{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6471ed50-4a55-4e5f-9a6f-04c0c4a9c666",
   "metadata": {},
   "outputs": [],
   "source": [
    "import re\n",
    "from pathlib import Path\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import h5py\n",
    "from matplotlib.lines import Line2D\n",
    "from matplotlib.ticker import AutoMinorLocator, MultipleLocator\n",
    "from mpl_toolkits.axes_grid1.inset_locator import inset_axes, zoomed_inset_axes\n",
    "import matplotlib.patheffects as pe\n",
    "import matplotlib\n",
    "from matplotlib.patches import FancyBboxPatch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0722f880-aea9-495f-8994-314a9fcff426",
   "metadata": {},
   "outputs": [],
   "source": [
    "ω1 = 5.089\n",
    "ω2 = 6.189\n",
    "ωtb = 8.1\n",
    "ωtb_red = ωtb*0.9405\n",
    "α1 = -0.310\n",
    "α2 = -0.286\n",
    "ω_ϕ = 0.81658"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6bff992b-1592-40c1-baf1-3ab5be536774",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams.update(\n",
    "    {\n",
    "        \"text.usetex\": True,\n",
    "        \"font.family\": \"serif\",\n",
    "        \"font.serif\": [\"Computer Modern Roman\"],\n",
    "        \"font.size\": 10,\n",
    "    }\n",
    ")\n",
    "\n",
    "π = np.pi\n",
    "ϕ = 0.5 * (1 + np.sqrt(5))\n",
    "\n",
    "columnwidth = 246 * 1 / 72.27  # 246pt to inch\n",
    "textwidth = 510 * 1 / 72.27  # 510pt to inch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77b096e6-77b7-4389-9135-a57338a713d0",
   "metadata": {},
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "f9855738-268c-45de-a747-f7264ed1246f",
   "metadata": {},
   "outputs": [],
   "source": [
    "df_vary_theta = pd.read_pickle(\"ganzhorn_optimized_vary_theta.pickle\")\n",
    "df_res = pd.read_csv(\"ganzhorn_optimizations.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e80a7828-0391-4d44-898a-902110a0ec05",
   "metadata": {},
   "outputs": [],
   "source": [
    "imgfldr = Path(\"images\")\n",
    "imgfldr.mkdir(exist_ok=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5efc4dba-2279-4b0c-b3d2-4785612a6c29",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "2e89fc9b-fd33-493b-ac64-d790eed67bbf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>T</th>\n",
       "      <th>dt</th>\n",
       "      <th>error</th>\n",
       "      <th>g_3</th>\n",
       "      <th>guess_Θ</th>\n",
       "      <th>guess_δ</th>\n",
       "      <th>guess_ωφ</th>\n",
       "      <th>lb_Θ</th>\n",
       "      <th>lb_δ</th>\n",
       "      <th>lb_ωφ</th>\n",
       "      <th>ub_Θ</th>\n",
       "      <th>ub_δ</th>\n",
       "      <th>ub_ωφ</th>\n",
       "      <th>u_Θ</th>\n",
       "      <th>u_δ</th>\n",
       "      <th>u_ωφ</th>\n",
       "      <th>α_3</th>\n",
       "      <th>ω_3</th>\n",
       "      <th>ω_c_0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>800.0</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.179023</td>\n",
       "      <td>0.534071</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.19</td>\n",
       "      <td>5.130723</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.12</td>\n",
       "      <td>5.026548</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.25</td>\n",
       "      <td>5.215044</td>\n",
       "      <td>0.179685</td>\n",
       "      <td>0.190402</td>\n",
       "      <td>5.180487</td>\n",
       "      <td>0.628319</td>\n",
       "      <td>35.361767</td>\n",
       "      <td>50.893801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>800.0</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.030405</td>\n",
       "      <td>0.534071</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.19</td>\n",
       "      <td>5.130723</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.12</td>\n",
       "      <td>5.026548</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.25</td>\n",
       "      <td>5.215044</td>\n",
       "      <td>0.175793</td>\n",
       "      <td>0.122787</td>\n",
       "      <td>5.118527</td>\n",
       "      <td>0.628319</td>\n",
       "      <td>29.530971</td>\n",
       "      <td>50.893801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>800.0</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.065212</td>\n",
