Ion Shuttling Simulation (new) 20241205.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a30fa971",
   "metadata": {},
   "source": [
    "This is a notebook set up by Maggie Ke and later optimized by Bingran You"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e426e133",
   "metadata": {},
   "source": [
    "### Generate shuttling function CSV file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5a7c8e95",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "          Value\n",
      "1  0.000000e+00\n",
      "2  0.000000e+00\n",
      "3  0.000000e+00\n",
      "4  1.234871e-08\n",
      "5  1.784066e-04\n"
     ]
    },
    {
     "ename": "KeyError",
     "evalue": "'Time (us)'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "File \u001b[0;32m~/Library/CloudStorage/OneDrive-Personal/UCB STUDY/Research/Multiplexing/multiplexing/lib/python3.9/site-packages/pandas/core/indexes/base.py:3805\u001b[0m, in \u001b[0;36mIndex.get_loc\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m   3804\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m-> 3805\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_engine\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget_loc\u001b[49m\u001b[43m(\u001b[49m\u001b[43mcasted_key\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   3806\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mKeyError\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m err:\n",
      "File \u001b[0;32mindex.pyx:167\u001b[0m, in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n",
      "File \u001b[0;32mindex.pyx:196\u001b[0m, in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n",
      "File \u001b[0;32mpandas/_libs/hashtable_class_helper.pxi:7081\u001b[0m, in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[0;34m()\u001b[0m\n",
      "File \u001b[0;32mpandas/_libs/hashtable_class_helper.pxi:7089\u001b[0m, in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;31mKeyError\u001b[0m: 'Time (us)'",
      "\nThe above exception was the direct cause of the following exception:\n",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[1], line 144\u001b[0m\n\u001b[1;32m    142\u001b[0m plt\u001b[38;5;241m.\u001b[39mfigure(figsize\u001b[38;5;241m=\u001b[39m(half_column_width_inches, half_column_width_inches \u001b[38;5;241m/\u001b[39m aspect_ratio))\n\u001b[1;32m    143\u001b[0m \u001b[38;5;66;03m# plt.title('Shuttling function', fontdict={'family': 'STIXGeneral', 'size': 12})\u001b[39;00m\n\u001b[0;32m--> 144\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot(\u001b[43mdata_resampled\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43mr\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[38;5;124;43mTime (us)\u001b[39;49m\u001b[38;5;124;43m'\u001b[39;49m\u001b[43m]\u001b[49m \u001b[38;5;241m*\u001b[39m (\u001b[38;5;241m0.85\u001b[39m) \u001b[38;5;241m*\u001b[39m \u001b[38;5;241m1e6\u001b[39m, data_resampled[\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mValue\u001b[39m\u001b[38;5;124m'\u001b[39m] \u001b[38;5;241m*\u001b[39m (\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m0.0682\u001b[39m\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m1e6\u001b[39m) \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m20.17\u001b[39m, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mC0\u001b[39m\u001b[38;5;124m'\u001b[39m, linewidth\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m2.5\u001b[39m, label\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mProgrammed waveform\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m    145\u001b[0m plt\u001b[38;5;241m.\u001b[39maxvline(\u001b[38;5;241m10.5\u001b[39m, color\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mr\u001b[39m\u001b[38;5;124m'\u001b[39m, linewidth\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0.5\u001b[39m, linestyle\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m--\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m    146\u001b[0m plt\u001b[38;5;241m.\u001b[39maxvline(\u001b[38;5;241m10.5\u001b[39m \u001b[38;5;241m+\u001b[39m \u001b[38;5;241m1.7\u001b[39m, color\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mr\u001b[39m\u001b[38;5;124m'\u001b[39m, linewidth\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0.5\u001b[39m, linestyle\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m--\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
      "File \u001b[0;32m~/Library/CloudStorage/OneDrive-Personal/UCB STUDY/Research/Multiplexing/multiplexing/lib/python3.9/site-packages/pandas/core/frame.py:4102\u001b[0m, in \u001b[0;36mDataFrame.__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m   4100\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcolumns\u001b[38;5;241m.\u001b[39mnlevels \u001b[38;5;241m>\u001b[39m \u001b[38;5;241m1\u001b[39m:\n\u001b[1;32m   4101\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_getitem_multilevel(key)\n\u001b[0;32m-> 4102\u001b[0m indexer \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcolumns\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mget_loc\u001b[49m\u001b[43m(\u001b[49m\u001b[43mkey\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   4103\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m is_integer(indexer):\n\u001b[1;32m   4104\u001b[0m     indexer \u001b[38;5;241m=\u001b[39m [indexer]\n",
      "File \u001b[0;32m~/Library/CloudStorage/OneDrive-Personal/UCB STUDY/Research/Multiplexing/multiplexing/lib/python3.9/site-packages/pandas/core/indexes/base.py:3812\u001b[0m, in \u001b[0;36mIndex.get_loc\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m   3807\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28misinstance\u001b[39m(casted_key, \u001b[38;5;28mslice\u001b[39m) \u001b[38;5;129;01mor\u001b[39;00m (\n\u001b[1;32m   3808\u001b[0m         \u001b[38;5;28misinstance\u001b[39m(casted_key, abc\u001b[38;5;241m.\u001b[39mIterable)\n\u001b[1;32m   3809\u001b[0m         \u001b[38;5;129;01mand\u001b[39;00m \u001b[38;5;28many\u001b[39m(\u001b[38;5;28misinstance\u001b[39m(x, \u001b[38;5;28mslice\u001b[39m) \u001b[38;5;28;01mfor\u001b[39;00m x \u001b[38;5;129;01min\u001b[39;00m casted_key)\n\u001b[1;32m   3810\u001b[0m     ):\n\u001b[1;32m   3811\u001b[0m         \u001b[38;5;28;01mraise\u001b[39;00m InvalidIndexError(key)\n\u001b[0;32m-> 3812\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mKeyError\u001b[39;00m(key) \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01merr\u001b[39;00m\n\u001b[1;32m   3813\u001b[0m \u001b[38;5;28;01mexcept\u001b[39;00m \u001b[38;5;167;01mTypeError\u001b[39;00m:\n\u001b[1;32m   3814\u001b[0m     \u001b[38;5;66;03m# If we have a listlike key, _check_indexing_error will raise\u001b[39;00m\n\u001b[1;32m   3815\u001b[0m     \u001b[38;5;66;03m#  InvalidIndexError. Otherwise we fall through and re-raise\u001b[39;00m\n\u001b[1;32m   3816\u001b[0m     \u001b[38;5;66;03m#  the TypeError.\u001b[39;00m\n\u001b[1;32m   3817\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_check_indexing_error(key)\n",
