerical atmosphere"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Creating parameter:\n",
      "    > Named \"mode_frequency\" with fixed value 3.000e+02.\n",
      "    > Coordinate frequency of the mode of radiative asymmetry in the\n",
      "photosphere that is assumed to generate the pulsed signal [Hz].\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Free parameters\n",
       "---------------\n",
       "p__phase_shift: The phase of the hot region, a periodic parameter [cycles].\n",
       "p__super_colatitude: The colatitude of the centre of the superseding region [radians].\n",
       "p__super_radius: The angular radius of the (circular) superseding region [radians].\n",
       "p__super_temperature: log10(superseding region effective temperature [K]).\n",
       "s__phase_shift: The phase of the hot region, a periodic parameter [cycles].\n",
       "s__super_colatitude: The colatitude of the centre of the superseding region [radians].\n",
       "s__super_radius: The angular radius of the (circular) superseding region [radians].\n",
       "s__super_temperature: log10(superseding region effective temperature [K]).\n",
       "\n",
       "Derived/fixed parameters\n",
       "------------------------\n",
       "mode_frequency: Coordinate frequency of the mode of radiative asymmetry in the\n",
       "photosphere that is assumed to generate the pulsed signal [Hz]."
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "class CustomPhotosphere_num(xpsi.Photosphere):\n",
    "    \"\"\" A photosphere extension to preload the numerical atmosphere NSX. \"\"\"\n",
    "\n",
    "    @xpsi.Photosphere.hot_atmosphere.setter\n",
    "    def hot_atmosphere(self, path):\n",
    "        \n",
    "        size=(35, 14, 67, 166)\n",
    "        # USING THE PRELOAD FUNCTION DEFINED ABOVE\n",
    "        self._hot_atmosphere = preload(path, size)\n",
    "\n",
    "                \n",
    "photosphere_num = CustomPhotosphere_num(hot = hot_Num4D,\n",
    "                                        elsewhere = None,\n",
    "                                        values=dict(mode_frequency = spacetime['frequency']))\n",
    "\n",
    "photosphere_num"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pre-loading the numerical atmosphere by providing the model table (NSX)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "photosphere_num.hot_atmosphere = '../../examples/examples_modeling_tutorial/model_data/nsx_H_v200804.out' "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constructing the star with emission from a numerical atmosphere"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Gravitational mass [solar masses] = 1.400e+00,\n",
       " Coordinate equatorial radius [km] = 1.200e+01,\n",
       " Earth distance [kpc] = 2.000e-01,\n",
       " Cosine of Earth inclination to rotation axis = 3.153e-01,\n",
       " The phase of the hot region, a periodic parameter [cycles] = 0.000e+00,\n",
       " The colatitude of the centre of the superseding region [radians] = 1.000e+00,\n",
       " The angular radius of the (circular) superseding region [radians] = 7.500e-02,\n",
       " log10(superseding region effective temperature [K]) = 6.000e+00,\n",
       " The phase of the hot region, a periodic parameter [cycles] = 2.500e-02,\n",
       " The colatitude of the centre of the superseding region [radians] = 2.142e+00,\n",
       " The angular radius of the (circular) superseding region [radians] = 2.000e-01,\n",
       " log10(superseding region effective temperature [K]) = 6.000e+00]"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "star_num4D = xpsi.Star(spacetime = spacetime, photospheres = photosphere_num)\n",
    "star_num4D(Star_params)  # Same parameters as the blackbody star\n",
    "star_num4D.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the pulse profile of the two stars for comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Defining the energy range to use\n",
    "energies = np.logspace(-1.0, np.log10(3.0), 128, base=10.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "star_BB['cos_inclination'] = np.cos(2.0)\n",
    "star_BB.update()\n",
    "photosphere_BB.integrate(energies, threads=1) # the number of OpenMP threads to use\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "star_num4D['cos_inclination'] = np.cos(2.0)\n",
    "star_num4D.update()\n",
    "photosphere_num.integrate(energies, threads=1) # the number of OpenMP threads to use\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fdf6bd77c10>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(8,8))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.set_ylabel('Signal [arbitrary normalisation]')\n",
    "ax.set_xlabel('Phase [cycles]')\n",
    "    \n",
    "tempY = np.sum(photosphere_BB.signal[0][0], axis=0)\n",
    "ax.plot(hot_BB.phases_in_cycles[0], tempY/np.max(tempY), \n",
    "        'o-', color='k', lw=0.5, markersize=2,\n",
    "         label='Blackbody')\n",
    "\n",
    "    \n",
    "tempY = np.sum(photosphere_num.signal[0][0], axis=0)\n",
    "ax.plot(hot_Num4D.phases_in_cycles[0], tempY/np.max(tempY), 'o-', color='r', lw=0.5, markersize=2,\n",
    "         label='Num. Atmosphere')\n",
    "\n",
    "ax.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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