Torch.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PyTorch入门\n",
    "\n",
    "随着神经网络，特别是深度神经网络的出现，如何使用计算机高效的完成参数量巨大的神经网络的训练就成了一个难题。为此，出现了诸如TensorFlow、PyTorch等深度学习框架。在工业界中，TensorFlow出现的早而且应用较多，而PyTorch虽然出现的晚，不过由于其与Python结合更加紧密，且具有动态图等一系列优良特性，我们在这里以PyTorch为例讲解深度学习框架的使用。\n",
    "\n",
    "在这一节中，我们首先学习PyTorch的一些基础操作。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tensor的使用\n",
    "\n",
    "在机器学习中，Tensor是向量、矩阵的一个自然推广，即一个任意维的数组，比如：标量、向量（1维数组）、矩阵（2维数组）以及更高维的数组都可以看作是Tensor。\n",
    "\n",
    "## Tensor的创建\n",
    "\n",
    "在PyTorch中提供了Tensor数据类型，其使用方法与NumPy类似，但是也有一些差别。比如，为了创建一个Tensor，使用torch中的 **tensor()** 函数就可以了，这与NumPy里面的numpy.array()函数用法是一样的："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1., 2., 3., 4.])"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import torch\n",
    "\n",
    "a = torch.tensor([1., 2, 3, 4])\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "也可以通过NumPy的array创建："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.8688, 0.6350, 0.6659, 0.5229, 0.2616], dtype=torch.float64)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "b = np.random.random(5)\n",
    "b_torch = torch.from_numpy(b)\n",
    "b_torch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "反过来，也可以使用Tensor的numpy()函数转化为NumPy的array，此时也是共享内存的："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b= [1. 2. 3. 4.]\n",
      "b= [10.  2.  3.  4.]\n",
      "a= tensor([10.,  2.,  3.,  4.])\n"
     ]
    }
   ],
   "source": [
    "a = torch.tensor([1., 2, 3, 4])\n",
    "b = a.numpy()\n",
    "print(\"b=\", b)\n",
    "b[0] = 10\n",
    "print(\"b=\", b)\n",
    "print(\"a=\", a)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "或者，使用 **Tensor()** （*注意大小写！*）需要创建的Tensor的维数，从而创建一个未初始化的tensor："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[ 6.1365e-37,  0.0000e+00,  5.6052e-45],\n",
       "        [ 0.0000e+00,  0.0000e+00,  0.0000e+00],\n",
       "        [ 0.0000e+00,  0.0000e+00,  0.0000e+00],\n",
       "        [ 0.0000e+00,  0.0000e+00,  0.0000e+00],\n",
       "        [ 6.1365e-37,  0.0000e+00,  6.1365e-37],\n",
       "        [ 0.0000e+00,  6.1366e-37,  0.0000e+00],\n",
       "        [ 1.4013e-45,  0.0000e+00,  2.4663e-43],\n",
       "        [ 0.0000e+00,  1.5695e-43,  0.0000e+00],\n",
       "        [ 3.3936e-38,  0.0000e+00, -2.9040e+22],\n",
       "        [ 4.5626e-41,  0.0000e+00,  0.0000e+00]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c = torch.Tensor(10, 3)\n",
    "c"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用torch.Tensor()也可以转化NumPy的array为Tensor，两者的区别是使用b=torch.from_numpy(a)函数引入时，a和b是共享内存的；而如果使用b=torch.Tensor(a)函数时，如果a的类型不是Float32，则会新建，此时可能不共享内存。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([10.,  2.,  3.,  4.])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b_torch1 = torch.Tensor(b)\n",
    "b_torch1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "注意以上新创建的Tensor的值是凌乱的，因为没有对其进行初始化，所以里面的值是完全无意义的。\n",
    "\n",
    "几乎所有的神经网络工具箱都需要支持GPU计算，而GPU计算最常用的工具是NVIDIA公司的CUDA工具箱。如果你有支持CUDA的显卡，并且配置好了CUDA，可以在创建时通过 **cuda()** 函数将Tensor放在显卡的内存（显存）中，而非内存中："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1., 2., 3., 4.], device='cuda:0')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "if torch.cuda.is_available():\n",
    "    ac = torch.tensor([1., 2, 3, 4]).cuda()\n",
    "ac"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其中我们使用了“torch.cuda.is_available()”来判断计算机上是否有GPU和CUDA可用。上面的结果除了展示了Tensor的取值之外，还有一个 *device='cuda:0'* ，显示了这个Tensor所出的CUDA设备编号为0。如果有不止一块GPU，可以在括号中加入数字（从0开始计数），指定将其放在哪一块GPU上。\n",
    "\n",
    "我们可以使用cup()函数和cuda()函数在两者之间转换："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1., 2., 3., 4.])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ac_cpu = ac.cpu()\n",
    "ac_cpu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "另一种直接将Tensor放到GPU中的方法是在创建Tensor时直接指定其所处的device，比如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0., 1.], device='cuda:0')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gpu_tensor = torch.tensor([0., 1], device=0)\n",
    "gpu_tensor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下来介绍的创建Tensor的函数也都支持这种创建方法，特别是如果该Tensor需要被求导，一定要使用这种方法进行创建。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在这里值得一提的是Tensor的数据类型。在PyTorch中，Tensor有如下数据类型可以使用：\n",
    "* 浮点类型\n",
    "  * torch.FloatTensor（torch.cuda.FloatTensor）: 32位浮点型\n",
    "  * torch.DoubleTensor（torch.cuda.DoubleTensor）: 64位浮点型\n",
    "  * （torch.cuda.HalfTensor）: 16位浮点型\n",
    "* 整型\n",
    "  * torch.IntTensor（torch.cuda.IntTensor）: 32位整型\n",
    "  * torch.LongTensor（torch.cuda.LongTensor）: 64位整型\n",
    "  * torch.ShortTensor（torch.cuda.ShortTensor）: 16位整型\n",
    "  * torch.ByteTensor（torch.cuda.ByteTensor）：8位无符号整型\n",
    "  * torch.CharTensor（torch.cuda.CharTensor）：8位有符号整型\n",
    "  \n",
    "其中括号里面表示的是在CUDA中的类型。\n",
    "\n",
    "不管是在CPU上还是GPU上，位数更小的类型总是需要更少的内存（显存），并且具有更高的计算速度。然而位数更小的类型可能具有更差的精度或者更高的误差（特别是对于浮点类型）、更小的表示范围（特别是对于整数类型），所以在创建Tensor时可以按照需求指定类型。\n",
    "\n",
    "我们可以使用Tensor.type()函数展示其类型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.cuda.FloatTensor\n",
      "torch.FloatTensor\n"
     ]
    }
   ],
   "source": [
    "print(ac.type())\n",
    "print(c.type())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "根据上面的输出可以知道，默认的类型是32位浮点型，我们可以使用double()（以及float(), int(), long(), short()等）将其换为64位浮点型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.cuda.DoubleTensor\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([1., 2., 3., 4.], device='cuda:0', dtype=torch.float64)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ac_64 = ac.double()\n",
    "print(ac_64.type())\n",
    "ac_64"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "也可以使用type_as()方法产生相同类型的Tensor："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "e的类型： torch.LongTensor\n",
      "e_64的类型： torch.DoubleTensor\n",
      "tensor([1, 2, 3])\n",
      "tensor([1., 2., 3.], dtype=torch.float64)\n"
     ]
    }
   ],
   "source": [
    "d = c.double()\n",
    "e = torch.tensor([1, 2, 3])\n",
    "print(\"e的类型：\", e.type())\n",
    "e_64 = e.type_as(d)\n",
    "print(\"e_64的类型：\", e_64.type())\n",
    "print(e)\n",
    "print(e_64)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果需要改变所有的默认类型，可以使用torch.set_default_tensor_type()函数，比如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.FloatTensor\n",
      "torch.DoubleTensor\n"
     ]
    }
   ],
   "source": [
    "a = torch.tensor([1., 2, 3, 4])\n",
    "print(a.type())\n",
    "torch.set_default_tensor_type(\"torch.DoubleTensor\")\n",
    "a = torch.tensor([1., 2, 3, 4])\n",
    "print(a.type())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "一般而言，32位的浮点数已经足够用了，用Double会比较慢，特别是涉及到神经网络中大规模的计算，使用Double的计算开销比较大，所以不妨换回去："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "torch.set_default_tensor_type(\"torch.FloatTensor\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "与NumPy类似，PyTorch也有很多创建特殊Tensor的方法，比如：\n",
    "\n",
    "* 全为0的Tensor：torch.zeors()\n",
    "* 全为1的Tensor：torch.ones()\n",
    "* 单位阵：torch.eye()\n",
    "* U(0,1)的随机数：torch.rand()\n",
    "* 标准正态分布的随机数：torch.randn()\n",
    "* 从start到end，步长为step：torch.arange(start,end,step)\n",
    "* 从start到end，切成m份：torch.linspace(start,end,m)\n",
    "* 从10^start到10^end，切成m份：torch.linspace(start,end,m)\n",
    "* 随机排列：torch.randperm(m)\n",
    "\n",
    "比如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "维数为5-by-4的全为0的矩阵：\n",
      " tensor([[0., 0., 0., 0.],\n",
      "        [0., 0., 0., 0.],\n",
      "        [0., 0., 0., 0.],\n",
      "        [0., 0., 0., 0.],\n",
      "        [0., 0., 0., 0.]])\n",
      "维数为5-by-4的全为1的矩阵：\n",
      " tensor([[1., 1., 1., 1.],\n",
      "        [1., 1., 1., 1.],\n",
