d2l/torch.py

DATA_HUB = dict()
DATA_URL = 'http://d2l-data.s3-accelerate.amazonaws.com/'

import numpy as np
import torch
import torchvision
from PIL import Image
from torch import nn
from torch.nn import functional as F
from torch.utils import data
from torchvision import transforms

nn_Module = nn.Module

#################   WARNING   ################
# The below part is generated automatically through:
#    d2lbook build lib
# Don't edit it directly

import collections
import hashlib
import inspect
import math
import os
import random
import re
import shutil
import sys
import tarfile
import time
import zipfile
from collections import defaultdict
import gym
import pandas as pd
import requests
from IPython import display
from matplotlib import pyplot as plt
from matplotlib_inline import backend_inline
from scipy.spatial import distance_matrix

d2l = sys.modules[__name__]

import numpy as np
import torch
import torchvision
from PIL import Image
from torch import nn
from torch.nn import functional as F
from torchvision import transforms

def use_svg_display():
    """Use the svg format to display a plot in Jupyter.

    Defined in :numref:`sec_calculus`"""
    backend_inline.set_matplotlib_formats('svg')

def set_figsize(figsize=(3.5, 2.5)):
    """Set the figure size for matplotlib.

    Defined in :numref:`sec_calculus`"""
    use_svg_display()
    d2l.plt.rcParams['figure.figsize'] = figsize

def set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend):
    """Set the axes for matplotlib.

    Defined in :numref:`sec_calculus`"""
    axes.set_xlabel(xlabel), axes.set_ylabel(ylabel)
    axes.set_xscale(xscale), axes.set_yscale(yscale)
    axes.set_xlim(xlim),     axes.set_ylim(ylim)
    if legend:
        axes.legend(legend)
    axes.grid()

def plot(X, Y=None, xlabel=None, ylabel=None, legend=[], xlim=None,
         ylim=None, xscale='linear', yscale='linear',
         fmts=('-', 'm--', 'g-.', 'r:'), figsize=(3.5, 2.5), axes=None):
    """Plot data points.

    Defined in :numref:`sec_calculus`"""

    def has_one_axis(X):  # True if `X` (tensor or list) has 1 axis
        return (hasattr(X, "ndim") and X.ndim == 1 or isinstance(X, list)
                and not hasattr(X[0], "__len__"))

    if has_one_axis(X): X = [X]
    if Y is None:
        X, Y = [[]] * len(X), X
    elif has_one_axis(Y):
        Y = [Y]
    if len(X) != len(Y):
        X = X * len(Y)

    set_figsize(figsize)
    if axes is None: axes = d2l.plt.gca()
    axes.cla()
    for x, y, fmt in zip(X, Y, fmts):
        axes.plot(x,y,fmt) if len(x) else axes.plot(y,fmt)
    set_axes(axes, xlabel, ylabel, xlim, ylim, xscale, yscale, legend)

def add_to_class(Class):
    """Defined in :numref:`sec_oo-design`"""
    def wrapper(obj):
        setattr(Class, obj.__name__, obj)
    return wrapper

class HyperParameters:
    def save_hyperparameters(self, ignore=[]):
        """Defined in :numref:`sec_oo-design`"""
        raise NotImplemented

    def save_hyperparameters(self, ignore=[]):
        """Save function arguments into class attributes.
    
        Defined in :numref:`sec_utils`"""
        frame = inspect.currentframe().f_back
        _, _, _, local_vars = inspect.getargvalues(frame)
        self.hparams = {k:v for k, v in local_vars.items()
                        if k not in set(ignore+['self']) and not k.startswith('_')}
        for k, v in self.hparams.items():
            setattr(self, k, v)

class ProgressBoard(d2l.HyperParameters):
    """Plot data points in animation.

    Defined in :numref:`sec_oo-design`"""
    def __init__(self, xlabel=None, ylabel=None, xlim=None,
                 ylim=None, xscale='linear', yscale='linear',
                 ls=['-', '--', '-.', ':'], colors=['C0', 'C1', 'C2', 'C3'],
                 fig=None, axes=None, figsize=(3.5, 2.5), display=True):
        self.save_hyperparameters()

    def draw(self, x, y, label, every_n=1):
        raise NotImplemented

    def draw(self, x, y, label, every_n=1):
        """Defined in :numref:`sec_utils`"""
        Point = collections.namedtuple('Point', ['x', 'y'])
        if not hasattr(self, 'raw_points'):
            self.raw_points = collections.OrderedDict()
            self.data = collections.OrderedDict()
        if label not in self.raw_points:
            self.raw_points[label] = []
            self.data[label] = []
        points = self.raw_points[label]
        line = self.data[label]
        points.append(Point(x, y))
        if len(points) != every_n:
            return
        mean = lambda x: sum(x) / len(x)
        line.append(Point(mean([p.x for p in points]),
                          mean([p.y for p in points])))
        points.clear()
        if not self.display:
            return
        d2l.use_svg_display()
        if self.fig is None:
            self.fig = d2l.plt.figure(figsize=self.figsize)
        plt_lines, labels = [], []
        for (k, v), ls, color in zip(self.data.items(), self.ls, self.colors):
            plt_lines.append(d2l.plt.plot([p.x for p in v], [p.y for p in v],
                                          linestyle=ls, color=color)[0])
            labels.append(k)
        axes = self.axes if self.axes else d2l.plt.gca()
        if self.xlim: axes.set_xlim(self.xlim)
        if self.ylim: axes.set_ylim(self.ylim)
        if not self.xlabel: self.xlabel = self.x
        axes.set_xlabel(self.xlabel)
        axes.set_ylabel(self.ylabel)
        axes.set_xscale(self.xscale)
        axes.set_yscale(self.yscale)
        axes.legend(plt_lines, labels)
        display.display(self.fig)
        display.clear_output(wait=True)

class Module(d2l.nn_Module, d2l.HyperParameters):
    """Defined in :numref:`sec_oo-design`"""
    def __init__(self, plot_train_per_epoch=2, plot_valid_per_epoch=1):
        super().__init__()
        self.save_hyperparameters()
        self.board = ProgressBoard()
    def loss(self, y_hat, y):
        raise NotImplementedError

    def forward(self, X):
        assert hasattr(self, 'net'), 'Neural network is defined'
        return self.net(X)

    def plot(self, key, value, train):
        """Plot a point in animation."""
        assert hasattr(self, 'trainer'), 'Trainer is not inited'
        self.board.xlabel = 'epoch'
        if train:
            x = self.trainer.train_batch_idx / \
                self.trainer.num_train_batches
            n = self.trainer.num_train_batches / \
                self.plot_train_per_epoch
        else:
            x = self.trainer.epoch + 1
            n = self.trainer.num_val_batches / \
                self.plot_valid_per_epoch
        self.board.draw(x, d2l.numpy(d2l.to(value, d2l.cpu())),
                        ('train_' if train else 'val_') + key,
                        every_n=int(n))
    def training_step(self, batch):
        l = self.loss(self(*batch[:-1]), batch[-1])
        self.plot('loss', l, train=True)
        return l

    def validation_step(self, batch):
        l = self.loss(self(*batch[:-1]), batch[-1])
        self.plot('loss', l, train=False)

    def configure_optimizers(self):
        raise NotImplementedError

    def configure_optimizers(self):
        """Defined in :numref:`sec_classification`"""
        return torch.optim.SGD(self.parameters(), lr=self.lr)

    def apply_init(self, inputs, init=None):
        """Defined in :numref:`sec_lazy_init`"""
        self.forward(*inputs)
        if init is not None:
            self.net.apply(init)

class DataModule(d2l.HyperParameters):
    """Defined in :numref:`subsec_oo-design-models`"""
    def __init__(self, root='../data', num_workers=4):
        self.save_hyperparameters()

    def get_dataloader(self, train):
        raise NotImplementedError

    def train_dataloader(self):
        return self.get_dataloader(train=True)

    def val_dataloader(self):
        return self.get_dataloader(train=False)

    def get_tensorloader(self, tensors, train, indices=slice(0, None)):
        """Defined in :numref:`sec_synthetic-regression-data`"""
        tensors = tuple(a[indices] for a in tensors)
        dataset = torch.utils.data.TensorDataset(*tensors)
        return torch.utils.data.DataLoader(dataset, self.batch_size,
                                           shuffle=train)

class Trainer(d2l.HyperParameters):
    """Defined in :numref:`subsec_oo-design-models`"""
    def __init__(self, max_epochs, num_gpus=0, gradient_clip_val=0):
        self.save_hyperparameters()
        assert num_gpus == 0, 'No GPU support yet'

    def prepare_data(self, data):
        self.train_dataloader = data.train_dataloader()
        self.val_dataloader = data.val_dataloader()
        self.num_train_batches = len(self.train_dataloader)
        self.num_val_batches = (len(self.val_dataloader)
                                if self.val_dataloader is not None else 0)

    def prepare_model(self, model):
        model.trainer = self
        model.board.xlim = [0, self.max_epochs]
        self.model = model

    def fit(self, model, data):
        self.prepare_data(data)
        self.prepare_model(model)
        self.optim = model.configure_optimizers()
        self.epoch = 0
        self.train_batch_idx = 0
        self.val_batch_idx = 0
        for self.epoch in range(self.max_epochs):
            self.fit_epoch()

    def fit_epoch(self):
        raise NotImplementedError

    def prepare_batch(self, batch):
        """Defined in :numref:`sec_linear_scratch`"""
        return batch

    def fit_epoch(self):
        """Defined in :numref:`sec_linear_scratch`"""
        self.model.train()
        for batch in self.train_dataloader:
            loss = self.model.training_step(self.prepare_batch(batch))
            self.optim.zero_grad()
            with torch.no_grad():
                loss.backward()
                if self.gradient_clip_val > 0:  # To be discussed later
                    self.clip_gradients(self.gradient_clip_val, self.model)
                self.optim.step()
            self.train_batch_idx += 1
        if self.val_dataloader is None:
            return
        self.model.eval()
        for batch in self.val_dataloader:
            with torch.no_grad():
                self.model.validation_step(self.prepare_batch(batch))
            self.val_batch_idx += 1

    def __init__(self, max_epochs, num_gpus=0, gradient_clip_val=0):
        """Defined in :numref:`sec_use_gpu`"""
        self.save_hyperparameters()
        self.gpus = [d2l.gpu(i) for i in range(min(num_gpus, d2l.num_gpus()))]
    

    def prepare_batch(self, batch):
        """Defined in :numref:`sec_use_gpu`"""
        if self.gpus:
            batch = [d2l.to(a, self.gpus[0]) for a in batch]
        return batch
    

    def prepare_model(self, model):
        """Defined in :numref:`sec_use_gpu`"""
        model.trainer = self
        model.board.xlim = [0, self.max_epochs]
        if self.gpus:
            model.to(self.gpus[0])
        self.model = model

    def clip_gradients(self, grad_clip_val, model):
        """Defined in :numref:`sec_rnn-scratch`"""
        params = [p for p in model.parameters() if p.requires_grad]
        norm = torch.sqrt(sum(torch.sum((p.grad ** 2)) for p in params))
        if norm > grad_clip_val:
            for param in params:
                param.grad[:] *= grad_clip_val / norm

class SyntheticRegressionData(d2l.DataModule):
    """Defined in :numref:`sec_synthetic-regression-data`"""
    def __init__(self, w, b, noise=0.01, num_train=1000, num_val=1000,
                 batch_size=32):
        super().__init__()
        self.save_hyperparameters()
        n = num_train + num_val
        self.X = d2l.randn(n, len(w))
        noise = d2l.randn(n, 1) * noise
        self.y = d2l.matmul(self.X, d2l.reshape(w, (-1, 1))) + b + noise

    def get_dataloader(self, train):
        """Defined in :numref:`sec_synthetic-regression-data`"""
        i = slice(0, self.num_train) if train else slice(self.num_train, None)
        return self.get_tensorloader((self.X, self.y), train, i)

class LinearRegressionScratch(d2l.Module):
    """Defined in :numref:`sec_linear_scratch`"""
    def __init__(self, num_inputs, lr, sigma=0.01):
        super().__init__()
        self.save_hyperparameters()
        self.w = d2l.normal(0, sigma, (num_inputs, 1), requires_grad=True)
        self.b = d2l.zeros(1, requires_grad=True)

    def forward(self, X):
        """The linear regression model.
    
        Defined in :numref:`sec_linear_scratch`"""
        return d2l.matmul(X, self.w) + self.b

    def loss(self, y_hat, y):
        """Defined in :numref:`sec_linear_scratch`"""
        l = (y_hat - y) ** 2 / 2
        return d2l.reduce_mean(l)

    def configure_optimizers(self):
        """Defined in :numref:`sec_linear_scratch`"""
        return SGD([self.w, self.b], self.lr)

class SGD(d2l.HyperParameters):
    """Defined in :numref:`sec_linear_scratch`"""
    def __init__(self, params, lr):
        """Minibatch stochastic gradient descent."""
        self.save_hyperparameters()

    def step(self):
        for param in self.params:
            param -= self.lr * param.grad

    def zero_grad(self):
        for param in self.params:
            if param.grad is not None:
                param.grad.zero_()

class LinearRegression(d2l.Module):
    """Defined in :numref:`sec_linear_concise`"""
    def __init__(self, lr):
        super().__init__()
        self.save_hyperparameters()
        self.net = nn.LazyLinear(1)
        self.net.weight.data.normal_(0, 0.01)
        self.net.bias.data.fill_(0)

    def forward(self, X):
        """The linear regression model.
    
        Defined in :numref:`sec_linear_concise`"""
        return self.net(X)

    def loss(self, y_hat, y):
        """Defined in :numref:`sec_linear_concise`"""
        fn = nn.MSELoss()
        return fn(y_hat, y)

    def configure_optimizers(self):
        """Defined in :numref:`sec_linear_concise`"""
        return torch.optim.SGD(self.parameters(), self.lr)

    def get_w_b(self):
        """Defined in :numref:`sec_linear_concise`"""
        return (self.net.weight.data, self.net.bias.data)

class FashionMNIST(d2l.DataModule):
    """Defined in :numref:`sec_fashion_mnist`"""
    def __init__(self, batch_size=64, resize=(28, 28)):
        super().__init__()
        self.save_hyperparameters()
        trans = transforms.Compose([transforms.Resize(resize),
                                    transforms.ToTensor()])
        self.train = torchvision.datasets.FashionMNIST(
            root=self.root, train=True, transform=trans, download=True)
        self.val = torchvision.datasets.FashionMNIST(
            root=self.root, train=False, transform=trans, download=True)

    def text_labels(self, indices):
        """Return text labels.
    
        Defined in :numref:`sec_fashion_mnist`"""
        labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',
                  'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']
        return [labels[int(i)] for i in indices]

    def get_dataloader(self, train):
        """Defined in :numref:`sec_fashion_mnist`"""
        data = self.train if train else self.val
        return torch.utils.data.DataLoader(data, self.batch_size, shuffle=train,
                                           num_workers=self.num_workers)

    def visualize(self, batch, nrows=1, ncols=8, labels=[]):
        """Defined in :numref:`sec_fashion_mnist`"""
        X, y = batch
        if not labels:
            labels = self.text_labels(y)
        d2l.show_images(X.squeeze(1), nrows, ncols, titles=labels)

def show_images(imgs, num_rows, num_cols, titles=None, scale=1.5):
    """Plot a list of images.

    Defined in :numref:`sec_fashion_mnist`"""
    raise NotImplementedError

class Classifier(d2l.Module):
    """Defined in :numref:`sec_classification`"""
    def validation_step(self, batch):
        Y_hat = self(*batch[:-1])
        self.plot('loss', self.loss(Y_hat, batch[-1]), train=False)
        self.plot('acc', self.accuracy(Y_hat, batch[-1]), train=False)

    def accuracy(self, Y_hat, Y, averaged=True):
        """Compute the number of correct predictions.
    
        Defined in :numref:`sec_classification`"""
        Y_hat = d2l.reshape(Y_hat, (-1, Y_hat.shape[-1]))
        preds = d2l.astype(d2l.argmax(Y_hat, axis=1), Y.dtype)
        compare = d2l.astype(preds == d2l.reshape(Y, -1), d2l.float32)
        return d2l.reduce_mean(compare) if averaged else compare

    def loss(self, Y_hat, Y, averaged=True):
        """Defined in :numref:`sec_softmax_concise`"""
        Y_hat = d2l.reshape(Y_hat, (-1, Y_hat.shape[-1]))
        Y = d2l.reshape(Y, (-1,))
        return F.cross_entropy(
            Y_hat, Y, reduction='mean' if averaged else 'none')

    def layer_summary(self, X_shape):
        """Defined in :numref:`sec_lenet`"""
        X = d2l.randn(*X_shape)
        for layer in self.net:
            X = layer(X)
            print(layer.__class__.__name__, 'output shape:\t', X.shape)

class SoftmaxRegression(d2l.Classifier):
    """Defined in :numref:`sec_softmax_concise`"""
    def __init__(self, num_outputs, lr):
        super().__init__()
        self.save_hyperparameters()
        self.net = nn.Sequential(nn.Flatten(),
                                 nn.LazyLinear(num_outputs))
    def forward(self, X):
        return self.net(X)

def cpu():
    """Defined in :numref:`sec_use_gpu`"""
    return torch.device('cpu')
def gpu(i=0):
    """Defined in :numref:`sec_use_gpu`"""
    return torch.device(f'cuda:{i}')

def num_gpus():
    """Defined in :numref:`sec_use_gpu`"""
    return torch.cuda.device_count()

def try_gpu(i=0):
    """Return gpu(i) if exists, otherwise return cpu().

    Defined in :numref:`sec_use_gpu`"""
    if num_gpus() >= i + 1:
        return gpu(i)
    return cpu()

def try_all_gpus():
    """Return all available GPUs, or [cpu(),] if no GPU exists.

    Defined in :numref:`sec_use_gpu`"""
    return [gpu(i) for i in range(num_gpus())]

def corr2d(X, K):
    """Compute 2D cross-correlation.

