gradient descent / gradient ascent

author: chzhang <zch921005@126.com> 2023-04-02 14:31:11 +0800
committer: chzhang <zch921005@126.com> 2023-04-02 14:31:11 +0800
commit: 2c5dc53a4c2d64866a3b567cf971a9e9c335923f (patch)
tree: 6b948a2d55e8c83ff59736e43665809195f0332a
parent: 8dfef0bfbe2237de25a043a64b969d814654114b (diff)
1 files changed, 1613 insertions, 0 deletions
diff --git a/ml_core/tutorials/01_grad_descent_details_visualization.ipynb b/ml_core/tutorials/01_grad_descent_details_visualization.ipynb
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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "45f644da",
+   "metadata": {},
+   "source": [
+    "## summary"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "56901f0b",
+   "metadata": {},
+   "source": [
+    "- 一种优化算法（optimizer），迭代算法\n",
+    "- gradient descent / gradient ascent：parameter learning （from data）\n",
+    "    - gradient descent：最小化目标（objective，loss，deep learning），沿着负梯度方向更新\n",
+    "        $$\n",
+    "        w=w-\\eta\\nabla_wJ(w)\n",
+    "        $$\n",
+    "    - gradient ascent：最大化目标（objective，reward），沿着正梯度方向更新\n",
+    "        $$\n",
+    "        w=w+\\eta\\nabla_wJ(w)\n",
+    "        $$\n",
+    "- 一些简单分析\n",
+    "    - $\\eta\\nabla_wJ(w)$：刻画着 update/diff/step\n",
+    "        - 由两两部分组成 \n",
+    "            - $\\eta$：learning rate\n",
+    "            - $\\nabla_wJ(w)$：gradient"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a8a51e3d",
+   "metadata": {},
+   "source": [
+    "## example 1: $f(x)=x^2$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 33,
+   "id": "647e233f",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2023-04-02T06:10:18.540777Z",
+     "start_time": "2023-04-02T06:10:18.534462Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 37,
+   "id": "66aaea24",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2023-04-02T06:13:15.401856Z",
+     "start_time": "2023-04-02T06:13:15.394855Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "def gradient_descent(grad_fn, x0, learn_rate, n_iter=50, tolerance=1e-06, verbose=False):\n",
+    "    x = x0\n",
+    "    xs = [x0]\n",
+    "    for i in range(n_iter):\n",
+    "        diff = -learn_rate * grad_fn(x)\n",
+    "        if np.all(np.abs(diff) <= tolerance):\n",
+    "            break\n",
+    "        x += diff\n",
+    "        xs.append(x)\n",
+    "        if verbose:\n",
+    "            print(f'{i}: {xs[-2]:.3f}, {diff:.2f}={learn_rate:.3f}*{grad_fn(xs[-2]):.3f}, {xs[-1]:.3f}')\n",
+    "    return x, xs\n",
+    "\n",
+    "def gradient_ascent(grad_fn, x0, learn_rate, n_iter=50, tolerance=1e-06, verbose=False):\n",
+    "    x = x0\n",
+    "    xs = [x0]\n",
+    "    for i in range(n_iter):\n",
+    "        diff = learn_rate * grad_fn(x)\n",
+    "        if np.all(np.abs(diff) <= tolerance):\n",
+    "            break\n",
+    "        x += diff\n",
+    "        xs.append(x)\n",
+    "        if verbose:\n",
+    "            print(f'{i}: {xs[-2]:.3f}, {diff:.2f}={learn_rate:.3f}*{grad_fn(xs[-2]):.3f}, {xs[-1]:.3f}')\n",
+    "    return x, xs"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "id": "fc7d5476",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2023-04-02T06:13:17.249185Z",
+     "start_time": "2023-04-02T06:13:17.235808Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0: 10.000, -4.00=0.200*20.000, 6.000\n",
+      "1: 6.000, -2.40=0.200*12.000, 3.600\n",
+      "2: 3.600, -1.44=0.200*7.200, 2.160\n",
+      "3: 2.160, -0.86=0.200*4.320, 1.296\n",
+      "4: 1.296, -0.52=0.200*2.592, 0.778\n",
+      "5: 0.778, -0.31=0.200*1.555, 0.467\n",
+      "6: 0.467, -0.19=0.200*0.933, 0.280\n",
+      "7: 0.280, -0.11=0.200*0.560, 0.168\n",
+      "8: 0.168, -0.07=0.200*0.336, 0.101\n",
+      "9: 0.101, -0.04=0.200*0.202, 0.060\n",
+      "10: 0.060, -0.02=0.200*0.121, 0.036\n",
+      "11: 0.036, -0.01=0.200*0.073, 0.022\n",
+      "12: 0.022, -0.01=0.200*0.044, 0.013\n",
+      "13: 0.013, -0.01=0.200*0.026, 0.008\n",
+      "14: 0.008, -0.00=0.200*0.016, 0.005\n",
+      "15: 0.005, -0.00=0.200*0.009, 0.003\n",
+      "16: 0.003, -0.00=0.200*0.006, 0.002\n",
+      "17: 0.002, -0.00=0.200*0.003, 0.001\n",
+      "18: 0.001, -0.00=0.200*0.002, 0.001\n",
+      "19: 0.001, -0.00=0.200*0.001, 0.000\n",
+      "20: 0.000, -0.00=0.200*0.001, 0.000\n",
+      "21: 0.000, -0.00=0.200*0.000, 0.000\n",
+      "22: 0.000, -0.00=0.200*0.000, 0.000\n",
+      "23: 0.000, -0.00=0.200*0.000, 0.000\n",
+      "24: 0.000, -0.00=0.200*0.000, 0.000\n",
+      "25: 0.000, -0.00=0.200*0.000, 0.000\n",
+      "26: 0.000, -0.00=0.200*0.000, 0.000\n",
+      "27: 0.000, -0.00=0.200*0.000, 0.000\n",
+      "28: 0.000, -0.00=0.200*0.000, 0.000\n",
+      "29: 0.000, -0.00=0.200*0.000, 0.000\n"
+     ]
+    }
+   ],
+   "source": [
+    "f = lambda x: x**2\n",
+    "grad_fn = lambda x: 2*x\n",
+    "x, xs = gradient_descent(grad_fn=grad_fn, x0=10.0, learn_rate=0.2, verbose=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "id": "e4d25ca8",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2023-04-02T06:13:36.049941Z",
+     "start_time": "2023-04-02T06:13:35.828677Z"
+    },
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0, 0.5, 'f(x)')"
+      ]
+     },
+     "execution_count": 39,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(np.arange(-12, 12, 0.01), [f(x) for x in np.arange(-12, 12, 0.01)])\n",
+    "plt.plot(xs, [f(x) for x in xs], 'o-', color='g')\n",
+    "plt.xlabel('x')\n",
+    "plt.ylabel('f(x)')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6679c798",
+   "metadata": {},
+   "source": [
+    "- 可以看到，update/diff/step 其实越来越小\n",
+    "    $$\\eta\\cdot\\nabla_wJ(w)$$\n",
+    "    - 如前所说，update/diff/step 由两部分组成，因为 learning rate（$\\eta$） 是 fixed 的，因此 step/update/diff 的减少最要是 grad （$\\nabla_wJ(w)$）的减少造成的；\n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "id": "0172f81b",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2023-04-02T06:16:52.888060Z",
+     "start_time": "2023-04-02T06:16:52.699113Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Text(0, 0.5, 'f(x)')"
+      ]
+     },
+     "execution_count": 40,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "f = lambda x: x**2\n",
+    "grad_fn = lambda x: 2*x\n",
+    "x, xs = gradient_descent(grad_fn=grad_fn, x0=-10.0, learn_rate=0.2)\n",
+    "plt.plot(np.arange(-12, 12, 0.01), [f(x) for x in np.arange(-12, 12, 0.01)])\n",
+    "plt.plot(xs, [f(x) for x in xs], 'o-', color='g')\n",
+    "plt.xlabel('x')\n",
+    "plt.ylabel('f(x)')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "id": "bcd26b4c",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2023-04-02T06:17:50.315461Z",
+     "start_time": "2023-04-02T06:17:50.138547Z"
+    },
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x1203dd7c0>]"
+      ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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pGB7s9iBgcDRgKsXs4dGZyXyVot2BxbPpJ6aIiXZk53P3e2soKnXSu3UEr6vISC2yWCy8OvBVrmlxDWWuYxQ0eJ4yI5c/zdjA8l0HzY4nct5M+6mZmprKvffeS/PmzQkICKBly5aMHz+e0tLSas9LS0tj8ODBBAUFERERwcMPP3zSc0Q8UdrhIkb+ZzV5x8ro0rQhb4/sit1Hy6+ldvnafPnklk+4KPwi8suzKW34N0qcxdz/4To2pOWaHU/kvJhWZrZv347L5eLtt99my5YtvPzyy7z11ls89dRTVc9xOp0MGjSIwsJCVqxYwYwZM5g9ezaPPfaYWbFFasQBRzF3/OfHqiMK3ht1KYF+OipN6kZYQBhf3v4lYf5h5JRswdroLQpLy7l72hp2Hsg3O57IOXOrfWZeeOEF3nzzTfbs2QPA119/zfXXX096ejoxMTEAzJgxg1GjRpGTk3PWe8ZonxlxJ0eLSrnt7R/ZcSCfZuGBfHp/Ek1CdESB1L1lqcvo92E/yl3ltA28l2OHbyIyxM6sB3oS3yjQ7HginrnPTF5eHo0aNar6eNWqVXTs2LGqyAAMGDCAkpIS1q1bd9rXKSkpweFwVLuJuIPiMif3TFvDjgP5NAm28797e6jIiGn6JvTlzUFvArC96D+EhK3hgKOE3/33Jw4VlJicTuTsuU2Z+fnnn3nttdd44IEHqu7Lzs4mMjKy2vPCwsLw8/MjOzv7tK81ZcoUQkNDq27x8fG1llvkbDldBn+asYH1aUcJ8ffhw3t76LdfMd19Xe5j7GVjAdhV9ndCQvax91Ah976/lmOlTpPTiZydGi8zEyZMwGKxnPG2du3aap+TmZnJwIEDGTZsGPfdd1+1xyyWk0+BNQzjlPdXGjduHHl5eVW39HTtdCnme27+Vr7ZcgA/m5V3fteNNlHBZkcSAeAf/f7BoNaDKHYWk+07icCAXDamH+XhGRtwutxmJoLIadX4jMMxY8YwfPjwMz4nISGh6r8zMzO58sorSUpK4t///ne150VFRbF69epq9+Xm5lJWVnbSiM2J7HY7drv93MOL1JL/rNjLez+kAjD11k70aBFubiCRE9isNj66+SN6/bcXm3M2E9boH/gcmMiirQf465dbmXBDB7MjipxRjZeZiIgIIiIizuq5GRkZXHnllXTt2pX33nsPq7X6QFFSUhKTJ08mKyuL6OhoABYuXIjdbqdr1641HV2kVnydksVz87cC8OS1bbmhU8xvfIZI3QuxhzDv9nlc+s6l7DySwmVN/03mnoeYtjKV+EaB3Ht5c7MjipyWaXNmMjMz6du3L/Hx8UydOpWDBw+SnZ1dbS5M//79ad++PSNHjmTDhg0sXryYxx9/nNGjR2tVkniEdfuO8MjMZAwDRl7WjPuvaGF2JJHTSmiYwGfDP8PP5sePWQto12Y+UHGJdMFm7RIs7su0MrNw4UJ2797NkiVLiIuLIzo6uupWyWazMX/+fPz9/enVqxe33norN954I1OnTjUrtshZSz9SxOgP1lUdUzB+cPszzvUScQc943vy3xv+C8A3aW9zcesNGAb8aUayNtUTt+VW+8zUFu0zI3WtoKScW95cyfbsfDrGhvDJ/UnaFE88yjNLnmHy8sn4Wn3p1/h1tqTG0DjYzhdjehEdGmB2PPESHrnPjEh94HIZPDIjme3Z+TQOtvPO77qpyIjHmXTlJG5udzNlrjJWO56iaZMCDuaX8PsP1mnJtrgdlRmRGjZ14Q6+3XYAPx8r/x7ZVb/FikeyWqy8f+P7dInuwuFjhzjgO5HQwDJSMvL48+xNeMGgvngQlRmRGvR5cgZvLPsZgL/ffDGJTcNMTiRy/oL8gvhi+BfEBMew88g2gqJfx2Z1MW9jZtX3uYg7UJkRqSHJ6Ud5YtYmAB7s25KbEuNMTiRy4WJDYvli+BcE+ASwKvNbLrroMwBe+GYHC7ecfid2kbqkMiNSA3Icxfz+g7WUHl+59ET/NmZHEqkxXWO68sFNHwCwYN9/6dC6YjPTR2Ymsz1bZ9+J+VRmRC5QmdPFHz5aT05+CRdFNuCV4YlYrVqCLfXLLe1v4a9X/hWAbzKep0XcXopKndz/4TryjpWZnE68ncqMyAV6/qttrEnNJdjuw9sju9HArpVLUj893ftp7rj4DpyGk/UFf6FRyCH2HS7isU+ScekMJzGRyozIBfg8OaPqzKUXb+1E84ggcwOJ1CKLxcK7N7xLUlwSeSVHORLwV2w+hXy7LYc3v9OEYDGPyozIedqRnc+Ts1MA+MOVLenfIcrkRCK1z9/Hn7m3zaVpaFP2OX4mIOpVDMp5ceEOlu86aHY88VIqMyLnwVFcxgP/W8exMie9W0cwtp8m/Ir3iGwQyZe3f0kDvwZsObySsJgPcRoGD3+8gYyjx8yOJ15IZUbkHLlcBo99spG9hwqJbRjAq8MTsWnCr3iZiyMv5uObP8aChY25s2kQvojcojIe+t86Ssq1Q7DULZUZkXP0zvI9LNp6AD+blTfv7EKjID+zI4mY4vqLrueFfi8AsP3Yv7AGJLNxfx4T5201OZl4G5UZkXOwbl8uL3yzA4AJN3TgkriG5gYSMdnYpLHcm3gvLsPFAZ+/UWZN5aPVaczbmGl2NPEiKjMiZymvqIyHP95AuctgcKcYbr803uxIIqazWCy8MegN+jTrQ1F5AcdCpuDkKOPmpLDvcKHZ8cRLqMyInAXDMHhi1kYyjh6jWXggz9/UEYtF82REAPxsfsy+dTatGrUitySDYyH/IL/kGH/8eAOl5S6z44kXUJkROQsfrNrHwq0H8LVZ+NftXQj29zU7kohbCQ8MZ97t8wi1h3K4bBP5Aa+zcf9R/r5gu9nRxAuozIj8hs0ZeUyevw2Ap65rx8VxoSYnEnFPbSPa8umwT7FZbOTyLQ6fWfxnxV4WbztgdjSp51RmRM4gv7iMMR+tp9Tpol/7SEb1TDA7kohb69eyH/+89p8AHPV9nyLrSh77dCNZedp/RmqPyozIGTzz2WZSDxcR2zCAF265RPNkRM7CQ90fYkz3MQAcsb9EzrHtFZPnnZo/I7VDZUbkND5PzuDz5ExsVgv/vL0zDQO1n4zI2Xp54MsMaDkAJ8UctP+VVam7eXOZzm+S2qEyI3IK+3OLeOazzQA8fFVrujZrZHIiEc/iY/Vh5i0zaRfRjnLLIQ7an+OlxSlsTD9qdjSph1RmRH7Fefy4gvzichKbNuQPV7Y0O5KIRwr1D2Xe7fMIDwin1LqLHNsrPDJjPUWl5WZHk3pGZUbkV95ZvofVe48Q6Gfjlds642PT/yYi56tlo5bMuW0OvlZfinyWsyHv3arVgSI1RT+lRU6wOSOPFxceP65gcAeahQeZnEjE813R7Arevv5tAPJ8P+bfaz/Ucm2pUSozIscVlzl5ZGYyZU6DAR0iGdYtzuxIIvXG3Yl380TPJwA45PsKf/h0JgfzS0xOJfWFyozIcX/7eju7cwpoEmxnylAtwxapaVOunsL1rQeDpYxdrvGMmbmQcmc5y1KX8XHKxyxLXYbT5TQ7pnggi2EYhtkhapvD4SA0NJS8vDxCQkLMjiNuaPmug4z8z08AvH/PpfS5qLHJiUTqp4LSArr9uyc7DqdgczUhJMBCbskvl5ziQuJ4deCrDG031MSU4i7O9v1bIzPi9RzFZfzfrE0A3JXUTEVGpBY18GvAwpFfEuATjNOaQ25x9bkzGY4MbvnkFuZsm2NSQvFEKjPi9SZ/uY3MvGKahQfyf9e2NTuOSL0XGxxLA7+Aig9+dTXXoOJiwSMLHtElJzlrKjPi1ZbtyGHm2nQsFnjhlk4E+vmYHUmk3luetpyDRTmnfdzAIN2RzvK05XWYSjyZyox4rbxjZTw5OwWAUT0TuLS5dvkVqQtZ+Vk1+jwRlRnxWs99uZVsRzEJ4YH8eYAuL4nUlejg6Bp9nojKjHilpdtz+HTdfiwWmDqsEwF+NrMjiXiN3k17ExcSh+XXE2aOs2AhPiSe3k1713Ey8VQqM+J18orKeHJOxeqle3s1p1uCLi+J1CWb1carA18FOLnQHN8s5JWBr2Cz6pcMOTsqM+J1npu/lQOOElpEBPH4gDZmxxHxSkPbDWXWrbOIDYk96bFuIeO4sc1NJqQST6UyI15lxa5DVZeXXhh2Cf6++s1PxCxD2w0l9U+pLL1rKdOHTqd5aCuwwI7DO5i5Nt3seOJB3KLMlJSU0LlzZywWC8nJydUeS0tLY/DgwQQFBREREcHDDz9MaWmpOUHFox0rdfLU3IrVS7+7rBldm+nykojZbFYbfRP6MuLiEfzzupcByPf5kklfrSLHUWxyOvEUblFm/vznPxMTE3PS/U6nk0GDBlFYWMiKFSuYMWMGs2fP5rHHHjMhpXi6VxbvJO1IEdGh/jwxUKuXRNzNoNaD6BbTHcNSQmb5J0yYt8XsSOIhTC8zX3/9NQsXLmTq1KknPbZw4UK2bt3K//73PxITE7nmmmt48cUXeeedd3A4HCakFU+1OSOPd5fvBeC5GzvSwK7N8UTcjcViYWLfCQDk+8xnXsp2Fm7JNjeUeARTy8yBAwcYPXo0H374IYGBgSc9vmrVKjp27Fht1GbAgAGUlJSwbt26075uSUkJDoej2k28V7nTxZNzNuF0GQy6JJqr20WaHUlETuPaVtdyaeylGJYSHD6zefbzLeQXl5kdS9ycaWXGMAxGjRrFAw88QLdu3U75nOzsbCIjq7/xhIWF4efnR3b26dv6lClTCA0NrbrFx8fXaHbxLP/9YS+bMxyEBvgyYXAHs+OIyBlYLBYm9JkAQIHvV2Q4svjHgh3mhhK3V+NlZsKECVgsljPe1q5dy2uvvYbD4WDcuHFnfD2L5eRNlQzDOOX9lcaNG0deXl7VLT1ds+K9VdrhIl5atBOAp69rR+Ngu8mJROS3DGw1kB6xPXBRQp7vLP63eh/r9h0xO5a4sRovM2PGjGHbtm1nvHXs2JElS5bw448/Yrfb8fHxoVWrVgB069aNu+66C4CoqKiTRmByc3MpKys7acTmRHa7nZCQkGo38T6GYfDU3BSKy1wktQhnWLc4syOJyFmomDszEYBjvgsoM47w5OwUSsp1iracWo3PgoyIiCAiIuI3n/fPf/6T5557rurjzMxMBgwYwMyZM+nRowcASUlJTJ48maysLKKjK87oWLhwIXa7na5du9Z0dKlnPkvOYMXuQ9h9rDw/9OIzjuaJiHvp37I/SXFJrNq/irLAuezKuZe3lu3hT9e0NjuauCHT5sw0bdqUjh07Vt0uuugiAFq2bElcXMVv0P3796d9+/aMHDmSDRs2sHjxYh5//HFGjx6t0RY5o7xjZUyevw2Ah69uTfOIIJMTici5OHF0JtfyFeUc5vVlu9l3uNDkZOKOTF+afSY2m4358+fj7+9Pr169uPXWW7nxxhtPuYxb5EQvLtzBoYJSWjYOYnTvFmbHEZHzcE2La+gV34syVwkNGn9JabmLZz/fgmEYZkcTN2MxvOC7wuFwEBoaSl5enkZ0vEDK/jxueH0FhgEfje5Bz5a/fdlTRNzT4j2LuebDa/Cz2Yk99g4uZyPeurMLAztGmx1N6sDZvn+79ciMyLlyugye+SwFw4AhnWNUZEQ83FXNr6J3096UOkuIafoNABPnbaWwpNzkZOJOVGakXvn4pzQ27s8j2O7D09e1MzuOiFygE+fOrDn4KU3CCsjKK+afS3aZnEzcicqM1BuHCkr4x4LtADzW/yKahPibnEhEakLfhL5c0ewKSp2lRMcuAOA/y/ey80C+ycnEXajMSL0x5avtOIrL6RATwp2XNTM7jojUkBNHZxakfkTSRQblLoNnPtusycACqMxIPfHT3iPMXr8fi6XiIEkfm761ReqTvgl96ZvQl1JnKT4NP8ff18pPe48wd0OG2dHEDegnvni8MqeLv3y2GYDh3ZuS2DTM5EQiUhsqR2dmbnmfO3pVHE78/FfbyDumgyi9ncqMeLwPV+1jx4F8wgJ9+fOANmbHEZFackWzK7iq+VWUucrYVzqdlo2DOFRQyivf7jQ7mphMZUY82uGCEl4+/oPsiQFtCQvyMzmRiNSmytGZ9ze+x/1XBQPwwap97NJkYK+mMiMeberCneQfn/R7W/d4s+OISC27vOnlXNPiGspd5SxKf4t+7SNxugwmfblVk4G9mMqMeKzNGXnMWJMGwPjBHbBZdZCkiDeY0GcCANM2TuOu3gH42aws33WIRVsPmBtMTKMyIx7JMAwmztuCYcDgTjFc2ryR2ZFEpI70atqLfi36Ue4qZ1rKy9zXuzkAz83fRnGZ0+R0YgaVGfFI8zZlsSY1F39fK+OubWt2HBGpY5VzZ6YlT+O6RCuRIXbSjhTxnxV7TU4mZlCZEY9TVFrOlK+2AfBQ31bENAwwOZGI1LWk+CQGtByA03Dy0o9/48njv9S8vnQ32XnFJqeTuqYyIx7nrWU/k5VXTFxYAL+/ooXZcUTEJJWjMx9s/ICOTY/RpWlDikqd/P34sSbiPVRmxKOkHyni7e/3APD0de3w97WZnEhEzNIjrgfXtroWp+Fk8vLJTLihAxYLzN2Qwbp9uWbHkzqkMiMeZcrX2ygpd5HUIpyBHaPMjiMiJpvQdwIAH276kICAgwzrGgfAxHlbcLm0VNtbqMyIx/hp7xG+SsnGaoHxN7THYtFSbBFvd2nspQxqPQiX4eKv3/+VJwa0Jdjuw6b9eTq3yYuozIhHcLkMJs/fCsDwS5vSNirE5EQi4i4qR2emp0wnt3QfD13ZCoCpC3dwrFRLtb2Byox4hHmbMtm4P48gPxuPXnOR2XFExI10i+nG4IsGV43O3N0rgdiGAWTlFfOfFXvMjid1QGVG3F5xmZN/LNgBwIN9W9I42G5yIhFxN+P7jAfgo5SP2Je3mz8PrDh09s1lP3Mwv8TMaFIHVGbE7U1bmUrG0WNEhfhz7+Vaii0iJ+sa05Ub2tyAy3Ax6ftJDL4khk5xoRSWOqsOo5X6S2VG3NrhghJeX7IbgCcGtCHAT0uxReTUKs9s+jjlY3Yc3s5T17UDYMZPaTpVu55TmRG39s/Fu8gvKad9dAg3JcaaHUdE3FhidCI3tr0RA4NJ30+iR4tw+rePxGXA88d3DZf6SWVG3NbPBwuYvrriVOxnBrXDqlOxReQ3VI7OzNw8ky05W3jy2rb4WC0s3XGQFbsOmRtOao3KjLitv329nXKXwdVtm9CzVYTZcUTEA3SK6sTQdkOrRmdaNG7AnZc1A2DyV9twaiO9ekllRtzSj3sOs2jrAWxWC+Ou06nYInL2Klc2fbrlUzbnbObhq1sT7O/DtiwHs9fvNzmd1AaVGXE7LpdRdX17ePd4WjUJNjmRiHiSSyIv4Zb2t1SMznw3iUZBfow5vpHei9pIr15SmRG389XmLDYd3yDvEW2QJyLnoWp0ZuunpBxI4a6eFRvpHXCUMG1lqrnhpMapzIhbKXO6mPpNxQZ5v79CG+SJyPnp2KQjw9oPA2DidxPx97Uxtl/FL0dvLttNXlGZmfGkhqnMiFv5ZG06qYeLCA/y497ezc2OIyIebHyf8ViwMHvbbDZmb+TGxFjaRAbjKC7nze9+Njue1CCVGXEbx0qdvPrtLgDGXNWKBnYfkxOJiCfr0KQDt3a4FagYnbFZLTwxoOKYg/d+2Et2XrGZ8aQGqcyI23hv5V5y8kuICwtgRI+mZscRkXrg2T7PYsHC3O1zSc5O5up2TejWLIySchevLt5ldjypISoz4hbyisp4a1nFsO/Yfhdh99GxBSJy4do3bs/wjsMBmLBsAhaLhf+7tmK7h0/WpvPzwQIz40kNUZkRt/DGd7txFJfTNiqYIZ11bIGI1Jxn+zyL1WLl8x2fsz5rPd0TGnF12yY4XQYvLdQhlPWByoyYLjuvmGk/pAIVh0nadGyBiNSgthFtub3j7UDF6AzAEwPbYLHA/JQsNu0/al44qRGml5n58+fTo0cPAgICiIiIYOjQodUeT0tLY/DgwQQFBREREcHDDz9MaWmpSWmlNry6eCcl5S66J4RxVdsmZscRkXqocnRm3s55rMtcR9uoEG46Pgr8jwU7TE4nF8rUMjN79mxGjhzJ3XffzcaNG/nhhx8YMWJE1eNOp5NBgwZRWFjIihUrmDFjBrNnz+axxx4zMbXUpJ8PFvDJ2ortxf88sC0Wi0ZlRKTmXRR+EXdcfAcAE76bAMCj/S7C12Zhxe5DOoTSw1kMwzDl1K3y8nISEhKYOHEi99577ymf8/XXX3P99deTnp5OTEwMADNmzGDUqFHk5OQQEhJyVn+Ww+EgNDSUvLy8s/4cqRsPTV/HVynZXN22Cf8Z1d3sOCJSj+08vJN2r7fDZbj46b6f6B7bnQlfbGHaylQujg3lizG99AuVmznb92/TRmbWr19PRkYGVquVxMREoqOjufbaa9myZUvVc1atWkXHjh2rigzAgAEDKCkpYd26dad97ZKSEhwOR7WbuJ/NGXl8lZKNxVJx/VpEpDZdFH4Rd15yJ/DL6Mwfr2pFkJ+NlIw8vtlywMR0ciFMKzN79uwBYMKECTzzzDN8+eWXhIWF0adPH44cOQJAdnY2kZGR1T4vLCwMPz8/srOzT/vaU6ZMITQ0tOoWHx9fe38ROW8vL6pYRXBDpxjaRmnETERq31+u+As2i42vdn3F6v2rCW9g5+5eFbuNv7xoJy6XKRcr5ALVeJmZMKFiHf+ZbmvXrsXlcgHw9NNPc/PNN9O1a1fee+89LBYLn376adXrnWrIzzCMMw4Fjhs3jry8vKpbenp6Tf815QJtSMtl8fYcrBb409WtzY4jIl6iVaNWjOw0EvhldGZ07xYE+/uw40A+81OyTEwn56vG94sfM2YMw4cPP+NzEhISyM/PB6B9+/ZV99vtdlq0aEFaWhoAUVFRrF69utrn5ubmUlZWdtKIzYnsdjt2uw4odGcvHR+VGdoljhaNG5icRkS8yTO9n+HDjR+yYPcCVqWvIik+ifsub8HL3+7klW93ct3F0doiwsPU+MhMREQEbdu2PePN39+frl27Yrfb2bHjlyVxZWVlpKam0qxZMwCSkpLYvHkzWVm/NOWFCxdit9vp2rVrTUeXOrIm9QjLdx3Cx2rRqIyI1LmWjVpyV6e7gF9GZ+65PIGGgb78fLCQz5MzTEwn58O0OTMhISE88MADjB8/noULF7Jjxw4efPBBAIYNqzi2vX///rRv356RI0eyYcMGFi9ezOOPP87o0aO1KsmDVe64OaxbPPGNAk1OIyLe6JkrnsHH6sPCnxeyMn0lwf6+/P6KFgC8ungXZU6XyQnlXJi6z8wLL7zA8OHDGTlyJN27d2ffvn0sWbKEsLAwAGw2G/Pnz8ff359evXpx6623cuONNzJ16lQzY8sFWPnzIVbtOYyfzcqYq1qZHUdEvFTzsOaM6jQK+GVX4LuSEggP8mPf4SLmrN9vXjg5Z6btM1OXtM+MezAMg2FvrWLtvlx+l9SMSUM6mh1JRLxY6tFUWr/WmnJXOSvuXkGvpr14d/kenpu/jdiGASx9vC9+PqZvlO/V3H6fGfE+3+86xNp9udh9rPzhSo3KiIi5EhomcHfnuwEYv2w8AHde1owmwXYyjh5j5lqthPUUKjNSJwzDqFrBdOdlzYgM8Tc5kYgIPN37aXytvizeu5jl+5bj72ur+mXr9SW7KS5zmpxQzobKjNSJJdtz2Jh+lABfGw/0aWl2HBERAJo1bMY9ifcAv4zODL80nphQf7IdxXy0Os3MeHKWVGak1p04KvO7ns1oHKw9gETEfTzV+yl8rb4sTV3Kd6nfYfexMeaqim0j3lj2M8dKNTrj7lRmpNYt3HqALZkOgvxs3H+FRmVExL00DW3KfV3uA34ZnRnWLY64sAAOFZTw8U8anXF3KjNSqwzD4J+LdwEwqlcCjYL8TE4kInKyp3o/hZ/Nj+/2fcfSvUvxtf2yUOGt737W3Bk3pzIjtWrpjhy2ZDoI9LNx7+UtzI4jInJKcSFxjO4yGqjYFdgwDG7uEkdMqD85+SV8qpVNbk1lRmpNxajMbgBGXtZMozIi4tbGXT4OP5sf3+/7nqWpS/HzsfLg8dGZN5b9TEm5RmfclcqM1Jrluw6RnH4Uf18r9/XWqIyIuLfYkFh+3+X3QMXcGcMwGNY1jsgQO1l5xcxepzOb3JXKjNSKE+fKjLhUK5hExDOM6z0Ou83OirQVLN67GP8TtpN4felundnkplRmpFas2nOYtfty8fOxcn8fjcqIiGeICY7h/q73A7+Mztx+aVMiGlTsCjx3vUZn3JHKjNSK147PlRnePV67/YqIR3ny8ifx9/FnZfpKFu1ZdHx0puKXsn8t3U25RmfcjsqM1Lg1qUdYtecwvjaLdvsVEY8THRzNA10fAH4ZnRnRoynhQX6kHSnii42ZJieUX1OZkRpXOVfmlq7xxDQMMDmNiMi5+7/L/48AnwB+3P8j3/z8DYF+Poy+4vjozJLdOF2GyQnlRCozUqM2pOWyfNchfKwWHuqrURkR8UxRDaJ4sNuDwC+jM3de1oyGgb7sOVTIl5s0OuNOVGakRr22pGKuzE2JscQ3CjQ5jYjI+ftzrz8T4BPATxk/sWD3AhrYfbjv8uZAxc86l0Zn3IbKjNSYlP15LNmeg9VC1TbgIiKeKrJBJH/o/gfgl9GZ3/VMIMTfh905BXyzJdvkhFJJZUZqzBvLKkZlhnSOJSEiyOQ0IiIX7oleTxDoG8iazDV8tesrQvx9GdUzAajYFdgwNDrjDlRmpEbszilgwfHfUh7UXBkRqSeaBDWpGp2pPLNpVK/mBPjaSMnIY8XuQyYnFFCZkRry7+9/xjCgX/tILooMNjuOiEiNeaLnEwT5BrE2cy1f7vySRkF+DL80HoA3lv5scjoBlRmpAVl5x5i7oWJXTI3KiEh90zioMWMuHQP8MjozuncLfG0WVu05zIa0XJMTisqMXLB3vt9LmdPgshaN6NI0zOw4IiI17vGej9PArwHrs9bzxY4viGkYwI2dY4GKuTNiLpUZuSC5haV8/FMaAA/11QomEamfIgIj+OOlfwR+GZ25v09LLBZYtPUAOw/km5zQu6nMyAWZtjKVY2VOOsSE0Lt1hNlxRERqzWNJjxHsF0xydjKf7/icVk0aMKB9FABvaXTGVCozct4KS8p5f1UqUDEqY7FYzA0kIlKLwgPDebjHwwBMWDYBl+HioSsr5gl+vjGT9CNFZsbzaiozct4+/imNo0VlNI8IYmDHKLPjiIjUurFJYwn2C2bjgY18tv0zLolryOWtInC6DN5ZvsfseF5LZUbOS0m5k3eX7wXg/itaYLNqVEZE6r9GAY34U48/ASeMzhxfxTlzTToH80vMjOe1VGbkvHy+IZNsRzGRIXZu6hJrdhwRkTozNmksIfYQUnJSmLNtDkktw+kU35CSchfv/bDX7HheSWVGzpnTZfDWdxWT3e67vAV2H5vJiURE6k5YQBiP9HgEgInfTcTAqBqd+XDVPhzFZSam804qM3LOFm7JZs+hQkIDfLm9R1Oz44iI1LlHkx4l1B7K5pzNzNo6i37tImndpAH5JeVM/zHN7HheR2VGzolhGLx5fFTmrqRmNLD7mJxIRKTuNfRvyKOXPQpUjs64+P0VLQB474e9lJa7zIzndVRm5Jz8uOcIm/bnYfexctfxk2NFRLzRI5c9QkP/hmw9uJVPt37KkM6xRIbYyckv4YuNmWbH8yoqM3JOKpceDusWR3gDu8lpRETME+ofytjLxgIw6btJ2KwGo3o2B+Cd7/dgGIaZ8byKyoyctV0H8lmyPQeLBe69vIXZcURETPdwj4cJ8w9j26FtfLLlE0b0aEqQn40dB/L5budBs+N5DZUZOWuV+8r0bx9J84ggk9OIiJgv1D+UsUnHR2e+n0QDu5Xhl1YsjNAmenVHZUbOSk5+MXM3ZABUTXITEZGK0ZlGAY3Yfmg7MzbP4O5eCdisFn7YfZjNGXlmx/MKppaZnTt3MmTIECIiIggJCaFXr14sXbq02nPS0tIYPHgwQUFBRERE8PDDD1NaWmpSYu/1wcp9lDpddGnakK7NGpkdR0TEbYTYQ3gs6TGgYnQmKtSP6y+JBjQ6U1dMLTODBg2ivLycJUuWsG7dOjp37sz1119PdnY2AE6nk0GDBlFYWMiKFSuYMWMGs2fP5rHHHjMzttcpKi3nwx/3ARqVERE5lT9e+kfCA8LZeXgnH6d8zOjeFT8rv9yURcbRYyanq/9MKzOHDh1i9+7dPPnkk1xyySW0bt2av/3tbxQVFbFlyxYAFi5cyNatW/nf//5HYmIi11xzDS+++CLvvPMODofDrOhe59O1+8k7Vkaz8ED6tdeBkiIivxZsD+bxno8DFaMzbaOD6NkyHKfL4L0VOuKgtplWZsLDw2nXrh0ffPABhYWFlJeX8/bbbxMZGUnXrl0BWLVqFR07diQmJqbq8wYMGEBJSQnr1q077WuXlJTgcDiq3eT8OF0G766oGCa97/LmOlBSROQ0xlw6hojACHYf2c30TdOrRrI//imNvGM64qA2mVZmLBYLixYtYsOGDQQHB+Pv78/LL7/MggULaNiwIQDZ2dlERkZW+7ywsDD8/PyqLkWdypQpUwgNDa26xcfH1+ZfpV77Zks26UeOERboyy1d9XUUETmdBn4NeKLnEwD89fu/0qtVGG0igyksdfLxTzrioDbVeJmZMGECFovljLe1a9diGAYPPfQQTZo0Yfny5fz0008MGTKE66+/nqysrKrXs1hOHgkwDOOU91caN24ceXl5Vbf09PSa/mt6BcMwePv7ilGZkZc1I8BPB0qKiJzJH7r/gcaBjfk592emp0znvt4Vm+jpiIPaVeMH64wZM4bhw4ef8TkJCQksWbKEL7/8ktzcXEJCQgB44403WLRoEe+//z5PPvkkUVFRrF69utrn5ubmUlZWdtKIzYnsdjt2u3anvVBr9+WyMf0ofj5WRiYlmB1HRMTtBfkF8edef+aJRU/w1+//yqb7b2fqQjsHHBVHHNzSNc7siPVSjY/MRERE0LZt2zPe/P39KSoqqghgrR7BarXiclW016SkJDZv3lxtpGbhwoXY7faqeTVSe/59fFTm5i6xNA5WORQRORsPdnuQJkFN2JO7h5lbp1cdcfDuch1xUFtMmzOTlJREWFgYd911Fxs3bmTnzp088cQT7N27l0GDBgHQv39/2rdvz8iRI9mwYQOLFy/m8ccfZ/To0VWjOVI79hws4NttBwAdXSAici6C/IL4c88/A/Dc988xrFs0gX42tmfns+rnwyanq59MKzMREREsWLCAgoICrrrqKrp168aKFSv4/PPP6dSpEwA2m4358+fj7+9Pr169uPXWW7nxxhuZOnWqWbG9xrSVqRgGXNW2Ca2aNDA7joiIR3mw+4NEBkWy9+hePtv5UdXlpf/+oGXatcFieMGYl8PhIDQ0lLy8PI3onIW8Y2UkTVlMUamT6ff1oFerCLMjiYh4nJdXvczYhWNpFtqMBcPXM/CVVVgssOSxvjrf7iyd7fu3zmaSk3yyJp2iUidtIoPp2TLc7DgiIh7pgW4PENUgin15+/g+YxZXtW2CYcA0jc7UOJUZqabc6WLaylQA7u6VcMYl8CIicnoBvgE82etJACYvn8zIy2IB+HTdfm2iV8NUZqSaRVsPkHG0YpO8GxNjzY4jIuLRft/190Q3iCYtL43t+Z/TJjKYolInn6zR/mc1SWVGqnnvh1QA7ujRDH9fbZInInIhAnwDGHf5OACmrJjCyKSK07SnrUyl3KlN9GqKyoxU2ZyRx0+pR/CxWhiZ1MzsOCIi9cLorqOJCY4h3ZHOERbSKMiPjKPHWLT1gNnR6g2VGalSuWRw0CXRRIb4m5xGRKR+8PfxrxqdeWHV37itexSgZdo1SWVGAMjJL2bexkwA7u7V3OQ0IiL1y31d7iM2OJb9jv24Ahfja7OwJjWXTfuPmh2tXlCZEQD+92MaZU6DLk0b0jm+odlxRETqFX8ff57q/RQA/1r7AgM7Vmx7UTlPUS6MyoxQXObko9X7ALjnco3KiIjUhnsT7yU+JJ7M/EwaNPoOgHkbMzngKDY5medTmRHmbczkUEEpMaH+DOwQZXYcEZF6ye5jrxqdeX/zK3RpFki5y+DDVftMTub5VGa8nGEYVcOcI5MS8LHpW0JEpLbck3gPTUObklWQReOoFQBMX72P4jKnyck8m965vNzqvUfYmuXA39fK7ZfGmx1HRKRe87P58XTvpwH4Ys8bRIVayS0q44vkTJOTeTaVGS/33xUVSwNv7hJHw0A/k9OIiNR/ozqPolloM7ILsomP/wGo2ETPC859rjUqM15sf24R326r2LRpVM8Ec8OIiHgJP5sfz1zxDADfZ72Lr08pW7McrE/LNTmZ51KZ8WLTV6fhMqBXq3BaRwabHUdExGvc1ekuEhomkFN0gLi4itGZ91dqIvD5UpnxUsVlTmYeP+hs5GUJ5oYREfEyvjZfnuldMTqzKe8DXBTzVUoWOVqmfV5UZrzU/E1ZHCmsWI59TbsmZscREfE6v+v0O1qEteBI8UFCI5ZQ7jL4+Cedpn0+VGa81Ac/Vgxn3nFZMy3HFhExwYmjM+llM3FRzPTV+yjTadrnTO9iXig5/Sgb04/iZ7MyvLuWY4uImGVkp5G0DGtJXulhXIELyMkv4Zst2WbH8jgqM17og1WpAFx/STThDezmhhER8WI+Vh/+csVfADhqm42LY3ygicDnTGXGyxwuKOHLTVkAjExqZnIaERG545I7aN2oNYXluRT6zuen1CNszXSYHcujqMx4mZlr0yktd3FJXKhOxxYRcQMnjs4U+c3FRREf/phqbigPozLjRZwug+k/pgEw8rJmWCwWkxOJiAjA7RffTutGrSl25ZHv8yVzN2SQV1RmdiyPoTLjRRZvO0DG0WOEBfoyuFOM2XFEROQ4H6sPz/Z5FoBCv88oKivg03Vapn22VGa8yAfHj5m/rXtT/H1tJqcREZET3d7xdtqEt6HMcJDvM48PVu3D5dJ5TWdDZcZL7M4pYMXuQ1gscEePpmbHERGRX7FZbVWjM/k+c0k9cpDvdh40OZVnUJnxEv87vkne1W0jiW8UaHIaERE5lds63Ea7iHY4LQU4fL7g/eNbaciZqcx4gYKScmav2w/A77QcW0TEbVUfnfmMJTv3kn6kyORU7k9lxgt8tiGD/JJyWkQEcXmrCLPjiIjIGQxrP4z2jdvjshTisH3Bxz+lmR3J7anM1HOGYTB9dcX/CCN6NMVq1XJsERF3ZrPaGN9nPAAOn8/5aM02Sst1XtOZqMzUcxvSj7Ity4Hdx8otXePMjiMiImfhlva30L5xBwxLIakln7Jwq85rOhOVmXqucpO86y+JoWGgn8lpRETkbFgtViacMDrz35UpJidybyoz9VheURlfbsoE4I7LtBxbRMST3Nz+ZtqFd8SwFLFk/zR25xSYHcltqczUY7PX76ek3EXbqGASdQ6TiIhHsVqs/PWqCUDF6My7P2wyNY87U5mppyom/lbsLXOHzmESEfFIN7W7iRYN22NYjvHfja9RXOY0O5JbUpmpp37ae4SfDxYS6Gfjxs46h0lExBNZLVb+0e+vABzkM8YvfJ+PUz5mWeoynC4Vm0q1WmYmT55Mz549CQwMpGHDhqd8TlpaGoMHDyYoKIiIiAgefvhhSktLqz0nJSWFPn36EBAQQGxsLJMmTcIwdF7FmVQuxx7SOZZgf1+T04iIyPka2u4mwu2xYCnmH2vvZcScEVz5/pUkvJrAnG1zzI7nFmq1zJSWljJs2DAefPDBUz7udDoZNGgQhYWFrFixghkzZjB79mwee+yxquc4HA769etHTEwMa9as4bXXXmPq1Km89NJLtRndox0uKOHrzVmAzmESEfF0c7fP5XBJxkn3ZzgyuOWTW1RoAJ/afPGJEycCMG3atFM+vnDhQrZu3Up6ejoxMRWXQl588UVGjRrF5MmTCQkJYfr06RQXFzNt2jTsdjsdO3Zk586dvPTSS4wdO1ZzQU5h1rr9lDkNOsWF0jE21Ow4IiJynpwuJ39a8KdTPmZgYMHCIwseYUibIdistjpO5z5MnTOzatUqOnbsWFVkAAYMGEBJSQnr1q2rek6fPn2w2+3VnpOZmUlqauopX7ekpASHw1Ht5i1cLoOPjm99fUcPncMkIuLJlqctZ79j/2kfNzBId6SzPG15HaZyP6aWmezsbCIjI6vdFxYWhp+fH9nZ2ad9TuXHlc/5tSlTphAaGlp1i4+Pr4X07umHnw+x73ARwf4+XN8p2uw4IiJyAbLys2r0efXVOZeZCRMmYLFYznhbu3btWb/eqS4TGYZR7f5fP6dy8u/pLjGNGzeOvLy8qlt6evpZ5/F0lTv+Dk2MJdCvVq8iiohILYsOPrtfSs/2efXVOb/bjRkzhuHDh5/xOQkJCWf1WlFRUaxevbrafbm5uZSVlVWNvkRFRZ00ApOTkwNw0ohNJbvdXu2ylLc44Chm0bYDAIzQJSYREY/Xu2lv4kLiyHBkYHDyKl4LFuJC4ujdtLcJ6dzHOZeZiIgIIiIiauQPT0pKYvLkyWRlZREdXdEqFy5ciN1up2vXrlXPeeqppygtLcXPz6/qOTExMWddmrzFJ2vScboMuieE0SYq2Ow4IiJygWxWG68OfJVbPrkFC5ZfFZqKqxOvDHzFqyf/Qi3PmUlLSyM5OZm0tDScTifJyckkJydTUFBxvkT//v1p3749I0eOZMOGDSxevJjHH3+c0aNHExISAsCIESOw2+2MGjWKzZs3M3fuXJ5//nmtZPoVp8vgY038FRGpd4a2G8qsW2cRGxJb7X4fI4IPb5zB0HZDTUrmPmp1UsWzzz7L+++/X/VxYmIiAEuXLqVv377YbDbmz5/PQw89RK9evQgICGDEiBFMnTq16nNCQ0NZtGgRf/jDH+jWrRthYWGMHTuWsWPH1mZ0j/P9zoNk5hXTMNCXgR2jzI4jIiI1aGi7oQxpM4TlacvJzM/kxa9zOHSkBRR3MjuaW7AYXrCVrsPhIDQ0lLy8vKoRn/rm/g/X8s2WA9x7eXP+cn17s+OIiEgtenf5Hp6bv42LY0OZ98fLzY5Ta872/VtnM9UDOfnFLN5WMSn6tu7eswxdRMRbDe0Sh5/NSkpGHpsz8syOYzqVmXpgzvoMyl0GXZo25KJITfwVEanvGgX50b9DxYremWu8Z/uR01GZ8XCGYVR9Iw/vrnOYRES8ReXP/M+SMzhW6t0naKvMeLif9h5h76FCgvxsDLrEuzdNEhHxJj1bhhPfKID84nK+StEOwOLBZhwflbmhcwxBdu34KyLiLaxWC7d1q5gnOWNNmslpzKUy48Hyisqq2vhtusQkIuJ1hnWLx2a1sCY1l905+WbHMY3KjAf7fGMGJeUu2kYF0yku1Ow4IiJSxyJD/LmyTRPAuycCq8x4KMMw+Pinim/c27rHazdkEREvNfz4lhyz12dQUu6dE4FVZjzU5gwH27Ic+PlYuSkx9rc/QURE6qW+bRoTGWLnSGEpi7YeMDuOKVRmPFTlZK9rO0bRMNDP5DQiImIWH5uVYV0rRme89VKTyowHKiot54vkTEA7/oqIyC/vBct3HSL9SJHJaeqeyowHmr8pi/yScpqFB3JZ83Cz44iIiMniGwXSu3UE4J2jMyozHqjyG/XWbvFYrZr4KyIiv4zOfLounXKny+Q0dUtlxsPszsln7b5cbFYLt3SNMzuOiIi4iX7tI2kU5McBRwnf7zpodpw6pTLjYSpHZa5s04TIEH+T04iIiLuw+9gY0jkGgE/X7jc5Td1SmfEgpeUu5qzPAH7ZV0BERKRS5aqmb7cd4Ehhqclp6o7KjAdZsj2Hw4WlNA6207dNY7PjiIiIm2kfE0LH2BDKnAafJ2eYHafOqMx4kFnrKoYNhybG4mPTP52IiJyscnTmEy+61KR3RA9xML+EpTtyABjWTRN/RUTk1IZ0jsHPZmVbloPNGXlmx6kTKjMe4rMNGThdBp3jG9KqSbDZcURExE01DPSjX/tI4JcR/fpOZcYDGIZR9Q2p5dgiIvJbbjk+gv9ZsnccPqky4wFSMvLYcSAfu4+VwZ1izI4jIiJu7orWjYkK8edoURmLt+WYHafWqcx4gMr9AgZ0iCI0wNfkNCIi4u5sVgtDu8QC8Ona+n+8gcqMmysuc/LFxopDJXWJSUREzlble8Z3Ow+SnVdscprapTLj5r7ddoC8Y2VEh/rTq1WE2XFERMRDtGjcgG7NwnAZMGdD/Z4IrDLj5ion/t7cJQ6bDpUUEZFzULmVx6y1+zEMw+Q0tUdlxo1l5xXz/c6Kw8Ju1iUmERE5R4MuiSHA18aeQ4WsT8s1O06tUZlxY3M27MdlQPeEMJpHBJkdR0REPEwDuw/XXhwF1O/DJ1Vm3NSJe8tUbk0tIiJyrm7tVvEe8uWmLIpKy01OUztUZtzU+rSj7DlYSICvjesuiTY7joiIeKgezRvRtFEgBSXlfJ2SbXacWqEy46ZmravYF+Dai6NoYPcxOY2IiHgqi8VStUz703X1c88ZlRk3dKzUyZcbswBdYhIRkQtXuYjkxz1H2J9bZHKamqcy44a+2ZJNfkk5cWEB9GjeyOw4IiLi4WIbBpDUIhyoOLi4vlGZcUOVw4C3dI3Dqr1lRESkBlQebzBnfUa923NGZcbNZOUdY+XPh4GKjfJERERqwrUXR+Pva2XPoUKS04+aHadG1WqZmTx5Mj179iQwMJCGDRue9PjGjRu5/fbbiY+PJyAggHbt2vHqq6+e9LyUlBT69OlDQEAAsbGxTJo0qd61ykqfbcjEMODS5o2IbxRodhwREaknGth9GNihYs+ZOevr16WmWi0zpaWlDBs2jAcffPCUj69bt47GjRvzv//9jy1btvD0008zbtw4/vWvf1U9x+Fw0K9fP2JiYlizZg2vvfYaU6dO5aWXXqrN6KYwDIM56yv2lhmaGGtyGhERqW+GHh/xn7cpk5Jyp8lpak6trvmdOHEiANOmTTvl4/fcc0+1j1u0aMGqVauYM2cOY8aMAWD69OkUFxczbdo07HY7HTt2ZOfOnbz00kuMHTsWi6X+zCnZkulgV04Bfj5W7S0jIiI1rlerCJoE28nJL2Hp9oMM7BhldqQa4XZzZvLy8mjU6JcVPKtWraJPnz7Y7faq+wYMGEBmZiapqamnfI2SkhIcDke1myeYfXxUpl/7SEL8fU1OIyIi9Y3NauGmxMqJwPXneAO3KjOrVq3ik08+4f7776+6Lzs7m8jIyGrPq/w4O/vUOxlOmTKF0NDQqlt8vPvv1VLudDFvYyYAN3fRJSYREakdlZealu7I4UhhqclpasY5l5kJEyZgsVjOeFu7du05B9myZQtDhgzh2WefpV+/ftUe+/WlpMrJv6e7xDRu3Djy8vKqbunp7r/j4fJdhzhUUEp4kB+9Wzc2O46IiNRTbaKC6RATQpnT4MtNmWbHqRHnPGdmzJgxDB8+/IzPSUhIOKfX3Lp1K1dddRWjR4/mmWeeqfZYVFTUSSMwOTk5ACeN2FSy2+3VLkt5gspLTIM7xeBrc6sBMxERqWeGdoljS+ZW5qzP4HdJCWbHuWDnXGYiIiKIiIiosQBbtmzhqquu4q677mLy5MknPZ6UlMRTTz1FaWkpfn5+ACxcuJCYmJhzLk3uylFcxqKtBwDtLSMiIrXvhk4xPP/VNpLTj/LzwQJaNm5gdqQLUqtDAGlpaSQnJ5OWlobT6SQ5OZnk5GQKCgqAiiJz5ZVX0q9fP8aOHUt2djbZ2dkcPHiw6jVGjBiB3W5n1KhRbN68mblz5/L888/Xq5VMC1KyKSl30apJAzrGhpgdR0RE6rnGwXb6XFQxpWFuPdhzplbLzLPPPktiYiLjx4+noKCAxMREEhMTq+bUfPrppxw8eJDp06cTHR1ddevevXvVa4SGhrJo0SL2799Pt27deOihhxg7dixjx46tzeh1qvIS002JsfWmoImIiHurPN5g7oYMXC7P3ojWYtTXrXRP4HA4CA0NJS8vj5AQ9xr52J9bxOV/X4rFAiv+7ypiGwaYHUlERLxAcZmT7pO/Jb+4nI9HX0ZSy3CzI53kbN+/NdPUZJ8nV8wkv6x5uIqMiIjUGX9fG9cf36DV0/ecUZkxkWEYVZeYhmpvGRERqWOVe858lZLFsVLPPd5AZcZEm/bnsedgIf6+Vq69WMcXiIhI3erWLIz4RgEUljpZuPXUG9F6ApUZE1UO6/VvH0UDe60ekyUiInISi8XC0MSK0ZlZ6zz3UpPKjEnKnC7mbcoCdIlJRETMU/ke9MPuQ+TkF5uc5vyozJjkux0HOVJYSkQDO5e3qrlNCEVERM5Fs/AgEps2xGXAlxuzzI5zXlRmTDJnQ8Vw3pDOMfjo+AIRETHRkE4xAHye7Jkb6Old1AR5x8r4dlvF+VK6xCQiIma7vlMMNquFjfvz2Huo0Ow450xlxgTfbM6mtNxF6yYNaB/tXpv4iYiI9zlxysNnGzxvdEZlxgSfb6z4RrlRxxeIiIibuDHxl0tNnnY4gMpMHctxFLPy58NAxamlIiIi7qB/+ygCfG2kHi5i4/48s+OcE5WZOvbFxkwMA7o2CyO+UaDZcURERAAIsvvQr30k4HkTgVVm6tgXGyvOYhrSWaMyIiLiXiovNc3bmEW502VymrOnMlOH9hwsYNP+PGxWC4N0fIGIiLiZ3q0bExboy6GCkqopEZ5AZaYOVZ6Q3bt1BOEN7CanERERqc7XZmXQ8ZO0P/OgS00qM3XEMAxdYhIREbd3Y+eK/c++2ZztMSdpq8zUkZSMio2I/H2t9GsfZXYcERGRU+raLIy4sIqTtL/ddsDsOGdFZaaOfLahYlSmn07IFhERN2axWKquIHjKqiaVmTrgdBnM23T8EpP2lhERETdXealp2Y6D5BaWmpzmt6nM1IEf9xzmYH4JDQN9ueKixmbHEREROaPWkcG0jw6h3GUwP8X9T9JWmakDledcXHdxNH4++pKLiIj7O/F4A3end9ZaVlzmZMHmbECXmERExHMM7hSDxQJrUnPZn1tkdpwzUpmpZct25JBfUk5MqD/dExqZHUdEROSsRIcG0KN5xftW5T5p7kplppZVrmIa3DkGq1UnZIuIiOeonAj8hcqM98o7VsaSHTkADOkUa3IaERGRc3Ntx2h8bRZ2HMhnR3a+2XFOS2WmFn2zJZvSchetmzSgXXSw2XFERETOSWigL32Or8L9cpP7js6ozNSiyhngNybGYrHoEpOIiHiewZ0qT9LOxDAMk9OcmspMLclxFFedOHqDVjGJiIiHuqZdJP6+VlIPF7El02F2nFNSmakl81OyMAxIbNqQ+EaBZscRERE5L0F2H65uGwlUjM64I5WZWvLlpoodEwdfolEZERHxbIM7RQMV720ul/tdalKZqQUZR4+xbl8uFgsMuiTa7DgiIiIXpG+bJjSw+5Bx9Bgb0nPNjnMSlZlaMP/4jO9LExoRGeJvchoREZEL4+9ro3/7yktN7ndWk8pMLai8xHS9Jv6KiEg9Ubmq6ctNWTjd7FKTykwNSz1UyKb9eVgtcG3HKLPjiIiI1IherSJoGOjLoYISVu85bHacalRmaljlUem9WkUQ0cBuchoREZGa4edjrfolfZ6bbaCnMlPDKpetXa+JvyIiUs9UrtD9enPFDvfuolbLzOTJk+nZsyeBgYE0bNjwjM89fPgwcXFxWCwWjh49Wu2xlJQU+vTpQ0BAALGxsUyaNMktdyHcnZPP9ux8fKwWBnTQJSYREalferQIJ6KBnaNFZfyw+5DZcarUapkpLS1l2LBhPPjgg7/53HvvvZdLLrnkpPsdDgf9+vUjJiaGNWvW8NprrzF16lReeuml2oh8QSpneF9xUWMaBvqZnEZERKRm2ayWqisP7rSBXq2WmYkTJ/Loo49y8cUXn/F5b775JkePHuXxxx8/6bHp06dTXFzMtGnT6NixI0OHDuWpp57ipZdecqvRGcMwqg7h0iUmERGpryo30Fu49QDFZU6T01Qwfc7M1q1bmTRpEh988AFW68lxVq1aRZ8+fbDbf5lMO2DAADIzM0lNTT3la5aUlOBwOKrdatu2rHx+PliIn4+VfsfX4ouIiNQ3ifFhxDYMoKCknGU7csyOA5hcZkpKSrj99tt54YUXaNq06Smfk52dTWRk9XJQ+XF2dvYpP2fKlCmEhoZW3eLj42s2+ClUjspc2aYxwf6+tf7niYiImMFa7VKTe2ygd85lZsKECVgsljPe1q5de1avNW7cONq1a8edd955xudZLJZqH1deXvr1/Se+bl5eXtUtPT39rPKcr4pLTMc3ytNZTCIiUs9VbqC3ePsBCkrKTU4DPuf6CWPGjGH48OFnfE5CQsJZvdaSJUtISUlh1qxZwC8lJSIigqeffpqJEycSFRV10ghMTk7FsNavR2wq2e32apelatum/XmkHSkiwNfG1e2a1NmfKyIiYoYOMSE0jwhi76FCFm87wJDOsabmOecyExERQURERI384bNnz+bYsWNVH69Zs4Z77rmH5cuX07JlSwCSkpJ46qmnKC0txc+vYoXQwoULiYmJOevSVNsqLzFd3a4JgX7n/CUVERHxKBaLhcGXRPPPJbuZtzHT9DJTq3Nm0tLSSE5OJi0tDafTSXJyMsnJyRQUFADQsmVLOnbsWHVr3rw5AO3ataNJk4oRjhEjRmC32xk1ahSbN29m7ty5PP/884wdO/a0l5nqkstlMF+XmERExMtUXmr6budB8o6VmZqlVsvMs88+S2JiIuPHj6egoIDExEQSExPPek4NQGhoKIsWLWL//v1069aNhx56iLFjxzJ27NhaTH721qflkplXTAO7D33bNDY7joiISJ1oHRnMRZENKHMaLNp6wNQsFsOdNmupJQ6Hg9DQUPLy8ggJCanR157wxRamrUxlaGIsL93WuUZfW0RExJ39c/EuXlq0k75tGjPt7ktr/PXP9v3b9H1mPJnTZVQdLHl9J22UJyIi3uW6iyve+1bsOsTRolLTcqjMXIDVew9zML+E0ABfLm+lS0