cylinder_fdm_poisson_tests.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from cylinder_fdm_3d import CylinderFDM\n",
    "from icecream import ic\n",
    "import numpy as np\n",
    "from scipy.sparse.linalg import eigsh, cg, gmres, bicgstab\n",
    "from matplotlib import pyplot as plt\n",
    "from fft_tdse.simulator import LaserPulse\n",
    "from erfgau import ErfgauPotential\n",
    "from rich.console import Console\n",
    "from rich.table import Table\n",
    "import timeit\n",
    "from time import time\n",
    "from scipy.sparse.linalg import LinearOperator\n",
    "from scipy.sparse.linalg import spilu\n",
    "from scipy.sparse import csc_matrix\n",
    "from scipy.linalg import lu_factor, lu_solve\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| self.m_i: array([ 0.,  1., -2., -1.])\n",
      "ic| cylinder_fdm_3d.py:170 in __init__() at 13:55:02.455\n",
      "ic| self.n_r: 6, self.n_z: 4, self.n_m: 4\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 96\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d0fb70588c5a4eaaba970310f5cc85a3",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' 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       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "853c52ecc9f2496d9134745cdb98c188",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_r = 6\n",
    "n_z = 4\n",
    "n_theta = 4\n",
    "r_max = 20\n",
    "z_max = 20\n",
    "solver = CylinderFDM(r_max, z_max, n_r, n_z, n_theta)\n",
    "L_vec_zr = solver.get_laplacian_fast(ordering='zr')\n",
    "L_vec_rz = solver.get_laplacian_fast(ordering='rz')\n",
    "\n",
    "%matplotlib widget\n",
    "plt.figure()\n",
    "plt.imshow(L_vec_rz[1].todense())\n",
    "plt.title('Laplacian, ordering rz')\n",
    "plt.figure()\n",
    "plt.imshow(L_vec_zr[1].todense())\n",
    "plt.title('Laplacian, ordering zr')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_timing(solve, setup, n_r, n_z, m, number=10):\n",
    "    # n_r = 100\n",
    "    # n_z = 200\n",
    "    n_theta = 2*m + 1\n",
    "    r_max = 20\n",
    "    z_max = 20\n",
    "    fdm_solver = CylinderFDM(r_max, z_max, n_r, n_z, n_theta)\n",
    "    L_vec = fdm_solver.get_laplacian_fast()\n",
    "    rr, zz = fdm_solver.get_rz_meshgrid()\n",
    "\n",
    "    u = rr**(np.abs(m) + .5) * np.exp(-(rr**2 - zz**2)/2)\n",
    "    rhs = -4*np.pi*u.flatten()\n",
    "\n",
    "    ic('system dimension = ', L_vec[0].shape[0])\n",
    "    start = time()\n",
    "    solve_args = setup(fdm_solver, m, rhs)\n",
    "    setup_time = time() - start\n",
    "    ic(setup_time)\n",
    "    code = lambda: solve(*solve_args)\n",
    "    time_total = timeit.timeit(code, number=number)\n",
    "    time_per_solve = time_total/20\n",
    "    ic(time_per_solve)\n",
    "    return time_per_solve, setup_time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def timing_table(solve, setup, n_list, m_list):\n",
    "\n",
    "    \n",
    "    times = np.zeros((len(n_list), len(m_list)))\n",
    "    setup_times = np.zeros((len(n_list), len(m_list)))\n",
    "    for j,n in enumerate(n_list):\n",
    "        for i,m in enumerate(m_list):\n",
    "            times[j,i], setup_times[j,i] = solve_timing(solve, setup, n, n, m)\n",
    "\n",
    "    table = Table('Timings')\n",
    "    for m in m_list:\n",
    "        table.add_column(f'm = {m}')\n",
    "    for j,n in enumerate(n_list):\n",
    "        table.add_row(f'n = {n}', *map(str,times[j]))\n",
    "\n",
    "    display(table)\n",
    "    return times, setup_times, table\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:170 in __init__() at 14:03:52.246\n",
      "ic| self.n_r: 100, self.n_z: 100, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 10000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 10000\n",
      "ic| setup_time: 0.0824580192565918\n",
      "ic| time_per_solve: 0.0008329978911206127\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:170 in __init__() at 14:03:52.419\n",
      "ic| self.n_r: 100, self.n_z: 100, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 30000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 10000\n",
      "ic| setup_time: 0.011793851852416992\n",
      "ic| time_per_solve: 0.00015722709940746427\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:170 in __init__() at 14:03:52.534\n",
      "ic| self.n_r: 200, self.n_z: 200, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 40000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 40000\n",
      "ic| setup_time: 0.014158964157104492\n",
      "ic| time_per_solve: 0.009251304157078265\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:170 in __init__() at 14:03:52.861\n",
      "ic| self.n_r: 200, self.n_z: 200, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 120000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 40000\n",
      "ic| setup_time: 0.17183995246887207\n",
      "ic| time_per_solve: 0.003758333355654031\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:170 in __init__() at 14:03:53.255\n",
      "ic| self.n_r: 400, self.n_z: 400, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 160000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 160000\n",
      "ic| setup_time: 0.08563971519470215\n",
      "ic| time_per_solve: 0.003860581258777529\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:170 in __init__() at 14:03:53.610\n",
      "ic| self.n_r: 400, self.n_z: 400, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 480000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 160000\n",
      "ic| setup_time: 0.0955348014831543\n",
      "ic| time_per_solve: 0.0028326667030341922\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:170 in __init__() at 14:03:54.026\n",
      "ic| self.n_r: 1000, self.n_z: 1000, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 1000000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 1000000\n",
      "ic| setup_time: 0.2948768138885498\n",
      "ic| time_per_solve: 0.03470109795453027\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:170 in __init__() at 14:03:55.313\n",
      "ic| self.n_r: 1000, self.n_z: 1000, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 3000000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 1000000\n",
      "ic| setup_time: 0.5905258655548096\n",
      "ic| time_per_solve: 0.03136621459852904\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">┏━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓\n",
       "┃<span style=\"font-weight: bold\"> Timings  </span>┃<span style=\"font-weight: bold\"> m = 0                 </span>┃<span style=\"font-weight: bold\"> m = 1                  </span>┃\n",
       "┡━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━┩\n",
       "│ n = 100  │ 0.0008329978911206127 │ 0.00015722709940746427 │\n",
       "│ n = 200  │ 0.009251304157078265  │ 0.003758333355654031   │\n",
       "│ n = 400  │ 0.003860581258777529  │ 0.0028326667030341922  │\n",
       "│ n = 1000 │ 0.03470109795453027   │ 0.03136621459852904    │\n",
       "└──────────┴───────────────────────┴────────────────────────┘\n",
       "</pre>\n"
      ],
      "text/plain": [
       "┏━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━━━┓\n",
       "┃\u001b[1m \u001b[0m\u001b[1mTimings \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mm = 0                \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mm = 1                 \u001b[0m\u001b[1m \u001b[0m┃\n",
       "┡━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━━━┩\n",
       "│ n = 100  │ 0.0008329978911206127 │ 0.00015722709940746427 │\n",
       "│ n = 200  │ 0.009251304157078265  │ 0.003758333355654031   │\n",
       "│ n = 400  │ 0.003860581258777529  │ 0.0028326667030341922  │\n",
       "│ n = 1000 │ 0.03470109795453027   │ 0.03136621459852904    │\n",
       "└──────────┴───────────────────────┴────────────────────────┘\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(array([[0.000833  , 0.00015723],\n",
       "        [0.0092513 , 0.00375833],\n",
       "        [0.00386058, 0.00283267],\n",
       "        [0.0347011 , 0.03136621]]),\n",
       " array([[0.08245802, 0.01179385],\n",
       "        [0.01415896, 0.17183995],\n",
       "        [0.08563972, 0.0955348 ],\n",
       "        [0.29487681, 0.59052587]]),\n",
       " <rich.table.Table at 0x29301fa90>)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#\n",
    "# Timing of fast Poisson solver\n",
    "#\n",
    "def setup(fdm_solver, m, rhs):\n",
    "    fdm_solver.prepare_poisson_solver()\n",
    "    return fdm_solver, m, rhs\n",
    "\n",
    "def solve(fdm_solver, m, rhs):\n",
    "    return fdm_solver.solve_poisson(rhs.reshape((fdm_solver.n_r, fdm_solver.n_z)), np.abs(m))\n",
    "\n",
    "n_list = np.array([100, 200, 400, 1000])\n",
    "m_list = np.array([0, 1])\n",
    "timing_table(solve, setup, n_list, m_list)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 207,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:40:46.318\n",
      "ic| self.n_r: 100, self.n_z: 100, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 10000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 10000\n",
      "ic| setup_time: 5.0067901611328125e-06\n",
      "ic| time_per_solve: 0.008025954151526094\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:40:46.542\n",
      "ic| self.n_r: 100, self.n_z: 100, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 30000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 10000\n",
      "ic| setup_time: 1.1920928955078125e-06\n",
      "ic| time_per_solve: 0.006283968745265156\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:40:46.710\n",
      "ic| self.n_r: 200, self.n_z: 200, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 40000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 40000\n",
      "ic| setup_time: 5.245208740234375e-06\n",
      "ic| time_per_solve: 0.09758887080242858\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:40:48.770\n",
      "ic| self.n_r: 200, self.n_z: 200, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 120000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 40000\n",
      "ic| setup_time: 3.814697265625e-06\n",
      "ic| time_per_solve: 0.11165563125396147\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:40:51.140\n",
      "ic| self.n_r: 400, self.n_z: 400, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 160000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 160000\n",
      "ic| setup_time: 3.814697265625e-06\n",
      "ic| time_per_solve: 0.5277262000017799\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:41:01.892\n",
      "ic| self.n_r: 400, self.n_z: 400, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 480000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 160000\n",
      "ic| setup_time: 7.152557373046875e-06\n",