      "        [1., 1., 1., 1.],\n",
      "        [1., 1., 1., 1.],\n",
      "        [1., 1., 1., 1.]])\n",
      "维数为5-by-4的单位阵：\n",
      " tensor([[1., 0., 0., 0.],\n",
      "        [0., 1., 0., 0.],\n",
      "        [0., 0., 1., 0.],\n",
      "        [0., 0., 0., 1.],\n",
      "        [0., 0., 0., 0.]])\n",
      "维数为5-by-4的(0,1)上均匀分布随机数矩阵：\n",
      " tensor([[0.5356, 0.7557, 0.6717, 0.7953],\n",
      "        [0.3835, 0.8052, 0.7999, 0.6437],\n",
      "        [0.5057, 0.7549, 0.2026, 0.9213],\n",
      "        [0.4062, 0.1923, 0.1493, 0.7789],\n",
      "        [0.8646, 0.0785, 0.7154, 0.7986]])\n",
      "维数为5-by-4的标准正态分布矩阵：\n",
      " tensor([[ 0.1853, -0.0638,  1.3071,  0.2842],\n",
      "        [ 0.7994, -0.0534,  1.7484, -1.7582],\n",
      "        [ 1.0289,  0.0339, -0.2238,  0.0794],\n",
      "        [-0.3025, -1.4059, -0.0330, -0.0538],\n",
      "        [-0.2911, -0.7687,  2.1184,  0.8377]])\n",
      "从1到10，步长为2：\n",
      " tensor([1, 3, 5, 7, 9])\n",
      "从1到10，4等分（5个数字）：：\n",
      " tensor([ 1.0000,  3.2500,  5.5000,  7.7500, 10.0000])\n",
      "从10^1到10^3，4等分（5个数字）：：\n",
      " tensor([   1.0000,    5.6234,   31.6228,  177.8279, 1000.0000])\n",
      "0-9共10个数字的随机排列：\n",
      " tensor([7, 2, 8, 3, 6, 4, 0, 1, 9, 5])\n"
     ]
    }
   ],
   "source": [
    "a = torch.zeros(5, 4)\n",
    "print(\"维数为5-by-4的全为0的矩阵：\\n\", a)\n",
    "b = torch.ones(5, 4)\n",
    "print(\"维数为5-by-4的全为1的矩阵：\\n\", b)\n",
    "c = torch.eye(5, 4)\n",
    "print(\"维数为5-by-4的单位阵：\\n\", c)\n",
    "d = torch.rand(5, 4)\n",
    "print(\"维数为5-by-4的(0,1)上均匀分布随机数矩阵：\\n\", d)\n",
    "e = torch.randn(5, 4)\n",
    "print(\"维数为5-by-4的标准正态分布矩阵：\\n\", e)\n",
    "f = torch.arange(1, 10, 2)\n",
    "print(\"从1到10，步长为2：\\n\", f)\n",
    "g = torch.linspace(1, 10, 5)\n",
    "print(\"从1到10，4等分（5个数字）：：\\n\", g)\n",
    "h = torch.logspace(0, 3, 5)\n",
    "print(\"从10^1到10^3，4等分（5个数字）：：\\n\", h)\n",
    "i = torch.randperm(10)\n",
    "print(\"0-9共10个数字的随机排列：\\n\", i)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "此外，还可以使用如下命令产生形状相同的Tensor：\n",
    "\n",
    "* 创建与T形状相同的全为1的Tensor：torch.ones_like(T)\n",
    "* 创建与T形状相同的全为0的Tensor：torch.zeros_like(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "与i形状相同的全为1的Tensor：\n",
      " tensor([1, 1, 1, 1, 1, 1, 1, 1, 1, 1])\n",
      "与g形状相同的全为0的Tensor：\n",
      " tensor([0., 0., 0., 0., 0.])\n"
     ]
    }
   ],
   "source": [
    "j = torch.ones_like(i)\n",
    "print(\"与i形状相同的全为1的Tensor：\\n\", j)\n",
    "k = torch.zeros_like(g)\n",
    "print(\"与g形状相同的全为0的Tensor：\\n\", k)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "与NumPy类似，对于一个Tensor，可以通过shape、size等属性和方法查看Tensor的形状，但是值得注意的是PyTorch的方法、属性与NumPy略有区别："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "np_a=\n",
      " [[0.37807887 0.93018719 0.69036538 0.8614119  0.27931302 0.39179632]\n",
      " [0.54783785 0.77491369 0.18787534 0.20792254 0.18638006 0.54511025]\n",
      " [0.40004818 0.46726855 0.00308457 0.42465231 0.97812506 0.325218  ]\n",
      " [0.8305741  0.02855473 0.75274481 0.05924857 0.95954737 0.12115339]\n",
      " [0.55932785 0.65351854 0.33341192 0.2160422  0.51384614 0.94953161]]\n",
      "np_a的维度： 2\n",
      "np_a的形状： (5, 6)\n",
      "np_a的长度： 30\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "np_a = np.random.random((5, 6))\n",
    "print(\"np_a=\\n\", np_a)\n",
    "print(\"np_a的维度：\", np_a.ndim)\n",
    "print(\"np_a的形状：\", np_a.shape)\n",
    "print(\"np_a的长度：\", np_a.size)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a=\n",
      " [[0.37807887 0.93018719 0.69036538 0.8614119  0.27931302 0.39179632]\n",
      " [0.54783785 0.77491369 0.18787534 0.20792254 0.18638006 0.54511025]\n",
      " [0.40004818 0.46726855 0.00308457 0.42465231 0.97812506 0.325218  ]\n",
      " [0.8305741  0.02855473 0.75274481 0.05924857 0.95954737 0.12115339]\n",
      " [0.55932785 0.65351854 0.33341192 0.2160422  0.51384614 0.94953161]]\n",
      "a的维度： 2\n",
      "a的形状： torch.Size([5, 4])\n",
      "a的长度： torch.Size([5, 4])\n",
      "a的元素的个数： 20\n"
     ]
    }
   ],
   "source": [
    "print(\"a=\\n\", np_a)\n",
    "print(\"a的维度：\", a.dim())\n",
    "print(\"a的形状：\", a.shape)\n",
    "print(\"a的长度：\", a.size())\n",
    "print(\"a的元素的个数：\", a.numel())\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以发现：\n",
    "\n",
    "* NumPy中array的ndim, shape, size都是属性\n",
    "* PyTorch中Tensor的dim(), size()都是函数，shape为属性\n",
    "* NumPy中size代表元素的个数，而PyTorch中Tensor元素的个数是使用numel()方法。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 索引、视图与形状调整与\n",
    "\n",
    "与NumPy类似，Tensor也可以通过切片等操作产生Tensor的视图（view），与NumPy一样，视图并不会对Tensor进行复制，仅仅是一个引用。与NumPy类似，可以使用切片操作："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a= tensor([1, 2, 3, 4])\n",
      "b= tensor([1, 2])\n",
      "b= tensor([3, 2])\n",
      "a= tensor([3, 2, 3, 4])\n"
     ]
    }
   ],
   "source": [
    "a = torch.tensor([1, 2, 3, 4])\n",
    "print(\"a=\", a)\n",
    "b = a[0:2]\n",
    "print(\"b=\", b)\n",
    "b[0] = 3\n",
    "print(\"b=\", b)\n",
    "print(\"a=\", a)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "跟NumPy类似的是，也可以使用掩码操作，不过掩码操作所创建的是一个拷贝，而非视图："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a= tensor([1, 2, 3, 4])\n",
      "c= tensor([3, 4])\n",
      "c= tensor([3, 5])\n",
      "a= tensor([1, 2, 3, 4])\n",
      "b= tensor([3, 2])\n"
     ]
    }
   ],
   "source": [
    "a = torch.tensor([1, 2, 3, 4])\n",
    "print(\"a=\", a)\n",
    "c = a[a >= 3]\n",
    "print(\"c=\", c)\n",
    "c[-1] = 5\n",
    "print(\"c=\", c)\n",
    "print(\"a=\", a)\n",
    "print(\"b=\", b)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果需要调整Tensor的形状，可以使用Tensor的view()函数以及reshape()方法，其中view()和reshape()接受的参数为修改后的形状，区别在于view()一定会创建视图，而reshape()则不一定，也可能创建原Tensor的拷贝。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a= tensor([1, 2, 3, 4])\n",
      "b=\n",
      " tensor([[1, 2],\n",
      "        [3, 4]])\n",
      "c=\n",
      " tensor([[1, 2],\n",
      "        [3, 4]])\n",
      "现在对b重新赋值\n",
      "a= tensor([1, 2, 3, 4])\n",
      "b=\n",
      " tensor([[1, 2],\n",
      "        [3, 4]])\n",
      "c=\n",
      " tensor([[1, 2],\n",
      "        [3, 4]])\n"
     ]
    }
   ],
   "source": [
    "a = torch.tensor([1, 2, 3, 4])\n",
    "print(\"a=\", a)\n",
    "b = a.view(2, 2)\n",
    "print(\"b=\\n\", b)\n",
    "c = a.reshape(2, 2)\n",
    "print(\"c=\\n\", c)\n",
    "print(\"现在对b重新赋值\")\n",
    "b[0, 0] = 1\n",
    "print(\"a=\", a)\n",
    "print(\"b=\\n\", b)\n",
    "print(\"c=\\n\", c)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "也可以使用torch.reshape()函数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a= tensor([5, 2, 3, 4])\n",
      "d=\n",
      " tensor([[5, 2],\n",
      "        [3, 4]])\n"
     ]
    }
   ],
   "source": [
    "d = torch.reshape(a, (2, 2))\n",
    "d[0, 0] = 5\n",
    "print(\"a=\", a)\n",
    "print(\"d=\\n\", d)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "形状也可以使用-1来描述，当使用-1时，自动计算该维度的大小："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a= tensor([1, 2, 3, 4, 5, 6])\n",
      "b=\n",
      " tensor([[1, 2],\n",
      "        [3, 4],\n",
      "        [5, 6]])\n"
     ]
    }
   ],
   "source": [
    "a = torch.tensor([1, 2, 3, 4, 5, 6])\n",
    "print(\"a=\", a)\n",
    "b = a.view(-1, 2)\n",
    "print(\"b=\\n\", b)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以使用该特性将Tensor转化为向量："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a=\n",
      " tensor([[1, 2, 3],\n",
      "        [4, 5, 6]])\n",
      "b=\n",
      " tensor([1, 2, 3, 4, 5, 6])\n"
     ]
    }
   ],
   "source": [
    "a = torch.tensor([[1, 2, 3], [4, 5, 6]])\n",
