notebooks/chapter07_optimization/7.1_optimization-intro.ipynb

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   "source": [
    "# 7.1 优化与深度学习\n",
    "## 7.1.2 优化在深度学习中的挑战"
   ]
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   "source": [
    "%matplotlib inline\n",
    "import sys\n",
    "sys.path.append(\"..\") \n",
    "import L0CV as d2l\n",
    "from mpl_toolkits import mplot3d # 三维画图\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.1.2.1 局部最小值"
   ]
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   "cell_type": "code",
   "execution_count": 2,
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    "def f(x):\n",
    "    return x * np.cos(np.pi * x)\n",
    "\n",
    "L0CV.set_figsize((4.5, 2.5))\n",
    "x = np.arange(-1.0, 2.0, 0.1)\n",
    "fig,  = L0CV.plt.plot(x, f(x))\n",
    "fig.axes.annotate('local minimum', xy=(-0.3, -0.25), xytext=(-0.77, -1.0),\n",
    "                  arrowprops=dict(arrowstyle='->'))\n",
    "fig.axes.annotate('global minimum', xy=(1.1, -0.95), xytext=(0.6, 0.8),\n",
    "                  arrowprops=dict(arrowstyle='->'))\n",
    "L0CV.plt.xlabel('x')\n",
    "L0CV.plt.ylabel('f(x)');"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.1.2.2 鞍点"
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  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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    "x = np.arange(-2.0, 2.0, 0.1)\n",
    "fig, = d2l.plt.plot(x, x**3)\n",
    "fig.axes.annotate('saddle point', xy=(0, -0.2), xytext=(-0.52, -5.0),\n",
    "                  arrowprops=dict(arrowstyle='->'))\n",
    "d2l.plt.xlabel('x')\n",
    "d2l.plt.ylabel('f(x)');"
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   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
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    "x, y = np.mgrid[-1: 1: 31j, -1: 1: 31j]\n",
    "z = x**2 - y**2\n",
    "\n",
    "ax = d2l.plt.figure().add_subplot(111, projection='3d')\n",
    "ax.plot_wireframe(x, y, z, **{'rstride': 2, 'cstride': 2})\n",
    "ax.plot([0], [0], [0], 'rx')\n",
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    "d2l.plt.yticks(ticks)\n",
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