"""
.. _model-tree-lstm:

Tree-LSTM in DGL
==========================

**Author**: Zihao Ye, Qipeng Guo, `Minjie Wang
<https://jermainewang.github.io/>`_, `Jake Zhao
<https://cs.nyu.edu/~jakezhao/>`_, Zheng Zhang

.. warning::

    The tutorial aims at gaining insights into the paper, with code as a mean
    of explanation. The implementation thus is NOT optimized for running
    efficiency. For recommended implementation, please refer to the `official
    examples <https://github.com/dmlc/dgl/tree/master/examples>`_.

"""
 
##############################################################################
#
# In this tutorial, you learn to use Tree-LSTM networks for sentiment analysis. 
# The Tree-LSTM is a generalization of long short-term memory (LSTM) networks to tree-structured network topologies.
# 
# The Tree-LSTM structure was first introduced by Kai et. al in an ACL 2015 
# paper: `Improved Semantic Representations From Tree-Structured Long
# Short-Term Memory Networks <https://arxiv.org/pdf/1503.00075.pdf>`__.
# The core idea is to introduce syntactic information for language tasks by 
# extending the chain-structured LSTM to a tree-structured LSTM. The dependency 
# tree and constituency tree techniques are leveraged to obtain a ''latent tree''.
#
# The challenge in training Tree-LSTMs is batching --- a standard 
# technique in machine learning to accelerate optimization. However, since trees 
# generally have different shapes by nature, parallization is non-trivial. 
# DGL offers an alternative. Pool all the trees into one single graph then 
# induce the message passing over them, guided by the structure of each tree.
#
# The task and the dataset
# ------------------------
# 
# The steps here use the
# `Stanford Sentiment Treebank <https://nlp.stanford.edu/sentiment/>`__ in
# ``dgl.data``. The dataset provides a fine-grained, tree-level sentiment
# annotation. There are five classes: Very negative, negative, neutral, positive, and
# very positive, which indicate the sentiment in the current subtree. Non-leaf
# nodes in a constituency tree do not contain words, so use a special
# ``PAD_WORD`` token to denote them. During training and inference
# their embeddings would be masked to all-zero.
#
# .. figure:: https://i.loli.net/2018/11/08/5be3d4bfe031b.png
#    :alt: 
#
# The figure displays one sample of the SST dataset, which is a
# constituency parse tree with their nodes labeled with sentiment. To
# speed up things, build a tiny set with five sentences and take a look
# at the first one.
#

from collections import namedtuple

import dgl
from dgl.data.tree import SSTDataset


SSTBatch = namedtuple('SSTBatch', ['graph', 'mask', 'wordid', 'label'])

# Each sample in the dataset is a constituency tree. The leaf nodes
# represent words. The word is an int value stored in the "x" field.
# The non-leaf nodes have a special word PAD_WORD. The sentiment
# label is stored in the "y" feature field.
trainset = SSTDataset(mode='tiny')  # the "tiny" set has only five trees
tiny_sst = trainset.trees
num_vocabs = trainset.num_vocabs
num_classes = trainset.num_classes

vocab = trainset.vocab # vocabulary dict: key -> id
inv_vocab = {v: k for k, v in vocab.items()} # inverted vocabulary dict: id -> word

a_tree = tiny_sst[0]
for token in a_tree.ndata['x'].tolist():
    if token != trainset.PAD_WORD:
        print(inv_vocab[token], end=" ")

##############################################################################
# Step 1: Batching
# ----------------
#
# Add all the trees to one graph, using
# the :func:`~dgl.batched_graph.batch` API.
#

import networkx as nx
import matplotlib.pyplot as plt

graph = dgl.batch(tiny_sst)
def plot_tree(g):
    # this plot requires pygraphviz package
    pos = nx.nx_agraph.graphviz_layout(g, prog='dot')
    nx.draw(g, pos, with_labels=False, node_size=10,
            node_color=[[.5, .5, .5]], arrowsize=4)
    plt.show()

plot_tree(graph.to_networkx())

