Set1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Required Python packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {
    "is_executing": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.lines as mlines\n",
    "import numpy as np\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from scipy.special import erfc\n",
    "import os\n",
    "from tqdm import tqdm\n",
    "from numba import jit, prange"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We require a local installation of `ffmpeg` to be present for animation generation. If not installed, please refer to the [ffmpeg installation guide](https://ffmpeg.org/) or refer to [matplotlib documentation](https://matplotlib.org/stable/users/explain/animations/animations.html) for alternatives."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(42)\n",
    "SAVE_PATH = 'media/ex1'\n",
    "ANIM_BACKEND = 'ffmpeg'\n",
    "os.makedirs(SAVE_PATH, exist_ok=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 Vibrating string"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A. (0.5 point) Discretize the wave equation, and write it in a form suitable for\n",
    "implementing in a computer program. Assume that the boundaries are fixed, \t(x =\n",
    "0, t) = 0, \t(x = L, t) = 0. L is the length of the string. Take L = 1 for simplicity.\n",
    "Divide the string in N intervals, so that the interval length is \u0001x = L/N. Also\n",
    "consider the boundary cases."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_wave(psi_init, L, c, T, Nx, dt):\n",
    "    '''Solves the wave equation using the finite difference method (explicit scheme) and returns the vibration amplitude psi(x,t) matrix of all time steps.\n",
    "\n",
    "    Args:\n",
    "    psi_init (function): Initial condition function to generate psi(x,0)\n",
    "    L (float): Length of the string\n",
    "    c (float): Wave speed\n",
    "    T (float): Total time to simulate\n",
    "    Nx (int): Total number of spatial intervals\n",
    "    dt (float): Time step size\n",
    "    '''\n",
    "    # Discretization\n",
    "    dx = L/Nx  # spatial step size\n",
    "    Nt = int(T/dt)+1  # Total number of time steps\n",
    "    psi = np.zeros((Nx, Nt))  # Vibration amplitude psi(x,t) matrix\n",
    "    x = np.linspace(0, L, Nx)  # spatial grid\n",
    "\n",
    "    # Initial conditions\n",
    "    psi[:, 0] = psi_init(x)\n",
    "    psi[:, 1] = (1+dt)*psi[:, 0]  # approximated state at t=1\n",
    "\n",
    "    # Physical boundaries at x=0 and x=L\n",
    "    psi[0, :] = 0\n",
    "    psi[-1, :] = 0\n",
    "\n",
    "    # Stepping through time\n",
    "    for t in range(2, Nt):\n",
    "        psi[1:-1, t] = c**2 * (dt**2)/(dx**2) * (psi[2:, t-1] + psi[:-2,\n",
    "                                                                    t-1] - 2*psi[1:-1, t-1]) - psi[1:-1, t-2] + 2*psi[1:-1, t-1]\n",
    "\n",
    "    return psi\n",
    "\n",
    "\n",
    "# Parameters\n",
    "L = 1  # Length of the string\n",
    "c = 1  # Wave speed\n",
    "def psi_init(x): return np.sin(2 * np.pi * x)\n",
    "\n",
    "\n",
    "# Discretization\n",
    "Nx = 100  # Total number of spatial intervals\n",
    "dx = L / Nx  # Spatial step size\n",
    "Nt = 1000  # Number of time steps to simulate\n",
    "dt = 0.001  # Time step size\n",
    "\n",
    "psi_matrix = solve_wave(psi_init, L, c, Nt * dt, Nx, dt)\n",
    "x = np.linspace(0, L, Nx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "B. (1 point) Implement the time stepping. Determine the time development of\n",
    "the string, with the following initial conditions. The string is at rest at t = 0, i.e.\n",
    "\t′(x, t = 0) = 0.\n",
    "\n",
    "i. \t(x, t = 0) = sin(2πx).\n",
    "\n",
    "ii. \t(x, t = 0) = sin(5πx).\n",
    "\n",
    "iii. \t(x, t = 0) = sin(5πx) if 1/5 < x < 2/5, else \t = 0.\n",
    "\n",
    "Take c = 1 and use the time step dt = 0.001. Plot the result at several times in\n",
    "the same figure, e.g. varying the color of the curve."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1100x300 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Parameters\n",
    "c = 1\n",
    "L = 1\n",
    "\n",
    "# Discretization\n",
    "dt = 0.001\n",
    "T = 0.5\n",
    "Nx = 500\n",
    "dx = L / Nx\n",
    "Nt = int(T / dt)\n",
    "\n",
    "init_conditions = [\n",
    "    lambda x: np.sin(2 * np.pi * x),\n",
    "    lambda x: np.sin(5 * np.pi * x),\n",
    "    lambda x: np.where((1/5 < x) & (x < 2/5), np.sin(5 * np.pi * x), 0)\n",
    "]\n",
    "\n",
    "init_labels = [\n",
    "    '$\\\\sin(2\\\\pi x)$',\n",
    "    '$\\\\sin(5\\\\pi x)$',\n",
    "    '$\\\\sin(5\\\\pi x)$ if $0.2 < x < 0.4$, else $0$'\n",
    "]\n",
    "\n",
    "psis = []\n",
    "for i, (f0, init_label) in enumerate(zip(init_conditions, init_labels)):\n",
    "    psi_matrix = solve_wave(f0, L, c, T, Nx, dt)\n",
    "    psis.append(psi_matrix)\n",
    "\n",
    "\n",
    "fig, axs = plt.subplots(1, 3, figsize=(11, 3), sharey=True, layout='tight')\n",
    "times = np.linspace(0, T, 5)\n",
    "time_labels = [f't={t}s' for t in times]\n",
    "colors = ['blue', 'green', 'red', 'cyan', 'magenta']\n",
    "x = np.linspace(0, L, Nx)\n",
    "\n",
    "for i, (c, init_label) in enumerate(zip(psis, init_labels)):\n",
    "    for j, (t, time_label, color) in enumerate(zip(times, time_labels, colors)):\n",
    "        axs[i].plot(x, c[:, int(Nt*t)], label=time_label, color=color)\n",
    "    axs[i].set_title(f'$\\\\Psi(x,0)=${init_label}')\n",
    "    axs[i].grid(True)\n",
    "    axs[i].set_xlabel('Position ($x$)')\n",
    "    axs[i].set_yticks([-1, -0.5, 0, 0.5, 1])\n",
    "axs[0].set_ylabel('Vibration amplitude $\\\\Psi$')\n",
    "axs[-1].legend(loc='upper right')\n",
    "\n",
    "plt.suptitle(\n",
    "    'Vibration amplitude $\\\\Psi$ at selected time steps with different initial conditions $\\\\Psi(x,0)$')\n",
    "plt.xlabel('Position $x$')\n",
    "plt.savefig(f'{SAVE_PATH}/wave_equation.png', dpi=300, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "C. (1 point) Make an animated plot of the time development."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Animating wave:   0%|          | 0/3 [00:03<?, ?animation/s]\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[143], line 39\u001b[0m\n\u001b[1;32m     37\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i, (init_condition, init_label) \u001b[38;5;129;01min\u001b[39;00m tqdm(\u001b[38;5;28menumerate\u001b[39m(\u001b[38;5;28mzip\u001b[39m(init_conditions, init_labels)), total\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mlen\u001b[39m(init_conditions), desc\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mAnimating wave\u001b[39m\u001b[38;5;124m'\u001b[39m, unit\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124manimation\u001b[39m\u001b[38;5;124m'\u001b[39m):\n\u001b[1;32m     38\u001b[0m     psi \u001b[38;5;241m=\u001b[39m solve_wave(init_condition, L, c, T, Nx, dt)\n\u001b[0;32m---> 39\u001b[0m     anim \u001b[38;5;241m=\u001b[39m animate_wave(psi, \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m$\u001b[39m\u001b[38;5;130;01m\\\\\u001b[39;00m\u001b[38;5;124mPsi(x,0) =$ \u001b[39m\u001b[38;5;132;01m{\u001b[39;00minit_label\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124manimated_wave_\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mi\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m'\u001b[39m, T\u001b[38;5;241m=\u001b[39mT, total_frames\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m80\u001b[39m, save\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m)\n",
      "Cell \u001b[0;32mIn[143], line 23\u001b[0m, in \u001b[0;36manimate_wave\u001b[0;34m(psi, title, file_title, L, T, total_frames, save)\u001b[0m\n\u001b[1;32m     20\u001b[0m anim \u001b[38;5;241m=\u001b[39m FuncAnimation(fig, animate, frames\u001b[38;5;241m=\u001b[39mtotal_frames,\n\u001b[1;32m     21\u001b[0m                      interval\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m1000\u001b[39m\u001b[38;5;241m/\u001b[39m\u001b[38;5;241m/\u001b[39m\u001b[38;5;241m60\u001b[39m, blit\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m, repeat\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m)\n\u001b[1;32m     22\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m save:\n\u001b[0;32m---> 23\u001b[0m     anim\u001b[38;5;241m.\u001b[39msave(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mSAVE_PATH\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m/\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mfile_title\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m.gif\u001b[39m\u001b[38;5;124m'\u001b[39m, writer\u001b[38;5;241m=\u001b[39mANIM_BACKEND)\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/animation.py:1109\u001b[0m, in \u001b[0;36mAnimation.save\u001b[0;34m(self, filename, writer, fps, dpi, codec, bitrate, extra_args, metadata, extra_anim, savefig_kwargs, progress_callback)\u001b[0m\n\u001b[1;32m   1107\u001b[0m         progress_callback(frame_number, total_frames)\n\u001b[1;32m   1108\u001b[0m         frame_number \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m\n\u001b[0;32m-> 1109\u001b[0m writer\u001b[38;5;241m.\u001b[39mgrab_frame(\u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39msavefig_kwargs)\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/animation.py:371\u001b[0m, in \u001b[0;36mMovieWriter.grab_frame\u001b[0;34m(self, **savefig_kwargs)\u001b[0m\n\u001b[1;32m    369\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfig\u001b[38;5;241m.\u001b[39mset_size_inches(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_w, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_h)\n\u001b[1;32m    370\u001b[0m \u001b[38;5;66;03m# Save the figure data to the sink, using the frame format and dpi.\u001b[39;00m\n\u001b[0;32m--> 371\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfig\u001b[38;5;241m.\u001b[39msavefig(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_proc\u001b[38;5;241m.\u001b[39mstdin, \u001b[38;5;28mformat\u001b[39m\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mframe_format,\n\u001b[1;32m    372\u001b[0m                  dpi\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mdpi, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39msavefig_kwargs)\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/figure.py:3390\u001b[0m, in \u001b[0;36mFigure.savefig\u001b[0;34m(self, fname, transparent, **kwargs)\u001b[0m\n\u001b[1;32m   3388\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m ax \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39maxes:\n\u001b[1;32m   3389\u001b[0m         _recursively_make_axes_transparent(stack, ax)\n\u001b[0;32m-> 3390\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcanvas\u001b[38;5;241m.