tesk3 线性回归和softmax.ipynb

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    "#线性回归\n",
    "\n",
    "首先，假设自变量x和因变量y之间的关系是线性的， 即可以表示为中元素的加权和，这里通常允许包含观测值的一些噪声； 其次，我们假设任何噪声都比较正常，如噪声遵循正态分布\n",
    "\n",
    "其训练过程就是梯度下降，通过计算loss，也就是预测值与真实值之间的差距调整，权重w的大小，在多次训练后拉小预测值与真实值的差距"
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    "%matplotlib inline\n",
    "import math\n",
    "import time\n",
    "import numpy as np\n",
    "import torch\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "4feba7e7",
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   "source": [
    "n = 10000\n",
    "a = torch.ones([n])\n",
    "b = torch.ones([n])"
   ]
  },
  {
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   "execution_count": 79,
   "id": "ccc75dca",
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   "source": [
    "class Timer:  #@save\n",
    "    \"\"\"记录多次运行时间\"\"\"\n",
    "    def __init__(self):\n",
    "        self.times = []\n",
    "        self.start()\n",
    "\n",
    "    def start(self):\n",
    "        \"\"\"启动计时器\"\"\"\n",
    "        self.tik = time.time()\n",
    "\n",
    "    def stop(self):\n",
    "        \"\"\"停止计时器并将时间记录在列表中\"\"\"\n",
    "        self.times.append(time.time() - self.tik)\n",
    "        return self.times[-1]\n",
    "\n",
    "    def avg(self):\n",
    "        \"\"\"返回平均时间\"\"\"\n",
    "        return sum(self.times) / len(self.times)\n",
    "\n",
    "    def sum(self):\n",
    "        \"\"\"返回时间总和\"\"\"\n",
    "        return sum(self.times)\n",
    "\n",
    "    def cumsum(self):\n",
    "        \"\"\"返回累计时间\"\"\"\n",
    "        return np.array(self.times).cumsum().tolist()"
   ]
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  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "5298b142",
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   "source": [
    "def normal(x, mu, sigma):\n",
    "    p = 1 / math.sqrt(2 * math.pi * sigma**2)\n",
    "    return p * np.exp(-0.5 / sigma**2 * (x - mu)**2)"
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    "正态分布 \n",
    "有两个变量 一个是 mu 另一个是 sigma，\n",
    "mu是平均数代表 样本的母体平均 例如 mu=0 就是指这个样本的均值为0\n",
    "sigma 指 变异数（var）从图中简单来说就是sigma越大 分布越扁平\n",
    "表现在样本中就是 数据分散的程度"
   ]
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     "metadata": {},
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    }
   ],
   "source": [
    "# 再次使用numpy进行可视化\n",
    "x = np.arange(-7, 7, 0.01)\n",
    "\n",
    "# 均值和标准差对\n",
    "params = [(0, 1), (0, 2), (3, 1)]\n",
    "d2l.plot(x, [normal(x, mu, sigma) for mu, sigma in params], xlabel='x',\n",
    "         ylabel='p(x)', figsize=(4.5, 2.5),\n",
    "         legend=[f'mean {mu}, std {sigma}' for mu, sigma in params])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7d5771e8",
   "metadata": {},
   "source": [
    "正太分布和均方损失的关系\n",
    "\n",
    "\n",
    "误差项服从正态分布；\n",
    "误差项之间相互独立；\n",
    "误差项均值为0；\n",
    "误差项的方差为常数\n",
    "\n",
    "Reference\n",
    "\n",
    "https://zhuanlan.zhihu.com/p/450279508"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d9339557",
   "metadata": {},
   "source": [
    "线性回归的从零开始实现\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "d51dc694",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import random\n",
    "import torch\n",
    "import math\n",
    "from d2l import torch as d2l"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c891f4f1",
   "metadata": {},
   "source": [
    "生成数据 w 为 [2,-3.4] b 为 [4.2] 在其中混入 normal分布的噪声（增加训练难度，现实中也没有规整的数据都含有噪声）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "b8b6878b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def synthetic_data(w, b, num_examples):  #@save\n",
    "    \"\"\"生成y=Xw+b+噪声\"\"\"\n",
    "    X = torch.normal(0, 1, (num_examples, len(w)))\n",
    "    y = torch.matmul(X, w) + b\n",
    "    y += torch.normal(0, 0.01, y.shape)\n",
    "    return X, y.reshape((-1, 1))\n",
    "\n",
    "true_w = torch.tensor([2, -3.4])\n",
    "true_b = 4.2\n",
    "features, labels = synthetic_data(true_w, true_b, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "6c60094b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "features: tensor([0.1617, 0.7707]) \n",
