softmax.ipynb

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   "source": [
    "%matplotlib inline\n",
    "from matplotlib_inline import backend_inline\n",
    "from mxnet import autograd, gluon, np, npx, init\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "import sys\n",
    "from mxnet.gluon import nn\n",
    "import time\n",
    "from mxnet import gluon\n",
    "from IPython import display\n",
    " \n",
    "\n",
    "npx.set_np()\n",
    "\n",
    "net = nn.Sequential()\n",
    "net.add(nn.Dense(10))\n",
    "net.initialize(init.Normal(sigma=0.01))\n",
    "\n",
    "\n",
    "    \n",
    "def use_svg_display():  #@save\n",
    "    \"\"\"使用svg格式在Jupyter中显示绘图\"\"\"\n",
    "    backend_inline.set_matplotlib_formats('svg')\n",
    "\n",
    "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]\n",
    "\n",
    "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 = plt.subplots(num_rows, num_cols, figsize=figsize)\n",
    "    axes = axes.flatten()\n",
    "    for i, (ax, img) in enumerate(zip(axes, imgs)):\n",
    "        ax.imshow(img.asnumpy())\n",
    "        ax.axes.get_xaxis().set_visible(True)\n",
    "        ax.axes.get_yaxis().set_visible(True)\n",
    "        if titles:\n",
    "            ax.set_title(titles[i])\n",
    "    return axes\n",
    "\n",
    "def get_dataloader_workers():  #@save\n",
    "    \"\"\"在非Windows的平台上，使用4个进程来读取数据\"\"\"\n",
    "    return 0 if sys.platform.startswith('win') else 4\n",
    "\n",
    "def linreg(X, w, b):  #@save\n",
    "    \"\"\"线性回归模型\"\"\"\n",
    "    return np.dot(X, w) + b\n",
    "\n",
    "\n",
    "def squared_loss(y_hat, y):  #@save\n",
    "    \"\"\"均方损失\"\"\"\n",
    "    return (y_hat - y.reshape(y_hat.shape)) ** 2 / 276\n",
    "\n",
    "def sgd(params, lr, batch_size):  #@save\n",
    "    \"\"\"小批量随机梯度下降\"\"\"\n",
    "    for param in params:\n",
    "        param[:] = param - lr * param.grad / batch_size\n",
    "\n",
    "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",
    "    dataset = gluon.data.vision\n",
    "    trans = [dataset.transforms.ToTensor()]\n",
    "    if resize:\n",
    "        trans.insert(0, dataset.transforms.Resize(resize))\n",
    "    trans = dataset.transforms.Compose(trans)\n",
    "    mnist_train = dataset.FashionMNIST(train=True).transform_first(trans)\n",
    "    mnist_test = dataset.FashionMNIST(train=False).transform_first(trans)\n",
    "    return (gluon.data.DataLoader(mnist_train, batch_size, shuffle=True,\n",
    "                                  num_workers=get_dataloader_workers()),\n",
    "            gluon.data.DataLoader(mnist_test, batch_size, shuffle=False,\n",
    "                                  num_workers=get_dataloader_workers()))\n",
    "\n",
    "\n",
    "batch_size = 256\n",
    "train_iter, test_iter = load_data_fashion_mnist(batch_size)\n",
    "    \n",
    "\n",
    "'''\n",
    "weight 784×10\n",
    "offset 1×10\n",
    "'''   \n",
    "num_inputs = 784\n",
    "num_outputs = 10\n",
    "W = np.random.normal(0, 0.01, (num_inputs, num_outputs))\n",
    "b = np.zeros(num_outputs)\n",
    "W.attach_grad()\n",
    "b.attach_grad()\n",
    "\n",
    "X = np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])\n",
    "X.sum(0, keepdims=True), X.sum(1, keepdims=True)\n",
    "\n",
    "def softmax(X):\n",
    "    X_exp = np.exp(X)\n",
    "    partition = X_exp.sum(1, keepdims=True)\n",
    "    return X_exp / partition  # 这里应用了广播机制\n",
    "\n",
    "X = np.random.normal(0, 1, (2, 5))\n",
    "X_prob = softmax(X)\n",
    "X_prob, X_prob.sum(1)\n",
    "\n",