\u001b[39mprint_figure(fname, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/backend_bases.py:2158\u001b[0m, in \u001b[0;36mFigureCanvasBase.print_figure\u001b[0;34m(self, filename, dpi, facecolor, edgecolor, orientation, format, bbox_inches, pad_inches, bbox_extra_artists, backend, **kwargs)\u001b[0m\n\u001b[1;32m   2155\u001b[0m     \u001b[38;5;66;03m# we do this instead of `self.figure.draw_without_rendering`\u001b[39;00m\n\u001b[1;32m   2156\u001b[0m     \u001b[38;5;66;03m# so that we can inject the orientation\u001b[39;00m\n\u001b[1;32m   2157\u001b[0m     \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mgetattr\u001b[39m(renderer, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m_draw_disabled\u001b[39m\u001b[38;5;124m\"\u001b[39m, nullcontext)():\n\u001b[0;32m-> 2158\u001b[0m         \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfigure\u001b[38;5;241m.\u001b[39mdraw(renderer)\n\u001b[1;32m   2159\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m bbox_inches:\n\u001b[1;32m   2160\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m bbox_inches \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mtight\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/artist.py:95\u001b[0m, in \u001b[0;36m_finalize_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer, *args, **kwargs)\u001b[0m\n\u001b[1;32m     93\u001b[0m \u001b[38;5;129m@wraps\u001b[39m(draw)\n\u001b[1;32m     94\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mdraw_wrapper\u001b[39m(artist, renderer, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[0;32m---> 95\u001b[0m     result \u001b[38;5;241m=\u001b[39m draw(artist, renderer, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m     96\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m renderer\u001b[38;5;241m.\u001b[39m_rasterizing:\n\u001b[1;32m     97\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstop_rasterizing()\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer)\u001b[0m\n\u001b[1;32m     69\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     70\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[0;32m---> 72\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m draw(artist, renderer)\n\u001b[1;32m     73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m     74\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/figure.py:3154\u001b[0m, in \u001b[0;36mFigure.draw\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m   3151\u001b[0m         \u001b[38;5;66;03m# ValueError can occur when resizing a window.\u001b[39;00m\n\u001b[1;32m   3153\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpatch\u001b[38;5;241m.\u001b[39mdraw(renderer)\n\u001b[0;32m-> 3154\u001b[0m mimage\u001b[38;5;241m.\u001b[39m_draw_list_compositing_images(\n\u001b[1;32m   3155\u001b[0m     renderer, \u001b[38;5;28mself\u001b[39m, artists, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39msuppressComposite)\n\u001b[1;32m   3157\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m sfig \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39msubfigs:\n\u001b[1;32m   3158\u001b[0m     sfig\u001b[38;5;241m.\u001b[39mdraw(renderer)\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/image.py:132\u001b[0m, in \u001b[0;36m_draw_list_compositing_images\u001b[0;34m(renderer, parent, artists, suppress_composite)\u001b[0m\n\u001b[1;32m    130\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m not_composite \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m has_images:\n\u001b[1;32m    131\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m a \u001b[38;5;129;01min\u001b[39;00m artists:\n\u001b[0;32m--> 132\u001b[0m         a\u001b[38;5;241m.\u001b[39mdraw(renderer)\n\u001b[1;32m    133\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    134\u001b[0m     \u001b[38;5;66;03m# Composite any adjacent images together\u001b[39;00m\n\u001b[1;32m    135\u001b[0m     image_group \u001b[38;5;241m=\u001b[39m []\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer)\u001b[0m\n\u001b[1;32m     69\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     70\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[0;32m---> 72\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m draw(artist, renderer)\n\u001b[1;32m     73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m     74\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/axes/_base.py:3070\u001b[0m, in \u001b[0;36m_AxesBase.draw\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m   3067\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m artists_rasterized:\n\u001b[1;32m   3068\u001b[0m     _draw_rasterized(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfigure, artists_rasterized, renderer)\n\u001b[0;32m-> 3070\u001b[0m mimage\u001b[38;5;241m.\u001b[39m_draw_list_compositing_images(\n\u001b[1;32m   3071\u001b[0m     renderer, \u001b[38;5;28mself\u001b[39m, artists, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfigure\u001b[38;5;241m.\u001b[39msuppressComposite)\n\u001b[1;32m   3073\u001b[0m renderer\u001b[38;5;241m.\u001b[39mclose_group(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124maxes\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m   3074\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mstale \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/image.py:132\u001b[0m, in \u001b[0;36m_draw_list_compositing_images\u001b[0;34m(renderer, parent, artists, suppress_composite)\u001b[0m\n\u001b[1;32m    130\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m not_composite \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m has_images:\n\u001b[1;32m    131\u001b[0m     \u001b[38;5;28;01mfor\u001b[39;00m a \u001b[38;5;129;01min\u001b[39;00m artists:\n\u001b[0;32m--> 132\u001b[0m         a\u001b[38;5;241m.\u001b[39mdraw(renderer)\n\u001b[1;32m    133\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    134\u001b[0m     \u001b[38;5;66;03m# Composite any adjacent images together\u001b[39;00m\n\u001b[1;32m    135\u001b[0m     image_group \u001b[38;5;241m=\u001b[39m []\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer)\u001b[0m\n\u001b[1;32m     69\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     70\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[0;32m---> 72\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m draw(artist, renderer)\n\u001b[1;32m     73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m     74\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/axis.py:1395\u001b[0m, in \u001b[0;36mAxis.draw\u001b[0;34m(self, renderer, *args, **kwargs)\u001b[0m\n\u001b[1;32m   1393\u001b[0m \u001b[38;5;66;03m# Shift label away from axes to avoid overlapping ticklabels.\u001b[39;00m\n\u001b[1;32m   1394\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_update_label_position(renderer)\n\u001b[0;32m-> 1395\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mlabel\u001b[38;5;241m.\u001b[39mdraw(renderer)\n\u001b[1;32m   1397\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_update_offset_text_position(tlb1, tlb2)\n\u001b[1;32m   1398\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39moffsetText\u001b[38;5;241m.\u001b[39mset_text(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mmajor\u001b[38;5;241m.\u001b[39mformatter\u001b[38;5;241m.\u001b[39mget_offset())\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization.<locals>.draw_wrapper\u001b[0;34m(artist, renderer)\u001b[0m\n\u001b[1;32m     69\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m     70\u001b[0m         renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[0;32m---> 72\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m draw(artist, renderer)\n\u001b[1;32m     73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[1;32m     74\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/text.py:748\u001b[0m, in \u001b[0;36mText.draw\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m    745\u001b[0m renderer\u001b[38;5;241m.\u001b[39mopen_group(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mtext\u001b[39m\u001b[38;5;124m'\u001b[39m, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_gid())\n\u001b[1;32m    747\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_cm_set(text\u001b[38;5;241m=\u001b[39m\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_get_wrapped_text()):\n\u001b[0;32m--> 748\u001b[0m     bbox, info, descent \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_get_layout(renderer)\n\u001b[1;32m    749\u001b[0m     trans \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_transform()\n\u001b[1;32m    751\u001b[0m     \u001b[38;5;66;03m# don't use self.get_position here, which refers to text\u001b[39;00m\n\u001b[1;32m    752\u001b[0m     \u001b[38;5;66;03m# position in Text:\u001b[39;00m\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/text.py:502\u001b[0m, in \u001b[0;36mText._get_layout\u001b[0;34m(self, renderer)\u001b[0m\n\u001b[1;32m    499\u001b[0m xmin \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m=\u001b[39m offsetx\n\u001b[1;32m    500\u001b[0m ymin \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m=\u001b[39m offsety\n\u001b[0;32m--> 502\u001b[0m bbox \u001b[38;5;241m=\u001b[39m Bbox\u001b[38;5;241m.\u001b[39mfrom_bounds(xmin, ymin, width, height)\n\u001b[1;32m    504\u001b[0m \u001b[38;5;66;03m# now rotate the positions around the first (x, y) position\u001b[39;00m\n\u001b[1;32m    505\u001b[0m xys \u001b[38;5;241m=\u001b[39m M\u001b[38;5;241m.\u001b[39mtransform(offset_layout) \u001b[38;5;241m-\u001b[39m (offsetx, offsety)\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/transforms.py:811\u001b[0m, in \u001b[0;36mBbox.from_bounds\u001b[0;34m(x0, y0, width, height)\u001b[0m\n\u001b[1;32m    804\u001b[0m \u001b[38;5;129m@staticmethod\u001b[39m\n\u001b[1;32m    805\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mfrom_bounds\u001b[39m(x0, y0, width, height):\n\u001b[1;32m    806\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    807\u001b[0m \u001b[38;5;124;03m    Create a new `Bbox` from *x0*, *y0*, *width* and *height*.\u001b[39;00m\n\u001b[1;32m    808\u001b[0m \n\u001b[1;32m    809\u001b[0m \u001b[38;5;124;03m    *width* and *height* may be negative.\u001b[39;00m\n\u001b[1;32m    810\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m--> 811\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m Bbox\u001b[38;5;241m.\u001b[39mfrom_extents(x0, y0, x0 \u001b[38;5;241m+\u001b[39m width, y0 \u001b[38;5;241m+\u001b[39m height)\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/matplotlib/transforms.py:829\u001b[0m, in \u001b[0;36mBbox.from_extents\u001b[0;34m(minpos, *args)\u001b[0m\n\u001b[1;32m    813\u001b[0m \u001b[38;5;129m@staticmethod\u001b[39m\n\u001b[1;32m    814\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mfrom_extents\u001b[39m(\u001b[38;5;241m*\u001b[39margs, minpos\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m):\n\u001b[1;32m    815\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    816\u001b[0m \u001b[38;5;124;03m    Create a new Bbox from *left*, *bottom*, *right* and *top*.\u001b[39;00m\n\u001b[1;32m    817\u001b[0m \n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    827\u001b[0m \u001b[38;5;124;03m        scales where negative bounds result in floating point errors.\u001b[39;00m\n\u001b[1;32m    828\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[0;32m--> 829\u001b[0m     bbox \u001b[38;5;241m=\u001b[39m Bbox(np\u001b[38;5;241m.\u001b[39mreshape(args, (\u001b[38;5;241m2\u001b[39m, \u001b[38;5;241m2\u001b[39m)))\n\u001b[1;32m    830\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m minpos \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m    831\u001b[0m         bbox\u001b[38;5;241m.\u001b[39m_minpos[:] \u001b[38;5;241m=\u001b[39m minpos\n",