      "\u001b[0;31mKeyError\u001b[0m: 'Time (us)'"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 425x212.5 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "matplotlib.rcParams.update(\n",
    "        {\"font.family\": \"STIXGeneral\",\n",
    "         \"xtick.labelsize\": 12,\n",
    "         \"xtick.direction\": \"in\",\n",
    "         \"xtick.major.pad\": 3,\n",
    "         \"xtick.top\": True,\n",
    "         \"ytick.labelsize\": 12,\n",
    "         \"ytick.direction\": \"in\",\n",
    "         \"ytick.right\": True,\n",
    "         \"axes.labelsize\": 12,\n",
    "         \"axes.labelpad\": 3,\n",
    "         \"axes.grid\": True\n",
    "    }\n",
    ")\n",
    "\n",
    "def evaluate_shuttling_function(t):\n",
    "    # Constants\n",
    "    k1 = 1.0\n",
    "    k2 = -1.5e5\n",
    "    k3 = 6.0e9\n",
    "\n",
    "    # Check the time range and apply the corresponding formula\n",
    "    if 0 <= t < 2e-6:  # range 0us to 5us\n",
    "        return 0\n",
    "    elif 2e-6 <= t < 13e-6:  # range 5us to 15us\n",
    "        t0 = 2e-6\n",
    "        t_adjusted = t - t0\n",
    "        # -11.056e-6 * 1.0e16*(k1*(t^3)+k2*(t^4)+k3*(t^5)) -(0.000e-6)\n",
    "        return -11.056e-6 * 1.0e16 * (k1 * (t_adjusted**3) + k2 * (t_adjusted**4) + k3 * (t_adjusted**5)) - 0.000e-6\n",
    "    elif 13e-6 <= t < 15e-6:  # range 15us to 25us\n",
    "        t0 = 13e-6\n",
    "        return -11.056e-6\n",
    "    elif 15e-6 <= t < 25e-6:  # range 25us to 35us\n",
    "        t0 = 15e-6\n",
    "        t_adjusted = t - t0\n",
    "        # -9.373e-6 * 1.0e16*(k1*(t^3)+k2*(t^4)+k3*(t^5)) -(11.056e-6)\n",
    "        return -9.373e-6 * 1.0e16 * (k1 * (t_adjusted**3) + k2 * (t_adjusted**4) + k3 * (t_adjusted**5)) - 11.056e-6\n",
    "    elif 25e-6 <= t < 27e-6:  # range 35us to 45us\n",
    "        t0 = 25e-6\n",
    "        return -20.429e-6\n",
    "    elif 27e-6 <= t < 37e-6:  # range 45us to 55us\n",
    "        t0 = 27e-6\n",
    "        t_adjusted = t - t0\n",
    "        # -8.669e-6 * 1.0e16*(k1*(t^3)+k2*(t^4)+k3*(t^5)) -(20.429e-6)\n",
    "        return -8.669e-6 * 1.0e16 * (k1 * (t_adjusted**3) + k2 * (t_adjusted**4) + k3 * (t_adjusted**5)) - 20.429e-6\n",
    "    elif 37e-6 <= t < 39e-6:  # range 55us to 65us\n",
    "        t0 = 37e-6\n",
    "        return -29.098e-6\n",
    "    elif 39e-6 <= t < 49e-6:  # range 65us to 75us\n",
    "        t0 = 39e-6\n",
    "        t_adjusted = t - t0\n",
    "        # -8.385e-6 * 1.0e16*(k1*(t^3)+k2*(t^4)+k3*(t^5)) -(29.098e-6)\n",
    "        return -8.385e-6 * 1.0e16 * (k1 * (t_adjusted**3) + k2 * (t_adjusted**4) + k3 * (t_adjusted**5)) - 29.098e-6\n",
    "    elif 49e-6 <= t < 51e-6:  # range 75us to 85us\n",
    "        t0 = 49e-6\n",
    "        return -37.483e-6\n",
    "    elif 51e-6 <= t < 61e-6:  # range 85us to 95us\n",
    "        t0 = 51e-6\n",
    "        t_adjusted = t - t0\n",
    "        # -8.385e-6 * 1.0e16*(k1*(t^3)+k2*(t^4)+k3*(t^5)) -(37.483e-6)\n",
    "        return -8.385e-6 * 1.0e16 * (k1 * (t_adjusted**3) + k2 * (t_adjusted**4) + k3 * (t_adjusted**5)) - 37.483e-6\n",
    "    elif 61e-6 <= t < 63e-6:  # range 95us to 105us\n",
    "        t0 = 61e-6\n",
    "        return -45.869e-6\n",
    "    elif 63e-6 <= t < 73e-6:  # range 105us to 115us\n",
    "        t0 = 63e-6\n",
    "        t_adjusted = t - t0\n",
    "        # -8.669e-6 * 1.0e16*(k1*(t^3)+k2*(t^4)+k3*(t^5)) -(45.869e-6)\n",
    "        return -8.669e-6 * 1.0e16 * (k1 * (t_adjusted**3) + k2 * (t_adjusted**4) + k3 * (t_adjusted**5)) - 45.869e-6\n",
    "    elif 73e-6 <= t < 75e-6:  # range 115us to 125us\n",
    "        t0 = 73e-6\n",
    "        return -54.538e-6\n",
    "    elif 75e-6 <= t < 85e-6:  # range 125us to 135us\n",
    "        t0 = 75e-6\n",
    "        t_adjusted = t - t0\n",
    "        # -9.373e-6 * 1.0e16*(k1*(t^3)+k2*(t^4)+k3*(t^5)) -(54.538e-6)\n",
    "        return -9.373e-6 * 1.0e16 * (k1 * (t_adjusted**3) + k2 * (t_adjusted**4) + k3 * (t_adjusted**5)) - 54.538e-6\n",
    "    elif 85e-6 <= t < 87e-6:  # range 135us to 145us\n",
    "        t0 = 85e-6\n",
    "        return -63.911e-6\n",
    "    elif 87e-6 <= t < 97e-6:  # range 145us to 155us\n",
    "        t0 = 87e-6\n",
    "        t_adjusted = t - t0\n",
    "        # -11.056e-6 * 1.0e16*(k1*(t^3)+k2*(t^4)+k3*(t^5)) -(63.911e-6)\n",
    "        return -11.056e-6 * 1.0e16 * (k1 * (t_adjusted**3) + k2 * (t_adjusted**4) + k3 * (t_adjusted**5)) - 63.911e-6\n",
    "    elif 97e-6 <= t < 99e-6:  # range 155us to 165us\n",
    "        t0 = 97e-6\n",
    "        return -74.967e-6\n",
    "    elif 99e-6 <= t < 134e-6:\n",
    "        t_adjusted = t - 99e-6\n",
    "        return 1.7485e10 * (t_adjusted**3) - 7.49358e14 * (t_adjusted**4) + 8.56409e18 * (t_adjusted**5) -74.967e-6\n",
    "    else:\n",
    "        return 0\n",
    "\n",
    "# Total number of points and samples per second\n",
    "num_points = 16384\n",
    "samples_per_second = 5e7  # 50,000,000 samples per second\n",
    "\n",
    "# Total time range in microseconds\n",
    "total_time_us = 134 * 1e-6\n",
    "\n",
    "# Generate time points\n",
    "time_points = np.linspace(0, total_time_us, int(num_points))\n",
    "\n",
    "# Calculate values for each time point using evaluate_shuttling_function\n",
    "calculated_values = [evaluate_shuttling_function(t) for t in time_points]\n",
    "calculated_values = np.array(calculated_values)\n",
    "calculated_values = calculated_values * (-0.0682*1e6)\n",
    "\n",
    "# Create DataFrame\n",
    "df = pd.DataFrame({\n",
    "    'Time (us)': time_points,\n",
    "    'Value': calculated_values\n",
    "})\n",
    "\n",
    "df = pd.DataFrame({\n",
    "    'Value': calculated_values\n",
    "})\n",
    "\n",
    "# Save to CSV\n",
    "csv_filename = 'shuttling_function.csv'\n",
    "df.to_csv(csv_filename, index=False)\n",
    "\n",
    "# Load the CSV file\n",
    "file_path = csv_filename\n",
    "data = pd.read_csv(file_path)\n",
    "\n",
    "# Resample the data if necessary\n",
    "data_resampled = data.groupby(np.arange(len(data)) // 50).mean()\n",
    "data_resampled = data_resampled.iloc[1:]\n",
