dive_2deep_learning.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import torch\n",
    "import math\n",
    "import sys\n",
    "sys.path.append(\"..\") \n",
    "import d2lzh_pytorch as d2l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 10, x: 0.06046617599999997\n"
     ]
    }
   ],
   "source": [
    "\"\"\"\n",
    "下面以f(x)=x^2为例， 虽然我们知道最小化f(x)的解为x=0，\n",
    "\n",
    "看一下梯度下降是如何工作的\n",
    "\n",
    "使用x=10作为初始值，并设η=0.2。使用梯度下降对x迭代10次，可见最终x的值较接近最优解。\n",
    "\"\"\"\n",
    "def gd(eta):\n",
    "    x = 10\n",
    "    results = [x]\n",
    "    for i in range(10):\n",
    "        x -= eta * 2 * x  # f(x) = x * x的导数为f'(x) = 2 * x\n",
    "        results.append(x)\n",
    "    print('epoch 10, x:', x)\n",
    "    return results\n",
    "\n",
    "res = gd(0.2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"180.65625pt\" version=\"1.1\" viewBox=\"0 0 249.465625 180.65625\" width=\"249.465625pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 180.65625 \n",
       "L 249.465625 180.65625 \n",
       "L 249.465625 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 46.965625 143.1 \n",
       "L 242.265625 143.1 \n",
       "L 242.265625 7.2 \n",
       "L 46.965625 7.2 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"m7f9c17065e\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"55.842898\" xlink:href=\"#m7f9c17065e\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- −10 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.59375 35.5 \n",
       "L 73.1875 35.5 \n",
       "L 73.1875 27.203125 \n",
       "L 10.59375 27.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-8722\"/>\n",
       "       <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "       <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(45.290554 157.698438)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"100.229261\" xlink:href=\"#m7f9c17065e\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- −5 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(92.858168 157.698438)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"144.615625\" xlink:href=\"#m7f9c17065e\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(141.434375 157.698438)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"189.001989\" xlink:href=\"#m7f9c17065e\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- 5 -->\n",
       "      <g transform=\"translate(185.820739 157.698438)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"233.388352\" xlink:href=\"#m7f9c17065e\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- 10 -->\n",
       "      <g transform=\"translate(227.025852 157.698438)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_6\">\n",
       "     <!-- x -->\n",
       "     <defs>\n",
       "      <path d=\"M 54.890625 54.6875 \n",
       "L 35.109375 28.078125 \n",
       "L 55.90625 0 \n",
       "L 45.3125 0 \n",
       "L 29.390625 21.484375 \n",
       "L 13.484375 0 \n",
       "L 2.875 0 \n",
       "L 24.125 28.609375 \n",
       "L 4.6875 54.6875 \n",
       "L 15.28125 54.6875 \n",
       "L 29.78125 35.203125 \n",
       "L 44.28125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-120\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(141.65625 171.376563)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"m4b4c52df9a\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"46.965625\" xlink:href=\"#m4b4c52df9a\" y=\"136.922727\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(33.603125 140.721946)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"46.965625\" xlink:href=\"#m4b4c52df9a\" y=\"112.213636\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 20 -->\n",
       "      <defs>\n",
       "       <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(27.240625 116.012855)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"46.965625\" xlink:href=\"#m4b4c52df9a\" y=\"87.504545\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- 40 -->\n",
       "      <defs>\n",
       "       <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(27.240625 91.303764)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-52\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"46.965625\" xlink:href=\"#m4b4c52df9a\" y=\"62.795455\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- 60 -->\n",
       "      <defs>\n",
       "       <path d=\"M 33.015625 40.375 \n",
       "Q 26.375 40.375 22.484375 35.828125 \n",
       "Q 18.609375 31.296875 18.609375 23.390625 \n",
       "Q 18.609375 15.53125 22.484375 10.953125 \n",
       "Q 26.375 6.390625 33.015625 6.390625 \n",
       "Q 39.65625 6.390625 43.53125 10.953125 \n",
       "Q 47.40625 15.53125 47.40625 23.390625 \n",
       "Q 47.40625 31.296875 43.53125 35.828125 \n",
       "Q 39.65625 40.375 33.015625 40.375 \n",
       "z\n",
       "M 52.59375 71.296875 \n",
       "L 52.59375 62.3125 \n",
       "Q 48.875 64.0625 45.09375 64.984375 \n",
       "Q 41.3125 65.921875 37.59375 65.921875 \n",
       "Q 27.828125 65.921875 22.671875 59.328125 \n",
       "Q 17.53125 52.734375 16.796875 39.40625 \n",
       "Q 19.671875 43.65625 24.015625 45.921875 \n",
       "Q 28.375 48.1875 33.59375 48.1875 \n",
       "Q 44.578125 48.1875 50.953125 41.515625 \n",
       "Q 57.328125 34.859375 57.328125 23.390625 \n",
       "Q 57.328125 12.15625 50.6875 5.359375 \n",
       "Q 44.046875 -1.421875 33.015625 -1.421875 \n",
       "Q 20.359375 -1.421875 13.671875 8.265625 \n",
       "Q 6.984375 17.96875 6.984375 36.375 \n",
       "Q 6.984375 53.65625 15.1875 63.9375 \n",
       "Q 23.390625 74.21875 37.203125 74.21875 \n",
       "Q 40.921875 74.21875 44.703125 73.484375 \n",
       "Q 48.484375 72.75 52.59375 71.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-54\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(27.240625 66.594673)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-54\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"46.965625\" xlink:href=\"#m4b4c52df9a\" y=\"38.086364\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- 80 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 34.625 \n",
       "Q 24.75 34.625 20.71875 30.859375 \n",
       "Q 16.703125 27.09375 16.703125 20.515625 \n",
       "Q 16.703125 13.921875 20.71875 10.15625 \n",
       "Q 24.75 6.390625 31.78125 6.390625 \n",
       "Q 38.8125 6.390625 42.859375 10.171875 \n",
       "Q 46.921875 13.96875 46.921875 20.515625 \n",
       "Q 46.921875 27.09375 42.890625 30.859375 \n",
       "Q 38.875 34.625 31.78125 34.625 \n",
       "z\n",
       "M 21.921875 38.8125 \n",
       "Q 15.578125 40.375 12.03125 44.71875 \n",
       "Q 8.5 49.078125 8.5 55.328125 \n",
       "Q 8.5 64.0625 14.71875 69.140625 \n",
       "Q 20.953125 74.21875 31.78125 74.21875 \n",
       "Q 42.671875 74.21875 48.875 69.140625 \n",
       "Q 55.078125 64.0625 55.078125 55.328125 \n",
       "Q 55.078125 49.078125 51.53125 44.71875 \n",
       "Q 48 40.375 41.703125 38.8125 \n",
       "Q 48.828125 37.15625 52.796875 32.3125 \n",
       "Q 56.78125 27.484375 56.78125 20.515625 \n",
       "Q 56.78125 9.90625 50.3125 4.234375 \n",
       "Q 43.84375 -1.421875 31.78125 -1.421875 \n",
       "Q 19.734375 -1.421875 13.25 4.234375 \n",
       "Q 6.78125 9.90625 6.78125 20.515625 \n",
       "Q 6.78125 27.484375 10.78125 32.3125 \n",
       "Q 14.796875 37.15625 21.921875 38.8125 \n",
       "z\n",
       "M 18.3125 54.390625 \n",
       "Q 18.3125 48.734375 21.84375 45.5625 \n",
       "Q 25.390625 42.390625 31.78125 42.390625 \n",
       "Q 38.140625 42.390625 41.71875 45.5625 \n",
       "Q 45.3125 48.734375 45.3125 54.390625 \n",
       "Q 45.3125 60.0625 41.71875 63.234375 \n",
       "Q 38.140625 66.40625 31.78125 66.40625 \n",
       "Q 25.390625 66.40625 21.84375 63.234375 \n",
       "Q 18.3125 60.0625 18.3125 54.390625 \n",
       "z\n",
       "\" id=\"DejaVuSans-56\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(27.240625 41.885582)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-56\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"46.965625\" xlink:href=\"#m4b4c52df9a\" y=\"13.377273\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- 100 -->\n",
       "      <g transform=\"translate(20.878125 17.176491)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_13\">\n",
       "     <!-- f(x) -->\n",
       "     <defs>\n",
       "      <path d=\"M 37.109375 75.984375 \n",
       "L 37.109375 68.5 \n",
       "L 28.515625 68.5 \n",
       "Q 23.6875 68.5 21.796875 66.546875 \n",
       "Q 19.921875 64.59375 19.921875 59.515625 \n",
       "L 19.921875 54.6875 \n",
       "L 34.71875 54.6875 \n",
       "L 34.71875 47.703125 \n",
       "L 19.921875 47.703125 \n",
       "L 19.921875 0 \n",
       "L 10.890625 0 \n",
       "L 10.890625 47.703125 \n",
       "L 2.296875 47.703125 \n",
       "L 2.296875 54.6875 \n",
       "L 10.890625 54.6875 \n",
       "L 10.890625 58.5 \n",
       "Q 10.890625 67.625 15.140625 71.796875 \n",
       "Q 19.390625 75.984375 28.609375 75.984375 \n",
       "z\n",
       "\" id=\"DejaVuSans-102\"/>\n",
       "      <path d=\"M 31 75.875 \n",
       "Q 24.46875 64.65625 21.28125 53.65625 \n",
       "Q 18.109375 42.671875 18.109375 31.390625 \n",
       "Q 18.109375 20.125 21.3125 9.0625 \n",
       "Q 24.515625 -2 31 -13.1875 \n",
       "L 23.1875 -13.1875 \n",
       "Q 15.875 -1.703125 12.234375 9.375 \n",
       "Q 8.59375 20.453125 8.59375 31.390625 \n",
       "Q 8.59375 42.28125 12.203125 53.3125 \n",
       "Q 15.828125 64.359375 23.1875 75.875 \n",
       "z\n",
       "\" id=\"DejaVuSans-40\"/>\n",
       "      <path d=\"M 8.015625 75.875 \n",
       "L 15.828125 75.875 \n",
       "Q 23.140625 64.359375 26.78125 53.3125 \n",
       "Q 30.421875 42.28125 30.421875 31.390625 \n",
       "Q 30.421875 20.453125 26.78125 9.375 \n",
       "Q 23.140625 -1.703125 15.828125 -13.1875 \n",
       "L 8.015625 -13.1875 \n",
       "Q 14.5 -2 17.703125 9.0625 \n",
       "Q 20.90625 20.125 20.90625 31.390625 \n",
       "Q 20.90625 42.671875 17.703125 53.65625 \n",
       "Q 14.5 64.65625 8.015625 75.875 \n",
       "z\n",
       "\" id=\"DejaVuSans-41\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(14.798438 83.771094)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-102\"/>\n",
       "      <use x=\"35.205078\" xlink:href=\"#DejaVuSans-40\"/>\n",
       "      <use x=\"74.21875\" xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"133.398438\" xlink:href=\"#DejaVuSans-41\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"line2d_12\">\n",
       "    <path clip-path=\"url(#pa4fad64422)\" d=\"M 55.842898 13.377273 \n",
       "L 60.281534 25.422955 \n",
       "L 64.72017 36.850909 \n",
       "L 69.158807 47.661136 \n",
       "L 73.597443 57.853636 \n",
       "L 78.03608 67.428409 \n",
       "L 82.474716 76.385455 \n",
       "L 86.025625 83.106327 \n",
       "L 89.576534 89.431855 \n",
       "L 93.127443 95.362036 \n",
       "L 96.678352 100.896873 \n",
       "L 100.229261 106.036364 \n",
       "L 103.78017 110.780509 \n",
       "L 107.33108 115.129309 \n",
       "L 110.881989 119.082764 \n",
       "L 114.432898 122.640873 \n",
       "L 117.983807 125.803636 \n",
       "L 120.646989 127.916264 \n",
       "L 123.31017 129.806509 \n",
       "L 125.973352 131.474373 \n",
       "L 128.636534 132.919855 \n",
       "L 131.299716 134.142955 \n",
       "L 133.962898 135.143673 \n",
       "L 136.62608 135.922009 \n",
       "L 139.289261 136.477964 \n",
       "L 141.952443 136.811536 \n",
       "L 144.615625 136.922727 \n",
       "L 147.278807 136.811536 \n",
       "L 149.941989 136.477964 \n",
       "L 152.60517 135.922009 \n",
       "L 155.268352 135.143673 \n",
       "L 157.931534 134.142955 \n",
       "L 160.594716 132.919855 \n",
       "L 163.257898 131.474373 \n",
       "L 165.92108 129.806509 \n",
       "L 168.584261 127.916264 \n",
       "L 171.247443 125.803636 \n",
       "L 173.910625 123.468627 \n",
       "L 177.461534 120.009355 \n",
       "L 181.012443 116.154736 \n",
       "L 184.563352 111.904773 \n",
       "L 188.114261 107.259464 \n",
       "L 191.66517 102.218809 \n",
       "L 195.21608 96.782809 \n",
       "L 198.766989 90.951464 \n",
       "L 202.317898 84.724773 \n",
       "L 205.868807 78.102736 \n",
       "L 209.419716 71.085355 \n",
       "L 213.858352 61.757673 \n",
       "L 218.296989 51.812264 \n",
       "L 222.735625 41.249127 \n",
       "L 227.174261 30.068264 \n",
       "L 231.612898 18.269673 \n",
       "L 232.500625 15.835827 \n",
       "L 232.500625 15.835827 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"line2d_13\">\n",
       "    <path clip-path=\"url(#pa4fad64422)\" d=\"M 233.388352 13.377273 \n",
       "L 197.879261 92.446364 \n",
       "L 176.573807 120.911236 \n",
       "L 163.790534 131.158591 \n",
       "L 156.12057 134.847638 \n",
       "L 151.518592 136.175695 \n",
       "L 148.757405 136.653796 \n",
       "L 147.100693 136.825912 \n",
       "L 146.106666 136.887874 \n",
       "L 145.51025 136.91018 \n",
       "L 145.1524 136.91821 \n",
       "\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    <defs>\n",
       "     <path d=\"M 0 3 \n",
       "C 0.795609 3 1.55874 2.683901 2.12132 2.12132 \n",
       "C 2.683901 1.55874 3 0.795609 3 0 \n",
       "C 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \n",
       "C 1.55874 -2.683901 0.795609 -3 0 -3 \n",
       "C -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \n",
       "C -2.683901 -1.55874 -3 -0.795609 -3 0 \n",
       "C -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \n",
       "C -1.55874 2.683901 -0.795609 3 0 3 \n",
       "z\n",
       "\" id=\"md149f6c9e5\" style=\"stroke:#ff7f0e;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#pa4fad64422)\">\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"233.388352\" xlink:href=\"#md149f6c9e5\" y=\"13.377273\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"197.879261\" xlink:href=\"#md149f6c9e5\" y=\"92.446364\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"176.573807\" xlink:href=\"#md149f6c9e5\" y=\"120.911236\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"163.790534\" xlink:href=\"#md149f6c9e5\" y=\"131.158591\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"156.12057\" xlink:href=\"#md149f6c9e5\" y=\"134.847638\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"151.518592\" xlink:href=\"#md149f6c9e5\" y=\"136.175695\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"148.757405\" xlink:href=\"#md149f6c9e5\" y=\"136.653796\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"147.100693\" xlink:href=\"#md149f6c9e5\" y=\"136.825912\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"146.106666\" xlink:href=\"#md149f6c9e5\" y=\"136.887874\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"145.51025\" xlink:href=\"#md149f6c9e5\" y=\"136.91018\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"145.1524\" xlink:href=\"#md149f6c9e5\" y=\"136.91821\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 46.965625 143.1 \n",
       "L 46.965625 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 242.265625 143.1 \n",
       "L 242.265625 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 46.965625 143.1 \n",
       "L 242.265625 143.1 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 46.965625 7.2 \n",
       "L 242.265625 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"pa4fad64422\">\n",
       "   <rect height=\"135.9\" width=\"195.3\" x=\"46.965625\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"下面将绘制出自变量x的迭代轨迹。\"\"\"\n",
    "def show_trace(res):\n",
    "    n = max(abs(min(res)), abs(max(res)), 10)\n",
    "    f_line = np.arange(-n, n, 0.1)\n",
    "    d2l.set_figsize()\n",
    "    d2l.plt.plot(f_line, [x * x for x in f_line])\n",
    "    d2l.plt.plot(res, [x * x for x in res], '-o')\n",
    "    d2l.plt.xlabel('x')\n",
    "    d2l.plt.ylabel('f(x)')\n",
    "\n",
    "show_trace(res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "下面我们查看二维的情况\n",
    "\n",
    "构造一个输入为二维向量x=[x1,x2]⊤\n",
    "\n",
    "输出为目标函数f(x)= x1^2+x2^2\n",
    "\n",
    "初始位置[−5,−2][−5,−2]\n",
    "\n",
    "迭代自变量x20次\n",
    "\"\"\"\n",
    "def train_2d(trainer):  # 本函数将保存在d2lzh_pytorch包中方便以后使用\n",
    "    x1, x2, s1, s2 = -5, -2, 0, 0  # s1和s2是自变量状态，本章后续几节会使用\n",
    "    results = [(x1, x2)]\n",
    "    for i in range(20):\n",
    "        x1, x2, s1, s2 = trainer(x1, x2, s1, s2)\n",
    "        results.append((x1, x2))\n",
    "    print('epoch %d, x1 %f, x2 %f' % (i + 1, x1, x2))\n",
    "    return results\n",
    "\n",
    "def show_trace_2d(f, results):  # 本函数将保存在d2lzh_pytorch包中方便以后使用\n",
    "    d2l.plt.plot(*zip(*results), '-o', color='#ff7f0e')\n",
    "    x1, x2 = np.meshgrid(np.arange(-5.5, 1.0, 0.1), np.arange(-3.0, 1.0, 0.1))\n",
    "    d2l.plt.contour(x1, x2, f(x1, x2), colors='#1f77b4')\n",
    "    d2l.plt.xlabel('x1')\n",
    "    d2l.plt.ylabel('x2')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.057646, x2 -0.000073\n"
     ]
    },
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"180.65625pt\" version=\"1.1\" viewBox=\"0 0 245.120313 180.65625\" width=\"245.120313pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 180.65625 \n",
       "L 245.120313 180.65625 \n",
       "L 245.120313 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 42.620312 143.1 \n",
       "L 237.920313 143.1 \n",
       "L 237.920313 7.2 \n",
       "L 42.620312 7.2 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"mb020f047a1\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"88.39375\" xlink:href=\"#mb020f047a1\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- −4 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.59375 35.5 \n",
       "L 73.1875 35.5 \n",
       "L 73.1875 27.203125 \n",
       "L 10.59375 27.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-8722\"/>\n",
       "       <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(81.022656 157.698438)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"149.425\" xlink:href=\"#mb020f047a1\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- −2 -->\n",
       "      <defs>\n",
       "       <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(142.053906 157.698438)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"210.45625\" xlink:href=\"#mb020f047a1\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(207.275 157.698438)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_4\">\n",
       "     <!-- x1 -->\n",
       "     <defs>\n",
       "      <path d=\"M 54.890625 54.6875 \n",
       "L 35.109375 28.078125 \n",
       "L 55.90625 0 \n",
       "L 45.3125 0 \n",
       "L 29.390625 21.484375 \n",
       "L 13.484375 0 \n",
       "L 2.875 0 \n",
       "L 24.125 28.609375 \n",
       "L 4.6875 54.6875 \n",
       "L 15.28125 54.6875 \n",
       "L 29.78125 35.203125 \n",
       "L 44.28125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-120\"/>\n",
       "      <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(134.129687 171.376563)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"m7f84007b7f\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620312\" xlink:href=\"#m7f84007b7f\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- −3 -->\n",
       "      <defs>\n",
       "       <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(20.878125 146.899219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620312\" xlink:href=\"#m7f84007b7f\" y=\"108.253846\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- −2 -->\n",
       "      <g transform=\"translate(20.878125 112.053065)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620312\" xlink:href=\"#m7f84007b7f\" y=\"73.407692\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- −1 -->\n",
       "      <g transform=\"translate(20.878125 77.206911)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620312\" xlink:href=\"#m7f84007b7f\" y=\"38.561538\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(29.257812 42.360757)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_9\">\n",
       "     <!-- x2 -->\n",
       "     <g transform=\"translate(14.798437 81.290625)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_1\"/>\n",
       "   <g id=\"LineCollection_2\">\n",
       "    <path clip-path=\"url(#p114e8cd123)\" d=\"M 237.920313 104.627963 \n",
       "L 237.381801 104.769231 \n",
       "L 234.86875 105.394675 \n",
       "L 231.817188 106.064793 \n",
       "L 228.765625 106.645562 \n",
       "L 225.714063 107.136982 \n",
       "L 222.6625 107.539053 \n",
       "L 219.610938 107.851775 \n",
       "L 216.559375 108.075148 \n",
       "L 213.507813 108.209172 \n",
       "L 210.45625 108.253846 \n",
       "L 210.45625 108.253846 \n",
       "L 210.45625 108.253846 \n",
       "L 207.404688 108.209172 \n",
       "L 204.353125 108.075148 \n",
       "L 201.301563 107.851775 \n",
       "L 198.25 107.539053 \n",
       "L 195.198438 107.136982 \n",
       "L 192.146875 106.645562 \n",
       "L 189.095313 106.064793 \n",
       "L 186.04375 105.394675 \n",
       "L 183.530699 104.769231 \n",
       "L 182.992188 104.627963 \n",
       "L 179.940625 103.733264 \n",
       "L 176.889063 102.744387 \n",
       "L 173.8375 101.661331 \n",
       "L 172.861 101.284615 \n",
       "L 170.785938 100.438352 \n",
       "L 167.734375 99.094286 \n",
       "L 164.998491 97.8 \n",
       "L 164.682813 97.641608 \n",
       "L 161.63125 96.004895 \n",
       "L 158.672159 94.315385 \n",
       "L 158.579688 94.259181 \n",
       "L 155.528125 92.29206 \n",
       "L 153.383784 90.830769 \n",
       "L 152.476563 90.169894 \n",
       "L 149.425 87.82679 \n",
       "L 148.829573 87.346154 \n",
       "L 146.373438 85.216667 \n",
       "L 144.88314 83.861538 \n",
       "L 143.321875 82.328308 \n",
       "L 141.423125 80.376923 \n",
       "L 140.270313 79.08913 \n",
       "L 138.387434 76.892308 \n",
       "L 137.21875 75.398901 \n",
       "L 135.724107 73.407692 \n",
       "L 134.167188 71.115182 \n",
       "L 133.389338 69.923077 \n",
       "L 131.354963 66.438462 \n",
       "L 131.115625 65.973846 \n",
       "L 129.618632 62.953846 \n",
       "L 128.121639 59.469231 \n",
       "L 128.064063 59.310839 \n",
       "L 126.89892 55.984615 \n",
       "L 125.900227 52.5 \n",
       "L 125.123466 49.015385 \n",
       "L 125.0125 48.318462 \n",
       "L 124.584211 45.530769 \n",
       "L 124.262993 42.046154 \n",
       "L 124.155921 38.561538 \n",
       "L 124.262993 35.076923 \n",
       "L 124.584211 31.592308 \n",
       "L 125.0125 28.804615 \n",
       "L 125.123466 28.107692 \n",
       "L 125.900227 24.623077 \n",
       "L 126.89892 21.138462 \n",
       "L 128.064063 17.812238 \n",
       "L 128.121639 17.653846 \n",
       "L 129.618632 14.169231 \n",
       "L 131.115625 11.149231 \n",
       "L 131.354963 10.684615 \n",
       "L 133.389338 7.2 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_3\">\n",
       "    <path clip-path=\"url(#p114e8cd123)\" d=\"M 237.920313 134.578531 \n",
       "L 234.86875 135.117063 \n",
       "L 231.817188 135.592238 \n",
       "L 228.765625 136.004056 \n",
       "L 227.655966 136.130769 \n",
       "L 225.714063 136.344737 \n",
       "L 222.6625 136.619838 \n",
       "L 219.610938 136.833806 \n",
       "L 216.559375 136.98664 \n",
       "L 213.507813 137.07834 \n",
       "L 210.45625 137.108907 \n",
       "L 207.404688 137.07834 \n",
       "L 204.353125 136.98664 \n",
       "L 201.301563 136.833806 \n",
       "L 198.25 136.619838 \n",
       "L 195.198438 136.344737 \n",
       "L 193.256534 136.130769 \n",
       "L 192.146875 136.004056 \n",
       "L 189.095313 135.592238 \n",
       "L 186.04375 135.117063 \n",
       "L 182.992188 134.578531 \n",
       "L 179.940625 133.976643 \n",
       "L 176.889063 133.311399 \n",
       "L 174.102853 132.646154 \n",
       "L 173.8375 132.580406 \n",
       "L 170.785938 131.758563 \n",
       "L 167.734375 130.870972 \n",
       "L 164.682813 129.917634 \n",
       "L 162.41875 129.161538 \n",
       "L 161.63125 128.888235 \n",
       "L 158.579688 127.76086 \n",
       "L 155.528125 126.565158 \n",
       "L 153.383784 125.676923 \n",
       "L 152.476563 125.285793 \n",
       "L 149.425 123.899058 \n",
       "L 146.373438 122.441209 \n",
       "L 145.876672 122.192308 \n",
       "L 143.321875 120.857774 \n",
       "L 140.270313 119.189607 \n",
       "L 139.426263 118.707692 \n",
       "L 137.21875 117.391282 \n",
       "L 134.167188 115.494103 \n",
       "L 133.748346 115.223077 \n",
       "L 131.115625 113.44025 \n",
       "L 128.697406 111.738462 \n",
       "L 128.064063 111.271013 \n",
       "L 125.0125 108.933771 \n",
       "L 124.155921 108.253846 \n",
       "L 121.960938 106.422189 \n",
       "L 120.047246 104.769231 \n",
       "L 118.909375 103.733264 \n",
       "L 116.308043 101.284615 \n",
       "L 115.857813 100.836593 \n",
       "L 112.903125 97.8 \n",
       "L 112.80625 97.694406 \n",
       "L 109.801635 94.315385 \n",
       "L 109.754688 94.259181 \n",
       "L 106.976399 90.830769 \n",
       "L 106.703125 90.470292 \n",
       "L 104.403397 87.346154 \n",
       "L 103.651563 86.249145 \n",
       "L 102.061312 83.861538 \n",
       "L 100.6 81.492 \n",
       "L 99.931164 80.376923 \n",
       "L 98.008262 76.892308 \n",
       "L 97.548438 75.97967 \n",
       "L 96.287125 73.407692 \n",
       "L 94.741 69.923077 \n",
       "L 94.496875 69.308145 \n",
       "L 93.387216 66.438462 \n",
       "L 92.198295 62.953846 \n",
       "L 91.445313 60.407396 \n",
       "L 91.174921 59.469231 \n",
       "L 90.325119 55.984615 \n",
       "L 89.629826 52.5 \n",
       "L 89.089043 49.015385 \n",
       "L 88.702769 45.530769 \n",
       "L 88.471005 42.046154 \n",
       "L 88.39375 38.561538 \n",
       "L 88.471005 35.076923 \n",
       "L 88.702769 31.592308 \n",
       "L 89.089043 28.107692 \n",
       "L 89.629826 24.623077 \n",
       "L 90.325119 21.138462 \n",
       "L 91.174921 17.653846 \n",
       "L 91.445313 16.71568 \n",
       "L 92.198295 14.169231 \n",
       "L 93.387216 10.684615 \n",
       "L 94.496875 7.814932 \n",
       "L 94.741 7.2 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_4\">\n",
       "    <path clip-path=\"url(#p114e8cd123)\" d=\"M 135.724107 143.1 \n",
       "L 134.167188 142.361734 \n",
       "L 131.115625 140.855671 \n",
       "L 128.697406 139.615385 \n",
       "L 128.064063 139.27915 \n",
       "L 125.0125 137.597976 \n",
       "L 122.442763 136.130769 \n",
       "L 121.960938 135.845664 \n",
       "L 118.909375 133.976643 \n",
       "L 116.808299 132.646154 \n",
       "L 115.857813 132.021553 \n",
       "L 112.80625 129.950508 \n",
       "L 111.679519 129.161538 \n",
       "L 109.754688 127.76086 \n",
       "L 106.976399 125.676923 \n",
       "L 106.703125 125.463579 \n",
       "L 103.651563 123.010126 \n",
       "L 102.663028 122.192308 \n",
       "L 100.6 120.41293 \n",
       "L 98.677098 118.707692 \n",
       "L 97.548438 117.662308 \n",
       "L 94.985125 115.223077 \n",
       "L 94.496875 114.736852 \n",
       "L 91.564205 111.738462 \n",
       "L 91.445313 111.610976 \n",
       "L 88.39375 108.253846 \n",
       "L 88.39375 108.253846 \n",
       "L 85.455208 104.769231 \n",
       "L 85.342188 104.627963 \n",
       "L 82.731815 101.284615 \n",
       "L 82.290625 100.687253 \n",
       "L 80.208382 97.8 \n",
       "L 79.239063 96.374476 \n",
       "L 77.871121 94.315385 \n",
       "L 76.1875 91.617618 \n",
       "L 75.707479 90.830769 \n",
       "L 73.71882 87.346154 \n",
       "L 73.135938 86.249145 \n",
       "L 71.895192 83.861538 \n",
       "L 70.21851 80.376923 \n",
       "L 70.084375 80.073913 \n",
       "L 68.70625 76.892308 \n",
       "L 67.328125 73.407692 \n",
       "L 67.032813 72.582389 \n",
       "L 66.101283 69.923077 \n",
       "L 65.009145 66.438462 \n",
       "L 64.045493 62.953846 \n",
       "L 63.98125 62.685799 \n",
       "L 63.226224 59.469231 \n",
       "L 62.534117 55.984615 \n",
       "L 61.967848 52.5 \n",
       "L 61.527416 49.015385 \n",
       "L 61.212822 45.530769 \n",
       "L 61.024066 42.046154 \n",
       "L 60.961147 38.561538 \n",
       "L 61.024066 35.076923 \n",
       "L 61.212822 31.592308 \n",
       "L 61.527416 28.107692 \n",
       "L 61.967848 24.623077 \n",
       "L 62.534117 21.138462 \n",
       "L 63.226224 17.653846 \n",
       "L 63.98125 14.437278 \n",
       "L 64.045493 14.169231 \n",
       "L 65.009145 10.684615 \n",
       "L 66.101283 7.2 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_5\">\n",
       "    <path clip-path=\"url(#p114e8cd123)\" d=\"M 96.287125 143.1 \n",
       "L 94.496875 141.800652 \n",
       "L 91.564205 139.615385 \n",
       "L 91.445313 139.523684 \n",
       "L 88.39375 137.108907 \n",
       "L 87.188194 136.130769 \n",
       "L 85.342188 134.578531 \n",
       "L 83.099473 132.646154 \n",
       "L 82.290625 131.922932 \n",
       "L 79.274963 129.161538 \n",
       "L 79.239063 129.127376 \n",
       "L 76.1875 126.155204 \n",
       "L 75.707479 125.676923 \n",
       "L 73.135938 123.010126 \n",
       "L 72.364663 122.192308 \n",
       "L 70.084375 119.671522 \n",
       "L 69.23125 118.707692 \n",
       "L 67.032813 116.11359 \n",
       "L 66.294013 115.223077 \n",
       "L 63.98125 112.305725 \n",
       "L 63.540818 111.738462 \n",
       "L 60.961147 108.253846 \n",
       "L 60.929688 108.209172 \n",
       "L 58.55625 104.769231 \n",
       "L 57.878125 103.733264 \n",
       "L 56.307024 101.284615 \n",
       "L 54.826563 98.845385 \n",
       "L 54.204399 97.8 \n",
       "L 52.249029 94.315385 \n",
       "L 51.775 93.416129 \n",
       "L 50.438125 90.830769 \n",
       "L 48.7525 87.346154 \n",
       "L 48.723438 87.281624 \n",
       "L 47.211916 83.861538 \n",
       "L 45.785952 80.376923 \n",
       "L 45.671875 80.073913 \n",
       "L 44.496044 76.892308 \n",
       "L 43.320212 73.407692 \n",
       "L 42.620313 71.115182 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_6\">\n",
       "    <path clip-path=\"url(#p114e8cd123)\" d=\"M 67.328125 143.1 \n",
       "L 67.032813 142.834224 \n",
       "L 63.98125 140.028814 \n",
       "L 63.540818 139.615385 \n",
       "L 60.929688 137.07834 \n",
       "L 59.974148 136.130769 \n",
       "L 57.878125 133.976643 \n",
       "L 56.609158 132.646154 \n",
       "L 54.826563 130.706604 \n",
       "L 53.434102 129.161538 \n",
       "L 51.775 127.248416 \n",
       "L 50.438125 125.676923 \n",
       "L 48.723438 123.579042 \n",
       "L 47.611186 122.192308 \n",
       "L 45.671875 119.671522 \n",
       "L 44.943979 118.707692 \n",
       "L 42.620313 115.494103 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_7\">\n",
       "    <path clip-path=\"url(#p114e8cd123)\" d=\"M 43.320212 143.1 \n",
       "L 42.620313 142.361734 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_8\"/>\n",
       "   <g id=\"line2d_8\">\n",
       "    <path clip-path=\"url(#p114e8cd123)\" d=\"M 57.878125 108.253846 \n",
       "L 88.39375 80.376923 \n",
       "L 112.80625 63.650769 \n",
       "L 132.33625 53.615077 \n",
       "L 147.96025 47.593662 \n",
       "L 160.45945 43.980812 \n",
       "L 170.45881 41.813103 \n",
       "L 178.458298 40.512477 \n",
       "L 184.857888 39.732102 \n",
       "L 189.977561 39.263876 \n",
       "L 194.073299 38.982941 \n",
       "L 197.349889 38.81438 \n",
       "L 199.971161 38.713243 \n",
       "L 202.068179 38.652561 \n",