    Defined in :numref:`sec_conv_layer`"""
    h, w = K.shape
    Y = d2l.zeros((X.shape[0] - h + 1, X.shape[1] - w + 1))
    for i in range(Y.shape[0]):
        for j in range(Y.shape[1]):
            Y[i, j] = d2l.reduce_sum((X[i: i + h, j: j + w] * K))
    return Y

def init_cnn(module):
    """Initialize weights for CNNs.

    Defined in :numref:`sec_lenet`"""
    if type(module) == nn.Linear or type(module) == nn.Conv2d:
        nn.init.xavier_uniform_(module.weight)

class LeNet(d2l.Classifier):
    """Defined in :numref:`sec_lenet`"""
    def __init__(self, lr=0.1, num_classes=10):
        super().__init__()
        self.save_hyperparameters()
        self.net = nn.Sequential(
            nn.LazyConv2d(6, kernel_size=5, padding=2), nn.Sigmoid(),
            nn.AvgPool2d(kernel_size=2, stride=2),
            nn.LazyConv2d(16, kernel_size=5), nn.Sigmoid(),
            nn.AvgPool2d(kernel_size=2, stride=2),
            nn.Flatten(),
            nn.LazyLinear(120), nn.Sigmoid(),
            nn.LazyLinear(84), nn.Sigmoid(),
            nn.LazyLinear(num_classes))

class Residual(nn.Module):
    """The Residual block of ResNet."""
    def __init__(self, num_channels, use_1x1conv=False, strides=1):
        super().__init__()
        self.conv1 = nn.LazyConv2d(num_channels, kernel_size=3, padding=1,
                                   stride=strides)
        self.conv2 = nn.LazyConv2d(num_channels, kernel_size=3, padding=1)
        if use_1x1conv:
            self.conv3 = nn.LazyConv2d(num_channels, kernel_size=1,
                                       stride=strides)
        else:
            self.conv3 = None
        self.bn1 = nn.LazyBatchNorm2d()
        self.bn2 = nn.LazyBatchNorm2d()

    def forward(self, X):
        Y = F.relu(self.bn1(self.conv1(X)))
        Y = self.bn2(self.conv2(Y))
        if self.conv3:
            X = self.conv3(X)
        Y += X
        return F.relu(Y)

class ResNeXtBlock(nn.Module):
    """The ResNeXt block.

    Defined in :numref:`subsec_residual-blks`"""
    def __init__(self, num_channels, groups, bot_mul, use_1x1conv=False,
                 strides=1):
        super().__init__()
        bot_channels = int(round(num_channels * bot_mul))
        self.conv1 = nn.LazyConv2d(bot_channels, kernel_size=1, stride=1)
        self.conv2 = nn.LazyConv2d(bot_channels, kernel_size=3,
                                   stride=strides, padding=1,
                                   groups=bot_channels//groups)
        self.conv3 = nn.LazyConv2d(num_channels, kernel_size=1, stride=1)
        self.bn1 = nn.LazyBatchNorm2d()
        self.bn2 = nn.LazyBatchNorm2d()
        self.bn3 = nn.LazyBatchNorm2d()
        if use_1x1conv:
            self.conv4 = nn.LazyConv2d(num_channels, kernel_size=1,
                                       stride=strides)
            self.bn4 = nn.LazyBatchNorm2d()
        else:
            self.conv4 = None

    def forward(self, X):
        Y = F.relu(self.bn1(self.conv1(X)))
        Y = F.relu(self.bn2(self.conv2(Y)))
        Y = self.bn3(self.conv3(Y))
        if self.conv4:
            X = self.bn4(self.conv4(X))
        return F.relu(Y + X)

class TimeMachine(d2l.DataModule):
    """Defined in :numref:`sec_text-sequence`"""
    def _download(self):
        fname = d2l.download(d2l.DATA_URL + 'timemachine.txt', self.root,
                             '090b5e7e70c295757f55df93cb0a180b9691891a')
        with open(fname) as f:
            return f.read()

    def _preprocess(self, text):
        """Defined in :numref:`sec_text-sequence`"""
        return re.sub('[^A-Za-z]+', ' ', text).lower()

    def _tokenize(self, text):
        """Defined in :numref:`sec_text-sequence`"""
        return list(text)

    def build(self, raw_text, vocab=None):
        """Defined in :numref:`sec_text-sequence`"""
        tokens = self._tokenize(self._preprocess(raw_text))
        if vocab is None: vocab = Vocab(tokens)
        corpus = [vocab[token] for token in tokens]
        return corpus, vocab

    def __init__(self, batch_size, num_steps, num_train=10000, num_val=5000):
        """Defined in :numref:`subsec_perplexity`"""
        super(d2l.TimeMachine, self).__init__()
        self.save_hyperparameters()
        corpus, self.vocab = self.build(self._download())
        array = d2l.tensor([corpus[i:i+num_steps+1]
                            for i in range(len(corpus)-num_steps)])
        self.X, self.Y = array[:,:-1], array[:,1:]

    def get_dataloader(self, train):
        """Defined in :numref:`subsec_partitioning-seqs`"""
        idx = slice(0, self.num_train) if train else slice(
            self.num_train, self.num_train + self.num_val)
        return self.get_tensorloader([self.X, self.Y], train, idx)

class Vocab:
    """Vocabulary for text."""
    def __init__(self, tokens=[], min_freq=0, reserved_tokens=[]):
        """Defined in :numref:`sec_text-sequence`"""
        # Flatten a 2D list if needed
        if tokens and isinstance(tokens[0], list):
            tokens = [token for line in tokens for token in line]
        # Count token frequencies
        counter = collections.Counter(tokens)
        self.token_freqs = sorted(counter.items(), key=lambda x: x[1],
                                  reverse=True)
        # The list of unique tokens
        self.idx_to_token = list(sorted(set(['<unk>'] + reserved_tokens + [
            token for token, freq in self.token_freqs if freq >= min_freq])))
        self.token_to_idx = {token: idx
                             for idx, token in enumerate(self.idx_to_token)}

    def __len__(self):
        return len(self.idx_to_token)

    def __getitem__(self, tokens):
        if not isinstance(tokens, (list, tuple)):
            return self.token_to_idx.get(tokens, self.unk)
        return [self.__getitem__(token) for token in tokens]

    def to_tokens(self, indices):
        if hasattr(indices, '__len__') and len(indices) > 1:
            return [self.idx_to_token[int(index)] for index in indices]
        return self.idx_to_token[indices]

    @property
    def unk(self):  # Index for the unknown token
        return self.token_to_idx['<unk>']

class RNNScratch(d2l.Module):
    """Defined in :numref:`sec_rnn-scratch`"""
    def __init__(self, num_inputs, num_hiddens, sigma=0.01):
        super().__init__()
        self.save_hyperparameters()
        self.W_xh = nn.Parameter(
            d2l.randn(num_inputs, num_hiddens) * sigma)
        self.W_hh = nn.Parameter(
            d2l.randn(num_hiddens, num_hiddens) * sigma)
        self.b_h = nn.Parameter(d2l.zeros(num_hiddens))

    def forward(self, inputs, state=None):
        """Defined in :numref:`sec_rnn-scratch`"""
        if state is None:
            # Initial state with shape: (batch_size, num_hiddens)
            state = d2l.zeros((inputs.shape[1], self.num_hiddens),
                              device=inputs.device)
        else:
            state, = state
        outputs = []
        for X in inputs:  # Shape of inputs: (num_steps, batch_size, num_inputs)
            state = d2l.tanh(d2l.matmul(X, self.W_xh) +
                             d2l.matmul(state, self.W_hh) + self.b_h)
            outputs.append(state)
        return outputs, state

def check_len(a, n):
    """Defined in :numref:`sec_rnn-scratch`"""
    assert len(a) == n, f'list\'s len {len(a)} != expected length {n}'

def check_shape(a, shape):
    """Defined in :numref:`sec_rnn-scratch`"""
    assert a.shape == shape, \
            f'tensor\'s shape {a.shape} != expected shape {shape}'

class RNNLMScratch(d2l.Classifier):
    """Defined in :numref:`sec_rnn-scratch`"""
    def __init__(self, rnn, vocab_size, lr=0.01):
        super().__init__()
        self.save_hyperparameters()
        self.init_params()

    def init_params(self):
        self.W_hq = nn.Parameter(
            d2l.randn(
                self.rnn.num_hiddens, self.vocab_size) * self.rnn.sigma)
        self.b_q = nn.Parameter(d2l.zeros(self.vocab_size))
    def training_step(self, batch):
        l = self.loss(self(*batch[:-1]), batch[-1])
        self.plot('ppl', d2l.exp(l), train=True)
        return l

    def validation_step(self, batch):
        l = self.loss(self(*batch[:-1]), batch[-1])
        self.plot('ppl', d2l.exp(l), train=False)

    def one_hot(self, X):
        """Defined in :numref:`sec_rnn-scratch`"""
        # Output shape: (num_steps, batch_size, vocab_size)
        return F.one_hot(X.T, self.vocab_size).type(torch.float32)

    def output_layer(self, rnn_outputs):
        """Defined in :numref:`sec_rnn-scratch`"""
        outputs = [d2l.matmul(H, self.W_hq) + self.b_q for H in rnn_outputs]
        return d2l.stack(outputs, 1)
    

    def forward(self, X, state=None):
        """Defined in :numref:`sec_rnn-scratch`"""
        embs = self.one_hot(X)
        rnn_outputs, _ = self.rnn(embs, state)
        return self.output_layer(rnn_outputs)

    def predict(self, prefix, num_preds, vocab, device=None):
        """Defined in :numref:`sec_rnn-scratch`"""
        state, outputs = None, [vocab[prefix[0]]]
        for i in range(len(prefix) + num_preds - 1):
            X = d2l.tensor([[outputs[-1]]], device=device)
            embs = self.one_hot(X)
            rnn_outputs, state = self.rnn(embs, state)
            if i < len(prefix) - 1:  # Warm-up period
                outputs.append(vocab[prefix[i + 1]])
            else:  # Predict `num_preds` steps
                Y = self.output_layer(rnn_outputs)
                outputs.append(int(d2l.reshape(d2l.argmax(Y, axis=2), 1)))
        return ''.join([vocab.idx_to_token[i] for i in outputs])

class RNN(d2l.Module):
    """Defined in :numref:`sec_rnn-concise`"""
    def __init__(self, num_inputs, num_hiddens):
        super().__init__()
        self.save_hyperparameters()
        self.rnn = nn.RNN(num_inputs, num_hiddens)

    def forward(self, inputs, H=None):
        return self.rnn(inputs, H)

class RNNLM(d2l.RNNLMScratch):
    """Defined in :numref:`sec_rnn-concise`"""
    def init_params(self):
        self.linear = nn.LazyLinear(self.vocab_size)
    def output_layer(self, hiddens):
        return d2l.swapaxes(self.linear(hiddens), 0, 1)

class GRU(d2l.RNN):
    """Defined in :numref:`sec_deep_rnn`"""
    def __init__(self, num_inputs, num_hiddens, num_layers, dropout=0):
        d2l.Module.__init__(self)
        self.save_hyperparameters()
        self.rnn = nn.GRU(num_inputs, num_hiddens, num_layers,
                          dropout=dropout)

class MTFraEng(d2l.DataModule):
    """Defined in :numref:`sec_machine_translation`"""
    def _download(self):
        d2l.extract(d2l.download(
            d2l.DATA_URL+'fra-eng.zip', self.root,
            '94646ad1522d915e7b0f9296181140edcf86a4f5'))
        with open(self.root + '/fra-eng/fra.txt', encoding='utf-8') as f:
            return f.read()

    def _preprocess(self, text):
        """Defined in :numref:`sec_machine_translation`"""
        # Replace non-breaking space with space
        text = text.replace('\u202f', ' ').replace('\xa0', ' ')
        # Insert space between words and punctuation marks
        no_space = lambda char, prev_char: char in ',.!?' and prev_char != ' '
        out = [' ' + char if i > 0 and no_space(char, text[i - 1]) else char
               for i, char in enumerate(text.lower())]
        return ''.join(out)

    def _tokenize(self, text, max_examples=None):
        """Defined in :numref:`sec_machine_translation`"""
        src, tgt = [], []
        for i, line in enumerate(text.split('\n')):
            if max_examples and i > max_examples: break
            parts = line.split('\t')
            if len(parts) == 2:
                # Skip empty tokens
                src.append([t for t in f'{parts[0]} <eos>'.split(' ') if t])
                tgt.append([t for t in f'{parts[1]} <eos>'.split(' ') if t])
        return src, tgt

    def __init__(self, batch_size, num_steps=9, num_train=512, num_val=128):
        """Defined in :numref:`sec_machine_translation`"""
        super(MTFraEng, self).__init__()
        self.save_hyperparameters()
        self.arrays, self.src_vocab, self.tgt_vocab = self._build_arrays(
            self._download())
    

    def _build_arrays(self, raw_text, src_vocab=None, tgt_vocab=None):
        """Defined in :numref:`sec_machine_translation`"""
        def _build_array(sentences, vocab, is_tgt=False):
            pad_or_trim = lambda seq, t: (
                seq[:t] if len(seq) > t else seq + ['<pad>'] * (t - len(seq)))
            sentences = [pad_or_trim(s, self.num_steps) for s in sentences]
            if is_tgt:
                sentences = [['<bos>'] + s for s in sentences]
            if vocab is None:
                vocab = d2l.Vocab(sentences, min_freq=2)
            array = d2l.tensor([vocab[s] for s in sentences])
            valid_len = d2l.reduce_sum(
                d2l.astype(array != vocab['<pad>'], d2l.int32), 1)
            return array, vocab, valid_len
        src, tgt = self._tokenize(self._preprocess(raw_text),
                                  self.num_train + self.num_val)
        src_array, src_vocab, src_valid_len = _build_array(src, src_vocab)
        tgt_array, tgt_vocab, _ = _build_array(tgt, tgt_vocab, True)
        return ((src_array, tgt_array[:,:-1], src_valid_len, tgt_array[:,1:]),
                src_vocab, tgt_vocab)

    def get_dataloader(self, train):
        """Defined in :numref:`subsec_loading-seq-fixed-len`"""
        idx = slice(0, self.num_train) if train else slice(self.num_train, None)
        return self.get_tensorloader(self.arrays, train, idx)

    def build(self, src_sentences, tgt_sentences):
        """Defined in :numref:`subsec_loading-seq-fixed-len`"""
        raw_text = '\n'.join([src + '\t' + tgt for src, tgt in zip(
            src_sentences, tgt_sentences)])
        arrays, _, _ = self._build_arrays(
            raw_text, self.src_vocab, self.tgt_vocab)
        return arrays

def show_list_len_pair_hist(legend, xlabel, ylabel, xlist, ylist):
    """Plot the histogram for list length pairs.

    Defined in :numref:`sec_machine_translation`"""
    d2l.set_figsize()
    _, _, patches = d2l.plt.hist(
        [[len(l) for l in xlist], [len(l) for l in ylist]])
    d2l.plt.xlabel(xlabel)
    d2l.plt.ylabel(ylabel)
    for patch in patches[1].patches:
        patch.set_hatch('/')
    d2l.plt.legend(legend)

class Encoder(nn.Module):
    """The base encoder interface for the encoder-decoder architecture."""
    def __init__(self):
        super().__init__()

    # Later there can be additional arguments (e.g., length excluding padding)
    def forward(self, X, *args):
        raise NotImplementedError

class Decoder(nn.Module):
    """The base decoder interface for the encoder-decoder architecture.

    Defined in :numref:`sec_encoder-decoder`"""
    def __init__(self):
        super().__init__()

    # Later there can be additional arguments (e.g., length excluding padding)
    def init_state(self, enc_outputs, *args):
        raise NotImplementedError

    def forward(self, X, state):
        raise NotImplementedError

class EncoderDecoder(d2l.Classifier):
    """The base class for the encoder-decoder architecture.

    Defined in :numref:`sec_encoder-decoder`"""
    def __init__(self, encoder, decoder):
        super().__init__()
        self.encoder = encoder
        self.decoder = decoder

    def forward(self, enc_X, dec_X, *args):
        enc_outputs = self.encoder(enc_X, *args)
        dec_state = self.decoder.init_state(enc_outputs, *args)
        # Return decoder output only
        return self.decoder(dec_X, dec_state)[0]

    def predict_step(self, batch, device, num_steps,
                     save_attention_weights=False):
        """Defined in :numref:`sec_seq2seq_training`"""
        batch = [d2l.to(a, device) for a in batch]
        src, tgt, src_valid_len, _ = batch
        enc_outputs = self.encoder(src, src_valid_len)
        dec_state = self.decoder.init_state(enc_outputs, src_valid_len)
        outputs, attention_weights = [d2l.expand_dims(tgt[:,0], 1), ], []
        for _ in range(num_steps):
            Y, dec_state = self.decoder(outputs[-1], dec_state)
            outputs.append(d2l.argmax(Y, 2))
            # Save attention weights (to be covered later)
            if save_attention_weights:
                attention_weights.append(self.decoder.attention_weights)
        return d2l.concat(outputs[1:], 1), attention_weights

def init_seq2seq(module):
    """Initialize weights for Seq2Seq.

    Defined in :numref:`sec_seq2seq`"""
    if type(module) == nn.Linear:
         nn.init.xavier_uniform_(module.weight)
    if type(module) == nn.GRU:
        for param in module._flat_weights_names:
            if "weight" in param:
                nn.init.xavier_uniform_(module._parameters[param])

class Seq2SeqEncoder(d2l.Encoder):
    """The RNN encoder for sequence to sequence learning.

