frequency_principle/fprinciple.ipynb

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    "# Related papers\n",
    "\n",
    "[1] Zhi-Qin John Xu* , Yaoyu Zhang, and Yanyang Xiao, Training behavior of deep neural network in frequency domain, arXiv preprint: 1807.01251, (2018), 26th International Conference on Neural Information Processing (ICONIP 2019). [pdf](https://ins.sjtu.edu.cn/people/xuzhiqin/pub/training_behavior_ICONIP2019_XZX.pdf) and [web](https://link.springer.com/chapter/10.1007/978-3-030-36708-4_22)\n",
    "\n",
    "[2] Zhi-Qin John Xu* , Yaoyu Zhang, Tao Luo, Yanyang Xiao, Zheng Ma, Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks, arXiv preprint: 1901.06523, Communications in Computational Physics (CiCP). [pdf](https://ins.sjtu.edu.cn/people/xuzhiqin/pub/shedlightCiCP.pdf) and in [web](https://www.global-sci.org/intro/article_detail/cicp/18395.html), some code is in [github](https://github.com/xuzhiqin1990/F-Principle) \n",
    "\n",
    "[3] Zhi-Qin John Xu*, Yaoyu Zhang, Tao Luo, Overview frequency principle/spectral bias in deep learning. arxiv 2201.07395 (2022) . [pdf](https://ins.sjtu.edu.cn/people/xuzhiqin/pub/fpoverview2201.07395.pdf), and in [arxiv](https://arxiv.org/abs/2201.07395).\n",
    "\n",
    "For more details, refer to [Zhi-Qin John Xu's homepage](https://ins.sjtu.edu.cn/people/xuzhiqin/pub.html)"
   ]
  },
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    "# Frequency Principle (1D)\n",
    "\n",
    "DNNs often fit target functions from low to high frequencies.  \n",
    "\n",
    "The first figure shows the evolution of the function in spatial domain, the red line is the target function, and the blue line is the DNN output. *Ordinate vs. Abscissa : y vs. x*. \n",
    "\n",
    "The second figure shows the evolution of the function in Fourier domain, the red line is the FFT of the target function, and the blue line is the FFT of DNN output. *Ordinate vs. Abscissa: amplitude vs. frequency*. \n",
    "\n",
    "<!-- ![Title](https://ins.sjtu.edu.cn/people/xuzhiqin/index.html) -->\n",
    "![value](./pic/value.gif)![freq](./pic/F-Principle_one_dim.gif)\n",
    "\n",
    "\n",
    "## Which variables were not controlled in the experiment? \n",
    "\n",
    "Is it the frequency differences or amplitude differences between different frequencies that affect the fitting speed of the target function?\n",
    "\n",
    "核心目标：探索频率原则的一般性。是否是一个普遍的规律？我们应该在实验上做哪些设计？\n",
    "\n",
    "报告要求：频率原则和一系列超参的关系。报告选一到两个超参进行实验研究。\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import time\n",
    "import warnings\n",
    "import numpy as np\n",
    "import torch\n",
    "import math\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "from typing import List\n",
    "import argparse\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import datetime\n",
    "import re\n"
   ]
  },
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   "source": [
    "#   Default configuration parameter settings.\n",
    "\n",
    "`argparse` is a Python package that provides a convenient way to parse command line arguments. It allows us to define the arguments our program expects and will parse them for us. This makes it easy to write user-friendly command-line interfaces for our programs.\n",
    "\n",
    "To use `argparse`, we first create an `ArgumentParser` object, which will hold all the information necessary to parse the command-line arguments. We then define the arguments we expect using the `add_argument` method. This method takes several parameters, such as the name of the argument, its type, and a help message.\n",
    "\n",
    "In this code, we are using `argparse` to parse the command-line arguments that are passed to the program. We define several arguments, such as the learning rate, optimizer, and number of epochs, and then parse them using `args, _ = parser.parse_known_args()`. This allows us to easily customize the behavior of our program without having to modify the code itself.\n",
    "\n"
   ]
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   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Namespace(lr=0.0002, optimizer='adam', epochs=1000, batch_size=101, training_size=101, test_size=1000, t=0.5, boundary=['-3.1415', '3.1415'], act_func_name='tanh', hidden_layers_width=[200, 200, 200, 100], input_dim=1, output_dim=1, device='cuda', plot_epoch=1000, ini_path='')\n",
      "['--ip=127.0.0.1', '--stdin=9003', '--control=9001', '--hb=9000', '--Session.signature_scheme=\"hmac-sha256\"', '--Session.key=b\"74d89f19-f25c-4b3b-abe5-420cca19a691\"', '--shell=9002', '--transport=\"tcp\"', '--iopub=9004', '--f=c:\\\\Users\\\\15853\\\\AppData\\\\Roaming\\\\jupyter\\\\runtime\\\\kernel-v2-33692Sm0n9UZd53pC.json']\n"
     ]
    }
   ],
   "source": [
    "parser = argparse.ArgumentParser(description='PyTorch Training for Frequency Principle')\n",
    "\n",
    "\n",
    "\n",
    "parser.add_argument('--lr', default=2e-4, type=float, help='learning rate')\n",
    "parser.add_argument('--optimizer', default='adam',\n",
    "                    help='optimizer: sgd | adam')\n",
    "parser.add_argument('--epochs', default=1000, type=int,\n",
    "                    metavar='N', help='number of total epochs to run')\n",
    "parser.add_argument('--batch_size',   default=101, type=int,\n",
    "                    help='the batch size for model (default: 101)')\n",
    "parser.add_argument('--training_size',   default=101, type=int,\n",
    "                    help='the training data size for model (default: 101)')\n",
    "parser.add_argument('--test_size',   default=1000, type=int,\n",
    "                    help='the test data size for model (default: 1000)')\n",
    "parser.add_argument('--t', type=float, default=0.5,\n",
    "                    help='parameter initialization distribution variance power(We first assume that each layer is the same width.)')\n",
    "parser.add_argument('--boundary', nargs='+', type=str, default=['-3.1415', '3.1415'],\n",
    "                    help='the boundary of 1D data')\n",
    "parser.add_argument('--act_func_name', default='tanh',\n",
    "                    help='activation function: tanh | ReLU | Sigmoid | hat')\n",
    "parser.add_argument('--hidden_layers_width',\n",
    "                    nargs='+', type=int, default=[200,200,200,100])\n",
    "parser.add_argument('--input_dim',   default=1, type=int,\n",
    "                    help='the input dimension for model (default: 1)')\n",
    "parser.add_argument('--output_dim',   default=1, type=int,\n",
    "                    help='the output dimension for model (default: 1)')\n",
    "parser.add_argument('--device',   default='cuda', type=str,\n",
    "                    help='device used to train (cpu or cuda)')\n",
    "parser.add_argument('--plot_epoch',   default=1000, type=int,\n",
    "                    help='step size of plotting interval (default: 1000)')\n",
    "parser.add_argument('--ini_path', type=str,\n",
    "                    default='')\n",
    "\n",
    "args, unknown = parser.parse_known_args()\n",
    "\n",
    "print(args)\n",
    "\n",
    "print(unknown)"
   ]
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   "source": [
    "\n",
    "\n",
    "# Discrete Fourier Transform (DFT) and Inverse Transform\n",
    "\n",
    "The **Discrete Fourier Transform (DFT)** is defined by: $$X_k = \\sum_{n=0}^{N-1} x_n exp(-2\\pi i k n/N); 0 \\leq k \\leq N-1.$$\n",
    "And the **Inverse Discrete Fourier Transform (IDFT)** is defined by: $$x_n = \\frac{1}{N} \\sum_{k=0}^{N-1} X_k exp(2\\pi i k n/N).$$ \n",
    "\n",
    "`SelectPeakIndex` is a function for selecting frequency peaks, which are used to compare the convergence rates of different frequencies. The reason for choosing the frequency peak is explained later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def my_fft(data, freq_len=40, x_input=np.zeros(10), kk=0, min_f=0, max_f=np.pi/3, isnorm=1):\n",
    "\n",
    "    \"\"\"\n",
    "    This function performs FFT on the given data.\n",
    "    \n",
    "    Args:\n",
    "    data (numpy.ndarray): The input data.\n",
    "    freq_len (int): The length of the frequency.\n",
    "    x_input (numpy.ndarray): The input array.\n",
    "    kk (int): The value of k.\n",
    "    min_f (float): The minimum value of frequency.\n",
    "    max_f (float): The maximum value of frequency.\n",
    "    isnorm (int): The normalization factor.\n",
    "    \n",
    "    Returns:\n",
    "    return_fft (numpy.ndarray): The FFT output array.\n",
    "    \"\"\"\n",
    "\n",
    "    # second_diff_input = np.mean(np.diff(np.diff(np.squeeze(x_input))))\n",
    "    # if abs(second_diff_input) < 1e-10:\n",
    "    datat = np.squeeze(data)\n",
    "    datat_fft = np.fft.fft(datat)\n",
    "    ind2 = range(freq_len)\n",
    "    fft_coe = datat_fft[ind2]\n",
    "    if isnorm == 1:\n",
    "        return_fft = np.absolute(fft_coe)\n",
    "    else:\n",
    "        return_fft = fft_coe\n",
    "    # else:\n",
    "    #     return_fft = get_ft_multi(\n",
    "    #         x_input, data, kk=kk, freq_len=freq_len, min_f=min_f, max_f=max_f, isnorm=isnorm)\n",
    "    return return_fft\n",
    "\n",
    "\n",
    "# def get_ft_multi(x_input, data, kk=0, freq_len=100, min_f=0, max_f=np.pi/3, isnorm=1):\n",
    "\n",
    "#     \"\"\"\n",
    "#     This function returns the FFT output array for non-uniformly spaced inputs.\n",
    "\n",
    "#     Args:\n",
    "#     x_input (numpy.ndarray): The input array.\n",
    "#     data (numpy.ndarray): The input data.\n",
    "#     kk (int): The value of k.\n",
    "#     freq_len (int): The length of the frequency.\n",
    "#     min_f (float): The minimum value of frequency.\n",
    "#     max_f (float): The maximum value of frequency.\n",
    "#     isnorm (int): The normalization factor.\n",
    "\n",
    "#     Returns:\n",
    "#     return_fft (numpy.ndarray): The FFT output array.\n",
    "\n",
    "#     \"\"\"\n",
    "\n",
    "#     n = x_input.shape[1]\n",
    "#     if np.max(abs(kk)) == 0:\n",
    "#         k = np.linspace(min_f, max_f, num=freq_len, endpoint=True)\n",
    "#         kk = np.matmul(np.ones([n, 1]), np.reshape(k, [1, -1]))\n",
    "#     tmp = np.matmul(np.transpose(data), np.exp(-1J * (np.matmul(x_input, kk))))\n",
    "#     if isnorm == 1:\n",
    "#         return_fft = np.absolute(tmp)\n",
    "#     else:\n",
    "#         return_fft = tmp\n",
    "#     return np.squeeze(return_fft)\n",
    "\n",
    "\n",
    "def SelectPeakIndex(FFT_Data, endpoint=True):\n",
    "\n",
    "    \"\"\"\n",
    "    This function selects the peak index from FFT data.\n",
    "    \n",
    "    Args:\n",
    "    FFT_Data (numpy.ndarray): The FFT data array.\n",
    "    endpoint (bool): Whether to include endpoints or not. Default is True.\n",
    "    \n",
    "    Returns:\n",
    "    sel_ind (numpy.ndarray): Selected index array with peaks. \n",
    "    \"\"\"\n",
    "    \n",
    "    D1 = FFT_Data[1:-1]-FFT_Data[0:-2]\n",
    "    D2 = FFT_Data[1:-1]-FFT_Data[2:]\n",
    "    D3 = np.logical_and(D1 > 0, D2 > 0)\n",
    "    tmp = np.where(D3 == True)\n",
    "    sel_ind = tmp[0]+1\n",
    "    if endpoint:\n",
    "        if FFT_Data[0]-FFT_Data[1] > 0:\n",
    "            sel_ind = np.concatenate([[0], sel_ind])\n",
    "        if FFT_Data[-1]-FFT_Data[-2] > 0:\n",
    "            Last_ind = len(FFT_Data)-1\n",
    "            sel_ind = np.concatenate([sel_ind, [Last_ind]])\n",
    "    return sel_ind\n",
    "\n"
   ]
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   "source": [
    "\n",
    "\n",
    "# DFT and False Frequencies with Insufficient Sampling\n",
    "\n",
    "### When the sampling rate is insufficient to satisfy the Nyquist criterion, aliasing can occur, leading to the appearance of false frequencies in the DFT.\n",
    "\n",
    "The Nyquist criterion states that in order to accurately reconstruct a signal from its samples, the sampling rate must be at least twice the highest frequency component in the signal. If the sampling rate is insufficient, aliasing can occur, which means that high-frequency components in the signal can be incorrectly interpreted as low-frequency components. This can lead to the appearance of false frequencies in the DFT, which can make it difficult to accurately analyze the signal. To avoid aliasing, it is important to choose a sampling rate that satisfies the Nyquist criterion for the signal being analyzed.\n",
    "\n",
    "Target func拿出来\n",
    "\n",
    "超过频率均匀采样就够\n",
    "\n",