       "L 203.745793 38.616152 \n",
       "L 205.087884 38.594307 \n",
       "L 206.161558 38.581199 \n",
       "L 207.020496 38.573335 \n",
       "L 207.707647 38.568616 \n",
       "L 208.257367 38.565785 \n",
       "L 208.697144 38.564087 \n",
       "\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    <defs>\n",
       "     <path d=\"M 0 3 \n",
       "C 0.795609 3 1.55874 2.683901 2.12132 2.12132 \n",
       "C 2.683901 1.55874 3 0.795609 3 0 \n",
       "C 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \n",
       "C 1.55874 -2.683901 0.795609 -3 0 -3 \n",
       "C -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \n",
       "C -2.683901 -1.55874 -3 -0.795609 -3 0 \n",
       "C -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \n",
       "C -1.55874 2.683901 -0.795609 3 0 3 \n",
       "z\n",
       "\" id=\"m99bca512a8\" style=\"stroke:#ff7f0e;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p114e8cd123)\">\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"57.878125\" xlink:href=\"#m99bca512a8\" y=\"108.253846\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"88.39375\" xlink:href=\"#m99bca512a8\" y=\"80.376923\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"112.80625\" xlink:href=\"#m99bca512a8\" y=\"63.650769\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"132.33625\" xlink:href=\"#m99bca512a8\" y=\"53.615077\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"147.96025\" xlink:href=\"#m99bca512a8\" y=\"47.593662\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"160.45945\" xlink:href=\"#m99bca512a8\" y=\"43.980812\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"170.45881\" xlink:href=\"#m99bca512a8\" y=\"41.813103\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"178.458298\" xlink:href=\"#m99bca512a8\" y=\"40.512477\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"184.857888\" xlink:href=\"#m99bca512a8\" y=\"39.732102\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"189.977561\" xlink:href=\"#m99bca512a8\" y=\"39.263876\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"194.073299\" xlink:href=\"#m99bca512a8\" y=\"38.982941\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"197.349889\" xlink:href=\"#m99bca512a8\" y=\"38.81438\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"199.971161\" xlink:href=\"#m99bca512a8\" y=\"38.713243\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"202.068179\" xlink:href=\"#m99bca512a8\" y=\"38.652561\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"203.745793\" xlink:href=\"#m99bca512a8\" y=\"38.616152\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"205.087884\" xlink:href=\"#m99bca512a8\" y=\"38.594307\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"206.161558\" xlink:href=\"#m99bca512a8\" y=\"38.581199\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"207.020496\" xlink:href=\"#m99bca512a8\" y=\"38.573335\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"207.707647\" xlink:href=\"#m99bca512a8\" y=\"38.568616\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"208.257367\" xlink:href=\"#m99bca512a8\" y=\"38.565785\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"208.697144\" xlink:href=\"#m99bca512a8\" y=\"38.564087\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 42.620312 143.1 \n",
       "L 42.620312 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 237.920313 143.1 \n",
       "L 237.920313 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 42.620313 143.1 \n",
       "L 237.920313 143.1 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 42.620313 7.2 \n",
       "L 237.920313 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p114e8cd123\">\n",
       "   <rect height=\"135.9\" width=\"195.3\" x=\"42.620312\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "然后，观察学习率为0.1时自变量的迭代轨迹。使用梯度下降对自变量x迭代20次后，\n",
    "\n",
    "可见最终x的值较接近最优解[0,0][0,0]。\n",
    "\"\"\"\n",
    "eta = 0.1\n",
    "\n",
    "def f_2d(x1, x2):  # 目标函数\n",
    "    return x1 ** 2 + 2 * x2 ** 2\n",
    "\n",
    "def gd_2d(x1, x2, s1, s2):\n",
    "    return (x1 - eta * 2 * x1, x2 - eta * 4 * x2, 0, 0)\n",
    "\n",
    "show_trace_2d(f_2d, train_2d(gd_2d))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.316638, x2 -0.117459\n"
     ]
    },
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"180.65625pt\" version=\"1.1\" viewBox=\"0 0 245.120313 180.65625\" width=\"245.120313pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 180.65625 \n",
       "L 245.120313 180.65625 \n",
       "L 245.120313 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 42.620312 143.1 \n",
       "L 237.920313 143.1 \n",
       "L 237.920313 7.2 \n",
       "L 42.620312 7.2 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"mbd9f0dd67c\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"88.39375\" xlink:href=\"#mbd9f0dd67c\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- −4 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.59375 35.5 \n",
       "L 73.1875 35.5 \n",
       "L 73.1875 27.203125 \n",
       "L 10.59375 27.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-8722\"/>\n",
       "       <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(81.022656 157.698438)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"149.425\" xlink:href=\"#mbd9f0dd67c\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- −2 -->\n",
       "      <defs>\n",
       "       <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(142.053906 157.698438)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"210.45625\" xlink:href=\"#mbd9f0dd67c\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- 0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(207.275 157.698438)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_4\">\n",
       "     <!-- x1 -->\n",
       "     <defs>\n",
       "      <path d=\"M 54.890625 54.6875 \n",
       "L 35.109375 28.078125 \n",
       "L 55.90625 0 \n",
       "L 45.3125 0 \n",
       "L 29.390625 21.484375 \n",
       "L 13.484375 0 \n",
       "L 2.875 0 \n",
       "L 24.125 28.609375 \n",
       "L 4.6875 54.6875 \n",
       "L 15.28125 54.6875 \n",
       "L 29.78125 35.203125 \n",
       "L 44.28125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-120\"/>\n",
       "      <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(134.129687 171.376563)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"mc20e553993\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620312\" xlink:href=\"#mc20e553993\" y=\"143.1\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- −3 -->\n",
       "      <defs>\n",
       "       <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(20.878125 146.899219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620312\" xlink:href=\"#mc20e553993\" y=\"108.253846\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- −2 -->\n",
       "      <g transform=\"translate(20.878125 112.053065)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620312\" xlink:href=\"#mc20e553993\" y=\"73.407692\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_7\">\n",
       "      <!-- −1 -->\n",
       "      <g transform=\"translate(20.878125 77.206911)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620312\" xlink:href=\"#mc20e553993\" y=\"38.561538\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(29.257812 42.360757)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_9\">\n",
       "     <!-- x2 -->\n",
       "     <g transform=\"translate(14.798437 81.290625)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_1\"/>\n",
       "   <g id=\"LineCollection_2\">\n",
       "    <path clip-path=\"url(#p5653fcfcd2)\" d=\"M 237.920313 104.627963 \n",
       "L 237.381801 104.769231 \n",
       "L 234.86875 105.394675 \n",
       "L 231.817188 106.064793 \n",
       "L 228.765625 106.645562 \n",
       "L 225.714063 107.136982 \n",
       "L 222.6625 107.539053 \n",
       "L 219.610938 107.851775 \n",
       "L 216.559375 108.075148 \n",
       "L 213.507813 108.209172 \n",
       "L 210.45625 108.253846 \n",
       "L 210.45625 108.253846 \n",
       "L 210.45625 108.253846 \n",
       "L 207.404688 108.209172 \n",
       "L 204.353125 108.075148 \n",
       "L 201.301563 107.851775 \n",
       "L 198.25 107.539053 \n",
       "L 195.198438 107.136982 \n",
       "L 192.146875 106.645562 \n",
       "L 189.095313 106.064793 \n",
       "L 186.04375 105.394675 \n",
       "L 183.530699 104.769231 \n",
       "L 182.992188 104.627963 \n",
       "L 179.940625 103.733264 \n",
       "L 176.889063 102.744387 \n",
       "L 173.8375 101.661331 \n",
       "L 172.861 101.284615 \n",
       "L 170.785938 100.438352 \n",
       "L 167.734375 99.094286 \n",
       "L 164.998491 97.8 \n",
       "L 164.682813 97.641608 \n",
       "L 161.63125 96.004895 \n",
       "L 158.672159 94.315385 \n",
       "L 158.579688 94.259181 \n",
       "L 155.528125 92.29206 \n",
       "L 153.383784 90.830769 \n",
       "L 152.476563 90.169894 \n",
       "L 149.425 87.82679 \n",
       "L 148.829573 87.346154 \n",
       "L 146.373438 85.216667 \n",
       "L 144.88314 83.861538 \n",
       "L 143.321875 82.328308 \n",
       "L 141.423125 80.376923 \n",
       "L 140.270313 79.08913 \n",
       "L 138.387434 76.892308 \n",
       "L 137.21875 75.398901 \n",
       "L 135.724107 73.407692 \n",
       "L 134.167188 71.115182 \n",
       "L 133.389338 69.923077 \n",
       "L 131.354963 66.438462 \n",
       "L 131.115625 65.973846 \n",
       "L 129.618632 62.953846 \n",
       "L 128.121639 59.469231 \n",
       "L 128.064063 59.310839 \n",
       "L 126.89892 55.984615 \n",
       "L 125.900227 52.5 \n",
       "L 125.123466 49.015385 \n",
       "L 125.0125 48.318462 \n",
       "L 124.584211 45.530769 \n",
       "L 124.262993 42.046154 \n",
       "L 124.155921 38.561538 \n",
       "L 124.262993 35.076923 \n",
       "L 124.584211 31.592308 \n",
       "L 125.0125 28.804615 \n",
       "L 125.123466 28.107692 \n",
       "L 125.900227 24.623077 \n",
       "L 126.89892 21.138462 \n",
       "L 128.064063 17.812238 \n",
       "L 128.121639 17.653846 \n",
       "L 129.618632 14.169231 \n",
       "L 131.115625 11.149231 \n",
       "L 131.354963 10.684615 \n",
       "L 133.389338 7.2 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_3\">\n",
       "    <path clip-path=\"url(#p5653fcfcd2)\" d=\"M 237.920313 134.578531 \n",
       "L 234.86875 135.117063 \n",
       "L 231.817188 135.592238 \n",
       "L 228.765625 136.004056 \n",
       "L 227.655966 136.130769 \n",
       "L 225.714063 136.344737 \n",
       "L 222.6625 136.619838 \n",
       "L 219.610938 136.833806 \n",
       "L 216.559375 136.98664 \n",
       "L 213.507813 137.07834 \n",
       "L 210.45625 137.108907 \n",
       "L 207.404688 137.07834 \n",
       "L 204.353125 136.98664 \n",
       "L 201.301563 136.833806 \n",
       "L 198.25 136.619838 \n",
       "L 195.198438 136.344737 \n",
       "L 193.256534 136.130769 \n",
       "L 192.146875 136.004056 \n",
       "L 189.095313 135.592238 \n",
       "L 186.04375 135.117063 \n",
       "L 182.992188 134.578531 \n",
       "L 179.940625 133.976643 \n",
       "L 176.889063 133.311399 \n",
       "L 174.102853 132.646154 \n",
       "L 173.8375 132.580406 \n",
       "L 170.785938 131.758563 \n",
       "L 167.734375 130.870972 \n",
       "L 164.682813 129.917634 \n",
       "L 162.41875 129.161538 \n",
       "L 161.63125 128.888235 \n",
       "L 158.579688 127.76086 \n",
       "L 155.528125 126.565158 \n",
       "L 153.383784 125.676923 \n",
       "L 152.476563 125.285793 \n",
       "L 149.425 123.899058 \n",
       "L 146.373438 122.441209 \n",
       "L 145.876672 122.192308 \n",
       "L 143.321875 120.857774 \n",
       "L 140.270313 119.189607 \n",
       "L 139.426263 118.707692 \n",
       "L 137.21875 117.391282 \n",
       "L 134.167188 115.494103 \n",
       "L 133.748346 115.223077 \n",
       "L 131.115625 113.44025 \n",
       "L 128.697406 111.738462 \n",
       "L 128.064063 111.271013 \n",
       "L 125.0125 108.933771 \n",
       "L 124.155921 108.253846 \n",
       "L 121.960938 106.422189 \n",
       "L 120.047246 104.769231 \n",
       "L 118.909375 103.733264 \n",
       "L 116.308043 101.284615 \n",
       "L 115.857813 100.836593 \n",
       "L 112.903125 97.8 \n",
       "L 112.80625 97.694406 \n",
       "L 109.801635 94.315385 \n",
       "L 109.754688 94.259181 \n",
       "L 106.976399 90.830769 \n",
       "L 106.703125 90.470292 \n",
       "L 104.403397 87.346154 \n",
       "L 103.651563 86.249145 \n",
       "L 102.061312 83.861538 \n",
       "L 100.6 81.492 \n",
       "L 99.931164 80.376923 \n",
       "L 98.008262 76.892308 \n",
       "L 97.548438 75.97967 \n",
       "L 96.287125 73.407692 \n",
       "L 94.741 69.923077 \n",
       "L 94.496875 69.308145 \n",
       "L 93.387216 66.438462 \n",
       "L 92.198295 62.953846 \n",
       "L 91.445313 60.407396 \n",
       "L 91.174921 59.469231 \n",
       "L 90.325119 55.984615 \n",
       "L 89.629826 52.5 \n",
       "L 89.089043 49.015385 \n",
       "L 88.702769 45.530769 \n",
       "L 88.471005 42.046154 \n",
       "L 88.39375 38.561538 \n",
       "L 88.471005 35.076923 \n",
       "L 88.702769 31.592308 \n",
       "L 89.089043 28.107692 \n",
       "L 89.629826 24.623077 \n",
       "L 90.325119 21.138462 \n",
       "L 91.174921 17.653846 \n",
       "L 91.445313 16.71568 \n",
       "L 92.198295 14.169231 \n",
       "L 93.387216 10.684615 \n",
       "L 94.496875 7.814932 \n",
       "L 94.741 7.2 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_4\">\n",
       "    <path clip-path=\"url(#p5653fcfcd2)\" d=\"M 135.724107 143.1 \n",
       "L 134.167188 142.361734 \n",
       "L 131.115625 140.855671 \n",
       "L 128.697406 139.615385 \n",
       "L 128.064063 139.27915 \n",
       "L 125.0125 137.597976 \n",
       "L 122.442763 136.130769 \n",
       "L 121.960938 135.845664 \n",
       "L 118.909375 133.976643 \n",
       "L 116.808299 132.646154 \n",
       "L 115.857813 132.021553 \n",
       "L 112.80625 129.950508 \n",
       "L 111.679519 129.161538 \n",
       "L 109.754688 127.76086 \n",
       "L 106.976399 125.676923 \n",
       "L 106.703125 125.463579 \n",
       "L 103.651563 123.010126 \n",
       "L 102.663028 122.192308 \n",
       "L 100.6 120.41293 \n",
       "L 98.677098 118.707692 \n",
       "L 97.548438 117.662308 \n",
       "L 94.985125 115.223077 \n",
       "L 94.496875 114.736852 \n",
       "L 91.564205 111.738462 \n",
       "L 91.445313 111.610976 \n",
       "L 88.39375 108.253846 \n",
       "L 88.39375 108.253846 \n",
       "L 85.455208 104.769231 \n",
       "L 85.342188 104.627963 \n",
       "L 82.731815 101.284615 \n",
       "L 82.290625 100.687253 \n",
       "L 80.208382 97.8 \n",
       "L 79.239063 96.374476 \n",
       "L 77.871121 94.315385 \n",
       "L 76.1875 91.617618 \n",
       "L 75.707479 90.830769 \n",
       "L 73.71882 87.346154 \n",
       "L 73.135938 86.249145 \n",
       "L 71.895192 83.861538 \n",
       "L 70.21851 80.376923 \n",
       "L 70.084375 80.073913 \n",
       "L 68.70625 76.892308 \n",
       "L 67.328125 73.407692 \n",
       "L 67.032813 72.582389 \n",
       "L 66.101283 69.923077 \n",
       "L 65.009145 66.438462 \n",
       "L 64.045493 62.953846 \n",
       "L 63.98125 62.685799 \n",
       "L 63.226224 59.469231 \n",
       "L 62.534117 55.984615 \n",
       "L 61.967848 52.5 \n",
       "L 61.527416 49.015385 \n",
       "L 61.212822 45.530769 \n",
       "L 61.024066 42.046154 \n",
       "L 60.961147 38.561538 \n",
       "L 61.024066 35.076923 \n",
       "L 61.212822 31.592308 \n",
       "L 61.527416 28.107692 \n",
       "L 61.967848 24.623077 \n",
       "L 62.534117 21.138462 \n",
       "L 63.226224 17.653846 \n",
       "L 63.98125 14.437278 \n",
       "L 64.045493 14.169231 \n",
       "L 65.009145 10.684615 \n",
       "L 66.101283 7.2 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_5\">\n",
       "    <path clip-path=\"url(#p5653fcfcd2)\" d=\"M 96.287125 143.1 \n",
       "L 94.496875 141.800652 \n",
       "L 91.564205 139.615385 \n",
       "L 91.445313 139.523684 \n",
       "L 88.39375 137.108907 \n",
       "L 87.188194 136.130769 \n",
       "L 85.342188 134.578531 \n",
       "L 83.099473 132.646154 \n",
       "L 82.290625 131.922932 \n",
       "L 79.274963 129.161538 \n",
       "L 79.239063 129.127376 \n",
       "L 76.1875 126.155204 \n",
       "L 75.707479 125.676923 \n",
       "L 73.135938 123.010126 \n",
       "L 72.364663 122.192308 \n",
       "L 70.084375 119.671522 \n",
       "L 69.23125 118.707692 \n",
       "L 67.032813 116.11359 \n",
       "L 66.294013 115.223077 \n",
       "L 63.98125 112.305725 \n",
       "L 63.540818 111.738462 \n",
       "L 60.961147 108.253846 \n",
       "L 60.929688 108.209172 \n",
       "L 58.55625 104.769231 \n",
       "L 57.878125 103.733264 \n",
       "L 56.307024 101.284615 \n",
       "L 54.826563 98.845385 \n",
       "L 54.204399 97.8 \n",
       "L 52.249029 94.315385 \n",
       "L 51.775 93.416129 \n",
       "L 50.438125 90.830769 \n",
       "L 48.7525 87.346154 \n",
       "L 48.723438 87.281624 \n",
       "L 47.211916 83.861538 \n",
       "L 45.785952 80.376923 \n",
       "L 45.671875 80.073913 \n",
       "L 44.496044 76.892308 \n",
       "L 43.320212 73.407692 \n",
       "L 42.620313 71.115182 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_6\">\n",
       "    <path clip-path=\"url(#p5653fcfcd2)\" d=\"M 67.328125 143.1 \n",
       "L 67.032813 142.834224 \n",
       "L 63.98125 140.028814 \n",
       "L 63.540818 139.615385 \n",
       "L 60.929688 137.07834 \n",
       "L 59.974148 136.130769 \n",
       "L 57.878125 133.976643 \n",
       "L 56.609158 132.646154 \n",
       "L 54.826563 130.706604 \n",
       "L 53.434102 129.161538 \n",
       "L 51.775 127.248416 \n",
       "L 50.438125 125.676923 \n",
       "L 48.723438 123.579042 \n",
       "L 47.611186 122.192308 \n",
       "L 45.671875 119.671522 \n",
       "L 44.943979 118.707692 \n",
       "L 42.620313 115.494103 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_7\">\n",
       "    <path clip-path=\"url(#p5653fcfcd2)\" d=\"M 43.320212 143.1 \n",
       "L 42.620313 142.361734 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_8\"/>\n",
       "   <g id=\"line2d_8\">\n",
       "    <path clip-path=\"url(#p5653fcfcd2)\" d=\"M 57.878125 108.253846 \n",
       "L 94.817852 83.821276 \n",
       "L 112.556491 67.740201 \n",
       "L 129.402627 50.371414 \n",
       "L 145.060876 50.804685 \n",
       "L 160.088809 44.433732 \n",
       "L 170.934431 47.661865 \n",
       "L 175.085885 46.553685 \n",
       "L 180.559373 50.433504 \n",
       "L 186.730248 38.198174 \n",
       "L 192.488951 41.682739 \n",
       "L 194.153115 41.737416 \n",
       "L 197.36105 37.987541 \n",
       "L 190.044981 28.249795 \n",
       "L 192.758429 30.648385 \n",
       "L 201.253855 32.574503 \n",
       "L 200.908403 39.278803 \n",
       "L 206.47522 42.609867 \n",
       "L 207.551966 41.361801 \n",
       "L 201.334005 42.960942 \n",
       "L 200.793857 42.654541 \n",
       "\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    <defs>\n",
       "     <path d=\"M 0 3 \n",
       "C 0.795609 3 1.55874 2.683901 2.12132 2.12132 \n",
       "C 2.683901 1.55874 3 0.795609 3 0 \n",
       "C 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \n",
       "C 1.55874 -2.683901 0.795609 -3 0 -3 \n",
       "C -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \n",
       "C -2.683901 -1.55874 -3 -0.795609 -3 0 \n",
       "C -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \n",
       "C -1.55874 2.683901 -0.795609 3 0 3 \n",
       "z\n",
       "\" id=\"m49078c969e\" style=\"stroke:#ff7f0e;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p5653fcfcd2)\">\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"57.878125\" xlink:href=\"#m49078c969e\" y=\"108.253846\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"94.817852\" xlink:href=\"#m49078c969e\" y=\"83.821276\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"112.556491\" xlink:href=\"#m49078c969e\" y=\"67.740201\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"129.402627\" xlink:href=\"#m49078c969e\" y=\"50.371414\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"145.060876\" xlink:href=\"#m49078c969e\" y=\"50.804685\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"160.088809\" xlink:href=\"#m49078c969e\" y=\"44.433732\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"170.934431\" xlink:href=\"#m49078c969e\" y=\"47.661865\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"175.085885\" xlink:href=\"#m49078c969e\" y=\"46.553685\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"180.559373\" xlink:href=\"#m49078c969e\" y=\"50.433504\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"186.730248\" xlink:href=\"#m49078c969e\" y=\"38.198174\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"192.488951\" xlink:href=\"#m49078c969e\" y=\"41.682739\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"194.153115\" xlink:href=\"#m49078c969e\" y=\"41.737416\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"197.36105\" xlink:href=\"#m49078c969e\" y=\"37.987541\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"190.044981\" xlink:href=\"#m49078c969e\" y=\"28.249795\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"192.758429\" xlink:href=\"#m49078c969e\" y=\"30.648385\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"201.253855\" xlink:href=\"#m49078c969e\" y=\"32.574503\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"200.908403\" xlink:href=\"#m49078c969e\" y=\"39.278803\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"206.47522\" xlink:href=\"#m49078c969e\" y=\"42.609867\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"207.551966\" xlink:href=\"#m49078c969e\" y=\"41.361801\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"201.334005\" xlink:href=\"#m49078c969e\" y=\"42.960942\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"200.793857\" xlink:href=\"#m49078c969e\" y=\"42.654541\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 42.620312 143.1 \n",
       "L 42.620312 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 237.920313 143.1 \n",
       "L 237.920313 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 42.620313 143.1 \n",
       "L 237.920313 143.1 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 42.620313 7.2 \n",
       "L 237.920313 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p5653fcfcd2\">\n",
       "   <rect height=\"135.9\" width=\"195.3\" x=\"42.620312\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 252x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "下面我们通过在梯度中添加均值为0的随机噪声来模拟随机梯度下降，以此来比较它与梯度下降的区别。\n",
    "\n",
    "\"\"\"\n",
    "def sgd_2d(x1, x2, s1, s2):\n",
    "    return (x1 - eta * (2 * x1 + np.random.normal(0.1)),\n",
    "            x2 - eta * (4 * x2 + np.random.normal(0.1)), 0, 0)\n",
    "\n",
    "show_trace_2d(f_2d, train_2d(sgd_2d))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.943467, x2 -0.000073\n"
     ]
    },
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"262.19625pt\" version=\"1.1\" viewBox=\"0 0 394.160937 262.19625\" width=\"394.160937pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 262.19625 \n",
       "L 394.160937 262.19625 \n",
       "L 394.160937 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 52.160938 224.64 \n",
       "L 386.960938 224.64 \n",
       "L 386.960938 7.2 \n",
       "L 52.160938 7.2 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"m77ee388964\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"78.317188\" xlink:href=\"#m77ee388964\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- −5 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.59375 35.5 \n",
       "L 73.1875 35.5 \n",
       "L 73.1875 27.203125 \n",
       "L 10.59375 27.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-8722\"/>\n",
       "       <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(70.946094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"130.629688\" xlink:href=\"#m77ee388964\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- −4 -->\n",
       "      <defs>\n",
       "       <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(123.258594 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"182.942188\" xlink:href=\"#m77ee388964\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- −3 -->\n",
       "      <defs>\n",
       "       <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(175.571094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"235.254688\" xlink:href=\"#m77ee388964\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- −2 -->\n",
       "      <defs>\n",
       "       <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(227.883594 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"287.567188\" xlink:href=\"#m77ee388964\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- −1 -->\n",
       "      <defs>\n",
       "       <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(280.196094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"339.879688\" xlink:href=\"#m77ee388964\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(336.698438 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_7\">\n",
       "     <!-- x1 -->\n",
       "     <defs>\n",
       "      <path d=\"M 54.890625 54.6875 \n",
       "L 35.109375 28.078125 \n",
       "L 55.90625 0 \n",
       "L 45.3125 0 \n",
       "L 29.390625 21.484375 \n",
       "L 13.484375 0 \n",
       "L 2.875 0 \n",
       "L 24.125 28.609375 \n",
       "L 4.6875 54.6875 \n",
       "L 15.28125 54.6875 \n",
       "L 29.78125 35.203125 \n",
       "L 44.28125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-120\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(213.420313 252.916562)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"mb11a6b724c\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#mb11a6b724c\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- −3.0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.6875 12.40625 \n",
       "L 21 12.40625 \n",
       "L 21 0 \n",
       "L 10.6875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-46\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(20.878125 228.439219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#mb11a6b724c\" y=\"199.986939\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- −2.5 -->\n",
       "      <g transform=\"translate(20.878125 203.786158)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#mb11a6b724c\" y=\"175.333878\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- −2.0 -->\n",
       "      <g transform=\"translate(20.878125 179.133096)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#mb11a6b724c\" y=\"150.680816\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- −1.5 -->\n",
       "      <g transform=\"translate(20.878125 154.480035)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#mb11a6b724c\" y=\"126.027755\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- −1.0 -->\n",
       "      <g transform=\"translate(20.878125 129.826974)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#mb11a6b724c\" y=\"101.374694\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- −0.5 -->\n",
       "      <g transform=\"translate(20.878125 105.173913)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#mb11a6b724c\" y=\"76.721633\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_14\">\n",
       "      <!-- 0.0 -->\n",
       "      <g transform=\"translate(29.257812 80.520851)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_8\">\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#mb11a6b724c\" y=\"52.068571\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- 0.5 -->\n",
       "      <g transform=\"translate(29.257812 55.86779)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_9\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#mb11a6b724c\" y=\"27.41551\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_16\">\n",
       "      <!-- 1.0 -->\n",
       "      <g transform=\"translate(29.257812 31.214729)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_17\">\n",
       "     <!-- x2 -->\n",
       "     <g transform=\"translate(14.798438 122.060625)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_1\"/>\n",
       "   <g id=\"LineCollection_2\">\n",
       "    <path clip-path=\"url(#p52d3279c6e)\" d=\"M 386.960938 136.273567 \n",
       "L 381.729688 136.441208 \n",
       "L 376.498437 136.589127 \n",
       "L 371.267187 136.717322 \n",
       "L 366.035937 136.825796 \n",
       "L 360.804688 136.914547 \n",
       "L 355.573438 136.983576 \n",
       "L 350.342187 137.032882 \n",
       "L 345.110937 137.062465 \n",
       "L 339.879687 137.072327 \n",
       "L 334.648438 137.062465 \n",
       "L 329.417188 137.032882 \n",
       "L 324.185937 136.983576 \n",
       "L 318.954687 136.914547 \n",
       "L 313.723437 136.825796 \n",
       "L 308.492188 136.717322 \n",
       "L 303.260938 136.589127 \n",
       "L 298.029687 136.441208 \n",
       "L 292.798437 136.273567 \n",
       "L 287.567187 136.086204 \n",
       "L 282.585045 135.88898 \n",
       "L 282.335938 135.878261 \n",
       "L 277.104688 135.63173 \n",
       "L 271.873438 135.363762 \n",
       "L 266.642187 135.074357 \n",
       "L 261.410937 134.763514 \n",
       "L 256.179688 134.431233 \n",
       "L 250.948437 134.077516 \n",
       "L 245.717187 133.70236 \n",
       "L 240.485937 133.305768 \n",
       "L 235.254687 132.887737 \n",
       "L 230.023438 132.44827 \n",
       "L 224.792188 131.987365 \n",
       "L 219.560937 131.505022 \n",
       "L 214.329687 131.001242 \n",
       "L 213.902647 130.958367 \n",
       "L 209.098437 130.430087 \n",
       "L 203.867188 129.83137 \n",
       "L 198.635937 129.209174 \n",
       "L 193.404687 128.563499 \n",
       "L 188.173438 127.894344 \n",
       "L 182.942187 127.20171 \n",
       "L 177.710938 126.485598 \n",
       "L 174.472545 126.027755 \n",
       "L 172.479688 125.716348 \n",
       "L 167.248437 124.872954 \n",
       "L 162.017188 124.003609 \n",
       "L 156.785937 123.108314 \n",
       "L 151.554688 122.187068 \n",
       "L 146.323437 121.239871 \n",
       "L 145.556187 121.097143 \n",
       "L 141.092187 120.169028 \n",
       "L 135.860938 119.052389 \n",
       "L 130.629687 117.906747 \n",
       "L 125.398438 116.732101 \n",
       "L 122.94038 116.166531 \n",
       "L 120.167187 115.443374 \n",
       "L 114.935937 114.046367 \n",
       "L 109.704688 112.61649 \n",
       "L 104.767328 111.235918 \n",
       "L 104.473437 111.141099 \n",
       "L 99.242188 109.415385 \n",
       "L 94.010937 107.651743 \n",
       "L 90.101266 106.305306 \n",
       "L 88.779687 105.767421 \n",
       "L 83.548437 103.593469 \n",
       "L 78.317187 101.374694 \n",
       "L 78.317187 101.374694 \n",
       "L 73.085938 98.608073 \n",
       "L 69.07362 96.444082 \n",
       "L 67.854688 95.598834 \n",
       "L 62.623438 91.900875 \n",
       "L 62.085645 91.513469 \n",
       "L 57.392187 86.780082 \n",
       "L 57.200215 86.582857 \n",
       "L 54.320628 81.652245 \n",
       "L 53.360765 76.721633 \n",
       "L 54.320628 71.79102 \n",
       "L 57.200215 66.860408 \n",
       "L 57.392187 66.663184 \n",
       "L 62.085645 61.929796 \n",
       "L 62.623438 61.542391 \n",
       "L 67.854688 57.844431 \n",