       "      <td>0.534071</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.19</td>\n",
       "      <td>5.130723</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.12</td>\n",
       "      <td>5.026548</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.25</td>\n",
       "      <td>5.215044</td>\n",
       "      <td>0.150255</td>\n",
       "      <td>0.191525</td>\n",
       "      <td>5.129422</td>\n",
       "      <td>0.628319</td>\n",
       "      <td>31.114334</td>\n",
       "      <td>50.893801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>800.0</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.081490</td>\n",
       "      <td>0.534071</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.19</td>\n",
       "      <td>5.130723</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.12</td>\n",
       "      <td>5.026548</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.25</td>\n",
       "      <td>5.215044</td>\n",
       "      <td>0.162688</td>\n",
       "      <td>0.188883</td>\n",
       "      <td>5.135918</td>\n",
       "      <td>0.628319</td>\n",
       "      <td>30.636812</td>\n",
       "      <td>50.893801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>800.0</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.169565</td>\n",
       "      <td>0.534071</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.19</td>\n",
       "      <td>5.130723</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.12</td>\n",
       "      <td>5.026548</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.25</td>\n",
       "      <td>5.215044</td>\n",
       "      <td>0.160015</td>\n",
       "      <td>0.170602</td>\n",
       "      <td>5.125624</td>\n",
       "      <td>0.628319</td>\n",
       "      <td>36.442475</td>\n",
       "      <td>50.893801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>210</th>\n",
       "      <td>900.0</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.074375</td>\n",
       "      <td>0.534071</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.12</td>\n",
       "      <td>5.158495</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.08</td>\n",
       "      <td>5.152212</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.15</td>\n",
       "      <td>5.177345</td>\n",
       "      <td>0.121681</td>\n",
       "      <td>0.149995</td>\n",
       "      <td>5.168010</td>\n",
       "      <td>0.628319</td>\n",
       "      <td>26.841768</td>\n",
       "      <td>50.893801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>211</th>\n",
       "      <td>900.0</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.068601</td>\n",
       "      <td>0.534071</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.12</td>\n",
       "      <td>5.158495</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.08</td>\n",
       "      <td>5.152212</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.15</td>\n",
       "      <td>5.177345</td>\n",
       "      <td>0.122571</td>\n",
       "      <td>0.149967</td>\n",
       "      <td>5.164681</td>\n",
       "      <td>0.628319</td>\n",
       "      <td>27.470086</td>\n",
       "      <td>50.893801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>212</th>\n",
       "      <td>900.0</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.041279</td>\n",
       "      <td>0.534071</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.12</td>\n",
       "      <td>5.158495</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.08</td>\n",
       "      <td>5.152212</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.15</td>\n",
       "      <td>5.177345</td>\n",
       "      <td>0.123806</td>\n",
       "      <td>0.149920</td>\n",
       "      <td>5.164564</td>\n",
       "      <td>0.628319</td>\n",
       "      <td>28.601060</td>\n",
       "      <td>50.893801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>213</th>\n",
       "      <td>900.0</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.043481</td>\n",
       "      <td>0.534071</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.12</td>\n",