    "只保留第一个实验，样本足够多，其他的都删掉。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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djqgKwHEfK7LEQKlVDNtKXkpRnlzy6isO0sKcVrkyv+i6z5YqQ2lRQ5mtsg27qMarklQHffR7DMOoZ+2KmycZJrFkTmLeU94F5BMhoJwAyzTHMBIT0iV51RnKkHACqw7P1VGmsgaA1nEv0hz9HkPcZ5WmbmIo6p4VQBQo6bT3teTlctxpXiDN+aYjIgrAaybQW9fCWhaZKaUSGUBHca9dTSDNN5j5qgMGHPV7GPR7TiZQrzlROG41AANl/fQI7xGwd2luE0JAOQFWWYGhoqUDZkfUcNxRjzCzXS9g14LXMSfKGsqkLDa2DXSq46ZaVMu0QI8BcZ859+I07aKULqXj7mMU96ybKOWeHjUxoJK81LkcOxx3vUZH2ixQS0Imw76dOaX5xnssuLgK2DeWjYASWQPdsmaX+jO2HSGgnACrNMco2pS8TItFbWmUv9NJS5vaMGCekPVFSNlVskxzjAabgc40XtIRqAGY1K4y0A0j+ybKJnPqk2fcw6hX7cUxMZSlJgBT1+jkGIwHfeO+ClmjUwNKVnCkFI47WwdgQKgG1qL8arNWAYBkzGQiJK++Hg8cgS7JNxIDKrsoEALKCbBMVYbSjgl0UfyeJ/nGYgcs3WcN5kTniNSNd8JJwrhXQsecyBhKth4vxpg1g6zXnIZxr3JkvrFK85KZsOozTYFuvcdnLeEkeUFy371OwjEFurrU60q8ToKlJmkzzfssL5DkxUY7M0DDBFaa8WpblJfjdqd0eoWAcgKssjVDcQWUhuMmlEo22oAjFxOoO8g+VoTMaaw47lFklj/0XXFUdhUYReulYCtoz+t2RX0kWWE9Jv24kMxJwuaImo67lEoIgt0yLTDoi1MVpF3G2mFt3g8djPkkqAJdtJahTUxgXmd0EWFAkQylTD7HLuaUBMnrrsQyLaoXvmYCjhpKR/sE5ALulV0lRsddZ07EgW6oOEhbC6muhrIkKpqqDEV+Ztuak3QSFOxpmRaVoxOfaWZOsmuoLnVS1FGWaV79v8VnRsYuwnmdNciAQtDptUxFd2PUX69JE3NabzakZ05ybqjJp70onyn7Y+gCHQVCQDkBVtm6y0tmbOYMUkyqLtoUF7XMdjzoG6WlpSbQUdmV5gWGfYUJWFpI645oFPdRcNFO7BureqCzZJBryWu9UQ8ACatblJKXhO0YjnqNbkToiNSERdrVlplTSjgLpaYJ2M/nWh/AWGcCNIGOlU0f4jPt57/Vmxjk1+4EhIByAqgMhTFmLQLKCdTF/oU041UBELB31jSkpUgUTSm09yQrMFDssslYdUck/z8UjQzqewTs2nujWYCwaKqXvOzNAvVaBVVAqdvllLwqJkAn4ahNH8Iui+RVTwwIGd0qK6rGCsA+v6q29Nr8ovIVvnHHBhTG2N9jjP0iY+xxxhhnjD3RtQ31hWWbKLoaSpLbTyc+LpK8QFxnAoYJ2dyHQqe9pzmvsjTALnnVFzwl9ddl3C4prpK8IkIHmRWb88uasNRqYY7a2UmwaIyXW/Kq1ypIivJpsWGXPTFoSqoAVcKy6Semg35Vw6mjKY2HGkpX+GEAfwbAYwBunoYBMvOQmDgmitzUByiZB8EEbjKB9hkkpVRSt8t2PEiTOZW1CgomUKuhjGN3l1d9vGhqKHmTObWsOcl5abua9/h2FQ0pzvUeqzZryqJ80pQIjTWURF9zojiheZVu+glbLayxvSBIXp3hD3HOL3HO/1sAnz4NA5oMJTIX5ZOiOkEUWDtICqmkwVAc2rs8KhugzYiSvMBA0bhtjQmmQEcRgPWSl2NjY53RnXKtYu2IBKMbEAaUenPFUWoolIFOrWkCdobSqIVRMhRN00eS6dUJI3MKkhctOOePn/Ln6xmKhQmok2pEmHkkNbtcNZSNQEc4gZOs2JS8LA0Ai0TP6MhqFYojstfCui1+15lT29qODCgrolrYhoO0XDLWkC6lXR1IqtNBZNyLU3fclAG4zlDWWwyaY7Z+j5tNH4GhnHGse8vbZ2qyIAnQOqI033TcLslLzYKHhP34SV6n/vYaymQj0FEygaLZzmzJbFVGR+kg9QmL/jpnWSOrHGSfTiJMsgIDZX5N4j7SXL/7vV6jo3TcdUlVjoVO9prXGLAcLxKJsC6pWvas6TbOUtlFgbsuoDDGXskYe4Qx9sjVq1eP/XNWyjlLEq6agDxBFKCl/o1ahU3yajAn6SCpAl3LGkqtY4f0aIw0bzhumxQ30TK6DmpOg77xvKlFkmmlS4qzqdK8aRegz6KrY1rKZKoKKBTMSSP1qjZs2FVjTgPKxMDIUDQBpVYLowx0FLjrAgrn/A2c84c55w/fc889x/450uE2i/Lmnbmqg6TK1IqCIys4Bn010Jk3NqoH0QFrhkKX2daaBYySV1azi7a2U3+PWcG170Y9CRag7orbdJDV+We6jLsmXcr3T5Kw1OyqgqrWrgz9HqveO6WD1Em9gH686rvqKZmmrunDZFddUu31GKIeQ5IHyetMY6ljKIPIuFFP3D64Hm6qTE3+vDjarFXYpKWxJtBRaO+6zNbGnMZxk6H4XvCc87JZoOkgdQt+mW6O1zoAd9MVB5gz20kHCQsApLXEwNaJVG9GWTOBbhiw0a40x6Dfq3bVUwa6ZpeXbbw2JUJAjFlgKGccshuk2T5p7g7amCREE1gGlA0m4KgJjOImE6BgTqJourng01y/ibIR6OR4ec7U8oKDc9SYQHkVgYZtqpcfAWuNm4KhJHnNcTu097GG0ZG0pecF4rYOMq3PL1rm1FaKq7cY98oGEJLj67NmV5y0oY56EwMQAspdAfmC65ma6ZKeRapnAr4nSirtqmW2K8MBhvXWVCq7qkCnybh1zrgru+RRLrpirp4JFBvS5ZBQWkpzXrPLLpV0MV7yZ2oZijbQbUqXslmEijlpGYqBaaqBDhBruROGYmFOVZdXLZmiCHQUCAHlmFjpHLe1aLo5gamKgDqGsnbc+gxSx5x831eRGpgTYHaQm46IKNCVP09XzDU6yA4cd16IK5B1NRRdu6lIWDazWgq7gCMygdr8YoxhEPVo2plNdhkkQtVpA3RMQHTrtdsyUO/yknbdKTc2Ru5HthOMsf8RwMvKv94DYMAY+/7y709yzn+W8vNTS8a9SDY3WAHNjLuSlnw77kxk3CYHqVJpoDvmlBiYE6AvtNelEvIArGEo+gwyx317ccMu/8zJEugMjkgNdFGPoce62e9hL35vMjoAGBIxASNzMozXuM5QiAJKkuXaGoquiWFRnpisvvc7SfK6YwMKgL8J4CtrX3tN+fvbAZAGFK3kpSz487XnG0VTIqlE1hi0RWbTwtIFFO8MRRPoHHbpurx8nza8ZnRNB2kqfqvj1S8dt29Gp2PAVu09zXDf7qj6u2QCvt+jZE4bXYTWQLfJ6ABRd6IIdMbmihYJCyCZAEWzQE26rOaXrkanCXREAZgCd2xA4Zz/6dP8fBdDUVHdq91FrULHUGxMoCPtXctQyr0JRkmigyaG1Cp5aaSlGhMAQOK40yMGunmSN5gAhSNKDV2EgPk93rOz6WaoHGSdOckArN2HkjYd9zDqE+6P2TwUFVhvRlVRT/CEXXeO5BVqKMeETns3ZUTyXm39PhS/GZFcEPp+/M1JqQ10fSppScOcLMdKiC6vtSOi6sfXS15RZUMdWu2dwEHqA3AZUAwb9RoOMvZ/++ZKw8xtmzt1MiuFhGNjTqf5HnW1MLk2tfM+7Wa8qBACyjFh1d5rE9jUW67+HF/QMieDJJHkBQre7CgB6JiTmnGPDHbl5abCLjRuXWLgqqE07fJ/372uhrLu8tIX5ScaB0llV9uakzh4k/496phTlbCY2qy1khf9eDHGjOfYLZJMP+9Dl9fZhquGoqJ+npH677pwkCbmJK9hVRc8VT++tW24HoCrc5Y2pyelI2rTHVQFOo0k0WUTgzHjbkg4hHZp5peZCWy+x2HUDXOS11/rJa9uAp2u6xIwX5ZW724ESikuMJSzDd3+BZOWXD+KHaDrx7c5IpNdusy2k64lQ6CrH8W+YZfvQGfYTwQ0HWT9KHYJygCsjle/dJD191gUvHsmULNrEOmP9zF2U3XAzAHzAaT6QEdglybBA+SBrZoaSkdSHBVCQDkmZO2jTVunTvKi6sdfO6JmEbCeqdWPPJeglJbaMDqT46aRJJqJQdzvIe6zRkDRJQby36Yd2AXoD66UY9JFMVeXsADlVQQtmlEA4ppTnQkYriLQBjqSREr/Hk3HDtW7G+W/DZLXGcdRGMrS4Igo+vHlz2uzM7c6IK/LgNLizCydRAgQOaK8mRjIz67XKnSJAUCz4I0OUnPbn5FpEko42vEyBLpG91lHzEl+dt0uY6AjDMB1u0wnWutrdIGhnHlomYDBcc9tjqhDacko4XSQEekckamdWbdbWNrle7/Hulmg6biNzOmUJEJAnB1nCsDaxIAo0A210tLmZ9kC8GkyJ1OgI6k5afwEIN6VcR+KpssrtA2fcdgkHFMGqd9I1QETKLXipuMupZIOJYnhhrTE0O8xYwDutGgabS543WVpRubUEaMTdjVvRzQ5borit26DqvzstkyT1nG7mZNNUqVKDBoBOG4GYKB59hkg16P/DZcUCAHlmJCbleSx3ICYNIw1HbeVCVB1LalHN/R76LEjFOU7aoOV7ZP14qSVCXRaNG3LNPud1MIAMSZtmwUomZO++F0LdJZ5T5VI6ZnTERIDIkanC3S6mtNc0/5N0SxAhRBQjon6nRCA6iDdRXmAZsHLhaoeL17ZZSjKdymV1B2R7pKtTpmAwUHaGEpzRzrrhNFJu4zj1UUNJTMEOsu8r88vkm6qozCnxJSw+G/PNQVg3WV8cgN0V4dWUiAElGOifieEhJgop5gRGfrerZmt1kH6lkpMmW1zn4C1+N1RrWKseY9Li11UpzPrirn192iSCEm6vAzvcaSRcLpkTsYaiiUAd9mMom0WqDHzqnaoGa+CQ3tv0LYhBJRjIs2bDAUQk9S8Ua8DB2koMuvaFLt03CsL9TcWmesbGwl2fptrFZb3eJoOMo7aM+CO2r8Bw/wySKoUR8KkJolQM7+sNZS80N5ndFzYajuNNn6Ln1B/1jYjBJRjYpUVjUkC6IuAiyQHY035gqoNNuox9HrNhdUo5qaWojwRc9IXJ/ULXnumUUeMbjKIGpJEp4mBkTk1NxCeSo2u8R413Wem5gpCqbeVpCqbUTS1CvVn+YCU4kzzXg1ei+pyrea8B8RFXduOEFCOiTTnjUkCGLT3srdcLeADINnYWL9mV2Js2b/QCHSEzElX/G5uuCwdUQcB2GZXawdJEOhMDlLb5WXspvLfXGHeV9Fss7YFYN8Sjq4ZRdhlYcCRPqD4fJfGovygL47yUT5rbpK8AkM5+0iyXOu4TUXm+mIH6M5aqjshQExSXffZOO432MyA4OygJM/R74k2YRUmqWTQ7yHq0wc6k126xGBpkHBoirkG6TLuY5luXufs2nDpU8IxMRRdALZJSwCN49btQ8kKvlHjsp0Vp/4sH7BJccD6PD1AvU++yeh820WFEFCOifqlORImB1nPagHpIP1qyaKduR1zmidZI3sExAT2fZFV/a4KCZNEOIqb/wea4rfeLtlNtSFJpEJOrI9vHNF1eemK8tIW1S6gWXOiyLhttbAkLzZYh627EfAr4diaK4DN8VpapDjAr+M2NTHo7DIxumFp552wuTEElGMiyQqzg9RkaibHTdGeq5PixjrqnzSPiAfo9gnomhhMNRTjeHVl16APzjcXse5YDKA8QoeACZiYk7RFYpnm6LEmm6FwkMaagNw8m6lMwFCriAkYioU5AZsnWtu6LgHPAcXUxKA5VWN9QkTzUFTfdlEhBJRjon7dqISuPVd3EB1AVzTV2qU5JG+Z6pnAkIA5rbICg6g5Btr2SYNESFWUN40X0HTc9T0o0i7A7/XEaW5IWEpns6w5Il2NTjpun8mBbaOetKWyy1Sjo2ACx2B0XXRTuZiTWg8zbZylYJpUCAHlmEgsXV46yUubcRPVUGwSTmu7CPZVDAyMTtfOXO90kXalOd+oH5zYLgNDmWgWvC0xAPxLS3a7Nh2kidEB/msCOuaku7VR1uh0zSiA50Bn6SIEauNVNX10J8XpajtAPTGQXV70zIkKIaAcE0ZpyVAT0DoigmKuqSg/HjT3L8w1t8MJu7prFpDtzPVaxdhQQwH8SyW6Darj6nbEmuM2jBfg33HbmZMS6Aw1Opnw+Kw71e9Hl9Bdm6y7Hx1Q23P9sWBjt56uhpLmGEa9RjOKrFX4vGba1uUFbF7LbSzKh4By9pFait+6Yq6pyEwh4Zjs0hVN63qttIuirVPfztxHUatVmBxR5bg926VlArrMNi0MklfpiDxLOKbaDrAZ6JYWiZDCLv17FF+rS0s2u3xKhMYuQkMNxTa//DInGej0dqnjZTwrrpr3fmVoCoSAckyYtPeRoZg77UjCMTmiSiqpTeB6NiTtAvy3dWrbmU0SjqHNWv4sn3aZArC0RWKZ6JmTdBY+mUBqOdoHaDIB3XuMCQJwkuuZue5uG2Mi1fcfgG1dhNKWyi6XdEmQGNRlP10NRdY0m238gaGceaSWGgqwubDmSY7J0OIgfWfclgW/rNnVlfZuCsDaWoVDwvFrl779e6RhAq6M23dNoG1iYBovigDsmvfLegDWBjr/AdiVSLViTn3/zMnYXKEZr7lFMQBC2/CZhtNBbkyUTD9RiDLItsXceZIZmRPQFRNo1iqWnWaQ+ZGK37r3SMOczCceAOsCrrCrMDZXAL6lJXN3o7ClfQDuImEZaaTLpWVfGOCfadpqYfXEs6saHRVCQDkmTBlRnfrnBccyNe/3kD/LF9JMn3HrA4pd8vKdcZuOqqnbtdDcCaHa5XfBc8SRpsgcyyLzZpeXzRF5TwwMJx5IWyRMAZiC0Rlrh7G+icHKNDtgKDLQLeuBzsKcuqk5yQCs7tsxbDQmSAyoEALKMeHavyAnsMzYphrJi8JBmoryVWZbHniYFxyrTJ/ZUklxtoVVD3Ta4jdF0dRV/G44oo5qAg676pKXvZ3Zb9eSNpEqx2XeolZBIsWZuvV0AdiQ4FHVnHTzXl7Gt6jtQ9EmUgTdelQIAeWYMB/Zsdk+OV/pTxAFlLbOzHNR3sIEZJuizLy7msBmjXuTCRQy0HXEBGzdekAt4zYyAYLMNi+0zGntiNwBeG2XT8mLWx33siYt2TNu+vk1MhTlO6s5GQ6R1V16Z5K8YgK7qBACyjGQFxx5wavMVEW9fVIGlqm1m8pjBmliArX9C6ZjHgAqqUQvxU1rDGWZ6VsngdPV3jnnLdpg6duZGWOY1E49MLUN05yem2PY1nEb7OpSiuv3GIZRr9lmbemK8xvo9IfIAs09a0uT1EvAnKgQAsoxUB2noMkg6zWUmZUJEGSQlrO8gGag07abEmWQVi25tMd0PSvQLXOqHFE5XlJmsx294luKMzoi5SoCW6BbM2D6mlPc7yHus1ZMgOxkAc28B5q3Nro2zvqu0dnsqku9XdV2qBACyjFQ3VVhaxtO3UyATsLRH70CKFKcJaBQ1CpMC74ueZmuZwW67cIRtvUbjM7GBHzXwmx2Se09zQVbtklLXRS/geYR9ktD9xkVQzHZVT+wtdO2dMNRSNKujbbhlb7rkjFWngAeAsqZhOl8HkBtgxXPzGxMgCrj1nYH1Wo7FXPSBTq5T8BvP77uLK96m7XpzhGAcsGbHPeaCZhOqKWyy+Yg1XPZbAGYYn6ZpCVpl3x/WV4gyYvGeVkA3UVWRiZQr1Ws9O3fFRPw3GZtZpqbgW6W5JgOm3ZJ2wJDOaMwHUkNNHfmLmyO27MkURQcWaHfvyC7cJYtJC+KriXTgh9GPfSYWOSqXfYuHJ+BTj9ewObdNqYTagHCInMLqcR0iZVqVxfvUdowr6Rec3cjRTOKqUkG2HyPSSYCna6mKZlAF2eyAc3L+MR+taZdgJChA0M5ozAdSQ2sHbcMJLOVu1bh6xpg050QgAhe/R6rmMncUquII6KjRExFZpUJtJGWTsFBmq7/BWjaTa2BTpFwDssuQm1beocbZ4FNBzmr7GomUvLMLe/tzC3eo5z/NibQRY0O2LyeOMkKpDk32kVxdxIFQkA5BkzXjQJrx10Vv6WEY1nwvhyk6V5toNkdVC0s2w5+z8zJXjQtA52FCfh23Jzz0kGaM9t5zXHvahY8lRRnr+3UHHcH7xGwZ9wqE3A5bt+3gtqkOLUob2NOgP8rJax2aQKwkaH0e16bd6gQAsoxkFgYStVfLvd7rGy1Cr8O0hbogE3N1trl5dlx25iTtKFy3EsxXjsaR+RbWsrKQzntxe9Nu3QOcl2U70p7jypHdGhhAr0eQ9Tzn3G3Y07i9x2D4/ZdE7B1eanNAjbmJOzyKy1Zu7zUgOIIwEOCk8kpEALKMSAXgq49F9ik/raagO822MTCUIBaMdciefne4OW2K6qkQduC990+abqrYm3XusvLtuB9MxTOeSmV6JnTJFbsqhy32UF2sZ8I0GfcOuYEiCP/fXYRurq8lq3t8uu4bQFYva10vV/NEuhCUf5sIs31l/lIqG2d8gjv+j0NgP8dsKZLhiRGG5KXe2Ojt0DnYE4TRfKSGffOyOK4Pdll69YDgHEcYVmetVTZZagJ9Fh3zGmsk7w6knCsXXHDqLLHxQQGvmsVzvbv2kZjW63C+8ZZc2KwrrWWSoblPYai/BmFU1qqZWrGbMhz15IscraRcOZJhmGkD3S+u4NsTQzSrnqtwlYT8NUd5GIo40FPYQItHLfnANymPdcW6OTP8DW/qpqTYX7tjqLKHpeE471W4Wj/lu/v0FGr8O24rcxJuYxPMk0zQ2FB8jqrWDtIdzHXdPsg4L9omjgYiuimWnd52QqAAAFDaaG9z1biWmJdoJM1AV/dQe7aTqQEOrck4TsA2xKWNOdI88LJBIYeHbdk5iYpbncY4WApHbe9+O27VuEKdLMkR17wFl1e3TG6nWGEgou1uA7A3TBNKoSAcgysHAxldxRhf7nO1GzZEOC/hmKq7UyH/SoTMl3mA/ivVbgc5HQYVQvqcJVp5a61bf66g9oEulVWIC84ZivxHuu36UkMPWa2tqYPYPOE5lmSgzF9jU78DH/Skus97gwjrLICSVZUzSjWWoXHmpOtzXq3nE+Hy6xFoGP+N/Qa/UQMADhYZtauS2FXKMqfWdjacwFgbxzjYJkCkOfzbIfj3hut7ZqtMuOiqjZ4eVpYK4eEszOMqi6qw1VulG8Av46oTS0MEHUwMV72QOe7WcDGnADBfmerDJPYHOh8jpdLiqsc9yrDbJWBMbu05LuL0JRI7UnHvUo7DXRF0S7QHSzT9X41E0MJR6+cXbgW/N5oTf0Plhn2DBl3v8fAPBZz3Qs+rpjT7UWKc+PY+LMoHJFxwY8FoxNacmYNKD4ztTZt1oBw3Ict7PLHBKS0ZA908yRrFeg6Yyil45ZMYDqIGnepq3b5Twz0n7VTOe6sBaPzN7/Swq1kAMD+MmvXfRYkr7MJV5F5bxRjfyGYwP4ixZ7Bcfs+6sFVE9gbi6JplhfYX6ZV5qaDX6nEzgTOjeNS385xuDQzJ6DsDvI8XrbD+4B1QLHaFRFIcY5AN28R6HwygTZMExBMwMaAAb/7KlzS5a4SUA6XokmmC+nSlRisJa8Utxcpoh6z1jXDjY1nFC7HvTsSWvIqy91MgCDjNjlIGUAOV9mpMBSbFAcI1tTGQXaVcVcnIadZK+bka19Fm644oJ0U5zNhSZ3S0tpxH6zSymHqQMOc9M54t5r3KW4tEuu8p5AuzetxPV5yPZoYXWAoZxhtpCVgc6KY0K20tLbLxpyAbqUSacf+MsUsaVGr6CizVY/8P1hm2Bna36Ov8Vo5HJHKnG7OU5yfOOZXR80CO0rx++YsxQWbXR06bpWh3G4xXr7nve6GS2HXej3eWqQ4Z7ErFOXPMJxFwLGYwM/vL5EV3JkReZ/ARilO2HVrnuJgZa7tAGJh+Tq00uUgJUPZX2S4OUtw3plB+qH+zvbcgeq4E1yc2hykv6NE2to1T3Lcmie4MBlY7PLIUBxt6ZLBHa4y3JwnODc22xX7lAhdisFwXau4tbAHFJLmihZF+X1H4ulTiqNECCjHgGth7ZaZ7NM3FgCwNdKSzIievbUA57AylIHHox5cAViOz43ZCvvLDBenQ7NdPttzHUxTOp4bs0Rk3FOLg/SYGLgc0abjtjMBr3Y5Ns7WawJdM5Q2tYpb8wTnbYHOY3djmzPs+j2G/WWKW3N7QAn3oZxhJHleHcGtg3TUz9ycA7AHFJ99706GUjInaZc1oHiUSlKH45Z2PXFd2HVxp5uM2yXhXCoD21M35kjyAhdtTKDD2s6lHWHX8/tL3F6kOO+wy//GWf28XycGKW7Ok86kONd4jeIeBv0ebi/ScrzsTCDJ/Gycda1Hxhh2ys2gtxeplZmHo1fOMGyX+QDrhfX0DXdAGUR97104ruJ3G7v8Zrbt7Hri2gwArI47jvx1n7lqThenAzAGPPbCIQA4GYqvoryLOU0HfYziHh6/KsbLzVD8Ztym8RpEPVyYxHj65hzLtLAHOo8Zt2u8GGO4vDPA1YMVbjlqKF4TvMze5QWIOXZ9luDW3N0skOYcRbHdnV4hoBwDtktzAODeXZFBfvx54YjsXV4+tXf7BJYOUTIBW9swRXeQbYMXY6gc5EWL4/a5wcvVztzvMVycDPCJMqBYGUqHAVg4yCE+8cIBAHugG0Qeu88cjhsA7tkdVuPlZCgdtcsDwD17I3zq2gxZwa2Sl1dJtZQITUV5ALhvb4grtxY4WGU452CawHpvy7bijg0ojLEeY+y7GGOPMsaWjLGnGWOvZYxNqT/bdm4QIBbSMOrhQ5++DcC94LvS3qeDPsZxHx+5sg9ALH4T4sijluxgTlG/h4uTAT72vHCQlyySF0V7ru1dXtoZtHbcXR0JA0AElDJhsRflPTK6No57d4hPlu/RZhdFzckW6O7dXY+Xq5sqK/wwgaQFQ7lvb4RPPH8Izl2Jp99z/6hwxwYUAP8EwI8D+AiAvw3gFwH8HQC/zhgj/X+5GApjDA+cG+FgKY6fuNfmuL3WBHJEPWbctMUYwz27Q1w9WAEA7t2zFL8pNlw6Mtvb5WZQq4MkKcqb5ctL02F1hL2NOfksmlZM0+K4L+8MqhOtXePVFdMEgHt2htWtiC67fDluOV4mKQ4Qa1CeNHzZVqPzeOndOgCb59f9eyMclHbdvzcyPrc+sPUMSV6MsR9ipp034vsXGWO/emKr3HZ8AUQQ+RXO+V/hnL+Rc/7dAL4bwFcB+HrKz0/zwkpjAZF5AMIh2Rag32Ku+dwgCTlpR3FPe53t2i7/tQpXpgYImcnZHdRhxq2yJVtiQLJ/wcFQJF503uyIKPbHuBIDiRdfGBuf83m3TTuGsh6jB89PjM8NPNrVRiK8VwkiDzjeI3D2GMoPAHgrY+zB+jcYY18J4AMAvtqHYQ68AgAD8E9rX38jgDmAb6T8cBdDAYAHzonJ8dKL5kUF+C/m2pwjADx0WSyml1/eMe7KBfy3ddqYk7BHKJUvuTBGZBlbcXOd5/tQeubPe8lFMV4XJvHWHA4JAA+eX88rO3PyyQTcdt2nOMj7z5kd5NAjE2hnV7sAXDEBD+/yqHa9+Lw7AG97p9dRA8rfAvBlAD7AGPs6oKplvAbAfwCQAfhKvyZq8WUACgDvUr/IOV8CeH/5fTKkufmOA4nPvHcHwNohmdAmg1ymOX7irZ/EldsL63O2e8glPuf+PQB22g+007gXSY5/+fbH8FRZ5DehzXh97v27AOytzEC78UqyAj/5tsfw7C37eKW5O9B93gNivGwdS0A75pTlwq7Hrh5an3OdMQYAX/CgsOuBcyN7YtDCcRcFxz/+7Y/hI5/et9vVgqF84YPnAIhNtC5mDrgd9+v+4yfwyBM3WtllGy9pFwDrkTBtJa+f+v1P4e0fv2q3qwXTlPML2GQrx7XrV9/3LN72sReszzzyxA18+8+9x+lPjoMjBRTO+RsAfDmAKwB+hTH2LwD8LoDvA/ArAL6Ec/5O71Y28SIA1zjnK833ngVwmTGm9QCMsVcyxh5hjD1y9ap9Qphw394IL7/HXvv/6w+/BF/zhx/A//JnP8v6XBtH9IuPPI0f++2P4Sfe+knrc0lWWHVkAPjLf+RBfMVnXcb3/vnPs9vVQnt/y4eu4Efe8ih+9LcfddrlYk5f88Uvwld9zj34wa/9AutzbZjAWz/2An70tx7Fd//C+09s15/7/Pvw57/ofrz66+x2tQl073j8On70tx7Ft/2bR5x2AXbm9Cc/8x58wx97KX74r3yR3a4WEs77nr6J17/1k/j6N7zD+rNcR4kAwJc9dBHf9hUvxz/6a19s/VltJK+PfHofr/2dj+Ov/Qu7XW2ky897YA/f8l8/hNe94o+0ssvGgj91bYZX/8ZH8E0/9S7jM0C7APwZl6f41j/5cqddgxZXXTx3e4nv/IX345t/+t3g3Gz/MzcXeMuHnqtqgz5h5vAGcM4/zBj7MghG8m3ll7+Xc/4PvVpmxwSALpgAwFJ5Jql/swyKbwCAhx9++Fg6wP/5l+2LGBBB5/Xf8Eedz8V95pRwPvCM6Bb7sCODtF3mI3FxOsDP/s0/1sIud6D7wNO3AAAff+7A+lySc6ddO8MIP/0tX+62K3Jfhfr+0q6nbpycOY3iPv75//Clbrv6PRRcsBCTZPfB8j1eubXUfn/TLjtzGkQ9/HCLedhGe5fMRF4hYGI8bRxkv8fwfX/h8912teha+tCzt6s/28a1rV2uZAVoxwRUu+ZJZryork1zBWMM3/81LcarxWV8ql3XZ8lGnU1FGwZ8XBy5G6rM/P8RgD8B4HEImes7yhpKV5gDMFVIR8ozW482O4alpCSPcjFBXDfqZ5K0uTr2ym3hGD99a2HNiNrUnFrb1UKKe76064WDFTLLs67276OgTRfO8/vCLnlKsNEuy7Wxx7fLPA7yPQKoOgC1djnuHTmSXS0c5GPX1tLg0zfNc79NraIt2jCBT5UbcOt/rkPuuPfxLuMWAVhNoJ60yNCuCwJPgqN2eX02gHcC+A4APwngCwF8BQQT+A+MsVdTt+yW+DSErKULKg9CyGENdrKNiFucmXVlXyyma4crLFPzsRBtGMqR7HI47hdK5zNL8qrlVwffjlsyAZddecGrP2vtyri3RdUms31OcdzP7ZtZis/32IYJqAHFNl5pLhIDW83mqHbZGlLU4Pa8ZbzadHm1tqtFoLt2uLbLPl7+AnAb6VK1y1Y/9DledRz1J74HwEMA/irn/FWc8xXn/F0AvhjALwH4fgBv82qhHu+GsH1DI2GMjQB8CQC7SL1FcJ3qyznH87dX1cnAN+fmOLnymNkOIuG4c0t30NWDVTXR1clcR+qROa0zWzsTkHZ157jdme3z+8vq89TgUkeb5oq2aMMErtxerMfLZpdnBizsMr/HG7OkOqrfFegYAyKLRNgWbWo712cJ5EfdODSvxza1ndZ2tZAurx8m1fmCtyx+ok0t7Lg46k/8AETh/c3qFznnB5zzV0DUVNyFg5PjFwBwAN9Z+/q3QdRO3tSBDV4gj+wwSUazJEeSF3j5PaJr7ObMwgQ8Sksuis05x9WDFT7rvtKueTcMpU2m9vz+Ep9Tdo1ZmZNHB9kms31uf4nPL7t6bswsjsgnc2rBBJ67vcQXvVh0QVkTAwKJ0OYgb8yS6j2+YEkMVmUA9sGc2rQNXz9cVV2ctgSvTXNFWwxaSKrXZyv8obJZyOYnXEc0nQRH/YlfyTl/yvRNzvm/AuCuYJ4QnPM/APATAP4KY+xXGGPfyhh7LcTO+bcD+HlqG3xh0O+BcyAzMAHpEF9+SbQfuzIPb47bIeHsLzIkeYHPvm+3tMs2gf1n3CZHtExz7C+zyq7bDru6cpBZXuDqwQqfXQbgriRCuUvbzuhW6/FyBmDP88sRUF5+eQrGUF2prUOacQw922VTDW7MEjx0aYqox6yJQZvmiqPaZRuvq4cJ7tsbYW8UtQt0p12U55w7z3XmnH/s+OYcCd8J4H8D8AUQweXrAbwOwNdwzrd7948ClyQhHeLLLpWZh4sJeMts7RLO1UORMcpMzRboVh6Zk7TLNF5Sd29jl1dpyVH83l9mKDjwGfe4A0rqdbyEZGR6j0lWYJHmeNG5EaIe67AWZn+PgHDcl6YD7I1ih125N/lm0IqhJLi0M8SF6cDBNLttrrh+uMLlFnbJQOeD0dVx5LbhbUEZ3F5b/rpjsZ7AHNDsnLm1EBND7iSXf9chzdxHr7S2yxHoZGD7DGmXLdBlRXU7HbVd+0thx0vKEwpuL7rppnIxuoPSrss7Qwyjnj3jzgvElvOfjmOXabykXXvjGHvjuBo/HXxKqhUTsDDNeZLjwnSAvXGE/aX5PaYEzRUmRpcXHDfnCS7vDHBx0sZxd9f0cf1Q2HVhMnAyFIqCPHBnHw55JhBXFFtP/qTjeVkleXXXTQWYM1vpiB44P0a/x+yBziNzctl1WDqeC5MBdoeR1a4kd28EbQtXN9VBadfuKMK5sSvj9pnZ2pmmdNR7Y2mXxXET1MJMge566aglQ7EF4MRjAF4X5fXr8fYiRcHF/Lowje2Ou8X+q/Z22d/jKsuxSHOcnwxwcWoPKD4DXR0hoJwyho5imwwg9+6NMI77uOmg2L5rKObMdu0gz49jJ0Ppqii/4bgnsbOG4l+S0L9HmfnLgOIcr46YgHTUu8MYe6Noa2ooUqo8P4lFQLExJ59Sb3UkjKFJptw/tDOKcLGF5OVv/5WQLk3rcVGe8DyO+zg/ie3NOx4DXR0hoJwyZGZlWlhygZ8fx7gwiZ01FN8O0uSIKsc9FI57W4ryByvpuGMnE6CRSuzjtdfCLoquOKddpeRlHS+Pjsg1XodVYtBivLzWKsR6NBXl56Xjngz62BlG1ZH4OshahRe7HH5CXmUwGfRxfjxwvEd/ga6OEFBOGQNH5nF7kSLqMUwGfeyN40pq0qHNWV6t7WrNUMSCt0pLBAzFxAQ2mNMkxi2nVNKRtFTa0Sag+FzwLiZQZ05WacnnfiIH05wl4j1Oh5GooTikON/SpakoPy/tEgElrgKfya6uEgMZ6MaDPnaGfcySzLgVwWegqyMElFOGyxHdXqQ4N47BmAgqcuLo4HOiuGoCh6sU/R7DKO6VmZrZLp8Uu22g2xlG7u4gAmmptRTXWcbtaGKQgU4W5Z3Mqe/FLlegk/NJvkdXs0BXxW/JBMZxVDru3Hg1gE+7+j0GxiwMRZG8psMInMPoK0JR/gzDOYGTHJOhWMRTB8WmqaGYmYC4C55hOogwt9qVd1aU31+mGPR7GJULa2EJwMJBdhOAq0A3irDrlEr8B2BXoNtTmgVMma0IwJ7HyyF57QyFXfMkNwZFiv1EJoayUJiAvB9nbjgOyad0yRgrD2zVv5u1FBdVdpnOiwtF+TMMlyOaJ3l1/MTOMDJOkqLgyAp/bcOubpfDZYadcuJOLXaJn+F//4LNEckW5emg30Lj7oYJHCxTjOM+4n4P02FUSSc6UDAUWwBmDJgOIkwHfWQFN44txXiZ7JLzaTrsV+/zwCAv+RyvqGQCLmlpogQU09z3zQSGlqsb5Hwal7UdAMa5H4ryZxguCWeR5hgP3I7b57lBgBroTF1LWXVRkaT+JoiriX2fAWXOuKuA0sJxd1mUV+1Kc27ebOgxALtuRjwoE4Nej1XzzMTqfNrV7zH0e+ZrpqUznA6i6nh407v06SAlEzAV5VVpyRXofBe/Y8udO8tUF+j079Hnxtk6QkA5ZbgytUWSYxyLZ3aGkdFx+z6SWkpBto168k76SRnodFJJXnDkBa+aD06KNvtjZKBzOe7Ua1HeURNIMuyUDmgyEGNhdJAepSXXhVGLJK/smVZ2mR2Rz4zbds304SrDdNAvA12/slUHn5IqUF6RYBgvtSg/HbikJb9MwDZem8xJjJeZofjbt1NHCCinDJdUskjzKkObDPpGx93mHvKjoOo+syx46SB3hpFRKvF5VwXgHq9ZklcLSjpK3YLnnIsF7/kQRpPGvem47ZKET2lJMgGTdDlP15Lq2BXoPDIUQN5yad7vMa0kVUeg8+y446hnHK9Fecthm1qFz644YZeZ0c3Vorwz0IUaypmFa+PZPMmqBT8tHbfuWd8niMYOhqI6yLXjbi5CaavvU31NjnupOMhqwWscpHeJ0CVdKrWwidNBenbclsx2kSiSaiUtmbuDvEo4/Z5x3qsJyzh22+XVcVtuUV2Uc2kY9Zy1Ct+O23ZduK5ZQDfvAf/vUUUIKKcM176KZVpUmeOOJSPyfWmOq+99oXPcFrt87RNoJRHWmIDOEXkPwI7270WaYxRv2qUbr6LgZc3Jp+Nmlvm1llRtiQHgn6HYbgU9XK2bPlwSofcAbLlFVTbJ9HqsCnhGx+3ZrriV5BW1C3ShKH824erHrzMU8bXmgpcU3Zu05LBLNAvUHKRmYVWX+XQY6EY1JqBbWL6P8I76PfQs3UE6RqcNdIVf5iR+Vt/KgKWkWtUqUnNNwDsTMEmXq6yaV7bxAvx3U8UWJjBPFelSzi9L95nX2o6lKD9PMwyiHvo9Vtllre0EhnI24TrGe5E2i6Z6BymvG/VdE7BkarWFpctsvdd2qrOW3I5bZmpzjV3r2o6fZgHAnkEeldH5XPADi+NepMWaOVkSFt/NFUDJBIxtw3llz2TYXfcZUF56ZzoFWZn3ayZgli67CnRLbY2uG4lQRQgopwwbQykKjqVmwWsdUe5XWrLtj8kL0TnVxkH6Zij9HkOP2XcyV7UKKeHoaigElwxZNW6V0Vk07kqK8y3hWI6Jl3bJcbMFYJ/dQXHf3gYr7ZrEZsmLc+71cEigneQFAKMyGVkaNjZ6bxawdp+t7eqVRzWZNhuHovwZhu1Mo2W2bgUEFCagrQn4ddy9HkNk2CewTNcdJYC9JrDyzFDkz9KNF+d8kwlY7PJdlJc/y+ggE7WG4mZ0vjNbc3dQVjnsNUOxvMeOHPdCqe2MB+Z5nxccnPtmdDZpac0EeuXRQ6aA4luKG0Tm/TFzJQADYm0uOtjBX0cIKKcMW01A7dwAUDkk3QT2LS0BZgmnOs+oFuh0E5jCcZvsWmUFOAdGdSbQkbRksotzvuGIJhbH7bvNWv6sNk0ME4vjJrHLUWSWtZ1hJOpTOskrqZhTN8XvRZI1HLdOIqyYk3eG4pZ6AeErTAElnDZ8hiGZgG4Cq73l6u/agEKWcTcptlzYo5pdugmcktQE9BmktGtSk7y0dnlmdIDcJ9AcrzQX9YdKiotlLYy+zRqwMwFVUrU67lNgKNKu6rw4XaDL/HbrAXIfiqFtWNkXBpiZwLqL0N97HFqluAyTWLFr0LdKcUHyOsMwSSXLGhOw7RimqAmY9gmody8Aa0ZgyyC9BzqNllxnTlVNoMuMWxfo0s0ALKWShY2hdMCcsrxAkhfVexQnWhscN0EANjGUeo0OEO9UK8WV3Y0+GYqLOakMZTQwBRQK6dLeXNGQvCzNFSGgnGGYFrx6nAJgZwK+93vIn2WV4lowJ5qFdVTHbWMCHUiEyh4BCZPjppAuje+xVgsDzI6bIgCbajv1hEX+2TpeXhmdxXErxW9AjN2yo/coEimzFDdpUUOhaK5QEQLKFmBgoNh1BzmySUtEGZG1hlLaE/d7iHrMGuj8ZtxMH1ASjYM0aNwU3VROxz1Yf5ZzwXcZgBVHNDU4booAbKrtVJLqRkAxMSeCrjhrE0PeynGT1Q5bdJ8Bkjk1n00IGLCKEFC2ACaKXc9spcbdaUbU0hEJiq2bwBRtsH1tprbObI/ABDpkKOqCnwz0kgTJe3TNrw2GYh8vnwxYMBRzja4xXpoNl+v32NF+oprkNTZIXmQ1p7Z2xT2tn0gJ5peKEFC2AC7HPVaKk51ntpoJvNQseJOWTLVRz8pQVCZgKE52ua+izjQBi4RD0ixgcNy1mhMgGYrFcXtOWNrU6KSNXWyclT9L9x6rmlNcK8pbGF0XNTqgyZwmg8jaLBBqKGcYJmmpXkMBzBlRl/s9tAs+1jtuqnbmoznujnakm6RLTQ1lZHBEFEzAxVCaNZRuJJyj1HaMjM7zkUOAuxmlnrB0yVB0iUFR8I17kwBz2zDFPicVIaBsAY7iIEcGacn3YYfSrjbtzPLPugW/Zk5+22B1XV71DZfyz50xAde+nXqg00k4JF1xLkZ3OgHYnEitbx+UmA4i7XhRbbi07wtzMxSqJgbZpaVCjkEjwbPO+1CUP7MwMgHlMh8JJxPoYL/HUlNDcUpevjNIjV1zDRNwMTqvTMDQHaTLbLus7RgZiibQmfZ7UGS2pnmvTQy2oOY019ScjEyAKKAAzU3QVQDeGK8e5mneuDtJ/luf815FCChbAHMxV3xtVF9YhppA1GPo9eg3xOm7qXqdLixtUd5QzO2qPde84VJm3LWNZx3Z5WLAjSJzR5KXKeOW877OnGw1FN/NAgVH0y5DbaezBM9wd9JcwzTHcR95eRWCCopaq4oQULYAph2w6pHUEkbtneDAN9NFQ4s0R9RjG59nYk4UkoRLex9ttOdGjloFfXeQMdB1eOLBkaTLzhjdUTJuUWSuZ9xU46W3S9/dmOa88SxNwqI/mVwX6ExbDEIN5S6AKYNc1jo3AMuCT3MMY7+vcxD1jUX5cd0uiyQx6PfAmN97NExSSY9tBq9Jh1KcuVuvzLjbFL+J7MoKjqKWcddPYpB/1jpuIkYHNA9G1dpVjl09O6eq7eg+S9tmbdjUS9UkA5gDXZ056eyiqB2qCAFlC2DTbFUnBJiLgL6P8AYsGxs1do0is+P23fNu2jEsDxRUg5exyJzn1X3rvuDqDlKz+0kcIckKY4HVd3MF0HTcOuY0ivvgvBvHbbq6wdTEoNrcsMtz9xlgZk71Gp1qc2UXQa3CdFvp+j1uNguo36vsCvtQzj5s+wS0TMAgSfieJCYpTmfXyKAlr7LcewHQtvN7VA90cR/LtGhk5xT3apu7g7Lq2lgJWaCvBzsKxy3Hvz5mOslr4shsKRiKKeOuS3EAGjIhVbceYAl0Gua0TPQB2HcTA6CTvPTNO6rNdbtCUf4Mw7ZPoMEELP3lvgOKsZh7FOZEZJdpw6XaSQWYTxwmYU6mnd/axEB/C6Gohfltrqi6g2pjtkxFsN8IdIYDNamaBdSfLbHQ2GU6gJTSrobjtkhL9ZZmqrZhoF1RfmSY9xS1MBUhoGwBjPsEUn0NRdcdtMoKrwVmwN5uWmcCsrajK5pSMCej467ZZbqPnMIuW9dSwy6D416lNMwJ0EheBgYsv6ciyQowBkSeuwjlz96wy1A7BMzMiaJZoG6XjTkZAx0JQ9mcXza76r4iSF53AUztpvNE47gHhvZcCiZgOVa/seAHfRS86bQopCWb5KW25gq7ospmFSsKuyJTF07WcNxG5pTnJIEOQKNjb57kGwVmQOkO0gVg780V5tqOjgEDZgmnk5qTRvJydVORNDGYmgVqbdZauwiYk4oQULYARgnHwFCyQt+mOPSd2ZYSTr3+oGsWGFm05K6YgLBLL3k1mEBWeKf9pq4lrYM0MSeiJgZh1+ZnLdJ8owUWsDABohqd/NlOuyzj5Xv/1dDIBDL02CYbcnVTdbOxUbOh1xDoVlWDiF81QyIElC2AqZhrc9y6zIPKEaVFiwVvmsCEDrI+ZkuN5LWuCTSL32SOW+Mgm1KcoYZCUtth5c+utQ1bAp3uPVI0VwBNx217j12Ml7mbqmh0Ea7t2nyW6kgYrV1pDsaAkZJM2Zim+rN8IwSULUBsYAJ6CUevjVJ0U5kott4R9SqbVSQkjqh0kDomYKoJaBwR1Xg1Ja+iEYDXzKkW6Ajav001lPoJtYDDcVPZpXGQOkkV0DOBrhKWRZo1JGhr0wfB/itAN+9FF+FGoLPYBYT7UM40jEzgiFqy/0xN1gQ0ga5lBrnKCwx8NwvI8dJJJW2L8p1mtpm5VqENwL6bK8TP0+2wbtbo9HalhI67IcXpaoe2eU+w/0r+bBW6AGx7j74PYDTvjznCeiybK8LhkGcYOibAOTd2eQEdtcGWjq1NBmlbWN4zW4NUousOshUnKZoYhF3ubipbbYcqMWgwzVOXlvRS3CJtdsWdiuTVhtFVDLjZNtxdwqLZF+ZYjz6Zk4oQULYAOiaQ5GIXtW4DIdCNJBFrzg4qCo5lWhgzyGYxl2Zjo/jZ7lqFcb8HYaBrOMikOV5dMqdjSV4dBGDThsvlEdqZV5R26QJwfT2Wz9ZrKJTvUcdQ6u+x32MYRM2OUIqERUUIKFsAHROQ3VJtJa9VVhCc5dXcSLXMmq2T6t91FJuKCaiOSDK60y3KmzXuo9QEOg3AR9iHQtH+DWikS42EE/fFMTndJFLtHXfU72HQbzpuqn1OgOk9Ro3ndXvWKParqQgBZQugYwK6nnfA0dbp8V5tQF9k1p3/pP69i6K8zq5VVoBzmIvf2gXvd7x0jsgU6AZ9cYq0NtB5dpDGjFtTqxhGPTCm3xDXFXPS1XZM11+TzK8j1CoA0V2lX49U46WRejV2dTVeKkJA2QLomMBcc7kWoDKBWpsiZdE00wS6U21nbtYEdCfBAmsH2WBOaU5X21HsSvICBW8mBowxTOLmicOUNYF6oJtramEmx03RXGE84kTDnAD9sUOi+N1dc4WWCWhO2hbMnCbBazQLaDbOVnalNSmOYD2qCAFlC6BlAvJujxZMgHPemSPSHS2u/r2TTE3TtWRidNJxa3d+E0lx6m2SS80laRI6R0TZBqs6ojQXG0N1Gbfu2uSu2obzQsxlnV0TzaVkpOOl6W7UMYFJeVcLtV02Kc4YgDWJVGAoZxxaJqA5TgHQMwGK84xMdunODVL/3m13kDsAA6IwX5e8KHfKqwxlrjkJdm1XN45b54hs46VnAnT7nDZqdAYGLL9WHy+SdmYTE7A47uZ7zKsNpb4gr1vQnn2mHS+NFBcYytmHbcGbdjKrmRrVkdS69smqhtIi0OUFR1bwToryptqOsLXXzcbGo9rVkeSlk1TXCYtewulkA6Et0Okct+bqhq66GwF9ey6gd9xp7n/eS9vaNAsA4t3qanSBoZxxWJmAoSg/1wSULtonTZmtrk2R4ppdQL8PZX0NatNBTuLNhcU570ySsDGBic5xEx2rL+xqjlf9uH9AfxUBhePu9RiiWsZtD8CabiqC8Yr6PfTY5rxPsgJZwY2SVxfNFYB4l42bJA1dXoJpNo+ECQzljEPHBEzUX+e4qe440J215JIkFh0EOptEqHWQNWkpKzg493/8xHoHv+K4DdKl+FrTEXXWXOFgTl04bqB5545rfmlPje7ALlONDtA7bqrxqp/7J2tO+vnVb2y4pAp0EiGgbAF0p5vqThCVqE8UcsetHI1hW1iTWpF5Vf67bWACXQS66i7ylo6oHuhkc4XvU6Ol9r45Xllpg6FrqUMHqe0i1CQGk0GkbWKgkHAGUU8rXbZZj9Iu311eQPOqC5mQtJVUxZl/YR/KmYauTdGWQdbbTasTRD3vQ6m05EwX6NyZbSV5ETGBVbb+LFtmOxno7SKTltq+x5pdMqGg0t43HaR+46z8mt5BUjnuJqMzNQt00cQANC+Xqxy3QSLsyq64HoAN0rj8WldMU+KODSiMsf+JMfYmxtijjLGcMda8wu8OgW4jlZViD/obXUvUDGWlydRMC37ZgV2jKqA0a066DLLePkl1hLe2KO9gTtrEgMJx9/VMwNR9pjqiouCiyNyB4zY1owi7DBsIO5CW1t2NJkbXjRRXv2baluDVmTlAH1Cao3Pn4O8BuATgfQCmAF58uuYcH9o22CRHv8e0p4LW+/Flpt5FG6yLCcw37CJqFig/e5W2ZwIbdqU0R3hLKUFnl27BNwId4dHidQlHZtzGtmFl4yxpoKvZZdrnBBhqO0TMqX7pnTMAd9A2LO1atbUrFpfxqUGEol1exR3LUAD8aQDnOOd/CsAHTtmWE0GX2crrWXWngoquJXrHbcq4TYGunqlRtTOPNJLXut1Ur72rxe+EqLYjx2Wpscsc6DJwLjLONaOj0d4TXWJgcEQbTJNonxNQtsG2ZShlQJHjJW/t9C31VnZppDgtE4ibt6iSBToTczLUwgA01mSQvDTgnD/BOS/cT24/dBupdLciSow7krx0h/ctkqJxmU9lV0fSUlSeg7VMNx1kj+mz+3qgW3fF+XdEo6i/wVBM7d+ACHQFX4+TDJBdOiLthrhBb8NxU80v+TNb13YGEThfvz9pVxz5ZwKDqK+VVE21CvUZzvUncvvAsM6cHF2E6jMATRehijs2oJwlaGso5S1sOtSLplRSSdRjYKzJUHSLCjAzFAoJZxj1NhiKPLhPz+j6SPN1BknFnABgGPc2GUoirmfVfVb9dAFSx90oMtsDXV7WTTbsoigyG9pzdcnUuDxNW46XZFEjCkZXD3SppZuqduyQ/HcUASWOWPsur5Kty2eqLsLQ5eUPjLFXMsYeYYw9cvXq1dM2B4Chy0tzcJ9EvTtIZlIjz8fXM8aEllwLdKbP6WofCiAbADYdpI72A03qT2nXMNqUi6zSZS2zpbiHXKLhuBPB6HSBrn4fufz/+L4eAWhu1LPuQ6m9x/W8p2CavcZ7BMxtw+ozcl6StDPX16NVuow2nqGULiVOtSjPGDsP4DuP8E/+L875jZN8Juf8DQDeAAAPP/zwVnSG6ZjAXHO0uES9CLjOIOkp9jzJMbU47g16TSjh1BmK7s4R1S7xTI69UUxaZB7G9aKp/oRa1a56QCFx3FGvIeHYpEtAOKJziCsHScUEDldrtr1IckQ9pj1BuH68T8VQCMZrFPdxa55s2AWYa07qMytLZ58Pu/SBTl+jU+2ivk8eOP0ur/MAfvAIz/8cgBMFlG0EY6x0kJuZmtFBmvahEGnvdeZklLziDmsVGoZiY3TyGYCuywuQNZQaQzHatalxryzZ+UlRb4O1B7pSWpKOO6NzkLq2YZvUCyjMidAuccdJu1pFdStoKYtRMpT6vF9f22AuyneRsEicakDhnD8BgOZy4zsMdblonuS4fy/WPislL845GGOVIyKRlmqBbrayMIFamyJpraLOUKwBWExzqSWbbp30YlfcZAK28dLZReW41U63NnY1ahVEga5tM0oVgCuGQiP1ip/Z36iFzVMzc6qfr7ciDnRq0maXvAxSbzh65eyjTmXtxe9atwshQ9FRbJ2OLOwySRIUjruvCXR6u6TjlPbY9qycFKNaDcV0Qi3QHC9bh9NJ0dyHYg4odWlpRei4G2d5GW5FBBTm1EFR/ijvsS4trQMdwbxv1Ogyaxu/ahdl7VAiBJQtgciINqmsaWGZioAkDlIT6Fy1imUHGeRQUzR1Oe5qvAipf5OhmBld0xHR1QTEfo/NfRVmBxlt2NM1QzHNY1MNZdiR5NU2AK+Zpv/3OB4029JdTR/1JoawU14DxtjXAvji8q+fWX7t+8u/3+Kcv/5UDDsm6rum7RLOWiq5OB1gkebVHeX+7dpcWLNV+1qF7diRk2JYL+a2Gq9ywXfIUOZJjovTofbZRmJAKJUMo36tzdouXXZll+gi3DxW37j/Ku4uYWkw89TMzM2JAc38SvICecHR7zF7YlBJvZt2Ucx7iTs2oAD4qwC+qfa115S/PwngDgsozX0Vto2NwHoCL5KcZFHJz9rQbBOztFTX3hdpjriv151PilHcx7XDdRdOm6J8Fwt+WM9sWzC6ed1BEkg49YYJW6BrFOWJmeaqtm9nbGpLr71HylqFlFRlndK2L6zLtmH5DlZZXl09bGROlUQoEi/bKQS+cMdKXpzzb+acM8Ovh07bvqNiFK0ZSnXHgaZzA2hS2aWl3uLDLumAOedlptZekqBwjoDeEZkzyM1MbX18DFGXVy0xcHd5ye4guamPRippy4Dle1zWAzBFoKtdMra0SF71jHtFWKtYO+6i+kzTGmvUnEiL8pKlqXbp571ULaoanWXTqC/csQHlrGE8WHeV2O6EkM8Cmw6SKutQr11dpgU4N3dH1dtglxb54sR2xWstmXNul3AaAbigGy+N9m5rswY2JQlmOD7m5Ha1b7OudwdRSpfj2ikGtmaUkaGdmYQJRJvymm28hpG44bFRlCdpl98cA1tthzG2cdWFTBBMz/tACChbAtURzcvawHTYTlpapuZNkCe2SzmbSrad6s5/2rBLmexUjltlKKusQGENdHK81u25VBKhkEoURmcJdNXtm+p7jPQF1pNiHAvtPSsd9/II3WeUEk6jA88ylwfl1bxdNAvUmYCNOTHGNiRF6g2X6mfY5hdQJoS1mmaQvO4CqJLXrPzdtCO9KeHQHEQHrA8KVD9vYgp0FXNab/Aic9wbga60yzAGcb+HqMc2MjW6ANwrmRyvAp1JigM2j9FZpgWZdCnZ7rKsC1ily6hWq0hzDKIeeiRNH7p6oMNxN5gAXa1COu5ZkhkTPEC08teL31QbejfsWplPrgA251cXAeVOLsqfKYwG68x2VjIUZ5E5XTtIMglHCXS2Yx6AZtswqRSnHMJYMSfLwlKv2xUMhYg5lT83yYtW+11USWKR5iTOEVB2cyeiUSIvuHG8ej22sYFuSWlXjdUKB2ker/FgkwlEPYaISCIE1rKarbtR2NWrGDDljvQ6c5olGSZDi13q/EpCDeWugSh+b2bcRsmrJuHYdOeTQtZ2pHwDWAKKRoqj2CMgbUhz0bxgO2dJfV7NgimlOEAseNm9ZXdE/U6kS7Xl1nbrpvq8ygSo7FKTo7zgWKS5gwl0Y9eaoZSOe5Vhx2LXJI6UjaDmE6ZPbJe8C0hRDWwMpT6/gCB53RVQM8JZS8fdSVE+7le78tfnGdm7z+ZKBklll9oAsA7AtoASbbTnUklx0hkukrwK+CaJsLJrQyKkDShzZbysgU6tCRAyutFAtUuMg81xN+2ieY9qUT7LC6yywsqARxsMWNyKSFELq3eUHa7sDKUueZmOj/GFEFC2BOO4X95BUWC+cjCUekChrAmUP3eVFlVtx9XtIiU7ykAnbZglmfW+bwk147YVfinsMtV2gE0pbkXoINW9JW0CyqgmLVG9x4o5JTlmK3vCIp9X7aK622OoMLpZm4RF2QhJyYBVySvNCyRZgR3HeK39BF13o0QIKFuC0cYEtjMUqXHLCbzKcmOL8UmhatwuyYsxhp1hVDkGSiYgs341s3VKS+l6vwdVQJHyw3zVznFvZJAdJAaCObmlj3HcV/ahEL5HRfI6rLobLYEu3pRwqFpgVYlQzi+XFCff92xlL+CfBGqzgKtJRtgVbUjjlPUTIASUrYHaXy4zfKtmq3SVLBK6DYTqBHZJXoCw+WBJX9uZVlJJ1tpxq8d4kzGU4ZqhtKntqBkkpbSkc5C29zgdRJWDnycZXY1Ok7BYJS8lAB+u7PWWk0AGtcNV7mySqds1SzJrXeMk0I2XrYlhEnfDNCVCQNkSjDU1ARf1nyeiWE5alFcmsEvyAoCdUVQtwGVCJ0nIsZmt8taOe6M1lahrqWIoSaYwzXZF0zmhg1T3lshakm28dkbrgHK4yq1O/iSQAXSerBmKNdAN13YJJkCUsAzl/Moqxm0vyitt/6uczK6dkWqXu0anMidKKU4iBJQtgZysh+VEifvMeiqolHCSXOx1oNuHsmYCkjpbHVG54KkD3VoqyZRMzd6Pr0oScmH6hnQks2NIXgerDDtEjkjtwJu1kJZ2R5uOmyqgqBsb2zjuvdGaAc9WdEygvh6FrY5At8yqf0OWGMR99Ji0S46Xm5nL9Rgkr7sEu6WDO1xm1jtHJKaDPg5X7fRwH3YdlHZFPWY9GkRmkKusQFZwMkekOu5ZG4ZSHqRXFByHSYZdMge5ZijSwbily9IRLekct8pQpEPeG+kvcAM2pUtSBzk4WqATdqWVXVTjNYzEOVizVVbNL2ugG8c4WGXIC9FeTxXoGGPVGmvDgHdHMfKCY5kW1oM3fSEElC1BPSOy6aJAOYGXabXod4ky7t3S6Ui7JgP70SAys90vF/0ekV2q4z5YZhhEvVb7KuZpDs5Bx1AUKa7NuxmXZ2yleYFFmmNnaHbyJ4F65YF0yHtj82ftjuKNjJtM8orWktesRfF7dxRX40VZ/GaMYTro16Ql8/yS81wyByq7gFIFWGbrblBLQNkbi+/tL1OxCZIo0EmEgLIl2FEm5MHSLcnsjWLsL9LKce9ass0T2TVcM5TbixTnJvbPmQ5EDeWwcqY0dlXtuasctxepNduWz6vOlMxxKxLh/jLFdNC37uSW/49rhythF2GgY0ywoP1Fhh6zF3N3RxGSvMDhKkOSFWQOstdjZT0wUxiKLaCsmXwnjnu1DnS2oLpm8ml5TAudtLQzjDBTa3RW6VLM8/2FSD6pEjyJcPTKlmBXYSi3FynOWbJHQGSX+8tMkS+oGMp6Ae8vM6fj3hmJ7OmghdxzEqj3i+8v0yoTM2E86KPgwPXyDhUqRjeIehj0e5glOfYXqZUFAOuA8sJ+GVCIHFGvx7A7jLC/FPWt3VHsZJoA8NztRWkXnavYG0fYX2RVY4pt3450kNdnCZK8IBsvQAQ2NTlyMSdAJF6UzEnaIRM8AFZfIf3C/lIkOFQJnkQIKFuCHcVx31qkePD8yPq8WIQp9he0DEVmtgctA93OMMJhkinMic5xx32hce+3sEs67qsHtEwAEBnjvJT9XAFYynSVXUTMCSiTkEUKDvd7kd+/cntZ2kUYUEYxbi9SjAd97A4j6yGU0q7n94Vd1I57loj1GPWYldHJ93xjliDNuVOyPgl2y07KW/MWAWVcYyiOxOukCJLXlkDt3hAOcmB9fm8UY5UVuD4TGTfVROn1GHYGohDaNqBwvs64KTMi2Tq931LyAoAXDoQjoirKA6Xsl+TYX7gXsGRaV4klL2DtuA9aZKoysMmAQum4z41j7C9T3JonOD+121UPdNSS18EyE3ZNBq0YXRd2yT1Ct+YpdoaR9SgVuS6e218iL7hznZwUIaBsCWT3hpzAbSQvAHj2ppAkKB23lLHaSnEA8OwtaRelVCIc5P4yc0pLUk55fr8DhlIWc9swlK4kL6BktctyvFoylOckQyEcr3Ple7w5T3Fh4k6khF30UtzOcM0Ezjtqh3WJkDTQjcRpFLcWLfxEadczN+fi747nT4oQULYIu8MIt+YJZkl+5IlC6bh3y97/NtLSpalwCE9cm5HbdWk6wPVZUhbl7Z9zvrT76RtivCgd0YXSLlHbcdecAOC5fekg6Rb8uXGM/YV4j26GUpe8KAOdCCi35okzoNTtIpe8VhluzhNccAaUGqMj7KaSrdO350dI8G7SJ3hACChbhZ1RVGX2roxITpRnbi4winukJ4juDCNcn62wygqng7y0MwQAfOr6rPq3VLg4HeDGbNUq0N2zW9olAx2h4768M8D1w5WQvBwL+PLOpl3Uktf+sp2WfmlHOPanbgi7qCWv24sUN1o4bjn/nu7AQcpESjAUe6CTdjxVJiyu/8dJILq8ctycJ04/MSybRJ4pxytIXncRdkcxnr4hXryboaylJerOjd1RXE1Ip+MuHeQT12aYOFpmT4qL0yGeublAVnBnoKs7bsq2zss7Q1w9WLWqVdxbBrpPvnAIgF4i3F+0q4Vd3hmCMeDRKwcAgIsOh3pSuw6WGW4cJk7HfX4co8eATz4v7JKMmAIXJgMcrDJcPVhVDNeEUdzHZNDH41fF/HL9P06C8xOxWfGZmwtnQGGMYW8c4+kged19uDQd4Lmye6WttHTl9pK8t/zCJK6ovNOuMrO92YKOnxSXdgZVp4srI7w4HaDHRLvp+UlMGuguTYfYX2YouGArNkyHESaDPq4dJhhEPdJmgb1RjFl5ZpZkbCbE/R4uTYdV08cFQsct58ksyZ2SV6/HcHE6xKfL+Uhp18Xy3V2fJa0+5/LOsFIYLhLaJdfYCwcrZ/OOsGtQ1Q6pfUUIKFsEdZHLjNqEe/fW33c5h5Pi3r11C/N9e/Z25smgX51QfK/j2ZNCXbQuu/o9Vj1/j2NsT4pLShBpMwaSpdyzMyS5lEnigtJB1WYMpF3nxjGppKomHhccXV7AOkjHfUYagC8r88vFBFS72j5/XFyart9dG2lN9Q+UgQ4IAWWroAaRBy+Mrc9OBlG1mB44Z3/2pFCdzwPn7A6SMVb9P+4lDnRHCSjAenypA7DqWNqMgbTHxWZOCnWetAl09+118x7vV2xp81n3l3Pwvr0RaQBWx+hFLdaYnIOXdwZkh7UCm/P3xRcmzufv3RV2jeM+uWoQAsoW4aHL68nRJvN4oNz86HLyJ8VLLqqOyL3g5cJ68DxtoFODyIsdAVh9/qUX3YvwJFAX/EOXp87n5YJv8+xJoL6Pz2jxWXK8qO1S51ebz3rokniG+j0+dGn981/S4rNeXtreJrk5CV6m2OVKPAHgM+4Rdp0b209H8IEQULYIn//AOQBi4bd58S8qHcQffvF5SrPwBS8Sdl2cDlrdbyKd1Rc9eI7ULvXnt2lM+LwH9gAAn/+iPTKbAOBz71//fJd0CQCf98AugLVDooJ0LMB67tjwWfcJu15EnLCogU4GCxs+935hV5uxPQlUBvxZ9+04n5fzijqgqAc8fmGLufz55bxX3z8ZOOd37a8v/dIv5duGX3rkaf6+p262eva52wv+hrc/xldpTmsU5/yX3/M0f8+TN1o9e+XWgv/fv/c4n68yYqs4f/N7n+EffPpWq2evHiz5G3/3Mb5I6O361fc9w9/1qeutnr16sOQ/9luP8oNlSmwV5//u3U/x3/nwc62evb1I+Gt+/cP85mxFbBXn/8/7n+Vvfu8zrZ6drzL+93/tw/zKrQWxVZz/x48+x9/0zidbPZtkOf+Hb/kof/zqIbFVnP+Xx6/zn/r9x1s9m+cFf/3/9wn+0Su3vX0+gEe4xqcy8b27Ew8//DB/5JFHTtuMgICAgDsKjLH3cM4frn89SF4BAQEBAV4QAkpAQEBAgBeEgBIQEBAQ4AUhoAQEBAQEeEEIKAEBAQEBXhACSkBAQECAF4SAEhAQEBDgBSGgBAQEBAR4wV29sZExdhXAk8f855cBXPNozllHGK+jIYzX0RDG62g46Xi9jHN+T/2Ld3VAOQkYY4/odooG6BHG62gI43U0hPE6GqjGK0heAQEBAQFeEAJKQEBAQIAXhIByfLzhtA24wxDG62gI43U0hPE6GkjGK9RQAgICAgK8IDCUgICAgAAvCAElICAgIMALQkAJCAgICPCCEFBagjHWY4x9F2PsUcbYkjH2NGPstYyxDi5qvvPAGPtsxtirGWPvZIxdZYwdMMbezxj7vjBmbjDGJoyxTzHGOGPs9adtz7aCMXaRMfaPGWOfLNflVcbYWxljX3Hatm0bGGM7jLHvZYz9QbkerzHG/jNj7JsZY8zHZ0TuRwJK/BMAfwfAmwG8FsDnlX//I4yx/4ZzXpymcVuIvwHgVQB+DcCbAKQAvgrAPwDw3zHG/jjnfHGK9m07Xg2xmznAAMbYywC8DcAOgH8F4OMAzgH4wwAePD3Ltg+MsR6AtwD4EwD+NYDXAZgAeAWAn4bwZ3/3xB+ku2g+/Nr8BeALABQAfrn29b8NgAP4htO2cdt+AXgYwDnN1/9BOWbfcdo2busvAH8UQAbgu8uxev1p27SNvwD8HoCnATxw2rZs+y8A/1U5l/5J7esDAI8DuOXjc4Lk1Q6vAMAA/NPa198IYA7gG7s2aNvBOX+Ec35b861fKH//wi7tuVPAGOtDzKvfAvArp2zO1oIx9qcA/EkA/4hzfoUxFjPGJqdt1xZjr/z90+oXOecJxJleMx8fEgJKO3wZBEN5l/pFzvkSwPvL7we0w4vL358/VSu2F98F4HMBfMdpG7Ll+PPl708xxn4dwALAjDH2ccZYSPCaeBeAWwC+hzH21xljL2WMfQ5j7EcAfCmAH/LxISGgtMOLAFzjnK8033sWwGXG2KBjm+44lNn3D0DIOT9/yuZsHRhjLwfw9wG8mnP+xCmbs+34nPL3NwK4COCbAPxNAAmAn2WMfctpGbaN4JzfBPAXAdwA8O8gTll/FKLO+Vc552/08TmhKN8OEwC6YAIAS+WZpBtz7lj8UwB/HMD3cs4/dsq2bCN+EsCnAPz4aRtyB2C3/P0AwFeV0g0YY2+GqAn8MGPsX/PQLKPiEMCHIBpl/jNEIH4VgJ9njH0d5/x3TvoBgaG0wxzA0PC9kfJMgAGMsddAyDhv4Jz/yGnbs20oZZo/B+Bvcc7T07bnDoDsEPy3MpgAVSb+awDux5rF3PVgjH0RRBD5Hc75/845fzPn/F9B1KGeA/DGUkE4EUJAaYdPQ8hauqDyIIQcFtiJAYyxHwLw/RDtiX/rdK3ZPpTz6scB/L8AnmOMfSZj7DMBvKx85Fz5tfOnZeMW4pny9+c037tS/n6hI1vuBHwXRPL7i+oXOedzAL8JMdceOumHhIDSDu+GGKsvV7/IGBsB+BIAj5yCTXcEGGM/COAHAfwbAN/Ky17FgA2MAdwD4C8A+ITy623l97+x/Pu3noZxWwrZIPNizffk117oyJY7AXJfjo6FRLXfj40QUNrhFyB6uL+z9vVvg6idvKlrg+4EMMZ+AKJ75GcBfEvQs42YAfjrml//c/n93yr//munYt124lch6iffyBjbkV9kjD0A4C8B+ATn/JOnY9pW4iPl79+sfrFkvV8H4CaAx076IeH4+pZgjL0OogbwZghpQu6U/08A/kxwlptgjL0KwOsBPAXg/4Bou1bxvI8i4FkGY+whiCL9T3DOQxtxDYyxVwL4lwA+DOCnIDbpfTuABwB8Def835+ieVuF8lSB90LIgG+C8FsXIZLihwC8inP+z0/6OaHLqz2+E8ATAF4JIU1cgzi+4AdCMNFC7s15KcRRD3W8HUAIKAHHBuf8DYyxawC+B8BrIJKWd0CcXPGfTtW4LQPn/EnG2JdDtO3/WQBfD9HY8H4A/yvn3Msm2sBQAgICAgK8INRQAgICAgK8IASUgICAgAAvCAElICAgIMALQkAJCAgICPCCEFACAgICArwgBJSAgICAAC8IASUgICAgwAtCQAkICAgI8IIQUAICtgiMsS9hjP1QeexKQMAdhRBQAgK2C18CcTrzQ6drRkDA0RECSkBAQECAF4SAEhCwJSgvIvvp8q9vZYzx8tfPnJ5VAQHtEU4bDgjYHvwKxNHrrwTwwwA+Wn79xPdUBAR0gXDacEDAFoEx9s0QLOWrOOdvO11rAgKOhiB5BQQEBAR4QQgoAQEBAQFeEAJKQEBAQIAXhIASELBdCEXNgDsWIaAEBGwXDsvfL56qFQEBx0BoGw4I2C68G0AB4PsYYxcAzAB8inP+X07XrIAANwJDCQjYInDOnwLwNwCMAfwkgH8L4NtP1aiAgJYI+1ACAgICArwgMJSAgICAAC8IASUgICAgwAtCQAkICAgI8IIQUAICAgICvCAElICAgIAALwgBJSAgICDAC0JACQgICAjwghBQAgICAgK8IASUgICAgAAv+P8Bv/JoLiDjKCAAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample size=100: \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x388.8 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample size=10: \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x388.8 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def dft_analysis(f, T, N):\n",
    "\n",
    "    \"\"\"\n",
    "    Perform DFT analysis on a given function f with a total time of T and N samples.\n",
    "\n",
    "    Args:\n",
    "        f (function): The function to be analyzed.\n",
    "        T (float): The total time of the signal.\n",
    "        N (int): The number of samples.\n",
    "\n",
    "    Returns:\n",
    "        None\n",
    "    \"\"\"\n",
    "\n",
    "    \n",
    "\n",
    "    t = np.linspace(0, T, N, endpoint=False)\n",
    "    x = f(t)\n",
    "    X = np.fft.fft(x)\n",
    "\n",
    "    freqs = np.fft.fftfreq(N, d=T/N)\n",
    "\n",
    "    fig = plt.figure(figsize=(12.0, 5.4))\n",
    "    axes = [fig.add_axes(\n",
    "    [.1, .25, .25, .6]),fig.add_axes(\n",
    "    [.45, .25, .25, .6])]\n",
    "    axes[0].stem(freqs, np.abs(X))\n",
    "    axes[0].set_xlabel('frequence', fontsize=18)\n",
    "    axes[0].set_ylabel('amplitude', fontsize=18)\n",
    "    axes[1].plot(t,x)\n",
    "    axes[1].scatter(t,x, color='r')\n",
    "    axes[1].set_xlabel('t', fontsize=18)\n",
    "    axes[1].set_ylabel('x', fontsize=18)\n",
    "    axes[0].tick_params(labelsize=18)\n",
    "    axes[1].tick_params(labelsize=18)\n",
    "    plt.show()\n",
    "    plt.close()\n",
    "\n",
    "def dft_target(f, T, N):\n",
    "\n",
    "    \"\"\"\n",
    "    Perform DFT analysis on a given function f with a total time of T and N samples.\n",
    "\n",
    "    Args:\n",
    "        f (function): The function to be analyzed.\n",
    "        T (float): The total time of the signal.\n",
    "        N (int): The number of samples.\n",
    "\n",
    "    Returns:\n",
    "        None\n",
    "    \"\"\"\n",
    "\n",
    "    \n",
    "\n",
    "    t = np.linspace(0, T, N)\n",
    "    x = f(t)\n",
    "    \n",
    "    plt.plot(t,x)\n",
    "    plt.xlabel('t', fontsize=18)\n",
    "    plt.ylabel('x', fontsize=18)\n",
    "\n",
    "    plt.tick_params(labelsize=18)\n",
    "    plt.show()\n",
    "    plt.close()\n",
    "\n",
    "def f(t): \n",
    "    return np.sin(2*np.pi*t) + np.sin(6*np.pi*t)\n",
    "\n",
    "dft_target(f, 8, 1000)\n",
    "\n",
    "print('sample size=100: ')\n",
    "dft_analysis(f, 8, 64)\n",
    "print('sample size=10: ')\n",
    "dft_analysis(f, 8, 10)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Spectral Leakage \n",
    "\n",
    "If the number of samples in a Discrete Fourier Transform (DFT) is not an integer multiple of the signal’s period, the transform may be affected. This phenomenon is known as **spectral leakage**, where the energy of the original signal is spread across multiple frequency components instead of being concentrated at a single frequency component. \n",
    "\n",
    "Aperiodic truncation makes the energy of the original signal spread across multiple frequency components, so we choose frequency peaks to avoid the effects of aperiodic truncation.\n",
    "\n",
    "取一个半周期，或者多点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample size=100: \n"
     ]
    },
    {
     "data": {
      "image/png": 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2vj6org7P8aaJg76+UzFsPLI/rHGUF+Wwv62HsbHYmtBUokMJlYjIHFfX2sPawhySw1RPRGMjAJVH9nNg4TJ60zLPaI8Y3/F2LVlLYc9xCntPhDWO8qIc+oZGaeroD8v+Jb4ooRIRmePq2nrCMkP6KaWlAJzf+gzOkti7aMUZ7RHjO15t4SrObz1wVnuonbrST3VUghIqEZG5q6aGE2s30N4zSPk3vxC+mqatWyEri4q2gwDUFq2CrCyvPZK2bqUvt4CDC0pOxRLOONbe9zsA6t71gegW4ktMUEIlIjIX+Qq09w16E3mW738yfIXiVVWwbRuLF+ayqPcEtasqYds2rz2SqqrY+9k7cJbkJVTLl4cvjpoasm/cQklnK/sWLY9eIb7EDCVUIiJzka9Au25RGQDl7fXhLRSvqoL6eiqeW87uS6+JfDLlU1txCQAVO+6H+vrwxeE7v+vaG6hbtNxri0YhvsQMJVQiInORrxD74PwS8vp7WHSy84z2cKkozuPA0V4GhkfDepyp1DZ3sTA7jcLc9PAeyHce1xxr5NmCYkYt6Yx2STxKqERE5iJfIXZTXiGlna3YhPZw2bA0j9ExF7X5mWpbutmwNA+zMF3R6Oc7j8u6WhlJTqEte/4Z7ZJ4lFCJiMxFvkLxprzFFHcf9doiUCheUezd3qa2uSusx5nMwPAoB9p6TsUQVr7zW9zdDniJa1QK8SVmpEQ7ABERCYOqKpyD5p2ZbH72ca9Ae+vWsNc2Fednkp+Vyu6WyCdU+9t6GBlzVCzNC//BfOex5NYvANC8cj3cenPUasck+tRDJSIyR5149evpT0mn5L+rw1ugPY6ZUbE0j9rm7rAfayL/MSuKI5BQAVRVUfzE3wFo+uinlEwlOCVUIiJzlH8G7+KCMN1yZgobinOpa+1haGQsosetbekiNyOFkoLMiB0zIzWZhdnpmi1dlFCJiMxVzZ3eH/lIJhgAFUvzGBod48DRyBam727uoqI4AgXpE5QUZJ4615K4lFCJiMxRTR19ABRHOqHyDbntjuCw3/DoGHtbeyI33DdOcUHmqXMtiUsJlYjIHNXU0U9uRgq5GakRPe7y+Vlkp6dQG8HC9GeO9jI0MsaGpRG4wm+CkoJMWjoHGBtzET+2xA4lVCIic1RzRz8lEa6fAkhKMs5bmhvRqRP8x4pGD1VJQRZDo2O09w5G/NgSO5RQiYjMUU0d/REf7vOrWJrHniPdjEao12Z3Szfz0pJZsWBeRI43Xkm+d4417JfYlFCJiMxBzjmaO/sjXpDuV1Gcy8DwGIfaeyNyvNrmLs5bmktSUmQL0uF00b+u9EtsSqhEROagrv5hegdHKM6PVkLlDb1Foo5qdMyx54h3y5loKFZCJQSRUJnZajO7zMyi8wkWEZEp+f+4R6OGCmDlwnlkpCbxdFP4r/R79lgvfUOjUamfAshKS2H+vDQlVAku4ITKzF5uZgeBOuAB4Lm+9sVm9oyZvT6Afd1sZj8zs0Nm5sys/hzrl5vZ3WbWYWYnzexBM7sq0NcgIjLXnU6ootNDlZKcxPoluRHpoTo9Q3rkr/Dz01xUElBCZWabgV8CJ4BPwOkbmDvnjgIHgTcFsMtPAVf5tus4x7FXAX8DLgX+B/gwkA380cyuDuCYIiJznr9AOloJFfgK01u6wz6dQG1zF+kpSaxelB3W40ynOF9zUSW6QHuoPgrsAi4GvjLJ8r8Dzwlgf6uccwucc9cALedY99NAPnCtc+7Tzrk7gMt9233FIj01rohIDGvq6Cc7PYW8zMjOQTVeRXEuvYMjNJwIb6JR29LFuiW5pCRHryy4pCCT5o5+nNNcVIkq0E/fJqDGOTfVDZqagKKZ7sw5d2gm65nZPOCVwH3OuZ3jtu8FvgmsBZ430+OKiMx1/iv8ovl/TX+ReDjnoxobc+xu7qYiChN6jldSkMXgyBjHeoeiGodET6AJVTIw3cxlC4FwfJouANLxesAmetj3rIRKRMSnqaM/alf4+a0tzCEtOSmsdVSHO/roGRyJWkG6X7Hmokp4gSZUe/GG2abycrwhwVBb6ntunmSZv604DMcVEYlLzR19Ua2fAkhLSaK8KCes9/TzF6SfH+WEqmS+d65VmJ64Ak2ovgW83szeOW5bZ2ZZZvZFvILxbaEM0Md/3e9kvWMDE9Y5g5ltMbMdZrajvb09DKGJiMSWrv5hugdGojZL+ngVxd6VfuGqLapt6SI12VhTGL2CdBjfQ6WEKlEFlFA5574K/AT4BnAAcMCPgC7gJuC7zrmaUAcJ+PtQ0ydZljFhnTM457Y55zY55zYtWrQoDKGJiMSW5ijPQTXehqV5dPYNh63npra5i7WFOaSnJIdl/zOVk5FKXmbqqXMviSfgSyKcc28BXgf8GdiHN4XC74A3OOfeGdrwTvFfATjZsJ6/bbLhQBGRhONPXqI95AfjZkwPw7Cfc47dLd1URGmG9IlKCjR1QiJLmc1Gzrlf4s1HFSlP4w33XTrJskt8zzsiF46ISOzy/1GPdlE6wLqiHJKTjN0tXbykYsYXgc/Ika4BTpwciuqEnuMV52fy7LGT0Q5DoiQu7uXnmx7hN8BmM6v0t5tZNvAuvOHHR6MUnohITGnq6CczNZn589KiHQoZqcmsWZwdlqkT/PvcEOWCdL+SgiyaOzUXVaKatofKzD46i30659wnZ7Kimb0VWO77cRGQZma3+H5ucM79YNzqNwMvAv5kZp8HuoF34w35vczpEywiAng1VMVRnoNqvA1L83jgQOgvCqpt6SbJYH1RbPRQlRRk0jc0SkffcEwksxJZ5xry+/gkbf7EZeJvqvO1OWBGCRXwTuDKCW3+be8HTiVUzrlnzOwy4FbgI0Aa8ATwEufcPTM8nojInNfUGf0pE8arKM7lF080cbR7gMW5GefeYIZ2N3exenE2mWnRLUj3819V2dTRp4QqAZ1ryG/FhMf5wE68eqXrgY3AhUAV8DhegnP+TA/unNvsnLMpHpsnWX+vc+5Vzrl851yWc+4FSqZERM7U3NEfWwnV7kcAqH3OFVBWBjVBXgxeUwNlZdQ+tpeKh/8c/P5CxH/OdaVfYpo2oXLONYx/ADfgFYdf5pz7sXPuKefcLufcj4DLgGHgPeEPW0REJtM7OEJH3zDF+dGfMgGAmhrW//s/Y26M2sJV0NAAW7bMPgmqqYEtWzh6rIu2nAVsOLQruP2FUInvnGsuqsQUaFH6PwA/ds6NTFzgnBsGfuxbR0REouD0HFQx0kNVXU121wlWnGjm6cJVXltfH1RXz3p/9PWx27evitaDwe0vhHIzU8hJT9Fs6Qkq0IQqF5jucop83zoiIhIFzZ2+KRNiJaFqbATgOS37eHRZBSOWdEb7bPf399ILSB0dZsPRQ8HtL4TMjGLNRZWwAk2ongRuMrNVExeY2Wrgn/HqqEREJAqaYq2HqrQUgKufeZSuzBweK9lwRvts9ueA7Wsu4dKGp8ge6g9ufyHmTe6pHqpEFGhC9R94PVC7zezHZvYJM/u4mf0EqAVy8K7AExGRKGju6Cc9JYlF2ZPdqSsKtm6FrCwuf/ZJ0kaG2L7mYsjK8tpnub+DxWt4dn4x1zzjFbsHtb8QKynIorlDc1ElooBmSnfOPWRmm4HPc3at1MPAvzrnHg5NaCIiEqimjn6K82NnDiqqqgCYV13NZQ272L7+BfzXOzZjvvbZ7G97ezq0er1eLF/uJVOz3V+IlRRk0jM4Qnf/CHlZqdEORyIo4FvPOOceAZ5vZouAlXhzTx10zoV+1jYREQlIU0df7NRP+VVVQVUV1zzSyF9++TT7r76C8iB2tz1tCecXO5Z0x96fHf/tfpo6+8jLio0Z3CUyZn3rGedcu3PuEefcw0qmRERiQ3NnbM1BNd6L1i8GYPue1lnvo71nkCcPd3L1+sJQhRVSJQWaOiFRBdRDZWYzqvpzzkX/cgsRkQTTPzTKsd6hU3/UY01hbgaVy/LZvqeNm65aM6t93LuvDefgmvNiM6E6PVu6EqpEE+iQXz2nbz0zndi4D4CISALxT5kQqz1UAC8+r5DP/rGOtu4BCmdxG5rte9oozs9k/ZKcMEQXvIKsVLLSkjVbegIKNKH6b85OqFKAVcCrgKeB34cgLhERCZC/V8RfxxOLrl7vJVT37G2j6uLlAW3bPzTKgweO8eaLSmOn6H4CM/NNnaC5qBJNoFf5fXyqZWa2Evg73n3+REQkwk7PQRWbQ34AawuzKZ2fxfY9gSdUDx5oZ3BkLGaH+/yK8zUXVSKadVH6RM65Q8DXgU+Eap8iIjJzzZ39pCYbi3NiZA6qSZgZV68v5G/PHOfk4Fl3MZvW9j1t5GSkcNGK+WGKLjRKCrJ0+5kEFLKEyqcZOC/E+xQRkRlo6uhnaX4mSUmxORzmd815hQyNjvHA/plfID465rh331FeWL6Y1ORQ/+kKrZKCTLr6h+kZGI52KBJBof5UvhroCPE+RURkBpo6+mK6IN3veWUF5GWmsn1P24y3ebKxg+Mnh2J+uA9OX+mnXqrEEui0CR+dYtF84CqgAvifYIMSEZHANXf0s7l8UbTDOKeU5CSuWreYe+uOMjI6RsoMepy272kjNdm4Mg5e36m5qE70s64oN8rRSKQEepXfx6dZ1grcAnxm1tGIiMisDAyPcrRnMKYL0se75rxCfvlkMzsaOrhk5YJzrr99bxuXrFxAbkbs387l1GzputIvoQSaUK2YpM0BJ5xzvSGIR0REZqGl03+FX+wP+QFcsXYRaclJbN/Tds6E6mB7L4faT/L255dFJrggLcxOIz0lSUN+CSagGirnXMMkj0YlUyIi0eX/4x3Lc1CNl52ewqWrFnDP3jacm36+6Ht8tVYvitHbzUx0ei4qJVSJJKCEysxGzez6aZa/0cxGgw9LREQCcWoOqvnxMeQH3rBfw/E+Dhyd/v/k2/e0sWFpbtwkiwDFmjoh4QR6ld+5rsWN7Wt1RUTmqOaOfpKTjMIYnoNqIv8Njqe72u9Y7yCPN3bExdV946mHKvGEetqEUqAnxPsUEZFzaOroY0lexoyumIsVRXkZXJA5wvaaP0BSEpSVQU3N6RVqarj3FW/DObj6Q/905rIYV5yfyYmTQ/QNBTZ5qcSvcxalm9mr8O7T57fFzK6eZNX5wNXAQyGKTUQk7plZEvAB4AagDGgHfgp81Dl3MlTHaeroj5uC9FNqarjm3j9w26Vv4mhWPosbGmDLltPLt2xh+7X/wtLuo2zY9VfY8qTXXlUVnXgD4H8vmjv6WVMYmzdyltCayVV+G4G3+/7tgCt8j4l6gb8BN4UiMBGROeLzwPuBXwK3Aet9P19oZlc758ZCcZDmzn6ev2phKHYVOdXVXN1n3Hbpm/jwSz/Ask7f0N9dT3nPl72NB1dcyD88dY9XT9LXB9XVcZJQ+eaiUkKVMM7ZN+yc+4RzLsk5l4RXI/UW/88THrnOuRc7554Jf9giIpMzs4+b2ZT1nGY238zujlAsG4D3AXc5517rnPuGc+5fgX8FXgi8KeiD1NQwtHIVrZ19lHz/63E1LEZjI+va67n82SeoLVzN78sv8x5LL/Ae5ZdR0N/D62r/fMY28aDkL78HoOn6fzp7KFPmpNnMQzXzmy+JiETeR4HNZlblnGsev8DMrgTuBBZHKJY34/1H9H8ntH8DuBV4C/DDWe+9pga2bOFIWi7OkihuPABbvucti4NeHEpLsYYGfvDTCTfhWL7ce25omHSbmFdTw6J/voG0G++kKXcRPDluKDMe3heZldnMQ6WpX0Uklr0HeB6wy1cDipklmdkngXuAEeDKCMXyPGAMeHR8o3NuANjpWz571dXQ10dzrpcflnS1nR4Wiwdbt0LWhGkesrK89umWxbrqapL6TlLcfZSmPF/uHk/vi8zKtAmVmX3bzL5lZsnjfj7X41uRCV1E5GzOuW3ARcAR4C4z+xrwAFAN3AVsdM49HKFwlgLHnHODkyxrBhaaWdpkG5rZFjPbYWY72tunGBjwDX/1pGeR399NSdfRM9pjXlUVbNvm9UiZec/btnnt0y2Ldb7z7yVUhWe1x7yaGm+YcoorL6dcluDONeT3drxC9BuBUU4Xp0/HAe8MKioRkSA453ab2fPweqTe7Wv+T+fcrREOJQuYLJkCGBi3ztDEhb7EcBvApk2bJp9KvLQUGhq49sDDXHvg4TPb44U/eQp0WSzzvS8lXUe5Z9VFZ7bHOt8wMn2+wahJrrycdFk8vk8hNm1C5StEn/JnEZFY5Ov1+R/g+cBBvDnybjKzvzvn7o9gKH1MXa+VMW6d2dm69cw/cBA/w2Jzme99Ke46yrHsAgZS0shIS4mP98U3jNyWPZ87LnkDw0m+NOGXT3vPL3gHABVtz3D9rj/G1ZWX4RZoUbqISEwzs7XAj/GmfPkq3hV1lb62e8zs08DHQzVdwTm0AOeZWfokw37FeMOBZ/VOzZj/j1h1tTecVFrq/dHWH7fo8p3/km13A9C8rpJVH/lAfLwvvmHJmo3X8b3nvoKFvR1nLi+CgdR0flL5Yl627yHyBk/Gz1BmmCmhEpG55nFgGHidc+6XvrZHzawSbwjtFmAzk8+nF2qPAS/Gq+l60N9oZhl4Cd8DQR8hXofF5rqqKkouuw6+9neafvFbVq1dFO2IZsY3XPmnNZdwUePT/PRHN3vt4668fGJpOa99623ct3ITr9p7f3wMZUbAtAmVmX10uuVTcM65T84yHhGRYO0CrnfOnfHfZudcD/BmM7sH+EKEYvkJ8J/ABxmXUOHVdWUBquidw/w3c26Op3v6bd3K4Q9Vs2/xCm6595te2/hh5C1b2Niyn4W9HfxpzcW8quGx+BjKjIBz9VB9fBb7dIASKhGJliudc6NTLXTOfcvMInKLLOfc02b2Fbz6rbuA33F6pvT7CWYOKol5hbkZpCQZTR1xNNtQVRX3HEuDI3D1M496PVMThpGTqqu5+uCj/N95VzD0+m2kqYcUOHdCtSIiUYiIhMh0ydS4deoiEYvPB4F6YAvwMuAY8CW8e/lFoo5LoiQ5yVian0lTPPVQAduzlrFm8SBlJ5rPXugbYr5mbxs//t4OHr74yoiMnceDc13lN8k0tSIiMlO+BO8230MSTHF+Js2d8ZNQdfUN88izJ7jhipXTrnfZ6oVkpiazfU8bV8RLfViYBTUNgpllmlmc3d5cREQkMkoKMuNqyO++/UcZHXNcfV7htOtlpCZz+ZqF3LO3DecmnyYt0QScUJnZYjO7w8xagF6g18yO+NqmfwdEREQSSHFBJm3dgwyOnHMkOib8aU8bi3LS2ViSf851rzmvkCNdA+xu6Q5/YHEgoITKzFYAT+LdK6sL+BXwa6DT1/aEmU3fTygiIpIgSgq8+xEe6Rw4x5rRNzgyyv117Vy9fjFJSXbO9a9at5gk85IwCbyH6jZgAfBa59x659xrnXOvcc6tB17nW/a5UAcpIiISj0oKvKqYeChMf