      "label: tensor([1.9095])\n"
     ]
    }
   ],
   "source": [
    "print('features:', features[0],'\\nlabel:', labels[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "d985b782",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([1000, 2])\n",
      "torch.Size([1000, 1])\n"
     ]
    }
   ],
   "source": [
    "print(features.shape)\n",
    "print(labels.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b58456b",
   "metadata": {},
   "source": [
    "目标是将大批的数据以小批次的方式随机抽取\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "f5522b4e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def data_iter(batch_size, features, labels):\n",
    "    num_examples = len(features)\n",
    "    indices = list(range(num_examples))\n",
    "    # 这些样本是随机读取的，没有特定的顺序\n",
    "    random.shuffle(indices)\n",
    "    for i in range(0, num_examples, batch_size):\n",
    "    #一个小问题 这里的range在num_example 不被batch_size整除时会取不全\n",
    "        batch_indices = torch.tensor(\n",
    "            indices[i: min(i + batch_size, num_examples)])\n",
    "        yield features[batch_indices], labels[batch_indices]\n",
    "        # yield产生的值不会被内存占用 ，可以想成用一次 扔一次"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "f5a9ac55",
   "metadata": {},
   "outputs": [],
   "source": [
    "def data_iter(batch_size, features, labels):\n",
    "    num_examples = len(features)\n",
    "    indices = list(range(num_examples))\n",
    "    \n",
    "    random.shuffle(indices)\n",
    "    for i in range(math.ceil(num_examples/batch_size)):\n",
    "    # 一般改成ceil 向上取整 能解决这个问题\n",
    "        batch_indices = torch.tensor(\n",
    "            indices[i*batch_size : min(i*batch_size + batch_size, num_examples)])\n",
    "        yield features[batch_indices], labels[batch_indices]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "9dbc2fd2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([[ 0.7472,  0.4861],\n",
      "        [-0.1258, -0.3344],\n",
      "        [ 0.9924,  2.2822],\n",
      "        [ 1.2700, -1.2308],\n",
      "        [ 0.5503, -0.0372],\n",
      "        [ 0.0602,  2.5784],\n",
      "        [ 0.9472, -0.7022],\n",
      "        [-0.4092, -0.5871],\n",
      "        [ 0.5288, -0.7221],\n",
      "        [ 0.6072,  0.3052],\n",
      "        [-0.6505,  2.0106],\n",
      "        [-0.0896,  1.6997],\n",
      "        [-0.2057,  0.6627],\n",
      "        [-0.7126, -0.9078],\n",
      "        [ 1.0067,  1.3837]]) \n",
      " tensor([[ 4.0438],\n",
      "        [ 5.1041],\n",
      "        [-1.5825],\n",
      "        [10.9234],\n",
      "        [ 5.4356],\n",
      "        [-4.4389],\n",
      "        [ 8.4903],\n",
      "        [ 5.3755],\n",
      "        [ 7.7212],\n",
      "        [ 4.3752],\n",
      "        [-3.9428],\n",
      "        [-1.7458],\n",
      "        [ 1.5419],\n",
      "        [ 5.8750],\n",
      "        [ 1.5048]])\n"
     ]
    }
   ],
   "source": [
    "batch_size = 15\n",
    "\n",
    "for X, y in data_iter(batch_size, features, labels):\n",
    "    print(X, '\\n', y)\n",
    "    break\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "e8c65e60",
   "metadata": {},
   "outputs": [],
   "source": [
    "# initial\n",
    "w = torch.normal(0, 0.01, size=(2,1), requires_grad=True)\n",
    "b = torch.zeros(1, requires_grad=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "9e732f24",
   "metadata": {},
   "outputs": [],
   "source": [
    "def linreg(X, w, b):  #@save\n",
    "    \"\"\"线性回归模型\"\"\"\n",
    "    return torch.matmul(X, w) + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "e5d4b89f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def squared_loss(y_hat, y):  #@save\n",
    "    \"\"\"均方损失\"\"\"\n",
    "    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0e6df7d8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "a44d9aef",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sgd(params, lr, batch_size):  #@save\n",
    "    \"\"\"小批量随机梯度下降\"\"\"\n",
    "    with torch.no_grad():\n",
    "        for param in params:\n",
    "            param -= lr * param.grad / batch_size \n",