    "data_resampled = data_resampled.iloc[:-1]\n",
    "print(data_resampled.head())\n",
    "\n",
    "# Plotting\n",
    "half_column_width_inches = 4.25\n",
    "aspect_ratio = 2  # You can adjust this for your desired aspect ratio\n",
    "plt.figure(figsize=(half_column_width_inches, half_column_width_inches / aspect_ratio))\n",
    "# plt.title('Shuttling function', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.plot(data_resampled[r'Time (us)'] * (0.85) * 1e6, data_resampled['Value'] * (-0.0682*1e6) + 20.17, 'C0', linewidth=2.5, label='Programmed waveform')\n",
    "plt.axvline(10.5, color='r', linewidth=0.5, linestyle='--')\n",
    "plt.axvline(10.5 + 1.7, color='r', linewidth=0.5, linestyle='--')\n",
    "# plt.xlabel(r'Time ($\\mu$$s$)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "# plt.ylabel('Voltage (V)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.grid(True)\n",
    "legend_fontsize = 12\n",
    "# plt.legend(fontsize=legend_fontsize)\n",
    "pdf_filename = 'Shuttling_function_new_test.pdf'\n",
    "plt.savefig(pdf_filename, format='pdf', bbox_inches='tight')\n",
    "plt.show()\n",
    "\n",
    "# Plotting\n",
    "half_column_width_inches = 4.25\n",
    "aspect_ratio = 2  # You can adjust this for your desired aspect ratio\n",
    "plt.figure(figsize=(half_column_width_inches, half_column_width_inches / aspect_ratio))\n",
    "# plt.title('Shuttling function', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.plot(data_resampled[r'Time (us)'] * (0.85) * 1e6, -data_resampled['Value'] * (-0.0682*1e6) + 20.17, 'C0', linewidth=2.5, label='Programmed waveform')\n",
    "plt.axvline(10.5, color='r', linewidth=0.5, linestyle='--')\n",
    "plt.axvline(10.5 + 1.7, color='r', linewidth=0.5, linestyle='--')\n",
    "# plt.xlabel(r'Time ($\\mu$$s$)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "# plt.ylabel('Voltage (V)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.grid(True)\n",
    "legend_fontsize = 12\n",
    "# plt.legend(fontsize=legend_fontsize)\n",
    "pdf_filename = 'Shuttling_function_new_test_2.pdf'\n",
    "plt.savefig(pdf_filename, format='pdf', bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bb9f4ec",
   "metadata": {},
   "source": [
    "### Set up parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "6532267d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import standard libraries\n",
    "import math\n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "from scipy.integrate import solve_ivp\n",
    "from scipy.ndimage import gaussian_filter\n",
    "from scipy.optimize import fsolve, leastsq,root,brentq,newton,curve_fit\n",
    "from sympy.utilities.lambdify import lambdify\n",
    "from sympy import sympify\n",
    "from sympy import var\n",
    "\n",
    "import timeit\n",
    "from time import time\n",
    "from mpl_toolkits import mplot3d\n",
    "\n",
    "# Set matplotlib parameters for consistent figure styling\n",
    "plt.rcParams.update({\n",
    "    \"font.family\": \"STIXGeneral\",\n",
    "    \"xtick.labelsize\": 12,\n",
    "    \"xtick.direction\": \"in\",\n",
    "    \"xtick.major.pad\": 3,\n",
    "    \"xtick.top\": True,\n",
    "    \"ytick.labelsize\": 12,\n",
    "    \"ytick.direction\": \"in\",\n",
    "    \"ytick.right\": True,\n",
    "    \"axes.labelsize\": 12,\n",
    "    \"axes.labelpad\": 3,\n",
    "    \"axes.grid\": True,\n",
    "})\n",
    "\n",
    "# Constants\n",
    "E0 = 8.85e-12\n",
    "e = 1.6e-19\n",
    "m = 6.64215627e-26\n",
    "pi = math.pi\n",
    "h_bar = 1.0546e-34\n",
    "\n",
    "# Parameters for the simulation\n",
    "T_factor = (121 / 133.93969396934) * 1.1625  # The time factor for the simulation\n",
    "NUM_VOLTAGE_POINTS = 500  # The points for voltage sampling\n",
    "T = 150 * 1e-6 * T_factor # Total time duration in s unit\n",
    "points = 3000000  # Number of points at which to evaluate the solution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65da1f50",
   "metadata": {},
   "source": [
    "### Load useful functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "cca29eee",
   "metadata": {},
   "outputs": [],
   "source": [
    "def pfit(x_data, y_data, degree, plot=False):\n",
    "    \"\"\"\n",
    "    Polynomial fit of data.\n",
    "\n",
    "    Parameters:\n",
    "    - x_data: x data points\n",
    "    - y_data: y data points\n",
    "    - degree: Degree of the polynomial\n",
    "    - plot: Boolean to plot the original data and the fit\n",
    "\n",
    "    Returns:\n",
    "    - coeffs: Coefficients of the polynomial fit\n",
    "    \"\"\"\n",
    "    coeffs = np.polyfit(x_data, y_data, degree)\n",
    "    poly = np.poly1d(coeffs)\n",
    "    y_fit = poly(x_data)\n",
    "    if plot:\n",
    "        plt.plot(x_data, y_data, label='Original')\n",
    "        plt.plot(x_data, y_fit, label='Fit')\n",
    "        plt.legend()\n",
    "        plt.show()\n",
    "    return coeffs\n",
    "\n",
    "def v_har(delta_x, x_data, y_data, plot=False):\n",
    "    \"\"\"\n",
    "    Harmonic fit around a minimum point within a specified range.\n",
    "\n",
    "    Parameters:\n",
    "    - delta_x: Range around the minimum point to consider for the fit\n",
    "    - x_data: x data points\n",
    "    - y_data: y data points\n",
    "    - plot: Boolean to plot the original data and the fit\n",
    "\n",
    "    Returns:\n",
    "    - coeffs: Coefficients of the polynomial fit\n",
    "    \"\"\"\n",
    "    def mini(x_data, y_data):\n",
    "        \"\"\"Find the minimum point of the potential.\"\"\"\n",
    "        min_index = np.argmin(y_data)\n",
    "        return x_data[min_index]\n",
    "\n",
    "    min_x = mini(x_data, y_data)\n",
    "    mask = (x_data >= min_x - delta_x) & (x_data <= min_x + delta_x)\n",
    "    fit_x_data = x_data[mask]\n",
    "    fit_y_data = y_data[mask]\n",
    "\n",
    "    coeffs = np.polyfit(fit_x_data, fit_y_data, 2)  # Degree is always 2 for harmonic fit\n",
    "    poly = np.poly1d(coeffs)\n",
    "    y_fit = poly(x_data)\n",
    "\n",
    "    if plot:\n",
    "        plt.plot(x_data, y_data, label='Original')\n",
    "        plt.plot(x_data, y_fit, label='Fit')\n",
    "        plt.xlabel('x/m')\n",
    "        plt.ylabel('Potential Energy/J')\n",
    "        plt.legend()\n",
    "        plt.show()\n",
    "\n",
    "    return coeffs"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b48836af",
   "metadata": {},
   "source": [
    "### Display shuttling functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "60da2c22",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Length of time_array: 10000, Length of scaled_voltage_array: 10000\n",