#################################################################################
# You can read more about the definition of :func:`~dgl.batch`, or
# skip ahead to the next step:
# .. note::
#
#    **Definition**: :func:`~dgl.batch` unions a list of :math:`B`
#      :class:`~dgl.DGLGraph`\ s and returns a :class:`~dgl.DGLGraph` of batch 
#      size :math:`B`. 
#    
#    - The union includes all the nodes,
#      edges, and their features. The order of nodes, edges, and features are
#      preserved. 
#     
#        - Given that you have :math:`V_i` nodes for graph
#          :math:`\mathcal{G}_i`, the node ID :math:`j` in graph
#          :math:`\mathcal{G}_i` correspond to node ID
#          :math:`j + \sum_{k=1}^{i-1} V_k` in the batched graph. 
#    
#        - Therefore, performing feature transformation and message passing on
#          the batched graph is equivalent to doing those
#          on all ``DGLGraph`` constituents in parallel. 
#
#    - Duplicate references to the same graph are
#      treated as deep copies; the nodes, edges, and features are duplicated,
#      and mutation on one reference does not affect the other. 
#    - The batched graph keeps track of the meta
#      information of the constituents so it can be
#      :func:`~dgl.batched_graph.unbatch`\ ed to list of ``DGLGraph``\ s.
#
# Step 2: Tree-LSTM cell with message-passing APIs
# ------------------------------------------------
#
# Researchers have proposed two types of Tree-LSTMs: Child-Sum
# Tree-LSTMs, and :math:`N`-ary Tree-LSTMs. In this tutorial you focus 
# on applying *Binary* Tree-LSTM to binarized constituency trees. This 
# application is also known as *Constituency Tree-LSTM*. Use PyTorch 
# as a backend framework to set up the network.
#
# In `N`-ary Tree-LSTM, each unit at node :math:`j` maintains a hidden
# representation :math:`h_j` and a memory cell :math:`c_j`. The unit
# :math:`j` takes the input vector :math:`x_j` and the hidden
# representations of the child units: :math:`h_{jl}, 1\leq l\leq N` as
# input, then update its new hidden representation :math:`h_j` and memory
# cell :math:`c_j` by: 
#
# .. math::
#
#    i_j & = & \sigma\left(W^{(i)}x_j + \sum_{l=1}^{N}U^{(i)}_l h_{jl} + b^{(i)}\right),  & (1)\\
#    f_{jk} & = & \sigma\left(W^{(f)}x_j + \sum_{l=1}^{N}U_{kl}^{(f)} h_{jl} + b^{(f)} \right), &  (2)\\
#    o_j & = & \sigma\left(W^{(o)}x_j + \sum_{l=1}^{N}U_{l}^{(o)} h_{jl} + b^{(o)} \right), & (3)  \\
#    u_j & = & \textrm{tanh}\left(W^{(u)}x_j + \sum_{l=1}^{N} U_l^{(u)}h_{jl} + b^{(u)} \right), & (4)\\
#    c_j & = & i_j \odot u_j + \sum_{l=1}^{N} f_{jl} \odot c_{jl}, &(5) \\
#    h_j & = & o_j \cdot \textrm{tanh}(c_j), &(6)  \\
#
# It can be decomposed into three phases: ``message_func``,
# ``reduce_func`` and ``apply_node_func``.
#
# .. note::
#    ``apply_node_func`` is a new node UDF that has not been introduced before. In
#    ``apply_node_func``, a user specifies what to do with node features,
#    without considering edge features and messages. In a Tree-LSTM case,
#    ``apply_node_func`` is a must, since there exists (leaf) nodes with
#    :math:`0` incoming edges, which would not be updated with 
#    ``reduce_func``.
#

import torch as th
import torch.nn as nn

class TreeLSTMCell(nn.Module):
    def __init__(self, x_size, h_size):
        super(TreeLSTMCell, self).__init__()
        self.W_iou = nn.Linear(x_size, 3 * h_size, bias=False)
        self.U_iou = nn.Linear(2 * h_size, 3 * h_size, bias=False)
        self.b_iou = nn.Parameter(th.zeros(1, 3 * h_size))
        self.U_f = nn.Linear(2 * h_size, 2 * h_size)

    def message_func(self, edges):
        return {'h': edges.src['h'], 'c': edges.src['c']}

    def reduce_func(self, nodes):
        # concatenate h_jl for equation (1), (2), (3), (4)
        h_cat = nodes.mailbox['h'].view(nodes.mailbox['h'].size(0), -1)
        # equation (2)
        f = th.sigmoid(self.U_f(h_cat)).view(*nodes.mailbox['h'].size())
        # second term of equation (5)
        c = th.sum(f * nodes.mailbox['c'], 1)
        return {'iou': self.U_iou(h_cat), 'c': c}

    def apply_node_func(self, nodes):
        # equation (1), (3), (4)
        iou = nodes.data['iou'] + self.b_iou
        i, o, u = th.chunk(iou, 3, 1)
        i, o, u = th.sigmoid(i), th.sigmoid(o), th.tanh(u)
        # equation (5)
        c = i * u + nodes.data['c']
        # equation (6)
        h = o * th.tanh(c)
        return {'h' : h, 'c' : c}

##############################################################################
# Step 3: Define traversal
# ------------------------
#
# After you define the message-passing functions, induce the
# right order to trigger them. This is a significant departure from models
# such as GCN, where all nodes are pulling messages from upstream ones
# *simultaneously*.
#
# In the case of Tree-LSTM, messages start from leaves of the tree, and
# propagate/processed upwards until they reach the roots. A visualization
# is as follows:
#
# .. figure:: https://i.loli.net/2018/11/09/5be4b5d2df54d.gif
#    :alt:
#
# DGL defines a generator to perform the topological sort, each item is a
# tensor recording the nodes from bottom level to the roots. One can
# appreciate the degree of parallelism by inspecting the difference of the
# followings:
#

# to heterogenous graph
trv_a_tree = dgl.graph(a_tree.edges())
print('Traversing one tree:')
print(dgl.topological_nodes_generator(trv_a_tree))