       "      <td>5.158495</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.08</td>\n",
       "      <td>5.152212</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.15</td>\n",
       "      <td>5.177345</td>\n",
       "      <td>0.125258</td>\n",
       "      <td>0.149813</td>\n",
       "      <td>5.161589</td>\n",
       "      <td>0.628319</td>\n",
       "      <td>29.229378</td>\n",
       "      <td>50.893801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>214</th>\n",
       "      <td>900.0</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.103925</td>\n",
       "      <td>0.534071</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.12</td>\n",
       "      <td>5.158495</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.08</td>\n",
       "      <td>5.152212</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.15</td>\n",
       "      <td>5.177345</td>\n",
       "      <td>0.122031</td>\n",
       "      <td>0.150000</td>\n",
       "      <td>5.174587</td>\n",
       "      <td>0.628319</td>\n",
       "      <td>33.753271</td>\n",
       "      <td>50.893801</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>215 rows × 19 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         T    dt     error       g_3  guess_Θ  guess_δ  guess_ωφ  lb_Θ  lb_δ  \\\n",
       "0    800.0  0.01  0.179023  0.534071     0.15     0.19  5.130723   0.1  0.12   \n",
       "1    800.0  0.01  0.030405  0.534071     0.15     0.19  5.130723   0.1  0.12   \n",
       "2    800.0  0.01  0.065212  0.534071     0.15     0.19  5.130723   0.1  0.12   \n",
       "3    800.0  0.01  0.081490  0.534071     0.15     0.19  5.130723   0.1  0.12   \n",
       "4    800.0  0.01  0.169565  0.534071     0.15     0.19  5.130723   0.1  0.12   \n",
       "..     ...   ...       ...       ...      ...      ...       ...   ...   ...   \n",
       "210  900.0  0.01  0.074375  0.534071     0.11     0.12  5.158495   0.1  0.08   \n",
       "211  900.0  0.01  0.068601  0.534071     0.11     0.12  5.158495   0.1  0.08   \n",
       "212  900.0  0.01  0.041279  0.534071     0.11     0.12  5.158495   0.1  0.08   \n",
       "213  900.0  0.01  0.043481  0.534071     0.11     0.12  5.158495   0.1  0.08   \n",
       "214  900.0  0.01  0.103925  0.534071     0.11     0.12  5.158495   0.1  0.08   \n",
       "\n",
       "        lb_ωφ  ub_Θ  ub_δ     ub_ωφ       u_Θ       u_δ      u_ωφ       α_3  \\\n",
       "0    5.026548  0.22  0.25  5.215044  0.179685  0.190402  5.180487  0.628319   \n",
       "1    5.026548  0.22  0.25  5.215044  0.175793  0.122787  5.118527  0.628319   \n",
       "2    5.026548  0.22  0.25  5.215044  0.150255  0.191525  5.129422  0.628319   \n",
       "3    5.026548  0.22  0.25  5.215044  0.162688  0.188883  5.135918  0.628319   \n",
       "4    5.026548  0.22  0.25  5.215044  0.160015  0.170602  5.125624  0.628319   \n",
       "..        ...   ...   ...       ...       ...       ...       ...       ...   \n",
       "210  5.152212  0.15  0.15  5.177345  0.121681  0.149995  5.168010  0.628319   \n",
       "211  5.152212  0.15  0.15  5.177345  0.122571  0.149967  5.164681  0.628319   \n",
       "212  5.152212  0.15  0.15  5.177345  0.123806  0.149920  5.164564  0.628319   \n",
       "213  5.152212  0.15  0.15  5.177345  0.125258  0.149813  5.161589  0.628319   \n",
       "214  5.152212  0.15  0.15  5.177345  0.122031  0.150000  5.174587  0.628319   \n",
       "\n",
       "           ω_3      ω_c_0  \n",
       "0    35.361767  50.893801  \n",
       "1    29.530971  50.893801  \n",
       "2    31.114334  50.893801  \n",
       "3    30.636812  50.893801  \n",
       "4    36.442475  50.893801  \n",
       "..         ...        ...  \n",
       "210  26.841768  50.893801  \n",
       "211  27.470086  50.893801  \n",
       "212  28.601060  50.893801  \n",
       "213  29.229378  50.893801  \n",
       "214  33.753271  50.893801  \n",
       "\n",
       "[215 rows x 19 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f08db0b8-1bd6-4038-9db5-f38caffc2023",
   "metadata": {},
   "outputs": [],
   "source": [