/jQCXoHR7h6/cwGmxZkp/Pc5QVsV0IFBJ5QvQj4inPu7okLfBPofdW3joiISMI7NRdVZ+zXUd2zp43M1GQuW71wxttcc14he490x1WdWLgEmlA54MA0y/f71hEREUl4S/IySE6ymO+hcs5xz942rli7kIzU5Blvd815RYCXjCW6QBOq+4EXTrN8M3DfbIMRERGZS1KSkyjKzYj5hKq2uZsjXQMzHu7zW7FwHqsWzWP7XiVUgSZUHwQuNrPbzOzUHdR9V/7dDlzsW0dERETwrvSL9dvPbN/bRpLBiwJMqMDrpXrk0Am6+ofDEFn8CDSh+jOQiZc0HTGz42Z2DDgCfMC37F4zOzTucTCkEYuIiMSReJiLavueNjYtn8/8eWkBb3vNeYWMjDnuqzsahsjix7luPTNRI6qREhERmbGS/ExauwcYHh0jNTmo+bTD4vCJPvYe6eY/X7puVttvXJbPwuw0tu9p41Ubi0McXfwIKKFyzm0OUxwiIiJzUklBFmMOWrsGWDY/K9rhnOXPvvonf4F5oJKTjBetK+R3Tx9haGSMtJTYSxojITFftYiISIT456I6HKPDftv3trF6cTYrFs6b9T6uOa+QnsERHnn2eAgjiy+zTqjMLMvMlplZ6cRHKAMUERGJZ8W+hCoWC9O7+od55NCJgK/um+iy1QvJSE1K6Ek+A731TLKZ/aeZNQM9QD3w7CQPERERAZbkZWIWg7Ol19Rw37VvYmTMcc0tN0JNzax3lZmWzOWZg9xzz5O4pCQoKwtqf/Eo0KL024H3AU8APwM6Qh6RiIjIHJKWkkRhTozNRVVTA1u2sP3qm1h4soMLn7gftjzqLauqmtX+rrnrh2y/+r3sXrSCioZDsGXL7PcXhwJNqKqAu5xzrw9HMCIiInNRSUFmbN1+prqaoYEh7l/5XF667yGScNDXB9XVs0uAqqu5qr0Te9F72L7mEiqOHgpuf3Eo0BqqVOBP4QhERERkrvLmooqhHqrGRnYXrqQnfR6bDz1+Rvts97ewr4sLjhzg4dLzg99fHAo0ofobcF44AhEREZmrigsyae0aYGR0LNqheEpLqS1cBcAFRw6c0T7b/QFc0HqAPYUrGcOC218cCjSh+nfgejN7VTiCERERmYtKCrIYGXO09QxGOxTP1q3sLllHQV8XS3vavbasLNi6ddb7IyuLiraD9KTP43B+YXD7i0OBTuz5tJm9G/iFmbXgXdE3evZq7kWhClBERCTeFed7Uyc0neg79e+oqqqi9kA2FfUHMDOvJ2nr1tnXO/m22/DZrwJQW3EJy9/z+oSpn4LAp014KfBT33a5QCmwYsJjZYhjFBERiWv+yT2bO2OjjmpoZIy64VQ2vPHlMDYG9fXBJz9VVazd8QCpyUZt9acTKpmCwK/yuxU4DLzGOfd0GOKZlplNdR/Bk8657IgGIyIiMkNL/T1UMVKYvr+th+FRR0Vxbkj3m5aSRHlRDrXNXSHdbzwINKFaA/xHNJKpcR4Etk1oG45GICIiIjORkZrMopx0mmLk9jO7W7yEp2JpXsj3XbE0jz/ubsU55w0nJohAE6oGICMcgQTgkHPuzijHICIiEhBvLqrY6KGqbe4mJz2F0jDcrHlDcR4/fuwwLV0DsVEvFiGBXuX3ReBdZhbV4TUzS4t2DCIiIoEoKciKmSG/2pYuzluaS1JS6HuQKpZ6w4iJNuwXaELVC3QCe83sv83sHWb2jxMfoQ/zDK8H+oAeMztqZl8ys9D3WYqIiIRQcX4mLZ39jI1NVQ4cGSOjY+w90k1FcXj+dK5fkktykrE7wRKqQIf8vjvu37dMsY4Dvj+raM7tUbx7CD6Dd5XhS4GbgCvN7PnOud4wHVdERCQoJQWZDI86jvYMUpQXveqZg+0nGRgeC3lBul9GajKrF2VT29Idlv3HqkATqheGJYoZcs5dPKHp+2b2FLAV+IDv+QxmtgXYAlCaQDO2iohIbCku8F/p1xfVhMo/FBeOgnS/DcW5PHTgWNj2H4sCndjz/nAFEoTPAh8DXsYkCZVzbhu+qwI3bdoU3X5WERFJWMvGzUW1KYpx1LZ0kZGaxMpF4StFrliax11PNHO0e4DFudG+li0yAu2hAsDMNgEXAwWcXYflnHOfDDawmXLODftmbV8YqWOKiIgEqjjfu6Iu2oXpu5u7Oc9X5xQu/vqs3S3dSqgmY2aZwF3AiwHDq5fyvyNuXFvEEiozywBKgIcjdUwREZFAZaYls2BeWlQTqrExx+6WLl733JKwHue8cVf6vXDd4rAeK1YEepXfR/GSqa149VQGvA24Dm/CzceA80IZoJ+ZLZhi0SfxEsPfhOO4IiIioVJSkBnVyT3rj5/k5NBoWOunALLTU1i5cB61LYlzpV+gQ36vB37mnPvouASn2Tl3r5n9GS+hejtwcwhj9LvFzC4B/gI0Atl4V/m9EHgE+FIYjikiIhIyxQWZ7DvSE7Xj+6+82xCmK/zG21CcxxMNHWE/TqwItIdqGeAvTB/1PacBOOdGgB8BbwpNaGe5D+jG6xH7X+ATwHygGtjsnIuN2dJERESmUFKQRXNnP85F5xqp3c1dpCUnsWZxTtiPVbE0l+bOfjpODoX9WLEg0B6qnnHb9ABjwNJxy7uAohDEdRbn3K+AX4Vj3yIiIpFQUpDJ4MgY7b2DLM6JfLF2bUsX5UU5pKUE2p8SuPGF6S9YM/evGwv0jB4E1gI450aB3XjDgJh3B8TXAodDGaCIiMhc4b+3XTQK051z1DZ3h21Cz4k2+AvTE6SOKtCE6h7gdWaW7Pv568BLzOwgcAC4GvhWCOMTERGZM0oKvKkTmqOQUDV19NPVP8yGMBek++VnpVFSkJkw9/QLdMjvVuAH+KZKcM7d4Zu24C14NVXfAP4npBGKiIjMEadnS498QrXb11MUrnv4TaZiaZ4Sqsn47pVXN6HtduD2UAYlIiIyF2Wnp5CflUpzZ+SnTqht7iY5yVhXFP6CdL+K4lz+sLuV7oFhcjNSI3bcaAh/VZqIiIic4s1FFfkeqtqWLtYsziYjNfncK4fIBl9v2J4EuFGyEioREZEIKs6PfELlFaR3Rax+ys8/gWgiDPspoRIREYmgkoIsmjsiOxfV0Z5BjvUORewKP79FOekU5qazWz1UIiIiEkolBZn0D49yIoITXvp7iCJZkO6XKIXpSqhEREQiqPipRwFoXns+lJVBTU3Yj1nb3I0ZrF8S2R4q8OqoDrb30jc0EpkD1tR45zUpKWLnF5RQiYiIRE5NDSW3fgKAptzF0NAAW7aE/Y9+bUsXKxbOIzs90NmSglexNJcxB3sjcQ/DmhrvfDY0gHMRO7+ghEpERCRyqqspbmsEoClvsdfW1wfV1WE97O7mrlMF4pF2+hY0ERj2q66Gvj6uf+NW7tx4ndcWgfMLSqhEREQip7GRvMGTzO/r4uD8kjPaw+V47yAtXQMRL0j3W5KXwfx5aZGpo2pspCMjh7+VVdKXlnFGe7gpoRIREYmU0lIAytvrqVu0/Kz2cPBfYRetHiozY8PSXGqbI3ClX2npqfNa3t5wRnu4KaESERGJlK1bISuL8vYG9i9czhgGWVleezjU1FD7gf8EYMN1l0esQHuiis4m9jd3MJiaFt5C8a1bqSteA8C69nqvLZzndxwlVCIiIpFSVQXbtlE+1kNfWiZN510I27Z57aHmK9Denb6AZZ2t5D2zL2IF2hPjqPj+HYwkJbN/QWl4C8Wrqtj3mreQP9jL4pMdsHx5+M7vBEqoREREIqmqivLvfgWAfT/9bfj+2PsKtJ8uXM2GtoNeW4QKtCfGUdG4B4Cni1aHPY667ELWrivFxsagvj4iyRQooRIREYm4tYXeDYr3t4VxKgFfgXZjwRIuOHLgjPaIamyktLOV3IFenlqyNqxxOOfY39Yb0RtA+ymhEhERibDs9BSWzc9kX2sYE6rSUnYt8eqJNh7Zf0Z7RJWWYkDlkf3sHJ9QhSGO5s5+egdHKFdCJSIikhjKC3OoC2dCtXUru0o3YG6M81t9PVQRKtCeGAdZWVzYUsf+haX0paaHLQ7/+SwvVEIlIiKSEMqLcjh07CSDI6PhOUBVFbuueS2ru9vIGR6IaIH2xDjYto3K0U7GkpKprbwsbHH4e/zWqodKRGRuMbMbzKzGzPaZ2aiZuWjHJLGhvCiX0THHofaTYdm/c45dY/OovOp5EOEC7bNUVXHBH38BwK7bvhG2OPa39VCcn0luRmpY9j8dJVQiIuF1M/BK4CjQEuVYJIb4C6fDNezX1NHP8ZNDVC7LD8v+A7UoJ53i/Ex2NnWG7Rh1rT1RqZ8CJVQiIuG2Gchzzl0B7IpyLBJDViycR2qyha0wfZcvcdlYkh+W/c/GxmX57DrcGZZ9D4+OcbC999QVlJGmhEpEJIycc/XOubFoxyGxJzU5iVWLsqlrDc8tWXYd7iQtJSlqPTaTqVyWR1NHP8d6B0O+70PtJxkedVGZMgGUUImIiERNeVEO+9t6w7LvXYe72LA0l7SU2PlTX+nrLXsqDMN+db45vTTkJyIip5jZFjPbYWY72tvbox2OhEl5UQ7Nnf10DwyHdL8jo2M83dx1KoGJFRXFeSQZ7GzsDPm+61q7SUkyVi3KDvm+ZyIlKkcVEYkjZpYPfDCATb7onDsRzDGdc9uAbQCbNm3SlYFzlH++pP2tPWwqmx+y/e5v66V/eJQLS/NDts9QmJeewtrCHHY2dYV833WtPaxYOC9qPXJKqEREzi0f+FgA698JBJVQSWLwD0/tC3FC5S9Ij7UeKvAK039f24pzDjML2X73tfawMYpXNGrIT0TkHHyF5RbA45loxyzxoTg/k5z0lJDf02/X4U7yMlNZviArpPsNhcpl+XT1D9NwvC9k++wdHKGpoz9qBemghEpERCRqzIy1RTkhnzph5+FOKpflh7QHKFT8vWa7QliYvv9UQXpuyPYZKCVUIiIiUbTWd08/50JTKtc3NML+th42luSFZH+htrYwm4zUJHaGcD6qaN7Dz081VCIiYWRmrwAqfT+u9rXd4vu50zn35agEJjFjXVEOP3q0kbbuQYryMoLeX21zN2OOmJkhfaKU5CTOL84L6QSfda09ZKUlU1KQGbJ9BkoJlYhIeL0OeNuEtk/6nhsAJVQJzl+YXtfWE5KEyp+oXBCDBel+lSX5fP/hBoZHx0hNDn6wrK61h7WFOSQlRW+IU0N+IiJh5Jx7+zTF62XRjk+izz9MFaoZ03c2dVKcn8minPSQ7C8cKpflMzQyFpL7GDrnqGvriWpBOiihEhERiaqCeWkszkkPWWH6rsOdbIyx+acm8k9vEIo6qvbeQU6cHIraPfz8lFCJiIhEWXlRTkh6a471DtLU0R9TN0SeTElBJgvmpYWkjsp/3tRDJSIikuDWFeVw4Ggvo2PBXennT1BitSDdz8yoXJYfkh6qU1f4KaESERFJbGsLcxgaGaP++Mmg9rPrcCdJBhXF0ZuPaaYqS/J5pr2XniDvY1jX2sPC7HQWZEe3ZkwJlYiISJSt801IGeyw386mLtYW5pCVFvsX8Vcuy8M5eLo5uPv61bX1UF4UnRsij6eESkREJMrWFGaTZARVmO6c8wrSY3y4z+/UjOmHZ59QjY459rf1UF4Y/R45JVQiIiJRlpGaTNmCeewPIqFqON5HV/9wzNdP+RXMS2P5gqygCtMPn+hjYHgs6gXpoIRKREQkJqwtzKEuiJsk+++NVxnjV/iNV1mSH9Q9/fw9emuVUImIiAh4V6nVHz9J/9DorLbfebiTzNRk1hZGv55opjYuy+dI1wBt3QOz2r6utQczYuI1K6ESERGJAeuKcnAODhydXS/VrsOdnF+cR0oIbuUSKf7hydkO+9W1dVM6PysmivDj56yLiIjMYafu6TeLOqrh0TFqW7qpXJYX6rDCasPSXFKSbNbDfnWtPadu3RNtSqhERERiwPIF80hPSQo8oaqpoW7TlQyNjFF56y1QUxOeAMMg46c/Zt2xBnZ95+dQVhZQ7APDo9Qf74v6hJ5+SqhERERiQHKSsaYwO7DC9Joa2LKFnXhJReVTf4UtW+IjqfLFXtlQy66iNYw1NAYU+zO+meWVUImIiMgZyk8eY99TByEpaWY9NtXV0NfH48XrWXCyk5Luo9DX57XHOl/slUf205ORzf6FpTOPvaaGuqp3A7DuLa+JiQRSCZWIiEgsqKlh3f/9mPbMPE5k5EBDw7l7bBobOTovn9+uewEvPvAwNq495vli3HxoB2kjw3z/OS8/o31Kvp6t/ZZN2sgwZbU7YqJXTgmViIhILKiuprz5AACPF6/z2s7VY1Nayrc3vYqRpGS2PHrXGe0xzxfj4pOdvK72Hn5+/tUcnVdw7thP9cqtY9Xxw6S4sZjolVNCJSIiEgsaG7nocC3FXUf5wmXXM+bvb5qmx6brvz/Fnc95GdfV/ZUVHS1eY1YWbN0agYCDtHWrFyvwnkd+wUhSEt+69PXnjr2xkQfLNrKjZAOvr73njPZoUkIlIiISC0pLyRgd5t8e/AG1Rav5zfrLT7VP5c5lF9GblsV7G/4KZrB8OWzbBlVVEQo6CFVVXqzLl7O8q42XH36CO5/3Srpe8w/TbjZWupxbr3w7JZ2tvOXJ351eEOVeOSVUIiIiscDXY/Pq3fexvu0Qn7viHxnMzp2yx6Z/aJRvP/Qsm8sXsWHnQzA2BvX18ZFM+VVVeTGPjXHj7f/KyTHj+3+vn3aTX3/oM+wuWs2HHryT9NERrzEGeuWUUImIiMQCX49N0vJSPnL/dzmcX0TN//vmlAnST3cc5vjJId67eXWEAw2P9UtyuWrdYr7zt/opb78zODLK504uZEPGCK88WR9TvXJKqERERGKFr8fmioM7uGz1Ar7UlUf3wPBZqw2PjrHtgUNsWl7ARSvmRyHQ8Hjv5lWcODnEjx+bvB7qB39voKmjn49UPZ+k+mdjqldOCZWIiEiMMTM+8pL1dPQN8/X7D561/Nc7W2ju7Oe9L1wVhejCZ1PZfC4qm883HjjE0MjYGcu6+of58l+e4fI1C7l8zaIoRTg1JVQiIiIx6PySPF5ZuZRvPfQsrV0Dp9rHxhxfvf8g64pyeGH54ihGGB43vnAVLV0D/Gpn8xntX7v/IJ19w/zHS9ZFKbLpxVVCZWZJZvYvZrbPzAbM7LCZ3WZm86Idm4iISKh96MXljI45/vee/afatu9t45mjvdy4eRVmNs3W8Wnz2kWctySXr91/kLExB8CRrn6+/dCzvHrjUiqKY/MG0HGVUAGfB24H9gDvA34GvB/4jZnF22sRERGZVumCLKouXs5PdxzmQFsPzjnuuO8gpfOzeNn5S6IdXliYGTduXsXB9pP8aU8rAJ/fvh/n4N9eXB7l6KaWEu0AZsrMNuAlUXc55143rv1Z4IvAm4AfBnOMu59s5rN/rKOls5+l+Zl8+NpyXn1h8ayXhXp/sXKscy2bzfkN9XahPlasnN9YOZaIRM77rlrNzx9+ls/825f5p4d+wq43bWXr0j5SkuduP8JLz1/Cbb/YwR1f+CUr7/4ffv6OL/GORUMsm58V7dCmFDcJFfBmwID/ndD+DeBW4C0EkVDd/WQzN9/1NP3D3qWazZ393HzX06eWB7psR8MJfvF4c8j2FyvHOteyqf7gTnd+p/sjPZvtQn2sWDm/sfKZUlIlElkLfvVz3vPX3/O5S9/MMy9eyKLeE7zulvfBgqGYuLotHJJ/9ENu+MNPuPmqG9jymmrmDfVx063vh6UDMfuazTkX7RhmxMz+CFwNZDnnBics+yuw1jk3bdn/pk2b3I4dOyZddtmt99Lc2c8NT/2KlV2nC+HSU5IBb+6LiaZbZmZMdm5nu79YOda5ll1Yms+eI90AnLck99SyJxs7p90GmNV2kThWrJzfaH2mDuUV8/ULXgVAcX4mf/3IVWet79vmcefcpkkXSlCm++6SBFBWRl9LK5vfvY2jOQu4+S/f5oZH7/LmX6qvj3Z04VFWxmBTM1fc8C3achbw7/d9l/c+8vOwvOZQfXfFUw/VUuDYxGTKpxl4vpmlOeeGxi8wsy3AFoDSaaalb+nsn7R9sj82M1k2VaI62/3FyrFmsmx8knKu7ca3z2a7SBwrVs5vLHympvo9EZEwamwkyzn+695vcsclb+D6nb8/1T5nNTaS7hz/9uCd1Gx8Ce94/Den2mNVPCVUWcBkyRTAwLh1zkionHPbgG3g/S9vqp0vzc+kubP/1P/E/YrzMwFvyGOi6ZYlmzE6yR+l2e4vVo51rmVvnKL34npfD2Ag28x2u1AfK1bObyx8ppb6thGRCCothYYGXrHvQV6x78Ez2+cq32v+h6e38w9Pbz+zPUbFU0VbH5A+xbKMcevMyoevLSczNfmMtszUZD58bfmslr354mUh3V+sHOtcy6Yym21mu12ojxUr5zdWPlMiEmG+e/ydIQbuXRdWcfia46mHqgU4z8zSJxn2K8YbDhyaZLsZ8RfaTndVU6DLNi2fH9L9xcqxZrJsNuc3VNuF41ixcn5j6TMlIhHiL8KurvaGvEpLvcQiRouzQyIOX3M8FaX/P6AauMI59+C49gzgOPCAc+666fahwk6R8FFRevjou0skfEL13RVPQ34/ARzwwQnt78arnaqJdEAiIiIiEEdDfs65p83sK8BNZnYX8DtgPd5M6fcT5KSeIiIiIrMVNwmVzweBerxpEF4GHAO+BHzUOTc29WYiIiIi4RNXCZVzbhS4zfcQERERiQnxVEMlIiIiEpOUUImIiIgEKW6mTQgFM2sHGqIdRwAW4tWJiUfn47RYPBfLz3U/TZmdGX53xeJnQvS+xKrx70tIvrsSKqGKN2a2Q/P6nKbzcZrOhUykz0Rs0vsSm8LxvmjIT0RERCRISqhEREREgqSEKrZti3YAMUbn4zSdC5lIn4nYpPclNoX8fVENlYiIiEiQ1EMlIiIiEiQlVCIiIiJBUkIVg8zsBjOrMbN9ZjZqZtOOy5rZUjP7vpm1m1m/me0wszdEKt5wMbMkM/sX33kYMLPDZnabmc2LdmzhZGY3m9nPzOyQmTkzqz/H+uVmdreZdZjZSTN70MyuilC4Eiah+Pyb2UvN7G++z8UJ3+dqRTjjnuuCfV/M7D7f7/VkD02vMAuBfmdOs5+gfl9UQxWDfB+GBcCTwAqgxDlnU6w7H9gBLAZuB5qA64ErgX9yzn0nEjGHg5l9AXg/8Evg98B64H3Ag8DVc/WG2L4E+gTwBPBcoNs5VzbFuquAR4ER4H+BLuDdQAVwnXPungiELGEQ7OffzF4L/BzYBXwDyMO7wfwosMk51xK24OewELwv9wEbgH+ZZPHvnHMnQhpwAgjkO3OafQT/++Kc0yPGHkAZkOT79/95b9OU6/4P4IBXjGtLxvsjexzIjvbrmeU52ACMAb+Y0P4+3+u9PtoxhvG1rxz371qgfpp1f+r7hd84ri0bb1btOnz/adIjvh7Bfv6BVKDZ9znIHte+0fd52Rbt1xiPj1B8LwH3Tfc7rces3pcZf2dOsX1Ifl805BeDnHP1bua9L9cDB51zvxm3/SjwJWA+8NIwhBgJbwYMr9dlvG8AfcBbIh1QpDjnDs1kPd8QwyuB+5xzO8dt3wt8E1gLPC8cMUrYBfv5vxJYCnzT93kAwPc5uQ94o5mlhijWRBKy7yXf0GGumU06+iAzN9PvzGmE5PdFCVUcM7MlQDHw8CSL/W3x+gf1eXj/E3x0fKNzbgDYSfy+rlC6AEgH/j7Jsnh//xNdsJ9///KpPhu5eAm3BCZU30vFQC/eEH2vmd1lZutCGKcEJiS/L0qo4ttS33PzJMv8bcURiiXUlgLHnHODkyxrBhaaWVqEY4o1c/n9T3TBfv712QiPUHwvPYtXqvEO4A3AHcB1wCNmdn4og5UZC8nvS0rIwpEzmFk+XkHbTH3RBV6MmOV7nuyXe2DCOvEmi8lfF5z52oYiE05Mmsvvf6IL9vOvz0Z4BP295Jx7x4Smn5vZr/GGlm4HrgkyRglcSH5flFCFTz7wsQDWvxPvKoVA9Pme0ydZljFhnXjTh3fl4mTi/bWFylx+/xNdsJ9/fTbCIyzfS865B83sAeCFZpbpnOufbYAyKyH5fdGQX5j4CsstgMczsziM/zLOyboi/W2TdWHGgxa87vPJPuDFeN3uidw7BXP7/U90wX7+9dkIj3B+L9XjXaFdMMvtZfZC8vuihCqOOeeO4L3Jl0yy2N+2I3IRhdRjeJ/Pi8Y3mlkG3qWs8fq6QulpvC7qSydZFu/vf6IL9vP/mO95qs9GN7A/uBATUji/l9bgzSeneagiLyS/L0qo4t+PgFVm9gp/g5kl482L0gn8LkpxBesnePO6fHBC+7vxxrJrIh1QrPFd3vsbYLOZVfrbzSwbeBdwgAlXI0ncmPHn38yWmNk6Mxtf43E/cAR4l+/z4F+3EtgM/Mw5Nxye0Oe0oN4XM8vzfT+fwcxeBlwGbPddMShhEs7fF82UHoN8yZH/D+RbgHLgv3w/dzrnvjxu3QXA43gzq9+O12P1ZrwPwbucc9+KUNghZ2ZfAm7Cm5H4d3gzEr8f+CtwVQBzdcUVM3srsNz34/uANOA2388NzrkfjFt3NV7SNAx8Hu9/Uu8Gzgde5pz7Y6TiltCa6effzL4LvA14oXPuvnHbvwEvAfDP/JyLNzu3A57rnNOQ3ywE876Y2avxvqd/AxzC65G6CO97/gRwmXNOPYcBCvA787uE6/cl2jOc6jHprK3f9b2Jkz3qJ1m/GPgBcAzvioQngDdG+3WE4DwkA/+GN+P3IF6yeDtxOvt7AK/7vmne//smWX898Cu8Hsk+4CG8W2BE/bXoEdTnYEaf/3HfF5sn2cfL8ebR6QM68G6tsSrary2eH8G8L77f1Z8BB/HmoRr0/fsrQHG0X1u8PgL5zgzn74t6qERERESCpBoqERERkSApoRIREREJkhIqERERkSApoRIREREJkhIqERERkSApoRIREREJkhIqERERkSApoUowZrbCzO42s3Yzc75ZY0VERCQIKdEOQCLuu8AFwFagFW+WXhERCZKZbQReDXzXOVcf1WAk4pRQJRAzSwcuB77snPtctOMREZljNgIfw7sVSn00A5HI05BfYikEDO8mnNMys5zwhyMiIjI3KKFKEL5aqQbfjx/z1U85M3u77/njZvZGM3vczPqBL43b9moz+5OZdZrZgJk9ZWbvmeI47zKzfWY2aGbPmNkHzOwdvmNsHh+PmU16I8mpart88T1kZj1m1mdmj5jZ66fa3swuNbP7zeykmR0zs2+aWfYk6xeZ2RfN7JAv7qNmtt3Mrpmw3hoz+4GZHTGzITOrN7PPmtm8yV6HiCQOM/s48B3fj38Z9x373ehFJZGkIb/E8XVgJ/B54JfAXb72A77nVwPvB74KfA3oBjCzLb6fH8aruzoJXAN81cxWOec+7D+AmX3Qt/9dwH8CWcCHgaPBBm9m/w+oBv4A/BcwBrwG+JmZ3eSc+8qETTYC/4f3BfdDYDPwTt92W8bttwz4K17v3feBHcA84BLgamC7b73nAvcCnXjnshmoxDtnl5nZlc654WBfp4jErbuAJXjfL58C9vraVaeaKJxzeiTIAygDHPDxSdqGgfUT1l8CDAA/nGRfXwBGgVW+n/Pxkq09QNa49UqAXt8xNo9r/6738Zs0TodX1On/+Tm+tk9Nsu7deMlfzoTtx4BLJqz7W9/rzB7X9jvf+tdOsu+kcf/eBewbfxxf+2t827892u+vHnroEd0H8PaJ33V6JM5DQ37i91vn3N4Jba8H0oFvmdnC8Q/gN3hDxi/yrftivB6przjn+vw7cM41ATVBxlaF9yX1vUni+DWQA1w6YZu/O+centB2L16vbBmAmc0HXgL8wTn3x4kHdc6N+dY7H+/KyB8C6ROO/xBeIvniIF+jiIjEMQ35id/+SdrW+57vmWa7Qt/zSt/zvknW2TPboMbFYVPse2IcfocmWee473mB73m1b79PzuD4AJ/wPWZyfBERSSBKqMSvb5I28z3/I3Bkiu0OTVh3skJzm6RtqoL0yT6T5lv/OrxhxsnsnvDzVOuNj2e6mCdb/za8Gq7JdJxjHyIiMocpoZLp+AvWjznnpuulgtOFl+vxhtbGW8/ZToA37OacGz+Nw8pJ1j2ANzTXOMmwZDAO4CVTF85gPYDRGZwHEUlc5/rPmcxhqqGS6fwUGAQ+YWaZExeaWZ5vslDwrobrB/7ZzLLGrVMCXD/Jvv1DjFdPaP+3Sdb9ge/5U2aWPEkci6d9FVPwJXK/B64zs4lxYGb+nqkngVrgPWZ2VsJnZim+eiwRSWy9vmd9HyQg9VDJlJxzTWZ2I/BNYK+Z/QBvLqtFwPl4Uy2cB9Q75zrM7L+AzwF/M7Pv4xWpvwevh2diL9CP8C4t3mZm6/Dqm64DFk4Sx2Nm9jG8+qWdZvYzoAXvKsTnAi8F0mb5Mm8C/gb83sy+BzwOZAIX4810/B/OOWdmb8XreXvKzL6NN8SYhVeH9VrgZrwrF0UkcT2Gd4VxtZkV4F2w8qxz7pHohiWRoIRKpuWc+46Z7Qc+BNyANz3CMaAObz6o1nHr3mZmvcC/Ap8GDuMlWF3Atyfst9vMXgrcjjdnVS/ePC5vYZJ6JOfcf5vZ43jzPn0Qb66oo3g9Rx8I4vU9a2abfK/lpXj1Yh140yRsG7feTjO7EC9xeiVeotiDl3R9F/jzbGMQkbnBOddoZv8E/AfenH6pwPcAJVQJwJzTkK+El5m9HW+CzRc65+6LbjQiIiKhpxoqERERkSApoRIREREJkhIqERERkSCphkpEREQkSOqhEhEREQmSEioRERGRICmhEhEREQmSEioRERGRICmhEhEREQmSEioRERGRIP1/40tnRdgGwK4AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 864x388.8 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample size=10: \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x388.8 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sample size=10: \n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x388.8 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('sample size=100: ')\n",
    "dft_analysis(f, 1, 30)\n",
    "print('sample size=10: ')\n",
    "dft_analysis(f, 0.5, 30)\n",
    "print('sample size=10: ')\n",
    "dft_analysis(f, 0.9, 30)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#   The storage path of the output file.\n",
    "\n",
    "The storage path is mainly based on the current time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "save path: 20230821203535106618\n"
     ]
    }
   ],
   "source": [
    "def mkdirs(fn):  \n",
    "    \n",
    "    \"\"\"\n",