    "print(\"a=\\n\", a)\n",
    "b = a.view(-1)\n",
    "print(\"b=\\n\", b)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "此外还可以使用squeeze()和unsqueeze()方法对某一个维度压缩一个1或者增加一个1，比如如下的Tensor中，第0个维度的个数为1，可以使用squeeze()方法删掉这个维度："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[1, 2, 3, 4, 5, 6]])\n",
      "torch.Size([1, 6])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([1, 2, 3, 4, 5, 6])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = torch.tensor([[1, 2, 3, 4, 5, 6]])\n",
    "print(a)\n",
    "print(a.shape)\n",
    "b = a.squeeze(0)\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "反过来也可以在指定维度上增加一个维度："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([1, 2, 3, 4, 5, 6])\n",
      "torch.Size([6])\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor([[1],\n",
       "        [2],\n",
       "        [3],\n",
       "        [4],\n",
       "        [5],\n",
       "        [6]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = torch.tensor([1, 2, 3, 4, 5, 6])\n",
    "print(a)\n",
    "print(a.shape)\n",
    "b = a.unsqueeze(1)\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tensor的计算\n",
    "\n",
    "与NumPy类似，Tensor也有很多计算功能，这与我们之前所学的NumPy几乎是相同的。\n",
    "\n",
    "一个与NumPy有点区别的地方是，在Tensor中，很多运算函数都有带下划线的版本，比如Tensor的add()方法同样有add_()方法，两者的区别在于：\n",
    "\n",
    "* 使用a.add(b)会返回计算结果a+b，而不改变a\n",
    "* 使用a.add_()会改变a，计算结束后a=a+b\n",
    "\n",
    "比如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c= tensor([5, 7, 9])\n",
      "a= tensor([1, 2, 3])\n",
      "c= tensor([5, 7, 9])\n",
      "a= tensor([1, 2, 3])\n",
      "a= tensor([5, 7, 9])\n"
     ]
    }
   ],
   "source": [
    "a = torch.tensor([1, 2, 3])\n",
    "b = torch.tensor([4, 5, 6])\n",
    "c = a + b\n",
    "print(\"c=\", c)\n",
    "print(\"a=\", a)\n",
    "c = a.add(b)\n",
    "print(\"c=\", c)\n",
    "print(\"a=\", a)\n",
    "a.add_(b)\n",
    "print(\"a=\", a)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PyTorch中支持NumPy中支持的很多运算，比如：\n",
    "\n",
    "* 逐元素的算数运算\n",
    "  * 加（+,add()）\n",
    "  * 减（-,sub()）\n",
    "  * 乘（*,mul()）\n",
    "  * 除（/,div()）\n",
    "  * 取反（-，neg()）\n",
    "* 比较运算\n",
    "  * 大于（>,gt()）、大于等于（>=,ge()）、小于（<,lt()）、小于等于（>,le()）\n",
    "  * 等于（==, eq()）、不等于（!=,ne()）\n",
    "  * 排序：sort()\n",
    "  * 最大值（max()）、最小值（min()）\n",
    "  * 最大的k个数：topk()\n",
    "* 函数运算\n",
    "  * 绝对值（abs()）、平方根（sqrt()）\n",
    "  * 三角函数：sin(), cos(), asin(), tan(), atan(), cosh(), tanh().....\n",
    "  * 向上取整（ceil()）、向下取整（floor()）、四舍五入（round()）、取整数部分（trunc()）、取余（fmod()）、符号函数（sign()）\n",
    "  * 指数（exp()）、对数（log()）\n",
    "  * 激活函数\n",
    "    * sigmoid()\n",
    "    * tanh()\n",
    "    * softmax()\n",
    "* 归并函数\n",
    "  * 均值（mean()）、求和（sum()）、中位数（median()）、众数（mode()）\n",
    "  * 标准差（std()）、方差（var()）\n",
    "  * 范数（norm()）、距离（dist()）\n",
    "  * 累加（cumsum()）、累乘（cumprod()）\n",
    "* 矩阵运算\n",
    "  * 内积（dot()）、外积（cross()）\n",
    "  * 转置（t()）\n",
    "  * 矩阵乘法（mm()）\n",
    "  * 矩阵与向量乘法（mv()）\n",
    "  * 迹（trace()）\n",
    "  * 求逆（inverse()）\n",
    "  * 对角线元素（diag()）\n",
    "  * 奇异值分解（svd()）\n",
    "  \n",
    "等等非常多的运算。\n",
    "\n",
    "比如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "---\n",
      "a+b=\n",
      " tensor([ 3., 11., 18.])\n",
      "---\n",
      "a/b=\n",
      " tensor([0.5000, 0.2222, 1.2500])\n",
      "---\n",
      "a>=b\n",
      " tensor([False, False,  True])\n",
      "---\n",
      "b.sort()=\n",
      " torch.return_types.sort(\n",
      "values=tensor([2., 8., 9.]),\n",
      "indices=tensor([0, 2, 1]))\n",
      "---\n",
      "torch.max(a,b)=\n",
      " tensor([ 2.,  9., 10.])\n",
      "---\n",
      "b.max()=\n",
      " tensor(9.)\n",
      "---\n",
      "b.topk(2)=\n",
      " torch.return_types.topk(\n",
      "values=tensor([9., 8.]),\n",
      "indices=tensor([1, 2]))\n",
      "---\n",
      "torch.sqrt(b)=\n",
      " tensor([1.4142, 3.0000, 2.8284])\n",
      "---\n",
      "torch.sigmoid(b)=\n",
      " tensor([0.8808, 0.9999, 0.9997])\n",
      "---\n",
      "a.sum()=\n",
      " tensor(13.)\n",
      "---\n",
      "a.std()=\n",
      " tensor(4.9329)\n",
      "---\n",
      "a.norm(2)=\n",
      " tensor(10.2470)\n",
      "---\n",
      "torch.dist(a,b,2)=\n",
      " tensor(7.3485)\n",
      "---\n",
      "a.cumsum()=\n",
      " tensor([ 1.,  3., 13.])\n"
     ]
    }
   ],
   "source": [
    "a = torch.tensor([1., 2, 10])\n",
    "b = torch.tensor([2., 9, 8])\n",
    "print(\"---\\na+b=\\n\", a + b)\n",
    "print(\"---\\na/b=\\n\", a / b)\n",
    "print(\"---\\na>=b\\n\", a >= b)\n",
    "print(\"---\\nb.sort()=\\n\", b.sort())\n",
    "print(\"---\\ntorch.max(a,b)=\\n\", torch.max(a, b))\n",
    "print(\"---\\nb.max()=\\n\", b.max())\n",
    "print(\"---\\nb.topk(2)=\\n\", b.topk(2))\n",
    "print(\"---\\ntorch.sqrt(b)=\\n\", torch.sqrt(b))\n",
    "print(\"---\\ntorch.sigmoid(b)=\\n\", torch.sigmoid(b))\n",
    "print(\"---\\na.sum()=\\n\", a.sum())\n",
    "print(\"---\\na.std()=\\n\", a.std())\n",
    "print(\"---\\na.norm(2)=\\n\", a.norm(2))\n",
    "print(\"---\\ntorch.dist(a,b,2)=\\n\", torch.dist(a, b, 2))\n",
    "print(\"---\\na.cumsum()=\\n\", a.cumsum(0))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a=\n",
      " tensor([[1., 2., 3.],\n",
      "        [5., 6., 4.],\n",
      "        [8., 1., 0.]])\n",
      "b=\n",
      " tensor([[ 2.,  4.,  3.],\n",
      "        [ 5.,  7.,  1.],\n",
      "        [ 8., 10.,  2.]])\n",
      "c=\n",
      " tensor([1., 2., 3.])\n",
      "---\n",
      "a+b=\n",
      " tensor([[ 3.,  6.,  6.],\n",
      "        [10., 13.,  5.],\n",
      "        [16., 11.,  2.]])\n",
      "---\n",
      "torch.exp(a)=\n",
      " tensor([[2.7183e+00, 7.3891e+00, 2.0086e+01],\n",
      "        [1.4841e+02, 4.0343e+02, 5.4598e+01],\n",
      "        [2.9810e+03, 2.7183e+00, 1.0000e+00]])\n",
      "---\n",
      "a.diag()=\n",
      " tensor([1., 6., 0.])\n",
      "---\n",
      "a.t()=\n",
      " tensor([[1., 5., 8.],\n",
      "        [2., 6., 1.],\n",
      "        [3., 4., 0.]])\n",
      "---\n",
      "torch.dot(c,d)=\n",
      " tensor(10.)\n",
      "---\n",
      "torch.mm(a,b)=\n",
      " tensor([[ 36.,  48.,  11.],\n",
      "        [ 72., 102.,  29.],\n",
      "        [ 21.,  39.,  25.]])\n",
      "---\n",
      "a.mm(b)=\n",
      " tensor([[ 36.,  48.,  11.],\n",
      "        [ 72., 102.,  29.],\n",
      "        [ 21.,  39.,  25.]])\n",
      "---\n",
      "a.trace()= tensor(7.)\n",
      "---\n",
      "a.inverse()= tensor([[ 0.0580, -0.0435,  0.1449],\n",
      "        [-0.4638,  0.3478, -0.1594],\n",
      "        [ 0.6232, -0.2174,  0.0580]])\n",
      "---\n",
      "a.mm(a.inverse())= tensor([[1.0000e+00, 2.9802e-08, 0.0000e+00],\n",
      "        [0.0000e+00, 1.0000e+00, 2.9802e-08],\n",
      "        [0.0000e+00, 0.0000e+00, 1.0000e+00]])\n",
      "---\n",
      "torch.mv(a,c)=\n",
      " tensor([14., 29., 10.])\n",
      "---\n",
      "torch.mv(a.t(),c)=\n",
      " tensor([35., 17., 11.])\n"
     ]
    }
   ],
   "source": [
    "a = torch.tensor([[1., 2, 3], [5, 6, 4], [8, 1, 0]])\n",
    "b = torch.tensor([[2., 4, 3], [5, 7, 1], [8, 10, 2]])\n",
    "c = torch.tensor([1, 2, 3.])\n",
    "d = torch.tensor([3, 2, 1.])\n",
    "print(\"a=\\n\", a)\n",
    "print(\"b=\\n\", b)\n",
    "print(\"c=\\n\", c)\n",
    "print(\"---\\na+b=\\n\", a + b)\n",
    "print(\"---\\ntorch.exp(a)=\\n\", torch.exp(a))\n",
    "print(\"---\\na.diag()=\\n\", a.diag())\n",
    "print(\"---\\na.t()=\\n\", a.t())\n",
    "print(\"---\\ntorch.dot(c,d)=\\n\", torch.dot(c, d))\n",
    "print(\"---\\ntorch.mm(a,b)=\\n\", torch.mm(a, b))\n",