    "res_min = df_res.iloc[df_res.sort_values(\"ω_3\").groupby(\"ω_3\")[\"error\"].idxmin()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "cac1a596-fd1d-4952-8f0a-fcf3423bae65",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_J_T_PEs(w_u):\n",
    "    def J_T_PE_0(row):\n",
    "        return np.amin(w_u * row.du0 + (1 - w_u) * row.pe0)\n",
    "\n",
    "    def J_T_PE_1(row):\n",
    "        return np.amin(w_u * row.du1 + (1 - w_u) * row.pe1)\n",
    "\n",
    "    def J_T_PE_01(row):\n",
    "        return np.amin(\n",
    "            w_u * row.du0 + (1 - w_u) * row.pe0 +\n",
    "            w_u * row.du1 + (1 - w_u) * row.pe1 +\n",
    "            row.simil\n",
    "        )\n",
    "\n",
    "    return J_T_PE_0, J_T_PE_1, J_T_PE_01\n",
    "\n",
    "w_unitarity = 0.8\n",
    "w_unit_tot = 0.8\n",
    "J_T_PE_0, J_T_PE_1, J_T_PE_01 = get_J_T_PEs(w_unitarity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "9e959eac-c3a7-4a0d-8ac3-a313de77994d",
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_sel = .15\n",
    "df_orig = df_vary_theta[df_vary_theta.theta==theta_sel]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79a8298b-e28f-4818-bbc0-21422489fbdf",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "dac06ec1-3d79-4641-81b9-840cba1a0c56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 705.687x211.706 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(\n",
    "    1,\n",
    "    1,\n",
    "    figsize=(textwidth, textwidth*0.30),\n",
    "    sharex=True,\n",
    "    sharey=True,\n",
    ")\n",
    "\n",
    "α3 = -0.100\n",
    "c_sr = \"dodgerblue\"\n",
    "α_sr = 0.9\n",
    "df_g = df_orig\n",
    "\n",
    "\n",
    "ax.plot(\n",
    "    df_g.ω3,\n",
    "    df_g.apply(J_T_PE_01, axis=1),\n",
    "    label=f\"\",\n",
    "    ls=\"-\",\n",
    "    alpha=0.6,\n",
    "    c=\"gray\",\n",
    ")\n",
    "for omega_i, alpha_i in zip([ω1, ω2], [α1, α2]):\n",
    "    ax.axvline(omega_i, ls=(0,(2,.5)), c=c_sr, alpha=α_sr)\n",
    "    ax.axvline(omega_i - α3, ls=\"--\", c=c_sr, alpha=α_sr)\n",
    "    ax.axvline(omega_i + alpha_i, ls=\"-.\", c=c_sr, alpha=α_sr)\n",
    "ax.axvline(ω2 + 2*α2, ls=(0, (1.0, 1.0, 1.0, 1.0, 3.0, 1.0)), c=c_sr, alpha=α_sr)\n",
    "\n",
    "#===============================================================\n",
    "vleg = ax.legend(\n",
    "    [\n",
    "        Line2D([], [], ls=\"-\", c=\"gray\", alpha=0.6),\n",
    "        Line2D([], [], ls=(0,(2,.5)), c=c_sr, alpha=α_sr),\n",
    "        Line2D([], [], ls=\"-.\", c=c_sr, alpha=α_sr),\n",
    "        Line2D([], [], ls=\"--\", c=c_sr, alpha=α_sr),\n",
    "        Line2D([], [], ls=(0, (1.0, 1.0, 1.0, 1.0, 3.0, 1.0)), c=c_sr, alpha=α_sr),\n",
    "    ],\n",
    "    [\n",
    "        r\"$\\mathcal{J}^{\\mathrm{orig.}}_\\mathrm{PE}$\",\n",
    "        r\"$\\omega_3 = \\omega_i$\",\n",
    "        r\"$\\omega_3 = \\omega_i + \\alpha_i$\",\n",
    "        r\"$\\omega_3+\\alpha_3 = \\omega_i$\",\n",
    "        r\"$\\omega_3 = \\omega_2 + 2\\alpha_2$\",\n",
    "    ], bbox_to_anchor=(-.01, 0.97), loc=\"lower left\", ncol=5, frameon=False,\n",
    ")\n",
    "ax.add_artist(vleg)\n",
    "\n",
    "#================================================================\n",
    "ax.scatter(res_min.ω_3/(2*np.pi), res_min.error, label=\"parameter optimization\", marker=\"x\", c=\"red\")\n",
    "ax.legend(loc=\"upper left\", frameon=False, bbox_to_anchor=(.02, 1.03), handletextpad=0.0)\n",
    "#===============================================================\n",
    "\n",
    "ax.set_xlabel(\"$\\\\omega_3$ (GHz)\")\n",
    "ax.set_ylabel(r\"$\\mathcal{J}_\\mathrm{PE}$\")\n",
    "ax.set_xlim(4.0, 6.0)\n",
    "ax.set_ylim(0.0, 1.5)\n",
    "\n",
    "\n",
    "bbox_props = dict(boxstyle='round', facecolor='none', pad=.5, lw=0.5)\n",
    "\n",
    "fig.subplots_adjust(left=0.065, right=0.980, bottom=0.200, top=0.875, hspace=0.1)\n",
    "\n",
    "plt.savefig(imgfldr/\"ganzhorn.optimized_spectrum.pdf\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1cfa5fc-7e98-405a-b3ef-36b637de2bc4",
   "metadata": {},
   "source": [
    "---"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv-pepaper",
   "language": "python",
   "name": "venv-pepaper"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
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