# to heterogenous graph
trv_graph = dgl.graph(graph.edges())
print('Traversing many trees at the same time:')
print(dgl.topological_nodes_generator(trv_graph))

##############################################################################
# Call :meth:`~dgl.DGLGraph.prop_nodes` to trigger the message passing:

import dgl.function as fn
import torch as th

trv_graph.ndata['a'] = th.ones(graph.number_of_nodes(), 1)
traversal_order = dgl.topological_nodes_generator(trv_graph)
trv_graph.prop_nodes(traversal_order,
                     message_func=fn.copy_src('a', 'a'),
                     reduce_func=fn.sum('a', 'a'))

# the following is a syntax sugar that does the same
# dgl.prop_nodes_topo(graph)

##############################################################################
# .. note::
#
#    Before you call :meth:`~dgl.DGLGraph.prop_nodes`, specify a
#    `message_func` and `reduce_func` in advance. In the example, you can see built-in
#    copy-from-source and sum functions as message functions, and a reduce
#    function for demonstration.
#
# Putting it together
# -------------------
#
# Here is the complete code that specifies the ``Tree-LSTM`` class.
#

class TreeLSTM(nn.Module):
    def __init__(self,
                 num_vocabs,
                 x_size,
                 h_size,
                 num_classes,
                 dropout,
                 pretrained_emb=None):
        super(TreeLSTM, self).__init__()
        self.x_size = x_size
        self.embedding = nn.Embedding(num_vocabs, x_size)
        if pretrained_emb is not None:
            print('Using glove')
            self.embedding.weight.data.copy_(pretrained_emb)
            self.embedding.weight.requires_grad = True
        self.dropout = nn.Dropout(dropout)
        self.linear = nn.Linear(h_size, num_classes)
        self.cell = TreeLSTMCell(x_size, h_size)

    def forward(self, batch, h, c):
        """Compute tree-lstm prediction given a batch.

        Parameters
        ----------
        batch : dgl.data.SSTBatch
            The data batch.
        h : Tensor
            Initial hidden state.
        c : Tensor
            Initial cell state.

        Returns
        -------
        logits : Tensor
            The prediction of each node.
        """
        g = batch.graph
        # to heterogenous graph
        g = dgl.graph(g.edges())
        # feed embedding
        embeds = self.embedding(batch.wordid * batch.mask)
        g.ndata['iou'] = self.cell.W_iou(self.dropout(embeds)) * batch.mask.float().unsqueeze(-1)
        g.ndata['h'] = h
        g.ndata['c'] = c
        # propagate
        dgl.prop_nodes_topo(g,
                            message_func=self.cell.message_func,
                            reduce_func=self.cell.reduce_func,
                            apply_node_func=self.cell.apply_node_func)
        # compute logits
        h = self.dropout(g.ndata.pop('h'))
        logits = self.linear(h)
        return logits

##############################################################################
# Main Loop
# ---------
#
# Finally, you could write a training paradigm in PyTorch.
#

from torch.utils.data import DataLoader
import torch.nn.functional as F

device = th.device('cpu')
# hyper parameters
x_size = 256
h_size = 256
dropout = 0.5
lr = 0.05
weight_decay = 1e-4
epochs = 10

# create the model
model = TreeLSTM(trainset.num_vocabs,
                 x_size,
                 h_size,
                 trainset.num_classes,
                 dropout)
print(model)

# create the optimizer
optimizer = th.optim.Adagrad(model.parameters(),
                          lr=lr,
                          weight_decay=weight_decay)

def batcher(dev):
    def batcher_dev(batch):
        batch_trees = dgl.batch(batch)
        return SSTBatch(graph=batch_trees,
                        mask=batch_trees.ndata['mask'].to(device),
                        wordid=batch_trees.ndata['x'].to(device),
                        label=batch_trees.ndata['y'].to(device))
    return batcher_dev

train_loader = DataLoader(dataset=tiny_sst,
                          batch_size=5,
                          collate_fn=batcher(device),
                          shuffle=False,
                          num_workers=0)

# training loop
for epoch in range(epochs):
    for step, batch in enumerate(train_loader):
        g = batch.graph
        n = g.number_of_nodes()
        h = th.zeros((n, h_size))
        c = th.zeros((n, h_size))
        logits = model(batch, h, c)
        logp = F.log_softmax(logits, 1)
        loss = F.nll_loss(logp, batch.label, reduction='sum') 
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()
        pred = th.argmax(logits, 1)
        acc = float(th.sum(th.eq(batch.label, pred))) / len(batch.label)
        print("Epoch {:05d} | Step {:05d} | Loss {:.4f} | Acc {:.4f} |".format(
            epoch, step, loss.item(), acc))

##############################################################################
# To train the model on a full dataset with different settings (such as CPU or GPU),
# refer to the `PyTorch example <https://github.com/dmlc/dgl/tree/master/examples/pytorch/tree_lstm>`__.
# There is also an implementation of the Child-Sum Tree-LSTM.