    "    Create directories if they don't exist.\n",
    "\n",
    "    Args:\n",
    "    fn: The directory path to create.\n",
    "    \"\"\"\n",
    "\n",
    "    if not os.path.isdir(fn):\n",
    "        os.makedirs(fn)\n",
    "\n",
    "\n",
    "def create_save_dir(path_ini):\n",
    "    \"\"\"\n",
    "    Create a new directory with the current date and time as its name and return the path of the new directory.\n",
    "\n",
    "    Args:\n",
    "    path_ini: The initial path to create the new directory.\n",
    "\n",
    "    Return:\n",
    "    The path of the new directory.\n",
    "    \"\"\"\n",
    "    subFolderName = re.sub(r'[^0-9]', '', str(datetime.datetime.now()))\n",
    "    path = os.path.join(path_ini, subFolderName)\n",
    "    mkdirs(path)\n",
    "    mkdirs(os.path.join(path, 'output'))\n",
    "    return path\n",
    "\n",
    "\n",
    "args.path = create_save_dir(args.ini_path)\n",
    "print('save path: %s' % (args.path))\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Generation of training and test sets.\n",
    "\n",
    "Target function: $f(x)=sin(x)+sin(3x)+sin(5x)$\n",
    "\n",
    "Training data interval: $[-\\pi, \\pi]$\n",
    "\n",
    "Test data interval: $[-\\pi-0.5, \\pi+0.5]$\n",
    "\n",
    "出一个sinx的整数化，这个实验是不是验证了低频先收敛？第二种，sinx+alpha sin5x, 让他们自己选alpha。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The target function:\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def get_y(x):  \n",
    "\n",
    "    \"\"\"\n",
    "    Function to fit.\n",
    "\n",
    "    Args:\n",
    "        x (float): input value.\n",
    "\n",
    "    Returns:\n",
    "        float: output value.\n",
    "    \"\"\"\n",
    "\n",
    "    y = np.sin(x)+np.sin(3*x)+np.sin(5*x)\n",
    "    return y\n",
    "\n",
    "for i in range(2):\n",
    "    if isinstance(args.boundary[i], str):\n",
    "        args.boundary[i] = eval(args.boundary[i])\n",
    "\n",
    "args.test_input = torch.reshape(torch.linspace(args.boundary[0] - 0.5, args.boundary[1] + 0.5, steps=args.test_size), [args.test_size, 1])\n",
    "\n",
    "\n",
    "args.training_input = torch.reshape(torch.linspace(args.boundary[0], args.boundary[1], steps=args.training_size), [args.training_size, 1])\n",
    "args.test_target = get_y(args.test_input)\n",
    "args.training_target = get_y(args.training_input)\n",
    "\n",
    "\n",
    "def plot_target(args):\n",
    "\n",
    "    \"\"\"\n",
    "    Plot the target.\n",
    "\n",
    "    Args:\n",
    "        args (object): object containing training and test input and target.\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    plt.figure()\n",
    "    ax = plt.gca()\n",
    "\n",
    "    plt.plot(args.training_input.detach().cpu().numpy(),\n",
    "             args.training_target.detach().cpu().numpy(), 'b*', label='True')\n",
    "    plt.plot(args.test_input.detach().cpu().numpy(),\n",
    "             args.test_target.detach().cpu().numpy(), 'r-', label='Test')\n",
    "\n",
    "    ax.tick_params(labelsize=18)\n",
    "    plt.legend(fontsize=18)\n",
    "    plt.show()\n",
    "\n",
    "print(\"The target function:\")\n",
    "plot_target(args)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Activation Functions\n",
    "\n",
    "We mainly give four activation functions: Tanh, ReLU, Sigmoid, Hat.\n",
    "\n",
    "Tanh function：\n",
    "\n",
    "$$f(x) = \\frac{e^x - e^{-x}}{e^x + e^{-x}}$$\n",
    "\n",
    "ReLU function：\n",
    "\n",
    "$$f(x) = \\max(0, x)$$\n",
    "\n",
    "Sigmoid function：\n",
    "\n",
    "$$f(x) = \\frac{1}{1 + e^{-x}}$$\n",
    "\n",
    "Hat function：\n",
    "\n",
    "$$f(x) = \\begin{cases} x, & 0 \\leq x < 1 \\\\  2 - x, & 1 \\leq x < 2 \\\\ 0, & \\text{otherwise}  \\end{cases}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# Define the activation functions\n",
    "def tanh(x):\n",
    "    return np.tanh(x)\n",
    "\n",
    "def relu(x):\n",
    "    return np.maximum(0, x)\n",
    "\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "def hat(x):\n",
    "    return np.piecewise(x, [np.logical_and(0 <= x, x < 1), np.logical_and(1 <= x, x < 2), x >= 2], [lambda x: x, lambda x: 2 - x, 0])\n",
    "\n",
    "# Define the input range\n",
    "x = np.linspace(-2, 2, 1000)\n",
    "\n",
    "# Create a figure with four subplots\n",
    "fig, axs = plt.subplots(2, 2)\n",
    "\n",
    "# Plot the activation functions in the subplots\n",
    "axs[0, 0].plot(x, tanh(x))\n",
    "axs[0, 0].set_title('Tanh')\n",
    "\n",
    "axs[0, 1].plot(x, relu(x))\n",
    "axs[0, 1].set_title('ReLU')\n",
    "\n",
    "axs[1, 0].plot(x, sigmoid(x))\n",
    "axs[1, 0].set_title('Sigmoid')\n",
    "\n",
    "axs[1, 1].plot(x, hat(x))\n",
    "axs[1, 1].set_title('Hat')\n",
    "\n",
    "# Add labels to the subplots\n",
    "for ax in axs.flat:\n",
    "    ax.set(xlabel='Input', ylabel='Output')\n",
    "\n",
    "# Adjust the layout of the subplots\n",
    "plt.tight_layout()\n",
    "\n",
    "# Show the plot\n",
    "plt.show()\n",
    "plt.close()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Network model and parameter initialization.\n",
    "\n",
    "Given $\\theta\\in \\mathbb{R}^M$, the FNN function $f_{\\theta}(\\cdot)$ is defined recursively. First, we denote $f^{[0]}_{\\theta}(x)=x$ for all $x\\in\\mathbb{R}^d$. Then, for $l\\in[L-1]$, $f^{[l]}_{\\theta}$ is defined recursively as \n",
    "$f^{[l]}_{\\theta}(x)=\\sigma (W^{[l]} f^{[l-1]}_{\\theta}(x)+b^{[l]})$, where $\\sigma$ is a non-linear activation function.\n",
    "Finally, we denote\n",
    "\\begin{equation*}\n",
    "    f_{\\theta}(x)=f(x,\\theta)=f^{[L]}_{\\theta}(x)=W^{[L]} f^{[L-1]}_{\\theta}(x)+b^{[L]}.\n",
    "\\end{equation*}\n",
    "\n",
    "The parameter initialization is under the Gaussian distribution as follows,\n",
    "\n",
    "\\begin{equation*}\n",
    "    \\theta|_{l} \\sim N(0, \\frac{1}{m_{l}^t}),\n",
    "\\end{equation*}\n",
    "where the $l$ th layer parameters of $\\theta$ is the ordered pair $\\theta|_{l}=\\Big(W^{[l]},b^{[l]}\\Big),\\quad l\\in[L]$, $m_{l}$ is the width of the $l$ th layer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The network structure:\n",
      "Linear(\n",
      "  (features): Sequential(\n",
      "    (0): Linear(in_features=1, out_features=200, bias=True)\n",
      "    (1): Tanh()\n",
      "    (2): Linear(in_features=200, out_features=200, bias=True)\n",
      "    (3): Tanh()\n",
      "    (4): Linear(in_features=200, out_features=200, bias=True)\n",
      "    (5): Tanh()\n",
      "    (6): Linear(in_features=200, out_features=100, bias=True)\n",
      "    (7): Tanh()\n",
      "    (8): Linear(in_features=100, out_features=1, bias=True)\n",
      "  )\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "class Linear(nn.Module):\n",
    "    def __init__(self, t, hidden_layers_width=[100],  input_size=20, num_classes: int = 1000, act_layer: nn.Module = nn.ReLU()):\n",
    "        super(Linear, self).__init__()\n",
    "        self.num_classes = num_classes\n",
    "        self.input_size = input_size\n",
    "        self.hidden_layers_width = hidden_layers_width\n",
    "        self.t = t\n",
    "        layers: List[nn.Module] = []\n",
    "        self.layers_width = [self.input_size]+self.hidden_layers_width\n",
    "        for i in range(len(self.layers_width)-1):\n",
    "            layers += [nn.Linear(self.layers_width[i],\n",
    "                                    self.layers_width[i+1]), act_layer]\n",
    "        layers += [nn.Linear(self.layers_width[-1], num_classes)]\n",
    "        self.features = nn.Sequential(*layers)\n",
    "        self._initialize_weights()\n",
    "\n",
    "\n",
    "    def forward(self, x):\n",
    "\n",
    "        x = x.view(x.size(0), -1)\n",
    "        x = self.features(x)\n",
    "        return x\n",
    "\n",
    "    def _initialize_weights(self) -> None:\n",
    "\n",
    "        for obj in self.modules():\n",
    "            if isinstance(obj, (nn.Linear, nn.Conv2d)):\n",
    "                nn.init.normal_(obj.weight.data, 0, 1 /\n",
    "                                self.hidden_layers_width[0]**(self.t))\n",
    "                if obj.bias is not None:\n",
    "                    nn.init.normal_(obj.bias.data, 0, 1 /\n",
    "                                    self.hidden_layers_width[0]**(self.t))\n",
    "\n",
    "class hat_torch(nn.Module):  # Custom activation function\n",
    "    def __init__(self):\n",
    "        super(hat_torch, self).__init__()\n",
    "\n",
    "    def forward(self, x):\n",
    "        y = torch.where((x > 0) & (x < 1), x,  torch.tensor(0.0))\n",
    "        y = torch.where((x >= 1) & (x < 2), 2 - x, y)\n",
    "        return y\n",
    "\n",
    "\n",
    "\n",
    "def get_act_func(act_func):\n",
    "\n",
    "    \"\"\"\n",
    "    Get activation function.\n",
    "\n",
    "    Args:\n",
    "        act_func (str): activation function name.\n",
    "\n",
    "    Returns:\n",
    "        nn.Module: activation function.\n",
    "    \"\"\"\n",
    "\n",
    "    if act_func == 'tanh':\n",
    "        return nn.Tanh()\n",
    "    elif act_func == 'ReLU':\n",
    "        return nn.ReLU()\n",
    "    elif act_func == 'Sigmoid':\n",
    "        return nn.Sigmoid()\n",
    "    elif act_func == 'hat':\n",
    "        return hat_torch()\n",
    "    else:\n",
    "        raise NameError('No such act func!')\n",
    "\n",
    "\n",
    "act_func = get_act_func(args.act_func_name)\n",
    "\n",
    "model = Linear(args.t, args.hidden_layers_width, args.input_dim,\n",
    "               args.output_dim, act_func).to(args.device)\n",
    "print(\"The network structure:\")\n",
    "print(model)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# One-step training function.\n",
    "\n",
    "The training data set is denoted as  $S=\\{(x_i,y_i)\\}_{i=1}^n$, where $x_i\\in\\mathbb{R}^d$ and $y_i\\in \\mathbb{R}^{d'}$. For simplicity, we assume an unknown function $y$ satisfying $y(x_i)=y_i$ for $i\\in[n]$. The empirical risk reads as\n",
    "\\begin{equation*}\n",
    "    R_S(\\theta)=\\frac{1}{n}\\sum_{i=1}^n\\ell(f(x_i,\\theta),y(x_i)),\n",
    "\\end{equation*}\n",
    "where the loss function $\\ell(\\cdot,\\cdot)$ is differentiable and the derivative of $\\ell$ with respect to its first argument is denoted by $\\nabla\\ell(y,y^*)$. \n",
    "\n",
    "For a one-step gradient descent, we have, \n",
    "\n",
    "\\begin{equation*}\n",
    "    \\theta_{t+1}=\\theta_t-\\eta\\nabla R_S(\\theta).\n",
    "\\end{equation*}\n",
    "\n",
    "\n",
    "加一下SGD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_one_step(model, optimizer, loss_fn,  args):\n",
    "\n",
    "    \"\"\"\n",
    "    Train one step.\n",
    "\n",
    "    Args:\n",
    "        model (nn.Module): model.\n",
    "        optimizer (optim.Optimizer): optimizer.\n",
    "        loss_fn (nn.Module): loss function.\n",
    "        args (object): object containing training and test input and target.\n",
    "\n",
    "    Returns:\n",
    "        tuple: tuple containing loss and outputs.\n",
    "    \"\"\"\n",
    "\n",
    "    # Set the model to training mode (Dropout, BN, etc.)\n",
    "    model.train()\n",
    "\n",
    "    # Get the device to use for computation\n",
    "    device = args.device\n",
    "\n",
    "    training_loss = 0.0\n",
    "    total = 0\n",
    "\n",
    "    # Move the training input and target to the device and convert the target to float\n",
    "    data, target = args.training_input.to(device), args.training_target.to(device).to(torch.float)\n",
    "\n",
    "    # Loop over the training data in batches\n",
    "    for i in range(args.training_size // args.batch_size ):  \n",
    "\n",
    "        # Zero the gradients of the optimizer\n",
    "        optimizer.zero_grad()\n",
    "\n",
    "        # Randomly select a batch of data\n",
    "        mask = np.random.choice(args.training_size, args.batch_size, replace=False)\n",
    "\n",
    "        # Get the model's predictions for the selected data\n",
    "        y_train = model(data[mask])\n",
    "\n",
    "        # Calculate the loss between the predictions and the target\n",
    "        loss = loss_fn(y_train, target[mask])\n",
    "\n",
    "        # Compute the gradients of the loss with respect to the model parameters\n",
    "        loss.backward()\n",
    "\n",
    "        #loss.grad.data\n",
    "\n",
    "        # Update the model parameters using the optimizer\n",
    "        optimizer.step()\n",
    "\n",
    "        training_loss+=loss.item()*args.batch_size\n",
    "        total += args.batch_size\n",
    "\n",
    "    # Get the model's predictions for all the training data\n",
    "    outputs = model(data)\n",
    "\n",
    "    return training_loss/total, outputs\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# One-step test function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def test(model, loss_fn, args):\n",
    "    \"\"\"\n",
    "    Test.\n",
    "\n",
    "    Args:\n",
    "        model (nn.Module): model.\n",
    "        loss_fn (nn.Module): loss function.\n",
    "        args (object): object containing training and test input and target.\n",
    "\n",
    "    Returns:\n",
    "        tuple: tuple containing loss and outputs.\n",
    "    \"\"\"\n",
    "\n",
    "    model.eval()\n",
    "    device = args.device\n",
    "    with torch.no_grad():\n",
    "        data, target = args.test_input.to(\n",
    "            device), args.test_target.to(device).to(torch.float)\n",
    "        outputs = model(data)\n",
    "        loss = loss_fn(outputs, target)\n",
    "\n",