    "            param.grad.zero_()#将 grad清除 不然多次计算 grad会累加"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "054001fe",
   "metadata": {},
   "source": [
    "我看到好像有朋友对 这部分没有return数值 有疑问，params是输入进来的值，这个for 就是为了修改 params 内部的数值，省略了一个单独计算 update 的函数，就不用return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "0b198928",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss 0.317321\n",
      "epoch 2, loss 0.006428\n",
      "epoch 3, loss 0.000182\n"
     ]
    }
   ],
   "source": [
    "lr = 0.03\n",
    "num_epochs = 3\n",
    "net = linreg\n",
    "loss = squared_loss\n",
    "\n",
    "for epoch in range(num_epochs):\n",
    "    for X, y in data_iter(batch_size, features, labels):\n",
    "        l = loss(net(X, w, b), y)  # X和y的小批量损失\n",
    "        # 因为l形状是(batch_size,1)，而不是一个标量。l中的所有元素被加到一起，\n",
    "        # 并以此计算关于[w,b]的梯度\n",
    "        l.sum().backward()\n",
    "        sgd([w, b], lr, batch_size)  # 使用参数的梯度更新参数\n",
    "    with torch.no_grad():\n",
    "        train_l = loss(net(features, w, b), labels)\n",
    "        print(f'epoch {epoch + 1}, loss {float(train_l.mean()):f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a0b37e23",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "cf0d2046",
   "metadata": {},
   "source": [
    "线性回归的简洁实现"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec88ffc5",
   "metadata": {},
   "source": [
    "和上面的操作是一样的，换成了pytorch内建语法"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "5304b2ad",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import torch\n",
    "from torch.utils import data\n",
    "from d2l import torch as d2l\n",
    "\n",
    "true_w = torch.tensor([2, -3.4])\n",
    "true_b = 4.2\n",
    "features, labels = d2l.synthetic_data(true_w, true_b, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "72855ed7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_array(data_arrays, batch_size, is_train=True):  #@save\n",
    "    \"\"\"构造一个PyTorch数据迭代器\"\"\"\n",
    "    dataset = data.TensorDataset(*data_arrays)#这个星号没看懂\n",
    "    return data.DataLoader(dataset, batch_size, shuffle=is_train)\n",
    "\n",
    "batch_size = 10\n",
    "data_iter = load_array((features, labels), batch_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "f32d0ee0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[tensor([[ 1.0149e+00,  3.1135e-01],\n",
       "         [ 1.0245e+00, -2.0513e-01],\n",
       "         [ 8.7568e-01,  3.7828e-01],\n",
       "         [-1.6846e+00, -2.5682e+00],\n",
       "         [-9.5389e-01, -1.7107e+00],\n",
       "         [-8.4295e-01, -1.3658e+00],\n",
       "         [ 2.3155e-01,  9.1670e-01],\n",
       "         [-2.4342e-01,  1.9945e+00],\n",
       "         [ 1.0417e-01, -1.2864e-03],\n",
       "         [-7.5100e-01,  1.1887e+00]]),\n",
       " tensor([[ 5.1804],\n",
       "         [ 6.9357],\n",
       "         [ 4.6810],\n",
       "         [ 9.5703],\n",
       "         [ 8.0967],\n",
       "         [ 7.1574],\n",
       "         [ 1.5375],\n",
       "         [-3.0778],\n",
       "         [ 4.4127],\n",
       "         [-1.3419]])]"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next(iter(data_iter))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "e709b8bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[tensor([[ 0.4506,  0.8625],\n",
       "         [ 0.2434,  0.0932],\n",
       "         [ 0.2698,  0.3096],\n",
       "         [-1.7149,  1.7543],\n",
       "         [-0.7350, -1.7231],\n",
       "         [-0.5838,  0.2832],\n",
       "         [-0.4024,  0.3614],\n",
       "         [ 1.3470, -0.5828],\n",
       "         [ 2.2468, -0.9336],\n",
       "         [ 0.8501, -1.3048]]),\n",
       " tensor([[ 2.1539],\n",
       "         [ 4.3646],\n",
       "         [ 3.6812],\n",
       "         [-5.2036],\n",
       "         [ 8.5873],\n",
       "         [ 2.0636],\n",
       "         [ 2.1621],\n",
       "         [ 8.8809],\n",
       "         [11.8769],\n",
       "         [10.3312]])]"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "next(iter(data_iter))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14cee002",