      "ic| time_per_solve: 0.443043818755541\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">┏━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┓\n",
       "┃<span style=\"font-weight: bold\"> Timings </span>┃<span style=\"font-weight: bold\"> m = 0                </span>┃<span style=\"font-weight: bold\"> m = 1                </span>┃\n",
       "┡━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━┩\n",
       "│ n = 100 │ 0.008025954151526094 │ 0.006283968745265156 │\n",
       "│ n = 200 │ 0.09758887080242858  │ 0.11165563125396147  │\n",
       "│ n = 400 │ 0.5277262000017799   │ 0.443043818755541    │\n",
       "└─────────┴──────────────────────┴──────────────────────┘\n",
       "</pre>\n"
      ],
      "text/plain": [
       "┏━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┓\n",
       "┃\u001b[1m \u001b[0m\u001b[1mTimings\u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mm = 0               \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mm = 1               \u001b[0m\u001b[1m \u001b[0m┃\n",
       "┡━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━┩\n",
       "│ n = 100 │ 0.008025954151526094 │ 0.006283968745265156 │\n",
       "│ n = 200 │ 0.09758887080242858  │ 0.11165563125396147  │\n",
       "│ n = 400 │ 0.5277262000017799   │ 0.443043818755541    │\n",
       "└─────────┴──────────────────────┴──────────────────────┘\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(array([[0.00802595, 0.00628397],\n",
       "        [0.09758887, 0.11165563],\n",
       "        [0.5277262 , 0.44304382]]),\n",
       " array([[5.00679016e-06, 1.19209290e-06],\n",
       "        [5.24520874e-06, 3.81469727e-06],\n",
       "        [3.81469727e-06, 7.15255737e-06]]),\n",
       " <rich.table.Table at 0x2c66a8ac0>)"
      ]
     },
     "execution_count": 207,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#\n",
    "# Timing of plain CG\n",
    "#\n",
    "setup = lambda _, A, b: {'A': A, 'b': b, 'tol': 1e-10, 'maxiter': 1000}\n",
    "solve = cg\n",
    "n_list = np.array([100, 200, 400])\n",
    "m_list = np.array([0, 1])\n",
    "timing_table(solve, setup, n_list, m_list)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 209,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:43:02.421\n",
      "ic| self.n_r: 100, self.n_z: 100, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 10000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 10000\n",
      "ic| setup_time: 4.0531158447265625e-06\n",
      "ic| time_per_solve: 0.011314154148567467\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:43:02.710\n",
      "ic| self.n_r: 100, self.n_z: 100, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 30000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 10000\n",
      "ic| setup_time: 2.1457672119140625e-06\n",
      "ic| time_per_solve: 0.008620060398243368\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:43:02.928\n",
      "ic| self.n_r: 200, self.n_z: 200, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 40000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 40000\n",
      "ic| setup_time: 2.1457672119140625e-06\n",
      "ic| time_per_solve: 0.2745467104017735\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:43:08.543\n",
      "ic| self.n_r: 200, self.n_z: 200, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 120000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 40000\n",
      "ic| setup_time: 1.9073486328125e-06\n",
      "ic| time_per_solve: 0.2807751042069867\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:43:14.315\n",
      "ic| self.n_r: 400, self.n_z: 400, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 160000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 160000\n",
      "ic| setup_time: 1.9073486328125e-06\n",
      "ic| time_per_solve: 0.9695732229040004\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:43:33.998\n",
      "ic| self.n_r: 400, self.n_z: 400, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 480000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 160000\n",
      "ic| setup_time: 4.0531158447265625e-06\n",
      "ic| time_per_solve: 1.1364051937591284\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">┏━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┓\n",
       "┃<span style=\"font-weight: bold\"> Timings </span>┃<span style=\"font-weight: bold\"> m = 0                </span>┃<span style=\"font-weight: bold\"> m = 1                </span>┃\n",
       "┡━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━┩\n",
       "│ n = 100 │ 0.011314154148567467 │ 0.008620060398243368 │\n",
       "│ n = 200 │ 0.2745467104017735   │ 0.2807751042069867   │\n",
       "│ n = 400 │ 0.9695732229040004   │ 1.1364051937591284   │\n",
       "└─────────┴──────────────────────┴──────────────────────┘\n",
       "</pre>\n"
      ],
      "text/plain": [
       "┏━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┓\n",
       "┃\u001b[1m \u001b[0m\u001b[1mTimings\u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mm = 0               \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mm = 1               \u001b[0m\u001b[1m \u001b[0m┃\n",
       "┡━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━┩\n",
       "│ n = 100 │ 0.011314154148567467 │ 0.008620060398243368 │\n",
       "│ n = 200 │ 0.2745467104017735   │ 0.2807751042069867   │\n",
       "│ n = 400 │ 0.9695732229040004   │ 1.1364051937591284   │\n",
       "└─────────┴──────────────────────┴──────────────────────┘\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(array([[0.01131415, 0.00862006],\n",
       "        [0.27454671, 0.2807751 ],\n",
       "        [0.96957322, 1.13640519]]),\n",
       " array([[4.05311584e-06, 2.14576721e-06],\n",
       "        [2.14576721e-06, 1.90734863e-06],\n",
       "        [1.90734863e-06, 4.05311584e-06]]),\n",
       " <rich.table.Table at 0x2c66a9ed0>)"
      ]
     },
     "execution_count": 209,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#\n",
    "# Timing of plain gmres\n",
    "#\n",
    "setup = lambda _, A, b: {'A': A, 'b': b, 'tol': 1e-10, 'maxiter': 1000}\n",
    "solve = bicgstab\n",
    "n_list = np.array([100, 200, 400])\n",
    "m_list = np.array([0, 1])\n",
    "timing_table(solve, setup, n_list, m_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 210,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:44:45.973\n",
      "ic| self.n_r: 100, self.n_z: 100, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 10000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 10000\n",
      "ic| setup_time: 0.020043134689331055\n",
      "ic| time_per_solve: 0.1417937207967043\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:44:48.880\n",
      "ic| self.n_r: 100, self.n_z: 100, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 30000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 10000\n",
      "ic| setup_time: 0.019572019577026367\n",
      "ic| time_per_solve: 0.1410190249909647\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:44:51.767\n",
      "ic| self.n_r: 200, self.n_z: 200, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 40000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 40000\n",
      "ic| setup_time: 0.09102416038513184\n",
      "ic| time_per_solve: 0.9976069979020394\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:45:11.951\n",
      "ic| self.n_r: 200, self.n_z: 200, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 120000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 40000\n",
      "ic| setup_time: 0.10575199127197266\n",
      "ic| time_per_solve: 0.9545787021052092\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:45:31.339\n",
      "ic| self.n_r: 400, self.n_z: 400, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 160000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 160000\n",
      "ic| setup_time: 0.42995309829711914\n",
      "ic| time_per_solve: 3.474452425003983\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:46:41.427\n",
      "ic| self.n_r: 400, self.n_z: 400, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 480000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 160000\n",
      "ic| setup_time: 0.423551082611084\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[210], line 13\u001b[0m\n\u001b[1;32m     11\u001b[0m n_list \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray([\u001b[38;5;241m100\u001b[39m, \u001b[38;5;241m200\u001b[39m, \u001b[38;5;241m400\u001b[39m])\n\u001b[1;32m     12\u001b[0m m_list \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marray([\u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m1\u001b[39m])\n\u001b[0;32m---> 13\u001b[0m \u001b[43mtiming_table\u001b[49m\u001b[43m(\u001b[49m\u001b[43msolve\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msetup\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mn_list\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mm_list\u001b[49m\u001b[43m)\u001b[49m\n",
      "Cell \u001b[0;32mIn[206], line 8\u001b[0m, in \u001b[0;36mtiming_table\u001b[0;34m(solve, setup, n_list, m_list)\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m j,n \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(n_list):\n\u001b[1;32m      7\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m i,m \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28menumerate\u001b[39m(m_list):\n\u001b[0;32m----> 8\u001b[0m         times[j,i], setup_times[j,i] \u001b[38;5;241m=\u001b[39m \u001b[43msolve_timing\u001b[49m\u001b[43m(\u001b[49m\u001b[43msolve\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msetup\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mn\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mn\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mm\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     10\u001b[0m table \u001b[38;5;241m=\u001b[39m Table(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mTimings\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m     11\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m m \u001b[38;5;129;01min\u001b[39;00m m_list:\n",
      "Cell \u001b[0;32mIn[205], line 20\u001b[0m, in \u001b[0;36msolve_timing\u001b[0;34m(solve, setup, n_r, n_z, m, number)\u001b[0m\n\u001b[1;32m     18\u001b[0m ic(setup_time)\n\u001b[1;32m     19\u001b[0m code \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mlambda\u001b[39;00m: solve(\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39msolve_args)\n\u001b[0;32m---> 20\u001b[0m time_total \u001b[38;5;241m=\u001b[39m \u001b[43mtimeit\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtimeit\u001b[49m\u001b[43m(\u001b[49m\u001b[43mcode\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnumber\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mnumber\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     21\u001b[0m time_per_solve \u001b[38;5;241m=\u001b[39m time_total\u001b[38;5;241m/\u001b[39m\u001b[38;5;241m20\u001b[39m\n\u001b[1;32m     22\u001b[0m ic(time_per_solve)\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.10/timeit.py:234\u001b[0m, in \u001b[0;36mtimeit\u001b[0;34m(stmt, setup, timer, number, globals)\u001b[0m\n\u001b[1;32m    231\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mtimeit\u001b[39m(stmt\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpass\u001b[39m\u001b[38;5;124m\"\u001b[39m, setup\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpass\u001b[39m\u001b[38;5;124m\"\u001b[39m, timer\u001b[38;5;241m=\u001b[39mdefault_timer,\n\u001b[1;32m    232\u001b[0m            number\u001b[38;5;241m=\u001b[39mdefault_number, \u001b[38;5;28mglobals\u001b[39m\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m    233\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"Convenience function to create Timer object and call timeit method.\"\"\"\u001b[39;00m\n\u001b[0;32m--> 234\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mTimer\u001b[49m\u001b[43m(\u001b[49m\u001b[43mstmt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msetup\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtimer\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mglobals\u001b[39;49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtimeit\u001b[49m\u001b[43m(\u001b[49m\u001b[43mnumber\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.10/timeit.py:178\u001b[0m, in \u001b[0;36mTimer.timeit\u001b[0;34m(self, number)\u001b[0m\n\u001b[1;32m    176\u001b[0m gc\u001b[38;5;241m.\u001b[39mdisable()\n\u001b[1;32m    177\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[0;32m--> 178\u001b[0m     timing \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43minner\u001b[49m\u001b[43m(\u001b[49m\u001b[43mit\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mtimer\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    179\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m    180\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m gcold:\n",
      "File \u001b[0;32m<timeit-src>:6\u001b[0m, in \u001b[0;36minner\u001b[0;34m(_it, _timer, _stmt)\u001b[0m\n",
      "Cell \u001b[0;32mIn[205], line 19\u001b[0m, in \u001b[0;36msolve_timing.<locals>.<lambda>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     17\u001b[0m setup_time \u001b[38;5;241m=\u001b[39m time() \u001b[38;5;241m-\u001b[39m start\n\u001b[1;32m     18\u001b[0m ic(setup_time)\n\u001b[0;32m---> 19\u001b[0m code \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mlambda\u001b[39;00m: \u001b[43msolve\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43msolve_args\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     20\u001b[0m time_total \u001b[38;5;241m=\u001b[39m timeit\u001b[38;5;241m.\u001b[39mtimeit(code, number\u001b[38;5;241m=\u001b[39mnumber)\n\u001b[1;32m     21\u001b[0m time_per_solve \u001b[38;5;241m=\u001b[39m time_total\u001b[38;5;241m/\u001b[39m\u001b[38;5;241m20\u001b[39m\n",
      "File \u001b[0;32m<decorator-gen-3>:2\u001b[0m, in \u001b[0;36mcg\u001b[0;34m(A, b, x0, tol, maxiter, M, callback, atol)\u001b[0m\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.10/site-packages/scipy/_lib/_threadsafety.py:44\u001b[0m, in \u001b[0;36mReentrancyLock.decorate.<locals>.caller\u001b[0;34m(func, *a, **kw)\u001b[0m\n\u001b[1;32m     42\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mcaller\u001b[39m(func, \u001b[38;5;241m*\u001b[39ma, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkw):\n\u001b[1;32m     43\u001b[0m     \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m:\n\u001b[0;32m---> 44\u001b[0m         \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfunc\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43ma\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkw\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/anaconda3/lib/python3.10/site-packages/scipy/sparse/linalg/_isolve/iterative.py:358\u001b[0m, in \u001b[0;36mcg\u001b[0;34m(A, b, x0, tol, maxiter, M, callback, atol)\u001b[0m\n\u001b[1;32m    355\u001b[0m \u001b[38;5;28;01mwhile\u001b[39;00m \u001b[38;5;28;01mTrue\u001b[39;00m:\n\u001b[1;32m    356\u001b[0m     olditer \u001b[38;5;241m=\u001b[39m iter_\n\u001b[1;32m    357\u001b[0m     x, iter_, resid, info, ndx1, ndx2, sclr1, sclr2, ijob \u001b[38;5;241m=\u001b[39m \\\n\u001b[0;32m--> 358\u001b[0m        \u001b[43mrevcom\u001b[49m\u001b[43m(\u001b[49m\u001b[43mb\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mwork\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43miter_\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mresid\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43minfo\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mndx1\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mndx2\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mijob\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    359\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m callback \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;129;01mand\u001b[39;00m iter_ \u001b[38;5;241m>\u001b[39m olditer:\n\u001b[1;32m    360\u001b[0m         callback(x)\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "#\n",
    "# Timing of  ILU-preconditioned GG\n",
    "#\n",
    "def setup(fdm_solver, A, b):\n",
    "\n",
    "    LU = spilu(csc_matrix(A))\n",
    "    M = LinearOperator(A.shape, LU.solve)\n",
    "    return {'A': A, 'b': b, 'tol': 1e-10, 'maxiter': 1000, 'M': M}\n",
    "\n",
    "solve = cg\n",
    "n_list = np.array([100, 200, 400])\n",
    "m_list = np.array([0, 1])\n",
    "timing_table(solve, setup, n_list, m_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:47:32.623\n",
      "ic| self.n_r: 100, self.n_z: 100, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 10000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 10000\n",
      "/Users/simenkva/anaconda3/lib/python3.10/site-packages/scipy/sparse/linalg/_dsolve/linsolve.py:395: SparseEfficiencyWarning: splu converted its input to CSC format\n",
      "  warn('splu converted its input to CSC format', SparseEfficiencyWarning)\n",
      "ic| setup_time: 0.0048520565032958984\n",
      "ic| time_per_solve: 0.022505481250118465\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:47:33.148\n",
      "ic| self.n_r: 100, self.n_z: 100, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 30000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 10000\n",
      "ic| setup_time: 0.00910186767578125\n",
      "ic| time_per_solve: 0.020310118747875094\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:47:33.625\n",
      "ic| self.n_r: 200, self.n_z: 200, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 40000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 40000\n",
      "ic| setup_time: 0.01325082778930664\n",
      "ic| time_per_solve: 0.3341591187519953\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:47:40.412\n",
      "ic| self.n_r: 200, self.n_z: 200, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 120000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 40000\n",
      "ic| setup_time: 0.026705026626586914\n",
      "ic| time_per_solve: 0.2666449479060248\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:47:45.944\n",
      "ic| self.n_r: 400, self.n_z: 400, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 160000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 160000\n",
      "ic| setup_time: 0.05185103416442871\n",
      "ic| time_per_solve: 1.419138945848681\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:48:14.718\n",
      "ic| self.n_r: 400, self.n_z: 400, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 480000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 160000\n",
      "ic| setup_time: 0.05710911750793457\n",
      "ic| time_per_solve: 1.4083655500086025\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">┏━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┓\n",
       "┃<span style=\"font-weight: bold\"> Timings </span>┃<span style=\"font-weight: bold\"> m = 0                </span>┃<span style=\"font-weight: bold\"> m = 1                </span>┃\n",
       "┡━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━┩\n",
       "│ n = 100 │ 0.022505481250118465 │ 0.020310118747875094 │\n",
       "│ n = 200 │ 0.3341591187519953   │ 0.2666449479060248   │\n",
       "│ n = 400 │ 1.419138945848681    │ 1.4083655500086025   │\n",
       "└─────────┴──────────────────────┴──────────────────────┘\n",
       "</pre>\n"
      ],
      "text/plain": [
       "┏━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┓\n",
       "┃\u001b[1m \u001b[0m\u001b[1mTimings\u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mm = 0               \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mm = 1               \u001b[0m\u001b[1m \u001b[0m┃\n",
       "┡━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━┩\n",
       "│ n = 100 │ 0.022505481250118465 │ 0.020310118747875094 │\n",
       "│ n = 200 │ 0.3341591187519953   │ 0.2666449479060248   │\n",
       "│ n = 400 │ 1.419138945848681    │ 1.4083655500086025   │\n",
       "└─────────┴──────────────────────┴──────────────────────┘\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(array([[0.02250548, 0.02031012],\n",
       "        [0.33415912, 0.26664495],\n",
       "        [1.41913895, 1.40836555]]),\n",
       " array([[0.00485206, 0.00910187],\n",
       "        [0.01325083, 0.02670503],\n",
       "        [0.05185103, 0.05710912]]),\n",
       " <rich.table.Table at 0x2c7c8cfa0>)"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.sparse import diags, spdiags\n",
    "from scipy.sparse.linalg import splu\n",
    "\n",
    "\n",
    "#\n",
    "# Timing of tridiagonal-preconditioned GG\n",
    "#\n",
    "def setup(fdm_solver, A, b):\n",
    "\n",
    "    data = np.array([np.append(A.diagonal(-1), 0), A.diagonal(), np.insert(A.diagonal(1), 0, 0)])\n",
    "    T = spdiags(data, [-1, 0, 1], A.shape[0], A.shape[0])    # get the diagonal of the sparse matrix  A\n",
    "    \n",
    "    LU = splu(T)\n",
    "    M = LinearOperator(A.shape, LU.solve)\n",
    "    return {'A': A, 'b': b, 'tol': 1e-10, 'maxiter': 1000, 'M': M}\n",
    "\n",
    "solve = cg\n",
    "n_list = np.array([100, 200, 400])\n",
    "m_list = np.array([0, 1])\n",
    "timing_table(solve, setup, n_list, m_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 22:04:43.012\n",
      "ic| self.n_r: 100, self.n_z: 100, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 10000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 10000\n",
      "ic| setup_time: 0.7746078968048096\n",
      "ic| time_per_solve: 0.014169149997178465\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 22:04:44.286\n",