    "    return loss.item(), outputs\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot the loss value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_loss(path, loss_train, x_log=False):\n",
    "\n",
    "    \"\"\"\n",
    "    Plot loss.\n",
    "\n",
    "    Args:\n",
    "        path (str): path.\n",
    "        loss_train (list): list of training loss.\n",
    "        x_log (bool): whether to use log scale for x-axis.\n",
    "\n",
    "    Returns:\n",
    "        None.\n",
    "    \"\"\"\n",
    "\n",
    "    plt.figure()\n",
    "    ax = plt.gca()\n",
    "    y2 = np.asarray(loss_train)\n",
    "    plt.plot(y2, 'k-', label='Train')\n",
    "    plt.xlabel('epoch', fontsize=18)\n",
    "    ax.tick_params(labelsize=18)\n",
    "    plt.yscale('log')\n",
    "    if x_log == False:\n",
    "        fntmp = os.path.join(path, 'loss.png')\n",
    "\n",
    "    else:\n",
    "        plt.xscale('log')\n",
    "        fntmp = os.path.join(path, 'loss_log.png')\n",
    "    plt.tight_layout()\n",
    "    plt.savefig(fntmp,dpi=300)\n",
    "\n",
    "\n",
    "    plt.close()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot the output figure.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_model_output(path, args, output, epoch):\n",
    "\n",
    "    plt.figure()\n",
    "    ax = plt.gca()\n",
    "\n",
    "    plt.plot(args.training_input.detach().cpu().numpy(),\n",
    "             args.training_target.detach().cpu().numpy(), 'b*', label='True')\n",
    "    plt.plot(args.test_input.detach().cpu().numpy(),\n",
    "             output.detach().cpu().numpy(), 'r-', label='Test')\n",
    "\n",
    "    ax.tick_params(labelsize=18)\n",
    "    plt.legend(fontsize=18)\n",
    "    fntmp = os.path.join(path, 'output', str(epoch)+'.png')\n",
    "\n",
    "    plt.savefig(fntmp, dpi=300)\n",
    "\n",
    "\n",
    "    plt.close()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Training Process"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] loss: 1.360981 valloss: 1.627375 time: 3.39 s\n",
      "[1001] loss: 0.017432 valloss: 0.292552 time: 10.00 s\n"
     ]
    }
   ],
   "source": [
    "if args.optimizer=='sgd':\n",
    "    optimizer = torch.optim.SGD(model.parameters(), lr=args.lr)\n",
    "else:\n",
    "    optimizer = torch.optim.Adam(model.parameters(), lr=args.lr)\n",
    "loss_fn = nn.MSELoss(reduction='mean')\n",
    "t0 = time.time()\n",
    "args.loss_training_lst=[]\n",
    "args.loss_test_lst = []\n",
    "args.training_output=[]\n",
    "for epoch in range(args.epochs+1):\n",
    "\n",
    "      model.train()\n",
    "      loss, training_output = train_one_step(\n",
    "        model, optimizer, loss_fn, args)\n",
    "      loss_test, output = test(\n",
    "          model, loss_fn, args)\n",
    "      args.loss_training_lst.append(loss)\n",
    "      args.loss_test_lst.append(loss_test)\n",
    "      args.training_output.append(training_output.detach().cpu().numpy())\n",
    "      if epoch % args.plot_epoch == 0:\n",
    "            print(\"[%d] loss: %.6f valloss: %.6f time: %.2f s\" %\n",
    "                  (epoch + 1, loss, loss_test, (time.time()-t0)))\n",
    "  \n",
    "      if (epoch+1) % (args.plot_epoch) == 0:\n",
    "          plot_loss(path=args.path,\n",
    "                    loss_train=args.loss_training_lst, x_log=True)\n",
    "          plot_loss(path=args.path,\n",
    "                    loss_train=args.loss_training_lst, x_log=False)\n",
    "\n",
    "          plot_model_output(args.path, args, output, epoch)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot the frequency distribution figure\n",
    "\n",
    "To avoid the interference of amplitude on the experiment, we study the changes in relative error at different frequencies. We consider the following quantities:\n",
    "$$\n",
    "\\Delta_F(k)=\\frac{\\left|\\hat{h}_k-\\hat{f}_k\\right|} {\\left|\\hat{f}_k\\right|}\n",
    "$$\n",
    "\n",
    "where $\\hat{h}_k$ and $\\hat{f}_k$ are the discrete Fourier transform (DFT) of the DNN output $h(x)$ and the  target function $f(x)$,  $|·|$ denotes the norm of a complex number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_freq_distr(args):\n",
    "\n",
    "    \"\"\"\n",
    "    Plot frequency distribution and the heatmap of the given training target and output.\n",
    "    \n",
    "    Args:\n",
    "    args: A dictionary containing training target and output.\n",
    "    \n",
    "    Returns:\n",
    "    None\n",
    "    \"\"\"\n",
    "\n",
    "    y_fft = my_fft(args.training_target.detach().cpu().numpy()) / \\\n",
    "        args.training_size\n",
    "    plt.figure()\n",
    "    ax = plt.gca()\n",
    "    plt.semilogy(y_fft+1e-5, label='Target')\n",
    "    idx = SelectPeakIndex(y_fft, endpoint=False)\n",
    "    plt.semilogy(idx, y_fft[idx]+1e-5, 'o')\n",
    "    y_fft_pred = my_fft(args.training_output[-1])/args.training_size\n",
    "    plt.semilogy(y_fft_pred+1e-5, label='Model output')\n",
    "    plt.semilogy(idx, y_fft_pred[idx]+1e-5, 'o')\n",
    "    plt.legend(fontsize=22)\n",
    "    plt.xlabel('freq idx', fontsize=22)\n",
    "    plt.ylabel('freq', fontsize=22)\n",
    "    plt.gca().tick_params(axis='y', labelsize=22)\n",
    "    plt.gca().tick_params(axis='x', labelsize=22)\n",
    "    plt.tight_layout()\n",
    "    plt.savefig(os.path.join(args.path, 'fft.png'), dpi=300)\n",
    "    plt.show()\n",
    "    plt.close()\n",
    "\n",
    "    y_pred_epoch = np.squeeze(args.training_output)\n",
    "    idx1 = idx[:3]\n",
    "    abs_err = np.zeros([len(idx1), len(args.training_output)])\n",
    "    y_fft = my_fft(args.training_target)\n",
    "    tmp1 = y_fft[idx1]\n",
    "    for i in range(len(y_pred_epoch)):\n",
    "        tmp2 = my_fft(y_pred_epoch[i])[idx1]\n",
    "        abs_err[:, i] = np.abs(tmp1 - tmp2)/(1e-5 + tmp1)\n",
    "\n",
    "    \n",
    "\n",
    "    plt.figure(figsize=(8, 6))\n",
    "    ax = plt.gca()\n",
    "    plt.pcolor(abs_err, cmap='RdBu', vmin=0.1, vmax=1, linewidths=0.4)\n",
    "    plt.colorbar()\n",
    "\n",
    "   \n",
    "    plt.xlabel('Epoch', fontsize=22)\n",
    "\n",
    "    # Set the y-axis ticks and labels to 1, 2, 3, and rotate the labels\n",
    "    plt.yticks([0.5, 1.5, 2.5], [1, 2, 3], rotation=0, fontsize=22)\n",
    "\n",
    "    # Set the y-axis tick parameters to hide the tick marks and set the tick label size\n",
    "    plt.gca().yaxis.set_tick_params(size=0)\n",
    "    plt.gca().tick_params(axis='y', labelsize=22)\n",
    "    plt.gca().tick_params(axis='x', labelsize=22)\n",
    "\n",
    "\n",
    "    plt.title('Absolute Error', fontsize=22)\n",
    "\n",
    "    plt.tight_layout()\n",
    "\n",
    "    plt.savefig(os.path.join(args.path, 'hot.png'))\n",
    "    plt.show()\n",
    "    plt.close()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_freq_distr(args)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task\n",
    "\n",
    "受到很多因素的影响，比如初始化，学习率，目标函数，激活函数等，观察这些参数对fprinciple的影响\n",
    "\n",
    "\n",
    "\n",
    "3. Study how different frequency amplitudes affect the convergence speed of the model. Taking the objective function $sin(x)+a*sin(4x)$ as an example, where $a$ is a given parameter. We can plot the horizontal axis as $a$ and the vertical axis as (the number of steps required for high-frequency relative error <10%) / (the number of steps required for low-frequency relative error <10%) under this objective function.\n",
    "\n",
    "4. Study how different high frequency affect the convergence speed of the model. Taking the objective function $sin(x)+0.2*sin(k\\cdot x)$ as an example, where $k$ is a given parameter. We can plot the horizontal axis as $k$ and the vertical axis as (the number of steps required for high-frequency relative error <10%) / (the number of steps required for low-frequency relative error <10%) under this objective function.\n",
    "\n",
    "\n",
    "    (10\\% in the two tasks above is optional.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task3: Different amplitudes (Code generated by New Bing) \n",
    "\n",
    "prompt1: 帮我构造一个神经网络拟合目标函数的例子，目标函数是$sin(x)+a*sin(4x)$。我们假设a为[0.5,2]中的linspace采样，对于不同的a，我们均训练8000步，并记录每一步神经网络的输出，并保存到以a为key的字典中，每个key对应的值是一个列表，这个列表记录了每10步网络的输出值。神经网络的结构为五层神经网络，宽度为256,以Tanh作为激活函数. 我们使用full batch的Adam进行训练，学习率为1e-4. 对于input data，我们希望它是在[-pi, pi]上的linspace采样。你需要注意，模型的input与output应该具有相同的size。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a=1.00, Step 0: Loss = 0.9677\n",
      "a=1.00, Step 1000: Loss = 0.0670\n",
      "a=1.00, Step 2000: Loss = 0.0024\n",
      "a=1.00, Step 3000: Loss = 0.0001\n",
      "a=1.10, Step 0: Loss = 1.0931\n",
      "a=1.10, Step 1000: Loss = 0.0691\n",
      "a=1.10, Step 2000: Loss = 0.0005\n",
      "a=1.10, Step 3000: Loss = 0.0001\n",
      "a=1.20, Step 0: Loss = 1.2346\n",
      "a=1.20, Step 1000: Loss = 0.0752\n",
      "a=1.20, Step 2000: Loss = 0.0007\n",
      "a=1.20, Step 3000: Loss = 0.0003\n",
      "a=1.30, Step 0: Loss = 1.2740\n",
      "a=1.30, Step 1000: Loss = 0.0807\n",
      "a=1.30, Step 2000: Loss = 0.0009\n",
      "a=1.30, Step 3000: Loss = 0.0004\n",
      "a=1.40, Step 0: Loss = 1.4400\n",
      "a=1.40, Step 1000: Loss = 0.0689\n",
      "a=1.40, Step 2000: Loss = 0.0007\n",
      "a=1.40, Step 3000: Loss = 0.0002\n",
      "a=1.50, Step 0: Loss = 1.6504\n",
      "a=1.50, Step 1000: Loss = 0.0817\n",
      "a=1.50, Step 2000: Loss = 0.0016\n",
      "a=1.50, Step 3000: Loss = 0.0002\n",
      "a=1.60, Step 0: Loss = 1.7760\n",
      "a=1.60, Step 1000: Loss = 0.0917\n",
      "a=1.60, Step 2000: Loss = 0.0014\n",
      "a=1.60, Step 3000: Loss = 0.0002\n",
      "a=1.70, Step 0: Loss = 1.9374\n",
      "a=1.70, Step 1000: Loss = 0.1449\n",
      "a=1.70, Step 2000: Loss = 0.0026\n",
      "a=1.70, Step 3000: Loss = 0.0007\n",
      "a=1.80, Step 0: Loss = 2.1343\n",
      "a=1.80, Step 1000: Loss = 0.0438\n",
      "a=1.80, Step 2000: Loss = 0.0029\n",
      "a=1.80, Step 3000: Loss = 0.0005\n",
      "a=1.90, Step 0: Loss = 2.4081\n",
      "a=1.90, Step 1000: Loss = 0.1252\n",
      "a=1.90, Step 2000: Loss = 0.0035\n",
      "a=1.90, Step 3000: Loss = 0.0012\n",
      "a=2.00, Step 0: Loss = 2.5500\n",
      "a=2.00, Step 1000: Loss = 0.0612\n",
      "a=2.00, Step 2000: Loss = 0.0025\n",
      "a=2.00, Step 3000: Loss = 0.0004\n",
      "a=2.10, Step 0: Loss = 2.7408\n",
      "a=2.10, Step 1000: Loss = 0.0588\n",
      "a=2.10, Step 2000: Loss = 0.0032\n",
      "a=2.10, Step 3000: Loss = 0.0004\n",
      "a=2.20, Step 0: Loss = 2.9117\n",
      "a=2.20, Step 1000: Loss = 0.1008\n",
      "a=2.20, Step 2000: Loss = 0.0056\n",
      "a=2.20, Step 3000: Loss = 0.0006\n",
      "a=2.30, Step 0: Loss = 3.1440\n",
      "a=2.30, Step 1000: Loss = 0.0421\n",
      "a=2.30, Step 2000: Loss = 0.0043\n",
      "a=2.30, Step 3000: Loss = 0.0024\n",
      "a=2.40, Step 0: Loss = 3.3815\n",
      "a=2.40, Step 1000: Loss = 0.0404\n",
      "a=2.40, Step 2000: Loss = 0.0029\n",
      "a=2.40, Step 3000: Loss = 0.0003\n",
      "a=2.50, Step 0: Loss = 3.6021\n",
      "a=2.50, Step 1000: Loss = 0.0336\n",
      "a=2.50, Step 2000: Loss = 0.0024\n",
      "a=2.50, Step 3000: Loss = 0.0019\n",
      "a=2.60, Step 0: Loss = 3.9406\n",
      "a=2.60, Step 1000: Loss = 0.0625\n",
      "a=2.60, Step 2000: Loss = 0.0043\n",
      "a=2.60, Step 3000: Loss = 0.0004\n",
      "a=2.70, Step 0: Loss = 4.2083\n",
      "a=2.70, Step 1000: Loss = 0.0584\n",
      "a=2.70, Step 2000: Loss = 0.0055\n",
      "a=2.70, Step 3000: Loss = 0.0004\n",
      "a=2.80, Step 0: Loss = 4.4271\n",
      "a=2.80, Step 1000: Loss = 0.0611\n",
      "a=2.80, Step 2000: Loss = 0.0080\n",
      "a=2.80, Step 3000: Loss = 0.0005\n",
      "a=2.90, Step 0: Loss = 4.7065\n",
      "a=2.90, Step 1000: Loss = 0.0526\n",
      "a=2.90, Step 2000: Loss = 0.0033\n",
      "a=2.90, Step 3000: Loss = 0.0003\n",
      "a=3.00, Step 0: Loss = 5.1024\n",
      "a=3.00, Step 1000: Loss = 0.0445\n",
      "a=3.00, Step 2000: Loss = 0.0009\n",
      "a=3.00, Step 3000: Loss = 0.0006\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "from torch.optim import Adam\n",
    "import numpy as np\n",
    "\n",
    "class Net(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(Net, self).__init__()\n",
    "        self.fc1 = nn.Linear(1, 256)\n",
    "        self.fc2 = nn.Linear(256, 256)\n",
    "        self.fc3 = nn.Linear(256, 256)\n",
    "        self.fc4 = nn.Linear(256, 256)\n",
    "        self.fc5 = nn.Linear(256, 1)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = torch.tanh(self.fc1(x))\n",
    "        x = torch.tanh(self.fc2(x))\n",
    "        x = torch.tanh(self.fc3(x))\n",
    "        x = torch.tanh(self.fc4(x))\n",
    "        x = self.fc5(x)\n",
    "        return x\n",
    "    \n",
    "\n",
    "\n",
    "def train(a):\n",
    "    net = Net()\n",
    "    optimizer = Adam(net.parameters(), lr=5e-5)\n",
    "    criterion = nn.MSELoss()\n",
    "    x = np.linspace(-np.pi, np.pi, 1000).reshape(-1, 1)\n",
    "    y = np.sin(x) + a * np.sin(4 * x)\n",
    "    x = torch.from_numpy(x).float()\n",
    "    y = torch.from_numpy(y).float()\n",
    "    res_dict = {}\n",
    "    res_list = []\n",
    "    for i in range(4000):\n",
    "        optimizer.zero_grad()\n",
    "        y_pred = net(x)\n",
    "        loss = criterion(y_pred, y)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        # if i % 10 == 0:\n",
    "        res_list.append(y_pred.detach().numpy())\n",
    "        if i % 1000 == 0:\n",
    "            print(f'a={a:.2f}, Step {i}: Loss = {loss.item():.4f}')\n",
    "    res_dict[a] = res_list\n",
    "    return res_dict\n",
    "\n",
    "\n",
    "a_list = np.linspace(1, 3, 21)\n",