    Defined in :numref:`sec_seq2seq`"""
    def __init__(self, vocab_size, embed_size, num_hiddens, num_layers,
                 dropout=0):
        super().__init__()
        self.embedding = nn.Embedding(vocab_size, embed_size)
        self.rnn = d2l.GRU(embed_size, num_hiddens, num_layers, dropout)
        self.apply(init_seq2seq)

    def forward(self, X, *args):
        # X shape: (batch_size, num_steps)
        embs = self.embedding(d2l.astype(d2l.transpose(X), d2l.int64))
        # embs shape: (num_steps, batch_size, embed_size)
        output, state = self.rnn(embs)
        # output shape: (num_steps, batch_size, num_hiddens)
        # state shape: (num_layers, batch_size, num_hiddens)
        return output, state

class Seq2Seq(d2l.EncoderDecoder):
    """Defined in :numref:`sec_seq2seq_decoder`"""
    def __init__(self, encoder, decoder, tgt_pad, lr):
        super().__init__(encoder, decoder)
        self.save_hyperparameters()

    def validation_step(self, batch):
        Y_hat = self(*batch[:-1])
        self.plot('loss', self.loss(Y_hat, batch[-1]), train=False)

    def configure_optimizers(self):
        # Adam optimizer is used here
        return torch.optim.Adam(self.parameters(), lr=self.lr)

def bleu(pred_seq, label_seq, k):
    """Compute the BLEU.

    Defined in :numref:`sec_seq2seq_training`"""
    pred_tokens, label_tokens = pred_seq.split(' '), label_seq.split(' ')
    len_pred, len_label = len(pred_tokens), len(label_tokens)
    score = math.exp(min(0, 1 - len_label / len_pred))
    for n in range(1, min(k, len_pred) + 1):
        num_matches, label_subs = 0, collections.defaultdict(int)
        for i in range(len_label - n + 1):
            label_subs[' '.join(label_tokens[i: i + n])] += 1
        for i in range(len_pred - n + 1):
            if label_subs[' '.join(pred_tokens[i: i + n])] > 0:
                num_matches += 1
                label_subs[' '.join(pred_tokens[i: i + n])] -= 1
        score *= math.pow(num_matches / (len_pred - n + 1), math.pow(0.5, n))
    return score

def show_heatmaps(matrices, xlabel, ylabel, titles=None, figsize=(2.5, 2.5),
                  cmap='Reds'):
    """Show heatmaps of matrices.

    Defined in :numref:`sec_queries-keys-values`"""
    d2l.use_svg_display()
    num_rows, num_cols, _, _ = matrices.shape
    fig, axes = d2l.plt.subplots(num_rows, num_cols, figsize=figsize,
                                 sharex=True, sharey=True, squeeze=False)
    for i, (row_axes, row_matrices) in enumerate(zip(axes, matrices)):
        for j, (ax, matrix) in enumerate(zip(row_axes, row_matrices)):
            pcm = ax.imshow(d2l.numpy(matrix), cmap=cmap)
            if i == num_rows - 1:
                ax.set_xlabel(xlabel)
            if j == 0:
                ax.set_ylabel(ylabel)
            if titles:
                ax.set_title(titles[j])
    fig.colorbar(pcm, ax=axes, shrink=0.6);

def masked_softmax(X, valid_lens):
    """Perform softmax operation by masking elements on the last axis.

    Defined in :numref:`sec_attention-scoring-functions`"""
    # X: 3D tensor, valid_lens: 1D or 2D tensor
    def _sequence_mask(X, valid_len, value=0):
        maxlen = X.size(1)
        mask = torch.arange((maxlen), dtype=torch.float32,
                            device=X.device)[None, :] < valid_len[:, None]
        X[~mask] = value
        return X

    if valid_lens is None:
        return nn.functional.softmax(X, dim=-1)
    else:
        shape = X.shape
        if valid_lens.dim() == 1:
            valid_lens = torch.repeat_interleave(valid_lens, shape[1])
        else:
            valid_lens = valid_lens.reshape(-1)
        # On the last axis, replace masked elements with a very large negative
        # value, whose exponentiation outputs 0
        X = _sequence_mask(X.reshape(-1, shape[-1]), valid_lens, value=-1e6)
        return nn.functional.softmax(X.reshape(shape), dim=-1)

class DotProductAttention(nn.Module):
    """Scaled dot product attention.

    Defined in :numref:`subsec_batch_dot`"""
    def __init__(self, dropout, num_heads=None):
        super().__init__()
        self.dropout = nn.Dropout(dropout)
        self.num_heads = num_heads  # To be covered later

    # Shape of queries: (batch_size, no. of queries, d)
    # Shape of keys: (batch_size, no. of key-value pairs, d)
    # Shape of values: (batch_size, no. of key-value pairs, value dimension)
    # Shape of valid_lens: (batch_size,) or (batch_size, no. of queries)
    def forward(self, queries, keys, values, valid_lens=None,
                window_mask=None):
        d = queries.shape[-1]
        # Swap the last two dimensions of keys with keys.transpose(1, 2)
        scores = torch.bmm(queries, keys.transpose(1, 2)) / math.sqrt(d)
        if window_mask is not None:  # To be covered later
            num_windows = window_mask.shape[0]
            n, num_queries, num_kv_pairs = scores.shape
            # Shape of window_mask: (num_windows, no. of queries,
            # no. of key-value pairs)
            scores = d2l.reshape(
                scores, (n//(num_windows*self.num_heads), num_windows,
                         self.num_heads, num_queries, num_kv_pairs
                        )) + d2l.expand_dims(
                d2l.expand_dims(window_mask, 1), 0)
            scores = d2l.reshape(scores, (n, num_queries, num_kv_pairs))
        self.attention_weights = masked_softmax(scores, valid_lens)
        return torch.bmm(self.dropout(self.attention_weights), values)

class AdditiveAttention(nn.Module):
    """Additive attention.

    Defined in :numref:`subsec_batch_dot`"""
    def __init__(self, num_hiddens, dropout, **kwargs):
        super(AdditiveAttention, self).__init__(**kwargs)
        self.W_k = nn.LazyLinear(num_hiddens, bias=False)
        self.W_q = nn.LazyLinear(num_hiddens, bias=False)
        self.w_v = nn.LazyLinear(1, bias=False)
        self.dropout = nn.Dropout(dropout)

    def forward(self, queries, keys, values, valid_lens):
        queries, keys = self.W_q(queries), self.W_k(keys)
        # After dimension expansion, shape of queries: (batch_size, no. of
        # queries, 1, num_hiddens) and shape of keys: (batch_size, 1, no. of
        # key-value pairs, num_hiddens). Sum them up with broadcasting
        features = queries.unsqueeze(2) + keys.unsqueeze(1)
        features = torch.tanh(features)
        # There is only one output of self.w_v, so we remove the last
        # one-dimensional entry from the shape. Shape of scores: (batch_size,
        # no. of queries, no. of key-value pairs)
        scores = self.w_v(features).squeeze(-1)
        self.attention_weights = masked_softmax(scores, valid_lens)
        # Shape of values: (batch_size, no. of key-value pairs, value
        # dimension)
        return torch.bmm(self.dropout(self.attention_weights), values)

class AttentionDecoder(d2l.Decoder):
    """The base attention-based decoder interface.

    Defined in :numref:`sec_seq2seq_attention`"""
    def __init__(self):
        super().__init__()

    @property
    def attention_weights(self):
        raise NotImplementedError

class MultiHeadAttention(d2l.Module):
    """Multi-head attention.

    Defined in :numref:`sec_multihead-attention`"""
    def __init__(self, num_hiddens, num_heads, dropout, bias=False, **kwargs):
        super().__init__()
        self.num_heads = num_heads
        self.attention = d2l.DotProductAttention(dropout, num_heads)
        self.W_q = nn.LazyLinear(num_hiddens, bias=bias)
        self.W_k = nn.LazyLinear(num_hiddens, bias=bias)
        self.W_v = nn.LazyLinear(num_hiddens, bias=bias)
        self.W_o = nn.LazyLinear(num_hiddens, bias=bias)

    def forward(self, queries, keys, values, valid_lens, window_mask=None):
        # Shape of queries, keys, or values:
        # (batch_size, no. of queries or key-value pairs, num_hiddens)
        # Shape of valid_lens: (batch_size,) or (batch_size, no. of queries)
        # After transposing, shape of output queries, keys, or values:
        # (batch_size * num_heads, no. of queries or key-value pairs,
        # num_hiddens / num_heads)
        queries = self.transpose_qkv(self.W_q(queries))
        keys = self.transpose_qkv(self.W_k(keys))
        values = self.transpose_qkv(self.W_v(values))

        if valid_lens is not None:
            # On axis 0, copy the first item (scalar or vector) for num_heads
            # times, then copy the next item, and so on
            valid_lens = torch.repeat_interleave(
                valid_lens, repeats=self.num_heads, dim=0)

        # Shape of output: (batch_size * num_heads, no. of queries,
        # num_hiddens / num_heads)
        output = self.attention(queries, keys, values, valid_lens,
                                window_mask)
        # Shape of output_concat: (batch_size, no. of queries, num_hiddens)
        output_concat = self.transpose_output(output)
        return self.W_o(output_concat)

    def transpose_qkv(self, X):
        """Transposition for parallel computation of multiple attention heads.
    
        Defined in :numref:`sec_multihead-attention`"""
        # Shape of input X: (batch_size, no. of queries or key-value pairs,
        # num_hiddens). Shape of output X: (batch_size, no. of queries or
        # key-value pairs, num_heads, num_hiddens / num_heads)
        X = X.reshape(X.shape[0], X.shape[1], self.num_heads, -1)
        # Shape of output X: (batch_size, num_heads, no. of queries or key-value
        # pairs, num_hiddens / num_heads)
        X = X.permute(0, 2, 1, 3)
        # Shape of output: (batch_size * num_heads, no. of queries or key-value
        # pairs, num_hiddens / num_heads)
        return X.reshape(-1, X.shape[2], X.shape[3])
    

    def transpose_output(self, X):
        """Reverse the operation of transpose_qkv.
    
        Defined in :numref:`sec_multihead-attention`"""
        X = X.reshape(-1, self.num_heads, X.shape[1], X.shape[2])
        X = X.permute(0, 2, 1, 3)
        return X.reshape(X.shape[0], X.shape[1], -1)

class PositionalEncoding(nn.Module):
    """Positional encoding.

    Defined in :numref:`sec_self-attention-and-positional-encoding`"""
    def __init__(self, num_hiddens, dropout, max_len=1000):
        super().__init__()
        self.dropout = nn.Dropout(dropout)
        # Create a long enough P
        self.P = d2l.zeros((1, max_len, num_hiddens))
        X = d2l.arange(max_len, dtype=torch.float32).reshape(
            -1, 1) / torch.pow(10000, torch.arange(
            0, num_hiddens, 2, dtype=torch.float32) / num_hiddens)
        self.P[:, :, 0::2] = torch.sin(X)
        self.P[:, :, 1::2] = torch.cos(X)

    def forward(self, X):
        X = X + self.P[:, :X.shape[1], :].to(X.device)
        return self.dropout(X)

class PositionWiseFFN(nn.Module):
    """Positionwise feed-forward network.

    Defined in :numref:`sec_transformer`"""
    def __init__(self, ffn_num_hiddens, ffn_num_outputs):
        super().__init__()
        self.dense1 = nn.LazyLinear(ffn_num_hiddens)
        self.relu = nn.ReLU()
        self.dense2 = nn.LazyLinear(ffn_num_outputs)

    def forward(self, X):
        return self.dense2(self.relu(self.dense1(X)))

class AddNorm(nn.Module):
    """Residual connection followed by layer normalization.

    Defined in :numref:`subsec_positionwise-ffn`"""
    def __init__(self, norm_shape, dropout):
        super().__init__()
        self.dropout = nn.Dropout(dropout)
        self.ln = nn.LayerNorm(norm_shape)

    def forward(self, X, Y):
        return self.ln(self.dropout(Y) + X)

class TransformerEncoderBlock(nn.Module):
    """Transformer encoder block.

    Defined in :numref:`subsec_positionwise-ffn`"""
    def __init__(self, num_hiddens, ffn_num_hiddens, num_heads, dropout,
                 use_bias=False):
        super().__init__()
        self.attention = d2l.MultiHeadAttention(num_hiddens, num_heads,
                                                dropout, use_bias)
        self.addnorm1 = AddNorm(num_hiddens, dropout)
        self.ffn = PositionWiseFFN(ffn_num_hiddens, num_hiddens)
        self.addnorm2 = AddNorm(num_hiddens, dropout)

    def forward(self, X, valid_lens):
        Y = self.addnorm1(X, self.attention(X, X, X, valid_lens))
        return self.addnorm2(Y, self.ffn(Y))

class TransformerEncoder(d2l.Encoder):
    """Transformer encoder.

    Defined in :numref:`subsec_transformer-encoder`"""
    def __init__(self, vocab_size, num_hiddens, ffn_num_hiddens,
                 num_heads, num_blks, dropout, use_bias=False):
        super().__init__()
        self.num_hiddens = num_hiddens
        self.embedding = nn.Embedding(vocab_size, num_hiddens)
        self.pos_encoding = d2l.PositionalEncoding(num_hiddens, dropout)
        self.blks = nn.Sequential()
        for i in range(num_blks):
            self.blks.add_module("block"+str(i), TransformerEncoderBlock(
                num_hiddens, ffn_num_hiddens, num_heads, dropout, use_bias))

    def forward(self, X, valid_lens):
        # Since positional encoding values are between -1 and 1, the embedding
        # values are multiplied by the square root of the embedding dimension
        # to rescale before they are summed up
        X = self.pos_encoding(self.embedding(X) * math.sqrt(self.num_hiddens))
        self.attention_weights = [None] * len(self.blks)
        for i, blk in enumerate(self.blks):
            X = blk(X, valid_lens)
            self.attention_weights[
                i] = blk.attention.attention.attention_weights
        return X

def annotate(text, xy, xytext):
    d2l.plt.gca().annotate(text, xy=xy, xytext=xytext,
                           arrowprops=dict(arrowstyle='->'))

def train_2d(trainer, steps=20, f_grad=None):
    """Optimize a 2D objective function with a customized trainer.

    Defined in :numref:`subsec_gd-learningrate`"""
    # `s1` and `s2` are internal state variables that will be used in Momentum, adagrad, RMSProp
    x1, x2, s1, s2 = -5, -2, 0, 0
    results = [(x1, x2)]
    for i in range(steps):
        if f_grad:
            x1, x2, s1, s2 = trainer(x1, x2, s1, s2, f_grad)
        else:
            x1, x2, s1, s2 = trainer(x1, x2, s1, s2)
        results.append((x1, x2))
    print(f'epoch {i + 1}, x1: {float(x1):f}, x2: {float(x2):f}')
    return results

def show_trace_2d(f, results):
    """Show the trace of 2D variables during optimization.

    Defined in :numref:`subsec_gd-learningrate`"""
    d2l.set_figsize()
    d2l.plt.plot(*zip(*results), '-o', color='#ff7f0e')
    x1, x2 = d2l.meshgrid(d2l.arange(-5.5, 1.0, 0.1),
                          d2l.arange(-3.0, 1.0, 0.1))
    d2l.plt.contour(x1, x2, f(x1, x2), colors='#1f77b4')
    d2l.plt.xlabel('x1')
    d2l.plt.ylabel('x2')

class Timer:
    """Record multiple running times."""
    def __init__(self):
        """Defined in :numref:`sec_minibatch_sgd`"""
        self.times = []
        self.start()

    def start(self):
        """Start the timer."""
        self.tik = time.time()

    def stop(self):
        """Stop the timer and record the time in a list."""
        self.times.append(time.time() - self.tik)
        return self.times[-1]

    def avg(self):
        """Return the average time."""
        return sum(self.times) / len(self.times)

    def sum(self):
        """Return the sum of time."""
        return sum(self.times)

    def cumsum(self):
        """Return the accumulated time."""
        return np.array(self.times).cumsum().tolist()

d2l.DATA_HUB['airfoil'] = (d2l.DATA_URL + 'airfoil_self_noise.dat',
                           '76e5be1548fd8222e5074cf0faae75edff8cf93f')

def get_data_ch11(batch_size=10, n=1500):
    """Defined in :numref:`sec_minibatches`"""
    data = np.genfromtxt(d2l.download('airfoil'),
                         dtype=np.float32, delimiter='\t')
    data = torch.from_numpy((data - data.mean(axis=0)) / data.std(axis=0))
    data_iter = d2l.load_array((data[:n, :-1], data[:n, -1]),
                               batch_size, is_train=True)
    return data_iter, data.shape[1]-1

def train_ch11(trainer_fn, states, hyperparams, data_iter,
               feature_dim, num_epochs=2):
    """Defined in :numref:`sec_minibatches`"""
    # Initialization
    w = torch.normal(mean=0.0, std=0.01, size=(feature_dim, 1),
                     requires_grad=True)
    b = torch.zeros((1), requires_grad=True)
    net, loss = lambda X: d2l.linreg(X, w, b), d2l.squared_loss
    # Train
    animator = d2l.Animator(xlabel='epoch', ylabel='loss',
                            xlim=[0, num_epochs], ylim=[0.22, 0.35])
    n, timer = 0, d2l.Timer()
    for _ in range(num_epochs):
        for X, y in data_iter:
            l = loss(net(X), y).mean()
            l.backward()
            trainer_fn([w, b], states, hyperparams)
            n += X.shape[0]
            if n % 200 == 0:
                timer.stop()
                animator.add(n/X.shape[0]/len(data_iter),
                             (d2l.evaluate_loss(net, data_iter, loss),))
                timer.start()
    print(f'loss: {animator.Y[0][-1]:.3f}, {timer.sum()/num_epochs:.3f} sec/epoch')
    return timer.cumsum(), animator.Y[0]

def train_concise_ch11(trainer_fn, hyperparams, data_iter, num_epochs=4):
    """Defined in :numref:`sec_minibatches`"""
    # Initialization
    net = nn.Sequential(nn.Linear(5, 1))
    def init_weights(module):
        if type(module) == nn.Linear:
            torch.nn.init.normal_(module.weight, std=0.01)
    net.apply(init_weights)

    optimizer = trainer_fn(net.parameters(), **hyperparams)
    loss = nn.MSELoss(reduction='none')
    animator = d2l.Animator(xlabel='epoch', ylabel='loss',
                            xlim=[0, num_epochs], ylim=[0.22, 0.35])
    n, timer = 0, d2l.Timer()
    for _ in range(num_epochs):
        for X, y in data_iter:
            optimizer.zero_grad()
            out = net(X)
            y = y.reshape(out.shape)
            l = loss(out, y)
            l.mean().backward()
            optimizer.step()
            n += X.shape[0]
            if n % 200 == 0:
                timer.stop()
                # `MSELoss` computes squared error without the 1/2 factor
                animator.add(n/X.shape[0]/len(data_iter),
                             (d2l.evaluate_loss(net, data_iter, loss) / 2,))
                timer.start()
    print(f'loss: {animator.Y[0][-1]:.3f}, {timer.sum()/num_epochs:.3f} sec/epoch')

class Benchmark:
    """For measuring running time."""
    def __init__(self, description='Done'):
        """Defined in :numref:`sec_hybridize`"""
        self.description = description

    def __enter__(self):
        self.timer = d2l.Timer()
        return self

    def __exit__(self, *args):
        print(f'{self.description}: {self.timer.stop():.4f} sec')

def split_batch(X, y, devices):
    """Split `X` and `y` into multiple devices.