      "File \u001b[0;32m/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/numpy/core/fromnumeric.py:200\u001b[0m, in \u001b[0;36mreshape\u001b[0;34m(a, newshape, order)\u001b[0m\n\u001b[1;32m    196\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m (a,)\n\u001b[1;32m    199\u001b[0m \u001b[38;5;66;03m# not deprecated --- copy if necessary, view otherwise\u001b[39;00m\n\u001b[0;32m--> 200\u001b[0m \u001b[38;5;129m@array_function_dispatch\u001b[39m(_reshape_dispatcher)\n\u001b[1;32m    201\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mreshape\u001b[39m(a, newshape, order\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mC\u001b[39m\u001b[38;5;124m'\u001b[39m):\n\u001b[1;32m    202\u001b[0m \u001b[38;5;250m    \u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    203\u001b[0m \u001b[38;5;124;03m    Gives a new shape to an array without changing its data.\u001b[39;00m\n\u001b[1;32m    204\u001b[0m \n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    283\u001b[0m \u001b[38;5;124;03m           [5, 6]])\u001b[39;00m\n\u001b[1;32m    284\u001b[0m \u001b[38;5;124;03m    \"\"\"\u001b[39;00m\n\u001b[1;32m    285\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m _wrapfunc(a, \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mreshape\u001b[39m\u001b[38;5;124m'\u001b[39m, newshape, order\u001b[38;5;241m=\u001b[39morder)\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def animate_wave(psi, title, file_title, L=1.0, T=1.0, total_frames=100, save=False):\n",
    "    '''Animates the wave equation amplitude psi over time'''\n",
    "    fig, ax = plt.subplots(figsize=(5, 3.5), layout='tight')\n",
    "    x = np.linspace(0, L, psi.shape[0])\n",
    "    plt.xlim(0, L)\n",
    "    plt.ylim(-1.2, 1.2)\n",
    "    plt.xlabel('Position (x)')\n",
    "    plt.ylabel('Vibration amplitude ($\\\\Psi$)')\n",
    "    plt.grid(True)\n",
    "    line, = ax.plot(x, psi[:, 0])\n",
    "\n",
    "    # Calculate the frame interval based on the total number of frames\n",
    "    frame_interval = int(psi.shape[1] / total_frames)\n",
    "\n",
    "    def animate(i):\n",
    "        line.set_ydata(psi[:, i * frame_interval])\n",
    "        plt.title(title + f' (t={i * frame_interval / psi.shape[1] * T:.2f}s)')\n",
    "        return line,\n",
    "\n",
    "    anim = FuncAnimation(fig, animate, frames=total_frames,\n",
    "                         interval=1000//60, blit=True, repeat=True)\n",
    "    if save:\n",
    "        anim.save(f'{SAVE_PATH}/{file_title}.gif', writer=ANIM_BACKEND)\n",
    "\n",
    "\n",
    "# Parameters\n",
    "c = 1\n",
    "L = 1\n",
    "\n",
    "# Discretization\n",
    "dt = 0.001\n",
    "T = 2.0\n",
    "Nx = 500\n",
    "dx = L / Nx\n",
    "Nt = int(T / dt)\n",
    "\n",
    "for i, (init_condition, init_label) in tqdm(enumerate(zip(init_conditions, init_labels)), total=len(init_conditions), desc='Animating wave', unit='animation'):\n",
    "    psi = solve_wave(init_condition, L, c, T, Nx, dt)\n",
    "    anim = animate_wave(psi, f'$\\\\Psi(x,0) =$ {init_label}', f'animated_wave_{i}', T=T, total_frames=80, save=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2: Time Dependent Diffusion Equation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "D. (0.5 point) Determine the equation to use at the boundaries of the domain.\n",
    "Clearly show the ranges of the indices of the grid. A figure is extremely helpful for\n",
    "figuring this out."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equations relevant for all boundaries are\n",
    "$$\n",
    "\\begin{align}\n",
    "c(x, 0; t) = 0 &\\land c(x, 1; t) = 1\\\\\n",
    "c(0, y; t) = c(N-1, y; t) &\\land c(N, y; t) = c(1, y; t)\n",
    "\\end{align}\n",
    "$$\n",
    "where equation 1 refers to the source and sink boundary conditions and equation 2 refers to the periodic boundary conditions in the x direction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The chosen dt=0.01 is larger than the maximum stable dt=0.0001.\n",
      "Setting dt to 5e-05 instead.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def diffusion_step(u, dt, dx):\n",
    "    '''Executes a single time step of the diffusion equation'''\n",
    "    u_new = np.copy(u)\n",
    "\n",
    "    # Left boundary (periodic boundary conditions)\n",
    "    u_new[0, 1:-1] = u[0, 1:-1] + (D * dt / dx**2) * (\n",
    "        u[1, 1:-1] + u[-1, 1:-1] + u[0, 2:] + u[0, :-2] - 4 * u[0, 1:-1])\n",
    "    \n",
    "    u_new[1:-1, 1:-1] = u[1:-1, 1:-1] + (D * dt / dx**2) * (\n",
    "        u[2:, 1:-1] + u[:-2, 1:-1] + u[1:-1, 2:] + u[1:-1, :-2] - 4 * u[1:-1, 1:-1])\n",
    "    \n",
    "    # Right boundary (periodic boundary conditions)\n",
    "    u_new[-1, 1:-1] = u_new[0, 1:-1]\n",
    "\n",
    "    return u_new\n",
    "\n",
    "\n",
    "def ensure_stable_dt(D, dx, dt):\n",
    "    '''Ensures that the time step dt is stable for the given model'''\n",
    "    dt_stable = (dx**2) / (4 * D)\n",
    "    if dt > dt_stable:\n",
    "        print(f'The chosen dt={dt} is larger than the maximum stable dt={dt_stable}.')\n",
    "        new_dt = dt_stable / 2  # Use half of the maximum stable dt instead\n",
    "        print(f'Setting dt to {new_dt} instead.')\n",
    "        return new_dt\n",
    "    return dt\n",
    "\n",
    "\n",
    "def solve_diffusion(Nx, D, dx, dt, T):\n",
    "    '''\n",
    "    Simulate diffusion (2D spatial + time) and return the concentration matrix.\n",
    "\n",
    "    Parameters:\n",
    "    - Nx: Number of spatial grid points in each dimension\n",
    "    - D: Diffusion constant\n",
    "    - dx: Distance between grid points\n",
    "    - dt: Time step size\n",
    "    - T: Total time to simulate\n",
    "\n",
    "    Returns:\n",
    "    - c: Concentration matrix at each time step\n",
    "    '''\n",
    "    dt = ensure_stable_dt(D, dx, dt)\n",
    "    Nt = int(T / dt)\n",
    "\n",
    "    # Initial & boundary conditions\n",
    "    c = np.zeros((Nx, Nx, Nt + 1))\n",
    "    c[:, -1] = 1\n",
    "\n",
    "    for t in range(1, Nt + 1):\n",
    "        # Left boundary\n",
    "        c[0, 1:-1, t] = c[0, 1:-1, t-1] + (D * dt / dx**2) * (c[1, 1:-1, t-1] + c[-1, 1:-1, t-1] + c[0, 2:, t-1] + c[0, :-2, t-1] - 4 * c[0, 1:-1, t-1])\n",
    "        # Main body\n",
    "        c[1:-1, 1:-1, t] = c[1:-1, 1:-1, t-1] + (D * dt / dx**2) * (\n",
    "            c[2:, 1:-1, t-1] + c[:-2, 1:-1, t-1] + c[1:-1, 2:, t-1] + c[1:-1, :-2, t-1] - 4 * c[1:-1, 1:-1, t-1])\n",
    "        # Right boundary\n",
    "        c[-1, 1:-1, t] = c[0, 1:-1, t]\n",
    "\n",
    "    return c\n",
    "\n",
    "\n",
    "# Parameters\n",
    "D = 1  # Diffusion coefficient\n",
    "L = 1  # Length of the square spatial domain\n",
    "\n",
    "# Discretization\n",
    "T = 1.0\n",
    "dt = 0.01\n",
    "Nx = 50\n",
    "dx = L / Nx\n",
    "\n",
    "dt = ensure_stable_dt(D, dx, dt)\n",
    "Nt = int(T / dt)\n",
    "\n",
    "c = solve_diffusion(Nx, D, dx, dt, T)\n",
    "\n",
    "# Plotting the final state\n",
    "plt.figure(figsize=(5, 4))\n",
    "plt.imshow(np.rot90(c[:, :, -1], 3), origin='lower',\n",
    "           extent=(0, L, 0, L))\n",
    "plt.colorbar(label='Concentration', shrink=0.9, pad=0.1)\n",
    "plt.title(f'Concentration at t={T:.2f}s (stable)')\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel('$y$')\n",
    "plt.savefig(f'{SAVE_PATH}/diffusion_stable.png', dpi=300, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "E. (1 point) Test the correctness of your simulation. Compare to the analytic\n",
    "solutions, plot c(y) for different times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def solve_diffusion_analytical(y, t, terms=50):\n",
    "    '''Computes the analytical solution of the concentration c(y,t) using the error function.'''\n",
    "    result = 0\n",
    "    for i in range(terms):\n",
    "        result += erfc((1 - y + 2*i) / np.sqrt(4*D*t)) - \\\n",
    "            erfc((1 + y + 2*i) / np.sqrt(4*D*t))\n",
    "    return result\n",
    "\n",
    "y = np.linspace(0, L, Nx)\n",
    "time_values = np.logspace(-3, 0, 4)\n",
    "colors = ['tab:blue', 'tab:orange', 'tab:green', 'tab:red']\n",
    "y_analyticals = []\n",
    "\n",
    "for t in time_values:\n",
    "    y_analyticals.append(solve_diffusion_analytical(y, t))\n",
    "\n",
    "# Compare the analytical solution with the numerical solution\n",
    "plt.figure(figsize=(5, 3.5), layout='tight')\n",
    "lines = []\n",
    "for i, (t, color) in enumerate(zip(time_values, colors)):\n",
    "    plt.plot(y, c[0, :, int(t*Nt)], color=color, linestyle='--')\n",
    "    plt.plot(y, y_analyticals[i], color=color, alpha=0.2, lw=3)\n",
    "    lines.append(mlines.Line2D([], [], color=color, label=f't={t}'))\n",
    "plt.title('Comparison of analytical and numerical solutions')\n",
    "plt.xlabel('Position $y$')\n",
    "plt.ylabel('Concentration $c(y,t)$')\n",
    "\n",
    "# Double legend\n",
    "analytical_line = mlines.Line2D(\n",
    "    [], [], color='black', alpha=0.2, lw=3, label='analytical')\n",
    "numerical_line = mlines.Line2D(\n",
    "    [], [], color='black', linestyle='--', label='numerical')\n",
    "type_legend = plt.legend(\n",
    "    handles=[analytical_line, numerical_line], loc='center left')\n",
    "plt.gca().add_artist(type_legend)\n",
    "plt.legend(handles=lines, loc='upper left')\n",
    "\n",
    "plt.grid(True)\n",
    "plt.savefig(f'{SAVE_PATH}/diffusion_comparison.png', dpi=300, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "F. (1 point) Plot the results, show the 2D domain, with a color representing the\n",
    "concentration at each point. Make a plot of the state of the system at several times:\n",
    "t = {0, 0.001, 0.01, 0.1, and 1}."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/tg/bfb__1d16td__2vd879zjkrh0000gn/T/ipykernel_29901/3133543208.py:25: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n",
      "  plt.savefig(f'{SAVE_PATH}/diffusion_at_different_times.png',\n",
      "/opt/homebrew/Caskroom/miniconda/base/envs/scientific/lib/python3.12/site-packages/IPython/core/pylabtools.py:152: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.\n",
      "  fig.canvas.print_figure(bytes_io, **kw)\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 900x300 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Time points to capture the concentration\n",
    "times_to_plot = np.array(np.array([0, 0.001, 0.01, 0.1, 1]) * Nt, dtype=int)\n",
    "\n",
    "# Recalculate the simulation with tolerance for capturing times\n",
    "c = solve_diffusion(Nx, D, dx, dt, T)\n",
    "\n",
    "# Plotting with corrected results\n",
    "fig, axs = plt.subplots(1, len(times_to_plot), figsize=(\n",
    "    9, 3), sharey=True, layout='tight')\n",
    "for i, t in enumerate(times_to_plot):\n",
    "    im = axs[i].imshow(np.rot90(c[:, :, t], 3), extent=[\n",
    "                       0, L, 0, L], origin='lower')\n",
    "    axs[i].set_title(f't={t/Nt}s')\n",
    "    axs[i].set_xlabel('x')\n",