       "L 69.07362 56.999184 \n",
       "L 73.085938 54.835193 \n",
       "L 78.317187 52.068571 \n",
       "L 78.317188 52.068571 \n",
       "L 83.548437 49.849796 \n",
       "L 88.779687 47.675844 \n",
       "L 90.101266 47.137959 \n",
       "L 94.010937 45.791523 \n",
       "L 99.242188 44.027881 \n",
       "L 104.473437 42.302166 \n",
       "L 104.767328 42.207347 \n",
       "L 109.704688 40.826776 \n",
       "L 114.935937 39.396898 \n",
       "L 120.167187 37.999891 \n",
       "L 122.94038 37.276735 \n",
       "L 125.398438 36.711164 \n",
       "L 130.629687 35.536519 \n",
       "L 135.860938 34.390876 \n",
       "L 141.092187 33.274238 \n",
       "L 145.556188 32.346122 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_3\">\n",
       "    <path clip-path=\"url(#p52d3279c6e)\" d=\"M 386.960938 161.52112 \n",
       "L 381.729688 161.640863 \n",
       "L 376.498437 161.746519 \n",
       "L 371.267187 161.838087 \n",
       "L 366.035937 161.915569 \n",
       "L 360.804688 161.978962 \n",
       "L 355.573438 162.028268 \n",
       "L 350.342187 162.063487 \n",
       "L 345.110937 162.084618 \n",
       "L 339.879687 162.091662 \n",
       "L 334.648438 162.084618 \n",
       "L 329.417188 162.063487 \n",
       "L 324.185937 162.028268 \n",
       "L 318.954687 161.978962 \n",
       "L 313.723437 161.915569 \n",
       "L 308.492188 161.838087 \n",
       "L 303.260938 161.746519 \n",
       "L 298.029687 161.640863 \n",
       "L 292.798437 161.52112 \n",
       "L 287.567187 161.387289 \n",
       "L 282.335938 161.23937 \n",
       "L 277.104688 161.077364 \n",
       "L 271.873438 160.901271 \n",
       "L 266.642187 160.71109 \n",
       "L 262.312877 160.542041 \n",
       "L 261.410937 160.504688 \n",
       "L 256.179688 160.273098 \n",
       "L 250.948438 160.026568 \n",
       "L 245.717188 159.765096 \n",
       "L 240.485938 159.488683 \n",
       "L 235.254687 159.197328 \n",
       "L 230.023438 158.891033 \n",
       "L 224.792188 158.569796 \n",
       "L 219.560937 158.233618 \n",
       "L 214.329687 157.882498 \n",
       "L 209.098437 157.516438 \n",
       "L 203.867188 157.135436 \n",
       "L 198.635937 156.739493 \n",
       "L 193.404687 156.328609 \n",
       "L 188.173438 155.902783 \n",
       "L 184.715493 155.611429 \n",
       "L 182.942187 155.452377 \n",
       "L 177.710938 154.967268 \n",
       "L 172.479687 154.466254 \n",
       "L 167.248437 153.949335 \n",
       "L 162.017188 153.416511 \n",
       "L 156.785937 152.867781 \n",
       "L 151.554688 152.303147 \n",
       "L 146.323437 151.722607 \n",
       "L 141.092187 151.126162 \n",
       "L 137.287642 150.680816 \n",
       "L 135.860938 150.502294 \n",
       "L 130.629687 149.830711 \n",
       "L 125.398438 149.142125 \n",
       "L 120.167187 148.436538 \n",
       "L 114.935937 147.713948 \n",
       "L 109.704688 146.974356 \n",
       "L 104.473437 146.217762 \n",
       "L 101.311693 145.750204 \n",
       "L 99.242188 145.421497 \n",
       "L 94.010937 144.572336 \n",
       "L 88.779687 143.704913 \n",
       "L 83.548437 142.819229 \n",
       "L 78.317187 141.915283 \n",
       "L 73.085938 140.993076 \n",
       "L 72.12095 140.819592 \n",
       "L 67.854688 139.991249 \n",
       "L 62.623438 138.95582 \n",
       "L 57.392187 137.900669 \n",
       "L 52.160937 136.825796 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_4\">\n",
       "    <path clip-path=\"url(#p52d3279c6e)\" d=\"M 386.960938 180.832084 \n",
       "L 381.729688 180.929549 \n",
       "L 376.498437 181.015548 \n",
       "L 371.267187 181.090081 \n",
       "L 366.035937 181.153147 \n",
       "L 360.804688 181.204746 \n",
       "L 355.573438 181.244879 \n",
       "L 350.342187 181.273545 \n",
       "L 345.110937 181.290745 \n",
       "L 339.879687 181.296478 \n",
       "L 334.648438 181.290745 \n",
       "L 329.417188 181.273545 \n",
       "L 324.185937 181.244879 \n",
       "L 318.954687 181.204746 \n",
       "L 313.723437 181.153147 \n",
       "L 308.492188 181.090081 \n",
       "L 303.260938 181.015548 \n",
       "L 298.029687 180.929549 \n",
       "L 292.798437 180.832084 \n",
       "L 287.567187 180.723151 \n",
       "L 282.335938 180.602753 \n",
       "L 277.104688 180.470888 \n",
       "L 271.873438 180.327556 \n",
       "L 269.742187 180.26449 \n",
       "L 266.642187 180.168283 \n",
       "L 261.410937 179.993907 \n",
       "L 256.179688 179.807506 \n",
       "L 250.948438 179.609079 \n",
       "L 245.717187 179.398626 \n",
       "L 240.485937 179.176147 \n",
       "L 235.254687 178.941643 \n",
       "L 230.023438 178.695112 \n",
       "L 224.792188 178.436556 \n",
       "L 219.560937 178.165973 \n",
       "L 214.329687 177.883365 \n",
       "L 209.098437 177.588731 \n",
       "L 203.867188 177.282071 \n",
       "L 198.635937 176.963385 \n",
       "L 193.404687 176.632673 \n",
       "L 188.173438 176.289935 \n",
       "L 182.942187 175.935172 \n",
       "L 177.710938 175.568382 \n",
       "L 174.472545 175.333878 \n",
       "L 172.479687 175.182166 \n",
       "L 167.248437 174.771282 \n",
       "L 162.017188 174.347755 \n",
       "L 156.785937 173.911586 \n",
       "L 151.554688 173.462773 \n",
       "L 146.323437 173.001319 \n",
       "L 141.092187 172.527221 \n",
       "L 135.860938 172.040481 \n",
       "L 130.629687 171.541099 \n",
       "L 125.398438 171.029074 \n",
       "L 120.167187 170.504406 \n",
       "L 119.182482 170.403265 \n",
       "L 114.935937 169.943519 \n",
       "L 109.704688 169.363839 \n",
       "L 104.473437 168.770833 \n",
       "L 99.242188 168.164501 \n",
       "L 94.010937 167.544843 \n",
       "L 88.779687 166.911859 \n",
       "L 83.548437 166.265549 \n",
       "L 78.317187 165.605913 \n",
       "L 77.281296 165.472653 \n",
       "L 73.085938 164.902111 \n",
       "L 67.854688 164.176606 \n",
       "L 62.623438 163.437015 \n",
       "L 57.392187 162.683335 \n",
       "L 52.160937 161.915569 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_5\">\n",
       "    <path clip-path=\"url(#p52d3279c6e)\" d=\"M 386.960938 197.06379 \n",
       "L 381.729688 197.149321 \n",
       "L 376.498437 197.22479 \n",
       "L 371.267187 197.290196 \n",
       "L 366.035937 197.345539 \n",
       "L 360.804688 197.39082 \n",
       "L 355.573438 197.426039 \n",
       "L 350.342187 197.451195 \n",
       "L 345.110937 197.466289 \n",
       "L 339.879687 197.47132 \n",
       "L 334.648438 197.466289 \n",
       "L 329.417188 197.451195 \n",
       "L 324.185937 197.426039 \n",
       "L 318.954687 197.39082 \n",
       "L 313.723437 197.345539 \n",
       "L 308.492188 197.290196 \n",
       "L 303.260938 197.22479 \n",
       "L 298.029687 197.149321 \n",
       "L 292.798437 197.06379 \n",
       "L 287.567187 196.968197 \n",
       "L 282.335938 196.862541 \n",
       "L 277.104688 196.746822 \n",
       "L 271.873438 196.621041 \n",
       "L 266.642187 196.485198 \n",
       "L 261.410937 196.339292 \n",
       "L 256.179688 196.183324 \n",
       "L 250.948438 196.017293 \n",
       "L 245.717187 195.8412 \n",
       "L 240.485937 195.655044 \n",
       "L 235.254687 195.458825 \n",
       "L 230.023438 195.252545 \n",
       "L 225.278815 195.056327 \n",
       "L 224.792188 195.035345 \n",
       "L 219.560937 194.799305 \n",
       "L 214.329687 194.552775 \n",
       "L 209.098437 194.295753 \n",
       "L 203.867188 194.028241 \n",
       "L 198.635937 193.750239 \n",
       "L 193.404687 193.461746 \n",
       "L 188.173438 193.162762 \n",
       "L 182.942187 192.853287 \n",
       "L 177.710938 192.533322 \n",
       "L 172.479687 192.202866 \n",
       "L 167.248437 191.861919 \n",
       "L 162.017188 191.510482 \n",
       "L 156.785937 191.148554 \n",
       "L 151.554688 190.776135 \n",
       "L 146.323437 190.393226 \n",
       "L 142.766187 190.125714 \n",
       "L 141.092187 189.994231 \n",
       "L 135.860937 189.57239 \n",
       "L 130.629687 189.139592 \n",
       "L 125.398438 188.695837 \n",
       "L 120.167187 188.241125 \n",
       "L 114.935937 187.775456 \n",
       "L 109.704688 187.29883 \n",
       "L 104.473437 186.811247 \n",
       "L 99.242188 186.312707 \n",
       "L 94.010937 185.803211 \n",
       "L 88.779687 185.282757 \n",
       "L 87.916801 185.195102 \n",
       "L 83.548437 184.730707 \n",
       "L 78.317187 184.163113 \n",
       "L 73.085938 183.584053 \n",
       "L 67.854688 182.993526 \n",
       "L 62.623438 182.391533 \n",
       "L 57.392187 181.778073 \n",
       "L 52.160937 181.153147 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_6\">\n",
       "    <path clip-path=\"url(#p52d3279c6e)\" d=\"M 386.960938 211.367688 \n",
       "L 381.729688 211.443889 \n",
       "L 376.498437 211.511124 \n",
       "L 371.267187 211.569395 \n",
       "L 366.035937 211.618701 \n",
       "L 360.804688 211.659043 \n",
       "L 355.573438 211.690419 \n",
       "L 350.342187 211.712831 \n",
       "L 345.110937 211.726278 \n",
       "L 339.879687 211.730761 \n",
       "L 334.648438 211.726278 \n",
       "L 329.417188 211.712831 \n",
       "L 324.185937 211.690419 \n",
       "L 318.954687 211.659043 \n",
       "L 313.723437 211.618701 \n",
       "L 308.492188 211.569395 \n",
       "L 303.260938 211.511124 \n",
       "L 298.029687 211.443889 \n",
       "L 292.798437 211.367688 \n",
       "L 287.567187 211.282523 \n",
       "L 282.335938 211.188393 \n",
       "L 277.104688 211.085299 \n",
       "L 271.873438 210.973239 \n",
       "L 266.642187 210.852215 \n",
       "L 261.410937 210.722226 \n",
       "L 256.179688 210.583273 \n",
       "L 250.948438 210.435354 \n",
       "L 245.717187 210.278471 \n",
       "L 240.485937 210.112623 \n",
       "L 235.254687 209.937811 \n",
       "L 232.702858 209.848163 \n",
       "L 230.023438 209.750481 \n",
       "L 224.792188 209.550466 \n",
       "L 219.560937 209.341147 \n",
       "L 214.329687 209.122526 \n",
       "L 209.098437 208.894601 \n",
       "L 203.867188 208.657374 \n",
       "L 198.635937 208.410843 \n",
       "L 193.404687 208.15501 \n",
       "L 188.173438 207.889873 \n",
       "L 182.942187 207.615433 \n",
       "L 177.710938 207.33169 \n",
       "L 172.479687 207.038645 \n",
       "L 167.248437 206.736296 \n",
       "L 162.017188 206.424644 \n",
       "L 156.785937 206.103689 \n",
       "L 151.554688 205.773431 \n",
       "L 146.323437 205.43387 \n",
       "L 141.092187 205.085006 \n",
       "L 138.646408 204.917551 \n",
       "L 135.860938 204.71936 \n",
       "L 130.629687 204.337479 \n",
       "L 125.398438 203.94593 \n",
       "L 120.167187 203.544714 \n",
       "L 114.935937 203.13383 \n",
       "L 109.704688 202.713277 \n",
       "L 104.473437 202.283057 \n",
       "L 99.242188 201.843169 \n",
       "L 94.010937 201.393613 \n",
       "L 88.779687 200.93439 \n",
       "L 83.548437 200.465498 \n",
       "L 78.317187 199.986939 \n",
       "L 78.317187 199.986939 \n",
       "L 73.085938 199.478784 \n",
       "L 67.854688 198.960566 \n",
       "L 62.623438 198.432287 \n",
       "L 57.392187 197.893944 \n",
       "L 52.160937 197.345539 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_7\">\n",
       "    <path clip-path=\"url(#p52d3279c6e)\" d=\"M 339.879687 224.64 \n",
       "L 334.648438 224.635822 \n",
       "L 329.417188 224.623286 \n",
       "L 324.185937 224.602394 \n",
       "L 318.954687 224.573144 \n",
       "L 313.723437 224.535538 \n",
       "L 308.492188 224.489575 \n",
       "L 303.260938 224.435254 \n",
       "L 298.029687 224.372577 \n",
       "L 292.798437 224.301543 \n",
       "L 287.567187 224.222152 \n",
       "L 282.335938 224.134403 \n",
       "L 277.104688 224.038298 \n",
       "L 271.873438 223.933836 \n",
       "L 266.642187 223.821017 \n",
       "L 261.410937 223.699841 \n",
       "L 256.179688 223.570308 \n",
       "L 250.948438 223.432418 \n",
       "L 245.717187 223.286171 \n",
       "L 240.485937 223.131567 \n",
       "L 235.254687 222.968606 \n",
       "L 230.023438 222.797288 \n",
       "L 224.792188 222.617613 \n",
       "L 219.560937 222.429581 \n",
       "L 214.329687 222.233193 \n",
       "L 209.098437 222.028447 \n",
       "L 203.867188 221.815344 \n",
       "L 198.635937 221.593884 \n",
       "L 193.404687 221.364068 \n",
       "L 188.173438 221.125894 \n",
       "L 182.942187 220.879364 \n",
       "L 177.710938 220.624476 \n",
       "L 172.479687 220.361231 \n",
       "L 167.248437 220.08963 \n",
       "L 162.017188 219.809671 \n",
       "L 160.197622 219.709388 \n",
       "L 156.785937 219.514758 \n",
       "L 151.554688 219.207676 \n",
       "L 146.323437 218.891944 \n",
       "L 141.092187 218.567562 \n",
       "L 135.860938 218.234529 \n",
       "L 130.629687 217.892846 \n",
       "L 125.398438 217.542513 \n",
       "L 120.167187 217.18353 \n",
       "L 114.935937 216.815897 \n",
       "L 109.704688 216.439613 \n",
       "L 104.473437 216.05468 \n",
       "L 99.242188 215.661096 \n",
       "L 94.010937 215.258861 \n",
       "L 88.779687 214.847977 \n",
       "L 87.916801 214.778776 \n",
       "L 83.548437 214.415703 \n",
       "L 78.317187 213.971948 \n",
       "L 73.085938 213.519228 \n",
       "L 67.854688 213.057544 \n",
       "L 62.623438 212.586894 \n",
       "L 57.392187 212.10728 \n",
       "L 52.160937 211.618701 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p52d3279c6e)\" d=\"M 386.960938 224.301543 \n",
       "L 381.729688 224.372577 \n",
       "L 376.498437 224.435254 \n",
       "L 371.267187 224.489575 \n",
       "L 366.035937 224.535538 \n",
       "L 360.804688 224.573144 \n",
       "L 355.573438 224.602394 \n",
       "L 350.342187 224.623286 \n",
       "L 345.110937 224.635822 \n",
       "L 339.879687 224.64 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_8\">\n",
       "    <path clip-path=\"url(#p52d3279c6e)\" d=\"M 53.360765 224.64 \n",
       "L 52.160937 224.535538 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_9\"/>\n",
       "   <g id=\"line2d_16\">\n",
       "    <path clip-path=\"url(#p52d3279c6e)\" d=\"M 78.317188 175.333878 \n",
       "L 99.242188 17.554286 \n",
       "L 118.493188 112.222041 \n",
       "L 136.204108 55.421388 \n",
       "L 152.498154 89.50178 \n",
       "L 167.488677 69.053544 \n",
       "L 181.279957 81.322486 \n",
       "L 193.967936 73.961121 \n",
       "L 205.640876 78.37794 \n",
       "L 216.379981 75.727848 \n",
       "L 226.259957 77.317903 \n",
       "L 235.349536 76.36387 \n",
       "L 243.711948 76.93629 \n",
       "L 251.405367 76.592838 \n",
       "L 258.483313 76.798909 \n",
       "L 264.995023 76.675267 \n",
       "L 270.985796 76.749452 \n",
       "L 276.497307 76.704941 \n",
       "L 281.567898 76.731648 \n",
       "L 286.232841 76.715624 \n",
       "L 290.524589 76.725238 \n",
       "\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    <defs>\n",
       "     <path d=\"M 0 3 \n",
       "C 0.795609 3 1.55874 2.683901 2.12132 2.12132 \n",
       "C 2.683901 1.55874 3 0.795609 3 0 \n",
       "C 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \n",
       "C 1.55874 -2.683901 0.795609 -3 0 -3 \n",
       "C -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \n",
       "C -2.683901 -1.55874 -3 -0.795609 -3 0 \n",
       "C -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \n",
       "C -1.55874 2.683901 -0.795609 3 0 3 \n",
       "z\n",
       "\" id=\"m1a62071d0c\" style=\"stroke:#ff7f0e;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p52d3279c6e)\">\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"78.317188\" xlink:href=\"#m1a62071d0c\" y=\"175.333878\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"99.242188\" xlink:href=\"#m1a62071d0c\" y=\"17.554286\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"118.493188\" xlink:href=\"#m1a62071d0c\" y=\"112.222041\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"136.204108\" xlink:href=\"#m1a62071d0c\" y=\"55.421388\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"152.498154\" xlink:href=\"#m1a62071d0c\" y=\"89.50178\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"167.488677\" xlink:href=\"#m1a62071d0c\" y=\"69.053544\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"181.279957\" xlink:href=\"#m1a62071d0c\" y=\"81.322486\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"193.967936\" xlink:href=\"#m1a62071d0c\" y=\"73.961121\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"205.640876\" xlink:href=\"#m1a62071d0c\" y=\"78.37794\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"216.379981\" xlink:href=\"#m1a62071d0c\" y=\"75.727848\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"226.259957\" xlink:href=\"#m1a62071d0c\" y=\"77.317903\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"235.349536\" xlink:href=\"#m1a62071d0c\" y=\"76.36387\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"243.711948\" xlink:href=\"#m1a62071d0c\" y=\"76.93629\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"251.405367\" xlink:href=\"#m1a62071d0c\" y=\"76.592838\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"258.483313\" xlink:href=\"#m1a62071d0c\" y=\"76.798909\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"264.995023\" xlink:href=\"#m1a62071d0c\" y=\"76.675267\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"270.985796\" xlink:href=\"#m1a62071d0c\" y=\"76.749452\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"276.497307\" xlink:href=\"#m1a62071d0c\" y=\"76.704941\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"281.567898\" xlink:href=\"#m1a62071d0c\" y=\"76.731648\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"286.232841\" xlink:href=\"#m1a62071d0c\" y=\"76.715624\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"290.524589\" xlink:href=\"#m1a62071d0c\" y=\"76.725238\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 52.160938 224.64 \n",
       "L 52.160938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 386.960938 224.64 \n",
       "L 386.960938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 52.160937 224.64 \n",
       "L 386.960938 224.64 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 52.160937 7.2 \n",
       "L 386.960938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p52d3279c6e\">\n",
       "   <rect height=\"217.44\" width=\"334.8\" x=\"52.160938\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"梯度下降的问题\"\"\"\n",
    "\n",
    "%matplotlib inline\n",
    "import sys\n",
    "sys.path.append(\"..\") \n",
    "import d2lzh_pytorch as d2l\n",
    "import torch\n",
    "\n",
    "eta = 0.4 # 学习率\n",
    "\n",
    "def f_2d(x1, x2):\n",
    "    return 0.1 * x1 ** 2 + 2 * x2 ** 2\n",
    "\n",
    "def gd_2d(x1, x2, s1, s2):\n",
    "    return (x1 - eta * 0.2 * x1, x2 - eta * 4 * x2, 0, 0)\n",
    "\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(gd_2d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.387814, x2 -1673.365109\n"
     ]
    },
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"262.19625pt\" version=\"1.1\" viewBox=\"0 0 403.707812 262.19625\" width=\"403.707812pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 262.19625 \n",
       "L 403.707812 262.19625 \n",
       "L 403.707812 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 61.707813 224.64 \n",
       "L 396.507812 224.64 \n",
       "L 396.507812 7.2 \n",
       "L 61.707813 7.2 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"m0445845627\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"87.864063\" xlink:href=\"#m0445845627\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- −5 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.59375 35.5 \n",
       "L 73.1875 35.5 \n",
       "L 73.1875 27.203125 \n",
       "L 10.59375 27.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-8722\"/>\n",
       "       <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(80.492969 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"140.176563\" xlink:href=\"#m0445845627\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- −4 -->\n",
       "      <defs>\n",
       "       <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(132.805469 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"192.489063\" xlink:href=\"#m0445845627\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- −3 -->\n",
       "      <defs>\n",
       "       <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(185.117969 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"244.801563\" xlink:href=\"#m0445845627\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- −2 -->\n",
       "      <defs>\n",
       "       <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(237.430469 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"297.114063\" xlink:href=\"#m0445845627\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- −1 -->\n",
       "      <defs>\n",
       "       <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(289.742969 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"349.426563\" xlink:href=\"#m0445845627\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(346.245313 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_7\">\n",
       "     <!-- x1 -->\n",
       "     <defs>\n",
       "      <path d=\"M 54.890625 54.6875 \n",
       "L 35.109375 28.078125 \n",
       "L 55.90625 0 \n",
       "L 45.3125 0 \n",
       "L 29.390625 21.484375 \n",
       "L 13.484375 0 \n",
       "L 2.875 0 \n",
       "L 24.125 28.609375 \n",
       "L 4.6875 54.6875 \n",
       "L 15.28125 54.6875 \n",
       "L 29.78125 35.203125 \n",
       "L 44.28125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-120\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(222.967188 252.916562)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"md0fa9a78dc\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"61.707813\" xlink:href=\"#md0fa9a78dc\" y=\"202.810033\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- −1500 -->\n",
       "      <g transform=\"translate(20.878125 206.609252)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "       <use x=\"211.035156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"274.658203\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"61.707813\" xlink:href=\"#md0fa9a78dc\" y=\"168.355779\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- −1000 -->\n",
       "      <g transform=\"translate(20.878125 172.154998)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"211.035156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"274.658203\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"61.707813\" xlink:href=\"#md0fa9a78dc\" y=\"133.901526\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- −500 -->\n",
       "      <g transform=\"translate(27.240625 137.700745)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"211.035156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"61.707813\" xlink:href=\"#md0fa9a78dc\" y=\"99.447273\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(48.345313 103.246491)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"61.707813\" xlink:href=\"#md0fa9a78dc\" y=\"64.993019\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- 500 -->\n",
       "      <g transform=\"translate(35.620312 68.792238)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-53\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"61.707813\" xlink:href=\"#md0fa9a78dc\" y=\"30.538766\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- 1000 -->\n",
       "      <g transform=\"translate(29.257812 34.337985)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"127.246094\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"190.869141\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_14\">\n",
       "     <!-- x2 -->\n",
       "     <g transform=\"translate(14.798438 122.060625)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_1\"/>\n",
       "   <g id=\"LineCollection_2\">\n",
       "    <path clip-path=\"url(#p6f01c307aa)\" d=\"M 396.507812 99.5305 \n",
       "L 391.276563 99.530735 \n",
       "L 386.045312 99.530941 \n",
       "L 380.814062 99.531121 \n",
       "L 375.582812 99.531272 \n",
       "L 370.351562 99.531396 \n",
       "L 365.120313 99.531493 \n",
       "L 359.889062 99.531562 \n",
       "L 354.657812 99.531603 \n",
       "L 349.426562 99.531617 \n",
       "L 344.195312 99.531603 \n",
       "L 338.964063 99.531562 \n",
       "L 333.732812 99.531493 \n",
       "L 328.501562 99.531396 \n",
       "L 323.270312 99.531272 \n",
       "L 318.039062 99.531121 \n",
       "L 312.807813 99.530941 \n",
       "L 307.576562 99.530735 \n",
       "L 302.345312 99.5305 \n",
       "L 297.114062 99.530239 \n",
       "L 292.13192 99.529963 \n",
       "L 291.882812 99.529948 \n",
       "L 286.651563 99.529603 \n",
       "L 281.420313 99.529229 \n",
       "L 276.189062 99.528824 \n",
       "L 270.957812 99.52839 \n",
       "L 265.726562 99.527926 \n",
       "L 260.495312 99.527431 \n",
       "L 255.264062 99.526907 \n",
       "L 250.032812 99.526353 \n",
       "L 244.801562 99.525769 \n",
       "L 239.570312 99.525154 \n",
       "L 234.339063 99.52451 \n",
       "L 229.107812 99.523836 \n",
       "L 223.876562 99.523132 \n",
       "L 223.449522 99.523072 \n",
       "L 218.645312 99.522334 \n",
       "L 213.414062 99.521497 \n",
       "L 208.182812 99.520627 \n",
       "L 202.951562 99.519725 \n",
       "L 197.720313 99.51879 \n",
       "L 192.489062 99.517822 \n",
       "L 187.257812 99.516821 \n",
       "L 184.01942 99.516181 \n",
       "L 182.026563 99.515746 \n",
       "L 176.795312 99.514567 \n",
       "L 171.564063 99.513352 \n",
       "L 166.332812 99.512101 \n",
       "L 161.101562 99.510814 \n",
       "L 155.870312 99.50949 \n",
       "L 155.103062 99.50929 \n",
       "L 150.639062 99.507993 \n",
       "L 145.407813 99.506433 \n",
       "L 140.176562 99.504832 \n",
       "L 134.945312 99.50319 \n",
       "L 132.487255 99.5024 \n",
       "L 129.714062 99.501389 \n",
       "L 124.482812 99.499436 \n",
       "L 119.251563 99.497438 \n",
       "L 114.314203 99.495509 \n",
       "L 114.020312 99.495376 \n",
       "L 108.789062 99.492964 \n",
       "L 103.557812 99.4905 \n",
       "L 99.648141 99.488618 \n",
       "L 98.326562 99.487866 \n",
       "L 93.095312 99.484828 \n",
       "L 87.864062 99.481727 \n",
       "L 87.864062 99.481727 \n",
       "L 82.632812 99.47786 \n",
       "L 78.620495 99.474836 \n",
       "L 77.401563 99.473655 \n",
       "L 72.170313 99.468487 \n",
       "L 71.63252 99.467945 \n",
       "L 66.939062 99.46133 \n",
       "L 66.74709 99.461054 \n",
       "L 63.867503 99.454164 \n",
       "L 62.90764 99.447273 \n",
       "L 63.867503 99.440382 \n",
       "L 66.74709 99.433491 \n",
       "L 66.939062 99.433215 \n",
       "L 71.63252 99.4266 \n",
       "L 72.170313 99.426059 \n",
       "L 77.401563 99.420891 \n",
       "L 78.620495 99.419709 \n",
       "L 82.632812 99.416685 \n",
       "L 87.864062 99.412818 \n",
       "L 87.864063 99.412818 \n",
       "L 93.095312 99.409718 \n",
       "L 98.326562 99.406679 \n",
       "L 99.648141 99.405928 \n",
       "L 103.557812 99.404046 \n",
       "L 108.789062 99.401581 \n",
       "L 114.020312 99.399169 \n",
       "L 114.314203 99.399037 \n",
       "L 119.251563 99.397107 \n",
       "L 124.482812 99.395109 \n",
       "L 129.714062 99.393157 \n",
       "L 132.487255 99.392146 \n",
       "L 134.945312 99.391356 \n",
       "L 140.176562 99.389714 \n",
       "L 145.407813 99.388113 \n",
       "L 150.639062 99.386552 \n",
       "L 155.103063 99.385255 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_3\">\n",
       "    <path clip-path=\"url(#p6f01c307aa)\" d=\"M 396.507812 99.565786 \n",
       "L 391.276563 99.565953 \n",
       "L 386.045312 99.566101 \n",
       "L 380.814062 99.566228 \n",
       "L 375.582812 99.566337 \n",
       "L 370.351562 99.566425 \n",
       "L 365.120313 99.566494 \n",
       "L 359.889062 99.566544 \n",
       "L 354.657812 99.566573 \n",
       "L 349.426562 99.566583 \n",
       "L 344.195312 99.566573 \n",
       "L 338.964063 99.566544 \n",
       "L 333.732812 99.566494 \n",
       "L 328.501562 99.566425 \n",
       "L 323.270312 99.566337 \n",
       "L 318.039062 99.566228 \n",
       "L 312.807813 99.566101 \n",
       "L 307.576562 99.565953 \n",
       "L 302.345312 99.565786 \n",
       "L 297.114062 99.565598 \n",
       "L 291.882812 99.565392 \n",
       "L 286.651563 99.565165 \n",
       "L 281.420313 99.564919 \n",
       "L 276.189062 99.564653 \n",
       "L 271.859752 99.564417 \n",
       "L 270.957812 99.564365 \n",
       "L 265.726562 99.564041 \n",
       "L 260.495313 99.563697 \n",
       "L 255.264063 99.563331 \n",
       "L 250.032813 99.562945 \n",
       "L 244.801562 99.562538 \n",
       "L 239.570312 99.56211 \n",
       "L 234.339063 99.561661 \n",
       "L 229.107812 99.561191 \n",
       "L 223.876562 99.5607 \n",
       "L 218.645312 99.560189 \n",
       "L 213.414062 99.559656 \n",
       "L 208.182812 99.559103 \n",
       "L 202.951562 99.558529 \n",
       "L 197.720313 99.557934 \n",
       "L 194.262368 99.557526 \n",
       "L 192.489062 99.557304 \n",
       "L 187.257812 99.556626 \n",
       "L 182.026562 99.555926 \n",
       "L 176.795312 99.555203 \n",
       "L 171.564063 99.554459 \n",
       "L 166.332812 99.553692 \n",
       "L 161.101562 99.552903 \n",
       "L 155.870312 99.552091 \n",
       "L 150.639062 99.551258 \n",
       "L 146.834517 99.550635 \n",
       "L 145.407813 99.550386 \n",
       "L 140.176562 99.549447 \n",
       "L 134.945312 99.548485 \n",
       "L 129.714062 99.547499 \n",
       "L 124.482812 99.546489 \n",
       "L 119.251563 99.545455 \n",
       "L 114.020312 99.544398 \n",
       "L 110.858568 99.543745 \n",
       "L 108.789062 99.543285 \n",
       "L 103.557812 99.542098 \n",
       "L 98.326562 99.540886 \n",
       "L 93.095312 99.539648 \n",
       "L 87.864062 99.538385 \n",
       "L 82.632812 99.537096 \n",
       "L 81.667825 99.536854 \n",
       "L 77.401563 99.535696 \n",
       "L 72.170313 99.534249 \n",
       "L 66.939062 99.532774 \n",
       "L 61.707812 99.531272 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_4\">\n",
       "    <path clip-path=\"url(#p6f01c307aa)\" d=\"M 396.507812 99.592774 \n",
       "L 391.276563 99.59291 \n",
       "L 386.045312 99.59303 \n",
       "L 380.814062 99.593134 \n",
       "L 375.582812 99.593223 \n",
       "L 370.351562 99.593295 \n",
       "L 365.120313 99.593351 \n",
       "L 359.889062 99.593391 \n",
       "L 354.657812 99.593415 \n",
       "L 349.426562 99.593423 \n",
       "L 344.195312 99.593415 \n",
       "L 338.964063 99.593391 \n",
       "L 333.732812 99.593351 \n",
       "L 328.501562 99.593295 \n",
       "L 323.270312 99.593223 \n",
       "L 318.039062 99.593134 \n",
       "L 312.807813 99.59303 \n",
       "L 307.576562 99.59291 \n",
       "L 302.345312 99.592774 \n",
       "L 297.114062 99.592622 \n",
       "L 291.882812 99.592453 \n",
       "L 286.651563 99.592269 \n",
       "L 281.420313 99.592069 \n",
       "L 279.289062 99.591981 \n",
       "L 276.189062 99.591846 \n",
       "L 270.957812 99.591602 \n",
       "L 265.726562 99.591342 \n",
       "L 260.495313 99.591065 \n",
       "L 255.264062 99.59077 \n",
       "L 250.032812 99.59046 \n",
       "L 244.801562 99.590132 \n",
       "L 239.570312 99.589787 \n",
       "L 234.339063 99.589426 \n",