      "ic| self.n_r: 100, self.n_z: 100, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 30000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 10000\n",
      "ic| setup_time: 0.4878251552581787\n",
      "ic| time_per_solve: 0.0145769500057213\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 22:04:45.194\n",
      "ic| self.n_r: 200, self.n_z: 200, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 40000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 40000\n",
      "ic| setup_time: 1.2766859531402588\n",
      "ic| time_per_solve: 0.019262914592400194\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 22:04:47.051\n",
      "ic| self.n_r: 200, self.n_z: 200, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 120000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 40000\n",
      "ic| setup_time: 0.9402029514312744\n",
      "ic| time_per_solve: 0.018405960395466537\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 22:04:48.506\n",
      "ic| self.n_r: 400, self.n_z: 400, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 160000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 160000\n",
      "ic| setup_time: 5.007488012313843\n",
      "ic| time_per_solve: 0.051602968748193236\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 22:04:54.755\n",
      "ic| self.n_r: 400, self.n_z: 400, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 480000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 160000\n",
      "ic| setup_time: 4.3116350173950195\n",
      "ic| time_per_solve: 0.04700287289451808\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 22:05:00.253\n",
      "ic| self.n_r: 800, self.n_z: 800, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 640000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 640000\n",
      "ic| setup_time: 37.47531008720398\n",
      "ic| time_per_solve: 0.23954424584517256\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 22:05:42.878\n",
      "ic| self.n_r: 800, self.n_z: 800, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 1920000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 640000\n",
      "ic| setup_time: 38.02315378189087\n",
      "ic| time_per_solve: 0.23393491039751096\n",
      "ic| self.m_i: array([0.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 22:06:25.942\n",
      "ic| self.n_r: 1000, self.n_z: 1000, self.n_m: 1\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 1000000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 1000000\n",
      "ic| setup_time: 86.98019814491272\n",
      "ic| time_per_solve: 2.126472829200793\n",
      "ic| self.m_i: array([ 0.,  1., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 22:08:36.490\n",
      "ic| self.n_r: 1000, self.n_z: 1000, self.n_m: 3\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 3000000\n",
      "ic| 'system dimension = ', L_vec[0].shape[0]: 1000000\n",
      "ic| setup_time: 81.35245394706726\n",
      "ic| time_per_solve: 1.9526557729113847\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">┏━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┓\n",
       "┃<span style=\"font-weight: bold\"> Timings  </span>┃<span style=\"font-weight: bold\"> m = 0                </span>┃<span style=\"font-weight: bold\"> m = 1                </span>┃\n",
       "┡━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━┩\n",
       "│ n = 100  │ 0.014169149997178465 │ 0.0145769500057213   │\n",
       "│ n = 200  │ 0.019262914592400194 │ 0.018405960395466537 │\n",
       "│ n = 400  │ 0.051602968748193236 │ 0.04700287289451808  │\n",
       "│ n = 800  │ 0.23954424584517256  │ 0.23393491039751096  │\n",
       "│ n = 1000 │ 2.126472829200793    │ 1.9526557729113847   │\n",
       "└──────────┴──────────────────────┴──────────────────────┘\n",
       "</pre>\n"
      ],
      "text/plain": [
       "┏━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┳━━━━━━━━━━━━━━━━━━━━━━┓\n",
       "┃\u001b[1m \u001b[0m\u001b[1mTimings \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mm = 0               \u001b[0m\u001b[1m \u001b[0m┃\u001b[1m \u001b[0m\u001b[1mm = 1               \u001b[0m\u001b[1m \u001b[0m┃\n",
       "┡━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━╇━━━━━━━━━━━━━━━━━━━━━━┩\n",
       "│ n = 100  │ 0.014169149997178465 │ 0.0145769500057213   │\n",
       "│ n = 200  │ 0.019262914592400194 │ 0.018405960395466537 │\n",
       "│ n = 400  │ 0.051602968748193236 │ 0.04700287289451808  │\n",
       "│ n = 800  │ 0.23954424584517256  │ 0.23393491039751096  │\n",
       "│ n = 1000 │ 2.126472829200793    │ 1.9526557729113847   │\n",
       "└──────────┴──────────────────────┴──────────────────────┘\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(array([[0.01416915, 0.01457695],\n",
       "        [0.01926291, 0.01840596],\n",
       "        [0.05160297, 0.04700287],\n",
       "        [0.23954425, 0.23393491],\n",
       "        [2.12647283, 1.95265577]]),\n",
       " array([[ 0.7746079 ,  0.48782516],\n",
       "        [ 1.27668595,  0.94020295],\n",
       "        [ 5.00748801,  4.31163502],\n",
       "        [37.47531009, 38.02315378],\n",
       "        [86.98019814, 81.35245395]]),\n",
       " <rich.table.Table at 0x2b708cfd0>)"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from block_lu import extract_tridiag_blocks, block_lu, block_lu_solve\n",
    "\n",
    "def setup(fdm_solver, X, b):\n",
    "    D, A, C = extract_tridiag_blocks(X, fdm_solver.n_z, fdm_solver.n_r)\n",
    "    L, lu_U, C = block_lu(D, A, C)\n",
    "    return {'L': L, 'lu_U': lu_U, 'C': C, 'b': b}\n",
    "\n",
    "def solve(L, lu_U, C, b):\n",
    "    return block_lu_solve(L, lu_U, C, b)\n",
    "\n",
    "\n",
    "n_list = np.array([100, 200, 400, 800, 1000])\n",
    "m_list = np.array([0, 1])\n",
    "timing_table(solve, setup, n_list, m_list)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.85060858e+85, 1.48093144e+85, 3.47885231e+84, 8.12106822e+83,\n",
       "       1.89470558e+83, 4.42024600e+82, 1.03120590e+82, 2.40536777e+81,\n",
       "       5.59584186e+80, 1.23808854e+80])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lu_solve(lu_U[0], rhs[:n_z])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| self.m_i: array([ 0.,  1., -2., -1.])\n",
      "ic| cylinder_fdm_3d.py:169 in __init__() at 21:08:53.243\n",
      "ic| self.n_r: 100, self.n_z: 20, self.n_m: 4\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 8000\n"
     ]
    }
   ],
   "source": [
    "from scipy.sparse.csgraph import reverse_cuthill_mckee\n",
    "n_r = 100\n",
    "n_z = 20\n",
    "n_theta = 4\n",
    "r_max = 20\n",
    "z_max = 20\n",
    "solver = CylinderFDM(r_max, z_max, n_r, n_z, n_theta)\n",
    "L_vec = solver.get_laplacian_fast()\n",
    "rr, zz = solver.get_rz_meshgrid()\n",
    "\n",
    "u = rr**.5 * np.exp(-(rr**2 - zz**2)/2)\n",
    "rhs = -4*np.pi*u.flatten()\n",
    "\n",
    "\n",
    "P = reverse_cuthill_mckee(L_vec[0], symmetric_mode=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2627bc3d3ce042dc8ef4e9be47c6bc2e",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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' 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       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "bd13ccc71166417682874d4c26e0cce1",
       "version_major": 2,
       "version_minor": 0
      },
      "image/png": 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fP9pKS0vVtm3bgN8d7HfUJy0tzfJzXFxcvcu9f9527NihCy64QN9++60eeeQR3z94vfcLN+Y9auhnz+umm27S4cOH1bZtW/3kJz9p1GsBL6qA0WIcDodmzJihhx56SJs2bbI8V1xcHLC+d5n3C/6ll15St27d9Oqrr1qCgrdIwO54o2833nijbrzxRlVVVem9997TjBkzlJeXpy+++CJgNKIhXC6XJk2apGeeeUbTp0/Xc889pwkTJiglJaVBr2+OY2+M9PR0SdKjjz563KpDe7hp6rntOnTooLVr18oYY9l2SUmJjhw54tvHxm5TkoqKigIqcXfv3h2wzYYeU4cOHfTRRx8FLA/2Pp6Kl156ScOHD9eTTz5pWV5ZWXlK2z3e5y0uLk7t27f3/e4bbrhBs2bNsqy3b9++Bn+u/Xnfi+P97q5du/p+Tk9Pl9PpPG7xkPd969Chg44cOaLS0lJLCGzq9+F4Fi1apKqqKi1YsMDyvbFhw4ZGb6sxf56qqqo0ceJE9ejRQ3v27NHNN98ctBAOOBFGANEsioqKgi73Xj7yeDyW5Z999pn+/e9/W5a9/PLLSkpK8s3HFxMTo7i4OMuXZXFx8Ul/+SUmJmrMmDG67777VFtbq88+++y469pHNOx+8pOfaN++fRo/frzKysp0xx13NHg/mvrYjzfidrxjGDp0qFJSUlRYWKhzzz036MM7+tFcLr74Yh08eDBg/sIXXnjB93xjeS/nvvTSS5bl69at0+bNm09qm5I0bNgwVVZWBlSwvvLKKye1veOJiYnxvWden3766SnPK7hgwQLLqHFlZaXefPNNXXDBBYqNjT3u7168eLG+/fbbk/qdgwYNUkJCgv76179alq9evTrgsndeXp6++uordejQIehn0RsWL7roIkkK2ObLL798UvvYWN4/i/7nyRijp59+OmDdhoyCN9Rtt92mHTt2aMGCBfrLX/6iN954Qw899FCTbBvRhRFANItLL71Up512msaOHauePXvq6NGj2rBhg/74xz+qffv2+p//+R/L+h6PR5dffrlmzpyprKwsvfTSS1q2bJlmz57tm2MuLy9PCxYs0O23367x48dr586d+s1vfqOsrCxt3bq1Qft1yy23yOl0aujQocrKylJxcbEefPBBuVwufec73znu63JyciRJs2fP1pgxYxQbG6t+/fr5glGPHj00evRovfXWWzr//PMD7umrT1Mfe05OjlauXKk333xTWVlZSkpK0llnnaW+fftKkp566iklJSUpISFB3bp1U4cOHfToo49q0qRJ2r9/v8aPH6/MzEzt3btX//73v7V3796AUaimdsMNN+jxxx/XpEmTtH37duXk5OiDDz7QrFmz9N3vfleXXHJJo7d51lln6dZbb9Wjjz6qNm3aaMyYMdq+fbt++ctfqnPnzrrrrrtOal8nTZqkhx56SNdff70eeOABnXnmmXrrrbf09ttvSwqc5uhk5eXl6Te/+Y1mzJihYcOG6fPPP9evf/1rdevWTUeOHDnp7cbGxmrkyJG6++67dfToUc2ePVsVFRWWic7z8vI0f/589ezZU/369dPHH3+s3//+9yc9p2FqaqqmT5+uBx54QDfffLO+//3va+fOnZo5c2bAJdupU6fqn//8py688ELddddd6tevn44ePaodO3Zo6dKlmjZtmnJzczVq1ChdeOGF+tnPfqaqqiqde+65+vDDD/Xiiy+e9LlpjJEjRyouLk7XXnutfvazn+nQoUN68skndeDAgYB1c3JytGDBAj355JMaOHCg2rRpo3PPPbfRv/OZZ57RSy+9pOeee059+vRRnz59dMcdd+iee+7R0KFDdd5550k69g+nm266Sc8++6xuuOGGUz5WtFKhrUFBa/Xqq6+aCRMmmO7du5v27dsbh8NhunTpYiZOnGgKCwst62ZnZ5vLLrvM/OMf/zB9+vQxcXFxpmvXrmbu3LkB2/3d735nunbtauLj402vXr3M008/HbTSUpL58Y9/HPD6559/3lx00UWmY8eOJi4uzng8HnP11VebTz/91LdOsCrgmpoac/PNN5uMjAwTExNjJJlt27ZZtj1//nwjybzyyisNPk/NcewbNmwwQ4cONe3atQuosHz44YdNt27dTGxsbECF4apVq8xll11m0tLSjMPhMJ06dTKXXXaZee2113zreH+f/xQq9mOxs1fRHk9paam57bbbTFZWlmnbtq3Jzs429957rzl06FDA9hpSBWzMscrM2bNnmx49ehiHw2HS09PN9ddfb3bu3NngbQbb/x07dpgrr7zStG/f3iQlJZmrrrrKLFmyxEgyr7/+um+941UBN+Q81dTUmOnTp5tOnTqZhIQEc84555hFixaZSZMmBVSUqhFVwLNnzzb333+/Oe2000xcXJwZMGCAefvtty3rHjhwwEyZMsVkZmaadu3amfPPP9+8//77Afvo/bPi/xnx/13+n6+jR4+aBx980HTu3NnExcWZfv36mTfffDPo+T148KD5xS9+Yc466ywTFxdnXC6XycnJMXfddZcpLi72rVdWVmZuuukmk5KSYtq1a2dGjhxptmzZ0qgqYPu+P/fcc0ZSQBVysM/+m2++afr3728SEhJMp06dzE9/+lNfdbL/98f+/fvN+PHjTUpKiu/7w/88+U/5dLxz+Omnnxqn0xlQ4X/o0CEzcOBA07VrV3PgwAHLMdgriAF/McbYZrAFWljXrl3Vt29f/etf/wr1rpySq666SmvWrNH27dsbXNHXWo4dx1rw/eIXv9COHTvo/gEg7HEJGDgFNTU1+uSTT/TRRx9p4cKFmjt3boPDHyLXY489Jknq2bOnDh8+rHfffVd/+tOfdP311xP+AEQEAiBwCoqKijRkyBAlJyfrhz/8oe68885Q7xJaQLt27fTQQw9p+/btqqmpUZcuXXTPPffoF7/4Rah3DQAahEvAAAAAUYZpYAAAAKIMARAAACDKEAABAACiDAEQAAAgyhAAAQAAogwBECfliSeeULdu3ZSQkKCBAwfq/fffD/UuRZyZM2cqJibG8vBvi2WM0cyZM+XxeOR0OjV8+PCAfsU1NTW68847lZ6ersTERF1++eXatWtXSx9K2Hrvvfc0duxYeTwexcTEBPQabqpzfODAAU2cOFEul0sul0sTJ05UWVlZMx9d+DnR+Z48eXLAZ37QoEGWdTjfQMsgAKLRXn31VU2dOlX33Xef1q9frwsuuEBjxozRjh07Qr1rEadPnz4qKiryPTZu3Oh7bs6cOZo7d64ee+wxrVu3Tm63WyNHjlRlZaVvnalTp2rhwoV65ZVX9MEHH+jgwYPKy8tTXV1dKA4n7FRVVal///6+iZvtmuocT5gwQRs2bFB+fr7y8/O1YcMGTZw4sdmPL9yc6HxL0ujRoy2f+SVLllie53wDLSSUfegQmc477zxz2223WZb17NnT/L//9/9CtEeRacaMGaZ///5Bnzt69Khxu93md7/7nW/ZoUOHjMvlMvPmzTPGHOuD6nA4LL2Hv/32W9OmTRuTn5/frPseiSSZhQsX+n5uqnNcWFhoJJk1a9b41ikoKDCSzJYtW5r5qMKX/XwbY8ykSZPMFVdccdzXcL6BlsMIIBqltrZWH3/8sUaNGmVZPmrUKK1evTpEexW5tm7dKo/Ho27duukHP/iBvv76a0nStm3bVFxcbDnP8fHxGjZsmO88f/zxxzp8+LBlHY/Ho759+/JeNEBTneOCggK5XC7l5ub61hk0aJBcLhfvQxArV65UZmamevTooVtuuUUlJSW+5zjfQMshAKJR9u3bp7q6OnXs2NGyvGPHjiouLg7RXkWm3NxcvfDCC3r77bf19NNPq7i4WEOGDFFpaanvXNZ3nouLixUXF6fU1NTjroPja6pzXFxcrMzMzIDtZ2Zm8j7YjBkzRn/961/17rvv6o9//KPWrVunESNGqKamRhLnG2hJ9ALGSYmJibH8bIwJWIb6jRkzxvf/OTk5Gjx4sM444ww9//zzvhvjT+Y88140TlOc42Dr8z4Euuaaa3z/37dvX5177rnKzs7W4sWLdeWVVx73dZxvoOkxAohGSU9PV2xsbMC/tEtKSgJGUtA4iYmJysnJ0datW33VwPWdZ7fbrdraWh04cOC46+D4muocu91u7dmzJ2D7e/fu5X04gaysLGVnZ2vr1q2SON9ASyIAolHi4uI0cOBALVu2zLJ82bJlGjJkSIj2qnWoqanR5s2blZWVpW7dusntdlvOc21trVatWuU7zwMHDpTD4bCsU1RUpE2bNvFeNEBTnePBgwervLxcH330kW+dtWvXqry8nPfhBEpLS7Vz505lZWVJ4nwDLSp09SeIVK+88opxOBzmL3/5iyksLDRTp041iYmJZvv27aHetYgybdo0s3LlSvP111+bNWvWmLy8PJOUlOQ7j7/73e+My+UyCxYsMBs3bjTXXnutycrKMhUVFb5t3Hbbbea0004z77zzjvnkk0/MiBEjTP/+/c2RI0dCdVhhpbKy0qxfv96sX7/eSDJz584169evN998840xpunO8ejRo02/fv1MQUGBKSgoMDk5OSYvL6/FjzfU6jvflZWVZtq0aWb16tVm27ZtZsWKFWbw4MGmU6dOnG8gBAiAOCmPP/64yc7ONnFxceacc84xq1atCvUuRZxrrrnGZGVlGYfDYTwej7nyyivNZ5995nv+6NGjZsaMGcbtdpv4+Hhz4YUXmo0bN1q2UV1dbe644w6TlpZmnE6nycvLMzt27GjpQwlbK1asMJICHpMmTTLGNN05Li0tNdddd51JSkoySUlJ5rrrrjMHDhxooaMMH/Wd7//85z9m1KhRJiMjwzgcDtOlSxczadKkgHPJ+QZaRowxxoRm7BEAAAChwD2AAAAAUYYACAAAEGUIgAAAAFGGAAgAABBlCIAAAABRhgAIAAAQZQiAAAAAUYYAGMWeeOIJdevWTQkJCRo4cKDef//9Br+2pqZGM2fOVE1NTTPuIfxxzlsW57tlcb6BlsVE0FHq1Vdf1cSJE/XEE09o6NCh+vOf/6xnnnlGhYWF6tKlywlfX1FRIZfLpfLyciUnJ7fAHoNz3rI43y2L8w20LEYAo9TcuXM1ZcoU3XzzzerVq5cefvhhde7cWU8++WSodw0AADQzAmAUqq2t1ccff6xRo0ZZlo8aNUqrV68O0V4BAICW0jbUO4CWt2/fPtXV1aljx46W5R07dlRxcXHQ19TU1FjuzSkrK5MklZeXN9t+wqqiosLyXzQvznfL4ny3PGOMKisr5fF41KYN40HRhgAYxWJiYiw/G2MClnk9+OCDuv/++wOWN+R+QTStzp07h3oXogrnu2Vxvlvezp07ddppp4V6N9DCCIBRKD09XbGxsQGjfSUlJQGjgl733nuv7r77bt/P5eXl6tKlizr9aL7axLdTUlwb5fXzaPnne3RailOTh56uEb2CbwsAEHoVFRXq3LmzkpKSQr0rCAECYBSKi4vTwIEDtWzZMn3ve9/zLV+2bJmuuOKKoK+Jj49XfHx8wPKzu7m1qfSIqiS982WFhvfO1odf79PDq3YqsX2SRvZxN9dhAACawPGu/KB1IwBGqbvvvlsTJ07Uueeeq8GDB+upp57Sjh07dNtttzVqO7mnp8nhrNH6XeUqrT6ilZ+XaPhZmfrw63166r0vJYkQCABAmCEARqlrrrlGpaWl+vWvf62ioiL17dtXS5YsUXZ2dqO2s+CTXep/ukcDTnP5QuCywmKN7O3Wh1/v05z8LdpfVatrzuNeQQAAwgUTQeOkeCdtvfbR5fqyvE693ckqrz6s9buOVQVnJjo0um+WPvhqr9rEtNE9o3syEggAYYTJt6Mbdd84JfNuOFe93cnauLtcLqdDA05zSZJKqg5rWWGxzj8jQwdrDuup977Uss+CTzEDAABaFgEQp2zWVf2U0T5Om/4vBPbISJQkFVXWallhsYaenq6dB6r128WFhEAAAMIAARCnzJPi1LM35qqvx6WNu8vlSXEGDYGHjtQxEggAQBggAKJJeFKclpFAT4rTdzm4ovaoZSRwTv4WvfrRjhDvMQAA0YsAiCZjHwl0JydYQuD7W/dqVC+36sxRPf3+14wEAgAQIgRANCnvSGAnV4I27i6TOzlBw7unSzpWGJK/qYjCEAAAQowAiCbnSXHq/nE5SkuM07pv9kuS+riPtRryhkAKQwAACB0CIJrFgC6pmjfxO77LwRlJ8eqW5pR0LASu/LyEwhAAAEKEAIhmYy8Mye6Q6Lsn0Ns2jsIQAABaHgEQzaq+wpDS6iMUhgAAEAIEQDS7YIUh/h1DKAwBAKBlEQDRIuyFIS6nw3JP4IoteygMAQCghRAA0WLshSHZHRJ9IXBneQ2FIQAAtBACIFrUiQpD6BgCAEDzIwCixdkLQ1xOR0DbOP/CEEIgAABNiwCIkLCPBNpD4KL1u3T+GRkqr67VM4RAAACaFAEQIeM/ElhYXCGX0+FrG1dRe1T5m4o0pk8WU8QAANDECIAIKU+KU/On5Kq3O1kbd5dLkqV3sHckkCliAABoOgRAhAX/y8GSLJeD39jwLVPEAADQhAiACAv1FYaU1dRp+eY9TBEDAEATIQAibAQrDBnUNVXSsRDIFDEAADQNAiDCir0wJMER6wuBFbVH6R0MAEATIAAi7NgLQxIcsZbewSu27KEwBACAU0AARNiyXw72bxtH72AAAE4eARBhy14YYu8d7L0nkMIQAAAahwCIsFZf72Bv2zgKQwAAaBwCIMKefSTQnZxgCYGrv9pHYQgAAI1AAERE8I4EdnIlaOPuMrmTE3zVwUWVtVpWWExhCAAADUQARMTwpDh1/7gcpSXGad03+5XgiFWPjERJx0Jg/qYiCkMAAGgAAiAiyoAuqZo38Tu+y8GeFKevMKSk6jAdQwAAaAACICJOfYUh/m3jKAwBACA4AiAiUrDCEP+2cXQMAQDg+AiAiFj2wpDUdnG+EFhSdVj5m4ooDAEAIAgCICJasMIQ/3sC6RgCAEAgAiAinr0wxN4xZOXnJRSGAADghwCIVqG+wpDS6iOWjiGMBAIAoh0BEK2GvTDE5XQEbRvHSCAAINoRANGq2EcC7SGQKWIAACAAohXyHwksLK6Qy+mwTBFD72AAQLQjAKJV8qQ4NX9Krnq7k7Vxd7kSHLGW3sFMEQMAiGYEQLRq/peD7VPE0DsYABCtCIBo1eyFIf5TxJRUHaYwBAAQlQiAaPWCTREzvHu6JGt1MIUhAIBoQQBEVLCPBDodsZYQSO9gAEA0IQAiath7Bzsdsb4pYrxt4ygMAQBEAwIgooq9d7DL6bC0jaN3MAAgGhAAEXVO1DuYwhAAQGtHAERUqq93MIUhAIDWjgCIqGUvDHEnJ1hC4EfbSikMAQC0SgRARDV7YYh/CPTeE0hhCACgtSEAIuqdqDCEjiEAgNaGAAio/sIQOoYAAFobAiDwfxpTGMJIIAAgkhEAAT/2whCX0xG0bRwjgQCASEYABGzsI4GS6B0MAGhVCIBAEP4jgYXFFZJkuRy8+qt9TBEDAIhYBEDgODwpTs2fkqve7mTf5WBvCCyqrNWywmKmiAEARCQCIHAC/peDXU6HemQkSjoWApkiBgAQiQiAwAnYC0M8KU5fCGSKGABAJCIAAg1gLwzxpDgt9wSu/LyEwhAAQMQgAAINVF/v4NLqI/QOBgBEDAIg0Agn6h2cv6mIwhAAQNgjAAKNVF/v4JKqwxSGAADCHgEQOAkn6h28fPMeCkMAAGGLAAicpGC9gwd1TZUkldXU+UIghSEAgHBDAAROgb0wJLVdnCUEvr91L4UhAICwQwAETpG9MCS1XZyvMMQ7TyCFIQCAcEIABJpAfYUh3rZxFIYAAMIFARBoIsEKQ/zbxtExBAAQLgiAQBMK1jHEe09gRe1RRgIBAGGBAAg0MXthSIIjNmjbOEYCAQChQgAEmoF9JNDldFjaxtE7GAAQSgRAoJn4jwQWFlcEhECmiAEAhAoBEGhGnhSn5k/JVW93sjbaRgK9beOYIgYA0NIIgEALsF8O9m8bR2EIAKClEQCBFmAvDLFPEUPvYABASyIAAi2kviliymrqLCOBFIYAAJoTARBoQcF6B/tPEUNhCACgJRAAgRZm7x3sTk6gMAQA0KIIgEAIBOsd3MedJOm/IZDCEABAcyEAAiFi7x2ckRRvCYH0DgYANBcCIBBC9sKQjKT4oG3jKAwBADQlAmCEmTlzpmJiYiwPt9vte94Yo5kzZ8rj8cjpdGr48OH67LPPLNuoqanRnXfeqfT0dCUmJuryyy/Xrl27WvpQ8H/shSH+9wSWVh/RR9tKKQwBADQpAmAE6tOnj4qKinyPjRs3+p6bM2eO5s6dq8cee0zr1q2T2+3WyJEjVVlZ6Vtn6tSpWrhwoV555RV98MEHOnjwoPLy8lRXVxeKw4HqLwzZWV5DYQgAoEkRACNQ27Zt5Xa7fY+MjAxJx0b/Hn74Yd1333268sor1bdvXz3//PP6z3/+o5dfflmSVF5err/85S/64x//qEsuuUQDBgzQSy+9pI0bN+qdd94J5WFFvWCFIf4dQygMAQA0FQJgBNq6das8Ho+6deumH/zgB/r6668lSdu2bVNxcbFGjRrlWzc+Pl7Dhg3T6tWrJUkff/yxDh8+bFnH4/Gob9++vnWCqampUUVFheWBpmcvDMnukGgJgd57AikMAQCcCgJghMnNzdULL7ygt99+W08//bSKi4s1ZMgQlZaWqrj4WBjo2LGj5TUdO3b0PVdcXKy4uDilpqYed51gHnzwQblcLt+jc+fOTXxk8LIXhmR3SLTcE+hfGMJIIADgZBAAI8yYMWN01VVXKScnR5dccokWL14sSXr++ed968TExFheY4wJWGZ3onXuvfdelZeX+x47d+48haPAidgLQ1xOhyUEMkUMAOBUEAAjXGJionJycrR161ZfNbB9JK+kpMQ3Kuh2u1VbW6sDBw4cd51g4uPjlZycbHmgedlHAv1DYEXtUXoHAwBOGgEwwtXU1Gjz5s3KyspSt27d5Ha7tWzZMt/ztbW1WrVqlYYMGSJJGjhwoBwOh2WdoqIibdq0ybcOwof/SGBhcUVACKR3MADgZBAAI8z06dO1atUqbdu2TWvXrtX48eNVUVGhSZMmKSYmRlOnTtWsWbO0cOFCbdq0SZMnT1a7du00YcIESZLL5dKUKVM0bdo0LV++XOvXr9f111/vu6SM8ONJcWr+lFz1dif7LgcP754uid7BAICT0zbUO4DG2bVrl6699lrt27dPGRkZGjRokNasWaPs7GxJ0s9+9jNVV1fr9ttv14EDB5Sbm6ulS5cqKSnJt42HHnpIbdu21dVXX63q6mpdfPHFmj9/vmJjY0N1WGiAWVf1003PrdWm3eXq63GpjztJnxVX+kLgBd0z9OHX+/TbxYWSpJF93CfYIgAgWsUYY0yodwKRp6KiQi6XS+Xl5dwP2IJ2l1Xr5//8VBt3lyvH49I3pVXatr9aktTB2VbDz8rUh1/vU+dUp2698ExCIIDj4ns8unEJGIggjZkihsIQAMDxEACBCHOi3sEUhgAAToQACESg+noHUxgCADgRAiAQoU7UO3jFlj10DAEABEUABCJYfb2Dd5bX0DsYABAUARCIcCcqDKFjCADAjgAItAL1FYbQMQQAYEcABFoJCkMAAA1FAARakWCFIX3cx7rAeEMghSEAAAIg0MrYC0MykuItIdB7TyCFIQAQvQiAQCtkLwzJSIq33BO4fDNTxABANCMAAq2UvTDE5XT4QmBZTZ0vBDISCADRhwAItGL2kUCX06FBXVMlHQuBTBEDANGJAAi0cv4jgYXFFUpwxPpCIFPEAEB0IgACUcCT4tT8Kbnq7U7Wxt3lSnDEWqaIWbFlD1PEAEAUIQACUcR+Odi/bRy9gwEgehAAgShiLwyx9w5mihgAiA4EQCDK1Nc7uKL2KIUhABAFCIBAFDpR7+DVX+2jMAQAWjECIBClgvUO9lYHF1XWallhMYUhANBKEQCBKGbvHZzgiFWPjERJx0IgvYMBoHUiAAJRzt472JPi9BWGlFQdpmMIALRCBEAA9RaG+LeNozAEAFoHAiAAScELQ/zbxtExBABaDwIgAB97YUhquzhfCCypOqz8TUUUhgBAK0AABGARrDDE/55AOoYAQOQjAAIIYC8MsXcMWfl5CYUhABDBCIAAgqqvMKS0+ggdQwAgghEAARyXvTDE5XQEtI3zLwwhBAJAZCAAAqiXfSTQHgLf2PCtzj8jQ+XVtXqGEAgAEYEACOCE/EcCC4sr5HI6LFPELCss1pg+WUwRAwARggAIoEE8KU7Nn5Kr3u5kbdxdrgRHrKV38KL1u5giBgAiBAEQQKP4Xw5OcMRaLgcvWr+LKWIAIAIQAAE0SkMKQ5giBgDCGwEQQKMFKwwZ3j1dkjUEMkUMAIQnAiCAk2IvDJFkCYH0DgaA8EUABHDS7IUhknyXg71t4ygMAYDwQwAEcMrsl4P928bROxgAwg8BEMApsxeG2HsHUxgCAOGFAAigSdTXO5jCEAAILwRAAE3GPhLoTk6whMCPtpVSGAIAYYAACKBJeUcCO7kStHF3mSUEeu8JpDAEAEKLAAigyXlSnLp/XI7SEuO07pv9AYUh+ZuKKAwBgBAiAAJoFgO6pGrexO8ELQwpqTpMYQgAhBABEECzoTAEAMITARBAswrWO9jeNs6/MIQQCADNjwAIoNnZRwIla9u4Ret36fwzMlReXatnCIEA0OwIgABaRLDewfbLwWP6ZDFFDAC0AAIggBZj7x3scjp8IbCoslZvbPiWKWIAoAUQAAG0OHvv4EFdUyVJZTV1WrR+F1PEAEAzIwACaHH2wpAER6wvBPpXBzNFDAA0DwIggJCwF4YkOGIt9wSu/LyEKWIAoJkQAAGEjL0wxP+ewNLqI/QOBoBmQgAEEFL1FYZ428ZRGAIATYsACCAs2AtD/NvG0TsYAJoWARBAWLAXhth7By/fvIfCEABoIgRAAGEjWO9g/ylivCGQwhAAODUEQABhxT4SmNouzhIC39+6l8IQADhFBEAAYcc7EtjJlaCNu8uU2i7OVxhSUnVYywqLKQwBgFNAAAQQljwpTt0/LkdpiXFa981+S2FIUWWtb7JoCkMAoPEIgADC1oAuqZo38TuWwpAeGYmSrCGQwhAAaBwCIICwZi8M8aQ4g7aNozAEABqOAAgg7AUrDPFvG0fHEABoHAIggIhgLwxxJydYOoas2LKHwhAAaCACIICIUV9hiLdtHIUhAHBiBEAAESVYYYh/xxAKQwDgxAiAACJOsI4h/vcE+ncMYSQQAAIRAAFEJHthiMvpCNo2jpFAAAhEAAQQsewjgQmOWEsIZIoYAAiOAAggovmPBBYWVyjBEWu5HEzvYAAIRAAEEPE8KU7Nn5Kr3u5k3+Vg/97B+ZuKmCIGAPwQAAG0Gv6Xg11Oh/q4kyT9NwRSGAIAxxAAAbQa9sKQjKR4SwhkihgAOIYACKBVsReGZCTFW+4JXPl5CYUhAKIeARBAq2MfCfRvG1dafYTewQCiHgEQQKt0ot7BFIYAiGYEQACtVn29gykMARDNCIAAWrUT9Q723hNIYQiAaEIABNDq1dc7uLT6CIUhAKIOARBAVDhRYQgdQwBEEwIggKhRX2EIHUMARBMCYJh57733NHbsWHk8HsXExGjRokWW540xmjlzpjwej5xOp4YPH67PPvvMsk5NTY3uvPNOpaenKzExUZdffrl27dplWefAgQOaOHGiXC6XXC6XJk6cqLKysmY+OiD0KAwBAAJg2KmqqlL//v312GOPBX1+zpw5mjt3rh577DGtW7dObrdbI0eOVGVlpW+dqVOnauHChXrllVf0wQcf6ODBg8rLy1NdXZ1vnQkTJmjDhg3Kz89Xfn6+NmzYoIkTJzb78QHhIFhhCB1DAESTGGOMCfVOILiYmBgtXLhQ48aNk3Rs9M/j8Wjq1Km65557JB0b7evYsaNmz56tH/7whyovL1dGRoZefPFFXXPNNZKk3bt3q3PnzlqyZIkuvfRSbd68Wb1799aaNWuUm5srSVqzZo0GDx6sLVu26KyzzjrhvlVUVMjlcqm8vFzJycnNcwKAZra7rFo3PbdW+w7Wqq/n2KXglVv3SZKS49poZG+3Pvx6nxLaxuq+y3prZB93KHcXaFJ8j0c3RgAjyLZt21RcXKxRo0b5lsXHx2vYsGFavXq1JOnjjz/W4cOHLet4PB717dvXt05BQYFcLpcv/EnSoEGD5HK5fOvY1dTUqKKiwvIAIp29MERS0LZxjAQCaG0IgBGkuPjYXz4dO3a0LO/YsaPvueLiYsXFxSk1NbXedTIzMwO2n5mZ6VvH7sEHH/TdL+hyudS5c+dTPh4gHNiniHE5HUwRA6DVIwBGoJiYGMvPxpiAZXb2dYKtX9927r33XpWXl/seO3fuPIk9B8KT/0hgYXFFQAhkihgArQ0BMIK43cfuP7KP0pWUlPhGBd1ut2pra3XgwIF619mzZ0/A9vfu3RswuugVHx+v5ORkywNoTTwpTs2fkqve7mRttI0EMkUMgNaGABhBunXrJrfbrWXLlvmW1dbWatWqVRoyZIgkaeDAgXI4HJZ1ioqKtGnTJt86gwcPVnl5uT766CPfOmvXrlV5eblvHSBa2S8H+08Rs2LLHqaIAdAqtA31DsDq4MGD+vLLL30/b9u2TRs2bFBaWpq6dOmiqVOnatasWerevbu6d++uWbNmqV27dpowYYIkyeVyacqUKZo2bZo6dOigtLQ0TZ8+XTk5ObrkkkskSb169dLo0aN1yy236M9//rMk6dZbb1VeXl6DKoCB1sx7Ofjn//xUG3eXK+f/qoO37a/WzvIa/efzEg0/K1Mffr1PT7137M8q1cEAIg3TwISZlStX6qKLLgpYPmnSJM2fP1/GGN1///3685//rAMHDig3N1ePP/64+vbt61v30KFD+ulPf6qXX35Z1dXVuvjii/XEE09YCjf279+vn/zkJ3rjjTckSZdffrkee+wxpaSkNGg/mT4ArZ19ipjy6sNav+tYpbD/FDFJ8Q7dfMHpuua8LiHeY6Bx+B6PbgRAnBS+OBANdpdV+0YCz8tOU3HFIV8IzEx0aHTfLH3w1V61iWmje0b3ZCQQEYXv8ejGPYAAcBz0DgbQWhEAAaAewXoH+7eNo3cwgEhEAASAE7D3Ds5Iiqd3MICIRgAEgAawdwzJSIq3tI1bvnkPHUMARAwCIAA0kL13sP89gWU1dVr91T46hgCICARAAGiEYIUhg7oe671dVFlLYQiAiEAABIBGsheGJDhi1SMjURKFIQAiAwEQAE6CvTDEk+K0tI1b+XkJhSEAwhYBEABOkr0wJLtDou+ewNLqI74QyEgggHBDAASAU2AvDHE5HZYQyBQxAMIRARAATpF9JNA/BFbUHvWFQKaIARAuCIAA0AT8RwILiysCQiBTxAAIJwRAAGginhSn5k/JVW93su9ysP8UMcsKi5kiBkBYIAACQBPzvxzsP0WMd55ACkMAhBoBEACamL0wxD5FjLdtHIUhAEKFAAgAzaC+KWLKauroHQwgpAiAANBMgvUO9t4TWFZTp/e37qUwBEBIEAABoBnZewentovzhUBv2zgKQwC0NAIgADSzYL2D/e8JXLFlD4UhAFoUARAAWoC9d3B2h0RfCNxZXkPvYAAtigAIAC3kRL2D6RgCoKUQAAGgBQUrDPHvGEJhCICWQAAEgBZmLwzxD4ElVYfpGAKg2REAASAE7IUhLqfD0jHE/3IwhSEAmhoBEABCxF4Y4klxBg2BFIYAaGoEQAAIIXthiCfFabknkJFAAM2BAAgAIWYvDHE5HUFDICOBAJoKARAAwoB9JNDldGh493RJgSOBTBED4FQRAAEgTPiPBBYWV0iSJQQyRQyApkIABIAw4klxav6UXPV2J2vj7nJJskwRs2LLHqaIAXDKCIAAEIbsl4P928bROxjAqSIAAkAYsheG2HsHUxgC4FQQAAEgTNXXO5jCEACnggAIAGHsRL2DP9pWSmEIgEYjAAJAmKuvd7D3nkAKQwA0BgEQACJAsN7B/vcE5m8qojAEQIMRAAEgQth7B/sXhpRUHaYwBECDEQABIIJQGAKgKRAAASDCBCsMoWMIgMYgAAJABLIXhjgdsb4QWFJ1WPmbiigMAXBcBEAAiFD2whBJQe8JpDAEgB0BEAAiWH2FIUWVtVq+eQ+FIQACEAABIMIFKwwZ1DVVklRWU8dIIIAABEAAaAXshSEJjlhfCPSvDmYkEIBEAASAVsM+