nn.py

#  Copyright (c) 2018 PaddlePaddle Authors. All Rights Reserve.
#
#Licensed under the Apache License, Version 2.0 (the "License");
#you may not use this file except in compliance with the License.
#You may obtain a copy of the License at
#
#    http://www.apache.org/licenses/LICENSE-2.0
#
#Unless required by applicable law or agreed to in writing, software
#distributed under the License is distributed on an "AS IS" BASIS,
#WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
#See the License for the specific language governing permissions and
#limitations under the License.
"""
All layers just related to the neural network.
"""

from ..layer_helper import LayerHelper
from ..initializer import Normal, Constant
from ..framework import Variable
from ..param_attr import ParamAttr
from tensor import concat

__all__ = [
    'fc',
    'embedding',
    'dynamic_lstm',
    'gru_unit',
    'linear_chain_crf',
    'crf_decoding',
    'cos_sim',
    'cross_entropy',
    'square_error_cost',
    'accuracy',
    'chunk_eval',
    'sequence_conv',
    'conv2d',
    'sequence_pool',
    'pool2d',
    'batch_norm',
    'beam_search_decode',
    'conv2d_transpose',
    'sequence_expand',
    'lstm_unit',
    'reduce_sum',
    'reduce_mean',
    'reduce_max',
    'reduce_min',
    'sequence_first_step',
    'sequence_last_step',
    'dropout',
    'split',
    'l2_normalize',
]


def fc(input,
       size,
       num_flatten_dims=1,
       param_attr=None,
       bias_attr=None,
       act=None,
       name=None):
    """
    **Fully Connected Layer**

    The fully connected layer can take multiple tensors as its inputs. It
    creates a variable (one for each input tensor) called weights for each input
    tensor, which represents a fully connected weight matrix from each input
    unit to each output unit. The fully connected layer multiplies each input
    tensor with its coresponding weight to produce an output Tensor. If
    multiple input tensors are given, the results of multiple multiplications
    will be sumed up. If bias_attr is not None, a biases variable will be
    created and added to the output. Finally, if activation is not None,
    it will be applied to the output as well.

    This process can be formulated as follows:

    .. math::

        Out = Act({\sum_{i=0}^{N-1}W_iX_i + b})

    In the above equation:

    * :math:`N`: Number of the input.
    * :math:`X_i`: The input tensor.
    * :math:`W`: The weights created by this layer.
    * :math:`b`: The bias parameter created by this layer (if needed).
    * :math:`Act`: The activation funtion.
    * :math:`Out`: The output tensor.

    Args:
       input(Variable|list): The input tensor(s) to the fully connected layer.
       size(int): The number of output units in the fully connected layer.
       num_flatten_dims(int): The fc layer can accept an input tensor with more
                              than two dimensions. If this happens, the
                              multidimensional tensor will first be flattened
                              into a 2-dimensional matrix. The parameter
                              `num_flatten_dims` determines how the input tensor
                              is flattened: the first `num_flatten_dims`
                              dimensions will be flatten to form the first
                              dimension of the final matrix (height of the
                              matrix), and the rest `rank(X) - num_flatten_dims`
                              dimensions are flattened to form the second
                              dimension of the final matrix (width of the matrix).
                              For example, suppose `X` is a 6-dimensional tensor
                              with a shape [2, 3, 4, 5, 6], and
                              `num_flatten_dims` = 3. Then, the flattened matrix
                              will have a shape [2 x 3 x 4, 5 x 6] = [24, 30].
                              By default, `num_flatten_dims` is set to 1.
       param_attr(ParamAttr|list): The parameter attribute for learnable
                                   parameters/weights of the fully connected
                                   layer.
       param_initializer(ParamAttr|list): The initializer used for the
                                          weight/parameter. If set None,
                                          XavierInitializer() will be used.
       bias_attr(ParamAttr|list): The parameter attribute for the bias parameter
                                  for this layer. If set None, no bias will be
                                  added to the output units.
       bias_initializer(ParamAttr|list): The initializer used for the bias.
                                        If set None, then ConstantInitializer()
                                        will be used.
       act(str): Activation to be applied to the output of the fully connected
                 layer.
       name(str): Name/alias of the fully connected layer.