    "    axs[i].set_xticks([0, 0.5, 1])\n",
    "    axs[i].set_yticks([0, 0.5, 1])\n",
    "axs[0].set_ylabel('y')\n",
    "\n",
    "# Add a colorbar on the bottom\n",
    "cbar_ax = fig.add_axes((0.25, 0, 0.5, 0.05))\n",
    "fig.colorbar(im, cax=cbar_ax, orientation='horizontal',\n",
    "             label='Concentration $c$')\n",
    "\n",
    "fig.suptitle('Concentration $c$ at different times during 2D diffusion', y=0.85)\n",
    "plt.savefig(f'{SAVE_PATH}/diffusion_at_different_times.png',\n",
    "            dpi=300, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "G. (1 point) Make an animated plot of the time dependent diffusion equation until\n",
    "equilibrium."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def has_converged(c_old, c_new, epsilon=1e-5):\n",
    "    '''Check if the concentration matrix has converged to a steady state'''\n",
    "    delta = np.max(np.abs(c_new - c_old))\n",
    "    return delta < epsilon\n",
    "\n",
    "\n",
    "def animate_diffusion(c, title, file_title, L, T, total_frames=100, save=False):\n",
    "    '''Animates the diffusion concentration c over time'''\n",
    "    fig, _ = plt.subplots(figsize=(5, 3.5), layout='tight')\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "    grid = plt.imshow(np.rot90(c[:, :, 0], 3), extent=[0, L, 0, L], origin='lower')\n",
    "    plt.colorbar(label='Concentration')\n",
    "\n",
    "    # Calculate the frame interval based on the total number of frames\n",
    "    frame_interval = int(c.shape[2] / total_frames)\n",
    "\n",
    "    def animate(i):\n",
    "        frame = i * frame_interval\n",
    "        grid.set_data(np.rot90(c[:, :, frame], 3))\n",
    "        plt.title(title + f' (t={frame / c.shape[2] * T:.2f}s)')\n",
    "        return grid,\n",
    "\n",
    "    anim = FuncAnimation(fig, animate, frames=total_frames,\n",
    "                         interval=1000//60, blit=True, repeat=True)\n",
    "    if save:\n",
    "        anim.save(f'{SAVE_PATH}/{file_title}.gif', writer=ANIM_BACKEND)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged after 11268 time steps at time 0.56s.\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x350 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Iterate until convergence\n",
    "c = np.zeros((Nx, Nx, Nt+1))\n",
    "c[:, -1, :] = 1\n",
    "\n",
    "epsilon = 1e-6\n",
    "timestep_equillibrium = 0\n",
    "for i in range(Nt):\n",
    "    c[:, :, i+1] = diffusion_step(c[:, :, i], dt, dx)\n",
    "    if has_converged(c[:, :, i], c[:, :, i+1], epsilon=epsilon):\n",
    "        timestep_equillibrium = i\n",
    "        print(f'Converged after {i} time steps at time {i*dt:.2f}s.')\n",
    "        break\n",
    "\n",
    "if timestep_equillibrium == 0:\n",
    "    print('No convergence reached.')\n",
    "\n",
    "anim = animate_diffusion(c[:, :, :i], f'2D Diffusion simulation until equillibrium',\n",
    "                         f'2d_diffusion_until_equillibrium', L=L, T=i*dt, total_frames=80, save=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Laplace Equation\n",
    "\n",
    "H. (1 point) Implement the Jacobi iteration, the Gauss-Seidel method and SOR.\n",
    "Try N = 50. Test the methods by comparing the result to the analytical result in\n",
    "eq. (5), i.e. the linear dependence of the concentration on y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "is_executing": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Jacobi method: 4068 iter(s), Gauss-Seidel method: 2385 iter(s), SOR method: 198 iter(s)\n"
     ]
    }
   ],
   "source": [
    "def jacobi_iter(c):\n",
    "    c_new = c.copy()\n",
    "    Nx = c.shape[0]\n",
    "    for i in range(0, Nx):\n",
    "        for j in range(1, Nx-1):\n",
    "            c_new[i, j] = 0.25 * \\\n",
    "                (c[(i+1)%Nx, j] + c[i-1, j] + c[i, j+1] + c[i, j-1])\n",
    "\n",
    "    return c_new\n",
    "\n",
    "\n",
    "def gauss_seidel(c):\n",
    "    Nx = c.shape[0]\n",
    "    for i in range(0, Nx):\n",
    "        for j in range(1, Nx-1):\n",
    "            c[i, j] = 0.25 * (c[(i+1)%Nx, j] + c[i-1, j] + c[i, j+1] + c[i, j-1])\n",
    "\n",
    "    return c\n",
    "\n",
    "\n",
    "def sor_iter(c, omega):\n",
    "    Nx = c.shape[0]\n",
    "    for i in range(0, Nx):\n",
    "        for j in range(1, Nx-1):\n",
    "            c[i, j] = (1-omega)*c[i, j] + omega*0.25 * \\\n",
    "                (c[(i+1)%Nx, j] + c[i-1, j] + c[i, j+1] + c[i, j-1])\n",
    "\n",
    "    return c\n",
    "\n",
    "\n",
    "def solve_laplace(method, c, Nx, epsilon, omega=None):\n",
    "    iteration = 0\n",
    "    while True:\n",
    "        c_old = c.copy()\n",
    "        if method == 'jacobi':\n",
    "            c = jacobi_iter(c)\n",
    "        elif method == 'gs':\n",
    "            c = gauss_seidel(c)\n",
    "        elif method == 'sor':\n",
    "            c = sor_iter(c, omega)\n",
    "        iteration += 1\n",
    "        if has_converged(c_old, c, epsilon):\n",
    "            break\n",
    "    return c, iteration\n",
    "\n",
    "\n",
    "# Parameters\n",
    "sor_omega = 1.9\n",
    "epsilon = 1e-5  # checking for convergence\n",
    "L = 1.0  # Length of the square spatial domain\n",
    "\n",
    "# Discretization\n",
    "Nx = 50\n",
    "x = np.linspace(0, L, Nx)\n",
    "dx = x[1] - x[0]\n",
    "\n",
    "# Initial conditions\n",
    "c = np.zeros((Nx, Nx))\n",
    "c[:, -1] = 1\n",
    "\n",
    "# Solve the Laplace equation using different methods\n",
    "c_jacobi, iterations_jacobi = solve_laplace('jacobi', c.copy(), Nx, epsilon)\n",
    "c_gs, iterations_gs = solve_laplace('gs', c.copy(), Nx, epsilon)\n",
    "c_sor, iterations_sor = solve_laplace('sor', c.copy(), Nx, epsilon, sor_omega)\n",
    "print(f'Jacobi method: {iterations_jacobi} iter(s), Gauss-Seidel method: ' + \n",
    "      f'{iterations_gs} iter(s), SOR method: {iterations_sor} iter(s)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Max error (Jacobi): 9.72e-03, Max error (Gauss-Seidel): 4.85e-03, Max error (SOR): 2.18e-04\n",
      "MSE (Jacobi): 4.63e-05, MSE (Gauss-Seidel): 1.15e-05, MSE (SOR): 2.15e-08\n",
      "RMSE (Jacobi): 6.81e-03, RMSE (Gauss-Seidel): 3.39e-03, RMSE (SOR): 1.47e-04\n"
     ]
    }
   ],
   "source": [
    "# Analytical solution (assuming a linear dependence on y)\n",
    "c_analytical = np.zeros((Nx, Nx))\n",
    "for i in range(Nx):\n",
    "    c_analytical[:, i] = x[i]\n",
    "\n",
    "# Calculate Errors compared to analytical solution\n",
    "error_jacobi = np.abs(c_jacobi - c_analytical)\n",
    "error_gs = np.abs(c_gs - c_analytical)\n",
    "error_sor = np.abs(c_sor - c_analytical)\n",
    "\n",
    "max_error_jacobi = np.max(error_jacobi)\n",
    "max_error_gs = np.max(error_gs)\n",
    "max_error_sor = np.max(error_sor)\n",
    "\n",
    "mse_jacobi = np.mean((c_analytical - c_jacobi) ** 2)\n",
    "mse_gs = np.mean((c_analytical - c_gs) ** 2)\n",
    "mse_sor = np.mean((c_analytical - c_sor) ** 2)\n",
    "\n",
    "rmse_jacobi = np.sqrt(mse_jacobi)\n",
    "rmse_gs = np.sqrt(mse_gs)\n",
    "rmse_sor = np.sqrt(mse_sor)\n",
    "\n",
    "print(f'Max error (Jacobi): {max_error_jacobi:.2e}, Max error (Gauss-Seidel): ' + \n",
    "      f'{max_error_gs:.2e}, Max error (SOR): {max_error_sor:.2e}')\n",
    "print(f'MSE (Jacobi): ' + \n",
    "      f'{mse_jacobi:.2e}, MSE (Gauss-Seidel): {mse_gs:.2e}, MSE (SOR): {mse_sor:.2e}')\n",
    "print(f'RMSE (Jacobi): ' + \n",
    "      f'{rmse_jacobi:.2e}, RMSE (Gauss-Seidel): {rmse_gs:.2e}, RMSE (SOR): {rmse_sor:.2e}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1000x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axs = plt.subplots(1, 2, figsize=(10, 4), layout='tight')\n",
    "methods = ['Jacobi', 'Gauss-Seidel', 'SOR']\n",
    "b = np.arange(len(methods))\n",
    "bar_width = 0.25\n",
    "\n",
    "axs[0].bar(b, [max_error_jacobi, max_error_gs, max_error_sor],\n",
    "           color='tab:blue', width=bar_width, label='Max Error')\n",
    "axs[0].bar(b+bar_width, [rmse_jacobi, rmse_gs, rmse_sor],\n",
    "           color='tab:orange', width=bar_width, label='RMSE')\n",
    "axs[0].bar(b+2*bar_width, [mse_jacobi, mse_gs, mse_sor],\n",
    "           color='tab:green', width=bar_width, label='MSE')\n",
    "axs[0].set_xlabel('Method')\n",
    "axs[0].set_xticks([r + bar_width for r in range(len(methods))])\n",
    "axs[0].set_xticklabels(methods)\n",
    "axs[0].set_ylabel('Error')\n",
    "axs[0].set_yscale('log')\n",
    "axs[0].set_title('Error of numerical solutions')\n",
    "axs[0].grid(True)\n",
    "axs[0].legend()\n",
    "\n",
    "iterations = [iterations_jacobi, iterations_gs, iterations_sor]\n",
    "axs[1].bar(methods, iterations, color=['tab:purple'])\n",
    "axs[1].set_xlabel('Method')\n",
    "axs[1].set_ylabel('Iterations $k$')\n",
    "axs[1].set_yscale('log')\n",
    "axs[1].set_yticks([100, 1000, 10000])\n",
    "axs[1].set_title('Iterations until convergence')\n",
    "axs[1].grid(True)\n",
    "\n",
    "plt.suptitle('Comparison of iterative methods for solving the Laplace equation')\n",
    "plt.savefig(f'{SAVE_PATH}/laplace_comparison.png', dpi=300, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I. (1 point) Show how the convergence measure δ in eq. (14) depends on the number\n",
    "of iterations k for each of the methods. A log-lin plot may be suitable. For SOR,\n",
    "choose a few representative values for ω."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def track_delta(method, c, Nx, omega=None):\n",
    "    '''Counts the number of iterations for each method to converge and returns the deltas (change in c) over time.'''\n",
    "    deltas = []\n",
    "    epsilon = 1e-5\n",
    "    iteration = 0\n",
    "    while True:\n",
    "        c_old = c.copy()\n",
    "        if method == 'jacobi':\n",
    "            c = jacobi_iter(c)\n",
    "        elif method == 'gs':\n",
    "            c = gauss_seidel(c)\n",
    "        elif method == 'sor':\n",
    "            c = sor_iter(c, omega)\n",
    "        delta = np.max(np.abs(c_old - c))\n",
    "        deltas.append(delta)\n",
    "        iteration += 1\n",
    "        if delta < epsilon:\n",
    "            break\n",
    "    return deltas\n",
    "\n",
    "\n",
    "c = np.zeros((Nx, Nx))\n",
    "c[:, -1] = 1\n",
    "delta_jacobi = track_delta('jacobi', c.copy(), Nx)\n",
    "\n",
    "c = np.zeros((Nx, Nx))\n",
    "c[:, -1] = 1\n",
    "delta_gs = track_delta('gs', c.copy(), Nx)\n",
    "\n",
    "omega_values = [1.7, 1.8, 1.9, 1.91]\n",
    "c = np.zeros((Nx, Nx))\n",
    "c[:, -1] = 1\n",
    "delta_sor = {omega: track_delta('sor', c.copy(), Nx, omega)\n",
    "             for omega in omega_values}\n",
    "\n",
    "plt.figure(figsize=(5, 3.5), layout='tight')\n",
    "plt.plot(delta_jacobi, label='Jacobi')\n",
    "plt.plot(delta_gs, label='Gauss-Seidel')\n",
    "for sor_omega, deltas in delta_sor.items():\n",
    "    plt.plot(deltas, label=f'SOR (ω={sor_omega})')\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Iterations $k$')\n",
    "plt.ylabel('Convergence measure $\\\\delta$')\n",