EpjgiLVMEbPy8xKmiAEgiQAIAK2K/0hgYXGFXE6HLwSWVh+hdzAASQRAAGh1PClOzZ+Sq97uZG3cXW4Jgd62cUwRA0Q3AiAAtFL+l4P9ewd75wmkMASIXgRAAGil7IUh9t7BTBEDRC8CIAC0YieaIsYbAikMAaILARAAWjn7SGBquzhLCKR3MBB9CIAAEAXsvYNT28X5CkO8beMoDAGiBwEQAKKEvXewf2FIUWUtHUOAKEIABIAoEqx3cI+MREnWEEhhCNC6EQABIMrYC0M8Kc6gbeMoDAFaLwIgAEShYIUh/m3j6BgCtG4EQACIUvbCEHdygqVjyIoteygMAVopAiAARLH6CkO8beMoDAFaHwIgAES5YIUh/h1DKAwBWh8CIAAgaMcQ/3sC6RgCtC4EQACApMDCEJfTEdA2zr8whBAIRC4CIADAxz4SmOCItYTARet36fwzMlReXatnCIFAxCIAAgAs/EcCC4srlOCItVwOzt9UpDF9spgiBohgBEAAQABPilPzp+SqtzvZdznYv3ewdySQKWKAyEQABAAcl//lYJfToeHd0yUdGwlctH4XU8QAEYoACAA4LnthiCRLCGSKGCAyEQABAPWyF4ZIstwTuPLzEqaIASIMARAAcEL2whD/ewJLq4/QOxiIMARAAECD1FcY4m0bR2EIEBkIgACARrEXhvi3jaN3MBAZCIAAgEaxF4bYewd77wmkMAQIXwRAAECj1dc7uLT6CIUhQJgjAAIATop9JNCdnGAJge9v3UthCBCmCIAAgJPmHQns5ErQxt1llhDovSeQwhAg/BAAAQCnxJPi1P3jcpSWGKd13+ynMASIAARAAMApG9AlVfMmfsdSGNLHnSTpWAikYwgQXgiAAIAmYS8MyUiKD9o2jsIQIPQIgACAJmMvDHE6Yi1t41Z/tY/CECAMEAABAE2qvsKQospaLSsspjAECDECIACgyQUrDOmRkSjpWAikMAQILQIgAKBZ2AtDPClOXwikMAQILQJgmHnvvfc0duxYeTwexcTEaNGiRZbnJ0+erJiYGMtj0KBBlnVqamp05513Kj09XYmJibr88su1a9cuyzoHDhzQxIkT5XK55HK5NHHiRJWVlTXz0QGINvbCEE+K03JPoH/HEEYCgZZDAAwzVVVV6t+/vx577LHjrjN69GgVFRX5HkuWLLE8P3XqVC1cuFCvvPKKPvjgAx08eFB5eXmqq6vzrTNhwgRt2LBB+fn5ys/P14YNGzRx4sRmOy4A0cteGOJyOoK2jWMkEGg5McYYE+qdQHAxMTFauHChxo0b51s2efJklZWVBYwMepWXlysjI0MvvviirrnmGknS7t271blzZy1ZskSXXnqpNm/erN69e2vNmjXKzc2VJK1Zs0aDBw/Wli1bdNZZZ51w3yoqKuRyuVReXq7k5ORTPlYArd/usmrd9Nxa7TtYq74el8qrD2v9rnJJUnJcG43s7daHX+9TUrxDN19wuq45r0uI97h143s8ujECGIFWrlypzMxM9ejRQ7fccotKSkp8z3388cc6fPiwRo0a5Vvm8XjUt29frV69WpJUUFAgl8vlC3+SNGjQILlcLt86ANDU/EcCC4srLCOBFbVH6R0MtCACYIQZM2aM/vrXv+rdd9/VH//4R61bt04jRoxQTU2NJKm4uFhxcXFKTU21vK5jx44qLi72rZOZmRmw7czMTN86djU1NaqoqLA8AKCxPClOzZ+Sq97u5IDLwfQOBloOATDCXHPNNbrsssvUt29fjR07Vm+99Za++OILLV68uN7XGWMUExPj+9n//4+3jr8HH3zQVzDicrnUuXPnUzsQAFHNvzDE5XRY2sYxRQzQ/AiAES4rK0vZ2dnaunWrJMntdqu2tlYHDhywrFdSUqKOHTv61tmzZ0/Atvbu3etbx+7ee+9VeXm577Fz584mPhIA0cReGJKRFE/vYKAFEQAjXGlpqXbu3KmsrCxJ0sCBA+VwOLRs2TLfOkVFRdq0aZOGDBkiSRo8eLDKy8v10Ucf+dZZu3atysvLfevYxcfHKzk52fIAgFMRrHew/z2ByzfvoXcw0EwIgGHm4MGD2rBhgzZs2CBJ2rZtmzZs2KAdO3bo4MGDmj59ugoKCrR9+3atXLlSY8eOVXp6ur73ve9Jklwul6ZMmaJp06Zp+fLlWr9+va6//nrl5OTokksukST16tVLo0eP1i233KI1a9ZozZo1uuWWW5SXl9egCmAAaCr2kUD/tnFlNXX0DgaaCQEwzPzv//6vBgwYoAEDBkiS7r77bg0YMEC/+tWvFBsbq40bN+qKK65Qjx49NGnSJPXo0UMFBQVKSkrybeOhhx7SuHHjdPXVV2vo0KFq166d3nzzTcXGxvrW+etf/6qcnByNGjVKo0aNUr9+/fTiiy+2+PECQLDewYO6Hitk87aNozAEaFrMA4iTwvxRAJra+h0HNOP1jdpddkh9PS7tLqvWF3urJEmZiQ5d0D1DH369TwltY3XfZb01so87xHsc2fgej26MAAIAwkKw3sHd0pySjhWG0DEEaDoEQABA2LAXhmR3SAzaNo7CEODUEAABAGGlvsKQ0uojdAwBmgABEAAQdoIVhtAxBGg6BEAAQFjypDh1/7gcpSXGad03++VyOiz3BHoni6ZjCNB4BEAAQNiyF4Zkd0hUj4xEScemiPFOFk1hCNA4BEAAQFizF4Z4Upy+eQLLauoYCQROAgEQABD27IUhCY7YoG3jGAkEGoYACACICPaRQJfTYWkbR+9goOEIgACAiOE/ElhYXCGX02G5HMwUMUDDEAABABHFk+LU/Cm56u1O9l0O9oZApogBGoYACACISP6XgxMcsZYpYlZs2UNhCFAPAiAAICLZC0OyOyT6QuDO8hp6BwP1IAACACLWiXoH+08RQ2EI8F8EQABARKuvd3BF7VEKQ4AgCIAAgIh3ot7BywqLKQwB/BAAAQCtQrDewf5t4+gYAvwXARAA0GrYewd7UpxBQyCFIYh2BEAAQKsSrHew/z2BFIYABEAAQCtEYQhQPwIgAKBVClYYMrx7uiQ6hgAEQABAq2UvDJGkPu4kSf8NgRSGIBoRAAEArZq9MCQjKd7SNo6OIYhGBEAAQKt3oo4h3hDISCCiBQEQABAV7IUhLqcjaNs4RgIRDQiAAICoYR8J9A+BTBGDaEIABABEFf+RwMLiioAQ+NG2UqaIQatHAAQARB1PilPzp+Sqtzs54HLwzvIardiyhyli0KoRAAEAUct+OdhbHbyzvIYpYtCqEQABAFHLXhiS3SHRMkUMhSForQiAAICoVt8UMRSGoLUiAAIAol6w3sHetnH0DkZrRAAEAECBvYOdjlh6B6PVIgACAPB/gvUODnZPIIUhiHQEQAAA/Nh7B/sXhhRV1mr55j0UhiDiEQABALAJVhgyqGuqJKmspo7CEEQ8AiAAAEHYC0NS28X5QiCFIYh0BEAAAI7DXhiS2i7ON0VMSdVhOoYgYhEAAQCoh70wxN4xZMWWPRSGIOIQAAEAOIH6CkN2ltfQMQQRhwAIAEADNKZjCCOBCHcEQAAAGsheGOJyOiwhkCliECkIgAAANIJ9JNDldFimiPGGQKaIQTgjAAIA0Ej+I4GFxRVKcMRaQiBTxCDcEQABADgJnhSn5k/JVW93sjbuLleCI9YyRcyywmKmiEHYIgACAHAK7JeD/dvGURiCcEUABADgFNgLQ7I7JKpHRqIkawikMAThhAAIAMApsheGeFKclrZx9A5GuCEAAgDQBIL1DvafIuajbaUUhiBsEAABAGgi9t7B7uQEXwj0to2jMAThgAAIAEATOlHv4PxNRRSGIOQIgAAANLH6egd7p4ihMAShRAAEAKAZnKh3MB1DEEoEQAAAmom9MMSdnGDpGLL6q30UhiAkCIAAADQje2FIars4XwgsqqxV/qYiCkPQ4giAAAA0M3thSIIj1nJPIIUhaGkEQAAAWgCFIQgnBEAAAFpIsMKQ4d3TJQV2DGEkEM2JAAgAQAuyF4ZIChoCGQlEcyIAAgDQwuwjgZIsU8Ss/LyEKWLQrAiAAACEgP9IYGFxhVxOhy8EllYfoXcwmhUBEACAEPGkODV/Sq56u5O1cXe5JQR628YxRQyaAwEQAIAQ878c7N87mCli0FwIgAAAhJi9MMQ+RYz3nkAKQ9BUCIAAAISB+noHl1YfoTAETYoACABAmAjWO9g/BL6/dS+FIWgSBEAAAMKIvXewfwj03hNIYQhOFQEQAIAwY+8dTGEImhoBEACAMBSsd3Afd5Ikegfj1BEAAQAIU/bCkIyk+OP2DqYwBI1BAAQAIIzZC0OcjlhL27jVX+2jMASNRgAEACDM1VcYUlRZq2WFxRSGoFEIgAAARIBghSE9MhIlHQuBFIagMQiAAABECHthiCfF6QuBFIagMQiAAABEEHthiCfFabknkI4haAgCIAAAEcZeGOJyOgLaxvkXhhACYUcABAAgAtlHAu0hcNH6XTr/jAyVV9fqGUIgbAiAAABEKP+RwMLiCksIrKg9qvxNRRrTJ4spYhCAAAgAQATzpDg1f0queruTAy4Hl1Qd1hsbvmWKGAQgAAIA0ArYLwcP6poqSSqrqdMbG75lihhYEAABAGgF7IUhCY5YSwi0TxHz7uY9Id5jhBIBEACAVsJeGJJgaxu3fPMe30jgI+98EeK9RSgRAAEAaEXqKwwpq6mz9A5G9CIAAgDQygQrDPFeDva2jbt7ZM8Q7yVCiQAIAEArZb8c7N827jdvbArx3iGU2oZ6BxCZjDGSpIqKihDvCQDgeNq3kR65qpfuf+Mzbfh6t84/I13VVUf1zYFD2lPzH0n//T5HdCEA4qSUlpZKkjp37hziPQEANNS/gyyrrKyUy+Vq8X1BaBEAcVLS0tIkSTt27OCLo4VUVFSoc+fO2rlzp5KTk0O9O60e57tlcb5bnjFGlZWV8ng8od4VhAABECelTZtjt4+6XC6+rFtYcnIy57wFcb5bFue7ZfEP+OhFEQgAAECUIQACAABEGQIgTkp8fLxmzJih+Pj4UO9K1OCctyzOd8vifAMtK8ZQ/w0AABBVGAEEAACIMgRAAACAKEMABAAAiDIEQAAAgChDAAQAAIgyBEAAAIAoQwAEAACIMgRAAACAKEMABAAAiDIEQAAAgChDAAQAAIgyBEAAAIAoQwAEAACIMgRAAACAKEMABAAAiDIEQAAAgChDAAQAAIgyBEAAAIAoQwAEAACIMgRAAACAKEMABAAAiDIEQAAAgChDAAQAAIgyBEAAAIAoQwAEAACIMgRAAACAKEMABAAAiDIEQAAAgChDAAQAAIgyBEAAAIAoQwAEAACIMgRAAACAKEMABAAAiDIEQAAAgChDAAQAAIgyBEAAAIAoQwAEAACIMgRAAACAKEMABAAAiDIEQAAAgChDAAQAAIgyBEAAAIAoQwAEAACIMgRAAACAKEMABAAAiDIEQAAAgCjz/wHrGD75TrP42wAAAABJRU5ErkJggg==",
      "text/html": [
       "\n",
       "            <div style=\"display: inline-block;\">\n",
       "                <div class=\"jupyter-widgets widget-label\" style=\"text-align: center;\">\n",
       "                    Figure\n",
       "                </div>\n",
       "                <img 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/use+3Zs0effvppwGcxKSlJxhjfP9pKS0vVtm3bgN8d7HfUJy0tzfJzXFxcvcu9f9527NihCy64QN9++60eeeQR3z94vfcLN+Y9auhnz+umm27S4cOH1bZtW/3kJz9p1GsBL6qA0WIcDodmzJihhx56SJs2bbI8V1xcHLC+d5n3C/6ll15St27d9Oqrr1qCgrdIwO54o2833nijbrzxRlVVVem9997TjBkzlJeXpy+++CJgNKIhXC6XJk2apGeeeUbTp0/Xc889pwkTJiglJaVBr2+OY2+M9PR0SdKjjz563KpDe7hp6rntOnTooLVr18oYY9l2SUmJjhw54tvHxm5TkoqKigIqcXfv3h2wzYYeU4cOHfTRRx8FLA/2Pp6Kl156ScOHD9eTTz5pWV5ZWXlK2z3e5y0uLk7t27f3/e4bbrhBs2bNsqy3b9++Bn+u/Xnfi+P97q5du/p+Tk9Pl9PpPG7xkPd969Chg44cOaLS0lJLCGzq9+F4Fi1apKqqKi1YsMDyvbFhw4ZGb6sxf56qqqo0ceJE9ejRQ3v27NHNN98ctBAOOBFGANEsioqKgi73Xj7yeDyW5Z999pn+/e9/W5a9/PLLSkpK8s3HFxMTo7i4OMuXZXFx8Ul/+SUmJmrMmDG67777VFtbq88+++y469pHNOx+8pOfaN++fRo/frzKysp0xx13NHg/mvrYjzfidrxjGDp0qFJSUlRYWKhzzz036MM7+tFcLr74Yh08eDBg/sIXXnjB93xjeS/nvvTSS5bl69at0+bNm09qm5I0bNgwVVZWBlSwvvLKKye1veOJiYnxvWden3766SnPK7hgwQLLqHFlZaXefPNNXXDBBYqNjT3u7168eLG+/fbbk/qdgwYNUkJCgv76179alq9evTrgsndeXp6++uordejQIehn0RsWL7roIkkK2ObLL798UvvYWN4/i/7nyRijp59+OmDdhoyCN9Rtt92mHTt2aMGCBfrLX/6iN954Qw899FCTbBvRhRFANItLL71Up512msaOHauePXvq6NGj2rBhg/74xz+qffv2+p//+R/L+h6PR5dffrlmzpyprKwsvfTSS1q2bJlmz57tm2MuLy9PCxYs0O23367x48dr586d+s1vfqOsrCxt3bq1Qft1yy23yOl0aujQocrKylJxcbEefPBBuVwufec73znu63JyciRJs2fP1pgxYxQbG6t+/fr5glGPHj00evRovfXWWzr//PMD7umrT1Mfe05OjlauXKk333xTWVlZSkpK0llnnaW+fftKkp566iklJSUpISFB3bp1U4cOHfToo49q0qRJ2r9/v8aPH6/MzEzt3btX//73v7V3796AUaimdsMNN+jxxx/XpEmTtH37duXk5OiDDz7QrFmz9N3vfleXXHJJo7d51lln6dZbb9Wjjz6qNm3aaMyYMdq+fbt++ctfqnPnzrrrrrtOal8nTZqkhx56SNdff70eeOABnXnmmXrrrbf09ttvSwqc5uhk5eXl6Te/+Y1mzJihYcOG6fPPP9evf/1rdevWTUeOHDnp7cbGxmrkyJG6++67dfToUc2ePVsVFRWWic7z8vI0f/589ezZU/369dPHH3+s3//+9yc9p2FqaqqmT5+uBx54QDfffLO+//3va+fOnZo5c2bAJdupU6fqn//8py688ELddddd6tevn44ePaodO3Zo6dKlmjZtmnJzczVq1ChdeOGF+tnPfqaqqiqde+65+vDDD/Xiiy+e9LlpjJEjRyouLk7XXnutfvazn+nQoUN68skndeDAgYB1c3JytGDBAj355JMaOHCg2rRpo3PPPbfRv/OZZ57RSy+9pOeee059+vRRnz59dMcdd+iee+7R0KFDdd5550k69g+nm266Sc8++6xuuOGGUz5WtFKhrUFBa/Xqq6+aCRMmmO7du5v27dsbh8NhunTpYiZOnGgKCwst62ZnZ5vLLrvM/OMf/zB9+vQxcXFxpmvXrmbu3LkB2/3d735nunbtauLj402vXr3M008/HbTSUpL58Y9/HPD6559/3lx00UWmY8eOJi4uzng8HnP11VebTz/91LdOsCrgmpoac/PNN5uMjAwTExNjJJlt27ZZtj1//nwjybzyyisNPk/NcewbNmwwQ4cONe3atQuosHz44YdNt27dTGxsbECF4apVq8xll11m0tLSjMPhMJ06dTKXXXaZee2113zreH+f/xQq9mOxs1fRHk9paam57bbbTFZWlmnbtq3Jzs429957rzl06FDA9hpSBWzMscrM2bNnmx49ehiHw2HS09PN9ddfb3bu3NngbQbb/x07dpgrr7zStG/f3iQlJZmrrrrKLFmyxEgyr7/+um+941UBN+Q81dTUmOnTp5tOnTqZhIQEc84555hFixaZSZMmBVSUqhFVwLNnzzb333+/Oe2000xcXJwZMGCAefvtty3rHjhwwEyZMsVkZmaadu3amfPPP9+8//77Afvo/bPi/xnx/13+n6+jR4+aBx980HTu3NnExcWZfv36mTfffDPo+T148KD5xS9+Yc466ywTFxdnXC6XycnJMXfddZcpLi72rVdWVmZuuukmk5KSYtq1a2dGjhxptmzZ0qgqYPu+P/fcc0ZSQBVysM/+m2++afr3728SEhJMp06dzE9/+lNfdbL/98f+/fvN+PHjTUpKiu/7w/88+U/5dLxz+Omnnxqn0xlQ4X/o0CEzcOBA07VrV3PgwAHLMdgriAF/McbYZrAFWljXrl3Vt29f/etf/wr1rpySq666SmvWrNH27dsbXNHXWo4dx1rw/eIXv9COHTvo/gEg7HEJGDgFNTU1+uSTT/TRRx9p4cKFmjt3boPDHyLXY489Jknq2bOnDh8+rHfffVd/+tOfdP311xP+AEQEAiBwCoqKijRkyBAlJyfrhz/8oe68885Q7xJaQLt27fTQQw9p+/btqqmpUZcuXXTPPffoF7/4Rah3DQAahEvAAAAAUYZpYAAAAKIMARAAACDKEAABAACiDAEQAAAgyhAAAQAAogwBECfliSeeULdu3ZSQkKCBAwfq/fffD/UuRZyZM2cqJibG8vBvi2WM0cyZM+XxeOR0OjV8+PCAfsU1NTW68847lZ6ersTERF1++eXatWtXSx9K2Hrvvfc0duxYeTwexcTEBPQabqpzfODAAU2cOFEul0sul0sTJ05UWVlZMx9d+DnR+Z48eXLAZ37QoEGWdTjfQMsgAKLRXn31VU2dOlX33Xef1q9frwsuuEBjxozRjh07Qr1rEadPnz4qKiryPTZu3Oh7bs6cOZo7d64ee+wxrVu3Tm63WyNHjlRlZaVvnalTp2rhwoV65ZVX9MEHH+jgwYPKy8tTXV1dKA4n7FRVVal///6+iZvtmuocT5gwQRs2bFB+fr7y8/O1YcMGTZw4sdmPL9yc6HxL0ujRoy2f+SVLllie53wDLSSUfegQmc477zxz2223WZb17NnT/L//9/9CtEeRacaMGaZ///5Bnzt69Khxu93md7/7nW/ZoUOHjMvlMvPmzTPGHOuD6nA4LL2Hv/32W9OmTRuTn5/frPseiSSZhQsX+n5uqnNcWFhoJJk1a9b41ikoKDCSzJYtW5r5qMKX/XwbY8ykSZPMFVdccdzXcL6BlsMIIBqltrZWH3/8sUaNGmVZPmrUKK1evTpEexW5tm7dKo/Ho27duukHP/iBvv76a0nStm3bVFxcbDnP8fHxGjZsmO88f/zxxzp8+LBlHY/Ho759+/JeNEBTneOCggK5XC7l5ub61hk0aJBcLhfvQxArV65UZmamevTooVtuuUUlJSW+5zjfQMshAKJR9u3bp7q6OnXs2NGyvGPHjiouLg7RXkWm3NxcvfDCC3r77bf19NNPq7i4WEOGDFFpaanvXNZ3nouLixUXF6fU1NTjroPja6pzXFxcrMzMzIDtZ2Zm8j7YjBkzRn/961/17rvv6o9//KPWrVunESNGqKamRhLnG2hJ9ALGSYmJibH8bIwJWIb6jRkzxvf/OTk5Gjx4sM444ww9//zzvhvjT+Y88140TlOc42Dr8z4Euuaaa3z/37dvX5177rnKzs7W4sWLdeWVVx73dZxvoOkxAohGSU9PV2xsbMC/tEtKSgJGUtA4iYmJysnJ0datW33VwPWdZ7fbrdraWh04cOC46+D4muocu91u7dmzJ2D7e/fu5X04gaysLGVnZ2vr1q2SON9ASyIAolHi4uI0cOBALVu2zLJ82bJlGjJkSIj2qnWoqanR5s2blZWVpW7dusntdlvOc21trVatWuU7zwMHDpTD4bCsU1RUpE2bNvFeNEBTnePBgwervLxcH330kW+dtWvXqry8nPfhBEpLS7Vz505lZWVJ4nwDLSp09SeIVK+88opxOBzmL3/5iyksLDRTp041iYmJZvv27aHetYgybdo0s3LlSvP111+bNWvWmLy8PJOUlOQ7j7/73e+My+UyCxYsMBs3bjTXXnutycrKMhUVFb5t3Hbbbea0004z77zzjvnkk0/MiBEjTP/+/c2RI0dCdVhhpbKy0qxfv96sX7/eSDJz584169evN998840xpunO8ejRo02/fv1MQUGBKSgoMDk5OSYvL6/FjzfU6jvflZWVZtq0aWb16tVm27ZtZsWKFWbw4MGmU6dOnG8gBAiAOCmPP/64yc7ONnFxceacc84xq1atCvUuRZxrrrnGZGVlGYfDYTwej7nyyivNZ5995nv+6NGjZsaMGcbtdpv4+Hhz4YUXmo0bN1q2UV1dbe644w6TlpZmnE6nycvLMzt27GjpQwlbK1asMJICHpMmTTLGNN05Li0tNdddd51JSkoySUlJ5rrrrjMHDhxooaMMH/Wd7//85z9m1KhRJiMjwzgcDtOlSxczadKkgHPJ+QZaRowxxoRm7BEAAAChwD2AAAAAUYYACAAAEGUIgAAAAFGGAAgAABBlCIAAAABRhgAIAAAQZQiAAAAAUYYAGMWeeOIJdevWTQkJCRo4cKDef//9Br+2pqZGM