   "metadata": {},
   "source": [
    "sequential的用处就是 将一串神经网络垒起来 不用手动的填入x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "1f91f86a",
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch import nn\n",
    "\n",
    "net = nn.Sequential(nn.Linear(2, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "8a0f9cd5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.])"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "net[0].weight.data.normal_(0, 0.01)\n",
    "net[0].bias.data.fill_(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09cb6336",
   "metadata": {},
   "source": [
    "重新初始化参数 \n",
    "现在我们能直接访问参数以设定它们的初始值。 我们通过net[0]选择网络中的第一个图层， 然后使用weight.data和bias.data方法访问参数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "7c0e3fa9",
   "metadata": {},
   "outputs": [],
   "source": [
    "loss = nn.MSELoss()\n",
    "trainer = torch.optim.SGD(net.parameters(), lr=0.03)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "7d14d508",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "epoch 1, loss 0.000169\n",
      "epoch 2, loss 0.000097\n",
      "epoch 3, loss 0.000097\n"
     ]
    }
   ],
   "source": [
    "num_epochs = 3\n",
    "for epoch in range(num_epochs):\n",
    "    for X, y in data_iter:\n",
    "        l = loss(net(X) ,y)\n",
    "        trainer.zero_grad()\n",
    "        l.backward()\n",
    "        trainer.step()\n",
    "    l = loss(net(features), labels)\n",
    "    print(f'epoch {epoch + 1}, loss {l:f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "a470c408",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w的估计误差： tensor([-0.0002, -0.0013])\n",
      "b的估计误差： tensor([-0.0006])\n"
     ]
    }
   ],
   "source": [
    "w = net[0].weight.data\n",
    "print('w的估计误差：', true_w - w.reshape(true_w.shape))\n",
    "b = net[0].bias.data\n",
    "print('b的估计误差：', true_b - b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20376887",
   "metadata": {},
   "source": [
    "softmax回归\n",
    "\n",
    "softmax的值域处于0~1之间 是为了将输出值以几率的形式输出，输出都是非负的且总和为1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cf764d82",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "fb7b98bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import torch\n",
    "import torchvision\n",
    "from torch.utils import data\n",
    "from torchvision import transforms\n",
    "from d2l import torch as d2l\n",
    "\n",
    "d2l.use_svg_display()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "f593cf43",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 通过ToTensor实例将图像数据从PIL类型变换成32位浮点数格式，\n",
    "# 并除以255使得所有像素的数值均在0～1之间\n",
    "trans = transforms.ToTensor()\n",
    "mnist_train = torchvision.datasets.FashionMNIST(\n",
    "    root=\"../data\", train=True, transform=trans, download=True)\n",
    "mnist_test = torchvision.datasets.FashionMNIST(\n",
    "    root=\"../data\", train=False, transform=trans, download=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "b0f7ffff",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_fashion_mnist_labels(labels):  #@save\n",
    "    \"\"\"返回Fashion-MNIST数据集的文本标签\"\"\"\n",
    "    text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',\n",
    "                   'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']\n",
    "    return [text_labels[int(i)] for i in labels]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "aa0a70f8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def show_images(imgs, num_rows, num_cols, titles=None, scale=1.5):  #@save\n",
    "    \"\"\"绘制图像列表\"\"\"\n",
    "    figsize = (num_cols * scale, num_rows * scale)\n",
    "    _, axes = d2l.plt.subplots(num_rows, num_cols, figsize=figsize)\n",
    "    axes = axes.flatten()\n",
    "    for i, (ax, img) in enumerate(zip(axes, imgs)):\n",
    "        if torch.is_tensor(img):\n",
    "            # 图片张量\n",
    "            ax.imshow(img.numpy())\n",
    "        else:\n",
    "            # PIL图片\n",
    "            ax.imshow(img)\n",
    "        ax.axes.get_xaxis().set_visible(False)\n",
    "        ax.axes.get_yaxis().set_visible(False)\n",
    "        if titles:\n",
    "            ax.set_title(titles[i])\n",