       "L 229.107812 99.589048 \n",
       "L 223.876562 99.588653 \n",
       "L 218.645312 99.588241 \n",
       "L 213.414062 99.587812 \n",
       "L 208.182812 99.587367 \n",
       "L 202.951562 99.586905 \n",
       "L 197.720313 99.586426 \n",
       "L 192.489062 99.58593 \n",
       "L 187.257812 99.585417 \n",
       "L 184.01942 99.58509 \n",
       "L 182.026562 99.584878 \n",
       "L 176.795312 99.584303 \n",
       "L 171.564063 99.583712 \n",
       "L 166.332812 99.583102 \n",
       "L 161.101562 99.582475 \n",
       "L 155.870312 99.58183 \n",
       "L 150.639062 99.581167 \n",
       "L 145.407813 99.580487 \n",
       "L 140.176562 99.579789 \n",
       "L 134.945312 99.579073 \n",
       "L 129.714062 99.57834 \n",
       "L 128.729357 99.578199 \n",
       "L 124.482812 99.577556 \n",
       "L 119.251563 99.576746 \n",
       "L 114.020312 99.575917 \n",
       "L 108.789062 99.57507 \n",
       "L 103.557812 99.574204 \n",
       "L 98.326562 99.573319 \n",
       "L 93.095312 99.572416 \n",
       "L 87.864062 99.571494 \n",
       "L 86.828171 99.571308 \n",
       "L 82.632812 99.570511 \n",
       "L 77.401563 99.569497 \n",
       "L 72.170313 99.568463 \n",
       "L 66.939062 99.56741 \n",
       "L 61.707812 99.566337 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_5\">\n",
       "    <path clip-path=\"url(#p6f01c307aa)\" d=\"M 396.507812 99.615459 \n",
       "L 391.276563 99.615578 \n",
       "L 386.045312 99.615684 \n",
       "L 380.814062 99.615775 \n",
       "L 375.582812 99.615852 \n",
       "L 370.351562 99.615916 \n",
       "L 365.120313 99.615965 \n",
       "L 359.889062 99.616 \n",
       "L 354.657812 99.616021 \n",
       "L 349.426562 99.616028 \n",
       "L 344.195312 99.616021 \n",
       "L 338.964063 99.616 \n",
       "L 333.732812 99.615965 \n",
       "L 328.501562 99.615916 \n",
       "L 323.270312 99.615852 \n",
       "L 318.039062 99.615775 \n",
       "L 312.807813 99.615684 \n",
       "L 307.576562 99.615578 \n",
       "L 302.345312 99.615459 \n",
       "L 297.114062 99.615325 \n",
       "L 291.882812 99.615177 \n",
       "L 286.651563 99.615016 \n",
       "L 281.420313 99.61484 \n",
       "L 276.189062 99.61465 \n",
       "L 270.957812 99.614446 \n",
       "L 265.726562 99.614228 \n",
       "L 260.495313 99.613996 \n",
       "L 255.264062 99.61375 \n",
       "L 250.032812 99.61349 \n",
       "L 244.801562 99.613216 \n",
       "L 239.570312 99.612927 \n",
       "L 234.82569 99.612653 \n",
       "L 234.339063 99.612624 \n",
       "L 229.107812 99.612294 \n",
       "L 223.876562 99.611949 \n",
       "L 218.645312 99.61159 \n",
       "L 213.414062 99.611216 \n",
       "L 208.182812 99.610828 \n",
       "L 202.951562 99.610425 \n",
       "L 197.720313 99.610007 \n",
       "L 192.489062 99.609574 \n",
       "L 187.257812 99.609127 \n",
       "L 182.026562 99.608665 \n",
       "L 176.795312 99.608189 \n",
       "L 171.564063 99.607698 \n",
       "L 166.332812 99.607192 \n",
       "L 161.101562 99.606671 \n",
       "L 155.870312 99.606136 \n",
       "L 152.313062 99.605762 \n",
       "L 150.639062 99.605579 \n",
       "L 145.407812 99.604989 \n",
       "L 140.176562 99.604384 \n",
       "L 134.945312 99.603764 \n",
       "L 129.714062 99.603128 \n",
       "L 124.482812 99.602478 \n",
       "L 119.251563 99.601812 \n",
       "L 114.020312 99.60113 \n",
       "L 108.789062 99.600433 \n",
       "L 103.557812 99.599721 \n",
       "L 98.326562 99.598994 \n",
       "L 97.463676 99.598871 \n",
       "L 93.095312 99.598222 \n",
       "L 87.864062 99.597429 \n",
       "L 82.632812 99.59662 \n",
       "L 77.401563 99.595795 \n",
       "L 72.170313 99.594953 \n",
       "L 66.939062 99.594096 \n",
       "L 61.707812 99.593223 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_6\">\n",
       "    <path clip-path=\"url(#p6f01c307aa)\" d=\"M 396.507812 99.635449 \n",
       "L 391.276563 99.635556 \n",
       "L 386.045312 99.63565 \n",
       "L 380.814062 99.635731 \n",
       "L 375.582812 99.6358 \n",
       "L 370.351562 99.635857 \n",
       "L 365.120313 99.6359 \n",
       "L 359.889062 99.635932 \n",
       "L 354.657812 99.63595 \n",
       "L 349.426562 99.635957 \n",
       "L 344.195312 99.63595 \n",
       "L 338.964063 99.635932 \n",
       "L 333.732812 99.6359 \n",
       "L 328.501562 99.635857 \n",
       "L 323.270312 99.6358 \n",
       "L 318.039062 99.635731 \n",
       "L 312.807813 99.63565 \n",
       "L 307.576562 99.635556 \n",
       "L 302.345312 99.635449 \n",
       "L 297.114062 99.63533 \n",
       "L 291.882812 99.635199 \n",
       "L 286.651563 99.635055 \n",
       "L 281.420313 99.634898 \n",
       "L 276.189062 99.634729 \n",
       "L 270.957812 99.634547 \n",
       "L 265.726562 99.634353 \n",
       "L 260.495313 99.634146 \n",
       "L 255.264062 99.633927 \n",
       "L 250.032812 99.633695 \n",
       "L 244.801562 99.633451 \n",
       "L 242.249733 99.633326 \n",
       "L 239.570312 99.633189 \n",
       "L 234.339063 99.63291 \n",
       "L 229.107812 99.632617 \n",
       "L 223.876562 99.632312 \n",
       "L 218.645312 99.631993 \n",
       "L 213.414062 99.631661 \n",
       "L 208.182812 99.631317 \n",
       "L 202.951562 99.630959 \n",
       "L 197.720313 99.630589 \n",
       "L 192.489062 99.630205 \n",
       "L 187.257812 99.629809 \n",
       "L 182.026562 99.629399 \n",
       "L 176.795312 99.628977 \n",
       "L 171.564063 99.628541 \n",
       "L 166.332812 99.628093 \n",
       "L 161.101562 99.627631 \n",
       "L 155.870312 99.627156 \n",
       "L 150.639062 99.626669 \n",
       "L 148.193283 99.626435 \n",
       "L 145.407813 99.626158 \n",
       "L 140.176562 99.625624 \n",
       "L 134.945312 99.625077 \n",
       "L 129.714062 99.624516 \n",
       "L 124.482812 99.623942 \n",
       "L 119.251563 99.623354 \n",
       "L 114.020312 99.622753 \n",
       "L 108.789062 99.622138 \n",
       "L 103.557812 99.62151 \n",
       "L 98.326562 99.620868 \n",
       "L 93.095312 99.620213 \n",
       "L 87.864062 99.619544 \n",
       "L 87.864062 99.619544 \n",
       "L 82.632812 99.618834 \n",
       "L 77.401563 99.61811 \n",
       "L 72.170313 99.617371 \n",
       "L 66.939062 99.616619 \n",
       "L 61.707812 99.615852 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_7\">\n",
       "    <path clip-path=\"url(#p6f01c307aa)\" d=\"M 349.426562 99.653998 \n",
       "L 344.195312 99.653992 \n",
       "L 338.964063 99.653975 \n",
       "L 333.732812 99.653946 \n",
       "L 328.501562 99.653905 \n",
       "L 323.270312 99.653852 \n",
       "L 318.039062 99.653788 \n",
       "L 312.807813 99.653712 \n",
       "L 307.576562 99.653625 \n",
       "L 302.345312 99.653525 \n",
       "L 297.114062 99.653414 \n",
       "L 291.882812 99.653292 \n",
       "L 286.651563 99.653157 \n",
       "L 281.420313 99.653011 \n",
       "L 276.189062 99.652854 \n",
       "L 270.957812 99.652684 \n",
       "L 265.726562 99.652503 \n",
       "L 260.495313 99.652311 \n",
       "L 255.264062 99.652106 \n",
       "L 250.032812 99.65189 \n",
       "L 244.801562 99.651662 \n",
       "L 239.570312 99.651423 \n",
       "L 234.339063 99.651172 \n",
       "L 229.107812 99.650909 \n",
       "L 223.876562 99.650635 \n",
       "L 218.645312 99.650348 \n",
       "L 213.414062 99.650051 \n",
       "L 208.182812 99.649741 \n",
       "L 202.951562 99.64942 \n",
       "L 197.720313 99.649087 \n",
       "L 192.489062 99.648743 \n",
       "L 187.257812 99.648386 \n",
       "L 182.026562 99.648018 \n",
       "L 176.795312 99.647639 \n",
       "L 171.564063 99.647248 \n",
       "L 169.744497 99.647107 \n",
       "L 166.332812 99.646835 \n",
       "L 161.101562 99.646406 \n",
       "L 155.870312 99.645965 \n",
       "L 150.639062 99.645512 \n",
       "L 145.407813 99.645046 \n",
       "L 140.176562 99.644569 \n",
       "L 134.945312 99.644079 \n",
       "L 129.714062 99.643577 \n",
       "L 124.482812 99.643064 \n",
       "L 119.251563 99.642538 \n",
       "L 114.020312 99.642 \n",
       "L 108.789062 99.64145 \n",
       "L 103.557812 99.640887 \n",
       "L 98.326562 99.640313 \n",
       "L 97.463676 99.640217 \n",
       "L 93.095312 99.639709 \n",
       "L 87.864062 99.639089 \n",
       "L 82.632812 99.638456 \n",
       "L 77.401563 99.637811 \n",
       "L 72.170313 99.637153 \n",
       "L 66.939062 99.636483 \n",
       "L 61.707812 99.6358 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p6f01c307aa)\" d=\"M 396.507812 99.653525 \n",
       "L 391.276563 99.653625 \n",
       "L 386.045312 99.653712 \n",
       "L 380.814062 99.653788 \n",
       "L 375.582812 99.653852 \n",
       "L 370.351562 99.653905 \n",
       "L 365.120313 99.653946 \n",
       "L 359.889062 99.653975 \n",
       "L 354.657812 99.653992 \n",
       "L 349.426562 99.653998 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_8\">\n",
       "    <path clip-path=\"url(#p6f01c307aa)\" d=\"M 62.90764 99.653998 \n",
       "L 61.707812 99.653852 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_9\"/>\n",
       "   <g id=\"line2d_13\">\n",
       "    <path clip-path=\"url(#p6f01c307aa)\" d=\"M 87.864063 99.58509 \n",
       "L 119.251563 99.254329 \n",
       "L 146.872563 99.717394 \n",
       "L 171.179043 99.069103 \n",
       "L 192.568745 99.976711 \n",
       "L 211.391683 98.70606 \n",
       "L 227.955869 100.484971 \n",
       "L 242.532352 97.994495 \n",
       "L 255.359657 101.481161 \n",
       "L 266.647686 96.599829 \n",
       "L 276.581151 103.433694 \n",
       "L 285.3226 93.866283 \n",
       "L 293.015076 107.260658 \n",
       "L 299.784454 88.508533 \n",
       "L 305.741507 114.761509 \n",
       "L 310.983714 78.007342 \n",
       "L 315.596856 129.463175 \n",
       "L 319.65642 57.425009 \n",
       "L 323.228838 158.278442 \n",
       "L 326.372565 17.083636 \n",
       "L 329.139044 214.756364 \n",
       "\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    <defs>\n",
       "     <path d=\"M 0 3 \n",
       "C 0.795609 3 1.55874 2.683901 2.12132 2.12132 \n",
       "C 2.683901 1.55874 3 0.795609 3 0 \n",
       "C 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \n",
       "C 1.55874 -2.683901 0.795609 -3 0 -3 \n",
       "C -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \n",
       "C -2.683901 -1.55874 -3 -0.795609 -3 0 \n",
       "C -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \n",
       "C -1.55874 2.683901 -0.795609 3 0 3 \n",
       "z\n",
       "\" id=\"m28eb8f1515\" style=\"stroke:#ff7f0e;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p6f01c307aa)\">\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"87.864063\" xlink:href=\"#m28eb8f1515\" y=\"99.58509\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"119.251563\" xlink:href=\"#m28eb8f1515\" y=\"99.254329\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"146.872563\" xlink:href=\"#m28eb8f1515\" y=\"99.717394\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"171.179043\" xlink:href=\"#m28eb8f1515\" y=\"99.069103\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"192.568745\" xlink:href=\"#m28eb8f1515\" y=\"99.976711\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"211.391683\" xlink:href=\"#m28eb8f1515\" y=\"98.70606\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"227.955869\" xlink:href=\"#m28eb8f1515\" y=\"100.484971\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"242.532352\" xlink:href=\"#m28eb8f1515\" y=\"97.994495\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"255.359657\" xlink:href=\"#m28eb8f1515\" y=\"101.481161\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"266.647686\" xlink:href=\"#m28eb8f1515\" y=\"96.599829\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"276.581151\" xlink:href=\"#m28eb8f1515\" y=\"103.433694\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"285.3226\" xlink:href=\"#m28eb8f1515\" y=\"93.866283\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"293.015076\" xlink:href=\"#m28eb8f1515\" y=\"107.260658\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"299.784454\" xlink:href=\"#m28eb8f1515\" y=\"88.508533\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"305.741507\" xlink:href=\"#m28eb8f1515\" y=\"114.761509\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"310.983714\" xlink:href=\"#m28eb8f1515\" y=\"78.007342\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"315.596856\" xlink:href=\"#m28eb8f1515\" y=\"129.463175\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"319.65642\" xlink:href=\"#m28eb8f1515\" y=\"57.425009\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"323.228838\" xlink:href=\"#m28eb8f1515\" y=\"158.278442\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"326.372565\" xlink:href=\"#m28eb8f1515\" y=\"17.083636\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"329.139044\" xlink:href=\"#m28eb8f1515\" y=\"214.756364\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 61.707813 224.64 \n",
       "L 61.707813 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 396.507812 224.64 \n",
       "L 396.507812 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 61.707812 224.64 \n",
       "L 396.507812 224.64 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 61.707812 7.2 \n",
       "L 396.507812 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p6f01c307aa\">\n",
       "   <rect height=\"217.44\" width=\"334.8\" x=\"61.707813\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "可以看到，同一位置上，目标函数在竖直方向（x2轴方向）比在水平方向（x1轴方向）的斜率的绝对值更大。\n",
    "因此，给定学习率，梯度下降迭代自变量时会使自变量在竖直方向比在水平方向移动幅度更大。\n",
    "那么，我们需要一个较小的学习率从而避免自变量在竖直方向上越过目标函数最优解。\n",
    "然而，这会造成自变量在水平方向上朝最优解移动变慢。\n",
    "\"\"\"\n",
    "\n",
    "\"\"\"\n",
    "当学习率变大时\n",
    "\"\"\"\n",
    "\n",
    "eta = 0.6\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(gd_2d))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\n此时自变量在竖直方向不断越过最优解并逐渐发散\\n'"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "此时自变量在竖直方向不断越过最优解并逐渐发散\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.062843, x2 0.001202\n"
     ]
    },
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"262.19625pt\" version=\"1.1\" viewBox=\"0 0 394.160937 262.19625\" width=\"394.160937pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 262.19625 \n",
       "L 394.160937 262.19625 \n",
       "L 394.160937 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 52.160938 224.64 \n",
       "L 386.960938 224.64 \n",
       "L 386.960938 7.2 \n",
       "L 52.160938 7.2 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"mc5f10a9a4d\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"78.317188\" xlink:href=\"#mc5f10a9a4d\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- −5 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.59375 35.5 \n",
       "L 73.1875 35.5 \n",
       "L 73.1875 27.203125 \n",
       "L 10.59375 27.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-8722\"/>\n",
       "       <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(70.946094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"130.629688\" xlink:href=\"#mc5f10a9a4d\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- −4 -->\n",
       "      <defs>\n",
       "       <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(123.258594 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"182.942188\" xlink:href=\"#mc5f10a9a4d\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- −3 -->\n",
       "      <defs>\n",
       "       <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(175.571094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"235.254688\" xlink:href=\"#mc5f10a9a4d\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- −2 -->\n",
       "      <defs>\n",
       "       <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(227.883594 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"287.567188\" xlink:href=\"#mc5f10a9a4d\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- −1 -->\n",
       "      <defs>\n",
       "       <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(280.196094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"339.879688\" xlink:href=\"#mc5f10a9a4d\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(336.698438 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_7\">\n",
       "     <!-- x1 -->\n",
       "     <defs>\n",
       "      <path d=\"M 54.890625 54.6875 \n",
       "L 35.109375 28.078125 \n",
       "L 55.90625 0 \n",
       "L 45.3125 0 \n",
       "L 29.390625 21.484375 \n",
       "L 13.484375 0 \n",
       "L 2.875 0 \n",
       "L 24.125 28.609375 \n",
       "L 4.6875 54.6875 \n",
       "L 15.28125 54.6875 \n",
       "L 29.78125 35.203125 \n",
       "L 44.28125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-120\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(213.420313 252.916562)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"m8ff580a0db\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m8ff580a0db\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- −3.0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.6875 12.40625 \n",
       "L 21 12.40625 \n",
       "L 21 0 \n",
       "L 10.6875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-46\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(20.878125 228.439219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m8ff580a0db\" y=\"199.986939\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- −2.5 -->\n",
       "      <g transform=\"translate(20.878125 203.786158)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m8ff580a0db\" y=\"175.333878\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- −2.0 -->\n",
       "      <g transform=\"translate(20.878125 179.133096)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m8ff580a0db\" y=\"150.680816\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- −1.5 -->\n",
       "      <g transform=\"translate(20.878125 154.480035)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m8ff580a0db\" y=\"126.027755\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- −1.0 -->\n",
       "      <g transform=\"translate(20.878125 129.826974)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m8ff580a0db\" y=\"101.374694\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- −0.5 -->\n",
       "      <g transform=\"translate(20.878125 105.173913)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m8ff580a0db\" y=\"76.721633\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_14\">\n",
       "      <!-- 0.0 -->\n",
       "      <g transform=\"translate(29.257812 80.520851)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_8\">\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m8ff580a0db\" y=\"52.068571\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- 0.5 -->\n",
       "      <g transform=\"translate(29.257812 55.86779)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_9\">\n",
       "     <g id=\"line2d_15\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m8ff580a0db\" y=\"27.41551\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_16\">\n",
       "      <!-- 1.0 -->\n",
       "      <g transform=\"translate(29.257812 31.214729)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_17\">\n",
       "     <!-- x2 -->\n",
       "     <g transform=\"translate(14.798438 122.060625)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_1\"/>\n",
       "   <g id=\"LineCollection_2\">\n",
       "    <path clip-path=\"url(#p8fba36b22d)\" d=\"M 386.960938 136.273567 \n",
       "L 381.729688 136.441208 \n",
       "L 376.498437 136.589127 \n",
       "L 371.267187 136.717322 \n",
       "L 366.035937 136.825796 \n",
       "L 360.804688 136.914547 \n",
       "L 355.573438 136.983576 \n",
       "L 350.342187 137.032882 \n",
       "L 345.110937 137.062465 \n",
       "L 339.879687 137.072327 \n",
       "L 334.648438 137.062465 \n",
       "L 329.417188 137.032882 \n",
       "L 324.185937 136.983576 \n",
       "L 318.954687 136.914547 \n",
       "L 313.723437 136.825796 \n",
       "L 308.492188 136.717322 \n",
       "L 303.260938 136.589127 \n",
       "L 298.029687 136.441208 \n",
       "L 292.798437 136.273567 \n",
       "L 287.567187 136.086204 \n",
       "L 282.585045 135.88898 \n",
       "L 282.335938 135.878261 \n",
       "L 277.104688 135.63173 \n",
       "L 271.873438 135.363762 \n",
       "L 266.642187 135.074357 \n",
       "L 261.410937 134.763514 \n",
       "L 256.179688 134.431233 \n",
       "L 250.948437 134.077516 \n",
       "L 245.717187 133.70236 \n",
       "L 240.485937 133.305768 \n",
       "L 235.254687 132.887737 \n",
       "L 230.023438 132.44827 \n",
       "L 224.792188 131.987365 \n",
       "L 219.560937 131.505022 \n",
       "L 214.329687 131.001242 \n",
       "L 213.902647 130.958367 \n",
       "L 209.098437 130.430087 \n",
       "L 203.867188 129.83137 \n",
       "L 198.635937 129.209174 \n",
       "L 193.404687 128.563499 \n",
       "L 188.173438 127.894344 \n",
       "L 182.942187 127.20171 \n",
       "L 177.710938 126.485598 \n",
       "L 174.472545 126.027755 \n",
       "L 172.479688 125.716348 \n",
       "L 167.248437 124.872954 \n",
       "L 162.017188 124.003609 \n",
       "L 156.785937 123.108314 \n",
       "L 151.554688 122.187068 \n",
       "L 146.323437 121.239871 \n",
       "L 145.556187 121.097143 \n",
       "L 141.092187 120.169028 \n",
       "L 135.860938 119.052389 \n",
       "L 130.629687 117.906747 \n",
       "L 125.398438 116.732101 \n",
       "L 122.94038 116.166531 \n",
       "L 120.167187 115.443374 \n",
       "L 114.935937 114.046367 \n",
       "L 109.704688 112.61649 \n",
       "L 104.767328 111.235918 \n",
       "L 104.473437 111.141099 \n",
       "L 99.242188 109.415385 \n",
       "L 94.010937 107.651743 \n",
       "L 90.101266 106.305306 \n",
       "L 88.779687 105.767421 \n",
       "L 83.548437 103.593469 \n",
       "L 78.317187 101.374694 \n",
       "L 78.317187 101.374694 \n",
       "L 73.085938 98.608073 \n",
       "L 69.07362 96.444082 \n",
       "L 67.854688 95.598834 \n",
       "L 62.623438 91.900875 \n",
       "L 62.085645 91.513469 \n",
       "L 57.392187 86.780082 \n",
       "L 57.200215 86.582857 \n",
       "L 54.320628 81.652245 \n",
       "L 53.360765 76.721633 \n",
       "L 54.320628 71.79102 \n",
       "L 57.200215 66.860408 \n",
       "L 57.392187 66.663184 \n",
       "L 62.085645 61.929796 \n",
       "L 62.623438 61.542391 \n",
       "L 67.854688 57.844431 \n",
       "L 69.07362 56.999184 \n",
       "L 73.085938 54.835193 \n",
       "L 78.317187 52.068571 \n",
       "L 78.317188 52.068571 \n",
       "L 83.548437 49.849796 \n",
       "L 88.779687 47.675844 \n",
       "L 90.101266 47.137959 \n",
       "L 94.010937 45.791523 \n",
       "L 99.242188 44.027881 \n",
       "L 104.473437 42.302166 \n",
       "L 104.767328 42.207347 \n",
       "L 109.704688 40.826776 \n",
       "L 114.935937 39.396898 \n",
       "L 120.167187 37.999891 \n",
       "L 122.94038 37.276735 \n",
       "L 125.398438 36.711164 \n",
       "L 130.629687 35.536519 \n",
       "L 135.860938 34.390876 \n",
       "L 141.092187 33.274238 \n",
       "L 145.556188 32.346122 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_3\">\n",
       "    <path clip-path=\"url(#p8fba36b22d)\" d=\"M 386.960938 161.52112 \n",
       "L 381.729688 161.640863 \n",
       "L 376.498437 161.746519 \n",
       "L 371.267187 161.838087 \n",
       "L 366.035937 161.915569 \n",
       "L 360.804688 161.978962 \n",
       "L 355.573438 162.028268 \n",
       "L 350.342187 162.063487 \n",
       "L 345.110937 162.084618 \n",
       "L 339.879687 162.091662 \n",
       "L 334.648438 162.084618 \n",
       "L 329.417188 162.063487 \n",
       "L 324.185937 162.028268 \n",
       "L 318.954687 161.978962 \n",
       "L 313.723437 161.915569 \n",
       "L 308.492188 161.838087 \n",
       "L 303.260938 161.746519 \n",
       "L 298.029687 161.640863 \n",
       "L 292.798437 161.52112 \n",
       "L 287.567187 161.387289 \n",
       "L 282.335938 161.23937 \n",
       "L 277.104688 161.077364 \n",
       "L 271.873438 160.901271 \n",
       "L 266.642187 160.71109 \n",
       "L 262.312877 160.542041 \n",
       "L 261.410937 160.504688 \n",
       "L 256.179688 160.273098 \n",
       "L 250.948438 160.026568 \n",
       "L 245.717188 159.765096 \n",
       "L 240.485938 159.488683 \n",
       "L 235.254687 159.197328 \n",
       "L 230.023438 158.891033 \n",
       "L 224.792188 158.569796 \n",
       "L 219.560937 158.233618 \n",
       "L 214.329687 157.882498 \n",
       "L 209.098437 157.516438 \n",
       "L 203.867188 157.135436 \n",
       "L 198.635937 156.739493 \n",
       "L 193.404687 156.328609 \n",
       "L 188.173438 155.902783 \n",
       "L 184.715493 155.611429 \n",
       "L 182.942187 155.452377 \n",
       "L 177.710938 154.967268 \n",
       "L 172.479687 154.466254 \n",
       "L 167.248437 153.949335 \n",
       "L 162.017188 153.416511 \n",
       "L 156.785937 152.867781 \n",
       "L 151.554688 152.303147 \n",
       "L 146.323437 151.722607 \n",
       "L 141.092187 151.126162 \n",
       "L 137.287642 150.680816 \n",
       "L 135.860938 150.502294 \n",
       "L 130.629687 149.830711 \n",
       "L 125.398438 149.142125 \n",
       "L 120.167187 148.436538 \n",
       "L 114.935937 147.713948 \n",
       "L 109.704688 146.974356 \n",
       "L 104.473437 146.217762 \n",
       "L 101.311693 145.750204 \n",
       "L 99.242188 145.421497 \n",
       "L 94.010937 144.572336 \n",
       "L 88.779687 143.704913 \n",
       "L 83.548437 142.819229 \n",
       "L 78.317187 141.915283 \n",
       "L 73.085938 140.993076 \n",
       "L 72.12095 140.819592 \n",
       "L 67.854688 139.991249 \n",
       "L 62.623438 138.95582 \n",
       "L 57.392187 137.900669 \n",
       "L 52.160937 136.825796 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_4\">\n",
       "    <path clip-path=\"url(#p8fba36b22d)\" d=\"M 386.960938 180.832084 \n",
       "L 381.729688 180.929549 \n",
       "L 376.498437 181.015548 \n",
       "L 371.267187 181.090081 \n",
       "L 366.035937 181.153147 \n",
       "L 360.804688 181.204746 \n",
       "L 355.573438 181.244879 \n",
       "L 350.342187 181.273545 \n",
       "L 345.110937 181.290745 \n",
       "L 339.879687 181.296478 \n",
       "L 334.648438 181.290745 \n",
       "L 329.417188 181.273545 \n",
       "L 324.185937 181.244879 \n",
       "L 318.954687 181.204746 \n",
       "L 313.723437 181.153147 \n",
       "L 308.492188 181.090081 \n",
       "L 303.260938 181.015548 \n",
       "L 298.029687 180.929549 \n",
       "L 292.798437 180.832084 \n",
       "L 287.567187 180.723151 \n",
       "L 282.335938 180.602753 \n",
       "L 277.104688 180.470888 \n",
       "L 271.873438 180.327556 \n",
       "L 269.742187 180.26449 \n",
       "L 266.642187 180.168283 \n",
       "L 261.410937 179.993907 \n",
       "L 256.179688 179.807506 \n",
       "L 250.948438 179.609079 \n",
       "L 245.717187 179.398626 \n",
       "L 240.485937 179.176147 \n",
       "L 235.254687 178.941643 \n",
       "L 230.023438 178.695112 \n",
       "L 224.792188 178.436556 \n",
       "L 219.560937 178.165973 \n",
       "L 214.329687 177.883365 \n",
       "L 209.098437 177.588731 \n",
       "L 203.867188 177.282071 \n",
       "L 198.635937 176.963385 \n",
       "L 193.404687 176.632673 \n",
       "L 188.173438 176.289935 \n",
       "L 182.942187 175.935172 \n",
       "L 177.710938 175.568382 \n",
       "L 174.472545 175.333878 \n",
       "L 172.479687 175.182166 \n",
       "L 167.248437 174.771282 \n",
       "L 162.017188 174.347755 \n",
       "L 156.785937 173.911586 \n",
       "L 151.554688 173.462773 \n",
       "L 146.323437 173.001319 \n",
       "L 141.092187 172.527221 \n",
       "L 135.860938 172.040481 \n",
       "L 130.629687 171.541099 \n",
       "L 125.398438 171.029074 \n",
       "L 120.167187 170.504406 \n",
       "L 119.182482 170.403265 \n",
       "L 114.935937 169.943519 \n",
       "L 109.704688 169.363839 \n",
       "L 104.473437 168.770833 \n",
       "L 99.242188 168.164501 \n",
       "L 94.010937 167.544843 \n",
       "L 88.779687 166.911859 \n",
       "L 83.548437 166.265549 \n",
       "L 78.317187 165.605913 \n",
       "L 77.281296 165.472653 \n",
       "L 73.085938 164.902111 \n",
       "L 67.854688 164.176606 \n",
       "L 62.623438 163.437015 \n",
       "L 57.392187 162.683335 \n",
       "L 52.160937 161.915569 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_5\">\n",
       "    <path clip-path=\"url(#p8fba36b22d)\" d=\"M 386.960938 197.06379 \n",
       "L 381.729688 197.149321 \n",
       "L 376.498437 197.22479 \n",
       "L 371.267187 197.290196 \n",
       "L 366.035937 197.345539 \n",
       "L 360.804688 197.39082 \n",
       "L 355.573438 197.426039 \n",
       "L 350.342187 197.451195 \n",
       "L 345.110937 197.466289 \n",
       "L 339.879687 197.47132 \n",
       "L 334.648438 197.466289 \n",
       "L 329.417188 197.451195 \n",
       "L 324.185937 197.426039 \n",
       "L 318.954687 197.39082 \n",
       "L 313.723437 197.345539 \n",
       "L 308.492188 197.290196 \n",
       "L 303.260938 197.22479 \n",
       "L 298.029687 197.149321 \n",
       "L 292.798437 197.06379 \n",
       "L 287.567187 196.968197 \n",
       "L 282.335938 196.862541 \n",
       "L 277.104688 196.746822 \n",
       "L 271.873438 196.621041 \n",
       "L 266.642187 196.485198 \n",
       "L 261.410937 196.339292 \n",
       "L 256.179688 196.183324 \n",
       "L 250.948438 196.017293 \n",
       "L 245.717187 195.8412 \n",
       "L 240.485937 195.655044 \n",
       "L 235.254687 195.458825 \n",
       "L 230.023438 195.252545 \n",
       "L 225.278815 195.056327 \n",
       "L 224.792188 195.035345 \n",
       "L 219.560937 194.799305 \n",
       "L 214.329687 194.552775 \n",
       "L 209.098437 194.295753 \n",
       "L 203.867188 194.028241 \n",
       "L 198.635937 193.750239 \n",
       "L 193.404687 193.461746 \n",
       "L 188.173438 193.162762 \n",
       "L 182.942187 192.853287 \n",
       "L 177.710938 192.533322 \n",
       "L 172.479687 192.202866 \n",
       "L 167.248437 191.861919 \n",
       "L 162.017188 191.510482 \n",
       "L 156.785937 191.148554 \n",
       "L 151.554688 190.776135 \n",
       "L 146.323437 190.393226 \n",
       "L 142.766187 190.125714 \n",
       "L 141.092187 189.994231 \n",
       "L 135.860937 189.57239 \n",
       "L 130.629687 189.139592 \n",
       "L 125.398438 188.695837 \n",
       "L 120.167187 188.241125 \n",
       "L 114.935937 187.775456 \n",
       "L 109.704688 187.29883 \n",
       "L 104.473437 186.811247 \n",
       "L 99.242188 186.312707 \n",
       "L 94.010937 185.803211 \n",
       "L 88.779687 185.282757 \n",
       "L 87.916801 185.195102 \n",
       "L 83.548437 184.730707 \n",
       "L 78.317187 184.163113 \n",
       "L 73.085938 183.584053 \n",
       "L 67.854688 182.993526 \n",
       "L 62.623438 182.391533 \n",
       "L 57.392187 181.778073 \n",
       "L 52.160937 181.153147 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_6\">\n",
       "    <path clip-path=\"url(#p8fba36b22d)\" d=\"M 386.960938 211.367688 \n",
       "L 381.729688 211.443889 \n",
       "L 376.498437 211.511124 \n",
       "L 371.267187 211.569395 \n",
       "L 366.035937 211.618701 \n",
       "L 360.804688 211.659043 \n",
       "L 355.573438 211.690419 \n",
       "L 350.342187 211.712831 \n",
       "L 345.110937 211.726278 \n",
