def _pairwise_distance(embeddings, squared=False):
    '''
       计算两两embedding的距离
       ------------------------------------------
       Args：
          embedding: 特征向量， 大小（batch_size, vector_size）
          squared:   是否距离的平方，即欧式距离
    
       Returns：
          distances: 两两embeddings的距离矩阵，大小 （batch_size, batch_size）
    '''    
    # 矩阵相乘,得到（batch_size, batch_size），因为计算欧式距离|a-b|^2 = a^2 -2ab + b^2, 
    # 其中 ab 可以用矩阵乘表示
    dot_product = tf.matmul(embeddings, tf.transpose(embeddings))   
    # dot_product对角线部分就是 每个embedding的平方
    square_norm = tf.diag_part(dot_product)
    # |a-b|^2 = a^2 - 2ab + b^2
    # tf.expand_dims(square_norm, axis=1)是（batch_size, 1）大小的矩阵，减去 （batch_size, batch_size）大小的矩阵，相当于每一列操作
    distances = tf.expand_dims(square_norm, axis=1) - 2.0 * dot_product + tf.expand_dims(square_norm, axis=0)
    distances = tf.maximum(distances, 0.0)   # 小于0的距离置为0
    if not squared:          # 如果不平方，就开根号，但是注意有0元素，所以0的位置加上 1e*-16
        distances = distances + mask * 1e-16
        distances = tf.sqrt(distances)
        distances = distances * (1.0 - mask)    # 0的部分仍然置为0
    return distances

def _get_triplet_mask(labels):
    '''
       得到一个3D的mask [a, p, n], 对应triplet（a, p, n）是valid的位置是True
       ----------------------------------
       Args:
          labels: 对应训练数据的labels, shape = (batch_size,)
       
       Returns:
          mask: 3D,shape = (batch_size, batch_size, batch_size)
    
    '''
    
    # 初始化一个二维矩阵，坐标(i, j)不相等置为1，得到indices_not_equal
    indices_equal = tf.cast(tf.eye(tf.shape(labels)[0]), tf.bool)
    indices_not_equal = tf.logical_not(indices_equal)
    # 因为最后得到一个3D的mask矩阵(i, j, k)，增加一个维度，则 i_not_equal_j 在第三个维度增加一个即，(batch_size, batch_size, 1), 其他同理
    i_not_equal_j = tf.expand_dims(indices_not_equal, 2) 
    i_not_equal_k = tf.expand_dims(indices_not_equal, 1)
    j_not_equal_k = tf.expand_dims(indices_not_equal, 0)
    # 想得到i!=j!=k, 三个不等取and即可, 最后可以得到当下标（i, j, k）不相等时才取True
    distinct_indices = tf.logical_and(tf.logical_and(i_not_equal_j, i_not_equal_k), j_not_equal_k)
    # 同样根据labels得到对应i=j, i!=k
    label_equal = tf.equal(tf.expand_dims(labels, 0), tf.expand_dims(labels, 1))
    i_equal_j = tf.expand_dims(label_equal, 2)
    i_equal_k = tf.expand_dims(label_equal, 1)
    valid_labels = tf.logical_and(i_equal_j, tf.logical_not(i_equal_k))
    # mask即为满足上面两个约束，所以两个3D取and
    mask = tf.logical_and(distinct_indices, valid_labels)
    return mask

def batch_all_triplet_loss(labels, embeddings, margin, squared=False):
    '''
       triplet loss of a batch
       -------------------------------
       Args:
          labels:     标签数据，shape = （batch_size,）
          embeddings: 提取的特征向量， shape = (batch_size, vector_size)
          margin:     margin大小， scalar
          
       Returns:
          triplet_loss: scalar, 一个batch的损失值
          fraction_postive_triplets : valid的triplets占的比例
    '''
    