    "    return axes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "8eb929b2",
   "metadata": {},
   "outputs": [
    {
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       "   <cc:Work>\n",
       "    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\n",
       "    <dc:date>2023-03-23T22:48:44.213973</dc:date>\n",
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      ],
      "text/plain": [
       "<Figure size 1350x300 with 18 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = next(iter(data.DataLoader(mnist_train, batch_size=18)))\n",
    "show_images(X.reshape(18, 28, 28), 2, 9, titles=get_fashion_mnist_labels(y));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c424820c",
   "metadata": {},
   "source": [
    "对于batchsize的大小 建议是越大越好，前提是你的电脑得受的住，越小的话 效率会越低，\n",
    "如果到1 那应该和 for 差不多吧"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "5f28afa3",
   "metadata": {},
   "outputs": [],
   "source": [
    "batch_size = 256\n",
    "\n",
    "def get_dataloader_workers():  #@save\n",
    "    \"\"\"使用4个进程来读取数据\"\"\"\n",
    "    return 4\n",
    "\n",
    "train_iter = data.DataLoader(mnist_train, batch_size, shuffle=True,\n",
    "                             num_workers=get_dataloader_workers())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3c8cf711",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "4c69ad87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'2.24 sec'"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "timer = d2l.Timer()\n",
    "for X, y in train_iter:\n",
    "    continue\n",
    "#     break\n",
    "f'{timer.stop():.2f} sec'# 在pytorch版本低的情況下 多线程大于0有可能报错"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "8fb12593",
   "metadata": {},
   "outputs": [],
   "source": [
    "def load_data_fashion_mnist(batch_size, resize=None):  #@save\n",
    "    \"\"\"下载Fashion-MNIST数据集，然后将其加载到内存中\"\"\"\n",
    "    trans = [transforms.ToTensor()]\n",
    "    if resize:\n",
    "        trans.insert(0, transforms.Resize(resize))\n",
    "    trans = transforms.Compose(trans)\n",
    "    mnist_train = torchvision.datasets.FashionMNIST(\n",
    "        root=\"../data\", train=True, transform=trans, download=True)\n",
    "    mnist_test = torchvision.datasets.FashionMNIST(\n",
    "        root=\"../data\", train=False, transform=trans, download=True)\n",
    "    return (data.DataLoader(mnist_train, batch_size, shuffle=True,\n",
    "                            num_workers=get_dataloader_workers()),\n",
    "            data.DataLoader(mnist_test, batch_size, shuffle=False,\n",
    "                            num_workers=get_dataloader_workers()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "8d3b0b85",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([32, 1, 64, 64]) torch.float32 torch.Size([32]) torch.int64\n"
     ]
    }
   ],
   "source": [
    "train_iter, test_iter = load_data_fashion_mnist(32, resize=64)\n",
    "for X, y in train_iter:\n",
    "    print(X.shape, X.dtype, y.shape, y.dtype)\n",
    "    break"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d59fdb0",
   "metadata": {},
   "source": [
    "softmax回归的从零开始实现"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "10aaad08",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "from IPython import display\n",
    "from d2l import torch as d2l\n",
    "\n",
    "batch_size = 256\n",
    "train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "d3fceba5",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_inputs = 784\n",
    "num_outputs = 10\n",
    "\n",
    "W = torch.normal(0, 0.01, size=(num_inputs, num_outputs), requires_grad=True)\n",
    "b = torch.zeros(num_outputs, requires_grad=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "b5e33320",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[5., 7., 9.]]),\n",
       " tensor([[ 6.],\n",
       "         [15.]]))"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = torch.tensor([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])\n",
    "X.sum(0, keepdim=True), X.sum(1, keepdim=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "92e9b588",
   "metadata": {},
   "outputs": [],
   "source": [