    "plt.title('Convergence behaviour of iterative methods')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.savefig(f'{SAVE_PATH}/convergence_measure.png', dpi=300, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "J. (1 point) In the SOR method, find the optimal ω. How does it depend on N?."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit(nopython=True, parallel=True)\n",
    "def sor_parallel(c, omega, epsilon=1e-6, max_iterations=10_000):\n",
    "    '''Solves the Laplace equation using the red-black parallel Successive Over-Relaxation (SOR) method introduced in Set 1'''\n",
    "    converged = False\n",
    "    Nx = c.shape[0] # Assume 2D square lattice\n",
    "\n",
    "    for n in range(max_iterations):\n",
    "        c_old = c.copy()  # Copy the grid for convergence check\n",
    "\n",
    "        # Red points\n",
    "        for i in prange(0, Nx):\n",
    "            for j in range(1, Nx-1): # exclude y=0 sink and y=Nx source\n",
    "                if (i + j) % 2 == 0:\n",
    "                    # for periodic boundaries, note use of (i+1)% Nx, i-1 pythonically wraps to index -1\n",
    "                    c[i, j] = (1-omega)*c[i, j] + omega*0.25 * \\\n",
    "                        (c[(i+1)%Nx, j] + c[i-1, j] + c[i, j+1] + c[i, j-1])\n",
    "\n",
    "        # Black points\n",
    "        for i in prange(0, Nx):\n",
    "            for j in range(1, Nx-1):\n",
    "                if (i + j) % 2 == 1:\n",
    "                    c[i, j] = (1-omega)*c[i, j] + omega*0.25 * \\\n",
    "                        (c[(i+1)%Nx, j] + c[i-1, j] + c[i, j+1] + c[i, j-1])\n",
    "\n",
    "        # Check for convergence\n",
    "        if np.max(np.abs(c - c_old)) < epsilon:\n",
    "            converged = True\n",
    "            # info(f'Converged after {n} iterations using omega={omega}.')\n",
    "            break\n",
    "    \n",
    "    return c, n, converged\n",
    "\n",
    "\n",
    "def find_best_omega(omega_values, Nx, tolerance=1e-6, max_iterations=10000):\n",
    "    '''Finds the best relaxation parameter omega for SOR'''\n",
    "    best_omega = 0\n",
    "    min_iterations = max_iterations\n",
    "    for omega in omega_values:\n",
    "        c = np.zeros((Nx, Nx))\n",
    "        c[:, -1] = 1\n",
    "        _, iterations, converged = sor_parallel(\n",
    "            c, omega, tolerance, max_iterations)\n",
    "        if converged and iterations < min_iterations:\n",
    "            min_iterations = iterations\n",
    "            best_omega = omega\n",
    "    return best_omega, min_iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE SOR Parallel: 1.2582164217609535e-05\n"
     ]
    }
   ],
   "source": [
    "# Check correctness of parallel SOR implementation\n",
    "c = np.zeros((Nx, Nx))  \n",
    "c[:, -1] = 1\n",
    "c_psor, _, _ = sor_parallel(c, 1.9, 1e-6)\n",
    "mse_psor = np.mean((c_analytical - c_psor) ** 2)\n",
    "rmse_psor = np.sqrt(mse_psor)\n",
    "print(f'RMSE SOR Parallel: {rmse_psor}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Finding best omega for each grid size:   0%|          | 0/39 [00:00<?, ?grid/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Finding best omega for each grid size: 100%|██████████| 39/39 [03:33<00:00,  5.48s/grid]\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x350 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid_sizes = np.arange(10, 205, 5)\n",
    "omega_range = np.arange(1.5, 2, 0.025)\n",
    "\n",
    "best_omegas = []\n",
    "min_iterations_list = []\n",
    "\n",
    "for Nx in tqdm(grid_sizes, desc='Finding best omega for each grid size', unit='grid'):\n",
    "    best_omega, min_iterations = find_best_omega(Nx, omega_range)\n",
    "    best_omegas.append(best_omega)\n",
    "    min_iterations_list.append(min_iterations)\n",
    "    # print(f'Grid Size: {N}, Best Omega: {best_omega:.4f}, Min Iterations: {min_iterations}')\n",
    "\n",
    "plt.figure(figsize=(5, 3.5), layout='tight')\n",
    "plt.plot(grid_sizes, best_omegas, '-o', label='Best $\\\\omega$')\n",
    "plt.xlabel('Grid size $N$')\n",
    "plt.ylabel('Omega $\\\\omega$')\n",
    "plt.title('Best SOR parameter omega $\\\\omega$ for grid size $N$')\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "plt.savefig(f'{SAVE_PATH}/best_omega.png', dpi=300, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "K. (2 points) Implement the possibility to include objects into the computational\n",
    "domain. The objects should be sinks. Experiment a little bit with some objects in\n",
    "the computational domain (e.g. a rectangle or a few rectangles, ...). What is the\n",
    "influence on the number of iterations. What about the optimal ω , is it influenced\n",
    "by the presence of objects? Look at the resulting concentration fields, and try to\n",
    "interpret what happens. The implementation in this exercise will also be used for\n",
    "diffusion-limited aggregation in Set 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "@jit(nopython=True, parallel=True)\n",
    "def update_with_sink(c, omega, objects):\n",
    "    c_new = c.copy()\n",
    "    Nx = c.shape[0]\n",
    "    for i in prange(0, Nx):\n",
    "        for j in range(1, Nx-1):\n",
    "            if objects[i, j] == 0:  # Check if the point is not part of an object\n",
    "                c_new[i, j] = (1 - omega) * c[i, j] + (omega / 4) * (\n",
    "                    c[(i+1)%Nx, j] + c_new[i-1, j] + c[i, j+1] + c_new[i, j-1]\n",
    "                )\n",
    "            else:\n",
    "                # Set concentration to zero if it's part of an object\n",
    "                c_new[i, j] = 0\n",
    "\n",
    "    return c_new\n",
    "\n",
    "@jit(nopython=True, parallel=True)\n",
    "def update_with_insulation(c, omega, objects):\n",
    "    c_new = c.copy()\n",
    "    Nx = c.shape[0]\n",
    "    for i in prange(0, Nx):\n",
    "        for j in range(1, Nx-1):\n",
    "            if objects[i, j] == 0:  # Not part of an object\n",
    "                contributions = []\n",
    "                # Check each neighbor and add it to the contributions if it's not an insulating material\n",
    "                if objects[(i+1)%Nx, j] != 2:\n",
    "                    contributions.append(c[(i+1)%Nx, j])\n",
    "                if objects[i-1, j] != 2:\n",
    "                    contributions.append(c_new[i-1, j])\n",
    "                if objects[i, j+1] != 2:\n",
    "                    contributions.append(c[i, j+1])\n",
    "                if objects[i, j-1] != 2:\n",
    "                    contributions.append(c_new[i, j-1])\n",
    "\n",
    "                if contributions:\n",
    "                    c_new[i, j] = (1 - omega) * c[i, j] + omega * \\\n",
    "                        sum(contributions) / len(contributions)\n",
    "                else:\n",
    "                    # No update if completely surrounded by insulators\n",
    "                    c_new[i, j] = c[i, j]\n",
    "            # No else case needed; insulating objects do not change concentration\n",
    "\n",
    "    return c_new\n",
    "\n",
    "\n",
    "def solve_laplace_with_objects(c, omega, objects, epsilon, max_iterations, object_type='sink', show_output=True):\n",
    "    if show_output:\n",
    "        iterator = tqdm(range(max_iterations), desc=f'Simulating SOR with {object_type}', unit='iteration')\n",
    "    else:\n",
    "        iterator = range(max_iterations)\n",
    "        \n",
    "    for iteration in iterator:\n",
    "        if object_type == 'sink':\n",
    "            c_new = update_with_sink(c, omega, objects)\n",
    "        elif object_type == 'insulator':\n",
    "            c_new = update_with_insulation(c, omega, objects)\n",
    "\n",
    "        # Check for convergence\n",
    "        delta = np.max(np.abs(c_new - c))\n",
    "        if delta < epsilon:\n",
    "            if show_output:\n",
    "                print(f'Converged in {iteration+1} iterations')\n",
    "            break\n",
    "        \n",
    "        c = c_new\n",
    "    if delta >= epsilon:\n",
    "        if show_output: \n",
    "            print('Maximum iterations reached without convergence')\n",
    "    return c, iteration, delta < epsilon\n",
    "\n",
    "\n",
    "def plot_laplace_grid(c, title, filename):\n",
    "    plt.figure(figsize=(5, 4), layout='tight')\n",
    "    plt.imshow(np.rot90(c, 3), interpolation='nearest', origin='lower')\n",
    "    plt.colorbar(label='Concentration')\n",
    "    plt.title(title)\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "    plt.savefig(f'{SAVE_PATH}/{filename}.png', dpi=300, bbox_inches='tight')\n",
    "    plt.show()\n",
    "\n",
    "\n",
    "def get_predefined_objects(Nx, object_type, object_shape):\n",
    "    objects = np.zeros((Nx, Nx), dtype=int)\n",
    "    if object_type == 'sink':\n",
    "        fill = 1\n",
    "    elif object_type == 'insulator':\n",
    "        fill = 2\n",
    "    else:\n",
    "        raise NotImplementedError('Unsupported object type')\n",
    "\n",
    "    if object_shape == 'rectangle':\n",
    "        objects[3*Nx//5:4*Nx//5, 9*Nx//10:Nx] = fill\n",
    "    elif object_shape == 'complex':\n",
    "        objects[15:20, 3*Nx//5:int(4.5*Nx//5)] = fill\n",
    "        objects[-20:-15, 3*Nx//5:int(4.5*Nx//5)] = fill\n",
    "        objects[:20, 3*Nx//5] = fill\n",
    "        objects[-20:, 3*Nx//5] = fill\n",
    "        objects[5:-5, 2*Nx//5] = fill\n",
    "    else:\n",
    "        raise NotImplementedError('Unsupported object shape')\n",
    "    return objects\n",
    "\n",
    "def find_best_omega_with_objects(omega_values, objects, Nx, epsilon=1e-6, max_iterations=5_000, object_type='sink'):\n",
    "    '''Finds the best relaxation parameter omega for SOR'''\n",
    "\n",
    "    best_omega = 0\n",
    "    min_iterations = max_iterations\n",
    "    for omega in omega_values:\n",
    "        c = np.zeros((Nx, Nx))\n",
    "        c[:, -1] = 1\n",
    "        c, iterations, converged = solve_laplace_with_objects(c, omega, objects, epsilon, max_iterations, object_type=object_type, show_output=False)\n",
    "        if converged and iterations < min_iterations:\n",
    "            min_iterations = iterations\n",
    "            best_omega = omega\n",
    "            c_converged = c.copy()\n",
    "        # else:\n",
    "            # print(f'Did not converge with {omega}')\n",
    "    if best_omega == 0:\n",
    "        ValueError(f'No convergence reached for {Nx}x{Nx} grid with max_iterations={max_iterations} and object type {object_type}.')\n",
    "    return c_converged, best_omega, min_iterations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Simulating SOR with sink:   0%|          | 0/10000 [00:00<?, ?iteration/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Simulating SOR with sink:   9%|▊         | 853/10000 [00:00<00:02, 4004.85iteration/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged in 854 iterations\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Parameters\n",
    "Nx = 50\n",
    "omega = 1.7\n",
    "epsilon = 1e-6\n",
    "max_iterations = 10000\n",
    "\n",