      "scaled_voltage_array_min = 23.33, scaled_voltage_array_max = 28.68\n",
      "First 5 elements of time_array: [0.00633273 0.02040545 0.03447817 0.0485509  0.06262362]\n",
      "First 5 elements of scaled_voltage_array: [28.68 28.68 28.68 28.68 28.68]\n",
      "The time range =  140.71950023228257  us\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 425x212.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 425x212.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def scale_voltage_array(voltage_array, original_min, original_max, new_min, new_max):\n",
    "    \"\"\"Scales the voltage array based on the original and new min/max values.\"\"\"\n",
    "    return ((voltage_array - original_min) / (original_max - original_min)) * (new_max - new_min) + new_min\n",
    "\n",
    "def load_and_process_data(filepath, smooth = False, smooth_window = 100):\n",
    "    \"\"\"Loads the CSV, processes the data, and saves time and scaled voltage arrays.\"\"\"\n",
    "    # Load the CSV file\n",
    "    df = pd.read_csv(filepath)\n",
    "    if(smooth == True):\n",
    "        df = df.groupby(np.arange(len(df)) // smooth_window).mean()\n",
    "\n",
    "    # Extract arrays of time and voltage, apply scaling and corrections\n",
    "    time_array = df['Time (us)'].to_numpy() * T_factor * 1e6\n",
    "    voltage_array = df['Value'].to_numpy() * (-0.0682 * 1e6) + 20.17\n",
    "    \n",
    "    # Scale the first voltage array\n",
    "    original_min, original_max = min(voltage_array), max(voltage_array)\n",
    "    scaled_voltage_array = scale_voltage_array(voltage_array, original_min, original_max, 20.21, 25.59)\n",
    "    \n",
    "    # Save arrays\n",
    "    np.save('time_array.npy', time_array)  # Unit: us\n",
    "    np.save('DC1_voltage_array.npy', scaled_voltage_array)\n",
    "    \n",
    "    # Process for the second voltage array with different scaling\n",
    "    voltage_array = -voltage_array\n",
    "    original_min, original_max = min(voltage_array), max(voltage_array)\n",
    "    scaled_voltage_array = scale_voltage_array(voltage_array, original_min, original_max, 23.33, 28.68)\n",
    "    \n",
    "    # Save the second voltage array\n",
    "    np.save('DC2_voltage_array.npy', scaled_voltage_array)\n",
    "    \n",
    "    return time_array, scaled_voltage_array\n",
    "\n",
    "def plot_voltage_time(time_array, scaled_voltage_array, pdf_filename):\n",
    "    \"\"\"Plots the voltage array over time and saves the plot to a PDF.\"\"\"\n",
    "    half_column_width_inches = 4.25\n",
    "    aspect_ratio = 2\n",
    "    plt.figure(figsize=(half_column_width_inches, half_column_width_inches / aspect_ratio))\n",
    "    plt.title('Shuttling function', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "    plt.plot(time_array, scaled_voltage_array, 'C0', linewidth=2.5, label='Programmed waveform')\n",
    "    plt.axvline(13 * T_factor, color='r', linewidth=0.5, linestyle='--')\n",
    "    plt.axvline((15) * T_factor, color='r', linewidth=0.5, linestyle='--')\n",
    "    plt.xlabel(r'Time ($\\mu$$s$)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "    plt.ylabel('Voltage (V)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "    plt.grid(True)\n",
    "    plt.legend()\n",
    "    plt.savefig(pdf_filename, format='pdf', bbox_inches='tight')\n",
    "    plt.show()\n",
    "\n",
    "filepath = 'shuttling_function.csv'\n",
    "# filepath = 'RigolDS0_123.csv'\n",
    "time_array, scaled_voltage_array = load_and_process_data(filepath, smooth = True, smooth_window = 10)\n",
    "# scaled_voltage_array = np.ones(len(scaled_voltage_array)) * scaled_voltage_array[0]\n",
    "\n",
    "# Displaying the first few elements to verify the extraction\n",
    "print(f\"Length of time_array: {len(time_array)}, Length of scaled_voltage_array: {len(scaled_voltage_array)}\")\n",
    "print(f\"scaled_voltage_array_min = {min(scaled_voltage_array)}, scaled_voltage_array_max = {max(scaled_voltage_array)}\")\n",
    "print(\"First 5 elements of time_array:\", time_array[:5])\n",
    "print(\"First 5 elements of scaled_voltage_array:\", scaled_voltage_array[:5])\n",
    "print(\"The time range = \", time_array[-1], \" us\")\n",
    "\n",
    "# Plotting\n",
    "time_array = np.load(\"time_array.npy\") * 1e-6\n",
    "DC1_voltage_array = np.load(\"DC1_voltage_array.npy\")\n",
    "# DC1_voltage_array = np.ones(len(DC1_voltage_array)) * DC1_voltage_array[0]\n",
    "DC2_voltage_array = np.load(\"DC2_voltage_array.npy\")\n",
    "# DC2_voltage_array = np.ones(len(DC2_voltage_array)) * DC2_voltage_array[0]\n",
    "plot_voltage_time(time_array * 1e6, scaled_voltage_array, 'Shuttling_function_new.pdf')\n",
    "\n",
    "half_column_width_inches = 4.25\n",
    "aspect_ratio = 2\n",
    "plt.figure(figsize=(half_column_width_inches, half_column_width_inches / aspect_ratio))\n",
    "plt.title('Shuttling function', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.plot(time_array * 1e6, DC1_voltage_array, linewidth=2.5, label='Endcap 1')\n",
    "plt.plot(time_array * 1e6, DC2_voltage_array, linewidth=2.5, label='Endcap 1')\n",
    "plt.axvline(13 * T_factor, color='r', linewidth=0.5, linestyle='--')\n",
    "plt.axvline((15) * T_factor, color='r', linewidth=0.5, linestyle='--')\n",
    "plt.xlabel(r'Time ($\\mu$$s$)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.ylabel('Voltage (V)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "pdf_filename = \"voltage_function_of_endcaps_new_test\"\n",
    "plt.savefig(pdf_filename, format='pdf', bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "afbc04b7",
   "metadata": {},
   "source": [
    "### Set up ODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "49dd8745",
   "metadata": {},
   "outputs": [],
   "source": [
    "data_dc1 = np.loadtxt('DC1.csv', delimiter=',', skiprows=9)\n",
    "data_dc2 = np.loadtxt('DC2.csv', delimiter=',', skiprows=9)\n",
    "\n",
    "# data_dc1 = DC1_voltage_array\n",
    "# data_dc2 = DC2_voltage_array\n",
    "\n",
    "def cal_omega(DC1, DC2, delta_x, plot):\n",
    "    V1 = 1.6e-19 * DC1 * data_dc1[:, 3]\n",
    "    V2 = 1.6e-19 * DC2 * data_dc2[:, 3]\n",
    "    V = V1 + V2\n",
    "    z = 1e-3 * data_dc1[:, 2]\n",
    "    a, b, c = v_har(delta_x, z, V, plot)\n",
    "    omega = np.sqrt(2 * a / m)\n",
    "    x_0 = -b / (m * omega ** 2)\n",
    "    return omega, x_0\n",
    "    # return 1076322.9794945174, 5.5703264876617695e-05\n",
    "\n",
    "def ode_csv(t, y):\n",
