notebooks/chapter07_optimization/7.2_gd-sgd.ipynb

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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 7.2 梯度下降和随机梯度下降"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import torch\n",
    "import math\n",
    "import sys\n",
    "sys.path.append(\"..\") \n",
    "import L0CV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.2.1 一维梯度下降"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 10, x: 0.06046617599999997\n"
     ]
    }
   ],
   "source": [
    "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
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   "source": [
    "def show_trace(res):\n",
    "    n = max(abs(min(res)), abs(max(res)), 10)\n",
    "    f_line = np.arange(-n, n, 0.1)\n",
    "    L0CV.set_figsize()\n",
    "    L0CV.plt.plot(f_line, [x * x for x in f_line])\n",
    "    L0CV.plt.plot(res, [x * x for x in res], '-o')\n",
    "    L0CV.plt.xlabel('x')\n",
    "    L0CV.plt.ylabel('f(x)')\n",
    "\n",
    "show_trace(res)"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.2.2 学习率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 10, x: 3.4867844009999995\n"
     ]
    },
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    "show_trace(gd(1.1))"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.2.3 多维梯度下降"
   ]
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  {
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   "execution_count": 6,
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    "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')"
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      "epoch 20, x1 -0.057646, x2 -0.000073\n"
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   "source": [
    "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))"
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  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.2.4 随机梯度下降"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
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     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 20, x1 -0.047150, x2 -0.075628\n"
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    "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))"
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