    Defined in :numref:`sec_multi_gpu`"""
    assert X.shape[0] == y.shape[0]
    return (nn.parallel.scatter(X, devices),
            nn.parallel.scatter(y, devices))

def resnet18(num_classes, in_channels=1):
    """A slightly modified ResNet-18 model.

    Defined in :numref:`sec_multi_gpu_concise`"""
    def resnet_block(in_channels, out_channels, num_residuals,
                     first_block=False):
        blk = []
        for i in range(num_residuals):
            if i == 0 and not first_block:
                blk.append(d2l.Residual(out_channels, use_1x1conv=True,
                                        strides=2))
            else:
                blk.append(d2l.Residual(out_channels))
        return nn.Sequential(*blk)

    # This model uses a smaller convolution kernel, stride, and padding and
    # removes the max-pooling layer
    net = nn.Sequential(
        nn.Conv2d(in_channels, 64, kernel_size=3, stride=1, padding=1),
        nn.BatchNorm2d(64),
        nn.ReLU())
    net.add_module("resnet_block1", resnet_block(64, 64, 2, first_block=True))
    net.add_module("resnet_block2", resnet_block(64, 128, 2))
    net.add_module("resnet_block3", resnet_block(128, 256, 2))
    net.add_module("resnet_block4", resnet_block(256, 512, 2))
    net.add_module("global_avg_pool", nn.AdaptiveAvgPool2d((1,1)))
    net.add_module("fc", nn.Sequential(nn.Flatten(),
                                       nn.Linear(512, num_classes)))
    return net

def train_batch_ch13(net, X, y, loss, trainer, devices):
    """Train for a minibatch with multiple GPUs (defined in Chapter 13).

    Defined in :numref:`sec_image_augmentation`"""
    if isinstance(X, list):
        # Required for BERT fine-tuning (to be covered later)
        X = [x.to(devices[0]) for x in X]
    else:
        X = X.to(devices[0])
    y = y.to(devices[0])
    net.train()
    trainer.zero_grad()
    pred = net(X)
    l = loss(pred, y)
    l.sum().backward()
    trainer.step()
    train_loss_sum = l.sum()
    train_acc_sum = d2l.accuracy(pred, y)
    return train_loss_sum, train_acc_sum

def train_ch13(net, train_iter, test_iter, loss, trainer, num_epochs,
               devices=d2l.try_all_gpus()):
    """Train a model with multiple GPUs (defined in Chapter 13).

    Defined in :numref:`sec_image_augmentation`"""
    timer, num_batches = d2l.Timer(), len(train_iter)
    animator = d2l.Animator(xlabel='epoch', xlim=[1, num_epochs], ylim=[0, 1],
                            legend=['train loss', 'train acc', 'test acc'])
    net = nn.DataParallel(net, device_ids=devices).to(devices[0])
    for epoch in range(num_epochs):
        # Sum of training loss, sum of training accuracy, no. of examples,
        # no. of predictions
        metric = d2l.Accumulator(4)
        for i, (features, labels) in enumerate(train_iter):
            timer.start()
            l, acc = train_batch_ch13(
                net, features, labels, loss, trainer, devices)
            metric.add(l, acc, labels.shape[0], labels.numel())
            timer.stop()
            if (i + 1) % (num_batches // 5) == 0 or i == num_batches - 1:
                animator.add(epoch + (i + 1) / num_batches,
                             (metric[0] / metric[2], metric[1] / metric[3],
                              None))
        test_acc = d2l.evaluate_accuracy_gpu(net, test_iter)
        animator.add(epoch + 1, (None, None, test_acc))
    print(f'loss {metric[0] / metric[2]:.3f}, train acc '
          f'{metric[1] / metric[3]:.3f}, test acc {test_acc:.3f}')
    print(f'{metric[2] * num_epochs / timer.sum():.1f} examples/sec on '
          f'{str(devices)}')

d2l.DATA_HUB['hotdog'] = (d2l.DATA_URL + 'hotdog.zip',
                         'fba480ffa8aa7e0febbb511d181409f899b9baa5')

def box_corner_to_center(boxes):
    """Convert from (upper-left, lower-right) to (center, width, height).

    Defined in :numref:`sec_bbox`"""
    x1, y1, x2, y2 = boxes[:, 0], boxes[:, 1], boxes[:, 2], boxes[:, 3]
    cx = (x1 + x2) / 2
    cy = (y1 + y2) / 2
    w = x2 - x1
    h = y2 - y1
    boxes = d2l.stack((cx, cy, w, h), axis=-1)
    return boxes

def box_center_to_corner(boxes):
    """Convert from (center, width, height) to (upper-left, lower-right).

    Defined in :numref:`sec_bbox`"""
    cx, cy, w, h = boxes[:, 0], boxes[:, 1], boxes[:, 2], boxes[:, 3]
    x1 = cx - 0.5 * w
    y1 = cy - 0.5 * h
    x2 = cx + 0.5 * w
    y2 = cy + 0.5 * h
    boxes = d2l.stack((x1, y1, x2, y2), axis=-1)
    return boxes

def bbox_to_rect(bbox, color):
    """Convert bounding box to matplotlib format.

    Defined in :numref:`sec_bbox`"""
    # Convert the bounding box (upper-left x, upper-left y, lower-right x,
    # lower-right y) format to the matplotlib format: ((upper-left x,
    # upper-left y), width, height)
    return d2l.plt.Rectangle(
        xy=(bbox[0], bbox[1]), width=bbox[2]-bbox[0], height=bbox[3]-bbox[1],
        fill=False, edgecolor=color, linewidth=2)

def multibox_prior(data, sizes, ratios):
    """Generate anchor boxes with different shapes centered on each pixel.

    Defined in :numref:`sec_anchor`"""
    in_height, in_width = data.shape[-2:]
    device, num_sizes, num_ratios = data.device, len(sizes), len(ratios)
    boxes_per_pixel = (num_sizes + num_ratios - 1)
    size_tensor = d2l.tensor(sizes, device=device)
    ratio_tensor = d2l.tensor(ratios, device=device)
    # Offsets are required to move the anchor to the center of a pixel. Since
    # a pixel has height=1 and width=1, we choose to offset our centers by 0.5
    offset_h, offset_w = 0.5, 0.5
    steps_h = 1.0 / in_height  # Scaled steps in y axis
    steps_w = 1.0 / in_width  # Scaled steps in x axis

    # Generate all center points for the anchor boxes
    center_h = (torch.arange(in_height, device=device) + offset_h) * steps_h
    center_w = (torch.arange(in_width, device=device) + offset_w) * steps_w
    shift_y, shift_x = torch.meshgrid(center_h, center_w, indexing='ij')
    shift_y, shift_x = shift_y.reshape(-1), shift_x.reshape(-1)

    # Generate `boxes_per_pixel` number of heights and widths that are later
    # used to create anchor box corner coordinates (xmin, xmax, ymin, ymax)
    w = torch.cat((size_tensor * torch.sqrt(ratio_tensor[0]),
                   sizes[0] * torch.sqrt(ratio_tensor[1:])))\
                   * in_height / in_width  # Handle rectangular inputs
    h = torch.cat((size_tensor / torch.sqrt(ratio_tensor[0]),
                   sizes[0] / torch.sqrt(ratio_tensor[1:])))
    # Divide by 2 to get half height and half width
    anchor_manipulations = torch.stack((-w, -h, w, h)).T.repeat(
                                        in_height * in_width, 1) / 2

    # Each center point will have `boxes_per_pixel` number of anchor boxes, so
    # generate a grid of all anchor box centers with `boxes_per_pixel` repeats
    out_grid = torch.stack([shift_x, shift_y, shift_x, shift_y],
                dim=1).repeat_interleave(boxes_per_pixel, dim=0)
    output = out_grid + anchor_manipulations
    return output.unsqueeze(0)

def show_bboxes(axes, bboxes, labels=None, colors=None):
    """Show bounding boxes.

    Defined in :numref:`sec_anchor`"""

    def make_list(obj, default_values=None):
        if obj is None:
            obj = default_values
        elif not isinstance(obj, (list, tuple)):
            obj = [obj]
        return obj

    labels = make_list(labels)
    colors = make_list(colors, ['b', 'g', 'r', 'm', 'c'])
    for i, bbox in enumerate(bboxes):
        color = colors[i % len(colors)]
        rect = d2l.bbox_to_rect(d2l.numpy(bbox), color)
        axes.add_patch(rect)
        if labels and len(labels) > i:
            text_color = 'k' if color == 'w' else 'w'
            axes.text(rect.xy[0], rect.xy[1], labels[i],
                      va='center', ha='center', fontsize=9, color=text_color,
                      bbox=dict(facecolor=color, lw=0))

def box_iou(boxes1, boxes2):
    """Compute pairwise IoU across two lists of anchor or bounding boxes.

    Defined in :numref:`sec_anchor`"""
    box_area = lambda boxes: ((boxes[:, 2] - boxes[:, 0]) *
                              (boxes[:, 3] - boxes[:, 1]))
    # Shape of `boxes1`, `boxes2`, `areas1`, `areas2`: (no. of boxes1, 4),
    # (no. of boxes2, 4), (no. of boxes1,), (no. of boxes2,)
    areas1 = box_area(boxes1)
    areas2 = box_area(boxes2)
    # Shape of `inter_upperlefts`, `inter_lowerrights`, `inters`: (no. of
    # boxes1, no. of boxes2, 2)
    inter_upperlefts = torch.max(boxes1[:, None, :2], boxes2[:, :2])
    inter_lowerrights = torch.min(boxes1[:, None, 2:], boxes2[:, 2:])
    inters = (inter_lowerrights - inter_upperlefts).clamp(min=0)
    # Shape of `inter_areas` and `union_areas`: (no. of boxes1, no. of boxes2)
    inter_areas = inters[:, :, 0] * inters[:, :, 1]
    union_areas = areas1[:, None] + areas2 - inter_areas
    return inter_areas / union_areas

def assign_anchor_to_bbox(ground_truth, anchors, device, iou_threshold=0.5):
    """Assign closest ground-truth bounding boxes to anchor boxes.

    Defined in :numref:`sec_anchor`"""
    num_anchors, num_gt_boxes = anchors.shape[0], ground_truth.shape[0]
    # Element x_ij in the i-th row and j-th column is the IoU of the anchor
    # box i and the ground-truth bounding box j
    jaccard = box_iou(anchors, ground_truth)
    # Initialize the tensor to hold the assigned ground-truth bounding box for
    # each anchor
    anchors_bbox_map = torch.full((num_anchors,), -1, dtype=torch.long,
                                  device=device)
    # Assign ground-truth bounding boxes according to the threshold
    max_ious, indices = torch.max(jaccard, dim=1)
    anc_i = torch.nonzero(max_ious >= iou_threshold).reshape(-1)
    box_j = indices[max_ious >= iou_threshold]
    anchors_bbox_map[anc_i] = box_j
    col_discard = torch.full((num_anchors,), -1)
    row_discard = torch.full((num_gt_boxes,), -1)
    for _ in range(num_gt_boxes):
        max_idx = torch.argmax(jaccard)  # Find the largest IoU
        box_idx = (max_idx % num_gt_boxes).long()
        anc_idx = (max_idx / num_gt_boxes).long()
        anchors_bbox_map[anc_idx] = box_idx
        jaccard[:, box_idx] = col_discard
        jaccard[anc_idx, :] = row_discard
    return anchors_bbox_map

def offset_boxes(anchors, assigned_bb, eps=1e-6):
    """Transform for anchor box offsets.

    Defined in :numref:`subsec_labeling-anchor-boxes`"""
    c_anc = d2l.box_corner_to_center(anchors)
    c_assigned_bb = d2l.box_corner_to_center(assigned_bb)
    offset_xy = 10 * (c_assigned_bb[:, :2] - c_anc[:, :2]) / c_anc[:, 2:]
    offset_wh = 5 * d2l.log(eps + c_assigned_bb[:, 2:] / c_anc[:, 2:])
    offset = d2l.concat([offset_xy, offset_wh], axis=1)
    return offset

def multibox_target(anchors, labels):
    """Label anchor boxes using ground-truth bounding boxes.

    Defined in :numref:`subsec_labeling-anchor-boxes`"""
    batch_size, anchors = labels.shape[0], anchors.squeeze(0)
    batch_offset, batch_mask, batch_class_labels = [], [], []
    device, num_anchors = anchors.device, anchors.shape[0]
    for i in range(batch_size):
        label = labels[i, :, :]
        anchors_bbox_map = assign_anchor_to_bbox(
            label[:, 1:], anchors, device)
        bbox_mask = ((anchors_bbox_map >= 0).float().unsqueeze(-1)).repeat(
            1, 4)
        # Initialize class labels and assigned bounding box coordinates with
        # zeros
        class_labels = torch.zeros(num_anchors, dtype=torch.long,
                                   device=device)
        assigned_bb = torch.zeros((num_anchors, 4), dtype=torch.float32,
                                  device=device)
        # Label classes of anchor boxes using their assigned ground-truth
        # bounding boxes. If an anchor box is not assigned any, we label its
        # class as background (the value remains zero)
        indices_true = torch.nonzero(anchors_bbox_map >= 0)
        bb_idx = anchors_bbox_map[indices_true]
        class_labels[indices_true] = label[bb_idx, 0].long() + 1
        assigned_bb[indices_true] = label[bb_idx, 1:]
        # Offset transformation
        offset = offset_boxes(anchors, assigned_bb) * bbox_mask
        batch_offset.append(offset.reshape(-1))
        batch_mask.append(bbox_mask.reshape(-1))
        batch_class_labels.append(class_labels)
    bbox_offset = torch.stack(batch_offset)
    bbox_mask = torch.stack(batch_mask)
    class_labels = torch.stack(batch_class_labels)
    return (bbox_offset, bbox_mask, class_labels)

def offset_inverse(anchors, offset_preds):
    """Predict bounding boxes based on anchor boxes with predicted offsets.

    Defined in :numref:`subsec_labeling-anchor-boxes`"""
    anc = d2l.box_corner_to_center(anchors)
    pred_bbox_xy = (offset_preds[:, :2] * anc[:, 2:] / 10) + anc[:, :2]
    pred_bbox_wh = d2l.exp(offset_preds[:, 2:] / 5) * anc[:, 2:]
    pred_bbox = d2l.concat((pred_bbox_xy, pred_bbox_wh), axis=1)
    predicted_bbox = d2l.box_center_to_corner(pred_bbox)
    return predicted_bbox

def nms(boxes, scores, iou_threshold):
    """Sort confidence scores of predicted bounding boxes.

    Defined in :numref:`subsec_predicting-bounding-boxes-nms`"""
    B = torch.argsort(scores, dim=-1, descending=True)
    keep = []  # Indices of predicted bounding boxes that will be kept
    while B.numel() > 0:
        i = B[0]
        keep.append(i)
        if B.numel() == 1: break
        iou = box_iou(boxes[i, :].reshape(-1, 4),
                      boxes[B[1:], :].reshape(-1, 4)).reshape(-1)
        inds = torch.nonzero(iou <= iou_threshold).reshape(-1)
        B = B[inds + 1]
    return d2l.tensor(keep, device=boxes.device)

def multibox_detection(cls_probs, offset_preds, anchors, nms_threshold=0.5,
                       pos_threshold=0.009999999):
    """Predict bounding boxes using non-maximum suppression.

    Defined in :numref:`subsec_predicting-bounding-boxes-nms`"""
    device, batch_size = cls_probs.device, cls_probs.shape[0]
    anchors = anchors.squeeze(0)
    num_classes, num_anchors = cls_probs.shape[1], cls_probs.shape[2]
    out = []
    for i in range(batch_size):
        cls_prob, offset_pred = cls_probs[i], offset_preds[i].reshape(-1, 4)
        conf, class_id = torch.max(cls_prob[1:], 0)
        predicted_bb = offset_inverse(anchors, offset_pred)
        keep = nms(predicted_bb, conf, nms_threshold)
        # Find all non-`keep` indices and set the class to background
        all_idx = torch.arange(num_anchors, dtype=torch.long, device=device)
        combined = torch.cat((keep, all_idx))
        uniques, counts = combined.unique(return_counts=True)
        non_keep = uniques[counts == 1]
        all_id_sorted = torch.cat((keep, non_keep))
        class_id[non_keep] = -1
        class_id = class_id[all_id_sorted]
        conf, predicted_bb = conf[all_id_sorted], predicted_bb[all_id_sorted]
        # Here `pos_threshold` is a threshold for positive (non-background)
        # predictions
        below_min_idx = (conf < pos_threshold)
        class_id[below_min_idx] = -1
        conf[below_min_idx] = 1 - conf[below_min_idx]
        pred_info = torch.cat((class_id.unsqueeze(1),
                               conf.unsqueeze(1),
                               predicted_bb), dim=1)
        out.append(pred_info)
    return d2l.stack(out)

d2l.DATA_HUB['banana-detection'] = (
    d2l.DATA_URL + 'banana-detection.zip',
    '5de26c8fce5ccdea9f91267273464dc968d20d72')

def read_data_bananas(is_train=True):
    """Read the banana detection dataset images and labels.