    "    # Unpack position and velocity variables\n",
    "    x1, x2, x3, x4, x5, x6, x7, x8, x9, v1, v2, v3, v4, v5, v6, v7, v8, v9 = y\n",
    "\n",
    "    # Determine the closest time index for 't' and calculate omega and x0 values\n",
    "    index_t = np.argmin(np.abs(time_array - t))\n",
    "    omega_value, x0_value = cal_omega(DC1_voltage_array[index_t], DC2_voltage_array[index_t], 1e-4, False)\n",
    "    omega_value = 1076322.9794945174\n",
    "\n",
    "    # Print omega and x0 at the beginning of the simulation\n",
    "    if t == 0:\n",
    "        print(omega_value, x0_value)\n",
    "\n",
    "    # Constants for the equations of motion\n",
    "    a = -m * omega_value**2\n",
    "    b = m * omega_value**2 * x0_value\n",
    "    coulomb_factor = e**2 / (4 * np.pi * E0)\n",
    "\n",
    "    # Derivatives of positions are the velocities\n",
    "    dx_dt = [v1, v2, v3, v4, v5, v6, v7, v8, v9]\n",
    "\n",
    "    # Calculate the derivatives of velocities (dv/dt) considering Coulomb repulsion\n",
    "    dv_dt = [\n",
    "        1/m * (a * x1 + b - coulomb_factor * (sum(1 / (x1 - x)**2 for x in [x2, x3, x4, x5, x6, x7, x8, x9]))),\n",
    "        1/m * (a * x2 + b - coulomb_factor * (-1 / (x2 - x1)**2 + sum(1 / (x2 - x)**2 for x in [x3, x4, x5, x6, x7, x8, x9]))),\n",
    "        1/m * (a * x3 + b - coulomb_factor * (sum(-1 / (x3 - x)**2 for x in [x1, x2]) + sum(1 / (x3 - x)**2 for x in [x4, x5, x6, x7, x8, x9]))),\n",
    "        1/m * (a * x4 + b - coulomb_factor * (sum(-1 / (x4 - x)**2 for x in [x1, x2, x3]) + sum(1 / (x4 - x)**2 for x in [x5, x6, x7, x8, x9]))),\n",
    "        1/m * (a * x5 + b - coulomb_factor * (sum(-1 / (x5 - x)**2 for x in [x1, x2, x3, x4]) + sum(1 / (x5 - x)**2 for x in [x6, x7, x8, x9]))),\n",
    "        1/m * (a * x6 + b - coulomb_factor * (sum(-1 / (x6 - x)**2 for x in [x1, x2, x3, x4, x5]) + sum(1 / (x6 - x)**2 for x in [x7, x8, x9]))),\n",
    "        1/m * (a * x7 + b - coulomb_factor * (sum(-1 / (x7 - x)**2 for x in [x1, x2, x3, x4, x5, x6]) + sum(1 / (x7 - x)**2 for x in [x8, x9]))),\n",
    "        1/m * (a * x8 + b - coulomb_factor * (sum(-1 / (x8 - x)**2 for x in [x1, x2, x3, x4, x5, x6, x7]) + 1 / (x8 - x9)**2)),\n",
    "        1/m * (a * x9 + b - coulomb_factor * (sum(-1 / (x9 - x)**2 for x in [x1, x2, x3, x4, x5, x6, x7, x8])))\n",
    "    ]\n",
    "\n",
    "    # Return the concatenated list of position and velocity derivatives\n",
    "    return dx_dt + dv_dt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48241f77",
   "metadata": {},
   "source": [
    "### Calculate initial state and solve ODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "21d40711",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The initial position:  5.5703264876617695e-05\n",
      "The trap frequency:  1076322.9794945174\n",
      "[17.08366553858873, 28.47476582463269, 38.132043127702964, 47.06397638554019, 55.703264876617695, 64.3425533676952, 73.27448662553242, 82.9317639286027, 94.32286421464666, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]\n",
      "1076322.9794945174 5.5703264876617695e-05\n"
     ]
    }
   ],
   "source": [
    "def Eqposition3(N):\n",
    "    # Define the equations to solve\n",
    "    def func(u):\n",
    "        return np.array([u[m] - np.sum(1 / (u[m] - u[:m])**2) + np.sum(1 / (u[m] - u[m+1:])**2) for m in range(N)])\n",
    "    \n",
    "    # Define the first-order derivative\n",
    "    def dfunc(u):\n",
    "        return np.array([1 + 2 * np.sum(1 / (u[m] - u[:m])**3) - 2 * np.sum(1 / (u[m] - u[m+1:])**3) for m in range(N)])\n",
    "    \n",
    "    # Define the second-order derivative (not used in newton method here but defined for completeness)\n",
    "    def ddfunc(u):\n",
    "        return np.array([np.sum(1 / (u[m] - u[:m])**4) - np.sum(1 / (u[m] - u[m+1:])**4) for m in range(N)])\n",
    "\n",
    "    # Initial guess for the Newton method\n",
    "    ni = np.arange(0, N)\n",
    "    guess = 3.94 * (N**0.387) * np.sin(1 / 3 * np.arcsin(1.75 * N**(-0.982) * ((ni + 1) - (N + 1) / 2)))\n",
    "    \n",
    "    # Solve for the equilibrium positions using the Newton method\n",
    "    x0 = newton(func, guess, fprime=dfunc, maxiter=100000)\n",
    "    \n",
    "    return np.round(x0, 5)\n",
    "\n",
    "# Initial conditions setup\n",
    "omega_value, x0_value = cal_omega(DC1_voltage_array[0], DC2_voltage_array[0], 1e-4, False)\n",
    "# print(omega_value, x0_value)\n",
    "x0 = x0_value\n",
    "print(\"The initial position: \", x0_value)\n",
    "omega0 = omega_value\n",
    "print(\"The trap frequency: \", omega0)\n",
    "l0 = math.pow(e**2 / (4 * math.pi * E0 * m * omega0**2), 1/3)\n",
    "\n",
    "# Calculate initial positions and scale\n",
    "initial_positions = Eqposition3(9) * l0\n",
    "initial_state = [x + x0 for x in initial_positions] + [0] * 9  # Append velocity initial conditions (zeros)\n",
    "\n",
    "# Convert units to micrometers (um) and back, demonstrating unit conversion without functional change\n",
    "initial_state_um = [x * 1e6 for x in initial_state]\n",
    "print(initial_state_um)  # In the unit of micrometers (um)\n",
    "initial_state = [x / 1e6 for x in initial_state_um]  # Convert back, though this step is redundant here\n",
    "initial_state = np.array([17.08369540791233, 28.474782827470513, 38.13198316843803, 47.06403315776806, 55.70326488240171, 64.34249658649416, 73.274546588792, 82.93174692487013, 94.32283434541237, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]) / 1e6\n",
    "\n",
    "initial_state = np.array([17.083695539177068, 28.47478293928541, 38.131983453958746, 47.06403296135834, 55.70326497471302, 64.34249664063852, 73.27454636648979, 82.93174679858147, 94.3228342153568, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]) / 1e6\n",
    "\n",
    "initial_state = np.array([17.08369553804403, 28.474782951113287, 38.131983421221584, 47.06403299876212, 55.70326497124225, 64.3424966085964, 73.27454639684315, 82.93174678729447, 94.32283421644193, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]) / 1e6\n",
    "\n",
    "initial_state = np.array([17.083695539177068, 28.47478293928541, 38.13198342382467, 47.06403296135834, 55.70326497634435, 64.34249664063852, 73.27454636648979, 82.93174679858147, 94.3228342153568, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]) / 1e6\n",
    "\n",
    "# Solve the differential equations using 'solve_ivp'\n",
    "# solution = solve_ivp(ode_csv, (0, T), initial_state, t_eval=np.linspace(0, T, points))\n",