       "L 339.879687 211.730761 \n",
       "L 334.648438 211.726278 \n",
       "L 329.417188 211.712831 \n",
       "L 324.185937 211.690419 \n",
       "L 318.954687 211.659043 \n",
       "L 313.723437 211.618701 \n",
       "L 308.492188 211.569395 \n",
       "L 303.260938 211.511124 \n",
       "L 298.029687 211.443889 \n",
       "L 292.798437 211.367688 \n",
       "L 287.567187 211.282523 \n",
       "L 282.335938 211.188393 \n",
       "L 277.104688 211.085299 \n",
       "L 271.873438 210.973239 \n",
       "L 266.642187 210.852215 \n",
       "L 261.410937 210.722226 \n",
       "L 256.179688 210.583273 \n",
       "L 250.948438 210.435354 \n",
       "L 245.717187 210.278471 \n",
       "L 240.485937 210.112623 \n",
       "L 235.254687 209.937811 \n",
       "L 232.702858 209.848163 \n",
       "L 230.023438 209.750481 \n",
       "L 224.792188 209.550466 \n",
       "L 219.560937 209.341147 \n",
       "L 214.329687 209.122526 \n",
       "L 209.098437 208.894601 \n",
       "L 203.867188 208.657374 \n",
       "L 198.635937 208.410843 \n",
       "L 193.404687 208.15501 \n",
       "L 188.173438 207.889873 \n",
       "L 182.942187 207.615433 \n",
       "L 177.710938 207.33169 \n",
       "L 172.479687 207.038645 \n",
       "L 167.248437 206.736296 \n",
       "L 162.017188 206.424644 \n",
       "L 156.785937 206.103689 \n",
       "L 151.554688 205.773431 \n",
       "L 146.323437 205.43387 \n",
       "L 141.092187 205.085006 \n",
       "L 138.646408 204.917551 \n",
       "L 135.860938 204.71936 \n",
       "L 130.629687 204.337479 \n",
       "L 125.398438 203.94593 \n",
       "L 120.167187 203.544714 \n",
       "L 114.935937 203.13383 \n",
       "L 109.704688 202.713277 \n",
       "L 104.473437 202.283057 \n",
       "L 99.242188 201.843169 \n",
       "L 94.010937 201.393613 \n",
       "L 88.779687 200.93439 \n",
       "L 83.548437 200.465498 \n",
       "L 78.317187 199.986939 \n",
       "L 78.317187 199.986939 \n",
       "L 73.085938 199.478784 \n",
       "L 67.854688 198.960566 \n",
       "L 62.623438 198.432287 \n",
       "L 57.392187 197.893944 \n",
       "L 52.160937 197.345539 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_7\">\n",
       "    <path clip-path=\"url(#p8fba36b22d)\" d=\"M 339.879687 224.64 \n",
       "L 334.648438 224.635822 \n",
       "L 329.417188 224.623286 \n",
       "L 324.185937 224.602394 \n",
       "L 318.954687 224.573144 \n",
       "L 313.723437 224.535538 \n",
       "L 308.492188 224.489575 \n",
       "L 303.260938 224.435254 \n",
       "L 298.029687 224.372577 \n",
       "L 292.798437 224.301543 \n",
       "L 287.567187 224.222152 \n",
       "L 282.335938 224.134403 \n",
       "L 277.104688 224.038298 \n",
       "L 271.873438 223.933836 \n",
       "L 266.642187 223.821017 \n",
       "L 261.410937 223.699841 \n",
       "L 256.179688 223.570308 \n",
       "L 250.948438 223.432418 \n",
       "L 245.717187 223.286171 \n",
       "L 240.485937 223.131567 \n",
       "L 235.254687 222.968606 \n",
       "L 230.023438 222.797288 \n",
       "L 224.792188 222.617613 \n",
       "L 219.560937 222.429581 \n",
       "L 214.329687 222.233193 \n",
       "L 209.098437 222.028447 \n",
       "L 203.867188 221.815344 \n",
       "L 198.635937 221.593884 \n",
       "L 193.404687 221.364068 \n",
       "L 188.173438 221.125894 \n",
       "L 182.942187 220.879364 \n",
       "L 177.710938 220.624476 \n",
       "L 172.479687 220.361231 \n",
       "L 167.248437 220.08963 \n",
       "L 162.017188 219.809671 \n",
       "L 160.197622 219.709388 \n",
       "L 156.785937 219.514758 \n",
       "L 151.554688 219.207676 \n",
       "L 146.323437 218.891944 \n",
       "L 141.092187 218.567562 \n",
       "L 135.860938 218.234529 \n",
       "L 130.629687 217.892846 \n",
       "L 125.398438 217.542513 \n",
       "L 120.167187 217.18353 \n",
       "L 114.935937 216.815897 \n",
       "L 109.704688 216.439613 \n",
       "L 104.473437 216.05468 \n",
       "L 99.242188 215.661096 \n",
       "L 94.010937 215.258861 \n",
       "L 88.779687 214.847977 \n",
       "L 87.916801 214.778776 \n",
       "L 83.548437 214.415703 \n",
       "L 78.317187 213.971948 \n",
       "L 73.085938 213.519228 \n",
       "L 67.854688 213.057544 \n",
       "L 62.623438 212.586894 \n",
       "L 57.392187 212.10728 \n",
       "L 52.160937 211.618701 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p8fba36b22d)\" d=\"M 386.960938 224.301543 \n",
       "L 381.729688 224.372577 \n",
       "L 376.498437 224.435254 \n",
       "L 371.267187 224.489575 \n",
       "L 366.035937 224.535538 \n",
       "L 360.804688 224.573144 \n",
       "L 355.573438 224.602394 \n",
       "L 350.342187 224.623286 \n",
       "L 345.110937 224.635822 \n",
       "L 339.879687 224.64 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_8\">\n",
       "    <path clip-path=\"url(#p8fba36b22d)\" d=\"M 53.360765 224.64 \n",
       "L 52.160937 224.535538 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_9\"/>\n",
       "   <g id=\"line2d_16\">\n",
       "    <path clip-path=\"url(#p8fba36b22d)\" d=\"M 78.317188 175.333878 \n",
       "L 99.242188 17.554286 \n",
       "L 128.955688 33.332245 \n",
       "L 160.686358 110.644245 \n",
       "L 190.887159 95.024065 \n",
       "L 217.906962 57.930083 \n",
       "L 241.174681 69.449571 \n",
       "L 260.704942 86.844613 \n",
       "L 276.804051 79.345365 \n",
       "L 289.899657 71.397769 \n",
       "L 300.445863 75.942153 \n",
       "L 308.873671 79.461512 \n",
       "L 315.568057 76.837385 \n",
       "L 320.86018 75.340118 \n",
       "L 325.027802 76.801908 \n",
       "L 328.299764 77.404363 \n",
       "L 330.862139 76.613222 \n",
       "L 332.86473 76.391109 \n",
       "L 334.427223 76.80889 \n",
       "L 335.644666 76.878169 \n",
       "L 336.592189 76.66235 \n",
       "\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    <defs>\n",
       "     <path d=\"M 0 3 \n",
       "C 0.795609 3 1.55874 2.683901 2.12132 2.12132 \n",
       "C 2.683901 1.55874 3 0.795609 3 0 \n",
       "C 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \n",
       "C 1.55874 -2.683901 0.795609 -3 0 -3 \n",
       "C -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \n",
       "C -2.683901 -1.55874 -3 -0.795609 -3 0 \n",
       "C -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \n",
       "C -1.55874 2.683901 -0.795609 3 0 3 \n",
       "z\n",
       "\" id=\"m7ad9bca6a9\" style=\"stroke:#ff7f0e;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p8fba36b22d)\">\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"78.317188\" xlink:href=\"#m7ad9bca6a9\" y=\"175.333878\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"99.242188\" xlink:href=\"#m7ad9bca6a9\" y=\"17.554286\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"128.955688\" xlink:href=\"#m7ad9bca6a9\" y=\"33.332245\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"160.686358\" xlink:href=\"#m7ad9bca6a9\" y=\"110.644245\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"190.887159\" xlink:href=\"#m7ad9bca6a9\" y=\"95.024065\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"217.906962\" xlink:href=\"#m7ad9bca6a9\" y=\"57.930083\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"241.174681\" xlink:href=\"#m7ad9bca6a9\" y=\"69.449571\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"260.704942\" xlink:href=\"#m7ad9bca6a9\" y=\"86.844613\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"276.804051\" xlink:href=\"#m7ad9bca6a9\" y=\"79.345365\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"289.899657\" xlink:href=\"#m7ad9bca6a9\" y=\"71.397769\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"300.445863\" xlink:href=\"#m7ad9bca6a9\" y=\"75.942153\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"308.873671\" xlink:href=\"#m7ad9bca6a9\" y=\"79.461512\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"315.568057\" xlink:href=\"#m7ad9bca6a9\" y=\"76.837385\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"320.86018\" xlink:href=\"#m7ad9bca6a9\" y=\"75.340118\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"325.027802\" xlink:href=\"#m7ad9bca6a9\" y=\"76.801908\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"328.299764\" xlink:href=\"#m7ad9bca6a9\" y=\"77.404363\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"330.862139\" xlink:href=\"#m7ad9bca6a9\" y=\"76.613222\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"332.86473\" xlink:href=\"#m7ad9bca6a9\" y=\"76.391109\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"334.427223\" xlink:href=\"#m7ad9bca6a9\" y=\"76.80889\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"335.644666\" xlink:href=\"#m7ad9bca6a9\" y=\"76.878169\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"336.592189\" xlink:href=\"#m7ad9bca6a9\" y=\"76.66235\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 52.160938 224.64 \n",
       "L 52.160938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 386.960938 224.64 \n",
       "L 386.960938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 52.160937 224.64 \n",
       "L 386.960938 224.64 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 52.160937 7.2 \n",
       "L 386.960938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p8fba36b22d\">\n",
       "   <rect height=\"217.44\" width=\"334.8\" x=\"52.160938\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "梯度下降在使用动量法后的迭代轨迹\n",
    "\"\"\"\n",
    "def momentum_2d(x1, x2, v1, v2):\n",
    "    v1 = gamma * v1 + eta * 0.2 * x1\n",
    "    v2 = gamma * v2 + eta * 4 * x2\n",
    "    return x1 - v1, x2 - v2, v1, v2\n",
    "\n",
    "eta, gamma = 0.4, 0.5\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(momentum_2d))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 0.007188, x2 0.002553\n"
     ]
    },
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"262.78207pt\" version=\"1.1\" viewBox=\"0 0 384.620312 262.78207\" width=\"384.620312pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 262.78207 \n",
       "L 384.620312 262.78207 \n",
       "L 384.620312 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 42.620313 225.22582 \n",
       "L 377.420313 225.22582 \n",
       "L 377.420313 7.78582 \n",
       "L 42.620313 7.78582 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"m1cf92d9f6a\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"68.776563\" xlink:href=\"#m1cf92d9f6a\" y=\"225.22582\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- −5 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.59375 35.5 \n",
       "L 73.1875 35.5 \n",
       "L 73.1875 27.203125 \n",
       "L 10.59375 27.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-8722\"/>\n",
       "       <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(61.405469 239.824257)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"121.089063\" xlink:href=\"#m1cf92d9f6a\" y=\"225.22582\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- −4 -->\n",
       "      <defs>\n",
       "       <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(113.717969 239.824257)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"173.401563\" xlink:href=\"#m1cf92d9f6a\" y=\"225.22582\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- −3 -->\n",
       "      <defs>\n",
       "       <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(166.030469 239.824257)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"225.714063\" xlink:href=\"#m1cf92d9f6a\" y=\"225.22582\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- −2 -->\n",
       "      <defs>\n",
       "       <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(218.342969 239.824257)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"278.026563\" xlink:href=\"#m1cf92d9f6a\" y=\"225.22582\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- −1 -->\n",
       "      <defs>\n",
       "       <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(270.655469 239.824257)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"330.339063\" xlink:href=\"#m1cf92d9f6a\" y=\"225.22582\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(327.157813 239.824257)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_7\">\n",
       "     <!-- x1 -->\n",
       "     <defs>\n",
       "      <path d=\"M 54.890625 54.6875 \n",
       "L 35.109375 28.078125 \n",
       "L 55.90625 0 \n",
       "L 45.3125 0 \n",
       "L 29.390625 21.484375 \n",
       "L 13.484375 0 \n",
       "L 2.875 0 \n",
       "L 24.125 28.609375 \n",
       "L 4.6875 54.6875 \n",
       "L 15.28125 54.6875 \n",
       "L 29.78125 35.203125 \n",
       "L 44.28125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-120\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(203.879688 253.502382)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"mf5801f35e2\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#mf5801f35e2\" y=\"225.22582\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- −3 -->\n",
       "      <g transform=\"translate(20.878125 229.025038)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#mf5801f35e2\" y=\"189.521386\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- −2 -->\n",
       "      <g transform=\"translate(20.878125 193.320605)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#mf5801f35e2\" y=\"153.816953\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- −1 -->\n",
       "      <g transform=\"translate(20.878125 157.616171)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#mf5801f35e2\" y=\"118.112519\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- 0 -->\n",
       "      <g transform=\"translate(29.257813 121.911738)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#mf5801f35e2\" y=\"82.408086\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- 1 -->\n",
       "      <g transform=\"translate(29.257813 86.207304)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#mf5801f35e2\" y=\"46.703652\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- 2 -->\n",
       "      <g transform=\"translate(29.257813 50.502871)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"42.620313\" xlink:href=\"#mf5801f35e2\" y=\"10.999219\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_14\">\n",
       "      <!-- 3 -->\n",
       "      <g transform=\"translate(29.257813 14.798438)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_15\">\n",
       "     <!-- x2 -->\n",
       "     <g transform=\"translate(14.798438 122.646445)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_1\"/>\n",
       "   <g id=\"LineCollection_2\">\n",
       "    <path clip-path=\"url(#pff06d154f3)\" d=\"M 377.420313 161.236334 \n",
       "L 372.189063 161.357729 \n",
       "L 366.957812 161.464842 \n",
       "L 361.726562 161.557674 \n",
       "L 356.495313 161.636224 \n",
       "L 351.264063 161.700492 \n",
       "L 346.032813 161.750478 \n",
       "L 340.801562 161.786182 \n",
       "L 335.570312 161.807605 \n",
       "L 330.339063 161.814746 \n",
       "L 325.107813 161.807605 \n",
       "L 319.876563 161.786182 \n",
       "L 314.645312 161.750478 \n",
       "L 309.414062 161.700492 \n",
       "L 304.182813 161.636224 \n",
       "L 298.951563 161.557674 \n",
       "L 293.720313 161.464842 \n",
       "L 288.489062 161.357729 \n",
       "L 283.257812 161.236334 \n",
       "L 278.026563 161.100657 \n",
       "L 273.04442 160.957839 \n",
       "L 272.795313 160.950078 \n",
       "L 267.564063 160.771555 \n",
       "L 262.332813 160.57751 \n",
       "L 257.101562 160.36794 \n",
       "L 251.870313 160.142847 \n",
       "L 246.639063 159.90223 \n",
       "L 241.407813 159.64609 \n",
       "L 236.176563 159.374425 \n",
       "L 230.945312 159.087238 \n",
       "L 225.714063 158.784526 \n",
       "L 220.482813 158.466291 \n",
       "L 215.251563 158.132532 \n",
       "L 210.020313 157.78325 \n",
       "L 204.789062 157.418443 \n",
       "L 204.362022 157.387396 \n",
       "L 199.557813 157.004849 \n",
       "L 194.326563 156.571295 \n",
       "L 189.095313 156.120739 \n",
       "L 183.864063 155.653181 \n",
       "L 178.632813 155.168621 \n",
       "L 173.401563 154.667058 \n",
       "L 168.170313 154.148494 \n",
       "L 164.93192 153.816953 \n",
       "L 162.939063 153.591451 \n",
       "L 157.707813 152.980717 \n",
       "L 152.476563 152.351192 \n",
       "L 147.245313 151.702874 \n",
       "L 142.014063 151.035765 \n",
       "L 136.782813 150.349864 \n",
       "L 136.015562 150.246509 \n",
       "L 131.551563 149.574426 \n",
       "L 126.320313 148.765826 \n",
       "L 121.089063 147.936223 \n",
       "L 115.857813 147.085617 \n",
       "L 113.399755 146.676066 \n",
       "L 110.626563 146.152401 \n",
       "L 105.395313 145.140775 \n",
       "L 100.164063 144.105347 \n",
       "L 95.226703 143.105623 \n",
       "L 94.932813 143.03696 \n",
       "L 89.701563 141.787305 \n",
       "L 84.470313 140.510185 \n",
       "L 80.560641 139.535179 \n",
       "L 79.239063 139.145676 \n",
       "L 74.007812 137.571435 \n",
       "L 68.776563 135.964736 \n",
       "L 68.776562 135.964736 \n",
       "L 63.545313 133.961321 \n",
       "L 59.532995 132.394293 \n",
       "L 58.314063 131.782217 \n",
       "L 53.082813 129.104384 \n",
       "L 52.54502 128.823849 \n",
       "L 47.851562 125.396224 \n",
       "L 47.65959 125.253406 \n",
       "L 44.780003 121.682963 \n",
       "L 43.82014 118.112519 \n",
       "L 44.780003 114.542076 \n",
       "L 47.65959 110.971633 \n",
       "L 47.851562 110.828815 \n",
       "L 52.54502 107.401189 \n",
       "L 53.082813 107.120654 \n",
       "L 58.314063 104.442822 \n",
       "L 59.532995 103.830746 \n",
       "L 63.545313 102.263718 \n",
       "L 68.776563 100.260302 \n",
       "L 68.776563 100.260302 \n",
       "L 74.007812 98.653603 \n",
       "L 79.239063 97.079362 \n",
       "L 80.560641 96.689859 \n",
       "L 84.470313 95.714853 \n",
       "L 89.701563 94.437733 \n",
       "L 94.932813 93.188078 \n",
       "L 95.226703 93.119416 \n",
       "L 100.164063 92.119692 \n",
       "L 105.395313 91.084263 \n",
       "L 110.626563 90.072637 \n",
       "L 113.399755 89.548972 \n",
       "L 115.857813 89.139422 \n",
       "L 121.089063 88.288816 \n",
       "L 126.320313 87.459213 \n",
       "L 131.551562 86.650613 \n",
       "L 136.015563 85.978529 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_3\">\n",
       "    <path clip-path=\"url(#pff06d154f3)\" d=\"M 377.420313 179.519044 \n",
       "L 372.189063 179.605755 \n",
       "L 366.957812 179.682264 \n",
       "L 361.726562 179.748573 \n",
       "L 356.495313 179.80468 \n",
       "L 351.264063 179.850585 \n",
       "L 346.032813 179.88629 \n",
       "L 340.801562 179.911793 \n",
       "L 335.570312 179.927095 \n",
       "L 330.339063 179.932196 \n",
       "L 325.107813 179.927095 \n",
       "L 319.876563 179.911793 \n",
       "L 314.645312 179.88629 \n",
       "L 309.414062 179.850585 \n",
       "L 304.182813 179.80468 \n",
       "L 298.951563 179.748573 \n",
       "L 293.720313 179.682264 \n",
       "L 288.489062 179.605755 \n",
       "L 283.257812 179.519044 \n",
       "L 278.026563 179.422132 \n",
       "L 272.795313 179.315019 \n",
       "L 267.564063 179.197704 \n",
       "L 262.332813 179.070188 \n",
       "L 257.101562 178.932471 \n",
       "L 252.772252 178.810056 \n",
       "L 251.870313 178.783007 \n",
       "L 246.639063 178.615305 \n",
       "L 241.407813 178.436783 \n",
       "L 236.176563 178.247441 \n",
       "L 230.945313 178.04728 \n",
       "L 225.714063 177.836299 \n",
       "L 220.482813 177.614499 \n",
       "L 215.251563 177.381879 \n",
       "L 210.020313 177.13844 \n",
       "L 204.789062 176.884181 \n",
       "L 199.557813 176.619102 \n",
       "L 194.326563 176.343204 \n",
       "L 189.095313 176.056487 \n",
       "L 183.864063 175.75895 \n",
       "L 178.632813 175.450594 \n",
       "L 175.174868 175.239613 \n",
       "L 173.401563 175.124437 \n",
       "L 168.170313 174.773152 \n",
       "L 162.939063 174.410349 \n",
       "L 157.707813 174.036028 \n",
       "L 152.476563 173.65019 \n",
       "L 147.245313 173.252834 \n",
       "L 142.014063 172.843961 \n",
       "L 136.782813 172.42357 \n",
       "L 131.551563 171.991661 \n",
       "L 127.747017 171.669169 \n",
       "L 126.320313 171.539895 \n",
       "L 121.089063 171.053576 \n",
       "L 115.857813 170.554945 \n",
       "L 110.626563 170.044002 \n",
       "L 105.395313 169.520748 \n",
       "L 100.164063 168.985181 \n",
       "L 94.932813 168.437303 \n",
       "L 91.771068 168.098726 \n",
       "L 89.701563 167.860697 \n",
       "L 84.470313 167.245787 \n",
       "L 79.239063 166.617653 \n",
       "L 74.007812 165.976296 \n",
       "L 68.776563 165.321715 \n",
       "L 63.545313 164.653909 \n",
       "L 62.580325 164.528283 \n",
       "L 58.314063 163.928448 \n",
       "L 53.082813 163.178655 \n",
       "L 47.851562 162.41458 \n",
       "L 42.620313 161.636224 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_4\">\n",
       "    <path clip-path=\"url(#pff06d154f3)\" d=\"M 377.420313 193.502846 \n",
       "L 372.189063 193.573424 \n",
       "L 366.957812 193.635699 \n",
       "L 361.726562 193.689671 \n",
       "L 356.495313 193.73534 \n",
       "L 351.264063 193.772705 \n",
       "L 346.032813 193.801767 \n",
       "L 340.801562 193.822525 \n",
       "L 335.570312 193.83498 \n",
       "L 330.339063 193.839132 \n",
       "L 325.107813 193.83498 \n",
       "L 319.876563 193.822525 \n",
       "L 314.645312 193.801767 \n",
       "L 309.414062 193.772705 \n",
       "L 304.182813 193.73534 \n",
       "L 298.951563 193.689671 \n",
       "L 293.720313 193.635699 \n",
       "L 288.489062 193.573424 \n",
       "L 283.257812 193.502846 \n",
       "L 278.026563 193.423964 \n",
       "L 272.795313 193.336779 \n",
       "L 267.564063 193.24129 \n",
       "L 262.332813 193.137498 \n",
       "L 260.201562 193.09183 \n",
       "L 257.101562 193.022162 \n",
       "L 251.870313 192.895891 \n",
       "L 246.639063 192.76091 \n",
       "L 241.407813 192.617222 \n",
       "L 236.176563 192.464825 \n",
       "L 230.945312 192.30372 \n",
       "L 225.714063 192.133906 \n",
       "L 220.482813 191.955384 \n",
       "L 215.251563 191.768153 \n",
       "L 210.020313 191.572214 \n",
       "L 204.789062 191.367567 \n",
       "L 199.557813 191.154211 \n",
       "L 194.326563 190.932147 \n",
       "L 189.095313 190.701374 \n",
       "L 183.864063 190.461893 \n",
       "L 178.632813 190.213704 \n",
       "L 173.401563 189.956806 \n",
       "L 168.170313 189.6912 \n",
       "L 164.93192 189.521386 \n",
       "L 162.939063 189.411526 \n",
       "L 157.707813 189.113989 \n",
       "L 152.476563 188.807298 \n",
       "L 147.245313 188.491451 \n",
       "L 142.014063 188.166449 \n",
       "L 136.782813 187.832292 \n",
       "L 131.551563 187.48898 \n",
       "L 126.320313 187.136513 \n",
       "L 121.089063 186.774891 \n",
       "L 115.857813 186.404115 \n",
       "L 110.626563 186.024183 \n",
       "L 109.641857 185.950943 \n",
       "L 105.395313 185.618023 \n",
       "L 100.164063 185.198255 \n",
       "L 94.932813 184.768837 \n",
       "L 89.701563 184.329769 \n",
       "L 84.470313 183.881051 \n",
       "L 79.239063 183.422683 \n",
       "L 74.007812 182.954665 \n",
       "L 68.776563 182.476998 \n",
       "L 67.740671 182.3805 \n",
       "L 63.545313 181.967348 \n",
       "L 58.314063 181.441983 \n",
       "L 53.082813 180.906416 \n",
       "L 47.851562 180.360649 \n",
       "L 42.620313 179.80468 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_5\">\n",
       "    <path clip-path=\"url(#pff06d154f3)\" d=\"M 377.420313 205.25684 \n",
       "L 372.189063 205.318776 \n",
       "L 366.957812 205.373426 \n",
       "L 361.726562 205.420789 \n",
       "L 356.495313 205.460865 \n",
       "L 351.264063 205.493655 \n",
       "L 346.032813 205.519158 \n",
       "L 340.801562 205.537375 \n",
       "L 335.570312 205.548305 \n",
       "L 330.339063 205.551948 \n",
       "L 325.107813 205.548305 \n",
       "L 319.876563 205.537375 \n",
       "L 314.645312 205.519158 \n",
       "L 309.414062 205.493655 \n",
       "L 304.182813 205.460865 \n",
       "L 298.951563 205.420789 \n",
       "L 293.720313 205.373426 \n",
       "L 288.489062 205.318776 \n",
       "L 283.257812 205.25684 \n",
       "L 278.026563 205.187617 \n",
       "L 272.795313 205.111108 \n",
       "L 267.564063 205.027312 \n",
       "L 262.332813 204.936229 \n",
       "L 257.101562 204.83786 \n",
       "L 251.870313 204.732204 \n",
       "L 246.639063 204.619261 \n",
       "L 241.407813 204.499032 \n",
       "L 236.176563 204.371516 \n",
       "L 230.945312 204.236713 \n",
       "L 225.714063 204.094624 \n",
       "L 220.482813 203.945249 \n",
       "L 215.73819 203.80316 \n",
       "L 215.251563 203.787966 \n",
       "L 210.020313 203.617041 \n",
       "L 204.789062 203.438519 \n",
       "L 199.557813 203.2524 \n",
       "L 194.326563 203.058684 \n",
       "L 189.095313 202.857372 \n",
       "L 183.864063 202.648463 \n",
       "L 178.632813 202.431957 \n",
       "L 173.401563 202.207855 \n",
       "L 168.170313 201.976156 \n",
       "L 162.939063 201.736861 \n",
       "L 157.707813 201.489968 \n",
       "L 152.476563 201.235479 \n",
       "L 147.245313 200.973393 \n",
       "L 142.014063 200.703711 \n",
       "L 136.782813 200.426432 \n",
       "L 133.225562 200.232716 \n",
       "L 131.551563 200.137504 \n",
       "L 126.320312 199.832033 \n",
       "L 121.089063 199.518628 \n",
       "L 115.857813 199.197288 \n",
       "L 110.626563 198.868013 \n",
       "L 105.395313 198.530805 \n",
       "L 100.164063 198.185662 \n",
       "L 94.932813 197.832585 \n",
       "L 89.701563 197.471573 \n",
       "L 84.470313 197.102628 \n",
       "L 79.239063 196.725747 \n",
       "L 78.376176 196.662273 \n",
       "L 74.007812 196.325987 \n",
       "L 68.776563 195.914971 \n",
       "L 63.545313 195.495651 \n",
       "L 58.314063 195.068028 \n",
       "L 53.082813 194.632102 \n",
       "L 47.851562 194.187873 \n",
       "L 42.620313 193.73534 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_6\">\n",
       "    <path clip-path=\"url(#pff06d154f3)\" d=\"M 377.420313 215.614835 \n",
       "L 372.189063 215.670015 \n",
       "L 366.957812 215.718703 \n",
       "L 361.726562 215.760899 \n",
       "L 356.495313 215.796603 \n",
       "L 351.264063 215.825816 \n",
       "L 346.032813 215.848537 \n",
       "L 340.801562 215.864766 \n",
       "L 335.570312 215.874504 \n",
       "L 330.339063 215.87775 \n",
       "L 325.107813 215.874504 \n",
       "L 319.876563 215.864766 \n",
       "L 314.645312 215.848537 \n",
       "L 309.414062 215.825816 \n",
       "L 304.182813 215.796603 \n",
       "L 298.951563 215.760899 \n",
       "L 293.720313 215.718703 \n",
       "L 288.489062 215.670015 \n",
       "L 283.257812 215.614835 \n",
       "L 278.026563 215.553164 \n",
       "L 272.795313 215.485001 \n",
       "L 267.564063 215.410346 \n",
       "L 262.332813 215.3292 \n",
       "L 257.101562 215.241562 \n",
       "L 251.870313 215.147432 \n",
       "L 246.639063 215.04681 \n",
       "L 241.407813 214.939697 \n",
       "L 236.176563 214.826092 \n",
       "L 230.945312 214.705995 \n",
       "L 225.714063 214.579407 \n",
       "L 223.162233 214.51449 \n",
       "L 220.482813 214.443754 \n",
       "L 215.251563 214.298916 \n",
       "L 210.020313 214.14734 \n",
       "L 204.789062 213.989028 \n",
       "L 199.557813 213.823979 \n",
       "L 194.326563 213.652194 \n",
       "L 189.095313 213.473672 \n",
       "L 183.864063 213.288413 \n",
       "L 178.632813 213.096417 \n",
       "L 173.401563 212.897685 \n",
       "L 168.170313 212.692216 \n",
       "L 162.939063 212.480011 \n",
       "L 157.707813 212.261068 \n",
       "L 152.476563 212.035389 \n",
       "L 147.245313 211.802974 \n",
       "L 142.014063 211.563821 \n",
       "L 136.782813 211.317932 \n",
       "L 131.551563 211.065307 \n",
       "L 129.105783 210.944046 \n",
       "L 126.320313 210.800529 \n",
       "L 121.089063 210.523994 \n",
       "L 115.857813 210.240459 \n",
       "L 110.626563 209.949923 \n",
       "L 105.395313 209.652386 \n",
       "L 100.164063 209.347848 \n",
       "L 94.932813 209.036309 \n",
       "L 89.701563 208.71777 \n",
       "L 84.470313 208.392229 \n",
       "L 79.239063 208.059688 \n",
       "L 74.007812 207.720146 \n",
       "L 68.776563 207.373603 \n",
       "L 68.776562 207.373603 \n",
       "L 63.545313 207.005629 \n",
       "L 58.314063 206.630368 \n",
       "L 53.082813 206.24782 \n",
       "L 47.851562 205.857986 \n",
       "L 42.620313 205.460865 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_7\">\n",
       "    <path clip-path=\"url(#pff06d154f3)\" d=\"M 330.339063 225.22582 \n",
       "L 325.107813 225.222794 \n",
       "L 319.876563 225.213717 \n",
       "L 314.645312 225.198588 \n",
       "L 309.414062 225.177407 \n",
       "L 304.182813 225.150175 \n",
       "L 298.951563 225.116891 \n",
       "L 293.720313 225.077556 \n",
       "L 288.489062 225.032169 \n",
       "L 283.257812 224.98073 \n",
       "L 278.026563 224.92324 \n",
       "L 272.795313 224.859698 \n",
       "L 267.564063 224.790105 \n",
       "L 262.332813 224.71446 \n",
       "L 257.101562 224.632763 \n",
       "L 251.870313 224.545015 \n",
       "L 246.639063 224.451215 \n",
       "L 241.407813 224.351364 \n",
       "L 236.176563 224.245461 \n",
       "L 230.945312 224.133506 \n",
       "L 225.714063 224.0155 \n",
       "L 220.482813 223.891442 \n",
       "L 215.251563 223.761333 \n",
       "L 210.020313 223.625172 \n",
       "L 204.789062 223.482959 \n",
       "L 199.557813 223.334695 \n",
       "L 194.326563 223.180379 \n",
       "L 189.095313 223.020012 \n",
       "L 183.864063 222.853593 \n",
       "L 178.632813 222.681122 \n",
       "L 173.401563 222.5026 \n",
       "L 168.170313 222.318026 \n",
       "L 162.939063 222.127401 \n",
       "L 157.707813 221.930724 \n",
       "L 152.476563 221.727996 \n",
       "L 150.656997 221.655376 \n",
       "L 147.245313 221.514438 \n",
       "L 142.014063 221.292068 \n",
       "L 136.782813 221.063434 \n",
       "L 131.551563 220.828537 \n",
       "L 126.320313 220.587375 \n",
       "L 121.089063 220.33995 \n",
       "L 115.857813 220.08626 \n",
       "L 110.626563 219.826307 \n",
       "L 105.395313 219.56009 \n",
       "L 100.164063 219.287609 \n",
       "L 94.932813 219.008864 \n",
       "L 89.701563 218.723854 \n",
       "L 84.470313 218.432581 \n",
       "L 79.239063 218.135045 \n",
       "L 78.376176 218.084933 \n",
       "L 74.007812 217.822019 \n",
       "L 68.776563 217.500679 \n",
       "L 63.545313 217.172847 \n",
       "L 58.314063 216.838524 \n",
       "L 53.082813 216.497709 \n",
       "L 47.851562 216.150402 \n",
       "L 42.620313 215.796603 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pff06d154f3)\" d=\"M 377.420313 224.98073 \n",
       "L 372.189063 225.032169 \n",
       "L 366.957812 225.077556 \n",
       "L 361.726562 225.116891 \n",
       "L 356.495313 225.150175 \n",
       "L 351.264063 225.177407 \n",
       "L 346.032813 225.198588 \n",
       "L 340.801562 225.213717 \n",
       "L 335.570312 225.222794 \n",
       "L 330.339063 225.22582 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_8\">\n",