    Defined in :numref:`sec_object-detection-dataset`"""
    data_dir = d2l.download_extract('banana-detection')
    csv_fname = os.path.join(data_dir, 'bananas_train' if is_train
                             else 'bananas_val', 'label.csv')
    csv_data = pd.read_csv(csv_fname)
    csv_data = csv_data.set_index('img_name')
    images, targets = [], []
    for img_name, target in csv_data.iterrows():
        images.append(torchvision.io.read_image(
            os.path.join(data_dir, 'bananas_train' if is_train else
                         'bananas_val', 'images', f'{img_name}')))
        # Here `target` contains (class, upper-left x, upper-left y,
        # lower-right x, lower-right y), where all the images have the same
        # banana class (index 0)
        targets.append(list(target))
    return images, torch.tensor(targets).unsqueeze(1) / 256

class BananasDataset(torch.utils.data.Dataset):
    """A customized dataset to load the banana detection dataset.

    Defined in :numref:`sec_object-detection-dataset`"""
    def __init__(self, is_train):
        self.features, self.labels = read_data_bananas(is_train)
        print('read ' + str(len(self.features)) + (f' training examples' if
              is_train else f' validation examples'))

    def __getitem__(self, idx):
        return (self.features[idx].float(), self.labels[idx])

    def __len__(self):
        return len(self.features)

def load_data_bananas(batch_size):
    """Load the banana detection dataset.

    Defined in :numref:`sec_object-detection-dataset`"""
    train_iter = torch.utils.data.DataLoader(BananasDataset(is_train=True),
                                             batch_size, shuffle=True)
    val_iter = torch.utils.data.DataLoader(BananasDataset(is_train=False),
                                           batch_size)
    return train_iter, val_iter

d2l.DATA_HUB['voc2012'] = (d2l.DATA_URL + 'VOCtrainval_11-May-2012.tar',
                           '4e443f8a2eca6b1dac8a6c57641b67dd40621a49')

def read_voc_images(voc_dir, is_train=True):
    """Read all VOC feature and label images.

    Defined in :numref:`sec_semantic_segmentation`"""
    txt_fname = os.path.join(voc_dir, 'ImageSets', 'Segmentation',
                             'train.txt' if is_train else 'val.txt')
    mode = torchvision.io.image.ImageReadMode.RGB
    with open(txt_fname, 'r') as f:
        images = f.read().split()
    features, labels = [], []
    for i, fname in enumerate(images):
        features.append(torchvision.io.read_image(os.path.join(
            voc_dir, 'JPEGImages', f'{fname}.jpg')))
        labels.append(torchvision.io.read_image(os.path.join(
            voc_dir, 'SegmentationClass' ,f'{fname}.png'), mode))
    return features, labels

VOC_COLORMAP = [[0, 0, 0], [128, 0, 0], [0, 128, 0], [128, 128, 0],
                [0, 0, 128], [128, 0, 128], [0, 128, 128], [128, 128, 128],
                [64, 0, 0], [192, 0, 0], [64, 128, 0], [192, 128, 0],
                [64, 0, 128], [192, 0, 128], [64, 128, 128], [192, 128, 128],
                [0, 64, 0], [128, 64, 0], [0, 192, 0], [128, 192, 0],
                [0, 64, 128]]

VOC_CLASSES = ['background', 'aeroplane', 'bicycle', 'bird', 'boat',
               'bottle', 'bus', 'car', 'cat', 'chair', 'cow',
               'diningtable', 'dog', 'horse', 'motorbike', 'person',
               'potted plant', 'sheep', 'sofa', 'train', 'tv/monitor']

def voc_colormap2label():
    """Build the mapping from RGB to class indices for VOC labels.

    Defined in :numref:`sec_semantic_segmentation`"""
    colormap2label = torch.zeros(256 ** 3, dtype=torch.long)
    for i, colormap in enumerate(VOC_COLORMAP):
        colormap2label[
            (colormap[0] * 256 + colormap[1]) * 256 + colormap[2]] = i
    return colormap2label

def voc_label_indices(colormap, colormap2label):
    """Map any RGB values in VOC labels to their class indices.

    Defined in :numref:`sec_semantic_segmentation`"""
    colormap = colormap.permute(1, 2, 0).numpy().astype('int32')
    idx = ((colormap[:, :, 0] * 256 + colormap[:, :, 1]) * 256
           + colormap[:, :, 2])
    return colormap2label[idx]

def voc_rand_crop(feature, label, height, width):
    """Randomly crop both feature and label images.

    Defined in :numref:`sec_semantic_segmentation`"""
    rect = torchvision.transforms.RandomCrop.get_params(
        feature, (height, width))
    feature = torchvision.transforms.functional.crop(feature, *rect)
    label = torchvision.transforms.functional.crop(label, *rect)
    return feature, label

class VOCSegDataset(torch.utils.data.Dataset):
    """A customized dataset to load the VOC dataset.

    Defined in :numref:`sec_semantic_segmentation`"""

    def __init__(self, is_train, crop_size, voc_dir):
        self.transform = torchvision.transforms.Normalize(
            mean=[0.485, 0.456, 0.406], std=[0.229, 0.224, 0.225])
        self.crop_size = crop_size
        features, labels = read_voc_images(voc_dir, is_train=is_train)
        self.features = [self.normalize_image(feature)
                         for feature in self.filter(features)]
        self.labels = self.filter(labels)
        self.colormap2label = voc_colormap2label()
        print('read ' + str(len(self.features)) + ' examples')

    def normalize_image(self, img):
        return self.transform(img.float() / 255)

    def filter(self, imgs):
        return [img for img in imgs if (
            img.shape[1] >= self.crop_size[0] and
            img.shape[2] >= self.crop_size[1])]

    def __getitem__(self, idx):
        feature, label = voc_rand_crop(self.features[idx], self.labels[idx],
                                       *self.crop_size)
        return (feature, voc_label_indices(label, self.colormap2label))

    def __len__(self):
        return len(self.features)

def load_data_voc(batch_size, crop_size):
    """Load the VOC semantic segmentation dataset.

    Defined in :numref:`sec_semantic_segmentation`"""
    voc_dir = d2l.download_extract('voc2012', os.path.join(
        'VOCdevkit', 'VOC2012'))
    num_workers = d2l.get_dataloader_workers()
    train_iter = torch.utils.data.DataLoader(
        VOCSegDataset(True, crop_size, voc_dir), batch_size,
        shuffle=True, drop_last=True, num_workers=num_workers)
    test_iter = torch.utils.data.DataLoader(
        VOCSegDataset(False, crop_size, voc_dir), batch_size,
        drop_last=True, num_workers=num_workers)
    return train_iter, test_iter

d2l.DATA_HUB['cifar10_tiny'] = (d2l.DATA_URL + 'kaggle_cifar10_tiny.zip',
                                '2068874e4b9a9f0fb07ebe0ad2b29754449ccacd')

def read_csv_labels(fname):
    """Read `fname` to return a filename to label dictionary.

    Defined in :numref:`sec_kaggle_cifar10`"""
    with open(fname, 'r') as f:
        # Skip the file header line (column name)
        lines = f.readlines()[1:]
    tokens = [l.rstrip().split(',') for l in lines]
    return dict(((name, label) for name, label in tokens))

def copyfile(filename, target_dir):
    """Copy a file into a target directory.

    Defined in :numref:`sec_kaggle_cifar10`"""
    os.makedirs(target_dir, exist_ok=True)
    shutil.copy(filename, target_dir)

def reorg_train_valid(data_dir, labels, valid_ratio):
    """Split the validation set out of the original training set.

    Defined in :numref:`sec_kaggle_cifar10`"""
    # The number of examples of the class that has the fewest examples in the
    # training dataset
    n = collections.Counter(labels.values()).most_common()[-1][1]
    # The number of examples per class for the validation set
    n_valid_per_label = max(1, math.floor(n * valid_ratio))
    label_count = {}
    for train_file in os.listdir(os.path.join(data_dir, 'train')):
        label = labels[train_file.split('.')[0]]
        fname = os.path.join(data_dir, 'train', train_file)
        copyfile(fname, os.path.join(data_dir, 'train_valid_test',
                                     'train_valid', label))
        if label not in label_count or label_count[label] < n_valid_per_label:
            copyfile(fname, os.path.join(data_dir, 'train_valid_test',
                                         'valid', label))
            label_count[label] = label_count.get(label, 0) + 1
        else:
            copyfile(fname, os.path.join(data_dir, 'train_valid_test',
                                         'train', label))
    return n_valid_per_label

def reorg_test(data_dir):
    """Organize the testing set for data loading during prediction.

    Defined in :numref:`sec_kaggle_cifar10`"""
    for test_file in os.listdir(os.path.join(data_dir, 'test')):
        copyfile(os.path.join(data_dir, 'test', test_file),
                 os.path.join(data_dir, 'train_valid_test', 'test',
                              'unknown'))

d2l.DATA_HUB['dog_tiny'] = (d2l.DATA_URL + 'kaggle_dog_tiny.zip',
                            '0cb91d09b814ecdc07b50f31f8dcad3e81d6a86d')

d2l.DATA_HUB['ptb'] = (d2l.DATA_URL + 'ptb.zip',
                       '319d85e578af0cdc590547f26231e4e31cdf1e42')

def read_ptb():
    """Load the PTB dataset into a list of text lines.

    Defined in :numref:`sec_word2vec_data`"""
    data_dir = d2l.download_extract('ptb')
    # Read the training set
    with open(os.path.join(data_dir, 'ptb.train.txt')) as f:
        raw_text = f.read()
    return [line.split() for line in raw_text.split('\n')]

def subsample(sentences, vocab):
    """Subsample high-frequency words.

    Defined in :numref:`sec_word2vec_data`"""
    # Exclude unknown tokens ('<unk>')
    sentences = [[token for token in line if vocab[token] != vocab.unk]
                 for line in sentences]
    counter = collections.Counter([
        token for line in sentences for token in line])
    num_tokens = sum(counter.values())

    # Return True if `token` is kept during subsampling
    def keep(token):
        return(random.uniform(0, 1) <
               math.sqrt(1e-4 / counter[token] * num_tokens))

    return ([[token for token in line if keep(token)] for line in sentences],
            counter)

def get_centers_and_contexts(corpus, max_window_size):
    """Return center words and context words in skip-gram.

    Defined in :numref:`sec_word2vec_data`"""
    centers, contexts = [], []
    for line in corpus:
        # To form a "center word--context word" pair, each sentence needs to
        # have at least 2 words
        if len(line) < 2:
            continue
        centers += line
        for i in range(len(line)):  # Context window centered at `i`
            window_size = random.randint(1, max_window_size)
            indices = list(range(max(0, i - window_size),
                                 min(len(line), i + 1 + window_size)))
            # Exclude the center word from the context words
            indices.remove(i)
            contexts.append([line[idx] for idx in indices])
    return centers, contexts

class RandomGenerator:
    """Randomly draw among {1, ..., n} according to n sampling weights."""
    def __init__(self, sampling_weights):
        """Defined in :numref:`sec_word2vec_data`"""
        # Exclude
        self.population = list(range(1, len(sampling_weights) + 1))
        self.sampling_weights = sampling_weights
        self.candidates = []
        self.i = 0

    def draw(self):
        if self.i == len(self.candidates):
            # Cache `k` random sampling results
            self.candidates = random.choices(
                self.population, self.sampling_weights, k=10000)
            self.i = 0
        self.i += 1
        return self.candidates[self.i - 1]

def get_negatives(all_contexts, vocab, counter, K):
    """Return noise words in negative sampling.

    Defined in :numref:`sec_word2vec_data`"""
    # Sampling weights for words with indices 1, 2, ... (index 0 is the
    # excluded unknown token) in the vocabulary
    sampling_weights = [counter[vocab.to_tokens(i)]**0.75
                        for i in range(1, len(vocab))]
    all_negatives, generator = [], RandomGenerator(sampling_weights)
    for contexts in all_contexts:
        negatives = []
        while len(negatives) < len(contexts) * K:
            neg = generator.draw()
            # Noise words cannot be context words
            if neg not in contexts:
                negatives.append(neg)
        all_negatives.append(negatives)
    return all_negatives

def batchify(data):
    """Return a minibatch of examples for skip-gram with negative sampling.

    Defined in :numref:`sec_word2vec_data`"""
    max_len = max(len(c) + len(n) for _, c, n in data)
    centers, contexts_negatives, masks, labels = [], [], [], []
    for center, context, negative in data:
        cur_len = len(context) + len(negative)
        centers += [center]
        contexts_negatives += [context + negative + [0] * (max_len - cur_len)]
        masks += [[1] * cur_len + [0] * (max_len - cur_len)]
        labels += [[1] * len(context) + [0] * (max_len - len(context))]
    return (d2l.reshape(d2l.tensor(centers), (-1, 1)), d2l.tensor(
        contexts_negatives), d2l.tensor(masks), d2l.tensor(labels))

def load_data_ptb(batch_size, max_window_size, num_noise_words):
    """Download the PTB dataset and then load it into memory.

    Defined in :numref:`subsec_word2vec-minibatch-loading`"""
    num_workers = d2l.get_dataloader_workers()
    sentences = read_ptb()
    vocab = d2l.Vocab(sentences, min_freq=10)
    subsampled, counter = subsample(sentences, vocab)
    corpus = [vocab[line] for line in subsampled]
    all_centers, all_contexts = get_centers_and_contexts(
        corpus, max_window_size)
    all_negatives = get_negatives(
        all_contexts, vocab, counter, num_noise_words)

    class PTBDataset(torch.utils.data.Dataset):
        def __init__(self, centers, contexts, negatives):
            assert len(centers) == len(contexts) == len(negatives)
            self.centers = centers
            self.contexts = contexts
            self.negatives = negatives

        def __getitem__(self, index):
            return (self.centers[index], self.contexts[index],
                    self.negatives[index])

        def __len__(self):
            return len(self.centers)

    dataset = PTBDataset(all_centers, all_contexts, all_negatives)

    data_iter = torch.utils.data.DataLoader(dataset, batch_size, shuffle=True,
                                      collate_fn=batchify,
                                      num_workers=num_workers)
    return data_iter, vocab

d2l.DATA_HUB['glove.6b.50d'] = (d2l.DATA_URL + 'glove.6B.50d.zip',
                                '0b8703943ccdb6eb788e6f091b8946e82231bc4d')

d2l.DATA_HUB['glove.6b.100d'] = (d2l.DATA_URL + 'glove.6B.100d.zip',
                                 'cd43bfb07e44e6f27cbcc7bc9ae3d80284fdaf5a')

d2l.DATA_HUB['glove.42b.300d'] = (d2l.DATA_URL + 'glove.42B.300d.zip',
                                  'b5116e234e9eb9076672cfeabf5469f3eec904fa')

d2l.DATA_HUB['wiki.en'] = (d2l.DATA_URL + 'wiki.en.zip',
                           'c1816da3821ae9f43899be655002f6c723e91b88')

class TokenEmbedding:
    """Token Embedding."""
    def __init__(self, embedding_name):
        """Defined in :numref:`sec_synonyms`"""
        self.idx_to_token, self.idx_to_vec = self._load_embedding(
            embedding_name)
        self.unknown_idx = 0
        self.token_to_idx = {token: idx for idx, token in
                             enumerate(self.idx_to_token)}

    def _load_embedding(self, embedding_name):
        idx_to_token, idx_to_vec = ['<unk>'], []
        data_dir = d2l.download_extract(embedding_name)
        # GloVe website: https://nlp.stanford.edu/projects/glove/
        # fastText website: https://fasttext.cc/
        with open(os.path.join(data_dir, 'vec.txt'), 'r') as f:
            for line in f:
                elems = line.rstrip().split(' ')
                token, elems = elems[0], [float(elem) for elem in elems[1:]]
                # Skip header information, such as the top row in fastText
                if len(elems) > 1:
                    idx_to_token.append(token)
                    idx_to_vec.append(elems)
        idx_to_vec = [[0] * len(idx_to_vec[0])] + idx_to_vec
        return idx_to_token, d2l.tensor(idx_to_vec)

    def __getitem__(self, tokens):
        indices = [self.token_to_idx.get(token, self.unknown_idx)
                   for token in tokens]
        vecs = self.idx_to_vec[d2l.tensor(indices)]
        return vecs

    def __len__(self):
        return len(self.idx_to_token)

def get_tokens_and_segments(tokens_a, tokens_b=None):
    """Get tokens of the BERT input sequence and their segment IDs.

    Defined in :numref:`sec_bert`"""
    tokens = ['<cls>'] + tokens_a + ['<sep>']
    # 0 and 1 are marking segment A and B, respectively
    segments = [0] * (len(tokens_a) + 2)
    if tokens_b is not None:
        tokens += tokens_b + ['<sep>']
        segments += [1] * (len(tokens_b) + 1)
    return tokens, segments

class BERTEncoder(nn.Module):
    """BERT encoder.

    Defined in :numref:`subsec_bert_input_rep`"""
    def __init__(self, vocab_size, num_hiddens, ffn_num_hiddens, num_heads,
                 num_blks, dropout, max_len=1000, **kwargs):
        super(BERTEncoder, self).__init__(**kwargs)
        self.token_embedding = nn.Embedding(vocab_size, num_hiddens)
        self.segment_embedding = nn.Embedding(2, num_hiddens)
        self.blks = nn.Sequential()
        for i in range(num_blks):
            self.blks.add_module(f"{i}", d2l.TransformerEncoderBlock(
                num_hiddens, ffn_num_hiddens, num_heads, dropout, True))
        # In BERT, positional embeddings are learnable, thus we create a
        # parameter of positional embeddings that are long enough
        self.pos_embedding = nn.Parameter(torch.randn(1, max_len,
                                                      num_hiddens))

    def forward(self, tokens, segments, valid_lens):
        # Shape of `X` remains unchanged in the following code snippet:
        # (batch size, max sequence length, `num_hiddens`)
        X = self.token_embedding(tokens) + self.segment_embedding(segments)
        X = X + self.pos_embedding[:, :X.shape[1], :]
        for blk in self.blks:
            X = blk(X, valid_lens)
        return X

class MaskLM(nn.Module):
    """The masked language model task of BERT.