    "solution = solve_ivp(ode_csv, (0, T), initial_state, method='RK45', t_eval=np.linspace(0, T, points), atol=1e-10, rtol=1e-8)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a08518bd",
   "metadata": {},
   "source": [
    "### Plot the movement of all the ions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "b95f01ef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 425x212.5 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 425x212.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Extract time points and positions from the solution\n",
    "time_points = solution.t\n",
    "positions = solution.y[:9]  # Extracting only the positions of the ions\n",
    "\n",
    "# Plotting\n",
    "half_column_width_inches = 4.25\n",
    "aspect_ratio = 2  # You can adjust this for your desired aspect ratio\n",
    "plt.figure(figsize=(half_column_width_inches, half_column_width_inches / aspect_ratio))\n",
    "\n",
    "# Time windows\n",
    "start_time_array = np.array([0, 13e-6, 25e-6, 37e-6, 49e-6, 61e-6, 73e-6, 85e-6, 97e-6, 140e-6]) * 1e6 * T_factor\n",
    "stop_time_array = np.array([2e-6, 15e-6, 27e-6, 39e-6, 51e-6, 63e-6, 75e-6, 87e-6, 99e-6, 150e-6]) * 1e6 * T_factor\n",
    "# Plotting\n",
    "half_column_width_inches = 4.25\n",
    "aspect_ratio = 2  # Desired aspect ratio\n",
    "plt.figure(figsize=(half_column_width_inches, half_column_width_inches / aspect_ratio))\n",
    "# Highlight the time windows\n",
    "for start, stop in zip(start_time_array, stop_time_array):\n",
    "    plt.axvspan(start, stop, color='C0', alpha=0.3)\n",
    "\n",
    "for i, pos in enumerate(positions, start=1):\n",
    "    if i == 5:\n",
    "        # plt.scatter(time_points * 1e6, pos * 1e6, s=0.2, c = 'black', label=f'Ion {i}')\n",
    "        plt.plot(time_points * 1e6, pos * 1e6, c = 'black', label=f'Ion {i}', linewidth=1.5)\n",
    "    else:\n",
    "        plt.plot(time_points * 1e6, pos * 1e6, label=f'Ion {i}', linewidth=1.5)\n",
    "\n",
    "plt.xlabel(r'Time (μs)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.ylabel(r'Position (μm)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.title('Positions of 9 ions chain', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "\n",
    "# Adjust the subplot params to give the plot more room for the legend\n",
    "plt.subplots_adjust(right=0.8)\n",
    "\n",
    "# Place the legend outside the plot\n",
    "plt.legend(bbox_to_anchor=(1.05, 0.5), loc=\"center left\", borderaxespad=0)\n",
    "# plt.grid(True)\n",
    "pdf_filename = 'positions_of_9_ions_chain_demo_new_test.pdf'\n",
    "plt.savefig(pdf_filename, format='pdf', bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "5492ac4a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-13.909610963416284\n",
      "-2.5185235426317045\n",
      "7.138676890005013\n",
      "16.07072656950908\n",
      "24.709958374572757\n",
      "33.34919017932469\n",
      "42.28123985905276\n",
      "51.93844029159467\n",
      "63.32952771241261\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 425x212.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "half_column_width_inches = 4.25\n",
    "aspect_ratio = 2  # You can adjust this for your desired aspect ratio\n",
    "plt.figure(figsize=(half_column_width_inches, half_column_width_inches / aspect_ratio))\n",
    "\n",
    "for i in range(9):\n",
    "    if(True):\n",
    "        plt.plot(time_points * 1e6, (positions[i] - positions[i][0]) * 1e6, lw=2, label=f'ion {i}')\n",
    "\n",
    "for i in range(9):\n",
    "    print(np.average(positions[i]) * 1e6)\n",
    "\n",
    "# print([17.08366553858873, 28.47476582463269, 38.132043127702964, 47.06397638554019, 55.703264876617695, 64.3425533676952, 73.27448662553242, 82.9317639286027, 94.32286421464666])\n",
    "\n",
    "plt.xlabel(r'Time (μs)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.ylabel(r'Position (μm)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.title('Ions position', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "\n",
    "# Calculate amplitude in these time windows\n",
    "time_points_us = time_points * 1e6  # Convert time_points to microseconds\n",
    "amplitudes = []\n",
    "# start_time = time_points_us[-15000]\n",
    "start_time = time_points_us[0]\n",
    "stop_time = time_points_us[-1]\n",
    "\n",
    "# Adjust the subplot params to give the plot more room for the legend\n",
    "plt.subplots_adjust(right=0.8)\n",
    "plt.legend(bbox_to_anchor=(1.05, 0.5), loc=\"center left\", borderaxespad=0)\n",
    "plt.grid(True)\n",
    "plt.xlim(start_time, stop_time+ 1)\n",
    "# plt.ylim(-0.18, 0.2)\n",
    "# plt.ylim(-1.2, 0.5)\n",
    "pdf_filename = 'positions_modes_of_9_ions_chain_demo_new_test.pdf'\n",
    "plt.savefig(pdf_filename, format='pdf', bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ccf16c59",
   "metadata": {},
   "source": [
    "### Calculate mode excitation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "abb1c5dc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3000000\n"
     ]
    }
   ],
   "source": [
    "# def nor_cor9(x1,x2,x3,x4,x5,x6,x7,x8,x9):\n",
    "#     y1=0.333384*x1+0.333368*x2+0.333329*x3+0.333377*x4+0.333383*x5+0.333377*x6+0.333329*x7+0.333368*x8+0.333384*x9\n",
    "#     y2=-0.533933*x1-0.376401*x2-0.24288*x3-0.119431*x4+6.89694*10**(-19)*x5+0.119431*x6+0.24288*x7+0.376401*x8+0.533933*x9\n",
    "#     y3=-0.553209*x1-0.096929*x2+0.165769*x3+0.30783*x4+0.353079*x5+0.30783*x6+0.165769*x7-0.096929*x8-0.553209*x9\n",
    "#     y4=-0.439418*x1+0.282817*x2+0.401852*x3+0.255804*x4-9.57488*10**(-17)*x5-0.255804*x6-0.401852*x7-0.282817*x8+0.439418*x9\n",
    "#     y5=0.281185*x1-0.510756*x2-0.187306*x3+0.22284*x4+0.388073*x5+0.22284*x6-0.187306*x7-0.510756*x8+0.281185*x9\n",
    "#     y6=0.146521*x1-0.501459*x2+0.258135*x3+0.400506*x4-9.81546*10**(-17)*x5-0.400506*x6-0.258135*x7+0.501459*x8-0.146521*x9\n",
    "#     y7=0.0613199*x1-0.340712*x2+0.527405*x3-0.0227322*x4-0.450561*x5-0.0227322*x6+0.527405*x7-0.340712*x8+0.0613199*x9\n",
    "#     y8=-0.0196748*x1+0.163883*x2-0.461312*x3+0.509813*x4+3.83695*10**(-18)*x5-0.509813*x6+0.461312*x7-0.163883*x8+0.0196748*x9\n",
    "#     y9=-0.0042412*x1+0.0501759*x2-0.219504*x3+0.493967*x4-0.640796*x5+0.493967*x6-0.219504*x7+0.0501759*x8-0.0042412*x9\n",
    "#     return [y1,y2,y3,y4,y5,y6,y7,y8,y9]\n",
    "\n",
    "def nor_cor9(positions_minus_x0_values):\n",
    "    # Assuming positions_minus_x0_values is a 2D array where each column corresponds to x1 through x9\n",
    "    \n",
    "    # Coefficients for each y computation as rows in a matrix\n",
    "    coefficients = np.array([\n",