    # 得到每两两embeddings的距离，然后增加一个维度，一维需要得到（batch_size, batch_size, batch_size）大小的3D矩阵
    # 然后再点乘上valid 的 mask即可
    pairwise_dis = _pairwise_distance(embeddings, squared=squared)
    anchor_positive_dist = tf.expand_dims(pairwise_dis, 2)
    assert anchor_positive_dist.shape[2] == 1, "{}".format(anchor_positive_dist.shape)
    anchor_negative_dist = tf.expand_dims(pairwise_dis, 1)
    assert anchor_negative_dist.shape[1] == 1, "{}".format(anchor_negative_dist.shape)
    triplet_loss = anchor_positive_dist - anchor_negative_dist + margin
    
    mask = _get_triplet_mask(labels)
    mask = tf.to_float(mask)
    triplet_loss = tf.multiply(mask, triplet_loss)
    triplet_loss = tf.maximum(triplet_loss, 0.0)
    
    # 计算valid的triplet的个数，然后对所有的triplet loss求平均
    valid_triplets = tf.to_float(tf.greater(triplet_loss, 1e-16))
    num_positive_triplets = tf.reduce_sum(valid_triplets)
    num_valid_triplets = tf.reduce_sum(mask)
    fraction_postive_triplets = num_positive_triplets / (num_valid_triplets + 1e-16)
    
    triplet_loss = tf.reduce_sum(triplet_loss) / (num_positive_triplets + 1e-16)
    return triplet_loss, fraction_postive_triplets

def main(argv):
    args = parser.parse_args(argv[1:])
    tf.logging.info("创建模型....")
    with open(args.model_config) as f:
        params = json.load(f)
    config = tf.estimator.RunConfig(model_dir=args.model_dir, tf_random_seed=100)  # config
    cls = tf.estimator.Estimator(model_fn=my_model, config=config, params=params)  # 建立模型
    tf.logging.info("开始训练模型,共{} epochs....".format(params['num_epochs']))
    cls.train(input_fn = lambda: train_input_fn(args.data_dir, params))            # 训练模型，指定输入
    
    tf.logging.info("测试集评价模型....")
    res = cls.evaluate(input_fn = lambda: test_input_fn(args.data_dir, params))    # 测试模型，指定输入
    for key in res:
        print("评价---{} : {}".format(key, res[key]))

def my_model(features, labels, mode, params):
    '''
       model_fn指定函数，构建模型，训练等
       ---------------------------------
       Args:
          features: 输入，shape = (batch_size, 784)
          labels:   输出，shape = (batch_size, )
          mode:     str, 阶段
          params:   dict, 超参数
    '''
    is_training = (mode == tf.estimator.ModeKeys.TRAIN)
    images = features
    images = tf.reshape(images, shape=[-1, params['image_size'], params['image_size'], 1])  # reshape (batch_size, img_size, img_size, 1)
    with tf.variable_scope("model"):
        embeddings = build_model(is_training, images, params)  # 简历模型
    
    if mode == tf.estimator.ModeKeys.PREDICT:     # 如果是预测阶段，直接返回得到embeddings
        predictions = {'embeddings': embeddings}
        return tf.estimator.EstimatorSpec(mode=mode, predictions=predictions)
    
    '''调用对应的triplet loss'''
    labels = tf.cast(labels, tf.int64)
    if params['triplet_strategy'] == 'batch_all':
        loss, fraction = batch_all_triplet_loss(labels, embeddings, margin=params['margin'], squared=params['squared'])
    elif params['triplet_strategy'] == 'batch_hard':
        loss = batch_hard_triplet_loss(labels, embeddings, margin=params['margin'], squared=params['squared'])
    else:
        raise ValueError("triplet_strategy 配置不正确: {}".format(params['triplet_strategy']))
    
    embedding_mean_norm = tf.reduce_mean(tf.norm(embeddings, axis=1))     # 这里计算了embeddings的二范数的均值 
    tf.summary.scalar("embedding_mean_norm", embedding_mean_norm)
    with tf.variable_scope("metrics"):
        eval_metric_ops = {'embedding_mean_norm': tf.metrics.mean(embedding_mean_norm)}
        if params['triplet_strategy'] == 'batch_all':
            eval_metric_ops['fraction_positive_triplets'] = tf.metrics.mean(fraction)
    if mode == tf.estimator.ModeKeys.EVAL:
        return tf.estimator.EstimatorSpec(mode, loss=loss, eval_metric_ops=eval_metric_ops)
    