wiIuJdWjVpQNuoYMpdBgu3mHepSWXmAlTuLTOwQxR+PvpSioiI9xncKYYAXxuHCktMy6B1xBdgWNc4fK0WBmkVk4iIeKmRSc24p1dzAvxspmVQmbkAiU3DSGwaZnYMERER04S4wRE+ujYiIiIiHk1lRkRERDyayoyIiIh4NJUZERER8WgqMyIiIuLRVGZERETEo6nMiIiIiEdTmRERERGPpjIjIiIiHk1lRkRERDyayoyIiIh4NJUZERER8WgqMyIiIuLRvOLUbMMwAHA4HCYnERERkbNV+b5d+T5+Ol5RZvLz8wGIj483OYmIiIicq/z8fEJDQ0/7uMX4rbpTD7hcLjIzMwkODsZisZgdp9Y5HA7i4+NJT08nJCTE7DheQ193c+jrbg593c3hbV93wzDIz88nJiYGq/X0M2O8YmTGarUSFxdndow6FxIS4hXf7O5GX3dz6OtuDn3dzeFNX/czjchU0gRgERER8WgqMyIiIuLRVGbqIbvdzvjx47Hb7WZH8Sr6uptDX3dz6OtuDn3dT80rJgCLiIhI/aWRGREREfFoKjMiIiLi0VRmRERExKOpzIiIiIhHU5mpZyZPnkzPnj0JDAykYcOGp3xOWloagwcPJigoiIiICB5++GFKS0vrNmg9l5CQgMViqXZ78sknzY5VL73xxhs0b94cf39/unbtyvLly82OVK9NmDDhpO/tqKgos2PVO99//z2DBw8mJiYGi8XCZ599Vu1xwzCYMGECMTExBAQE0LdvX7Zs2WJOWDegMlPPlJaWMmzYMB588MFTPu50Ohk0aBCFhYWsWLGCGTNmMHv2bB577LE6Tlr/TZo0iaysrKrbM888Y3akemfmzJk88sgjPP3002zYsIHevXtz7bXXkpaWZna0eq1Dhw7VvrdTUlLMjlTvFBYW0qlTJ/71r3+d8vF//OMfvPTSS/zrX/9izZo1REVF0a9fv6qzCL2OIfXSe++9Z4SGhp50/1dffWVYrVYjIyOj6r6PP/7YsNvtRl5eXh0mrN+aNWtmvPzyy2bHqPcuvfRS44EHHqh2X9u2bY0nn3zSpET13/jx441OnTqZHcOrAMbcuXOrPna5XEZUVJTxt7/9req+4uJiIzQ01HjrrbdMSGg+jcx4mVWrVtGxY0diYmKq7hswYAAlJSWsW7fOxGT1z9///nfCw8Pp3LkzkydP1qW8GlZaWsq6devo379/tfv79+/PypUrTUrlHXbt2kVMTAzNmzdn+PDh7Nmzx+xIXmXv3r1kZ2dX+9632+306dPHa7/3veKgSflFdnY2kZGR1e4LCwvDz8+P7Oxsk1LVP3/605/o0qULYWFh/PTTT4wbN469e/fy7rvvmh2t3jh06BBOp/Ok7+fIyEh9L9eiHj168MEHH3DRRRdx4MABnnvuOXr27MmWLVsIDw83O55XqPz+PtX3/r59+8yIZDqNzHiAU024+/Vt7dq1Z/16FovlpPsMwzjl/fKLc/l3ePTRR+nTpw+XXHIJ9913H2+99Rb/+c9/OHz4sMl/i/rn19+3+l6uXddeey0333wzF198Mddccw3z588H4P333zc5mffR9/4vNDLjAcaMGcPw4cPP+JyEhISzeq2oqChWr15d7b7c3FzKyspOavlS3YX8O1x22WUA7N69W7+91pCIiAhsNttJozA5OTn6Xq5DQUFBXHzxxezatcvsKF6jcvVYdnY20dHRVfd78/e+yowHiIiIICIiokZeKykpicmTJ5OVlVX1P8HChQux2+107dq1Rv6M+upC/h02bNgAUO0Hj1wYPz8/unbtyqJFi7jpppuq7l+0aBFDhgwxMZl3KSkpYdu2bfTu3dvsKF6jefPmREVFsWjRIhITE4GKOWTfffcdf//7301OZw6VmXomLS2NI0eOkJaWhtPpJDk5GYBWrVrRoEED+vfvT/v27Rk5ciQvvPACR44c4fHHH2f06NGEhISYG76eWLVqFT/++CNXXnkloaGhrFmzhkcffZQbbriBpk2bmh2vXhk7diwjR46kW7duJCUl8e9//5u0tDQeeOABs6PVW48//jiDBw+madOm5OTk8Nxzz+FwOLjrrrvMjlavFBQUsHv37qqP9+7dS3JyMo0aNaJp06Y88sgjPP/887Ru3ZrWrVvz/PPPExgYyIgRI0xMbSKTV1NJDbvrrrsM4KTb0qVLq56zb98+Y9CgQUZAQIDRqFEjY8yYMUZxcbF5oeuZdevWGT169DBCQ0MNf39/o02bNsb48eONwsJCs6PVS6+//rrRrFkzw8/Pz+jSpYvx3XffmR2pXrvtttuM6Ohow9fX14iJiTGGDh1qbNmyxexY9c7SpUtP+bP8rrvuMgyjYnn2+PHjjaioKMNutxtXXHGFkZKSYm5oE1kMwzDMKlIiIiIiF0qrmURERMSjqcyIiIiIR1OZEREREY+mMiMiIiIeTWVGREREPJrKjIiIiHg0lRkRERHxaCozIiIi4tFUZkRERMSjqcyIiIiIR1OZEREREY+mMiMiIiIe7f8BWUzg4HVrEAEAAAAASUVORK5CYII=\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "f = lambda x: -x**2\n",
+    "grad_fn = lambda x: -2*x\n",
+    "x, xs = gradient_ascent(grad_fn=grad_fn, x0=10.0, learn_rate=0.2)\n",
+    "plt.plot(np.arange(-12, 12, 0.01), [f(x) for x in np.arange(-12, 12, 0.01)])\n",
+    "plt.plot(xs, [f(x) for x in xs], 'o-', color='g')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6bc6d772",
+   "metadata": {},
+   "source": [
+    "## learning rate"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "id": "65ccee71",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2023-04-02T06:18:47.389364Z",
+     "start_time": "2023-04-02T06:18:47.213790Z"
+    },
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0: 10.000, -16.00=0.800*20.000, -6.000\n",
+      "1: -6.000, 9.60=0.800*-12.000, 3.600\n",
+      "2: 3.600, -5.76=0.800*7.200, -2.160\n",
+      "3: -2.160, 3.46=0.800*-4.320, 1.296\n",
+      "4: 1.296, -2.07=0.800*2.592, -0.778\n",
+      "5: -0.778, 1.24=0.800*-1.555, 0.467\n",
+      "6: 0.467, -0.75=0.800*0.933, -0.280\n",
+      "7: -0.280, 0.45=0.800*-0.560, 0.168\n",
+      "8: 0.168, -0.27=0.800*0.336, -0.101\n",
+      "9: -0.101, 0.16=0.800*-0.202, 0.060\n",
+      "10: 0.060, -0.10=0.800*0.121, -0.036\n",
+      "11: -0.036, 0.06=0.800*-0.073, 0.022\n",
+      "12: 0.022, -0.03=0.800*0.044, -0.013\n",
+      "13: -0.013, 0.02=0.800*-0.026, 0.008\n",
+      "14: 0.008, -0.01=0.800*0.016, -0.005\n",
+      "15: -0.005, 0.01=0.800*-0.009, 0.003\n",
+      "16: 0.003, -0.00=0.800*0.006, -0.002\n",
+      "17: -0.002, 0.00=0.800*-0.003, 0.001\n",
+      "18: 0.001, -0.00=0.800*0.002, -0.001\n",
+      "19: -0.001, 0.00=0.800*-0.001, 0.000\n",
+      "20: 0.000, -0.00=0.800*0.001, -0.000\n",
+      "21: -0.000, 0.00=0.800*-0.000, 0.000\n",
+      "22: 0.000, -0.00=0.800*0.000, -0.000\n",
+      "23: -0.000, 0.00=0.800*-0.000, 0.000\n",
+      "24: 0.000, -0.00=0.800*0.000, -0.000\n",
+      "25: -0.000, 0.00=0.800*-0.000, 0.000\n",
+      "26: 0.000, -0.00=0.800*0.000, -0.000\n",
+      "27: -0.000, 0.00=0.800*-0.000, 0.000\n",
+      "28: 0.000, -0.00=0.800*0.000, -0.000\n",
+      "29: -0.000, 0.00=0.800*-0.000, 0.000\n",
+      "30: 0.000, -0.00=0.800*0.000, -0.000\n",
+      "31: -0.000, 0.00=0.800*-0.000, 0.000\n",
+      "32: 0.000, -0.00=0.800*0.000, -0.000\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x12054dfd0>]"
+      ]
+     },
+     "execution_count": 43,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "f = lambda x: x**2\n",
+    "grad_fn = lambda x: 2*x\n",
+    "x, xs = gradient_descent(grad_fn=grad_fn, x0=10.0, learn_rate=0.8, verbose=True)\n",
+    "plt.plot(np.arange(-12, 12, 0.01), [f(x) for x in np.arange(-12, 12, 0.01)])\n",
+    "plt.plot(xs, [f(x) for x in xs], 'o-', color='g')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "id": "ef9530f2",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2023-04-02T06:20:23.702780Z",
+     "start_time": "2023-04-02T06:20:23.511108Z"
+    },
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x11fd26340>]"
+      ]
+     },
+     "execution_count": 45,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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tEZRt27ahQ4cO6NChAwBg7Nix6NChA1599VWcOHEC33zzDU6cOIH27dujfv36zselK3Rmz56NwYMHY/jw4ejRowciIyOxYsUKhIQE3lLcetHh6NmMW98TEZHnVe61NbCdAWHqwNocvlb7oIjiD/ugXGrF73l45sudMOjCseGlvwTEBjpERCRWYVk5Or/xEywVdnz9VA+0S6orOtJ1KWofFAL63ZQIbbgaeaYybPzjnOg4REQUAL7fY4Slwo4bEqLQtqFOdByPY0HxgfDQEAxs79gTZcl2/1giTUREyrascmv7jg2vuk2HP2NB8ZGhnRyby/2w1whzWbngNERE5M9yzpVgS3YBJOnP1aKBhgXFR9o11KFZvTqwVNix8vdTouMQEZEfW3pxNP7WG+NhqBshOI13sKD4iCRJGNbZsbMsb/MQEVFN2ewylm533N4Z1ln5R7/UFAuKDw3u0AAhKgk7cy7gSH6R6DhEROSHNv5xFnmmMmjD1Ui9qfod2AMBC4oP1YsOR+/mCQDgbL9ERETuWLLN8fkxsL0B4aGBt39YJRYUH6u8zZO+4wQqbHbBaYiIyJ+YSsvxY5Zjh/ZhnQL39g7AguJzf2mZiJjIUOQXWrD+yFnRcYiIyI+s+D0Plgo7mifWCci9Ty7FguJjYWoVBrV3LAlbuo23eYiIyHVLtjkWWQzvnBSQe59cigVFgMrbPJn7TuNCiVVwGiIi8geHThfi9xMmqFUSBgfo3ieXYkERoLVBh1b1tbDa7Pjm9zzRcYiIyA9Ujp70aVkP8XU0gtN4HwuKIMM6XdwThbd5iIjoOsptdmTsdJxcXPn5EehYUAQZ3KEBQkMk7DlpwgGjWXQcIiJSsDUHz+BskRXxdcLQp2U90XF8ggVFkNioMPzl4i8ZJ8sSEdG1VN7eGdy+AUJDguOjOzj+lgpVuYZ9+a6TKOeeKEREVI2zRRb8ciAfQGBvbX85FhSBerVIQHwdDc4WWbH64i8fERHRpZbvPIkKu4x2DXVooY8WHcdnWFAECg1R4d4OBgDAV7zNQ0REl5Fl2bmYYmgQjZ4ALCjCjbjZ8Qu3+mA+TpvLBKchIiIl2XPShIOnCxGmVmFgW4PoOD7FgiLYjfWicXPjmCrHZxMREQHAVxcnx/ZvrYcuMlRwGt9iQVGAETcnAwAWb82F3S4LTkNEREpQYq3A1zsdm3mOCLLbOwALiiLc1UaPaI0aOQUl2Hz0nOg4RESkAN/tMaLQUoGk2Ah0vyFOdByfY0FRgMgwNQa2d9xbXLQ1V3AaIiJSgkW/5QBwjJ6oVIF9MGB1WFAUYuTF2zw/7DXifDEPECQiCmZH8gux7fh5hKikoNr75FIsKAqR0kCLmy4eILh810nRcYiISKBFv108GLBFPSRqwwWnEYMFRSEkScLILo6WvOi3XMgyJ8sSEQUjS4UN6RcPBhx5c3COngAsKIoyqH0DaNQqHDxdiN9PmETHISIiATL3nUZBsRWJWg16t0gQHUcYFhQF0UWE4u429QEAi7fmCE5DREQiVN7eGd45CeogORiwOsH7N1eoyp1lv9mVh2JLheA0RETkS7kFJdhw5CwAR0EJZiwoCtOlSSyaxEeh2GrDyt15ouMQEZEPLb641UTPZvFIio0UnEYsFhSFkSTJOYrCPVGIiIJHhc2OJdsd/+6PCOLJsZVYUBTovo4NoVZJ2JlzAQeNhaLjEBGRD6w5eAanzRbERoWh302JouMIx4KiQAnRGvRt5fjlXMxRFCKioFA5an5fxwbQqEMEpxGPBUWhRlzcEyV95wlYKmyC0xARkTedNpdh9cF8ALy9U4kFRaFua5aA+rpwXCgpxw97jaLjEBGRFy3ZlgubXcbNjWNwY71o0XEUgQVFoUJUf06WXbiFe6IQEQUam92GNcfW4IvdC/HBlhWQYXOey0Y1KCjr1q3DgAEDYDAYIEkSli9fXuX7sixj8uTJMBgMiIiIQO/evZGVlVXlGovFgmeeeQbx8fGIiorCwIEDceLEiVr9RQLRyJuTEaKSsCW7AEfyOVmWiChQpO9PR+P/NEaf+X3wQMZo7LWOQ174I7CGbRYdTTHcLijFxcVo164d5s6dW+33Z86ciVmzZmHu3LnYunUr9Ho9+vXrh8LCPz9g09LSkJGRgUWLFmHDhg0oKirCPffcA5uNcy0updeF4/aW9QAAX3AUhYgoIKTvT8fQr4bihLnq/5hXSOcwOn040venC0qmLJJci1PpJElCRkYGBg8eDMAxemIwGJCWloaXXnoJgGO0JDExETNmzMBjjz0Gk8mEhIQEfP755xgxYgQAIC8vD0lJSfjuu+/Qv3//6/65ZrMZOp0OJpMJWq22pvH9wpqD+Xjok63Qhqvx28t9ER7Kmd1ERP7KZreh8X8aX1FOKkmQ0FDbENnPZSNEFXj/3rvz+e3ROSjZ2dkwGo1ITU11PqfRaNCrVy9s3LgRALB9+3aUl5dXucZgMCAlJcV5zeUsFgvMZnOVR7C4rVkCGsZEwFxWgZW7T4mOQ0REtbA+Z/1VywkAyJCRa87F+pz1PkylTB4tKEajY7VJYmLVDWYSExOd3zMajQgLC0NMTMxVr7nc9OnTodPpnI+kpOBZgqVSSRjV1TFp6ostxwWnISKi2jhV6Nr/aLp6XSDzyioeSZKqfC3L8hXPXe5a10ycOBEmk8n5yM0Nrs3LhnVKcu4suy8veEaPiIgCTf3o+h69LpB5tKDo9XoAuGIkJD8/3zmqotfrYbVacf78+ateczmNRgOtVlvlEUwSojXon+L42S78jaMoRET+6mzx2etek6RNQs/knj5Io2weLShNmjSBXq9HZmam8zmr1Yq1a9eie/fuAIBOnTohNDS0yjWnTp3C3r17ndfQlUZfvM2TseMkiiwVgtMQEZG7bHYbnl/1/HWveyv1rYCcIOsutbsvKCoqwpEjR5xfZ2dnY9euXYiNjUVycjLS0tIwbdo0NGvWDM2aNcO0adMQGRmJUaNGAQB0Oh0eeeQRjBs3DnFxcYiNjcX48ePRpk0b9O3b13N/swDTrWkcmsZH4ejZYnyzK885L4WIiPzD9SbIVkqISvBBGuVzu6Bs27YNffr0cX49duxYAMCYMWPw6aef4sUXX0RpaSmefPJJnD9/Hl27dsWqVasQHf3n1r2zZ8+GWq3G8OHDUVpaittvvx2ffvopQkLYGK9GkhyTZd/4dj++2HIc93dJuu68HiIiUo6vD3zt0nWcIOtQq31QRAmmfVAudb7Yiq7Tf4a1wo6vn+qBdkl1RUciIiIXpO9Px31f3efStavHrEbvxr29G0gQYfugkHfFRIXhnjaOmd1cckxE5B9sdhue++E5l67lBNk/saD4mcq5J9/8ngdTabngNEREdD2uzj0BgDl3zOEE2YtYUPxMp0YxaJEYjbJyO5bvPCk6DhERXYerc0rSbknDkFZDvJzGf7Cg+BlJkjD6lj93lvXDKUREREHlcMFhl64b1GKQl5P4FxYUPzS4QwNEhIbg0OkibMkuEB2HiIiuIn1/OiavmXzNayRInHtSDRYUP6QND8W9HRsAAD7fxMmyRERKVDk5Vsa1R7plyJx7Ug0WFD/1126NAAA/ZBlhNJUJTkNERJdzdXLslN5TOPekGiwofqqlXosuTWJhs8tY+FuO6DhERHQZVzdmaxbbzMtJ/BMLih+rHEVZuCUH1gq74DRERFQpfX865myZ49K1PLm4eiwofqx/az3qRWtwtsiC7/dya2QiIiXgxmyewYLix0JDVM6N2zhZlohIGbgxm2ewoPi5UV2SoVZJ2Hb8PLLyTKLjEBEFPVfnnnBjtmtjQfFz9bThuPPi+TwcRSEiEsuduSfcmO3aWFACQOVk2eW7TsJUwvN5iIhE4NwTz2JBCQCdG8WgVX0tysrtWLI9V3QcIqKgxLknnsWCEgAkSXKOony26Tjsdp7PQ0TkazwU0LNYUALEoPYGaMPVyCkowdpDZ0THISIKOjwU0LNYUAJEZJgawzsnAQA+23RMbBgioiDDQwE9jwUlgDxwi+M2z5pDZ3D8XLHgNEREwYGHAnoHC0oAaRwfhd4tEiDLXHJMROQrPBTQO1hQAsyYbo0BAIu35aLIUiE2DBFREHB1ciwPBXQPC0qA6dU8AU3jo1BYVoFl211b7kZERDXn6uRYHgroHhaUAKNSSXioR2MAwKcbj3HJMRGRF9nsNvxv+/+ue13D6IacHOsmFpQAdF/HhogOVyP7bDHWHMoXHYeIKGCtz1