    "print(\"---\\na.mm(b)=\\n\", a.mm(b))\n",
    "print(\"---\\na.trace()=\", a.trace())\n",
    "print(\"---\\na.inverse()=\", a.inverse())\n",
    "print(\"---\\na.mm(a.inverse())=\", a.mm(a.inverse()))\n",
    "print(\"---\\ntorch.mv(a,c)=\\n\", torch.mv(a, c))\n",
    "print(\"---\\ntorch.mv(a.t(),c)=\\n\", torch.mv(a.t(), c))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最后，还记得如果我们使用torch.from_numpy()函数和Tensor的numpy()函数在NumPy的array和PyTorch的Tensor之间转换，内存是共享的，转换速度很快，可以直接进行操作而付出较小的性能代价："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a=\n",
      " tensor([[1., 2., 3.],\n",
      "        [5., 6., 4.],\n",
      "        [8., 1., 0.]])\n",
      "b=\n",
      " tensor([[ 2.,  4.,  3.],\n",
      "        [ 5.,  7.,  1.],\n",
      "        [ 8., 10.,  2.]])\n",
      "c=\n",
      " tensor([[ 36.,  48.,  11.],\n",
      "        [ 72., 102.,  29.],\n",
      "        [ 21.,  39.,  25.]])\n",
      "c_np=\n",
      " [[ 36.  48.  11.]\n",
      " [ 72. 102.  29.]\n",
      " [ 21.  39.  25.]]\n"
     ]
    }
   ],
   "source": [
    "a = torch.tensor([[1., 2, 3], [5, 6, 4], [8, 1, 0]])\n",
    "b = torch.tensor([[2., 4, 3], [5, 7, 1], [8, 10, 2]])\n",
    "print(\"a=\\n\", a)\n",
    "print(\"b=\\n\", b)\n",
    "a_np = a.numpy()\n",
    "b_np = b.numpy()\n",
    "c_np = a_np @ b_np\n",
    "c = torch.tensor(c_np)\n",
    "print(\"c=\\n\", c)\n",
    "print(\"c_np=\\n\", c_np)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最后，Tensor也支持广播操作，在这里不再赘述。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 自动求导\n",
    "\n",
    "在神经网络中，优化算法需要计算损失函数对于每个参数的导数，然而在动辄成千上万甚至数十万参数的情况下，靠人工取计算这些导数显然是不现实的。为此，在现代化的深度学习框架中，都包含了自动求导的模块。\n",
    "\n",
    "在PyTorch中，torch.autograd模块就是用来实现自动求导的。\n",
    "\n",
    "对于一个Tensor，在创建的时候可以通过加入\"requires_grad=True\"选项，表示需要对这个Tensor进行求导。比如，我们对一个最简单的线性函数：$$y=x'b$$进行求导，易得：$$\\frac{dy}{db}=x$$一般而言，如果$(x,y)$为数据，$b$为参数，我们需要对参数求导（而非数据），从而我们只需要要求Tensor b在创建时加入requires_grad=True选项就可以了，比如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x=\n",
      " tensor([0.0114, 0.7916, 0.4483])\n",
      "y= tensor(2.9397, grad_fn=<DotBackward>)\n",
      "dy/dx=\n",
      " None\n",
      "dy/db=\n",
      " tensor([0.0114, 0.7916, 0.4483])\n"
     ]
    }
   ],
   "source": [
    "x = torch.rand(3)\n",
    "b = torch.tensor([1., 2, 3], requires_grad=True)\n",
    "y = torch.dot(x, b)\n",
    "print(\"x=\\n\", x)\n",
    "print(\"y=\", y)\n",
    "y.backward()\n",
    "print(\"dy/dx=\\n\", x.grad)\n",
    "print(\"dy/db=\\n\", b.grad)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看到由于b加入了requires_grad=True选项，我们可以使用y.backward()选项，实现对b的求导；而x由于没有这个选项，从而没有对x进行求导。\n",
    "\n",
    "我们还可以使用更加复杂的函数，比如：$$y=x'b \\\\ z=e^{y}$$其对$b$的导数应该按照链式法则进行计算：$$\\frac{dz}{db}=\\frac{dz}{dy}\\cdot\\frac{dy}{db}=e^{y}\\cdot x=zx$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x=\n",
      " tensor([0.0565, 0.6628, 0.7080])\n",
      "y= tensor(3.5059, grad_fn=<DotBackward>)\n",
      "z= tensor(33.3118, grad_fn=<ExpBackward>)\n",
      "dz/db=\n",
      " tensor([ 1.8809, 22.0776, 23.5841])\n"
     ]
    }
   ],
   "source": [
    "x = torch.rand(3)\n",
    "b = torch.tensor([1., 2, 3], requires_grad=True)\n",
    "y = torch.dot(x, b)\n",
    "z = torch.exp(y)\n",
    "print(\"x=\\n\", x)\n",
    "print(\"y=\", y)\n",
    "print(\"z=\", z)\n",
    "z.backward()\n",
    "print(\"dz/db=\\n\", b.grad)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以上复合函数求导在PyTorch中是以 **计算图** 的方式进行的，比如上面的例子我们可以使用如下的计算图来表示：\n",
    "![](pic/compute_graph.gv.png \"计算图\")\n",
    "其中菱形代表计算。在计算导数时，使用一种“反向传播”算法，即使用链式法则，按照计算方向的反方向计算导数，如下图所示：\n",
    "![](pic/compute_graph_back.gv.png \"反向传播图\")\n",
    "上图中虚线代表计算导数的方向，每条虚线计算导数，然后在节点上从最终的节点$z$到该节点$b$的导数累乘起来，就得到了$\\frac{dz}{db}$。正因如此，计算节点导数的函数才被成为backward()。\n",
    "\n",
    "PyTorch的计算图有个非常重要的优势是使用了动态的计算图，意味着每次传播时，计算图可以动态重新构建。\n",
    "\n",
    "在中间节点加入参数也是完全可行的，比如：$$y=x'b \\\\ z=e^{cy}$$那么导数为：$$\\frac{dz}{dc}=ye^{cy}=yz \\\\ \\frac{dz}{db}=\\frac{dz}{dy}\\cdot\\frac{dy}{db}=ce^{cy}\\cdot x=czx$$使用计算图表示为：\n",
    "![](pic/compute_graph_back2.gv.png \"反向传播图\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x=\n",
      " tensor([0.7245, 0.1693, 0.5531])\n",
      "c= tensor([2.], requires_grad=True)\n",
      "y= tensor(2.7223, grad_fn=<DotBackward>)\n",
      "z= tensor([231.4855], grad_fn=<ExpBackward>)\n",
      "dz/db=\n",
      " tensor([335.4218,  78.3583, 256.0627])\n",
      "dz/dc=\n",
      " tensor([630.1633])\n"
     ]
    }
   ],
   "source": [
    "x = torch.rand(3)\n",
    "b = torch.tensor([1., 2, 3], requires_grad=True)\n",
    "y = torch.dot(x, b)\n",
    "c = torch.tensor([2.], requires_grad=True)\n",
    "z = torch.exp(c * y)\n",
    "print(\"x=\\n\", x)\n",
    "print(\"c=\", c)\n",
    "print(\"y=\", y)\n",
    "print(\"z=\", z)\n",
    "z.backward()\n",
    "print(\"dz/db=\\n\", b.grad)\n",
    "print(\"dz/dc=\\n\", c.grad)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在统计和机器学习中，计算的目标函数（损失函数）通常是一个求和的形式：$$Q(x,b)=\\sum_{i=1}^N q(x_i,b)$$此时我们对$b$求导：$$\\frac{dQ}{db}=\\sum_{i=1}^N \\frac{dq(x_i,b)}{db}$$在默认的情况下，每次调用backward()后，导数都会自动进行累加："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dy/db=\n",
      " tensor([1., 2., 3.])\n",
      "dy/db=\n",
      " tensor([5., 7., 9.])\n"
     ]
    }
   ],
   "source": [
    "x1 = torch.tensor([1, 2, 3.])\n",
    "x2 = torch.tensor([4, 5, 6.])\n",
    "b = torch.tensor([1., 2, 3], requires_grad=True)\n",
    "y = torch.dot(x1, b)\n",
    "y.backward()\n",
    "print(\"dy/db=\\n\", b.grad)\n",
    "y = torch.dot(x2, b)\n",
    "y.backward()\n",
    "print(\"dy/db=\\n\", b.grad)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果不需要累加，需要对梯度清零："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dy/db=\n",
      " tensor([1., 2., 3.])\n",
      "dy/db=\n",
      " tensor([4., 5., 6.])\n"
     ]
    }
   ],
   "source": [
    "x1 = torch.tensor([1, 2, 3.])\n",
    "x2 = torch.tensor([4, 5, 6.])\n",
    "b = torch.tensor([1., 2, 3], requires_grad=True)\n",
    "y = torch.dot(x1, b)\n",
    "y.backward()\n",
    "print(\"dy/db=\\n\", b.grad)\n",
    "b.grad.zero_()\n",
    "y = torch.dot(x2, b)\n",
    "y.backward()\n",
    "print(\"dy/db=\\n\", b.grad)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在PyTorch中，只允许一个标量对张量求导，而不允许张量对张量求导。如果需要张量对张量求导，需要手动计算。\n",
    "比如，对于函数：$$y_1=b_1 \\times x_1 + b_2 \\times x_2 +b_3 \\times x_1\\times x_2 \\\\ y_2= b_2\\times x_1^{b_1}+x_2^{b_3}$$参数为$\\left[b_1,b_2,b_3\\right]$，而输出为$\\left[y_1,y_2\\right]$，其导数为：$$\\frac{dy}{db}=\\left[\\begin{array}{ccc}\n",
    "x_{1} & x_{2} & x_{1}x_{2}\\\\\n",
    "b_{2}x_{1}^{b_{1}}\\ln\\left(x_{1}\\right) & x_{1}^{b_{1}} & x_{2}^{b_{3}}\\ln\\left(x_{2}\\right)\n",
    "\\end{array}\\right]$$\n",
    "\n",
    "为了计算该Jacobian矩阵，可以分开计算第一行和第二行。在backward()函数中，可以加入一个参数向量v，比如如果使用：\n",
    "```python\n",
    "y.backward(v)\n",
    "```\n",
    "\n",
    "那么该函数就将计算：$\\frac{d(vy')}{db}$，我们只需要分别令$v_1=\\left[1,0\\right],v_2=\\left[0,1\\right]$就可以分别计算出Jaccobian的两行，然后放在一起即可："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x= tensor([1., 2.])\n",
      "y= tensor([11., 10.], grad_fn=<CopySlices>)\n",
      "J1= tensor([0.0000, 1.0000, 5.5452])\n",
      "J2= tensor([0.0000, 1.0000, 5.5452])\n",
      "J=\n",
      " tensor([[0.0000, 1.0000, 5.5452],\n",
      "        [0.0000, 1.0000, 5.5452]])\n"
     ]
    }
   ],
   "source": [
    "x = torch.tensor([1., 2])\n",
    "b = torch.tensor([1, 2, 3.], requires_grad=True)\n",
    "y = torch.zeros(2)\n",
    "y[0] = b[0] * x[0] + b[1] * x[1] + b[2] * x[0] * x[1]\n",
    "y[1] = b[1] * (x[0]**b[0]) + x[1]**b[2]\n",
    "print(\"x=\", x)\n",
    "print(\"y=\", y)\n",
    "y.backward(torch.tensor([1., 0]), retain_graph=True)\n",
