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   "source": [
    "%matplotlib inline \n",
    "import json\n",
    "import numpy as np\n",
    "import os\n",
    "import pylab as plt"
   ]
  },
  {
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   "id": "18fece92",
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     "status": "completed"
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    "tags": []
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   "outputs": [],
   "source": [
    "import matplotlib as mpl\n",
    "mpl.rc('font', family='Times New Roman')\n",
    "plt.rcParams[\"mathtext.fontset\"] = \"stix\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c9f17f73",
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    "tags": [
     "parameters"
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   "source": [
    "input_file = 'output.json'"
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   "cell_type": "code",
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   "id": "8e658b4f",
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    "tags": [
     "injected-parameters"
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   "outputs": [],
   "source": [
    "# Parameters\n",
    "input_file = \"output.json\"\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d42b9775",
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   "source": [
    "# Values from a previous calculation can be inserted here to reproduce the results \n",
    "step_dict = {}\n",
    "if os.path.exists(input_file):\n",
    "    with open(input_file, 'r') as f:\n",
    "        step_dict_str = json.load(f)\n",
    "    for k,v in step_dict_str.items():\n",
    "        step_dict[int(k)] = v"
   ]
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   "source": [
    "ind, temp_lst = [], []\n",
    "for k,v in step_dict.items():\n",
    "    ind.append(k)\n",
    "    temp_lst.append(v['temperature_next'])"
   ]
  },
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   "source": [
    "temp_array = np.array(temp_lst)[np.array(ind)]"
   ]
  },
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    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Temperature (K)')"
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     "metadata": {},
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the convergence of loop calculations\n",
    "plt.plot(np.arange(1, len(temp_array)), temp_array[0:-1], 'ro-', label=r\"$T^e$\")\n",
    "plt.plot(np.arange(1, len(temp_array)), temp_array[1:], 'bo-', label=r\"$T^p$\")\n",
    "plt.legend(fontsize=14)\n",
    "plt.tick_params(axis='both', labelsize=14)\n",
    "plt.xlabel('Number of loops', fontsize=14)\n",
    "plt.ylabel('Temperature (K)', fontsize=14)\n"
   ]
  }
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