mPE4XXH61+tNOjnBzrJhaUABSlUeP+Lo5Tjj/ecExsGCKiAObqwYCcf+I+FpQA9ddujaCSgA1HzuKgsVB0HCKigOPOwYCcf+I+FpQA1TAmEv1b6wEAn27MFpyGiCiw8GBA72NBCWB/u7UJACB9x0kUFFsFpyEiChw8GND7WFACWOdGMUhpoIWlwo4vf8sRHYeIKGC4OveEBwPWHAtKAJMkCX/r4RhF+WzTMZTb7IITERH5P3fmnvBgwJpjQQlwd7etj4RoDU6bLfhuj2u7HRIRUfU498R3WFACnEYdgge6Og4R/PjXY2LDEBH5Oc498R0WlCAw+pZkhIWo8HvuBezIOS86DhGR3+LcE99hQQkC8XU0GNjeAAD4eAOXHBMR1QTnnvgWC0qQePji+Tzf7zUi70Kp2DBERH6Gc098jwUlSLQ26HBL01jY7DI+3XhMdBwiIr/CuSe+5/GCUlFRgVdeeQVNmjRBREQEmjZtitdeew12+59LXGVZxuTJk2EwGBAREYHevXsjKyvL01HoMv+4rSkAYOGWHJjLygWnISLyH5x74nseLygzZszA+++/j7lz52L//v2YOXMm3nzzTbz99tvOa2bOnIlZs2Zh7ty52Lp1K/R6Pfr164fCQp4Z4029m9fDjfXqoMhSgcW/5YqOQ0TkF2x2G77Y84VL13Luied4vKBs2rQJgwYNwt13343GjRtj6NChSE1NxbZt2wA4Rk/mzJmDl19+GUOGDEFKSgrmz5+PkpISLFy40NNx6BIqlYRHezo2bvv412xu3EZE5IL1OetxpuTMda9LiEzg3BMP8nhBufXWW/Hzzz/j0KFDAIDff/8dGzZswF133QUAyM7OhtFoRGpqqvM1Go0GvXr1wsaNG6t9T4vFArPZXOVBNTOofQPE19HglKkM3+7mxm1ERNfj6u2d0W1Hc+6JB3m8oLz00ku4//770bJlS4SGhqJDhw5IS0vD/fffDwAwGo0AgMTExCqvS0xMdH7vctOnT4dOp3M+kpKSPB07aISHhuCh7o6N2+atOwpZlgUnIiJSLi4tFsfjBWXx4sVYsGABFi5ciB07dmD+/Pn497//jfnz51e5TpKkKl/LsnzFc5UmTpwIk8nkfOTmcv5EbYzu2ggRoSHYd8qMjX+cEx2HiEiRuLRYLLWn3/CFF17AhAkTMHLkSABAmzZtcPz4cUyfPh1jxoyBXq8H4BhJqV+/vvN1+fn5V4yqVNJoNNBoNJ6OGrRiosIwvHNDzN90HPPWHUWPG+NFRyIiUhwuLRbL4yMoJSUlUKmqvm1ISIhzmXGTJk2g1+uRmZnp/L7VasXatWvRvXt3T8ehq/jbrU2gkoC1h87goJGrp4iILselxWJ5vKAMGDAAU6dOxbfffotjx44hIyMDs2bNwr333gvAcWsnLS0N06ZNQ0ZGBvbu3YuHHnoIkZGRGDVqlKfj0FU0iovCHSmO0az/rT8qOA0RkbJw7ol4Hr/F8/bbb+Of//wnnnzySeTn58NgMOCxxx7Dq6++6rzmxRdfRGlpKZ588kmcP38eXbt2xapVqxAdHe3pOHQNj/Zsiu/2GPH1rpN4oX8LJGrDRUciIhKOc0+UQZL9cBmH2WyGTqeDyWSCVqsVHcevDXt/I7YeO48net+Al+5oKToOEZFwa46tQZ/5fVy6dtnwZby94wZ3Pr95Fk+Qe7SnY/v7LzYfR5GlQnAaIiLxOPdEGVhQglzfVoloEh8Fc1kFFm/l8m0iCm7c1l45WFCCnGP7e8coykfrj8Jawe3viSh4cVt75WBBIQzp2AAJ0Rrkmcrw9a6TouMQEQnDbe2VgwWFEB4agkdudRwi+P7aP2C3+928aSKiWuPSYmVhQSEAwOiuydCGq/HHmWKs2ndadBwiIp+y2W149vtnXbqWS4t9gwWFAADR4aH4a7fGAID31hzhIYJEFFSmrp+Kk4Wu3eLmtva+wYJCTg/1aAyNWoXfT5iwiYcIElGQSN+fjklrJrl0LZcW+w4LCjnF19Fg5M1JAIB31/whOA0Rkfe5s2sswLknvsSCQlU8eltThKgkbDhyFrtPXBAdh4jIq9w5sZhzT3yLBYWqaBgTiUHtDACA9ziKQkQB7lThKZev5dwT32JBoSs83vsGAMAPWUb8caZIcBoiIu85XHDYpeum9J7CuSc+xoJCV2ieGI2+rRIhy8AHazmKQkSByWa3Yd62ede9rkF0A7zc82UfJKJLsaBQtZ7s4xhFydh5EqdMpYLTEBF53tT1U3Gy6PpLi//R6R+8tSMACwpVq2NyDG5pGotym4wP12eLjkNE5FHuLC1uFtvMy2moOiwodFVP9L4RALBwSw7OFVkEpyEi8gx3lxbXj67vxTR0NSwodFW3NYtH24Y6lJbb8NEGjqIQUWDg0mL/wIJCVyVJEp75i2No87NNx3GhxCo4ERFR7bl6YjHApcUisaDQNfVtVQ+t6mtRZKnAx78eEx2HiKhWbHYbFuxe4NK1XFosFgsKXZNjFMUxF+WTX7NhLisXnIiIqOamrp+Ks6Vnr3tdfGQ8lxYLxoJC13VHaz2a1auDwrIKzOcoChH5KXdW7jzQ9gHe2hGMBYWuS6WS8PTFUZSPfs1GkaVCcCIiIvfwUED/w4JCLrmnrQFN46NwoaQcn286LjoOEZFbuHLH/7CgkEtCVBKe6uMYRflw/VGUWDmKQkT+gyt3/A8LCrlsUHsDkmMjca7YioVbckTHISJyic1uwxd7vnDpWq7cUQ4WFHKZOkSFpy6e0fPBuqMoK7cJTkREdH3rc9bjTMmZ617HlTvKwoJCbrm3Q0M0qBuBM4UWLPqNoyhEpHyu3t7hyh1lYUEht4SpVXiit2MU5f21R2Gp4CgKESlX+v50zNkyx6VruXJHWVhQyG3DOjeEXhsOo7kMi37LFR2HiKha7iwt5sod5WFBIbdp1CF46uK+KO+sPsK5KESkSO4sLebKHeVhQaEaGd7ZMRclv9CCBZu5LwoRKU/G/gyXrku7JY0rdxSIBYVqRKMOcZ7R8/7aP7gvChEpytKspZi7da5L13LuiTKxoFCN3depIZJjI3G2yIr5GzmKQkTKkL4/HcOWDoNdtl/32oTIBM49USgWFKqx0BAVnru9GQDgg3V/oJAnHRORYO6euTO67WjOPVEoFhSqlUHt/zyj51OedExEgrkzMRbg7R0l80pBOXnyJB544AHExcUhMjIS7du3x/bt253fl2UZkydPhsFgQEREBHr37o2srCxvRCEvU4eo8FxfxyjK/9YfhamUoyhEJI47Z+5wabGyebygnD9/Hj169EBoaCi+//577Nu3D2+99Rbq1q3rvGbmzJmYNWsW5s6di61bt0Kv16Nfv34oLCz0dBzygQFtDWieWAfmsgp8tP6o6DhEFKRsdhsW7F7g8vVcWqxsHi8oM2bMQFJSEj755BN06dIFjRs3xu23344bbnDsPirLMubMmYOXX34ZQ4YMQUpKCubPn4+SkhIsXLjQ03HIB1QqCc/3bQ4A+PjXYzhfbBWciIiC0dT1U3G29Ox1r1NBha+GfsWlxQrn8YLyzTffoHPnzhg2bBjq1auHDh064H//+5/z+9nZ2TAajUhNTXU+p9Fo0KtXL2zcuLHa97RYLDCbzVUepCz9W+txU30tiiwVmMdRFCLysfT96Zi0ZpJL1z7T5RkMaz3My4motjxeUI4ePYr33nsPzZo1w48//ojHH38czz77LD777DMAgNFoBAAkJiZWeV1iYqLze5ebPn06dDqd85GUlOTp2FRLKpWE5/s5RlE+/fUYzhZZBCciomDh7sqdwa0Gey8MeYzHC4rdbkfHjh0xbdo0dOjQAY899hgeffRRvPfee1WukySpyteyLF/xXKWJEyfCZDI5H7m5PP9Fifq2qod2DXUoLbfhndVHRMchoiDhzsodToz1Hx4vKPXr18dNN91U5blWrVohJycHAKDX6wHgitGS/Pz8K0ZVKmk0Gmi12ioPUh5JkjC+fwsAwBebc5BbUCI4EREFA3dW7nBirP/weEHp0aMHDh48WOW5Q4cOoVGjRgCAJk2aQK/XIzMz0/l9q9WKtWvXonv37p6OQz7Ws1kCetwYB6vNjtk/HRIdh4gCnDsrd6b0nsKJsX7E4wXl+eefx+bNmzFt2jQcOXIECxcuxLx58/DUU08BcPxfdlpaGqZNm4aMjAzs3bsXDz30ECIjIzFq1ChPxyEBXuzfEgCQsfMkDhq5dJyIvMfVlTvxkfF4uefLPkhEnuLxgnLzzTcjIyMDX375JVJSUvD6669jzpw5GD16tPOaF198EWlpaXjyySfRuXNnnDx5EqtWrUJ0dLSn45AA7ZLq4q42esgy8OaPB0THIaIA5c7KnQfaPsBbO35GkmVZFh3CXWazGTqdDiaTifNRFOqPM0VInb0ONruMpY93Q+fGsaIjEVEAsdltSPx3Is6VnnPp+tVjVqN3497eDUXX5c7nN8/iIa+4IaEOhnVqCACY8cMB+GEPJiIFm7p+qsvlhCt3/BMLCnnNc32bQaNWYeux81h9MF90HCIKEDa7DXM2z3H5eq7c8U8sKOQ19XUReKh7YwDAzB8Owm7nKAoR1d7U9VNxvuy8S9dy5Y7/YkEhr3qi9w2IDlfjgLEQX/9+UnQcIvJz7kyMjY2I5codP8aCQl5VNzIMj/dyHBT51qpDsFbYBSciIn9ls9vwjxX/cPn657o+x1s7fowFhbzu4R6NkRCtwYnzpViw+bjoOETkp9yZGBsXEcfREz/HgkJeFxmmxvN9HQcJ/veXwzCVlAtORET+xma34T9b/uPy9fMGzOPoiZ9jQSGfGN65IZrVq4MLJeV4Zw0PEiQi96zPWY+C0gKXruXE2MDAgkI+oQ5R4f/uagUA+PTXYzxIkIjckrE/w6XrODE2cLCgkM/0bpGAW2+Mh9Vmx4wfuAU+EblmadZSzN0616VrOTE2cLCgkM9IkoT/u6sVJAlYufsUduS4to8BEQWv9P3pGLZ0GOzy9VcAasO0HD0JICwo5FM3GbQY2tGxBf7Ub/dzC3wiuiqb3YbnfnjO5ev/1vFvHD0JICwo5HPjUlsgPFSF7cfP44e9RtFxiEih1uesxwnzCZevH9RikBfTkK+xoJDP6XXh+EfPpgCAf/1wgJu3EVG1vj7wtcvX8kDAwMOCQkI81usGxNfR4Pi5EnzOzduI6DI2uw0f7/zY5et5IGDgYUEhIaI0aoxLvbh528+HcaHEKjgRESnJ6+teh9lqvu51Kqjw1dCvuO9JAGJBIWGGd05Ci8RomErL8Z+fD4uOQ0QKsTRrKV5b+5pL1z7T5RkMaz3My4lIBBYUEiZEJeGVexybt3226TgOny4UnIiIRKtcVizDtRV+g1sN9m4gEoYFhYTq2SwB/W5KhM0u47WV+7jsmCiIubusODYilhNjAxgLCgn3yt2tEBaiwvrDZ5G577ToOEQkiLvLirlrbGBjQSHhGsVF4e89mwAA3vh2P8rKbYITEZEI7iwrjouI466xAY4FhRThqT43IlGrQU5BCT7akC06DhH5mLvLiucNmMfRkwDHgkKKEKVRY8KdLQEA76w+AqOpTHAiIvIlLiumy7GgkGIMbt8AHZProsRq42nHREGEy4qpOiwopBiSJGHywNaQJCBj50lsP87TjokCHZcV09WwoJCitG1YF8M6OU47nrIiC3Y7lx0TBSqb3YZ/rPiHy9dzWXFwYUEhxXmhf0tEa9TYfcKExdtyRcchIi+Zun4qzpWec/l6LisOLiwopDgJ0Rqk9XOc0zPjhwMoKOY5PUSBxma34c2Nb7p8PZcVBx8WFFKkMd0aoaU+GhdKyjHje06YJQo0U9dPRZG1yOXruaw4+LCgkCKpQ1SYem8KAGDxtlxsP14gOBEReYo7oycSJC4rDlIsKKRYnRrFYnhnx4TZlzP2osJmF5yIiDzh9XWvuzx6Mum2SVxWHKRYUEjRJtzZCnUjQ3HAWIj5m46LjkNEteTOnid1QuvglV6veDkRKRULCilabFQYXrrDscPs7MxDOG3mDrNE/srdPU9e6PEC550EMRYUUrwRnZPQPqkuiiwVeOPb/aLjEFENuLvnSZ3QOly1E+RYUEjxVCoJbwxOgUoCVvyehw2Hz4qORERucnfPE46eEAsK+YWUBjr8tVtjAMCrX+9FWblNbCAichn3PKGa8HpBmT59OiRJQlpamvM5WZYxefJkGAwGREREoHfv3sjKyvJ2FPJzY1ObIyFag6Nni/Hu6iOi4xCRi7jnCdWEVwvK1q1bMW/ePLRt27bK8zNnzsSsWbMwd+5cbN26FXq9Hv369UNhYaE345Cf04aHYsrA1gCAd9f8gYNG/r4QKR33PKGa8lpBKSoqwujRo/G///0PMTExzudlWcacOXPw8ssvY8iQIUhJScH8+fNRUlKChQsXeisOBYg7U/Tod1MiKuwyJqTvho2HCRIpmjujJ9zzhC7ltYLy1FNP4e6770bfvn2rPJ+dnQ2j0YjU1FTncxqNBr169cLGjRurfS+LxQKz2VzlQcFJkiS8PigFdTRq7My5gAWbuTcKkVK5M3rCPU/ocl4pKIsWLcKOHTswffr0K75nNBoBAImJiVWeT0xMdH7vctOnT4dOp3M+kpKSPB+a/IZeF46X7nTsjTLzhwPIu1AqOBERVcedHWO5aocu5/GCkpubi+eeew4LFixAeHj4Va+TJKnK17IsX/FcpYkTJ8JkMjkfubm5Hs1M/md0l2R0bhSDYqsN/1y+F7LMWz1ESrJ472JMWTvFpWu55wlVx+MFZfv27cjPz0enTp2gVquhVquxdu1a/Pe//4VarXaOnFw+WpKfn3/FqEoljUYDrVZb5UHBTaWSMH1IG4SFqPDzgXys3H1KdCQiuujFzBcxctlIl6/n6AlVx+MF5fbbb8eePXuwa9cu56Nz584YPXo0du3ahaZNm0Kv1yMzM9P5GqvVirVr16J79+6ejkMBrFliNJ7scwMAYMqKLFwosQpORERLs5a6tecJR0/oatSefsPo6GikpKRUeS4qKgpxcXHO59PS0jBt2jQ0a9YMzZo1w7Rp0xAZGYlRo0Z5Og4FuCd634CVu0/hSH4RXl+5H28Nbyc6ElHQstlteOSbR9x6DUdP6GqE7CT74osvIi0tDU8++SQ6d+6MkydPYtWqVYiOjhYRh/yYRh2CGfe1gSQBy3acwC8HTouORBS0pq6fCrPV9VWW3DGWrkWS/XB2odlshk6ng8lk4nwUAgC8sXIfPtyQjUStBqvSekEXGSo6ElFQsdlt0P1Lh+LyYpdfs2z4Mm7KFmTc+fzmWTwUEMb3b4Gm8VE4bbZgykoem0Dka6PTR7tcTlRQccdYui4WFAoI4aEheHNYO6gkIH3HSfy0j7d6iHxladZSLM5a7PL1C+9byB1j6bpYUChgdGoUg7/3bAoAmJixh6t6iHzA3YmxI1qPwIiUEV5MRIGCBYUCyth+zdE0IQpnCi2YsmKf6DhEAc+dibF1QuvgiyFfeDkRBQoWFAoo4aEh+PfFWz0ZO09iVVb1xycQUe3Z7DbM/HWmy9dzSTG5gwWFAk7H5Bg8epvjVs//ZexFQTFv9RB5gzsTY7VhWi4pJrewoFBAer5vczSrVwdniyyYsGw3z+oh8jB3J8Z+OPBDjp6QW1hQKCCFh4Zg9oj2CA2RsGrfaSzZdkJ0JKKAYa2wYszyMS5fP6L1CK7aIbexoFDASmmgw9h+LQAAk1dk4fg51zeQIqLqpe9PR8K/E1BSUeLS9ZwYSzXFgkIB7R+3NUWXJrEosdqQtngXKmx20ZGI/Fb6/nTc99V9MFtc386eE2OpplhQKKCFqCTMGt4O0eFq7My5gHdW/yE6EpFfstltePSbR916DSfGUm2woFDAaxgTiTcGO07S/u8vh7Ej57zgRET+Z3T6aBSUFbj1Gk6MpdpgQaGgMKh9AwxsZ4DNLuP5xbtQbKkQHYnIb7i7YgfgxFiqPRYUChqvD0qBQReO4+dKMPkbHihI5Aqb3Ya/ff03t14TFxHHibFUaywoFDR0kaF4a3h7SBKwZPsJZOzk0mOi67l/2f0oLC906zXzBszjrR2qNRYUCirdbojDs39pBgB4OWMvjp4pEpyISLleWPUCluxb4vL12jAtlg1fhiGthngxFQULFhQKOs/e3gy3NHUsPX5q4U6UldtERyJSnKVZS/HvTf92+frI0EiceeEMywl5DAsKBZ0QlYT/jOyA2Kgw7D9lxrTv9ouORKQoNZl38umgTxGmDvNSIgpGLCgUlBK14Zg1vB0A4LNNx/H9nlOCExEph7vzTrhih7yBBYWCVu8W9fBYL8epxy8u243cAte27iYKZDWZd8IVO+QNLCgU1MantkCH5LooLKvA01/uhLWCW+FT8HJ33gnAzdjIe1hQKKiFhqjw9v0doIsIxe+5F/D6yn2iIxEJUZN5J+O6jeOtHfIaFhQKeg1jIjFnRHsAwOebj2PZdu6PQsHH3Xknw28ajn+nujfaQuQOFhQiAH1a1sNztzv2R/m/jD3IyjMJTkTkO+N+HOf2vJOF9y30YiIiFhQip+dub4Y+LRJgqbDjiQU7YCopFx2JyOvG/TgOszbPcus1nHdCvsCCQnSRSiVh9oj2SIqNQE5BCdIW74TdLouOReQ1L6x6we1ywnkn5CssKESXqBsZhvdGd4JGrcLqg2fw9i9HREci8oqarNjhvBPyJRYUosukNNBh2r1tAABzfj6En/efFpyIyLNsdhse+eYRt17DeSfkaywoRNW4r1NDPHhLI8gy8OyXO3HQ6N5prkRKtubYGpitZrdew3kn5GssKERX8eqAm3BL01gUW234+2dbUVBsFR2JyCNe+fkVt67nvBMSgQWF6CpCQ1R4b3QnJMdGIregFE8s2M6dZsnvjftxHDbnbXb5+rG3jOW8ExKCBYXoGmKiwvDhmM6oo1FjS3YBJn2TBVnmyh7yT+4uKR7Wahje6v+WFxMRXR0LCtF1NE+Mxn/vbw9JAr78LQefbTouOhKR29wtJ+Eh4fhy6JdeTER0bSwoRC74S8tETLyzJQDgtZX7sO7QGcGJiFxXk83YJvacyEmxJBQLCpGLHu3ZFPd1bAibXcaTX+zA/lPurYIgEqEm5UQbpsXLPV/2UiIi17CgELlIkiRMG5KCrk1iUWSpwMOfbMUpU6noWERXVZOdYgEuKSZl8HhBmT59Om6++WZER0ejXr16GDx4MA4ePFjlGlmWMXnyZBgMBkRERKB3797IysrydBQij9OoQzDvwc5oVq8OjOYyPPzJVpjLeGYPKU9NdooFuKSYlMPjBWXt2rV46qmnsHnzZmRmZqKiogKpqakoLi52XjNz5kzMmjULc+fOxdatW6HX69GvXz8UFnIzLFI+XWQoPnn4ZiREa3DAWIgnF+zg8mNSFGuFFaPSR7n9Oi4pJiWRZC+vmTxz5gzq1auHtWvX4rbbboMsyzAYDEhLS8NLL70EALBYLEhMTMSMGTPw2GOPXfc9zWYzdDodTCYTtFqtN+MTXdXekyYM/2ATSqw23NexIf49rC0kSRIdi4LckqwleCD9AVjt7m0sOPaWsVxSTF7nzue31+egmEwmAEBsbCwAIDs7G0ajEampqc5rNBoNevXqhY0bN1b7HhaLBWazucqDSLSUBjq8M7ojQlQSlu04gbdWHRIdiYLc+FXjMXzpcJYTCgheLSiyLGPs2LG49dZbkZKSAgAwGo0AgMTExCrXJiYmOr93uenTp0On0zkfSUlJ3oxN5LI+Leph6mDH7/bc1Ufw4fqjghNRsHph1Qt4a5P7JYPlhJTKqwXl6aefxu7du/Hll1du9nP5ULgsy1cdHp84cSJMJpPzkZub65W8RDUxsksyXujfAgDwxrf78dU2/n6Sb9V0Qix3iiUlU3vrjZ955hl88803WLduHRo2bOh8Xq/XA3CMpNSvX9/5fH5+/hWjKpU0Gg00Go23ohLV2pO9b4CptBzz1h3FhGW7oQ0PxR0petGxKAjUdEJshDqCO8WSonl8BEWWZTz99NNIT0/HL7/8giZNmlT5fpMmTaDX65GZmel8zmq1Yu3atejevbun4xD5hCRJmHhnS4zonAS7DDz75U5sOHxWdCwKcOn706H7lw7ldveXus8fPJ97nZCiebygPPXUU1iwYAEWLlyI6OhoGI1GGI1GlJY6NrSSJAlpaWmYNm0aMjIysHfvXjz00EOIjIzEqFHu/18AkVI4NnJrg7va6GG12fGPz7dhR8550bEoQKXvT8d9X92HMluZ26/lXifkDzy+zPhq80g++eQTPPTQQwAcoyxTpkzBBx98gPPnz6Nr16545513nBNpr4fLjEnJLBU2/H3+Nqw/fBbR4Wp88feuaNuwruhYFECsFVboputQZne/nIzvNh5vpr7phVRE1+fO57fX90HxBhYUUroSawUe+ngrfjtWAG24Gl/8/Ra0aagTHYsCQPr+dIxeNtrtkZNQVSgWDlmIoa2HeikZ0fUpah8UomAUGabGJw/fjJsbx8BcVoEHPtqCvSdNomORn6vpbZ0wVRiKJhaxnJBfYUEh8pIojRqfPNwFnRrFwFRajtEfsqRQzVkrrBi9dHSNXrtgyAKEqcM8nIjIu1hQiLyojkaNTx++GR2T68JUWo4HPtqCrDyWFHJP5Wqdmsw54YRY8lcsKEReFh0eivl/64IOyXVxoaQc98/bjO3HubqHXLMka0mNV+vw8D/yZywoRD5QWVIq56Q8+NEW/HqE+6TQtS3euxjDlw6v0Wu5hT35OxYUIh/Rhofis791Rc9m8Six2vDwJ1uxKqv686eIxq8aj5HLRtbotSwnFAhYUIh8KCIsBB+O6Yw7Wjs2c3viix1YvvOk6FikMON+HFejg/8AlhMKHCwoRD6mUYdg7qgOGNKxAWx2Gc9/tQuf/potOhYpxPM/PI9Zm2fV6LUsJxRIvHZYIBFdnTpEhX8PbYc6GjU+23Qck1fsw8kLpZh4ZyuoVNXvxkyBzWa3oefHPbHp5KYavZ7lhAINR1CIBFGpJEwZ2Bov9G8BAPjf+mw8s2gnysptgpORry3JWoKIqREsJ0SXYEEhEkiSJDzV50bMHtEOoSESvt19Cn/96DdcKLGKjkY+MvbHsRi+dHiNTiQGWE4ocLGgECnAvR0a4tOHuyBao8Zvxwpw33sbcexssehY5GUDvhiA2Ztn1/j1LCcUyFhQiBSix43xWPJEN+i14fjjTDEGvfMrNhzmXimByGa3ocV/W2DlkZU1fo/x3caznFBAY0EhUpCWei2+froH2iU5tsYf88lv+OTXbPjhoeN0FZXzTQ6dP1Tj91h03yK8mfqmB1MRKQ8LCpHCJGrDsfgftziXIU9ZsQ8vLdsNSwUnz/q72s43AYAlQ5dgRMoID6YiUiYWFCIFCg8NwVvD2uGVu1tBJQFfbTuBkfM2I+9CqehoVAM2uw3dP+xeq/kmmhANlg1fhqGth3owGZFysaAQKZQkSfh7z6b45OEu0IarsTPnAu7673qsPpAvOhq5YfHexdC8oanxEmIA6NagG4r/rxhDWg3xYDIiZWNBIVK4Xs0TsPKZnmjTQIcLJeV4+NOtmPHDAVTY7KKj0TVUjpqMXDYSNrnmt+fG3jIWG/++ESGqEA+mI1I+FhQiP5AcF4mlT3TDmG6NAADvrfkDoz7cAqOpTHAyqs7ivYsR+nporUZN1FBjydAlXKlDQUuS/XB5gNlshk6ng8lkglarFR2HyKdW7s7DhGV7UGSpgC4iFFPvTcE9bQ2iYxFqv119peaxzbHvqX0cNaGA487nN0dQiPzMPW0N+ObpHmjbUAdTaTmeXrgTaYt2wlRa85UhVDs2uw2vrn4V6tfVtS4n9zS7BwefOchyQkGPBYXIDzVNqINlT3THs3+5ESoJWL4rD3fMWYeNR7ixm68tyVqC8DfC8fq612v9Xmld07Bi1AoPpCLyfywoRH4qNESFsaktsPSJ7mgcF4lTpjKM+nALJizbDVMJR1O8zWa3YdhXwzB86XBUyBW1fr/x3cZj9h01X4ZMFGhYUIj8XMfkGHz3XE88cEsyAGDR1lzcPmstVu7O4w60XmCz2/DPX/6J0NdDsXT/0lq/X6gUiiVDl3BnWKLLcJIsUQDZeqwAE5btxh9nHAcN3t6yHiYPbI2k2EjByQLDl3u+xKj0UR57v6GthmLR0EWcb0JBw53PbxYUogBjqbDhvTV/4J3VR1BukxGmVuGx25riid43IDJMLTqe37HZbfjpj58wbMkwFJYXeuQ9QxCCRUMXcVdYCjosKESEI/mF+OfyLGw6eg4AkKjVYMKdLTGoXQOoVJLgdP7hyz1fYnT6aMjw3D+T3Rp0w/q/reeoCQUlFhQiAgDIsowfs4yY+t1+5BY4zvFpl1QXL/ZvgR43xgtOp0zWCivmbJ6DSWsmoczmuY3wJEhYdN8iDE8Z7rH3JPI3LChEVEVZuQ0f/5qNub8cQYnVse16t6ZxGN+/OTo1ihWcThlKraXo8mEX7D2z1+PvzVETIgcWFCKqVn5hGd5d/QcWbsmB9eJZPr1bJOCZv9wYlEXFWmHF7E2zMWXtFJTaPH9SNEdNiKpiQSGiazp5oRRv/3wYS7afgM3u+Cegc6MYPNbrBtzesl5Az1GpLCVT10/12KTX6nDUhOhKLChE5JLss8V4f80fyNh50jmickNCFP52axMMat8AdTSBseqn1FqKZ79/FvN3z0e53bub2KklNb4Y8gVHTYiqwYJCRG45bS7DJ78ewxebj6PQ4tgVNSosBAPbN8DorslIaaATnNA9RWVFGL50OH7O/hlWu9Unf6YECa/0fAWTek/iqAnRVbCgEFGNFJaV46ttJ/DFluM4enGzNwBIaaDFoHYNcE+7+qivixCY8EpnzGfQ6cNOyC3MFZbh5VtfxpQ+U1hMiK6DBYWIakWWZWw+WoCFv+Xgh72nUG7785+JLo1jMaBdfdzeKhGGup4tK9IU/5r7cl/L+7B42GIWEyIX+U1Beffdd/Hmm2/i1KlTaN26NebMmYOePXte93UsKES+c67Igu/2GrFiVx5+O1ZQ5Xst9dHo07Ie+rSoh/ZJdRGmrvnxXv5UTno16oVVD6xCmDpMdBQiv+IXBWXx4sV48MEH8e6776JHjx744IMP8OGHH2Lfvn1ITk6+5mtZUIjEyLtQipW78/D9XiN25V7Apf96aNQqtE+qiy5NYtG5cSzaNtAhJsq1D3B/KScsJkS14xcFpWvXrujYsSPee+8953OtWrXC4MGDMX369Gu+lgWFSLyCYivWHz6DXw7kY/3hsygovnIyaqJWg5Z6LVrV16JpfBQaxkYgKSYSel04QkMcoy3+UE4ebPsgPhzwIYsJUS258/ktZA2h1WrF9u3bMWHChCrPp6amYuPGjVdcb7FYYLFYnF+bzWavZySia4uNCsOg9g0wqH0DyLKMP84UY9uxAvx2rADbj5/H8XMlOG224LT5DNYeOlPltSEqCbFRYagbESoo/fVpw7T44t4vcGfzOznHhEgAIQXl7NmzsNlsSExMrPJ8YmIijEbjFddPnz4dU6ZM8VU8InKTJEm4sV4d3FivDkZ2cdyiLbJU4KCxEAeMZhw4VYjjBSU4UVCCExdKYa2w40yhBWcKLYAGQM2nrnjc7U1ux4qRKxARpqzVSkTBRuguTJJUdWhXluUrngOAiRMnYuzYsc6vzWYzkpKSvJ6PiGqujkaNTo1i0KlRTJXn7XYZZ4osOFtkwYWSctz6haCAl0gIT8DHgz7maAmRgggpKPHx8QgJCblitCQ/P/+KURUA0Gg00Gg0vopHRF6kUklI1IYjURsuNEdsWCxe6PkCxt4ylnNLiBRIyMBqWFgYOnXqhMzMzCrPZ2Zmonv37iIiEZEg8iTfzdNvXKcxlg9bjop/VuDcxHOYcOsElhMihRJ2i2fs2LF48MEH0blzZ3Tr1g3z5s1DTk4OHn/8cVGRiEgQeZLsldU88aHx+GDQBxjUahBv3RD5GWEFZcSIETh37hxee+01nDp1CikpKfjuu+/QqFEjUZGISKDalhQ11FgwZAGGth7KMkIUALjVPREREfmEO5/fClrcR0REROTAgkJERESKw4JCREREisOCQkRERIrDgkJERESKw4JCREREisOCQkRERIrDgkJERESKw4JCREREiiNsq/vaqNz81mw2C05CRERErqr83HZlE3u/LCiFhYUAgKSkJMFJiIiIyF2FhYXQ6XTXvMYvz+Kx2+3Iy8tDdHQ0JMnzJ6AqjdlsRlJSEnJzc3n2kA/x5y4Gf+5i8OcuRrD93GVZRmFhIQwGA1Sqa88y8csRFJVKhYYNG4qO4XNarTYofoGVhj93MfhzF4M/dzGC6ed+vZGTSpwkS0RERIrDgkJERESKw4LiBzQaDSZNmgSNRiM6SlDhz10M/tzF4M9dDP7cr84vJ8kSERFRYOMIChERESkOCwoREREpDgsKERERKQ4LChERESkOC4rCTZ06Fd27d0dkZCTq1q1b7TU5OTkYMGAAoqKiEB8fj2effRZWq9W3QYNA48aNIUlSlceECRNExwo47777Lpo0aYLw8HB06tQJ69evFx0poE2ePPmK32u9Xi86VsBZt24dBgwYAIPBAEmSsHz58irfl2UZkydPhsFgQEREBHr37o2srCwxYRWCBUXhrFYrhg0bhieeeKLa79tsNtx9990oLi7Ghg0bsGjRIixbtgzjxo3zcdLg8Nprr+HUqVPOxyuvvCI6UkBZvHgx0tLS8PLLL2Pnzp3o2bMn7rzzTuTk5IiOFtBat25d5fd6z549oiMFnOLiYrRr1w5z586t9vszZ87ErFmzMHfuXGzduhV6vR79+vVznj0XlGTyC5988oms0+mueP67776TVSqVfPLkSedzX375pazRaGSTyeTDhIGvUaNG8uzZs0XHCGhdunSRH3/88SrPtWzZUp4wYYKgRIFv0qRJcrt27UTHCCoA5IyMDOfXdrtd1uv18r/+9S/nc2VlZbJOp5Pff/99AQmVgSMofm7Tpk1ISUmBwWBwPte/f39YLBZs375dYLLANGPGDMTFxaF9+/aYOnUqb6V5kNVqxfbt25Gamlrl+dTUVGzcuFFQquBw+PBhGAwGNGnSBCNHjsTRo0dFRwoq2dnZMBqNVX73NRoNevXqFdS/+355WCD9yWg0IjExscpzMTExCAsLg9FoFJQqMD333HPo2LEjYmJi8Ntvv2HixInIzs7Ghx9+KDpaQDh79ixsNtsVv8+JiYn8Xfairl274rPPPkPz5s1x+vRpvPHGG+jevTuysrIQFxcnOl5QqPz9ru53//jx4yIiKQJHUASoblLa5Y9t27a5/H6SJF3xnCzL1T5PVbnz3+L5559Hr1690LZtW/z973/H+++/j48++gjnzp0T/LcILJf/3vJ32bvuvPNO3HfffWjTpg369u2Lb7/9FgAwf/58wcmCD3/3q+IIigBPP/00Ro4cec1rGjdu7NJ76fV6bNmypcpz58+fR3l5+RVtnK5Um/8Wt9xyCwDgyJEj/D9ND4iPj0dISMgVoyX5+fn8XfahqKgotGnTBocPHxYdJWhUrpoyGo2oX7++8/lg/91nQREgPj4e8fHxHnmvbt26YerUqTh16pTzF3vVqlXQaDTo1KmTR/6MQFab/xY7d+4EgCr/oFDNhYWFoVOnTsjMzMS9997rfD4zMxODBg0SmCy4WCwW7N+/Hz179hQdJWg0adIEer0emZmZ6NChAwDHnKy1a9dixowZgtOJw4KicDk5OSgoKEBOTg5sNht27doFALjxxhtRp04dpKam4qabbsKDDz6IN998EwUFBRg/fjweffRRaLVaseEDyKZNm7B582b06dMHOp0OW7duxfPPP4+BAwciOTlZdLyAMXbsWDz44IPo3LkzunXrhnnz5iEnJwePP/646GgBa/z48RgwYACSk5ORn5+PN954A2azGWPGjBEdLaAUFRXhyJEjzq+zs7Oxa9cuxMbGIjk5GWlpaZg2bRqaNWuGZs2aYdq0aYiMjMSoUaMEphZM8Coiuo4xY8bIAK54rF692nnN8ePH5bvvvluOiIiQY2Nj5aefflouKysTFzoAbd++Xe7ataus0+nk8PBwuUWLFvKkSZPk4uJi0dECzjvvvCM3atRIDgsLkzt27CivXbtWdKSANmLECLl+/fpyaGiobDAY5CFDhshZWVmiYwWc1atXV/tv+ZgxY2RZdiw1njRpkqzX62WNRiPfdttt8p49e8SGFkySZVkWVY6IiIiIqsNVPERERKQ4LChERESkOCwoREREpDgsKERERKQ4LChERESkOCwoREREpDgsKERERKQ4LChERESkOCwoREREpDgsKERERKQ4LChERESkOCwoREREpDj/DwYCkXCqCdlfAAAAAElFTkSuQmCC\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "f = lambda x: x**2\n",
+    "grad_fn = lambda x: 2*x\n",
+    "x, xs = gradient_descent(grad_fn=grad_fn, x0=10.0, learn_rate=0.005, n_iter=2000)\n",
+    "plt.plot(np.arange(-12, 12, 0.01), [f(x) for x in np.arange(-12, 12, 0.01)])\n",
+    "plt.plot(xs, [f(x) for x in xs], 'o-', color='g')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "05d3daaf",
+   "metadata": {},
+   "source": [
+    "## example 2: $f(x)=x^4-5x^2-3x$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "id": "6d3959d7",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2023-04-02T06:20:56.668666Z",
+     "start_time": "2023-04-02T06:20:56.662319Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "f = lambda x: x**4-5*x**2-3*x\n",
+    "grad_fn = lambda x: 4*x**3-10*x-3"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "id": "1658310c",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2023-04-02T06:20:57.906740Z",
+     "start_time": "2023-04-02T06:20:57.720390Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0: 0.000, 0.60=0.200*-3.000, 0.600\n",
+      "1: 0.600, 1.63=0.200*-8.136, 2.227\n",
+      "2: 2.227, -3.78=0.200*18.919, -1.557\n",
+      "3: -1.557, 0.50=0.200*-2.522, -1.052\n",
+      "4: -1.052, -0.57=0.200*2.862, -1.625\n",
+      "5: -1.625, 0.78=0.200*-3.907, -0.843\n",
+      "6: -0.843, -0.61=0.200*3.034, -1.450\n",
+      "7: -1.450, 0.14=0.200*-0.695, -1.311\n",
+      "8: -1.311, -0.22=0.200*1.097, -1.530\n",
+      "9: -1.530, 0.41=0.200*-2.033, -1.124\n",
+      "10: -1.124, -0.51=0.200*2.561, -1.636\n",
+      "11: -1.636, 0.83=0.200*-4.155, -0.805\n",
+      "12: -0.805, -0.59=0.200*2.964, -1.398\n",
+      "13: -1.398, -0.01=0.200*0.054, -1.409\n",
+      "14: -1.409, 0.02=0.200*-0.093, -1.390\n",
+      "15: -1.390, -0.03=0.200*0.158, -1.422\n",
+      "16: -1.422, 0.06=0.200*-0.276, -1.366\n",
+      "17: -1.366, -0.09=0.200*0.459, -1.458\n",
+      "18: -1.458, 0.16=0.200*-0.821, -1.294\n",
+      "19: -1.294, -0.25=0.200*1.273, -1.549\n",
+      "20: -1.549, 0.47=0.200*-2.370, -1.075\n",
+      "21: -1.075, -0.56=0.200*2.782, -1.631\n",
+      "22: -1.631, 0.81=0.200*-4.047, -0.822\n",
+      "23: -0.822, -0.60=0.200*2.998, -1.421\n",
+      "24: -1.421, 0.05=0.200*-0.271, -1.367\n",
+      "25: -1.367, -0.09=0.200*0.452, -1.457\n",
+      "26: -1.457, 0.16=0.200*-0.807, -1.296\n",
+      "27: -1.296, -0.25=0.200*1.254, -1.547\n",
+      "28: -1.547, 0.47=0.200*-2.333, -1.080\n",
+      "29: -1.080, -0.55=0.200*2.761, -1.632\n",
+      "30: -1.632, 0.81=0.200*-4.072, -0.818\n",
+      "31: -0.818, -0.60=0.200*2.990, -1.416\n",
+      "32: -1.416, 0.04=0.200*-0.196, -1.377\n",
+      "33: -1.377, -0.07=0.200*0.328, -1.443\n",
+      "34: -1.443, 0.12=0.200*-0.581, -1.326\n",
+      "35: -1.326, -0.19=0.200*0.932, -1.513\n",
+      "36: -1.513, 0.34=0.200*-1.716, -1.169\n",
+      "37: -1.169, -0.46=0.200*2.298, -1.629\n",
+      "38: -1.629, 0.80=0.200*-3.999, -0.829\n",
+      "39: -0.829, -0.60=0.200*3.011, -1.431\n",
+      "40: -1.431, 0.08=0.200*-0.417, -1.348\n",
+      "41: -1.348, -0.14=0.200*0.683, -1.484\n",
+      "42: -1.484, 0.25=0.200*-1.240, -1.236\n",
+      "43: -1.236, -0.36=0.200*1.804, -1.597\n",
+      "44: -1.597, 0.67=0.200*-3.325, -0.932\n",
+      "45: -0.932, -0.62=0.200*3.082, -1.548\n",
+      "46: -1.548, 0.47=0.200*-2.366, -1.075\n",
+      "47: -1.075, -0.56=0.200*2.780, -1.631\n",
+      "48: -1.631, 0.81=0.200*-4.049, -0.821\n",
+      "49: -0.821, -0.60=0.200*2.997, -1.421\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x11fce2130>]"