    "c = np.zeros((Nx, Nx))\n",
    "c[:, -1] = 1\n",
    "\n",
    "objects = get_predefined_objects(Nx, 'sink', 'rectangle')\n",
    "\n",
    "c, _, _ = solve_laplace_with_objects(\n",
    "    c, omega, objects, epsilon, max_iterations, object_type='sink')\n",
    "plot_laplace_grid(\n",
    "    c, 'Steady-state concentration with a rectangular sink', 'sink_simple_object')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Simulating SOR with sink:   1%|▏         | 126/10000 [00:00<00:00, 14437.83iteration/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged in 127 iterations\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = np.zeros((Nx, Nx))\n",
    "c[:, -1] = 1\n",
    "\n",
    "objects = get_predefined_objects(Nx, 'sink', 'complex')\n",
    "\n",
    "c, _, _ = solve_laplace_with_objects(\n",
    "    c, omega, objects, epsilon, max_iterations, object_type='sink')\n",
    "plot_laplace_grid(\n",
    "    c, 'Steady-state concentration with a complex sink', 'sink_complex_object')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Temporary lists to store results\n",
    "rel_areas = []\n",
    "best_omegas = []\n",
    "iters_list = []\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "img = ax.imshow(np.rot90(c, 1), interpolation='nearest')\n",
    "\n",
    "Nt = 30\n",
    "omega_range = np.linspace(0.5, 2.0, 16)\n",
    "\n",
    "def simulate_and_animate(m):\n",
    "    # Barrier object\n",
    "    objects = np.zeros((Nx, Nx))\n",
    "    objects[((Nt-m)*Nx//Nt):Nx, (Nx//Nt):Nx] = 1\n",
    "\n",
    "    c_sink, best_omega, iters = find_best_omega_with_objects(omega_range, objects, Nx, epsilon, max_iterations=1_000, object_type='sink')\n",
    "    best_omegas.append(best_omega)\n",
    "    iters_list.append(iters)\n",
    "    fig.suptitle(f'Iterations = {iters}, optimal $\\\\omega$ = {best_omega}')\n",
    "    img.set_data(np.rot90(c_sink, 1))\n",
    "    plt.xlabel('x')\n",
    "    plt.ylabel('y')\n",
    "    return img,\n",
    "\n",
    "anim = FuncAnimation(fig, simulate_and_animate, frames=Nt, interval=250)\n",
    "anim.save(f'{SAVE_PATH}/sink_object_dynamic_best_omega.gif', writer=ANIM_BACKEND)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x350 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "length = np.linspace(0, Nx-4, len(best_omegas)-1) \n",
    "fig, ax = plt.subplots(figsize=(5, 3.5), layout='tight')\n",
    "ax2 = ax.twinx()\n",
    "ax.plot(length, best_omegas[:-1], 'tab:blue', label='Optimal $\\\\omega$', marker='o')\n",
    "ax2.plot(length, iters_list[:-1], 'tab:orange', label='Iterations $k$', marker='o')\n",
    "ax.set_xlabel('Length of blocking sink object')\n",
    "ax.set_ylabel('Optimal $\\\\omega$')\n",
    "ax2.set_ylabel('Iterations $k$')\n",
    "ax.grid(True)\n",
    "\n",
    "# Merge legends into one\n",
    "lines, labels = ax.get_legend_handles_labels()\n",
    "lines2, labels2 = ax2.get_legend_handles_labels()\n",
    "ax.legend(lines + lines2, labels + labels2, loc='upper right')\n",
    "\n",
    "plt.title('Optimal $\\\\omega$ and iterations $k$ for various length of blocking sink object')\n",
    "plt.savefig(f'{SAVE_PATH}/sink_object_omega_iterations.png', dpi=300, bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Optional. (1 point) Think of a way to incorporate objects with insulating material in your domain. What changes in the time evolution of the system? And in the ﬁnal state?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Simulating SOR with insulator:   0%|          | 0/10000 [00:00<?, ?iteration/s]"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Simulating SOR with insulator:  11%|█         | 1096/10000 [00:00<00:04, 2082.82iteration/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged in 1097 iterations\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAe4AAAGGCAYAAAC9sGJhAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy81sbWrAAAACXBIWXMAAA9hAAAPYQGoP6dpAABTeklEQVR4nO3de1hU1foH8O8Ml+GOispFETHvImpghuZdMG+Z2UmPHu+WhqmIlZIlaCZKpdTPW5aX0ynTU2plmYqWqKmJdzPzlKGggngFRLnNrN8fHuY4MIOzh2E2M/P9PM88j+7Zs/ZaM5t5Z6317rUVQggBIiIisgpKuStARERExmPgJiIisiIM3ERERFaEgZuIiMiKMHATERFZEQZuIiIiK8LATUREZEUYuImIiKwIAzcREZEVkRy4f/nlFwwZMgSNGjWCSqWCr68vIiIiMHPmTJ39VqxYgfXr15urnibp0aMHevToYdFjbtiwAcnJyVUqoya8d9bu3r17SEhIwN69e6ul/N9++w0JCQm4ePFihefGjh2Lxo0bV8txq8P69euhUCh02mLoPL548SIUCgXee+89y1VQBgsXLsTXX38tdzVMlpCQAIVCYZFj6Tt/5NK4cWOMHTvWpNda02cuKXB///336Ny5M/Ly8pCUlIRdu3bhgw8+QJcuXbBp0yadfe01+DBw1wz37t3DvHnzqjVwz5s3T++X1VtvvYWtW7dWy3Grw4ABA3Do0CH4+/trt5njPLZm1vQlLjd95481sqbP3FHKzklJSQgODsbOnTvh6Pi/lw4fPhxJSUlmrxyRpdy7dw9ubm5mKeuxxx4zSzmWUq9ePdSrV0/uapjs/v37cHV1lbsaNq2yvw9rP3+qU0lJCRQKhU68NAshQZs2bUSnTp0euV9QUJAAoPMICgrSPp+bmytmzpwpGjduLJycnERAQICYPn26uHv3rk45y5YtE127dhX16tUTbm5uIiQkRCxevFgUFxfr7KfRaMTixYtFo0aNhEqlEh06dBDbt28X3bt3F927dxdCCJGfny+8vb3FSy+9VKG+6enpQqlUiqSkpErblZOTI1588UXRsGFD4ezsLOrWrSs6d+4sUlJShBBCdO/evUK7H36LExISxBNPPCFq164tPD09RYcOHcQnn3wiNBqN2d87Q3744QfRq1cv4eXlJVxdXUXLli3FwoULdfb55ptvxJNPPilcXV2Fh4eH6NOnjzh48KDOPvHx8QKA+PXXX8Xw4cOFl5eXqF+/vhg3bpy4c+eOzr5qtVp8+OGHol27dsLFxUV4e3uLTp06iW+++UZnv40bN4onn3xSuLm5CXd3dxEVFSWOHz+us8+YMWOEu7u7+OOPP0S/fv2Eu7u7aNiwoYiNjRWFhYVCiAefp77PYcyYMTp1P3bsmBg6dKioVauW8PPzE0IIkZaWJoYNGyaCgoKEi4uLCAoKEsOHDxcXL17U1mHdunV6y1+3bp22jg9/ZkIIcf/+fTF79mydzy06Olrcvn1bZ7+goCAxYMAA8cMPP4gOHToIFxcX0aJFC7FmzZrKP1ghRHh4uOjfv7/OtpCQEAFAHDlyRLtt8+bNAoA4ffq0TnvS09OFEJWfx2Xv7bvvvivef/990bhxY+Hu7i6efPJJcejQoUfWMScnR7z88suiVatWwt3dXdSrV0/07NlT7Nu375Gvffj92bx5s2jfvr1QqVRi1qxZQgghsrKyxEsvvSQaNGggnJycROPGjUVCQoIoKSnRKaOwsFDMmzdPtGzZUqhUKlGnTh3Ro0cP8fPPPwshhN62l32PGFt/qe/T6tWrRbNmzYSzs7No1aqV+PzzzyucRz/99JMAIH766Se9xyo7/4T43zn+sI0bN4rIyEjh5+cnXFxcRMuWLcWsWbMqfHeU/Y2dPn1aREZGCg8PD/Hkk08a/EzKnz9CPDiH2rRpI44cOSKeeuop4erqKoKDg0ViYqJQq9Xa/dRqtXj77bdF8+bNtd8Nbdu2FcnJyTr1Kf/3ZKiNQUFB2r9zIR783cXGxop27doJLy8vUbt2bfHkk0+Kr7/+Wud1lX3mQghx5swZ8cwzz4hatWoJlUol2rVrJ9avX69TRtnn8+mnn4rY2FgREBAgFAqFOHfunMH3zlSSfgZERETgk08+wbRp0zBy5Eg8/vjjcHJyqrDf1q1b8fzzz8Pb2xsrVqwAAKhUKgAPfrl1794dly9fxhtvvIHQ0FCcPXsWc+fOxZkzZ7B7927t3MyFCxcwYsQIBAcHw9nZGadOncI777yD33//HWvXrtUeb968eZg3bx4mTJiA559/HpmZmXjxxRehVqvRokULAICHhwfGjx+P1atXIykpCd7e3trXr1ixAs7Ozhg/fnyl7R81ahSOHz+Od955B82bN8edO3dw/Phx3Lx5U1vOSy+9hAsXLugdKr148SImTZqERo0aAQAOHz6MqVOn4sqVK5g7d65Z3zt91qxZgxdffBHdu3fHqlWrUL9+ffznP//Br7/+qt1nw4YNGDlyJKKiovDFF1+gqKgISUlJ6NGjB/bs2YOnnnpKp8yhQ4di2LBhmDBhAs6cOYO4uDgA0Pl8xo4di88++wwTJkzA/Pnz4ezsjOPHj+sMMy9cuBBvvvkmxo0bhzfffBPFxcV499130bVrVxw5cgStW7fW7ltSUoJnnnkGEyZMwMyZM7Fv3z68/fbb8Pb2xty5c+Hv748dO3bg6aefxoQJEzBx4kQAqNAreO655zB8+HBMnjwZBQUF2s+oRYsWGD58OOrUqYOsrCysXLkSHTt2xG+//Ya6detiwIABWLhwId544w0sX74cjz/+OADDPW0hBJ599lns2bMHcXFx6Nq1K06fPo34+HgcOnQIhw4d0n7GAHDq1CnMnDkTs2fPhq+vLz755BNMmDABTZs2Rbdu3Qx+vn369MGyZctQUlICJycnXLt2Db/++itcXV2RkpKCjh07AgB2794NX19ftG3bVm85jzqPAWD58uVo2bKldjj9rbfeQv/+/ZGenq7zt1XerVu3AADx8fHw8/PD3bt3sXXrVu35ZUxOyvHjx3Hu3Dm8+eabCA4Ohru7O7Kzs/HEE09AqVRi7ty5eOyxx3Do0CEsWLAAFy9exLp16wAApaWl6NevH/bv34+YmBj06tULpaWlOHz4MDIyMtC5c2ccOnQIvXr1Qs+ePfHWW28BALy8vEyqvzHv0+rVqzFp0iQMHToUS5cuRW5uLubNm4eioqJHvhdS/PHHH+jfvz9iYmLg7u6O33//HYsXL8aRI0fw448/6uxbXFyMZ555BpMmTcLs2bNRWloq+XjZ2dkYOXIkZs6cifj4eGzduhVxcXEICAjA6NGjATwYxU1ISMCbb76Jbt26oaSkBL///jvu3LljjiajqKgIt27dwquvvooGDRqguLgYu3fvxnPPPYd169Zp61HZZ37+/Hl07twZ9evXx4cffggfHx989tlnGDt2LK5du4bXX39d55hxcXGIiIjAqlWroFQqUb9+fbO0RYeUKH/jxg3x1FNPaX+RODk5ic6dO4vExESRn5+vs2+bNm10frGUSUxMFEqlUqSlpels/+qrrwQAsX37dr3HVqvVoqSkRHz66afCwcFB3Lp1SwghxO3bt4WLi4sYMmSIzv4///xzhV9NFy5cEEqlUixdulS77f79+8LHx0eMGzfuke338PAQMTExle4zYMAAvb8ODbVn/vz5wsfHR6fXbe73TogHIw5eXl7iqaee0jlW+ToFBASItm3b6vwqzs/PF/Xr1xedO3fWbiv7tVt+lCI6Olq4uLhoj7Fv3z4BQMyZM8dg3TIyMoSjo6OYOnVqhTr7+fmJF154QbttzJgxAoD497//rbNv//79RYsWLbT/v379ugAg4uPjKxyvrO5z5841WKcypaWl4u7du8Ld3V188MEH2u1ffvml3t5PWR0fPgd27Nih973atGmTACBWr16t3VbW07906ZJ22/3790WdOnXEpEmTKq3r7t27BQBt7++zzz4Tnp6eIjo6WvTs2VO7X7NmzcSIESO0/9fXYzJ0Hpf17tq2bStKS0u1248cOSIAiC+++KLSOpZXWloqSkpKRO/evSv8DesTFBQkHBwcxPnz53W2T5o0SXh4eOi8b0II8d577wkA4uzZs0IIIT799FMBQHz88ceVHsfd3V2n5ya1/sa+T2q1Wvj5+VUYybx06ZJwcnIya4/7YRqNRpSUlIjU1FQBQJw6dUr7XNnf2Nq1ax/ZfiEM97gBiF9++UVn39atW4u+fftq/z9w4EDRvn37SsuvSo+7vLLPa8KECaJDhw46zxn6zIcPHy5UKpXIyMjQ2d6vXz/h5uamHWEs+3y6detWaXvMQVJymo+PD/bv34+0tDQsWrQIgwcPxn/+8x/ExcWhbdu2uHHjxiPL+O677xASEoL27dujtLRU++jbty8UCoVOMtGJEyfwzDPPwMfHBw4ODnBycsLo0aOhVqvxn//8B8CDX0qFhYUYOXKkznE6d+6MoKAgnW1NmjTBwIEDsWLFCoj/3oZ8w4YNuHnzJl555RXgwVmgU6+Hf2k+8cQTWL9+PRYsWIDDhw+jpKREytuHH3/8EX369IG3t7e2PXPnzsXNmzeRk5Nj1veuvIMHDyIvLw/R0dEGe+Xnz5/H1atXMWrUKCiV/zs1PDw8MHToUBw+fBj37t3Tec0zzzyj8//Q0FAUFhZq2/PDDz8AAKZMmWKwbjt37kRpaSlGjx6t0y4XFxd07969QrsUCgUGDRpU4biXLl0yeAx9hg4dWmHb3bt3MWvWLDRt2hSOjo5wdHSEh4cHCgoKcO7cOUnllynrzZTPdv3b3/4Gd3d37NmzR2d7+/bttaMyAODi4oLmzZs/sn1dunSBi4sLdu/eDQBISUlBjx498PTTT+PgwYO4d+8eMjMz8ccff6BPnz4mtaXMgAED4ODgoP1/aGgoABj1GaxatQqPP/44XFxc4OjoCCcnJ+zZs8fo9zc0NBTNmzfX2fbdd9+hZ8+eCAgI0DmH+vXrBwBITU0F8OB8dHFxeeTomrnq/6j36fz588jOzsYLL7yg87pGjRqhS5cuJtdRn7/++gsjRoyAn5+f9vune/fuAKC37vr+PqTw8/PDE088obOt/N/pE088gVOnTiE6Oho7d+5EXl5elY6pz5dffokuXbrAw8ND+3mtWbPG6PPtxx9/RO/evREYGKizfezYsbh37x4OHTqks72q75sxTLqOOzw8HLNmzcKXX36Jq1evYsaMGbh48aJRCWrXrl3D6dOn4eTkpPPw9PSEEEIb/DMyMtC1a1dcuXIFH3zwgfYHw/LlywE8SEgBoB2m9vPzq3AsfdumT5+OP/74AykpKQAeDGVFRERohztTU1Mr1K1sSHfTpk0YM2YMPvnkE0RERKBOnToYPXo0srOzH9nuI0eOICoqCgDw8ccf4+eff0ZaWhrmzJmj0x5zvHf6XL9+HQDQsGFDg/uUvZf6skMDAgKg0Whw+/Ztne0+Pj46/y8b8i1rz/Xr1+Hg4KD3s3i4XQDQsWPHCm3btGlThXa5ubnBxcWlwnELCwsNHkMffe0cMWIEli1bhokTJ2Lnzp04cuQI0tLSUK9ePaM+I31u3rwJR0fHCkP1CoUCfn5+2ve9TPn3FHjQvkcd38XFBV26dNEG7j179iAyMhI9evSAWq3G/v37ted9VQP3oz53Q5YsWYKXX34ZnTp1wubNm3H48GGkpaXh6aefNvr91fe5Xbt2Ddu2batw/rRp0wYAtOfQ9evXERAQoPPDVAqp9X/U+1T22fv6+lZ4rb5tprp79y66du2KX375BQsWLMDevXuRlpaGLVu26NSnjJubm3ao2FTGnMdxcXF47733cPjwYfTr1w8+Pj7o3bs3jh49WqVjl9myZQteeOEFNGjQAJ999hkOHTqEtLQ0jB8/3ujvi5s3bxr8Tix7/mGWyK6vcqqbk5MT4uPjsXTpUp25UkPq1q0LV1dXnTnQ8s8DwNdff42CggJs2bJFp+d88uRJnf3LTg59wTM7O7vC9bS9evVCSEgIli1bBg8PDxw/fhyfffaZ9vmwsDCkpaXpvKbsA6pbty6Sk5ORnJyMjIwMfPvtt5g9ezZycnKwY8eOStu9ceNGODk54bvvvtMJOlIuPzD2vdOnLGhcvnzZ4D5l72VWVlaF565evQqlUonatWsbXd+y46rVamRnZxs8ocvq/dVXX1UYJalO5UcecnNz8d133yE+Ph6zZ8/Wbi+bJzOVj48PSktLcf36dZ3gLYRAdna2du7ZHHr37o25c+fiyJEjuHz5MiIjI+Hp6YmOHTsiJSUFV69eRfPmzSv0Hizls88+Q48ePbBy5Uqd7fn5+UaXoW/EqG7duggNDcU777yj9zVlf8P16tXDgQMHoNFoTAre5qj/w8r+5sp+vD6s/Hda2fdG+blvY0Y6f/zxR1y9ehV79+7V9rIBGJxLttQ14I6OjoiNjUVsbCzu3LmD3bt344033kDfvn2RmZmp/ZGub77fmHZ/9tlnCA4OxqZNm3TaJCV/wMfHx+B3IlDxe9cS752kM1df5YH/DbOU/XEAhnsIAwcOxIULF+Dj44Pw8PAKj7JAW9b4h5N2hBD4+OOPdcp78skn4eLigs8//1xn+8GDBw0O202bNg3ff/894uLi4Ovri7/97W/a5zw9PSvUydnZuUIZjRo1wiuvvILIyEgcP378ke0uuyTg4WGz+/fv41//+leFfav63unTuXNneHt7Y9WqVdppgvJatGiBBg0aYMOGDTr7FBQUYPPmzYiIiJB8yVTZUGX5L7qH9e3bF46Ojrhw4YLedoWHh0s6JmB8D/BhCoUCQgidcw4APvnkE6jVapPL7927NwDo/EAEgM2bN6OgoED7vDn06dMHpaWleOutt9CwYUO0bNlSu3337t3a6ZpHMaaHbwqFQlHh/T19+nSF4UapBg4ciF9//RWPPfaY3vOn7LupX79+KCwsfOQ6CZX9HZuz/i1atICfnx/+/e9/62zPyMjAwYMHdbaV/X2fPn1aZ/u33377yOPo+z4FgI8++khqlatNrVq18Pzzz2PKlCm4deuWdqSzcePGyMnJ0flxU1xcjJ07dz6yTIVCAWdnZ51gmp2djW+++abCvoY+8969e2t/+Dzs008/hZubG5588kljm2g2knrcffv2RcOGDTFo0CC0bNkSGo0GJ0+exPvvvw8PDw9Mnz5du2/btm2xceNGbNq0CU2aNIGLiwvatm2LmJgYbN68Gd26dcOMGTMQGhoKjUaDjIwM7Nq1CzNnzkSnTp0QGRkJZ2dn/P3vf8frr7+OwsJCrFy5ssJQbe3atfHqq69iwYIFmDhxIv72t78hMzMTCQkJBodn//GPfyAuLg779u3Dm2++qTcwl5ebm4uePXtixIgRaNmyJTw9PZGWloYdO3bgueee02n3li1bsHLlSoSFhUGpVCI8PBwDBgzAkiVLMGLECLz00ku4efMm3nvvvQp/SOZ47/Tx8PDA+++/j4kTJ6JPnz548cUX4evriz///BOnTp3CsmXLoFQqkZSUhJEjR2LgwIGYNGkSioqK8O677+LOnTtYtGjRI9+n8rp27YpRo0ZhwYIFuHbtGgYOHAiVSoUTJ07Azc0NU6dORePGjTF//nzMmTMHf/31F55++mnUrl0b165dw5EjR+Du7o558+ZJOq6npyeCgoLwzTffoHfv3qhTpw7q1q1b6Y8bLy8vdOvWDe+++65239TUVKxZswa1atXS2TckJATAg4xgT09PuLi4IDg4WO/wYGRkJPr27YtZs2YhLy8PXbp00WaVd+jQAaNGjZLUtsqEhYWhdu3a2LVrF8aNG6fd3qdPH7z99tvafz+KofO4qgYOHIi3334b8fHx6N69O86fP4/58+cjODjYpMzlMvPnz0dKSgo6d+6MadOmoUWLFigsLMTFixexfft2rFq1Cg0bNsTf//53rFu3DpMnT8b58+fRs2dPaDQa/PLLL2jVqhWGDx+ubf/evXuxbds2+Pv7w9PTEy1atDB7/ZVKJebNm4dJkybh+eefx/jx43Hnzh3MmzcP/v7+OqMCfn5+6NOnDxITE1G7dm0EBQVhz5492uHuynTu3Bm1a9fG5MmTER8fDycnJ3z++ec4deqU5Dqb06BBgxASEoLw8HDUq1cPly5dQnJyMoKCgtCsWTMAwLBhwzB37lwMHz4cr732GgoLC/Hhhx9W+DGtz8CBA7FlyxZER0drrzh6++234e/vjz/++ENnX0OfeXx8vDaHYu7cuahTpw4+//xzfP/99xWuULIYKZlsmzZtEiNGjBDNmjUTHh4ewsnJSTRq1EiMGjVK/Pbbbzr7Xrx4UURFRQlPT88K1yLfvXtXvPnmm6JFixbC2dlZe+3ejBkzRHZ2tna/bdu2aa/9bdCggXjttdfEDz/8UCGzUqPRiMTERBEYGCicnZ1FaGio2LZtm8513OWNHTtWODo6isuXLxvV9sLCQjF58mQRGhqqvQa6RYsWIj4+XhQUFGj3u3Xrlnj++edFrVq1hEKh0Ml6XLt2rWjRooVQqVSiSZMmIjExUaxZs6ZCRqY53jtDyq5vd3d3F25ubqJ169Zi8eLFOvt8/fXXolOnTsLFxUW4u7uL3r17a69xLVOW0Xn9+nWd7foyTNVqtVi6dKkICQnR1jkiIkJs27atwnF79uwpvLy8hEqlEkFBQeL5558Xu3fv1u5Tdo1pefoyTHfv3i06dOggVCqV3uu4y9ddCCEuX74shg4dqr3W/umnnxa//vqr3mzV5ORkERwcLBwcHIy6jnvWrFkiKChIODk5CX9/f/Hyyy8bvI67vMrO5fKGDBkiAIjPP/9cu624uFi4u7sLpVJZ4Zj6PjND5/HD1yeXBwNZ/A8rKioSr776qmjQoIFwcXERjz/+uPj6668NZg6XZ+j9EeLBlQTTpk0TwcHBwsnJSdSpU0eEhYWJOXPm6FyrfP/+fTF37lztddM+Pj6iV69eOmsVnDx5UnTp0kW4ubnpXJ1ibP2lvk+rV68WTZs2Fc7OzqJ58+Zi7dq1YvDgwRUyn7OyssTzzz8v6tSpI7y9vcU//vEPcfToUaOyyg8ePCgiIiKEm5ubqFevnpg4caI4fvx4hdca+hszpLLruMsr/z69//77onPnzqJu3brC2dlZNGrUSEyYMEFn3QQhHnxvtW/fXri6uoomTZqIZcuWGZ1VvmjRItG4cWOhUqlEq1atxMcff6z3tYY+cyEeXMc9aNAg4e3tLZydnUW7du103jMh/pdV/uWXXz76TasihRAGxk1tWHFxMRo3boynnnqqwhAVEZHc7ty5g+bNm+PZZ5/F6tWr5a4O1TBmXoetZrt+/TrOnz+PdevW4dq1azoJSEREcsjOzsY777yDnj17wsfHB5cuXcLSpUuRn5+vM/1IVMauAvf333+PcePGwd/fHytWrNBeAkZEJBeVSoWLFy8iOjoat27d0iY8rVq1Sns5G9HD7HKonIiIyFqZtgoBERGRFdq3bx8GDRqEgIAAKBQKo9bSSE1NRVhYGFxcXNCkSROsWrWq+itaCQZuIiKyGwUFBWjXrh2WLVtm1P7p6eno378/unbtihMnTuCNN97AtGnTsHnz5mquqWEcKiciIrukUCiwdetWPPvsswb3mTVrFr799ludtc0nT56MU6dOVXnhIFPZVXKapWk0Gly9ehWenp4WW0KQiMjchBDIz8+v0jrvlSksLERxcbHJrxdCVPiOValUehe4kurQoUPa+0yU6du3L9asWaO9ha6lMXBXo6tXr8q2JjQRkbllZmZWeqMiUxQWFiI4yAPZOY9eCc0QDw8P3L17V2dbfHw8EhISqli7B5frlb/hi6+vL0pLS3Hjxg2L3FSkPAbuauTp6QkAuHS8Mbw8mE5ARNYp764GQY9f1H6nmVNxcTGyc9S4dKwxvDylf0/m5WsQFHYRmZmZOnc0M0dvu0z53nzZDLNcI6kM3NWo7EP18lCadEISEdUk1RmoPDwV8PCUXr4G//2e9fKq8q1I9fHz86twp7acnBw4OjrqvTeBJTBwExGR7NRCA7UJqdJqoTF/ZR4SERGBbdu26WzbtWsXwsPDZZnfBng5GBER1QAaCJMfUty9excnT57EyZMnATy43OvkyZPIyMgAAMTFxWH06NHa/SdPnoxLly4hNjYW586dw9q1a7FmzRq8+uqrZmu7VOxxExGR7DTQwJS+s9RXHT16FD179tT+PzY2FgAwZswYrF+/HllZWdogDgDBwcHYvn07ZsyYgeXLlyMgIAAffvghhg4dakJtzYPXcVejvLw8eHt74+Lv/lYxx60x06kwPLCzWcqxNhszD5qlHKUVXTroAOupK5kuL1+DwJZXkZuba/Z55LLvyczfG5icnBbY8kq11K2mqvnRhIiIiLQ4VE5ERLIzZb667HX2hoGbiIhkp4GAmoHbKAzcREQkO/a4jcfATUREslMLAbUJCbKmvMbaMXBbQJ5GDaGpvpPLlEUL9JF6KYaaGcU6rhv4jB0k9gjMmTHqUM0fEbNb7UO+pnoXOQEefP+YdjmY/WHgJiIi2alNnOM25TXWjj+YiYiIrAh73EREJDu1MG3az1xThdaEgZuIiGTHOW7jMXATEZHsNFCYlPCqscMkWQZuC8jVOEKtqVo6gUZIPzml/hEY2l8j9NedWeW6rqtd9W43lFWuVOjvK0jNQpe6/4Njm2d80ZRjk/W5q6n+v3WNePAw5XX2hoGbiIhkpzaxx22PHQhmlRMREVkR9riJiEh27HEbj4GbiIhkpxEKk3J5THmNtWPgJiIi2bHHbTwGbiIikp0aSqhNSLtSV0NdajoGbgvI1bigtMqXg5lyQuv/Jao2UJbGwB9NsXCQtL+9uq720rtdaWCJCGeF/q8cQ/s7mOnyMcDwpWhSOVhg+QtecvZo1d3rLLDATUaEiUPlwg6HyvnNS0REZEXY4yYiItlxjtt4DNxERCQ7tVAanMar/HXVUJkajoGbiIhkp4HCpLwZjR3mQDBwExGR7DhUbjwGbgu4q1FBo9HNzJY6JFTZL1FDZUm/aYj+7YUaJ/3bhf7tXU8X6t0OAPlqF73bizT6T8VSjaGMdml/rEoDv8odlfozu1XKUoNleTrob9+Vktp6t7soSvRvV+rfbihT25SbkhjKRDeUuS61HHNi9nj1MEdgu6ep/ouuTB8qt7/zhlnlREREVoQ9biIikt2DOW7ej9sYDNxERCQ7jYkrpzE5jYiISAac4zYeAzcREclOAyUvBzMSA7cF5GrcUKzWfavVEtfXNS2r3MCa5AaOXSL0nw4lBtYqN5htbmA7AINrthuqk6H5K6nvn6FpMEPHrWxt+UKF/vbllrrp3V5kIHvcUKauk0J/RrtSof8LqrL1ws2XVW6eL0dLrG0ulbnWba+MKfcaqG5ShqXvawxfZWEuaqGQ/ncNE74LbEDNO5uIiIjIIPa4iYhIdqbf1pND5URERBanEUqTphQ0TE4jIiKyPPa4jcfATUREstPAtESzmpfuWP0YuC3gjtoNRWrj3mrD64gbPqGlvsbQ/oayxw1uN7COuKF1xysrq1TiMaTSGPpRbkp6poFlmw1lqBcZyNZ3UhjKKte/3ZS1yqW+xlwZ1ubMHjeUTU//Y+jcM4W+Xu99dfVnlZt+OZj95VjbX4uJiIisGHvcREQkO9NXTrO//icDNxERyY43GTEeAzcREcmOPW7jMXATEZHsTL8cjIGbqkFeqSuKSw2v3/0wU4Z9DP3iNFSWoUxtQ38AhtbtlpohXtmxq3utckNrbWvUBt4jheE2lCr1Z30bej+cDKxJ7qg0lPGtf7uTgeMqK8kqN7RWuSGVlWWO8is9tgXWDLdH5lgnvVCtf719c9IIhUnZ8ebMqLcW9vdThYiIyIqxx01ERLLTmDhUbo/XcTNwExGR7Exfq5yBm4iIyOLUUFS6QmRlr7M39vdTxYDExEQoFArExMRotwkhkJCQgICAALi6uqJHjx44e/asfJUkIrJRZT1uUx72hj1uAGlpaVi9ejVCQ0N1ticlJWHJkiVYv349mjdvjgULFiAyMhLnz5+Hp6en0eUXqFUoVetmlUudy6ksc9LQc4aOYTCD2+Aa5obKMZCFXskfkqFscENlmStj1NBKy4bWwa4sw9lQ+xwNZKIXGSjLSaN/u6FjKw0suF7ZuuCG2ycxe1zi2uOWWF/cnBnt1sIS1yzr+5srKq3+UKGGab1nA7cOsGn291OlnLt372LkyJH4+OOPUbt2be12IQSSk5MxZ84cPPfccwgJCcE///lP3Lt3Dxs2bJCxxkREZM/sPnBPmTIFAwYMQJ8+fXS2p6enIzs7G1FRUdptKpUK3bt3x8GDBy1dTSIim2bJofIVK1YgODgYLi4uCAsLw/79+yvd//PPP0e7du3g5uYGf39/jBs3Djdv3jS1qVVm14F748aNOH78OBITEys8l52dDQDw9fXV2e7r66t9rryioiLk5eXpPIiI6NHKljw15SHFpk2bEBMTgzlz5uDEiRPo2rUr+vXrh4yMDL37HzhwAKNHj8aECRNw9uxZfPnll0hLS8PEiRPN0WyT2G3gzszMxPTp0/HZZ5/BxcXF4H4Khe6cixCiwrYyiYmJ8Pb21j4CAwPNWmciIlsl/nuTEakPIXFefMmSJZgwYQImTpyIVq1aITk5GYGBgVi5cqXe/Q8fPozGjRtj2rRpCA4OxlNPPYVJkybh6NGj5mi2Sew2cB87dgw5OTkICwuDo6MjHB0dkZqaig8//BCOjo7annb53nVOTk6FXniZuLg45Obmah+ZmZnV3g4iIltgiR53cXExjh07pjMFCgBRUVEGp0A7d+6My5cvY/v27RBC4Nq1a/jqq68wYMCAKrW3Kuw2q7x37944c+aMzrZx48ahZcuWmDVrFpo0aQI/Pz+kpKSgQ4cOAB586KmpqVi8eLHeMlUqFVQqVYXt+aWuKKrWtcrNk6ktdV3wUkPrjlfSBsMZ7dLaLXV/qVnOle1vMFPbwDrfjgbWGC+WWI4pGfCG1mg3ROpa5eZcX9wSmej2yBxXZhSrLZPNXpW1ystPTer7Pr5x4wbUarWkKdDOnTvj888/x7Bhw1BYWIjS0lI888wz+L//+z/JdTUXu+1xe3p6IiQkROfh7u4OHx8fhISEaK/pXrhwIbZu3Ypff/0VY8eOhZubG0aMGCF39YmI6CGBgYE6U5X6cpfKSJkC/e233zBt2jTMnTsXx44dw44dO5Ceno7Jkyebtf5S2G2P2xivv/467t+/j+joaNy+fRudOnXCrl27JF3DTUREj1bV23pmZmbCy8tLu13f6GfdunXh4OAgaQo0MTERXbp0wWuvvQYACA0Nhbu7O7p27YoFCxbA399fcp2rioH7IXv37tX5v0KhQEJCAhISEmSpDxGRvajqULmXl5dO4NbH2dkZYWFhSElJwZAhQ7TbU1JSMHjwYL2vuXfvHhwddUOlg8ODaUIh5JneYeAmIiLZaaA06U5fUl8TGxuLUaNGITw8HBEREVi9ejUyMjK0Q99xcXG4cuUKPv30UwDAoEGD8OKLL2LlypXo27cvsrKyEBMTgyeeeAIBAQGS62sODNxERCQ7tVAYTIR91OukGDZsGG7evIn58+cjKysLISEh2L59O4KCggAAWVlZOtd0jx07Fvn5+Vi2bBlmzpyJWrVqoVevXgaTlC1BIeTq69uBvLw8eHt7Y8LeF+DswazySo9th1nlhjK+mVVO5mSWrPK7Jfi4+1fIzc195HC0VGXfk5P2DYXKyO/JhxXdLcFH3TZXS91qKva4LaBA7YQStbPONqm/Ek27T620AC01qEq9WYkpx5ZLpYHbYGA1dHMQ/T9wpN4ARGpAr4zUgFvdPwBMYY+B3hJ/J/r+RotL7fYCpBqJgZuIiGQnTFx3XPC2nkRERJanhsLE23rWrNE6S2DgJiIi2WmEaVMBBm5Tb9MYuImISHam3qLTlNdYOwZuIiKSXdndvkx5nb1h4LaAe2pnlJTqZpWb8/Inqb84zZVVbrg+hvcXEjPd5VJZVrRCYja4wWOYKau88mMYyHQ34+VxcpRjCaa83zXtPK6MlL/rEv1XNJJMGLiJiEh2llqAxRYwcBMRkew4x208Bm4iIpKdBibeZMSKpifMhYGbiIhkJ0xMThMM3ERERJZX1dt62hMGbgsoKHGGY0nFm7rrY8pJaChT2+AxzLReuKH9pdbHlGNXN1Oyn6s929yELGdDdZJ6bHPtbwprykSXS3X//ZSUVmvxJBEDNxERyY7JacZj4CYiItlxqNx4DNxERCQ7rpxmPAZuIiKSHXvcxmPgJiIi2TFwG4+B2wLulzrBsdTJqH0tkZFtMBu8mo8LmNa+mqa6M7UNvUOmZFdLPrYNrEluC1nocgYjfccuLbH+99SWMHATEZHs2OM2HgM3ERHJjoHbeAzcREQkOwHTMsTtcRCfgZuIiGTHHrfxGLiJiEh2DNzGY+C2gKJSR5SW6r7V5syulnriSl7bXOJYlDnbVt1Z6ObKojalLKXEpplSV3NlWNtCtjnpkvK9oS5VV2NNHmDgNp79LfJKRERkxdjjJiIi2bHHbTwGbiIikp0QCpOmxmxhUSepGLiJiEh2vMmI8Ri4iYhIdhwqNx4DtwUUlTrCoaRqWeXmPDml5vVaU5a4JZgrw1pqOeZ85+Raw1zuY9gjc/zNWSKrnEPlxmNWORERkRVhj5uIiGTHoXLjMXATEZHsOFRuPAZuIiKSnTCxx83ATUREJAMBQJiQn2iPKY0M3BZQVFIxq1yqmpjZbcofmfRjWM9a5YaPYa5y5FtX3XA5ZinGxGPb31e2XL1Li6xVDgUUvI7bKMwqJyIisiLscRMRkeyYnGY8Bm4iIpKdRiigsOHLwTQaDf7880/k5ORAo9HoPNetWzdJZTFwExGR7IQwMTnNClIdDh8+jBEjRuDSpUsQ5SqsUCigVkvLIWDgJiIi2dnyUPnkyZMRHh6O77//Hv7+/lBUMauTgZuIiGRny4H7jz/+wFdffYWmTZuapTwGbgsoLVFCU+JQtUJq4OVgBsuv1tJrrur++jDr5U/VfCmVnJeJSWWJy8qsIbiU0Tf0rCnmBUhV0alTJ/z5558M3EREZDtsOTlt6tSpmDlzJrKzs9G2bVs4OTnpPB8aGiqpPAZuIiKSnS0npw0dOhQAMH78eO02hUIBIQST04iIyDo9CNymzHFXQ2XMLD093azl2e3ExcqVKxEaGgovLy94eXkhIiICP/zwg/Z5IQQSEhIQEBAAV1dX9OjRA2fPnpWxxkREtqssOc2UR00XFBRU6UMquw3cDRs2xKJFi3D06FEcPXoUvXr1wuDBg7XBOSkpCUuWLMGyZcuQlpYGPz8/REZGIj8/X+aaExHZHlGFhzW4cOECpk6dij59+iAyMhLTpk3DhQsXTCrLbofKBw0apPP/d955BytXrsThw4fRunVrJCcnY86cOXjuuecAAP/85z/h6+uLDRs2YNKkSZKOpS51gCitalZ51V5u1CEs8cvVWv7KKlPNb5PhLGczHrja21C95VP10ZtVXtXvLzu3c+dOPPPMM2jfvj26dOkCIQQOHjyINm3aYNu2bYiMjJRUnt32uB+mVquxceNGFBQUICIiAunp6cjOzkZUVJR2H5VKhe7du+PgwYMy1pSIyDZZcqh8xYoVCA4OhouLC8LCwrB///5K9y8qKsKcOXMQFBQElUqFxx57DGvXrjX6eLNnz8aMGTPwyy+/YMmSJVi6dCl++eUXxMTEYNasWZLrb7c9bgA4c+YMIiIiUFhYCA8PD2zduhWtW7fWBmdfX1+d/X19fXHp0iWD5RUVFaGoqEj7/7y8vOqpOBGRrTF13FviazZt2oSYmBisWLECXbp0wUcffYR+/frht99+Q6NGjfS+5oUXXsC1a9ewZs0aNG3aFDk5OSgtLTX6mOfOncO///3vCtvHjx+P5ORkaQ2AnQfuFi1a4OTJk7hz5w42b96MMWPGIDU1Vft8+WXpylL3DUlMTMS8efOqrb5ERDbL1EQzia9ZsmQJJkyYgIkTJwIAkpOTsXPnTqxcuRKJiYkV9t+xYwdSU1Px119/oU6dOgCAxo0bSzpmvXr1cPLkSTRr1kxn+8mTJ1G/fn1JZQF2PlTu7OyMpk2bIjw8HImJiWjXrh0++OAD+Pn5AQCys7N19s/JyanQC39YXFwccnNztY/MzMxqrT8Rka0ou47blIexiouLcezYMZ1pUACIiooyOA367bffIjw8HElJSWjQoAGaN2+OV199Fffv3zf6uC+++CJeeuklLF68GPv378eBAwewaNEiTJo0CS+99JLxDfgvu+5xlyeEQFFREYKDg+Hn54eUlBR06NABwIMPPDU1FYsXLzb4epVKBZVKZanqEhHZjKquVV5+alLf9/GNGzegVqv1ToOW76iV+euvv3DgwAG4uLhg69atuHHjBqKjo3Hr1i2j57nfeusteHp64v3330dcXBwAICAgAAkJCZg2bZpRZTzMbgP3G2+8gX79+iEwMBD5+fnYuHEj9u7dix07dkChUCAmJgYLFy5Es2bN0KxZMyxcuBBubm4YMWKE5GNpSpVASRUHN+w147u661QDs58tclmqBdbn1nvYGvh+2yspPVVNac0fnA0MDNT5f3x8PBISEvTuK2UaVKPRQKFQ4PPPP4e3tzeAB8Ptzz//PJYvXw5XV9dH1k2hUGDGjBmYMWOG9pJiT0/PR77OELsN3NeuXcOoUaOQlZUFb29vhIaGYseOHdq0/Ndffx33799HdHQ0bt++jU6dOmHXrl1VerOJiMgAoTDtV+t/X5OZmQkvLy/tZn2jn3Xr1oWDg4OkaVB/f380aNBAG7QBoFWrVhBC4PLlyxXmrR/FHDHEbgP3mjVrKn1eoVAgISHB4C82IiIyn6quVV62CmZlnJ2dERYWhpSUFAwZMkS7PSUlBYMHD9b7mi5duuDLL7/E3bt34eHhAQD4z3/+A6VSiYYNGxo81uOPP449e/agdu3a6NChQ6WJzcePH6+03uXZbeAmIqIaxEKXg8XGxmLUqFEIDw9HREQEVq9ejYyMDEyePBnAgyTjK1eu4NNPPwUAjBgxAm+//TbGjRuHefPm4caNG3jttdcwfvz4SofJBw8erO31Dx48uNLALRUDNxERya6qyWnGGjZsGG7evIn58+cjKysLISEh2L59u3bN8KysLGRkZGj39/DwQEpKCqZOnYrw8HD4+PjghRdewIIFCyo9Tnx8vPbf5h65ZeAmIqKawUI5k9HR0YiOjtb73Pr16ytsa9myJVJSUkw+XpMmTZCWlgYfHx+d7Xfu3MHjjz+Ov/76S1J5DNyWUKIEHKuaVW6eqph2bKYCVwuZMrsfHFuez7TSFvM0qx7mOM2qelWMnbt48aLee24XFRXh8uXLkstj4CYiItlZaqjckr799lvtv3fu3KmTma5Wq7Fnzx4EBwdLLpeBm4iI5Geh5DRLevbZZwE8uEppzJgxOs85OTmhcePGeP/99yWXy8BNREQ1gAKmzZfU3B63RqMBAAQHByMtLQ1169Y1S7kM3EREJD8b7HGXSU9PN2t5DNxERCQ/Gw7cAFBQUIDU1FRkZGSguLhY5zmp65UzcFtCqeLBowoUciZgWMkfhtWRceFuIWdGu1Q1dyS05qjuj7OK31/27sSJE+jfvz/u3buHgoIC1KlTBzdu3ICbmxvq168vOXAzx5+IiORXtla5KY8absaMGRg0aBBu3boFV1dXHD58GJcuXUJYWBjee+89yeUxcBMRkewscT9uuZw8eRIzZ86Eg4MDHBwcUFRUhMDAQCQlJeGNN96QXB4DNxERyU9U4VHDOTk5adcq9/X11S6p6u3trbO8qrE4x01ERPKr4m09a7IOHTrg6NGjaN68OXr27Im5c+fixo0b+Ne//oW2bdtKLo89biIikp1CmP6o6RYuXAh/f38AwNtvvw0fHx+8/PLLyMnJwerVqyWXxx63BShKlFBUca3yGnly1sQ61UQ1sUMgY0Z7tauRfywS1bBepIJrlZtMCIF69eqhTZs2AIB69eph+/btVSqTnwYREcnPRue4hRBo1qyZSTcTMYSBm4iI5Gejl4MplUo0a9YMN2/eNF+ZZiuJiIjIVDba4waApKQkvPbaa/j111/NUh7nuImISH42vOTpP/7xD9y7dw/t2rWDs7MzXF1ddZ6/deuWpPIYuImISH42HLiXLl2qvY7bHBi4LUBZCihLqlhIDZ/HeZgtJPWawoo+Iihs+kMy0wdhSjG2+raWyl0B6zZ27Fizlsc5biIikp+NJqcBgIODA3Jycipsv3nzJhwcHCSXxx43ERHJztTFVKxh8EgYWFC9qKgIzs7Okstj4CYiIvnZ4Bz3hx9+CABQKBT45JNP4OHhoX1OrVZj3759aNmypeRyrS5wjx07FuPHj0e3bt3krgoREZFBS5cuBfCgx71q1SqdYXFnZ2c0btwYq1atklyu1QXu/Px8REVFITAwEOPGjcOYMWPQoEEDuatFRERVoICJQ+Vmr4n5pKenAwB69uyJLVu2oHbt2mYp1+qS0zZv3owrV67glVdewZdffonGjRujX79++Oqrr1BSUtXUbSIiIvP66aefzBa0ASvscQOAj48Ppk+fjunTp+PEiRNYu3YtRo0aBQ8PD/zjH/9AdHQ0mjVrJnc1tZSlCihLjfxdWIPna6pVTWu3CT/ja/Iv/4oM1Na6GkGWYuz3V1XY8G091Wo11q9fjz179iAnJwcajUbn+R9//FFSeVYZuMtkZWVh165d2LVrFxwcHNC/f3+cPXsWrVu3RlJSEmbMmCF3FYmIyBg2mJxWZvr06Vi/fj0GDBiAkJCQKi/GYnWBu6SkBN9++y3WrVuHXbt2ITQ0FDNmzMDIkSPh6ekJANi4cSNefvllBm4iImthw4F748aN+Pe//43+/fubpTyrC9z+/v7QaDT4+9//jiNHjqB9+/YV9unbty9q1apl8boREZFpbPk6bmdnZzRt2tRs5VldctrSpUtx9epVLF++XG/QBoDatWtrs/mIiMgK2PDdwWbOnIkPPvjA4EIsUlldj3vUqFFyV4GIiMhoBw4cwE8//YQffvgBbdq0gZOTk87zW7ZskVSe1QVua6QoARRGLkdrDcM+ZLusIEGXZKCwxJW2NjzHXatWLQwZMsRs5TFwExGR7Gx5jnvdunVmLc/q5riJiMgG2fDdwQCgtLQUu3fvxkcffYT8/HwAwNWrV3H37l3JZbHHTURE8rPhofJLly7h6aefRkZGBoqKihAZGQlPT08kJSWhsLBQ8nrl7HETEZHsyobKTXnUdNOnT0d4eDhu374NV1dX7fYhQ4Zgz549kstjj5uIiORnwz3uAwcO4Oeff65w7+2goCBcuXJFcnkM3BagKFVAWWLcPIw1/Hok22Ul04VkYcISa5XbMI1GA7VaXWH75cuXtSt+SsGhciIikp+pw+RW0NmJjIxEcnKy9v8KhQJ3795FfHy8ScugssdNRETys+Gh8qVLl6Jnz55o3bo1CgsLMWLECPzxxx+oW7cuvvjiC8nlMXATEZH8bDhwBwQE4OTJk9i4cSOOHTsGjUaDCRMmYOTIkTrJasZi4CYiItnZ8gIsAODq6opx48Zh3LhxVS6Lc9xERETVKDExEWvXrq2wfe3atVi8eLHk8tjjtgBlCaDkTySyAswdJn2EJdYqt2EfffQRNmzYUGF7mzZtMHz4cMyaNUtSeQzcREQkPxue487Ozoa/v3+F7fXq1UNWVpbk8tgPJCIi2dnyymmBgYH4+eefK2z/+eefERAQILk89riJiKhmsIIgbIqJEyciJiYGJSUl6NWrFwBgz549eP311zFz5kzJ5TFwExGR/Gx4qPz111/HrVu3EB0djeLiYgCAi4sLZs2ahbi4OMnl2e1QeWJiIjp27AhPT0/Ur18fzz77LM6fP6+zjxACCQkJCAgIgKurK3r06IGzZ8/KVGMiIttly0PlCoUCixcvxvXr13H48GGcOnUKt27dwty5c00qz2573KmpqZgyZQo6duyI0tJSzJkzB1FRUfjtt9/g7u4OAEhKSsKSJUuwfv16NG/eHAsWLEBkZCTOnz8vaX1ZZSmgdDByZys4CcmGMa2c9BClctfANnh4eKBjx45VLsduA/eOHTt0/r9u3TrUr18fx44dQ7du3SCEQHJyMubMmYPnnnsOAPDPf/4Tvr6+2LBhAyZNmiRHtYmIbJMND5UXFBRg0aJF2LNnD3JycqDRaHSe/+uvvySVZ7eBu7zc3FwAQJ06dQAA6enpyM7ORlRUlHYflUqF7t274+DBg3oDd1FREYqKirT/z8vLq+ZaExHZBkuunLZixQq8++67yMrKQps2bZCcnIyuXbs+8nU///wzunfvjpCQEJw8edLo402cOBGpqakYNWoU/P39oVBUbWiLgRsP5rJjY2Px1FNPISQkBMCD6+4AwNfXV2dfX19fXLp0SW85iYmJmDdvXvVWlojIFlmox71p0ybExMRgxYoV6NKlCz766CP069cPv/32Gxo1amTwdbm5uRg9ejR69+6Na9euSTrmDz/8gO+//x5dunSRVlkD7DY57WGvvPIKTp8+rfcuLeV/GQkhDP5aiouLQ25urvaRmZlZLfUlIrI5ogoPCZYsWYIJEyZg4sSJaNWqFZKTkxEYGIiVK1dW+rpJkyZhxIgRiIiIkHZAALVr19aO5pqD3QfuqVOn4ttvv8VPP/2Ehg0barf7+fkB+F/Pu0xOTk6FXngZlUoFLy8vnQcRET1aVbPK8/LydB4PT1uWKS4uxrFjx3SmQAEgKioKBw8eNFi3devW4cKFC4iPjzepbW+//Tbmzp2Le/fumfT68ux2qFwIgalTp2Lr1q3Yu3cvgoODdZ4PDg6Gn58fUlJS0KFDBwAPPvTU1FTJi8JLWqvcChItyIYxq5z0sIa1ygMDA3X+Hx8fj4SEBJ1tN27cgFqt1jsFWr6TVuaPP/7A7NmzsX//fjg6mhYy33//fVy4cAG+vr5o3LgxnJycdJ4/fvy4pPLsNnBPmTIFGzZswDfffANPT0/th+bt7Q1XV1coFArExMRg4cKFaNasGZo1a4aFCxfCzc0NI0aMkLn2REQ2popz3JmZmTqjnCqVyuBLjJ0CVavVGDFiBObNm4fmzZubULkHnn32WZNfq4/dBu6y+YwePXrobF+3bh3Gjh0L4MFqN/fv30d0dDRu376NTp06YdeuXZKu4SYiIiNUMXAbMz1Zt25dODg4GD0Fmp+fj6NHj+LEiRN45ZVXAAAajQZCCDg6OmLXrl3aJUwrY+oQuyF2G7iFePQZolAokJCQUGG4hYiIzMsSl4M5OzsjLCwMKSkpGDJkiHZ7SkoKBg8eXGF/Ly8vnDlzRmfbihUr8OOPP+Krr76qMMX6KMeOHcO5c+egUCjQunVr7TSsVHYbuImIqAax0OVgsbGxGDVqFMLDwxEREYHVq1cjIyMDkydPBvDg6qArV67g008/hVKp1F4iXKZ+/fpwcXGpsL0yOTk5GD58OPbu3YtatWpBCIHc3Fz07NkTGzduRL169SS1we6zyomISH6WWqt82LBhSE5Oxvz589G+fXvs27cP27dvR1BQEAAgKysLGRkZZm3b1KlTkZeXh7Nnz+LWrVu4ffs2fv31V+Tl5WHatGmSy1MIY8aMySR5eXnw9vZGm5cWwsHZxbgX8dMgOTGrnPRQFxfi7Oo3kJuba/bLXMu+J1u9shAOKiO/Jx+uW1Ehzi2rnrqZi7e3N3bv3l1hnfIjR44gKioKd+7ckVQeh8qJiEh+NrxWuUajqXAJGAA4OTlVWLfcGBwqJyIi+Vlo5TQ59OrVC9OnT8fVq1e1265cuYIZM2agd+/ekstj4CYiItkpqvCo6ZYtW4b8/Hw0btwYjz32GJo2bYrg4GDk5+fj//7v/ySXx6FyIiKSnw0PlQcGBuL48eNISUnB77//DiEEWrdujT59+phUHnvcREQkO0tllVvSjz/+iNatW2tv8RwZGYmpU6di2rRp6NixI9q0aYP9+/dLLpc9bgtQlggojTy7avJJSLZPWMO4I1mcKOEXkymSk5Px4osv6s129/b2xqRJk7BkyRKj7gX+MPa4iYhIfjaYnHbq1Ck8/fTTBp+PiorCsWPHJJfLHjcREdUMNTgIm+LatWt6LwMr4+joiOvXr0sulz1uIiKSnS3OcTdo0KDCWucPO336NPz9/SWXy8BNRETys8Gh8v79+2Pu3LkoLCys8Nz9+/cRHx+PgQMHSi6XQ+VERCQ7S9wdzNLefPNNbNmyBc2bN8crr7yCFi1aQKFQ4Ny5c1i+fDnUajXmzJkjuVwGbiIiomrg6+uLgwcP4uWXX0ZcXJz2dtIKhQJ9+/bFihUr9N4H/FEYuC1AWQIojbzMpib/eiTbx8vBSB9RYomDwCYXYAkKCsL27dtx+/Zt/PnnnxBCoFmzZqhdu7bJZTJwExGR7GxxqPxhtWvXrnB3MFMxcBMRkfxstMddHRi4iYhIfgzcRmPgJiIi2dn6ULk58TpuIiIiK8IetwU4lAg4GPuz0A5/PVINwqxy0scSNxnhULnRGLiJiEh2CiGgENKjsCmvsXYM3EREJD/2uI3GwE1ERLJjcprxGLiJiEh+7HEbjVnlREREVoQ9bgtQlFZcq9weh3fIenENc/umKa3+Y3Co3HgM3EREJD8OlRuNgZuIiGTHHrfxGLiJiEh+7HEbjYGbiIhqBHvsPZuCWeVERERWhD1uC3AoEXAoP57DX5ZkTZhVbteERdYqFw8eprzOzjBwExGR7JicZjwGbiIikh+T04zGwE1ERLJTaB48THmdvWHgJiIi+bHHbTRmlRMREVkR9rgtQFksoCyX+WiPN38n6yUUTCu3Z0oLZJUzOc14DNxERCQ/Xg5mNAZuIiKSHXvcxmPgJiIi+TE5zWgM3EREJDv2uI3HrHIiIiIrwh63BShLNVBCd5UAe/yVSNZL8IS1a8pSC6xywuQ0ozFwExGR7DhUbjwGbiIikh+T04zGwE1ERLJjj9t4DNxERCQ/jXjwMOV1dsZus8r37duHQYMGISAgAAqFAl9//bXO80IIJCQkICAgAK6urujRowfOnj0rT2WJiIj+y2573AUFBWjXrh3GjRuHoUOHVng+KSkJS5Yswfr169G8eXMsWLAAkZGROH/+PDw9PSUdy6FYAwdNuaxM+/uRSNaMS5XbNWGRrHJwjttIdhu4+/Xrh379+ul9TgiB5ORkzJkzB8899xwA4J///Cd8fX2xYcMGTJo0yZJVJSKyeQqYOMdt9prUfHY7VF6Z9PR0ZGdnIyoqSrtNpVKhe/fuOHjwoMHXFRUVIS8vT+dBRERGKLuO25SHRCtWrEBwcDBcXFwQFhaG/fv3G9x3y5YtiIyMRL169eDl5YWIiAjs3LmzKi2tMgZuPbKzswEAvr6+Ott9fX21z+mTmJgIb29v7SMwMLBa60lEZCvKsspNeUixadMmxMTEYM6cOThx4gS6du2Kfv36ISMjQ+/++/btQ2RkJLZv345jx46hZ8+eGDRoEE6cOGGGVpuGgbsSinL3IBZCVNj2sLi4OOTm5mofmZmZ1V1FIiLbIKrwkGDJkiWYMGECJk6ciFatWiE5ORmBgYFYuXKl3v2Tk5Px+uuvo2PHjmjWrBkWLlyIZs2aYdu2bSY10xzsdo67Mn5+fgAe9Lz9/f2123Nycir0wh+mUqmgUqmqvX5ERLZGIQQUJgx7l72m/NSkvu/j4uJiHDt2DLNnz9bZHhUVVek06MM0Gg3y8/NRp04dyXU1F/a49QgODoafnx9SUlK024qLi5GamorOnTvLWDMiItInMDBQZ6oyMTGxwj43btyAWq2WPA36sPfffx8FBQV44YUXzFJvU9htj/vu3bv4888/tf9PT0/HyZMnUadOHTRq1AgxMTHaIZGy4RE3NzeMGDFC8rGUxRooK1wOZofXMJD1qmSKiGyfRW4yovnvw5TXAcjMzISXl5d2c2Wjn1KnQct88cUXSEhIwDfffIP69eubUFnzsNvAffToUfTs2VP7/9jYWADAmDFjsH79erz++uu4f/8+oqOjcfv2bXTq1Am7du2SfA03ERE9WlWHyr28vHQCtz5169aFg4NDhd71o6ZBgQdJbRMmTMCXX36JPn36SK6nOdlt4O7RowdEJSeJQqFAQkICEhISLFcpIiJ7ZYEFWJydnREWFoaUlBQMGTJEuz0lJQWDBw82+LovvvgC48ePxxdffIEBAwaYUEnzstvATURENYiF7scdGxuLUaNGITw8HBEREVi9ejUyMjIwefJkAA+uDrpy5Qo+/fRTAA+C9ujRo/HBBx/gySef1PbWXV1d4e3tLb2+ZsDATUREsrPU3cGGDRuGmzdvYv78+cjKykJISAi2b9+OoKAgAEBWVpbONd0fffQRSktLMWXKFEyZMkW7vWxaVQ4M3EREZFeio6MRHR2t97nywXjv3r3VXyGJGLgtQFmihlKj1t3IrHKyJswqt2tKtfrRO1WVhYbKbQEDNxERyU6hefAw5XX2hoGbiIjkxx630Ri4iYhIfrwft9EYuImISHZVXYDFnnCtciIiIivCHrcFKIrVUDiU6m60w1+JZMWYVW7XFMwqr1EYuImISH4Cpt1kxP7iNgM3ERHJj3PcxmPgJiIi+QmYOFRu9prUeAzcREQkP85xG41Z5URERFaEPW4LUBSXQuHgoLtRY3+/EsmKKZlVbs8U6tJH71RVGgCmnGZc8pSIiMjymJxmPAZuIiKSH+e4jcbATURE8mPgNhoDNxERyY+B22jMKiciIrIi7HFbgKK4BAplud9IdvgrkawY1yq3awpNSfUfhFnlRmPgJiIi2TGr3HgM3EREJD/OcRuNgZuIiOSnEYDChCBsh4tZMXATEZH82OM2GrPKiYiIrAh73JZQXAIwq5ysGbPK7ZslssphYo/bDu/rycBNRETy41C50Ri4iYhIfhoBk3rPTE4jIiKSgdA8eJjyOjvDwE1ERPLjULnRmFVORERkRdjjtgBRVAKhLJeVa4fDO2TFFPyNb8+ERdYq5xy3sRi4iYhIfhwqNxoDNxERyU/AxMBt9prUeAzcREQkP/a4jcbATURE8tNoYNLNtTX2ly/EjBMiIiIrwh43ERHJj0PlRmPgtoTiogr3mRV2eLKR9VLwJiP2TRRb4BgM3MZi4CYiIvnxOm6jMXATEZHshNBAmLAwlSmvsXYM3EREJD8hTOs92+FQObPKiYiIrAh73EREJD9h4hy3Hfa4GbgtQFNUDE25rHJ7TKgg61XhJjlkVzTCEjcZ0QAK3o/bGAzcREQkP/a4jcbATUREshMaDYQJPW5mlRMREcmBPW6jMavcCCtWrEBwcDBcXFwQFhaG/fv3y10lIiKyUwzcj7Bp0ybExMRgzpw5OHHiBLp27Yp+/fohIyND7qoREdkOjTD9YWc4VP4IS5YswYQJEzBx4kQAQHJyMnbu3ImVK1ciMTHRqDJEUZFJczdERDWBsERWuRAw6baeHCqnhxUXF+PYsWOIiorS2R4VFYWDBw/KVCsiItsjNMLkh1RSpz9TU1MRFhYGFxcXNGnSBKtWrTK1mWbBwF2JGzduQK1Ww9fXV2e7r68vsrOzK+xfVFSEvLw8nQcRERlBaEx/SCB1+jM9PR39+/dH165dceLECbzxxhuYNm0aNm/ebI5Wm4SB2wjlb2kohNB7m8PExER4e3trH4GBgZaqIhGRVbNUj/vh6c9WrVohOTkZgYGBWLlypd79V61ahUaNGiE5ORmtWrXCxIkTMX78eLz33nvmaLZJGLgrUbduXTg4OFToXefk5FTohQNAXFwccnNztY/MzExLVZWIiB7BlOnPQ4cOVdi/b9++OHr0KEpKLDD3rweT0yrh7OyMsLAwpKSkYMiQIdrtKSkpGDx4cIX9VSoVVCqV9v/iv0kTpSgx6fJEIqKaoBQPApSoxkSwUlFk0vKlZXUrPzVZ/vsYkD79CQDZ2dl69y8tLcWNGzfg7+8vuc5VxcD9CLGxsRg1ahTCw8MRERGB1atXIyMjA5MnT37ka/Pz8wEAB7C9uqtJRFTt8vPz4e3tbdYynZ2d4efnhwPZpn9Penh4VJiajI+PR0JCgt79jZ3+rGx/fdsthYH7EYYNG4abN29i/vz5yMrKQkhICLZv346goKBHvjYgIACZmZnw9PREfn4+AgMDkZmZCS8vLwvUvGbIy8uzu3azzfbRZsB+2i2EQH5+PgICAsxetouLC9LT01FcXGxyGfoCb/neNiB9+hMA/Pz89O7v6OgIHx8fk+tcFQzcRoiOjkZ0dLTk1ymVSjRs2BDA/36ZeXl52fQfuCH22G622X7YQ7vN3dN+mIuLC1xcXKqt/DJSpz8BICIiAtu2bdPZtmvXLoSHh8PJyala62sIk9OIiMhuxMbG4pNPPsHatWtx7tw5zJgxQ2f6My4uDqNHj9buP3nyZFy6dAmxsbE4d+4c1q5dizVr1uDVV1+VqwnscRMRkf141PRnVlaWzjXdwcHB2L59O2bMmIHly5cjICAAH374IYYOHSpXExi4LUWlUiE+Pl7vvIsts8d2s832w17bbe0qm/5cv359hW3du3fH8ePHq7lWxlOI6szvJyIiIrPiHDcREZEVYeAmIiKyIgzcREREVoSB20Kk3kbOmuzbtw+DBg1CQEAAFAoFvv76a53nhRBISEhAQEAAXF1d0aNHD5w9e1aeyppJYmIiOnbsCE9PT9SvXx/PPvsszp8/r7OPrbV75cqVCA0N1V6zHBERgR9++EH7vK21V5/ExEQoFArExMRot9lDu6lmYeC2AKm3kbM2BQUFaNeuHZYtW6b3+aSkJCxZsgTLli1DWloa/Pz8EBkZqV0S1hqlpqZiypQpOHz4MFJSUlBaWoqoqCgUFBRo97G1djds2BCLFi3C0aNHcfToUfTq1QuDBw/WBilba295aWlpWL16NUJDQ3W223q7qQYSVO2eeOIJMXnyZJ1tLVu2FLNnz5apRtUHgNi6dav2/xqNRvj5+YlFixZptxUWFgpvb2+xatUqGWpYPXJycgQAkZqaKoSwn3bXrl1bfPLJJzbf3vz8fNGsWTORkpIiunfvLqZPny6EsJ/PmWoW9rirmSm3kbMl6enpyM7O1mm/SqVC9+7dbar9ubm5AIA6deoAsP12q9VqbNy4EQUFBYiIiLD59k6ZMgUDBgxAnz59dLbberupZuICLNXMlNvI2ZKyNupr/6VLl+SoktkJIRAbG4unnnoKISEhAGy33WfOnEFERAQKCwvh4eGBrVu3onXr1togZWvtBYCNGzfi+PHjSEtLq/CcrX7OVLMxcFuI1NvI2Rpbbv8rr7yC06dP48CBAxWes7V2t2jRAidPnsSdO3ewefNmjBkzBqmpqdrnba29mZmZmD59Onbt2lXpTTBsrd1Us3GovJqZchs5W+Ln5wcANtv+qVOn4ttvv8VPP/2kvRMcYLvtdnZ2RtOmTREeHo7ExES0a9cOH3zwgc2299ixY8jJyUFYWBgcHR3h6OiI1NRUfPjhh3B0dNS2zdbaTTUbA3c1e/g2cg9LSUlB586dZaqV5QQHB8PPz0+n/cXFxUhNTbXq9gsh8Morr2DLli348ccfERwcrPO8rba7PCEEioqKbLa9vXv3xpkzZ3Dy5EntIzw8HCNHjsTJkyfRpEkTm2w31XDy5cXZj40bNwonJyexZs0a8dtvv4mYmBjh7u4uLl68KHfVzCI/P1+cOHFCnDhxQgAQS5YsESdOnBCXLl0SQgixaNEi4e3tLbZs2SLOnDkj/v73vwt/f3+Rl5cnc81N9/LLLwtvb2+xd+9ekZWVpX3cu3dPu4+ttTsuLk7s27dPpKeni9OnT4s33nhDKJVKsWvXLiGE7bXXkIezyoWwn3ZTzcHAbSHLly8XQUFBwtnZWTz++OPay4ZswU8//SQAVHiMGTNGCPHgkpn4+Hjh5+cnVCqV6Natmzhz5oy8la4ife0FINatW6fdx9baPX78eO05XK9ePdG7d29t0BbC9tprSPnAbS/tppqDdwcjIiKyIpzjJiIisiIM3ERERFaEgZuIiMiKMHATERFZEQZuIiIiK8LATUREZEUYuImIiKwIAzcREZEVYeAmIiKyIgzcREREVoSBm4iIyIowcBNZoevXr8PPzw8LFy7Ubvvll1/g7OyMXbt2yVgzIqpuvMkIkZXavn07nn32WRw8eBAtW7ZEhw4dMGDAACQnJ8tdNSKqRgzcRFZsypQp2L17Nzp27IhTp04hLS0NLi4ucleLiKoRAzeRFbt//z5CQkKQmZmJo0ePIjQ0VO4qEVE14xw3kRX766+/cPXqVWg0Gly6dEnu6hCRBbDHTWSliouL8cQTT6B9+/Zo2bIllixZgjNnzsDX11fuqhFRNWLgJrJSr732Gr766iucOnUKHh4e6NmzJzw9PfHdd9/JXTUiqkYcKieyQnv37kVycjL+9a9/wcvLC0qlEv/6179w4MABrFy5Uu7qEVE1Yo+biIjIirDHTUREZEUYuImIiKwIAzcREZEVYeAmIiKyIgzcREREVoSBm4iIyIowcBMREVkRBm4iIiIrwsBNRERkRRi4iYiIrAgDNxERkRVh4CYiIrIi/w+g921WFdYvwwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 500x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = np.zeros((Nx, Nx))\n",
    "c[:, -1] = 1\n",
    "\n",
    "objects = get_predefined_objects(Nx, 'insulator', 'rectangle')\n",
    "\n",
    "c, _, _ = solve_laplace_with_objects(\n",
    "    c, omega, objects, epsilon, max_iterations, object_type='insulator')\n",
    "plot_laplace_grid(\n",
    "    c, 'Steady-state concentration with a rectangular insulator', 'insulator_simple_object')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Simulating SOR with insulator:  17%|█▋        | 1656/10000 [00:00<00:01, 5961.21iteration/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Converged in 1657 iterations\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 500x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c = np.zeros((Nx, Nx))\n",
    "c[:, -1] = 1\n",
    "\n",
    "objects = get_predefined_objects(Nx, 'insulator', 'complex')\n",
    "\n",
    "c, _, _ = solve_laplace_with_objects(\n",
    "    c, omega, objects, epsilon, max_iterations, object_type='insulator')\n",
    "plot_laplace_grid(\n",
    "    c, 'Steady-state concentration with a complex insulator', 'insulator_complex_object')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}