       "    <path clip-path=\"url(#pff06d154f3)\" d=\"M 43.82014 225.22582 \n",
       "L 42.620313 225.150175 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_9\"/>\n",
       "   <g id=\"line2d_14\">\n",
       "    <path clip-path=\"url(#pff06d154f3)\" d=\"M 68.776563 189.521386 \n",
       "L 100.164063 18.140105 \n",
       "L 143.478813 172.383258 \n",
       "L 187.559418 119.255061 \n",
       "L 226.733277 89.948862 \n",
       "L 258.752902 142.88854 \n",
       "L 283.353053 109.895929 \n",
       "L 301.29145 113.11944 \n",
       "L 313.746362 126.714586 \n",
       "L 321.964942 112.867199 \n",
       "L 327.079126 118.532274 \n",
       "L 330.027411 120.3574 \n",
       "L 331.538951 115.882249 \n",
       "L 332.150735 118.997322 \n",
       "L 332.239226 118.431332 \n",
       "L 332.055452 117.383187 \n",
       "L 331.757598 118.609512 \n",
       "L 331.438447 118.029892 \n",
       "L 331.146945 117.938387 \n",
       "L 330.904248 118.310552 \n",
       "L 330.715078 118.021356 \n",
       "\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    <defs>\n",
       "     <path d=\"M 0 3 \n",
       "C 0.795609 3 1.55874 2.683901 2.12132 2.12132 \n",
       "C 2.683901 1.55874 3 0.795609 3 0 \n",
       "C 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \n",
       "C 1.55874 -2.683901 0.795609 -3 0 -3 \n",
       "C -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \n",
       "C -2.683901 -1.55874 -3 -0.795609 -3 0 \n",
       "C -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \n",
       "C -1.55874 2.683901 -0.795609 3 0 3 \n",
       "z\n",
       "\" id=\"mf2403a2ac9\" style=\"stroke:#ff7f0e;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#pff06d154f3)\">\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"68.776563\" xlink:href=\"#mf2403a2ac9\" y=\"189.521386\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"100.164063\" xlink:href=\"#mf2403a2ac9\" y=\"18.140105\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"143.478813\" xlink:href=\"#mf2403a2ac9\" y=\"172.383258\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"187.559418\" xlink:href=\"#mf2403a2ac9\" y=\"119.255061\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"226.733277\" xlink:href=\"#mf2403a2ac9\" y=\"89.948862\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"258.752902\" xlink:href=\"#mf2403a2ac9\" y=\"142.88854\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"283.353053\" xlink:href=\"#mf2403a2ac9\" y=\"109.895929\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"301.29145\" xlink:href=\"#mf2403a2ac9\" y=\"113.11944\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"313.746362\" xlink:href=\"#mf2403a2ac9\" y=\"126.714586\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"321.964942\" xlink:href=\"#mf2403a2ac9\" y=\"112.867199\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"327.079126\" xlink:href=\"#mf2403a2ac9\" y=\"118.532274\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"330.027411\" xlink:href=\"#mf2403a2ac9\" y=\"120.3574\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"331.538951\" xlink:href=\"#mf2403a2ac9\" y=\"115.882249\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"332.150735\" xlink:href=\"#mf2403a2ac9\" y=\"118.997322\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"332.239226\" xlink:href=\"#mf2403a2ac9\" y=\"118.431332\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"332.055452\" xlink:href=\"#mf2403a2ac9\" y=\"117.383187\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"331.757598\" xlink:href=\"#mf2403a2ac9\" y=\"118.609512\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"331.438447\" xlink:href=\"#mf2403a2ac9\" y=\"118.029892\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"331.146945\" xlink:href=\"#mf2403a2ac9\" y=\"117.938387\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"330.904248\" xlink:href=\"#mf2403a2ac9\" y=\"118.310552\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"330.715078\" xlink:href=\"#mf2403a2ac9\" y=\"118.021356\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 42.620313 225.22582 \n",
       "L 42.620313 7.78582 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 377.420313 225.22582 \n",
       "L 377.420313 7.78582 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 42.620313 225.22582 \n",
       "L 377.420313 225.22582 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 42.620313 7.78582 \n",
       "L 377.420313 7.78582 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"pff06d154f3\">\n",
       "   <rect height=\"217.44\" width=\"334.8\" x=\"42.620313\" y=\"7.78582\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "使用学习率0.6 也不在发散了\n",
    "\"\"\"\n",
    "\n",
    "eta = 0.6\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(momentum_2d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -2.382563, x2 -0.158591\n"
     ]
    },
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"262.19625pt\" version=\"1.1\" viewBox=\"0 0 394.160937 262.19625\" width=\"394.160937pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 262.19625 \n",
       "L 394.160937 262.19625 \n",
       "L 394.160937 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 52.160938 224.64 \n",
       "L 386.960938 224.64 \n",
       "L 386.960938 7.2 \n",
       "L 52.160938 7.2 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"m34bd6f35e4\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"78.317188\" xlink:href=\"#m34bd6f35e4\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- −5 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.59375 35.5 \n",
       "L 73.1875 35.5 \n",
       "L 73.1875 27.203125 \n",
       "L 10.59375 27.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-8722\"/>\n",
       "       <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(70.946094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"130.629688\" xlink:href=\"#m34bd6f35e4\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- −4 -->\n",
       "      <defs>\n",
       "       <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(123.258594 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"182.942188\" xlink:href=\"#m34bd6f35e4\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- −3 -->\n",
       "      <defs>\n",
       "       <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(175.571094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"235.254688\" xlink:href=\"#m34bd6f35e4\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- −2 -->\n",
       "      <defs>\n",
       "       <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(227.883594 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"287.567188\" xlink:href=\"#m34bd6f35e4\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- −1 -->\n",
       "      <defs>\n",
       "       <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(280.196094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"339.879688\" xlink:href=\"#m34bd6f35e4\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(336.698438 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_7\">\n",
       "     <!-- x1 -->\n",
       "     <defs>\n",
       "      <path d=\"M 54.890625 54.6875 \n",
       "L 35.109375 28.078125 \n",
       "L 55.90625 0 \n",
       "L 45.3125 0 \n",
       "L 29.390625 21.484375 \n",
       "L 13.484375 0 \n",
       "L 2.875 0 \n",
       "L 24.125 28.609375 \n",
       "L 4.6875 54.6875 \n",
       "L 15.28125 54.6875 \n",
       "L 29.78125 35.203125 \n",
       "L 44.28125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-120\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(213.420313 252.916562)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"m5b9c202f0b\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5b9c202f0b\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- −3.0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.6875 12.40625 \n",
       "L 21 12.40625 \n",
       "L 21 0 \n",
       "L 10.6875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-46\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(20.878125 228.439219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5b9c202f0b\" y=\"196.763077\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- −2.5 -->\n",
       "      <g transform=\"translate(20.878125 200.562296)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5b9c202f0b\" y=\"168.886154\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- −2.0 -->\n",
       "      <g transform=\"translate(20.878125 172.685373)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5b9c202f0b\" y=\"141.009231\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- −1.5 -->\n",
       "      <g transform=\"translate(20.878125 144.80845)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5b9c202f0b\" y=\"113.132308\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- −1.0 -->\n",
       "      <g transform=\"translate(20.878125 116.931526)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5b9c202f0b\" y=\"85.255385\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- −0.5 -->\n",
       "      <g transform=\"translate(20.878125 89.054603)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5b9c202f0b\" y=\"57.378462\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_14\">\n",
       "      <!-- 0.0 -->\n",
       "      <g transform=\"translate(29.257812 61.17768)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_8\">\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5b9c202f0b\" y=\"29.501538\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- 0.5 -->\n",
       "      <g transform=\"translate(29.257812 33.300757)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_16\">\n",
       "     <!-- x2 -->\n",
       "     <g transform=\"translate(14.798438 122.060625)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_1\"/>\n",
       "   <g id=\"LineCollection_2\">\n",
       "    <path clip-path=\"url(#p55e78729d1)\" d=\"M 386.960938 124.717957 \n",
       "L 381.729688 124.90752 \n",
       "L 376.498437 125.074782 \n",
       "L 371.267187 125.219742 \n",
       "L 366.035937 125.3424 \n",
       "L 360.804688 125.442757 \n",
       "L 355.573438 125.520812 \n",
       "L 350.342187 125.576566 \n",
       "L 345.110937 125.610018 \n",
       "L 339.879687 125.621169 \n",
       "L 334.648438 125.610018 \n",
       "L 329.417188 125.576566 \n",
       "L 324.185937 125.520812 \n",
       "L 318.954687 125.442757 \n",
       "L 313.723437 125.3424 \n",
       "L 308.492188 125.219742 \n",
       "L 303.260938 125.074782 \n",
       "L 298.029687 124.90752 \n",
       "L 292.798437 124.717957 \n",
       "L 287.567187 124.506092 \n",
       "L 282.585045 124.283077 \n",
       "L 282.335938 124.270957 \n",
       "L 277.104688 123.992187 \n",
       "L 271.873438 123.689177 \n",
       "L 266.642187 123.361926 \n",
       "L 261.410937 123.010435 \n",
       "L 256.179688 122.634702 \n",
       "L 250.948437 122.234729 \n",
       "L 245.717187 121.810515 \n",
       "L 240.485937 121.36206 \n",
       "L 235.254687 120.889365 \n",
       "L 230.023438 120.392428 \n",
       "L 224.792188 119.871251 \n",
       "L 219.560937 119.325833 \n",
       "L 214.329687 118.756174 \n",
       "L 213.902647 118.707692 \n",
       "L 209.098437 118.11033 \n",
       "L 203.867188 117.433319 \n",
       "L 198.635937 116.729758 \n",
       "L 193.404687 115.999648 \n",
       "L 188.173438 115.242989 \n",
       "L 182.942187 114.45978 \n",
       "L 177.710938 113.650022 \n",
       "L 174.472545 113.132308 \n",
       "L 172.479688 112.780178 \n",
       "L 167.248437 111.826494 \n",
       "L 162.017188 110.843466 \n",
       "L 156.785937 109.831093 \n",
       "L 151.554688 108.789377 \n",
       "L 146.323437 107.718316 \n",
       "L 145.556187 107.556923 \n",
       "L 141.092187 106.507439 \n",
       "L 135.860938 105.244778 \n",
       "L 130.629687 103.949321 \n",
       "L 125.398438 102.621068 \n",
       "L 122.94038 101.981538 \n",
       "L 120.167187 101.163815 \n",
       "L 114.935937 99.584123 \n",
       "L 109.704688 97.967262 \n",
       "L 104.767328 96.406154 \n",
       "L 104.473437 96.298935 \n",
       "L 99.242188 94.34755 \n",
       "L 94.010937 92.353278 \n",
       "L 90.101266 90.830769 \n",
       "L 88.779687 90.222545 \n",
       "L 83.548437 87.764308 \n",
       "L 78.317187 85.255385 \n",
       "L 78.317187 85.255385 \n",
       "L 73.085938 82.126974 \n",
       "L 69.07362 79.68 \n",
       "L 67.854688 78.72422 \n",
       "L 62.623438 74.542681 \n",
       "L 62.085645 74.104615 \n",
       "L 57.392187 68.752246 \n",
       "L 57.200215 68.529231 \n",
       "L 54.320628 62.953846 \n",
       "L 53.360765 57.378462 \n",
       "L 54.320628 51.803077 \n",
       "L 57.200215 46.227692 \n",
       "L 57.392187 46.004677 \n",
       "L 62.085645 40.652308 \n",
       "L 62.623438 40.214242 \n",
       "L 67.854688 36.032703 \n",
       "L 69.07362 35.076923 \n",
       "L 73.085938 32.629949 \n",
       "L 78.317187 29.501538 \n",
       "L 78.317188 29.501538 \n",
       "L 83.548437 26.992615 \n",
       "L 88.779687 24.534378 \n",
       "L 90.101266 23.926154 \n",
       "L 94.010937 22.403645 \n",
       "L 99.242188 20.409373 \n",
       "L 104.473437 18.457988 \n",
       "L 104.767328 18.350769 \n",
       "L 109.704688 16.789662 \n",
       "L 114.935937 15.1728 \n",
       "L 120.167187 13.593108 \n",
       "L 122.94038 12.775385 \n",
       "L 125.398438 12.135855 \n",
       "L 130.629687 10.807602 \n",
       "L 135.860938 9.512145 \n",
       "L 141.092187 8.249484 \n",
       "L 145.556188 7.2 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_3\">\n",
       "    <path clip-path=\"url(#p55e78729d1)\" d=\"M 386.960938 153.267112 \n",
       "L 381.729688 153.402514 \n",
       "L 376.498437 153.521987 \n",
       "L 371.267187 153.62553 \n",
       "L 366.035937 153.713143 \n",
       "L 360.804688 153.784826 \n",
       "L 355.573438 153.84058 \n",
       "L 350.342187 153.880404 \n",
       "L 345.110937 153.904299 \n",
       "L 339.879687 153.912264 \n",
       "L 334.648438 153.904299 \n",
       "L 329.417188 153.880404 \n",
       "L 324.185937 153.84058 \n",
       "L 318.954687 153.784826 \n",
       "L 313.723437 153.713143 \n",
       "L 308.492188 153.62553 \n",
       "L 303.260938 153.521987 \n",
       "L 298.029687 153.402514 \n",
       "L 292.798437 153.267112 \n",
       "L 287.567187 153.11578 \n",
       "L 282.335938 152.948519 \n",
       "L 277.104688 152.765327 \n",
       "L 271.873438 152.566207 \n",
       "L 266.642187 152.351156 \n",
       "L 262.312877 152.16 \n",
       "L 261.410937 152.117762 \n",
       "L 256.179688 151.855888 \n",
       "L 250.948438 151.577119 \n",
       "L 245.717188 151.281455 \n",
       "L 240.485938 150.968895 \n",
       "L 235.254687 150.639441 \n",
       "L 230.023438 150.293091 \n",
       "L 224.792188 149.929846 \n",
       "L 219.560937 149.549706 \n",
       "L 214.329687 149.152671 \n",
       "L 209.098437 148.738741 \n",
       "L 203.867188 148.307916 \n",
       "L 198.635937 147.860196 \n",
       "L 193.404687 147.39558 \n",
       "L 188.173438 146.91407 \n",
       "L 184.715493 146.584615 \n",
       "L 182.942187 146.404764 \n",
       "L 177.710938 145.856218 \n",
       "L 172.479687 145.289687 \n",
       "L 167.248437 144.705171 \n",
       "L 162.017188 144.10267 \n",
       "L 156.785937 143.482184 \n",
       "L 151.554688 142.843712 \n",
       "L 146.323437 142.187256 \n",
       "L 141.092187 141.512814 \n",
       "L 137.287642 141.009231 \n",
       "L 135.860938 140.807363 \n",
       "L 130.629687 140.047958 \n",
       "L 125.398438 139.269326 \n",
       "L 120.167187 138.471469 \n",
       "L 114.935937 137.654387 \n",
       "L 109.704688 136.81808 \n",
       "L 104.473437 135.962546 \n",
       "L 101.311693 135.433846 \n",
       "L 99.242188 135.062154 \n",
       "L 94.010937 134.101949 \n",
       "L 88.779687 133.121094 \n",
       "L 83.548437 132.11959 \n",
       "L 78.317187 131.097436 \n",
       "L 73.085938 130.054632 \n",
       "L 72.12095 129.858462 \n",
       "L 67.854688 128.921797 \n",
       "L 62.623438 127.750966 \n",
       "L 57.392187 126.557834 \n",
       "L 52.160937 125.3424 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_4\">\n",
       "    <path clip-path=\"url(#p55e78729d1)\" d=\"M 386.960938 175.103356 \n",
       "L 381.729688 175.213567 \n",
       "L 376.498437 175.310812 \n",
       "L 371.267187 175.395091 \n",
       "L 366.035937 175.466404 \n",
       "L 360.804688 175.524751 \n",
       "L 355.573438 175.570132 \n",
       "L 350.342187 175.602547 \n",
       "L 345.110937 175.621996 \n",
       "L 339.879687 175.628479 \n",
       "L 334.648438 175.621996 \n",
       "L 329.417188 175.602547 \n",
       "L 324.185937 175.570132 \n",
       "L 318.954687 175.524751 \n",
       "L 313.723437 175.466404 \n",
       "L 308.492188 175.395091 \n",
       "L 303.260938 175.310812 \n",
       "L 298.029687 175.213567 \n",
       "L 292.798437 175.103356 \n",
       "L 287.567187 174.980179 \n",
       "L 282.335938 174.844036 \n",
       "L 277.104688 174.694927 \n",
       "L 271.873438 174.532852 \n",
       "L 269.742187 174.461538 \n",
       "L 266.642187 174.35275 \n",
       "L 261.410937 174.155572 \n",
       "L 256.179688 173.944795 \n",
       "L 250.948438 173.72042 \n",
       "L 245.717187 173.482447 \n",
       "L 240.485937 173.230874 \n",
       "L 235.254687 172.965704 \n",
       "L 230.023438 172.686934 \n",
       "L 224.792188 172.394567 \n",
       "L 219.560937 172.0886 \n",
       "L 214.329687 171.769036 \n",
       "L 209.098437 171.435872 \n",
       "L 203.867188 171.089111 \n",
       "L 198.635937 170.72875 \n",
       "L 193.404687 170.354792 \n",
       "L 188.173438 169.967235 \n",
       "L 182.942187 169.566079 \n",
       "L 177.710938 169.151325 \n",
       "L 174.472545 168.886154 \n",
       "L 172.479687 168.714604 \n",
       "L 167.248437 168.249988 \n",
       "L 162.017188 167.771077 \n",
       "L 156.785937 167.27787 \n",
       "L 151.554688 166.770367 \n",
       "L 146.323437 166.248568 \n",
       "L 141.092187 165.712473 \n",
       "L 135.860938 165.162083 \n",
       "L 130.629687 164.597396 \n",
       "L 125.398438 164.018414 \n",
       "L 120.167187 163.425136 \n",
       "L 119.182482 163.310769 \n",
       "L 114.935937 162.790902 \n",
       "L 109.704688 162.135418 \n",
       "L 104.473437 161.464865 \n",
       "L 99.242188 160.779243 \n",
       "L 94.010937 160.078553 \n",
       "L 88.779687 159.362794 \n",
       "L 83.548437 158.631967 \n",
       "L 78.317187 157.886071 \n",
       "L 77.281296 157.735385 \n",
       "L 73.085938 157.090233 \n",
       "L 67.854688 156.269855 \n",
       "L 62.623438 155.433547 \n",
       "L 57.392187 154.58131 \n",
       "L 52.160937 153.713143 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_5\">\n",
       "    <path clip-path=\"url(#p55e78729d1)\" d=\"M 386.960938 193.45767 \n",
       "L 381.729688 193.554386 \n",
       "L 376.498437 193.639724 \n",
       "L 371.267187 193.713683 \n",
       "L 366.035937 193.776264 \n",
       "L 360.804688 193.827466 \n",
       "L 355.573438 193.86729 \n",
       "L 350.342187 193.895736 \n",
       "L 345.110937 193.912804 \n",
       "L 339.879687 193.918493 \n",
       "L 334.648438 193.912804 \n",
       "L 329.417188 193.895736 \n",
       "L 324.185937 193.86729 \n",
       "L 318.954687 193.827466 \n",
       "L 313.723437 193.776264 \n",
       "L 308.492188 193.713683 \n",
       "L 303.260938 193.639724 \n",
       "L 298.029687 193.554386 \n",
       "L 292.798437 193.45767 \n",
       "L 287.567187 193.349576 \n",
       "L 282.335938 193.230104 \n",
       "L 277.104688 193.099253 \n",
       "L 271.873438 192.957024 \n",
       "L 266.642187 192.803416 \n",
       "L 261.410937 192.63843 \n",
       "L 256.179688 192.462066 \n",
       "L 250.948438 192.274323 \n",
       "L 245.717187 192.075203 \n",
       "L 240.485937 191.864703 \n",
       "L 235.254687 191.642826 \n",
       "L 230.023438 191.40957 \n",
       "L 225.278815 191.187692 \n",
       "L 224.792188 191.163967 \n",
       "L 219.560937 190.897061 \n",
       "L 214.329687 190.618291 \n",
       "L 209.098437 190.32766 \n",
       "L 203.867188 190.025165 \n",
       "L 198.635937 189.710809 \n",
       "L 193.404687 189.384589 \n",
       "L 188.173438 189.046507 \n",
       "L 182.942187 188.696563 \n",
       "L 177.710938 188.334756 \n",
       "L 172.479687 187.961087 \n",
       "L 167.248437 187.575555 \n",
       "L 162.017188 187.17816 \n",
       "L 156.785937 186.768903 \n",
       "L 151.554688 186.347784 \n",
       "L 146.323437 185.914802 \n",
       "L 142.766187 185.612308 \n",
       "L 141.092187 185.463631 \n",
       "L 135.860937 184.986626 \n",
       "L 130.629687 184.497231 \n",
       "L 125.398438 183.995446 \n",
       "L 120.167187 183.481272 \n",
       "L 114.935937 182.954708 \n",
       "L 109.704688 182.415754 \n",
       "L 104.473437 181.86441 \n",
       "L 99.242188 181.300677 \n",
       "L 94.010937 180.724554 \n",
       "L 88.779687 180.136041 \n",
       "L 87.916801 180.036923 \n",
       "L 83.548437 179.5118 \n",
       "L 78.317187 178.869982 \n",
       "L 73.085938 178.215199 \n",
       "L 67.854688 177.547449 \n",
       "L 62.623438 176.866733 \n",
       "L 57.392187 176.173052 \n",
       "L 52.160937 175.466404 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_6\">\n",
       "    <path clip-path=\"url(#p55e78729d1)\" d=\"M 386.960938 209.632078 \n",
       "L 381.729688 209.718243 \n",
       "L 376.498437 209.794271 \n",
       "L 371.267187 209.860162 \n",
       "L 366.035937 209.915916 \n",
       "L 360.804688 209.961533 \n",
       "L 355.573438 209.997013 \n",
       "L 350.342187 210.022355 \n",
       "L 345.110937 210.037561 \n",
       "L 339.879687 210.042629 \n",
       "L 334.648438 210.037561 \n",
       "L 329.417188 210.022355 \n",
       "L 324.185937 209.997013 \n",
       "L 318.954687 209.961533 \n",
       "L 313.723437 209.915916 \n",
       "L 308.492188 209.860162 \n",
       "L 303.260938 209.794271 \n",
       "L 298.029687 209.718243 \n",
       "L 292.798437 209.632078 \n",
       "L 287.567187 209.535776 \n",
       "L 282.335938 209.429337 \n",
       "L 277.104688 209.312761 \n",
       "L 271.873438 209.186048 \n",
       "L 266.642187 209.049197 \n",
       "L 261.410937 208.90221 \n",
       "L 256.179688 208.745085 \n",
       "L 250.948438 208.577824 \n",
       "L 245.717187 208.400425 \n",
       "L 240.485937 208.21289 \n",
       "L 235.254687 208.015217 \n",
       "L 232.702858 207.913846 \n",
       "L 230.023438 207.80339 \n",
       "L 224.792188 207.577219 \n",
       "L 219.560937 207.340528 \n",
       "L 214.329687 207.093318 \n",
       "L 209.098437 206.835588 \n",
       "L 203.867188 206.567338 \n",
       "L 198.635937 206.288569 \n",
       "L 193.404687 205.99928 \n",
       "L 188.173438 205.699472 \n",
       "L 182.942187 205.389144 \n",
       "L 177.710938 205.068296 \n",
       "L 172.479687 204.736929 \n",
       "L 167.248437 204.395042 \n",
       "L 162.017188 204.042636 \n",
       "L 156.785937 203.67971 \n",
       "L 151.554688 203.306264 \n",
       "L 146.323437 202.922299 \n",
       "L 141.092187 202.527814 \n",
       "L 138.646408 202.338462 \n",
       "L 135.860938 202.114353 \n",
       "L 130.629687 201.682534 \n",
       "L 125.398438 201.239783 \n",
       "L 120.167187 200.7861 \n",
       "L 114.935937 200.321484 \n",
       "L 109.704688 199.845937 \n",
       "L 104.473437 199.359457 \n",
       "L 99.242188 198.862045 \n",
       "L 94.010937 198.353701 \n",
       "L 88.779687 197.834425 \n",
       "L 83.548437 197.304217 \n",
       "L 78.317187 196.763077 \n",
       "L 78.317187 196.763077 \n",
       "L 73.085938 196.188471 \n",
       "L 67.854688 195.602487 \n",
       "L 62.623438 195.005124 \n",
       "L 57.392187 194.396383 \n",
       "L 52.160937 193.776264 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_7\">\n",
       "    <path clip-path=\"url(#p55e78729d1)\" d=\"M 339.879687 224.64 \n",
       "L 334.648438 224.635275 \n",
       "L 329.417188 224.6211 \n",
       "L 324.185937 224.597476 \n",
       "L 318.954687 224.564402 \n",
       "L 313.723437 224.521877 \n",
       "L 308.492188 224.469904 \n",
       "L 303.260938 224.40848 \n",
       "L 298.029687 224.337606 \n",
       "L 292.798437 224.257283 \n",
       "L 287.567187 224.16751 \n",
       "L 282.335938 224.068287 \n",
       "L 277.104688 223.959614 \n",
       "L 271.873438 223.841492 \n",
       "L 266.642187 223.713919 \n",
       "L 261.410937 223.576897 \n",
       "L 256.179688 223.430425 \n",
       "L 250.948438 223.274503 \n",
       "L 245.717187 223.109132 \n",
       "L 240.485937 222.93431 \n",
       "L 235.254687 222.750039 \n",
       "L 230.023438 222.556318 \n",
       "L 224.792188 222.353147 \n",
       "L 219.560937 222.140527 \n",
       "L 214.329687 221.918456 \n",
       "L 209.098437 221.686936 \n",
       "L 203.867188 221.445966 \n",
       "L 198.635937 221.195546 \n",
       "L 193.404687 220.935677 \n",
       "L 188.173438 220.666357 \n",
       "L 182.942187 220.387588 \n",
       "L 177.710938 220.099369 \n",
       "L 172.479687 219.8017 \n",
       "L 167.248437 219.494581 \n",
       "L 162.017188 219.178013 \n",
       "L 160.197622 219.064615 \n",
       "L 156.785937 218.844534 \n",
       "L 151.554688 218.497296 \n",
       "L 146.323437 218.140275 \n",
       "L 141.092187 217.773474 \n",
       "L 135.860938 217.396891 \n",
       "L 130.629687 217.010526 \n",
       "L 125.398438 216.614381 \n",
       "L 120.167187 216.208453 \n",
       "L 114.935937 215.792745 \n",
       "L 109.704688 215.367255 \n",
       "L 104.473437 214.931984 \n",
       "L 99.242188 214.486931 \n",
       "L 94.010937 214.032097 \n",
       "L 88.779687 213.567482 \n",
       "L 87.916801 213.489231 \n",
       "L 83.548437 213.07868 \n",
       "L 78.317187 212.576895 \n",
       "L 73.085938 212.064973 \n",
       "L 67.854688 211.542915 \n",
       "L 62.623438 211.010719 \n",
       "L 57.392187 210.468386 \n",
       "L 52.160937 209.915916 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#p55e78729d1)\" d=\"M 386.960938 224.257283 \n",
       "L 381.729688 224.337606 \n",
       "L 376.498437 224.40848 \n",
       "L 371.267187 224.469904 \n",
       "L 366.035937 224.521877 \n",
       "L 360.804688 224.564402 \n",
       "L 355.573438 224.597476 \n",
       "L 350.342187 224.6211 \n",
       "L 345.110937 224.635275 \n",
       "L 339.879687 224.64 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_8\">\n",
       "    <path clip-path=\"url(#p55e78729d1)\" d=\"M 53.360765 224.64 \n",
       "L 52.160937 224.521877 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_9\"/>\n",
       "   <g id=\"line2d_15\">\n",
       "    <path clip-path=\"url(#p55e78729d1)\" d=\"M 78.317188 168.886154 \n",
       "L 99.242177 146.584616 \n",
       "L 113.409581 132.652955 \n",
       "L 124.654142 122.253454 \n",
       "L 134.171163 113.937166 \n",
       "L 142.513245 107.042156 \n",
       "L 149.988832 101.1992 \n",
       "L 156.790677 96.176142 \n",
       "L 163.048719 91.814739 \n",
       "L 168.855474 88.000652 \n",
       "L 174.279586 84.647559 \n",
       "L 179.373659 81.688035 \n",
       "L 184.179073 79.06798 \n",
       "L 188.72908 76.743049 \n",
       "L 193.050885 74.676263 \n",
       "L 197.16709 72.83636 \n",
       "L 201.096719 71.19661 \n",
       "L 204.85597 69.733959 \n",
       "L 208.458773 68.428372 \n",
       "L 211.917217 67.262342 \n",
       "L 215.241872 66.220495 \n",
       "\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    <defs>\n",
       "     <path d=\"M 0 3 \n",
       "C 0.795609 3 1.55874 2.683901 2.12132 2.12132 \n",
       "C 2.683901 1.55874 3 0.795609 3 0 \n",
       "C 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \n",
       "C 1.55874 -2.683901 0.795609 -3 0 -3 \n",
       "C -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \n",
       "C -2.683901 -1.55874 -3 -0.795609 -3 0 \n",
       "C -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \n",
       "C -1.55874 2.683901 -0.795609 3 0 3 \n",
       "z\n",
       "\" id=\"mcc7c03ac4c\" style=\"stroke:#ff7f0e;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#p55e78729d1)\">\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"78.317188\" xlink:href=\"#mcc7c03ac4c\" y=\"168.886154\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"99.242177\" xlink:href=\"#mcc7c03ac4c\" y=\"146.584616\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"113.409581\" xlink:href=\"#mcc7c03ac4c\" y=\"132.652955\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"124.654142\" xlink:href=\"#mcc7c03ac4c\" y=\"122.253454\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"134.171163\" xlink:href=\"#mcc7c03ac4c\" y=\"113.937166\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"142.513245\" xlink:href=\"#mcc7c03ac4c\" y=\"107.042156\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"149.988832\" xlink:href=\"#mcc7c03ac4c\" y=\"101.1992\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"156.790677\" xlink:href=\"#mcc7c03ac4c\" y=\"96.176142\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"163.048719\" xlink:href=\"#mcc7c03ac4c\" y=\"91.814739\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"168.855474\" xlink:href=\"#mcc7c03ac4c\" y=\"88.000652\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"174.279586\" xlink:href=\"#mcc7c03ac4c\" y=\"84.647559\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"179.373659\" xlink:href=\"#mcc7c03ac4c\" y=\"81.688035\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"184.179073\" xlink:href=\"#mcc7c03ac4c\" y=\"79.06798\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"188.72908\" xlink:href=\"#mcc7c03ac4c\" y=\"76.743049\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"193.050885\" xlink:href=\"#mcc7c03ac4c\" y=\"74.676263\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"197.16709\" xlink:href=\"#mcc7c03ac4c\" y=\"72.83636\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"201.096719\" xlink:href=\"#mcc7c03ac4c\" y=\"71.19661\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"204.85597\" xlink:href=\"#mcc7c03ac4c\" y=\"69.733959\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"208.458773\" xlink:href=\"#mcc7c03ac4c\" y=\"68.428372\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"211.917217\" xlink:href=\"#mcc7c03ac4c\" y=\"67.262342\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"215.241872\" xlink:href=\"#mcc7c03ac4c\" y=\"66.220495\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 52.160938 224.64 \n",
       "L 52.160938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 386.960938 224.64 \n",
       "L 386.960938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 52.160937 224.64 \n",
       "L 386.960938 224.64 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 52.160937 7.2 \n",
       "L 386.960938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"p55e78729d1\">\n",
       "   <rect height=\"217.44\" width=\"334.8\" x=\"52.160938\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "AdaGrad算法\n",
    "\"\"\"\n",
    "\n",
    "%matplotlib inline\n",
    "import math\n",
    "import torch\n",
    "import sys\n",
    "sys.path.append(\"..\") \n",
    "import d2lzh_pytorch as d2l\n",
    "\n",