    Defined in :numref:`subsec_bert_input_rep`"""
    def __init__(self, vocab_size, num_hiddens, **kwargs):
        super(MaskLM, self).__init__(**kwargs)
        self.mlp = nn.Sequential(nn.LazyLinear(num_hiddens),
                                 nn.ReLU(),
                                 nn.LayerNorm(num_hiddens),
                                 nn.LazyLinear(vocab_size))

    def forward(self, X, pred_positions):
        num_pred_positions = pred_positions.shape[1]
        pred_positions = pred_positions.reshape(-1)
        batch_size = X.shape[0]
        batch_idx = torch.arange(0, batch_size)
        # Suppose that `batch_size` = 2, `num_pred_positions` = 3, then
        # `batch_idx` is `torch.tensor([0, 0, 0, 1, 1, 1])`
        batch_idx = torch.repeat_interleave(batch_idx, num_pred_positions)
        masked_X = X[batch_idx, pred_positions]
        masked_X = masked_X.reshape((batch_size, num_pred_positions, -1))
        mlm_Y_hat = self.mlp(masked_X)
        return mlm_Y_hat

class NextSentencePred(nn.Module):
    """The next sentence prediction task of BERT.

    Defined in :numref:`subsec_mlm`"""
    def __init__(self, **kwargs):
        super(NextSentencePred, self).__init__(**kwargs)
        self.output = nn.LazyLinear(2)

    def forward(self, X):
        # `X` shape: (batch size, `num_hiddens`)
        return self.output(X)

class BERTModel(nn.Module):
    """The BERT model.

    Defined in :numref:`subsec_nsp`"""
    def __init__(self, vocab_size, num_hiddens, ffn_num_hiddens,
                 num_heads, num_blks, dropout, max_len=1000):
        super(BERTModel, self).__init__()
        self.encoder = BERTEncoder(vocab_size, num_hiddens, ffn_num_hiddens,
                                   num_heads, num_blks, dropout,
                                   max_len=max_len)
        self.hidden = nn.Sequential(nn.LazyLinear(num_hiddens),
                                    nn.Tanh())
        self.mlm = MaskLM(vocab_size, num_hiddens)
        self.nsp = NextSentencePred()

    def forward(self, tokens, segments, valid_lens=None, pred_positions=None):
        encoded_X = self.encoder(tokens, segments, valid_lens)
        if pred_positions is not None:
            mlm_Y_hat = self.mlm(encoded_X, pred_positions)
        else:
            mlm_Y_hat = None
        # The hidden layer of the MLP classifier for next sentence prediction.
        # 0 is the index of the '<cls>' token
        nsp_Y_hat = self.nsp(self.hidden(encoded_X[:, 0, :]))
        return encoded_X, mlm_Y_hat, nsp_Y_hat

d2l.DATA_HUB['wikitext-2'] = (
    'https://s3.amazonaws.com/research.metamind.io/wikitext/'
    'wikitext-2-v1.zip', '3c914d17d80b1459be871a5039ac23e752a53cbe')

def _read_wiki(data_dir):
    """Defined in :numref:`sec_bert-dataset`"""
    file_name = os.path.join(data_dir, 'wiki.train.tokens')
    with open(file_name, 'r') as f:
        lines = f.readlines()
    # Uppercase letters are converted to lowercase ones
    paragraphs = [line.strip().lower().split(' . ')
                  for line in lines if len(line.split(' . ')) >= 2]
    random.shuffle(paragraphs)
    return paragraphs

def _get_next_sentence(sentence, next_sentence, paragraphs):
    """Defined in :numref:`sec_bert-dataset`"""
    if random.random() < 0.5:
        is_next = True
    else:
        # `paragraphs` is a list of lists of lists
        next_sentence = random.choice(random.choice(paragraphs))
        is_next = False
    return sentence, next_sentence, is_next

def _get_nsp_data_from_paragraph(paragraph, paragraphs, vocab, max_len):
    """Defined in :numref:`sec_bert-dataset`"""
    nsp_data_from_paragraph = []
    for i in range(len(paragraph) - 1):
        tokens_a, tokens_b, is_next = _get_next_sentence(
            paragraph[i], paragraph[i + 1], paragraphs)
        # Consider 1 '<cls>' token and 2 '<sep>' tokens
        if len(tokens_a) + len(tokens_b) + 3 > max_len:
            continue
        tokens, segments = d2l.get_tokens_and_segments(tokens_a, tokens_b)
        nsp_data_from_paragraph.append((tokens, segments, is_next))
    return nsp_data_from_paragraph

def _replace_mlm_tokens(tokens, candidate_pred_positions, num_mlm_preds,
                        vocab):
    """Defined in :numref:`sec_bert-dataset`"""
    # For the input of a masked language model, make a new copy of tokens and
    # replace some of them by '<mask>' or random tokens
    mlm_input_tokens = [token for token in tokens]
    pred_positions_and_labels = []
    # Shuffle for getting 15% random tokens for prediction in the masked
    # language modeling task
    random.shuffle(candidate_pred_positions)
    for mlm_pred_position in candidate_pred_positions:
        if len(pred_positions_and_labels) >= num_mlm_preds:
            break
        masked_token = None
        # 80% of the time: replace the word with the '<mask>' token
        if random.random() < 0.8:
            masked_token = '<mask>'
        else:
            # 10% of the time: keep the word unchanged
            if random.random() < 0.5:
                masked_token = tokens[mlm_pred_position]
            # 10% of the time: replace the word with a random word
            else:
                masked_token = random.choice(vocab.idx_to_token)
        mlm_input_tokens[mlm_pred_position] = masked_token
        pred_positions_and_labels.append(
            (mlm_pred_position, tokens[mlm_pred_position]))
    return mlm_input_tokens, pred_positions_and_labels

def _get_mlm_data_from_tokens(tokens, vocab):
    """Defined in :numref:`subsec_prepare_mlm_data`"""
    candidate_pred_positions = []
    # `tokens` is a list of strings
    for i, token in enumerate(tokens):
        # Special tokens are not predicted in the masked language modeling
        # task
        if token in ['<cls>', '<sep>']:
            continue
        candidate_pred_positions.append(i)
    # 15% of random tokens are predicted in the masked language modeling task
    num_mlm_preds = max(1, round(len(tokens) * 0.15))
    mlm_input_tokens, pred_positions_and_labels = _replace_mlm_tokens(
        tokens, candidate_pred_positions, num_mlm_preds, vocab)
    pred_positions_and_labels = sorted(pred_positions_and_labels,
                                       key=lambda x: x[0])
    pred_positions = [v[0] for v in pred_positions_and_labels]
    mlm_pred_labels = [v[1] for v in pred_positions_and_labels]
    return vocab[mlm_input_tokens], pred_positions, vocab[mlm_pred_labels]

def _pad_bert_inputs(examples, max_len, vocab):
    """Defined in :numref:`subsec_prepare_mlm_data`"""
    max_num_mlm_preds = round(max_len * 0.15)
    all_token_ids, all_segments, valid_lens,  = [], [], []
    all_pred_positions, all_mlm_weights, all_mlm_labels = [], [], []
    nsp_labels = []
    for (token_ids, pred_positions, mlm_pred_label_ids, segments,
         is_next) in examples:
        all_token_ids.append(torch.tensor(token_ids + [vocab['<pad>']] * (
            max_len - len(token_ids)), dtype=torch.long))
        all_segments.append(torch.tensor(segments + [0] * (
            max_len - len(segments)), dtype=torch.long))
        # `valid_lens` excludes count of '<pad>' tokens
        valid_lens.append(torch.tensor(len(token_ids), dtype=torch.float32))
        all_pred_positions.append(torch.tensor(pred_positions + [0] * (
            max_num_mlm_preds - len(pred_positions)), dtype=torch.long))
        # Predictions of padded tokens will be filtered out in the loss via
        # multiplication of 0 weights
        all_mlm_weights.append(
            torch.tensor([1.0] * len(mlm_pred_label_ids) + [0.0] * (
                max_num_mlm_preds - len(pred_positions)),
                dtype=torch.float32))
        all_mlm_labels.append(torch.tensor(mlm_pred_label_ids + [0] * (
            max_num_mlm_preds - len(mlm_pred_label_ids)), dtype=torch.long))
        nsp_labels.append(torch.tensor(is_next, dtype=torch.long))
    return (all_token_ids, all_segments, valid_lens, all_pred_positions,
            all_mlm_weights, all_mlm_labels, nsp_labels)

class _WikiTextDataset(torch.utils.data.Dataset):
    """Defined in :numref:`subsec_prepare_mlm_data`"""
    def __init__(self, paragraphs, max_len):
        # Input `paragraphs[i]` is a list of sentence strings representing a
        # paragraph; while output `paragraphs[i]` is a list of sentences
        # representing a paragraph, where each sentence is a list of tokens
        paragraphs = [d2l.tokenize(
            paragraph, token='word') for paragraph in paragraphs]
        sentences = [sentence for paragraph in paragraphs
                     for sentence in paragraph]
        self.vocab = d2l.Vocab(sentences, min_freq=5, reserved_tokens=[
            '<pad>', '<mask>', '<cls>', '<sep>'])
        # Get data for the next sentence prediction task
        examples = []
        for paragraph in paragraphs:
            examples.extend(_get_nsp_data_from_paragraph(
                paragraph, paragraphs, self.vocab, max_len))
        # Get data for the masked language model task
        examples = [(_get_mlm_data_from_tokens(tokens, self.vocab)
                      + (segments, is_next))
                     for tokens, segments, is_next in examples]
        # Pad inputs
        (self.all_token_ids, self.all_segments, self.valid_lens,
         self.all_pred_positions, self.all_mlm_weights,
         self.all_mlm_labels, self.nsp_labels) = _pad_bert_inputs(
            examples, max_len, self.vocab)

    def __getitem__(self, idx):
        return (self.all_token_ids[idx], self.all_segments[idx],
                self.valid_lens[idx], self.all_pred_positions[idx],
                self.all_mlm_weights[idx], self.all_mlm_labels[idx],
                self.nsp_labels[idx])

    def __len__(self):
        return len(self.all_token_ids)

def load_data_wiki(batch_size, max_len):
    """Load the WikiText-2 dataset.

    Defined in :numref:`subsec_prepare_mlm_data`"""
    num_workers = d2l.get_dataloader_workers()
    data_dir = d2l.download_extract('wikitext-2', 'wikitext-2')
    paragraphs = _read_wiki(data_dir)
    train_set = _WikiTextDataset(paragraphs, max_len)
    train_iter = torch.utils.data.DataLoader(train_set, batch_size,
                                        shuffle=True, num_workers=num_workers)
    return train_iter, train_set.vocab

def _get_batch_loss_bert(net, loss, vocab_size, tokens_X,
                         segments_X, valid_lens_x,
                         pred_positions_X, mlm_weights_X,
                         mlm_Y, nsp_y):
    """Defined in :numref:`sec_bert-pretraining`"""
    # Forward pass
    _, mlm_Y_hat, nsp_Y_hat = net(tokens_X, segments_X,
                                  valid_lens_x.reshape(-1),
                                  pred_positions_X)
    # Compute masked language model loss
    mlm_l = loss(mlm_Y_hat.reshape(-1, vocab_size), mlm_Y.reshape(-1)) *\
    mlm_weights_X.reshape(-1, 1)
    mlm_l = mlm_l.sum() / (mlm_weights_X.sum() + 1e-8)
    # Compute next sentence prediction loss
    nsp_l = loss(nsp_Y_hat, nsp_y)
    l = mlm_l + nsp_l
    return mlm_l, nsp_l, l

d2l.DATA_HUB['aclImdb'] = (d2l.DATA_URL + 'aclImdb_v1.tar.gz',
                          '01ada507287d82875905620988597833ad4e0903')

def read_imdb(data_dir, is_train):
    """Read the IMDb review dataset text sequences and labels.

    Defined in :numref:`sec_sentiment`"""
    data, labels = [], []
    for label in ('pos', 'neg'):
        folder_name = os.path.join(data_dir, 'train' if is_train else 'test',
                                   label)
        for file in os.listdir(folder_name):
            with open(os.path.join(folder_name, file), 'rb') as f:
                review = f.read().decode('utf-8').replace('\n', '')
                data.append(review)
                labels.append(1 if label == 'pos' else 0)
    return data, labels

def load_data_imdb(batch_size, num_steps=500):
    """Return data iterators and the vocabulary of the IMDb review dataset.

    Defined in :numref:`sec_sentiment`"""
    data_dir = d2l.download_extract('aclImdb', 'aclImdb')
    train_data = read_imdb(data_dir, True)
    test_data = read_imdb(data_dir, False)
    train_tokens = d2l.tokenize(train_data[0], token='word')
    test_tokens = d2l.tokenize(test_data[0], token='word')
    vocab = d2l.Vocab(train_tokens, min_freq=5)
    train_features = torch.tensor([d2l.truncate_pad(
        vocab[line], num_steps, vocab['<pad>']) for line in train_tokens])
    test_features = torch.tensor([d2l.truncate_pad(
        vocab[line], num_steps, vocab['<pad>']) for line in test_tokens])
    train_iter = d2l.load_array((train_features, torch.tensor(train_data[1])),
                                batch_size)
    test_iter = d2l.load_array((test_features, torch.tensor(test_data[1])),
                               batch_size,
                               is_train=False)
    return train_iter, test_iter, vocab

def predict_sentiment(net, vocab, sequence):
    """Predict the sentiment of a text sequence.

    Defined in :numref:`sec_sentiment_rnn`"""
    sequence = torch.tensor(vocab[sequence.split()], device=d2l.try_gpu())
    label = torch.argmax(net(sequence.reshape(1, -1)), dim=1)
    return 'positive' if label == 1 else 'negative'

d2l.DATA_HUB['SNLI'] = (
    'https://nlp.stanford.edu/projects/snli/snli_1.0.zip',
    '9fcde07509c7e87ec61c640c1b2753d9041758e4')

def read_snli(data_dir, is_train):
    """Read the SNLI dataset into premises, hypotheses, and labels.

    Defined in :numref:`sec_natural-language-inference-and-dataset`"""
    def extract_text(s):
        # Remove information that will not be used by us
        s = re.sub('\\(', '', s)
        s = re.sub('\\)', '', s)
        # Substitute two or more consecutive whitespace with space
        s = re.sub('\\s{2,}', ' ', s)
        return s.strip()
    label_set = {'entailment': 0, 'contradiction': 1, 'neutral': 2}
    file_name = os.path.join(data_dir, 'snli_1.0_train.txt'
                             if is_train else 'snli_1.0_test.txt')
    with open(file_name, 'r') as f:
        rows = [row.split('\t') for row in f.readlines()[1:]]
    premises = [extract_text(row[1]) for row in rows if row[0] in label_set]
    hypotheses = [extract_text(row[2]) for row in rows if row[0] in label_set]
    labels = [label_set[row[0]] for row in rows if row[0] in label_set]
    return premises, hypotheses, labels

class SNLIDataset(torch.utils.data.Dataset):
    """A customized dataset to load the SNLI dataset.

    Defined in :numref:`sec_natural-language-inference-and-dataset`"""
    def __init__(self, dataset, num_steps, vocab=None):
        self.num_steps = num_steps
        all_premise_tokens = d2l.tokenize(dataset[0])
        all_hypothesis_tokens = d2l.tokenize(dataset[1])
        if vocab is None:
            self.vocab = d2l.Vocab(all_premise_tokens + all_hypothesis_tokens,
                                   min_freq=5, reserved_tokens=['<pad>'])
        else:
            self.vocab = vocab
        self.premises = self._pad(all_premise_tokens)
        self.hypotheses = self._pad(all_hypothesis_tokens)
        self.labels = torch.tensor(dataset[2])
        print('read ' + str(len(self.premises)) + ' examples')

    def _pad(self, lines):
        return torch.tensor([d2l.truncate_pad(
            self.vocab[line], self.num_steps, self.vocab['<pad>'])
                         for line in lines])

    def __getitem__(self, idx):
        return (self.premises[idx], self.hypotheses[idx]), self.labels[idx]

    def __len__(self):
        return len(self.premises)

def load_data_snli(batch_size, num_steps=50):
    """Download the SNLI dataset and return data iterators and vocabulary.

    Defined in :numref:`sec_natural-language-inference-and-dataset`"""
    num_workers = d2l.get_dataloader_workers()
    data_dir = d2l.download_extract('SNLI')
    train_data = read_snli(data_dir, True)
    test_data = read_snli(data_dir, False)
    train_set = SNLIDataset(train_data, num_steps)
    test_set = SNLIDataset(test_data, num_steps, train_set.vocab)
    train_iter = torch.utils.data.DataLoader(train_set, batch_size,
                                             shuffle=True,
                                             num_workers=num_workers)
    test_iter = torch.utils.data.DataLoader(test_set, batch_size,
                                            shuffle=False,
                                            num_workers=num_workers)
    return train_iter, test_iter, train_set.vocab

def predict_snli(net, vocab, premise, hypothesis):
    """Predict the logical relationship between the premise and hypothesis.