2fOVE1NTTPuIfxxzlsW57tlcb6BlsVE0FHq1Vdf1cSJE/XEE09o6NCh+vOf/6xnnnlGhYWF6tKlywlfX1FRIZfLpfLyciUnJ7fAHoNz3rI43y2L8w20LEYAo9TcuXM1ZcoU3XzzzerVq5cefvhhde7cWU8++WSodw0AADQzAmAUqq2t1ccff6xRo0ZZlo8aNUqrV68O0V4BAICW0jbUO4CWt2/fPtXV1aljx46W5R07dlRxcXHQ19TU1FjuzSkrK5MklZeXN9t+wqqiosLyXzQvznfL4ny3PGOMKisr5fF41KYN40HRhgAYxWJiYiw/G2MClnk9+OCDuv/++wOWN+R+QTStzp07h3oXogrnu2Vxvlvezp07ddppp4V6N9DCCIBRKD09XbGxsQGjfSUlJQGjgl733nuv7r77bt/P5eXl6tKlizr9aL7axLdTUlwb5fXzaPnne3RailOTh56uEb2CbwsAEHoVFRXq3LmzkpKSQr0rCAECYBSKi4vTwIEDtWzZMn3ve9/zLV+2bJmuuOKKoK+Jj49XfHx8wPKzu7m1qfSIqiS982WFhvfO1odf79PDq3YqsX2SRvZxN9dhAACawPGu/KB1IwBGqbvvvlsTJ07Uueeeq8GDB+upp57Sjh07dNtttzVqO7mnp8nhrNH6XeUqrT6ilZ+XaPhZmfrw63166r0vJYkQCABAmCEARqlrrrlGpaWl+vWvf62ioiL17dtXS5YsUXZ2dqO2s+CTXep/ukcDTnP5QuCywmKN7O3Wh1/v05z8LdpfVatrzuNeQQAAwgUTQeOkeCdtvfbR5fqyvE693ckqrz6s9buOVQVnJjo0um+WPvhqr9rEtNE9o3syEggAYYTJt6Mbdd84JfNuOFe93cnauLtcLqdDA05zSZJKqg5rWWGxzj8jQwdrDuup977Uss+CTzEDAABaFgEQp2zWVf2U0T5Om/4vBPbISJQkFVXWallhsYaenq6dB6r128WFhEAAAMIAARCnzJPi1LM35qqvx6WNu8vlSXEGDYGHjtQxEggAQBggAKJJeFKclpFAT4rTdzm4ovaoZSRwTv4WvfrRjhDvMQAA0YsAiCZjHwl0JydYQuD7W/dqVC+36sxRPf3+14wEAgAQIgRANCnvSGAnV4I27i6TOzlBw7unSzpWGJK/qYjCEAAAQowAiCbnSXHq/nE5SkuM07pv9kuS+riPtRryhkAKQwAACB0CIJrFgC6pmjfxO77LwRlJ8eqW5pR0LASu/LyEwhAAAEKEAIhmYy8Mye6Q6Lsn0Ns2jsIQAABaHgEQzaq+wpDS6iMUhgAAEAIEQDS7YIUh/h1DKAwBAKBlEQDRIuyFIS6nw3JP4IoteygMAQCghRAA0WLshSHZHRJ9IXBneQ2FIQAAtBACIFrUiQpD6BgCAEDzIwCixdkLQ1xOR0DbOP/CEEIgAABNiwCIkLCPBNpD4KL1u3T+GRkqr67VM4RAAACaFAEQIeM/ElhYXCGX0+FrG1dRe1T5m4o0pk8WU8QAANDECIAIKU+KU/On5Kq3O1kbd5dLkqV3sHckkCliAABoOgRAhAX/y8GSLJeD39jwLVPEAADQhAiACAv1FYaU1dRp+eY9TBEDAEATIQAibAQrDBnUNVXSsRDIFDEAADQNAiDCir0wJMER6wuBFbVH6R0MAEATIAAi7NgLQxIcsZbewSu27KEwBACAU0AARNiyXw72bxtH72AAAE4eARBhy14YYu8d7L0nkMIQAAAahwCIsFZf72Bv2zgKQwAAaBwCIMKefSTQnZxgCYGrv9pHYQgAAI1AAERE8I4EdnIlaOPuMrmTE3zVwUWVtVpWWExhCAAADUQARMTwpDh1/7gcpSXGad03+5XgiFWPjERJx0Jg/qYiCkMAAGgAAiAiyoAuqZo38Tu+y8GeFKevMKSk6jAdQwAAaAACICJOfYUh/m3jKAwBACA4AiAiUrDCEP+2cXQMAQDg+AiAiFj2wpDUdnG+EFhSdVj5m4ooDAEAIAgCICJasMIQ/3sC6RgCAEAgAiAinr0wxN4xZOXnJRSGAADghwCIVqG+wpDS6iOWjiGMBAIAoh0BEK2GvTDE5XQEbRvHSCAAINoRANGq2EcC7SGQKWIAACAAohXyHwksLK6Qy+mwTBFD72AAQLQjAKJV8qQ4NX9Krnq7k7Vxd7kSHLGW3sFMEQMAiGYEQLRq/peD7VPE0DsYABCtCIBo1eyFIf5TxJRUHaYwBAAQlQiAaPWCTREzvHu6JGt1MIUhAIBoQQBEVLCPBDodsZYQSO9gAEA0IQAiath7Bzsdsb4pYrxt4ygMAQBEAwIgooq9d7DL6bC0jaN3MAAgGhAAEXVO1DuYwhAAQGtHAERUqq93MIUhAIDWjgCIqGUvDHEnJ1hC4EfbSikMAQC0SgRARDV7YYh/CPTeE0hhCACgtSEAIuqdqDCEjiEAgNaGAAio/sIQOoYAAFobAiDwfxpTGMJIIAAgkhEAAT/2whCX0xG0bRwjgQCASEYABGzsI4GS6B0MAGhVCIBAEP4jgYXFFZJkuRy8+qt9TBEDAIhYBEDgODwpTs2fkqve7mTf5WBvCCyqrNWywmKmiAEARCQCIHAC/peDXU6HemQkSjoWApkiBgAQiQiAwAnYC0M8KU5fCGSKGABAJCIAAg1gLwzxpDgt9wSu/LyEwhAAQMQgAAINVF/v4NLqI/QOBgBEDAIg0Agn6h2cv6mIwhAAQNgjAAKNVF/v4JKqwxSGAADCHgEQOAkn6h28fPMeCkMAAGGLAAicpGC9gwd1TZUkldXU+UIghSEAgHBDAAROgb0wJLVdnCUEvr91L4UhAICwQwAETpG9MCS1XZyvMMQ7TyCFIQCAcEIABJpAfYUh3rZxFIYAAMIFARBoIsEKQ/zbxtExBAAQLgiAQBMK1jHEe09gRe1RRgIBAGGBAAg0MXthSIIjNmjbOEYCAQChQgAEmoF9JNDldFjaxtE7GAAQSgRAoJn4jwQWFlcEhECmiAEAhAoBEGhGnhSn5k/JVW93sjbaRgK9beOYIgYA0NIIgEALsF8O9m8bR2EIAKClEQCBFmAvDLFPEUPvYABASyIAAi2kviliymrqLCOBFIYAAJoTARBoQcF6B/tPEUNhCACgJRAAgRZm7x3sTk6gMAQA0KIIgEAIBOsd3MedJOm/IZDCEABAcyEAAiFi7x2ckRRvCYH0DgYANBcCIBBC9sKQjKT4oG3jKAwBADQlAmCEmTlzpmJiYiwPt9vte94Yo5kzZ8rj8cjpdGr48OH67LPPLNuoqanRnXfeqfT0dCUmJuryyy/Xrl27WvpQ8H/shSH+9wSWVh/RR9tKKQwBADQpAmAE6tOnj4qKinyPjRs3+p6bM2eO5s6dq8cee0zr1q2T2+3WyJEjVVlZ6Vtn6tSpWrhwoV555RV98MEHOnjwoPLy8lRXVxeKw4HqLwzZWV5DYQgAoEkRACNQ27Zt5Xa7fY+MjAxJx0b/Hn74Yd1333268sor1bdvXz3//PP6z3/+o5dfflmSVF5err/85S/64x//qEsuuUQDBgzQSy+9pI0bN+qdd94J5WFFvWCFIf4dQygMAQA0FQJgBNq6das8Ho+6deumH/zgB/r6668lSdu2bVNxcbFGjRrlWzc+Pl7Dhg3T6tWrJUkff/yxDh8+bFnH4/Gob9++vnWCqampUUVFheWBpmcvDMnukGgJgd57AikMAQCcCgJghMnNzdULL7ygt99+W08//bSKi4s1ZMgQlZaWqrj4WBjo2LGj5TUdO3b0PVdcXKy4uDilpqYed51gHnzwQblcLt+jc+fOTXxk8LIXhmR3SLTcE+hfGMJIIADgZBAAI8yYMWN01VVXKScnR5dccokWL14sSXr++ed968TExFheY4wJWGZ3onXuvfdelZeX+x47d+48haPAidgLQ1xOhyUEMkUMAOBUEAAjXGJionJycrR161ZfNbB9JK+kpMQ3Kuh2u1VbW6sDBw4cd51g4uPjlZycbHmgedlHAv1DYEXtUXoHAwBOGgEwwtXU1Gjz5s3KyspSt27d5Ha7tWzZMt/ztbW1WrVqlYYMGSJJGjhwoBwOh2WdoqIibdq0ybcOwof/SGBhcUVACKR3MADgZBAAI8z06dO1atUqbdu2TWvXrtX48eNVUVGhSZMmKSYmRlOnTtWsWbO0cOFCbdq0SZMnT1a7du00YcIESZLL5dKUKVM0bdo0LV++XOvXr9f111/vu6SM8ONJcWr+lFz1dif7LgcP754uid7BAICT0zbUO4DG2bVrl6699lrt27dPGRkZGjRokNasWaPs7GxJ0s9+9jNVV1fr9ttv14EDB5Sbm6ulS5cqKSnJt42HHnpIbdu21dVXX63q6mpdfPHFmj9/vmJjY0N1WGiAWVf1003PrdWm3eXq63GpjztJnxVX+kLgBd0z9OHX+/TbxYWSpJF93CfYIgAgWsUYY0yodwKRp6KiQi6XS+Xl5dwP2IJ2l1Xr5//8VBt3lyvH49I3pVXatr9aktTB2VbDz8rUh1/vU+dUp2698ExCIIDj4ns8unEJGIggjZkihsIQAMDxEACBCHOi3sEUhgAAToQACESg+noHUxgCADgRAiAQoU7UO3jFlj10DAEABEUABCJYfb2Dd5bX0DsYABAUARCIcCcqDKFjCADAjgAItAL1FYbQMQQAYEcABFoJCkMAAA1FAARakWCFIX3cx7rAeEMghSEAAAIg0MrYC0MykuItIdB7TyCFIQAQvQiAQCtkLwzJSIq33BO4fDNTxABANCMAAq2UvTDE5XT4QmBZTZ0vBDISCADRhwAItGL2kUCX06FBXVMlHQuBTBEDANGJAAi0cv4jgYXFFUpwxPpCIFPEAEB0IgACUcCT4tT8Kbnq7U7Wxt3lSnDEWqaIWbFlD1PEAEAUIQACUcR+Odi/bRy9gwEgehAAgShiLwyx9w5mihgAiA4EQCDK1Nc7uKL2KIUhABAFCIBAFDpR7+DVX+2jMAQAWjECIBClgvUO9lYHF1XWallhMYUhANBKEQCBKGbvHZzgiFWPjERJx0IgvYMBoHUiAAJRzt472JPi9BWGlFQdpmMIALRCBEAA9RaG+LeNozAEAFoHAiAAScELQ/zbxtExBABaDwIgAB97YUhquzhfCCypOqz8TUUUhgBAK0AABGARrDDE/55AOoYAQOQjAAIIYC8MsXcMWfl5CYUhABDBCIAAgqqvMKS0+ggdQwAgghEAARyXvTDE5XQEtI3zLwwhBAJAZCAAAqiXfSTQHgLf2PCtzj8jQ+XVtXqGEAgAEYEACOCE/EcCC4sr5HI6LFPELCss1pg+WUwRAwARggAIoEE8KU7Nn5Kr3u5kbdxdrgRHrKV38KL1u5giBgAiBAEQQKP4Xw5OcMRaLgcvWr+LKWIAIAIQAAE0SkMKQ5giBgDCGwEQQKMFKwwZ3j1dkjUEMkUMAIQnAiCAk2IvDJFkCYH0DgaA8EUABHDS7IUhknyXg71t4ygMAYDwQwAEcMrsl4P928bROxgAwg8BEMApsxeG2HsHUxgCAOGFAAigSdTXO5jCEAAILwRAAE3GPhLoTk6whMCPtpVSGAIAYYAACKBJeUcCO7kStHF3mSUEeu8JpDAEAEKLAAigyXlSnLp/XI7SEuO07pv9AYUh+ZuKKAwBgBAiAAJoFgO6pGrexO8ELQwpqTpMYQgAhBABEECzoTAEAMITARBAswrWO9jeNs6/MIQQCADNjwAIoNnZRwIla9u4Ret36fwzMlReXatnCIEA0OwIgABaRLDewfbLwWP6ZDFFDAC0AAIggBZj7x3scjp8IbCoslZvbPiWKWIAoAUQAAG0OHvv4EFdUyVJZTV1WrR+F1PEAEAzIwACaHH2wpAER6wvBPpXBzNFDAA0DwIggJCwF4YkOGIt9wSu/LyEKWIAoJkQAAGEjL0wxP+ewNLqI/QOBoBmQgAEEFL1FYZ428ZRGAIATYsACCAs2AtD/NvG0TsYAJoWARBAWLAXhth7By/fvIfCEABoIgRAAGEjWO9g/ylivCGQwhAAODUEQABhxT4SmNouzhIC39+6l8IQADhFBEAAYcc7EtjJlaCNu8uU2i7OVxhSUnVYywqLKQwBgFNAAAQQljwpTt0/LkdpiXFa981+S2FIUWWtb7JoCkMAoPEIgADC1oAuqZo38TuWwpAeGYmSrCGQwhAAaBwCIICwZi8M8aQ4g7aNozAEABqOAAgg7AUrDPFvG0fHEABoHAIggIhgLwxxJydYOoas2LKHwhAAaCACIICIUV9hiLdtHIUhAHBiBEAAESVYYYh/xxAKQwDgxAiAACJOsI4h/vcE+ncMYSQQAAIRAAFEJHthiMvpCNo2jpFAAAhEAAQQsewjgQmOWEsIZIoYAAiOAAggovmPBBYWVyjBEWu5HEzvYAAIRAAEEPE8KU7Nn5Kr3u5k3+Vg/97B+ZuKmCIGAPwQAAG0Gv6Xg11Oh/q4kyT9NwRSGAIAxxAAAbQa9sKQjKR4SwhkihgAOIYACKBVsReGZCTFW+4JXPl5CYUhAKIeARBAq2MfCfRvG1dafYTewQCiHgEQQKt0ot7BFIYAiGYEQACtVn29gykMARDNCIAAWrUT9Q723hNIYQiAaEIABNDq1dc7uLT6CIUhAKIOARBAVDhRYQgdQwBEEwIggKhRX2EIHUMARBMCYJh57733NHbsWHk8HsXExGjRokWW540xmjlzpjwej5xOp4YPH67PPvvMsk5NTY3uvPNOpaenKzExUZdffrl27dplWefAgQOaOHGiXC6XXC6XJk6cqLKysmY+OiD0KAwBAAJg2KmqqlL//v312GOPBX1+zpw5mjt3rh577DGtW7dObrdbI0eOVGVlpW+dqVOnauHChXrllVf0wQcf6ODBg8rLy1NdXZ1vnQkTJmjDhg3Kz89Xfn6+NmzYoIkTJzb78QHhIFhhCB1DAESTGGOMCfVOILiYmBgtXLhQ48aNk3Rs9M/j8Wjq1Km65557JB0b7evYsaNmz56tH/7whyovL1dGRoZefPFFXXPNNZKk3bt3q3PnzlqyZIkuvfRSbd68Wb1799aaNWuUm5srSVqzZo0GDx6sLVu26KyzzjrhvlVUVMjlcqm8vFzJycnNcwKAZra7rFo3PbdW+w7Wqq/n2KXglVv3SZKS49poZG+3Pvx6nxLaxuq+y3prZB93KHcXaFJ8j0c3RgAjyLZt21RcXKxRo0b5lsXHx2vYsGFavXq1JOnjjz/W4cOHLet4PB717dvXt05BQYFcLpcv/EnSoEGD5HK5fOvY1dTUqKKiwvIAIp29MERS0LZxjAQCaG0IgBGkuPjYXz4dO3a0LO/YsaPvueLiYsXFxSk1NbXedTIzMwO2n5mZ6VvH7sEHH/TdL+hyudS5c+dTPh4gHNiniHE5HUwRA6DVIwBGoJiYGMvPxpiAZXb2dYKtX9927r33XpWXl/seO3fuPIk9B8KT/0hgYXFFQAhkihgArQ0BMIK43cfuP7KP0pWUlPhGBd1ut2pra3XgwIF619mzZ0/A9vfu3RswuugVHx+v5ORkywNoTTwpTs2fkqve7mRttI0EMkUMgNaGABhBunXrJrfbrWXLlvmW1dbWatWqVRoyZIgkaeDAgXI4HJZ1ioqKtGnTJt86gwcPVnl5uT766CPfOmvXrlV5eblvHSBa2S8H+08Rs2LLHqaIAdAqtA31DsDq4MGD+vLLL30/b9u2TRs2bFBaWpq6dOmiqVOnatasWerevbu6d++uWbNmqV27dpowYYIkyeVyacqUKZo2bZo6dOigtLQ0TZ8+XTk5ObrkkkskSb169dLo0aN1yy236M9//rMk6dZbb1VeXl6DKoCB1sx7Ofjn//xUG3eXK+f/qoO37a/WzvIa/efzEg0/K1Mffr1PT7137M8q1cEAIg3TwISZlStX6qKLLgpYPmnSJM2fP1/GGN1///3685//rAMHDig3N1ePP/64+vbt61v30KFD+ulPf6qXX35Z1dXVuvjii/XEE09YCjf279+vn/zkJ3rjjTckSZdffrkee+wxpaSkNGg/mT4ArZ19ipjy6sNav+tYpbD/FDFJ8Q7dfMHpuua8LiHeY6Bx+B6PbgRAnBS+OBANdpdV+0YCz8tOU3HFIV8IzEx0aHTfLH3w1V61iWmje0b3ZCQQEYXv8ejGPYAAcBz0DgbQWhEAAaAewXoH+7eNo3cwgEhEAASAE7D3Ds5Iiqd3MICIRgAEgAawdwzJSIq3tI1bvnkPHUMARAwCIAA0kL13sP89gWU1dVr91T46hgCICARAAGiEYIUhg7oe671dVFlLYQiAiEAABIBGsheGJDhi1SMjURKFIQAiAwEQAE6CvTDEk+K0tI1b+XkJhSEAwhYBEABOkr0wJLtDou+ewNLqI74QyEgggHBDAASAU2AvDHE5HZYQyBQxAMIRARAATpF9JNA/BFbUHvWFQKaIARAuCIAA0AT8RwILiysCQiBTxAAIJwRAAGginhSn5k/JVW93su9ysP8UMcsKi5kiBkBYIAACQBPzvxzsP0WMd55ACkMAhBoBEACamL0wxD5FjLdtHIUhAEKFAAgAzaC+KWLKauroHQwgpAiAANBMgvUO9t4TWFZTp/e37qUwBEBIEAABoBnZewentovzhUBv2zgKQwC0NAIgADSzYL2D/e8JXLFlD4UhAFoUARAAWoC9d3B2h0RfCNxZXkPvYAAtigAIAC3kRL2D6RgCoKUQAAGgBQUrDPHvGEJhCICWQAAEgBZmLwzxD4ElVYfpGAKg2REAASAE7IUhLqfD0jHE/3IwhSEAmhoBEABCxF4Y4klxBg2BFIYAaGoEQAAIIXthiCfFabknkJFAAM2BAAgAIWYvDHE5HUFDICOBAJoKARAAwoB9JNDldGh493RJgSOBTBED4FQRAAEgTPiPBBYWV0iSJQQyRQyApkIABIAw4klxav6UXPV2J2vj7nJJskwRs2LLHqaIAXDKCIAAEIbsl4P928bROxjAqSIAAkAYsheG2HsHUxgC4FQQAAEgTNXXO5jCEACnggAIAGHsRL2DP9pWSmEIgEYjAAJAmKuvd7D3nkAKQwA0BgEQACJAsN7B/vcE5m8qojAEQIMRAAEgQth7B/sXhpRUHaYwBECDEQABIIJQGAKgKRAAASDCBCsMoWMIgMYgAAJABLIXhjgdsb4QWFJ1WPmbiigMAXBcBEAAiFD2whBJQe8JpDAEgB0BEAAiWH2FIUWVtVq+eQ+FIQACEAABIMIFKwwZ1DVVklRWU8dIIIAABEAAaAXshSEJjlhfCPSvDmYkEIBEAASAVsM+EpjgiLVMEbPy8xKmiAEgiQAIAK2K/0hgYXGFXE6HLwSWVh+hdzAASQRAAGh1PClOzZ+Sq97uZG3cXW4Jgd62cUwRA0Q3AiAAtFL+l4P9ewd75wmkMASIXgRAAGil7IUh9t7BTBEDRC8CIAC0YieaIsYbAikMAaILARAAWjn7SGBquzhLCKR3MBB9CIAAEAXsvYNT28X5CkO8beMoDAGiBwEQAKKEvXewf2FIUWUtHUOAKEIABIAoEqx3cI+MREnWEEhhCNC6EQABIMrYC0M8Kc6gbeMoDAFaLwIgAEShYIUh/m3j6BgCtG4EQACIUvbCEHdygqVjyIoteygMAVopAiAARLH6CkO8beMoDAFaHwIgAES5YIUh/h1DKAwBWh8CIAAgaMcQ/3sC6RgCtC4EQACApMDCEJfTEdA2zr8whBAIRC4CIADAxz4SmOCItYTARet36fwzMlReXatnCIFAxCIAAgAs/EcCC4srlOCItVwOzt9UpDF9spgiBohgBEAAQABPilPzp+SqtzvZdznYv3ewdySQKWKAyEQABAAcl//lYJfToeHd0yUdGwlctH4XU8QAEYoACAA4LnthiCRLCGSKGCAyEQABAPWyF4ZIstwTuPLzEqaIASIMARAAcEL2whD/ewJLq4/QOxiIMARAAECD1FcY4m0bR2EIEBkIgACARrEXhvi3jaN3MBAZCIAAgEaxF4bYewd77wmkMAQIXwRAAECj1dc7uLT6CIUhQJgjAAIATop9JNCdnGAJge9v3UthCBCmCIAAgJPmHQns5ErQxt1llhDovSeQwhAg/BAAAQCnxJPi1P3jcpSWGKd13+ynMASIAARAAMApG9AlVfMmfsdSGNLHnSTpWAikYwgQXgiAAIAmYS8MyUiKD9o2jsIQIPQIgACAJmMvDHE6Yi1t41Z/tY/CECAMEAABAE2qvsKQospaLSsspjAECDECIACgyQUrDOmRkSjpWAikMAQILQIgAKBZ2AtDPClOXwikMAQILQJgmHnvvfc0duxYeTwexcTEaNGiRZbnJ0+erJiYGMtj0KBBlnVqamp05513Kj09XYmJibr88su1a9cuyzoHDhzQxIkT5XK55HK5NHHiRJWVlTXz0QGINvbCEE+K03JPoH/HEEYCgZZDAAwzVVVV6t+/vx577LHjrjN69GgVFRX5HkuWLLE8P3XqVC1cuFCvvPKKPvjgAx08eFB5eXmqq6vzrTNhwgRt2LBB+fn5ys/P14YNGzRx4sRmOy4A0cteGOJyOoK2jWMkEGg5McYYE+qdQHAxMTFauHChxo0b51s2efJklZWVBYwMepWXlysjI0MvvviirrnmGknS7t271blzZy1ZskSXXnqpNm/erN69e2vNmjXKzc2VJK1Zs0aDBw/Wli1bdNZZZ51w3yoqKuRyuVReXq7k5ORTPlYArd/usmrd9Nxa7TtYq74el8qrD2v9rnJJUnJcG43s7daHX+9TUrxDN19wuq45r0uI97h143s8ujECGIFWrlypzMxM9ejRQ7fccotKSkp8z3388cc6fPiwRo0a5Vvm8XjUt29frV69WpJUUFAgl8vlC3+SNGjQILlcLt86ANDU/EcCC4srLCOBFbVH6R0MtCACYIQZM2aM/vrXv+rdd9/VH//4R61bt04jRoxQTU2NJKm4uFhxcXFKTU21vK5jx44qLi72rZOZmRmw7czMTN86djU1NaqoqLA8AKCxPClOzZ+Sq97u5IDLwfQOBloOATDCXHPNNbrsssvUt29fjR07Vm+99Za++OILLV68uN7XGWMUExPj+9n//4+3jr8HH3zQVzDicrnUuXPnUzsQAFHNvzDE5XRY2sYxRQzQ/AiAES4rK0vZ2dnaunWrJMntdqu2tlYHDhywrFdSUqKOHTv61tmzZ0/Atvbu3etbx+7ee+9VeXm577Fz584mPhIA0cReGJKRFE/vYKAFEQAjXGlpqXbu3KmsrCxJ0sCBA+VwOLRs2TLfOkVFRdq0aZOGDBkiSRo8eLDKy8v10Ucf+dZZu3atysvLfevYxcfHKzk52fIAgFMRrHew/z2ByzfvoXcw0EwIgGHm4MGD2rBhgzZs2CBJ2rZtmzZs2KAdO3bo4MGDmj59ugoKCrR9+3atXLlSY8eOVXp6ur73ve9Jklwul6ZMmaJp06Zp+fLlWr9+va6//nrl5OTokksukST16tVLo0eP1i233KI1a9ZozZo1uuWWW5SXl9egCmAAaCr2kUD/tnFlNXX0DgaaCQEwzPzv//6vBgwYoAEDBkiS7r77bg0YMEC/+tWvFBsbq40bN+qKK65Qjx49NGnSJPXo0UMFBQVKSkrybeOhhx7SuHHjdPXVV2vo0KFq166d3nzzTcXGxvrW+etf/6qcnByNGjVKo0aNUr9+/fTiiy+2+PECQLDewYO6Hitk87aNozAEaFrMA4iTwvxRAJra+h0HNOP1jdpddkh9PS7tLqvWF3urJEmZiQ5d0D1DH369TwltY3XfZb01so87xHsc2fgej26MAAIAwkKw3sHd0pySjhWG0DEEaDoEQABA2LAXhmR3SAzaNo7CEODUEAABAGGlvsKQ0uojdAwBmgABEAAQdoIVhtAxBGg6BEAAQFjypDh1/7gcpSXGad03++VyOiz3BHoni6ZjCNB4BEAAQNiyF4Zkd0hUj4xEScemiPFOFk1hCNA4BEAAQFizF4Z4Upy+eQLLauoYCQROAgEQABD27IUhCY7YoG3jGAkEGoYACACICPaRQJfTYWkbR+9goOEIgACAiOE/ElhYXCGX02G5HMwUMUDDEAABABHFk+LU/Cm56u1O9l0O9oZApogBGoYACACISP6XgxMcsZYpYlZs2UNhCFAPAiAAICLZC0OyOyT6QuDO8hp6BwP1IAACACLWiXoH+08RQ2EI8F8EQABARKuvd3BF7VEKQ4AgCIAAgIh3ot7BywqLKQwB/BAAAQCtQrDewf5t4+gYAvwXARAA0GrYewd7UpxBQyCFIYh2BEAAQKsSrHew/z2BFIYABEAAQCtEYQhQPwIgAKBVClYYMrx7uiQ6hgAEQABAq2UvDJGkPu4kSf8NgRSGIBoRAAEArZq9MCQjKd7SNo6OIYhGBEAAQKt3oo4h3hDISCCiBQEQABAV7IUhLqcjaNs4RgIRDQiAAICoYR8J9A+BTBGDaEIABABEFf+RwMLiioAQ+NG2UqaIQatHAAQARB1PilPzp+Sqtzs54HLwzvIardiyhyli0KoRAAEAUct+OdhbHbyzvIYpYtCqEQABAFHLXhiS3SHRMkUMhSForQiAAICoVt8UMRSGoLUiAAIAol6w3sHetnH0DkZrRAAEAECBvYOdjlh6B6PVIgACAPB/gvUODnZPIIUhiHQEQAAA/Nh7B/sXhhRV1mr55j0UhiDiEQABALAJVhgyqGuqJKmspo7CEEQ8AiAAAEHYC0NS28X5QiCFIYh0BEAAAI7DXhiS2i7ON0VMSdVhOoYgYhEAAQCoh70wxN4xZMWWPRSGIOIQAAEAOIH6CkN2ltfQMQQRhwAIAEADNKZjCCOBCHcEQAAAGsheGOJyOiwhkCliECkIgAAANIJ9JNDldFimiPGGQKaIQTgjAAIA0Ej+I4GFxRVKcMRaQiBTxCDcEQABADgJnhSn5k/JVW93sjbuLleCI9YyRcyywmKmiEHYIgACAHAK7JeD/dvGURiCcEUABADgFNgLQ7I7JKpHRqIkawikMAThhAAIAMApsheGeFKclrZx9A5GuCEAAgDQBIL1DvafIuajbaUUhiBsEAABAGgi9t7B7uQEXwj0to2jMAThgAAIAEATOlHv4PxNRRSGIOQIgAAANLH6egd7p4ihMAShRAAEAKAZnKh3MB1DEEoEQAAAmom9MMSdnGDpGLL6q30UhiAkCIAAADQje2FIars4XwgsqqxV/qYiCkPQ4giAAAA0M3thSIIj1nJPIIUhaGkEQAAAWgCFIQgnBEAAAFpIsMKQ4d3TJQV2DGEkEM2JAAgAQAuyF4ZIChoCGQlEcyIAAgDQwuwjgZIsU8Ss/LyEKWLQrAiAAACEgP9IYGFxhVxOhy8EllYfoXcwmhUBEACAEPGkODV/Sq56u5O1cXe5JQR628YxRQyaAwEQAIAQ878c7N87mCli0FwIgAAAhJi9MMQ+RYz3nkAKQ9BUCIAAAISB+noHl1YfoTAETYoACABAmAjWO9g/BL6/dS+FIWgSBEAAAMKIvXewfwj03hNIYQhOFQEQAIAwY+8dTGEImhoBEACAMBSsd3Afd5Ikegfj1BEAAQAIU/bCkIyk+OP2DqYwBI1BAAQAIIzZC0OcjlhL27jVX+2jMASNRgAEACDM1VcYUlRZq2WFxRSGoFEIgAAARIBghSE9MhIlHQuBFIagMQiAAABECHthiCfF6QuBFIagMQiAAABEEHthiCfFabknkI4haAgCIAAAEcZeGOJyOgLaxvkXhhACYUcABAAgAtlHAu0hcNH6XTr/jAyVV9fqGUIgbAiAAABEKP+RwMLiCksIrKg9qvxNRRrTJ4spYhCAAAgAQATzpDg1f0queruTAy4Hl1Qd1hsbvmWKGAQgAAIA0ArYLwcP6poqSSqrqdMbG75lihhYEAABAGgF7IUhCY5YSwi0TxHz7uY9Id5jhBIBEACAVsJeGJJgaxu3fPMe30jgI+98EeK9RSgRAAEAaEXqKwwpq6mz9A5G9CIAAgDQygQrDPFeDva2jbt7ZM8Q7yVCiQAIAEArZb8c7N827jdvbArx3iGU2oZ6BxCZjDGSpIqKihDvCQDgeNq3kR65qpfuf+Mzbfh6t84/I13VVUf1zYFD2lPzH0n//T5HdCEA4qSUlpZKkjp37hziPQEANNS/gyyrrKyUy+Vq8X1BaBEAcVLS0tIkSTt27OCLo4VUVFSoc+fO2rlzp5KTk0O9O60e57tlcb5bnjFGlZWV8ng8od4VhAABECelTZtjt4+6XC6+rFtYcnIy57wFcb5bFue7ZfEP+OhFEQgAAECUIQACAABEGQIgTkp8fLxmzJih+Pj4UO9K1OCctyzOd8vifAMtK8ZQ/w0AABBVGAEEAACIMgRAAACAKEMABAAAiDIEQAAAgChDAAQAAIgyBEAAAIAoQwAEAACIMgRAAACAKEMABAAAiDIEQAAAgChDAAQAAIgyBEAAAIAoQwAEAACIMgRAAACAKEMABAAAiDIEQAAAgChDAAQAAIgyBEAAAIAoQwAEAACIMgRAAACAKEMABAAAiDIEQAAAgChDAAQAAIgyBEAAAIAoQwAEAACIMgRAAACAKEMABAAAiDIEQAAAgChDAAQAAIgyBEAAAIAoQwAEAACIMgRAAACAKEMABAAAiDIEQAAAgChDAAQAAIgyBEAAAIAoQwAEAACIMgRAAACAKEMABAAAiDIEQAAAgChDAAQAAIgyBEAAAIAoQwAEAACIMgRAAACAKEMABAAAiDIEQAAAgCjz/wHrGD75TrP42wAAAABJRU5ErkJggg==' width=640.0/>\n",
       "            </div>\n",
       "        "
      ],
      "text/plain": [
       "Canvas(toolbar=Toolbar(toolitems=[('Home', 'Reset original view', 'home', 'home'), ('Back', 'Back to previous …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.spy(L_vec[0], markersize=.1)\n",
    "plt.title('Sparsity pattern of original banded matrix.')\n",
    "plt.figure()\n",
    "plt.spy(L_vec[0][P,:][:,P], markersize=.1)\n",
    "plt.title('Sparsity pattern of permuted banded matrix.')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on built-in function reverse_cuthill_mckee in module scipy.sparse.csgraph._reordering:\n",
      "\n",
      "reverse_cuthill_mckee(...)\n",
      "    reverse_cuthill_mckee(graph, symmetric_mode=False)\n",
      "    \n",
      "    Returns the permutation array that orders a sparse CSR or CSC matrix\n",
      "    in Reverse-Cuthill McKee ordering.  \n",
      "    \n",
      "    It is assumed by default, ``symmetric_mode=False``, that the input matrix \n",
      "    is not symmetric and works on the matrix ``A+A.T``. If you are \n",
      "    guaranteed that the matrix is symmetric in structure (values of matrix \n",
      "    elements do not matter) then set ``symmetric_mode=True``.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    graph : sparse matrix\n",
      "        Input sparse in CSC or CSR sparse matrix format.\n",
      "    symmetric_mode : bool, optional\n",
      "        Is input matrix guaranteed to be symmetric.\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    perm : ndarray\n",
      "        Array of permuted row and column indices.\n",
      "    \n",
      "    Notes\n",
      "    -----\n",
      "    .. versionadded:: 0.15.0\n",
      "    \n",
      "    References\n",
      "    ----------\n",
      "    E. Cuthill and J. McKee, \"Reducing the Bandwidth of Sparse Symmetric Matrices\",\n",
      "    ACM '69 Proceedings of the 1969 24th national conference, (1969).\n",
      "    \n",
      "    Examples\n",
      "    --------\n",
      "    >>> from scipy.sparse import csr_matrix\n",
      "    >>> from scipy.sparse.csgraph import reverse_cuthill_mckee\n",
      "    \n",
      "    >>> graph = [\n",
      "    ... [0, 1, 2, 0],\n",
      "    ... [0, 0, 0, 1],\n",
      "    ... [2, 0, 0, 3],\n",
      "    ... [0, 0, 0, 0]\n",
      "    ... ]\n",
      "    >>> graph = csr_matrix(graph)\n",
      "    >>> print(graph)\n",
      "      (0, 1)    1\n",
      "      (0, 2)    2\n",
      "      (1, 3)    1\n",
      "      (2, 0)    2\n",
      "      (2, 3)    3\n",
      "    \n",
      "    >>> reverse_cuthill_mckee(graph)\n",
      "    array([3, 2, 1, 0], dtype=int32)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(reverse_cuthill_mckee)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.fft import dst, idst\n",
    "\n",
    "def apply_inverse_fdm_laplacian(L, f, analytic=False):\n",
    "    \"\"\" Apply the inverse of the Laplacian to a function. \n",
    "    \n",
    "    The domain is [0, L] divided into len(f)+2 points, with the function\n",
    "    assumed evaluated at the interior points. (Homogenous Dirichlet boundary conditions.)\n",
    "    \n",
    "    Args:\n",
    "        L: the length of the domain\n",
    "        f: the function to apply the inverse Laplacian to\n",
    "        analytic: whether to use the analytic eigenvalues of the Laplacian or FDM eigenvalues\n",
    "    \"\"\"\n",
    "    n = len(f)\n",
    "    dx = L / (n+1)\n",
    "    k = np.arange(1, n+1) * np.pi / L\n",
    "    \n",
    "    if analytic:\n",
    "        evals = -k**2\n",
    "    else:\n",
    "        evals = (2*np.cos(k*dx) - 2)/dx**2\n",
    "    return idst(evals*dst(f, type=1), type=1)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "ic| self.m_i: array([ 0.,  1., -2., -1.])\n",
      "ic| cylinder_fdm_3d.py:170 in __init__() at 13:53:24.791\n",
      "ic| self.n_r: 6, self.n_z: 4, self.n_m: 4\n",
      "ic| self.r_max: 20, self.z_max: 20\n",
      "ic| self.n_dof: 96\n"
     ]
    }
   ],
   "source": [
    "from cylinder_fdm_3d import CylinderFDM\n",
    "from icecream import ic\n",
    "import numpy as np\n",
    "from scipy.sparse.linalg import eigsh, cg, gmres, bicgstab\n",
    "from matplotlib import pyplot as plt\n",
    "from fft_tdse.simulator import LaserPulse\n",
    "from erfgau import ErfgauPotential\n",
    "from rich.console import Console\n",
    "from rich.table import Table\n",
    "import timeit\n",
    "from time import time\n",
    "from scipy.sparse.linalg import LinearOperator\n",
    "from scipy.sparse.linalg import spilu\n",
    "from scipy.sparse import csc_matrix\n",
    "from scipy.linalg import lu_factor, lu_solve\n",
    "\n",
    "n_r = 6\n",
    "n_z = 4\n",
    "n_theta = 4\n",
    "r_max = 20\n",
    "z_max = 20\n",
    "solver = CylinderFDM(r_max, z_max, n_r, n_z, n_theta)\n",
    "L_vec_rz = solver.get_laplacian_fast(ordering='rz')\n",
    "solver.prepare_poisson_solver()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "rr,zz = solver.get_rz_meshgrid()\n",
    "m = 0\n",
    "rhs = np.random.rand(n_r,n_z)\n",
    "u = solver.solve_poisson(rhs, m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-9.99200722e-16, -1.44328993e-15, -2.88657986e-15, -1.11022302e-15,\n",
       "        2.22044605e-16, -1.77635684e-15, -4.10782519e-15, -1.77635684e-15,\n",
       "        2.22044605e-16, -4.44089210e-16, -4.44089210e-16, -3.33066907e-16,\n",
       "        3.33066907e-16, -8.88178420e-16, -6.66133815e-16, -3.33066907e-16,\n",
       "        2.22044605e-16, -2.10942375e-15,  2.22044605e-16,  3.33066907e-16,\n",
       "       -6.66133815e-16, -5.55111512e-17, -1.11022302e-15, -9.99200722e-16])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L_vec_rz[m] @ u.flatten() - rhs.flatten()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6, 4)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rhs.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.random.rand(4,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "type(A @ A.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -2.14159667,  -2.15722167,  -2.17653523,  -2.19216023],\n",
       "       [ -2.52718066,  -2.54280566,  -2.56211922,  -2.57774422],\n",
       "       [ -3.45136066,  -3.46698566,  -3.48629922,  -3.50192422],\n",
       "       [ -5.75153057,  -5.76715557,  -5.78646914,  -5.80209414],\n",
       "       [-13.29924208, -13.31486708, -13.33418064, -13.34980564],\n",
       "       [-68.68046632, -68.69609132, -68.71540488, -68.73102988]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solver.D_inverse[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.0061685 , -0.02467401, -0.05551652, -0.09869604])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solver.T_z_Lambda"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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