    "J1 = b.grad\n",
    "b.grad.zero_()\n",
    "J2 = y.backward(torch.tensor([0, 1.]))\n",
    "J2 = b.grad\n",
    "print(\"J1=\", J1)\n",
    "print(\"J2=\", J2)\n",
    "J = torch.zeros(2, 3)\n",
    "J[0] = J1\n",
    "J[1] = J2\n",
    "print(\"J=\\n\", J)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "注意以上代码中的两个细节：\n",
    "\n",
    "* 第一次调用backward时，使用了retain_graph=True选项，该选项代表在多次传播时，强制保留反向传播中的中间计算结果\n",
    "* 由于每一次传播时grad会累加，为了不让其累加，我们对b.grad进行了清零操作\n",
    "\n",
    "最后，值得注意的是，如果某个Tensor需要求导，而且要被放在GPU上，那么在创建该Tensor时，一定要用“device=0”的方式来创建："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([0.4966, 0.2575, 0.6404], device='cuda:0', requires_grad=True)\n",
      "tensor([0.9932, 0.5151, 1.2808], device='cuda:0')\n"
     ]
    }
   ],
   "source": [
    "b = torch.rand(3, requires_grad=True, device=0)\n",
    "f = torch.sum(b**2)\n",
    "f.backward()\n",
    "print(b)\n",
    "print(b.grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 数据读取\n",
    "\n",
    "在torch.utils.data模块中包含了读取数据的类，比如Dataset、IterableDataset和DataLoader等。其中：\n",
    "\n",
    "* Dataset提供了一个抽象类，用于用户自定义数据集，用户需要重载两个函数完成这个类：\n",
    "    * \\_\\_len\\_\\_()：数据量大小\n",
    "    * \\_\\_getitem\\_\\_()：获得一条数据\n",
    "* IterableDataset同样提供了一个抽象类，与Dataset不同的是该抽象类使用迭代器的方式返回数据，通常用来比较大型的数据或者从数据库、远程服务器中读取的数据等等，用户需要重载一个函数完成这个类：\n",
    "    * \\_\\_iter\\_\\_()：返回一个数据条目（可迭代）\n",
    "* DataLoader在Dataset的基础上定义一个迭代器，实现批量（batch）读取、随机读取等操作。\n",
    "\n",
    "我们首先以一个伪数据看一下Dataset的使用方法："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X=\n",
      " [[-1.04059995  1.3383255  -0.98178686]\n",
      " [ 2.05707228 -1.63339876  1.29662358]\n",
      " [-0.26122713 -0.89392098  0.70135701]\n",
      " [-1.59917975 -1.22977353  0.33054182]\n",
      " [-0.46870777  1.45681876  0.07663929]\n",
      " [ 0.06833739  0.69486777  0.63110193]\n",
      " [ 2.38313998  0.81204174 -0.80433736]\n",
      " [-1.41071764  0.5373097   0.0502901 ]\n",
      " [ 0.98213745 -0.47410963 -0.64930138]\n",
      " [ 0.14045357  1.30505332  0.23967886]] \n",
      "Y=\n",
      " [-1.30930954  2.68014549  0.05500196 -3.06710133  2.67484764  3.35137871\n",
      "  1.59421136 -0.18522796 -1.91398595  3.46959677]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "# 这里假设一个伪数据集，使用NumPy生成\n",
    "X = np.random.normal(0, 1, (10, 3))\n",
    "b = np.array([1, 2, 3.])\n",
    "Y = X @ b.T\n",
    "print(\"X=\\n\", X, \"\\nY=\\n\", Y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以上使用NumPy产生了10个观测，其中有3个特征，以及一个标签（Y），接下来我们定义Dataset："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch.utils.data import Dataset\n",
    "\n",
    "\n",
    "class fake_data(Dataset):\n",
    "\n",
    "    def __len__(self):\n",
    "        return X.shape[0]\n",
    "\n",
    "    def __getitem__(self, i):\n",
    "        x = X[i, :]\n",
    "        y = Y[i]\n",
    "        data = torch.from_numpy(x)\n",
    "        label = torch.tensor(y)\n",
    "        return data, label"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以上我们就定义了一个Dataset，我们可以使用如下方法获得给定下标的数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "共有10个观测\n",
      "第1个观测为：\n",
      " (tensor([-1.0406,  1.3383, -0.9818], dtype=torch.float64), tensor(-1.3093, dtype=torch.float64))\n"
     ]
    }
   ],
   "source": [
    "fd = fake_data()\n",
    "print(\"共有{}个观测\".format(fd.__len__()))\n",
    "print(\"第1个观测为：\\n\", fd[0])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以上的Dataset只提供了一个简单的数据抽取对象，而深度学习所需要的更多的操作可以由DataLoader来完成。\n",
    "\n",
    "为了创建一个DataLoader，需要提供以下信息：\n",
    "* Dataset：像上面定义的Dataset，数据源\n",
    "* shuffle：是否将数据打乱\n",
    "* batch_size: 批量处理每批的大小\n",
    "* sampler/batch_sampler：一个用于将数据打乱的类，可以使用默认\n",
    "* num_workers：载入数据使用的进程数，默认为0，即使用主进程，如果显存足够大，可以设置稍微大一点，这样在跑上一个epoch时下一个epoch的数据已经加载好了\n",
    "* pin_memory：是否将数据保存在CUDA的pinned memory区，从而放入GPU中会快一些\n",
    "* drop_last：是否扔掉最后一个不完整的batch（通常由于数据量/批大小不能整除）\n",
    "\n",
    "比如："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "第0批：\n",
      "tensor([[ 0.1405,  1.3051,  0.2397],\n",
      "        [-1.0406,  1.3383, -0.9818],\n",
      "        [ 2.0571, -1.6334,  1.2966]], dtype=torch.float64)\n",
      "tensor([ 3.4696, -1.3093,  2.6801], dtype=torch.float64)\n",
      "第1批：\n",
      "tensor([[-0.4687,  1.4568,  0.0766],\n",
      "        [ 0.0683,  0.6949,  0.6311],\n",
      "        [ 2.3831,  0.8120, -0.8043]], dtype=torch.float64)\n",
      "tensor([2.6748, 3.3514, 1.5942], dtype=torch.float64)\n",
      "第2批：\n",
      "tensor([[-0.2612, -0.8939,  0.7014],\n",
      "        [ 0.9821, -0.4741, -0.6493],\n",
      "        [-1.4107,  0.5373,  0.0503]], dtype=torch.float64)\n",
      "tensor([ 0.0550, -1.9140, -0.1852], dtype=torch.float64)\n"
     ]
    }
   ],
   "source": [
    "from torch.utils.data import DataLoader\n",
    "\n",
    "fdl = DataLoader(fd, shuffle=True, batch_size=3, drop_last=True)\n",
    "for d, l in enumerate(fdl):\n",
    "    print(\"第{}批：\".format(d))\n",
    "    print(l[0])\n",
    "    print(l[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "如果需要全部返回，设定batch_size为数据量即可："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[-1.4107,  0.5373,  0.0503],\n",
      "        [ 2.3831,  0.8120, -0.8043],\n",
      "        [ 2.0571, -1.6334,  1.2966],\n",
      "        [-1.0406,  1.3383, -0.9818],\n",
      "        [ 0.0683,  0.6949,  0.6311],\n",
      "        [-1.5992, -1.2298,  0.3305],\n",
      "        [ 0.1405,  1.3051,  0.2397],\n",
      "        [ 0.9821, -0.4741, -0.6493],\n",
      "        [-0.4687,  1.4568,  0.0766],\n",
      "        [-0.2612, -0.8939,  0.7014]], dtype=torch.float64)\n",
      "tensor([-0.1852,  1.5942,  2.6801, -1.3093,  3.3514, -3.0671,  3.4696, -1.9140,\n",
      "         2.6748,  0.0550], dtype=torch.float64)\n"
     ]
    }
   ],
   "source": [
    "fdl = DataLoader(fd, shuffle=True, batch_size=fd.__len__(), drop_last=True)\n",
    "for d in fdl:\n",
    "    print(d[0])\n",
    "    print(d[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 应用实例：使用PyTorch计算Logistic回归\n",
    "\n",
    "应用PyTorch可以自动计算导数的特性，我们可以轻松的计算线性回归、Logistic回归等多数简单的统计模型。接下来我们就使用PyTorch计算Logistic回归，并与真实概率进行比较。\n",
    "\n",
    "首先，我们在一个fake数据集上进行计算，并验证。我们使用如下代码产生数据："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "# 设置参数\n",
    "N = 200\n",
    "K = 5\n",
    "# 产生伪数据\n",
    "X = np.random.normal(0, 1, (N, K))\n",
    "beta = np.array([1., 2, -1, -2, 1])\n",
    "Xb = X @ beta.T + 0.5\n",
    "True_Prob = 1.0 / (1 + np.exp(-Xb))\n",
    "Y = (True_Prob >= np.random.random(N)).astype('int32')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下来我们构建Dataset和DataLoader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cuda:0\n"
     ]
    }
   ],
   "source": [
    "import torch\n",
    "from torch.utils.data import Dataset, DataLoader\n",
    "from torch.utils.data import Dataset\n",
    "\n",
    "device = torch.device('cuda:0' if torch.cuda.is_available() else 'cpu')\n",
    "\n",
    "\n",
    "class binary_data(Dataset):\n",
    "\n",
    "    def __len__(self):\n",
    "        return X.shape[0]\n",
    "\n",
    "    def __getitem__(self, i):\n",
    "        x = X[i, :]\n",
    "        y = Y[i]\n",
    "        data = torch.Tensor(x).to(device)\n",
    "        label = torch.tensor(y).to(device)\n",
    "        return data, label\n",
    "\n",
    "\n",
    "fd = binary_data()\n",
    "dl = DataLoader(fd, shuffle=False, batch_size=fd.__len__(), drop_last=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "然而以上代码有一个问题，即每次调用__getitem__都需要将内存中的数据调入显存，而这一过程是比较耗时的。为此，我们可以使用pin_memory选项，将其预先放置在预读区中："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "class binary_data(Dataset):\n",