    "def adagrad_2d(x1, x2, s1, s2):\n",
    "    g1, g2, eps = 0.2 * x1, 4 * x2, 1e-6  # 前两项为自变量梯度\n",
    "    s1 += g1 ** 2\n",
    "    s2 += g2 ** 2\n",
    "    x1 -= eta / math.sqrt(s1 + eps) * g1\n",
    "    x2 -= eta / math.sqrt(s2 + eps) * g2\n",
    "    return x1, x2, s1, s2\n",
    "\n",
    "def f_2d(x1, x2):\n",
    "    return 0.1 * x1 ** 2 + 2 * x2 ** 2\n",
    "\n",
    "eta = 0.4\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(adagrad_2d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.002295, x2 -0.000000\n"
     ]
    },
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"262.19625pt\" version=\"1.1\" viewBox=\"0 0 394.160937 262.19625\" width=\"394.160937pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 262.19625 \n",
       "L 394.160937 262.19625 \n",
       "L 394.160937 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 52.160938 224.64 \n",
       "L 386.960938 224.64 \n",
       "L 386.960938 7.2 \n",
       "L 52.160938 7.2 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"mf10a326e97\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"78.317188\" xlink:href=\"#mf10a326e97\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- −5 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.59375 35.5 \n",
       "L 73.1875 35.5 \n",
       "L 73.1875 27.203125 \n",
       "L 10.59375 27.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-8722\"/>\n",
       "       <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(70.946094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"130.629688\" xlink:href=\"#mf10a326e97\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- −4 -->\n",
       "      <defs>\n",
       "       <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(123.258594 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"182.942188\" xlink:href=\"#mf10a326e97\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- −3 -->\n",
       "      <defs>\n",
       "       <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(175.571094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"235.254688\" xlink:href=\"#mf10a326e97\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- −2 -->\n",
       "      <defs>\n",
       "       <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(227.883594 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"287.567188\" xlink:href=\"#mf10a326e97\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- −1 -->\n",
       "      <defs>\n",
       "       <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(280.196094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"339.879688\" xlink:href=\"#mf10a326e97\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(336.698438 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_7\">\n",
       "     <!-- x1 -->\n",
       "     <defs>\n",
       "      <path d=\"M 54.890625 54.6875 \n",
       "L 35.109375 28.078125 \n",
       "L 55.90625 0 \n",
       "L 45.3125 0 \n",
       "L 29.390625 21.484375 \n",
       "L 13.484375 0 \n",
       "L 2.875 0 \n",
       "L 24.125 28.609375 \n",
       "L 4.6875 54.6875 \n",
       "L 15.28125 54.6875 \n",
       "L 29.78125 35.203125 \n",
       "L 44.28125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-120\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(213.420313 252.916562)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"m31e324f1eb\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m31e324f1eb\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- −3.0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.6875 12.40625 \n",
       "L 21 12.40625 \n",
       "L 21 0 \n",
       "L 10.6875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-46\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(20.878125 228.439219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m31e324f1eb\" y=\"196.763077\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- −2.5 -->\n",
       "      <g transform=\"translate(20.878125 200.562296)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m31e324f1eb\" y=\"168.886154\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- −2.0 -->\n",
       "      <g transform=\"translate(20.878125 172.685373)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m31e324f1eb\" y=\"141.009231\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- −1.5 -->\n",
       "      <g transform=\"translate(20.878125 144.80845)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m31e324f1eb\" y=\"113.132308\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- −1.0 -->\n",
       "      <g transform=\"translate(20.878125 116.931526)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m31e324f1eb\" y=\"85.255385\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- −0.5 -->\n",
       "      <g transform=\"translate(20.878125 89.054603)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m31e324f1eb\" y=\"57.378462\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_14\">\n",
       "      <!-- 0.0 -->\n",
       "      <g transform=\"translate(29.257812 61.17768)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_8\">\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m31e324f1eb\" y=\"29.501538\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- 0.5 -->\n",
       "      <g transform=\"translate(29.257812 33.300757)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_16\">\n",
       "     <!-- x2 -->\n",
       "     <g transform=\"translate(14.798438 122.060625)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_1\"/>\n",
       "   <g id=\"LineCollection_2\">\n",
       "    <path clip-path=\"url(#pbca4dab793)\" d=\"M 386.960938 124.717957 \n",
       "L 381.729688 124.90752 \n",
       "L 376.498437 125.074782 \n",
       "L 371.267187 125.219742 \n",
       "L 366.035937 125.3424 \n",
       "L 360.804688 125.442757 \n",
       "L 355.573438 125.520812 \n",
       "L 350.342187 125.576566 \n",
       "L 345.110937 125.610018 \n",
       "L 339.879687 125.621169 \n",
       "L 334.648438 125.610018 \n",
       "L 329.417188 125.576566 \n",
       "L 324.185937 125.520812 \n",
       "L 318.954687 125.442757 \n",
       "L 313.723437 125.3424 \n",
       "L 308.492188 125.219742 \n",
       "L 303.260938 125.074782 \n",
       "L 298.029687 124.90752 \n",
       "L 292.798437 124.717957 \n",
       "L 287.567187 124.506092 \n",
       "L 282.585045 124.283077 \n",
       "L 282.335938 124.270957 \n",
       "L 277.104688 123.992187 \n",
       "L 271.873438 123.689177 \n",
       "L 266.642187 123.361926 \n",
       "L 261.410937 123.010435 \n",
       "L 256.179688 122.634702 \n",
       "L 250.948437 122.234729 \n",
       "L 245.717187 121.810515 \n",
       "L 240.485937 121.36206 \n",
       "L 235.254687 120.889365 \n",
       "L 230.023438 120.392428 \n",
       "L 224.792188 119.871251 \n",
       "L 219.560937 119.325833 \n",
       "L 214.329687 118.756174 \n",
       "L 213.902647 118.707692 \n",
       "L 209.098437 118.11033 \n",
       "L 203.867188 117.433319 \n",
       "L 198.635937 116.729758 \n",
       "L 193.404687 115.999648 \n",
       "L 188.173438 115.242989 \n",
       "L 182.942187 114.45978 \n",
       "L 177.710938 113.650022 \n",
       "L 174.472545 113.132308 \n",
       "L 172.479688 112.780178 \n",
       "L 167.248437 111.826494 \n",
       "L 162.017188 110.843466 \n",
       "L 156.785937 109.831093 \n",
       "L 151.554688 108.789377 \n",
       "L 146.323437 107.718316 \n",
       "L 145.556187 107.556923 \n",
       "L 141.092187 106.507439 \n",
       "L 135.860938 105.244778 \n",
       "L 130.629687 103.949321 \n",
       "L 125.398438 102.621068 \n",
       "L 122.94038 101.981538 \n",
       "L 120.167187 101.163815 \n",
       "L 114.935937 99.584123 \n",
       "L 109.704688 97.967262 \n",
       "L 104.767328 96.406154 \n",
       "L 104.473437 96.298935 \n",
       "L 99.242188 94.34755 \n",
       "L 94.010937 92.353278 \n",
       "L 90.101266 90.830769 \n",
       "L 88.779687 90.222545 \n",
       "L 83.548437 87.764308 \n",
       "L 78.317187 85.255385 \n",
       "L 78.317187 85.255385 \n",
       "L 73.085938 82.126974 \n",
       "L 69.07362 79.68 \n",
       "L 67.854688 78.72422 \n",
       "L 62.623438 74.542681 \n",
       "L 62.085645 74.104615 \n",
       "L 57.392187 68.752246 \n",
       "L 57.200215 68.529231 \n",
       "L 54.320628 62.953846 \n",
       "L 53.360765 57.378462 \n",
       "L 54.320628 51.803077 \n",
       "L 57.200215 46.227692 \n",
       "L 57.392187 46.004677 \n",
       "L 62.085645 40.652308 \n",
       "L 62.623438 40.214242 \n",
       "L 67.854688 36.032703 \n",
       "L 69.07362 35.076923 \n",
       "L 73.085938 32.629949 \n",
       "L 78.317187 29.501538 \n",
       "L 78.317188 29.501538 \n",
       "L 83.548437 26.992615 \n",
       "L 88.779687 24.534378 \n",
       "L 90.101266 23.926154 \n",
       "L 94.010937 22.403645 \n",
       "L 99.242188 20.409373 \n",
       "L 104.473437 18.457988 \n",
       "L 104.767328 18.350769 \n",
       "L 109.704688 16.789662 \n",
       "L 114.935937 15.1728 \n",
       "L 120.167187 13.593108 \n",
       "L 122.94038 12.775385 \n",
       "L 125.398438 12.135855 \n",
       "L 130.629687 10.807602 \n",
       "L 135.860938 9.512145 \n",
       "L 141.092187 8.249484 \n",
       "L 145.556188 7.2 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_3\">\n",
       "    <path clip-path=\"url(#pbca4dab793)\" d=\"M 386.960938 153.267112 \n",
       "L 381.729688 153.402514 \n",
       "L 376.498437 153.521987 \n",
       "L 371.267187 153.62553 \n",
       "L 366.035937 153.713143 \n",
       "L 360.804688 153.784826 \n",
       "L 355.573438 153.84058 \n",
       "L 350.342187 153.880404 \n",
       "L 345.110937 153.904299 \n",
       "L 339.879687 153.912264 \n",
       "L 334.648438 153.904299 \n",
       "L 329.417188 153.880404 \n",
       "L 324.185937 153.84058 \n",
       "L 318.954687 153.784826 \n",
       "L 313.723437 153.713143 \n",
       "L 308.492188 153.62553 \n",
       "L 303.260938 153.521987 \n",
       "L 298.029687 153.402514 \n",
       "L 292.798437 153.267112 \n",
       "L 287.567187 153.11578 \n",
       "L 282.335938 152.948519 \n",
       "L 277.104688 152.765327 \n",
       "L 271.873438 152.566207 \n",
       "L 266.642187 152.351156 \n",
       "L 262.312877 152.16 \n",
       "L 261.410937 152.117762 \n",
       "L 256.179688 151.855888 \n",
       "L 250.948438 151.577119 \n",
       "L 245.717188 151.281455 \n",
       "L 240.485938 150.968895 \n",
       "L 235.254687 150.639441 \n",
       "L 230.023438 150.293091 \n",
       "L 224.792188 149.929846 \n",
       "L 219.560937 149.549706 \n",
       "L 214.329687 149.152671 \n",
       "L 209.098437 148.738741 \n",
       "L 203.867188 148.307916 \n",
       "L 198.635937 147.860196 \n",
       "L 193.404687 147.39558 \n",
       "L 188.173438 146.91407 \n",
       "L 184.715493 146.584615 \n",
       "L 182.942187 146.404764 \n",
       "L 177.710938 145.856218 \n",
       "L 172.479687 145.289687 \n",
       "L 167.248437 144.705171 \n",
       "L 162.017188 144.10267 \n",
       "L 156.785937 143.482184 \n",
       "L 151.554688 142.843712 \n",
       "L 146.323437 142.187256 \n",
       "L 141.092187 141.512814 \n",
       "L 137.287642 141.009231 \n",
       "L 135.860938 140.807363 \n",
       "L 130.629687 140.047958 \n",
       "L 125.398438 139.269326 \n",
       "L 120.167187 138.471469 \n",
       "L 114.935937 137.654387 \n",
       "L 109.704688 136.81808 \n",
       "L 104.473437 135.962546 \n",
       "L 101.311693 135.433846 \n",
       "L 99.242188 135.062154 \n",
       "L 94.010937 134.101949 \n",
       "L 88.779687 133.121094 \n",
       "L 83.548437 132.11959 \n",
       "L 78.317187 131.097436 \n",
       "L 73.085938 130.054632 \n",
       "L 72.12095 129.858462 \n",
       "L 67.854688 128.921797 \n",
       "L 62.623438 127.750966 \n",
       "L 57.392187 126.557834 \n",
       "L 52.160937 125.3424 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_4\">\n",
       "    <path clip-path=\"url(#pbca4dab793)\" d=\"M 386.960938 175.103356 \n",
       "L 381.729688 175.213567 \n",
       "L 376.498437 175.310812 \n",
       "L 371.267187 175.395091 \n",
       "L 366.035937 175.466404 \n",
       "L 360.804688 175.524751 \n",
       "L 355.573438 175.570132 \n",
       "L 350.342187 175.602547 \n",
       "L 345.110937 175.621996 \n",
       "L 339.879687 175.628479 \n",
       "L 334.648438 175.621996 \n",
       "L 329.417188 175.602547 \n",
       "L 324.185937 175.570132 \n",
       "L 318.954687 175.524751 \n",
       "L 313.723437 175.466404 \n",
       "L 308.492188 175.395091 \n",
       "L 303.260938 175.310812 \n",
       "L 298.029687 175.213567 \n",
       "L 292.798437 175.103356 \n",
       "L 287.567187 174.980179 \n",
       "L 282.335938 174.844036 \n",
       "L 277.104688 174.694927 \n",
       "L 271.873438 174.532852 \n",
       "L 269.742187 174.461538 \n",
       "L 266.642187 174.35275 \n",
       "L 261.410937 174.155572 \n",
       "L 256.179688 173.944795 \n",
       "L 250.948438 173.72042 \n",
       "L 245.717187 173.482447 \n",
       "L 240.485937 173.230874 \n",
       "L 235.254687 172.965704 \n",
       "L 230.023438 172.686934 \n",
       "L 224.792188 172.394567 \n",
       "L 219.560937 172.0886 \n",
       "L 214.329687 171.769036 \n",
       "L 209.098437 171.435872 \n",
       "L 203.867188 171.089111 \n",
       "L 198.635937 170.72875 \n",
       "L 193.404687 170.354792 \n",
       "L 188.173438 169.967235 \n",
       "L 182.942187 169.566079 \n",
       "L 177.710938 169.151325 \n",
       "L 174.472545 168.886154 \n",
       "L 172.479687 168.714604 \n",
       "L 167.248437 168.249988 \n",
       "L 162.017188 167.771077 \n",
       "L 156.785937 167.27787 \n",
       "L 151.554688 166.770367 \n",
       "L 146.323437 166.248568 \n",
       "L 141.092187 165.712473 \n",
       "L 135.860938 165.162083 \n",
       "L 130.629687 164.597396 \n",
       "L 125.398438 164.018414 \n",
       "L 120.167187 163.425136 \n",
       "L 119.182482 163.310769 \n",
       "L 114.935937 162.790902 \n",
       "L 109.704688 162.135418 \n",
       "L 104.473437 161.464865 \n",
       "L 99.242188 160.779243 \n",
       "L 94.010937 160.078553 \n",
       "L 88.779687 159.362794 \n",
       "L 83.548437 158.631967 \n",
       "L 78.317187 157.886071 \n",
       "L 77.281296 157.735385 \n",
       "L 73.085938 157.090233 \n",
       "L 67.854688 156.269855 \n",
       "L 62.623438 155.433547 \n",
       "L 57.392187 154.58131 \n",
       "L 52.160937 153.713143 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_5\">\n",
       "    <path clip-path=\"url(#pbca4dab793)\" d=\"M 386.960938 193.45767 \n",
       "L 381.729688 193.554386 \n",
       "L 376.498437 193.639724 \n",
       "L 371.267187 193.713683 \n",
       "L 366.035937 193.776264 \n",
       "L 360.804688 193.827466 \n",
       "L 355.573438 193.86729 \n",
       "L 350.342187 193.895736 \n",
       "L 345.110937 193.912804 \n",
       "L 339.879687 193.918493 \n",
       "L 334.648438 193.912804 \n",
       "L 329.417188 193.895736 \n",
       "L 324.185937 193.86729 \n",
       "L 318.954687 193.827466 \n",
       "L 313.723437 193.776264 \n",
       "L 308.492188 193.713683 \n",
       "L 303.260938 193.639724 \n",
       "L 298.029687 193.554386 \n",
       "L 292.798437 193.45767 \n",
       "L 287.567187 193.349576 \n",
       "L 282.335938 193.230104 \n",
       "L 277.104688 193.099253 \n",
       "L 271.873438 192.957024 \n",
       "L 266.642187 192.803416 \n",
       "L 261.410937 192.63843 \n",
       "L 256.179688 192.462066 \n",
       "L 250.948438 192.274323 \n",
       "L 245.717187 192.075203 \n",
       "L 240.485937 191.864703 \n",
       "L 235.254687 191.642826 \n",
       "L 230.023438 191.40957 \n",
       "L 225.278815 191.187692 \n",
       "L 224.792188 191.163967 \n",
       "L 219.560937 190.897061 \n",
       "L 214.329687 190.618291 \n",
       "L 209.098437 190.32766 \n",
       "L 203.867188 190.025165 \n",
       "L 198.635937 189.710809 \n",
       "L 193.404687 189.384589 \n",
       "L 188.173438 189.046507 \n",
       "L 182.942187 188.696563 \n",
       "L 177.710938 188.334756 \n",
       "L 172.479687 187.961087 \n",
       "L 167.248437 187.575555 \n",
       "L 162.017188 187.17816 \n",
       "L 156.785937 186.768903 \n",
       "L 151.554688 186.347784 \n",
       "L 146.323437 185.914802 \n",
       "L 142.766187 185.612308 \n",
       "L 141.092187 185.463631 \n",
       "L 135.860937 184.986626 \n",
       "L 130.629687 184.497231 \n",
       "L 125.398438 183.995446 \n",
       "L 120.167187 183.481272 \n",
       "L 114.935937 182.954708 \n",
       "L 109.704688 182.415754 \n",
       "L 104.473437 181.86441 \n",
       "L 99.242188 181.300677 \n",
       "L 94.010937 180.724554 \n",
       "L 88.779687 180.136041 \n",
       "L 87.916801 180.036923 \n",
       "L 83.548437 179.5118 \n",
       "L 78.317187 178.869982 \n",
       "L 73.085938 178.215199 \n",
       "L 67.854688 177.547449 \n",
       "L 62.623438 176.866733 \n",
       "L 57.392187 176.173052 \n",
       "L 52.160937 175.466404 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_6\">\n",
       "    <path clip-path=\"url(#pbca4dab793)\" d=\"M 386.960938 209.632078 \n",
       "L 381.729688 209.718243 \n",
       "L 376.498437 209.794271 \n",
       "L 371.267187 209.860162 \n",
       "L 366.035937 209.915916 \n",
       "L 360.804688 209.961533 \n",
       "L 355.573438 209.997013 \n",
       "L 350.342187 210.022355 \n",
       "L 345.110937 210.037561 \n",
       "L 339.879687 210.042629 \n",
       "L 334.648438 210.037561 \n",
       "L 329.417188 210.022355 \n",
       "L 324.185937 209.997013 \n",
       "L 318.954687 209.961533 \n",
       "L 313.723437 209.915916 \n",
       "L 308.492188 209.860162 \n",
       "L 303.260938 209.794271 \n",
       "L 298.029687 209.718243 \n",
       "L 292.798437 209.632078 \n",
       "L 287.567187 209.535776 \n",
       "L 282.335938 209.429337 \n",
       "L 277.104688 209.312761 \n",
       "L 271.873438 209.186048 \n",
       "L 266.642187 209.049197 \n",
       "L 261.410937 208.90221 \n",
       "L 256.179688 208.745085 \n",
       "L 250.948438 208.577824 \n",
       "L 245.717187 208.400425 \n",
       "L 240.485937 208.21289 \n",
       "L 235.254687 208.015217 \n",
       "L 232.702858 207.913846 \n",
       "L 230.023438 207.80339 \n",
       "L 224.792188 207.577219 \n",
       "L 219.560937 207.340528 \n",
       "L 214.329687 207.093318 \n",
       "L 209.098437 206.835588 \n",
       "L 203.867188 206.567338 \n",
       "L 198.635937 206.288569 \n",
       "L 193.404687 205.99928 \n",
       "L 188.173438 205.699472 \n",
       "L 182.942187 205.389144 \n",
       "L 177.710938 205.068296 \n",
       "L 172.479687 204.736929 \n",
       "L 167.248437 204.395042 \n",
       "L 162.017188 204.042636 \n",
       "L 156.785937 203.67971 \n",
       "L 151.554688 203.306264 \n",
       "L 146.323437 202.922299 \n",
       "L 141.092187 202.527814 \n",
       "L 138.646408 202.338462 \n",
       "L 135.860938 202.114353 \n",
       "L 130.629687 201.682534 \n",
       "L 125.398438 201.239783 \n",
       "L 120.167187 200.7861 \n",
       "L 114.935937 200.321484 \n",
       "L 109.704688 199.845937 \n",
       "L 104.473437 199.359457 \n",
       "L 99.242188 198.862045 \n",
       "L 94.010937 198.353701 \n",
       "L 88.779687 197.834425 \n",
       "L 83.548437 197.304217 \n",
       "L 78.317187 196.763077 \n",
       "L 78.317187 196.763077 \n",
       "L 73.085938 196.188471 \n",
       "L 67.854688 195.602487 \n",
       "L 62.623438 195.005124 \n",
       "L 57.392187 194.396383 \n",
       "L 52.160937 193.776264 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_7\">\n",
       "    <path clip-path=\"url(#pbca4dab793)\" d=\"M 339.879687 224.64 \n",
       "L 334.648438 224.635275 \n",
       "L 329.417188 224.6211 \n",
       "L 324.185937 224.597476 \n",
       "L 318.954687 224.564402 \n",
       "L 313.723437 224.521877 \n",
       "L 308.492188 224.469904 \n",
       "L 303.260938 224.40848 \n",
       "L 298.029687 224.337606 \n",
       "L 292.798437 224.257283 \n",
       "L 287.567187 224.16751 \n",
       "L 282.335938 224.068287 \n",
       "L 277.104688 223.959614 \n",
       "L 271.873438 223.841492 \n",
       "L 266.642187 223.713919 \n",
       "L 261.410937 223.576897 \n",
       "L 256.179688 223.430425 \n",
       "L 250.948438 223.274503 \n",
       "L 245.717187 223.109132 \n",
       "L 240.485937 222.93431 \n",
       "L 235.254687 222.750039 \n",
       "L 230.023438 222.556318 \n",
       "L 224.792188 222.353147 \n",
       "L 219.560937 222.140527 \n",
       "L 214.329687 221.918456 \n",
       "L 209.098437 221.686936 \n",
       "L 203.867188 221.445966 \n",
       "L 198.635937 221.195546 \n",
       "L 193.404687 220.935677 \n",
       "L 188.173438 220.666357 \n",
       "L 182.942187 220.387588 \n",
       "L 177.710938 220.099369 \n",
       "L 172.479687 219.8017 \n",
       "L 167.248437 219.494581 \n",
       "L 162.017188 219.178013 \n",
       "L 160.197622 219.064615 \n",
       "L 156.785937 218.844534 \n",
       "L 151.554688 218.497296 \n",
       "L 146.323437 218.140275 \n",
       "L 141.092187 217.773474 \n",
       "L 135.860938 217.396891 \n",
       "L 130.629687 217.010526 \n",
       "L 125.398438 216.614381 \n",
       "L 120.167187 216.208453 \n",
       "L 114.935937 215.792745 \n",
       "L 109.704688 215.367255 \n",
       "L 104.473437 214.931984 \n",
       "L 99.242188 214.486931 \n",
       "L 94.010937 214.032097 \n",
       "L 88.779687 213.567482 \n",
       "L 87.916801 213.489231 \n",
       "L 83.548437 213.07868 \n",
       "L 78.317187 212.576895 \n",
       "L 73.085938 212.064973 \n",
       "L 67.854688 211.542915 \n",
       "L 62.623438 211.010719 \n",
       "L 57.392187 210.468386 \n",
       "L 52.160937 209.915916 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pbca4dab793)\" d=\"M 386.960938 224.257283 \n",
       "L 381.729688 224.337606 \n",
       "L 376.498437 224.40848 \n",
       "L 371.267187 224.469904 \n",
       "L 366.035937 224.521877 \n",
       "L 360.804688 224.564402 \n",
       "L 355.573438 224.597476 \n",
       "L 350.342187 224.6211 \n",
       "L 345.110937 224.635275 \n",
       "L 339.879687 224.64 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_8\">\n",
       "    <path clip-path=\"url(#pbca4dab793)\" d=\"M 53.360765 224.64 \n",
       "L 52.160937 224.521877 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_9\"/>\n",
       "   <g id=\"line2d_15\">\n",
       "    <path clip-path=\"url(#pbca4dab793)\" d=\"M 78.317188 168.886154 \n",
       "L 182.942135 57.378462 \n",
       "L 236.771247 57.378462 \n",
       "L 270.274817 57.378462 \n",
       "L 292.381268 57.378462 \n",
       "L 307.312321 57.378462 \n",
       "L 317.50116 57.378462 \n",
       "L 324.486755 57.378462 \n",
       "L 329.286694 57.378462 \n",
       "L 332.588235 57.378462 \n",
       "L 334.860242 57.378462 \n",
       "L 336.42412 57.378462 \n",
       "L 337.500693 57.378462 \n",
       "L 338.241844 57.378462 \n",
       "L 338.752091 57.378462 \n",
       "L 339.103376 57.378462 \n",
       "L 339.345223 57.378462 \n",
       "L 339.511726 57.378462 \n",
       "L 339.626358 57.378462 \n",
       "L 339.705278 57.378462 \n",
       "L 339.759613 57.378462 \n",
       "\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    <defs>\n",
       "     <path d=\"M 0 3 \n",
       "C 0.795609 3 1.55874 2.683901 2.12132 2.12132 \n",
       "C 2.683901 1.55874 3 0.795609 3 0 \n",
       "C 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \n",
       "C 1.55874 -2.683901 0.795609 -3 0 -3 \n",
       "C -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \n",
       "C -2.683901 -1.55874 -3 -0.795609 -3 0 \n",
       "C -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \n",
       "C -1.55874 2.683901 -0.795609 3 0 3 \n",
       "z\n",
       "\" id=\"m32f2a4b22e\" style=\"stroke:#ff7f0e;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#pbca4dab793)\">\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"78.317188\" xlink:href=\"#m32f2a4b22e\" y=\"168.886154\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"182.942135\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"236.771247\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"270.274817\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"292.381268\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"307.312321\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"317.50116\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"324.486755\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"329.286694\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"332.588235\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"334.860242\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"336.42412\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"337.500693\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"338.241844\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"338.752091\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"339.103376\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"339.345223\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"339.511726\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"339.626358\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"339.705278\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"339.759613\" xlink:href=\"#m32f2a4b22e\" y=\"57.378462\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 52.160938 224.64 \n",
       "L 52.160938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 386.960938 224.64 \n",
       "L 386.960938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 52.160937 224.64 \n",
       "L 386.960938 224.64 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 52.160937 7.2 \n",
       "L 386.960938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"pbca4dab793\">\n",
       "   <rect height=\"217.44\" width=\"334.8\" x=\"52.160938\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "下面将学习率增大到2。可以看到自变量更为迅速地逼近了最优解。\n",
    "\n",
    "\"\"\"\n",
    "eta = 2\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(adagrad_2d))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.010599, x2 0.000000\n"
     ]
    },
    {
     "data": {
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       "  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Created with matplotlib (https://matplotlib.org/) -->\n",
       "<svg height=\"262.19625pt\" version=\"1.1\" viewBox=\"0 0 394.160937 262.19625\" width=\"394.160937pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       " <defs>\n",
       "  <style type=\"text/css\">\n",
       "*{stroke-linecap:butt;stroke-linejoin:round;}\n",
       "  </style>\n",
       " </defs>\n",
       " <g id=\"figure_1\">\n",
       "  <g id=\"patch_1\">\n",
       "   <path d=\"M 0 262.19625 \n",
       "L 394.160937 262.19625 \n",
       "L 394.160937 0 \n",
       "L 0 0 \n",
       "z\n",
       "\" style=\"fill:none;\"/>\n",
       "  </g>\n",
       "  <g id=\"axes_1\">\n",
       "   <g id=\"patch_2\">\n",
       "    <path d=\"M 52.160938 224.64 \n",
       "L 386.960938 224.64 \n",
       "L 386.960938 7.2 \n",
       "L 52.160938 7.2 \n",
       "z\n",
       "\" style=\"fill:#ffffff;\"/>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_1\">\n",
       "    <g id=\"xtick_1\">\n",
       "     <g id=\"line2d_1\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L 0 3.5 \n",
       "\" id=\"m279389928f\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"78.317188\" xlink:href=\"#m279389928f\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_1\">\n",
       "      <!-- −5 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.59375 35.5 \n",
       "L 73.1875 35.5 \n",
       "L 73.1875 27.203125 \n",
       "L 10.59375 27.203125 \n",
       "z\n",
       "\" id=\"DejaVuSans-8722\"/>\n",
       "       <path d=\"M 10.796875 72.90625 \n",
       "L 49.515625 72.90625 \n",
       "L 49.515625 64.59375 \n",
       "L 19.828125 64.59375 \n",
       "L 19.828125 46.734375 \n",
       "Q 21.96875 47.46875 24.109375 47.828125 \n",
       "Q 26.265625 48.1875 28.421875 48.1875 \n",
       "Q 40.625 48.1875 47.75 41.5 \n",
       "Q 54.890625 34.8125 54.890625 23.390625 \n",
       "Q 54.890625 11.625 47.5625 5.09375 \n",
       "Q 40.234375 -1.421875 26.90625 -1.421875 \n",
       "Q 22.3125 -1.421875 17.546875 -0.640625 \n",
       "Q 12.796875 0.140625 7.71875 1.703125 \n",
       "L 7.71875 11.625 \n",
       "Q 12.109375 9.234375 16.796875 8.0625 \n",
       "Q 21.484375 6.890625 26.703125 6.890625 \n",
       "Q 35.15625 6.890625 40.078125 11.328125 \n",
       "Q 45.015625 15.765625 45.015625 23.390625 \n",
       "Q 45.015625 31 40.078125 35.4375 \n",
       "Q 35.15625 39.890625 26.703125 39.890625 \n",
       "Q 22.75 39.890625 18.8125 39.015625 \n",
       "Q 14.890625 38.140625 10.796875 36.28125 \n",
       "z\n",
       "\" id=\"DejaVuSans-53\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(70.946094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_2\">\n",
       "     <g id=\"line2d_2\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"130.629688\" xlink:href=\"#m279389928f\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_2\">\n",
       "      <!-- −4 -->\n",
       "      <defs>\n",
       "       <path d=\"M 37.796875 64.3125 \n",
       "L 12.890625 25.390625 \n",
       "L 37.796875 25.390625 \n",
       "z\n",
       "M 35.203125 72.90625 \n",
       "L 47.609375 72.90625 \n",
       "L 47.609375 25.390625 \n",
       "L 58.015625 25.390625 \n",
       "L 58.015625 17.1875 \n",
       "L 47.609375 17.1875 \n",
       "L 47.609375 0 \n",
       "L 37.796875 0 \n",
       "L 37.796875 17.1875 \n",
       "L 4.890625 17.1875 \n",
       "L 4.890625 26.703125 \n",
       "z\n",
       "\" id=\"DejaVuSans-52\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(123.258594 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-52\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_3\">\n",
       "     <g id=\"line2d_3\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"182.942188\" xlink:href=\"#m279389928f\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_3\">\n",
       "      <!-- −3 -->\n",
       "      <defs>\n",
       "       <path d=\"M 40.578125 39.3125 \n",
       "Q 47.65625 37.796875 51.625 33 \n",
       "Q 55.609375 28.21875 55.609375 21.1875 \n",
       "Q 55.609375 10.40625 48.1875 4.484375 \n",
       "Q 40.765625 -1.421875 27.09375 -1.421875 \n",
       "Q 22.515625 -1.421875 17.65625 -0.515625 \n",
       "Q 12.796875 0.390625 7.625 2.203125 \n",
       "L 7.625 11.71875 \n",
       "Q 11.71875 9.328125 16.59375 8.109375 \n",
       "Q 21.484375 6.890625 26.8125 6.890625 \n",
       "Q 36.078125 6.890625 40.9375 10.546875 \n",
       "Q 45.796875 14.203125 45.796875 21.1875 \n",
       "Q 45.796875 27.640625 41.28125 31.265625 \n",
       "Q 36.765625 34.90625 28.71875 34.90625 \n",
       "L 20.21875 34.90625 \n",
       "L 20.21875 43.015625 \n",
       "L 29.109375 43.015625 \n",
       "Q 36.375 43.015625 40.234375 45.921875 \n",
       "Q 44.09375 48.828125 44.09375 54.296875 \n",
       "Q 44.09375 59.90625 40.109375 62.90625 \n",
       "Q 36.140625 65.921875 28.71875 65.921875 \n",
       "Q 24.65625 65.921875 20.015625 65.03125 \n",
       "Q 15.375 64.15625 9.8125 62.3125 \n",