    Defined in :numref:`sec_natural-language-inference-attention`"""
    net.eval()
    premise = torch.tensor(vocab[premise], device=d2l.try_gpu())
    hypothesis = torch.tensor(vocab[hypothesis], device=d2l.try_gpu())
    label = torch.argmax(net([premise.reshape((1, -1)),
                           hypothesis.reshape((1, -1))]), dim=1)
    return 'entailment' if label == 0 else 'contradiction' if label == 1 \
            else 'neutral'

def rbfkernel(x1, x2, ls=4.):
    dist = distance_matrix(np.expand_dims(x1, 1), np.expand_dims(x2, 1))
    return np.exp(-(1. / ls / 2) * (dist ** 2))

class HPOTrainer(d2l.Trainer):
    """Defined in :numref:`sec_definition_hpo`"""
    def validation_error(self):
        self.model.eval()
        accuracy = 0
        val_batch_idx = 0
        for batch in self.val_dataloader:
            with torch.no_grad():
                x, y = self.prepare_batch(batch)
                y_hat = self.model(x)
                accuracy += self.model.accuracy(y_hat, y)
            val_batch_idx += 1
        return 1 -  accuracy / val_batch_idx

class HPOSearcher(d2l.HyperParameters):
    """Defined in :numref:`sec_api_hpo`"""
    def sample_configuration() -> dict:
        raise NotImplementedError

    def update(self, config: dict, error: float, additional_info=None):
        pass

class RandomSearcher(HPOSearcher):
    """Defined in :numref:`sec_api_hpo`"""
    def __init__(self, config_space: dict, initial_config=None):
        self.save_hyperparameters()

    def sample_configuration(self) -> dict:
        if self.initial_config is not None:
            result = self.initial_config
            self.initial_config = None
        else:
            result = {
                name: domain.rvs()
                for name, domain in self.config_space.items()
            }
        return result

class HPOScheduler(d2l.HyperParameters):
    """Defined in :numref:`sec_api_hpo`"""
    def suggest(self) -> dict:
        raise NotImplementedError

    def update(self, config: dict, error: float, info=None):
        raise NotImplementedError

class BasicScheduler(HPOScheduler):
    """Defined in :numref:`sec_api_hpo`"""
    def __init__(self, searcher: HPOSearcher):
        self.save_hyperparameters()

    def suggest(self) -> dict:
        return self.searcher.sample_configuration()

    def update(self, config: dict, error: float, info=None):
        self.searcher.update(config, error, additional_info=info)

class HPOTuner(d2l.HyperParameters):
    """Defined in :numref:`sec_api_hpo`"""
    def __init__(self, scheduler: HPOScheduler, objective: callable):
        self.save_hyperparameters()
        # Bookeeping results for plotting
        self.incumbent = None
        self.incumbent_error = None
        self.incumbent_trajectory = []
        self.cumulative_runtime = []
        self.current_runtime = 0
        self.records = []

    def run(self, number_of_trials):
        for i in range(number_of_trials):
            start_time = time.time()
            config = self.scheduler.suggest()
            print(f"Trial {i}: config = {config}")
            error = self.objective(**config)
            error = float(d2l.numpy(error.cpu()))
            self.scheduler.update(config, error)
            runtime = time.time() - start_time
            self.bookkeeping(config, error, runtime)
            print(f"    error = {error}, runtime = {runtime}")

    def bookkeeping(self, config: dict, error: float, runtime: float):
        """Defined in :numref:`sec_api_hpo`"""
        self.records.append({"config": config, "error": error, "runtime": runtime})
        # Check if the last hyperparameter configuration performs better
        # than the incumbent
        if self.incumbent is None or self.incumbent_error > error:
            self.incumbent = config
            self.incumbent_error = error
        # Add current best observed performance to the optimization trajectory
        self.incumbent_trajectory.append(self.incumbent_error)
        # Update runtime
        self.current_runtime += runtime
        self.cumulative_runtime.append(self.current_runtime)

def hpo_objective_lenet(learning_rate, batch_size, max_epochs=10):
    """Defined in :numref:`sec_api_hpo`"""
    model = d2l.LeNet(lr=learning_rate, num_classes=10)
    trainer = d2l.HPOTrainer(max_epochs=max_epochs, num_gpus=1)
    data = d2l.FashionMNIST(batch_size=batch_size)
    model.apply_init([next(iter(data.get_dataloader(True)))[0]], d2l.init_cnn)
    trainer.fit(model=model, data=data)
    validation_error = trainer.validation_error()
    return validation_error

class SuccessiveHalvingScheduler(d2l.HPOScheduler):
    """Defined in :numref:`sec_mf_hpo`"""
    def __init__(self, searcher, eta, r_min, r_max, prefact=1):
        self.save_hyperparameters()
        # Compute K, which is later used to determine the number of configurations
        self.K = int(np.log(r_max / r_min) / np.log(eta))
        # Define the rungs
        self.rung_levels = [r_min * eta ** k for k in range(self.K + 1)]
        if r_max not in self.rung_levels:
            # The final rung should be r_max
            self.rung_levels.append(r_max)
            self.K += 1
        # Bookkeeping
        self.observed_error_at_rungs = defaultdict(list)
        self.all_observed_error_at_rungs = defaultdict(list)
        # Our processing queue
        self.queue = []

    def suggest(self):
        """Defined in :numref:`sec_mf_hpo_sh`"""
        if len(self.queue) == 0:
            # Start a new round of successive halving
            # Number of configurations for the first rung:
            n0 = int(self.prefact * self.eta ** self.K)
            for _ in range(n0):
                config = self.searcher.sample_configuration()
                config["max_epochs"] = self.r_min  # Set r = r_min
                self.queue.append(config)
        # Return an element from the queue
        return self.queue.pop()

    def update(self, config: dict, error: float, info=None):
        """Defined in :numref:`sec_mf_hpo_sh`"""
        ri = int(config["max_epochs"])  # Rung r_i
        # Update our searcher, e.g if we use Bayesian optimization later
        self.searcher.update(config, error, additional_info=info)
        self.all_observed_error_at_rungs[ri].append((config, error))
        if ri < self.r_max:
            # Bookkeeping
            self.observed_error_at_rungs[ri].append((config, error))
            # Determine how many configurations should be evaluated on this rung
            ki = self.K - self.rung_levels.index(ri)
            ni = int(self.prefact * self.eta ** ki)
            # If we observed all configuration on this rung r_i, we estimate the
            # top 1 / eta configuration, add them to queue and promote them for
            # the next rung r_{i+1}
            if len(self.observed_error_at_rungs[ri]) >= ni:
                kiplus1 = ki - 1
                niplus1 = int(self.prefact * self.eta ** kiplus1)
                best_performing_configurations = self.get_top_n_configurations(
                    rung_level=ri, n=niplus1
                )
                riplus1 = self.rung_levels[self.K - kiplus1]  # r_{i+1}
                # Queue may not be empty: insert new entries at the beginning
                self.queue = [
                    dict(config, max_epochs=riplus1)
                    for config in best_performing_configurations
                ] + self.queue
                self.observed_error_at_rungs[ri] = []  # Reset

    def get_top_n_configurations(self, rung_level, n):
        """Defined in :numref:`sec_mf_hpo_sh`"""
        rung = self.observed_error_at_rungs[rung_level]
        if not rung:
            return []
        sorted_rung = sorted(rung, key=lambda x: x[1])
        return [x[0] for x in sorted_rung[:n]]

def update_D(X, Z, net_D, net_G, loss, trainer_D):
    """Update discriminator.

    Defined in :numref:`sec_basic_gan`"""
    batch_size = X.shape[0]
    ones = torch.ones((batch_size,), device=X.device)
    zeros = torch.zeros((batch_size,), device=X.device)
    trainer_D.zero_grad()
    real_Y = net_D(X)
    fake_X = net_G(Z)
    # Do not need to compute gradient for `net_G`, detach it from
    # computing gradients.
    fake_Y = net_D(fake_X.detach())
    loss_D = (loss(real_Y, ones.reshape(real_Y.shape)) +
              loss(fake_Y, zeros.reshape(fake_Y.shape))) / 2
    loss_D.backward()
    trainer_D.step()
    return loss_D

def update_G(Z, net_D, net_G, loss, trainer_G):
    """Update generator.

    Defined in :numref:`sec_basic_gan`"""
    batch_size = Z.shape[0]
    ones = torch.ones((batch_size,), device=Z.device)
    trainer_G.zero_grad()
    # We could reuse `fake_X` from `update_D` to save computation
    fake_X = net_G(Z)
    # Recomputing `fake_Y` is needed since `net_D` is changed
    fake_Y = net_D(fake_X)
    loss_G = loss(fake_Y, ones.reshape(fake_Y.shape))
    loss_G.backward()
    trainer_G.step()
    return loss_G

d2l.DATA_HUB['pokemon'] = (d2l.DATA_URL + 'pokemon.zip',
                           'c065c0e2593b8b161a2d7873e42418bf6a21106c')

def frozen_lake(seed):
    """Defined in :numref:`sec_utils`"""
    # See https://www.gymlibrary.dev/environments/toy_text/frozen_lake/ to learn more about this env
    # How to process env.P.items is adpated from https://sites.google.com/view/deep-rl-bootcamp/labs

    env = gym.make('FrozenLake-v1', is_slippery=False)
    env.seed(seed)
    env.action_space.np_random.seed(seed)
    env.action_space.seed(seed)
    env_info = {}
    env_info['desc'] = env.desc  # 2D array specifying what each grid item means
    env_info['num_states'] = env.nS  # Number of observations/states or obs/state dim
    env_info['num_actions'] = env.nA  # Number of actions or action dim
    # Define indices for (transition probability, nextstate, reward, done) tuple
    env_info['trans_prob_idx'] = 0  # Index of transition probability entry
    env_info['nextstate_idx'] = 1  # Index of next state entry
    env_info['reward_idx'] = 2  # Index of reward entry
    env_info['done_idx'] = 3  # Index of done entry
    env_info['mdp'] = {}
    env_info['env'] = env

    for (s, others) in env.P.items():
        # others(s) = {a0: [ (p(s'|s,a0), s', reward, done),...], a1:[...], ...}

        for (a, pxrds) in others.items():
            # pxrds is [(p1,next1,r1,d1),(p2,next2,r2,d2),..].
            # e.g. [(0.3, 0, 0, False), (0.3, 0, 0, False), (0.3, 4, 1, False)]
            env_info['mdp'][(s,a)] = pxrds

    return env_info

def make_env(name ='', seed=0):
    """Defined in :numref:`sec_utils`"""
    # Input parameters:
    # name: specifies a gym environment.
    # For Value iteration, only FrozenLake-v1 is supported.
    if name == 'FrozenLake-v1':
        return frozen_lake(seed)

    else:
        raise ValueError("%s env is not supported in this Notebook")

def show_value_function_progress(env_desc, V, pi):
    """Defined in :numref:`sec_utils`"""
    # This function visualizes how value and policy changes over time.
    # V: [num_iters, num_states]
    # pi: [num_iters, num_states]
    # How to visualize value function is adapted (but changed) from: https://sites.google.com/view/deep-rl-bootcamp/labs

    num_iters = V.shape[0]
    fig, ax  = plt.subplots(figsize=(15, 15))

    for k in range(V.shape[0]):
        plt.subplot(4, 4, k + 1)
        plt.imshow(V[k].reshape(4,4), cmap="bone")
        ax = plt.gca()
        ax.set_xticks(np.arange(0, 5)-.5, minor=True)
        ax.set_yticks(np.arange(0, 5)-.5, minor=True)
        ax.grid(which="minor", color="w", linestyle='-', linewidth=3)
        ax.tick_params(which="minor", bottom=False, left=False)
        ax.set_xticks([])
        ax.set_yticks([])

        # LEFT action: 0, DOWN action: 1
        # RIGHT action: 2, UP action: 3
        action2dxdy = {0:(-.25, 0),1: (0, .25),
                       2:(0.25, 0),3: (-.25, 0)}

        for y in range(4):
            for x in range(4):
                action = pi[k].reshape(4,4)[y, x]
                dx, dy = action2dxdy[action]

                if env_desc[y,x].decode() == 'H':
                    ax.text(x, y, str(env_desc[y,x].decode()),
                       ha="center", va="center", color="y",
                         size=20, fontweight='bold')

                elif env_desc[y,x].decode() == 'G':
                    ax.text(x, y, str(env_desc[y,x].decode()),
                       ha="center", va="center", color="w",
                         size=20, fontweight='bold')

                else:
                    ax.text(x, y, str(env_desc[y,x].decode()),
                       ha="center", va="center", color="g",
                         size=15, fontweight='bold')

                # No arrow for cells with G and H labels
                if env_desc[y,x].decode() != 'G' and env_desc[y,x].decode() != 'H':
                    ax.arrow(x, y, dx, dy, color='r', head_width=0.2, head_length=0.15)

        ax.set_title("Step = "  + str(k + 1), fontsize=20)

    fig.tight_layout()
    plt.show()

def show_Q_function_progress(env_desc, V_all, pi_all):
    """Defined in :numref:`sec_utils`"""
    # This function visualizes how value and policy changes over time.
    # V: [num_iters, num_states]
    # pi: [num_iters, num_states]

    # We want to only shows few values
    num_iters_all = V_all.shape[0]
    num_iters = num_iters_all // 10

    vis_indx = np.arange(0, num_iters_all, num_iters).tolist()
    vis_indx.append(num_iters_all - 1)
    V = np.zeros((len(vis_indx), V_all.shape[1]))
    pi = np.zeros((len(vis_indx), V_all.shape[1]))

    for c, i in enumerate(vis_indx):
        V[c]  = V_all[i]
        pi[c] = pi_all[i]

    num_iters = V.shape[0]
    fig, ax = plt.subplots(figsize=(15, 15))

    for k in range(V.shape[0]):
        plt.subplot(4, 4, k + 1)
        plt.imshow(V[k].reshape(4,4), cmap="bone")
        ax = plt.gca()
        ax.set_xticks(np.arange(0, 5)-.5, minor=True)
        ax.set_yticks(np.arange(0, 5)-.5, minor=True)
        ax.grid(which="minor", color="w", linestyle='-', linewidth=3)
        ax.tick_params(which="minor", bottom=False, left=False)
        ax.set_xticks([])
        ax.set_yticks([])

        # LEFT action: 0, DOWN action: 1
        # RIGHT action: 2, UP action: 3
        action2dxdy = {0:(-.25, 0),1:(0, .25),
                       2:(0.25, 0),3:(-.25, 0)}

        for y in range(4):
            for x in range(4):
                action = pi[k].reshape(4,4)[y, x]
                dx, dy = action2dxdy[action]

                if env_desc[y,x].decode() == 'H':
                    ax.text(x, y, str(env_desc[y,x].decode()),
                       ha="center", va="center", color="y",
                         size=20, fontweight='bold')

                elif env_desc[y,x].decode() == 'G':
                    ax.text(x, y, str(env_desc[y,x].decode()),
                       ha="center", va="center", color="w",
                         size=20, fontweight='bold')

                else:
                    ax.text(x, y, str(env_desc[y,x].decode()),
                       ha="center", va="center", color="g",
                         size=15, fontweight='bold')

                # No arrow for cells with G and H labels
                if env_desc[y,x].decode() != 'G' and env_desc[y,x].decode() != 'H':
                    ax.arrow(x, y, dx, dy, color='r', head_width=0.2, head_length=0.15)

        ax.set_title("Step = "  + str(vis_indx[k] + 1), fontsize=20)

    fig.tight_layout()
    plt.show()

def load_array(data_arrays, batch_size, is_train=True):
    """Construct a PyTorch data iterator.

    Defined in :numref:`sec_utils`"""
    dataset = torch.utils.data.TensorDataset(*data_arrays)
    return torch.utils.data.DataLoader(dataset, batch_size, shuffle=is_train)

def synthetic_data(w, b, num_examples):
    """Generate y = Xw + b + noise.

    Defined in :numref:`sec_utils`"""
    X = d2l.normal(0, 1, (num_examples, len(w)))
    y = d2l.matmul(X, w) + b
    y += d2l.normal(0, 0.01, y.shape)
    return X, d2l.reshape(y, (-1, 1))

def sgd(params, lr, batch_size):
    """Minibatch stochastic gradient descent.

    Defined in :numref:`sec_utils`"""
    with torch.no_grad():
        for param in params:
            param -= lr * param.grad / batch_size
            param.grad.zero_()

def get_dataloader_workers():
    """Use 4 processes to read the data.

    Defined in :numref:`sec_utils`"""
    return 4

def load_data_fashion_mnist(batch_size, resize=None):
    """Download the Fashion-MNIST dataset and then load it into memory.

    Defined in :numref:`sec_utils`"""
    trans = [transforms.ToTensor()]
    if resize:
        trans.insert(0, transforms.Resize(resize))
    trans = transforms.Compose(trans)
    mnist_train = torchvision.datasets.FashionMNIST(
        root="../data", train=True, transform=trans, download=True)
    mnist_test = torchvision.datasets.FashionMNIST(
        root="../data", train=False, transform=trans, download=True)
    return (torch.utils.data.DataLoader(mnist_train, batch_size, shuffle=True,
                                        num_workers=get_dataloader_workers()),
            torch.utils.data.DataLoader(mnist_test, batch_size, shuffle=False,
                                        num_workers=get_dataloader_workers()))

def evaluate_accuracy_gpu(net, data_iter, device=None):
    """Compute the accuracy for a model on a dataset using a GPU.

    Defined in :numref:`sec_utils`"""
    if isinstance(net, nn.Module):
        net.eval()  # Set the model to evaluation mode
        if not device:
            device = next(iter(net.parameters())).device
    # No. of correct predictions, no. of predictions
    metric = d2l.Accumulator(2)

    with torch.no_grad():
        for X, y in data_iter:
            if isinstance(X, list):
                # Required for BERT Fine-tuning (to be covered later)
                X = [x.to(device) for x in X]
            else:
                X = X.to(device)
            y = y.to(device)
            metric.add(d2l.accuracy(net(X), y), d2l.size(y))
    return metric[0] / metric[1]


def train_ch6(net, train_iter, test_iter, num_epochs, lr, device):
    """Train a model with a GPU (defined in Chapter 6).