    "\n",
    "    def __len__(self):\n",
    "        return X.shape[0]\n",
    "\n",
    "    def __getitem__(self, i):\n",
    "        x = X[i, :]\n",
    "        y = Y[i]\n",
    "        data = torch.Tensor(x)\n",
    "        label = torch.tensor(y)\n",
    "        return data, label\n",
    "\n",
    "\n",
    "fd = binary_data()\n",
    "dl = DataLoader(fd,\n",
    "                shuffle=False,\n",
    "                batch_size=fd.__len__(),\n",
    "                drop_last=True,\n",
    "                num_workers=4,\n",
    "                pin_memory=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下来，给定$b,b_0$，我们构造Logistic模型：$$Prob=\\frac{1}{1+e^{-\\left(b_0+x'b\\right)}}$$\n",
    "\n",
    "我们构造如下的计算图：\n",
    "\n",
    "![](pic/compute_graph_Logistic.gv.png \"Logistic计算图\")\n",
    "\n",
    "使用矩阵和向量的乘法，我们可以使用如下图简化：\n",
    "\n",
    "![](pic/compute_graph_Logistic2.gv.png \"Logistic计算图\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([0.5518, 0.3931, 0.5858, 0.6950, 0.9551, 0.6761, 0.9568, 0.6757, 0.8091,\n",
      "        0.8069, 0.6956, 0.2723, 0.2025, 0.0922, 0.5094, 0.8784, 0.6408, 0.3205,\n",
      "        0.5169, 0.7435, 0.6630, 0.3029, 0.9529, 0.3249, 0.2726, 0.2931, 0.7315,\n",
      "        0.8549, 0.6572, 0.7533, 0.8242, 0.6961, 0.2034, 0.2011, 0.7549, 0.5785,\n",
      "        0.4157, 0.5756, 0.6797, 0.9340, 0.3683, 0.7925, 0.2280, 0.6591, 0.4554,\n",
      "        0.1836, 0.5537, 0.3874, 0.8531, 0.7872, 0.1888, 0.9494, 0.4509, 0.0319,\n",
      "        0.7038, 0.8406, 0.3732, 0.6370, 0.8797, 0.2917, 0.6300, 0.1766, 0.7560,\n",
      "        0.1128, 0.2019, 0.2112, 0.0949, 0.1971, 0.8666, 0.1539, 0.4288, 0.7567,\n",
      "        0.2830, 0.5760, 0.2890, 0.4673, 0.7552, 0.3063, 0.7949, 0.9228, 0.3478,\n",
      "        0.6005, 0.3009, 0.0262, 0.4054, 0.4169, 0.6455, 0.4739, 0.6647, 0.7777,\n",
      "        0.4506, 0.5284, 0.1848, 0.9793, 0.7202, 0.0495, 0.2961, 0.0597, 0.6800,\n",
      "        0.2401, 0.7049, 0.3443, 0.3450, 0.7770, 0.5599, 0.5564, 0.8824, 0.1803,\n",
      "        0.4533, 0.3866, 0.8606, 0.5709, 0.4058, 0.8285, 0.4396, 0.2026, 0.6310,\n",
      "        0.8474, 0.9746, 0.6589, 0.8356, 0.8870, 0.1022, 0.3835, 0.3067, 0.2377,\n",
      "        0.6606, 0.0442, 0.5893, 0.3211, 0.3557, 0.7127, 0.7803, 0.3641, 0.4571,\n",
      "        0.8931, 0.1992, 0.3472, 0.6509, 0.9062, 0.7161, 0.3190, 0.6833, 0.4351,\n",
      "        0.3618, 0.1392, 0.3649, 0.6104, 0.2459, 0.7053, 0.7634, 0.4273, 0.8673,\n",
      "        0.7306, 0.1206, 0.5189, 0.7421, 0.3695, 0.7388, 0.5557, 0.8728, 0.5469,\n",
      "        0.7890, 0.3872, 0.4729, 0.8619, 0.6953, 0.1844, 0.6874, 0.0689, 0.7930,\n",
      "        0.8943, 0.2924, 0.6728, 0.8888, 0.5167, 0.7644, 0.8756, 0.3257, 0.9331,\n",
      "        0.8454, 0.2806, 0.5693, 0.8642, 0.5129, 0.4154, 0.6043, 0.8244, 0.9395,\n",
      "        0.6211, 0.2712, 0.1681, 0.2775, 0.3390, 0.5757, 0.9622, 0.4776, 0.8329,\n",
      "        0.1452, 0.1604], device='cuda:0', grad_fn=<SigmoidBackward>)\n"
     ]
    }
   ],
   "source": [
    "k = fd[0][0].numel()\n",
    "b = torch.rand(k, requires_grad=True, device=device)\n",
    "b0 = torch.rand(1, requires_grad=True, device=device)\n",
    "for x, y in dl:\n",
    "    Prob = torch.sigmoid(torch.mv(x.cuda(0), b) + b0)\n",
    "    print(Prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "有了概率预测后，可以计算极大似然函数：$$\\ln{L}=\\frac{1}{N}\\sum_{i=1}^{N}\\left[1\\left\\{y_i=1\\right\\}\\ln{Prob_i}+\\left(1\\left\\{y_i=0\\right\\}\\right)\\ln{\\left(1-Prob_i\\right)}\\right]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor(-1.0069, device='cuda:0', grad_fn=<MeanBackward0>)\n"
     ]
    }
   ],
   "source": [
    "y = y.to(device)\n",
    "LL = torch.mean(y * torch.log(Prob) + (1 - y) * torch.log(1 - Prob))\n",
    "print(LL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可以使用backward()计算b和b0的导数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.0604,  0.0024, -0.1533, -0.4495,  0.0749], device='cuda:0')\n",
      "tensor([0.0132], device='cuda:0')\n"
     ]
    }
   ],
   "source": [
    "LL.backward()\n",
    "print(b.grad)\n",
    "print(b0.grad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "为了使得似然函数能够达到最大值，我们需要引入最优化算法。\n",
    "\n",
    "一般最优化算法都以“最小化”为目标，而极大似然估计要求最大化对数似然函数，为此我们不妨对对数似然函数取相反数，从而把一个求最大化的问题转化为最小化的问题。\n",
    "\n",
    "为了求最小化，我们可以使用梯度下降法进行迭代。对于一个函数$f\\left(x\\right)$，为了求其最小值，我们可以从一个初始值$x^{(0)}$开始，并按照下降最快的方向进行迭代：$$x^{(t+1)}=x^{(t)}-\\eta\\nabla_x f\\left(x^{(t)}\\right)$$其中$\\nabla_x f\\left(x^{(t)}\\right)$为$f\\left(x^{(t)}\\right)$的梯度，而$\\eta$为一个步长（step size），或者在机器学习中，我们称为 **学习率** （**learning rate**）。\n",
    "\n",
    "![](pic/gradient_descent.gif \"动量\")\n",
    "\n",
    "对于以上的问题，我们令$b^{(0)}$为一个初始值（可以使用随机数选取），然后使用：$$b^{(t+1)}=b^{(t)}-\\eta\\nabla_b \\left(-\\ln{L}\\right)$$进行更新迭代，直到导数收敛到0为止。\n",
    "\n",
    "我们可以使用如下代码进行迭代："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([-0.0325, -0.0102,  0.0554,  0.0962, -0.0044,  0.0130], device='cuda:0')\n",
      "tensor([ 0.4059,  0.8298, -0.1768, -0.8985,  0.6773,  0.4781], device='cuda:0',\n",
      "       requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "# 参数\n",
    "# learning rate\n",
    "lr = 0.001\n",
    "# 初始化数据，只有1个batch，即全部数据\n",
    "fd = binary_data()\n",
    "dl = DataLoader(fd,\n",
    "                shuffle=False,\n",
    "                batch_size=fd.__len__(),\n",
    "                drop_last=True,\n",
    "                num_workers=4,\n",
    "                pin_memory=True)\n",
    "k = fd[0][0].numel()\n",
    "# 设置初始值\n",
    "b = torch.rand(k + 1, requires_grad=True, device=device)\n",
    "# 迭代8000次\n",
    "for i in range(8000):\n",
    "    # 计算梯度\n",
    "    for x, y in dl:\n",
    "        x = x.to(device)\n",
    "        y = y.to(device)\n",
    "        Xb = torch.mv(x, b[:-1]) + b[-1]\n",
    "        logeXb = torch.log1p(torch.exp(Xb))\n",
    "        LL = -torch.mean(y * (Xb - logeXb) + (1 - y) * (-logeXb))\n",
    "    LL.backward()\n",
    "    if i == 7999:\n",
    "        print(b.grad)\n",
    "    with torch.no_grad():\n",
    "        b.sub_(lr * b.grad)\n",
    "        # 梯度清零\n",
    "        b.grad.zero_()\n",
    "\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "注意在以上代码中我们使用了with torch.no_grad()作为上下文，该操作可以暂时切断自动求导操做，否则无法对b进行修改。\n",
    "\n",
    "此外，注意我们在计算时并没有使用$$y_i\\ln\\left(\\frac{x_i'\\beta}{1+x_i'\\beta}\\right)+\\left(1-y_i\\right)\\ln\\left(\\frac{1}{1+x_i'\\beta}\\right)$$而是使用：$$y_i\\left[x_i'\\beta-\\ln\\left(1+x_i'\\beta\\right)\\right]+\\left(1-y_i\\right)\\left[-\\ln\\left(1+x_i'\\beta\\right)\\right]$$其中$\\ln\\left(1+x\\right)$可以使用函数torch.log1p(x)来计算。这是由于当Xb非常大时，$\\frac{1}{1+x_i'\\beta}$可能会趋向于$0$，会造成下溢（underflow），计算机内部表示这个数时几乎就是$0$，再取对数就会得到-inf，从而出错。而使用以上的计算方法可以保证计算得到的数字在比较合理的范围内，避免下溢问题。\n",
    "\n",
    "以上结果可以看到梯度都几乎为0。接下来计算概率："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "Prob_pred = torch.sigmoid(torch.mv(x, b[:-1]) + b[-1])\n",
    "Prob_pred_np = Prob_pred.detach().cpu().numpy()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "画图进行比较："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (10.0, 10.0)\n",
    "\n",
    "l=np.linspace(0,1,50)\n",
    "plt.scatter(True_Prob,Prob_pred_np,color='pink') \n",
    "plt.plot(l,l,color='blue') \n",
    "plt.xlabel('True Prob')\n",
    "plt.ylabel(\"Predicted Prob\")\n",
    "plt.title('Predicted Probability v.s. True Probability')\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 随机梯度下降与最优化工具箱\n",
    "\n",
    "## 随机梯度下降\n",
    "\n",
    "以上虽然使用简单的梯度下降方法完成了最优化，然而在处理大型数据时，以上的计算方法需要计算一个很大的矩阵和向量的乘积，在更大的模型中这个运算更加复杂，而且每次迭代都需要计算一次，计算效率比较低。\n",