    "res_dict_a = {}\n",
    "for a in a_list:\n",
    "    res_dict_a.update(train(a))\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prompt2: 在上面这个代码中，我们获得了res_dict，包含每一个$a$对应的目标函数在训练过程中的输出。我们的目标函数是sin（x）+a*sin(4x), 现在我希望对每个a，计算模型每步训练时，在频率为1和频率为5处模型的输出与目标函数在傅里叶空间的相对误差。也就是对训练的每一步，对模型输出及目标函数进行傅里叶变换，取他们频率为1的模长，求相对误差，再取他们频率为5的模长，求相对误差。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.fft import fft\n",
    "\n",
    "error_1_list_all=[]\n",
    "error_5_list_all=[]\n",
    "\n",
    "def calc_relative_error(res_dict, a):\n",
    "    x = np.linspace(-np.pi, np.pi, 1000).reshape(-1, 1)\n",
    "    y = np.sin(x) + a * np.sin(4 * x)\n",
    "    y_fft = fft(y.squeeze())\n",
    "    error_1_list = []\n",
    "    error_5_list = []\n",
    "    for y_pred in res_dict[a]:\n",
    "        y_pred_fft = fft(y_pred.squeeze())\n",
    "        error_1 = abs(abs(y_fft[1]) - abs(y_pred_fft[1])) / abs(y_fft[1])\n",
    "        error_5 = abs(abs(y_fft[4]) - abs(y_pred_fft[4])) / abs(y_fft[4])\n",
    "        error_1_list.append(error_1)\n",
    "        error_5_list.append(error_5)\n",
    "    return error_1_list, error_5_list\n",
    "\n",
    "\n",
    "for a in a_list:\n",
    "    error_1_list, error_5_list = calc_relative_error(res_dict_a, a)\n",
    "    error_1_list_all.append(error_1_list)\n",
    "    error_5_list_all.append(error_5_list)   \n",
    "    # print(f'For a={a}, the relative errors at frequency 1 are {error_1_list}, the relative errors at frequency 5 are {error_5_list}')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prompt3: 假设对于a_list中的每个a，我们都得到了error_1_list和error_5_list，并把它们保存在列表error_1_list_all及error_5_list_all中，现在我们需要对每个a，找出其对应的error_1_list和error_5_list中error首次小于0.1的error的index，记为error_1_index及error_5_index，对于不同的a，我们都可以计算error_1_index/error_5_index的值。最后我们绘制一张横坐标为a，纵坐标为error_1_index/error_5_index的图像。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For a=5, the error 1 index is 121, the error 5 index is 1314\n",
      "For a=5, the error 1 index is 128, the error 5 index is 1132\n",
      "For a=5, the error 1 index is 128, the error 5 index is 1095\n",
      "For a=5, the error 1 index is 111, the error 5 index is 1054\n",
      "For a=5, the error 1 index is 123, the error 5 index is 971\n",
      "For a=5, the error 1 index is 127, the error 5 index is 992\n",
      "For a=5, the error 1 index is 117, the error 5 index is 958\n",
      "For a=5, the error 1 index is 112, the error 5 index is 1054\n",
      "For a=5, the error 1 index is 113, the error 5 index is 869\n",
      "For a=5, the error 1 index is 127, the error 5 index is 950\n",
      "For a=5, the error 1 index is 112, the error 5 index is 882\n",
      "For a=5, the error 1 index is 120, the error 5 index is 839\n",
      "For a=5, the error 1 index is 112, the error 5 index is 894\n",
      "For a=5, the error 1 index is 111, the error 5 index is 765\n",
      "For a=5, the error 1 index is 111, the error 5 index is 744\n",
      "For a=5, the error 1 index is 102, the error 5 index is 674\n",
      "For a=5, the error 1 index is 115, the error 5 index is 750\n",
      "For a=5, the error 1 index is 113, the error 5 index is 726\n",
      "For a=5, the error 1 index is 106, the error 5 index is 708\n",
      "For a=5, the error 1 index is 100, the error 5 index is 685\n",
      "For a=5, the error 1 index is 116, the error 5 index is 624\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def find_consecutive_index(arr):\n",
    "    for i in range(len(arr) - 10):\n",
    "        if all(arr[i+j] == arr[i] + j for j in range(10)):\n",
    "            return arr[i]\n",
    "\n",
    "def calc_error_index(error_1_list_all, error_5_list_all):\n",
    "    error_1_index_list = []\n",
    "    error_5_index_list = []\n",
    "    for error_1_list, error_5_list in zip(error_1_list_all, error_5_list_all):\n",
    "\n",
    "        error_1_index = np.where(np.array(error_1_list) < 0.1)[0]\n",
    "        error_5_index = np.where(np.array(error_5_list) < 0.1)[0]\n",
    "        error_1_index = find_consecutive_index(error_1_index)\n",
    "        error_5_index = find_consecutive_index(error_5_index)\n",
    "\n",
    "        error_1_index_list.append(error_1_index)\n",
    "        error_5_index_list.append(error_5_index)\n",
    "        print(f'For a={k}, the low freq index is {error_1_index}, the high freq index is {error_5_index}')\n",
    "\n",
    "\n",
    "    return error_1_index_list, error_5_index_list\n",
    "\n",
    "\n",
    "\n",
    "error_1_list_all = []\n",
    "error_5_list_all = []\n",
    "for a in a_list:\n",
    "    error_1_list, error_5_list = calc_relative_error(res_dict_a, a)\n",
    "    error_1_list_all.append(error_1_list)\n",
    "    error_5_list_all.append(error_5_list)\n",
    "\n",
    "error_1_index_list, error_5_index_list = calc_error_index(error_1_list_all, error_5_list_all)\n",
    "\n",
    "ratio = np.array(error_1_index_list) / np.array(error_5_index_list)\n",
    "plt.plot(a_list, ratio, 'o-')\n",
    "plt.xlabel('a', fontsize=14)\n",
    "plt.yscale('log')\n",
    "plt.ylabel('low freq index / high freq index', fontsize=14)\n",
    "# plt.yticks([0.02, 0.03])\n",
    "plt.xticks([1,1.5,2,2.5, 3])\n",
    "plt.gca().tick_params(axis='y', labelsize=14)\n",
    "plt.gca().tick_params(axis='x', labelsize=14)\n",
    "plt.tight_layout()\n",
    "plt.savefig(os.path.join(args.path, 'amplitudes.png'))\n",
    "plt.show()\n",
    "plt.close()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task4: Different high frequencies\n",
    "Network model and training process definition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "k=1.00, Step 0: Loss = 0.8964\n",
      "k=1.00, Step 1000: Loss = 0.0000\n",
      "k=1.00, Step 2000: Loss = 0.0000\n",
      "k=1.00, Step 3000: Loss = 0.0000\n",
      "k=1.00, Step 4000: Loss = 0.0000\n",
      "k=1.00, Step 5000: Loss = 0.0000\n",
      "k=1.00, Step 6000: Loss = 0.0000\n",
      "k=1.00, Step 7000: Loss = 0.0000\n",
      "k=1.00, Step 8000: Loss = 0.0000\n",
      "k=1.00, Step 9000: Loss = 0.0000\n",
      "k=2.00, Step 0: Loss = 0.7274\n",
      "k=2.00, Step 1000: Loss = 0.0000\n",
      "k=2.00, Step 2000: Loss = 0.0000\n",
      "k=2.00, Step 3000: Loss = 0.0000\n",
      "k=2.00, Step 4000: Loss = 0.0000\n",
      "k=2.00, Step 5000: Loss = 0.0000\n",
      "k=2.00, Step 6000: Loss = 0.0000\n",
      "k=2.00, Step 7000: Loss = 0.0000\n",
      "k=2.00, Step 8000: Loss = 0.0000\n",
      "k=2.00, Step 9000: Loss = 0.0000\n",
      "k=3.00, Step 0: Loss = 0.4543\n",
      "k=3.00, Step 1000: Loss = 0.0025\n",
      "k=3.00, Step 2000: Loss = 0.0002\n",
      "k=3.00, Step 3000: Loss = 0.0001\n",
      "k=3.00, Step 4000: Loss = 0.0000\n",
      "k=3.00, Step 5000: Loss = 0.0000\n",
      "k=3.00, Step 6000: Loss = 0.0001\n",
      "k=3.00, Step 7000: Loss = 0.0000\n",
      "k=3.00, Step 8000: Loss = 0.0000\n",
      "k=3.00, Step 9000: Loss = 0.0000\n",
      "k=4.00, Step 0: Loss = 0.5124\n",
      "k=4.00, Step 1000: Loss = 0.0035\n",
      "k=4.00, Step 2000: Loss = 0.0009\n",
      "k=4.00, Step 3000: Loss = 0.0003\n",
      "k=4.00, Step 4000: Loss = 0.0001\n",
      "k=4.00, Step 5000: Loss = 0.0000\n",
      "k=4.00, Step 6000: Loss = 0.0000\n",
      "k=4.00, Step 7000: Loss = 0.0001\n",
      "k=4.00, Step 8000: Loss = 0.0000\n",
      "k=4.00, Step 9000: Loss = 0.0000\n",
      "k=5.00, Step 0: Loss = 0.4329\n",
      "k=5.00, Step 1000: Loss = 0.0096\n",
      "k=5.00, Step 2000: Loss = 0.0046\n",
      "k=5.00, Step 3000: Loss = 0.0042\n",
      "k=5.00, Step 4000: Loss = 0.0036\n",
      "k=5.00, Step 5000: Loss = 0.0028\n",
      "k=5.00, Step 6000: Loss = 0.0018\n",
      "k=5.00, Step 7000: Loss = 0.0011\n",
      "k=5.00, Step 8000: Loss = 0.0007\n",
      "k=5.00, Step 9000: Loss = 0.0005\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "from torch import nn\n",
    "from torch.optim import Adam\n",
    "import numpy as np\n",
    "\n",
    "class Net(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(Net, self).__init__()\n",
    "        self.fc1 = nn.Linear(1, 256)\n",
    "        self.fc2 = nn.Linear(256, 256)\n",
    "        self.fc3 = nn.Linear(256, 256)\n",
    "        self.fc4 = nn.Linear(256, 256)\n",
    "        self.fc5 = nn.Linear(256, 1)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = torch.tanh(self.fc1(x))\n",
    "        x = torch.tanh(self.fc2(x))\n",
    "        x = torch.tanh(self.fc3(x))\n",
    "        x = torch.tanh(self.fc4(x))\n",
    "        x = self.fc5(x)\n",
    "        return x\n",
    "    \n",
    "\n",
    "\n",
    "def train(k):\n",
    "    net = Net()\n",
    "    optimizer = Adam(net.parameters(), lr=1e-4)\n",
    "    criterion = nn.MSELoss()\n",
    "    x = np.linspace(-np.pi, np.pi, 1000).reshape(-1, 1)\n",
    "    y = np.sin(x) + 0.2*np.sin(k * x)\n",
    "    x = torch.from_numpy(x).float()\n",
    "    y = torch.from_numpy(y).float()\n",
    "    res_dict = {}\n",
    "    res_list = []\n",
    "    for i in range(10000):\n",
    "        optimizer.zero_grad()\n",
    "        y_pred = net(x)\n",
    "        loss = criterion(y_pred, y)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        # if i % 10 == 0:\n",
    "        res_list.append(y_pred.detach().numpy())\n",
    "        if i % 1000 == 0:\n",
    "            print(f'k={k:.2f}, Step {i}: Loss = {loss.item():.4f}')\n",
    "    res_dict[k] = res_list\n",
    "    return res_dict\n",
    "\n",
    "\n",
    "# k_list = np.linspace(1, 3, 20)\n",
    "k_list=[1,2,3, 4, 5]\n",
    "res_dict_k = {}\n",
    "for k in k_list:\n",
    "    res_dict_k.update(train(k))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The relative error between the model output and the target function at different frequencies."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy.fft import fft\n",
    "\n",
    "error_1_list_all=[]\n",
    "error_5_list_all=[]\n",
    "\n",
    "def calc_relative_error(res_dict, k):\n",
    "    x = np.linspace(-np.pi, np.pi, 1000).reshape(-1, 1)\n",
    "    y = np.sin(x) + 0.2*np.sin(k * x)\n",
    "    y_fft = fft(y.squeeze())\n",
    "    error_1_list = []\n",
    "    error_5_list = []\n",
    "    for y_pred in res_dict[k]:\n",
    "        y_pred_fft = fft(y_pred.squeeze())\n",
    "        error_1 = abs(abs(y_fft[1]) - abs(y_pred_fft[1])) / abs(y_fft[1])\n",
    "        error_5 = abs(abs(y_fft[k]) - abs(y_pred_fft[k])) / abs(y_fft[k])\n",
    "        error_1_list.append(error_1)\n",
    "        error_5_list.append(error_5)\n",
    "    return error_1_list, error_5_list\n",
    "\n",
    "\n",
    "for k in k_list:\n",
    "    error_1_list, error_5_list = calc_relative_error(res_dict_k, k)\n",
    "    error_1_list_all.append(error_1_list)\n",
    "    error_5_list_all.append(error_5_list)   \n",
    "    # print(f'For a={a}, the relative errors at frequency 1 are {error_1_list}, the relative errors at frequency 5 are {error_5_list}')\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For a=5, the low freq index is 114, the high freq index is 114\n",
      "For a=5, the low freq index is 92, the high freq index is 225\n",
      "For a=5, the low freq index is 87, the high freq index is 1510\n",
      "For a=5, the low freq index is 91, the high freq index is 2432\n",
      "For a=5, the low freq index is 87, the high freq index is 8411\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def find_consecutive_index(arr):\n",
    "    for i in range(len(arr) - 10):\n",
    "        if all(arr[i+j] == arr[i] + j for j in range(10)):\n",
    "            return arr[i]\n",
    "    # return -1\n",
    "\n",
    "\n",
    "def calc_error_index(error_1_list_all, error_5_list_all):\n",
    "    error_1_index_list = []\n",
    "    error_5_index_list = []\n",
    "    for error_1_list, error_5_list in zip(error_1_list_all, error_5_list_all):\n",
    "\n",
    "        error_1_index = np.where(np.array(error_1_list) < 0.05)[0]\n",
    "        error_5_index = np.where(np.array(error_5_list) < 0.05)[0]\n",
    "        error_1_index = find_consecutive_index(error_1_index)\n",
    "        error_5_index = find_consecutive_index(error_5_index)\n",
    "\n",
    "        error_1_index_list.append(error_1_index)\n",
    "        error_5_index_list.append(error_5_index)\n",
    "        print(f'For a={k}, the low freq index is {error_1_index}, the high freq index is {error_5_index}')\n",
    "\n",
    "\n",
    "    return error_1_index_list, error_5_index_list\n",
    "\n",
    "\n",
    "\n",
    "error_1_list_all = []\n",
    "error_5_list_all = []\n",
    "for k in k_list:\n",
    "    error_1_list, error_5_list = calc_relative_error(res_dict_k, k)\n",
    "    error_1_list_all.append(error_1_list)\n",
    "    error_5_list_all.append(error_5_list)\n",
    "\n",
    "error_1_index_list, error_5_index_list = calc_error_index(error_1_list_all, error_5_list_all)\n",
    "\n",
    "ratio = np.array(error_1_index_list) / np.array(error_5_index_list)\n",
    "plt.plot(k_list, ratio, 'o-')\n",
    "plt.xticks([1,2,3,4,5])\n",
    "plt.xlabel('k', fontsize=14)\n",
    "plt.yscale('log')\n",
    "plt.ylabel('low freq index / high freq index', fontsize=14)\n",
    "# plt.yticks([0.02, 0.03])\n",
    "plt.xticks([1,2,3, 4, 5])\n",
    "plt.gca().tick_params(axis='y', labelsize=14)\n",
    "plt.gca().tick_params(axis='x', labelsize=14)\n",
    "plt.tight_layout()\n",
    "plt.ylabel('low freq index / high freq index')\n",
    "plt.savefig(os.path.join(args.path, 'frequencies.png'))\n",
    "plt.show()\n",
    "\n",
    "plt.close()\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "zzw",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.12"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}