    "'''\n",
    "(array([[0.10138504, 0.03572102, 0.04586977, 0.67316556, 0.1438586 ],\n",
    "        [0.03605377, 0.05437361, 0.6059516 , 0.08428083, 0.2193402 ]]),\n",
    " array([[1.],\n",
    "        [1.]]))\n",
    "'''\n",
    "# def net(X):\n",
    "#     return softmax(np.dot(X.reshape((-1, W.shape[0])), W) + b)\n",
    "\n",
    "y = np.array([0, 2])\n",
    "y_hat = np.array([[0.1, 0.3, 0.6], [0.3, 0.2, 0.5]])\n",
    "y_hat[[0, 1], y]\n",
    "print(y_hat)\n",
    "\n",
    "def cross_entropy(y_hat, y):\n",
    "    return - np.log(y_hat[range(len(y_hat)), y])\n",
    "\n",
    "cross_entropy(y_hat, y)\n",
    "\n",
    "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.astype(y.dtype) == y\n",
    "    return float(cmp.astype(y.dtype).sum())\n",
    "\n",
    "accuracy(y_hat, y) / len(y)\n",
    "\n",
    "def evaluate_accuracy(net, data_iter):  #@save\n",
    "    \"\"\"计算在指定数据集上模型的精度\"\"\"\n",
    "    metric = Accumulator(2)  # 正确预测数、预测总数\n",
    "    for X, y in data_iter:\n",
    "        metric.add(accuracy(net(X), y),y.size)\n",
    "    return metric[0] / metric[1]\n",
    "\n",
    "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]\n",
    "    \n",
    "evaluate_accuracy(net, test_iter)\n",
    "\n",
    "#@save\n",
    "def set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend):\n",
    "    \"\"\"设置matplotlib的轴\"\"\"\n",
    "    axes.set_xlabel(xlabel)\n",
    "    axes.set_ylabel(ylabel)\n",
    "    axes.set_xscale(xscale)\n",
    "    axes.set_yscale(yscale)\n",
    "    axes.set_xlim(xlim)\n",
    "    axes.set_ylim(ylim)\n",
    "    if legend:\n",
    "        axes.legend(legend)\n",
    "    axes.grid()\n",
    "\n",
    "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",
    "    # 训练损失总和、训练准确度总和、样本数\n",
    "    metric = Accumulator(3)\n",
    "    if isinstance(updater, gluon.Trainer):\n",
    "        updater = updater.step\n",
    "    for X, y in train_iter:\n",
    "        # 计算梯度并更新参数\n",
    "        with autograd.record():\n",
    "            y_hat = net(X)\n",
    "            l = loss(y_hat, y)\n",
    "        l.backward()\n",
    "        updater(X.shape[0])\n",
    "        metric.add(float(l.sum()), accuracy(y_hat, y), y.size)\n",
    "    # 返回训练损失和训练精度\n",
    "    return metric[0] / metric[2], metric[1] / metric[2]\n",
    "\n",
    "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",
    "        use_svg_display()\n",
    "        self.fig, self.axes = 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:  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)\n",
    "        \n",
    "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\n",
    "    \n",
    "lr = 0.1\n",
    "\n",
    "def updater(batch_size):\n",
    "    return  sgd([W, b], lr, batch_size)\n",
    "\n",
    "num_epochs = 10\n",
    "\n",
    "trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': 0.1})\n",
    "\n",
    "loss = gluon.loss.SoftmaxCrossEntropyLoss()\n",
    "\n",
    "# train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, updater)\n",
    "train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)\n",
    "\n",
    "\n",
    "\n",
    "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 = get_fashion_mnist_labels(y)\n",
    "    preds = get_fashion_mnist_labels(net(X).argmax(axis=1))\n",
    "    titles = [true +'\\n' + pred for true, pred in zip(trues, preds)]\n",
    "    show_images(\n",
    "        X[0:n].reshape((n, 28, 28)), 1, n, titles=titles[0:n])\n",
    "\n",
    "predict_ch3(net, test_iter)"
   ]
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