    tf.summary.scalar('loss', loss)
    if params['triplet_strategy'] == "batch_all":
        tf.summary.scalar('fraction_positive_triplets', fraction)
    tf.summary.image('train_image', images, max_outputs=1)   # 1代表1个channel
    
    optimizer = tf.train.AdamOptimizer(learning_rate=params['learning_rate'])
    global_step = tf.train.get_global_step()
    if params['use_batch_norm']:
        '''如果使用BN，需要估计batch上的均值和方差，tf.get_collection(tf.GraphKeys.UPDATE_OPS)就可以得到
        tf.control_dependencies计算完之后再进行里面的操作
        '''
        with tf.control_dependencies(tf.get_collection(tf.GraphKeys.UPDATE_OPS)):
            train_op = optimizer.minimize(loss, global_step=global_step)
    else:
        train_op = optimizer.minimize(loss, global_step=global_step)
    return tf.estimator.EstimatorSpec(mode, loss=loss, train_op=train_op)

def build_model(is_training, images, params):
    '''
       建立模型
       ----------------------------
       Args：
          is_training: bool, 是否是训练阶段，可以从mode中判断
          images：     (batch_size, 28*28*1), 输入mnist数据
          params:      dict, 一些超参数
          
       Returns:
          out: 输出的embeddings, shape = (batch_size, 64)
    '''
    num_channel = params['num_channels']
    bn_momentum = params['bn_momentum']
    channels = [num_channel, num_channel * 2]
    out = images
    for i, c in enumerate(channels):
        with tf.variable_scope("block_{}".format(i)):
            out = tf.layers.conv2d(out, c, 3, padding='same')
            if params['use_batch_norm']:
                out = tf.layers.batch_normalization(out, momentum=bn_momentum, training=is_training)
            out = tf.nn.relu(out)
            out = tf.layers.max_pooling2d(out, 2, 2)
    assert out.shape[1:] == [7, 7, num_channel * 2]
    out = tf.reshape(out, [-1, 7*7*num_channel*2])
    with tf.variable_scope("fc_1"):
        out = tf.layers.dense(out, params['embedding_size'])
    return out

args = parser.parse_args(argv[1:])
with open(args.model_config) as f:
    params = json.load(f)
tf.logging.info("创建模型....")
config = tf.estimator.RunConfig(model_dir=args.model_dir, tf_random_seed=100)  # config
cls = tf.estimator.Estimator(model_fn=my_model, config=config, params=params)  # 建立模型
tf.logging.info("预测....")
predictions = cls.predict(input_fn=lambda: test_input_fn(args.data_dir, params))
embeddings = np.zeros((10000, params['embedding_size']))
for i, p in enumerate(predictions):
    embeddings[i] = p['embeddings']
tf.logging.info("embeddings shape: {}".format(embeddings.shape))

with tf.Session() as sess:
    # Obtain the test labels
    dataset = mnist_dataset.test(args.data_dir)
    dataset = dataset.map(lambda img, lab: lab)
    dataset = dataset.batch(10000)
    labels_tensor = dataset.make_one_shot_iterator().get_next()
    labels = sess.run(labels_tensor)   
np.savetxt(os.path.join(args.log_dir, 'metadata.tsv'), labels, fmt='%d')

shutil.copy(args.sprite_filename, args.log_dir)
'''可视化embeddings'''
with tf.Session() as sess:
    # 1. Variable
    embedding_var = tf.Variable(embeddings, name="mnist_embeddings")
    #tf.global_variables_initializer().run()  # 不需要
    
    # 2. 保存到文件中，embeddings.ckpt
    saver = tf.train.Saver()
    sess.run(embedding_var.initializer)
    saver.save(sess, os.path.join(args.log_dir, 'embeddings.ckpt'))
    
    # 3. 关联metadata.tsv, 和mnist_10k_sprite.png
    summary_writer = tf.summary.FileWriter(args.log_dir)
    config = projector.ProjectorConfig()
    embedding = config.embeddings.add()
    embedding.tensor_name = embedding_var.name
    embedding.metadata_path = 'metadata.tsv'
    embedding.sprite.image_path = 'mnist_10k_sprite.png'
    embedding.sprite.single_image_dim.extend([28, 28])
    projector.visualize_embeddings(summary_writer, config)