+      ]
+     },
+     "execution_count": 47,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x, xs = gradient_descent(grad_fn=grad_fn, x0=0, learn_rate=0.2, verbose=True)\n",
+    "plt.plot(np.arange(-3, 3, 0.01), [f(x) for x in np.arange(-3, 3, 0.01)])\n",
+    "plt.plot(xs, [f(x) for x in xs], 'o-', color='g')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "id": "29e3fa19",
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2023-04-02T06:22:19.357039Z",
+     "start_time": "2023-04-02T06:22:19.027720Z"
+    },
+    "scrolled": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0: 0.000, 0.30=0.100*-3.000, 0.300\n",
+      "1: 0.300, 0.59=0.100*-5.892, 0.889\n",
+      "2: 0.889, 0.91=0.100*-9.080, 1.797\n",
+      "3: 1.797, -0.22=0.100*2.247, 1.573\n",
+      "4: 1.573, 0.32=0.100*-3.171, 1.890\n",
+      "5: 1.890, -0.51=0.100*5.092, 1.380\n",
+      "6: 1.380, 0.63=0.100*-6.283, 2.009\n",
+      "7: 2.009, -0.93=0.100*9.331, 1.076\n",
+      "8: 1.076, 0.88=0.100*-8.779, 1.953\n",
+      "9: 1.953, -0.73=0.100*7.282, 1.225\n",
+      "10: 1.225, 0.79=0.100*-7.895, 2.015\n",
+      "11: 2.015, -0.96=0.100*9.565, 1.058\n",
+      "12: 1.058, 0.88=0.100*-8.842, 1.942\n",
+      "13: 1.942, -0.69=0.100*6.891, 1.253\n",
+      "14: 1.253, 0.77=0.100*-7.658, 2.019\n",
+      "15: 2.019, -0.97=0.100*9.737, 1.045\n",
+      "16: 1.045, 0.89=0.100*-8.884, 1.934\n",
+      "17: 1.934, -0.66=0.100*6.591, 1.275\n",
+      "18: 1.275, 0.75=0.100*-7.461, 2.021\n",
+      "19: 2.021, -0.98=0.100*9.806, 1.040\n",
+      "20: 1.040, 0.89=0.100*-8.899, 1.930\n",
+      "21: 1.930, -0.65=0.100*6.467, 1.284\n",
+      "22: 1.284, 0.74=0.100*-7.376, 2.021\n",
+      "23: 2.021, -0.98=0.100*9.818, 1.039\n",
+      "24: 1.039, 0.89=0.100*-8.902, 1.930\n",
+      "25: 1.930, -0.64=0.100*6.444, 1.285\n",
+      "26: 1.285, 0.74=0.100*-7.361, 2.021\n",
+      "27: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "28: 1.039, 0.89=0.100*-8.902, 1.930\n",
+      "29: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "30: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "31: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "32: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "33: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "34: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "35: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "36: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "37: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "38: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "39: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "40: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "41: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "42: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "43: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "44: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "45: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "46: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "47: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "48: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "49: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "50: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "51: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "52: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "53: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "54: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "55: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "56: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "57: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "58: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "59: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "60: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "61: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "62: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "63: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "64: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "65: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "66: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "67: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "68: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "69: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "70: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "71: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "72: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "73: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "74: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "75: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "76: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "77: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "78: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "79: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "80: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "81: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "82: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "83: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "84: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "85: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "86: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "87: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "88: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "89: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "90: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "91: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "92: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "93: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "94: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "95: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "96: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "97: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "98: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "99: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "100: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "101: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "102: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "103: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "104: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "105: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "106: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "107: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "108: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "109: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "110: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "111: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "112: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "113: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "114: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "115: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "116: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "117: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "118: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "119: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "120: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "121: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "122: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "123: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "124: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "125: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "126: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "127: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "128: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "129: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "130: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "131: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "132: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "133: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "134: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "135: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "136: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "137: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "138: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "139: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "140: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "141: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "142: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "143: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "144: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "145: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "146: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "147: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "148: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "149: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "150: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "151: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "152: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "153: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "154: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "155: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "156: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "157: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "158: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "159: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "160: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "161: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "162: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "163: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "164: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "165: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "166: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "167: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "168: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "169: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "170: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "171: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "172: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "173: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "174: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "175: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "176: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "177: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "178: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "179: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "180: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "181: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "182: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "183: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "184: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "185: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "186: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "187: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "188: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "189: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "190: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "191: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "192: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "193: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "194: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "195: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "196: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "197: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "198: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "199: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "200: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "201: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "202: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "203: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "204: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "205: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "206: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "207: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "208: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "209: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "210: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "211: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "212: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "213: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "214: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "215: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "216: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "217: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "218: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "219: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "220: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "221: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "222: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "223: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "224: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "225: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "226: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "227: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "228: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "229: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "230: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "231: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "232: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "233: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "234: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "235: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "236: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "237: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "238: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "239: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "240: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "241: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "242: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "243: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "244: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "245: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "246: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "247: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "248: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "249: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "250: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "251: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "252: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "253: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "254: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "255: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "256: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "257: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "258: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "259: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "260: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "261: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "262: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "263: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "264: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "265: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "266: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "267: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "268: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "269: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "270: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "271: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "272: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "273: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "274: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "275: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "276: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "277: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "278: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "279: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "280: 1.039, 0.89=0.100*-8.903, 1.930\n",
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+      "287: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "288: 1.039, 0.89=0.100*-8.903, 1.930\n",
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+      "292: 1.039, 0.89=0.100*-8.903, 1.930\n",
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+      "903: 2.021, -0.98=0.100*9.819, 1.039\n",
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+      "911: 2.021, -0.98=0.100*9.819, 1.039\n",
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+      "913: 1.930, -0.64=0.100*6.442, 1.285\n",
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+      "917: 1.930, -0.64=0.100*6.442, 1.285\n",
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+      "919: 2.021, -0.98=0.100*9.819, 1.039\n",
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+      "921: 1.930, -0.64=0.100*6.442, 1.285\n",
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+      "923: 2.021, -0.98=0.100*9.819, 1.039\n",
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+      "925: 1.930, -0.64=0.100*6.442, 1.285\n",
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+      "943: 2.021, -0.98=0.100*9.819, 1.039\n",
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+      "981: 1.930, -0.64=0.100*6.442, 1.285\n",
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+      "983: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "984: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "985: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "986: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "987: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "988: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "989: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "990: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "991: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "992: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "993: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "994: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "995: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "996: 1.039, 0.89=0.100*-8.903, 1.930\n",
+      "997: 1.930, -0.64=0.100*6.442, 1.285\n",
+      "998: 1.285, 0.74=0.100*-7.359, 2.021\n",
+      "999: 2.021, -0.98=0.100*9.819, 1.039\n",
+      "1.0393324789193148\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[<matplotlib.lines.Line2D at 0x12188cfa0>]"
+      ]
+     },
+     "execution_count": 50,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x, xs = gradient_descent(grad_fn=grad_fn, x0=0, learn_rate=0.1, verbose=True, n_iter=1000)\n",
+    "print(x)\n",
+    "plt.plot(np.arange(-3, 3, 0.01), [f(x) for x in np.arange(-3, 3, 0.01)])\n",
+    "plt.plot(xs, [f(x) for x in xs], 'o-', color='g')"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.13"
+  },
+  "toc": {
+   "base_numbering": 1,
+   "nav_menu": {},
+   "number_sections": true,
+   "sideBar": true,
+   "skip_h1_title": false,
+   "title_cell": "Table of Contents",
+   "title_sidebar": "Contents",
+   "toc_cell": false,
+   "toc_position": {},
+   "toc_section_display": true,
+   "toc_window_display": true
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
author	chzhang <zch921005@126.com>	2023-04-02 14:31:11 +0800
committer	chzhang <zch921005@126.com>	2023-04-02 14:31:11 +0800
commit	2c5dc53a4c2d64866a3b567cf971a9e9c335923f (patch)
tree	6b948a2d55e8c83ff59736e43665809195f0332a
parent	8dfef0bfbe2237de25a043a64b969d814654114b (diff)