    "\n",
    "注意到，对于损失函数（目标函数）:$$\\ln{L}=\\frac{1}{N}\\sum_{i=1}^{N}\\left[1\\left\\{y_i=1\\right\\}\\ln{Prob_i}+\\left(1\\left\\{y_i=0\\right\\}\\right)\\ln{\\left(1-Prob_i\\right)}\\right]$$实际上是一个样本平均，根据大数定律应该收敛到其期望。\n",
    "\n",
    "一个很自然的想法是，我们可以不适用全部数据计算期望，而是将所有数据随机分成几个批次（batch），在每个批次（batch）上分别计算目标函数和梯度，并进行迭代即可。这种计算方法由于引入了随机性，因而被成为 **随机梯度下降** （ **stochastic gradient descent, SGD** ）。\n",
    "\n",
    "为了使用随机梯度下降方法，我们可以将$N$个数据分为$M$份，方便期间我们不妨假设每一份数据（批次）的数据量为$n$，那么随机梯度下降即在每个批次上执行：$$b^{(t+1)}=b^{(t)}-\\eta\\nabla_b \\left(-\\ln{L}\\right)^{(m)}$$其中$m=1,2,...,M$。\n",
    "\n",
    "比如，对于以上的Logistic回归，我们可以使用如下代码实现随机梯度下降：\n",
    "\n",
    "首先将Dataset使用DataLoader初始化，令shuffle=True，即打乱顺序（随机化），40个数据为一个batch（共5个batch）："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "fd = binary_data()\n",
    "dl = DataLoader(fd,\n",
    "                shuffle=True,\n",
    "                batch_size=50,\n",
    "                drop_last=False,\n",
    "                num_workers=4,\n",
    "                pin_memory=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "接下来进行迭代："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.8278,  1.1190, -0.6439, -1.8305,  0.9215,  0.5382], device='cuda:0',\n",
      "       requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "# 参数\n",
    "# learning rate\n",
    "lr = 0.001\n",
    "k = fd[0][0].numel()\n",
    "# 设置初始值\n",
    "b = torch.rand(k + 1, requires_grad=True, device=device)\n",
    "# 迭代8000次\n",
    "for i in range(8000):\n",
    "    for x, y in dl:\n",
    "        # 计算梯度\n",
    "        x = x.to(device)\n",
    "        y = y.to(device)\n",
    "        Xb = torch.mv(x, b[:-1]) + b[-1]\n",
    "        logeXb = torch.log1p(torch.exp(Xb))\n",
    "        LL = -torch.mean(y * (Xb - logeXb) + (1 - y) * (-logeXb))\n",
    "        LL.backward()\n",
    "        with torch.no_grad():\n",
    "            b.sub_(lr * b.grad)\n",
    "            # 梯度清零\n",
    "            b.grad.zero_()\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "以上代码与之前的版本相似度很高，然而在这里，我们将每次的迭代嵌入到了每个批次中，从而实现了随机梯度下降。在这里涉及到两个循环：\n",
    "\n",
    "* 外层的循环中我们循环了1000次，每一次都使用了所有数据，我们称为一个epoch\n",
    "* 内层的循环是对batches进行循环，每一次循环使用一个batch，我们称为一个iteration\n",
    "\n",
    "值得注意的是，如果在GPU上进行计算，一般为了保证计算速度，批次的选择一般会设置的使每次迭代尽量使用尽可能度的显存。在这里为了展示起见，虽然数据量很小，我们仍然使用多个批次。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## PyTorch中优化器的使用\n",
    "\n",
    "以上我们根据梯度下降的原理手写了原始的梯度下降方法和随机梯度下降方法。然而两种手写的优化方法使用起来比较繁琐且不够稳健。为了解决这个问题，我们可以使用PyTorch中自带的优化器。\n",
    "\n",
    "在PyTorch中，torch.optim包中提供了最优化所需要的函数。我们可以使用如下代码导入优化器："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.optim as optim"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "比如我们如果需要使用随机梯度下降，可以使用如下代码创建一个随机梯度下降的优化器："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = optim.SGD([b], lr=0.001)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "注意SGD的第一个参数为一个可迭代的参数列表，所以我们将b放在了一个列表里面。lr为学习率。\n",
    "\n",
    "接下来我们可以使用如下代码进行迭代："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 0.8149,  1.0950, -0.6292, -1.7976,  0.9025,  0.5203], device='cuda:0',\n",
      "       requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "k = fd[0][0].numel()\n",
    "\n",
    "# 设置初始值\n",
    "b = torch.rand(k + 1, requires_grad=True, device=device)\n",
    "ll_sgd = []\n",
    "# 初始化\n",
    "dl = DataLoader(fd,\n",
    "                shuffle=True,\n",
    "                batch_size=50,\n",
    "                drop_last=False,\n",
    "                num_workers=0)\n",
    "optimizer = optim.SGD([b], lr=0.001)\n",
    "for i in range(8000):\n",
    "    for x, y in dl:\n",
    "        x = x.to(device)\n",
    "        y = y.to(device)\n",
    "        Xb = torch.mv(x, b[:-1]) + b[-1]\n",
    "        logeXb = torch.log1p(torch.exp(Xb))\n",
    "        LL = -torch.mean(y * (Xb - logeXb) + (1 - y) * (-logeXb))\n",
    "        ll_sgd.append(LL)\n",
    "        # 梯度清零\n",
    "        optimizer.zero_grad()\n",
    "        # 计算梯度\n",
    "        LL.backward()\n",
    "        # 迭代\n",
    "        optimizer.step()\n",
    "print(b)\n",
    "ll_sgd = np.array(ll_sgd)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "随机梯度下降方法虽然解决了大量数据的计算问题，然而也有一些缺点，比如：\n",
    "\n",
    "* 在SGD中，学习率是恒定的，而选择合适的学习率就非常重要了。太小的学习率需要迭代太多次，而太大的学习率会导致结果不稳定甚至不收敛\n",
    "* 在SGD中，所有参数使用同样的学习率，然而每个变量的分布不相同、参数的大小不相同，对于不同参数设定不同的学习率，或者给予不同的更新幅度是必要的\n",
    "* 随机梯度下降仍然不能解决局部最优的问题。此外Dauphin等人(2014)发现在神经网络中，存在大量鞍点（saddle point），是梯度下降面临的主要问题。\n",
    "\n",
    "为此在随机梯度下降的基础上，有很多扩展的方法。我们这里介绍SGD的几种简单扩展和在PyTorch中的实现。\n",
    "\n",
    "### 加入动量\n",
    "\n",
    "**动量** （ **Momentum** ）就像在物理的意义一样，使得参数有保持其运动轨迹的趋势。令 $$v^{(t)}=\\alpha v^{(t-1)}+\\eta\\nabla_b Q\\left(b^{(t)}\\right)$$ 为动量（一个向量），其中 $\\eta$ 为学习率，而 $\\alpha$ 为一个衰减因子（在0到1之间，比如0.9），该因子决定了过去的导数决定现在方向的大小。从这个方程中可以看到，动量不仅仅使用了当前梯度的信息，还综合使用了过去所有期的梯度。接下来，使用： $$b^{(t+1)}=b^{(t)}-v^{(t)}$$ 进行迭代。\n",
    "\n",
    "![](pic/momentum.gif \"动量\")\n",
    "\n",
    "在PyTorch中，可以直接在optim.SGD中加入momentum参数加入动量："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 1.0896,  1.4805, -0.8775, -2.4161,  1.2117,  0.7630], device='cuda:0',\n",
      "       requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "k = fd[0][0].numel()\n",
    "\n",
    "# 设置初始值\n",
    "b = torch.rand(k + 1, requires_grad=True, device=device)\n",
    "\n",
    "# 初始化\n",
    "dl = DataLoader(fd,\n",
    "                shuffle=True,\n",
    "                batch_size=50,\n",
    "                drop_last=False,\n",
    "                num_workers=0)\n",
    "optimizer = optim.SGD([b], lr=0.001, momentum=0.9)\n",
    "ll_momentum = []\n",
    "for i in range(8000):\n",
    "    for x, y in dl:\n",
    "        x = x.to(device)\n",
    "        y = y.to(device)\n",
    "        Xb = torch.mv(x, b[:-1]) + b[-1]\n",
    "        logeXb = torch.log1p(torch.exp(Xb))\n",
    "        LL = -torch.mean(y * (Xb - logeXb) + (1 - y) * (-logeXb))\n",
    "        ll_momentum.append(LL)\n",
    "        # 梯度清零\n",
    "        optimizer.zero_grad()\n",
    "        # 计算梯度\n",
    "        LL.backward()\n",
    "        # 迭代\n",
    "        optimizer.step()\n",
    "print(b)\n",
    "ll_momentum = np.array(ll_momentum)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### AdaGrad\n",
    "\n",
    "为了解决每个参数的学习率都相同的文艺，一个解决方法是使用 **适应性梯度算法** （ **adaptive gradient algorithm** ），即 **AdaGrad** 。这个方法的思路是给那些变化比较小的特征（比如比较稀疏的特征）以更大的学习率，从而加快训练。\n",
    "\n",
    "如果我们记梯度为$g^{(t)}=\\nabla_b Q\\left(b^{(t)}\\right)$，令$$G=\\sum_{t=1}^T g^{(t)}g^{(t)'}$$为梯度的外积之和（每次迭代的和），那么$G$的对角线元素即为：$$G_{ii}=\\sum_{t=1}^T \\left(g_i^{(t)}\\right)^2$$ 接下来在每次更新中，对于第$i$个参数，使用：$$b^{(t+1)}_i=b^{(t)}_i-\\frac{\\eta}{\\sqrt{G_{ii}}}\\nabla_b Q\\left(b^{(t)}\\right)$$进行迭代更新。\n",
    "\n",
    "在AdaGrad中，每个参数的更新过程中，实际的学习率为$\\frac{\\eta}{\\sqrt{G_{ii}}}$，是随着梯度绝对大小的变化而变化的：如果梯度相对较小，会放大学习率；而如果梯度相对较大，会使用较小的学习率。\n",
    "\n",
    "![](pic/adagrad.gif \"AdaGrad\")\n",
    "\n",
    "在PyTorch中，可以使用optim.Adagrad来实现该算法："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([0.7022, 0.3477, 0.5030, 0.1416, 0.2845, 0.2538], device='cuda:0',\n",
      "       requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "k = fd[0][0].numel()\n",
    "# 设置初始值\n",
    "b = torch.rand(k + 1, requires_grad=True, device=0)\n",
    "\n",
    "# 初始化\n",
    "dl = DataLoader(fd,\n",
    "                shuffle=True,\n",
    "                batch_size=50,\n",
    "                drop_last=False,\n",
    "                num_workers=0)\n",
    "optimizer = optim.Adagrad([b], lr=0.001)\n",
    "ll_adagrad = []\n",
    "for i in range(8000):\n",
    "    for x, y in dl:\n",
    "        x = x.to(device)\n",