    "        [0.333384, 0.333368, 0.333329, 0.333377, 0.333383, 0.333377, 0.333329, 0.333368, 0.333384],\n",
    "        [-0.533933, -0.376401, -0.24288, -0.119431, 6.89694e-19, 0.119431, 0.24288, 0.376401, 0.533933],\n",
    "        [-0.553209, -0.096929, 0.165769, 0.30783, 0.353079, 0.30783, 0.165769, -0.096929, -0.553209],\n",
    "        [-0.439418, 0.282817, 0.401852, 0.255804, -9.57488e-17, -0.255804, -0.401852, -0.282817, 0.439418],\n",
    "        [0.281185, -0.510756, -0.187306, 0.22284, 0.388073, 0.22284, -0.187306, -0.510756, 0.281185],\n",
    "        [0.146521, -0.501459, 0.258135, 0.400506, -9.81546e-17, -0.400506, -0.258135, 0.501459, -0.146521],\n",
    "        [0.0613199, -0.340712, 0.527405, -0.0227322, -0.450561, -0.0227322, 0.527405, -0.340712, 0.0613199],\n",
    "        [-0.0196748, 0.163883, -0.461312, 0.509813, 3.83695e-18, -0.509813, 0.461312, -0.163883, 0.0196748],\n",
    "        [-0.0042412, 0.0501759, -0.219504, 0.493967, -0.640796, 0.493967, -0.219504, 0.0501759, -0.0042412]\n",
    "    ])\n",
    "\n",
    "    # Dot product of coefficients with positions_minus_x0_values to compute all y values at once\n",
    "    positions_modes = np.dot(coefficients, positions_minus_x0_values)\n",
    "\n",
    "    return positions_modes\n",
    "\n",
    "print(len(positions[1]))\n",
    "\n",
    "# Extract time points and positions from the solution\n",
    "time_points = solution.t\n",
    "positions = solution.y[:9]  # Extracting only the positions of the ions\n",
    "t_eval = np.linspace(0, T, points)\n",
    "dt = np.mean(np.diff(time_array))  # Assuming evenly spaced\n",
    "indices = np.floor((t_eval - time_array[0]) / dt).astype(int)\n",
    "indices = np.clip(indices, 0, len(time_array) - 1)  # Ensure indices are within bounds\n",
    "cal_omega_vectorized = np.vectorize(cal_omega, excluded=['eps', 'verbose'])\n",
    "omega_values, x0_values = cal_omega_vectorized(DC1_voltage_array[indices], DC2_voltage_array[indices], 1e-4, False)\n",
    "positions_um = positions * 1e6\n",
    "x0_value_array_um = np.array(x0_values) * 1e6\n",
    "\n",
    "positions_modes = nor_cor9(np.array([positions[0] - x0_values, positions[1] - x0_values, positions[2] - x0_values, positions[3] - x0_values, positions[4] - x0_values, positions[5] - x0_values, positions[6] - x0_values, positions[7] - x0_values, positions[8] - x0_values])) / 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "063c9d27",
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1500x700 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Updating the code to make the plot grid 3x3 instead of 9x1\n",
    "\n",
    "# Importing necessary libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Coefficients matrix for the 9 normal modes of a 9 ion chain\n",
    "coefficients = np.array([\n",
    "    [0.333384, 0.333368, 0.333329, 0.333377, 0.333383, 0.333377, 0.333329, 0.333368, 0.333384],\n",
    "    [-0.533933, -0.376401, -0.24288, -0.119431, 6.89694e-19, 0.119431, 0.24288, 0.376401, 0.533933],\n",
    "    [-0.553209, -0.096929, 0.165769, 0.30783, 0.353079, 0.30783, 0.165769, -0.096929, -0.553209],\n",
    "    [-0.439418, 0.282817, 0.401852, 0.255804, -9.57488e-17, -0.255804, -0.401852, -0.282817, 0.439418],\n",
    "    [0.281185, -0.510756, -0.187306, 0.22284, 0.388073, 0.22284, -0.187306, -0.510756, 0.281185],\n",
    "    [0.146521, -0.501459, 0.258135, 0.400506, -9.81546e-17, -0.400506, -0.258135, 0.501459, -0.146521],\n",
    "    [0.0613199, -0.340712, 0.527405, -0.0227322, -0.450561, -0.0227322, 0.527405, -0.340712, 0.0613199],\n",
    "    [-0.0196748, 0.163883, -0.461312, 0.509813, 3.83695e-18, -0.509813, 0.461312, -0.163883, 0.0196748],\n",
    "    [-0.0042412, 0.0501759, -0.219504, 0.493967, -0.640796, 0.493967, -0.219504, 0.0501759, -0.0042412]\n",
    "])\n",
    "\n",
    "# Setting up a 3x3 plot grid\n",
    "fig, axs = plt.subplots(3, 3, figsize=(15, 7))\n",
    "\n",
    "# Flattening the axs array for easier indexing\n",
    "axs = axs.flatten()\n",
    "\n",
    "# Ion positions for visualization\n",
    "ion_positions = np.arange(1, 10)\n",
    "\n",
    "for i in range(9):\n",
    "    axs[i].stem(ion_positions, coefficients[i], basefmt=\" \")\n",
    "    axs[i].set_title(f'Mode {i+1}')\n",
    "    axs[i].set_ylim([-0.7, 0.7])\n",
    "    axs[i].set_xticks(ion_positions)\n",
    "    axs[i].grid(True)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "6c69b457",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.7605349063991005\n",
      "[0.17983792609920252, 7.648864652765042e-09, 6.234020347247576e-08, 9.383457698353137e-09, 6.382734103717735e-08, 5.647543190642323e-09, 3.3694609497771626e-08, 3.441123338208431e-08, 1.3273285048573217e-07]\n",
      "[5.481084714468514, 9.915118191342069e-15, 6.586282796216854e-13, 1.492209306535191e-14, 6.904264943716884e-13, 5.405340604524519e-15, 1.924087411809906e-13, 2.0068015204644486e-13, 2.985800493714801e-12]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 425x212.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "half_column_width_inches = 4.25\n",
    "aspect_ratio = 2  # You can adjust this for your desired aspect ratio\n",
    "plt.figure(figsize=(half_column_width_inches, half_column_width_inches / aspect_ratio))\n",
    "factor = 0.34 * 1.0004196441454332\n",
    "for i, pos in enumerate(positions_modes, start=1):\n",
    "    # plt.scatter(time_points * 1e6, pos * 1e6, s=0.2, label=f'Mode {i}')\n",
    "    if(i != 2):\n",
    "        if(i == 8):\n",
    "            plt.plot(time_points * 1e6, np.abs(pos - pos[0]) * 1e6 / factor, lw=1, c=\"C1\", label=f'Mode {i}')\n",
    "            continue\n",
    "        if(i == 1):\n",
    "            plt.plot(time_points * 1e6, np.abs(pos - pos[0]) * 1e6 / factor, lw=1, c=\"black\", alpha = 0.7, label=f'Mode {i}')\n",
    "            print(np.max(np.abs(pos - pos[0]) * 1e6 / factor))\n",
    "            continue\n",
    "        plt.plot(time_points * 1e6, np.abs(pos - pos[0]) * 1e6 / factor, lw=1, label=f'Mode {i}')\n",
    "    else:\n",
    "        plt.plot(time_points * 1e6, np.abs(pos - pos[0]) * 1e6 / factor, lw=1, label=f'Mode {i}')\n",
    "\n",
    "plt.xlabel(r'Time (μs)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.ylabel(r'Relative amplitude', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.title('Modes excitation with half speed shuttling', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "\n",
    "# Calculate amplitude in these time windows\n",
    "time_points_us = time_points * 1e6  # Convert time_points to microseconds\n",
    "amplitudes = []\n",