    "def softmax(X):\n",
    "    X_exp = torch.exp(X)\n",
    "    partition = X_exp.sum(1, keepdim=True)\n",
    "    return X_exp / partition  # 这里应用了广播机制"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "698b22b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(tensor([[0.3685, 0.4588, 0.0492, 0.0537, 0.0697],\n",
       "         [0.1199, 0.1731, 0.2419, 0.0310, 0.4340]]),\n",
       " tensor([1., 1.]))"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = torch.normal(0, 1, (2, 5))\n",
    "X_prob = softmax(X)\n",
    "X_prob, X_prob.sum(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "013f3480",
   "metadata": {},
   "outputs": [],
   "source": [
    "def net(X):\n",
    "    return softmax(torch.matmul(X.reshape((-1, W.shape[0])), W) + b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "673362c8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([0.1000, 0.5000])"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = torch.tensor([0, 2])\n",
    "y_hat = torch.tensor([[0.1, 0.3, 0.6], [0.3, 0.2, 0.5]])\n",
    "y_hat[[0, 1], y]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "92b7c5db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([2.3026, 0.6931])"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def cross_entropy(y_hat, y):\n",
    "    return - torch.log(y_hat[range(len(y_hat)), y])\n",
    "\n",
    "cross_entropy(y_hat, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "167dcbee",
   "metadata": {},
   "outputs": [],
   "source": [
    "def accuracy(y_hat, y):  #@save\n",
    "    \"\"\"计算预测正确的数量\"\"\"\n",
    "    if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:\n",
    "        y_hat = y_hat.argmax(axis=1)\n",
    "    cmp = y_hat.type(y.dtype) == y\n",
    "    return float(cmp.type(y.dtype).sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "38219288",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy(y_hat, y) / len(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "222e8c51",
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaluate_accuracy(net, data_iter):  #@save\n",
    "    \"\"\"计算在指定数据集上模型的精度\"\"\"\n",
    "    if isinstance(net, torch.nn.Module):\n",
    "        net.eval()  # 将模型设置为评估模式\n",
    "    metric = Accumulator(2)  # 正确预测数、预测总数\n",
    "    with torch.no_grad():\n",
    "        for X, y in data_iter:\n",
    "            metric.add(accuracy(net(X), y), y.numel())\n",
    "    return metric[0] / metric[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "ac7995fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Accumulator:  #@save\n",
    "    \"\"\"在n个变量上累加\"\"\"\n",
    "    def __init__(self, n):\n",
    "        self.data = [0.0] * n\n",
    "\n",
    "    def add(self, *args):\n",
    "        self.data = [a + float(b) for a, b in zip(self.data, args)]\n",
    "\n",
    "    def reset(self):\n",
    "        self.data = [0.0] * len(self.data)\n",
    "\n",
    "    def __getitem__(self, idx):\n",
    "        return self.data[idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "e61ade69",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1359"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evaluate_accuracy(net, test_iter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "834e4972",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_epoch_ch3(net, train_iter, loss, updater):  #@save\n",
    "    \"\"\"训练模型一个迭代周期（定义见第3章）\"\"\"\n",
    "    # 将模型设置为训练模式\n",
    "    if isinstance(net, torch.nn.Module):\n",
    "        net.train()\n",
    "    # 训练损失总和、训练准确度总和、样本数\n",
    "    metric = Accumulator(3)\n",
    "    for X, y in train_iter:\n",
    "        # 计算梯度并更新参数\n",
    "        y_hat = net(X)\n",
    "        l = loss(y_hat, y)\n",
    "        if isinstance(updater, torch.optim.Optimizer):\n",
    "            # 使用PyTorch内置的优化器和损失函数\n",
    "            updater.zero_grad()\n",
    "            l.mean().backward()\n",
    "            updater.step()\n",
    "        else:\n",
    "            # 使用定制的优化器和损失函数\n",
    "            l.sum().backward()\n",
    "            updater(X.shape[0])\n",
    "        metric.add(float(l.sum()), accuracy(y_hat, y), y.numel())\n",
    "    # 返回训练损失和训练精度\n",