    "        y = y.to(device)\n",
    "        Xb = torch.mv(x, b[:-1]) + b[-1]\n",
    "        logeXb = torch.log1p(torch.exp(Xb))\n",
    "        LL = -torch.mean(y * (Xb - logeXb) + (1 - y) * (-logeXb))\n",
    "        ll_adagrad.append(LL)\n",
    "        # 梯度清零\n",
    "        optimizer.zero_grad()\n",
    "        # 计算梯度\n",
    "        LL.backward()\n",
    "        # 迭代\n",
    "        optimizer.step()\n",
    "print(b)\n",
    "ll_adagrad = np.array(ll_adagrad)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RMSProp\n",
    "\n",
    "**Root Mean Square Propagation**，简称**RMSProp**，同样也是一个适应性学习率的算法。该算法将AdaGrad中的权重$G_{ii}=\\sum_{t=1}^T \\left(g_i^{(t)}\\right)^2$使用类似于Momentum的方法来进行更新：$$v_i^{(t)}=\\gamma v_i^{(t-1)}+\\left(1-\\gamma\\right)\\left(g_i^{(t)}\\right)^2$$使用：$$b^{(t+1)}_i=b^{(t)}_i-\\frac{\\eta}{\\sqrt{v_i^{(t)}}}\\nabla_b Q\\left(b^{(t)}\\right)$$进行迭代更新。\n",
    "\n",
    "PyTorch中可以使用optim.RMSprop实现："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 1.0908,  1.4817, -0.8785, -2.4176,  1.2125,  0.7636], device='cuda:0',\n",
      "       requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "k = fd[0][0].numel()\n",
    "# 设置初始值\n",
    "b = torch.rand(k + 1, requires_grad=True, device=0)\n",
    "\n",
    "# 初始化\n",
    "dl = DataLoader(fd,\n",
    "                shuffle=True,\n",
    "                batch_size=50,\n",
    "                drop_last=False,\n",
    "                num_workers=0)\n",
    "optimizer = optim.RMSprop([b], lr=0.001)\n",
    "ll_rmsprop = []\n",
    "for i in range(8000):\n",
    "    for x, y in dl:\n",
    "        x = x.to(device)\n",
    "        y = y.to(device)\n",
    "        Xb = torch.mv(x, b[:-1]) + b[-1]\n",
    "        logeXb = torch.log1p(torch.exp(Xb))\n",
    "        LL = -torch.mean(y * (Xb - logeXb) + (1 - y) * (-logeXb))\n",
    "        ll_rmsprop.append(LL)\n",
    "        # 梯度清零\n",
    "        optimizer.zero_grad()\n",
    "        # 计算梯度\n",
    "        LL.backward()\n",
    "        # 迭代\n",
    "        optimizer.step()\n",
    "print(b)\n",
    "ll_rmsprop = np.array(ll_rmsprop)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Adam\n",
    "\n",
    "**Adaptive Moment Estimation**，简称**Adam**，同时结合了RMSProp和Momentum，分别使用两个学习率对动量和权重进行更新：$$m_i^{(t)}=\\gamma_1 v_i^{(m-1)}+\\left(1-\\gamma_1\\right)g_i^{(t)} \\\\ v_i^{(t)}=\\gamma_2 v_i^{(t-1)}+\\left(1-\\gamma_2\\right)\\left(g_i^{(t)}\\right)^2$$然后计算：$$\\hat{m_i}=\\frac{m_i^{(t)}}{1-\\gamma_1^t} \\\\ \\hat{v_i}=\\frac{v_i^{(t)}}{1-\\gamma_2^t}$$最后进行迭代更新：$$b^{(t+1)}_i=b^{(t)}_i-\\eta\\frac{\\hat{m_i}}{\\sqrt{\\hat{v_i}}}$$\n",
    "\n",
    "PyTorch中可以使用optim.Adam来完成："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 1.0908,  1.4812, -0.8783, -2.4178,  1.2122,  0.7637], device='cuda:0',\n",
      "       requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "k = fd[0][0].numel()\n",
    "# 设置初始值\n",
    "b = torch.rand(k + 1, requires_grad=True, device=device)\n",
    "\n",
    "# 初始化\n",
    "dl = DataLoader(fd,\n",
    "                shuffle=True,\n",
    "                batch_size=50,\n",
    "                drop_last=False,\n",
    "                num_workers=0)\n",
    "optimizer = optim.Adam([b], lr=0.001)\n",
    "ll_adam = []\n",
    "for i in range(8000):\n",
    "    for x, y in dl:\n",
    "        x = x.to(device)\n",
    "        y = y.to(device)\n",
    "        Xb = torch.mv(x, b[:-1]) + b[-1]\n",
    "        logeXb = torch.log1p(torch.exp(Xb))\n",
    "        LL = -torch.mean(y * (Xb - logeXb) + (1 - y) * (-logeXb))\n",
    "        ll_adam.append(LL)\n",
    "        # 梯度清零\n",
    "        optimizer.zero_grad()\n",
    "        # 计算梯度\n",
    "        LL.backward()\n",
    "        # 迭代\n",
    "        optimizer.step()\n",
    "print(b)\n",
    "ll_adam = np.array(ll_adam)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "除此之外还有AdaDelta、AdaMax、Nadam、AMSGrad等一系列算法，再次不再赘述。\n",
    "\n",
    "我们可以对比以上这些算法的迭代效果："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['figure.figsize'] = (15.0, 10.0)\n",
    "\n",
    "l = np.linspace(0, 1000, 1000)\n",
    "plt.plot(l, ll_sgd[0:4000:4], label='SGD')\n",
    "plt.plot(l, ll_momentum[0:4000:4], label='Momentum')\n",
    "plt.plot(l, ll_adagrad[0:4000:4], label='AdaGrad')\n",
    "plt.plot(l, ll_rmsprop[0:4000:4], label='RMSProp')\n",
    "plt.plot(l, ll_adam[0:4000:4], label='Adam')\n",
    "plt.xlabel('Iterations')\n",
    "plt.ylabel(\"Loss\")\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "值得注意的是，虽然适应性学习率可以自动调整学习率，对于鞍点问题等情况有较好的表现，并且相较于SGD和带Momentum的SGD有更快的速度，但是最终收敛结果可能没有使用优良参数的简单SGD好，所以不同模型究竟使用何种优化算法并不是一成不变的。一般而言，对于稀疏、高维的数据可以使用Adam等进行尝试，而简单模型SGD就可以达到足够好的效果。一个比较简单的方法是先使用Adam等方法迭代，经过一定时间迭代后再使用SGD。\n",
    "\n",
    "下图比较了不同方法对于局部最优的性能：\n",
    "\n",
    "![](pic/sgd_local_minimum.gif \"局部最优\")\n",
    "\n",
    "而下图则比较了不同方法逃离鞍点的性能：\n",
    "\n",
    "![](pic/sgd_saddle_point.gif \"局部最优\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 动态调整学习率\n",
    "\n",
    "无论是简单的SGD还是Adam，一个常见的做法是使用动态的学习率$\\eta$。比如，一个一般的做法是在迭代的初期使用较高的学习率，而后期则使用较低的学习率。在PyTorch中，可以使用optim.lr_scheduler根据epoch迭代的次数对学习率进行更新。\n",
    "\n",
    "一个比较一般化的调整方法是optim.lr_scheduler.LambdaLR，该方法需要提供：\n",
    "* optimizer：需要调整学习率的优化器\n",
    "* lr_lambda：一个根据epoch迭代次数计算出学习率的函数\n",
    "\n",
    "不过PyTorch本身集成了很多调整学习率的方案，比如：\n",
    "* StepLR: optim.lr_scheduler.StepLR(optimizer, step_size, gamma=0.1)：使用一个阶梯函数，step_size代表两次调整学习率之间epoch迭代次数，而gamma为每次更新学习率时，都将学习率乘以gamma，从而gamma越大衰减越慢\n",
    "* ExponentialLR：optim.lr_scheduler.ExponentialLR(optimizer, gamma)：每个epoch都将学习率乘以gamma\n",
    "* CosineAnnealingLR：optim.lr_scheduler.CosineAnnealingLR(optimizer, T_max, eta_min=0)：余弦退火算法，T_max为周期\n",
    "\n",
    "除此之外还有很多方案，https://pytorch.org/docs/stable/optim.html 中提供了方案列表。\n",
    "\n",
    "为了使用lr_scheduler，我们首先要进行初始化："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "optimizer = optim.SGD([b], lr=0.01, momentum=0.9)\n",
    "lr_scheduler = torch.optim.lr_scheduler.ExponentialLR(optimizer, gamma=0.999)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "然后在迭代时，每个epoch内进行一次step()即可："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([ 1.0905,  1.4814, -0.8781, -2.4175,  1.2123,  0.7637], device='cuda:0',\n",
      "       requires_grad=True)\n"
     ]
    }
   ],
   "source": [
    "LR = []\n",
    "for i in range(5000):\n",
    "    for x, y in dl:\n",
    "        x = x.to(device)\n",
    "        y = y.to(device)\n",
    "        Xb = torch.mv(x, b[:-1]) + b[-1]\n",
    "        logeXb = torch.log1p(torch.exp(Xb))\n",
    "        LL = -torch.mean(y * (Xb - logeXb) + (1 - y) * (-logeXb))\n",
    "        # 梯度清零\n",
    "        optimizer.zero_grad()\n",
    "        # 计算梯度\n",
    "        LL.backward()\n",
    "        # 迭代\n",
    "        optimizer.step()\n",
    "    lr_scheduler.step()\n",
    "    LR.append(lr_scheduler.get_last_lr())\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "注意我们更新学习率时是针对每一个epoch进行一次更新，而非每次迭代都更新。\n",
    "\n",
    "我们可以查看学习率的更新情况："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams['figure.figsize'] = (15.0, 10.0)\n",
    "\n",
    "l = np.linspace(0, len(LR), len(LR))\n",
    "plt.plot(l, np.array(LR), label='Learning Rate')\n",
    "plt.xlabel('Epoch')\n",
    "plt.ylabel(\"Learning Rate\")\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以发现按照这个计划，迭代结束时学习率几乎收敛到0。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 图片参考：\n",
    "    * https://towardsdatascience.com/a-visual-explanation-of-gradient-descent-methods-momentum-adagrad-rmsprop-adam-f898b102325c "
   ]
  }
 ],
 "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": "3.11.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}