    "# start_time = time_points_us[-15000 * 20]\n",
    "start_time = time_points_us[-15000 * 20]\n",
    "stop_time = time_points_us[-1]\n",
    "for i, pos in enumerate(positions_modes, start=1):\n",
    "    mask = (time_points_us >= start_time) & (time_points_us <= stop_time)\n",
    "    amplitude = (pos * 1e6)[mask].max() - (pos * 1e6)[mask].min()\n",
    "    amplitudes.append(amplitude)\n",
    "print(amplitudes)\n",
    "quantum = h_bar * omega_value\n",
    "real_amplitudes = np.array(amplitudes) * 1e-6\n",
    "n_bar = [0.25 * m * omega_value**2 * amplitude**2 / quantum for amplitude in real_amplitudes]\n",
    "print(n_bar)\n",
    "\n",
    "# Adjust the subplot params to give the plot more room for the legend\n",
    "plt.subplots_adjust(right=0.8)\n",
    "plt.legend(bbox_to_anchor=(1.05, 0.5), loc=\"center left\", borderaxespad=0)\n",
    "plt.grid(True)\n",
    "plt.xlim(140 * T_factor, 150 * T_factor)\n",
    "# plt.ylim(-0.08, 1.2)\n",
    "# plt.ylim(-1.2, 0.5)\n",
    "pdf_filename = 'positions_modes_of_9_ions_chain_demo_new_test.pdf'\n",
    "plt.savefig(pdf_filename, format='pdf', bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "2499d15a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 425x212.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(None,\n",
       " [2.046305525027492e-07,\n",
       "  0.17680866536089468,\n",
       "  0.10243410018335197,\n",
       "  0.057805462342177094,\n",
       "  0.08237597906010308,\n",
       "  0.1395671038008608,\n",
       "  0.18843369172484348,\n",
       "  0.18786423970968835,\n",
       "  0.14849940947125972,\n",
       "  0.17982001231715827])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Time windows\n",
    "start_time_array = np.array([0, 13e-6, 25e-6, 37e-6, 49e-6, 61e-6, 73e-6, 85e-6, 97e-6, 140e-6]) * 1e6 * T_factor\n",
    "stop_time_array = np.array([2e-6, 15e-6, 27e-6, 39e-6, 51e-6, 63e-6, 75e-6, 87e-6, 99e-6, 150e-6]) * 1e6 * T_factor\n",
    "\n",
    "# Plotting\n",
    "half_column_width_inches = 4.25\n",
    "aspect_ratio = 2  # Desired aspect ratio\n",
    "plt.figure(figsize=(half_column_width_inches, half_column_width_inches / aspect_ratio))\n",
    "\n",
    "# Plot the positions and center of trap\n",
    "plt.plot(time_points_us, positions_um[4], label='Center of mass (9 ions chain)')\n",
    "plt.plot(time_points_us, x0_value_array_um, color=\"black\", label=\"Center of trap\", linewidth=0.5)\n",
    "\n",
    "# Highlight the time windows\n",
    "for start, stop in zip(start_time_array, stop_time_array):\n",
    "    plt.axvspan(start, stop, color='red', alpha=0.3)\n",
    "\n",
    "# Calculate amplitude in these time windows\n",
    "amplitudes = []\n",
    "for start, stop in zip(start_time_array, stop_time_array):\n",
    "    mask = (time_points_us >= start) & (time_points_us <= stop)\n",
    "    amplitude = positions_um[4, mask].max() - positions_um[4, mask].min()\n",
    "    amplitudes.append(amplitude)\n",
    "\n",
    "# Set plot labels and title\n",
    "plt.xlabel('Time (μs)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.ylabel('Position (μm)', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.title('Position of trap center & ions chain center', fontdict={'family': 'STIXGeneral', 'size': 12})\n",
    "plt.legend()\n",
    "pdf_filename = 'trap_frequency_and_position_each_step_heating_half_speed_new_test.pdf'\n",
    "plt.savefig(pdf_filename, format='pdf', bbox_inches='tight')\n",
    "plt.grid(True)\n",
    "\n",
    "plt.show(), amplitudes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "cfeced5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 425x212.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Data provided by the user\n",
    "# data = np.array([3.3162240810623347, 9.915072138056101e-15, 4.1362428475472524e-13, 1.492133264609159e-14, 4.359650222624311e-13, 5.40290818828333e-15, 1.4931888325936294e-13, 2.0031599325987568e-13, 2.636743742477595e-12])/ 3.3162240810623347\n",
    "data = np.array(n_bar) / np.max(n_bar)\n",
    "\n",
    "# Generating mode numbers from 1 to the length of the data list\n",
    "mode_numbers = range(1, len(data) + 1)\n",
    "\n",
    "# Plotting the bar plot\n",
    "half_column_width_inches = 4.25\n",
    "aspect_ratio = 2  # Desired aspect ratio\n",
    "plt.figure(figsize=(half_column_width_inches, half_column_width_inches / aspect_ratio))\n",
    "plt.bar(mode_numbers, data, color='skyblue')\n",
    "plt.xlabel('Mode Number')\n",
    "plt.ylabel('Relative excitation')\n",
    "plt.title('Motianl excitation of different modes')\n",
    "plt.yscale('log')\n",
    "plt.xticks(mode_numbers)\n",
    "plt.grid(axis='y', linestyle='--')\n",
    "\n",
    "# plt.legend()\n",
    "pdf_filename = 'Heating of different motional modes.pdf'\n",
    "plt.savefig(pdf_filename, format='pdf', bbox_inches='tight')\n",
    "plt.grid(True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "c827a7c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 425x212.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Parameters for the simulation\n",
    "T_factor = (121 / 133.93969396934) * 1.65  # The time factor for the simulation\n",
    "NUM_VOLTAGE_POINTS = 500  # The points for voltage sampling\n",
    "T = 150 * 1e-6 * T_factor  # Total time duration in s unit\n",
    "points = 3000000  # Number of points at which to evaluate the solution\n",
    "\n",
    "shuttling_time = np.array([2.0, 1.9, 1.8, 1.7, 1.69, 1.68, 1.675, 1.67, 1.66, 1.6, 1.3, 1.2, 1.1, 1.0]) * 150 * (121 / 133.93969396934)\n",
    "phonon_number = [3.3162240810623347, 1.1686538823938188, 5.875925464087038, 6.619702650001575, 31.254016433807955, 71.98736367688507, 98.34855030356773, 130.87303629718585, 232.85274899348917, 2391.1302739952052, 95.51753401638237, 14.689732736191997, 1871.5136089051891, 822.7717571937637]\n",
    "\n",
    "# Plotting settings\n",
    "half_column_width_inches = 4.25\n",
    "aspect_ratio = 2  # Desired aspect ratio\n",
    "plt.figure(figsize=(half_column_width_inches, half_column_width_inches / aspect_ratio))\n",
    "\n",
    "plt.plot(shuttling_time, phonon_number, marker='o', linestyle='-', color='C0')\n",
    "\n",
    "plt.xlabel('Shuttling Time', fontsize=12)\n",
    "plt.ylabel('Phonon Number', fontsize=12)\n",
    "plt.title('Phonon Number vs Shuttling Time', fontsize=12)\n",
    "plt.yscale('log')\n",
    "plt.grid(True)\n",
    "plt.xticks(fontsize=10)\n",
    "plt.yticks(fontsize=10)\n",
    "\n",
    "# plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "32d639fc",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}