    "    return metric[0] / metric[2], metric[1] / metric[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "d31c0b2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Animator:  #@save\n",
    "    \"\"\"在动画中绘制数据\"\"\"\n",
    "    def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None,\n",
    "                 ylim=None, xscale='linear', yscale='linear',\n",
    "                 fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1,\n",
    "                 figsize=(3.5, 2.5)):\n",
    "        # 增量地绘制多条线\n",
    "        if legend is None:\n",
    "            legend = []\n",
    "        d2l.use_svg_display()\n",
    "        self.fig, self.axes = d2l.plt.subplots(nrows, ncols, figsize=figsize)\n",
    "        if nrows * ncols == 1:\n",
    "            self.axes = [self.axes, ]\n",
    "        # 使用lambda函数捕获参数\n",
    "        self.config_axes = lambda: d2l.set_axes(\n",
    "            self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)\n",
    "        self.X, self.Y, self.fmts = None, None, fmts\n",
    "\n",
    "    def add(self, x, y):\n",
    "        # 向图表中添加多个数据点\n",
    "        if not hasattr(y, \"__len__\"):\n",
    "            y = [y]\n",
    "        n = len(y)\n",
    "        if not hasattr(x, \"__len__\"):\n",
    "            x = [x] * n\n",
    "        if not self.X:\n",
    "            self.X = [[] for _ in range(n)]\n",
    "        if not self.Y:\n",
    "            self.Y = [[] for _ in range(n)]\n",
    "        for i, (a, b) in enumerate(zip(x, y)):\n",
    "            if a is not None and b is not None:\n",
    "                self.X[i].append(a)\n",
    "                self.Y[i].append(b)\n",
    "        self.axes[0].cla()\n",
    "        for x, y, fmt in zip(self.X, self.Y, self.fmts):\n",
    "            self.axes[0].plot(x, y, fmt)\n",
    "        self.config_axes()\n",
    "        display.display(self.fig)\n",
    "        display.clear_output(wait=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "4aaab3fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "def train_ch3(net, train_iter, test_iter, loss, num_epochs, updater):  #@save\n",
    "    \"\"\"训练模型（定义见第3章）\"\"\"\n",
    "    animator = Animator(xlabel='epoch', xlim=[1, num_epochs], ylim=[0.3, 0.9],\n",
    "                        legend=['train loss', 'train acc', 'test acc'])\n",
    "    for epoch in range(num_epochs):\n",
    "        train_metrics = train_epoch_ch3(net, train_iter, loss, updater)\n",
    "        test_acc = evaluate_accuracy(net, test_iter)\n",
    "        animator.add(epoch + 1, train_metrics + (test_acc,))\n",
    "    train_loss, train_acc = train_metrics\n",
    "    assert train_loss < 0.5, train_loss\n",
    "    assert train_acc <= 1 and train_acc > 0.7, train_acc\n",
    "    assert test_acc <= 1 and test_acc > 0.7, test_acc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "id": "32d6104a",
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = 0.1\n",
    "\n",
    "def updater(batch_size):\n",
    "    return d2l.sgd([W, b], lr, batch_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "64898cb1",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 350x250 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_epochs = 10\n",
    "train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, updater)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "5f490812",
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 900x150 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def predict_ch3(net, test_iter, n=6):  #@save\n",
    "    \"\"\"预测标签（定义见第3章）\"\"\"\n",
    "    for X, y in test_iter:\n",
    "        break\n",
    "    trues = d2l.get_fashion_mnist_labels(y)\n",
    "    preds = d2l.get_fashion_mnist_labels(net(X).argmax(axis=1))\n",
    "    titles = [true +'\\n' + pred for true, pred in zip(trues, preds)]\n",
    "    d2l.show_images(\n",
    "        X[0:n].reshape((n, 28, 28)), 1, n, titles=titles[0:n])\n",
    "\n",
    "predict_ch3(net, test_iter)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "52bca61b",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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