       "L 9.8125 71.09375 \n",
       "Q 15.4375 72.65625 20.34375 73.4375 \n",
       "Q 25.25 74.21875 29.59375 74.21875 \n",
       "Q 40.828125 74.21875 47.359375 69.109375 \n",
       "Q 53.90625 64.015625 53.90625 55.328125 \n",
       "Q 53.90625 49.265625 50.4375 45.09375 \n",
       "Q 46.96875 40.921875 40.578125 39.3125 \n",
       "z\n",
       "\" id=\"DejaVuSans-51\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(175.571094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_4\">\n",
       "     <g id=\"line2d_4\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"235.254688\" xlink:href=\"#m279389928f\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_4\">\n",
       "      <!-- −2 -->\n",
       "      <defs>\n",
       "       <path d=\"M 19.1875 8.296875 \n",
       "L 53.609375 8.296875 \n",
       "L 53.609375 0 \n",
       "L 7.328125 0 \n",
       "L 7.328125 8.296875 \n",
       "Q 12.9375 14.109375 22.625 23.890625 \n",
       "Q 32.328125 33.6875 34.8125 36.53125 \n",
       "Q 39.546875 41.84375 41.421875 45.53125 \n",
       "Q 43.3125 49.21875 43.3125 52.78125 \n",
       "Q 43.3125 58.59375 39.234375 62.25 \n",
       "Q 35.15625 65.921875 28.609375 65.921875 \n",
       "Q 23.96875 65.921875 18.8125 64.3125 \n",
       "Q 13.671875 62.703125 7.8125 59.421875 \n",
       "L 7.8125 69.390625 \n",
       "Q 13.765625 71.78125 18.9375 73 \n",
       "Q 24.125 74.21875 28.421875 74.21875 \n",
       "Q 39.75 74.21875 46.484375 68.546875 \n",
       "Q 53.21875 62.890625 53.21875 53.421875 \n",
       "Q 53.21875 48.921875 51.53125 44.890625 \n",
       "Q 49.859375 40.875 45.40625 35.40625 \n",
       "Q 44.1875 33.984375 37.640625 27.21875 \n",
       "Q 31.109375 20.453125 19.1875 8.296875 \n",
       "z\n",
       "\" id=\"DejaVuSans-50\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(227.883594 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_5\">\n",
       "     <g id=\"line2d_5\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"287.567188\" xlink:href=\"#m279389928f\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_5\">\n",
       "      <!-- −1 -->\n",
       "      <defs>\n",
       "       <path d=\"M 12.40625 8.296875 \n",
       "L 28.515625 8.296875 \n",
       "L 28.515625 63.921875 \n",
       "L 10.984375 60.40625 \n",
       "L 10.984375 69.390625 \n",
       "L 28.421875 72.90625 \n",
       "L 38.28125 72.90625 \n",
       "L 38.28125 8.296875 \n",
       "L 54.390625 8.296875 \n",
       "L 54.390625 0 \n",
       "L 12.40625 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-49\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(280.196094 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"xtick_6\">\n",
       "     <g id=\"line2d_6\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"339.879688\" xlink:href=\"#m279389928f\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_6\">\n",
       "      <!-- 0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 31.78125 66.40625 \n",
       "Q 24.171875 66.40625 20.328125 58.90625 \n",
       "Q 16.5 51.421875 16.5 36.375 \n",
       "Q 16.5 21.390625 20.328125 13.890625 \n",
       "Q 24.171875 6.390625 31.78125 6.390625 \n",
       "Q 39.453125 6.390625 43.28125 13.890625 \n",
       "Q 47.125 21.390625 47.125 36.375 \n",
       "Q 47.125 51.421875 43.28125 58.90625 \n",
       "Q 39.453125 66.40625 31.78125 66.40625 \n",
       "z\n",
       "M 31.78125 74.21875 \n",
       "Q 44.046875 74.21875 50.515625 64.515625 \n",
       "Q 56.984375 54.828125 56.984375 36.375 \n",
       "Q 56.984375 17.96875 50.515625 8.265625 \n",
       "Q 44.046875 -1.421875 31.78125 -1.421875 \n",
       "Q 19.53125 -1.421875 13.0625 8.265625 \n",
       "Q 6.59375 17.96875 6.59375 36.375 \n",
       "Q 6.59375 54.828125 13.0625 64.515625 \n",
       "Q 19.53125 74.21875 31.78125 74.21875 \n",
       "z\n",
       "\" id=\"DejaVuSans-48\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(336.698438 239.238437)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_7\">\n",
       "     <!-- x1 -->\n",
       "     <defs>\n",
       "      <path d=\"M 54.890625 54.6875 \n",
       "L 35.109375 28.078125 \n",
       "L 55.90625 0 \n",
       "L 45.3125 0 \n",
       "L 29.390625 21.484375 \n",
       "L 13.484375 0 \n",
       "L 2.875 0 \n",
       "L 24.125 28.609375 \n",
       "L 4.6875 54.6875 \n",
       "L 15.28125 54.6875 \n",
       "L 29.78125 35.203125 \n",
       "L 44.28125 54.6875 \n",
       "z\n",
       "\" id=\"DejaVuSans-120\"/>\n",
       "     </defs>\n",
       "     <g transform=\"translate(213.420313 252.916562)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"matplotlib.axis_2\">\n",
       "    <g id=\"ytick_1\">\n",
       "     <g id=\"line2d_7\">\n",
       "      <defs>\n",
       "       <path d=\"M 0 0 \n",
       "L -3.5 0 \n",
       "\" id=\"m5acb7501e8\" style=\"stroke:#000000;stroke-width:0.8;\"/>\n",
       "      </defs>\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5acb7501e8\" y=\"224.64\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_8\">\n",
       "      <!-- −3.0 -->\n",
       "      <defs>\n",
       "       <path d=\"M 10.6875 12.40625 \n",
       "L 21 12.40625 \n",
       "L 21 0 \n",
       "L 10.6875 0 \n",
       "z\n",
       "\" id=\"DejaVuSans-46\"/>\n",
       "      </defs>\n",
       "      <g transform=\"translate(20.878125 228.439219)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-51\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_2\">\n",
       "     <g id=\"line2d_8\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5acb7501e8\" y=\"196.763077\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_9\">\n",
       "      <!-- −2.5 -->\n",
       "      <g transform=\"translate(20.878125 200.562296)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_3\">\n",
       "     <g id=\"line2d_9\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5acb7501e8\" y=\"168.886154\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_10\">\n",
       "      <!-- −2.0 -->\n",
       "      <g transform=\"translate(20.878125 172.685373)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_4\">\n",
       "     <g id=\"line2d_10\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5acb7501e8\" y=\"141.009231\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_11\">\n",
       "      <!-- −1.5 -->\n",
       "      <g transform=\"translate(20.878125 144.80845)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_5\">\n",
       "     <g id=\"line2d_11\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5acb7501e8\" y=\"113.132308\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_12\">\n",
       "      <!-- −1.0 -->\n",
       "      <g transform=\"translate(20.878125 116.931526)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-49\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_6\">\n",
       "     <g id=\"line2d_12\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5acb7501e8\" y=\"85.255385\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_13\">\n",
       "      <!-- −0.5 -->\n",
       "      <g transform=\"translate(20.878125 89.054603)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-8722\"/>\n",
       "       <use x=\"83.789062\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"147.412109\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"179.199219\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_7\">\n",
       "     <g id=\"line2d_13\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5acb7501e8\" y=\"57.378462\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_14\">\n",
       "      <!-- 0.0 -->\n",
       "      <g transform=\"translate(29.257812 61.17768)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-48\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"ytick_8\">\n",
       "     <g id=\"line2d_14\">\n",
       "      <g>\n",
       "       <use style=\"stroke:#000000;stroke-width:0.8;\" x=\"52.160938\" xlink:href=\"#m5acb7501e8\" y=\"29.501538\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "     <g id=\"text_15\">\n",
       "      <!-- 0.5 -->\n",
       "      <g transform=\"translate(29.257812 33.300757)scale(0.1 -0.1)\">\n",
       "       <use xlink:href=\"#DejaVuSans-48\"/>\n",
       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-46\"/>\n",
       "       <use x=\"95.410156\" xlink:href=\"#DejaVuSans-53\"/>\n",
       "      </g>\n",
       "     </g>\n",
       "    </g>\n",
       "    <g id=\"text_16\">\n",
       "     <!-- x2 -->\n",
       "     <g transform=\"translate(14.798438 122.060625)rotate(-90)scale(0.1 -0.1)\">\n",
       "      <use xlink:href=\"#DejaVuSans-120\"/>\n",
       "      <use x=\"59.179688\" xlink:href=\"#DejaVuSans-50\"/>\n",
       "     </g>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_1\"/>\n",
       "   <g id=\"LineCollection_2\">\n",
       "    <path clip-path=\"url(#pf74528623a)\" d=\"M 386.960938 124.717957 \n",
       "L 381.729688 124.90752 \n",
       "L 376.498437 125.074782 \n",
       "L 371.267187 125.219742 \n",
       "L 366.035937 125.3424 \n",
       "L 360.804688 125.442757 \n",
       "L 355.573438 125.520812 \n",
       "L 350.342187 125.576566 \n",
       "L 345.110937 125.610018 \n",
       "L 339.879687 125.621169 \n",
       "L 334.648438 125.610018 \n",
       "L 329.417188 125.576566 \n",
       "L 324.185937 125.520812 \n",
       "L 318.954687 125.442757 \n",
       "L 313.723437 125.3424 \n",
       "L 308.492188 125.219742 \n",
       "L 303.260938 125.074782 \n",
       "L 298.029687 124.90752 \n",
       "L 292.798437 124.717957 \n",
       "L 287.567187 124.506092 \n",
       "L 282.585045 124.283077 \n",
       "L 282.335938 124.270957 \n",
       "L 277.104688 123.992187 \n",
       "L 271.873438 123.689177 \n",
       "L 266.642187 123.361926 \n",
       "L 261.410937 123.010435 \n",
       "L 256.179688 122.634702 \n",
       "L 250.948437 122.234729 \n",
       "L 245.717187 121.810515 \n",
       "L 240.485937 121.36206 \n",
       "L 235.254687 120.889365 \n",
       "L 230.023438 120.392428 \n",
       "L 224.792188 119.871251 \n",
       "L 219.560937 119.325833 \n",
       "L 214.329687 118.756174 \n",
       "L 213.902647 118.707692 \n",
       "L 209.098437 118.11033 \n",
       "L 203.867188 117.433319 \n",
       "L 198.635937 116.729758 \n",
       "L 193.404687 115.999648 \n",
       "L 188.173438 115.242989 \n",
       "L 182.942187 114.45978 \n",
       "L 177.710938 113.650022 \n",
       "L 174.472545 113.132308 \n",
       "L 172.479688 112.780178 \n",
       "L 167.248437 111.826494 \n",
       "L 162.017188 110.843466 \n",
       "L 156.785937 109.831093 \n",
       "L 151.554688 108.789377 \n",
       "L 146.323437 107.718316 \n",
       "L 145.556187 107.556923 \n",
       "L 141.092187 106.507439 \n",
       "L 135.860938 105.244778 \n",
       "L 130.629687 103.949321 \n",
       "L 125.398438 102.621068 \n",
       "L 122.94038 101.981538 \n",
       "L 120.167187 101.163815 \n",
       "L 114.935937 99.584123 \n",
       "L 109.704688 97.967262 \n",
       "L 104.767328 96.406154 \n",
       "L 104.473437 96.298935 \n",
       "L 99.242188 94.34755 \n",
       "L 94.010937 92.353278 \n",
       "L 90.101266 90.830769 \n",
       "L 88.779687 90.222545 \n",
       "L 83.548437 87.764308 \n",
       "L 78.317187 85.255385 \n",
       "L 78.317187 85.255385 \n",
       "L 73.085938 82.126974 \n",
       "L 69.07362 79.68 \n",
       "L 67.854688 78.72422 \n",
       "L 62.623438 74.542681 \n",
       "L 62.085645 74.104615 \n",
       "L 57.392187 68.752246 \n",
       "L 57.200215 68.529231 \n",
       "L 54.320628 62.953846 \n",
       "L 53.360765 57.378462 \n",
       "L 54.320628 51.803077 \n",
       "L 57.200215 46.227692 \n",
       "L 57.392187 46.004677 \n",
       "L 62.085645 40.652308 \n",
       "L 62.623438 40.214242 \n",
       "L 67.854688 36.032703 \n",
       "L 69.07362 35.076923 \n",
       "L 73.085938 32.629949 \n",
       "L 78.317187 29.501538 \n",
       "L 78.317188 29.501538 \n",
       "L 83.548437 26.992615 \n",
       "L 88.779687 24.534378 \n",
       "L 90.101266 23.926154 \n",
       "L 94.010937 22.403645 \n",
       "L 99.242188 20.409373 \n",
       "L 104.473437 18.457988 \n",
       "L 104.767328 18.350769 \n",
       "L 109.704688 16.789662 \n",
       "L 114.935937 15.1728 \n",
       "L 120.167187 13.593108 \n",
       "L 122.94038 12.775385 \n",
       "L 125.398438 12.135855 \n",
       "L 130.629687 10.807602 \n",
       "L 135.860938 9.512145 \n",
       "L 141.092187 8.249484 \n",
       "L 145.556188 7.2 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_3\">\n",
       "    <path clip-path=\"url(#pf74528623a)\" d=\"M 386.960938 153.267112 \n",
       "L 381.729688 153.402514 \n",
       "L 376.498437 153.521987 \n",
       "L 371.267187 153.62553 \n",
       "L 366.035937 153.713143 \n",
       "L 360.804688 153.784826 \n",
       "L 355.573438 153.84058 \n",
       "L 350.342187 153.880404 \n",
       "L 345.110937 153.904299 \n",
       "L 339.879687 153.912264 \n",
       "L 334.648438 153.904299 \n",
       "L 329.417188 153.880404 \n",
       "L 324.185937 153.84058 \n",
       "L 318.954687 153.784826 \n",
       "L 313.723437 153.713143 \n",
       "L 308.492188 153.62553 \n",
       "L 303.260938 153.521987 \n",
       "L 298.029687 153.402514 \n",
       "L 292.798437 153.267112 \n",
       "L 287.567187 153.11578 \n",
       "L 282.335938 152.948519 \n",
       "L 277.104688 152.765327 \n",
       "L 271.873438 152.566207 \n",
       "L 266.642187 152.351156 \n",
       "L 262.312877 152.16 \n",
       "L 261.410937 152.117762 \n",
       "L 256.179688 151.855888 \n",
       "L 250.948438 151.577119 \n",
       "L 245.717188 151.281455 \n",
       "L 240.485938 150.968895 \n",
       "L 235.254687 150.639441 \n",
       "L 230.023438 150.293091 \n",
       "L 224.792188 149.929846 \n",
       "L 219.560937 149.549706 \n",
       "L 214.329687 149.152671 \n",
       "L 209.098437 148.738741 \n",
       "L 203.867188 148.307916 \n",
       "L 198.635937 147.860196 \n",
       "L 193.404687 147.39558 \n",
       "L 188.173438 146.91407 \n",
       "L 184.715493 146.584615 \n",
       "L 182.942187 146.404764 \n",
       "L 177.710938 145.856218 \n",
       "L 172.479687 145.289687 \n",
       "L 167.248437 144.705171 \n",
       "L 162.017188 144.10267 \n",
       "L 156.785937 143.482184 \n",
       "L 151.554688 142.843712 \n",
       "L 146.323437 142.187256 \n",
       "L 141.092187 141.512814 \n",
       "L 137.287642 141.009231 \n",
       "L 135.860938 140.807363 \n",
       "L 130.629687 140.047958 \n",
       "L 125.398438 139.269326 \n",
       "L 120.167187 138.471469 \n",
       "L 114.935937 137.654387 \n",
       "L 109.704688 136.81808 \n",
       "L 104.473437 135.962546 \n",
       "L 101.311693 135.433846 \n",
       "L 99.242188 135.062154 \n",
       "L 94.010937 134.101949 \n",
       "L 88.779687 133.121094 \n",
       "L 83.548437 132.11959 \n",
       "L 78.317187 131.097436 \n",
       "L 73.085938 130.054632 \n",
       "L 72.12095 129.858462 \n",
       "L 67.854688 128.921797 \n",
       "L 62.623438 127.750966 \n",
       "L 57.392187 126.557834 \n",
       "L 52.160937 125.3424 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_4\">\n",
       "    <path clip-path=\"url(#pf74528623a)\" d=\"M 386.960938 175.103356 \n",
       "L 381.729688 175.213567 \n",
       "L 376.498437 175.310812 \n",
       "L 371.267187 175.395091 \n",
       "L 366.035937 175.466404 \n",
       "L 360.804688 175.524751 \n",
       "L 355.573438 175.570132 \n",
       "L 350.342187 175.602547 \n",
       "L 345.110937 175.621996 \n",
       "L 339.879687 175.628479 \n",
       "L 334.648438 175.621996 \n",
       "L 329.417188 175.602547 \n",
       "L 324.185937 175.570132 \n",
       "L 318.954687 175.524751 \n",
       "L 313.723437 175.466404 \n",
       "L 308.492188 175.395091 \n",
       "L 303.260938 175.310812 \n",
       "L 298.029687 175.213567 \n",
       "L 292.798437 175.103356 \n",
       "L 287.567187 174.980179 \n",
       "L 282.335938 174.844036 \n",
       "L 277.104688 174.694927 \n",
       "L 271.873438 174.532852 \n",
       "L 269.742187 174.461538 \n",
       "L 266.642187 174.35275 \n",
       "L 261.410937 174.155572 \n",
       "L 256.179688 173.944795 \n",
       "L 250.948438 173.72042 \n",
       "L 245.717187 173.482447 \n",
       "L 240.485937 173.230874 \n",
       "L 235.254687 172.965704 \n",
       "L 230.023438 172.686934 \n",
       "L 224.792188 172.394567 \n",
       "L 219.560937 172.0886 \n",
       "L 214.329687 171.769036 \n",
       "L 209.098437 171.435872 \n",
       "L 203.867188 171.089111 \n",
       "L 198.635937 170.72875 \n",
       "L 193.404687 170.354792 \n",
       "L 188.173438 169.967235 \n",
       "L 182.942187 169.566079 \n",
       "L 177.710938 169.151325 \n",
       "L 174.472545 168.886154 \n",
       "L 172.479687 168.714604 \n",
       "L 167.248437 168.249988 \n",
       "L 162.017188 167.771077 \n",
       "L 156.785937 167.27787 \n",
       "L 151.554688 166.770367 \n",
       "L 146.323437 166.248568 \n",
       "L 141.092187 165.712473 \n",
       "L 135.860938 165.162083 \n",
       "L 130.629687 164.597396 \n",
       "L 125.398438 164.018414 \n",
       "L 120.167187 163.425136 \n",
       "L 119.182482 163.310769 \n",
       "L 114.935937 162.790902 \n",
       "L 109.704688 162.135418 \n",
       "L 104.473437 161.464865 \n",
       "L 99.242188 160.779243 \n",
       "L 94.010937 160.078553 \n",
       "L 88.779687 159.362794 \n",
       "L 83.548437 158.631967 \n",
       "L 78.317187 157.886071 \n",
       "L 77.281296 157.735385 \n",
       "L 73.085938 157.090233 \n",
       "L 67.854688 156.269855 \n",
       "L 62.623438 155.433547 \n",
       "L 57.392187 154.58131 \n",
       "L 52.160937 153.713143 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_5\">\n",
       "    <path clip-path=\"url(#pf74528623a)\" d=\"M 386.960938 193.45767 \n",
       "L 381.729688 193.554386 \n",
       "L 376.498437 193.639724 \n",
       "L 371.267187 193.713683 \n",
       "L 366.035937 193.776264 \n",
       "L 360.804688 193.827466 \n",
       "L 355.573438 193.86729 \n",
       "L 350.342187 193.895736 \n",
       "L 345.110937 193.912804 \n",
       "L 339.879687 193.918493 \n",
       "L 334.648438 193.912804 \n",
       "L 329.417188 193.895736 \n",
       "L 324.185937 193.86729 \n",
       "L 318.954687 193.827466 \n",
       "L 313.723437 193.776264 \n",
       "L 308.492188 193.713683 \n",
       "L 303.260938 193.639724 \n",
       "L 298.029687 193.554386 \n",
       "L 292.798437 193.45767 \n",
       "L 287.567187 193.349576 \n",
       "L 282.335938 193.230104 \n",
       "L 277.104688 193.099253 \n",
       "L 271.873438 192.957024 \n",
       "L 266.642187 192.803416 \n",
       "L 261.410937 192.63843 \n",
       "L 256.179688 192.462066 \n",
       "L 250.948438 192.274323 \n",
       "L 245.717187 192.075203 \n",
       "L 240.485937 191.864703 \n",
       "L 235.254687 191.642826 \n",
       "L 230.023438 191.40957 \n",
       "L 225.278815 191.187692 \n",
       "L 224.792188 191.163967 \n",
       "L 219.560937 190.897061 \n",
       "L 214.329687 190.618291 \n",
       "L 209.098437 190.32766 \n",
       "L 203.867188 190.025165 \n",
       "L 198.635937 189.710809 \n",
       "L 193.404687 189.384589 \n",
       "L 188.173438 189.046507 \n",
       "L 182.942187 188.696563 \n",
       "L 177.710938 188.334756 \n",
       "L 172.479687 187.961087 \n",
       "L 167.248437 187.575555 \n",
       "L 162.017188 187.17816 \n",
       "L 156.785937 186.768903 \n",
       "L 151.554688 186.347784 \n",
       "L 146.323437 185.914802 \n",
       "L 142.766187 185.612308 \n",
       "L 141.092187 185.463631 \n",
       "L 135.860937 184.986626 \n",
       "L 130.629687 184.497231 \n",
       "L 125.398438 183.995446 \n",
       "L 120.167187 183.481272 \n",
       "L 114.935937 182.954708 \n",
       "L 109.704688 182.415754 \n",
       "L 104.473437 181.86441 \n",
       "L 99.242188 181.300677 \n",
       "L 94.010937 180.724554 \n",
       "L 88.779687 180.136041 \n",
       "L 87.916801 180.036923 \n",
       "L 83.548437 179.5118 \n",
       "L 78.317187 178.869982 \n",
       "L 73.085938 178.215199 \n",
       "L 67.854688 177.547449 \n",
       "L 62.623438 176.866733 \n",
       "L 57.392187 176.173052 \n",
       "L 52.160937 175.466404 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_6\">\n",
       "    <path clip-path=\"url(#pf74528623a)\" d=\"M 386.960938 209.632078 \n",
       "L 381.729688 209.718243 \n",
       "L 376.498437 209.794271 \n",
       "L 371.267187 209.860162 \n",
       "L 366.035937 209.915916 \n",
       "L 360.804688 209.961533 \n",
       "L 355.573438 209.997013 \n",
       "L 350.342187 210.022355 \n",
       "L 345.110937 210.037561 \n",
       "L 339.879687 210.042629 \n",
       "L 334.648438 210.037561 \n",
       "L 329.417188 210.022355 \n",
       "L 324.185937 209.997013 \n",
       "L 318.954687 209.961533 \n",
       "L 313.723437 209.915916 \n",
       "L 308.492188 209.860162 \n",
       "L 303.260938 209.794271 \n",
       "L 298.029687 209.718243 \n",
       "L 292.798437 209.632078 \n",
       "L 287.567187 209.535776 \n",
       "L 282.335938 209.429337 \n",
       "L 277.104688 209.312761 \n",
       "L 271.873438 209.186048 \n",
       "L 266.642187 209.049197 \n",
       "L 261.410937 208.90221 \n",
       "L 256.179688 208.745085 \n",
       "L 250.948438 208.577824 \n",
       "L 245.717187 208.400425 \n",
       "L 240.485937 208.21289 \n",
       "L 235.254687 208.015217 \n",
       "L 232.702858 207.913846 \n",
       "L 230.023438 207.80339 \n",
       "L 224.792188 207.577219 \n",
       "L 219.560937 207.340528 \n",
       "L 214.329687 207.093318 \n",
       "L 209.098437 206.835588 \n",
       "L 203.867188 206.567338 \n",
       "L 198.635937 206.288569 \n",
       "L 193.404687 205.99928 \n",
       "L 188.173438 205.699472 \n",
       "L 182.942187 205.389144 \n",
       "L 177.710938 205.068296 \n",
       "L 172.479687 204.736929 \n",
       "L 167.248437 204.395042 \n",
       "L 162.017188 204.042636 \n",
       "L 156.785937 203.67971 \n",
       "L 151.554688 203.306264 \n",
       "L 146.323437 202.922299 \n",
       "L 141.092187 202.527814 \n",
       "L 138.646408 202.338462 \n",
       "L 135.860938 202.114353 \n",
       "L 130.629687 201.682534 \n",
       "L 125.398438 201.239783 \n",
       "L 120.167187 200.7861 \n",
       "L 114.935937 200.321484 \n",
       "L 109.704688 199.845937 \n",
       "L 104.473437 199.359457 \n",
       "L 99.242188 198.862045 \n",
       "L 94.010937 198.353701 \n",
       "L 88.779687 197.834425 \n",
       "L 83.548437 197.304217 \n",
       "L 78.317187 196.763077 \n",
       "L 78.317187 196.763077 \n",
       "L 73.085938 196.188471 \n",
       "L 67.854688 195.602487 \n",
       "L 62.623438 195.005124 \n",
       "L 57.392187 194.396383 \n",
       "L 52.160937 193.776264 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_7\">\n",
       "    <path clip-path=\"url(#pf74528623a)\" d=\"M 339.879687 224.64 \n",
       "L 334.648438 224.635275 \n",
       "L 329.417188 224.6211 \n",
       "L 324.185937 224.597476 \n",
       "L 318.954687 224.564402 \n",
       "L 313.723437 224.521877 \n",
       "L 308.492188 224.469904 \n",
       "L 303.260938 224.40848 \n",
       "L 298.029687 224.337606 \n",
       "L 292.798437 224.257283 \n",
       "L 287.567187 224.16751 \n",
       "L 282.335938 224.068287 \n",
       "L 277.104688 223.959614 \n",
       "L 271.873438 223.841492 \n",
       "L 266.642187 223.713919 \n",
       "L 261.410937 223.576897 \n",
       "L 256.179688 223.430425 \n",
       "L 250.948438 223.274503 \n",
       "L 245.717187 223.109132 \n",
       "L 240.485937 222.93431 \n",
       "L 235.254687 222.750039 \n",
       "L 230.023438 222.556318 \n",
       "L 224.792188 222.353147 \n",
       "L 219.560937 222.140527 \n",
       "L 214.329687 221.918456 \n",
       "L 209.098437 221.686936 \n",
       "L 203.867188 221.445966 \n",
       "L 198.635937 221.195546 \n",
       "L 193.404687 220.935677 \n",
       "L 188.173438 220.666357 \n",
       "L 182.942187 220.387588 \n",
       "L 177.710938 220.099369 \n",
       "L 172.479687 219.8017 \n",
       "L 167.248437 219.494581 \n",
       "L 162.017188 219.178013 \n",
       "L 160.197622 219.064615 \n",
       "L 156.785937 218.844534 \n",
       "L 151.554688 218.497296 \n",
       "L 146.323437 218.140275 \n",
       "L 141.092187 217.773474 \n",
       "L 135.860938 217.396891 \n",
       "L 130.629687 217.010526 \n",
       "L 125.398438 216.614381 \n",
       "L 120.167187 216.208453 \n",
       "L 114.935937 215.792745 \n",
       "L 109.704688 215.367255 \n",
       "L 104.473437 214.931984 \n",
       "L 99.242188 214.486931 \n",
       "L 94.010937 214.032097 \n",
       "L 88.779687 213.567482 \n",
       "L 87.916801 213.489231 \n",
       "L 83.548437 213.07868 \n",
       "L 78.317187 212.576895 \n",
       "L 73.085938 212.064973 \n",
       "L 67.854688 211.542915 \n",
       "L 62.623438 211.010719 \n",
       "L 57.392187 210.468386 \n",
       "L 52.160937 209.915916 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "    <path clip-path=\"url(#pf74528623a)\" d=\"M 386.960938 224.257283 \n",
       "L 381.729688 224.337606 \n",
       "L 376.498437 224.40848 \n",
       "L 371.267187 224.469904 \n",
       "L 366.035937 224.521877 \n",
       "L 360.804688 224.564402 \n",
       "L 355.573438 224.597476 \n",
       "L 350.342187 224.6211 \n",
       "L 345.110937 224.635275 \n",
       "L 339.879687 224.64 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_8\">\n",
       "    <path clip-path=\"url(#pf74528623a)\" d=\"M 53.360765 224.64 \n",
       "L 52.160937 224.521877 \n",
       "\" style=\"fill:none;stroke:#1f77b4;stroke-width:1.5;\"/>\n",
       "   </g>\n",
       "   <g id=\"LineCollection_9\"/>\n",
       "   <g id=\"line2d_15\">\n",
       "    <path clip-path=\"url(#pf74528623a)\" d=\"M 78.317188 168.886154 \n",
       "L 144.487517 98.362502 \n",
       "L 185.424074 72.885056 \n",
       "L 215.743135 62.827911 \n",
       "L 239.688058 59.107555 \n",
       "L 259.157808 57.863437 \n",
       "L 275.199364 57.495617 \n",
       "L 288.47293 57.401956 \n",
       "L 299.439392 57.382157 \n",
       "L 308.448387 57.378874 \n",
       "L 315.783688 57.378488 \n",
       "L 321.687649 57.378462 \n",
       "L 326.374341 57.378462 \n",
       "L 330.036213 57.378462 \n",
       "L 332.847028 57.378462 \n",
       "L 334.962755 57.378462 \n",
       "L 336.521562 57.378462 \n",
       "L 337.643608 57.378462 \n",
       "L 338.431105 57.378462 \n",
       "L 338.96884 57.378462 \n",
       "L 339.325244 57.378462 \n",
       "\" style=\"fill:none;stroke:#ff7f0e;stroke-linecap:square;stroke-width:1.5;\"/>\n",
       "    <defs>\n",
       "     <path d=\"M 0 3 \n",
       "C 0.795609 3 1.55874 2.683901 2.12132 2.12132 \n",
       "C 2.683901 1.55874 3 0.795609 3 0 \n",
       "C 3 -0.795609 2.683901 -1.55874 2.12132 -2.12132 \n",
       "C 1.55874 -2.683901 0.795609 -3 0 -3 \n",
       "C -0.795609 -3 -1.55874 -2.683901 -2.12132 -2.12132 \n",
       "C -2.683901 -1.55874 -3 -0.795609 -3 0 \n",
       "C -3 0.795609 -2.683901 1.55874 -2.12132 2.12132 \n",
       "C -1.55874 2.683901 -0.795609 3 0 3 \n",
       "z\n",
       "\" id=\"m90c310ba1a\" style=\"stroke:#ff7f0e;\"/>\n",
       "    </defs>\n",
       "    <g clip-path=\"url(#pf74528623a)\">\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"78.317188\" xlink:href=\"#m90c310ba1a\" y=\"168.886154\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"144.487517\" xlink:href=\"#m90c310ba1a\" y=\"98.362502\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"185.424074\" xlink:href=\"#m90c310ba1a\" y=\"72.885056\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"215.743135\" xlink:href=\"#m90c310ba1a\" y=\"62.827911\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"239.688058\" xlink:href=\"#m90c310ba1a\" y=\"59.107555\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"259.157808\" xlink:href=\"#m90c310ba1a\" y=\"57.863437\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"275.199364\" xlink:href=\"#m90c310ba1a\" y=\"57.495617\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"288.47293\" xlink:href=\"#m90c310ba1a\" y=\"57.401956\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"299.439392\" xlink:href=\"#m90c310ba1a\" y=\"57.382157\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"308.448387\" xlink:href=\"#m90c310ba1a\" y=\"57.378874\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"315.783688\" xlink:href=\"#m90c310ba1a\" y=\"57.378488\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"321.687649\" xlink:href=\"#m90c310ba1a\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"326.374341\" xlink:href=\"#m90c310ba1a\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"330.036213\" xlink:href=\"#m90c310ba1a\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"332.847028\" xlink:href=\"#m90c310ba1a\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"334.962755\" xlink:href=\"#m90c310ba1a\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"336.521562\" xlink:href=\"#m90c310ba1a\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"337.643608\" xlink:href=\"#m90c310ba1a\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"338.431105\" xlink:href=\"#m90c310ba1a\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"338.96884\" xlink:href=\"#m90c310ba1a\" y=\"57.378462\"/>\n",
       "     <use style=\"fill:#ff7f0e;stroke:#ff7f0e;\" x=\"339.325244\" xlink:href=\"#m90c310ba1a\" y=\"57.378462\"/>\n",
       "    </g>\n",
       "   </g>\n",
       "   <g id=\"patch_3\">\n",
       "    <path d=\"M 52.160938 224.64 \n",
       "L 52.160938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_4\">\n",
       "    <path d=\"M 386.960938 224.64 \n",
       "L 386.960938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_5\">\n",
       "    <path d=\"M 52.160937 224.64 \n",
       "L 386.960938 224.64 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "   <g id=\"patch_6\">\n",
       "    <path d=\"M 52.160937 7.2 \n",
       "L 386.960938 7.2 \n",
       "\" style=\"fill:none;stroke:#000000;stroke-linecap:square;stroke-linejoin:miter;stroke-width:0.8;\"/>\n",
       "   </g>\n",
       "  </g>\n",
       " </g>\n",
       " <defs>\n",
       "  <clipPath id=\"pf74528623a\">\n",
       "   <rect height=\"217.44\" width=\"334.8\" x=\"52.160938\" y=\"7.2\"/>\n",
       "  </clipPath>\n",
       " </defs>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "RMSProp\n",
    "\"\"\"\n",
    "\n",
    "%matplotlib inline\n",
    "import math\n",
    "import torch\n",
    "import sys\n",
    "sys.path.append(\"..\") \n",
    "import d2lzh_pytorch as d2l\n",
    "\n",
    "def rmsprop_2d(x1, x2, s1, s2):\n",
    "    g1, g2, eps = 0.2 * x1, 4 * x2, 1e-6\n",
    "    s1 = gamma * s1 + (1 - gamma) * g1 ** 2\n",
    "    s2 = gamma * s2 + (1 - gamma) * g2 ** 2\n",
    "    x1 -= eta / math.sqrt(s1 + eps) * g1\n",
    "    x2 -= eta / math.sqrt(s2 + eps) * g2\n",
    "    return x1, x2, s1, s2\n",
    "\n",
    "def f_2d(x1, x2):\n",
    "    return 0.1 * x1 ** 2 + 2 * x2 ** 2\n",
    "\n",
    "eta, gamma = 0.4, 0.9\n",
    "d2l.show_trace_2d(f_2d, d2l.train_2d(rmsprop_2d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}