    Defined in :numref:`sec_utils`"""
    def init_weights(m):
        if type(m) == nn.Linear or type(m) == nn.Conv2d:
            nn.init.xavier_uniform_(m.weight)
    net.apply(init_weights)
    print('training on', device)
    net.to(device)
    optimizer = torch.optim.SGD(net.parameters(), lr=lr)
    loss = nn.CrossEntropyLoss()
    animator = d2l.Animator(xlabel='epoch', xlim=[1, num_epochs],
                            legend=['train loss', 'train acc', 'test acc'])
    timer, num_batches = d2l.Timer(), len(train_iter)
    for epoch in range(num_epochs):
        # Sum of training loss, sum of training accuracy, no. of examples
        metric = d2l.Accumulator(3)
        net.train()
        for i, (X, y) in enumerate(train_iter):
            timer.start()
            optimizer.zero_grad()
            X, y = X.to(device), y.to(device)
            y_hat = net(X)
            l = loss(y_hat, y)
            l.backward()
            optimizer.step()
            with torch.no_grad():
                metric.add(l * X.shape[0], d2l.accuracy(y_hat, y), X.shape[0])
            timer.stop()
            train_l = metric[0] / metric[2]
            train_acc = metric[1] / metric[2]
            if (i + 1) % (num_batches // 5) == 0 or i == num_batches - 1:
                animator.add(epoch + (i + 1) / num_batches,
                             (train_l, train_acc, None))
        test_acc = evaluate_accuracy_gpu(net, test_iter)
        animator.add(epoch + 1, (None, None, test_acc))
    print(f'loss {train_l:.3f}, train acc {train_acc:.3f}, '
          f'test acc {test_acc:.3f}')
    print(f'{metric[2] * num_epochs / timer.sum():.1f} examples/sec '
          f'on {str(device)}')

def show_images(imgs, num_rows, num_cols, titles=None, scale=1.5):
    """Plot a list of images.

    Defined in :numref:`sec_utils`"""
    figsize = (num_cols * scale, num_rows * scale)
    _, axes = d2l.plt.subplots(num_rows, num_cols, figsize=figsize)
    axes = axes.flatten()
    for i, (ax, img) in enumerate(zip(axes, imgs)):
        try:
            img = d2l.numpy(img)
        except:
            pass
        ax.imshow(img)
        ax.axes.get_xaxis().set_visible(False)
        ax.axes.get_yaxis().set_visible(False)
        if titles:
            ax.set_title(titles[i])
    return axes

def linreg(X, w, b):
    """The linear regression model.

    Defined in :numref:`sec_utils`"""
    return d2l.matmul(X, w) + b

def squared_loss(y_hat, y):
    """Squared loss.

    Defined in :numref:`sec_utils`"""
    return (y_hat - d2l.reshape(y, y_hat.shape)) ** 2 / 2

def get_fashion_mnist_labels(labels):
    """Return text labels for the Fashion-MNIST dataset.

    Defined in :numref:`sec_utils`"""
    text_labels = ['t-shirt', 'trouser', 'pullover', 'dress', 'coat',
                   'sandal', 'shirt', 'sneaker', 'bag', 'ankle boot']
    return [text_labels[int(i)] for i in labels]

class Animator:
    """For plotting data in animation."""
    def __init__(self, xlabel=None, ylabel=None, legend=None, xlim=None,
                 ylim=None, xscale='linear', yscale='linear',
                 fmts=('-', 'm--', 'g-.', 'r:'), nrows=1, ncols=1,
                 figsize=(3.5, 2.5)):
        """Defined in :numref:`sec_utils`"""
        # Incrementally plot multiple lines
        if legend is None:
            legend = []
        d2l.use_svg_display()
        self.fig, self.axes = d2l.plt.subplots(nrows, ncols, figsize=figsize)
        if nrows * ncols == 1:
            self.axes = [self.axes, ]
        # Use a lambda function to capture arguments
        self.config_axes = lambda: d2l.set_axes(
            self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)
        self.X, self.Y, self.fmts = None, None, fmts

    def add(self, x, y):
        # Add multiple data points into the figure
        if not hasattr(y, "__len__"):
            y = [y]
        n = len(y)
        if not hasattr(x, "__len__"):
            x = [x] * n
        if not self.X:
            self.X = [[] for _ in range(n)]
        if not self.Y:
            self.Y = [[] for _ in range(n)]
        for i, (a, b) in enumerate(zip(x, y)):
            if a is not None and b is not None:
                self.X[i].append(a)
                self.Y[i].append(b)
        self.axes[0].cla()
        for x, y, fmt in zip(self.X, self.Y, self.fmts):
            self.axes[0].plot(x, y, fmt)
        self.config_axes()
        display.display(self.fig)
        display.clear_output(wait=True)

class Accumulator:
    """For accumulating sums over `n` variables."""
    def __init__(self, n):
        """Defined in :numref:`sec_utils`"""
        self.data = [0.0] * n

    def add(self, *args):
        self.data = [a + float(b) for a, b in zip(self.data, args)]

    def reset(self):
        self.data = [0.0] * len(self.data)

    def __getitem__(self, idx):
        return self.data[idx]


def accuracy(y_hat, y):
    """Compute the number of correct predictions.

    Defined in :numref:`sec_utils`"""
    if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:
        y_hat = d2l.argmax(y_hat, axis=1)
    cmp = d2l.astype(y_hat, y.dtype) == y
    return float(d2l.reduce_sum(d2l.astype(cmp, y.dtype)))

def download(url, folder='../data', sha1_hash=None):
    """Download a file to folder and return the local filepath.

    Defined in :numref:`sec_utils`"""
    if not url.startswith('http'):
        # For back compatability
        url, sha1_hash = DATA_HUB[url]
    os.makedirs(folder, exist_ok=True)
    fname = os.path.join(folder, url.split('/')[-1])
    # Check if hit cache
    if os.path.exists(fname) and sha1_hash:
        sha1 = hashlib.sha1()
        with open(fname, 'rb') as f:
            while True:
                data = f.read(1048576)
                if not data:
                    break
                sha1.update(data)
        if sha1.hexdigest() == sha1_hash:
            return fname
    # Download
    print(f'Downloading {fname} from {url}...')
    r = requests.get(url, stream=True, verify=True)
    with open(fname, 'wb') as f:
        f.write(r.content)
    return fname

def extract(filename, folder=None):
    """Extract a zip/tar file into folder.

    Defined in :numref:`sec_utils`"""
    base_dir = os.path.dirname(filename)
    _, ext = os.path.splitext(filename)
    assert ext in ('.zip', '.tar', '.gz'), 'Only support zip/tar files.'
    if ext == '.zip':
        fp = zipfile.ZipFile(filename, 'r')
    else:
        fp = tarfile.open(filename, 'r')
    if folder is None:
        folder = base_dir
    fp.extractall(folder)

def download_extract(name, folder=None):
    """Download and extract a zip/tar file.

    Defined in :numref:`sec_utils`"""
    fname = download(name)
    base_dir = os.path.dirname(fname)
    data_dir, ext = os.path.splitext(fname)
    if ext == '.zip':
        fp = zipfile.ZipFile(fname, 'r')
    elif ext in ('.tar', '.gz'):
        fp = tarfile.open(fname, 'r')
    else:
        assert False, 'Only zip/tar files can be extracted.'
    fp.extractall(base_dir)
    return os.path.join(base_dir, folder) if folder else data_dir


def tokenize(lines, token='word'):
    """Split text lines into word or character tokens.

    Defined in :numref:`sec_utils`"""
    assert token in ('word', 'char'), 'Unknown token type: ' + token
    return [line.split() if token == 'word' else list(line) for line in lines]

def evaluate_loss(net, data_iter, loss):
    """Evaluate the loss of a model on the given dataset.

    Defined in :numref:`sec_utils`"""
    metric = d2l.Accumulator(2)  # Sum of losses, no. of examples
    for X, y in data_iter:
        out = net(X)
        y = d2l.reshape(y, out.shape)
        l = loss(out, y)
        metric.add(d2l.reduce_sum(l), d2l.size(l))
    return metric[0] / metric[1]

def grad_clipping(net, theta):
    """Clip the gradient.

    Defined in :numref:`sec_utils`"""
    if isinstance(net, nn.Module):
        params = [p for p in net.parameters() if p.requires_grad]
    else:
        params = net.params
    norm = torch.sqrt(sum(torch.sum((p.grad ** 2)) for p in params))
    if norm > theta:
        for param in params:
            param.grad[:] *= theta / norm

d2l.DATA_HUB['fra-eng'] = (d2l.DATA_URL + 'fra-eng.zip',
                           '94646ad1522d915e7b0f9296181140edcf86a4f5')

def read_data_nmt():
    """Load the English-French dataset.

    Defined in :numref:`sec_utils`"""
    data_dir = d2l.download_extract('fra-eng')
    with open(os.path.join(data_dir, 'fra.txt'), 'r', encoding='utf-8') as f:
        return f.read()

def preprocess_nmt(text):
    """Preprocess the English-French dataset.

    Defined in :numref:`sec_utils`"""
    def no_space(char, prev_char):
        return char in set(',.!?') and prev_char != ' '

    # Replace non-breaking space with space, and convert uppercase letters to
    # lowercase ones
    text = text.replace('\u202f', ' ').replace('\xa0', ' ').lower()
    # Insert space between words and punctuation marks
    out = [' ' + char if i > 0 and no_space(char, text[i - 1]) else char
           for i, char in enumerate(text)]
    return ''.join(out)

def tokenize_nmt(text, num_examples=None):
    """Tokenize the English-French dataset.

    Defined in :numref:`sec_utils`"""
    source, target = [], []
    for i, line in enumerate(text.split('\n')):
        if num_examples and i > num_examples:
            break
        parts = line.split('\t')
        if len(parts) == 2:
            source.append(parts[0].split(' '))
            target.append(parts[1].split(' '))
    return source, target


def truncate_pad(line, num_steps, padding_token):
    """Truncate or pad sequences.

    Defined in :numref:`sec_utils`"""
    if len(line) > num_steps:
        return line[:num_steps]  # Truncate
    return line + [padding_token] * (num_steps - len(line))  # Pad


def build_array_nmt(lines, vocab, num_steps):
    """Transform text sequences of machine translation into minibatches.

    Defined in :numref:`sec_utils`"""
    lines = [vocab[l] for l in lines]
    lines = [l + [vocab['<eos>']] for l in lines]
    array = d2l.tensor([truncate_pad(
        l, num_steps, vocab['<pad>']) for l in lines])
    valid_len = d2l.reduce_sum(
        d2l.astype(array != vocab['<pad>'], d2l.int32), 1)
    return array, valid_len


def load_data_nmt(batch_size, num_steps, num_examples=600):
    """Return the iterator and the vocabularies of the translation dataset.

    Defined in :numref:`sec_utils`"""
    text = preprocess_nmt(read_data_nmt())
    source, target = tokenize_nmt(text, num_examples)
    src_vocab = d2l.Vocab(source, min_freq=2,
                          reserved_tokens=['<pad>', '<bos>', '<eos>'])
    tgt_vocab = d2l.Vocab(target, min_freq=2,
                          reserved_tokens=['<pad>', '<bos>', '<eos>'])
    src_array, src_valid_len = build_array_nmt(source, src_vocab, num_steps)
    tgt_array, tgt_valid_len = build_array_nmt(target, tgt_vocab, num_steps)
    data_arrays = (src_array, src_valid_len, tgt_array, tgt_valid_len)
    data_iter = d2l.load_array(data_arrays, batch_size)
    return data_iter, src_vocab, tgt_vocab

def sequence_mask(X, valid_len, value=0):
    """Mask irrelevant entries in sequences.

    Defined in :numref:`sec_utils`"""
    maxlen = X.size(1)
    mask = torch.arange((maxlen), dtype=torch.float32,
                        device=X.device)[None, :] < valid_len[:, None]
    X[~mask] = value
    return X


class MaskedSoftmaxCELoss(nn.CrossEntropyLoss):
    """The softmax cross-entropy loss with masks.

    Defined in :numref:`sec_utils`"""
    # `pred` shape: (`batch_size`, `num_steps`, `vocab_size`)
    # `label` shape: (`batch_size`, `num_steps`)
    # `valid_len` shape: (`batch_size`,)
    def forward(self, pred, label, valid_len):
        weights = torch.ones_like(label)
        weights = sequence_mask(weights, valid_len)
        self.reduction='none'
        unweighted_loss = super(MaskedSoftmaxCELoss, self).forward(
            pred.permute(0, 2, 1), label)
        weighted_loss = (unweighted_loss * weights).mean(dim=1)
        return weighted_loss

def train_seq2seq(net, data_iter, lr, num_epochs, tgt_vocab, device):
    """Train a model for sequence to sequence.

    Defined in :numref:`sec_utils`"""
    def xavier_init_weights(m):
        if type(m) == nn.Linear:
            nn.init.xavier_uniform_(m.weight)
        if type(m) == nn.GRU:
            for param in m._flat_weights_names:
                if "weight" in param:
                    nn.init.xavier_uniform_(m._parameters[param])
    net.apply(xavier_init_weights)
    net.to(device)
    optimizer = torch.optim.Adam(net.parameters(), lr=lr)
    loss = MaskedSoftmaxCELoss()
    net.train()
    animator = d2l.Animator(xlabel='epoch', ylabel='loss',
                            xlim=[10, num_epochs])
    for epoch in range(num_epochs):
        timer = d2l.Timer()
        metric = d2l.Accumulator(2)  # Sum of training loss, no. of tokens
        for batch in data_iter:
            optimizer.zero_grad()
            X, X_valid_len, Y, Y_valid_len = [x.to(device) for x in batch]
            bos = torch.tensor([tgt_vocab['<bos>']] * Y.shape[0],
                               device=device).reshape(-1, 1)
            dec_input = d2l.concat([bos, Y[:, :-1]], 1)  # Teacher forcing
            Y_hat, _ = net(X, dec_input, X_valid_len)
            l = loss(Y_hat, Y, Y_valid_len)
            l.sum().backward()  # Make the loss scalar for `backward`
            d2l.grad_clipping(net, 1)
            num_tokens = Y_valid_len.sum()
            optimizer.step()
            with torch.no_grad():
                metric.add(l.sum(), num_tokens)
        if (epoch + 1) % 10 == 0:
            animator.add(epoch + 1, (metric[0] / metric[1],))
    print(f'loss {metric[0] / metric[1]:.3f}, {metric[1] / timer.stop():.1f} '
          f'tokens/sec on {str(device)}')


def predict_seq2seq(net, src_sentence, src_vocab, tgt_vocab, num_steps,
                    device, save_attention_weights=False):
    """Predict for sequence to sequence.

    Defined in :numref:`sec_utils`"""
    # Set `net` to eval mode for inference
    net.eval()
    src_tokens = src_vocab[src_sentence.lower().split(' ')] + [
        src_vocab['<eos>']]
    enc_valid_len = torch.tensor([len(src_tokens)], device=device)
    src_tokens = d2l.truncate_pad(src_tokens, num_steps, src_vocab['<pad>'])
    # Add the batch axis
    enc_X = torch.unsqueeze(
        torch.tensor(src_tokens, dtype=torch.long, device=device), dim=0)
    enc_outputs = net.encoder(enc_X, enc_valid_len)
    dec_state = net.decoder.init_state(enc_outputs, enc_valid_len)
    # Add the batch axis
    dec_X = torch.unsqueeze(torch.tensor(
        [tgt_vocab['<bos>']], dtype=torch.long, device=device), dim=0)
    output_seq, attention_weight_seq = [], []
    for _ in range(num_steps):
        Y, dec_state = net.decoder(dec_X, dec_state)
        # We use the token with the highest prediction likelihood as input
        # of the decoder at the next time step
        dec_X = Y.argmax(dim=2)
        pred = dec_X.squeeze(dim=0).type(torch.int32).item()
        # Save attention weights (to be covered later)
        if save_attention_weights:
            attention_weight_seq.append(net.decoder.attention_weights)
        # Once the end-of-sequence token is predicted, the generation of the
        # output sequence is complete
        if pred == tgt_vocab['<eos>']:
            break
        output_seq.append(pred)
    return ' '.join(tgt_vocab.to_tokens(output_seq)), attention_weight_seq


# Alias defined in config.ini
nn_Module = nn.Module

ones_like = torch.ones_like
ones = torch.ones
zeros_like = torch.zeros_like
zeros = torch.zeros
tensor = torch.tensor
arange = torch.arange
meshgrid = torch.meshgrid
sin = torch.sin
sinh = torch.sinh
cos = torch.cos
cosh = torch.cosh
tanh = torch.tanh
linspace = torch.linspace
exp = torch.exp
log = torch.log
normal = torch.normal
rand = torch.rand
randn = torch.randn
matmul = torch.matmul
int32 = torch.int32
int64 = torch.int64
float32 = torch.float32
concat = torch.cat
stack = torch.stack
abs = torch.abs
eye = torch.eye
sigmoid = torch.sigmoid
batch_matmul = torch.bmm
numpy = lambda x, *args, **kwargs: x.detach().numpy(*args, **kwargs)
size = lambda x, *args, **kwargs: x.numel(*args, **kwargs)
reshape = lambda x, *args, **kwargs: x.reshape(*args, **kwargs)
to = lambda x, *args, **kwargs: x.to(*args, **kwargs)
reduce_sum = lambda x, *args, **kwargs: x.sum(*args, **kwargs)
argmax = lambda x, *args, **kwargs: x.argmax(*args, **kwargs)
astype = lambda x, *args, **kwargs: x.type(*args, **kwargs)
transpose = lambda x, *args, **kwargs: x.t(*args, **kwargs)
reduce_mean = lambda x, *args, **kwargs: x.mean(*args, **kwargs)
expand_dims = lambda x, *args, **kwargs: x.unsqueeze(*args, **kwargs)
swapaxes = lambda x, *args, **kwargs: x.swapaxes(*args, **kwargs)
repeat = lambda x, *args, **kwargs: x.repeat(*args, **kwargs)