    Returns:
        Variable: The output tensor variable.

    Raises:
        ValueError: If rank of the input tensor is less than 2.

    Examples:
        .. code-block:: python

          data = fluid.layers.data(name="data", shape=[32, 32], dtype="float32")
          fc = fluid.layers.fc(input=data, size=1000, act="tanh")
    """

    helper = LayerHelper("fc", **locals())

    dtype = helper.input_dtype()

    mul_results = []
    for input_var, param_attr in helper.iter_inputs_and_params():
        input_shape = input_var.shape
        param_shape = [
            reduce(lambda a, b: a * b, input_shape[num_flatten_dims:], 1)
        ] + [size]
        w = helper.create_parameter(
            attr=param_attr, shape=param_shape, dtype=dtype, is_bias=False)
        tmp = helper.create_tmp_variable(dtype)
        helper.append_op(
            type="mul",
            inputs={
                "X": input_var,
                "Y": w,
            },
            outputs={"Out": tmp},
            attrs={"x_num_col_dims": num_flatten_dims,
                   "y_num_col_dims": 1})
        mul_results.append(tmp)

    # sum
    if len(mul_results) == 1:
        pre_bias = mul_results[0]
    else:
        pre_bias = helper.create_tmp_variable(dtype)
        helper.append_op(
            type="sum", inputs={"X": mul_results}, outputs={"Out": pre_bias})
    # add bias
    pre_activation = helper.append_bias_op(pre_bias)
    # add activation
    return helper.append_activation(pre_activation)


def embedding(input, size, is_sparse=False, param_attr=None, dtype='float32'):
    """
    **Embedding Layer**

    This layer is used to lookup a vector of IDs, provided by *input*, in a lookup table.
    The result of this lookup is the embedding of each ID in the *input*.

    All the input variables are passed in as local variables to the LayerHelper
    constructor.

    Args:
       input(Variable): Input to the function
       size(tuple|list|None): Shape of the look up table parameter
       is_sparse(bool): Boolean flag that specifying whether the input is sparse
       param_attr(ParamAttr): Parameters for this layer
       dtype(np.dtype|core.DataType|str): The type of data : float32, float_16, int etc

    Returns:
        Variable: The tensor variable storing the embeddings of the \
                  supplied inputs.

    Examples:
        .. code-block:: python

          dict_size = len(dataset.ids)
          data = fluid.layers.data(name='ids', shape=[32, 32], dtype='float32')
          fc = fluid.layers.embedding(input=data, size=[dict_size, 16])
    """

    helper = LayerHelper('embedding', **locals())
    w = helper.create_parameter(
        attr=helper.param_attr, shape=size, dtype=dtype, is_bias=False)
    tmp = helper.create_tmp_variable(dtype)
    helper.append_op(
        type='lookup_table',
        inputs={'Ids': input,
                'W': w},
        outputs={'Out': tmp},
        attrs={'is_sparse': is_sparse})
    return tmp


# TODO(qijun): expose H0 and C0
def dynamic_lstm(input,
                 size,
                 param_attr=None,
                 bias_attr=None,
                 use_peepholes=True,
                 is_reverse=False,
                 gate_activation='sigmoid',
                 cell_activation='tanh',
                 candidate_activation='tanh',
                 dtype='float32'):
    helper = LayerHelper('lstm', **locals())
    size = size / 4
    weight = helper.create_parameter(
        attr=helper.param_attr, shape=[size, 4 * size], dtype=dtype)
    bias_size = [1, 7 * size]
    if not use_peepholes:
        bias_size[1] = 4 * size
    bias = helper.create_parameter(
        attr=helper.bias_attr, shape=bias_size, dtype=dtype, is_bias=True)

    hidden = helper.create_tmp_variable(dtype)
    cell = helper.create_tmp_variable(dtype)
    batch_gate = helper.create_tmp_variable(dtype)
    batch_cell_pre_act = helper.create_tmp_variable(dtype)

    helper.append_op(
        type='lstm',
        inputs={'Input': input,
                'Weight': weight,
                'Bias': bias},
        outputs={
            'Hidden': hidden,
            'Cell': cell,
            'BatchGate': batch_gate,
            'BatchCellPreAct': batch_cell_pre_act
        },
        attrs={
            'use_peepholes': use_peepholes,
            'is_reverse': is_reverse,
            'gate_activation': gate_activation,
            'cell_activation': cell_activation,
            'candidate_activation': candidate_activation
        })
    return hidden, cell


def gru_unit(input,
             hidden,
             size,
             weight=None,
             bias=None,
             activation='tanh',
             gate_activation='sigmoid'):
    """
    GRU unit layer. The equation of a gru step is:

        .. math::
            u_t & = actGate(xu_{t} + W_u h_{t-1} + b_u)

            r_t & = actGate(xr_{t} + W_r h_{t-1} + b_r)

            m_t & = actNode(xm_t + W_c dot(r_t, h_{t-1}) + b_m)

            h_t & = dot((1-u_t), m_t) + dot(u_t, h_{t-1})

    The inputs of gru unit includes :math:`z_t`, :math:`h_{t-1}`. In terms
    of the equation above, the :math:`z_t` is split into 3 parts -
    :math:`xu_t`, :math:`xr_t` and :math:`xm_t`. This means that in order to
    implement a full GRU unit operator for an input, a fully
    connected layer has to be applied, such that :math:`z_t = W_{fc}x_t`.

    The terms :math:`u_t` and :math:`r_t` represent the update and reset gates
    of the GRU cell. Unlike LSTM, GRU has one lesser gate. However, there is
    an intermediate candidate hidden output, which is denoted by :math:`m_t`.
    This layer has three outputs :math:`h_t`, :math:`dot(r_t, h_{t-1})`
    and concatenation of :math:`u_t`, :math:`r_t` and :math:`m_t`.

    Args:
        input (Variable): The fc transformed input value of current step.
        hidden (Variable): The hidden value of lstm unit from previous step.
        size (integer): The input dimension value.
        weight (ParamAttr): The weight parameters for gru unit. Default: None
        bias (ParamAttr): The bias parameters for gru unit. Default: None
        activation (string): The activation type for cell (actNode). Default: 'tanh'
        gate_activation (string): The activation type for gates (actGate). Default: 'sigmoid'

    Returns:
        tuple: The hidden value, reset-hidden value and gate values.

    Examples:

        .. code-block:: python

             # assuming we have x_t_data and prev_hidden of size=10
             x_t = fluid.layers.fc(input=x_t_data, size=30)
             hidden_val, r_h_val, gate_val = fluid.layers.gru_unit(input=x_t,
                                                    hidden = prev_hidden)

    """
    activation_dict = dict(
        identity=0,
        sigmoid=1,
        tanh=2,
        relu=3, )
    activation = activation_dict[activation]
    gate_activation = activation_dict[gate_activation]

    helper = LayerHelper('gru_unit', **locals())
    dtype = helper.input_dtype()
    size = size / 3

    # create weight
    if weight is None:
        weight = helper.create_parameter(
            attr=helper.param_attr, shape=[size, 3 * size], dtype=dtype)

    # create bias

    if bias is None:
        bias_size = [1, 3 * size]
        bias = helper.create_parameter(
            attr=helper.bias_attr, shape=bias_size, dtype=dtype, is_bias=True)

    gate = helper.create_tmp_variable(dtype)
    reset_hidden_pre = helper.create_tmp_variable(dtype)
    updated_hidden = helper.create_tmp_variable(dtype)

    helper.append_op(
        type='gru_unit',
        inputs={'Input': input,
                'HiddenPrev': hidden,
                'Weight': weight},
        outputs={
            'Gate': gate,
            'ResetHiddenPrev': reset_hidden_pre,
            'Hidden': updated_hidden,
        },
        attrs={
            'activation': 0,
            'gate_activation': 1,
        })

    return updated_hidden, reset_hidden_pre, gate


def linear_chain_crf(input, label, param_attr=None):
    helper = LayerHelper('linear_chain_crf', **locals())
    size = input.shape[1]
    transition = helper.create_parameter(
        attr=helper.param_attr,
        shape=[size + 2, size],
        dtype=helper.input_dtype())
    alpha = helper.create_tmp_variable(dtype=helper.input_dtype())
    emission_exps = helper.create_tmp_variable(dtype=helper.input_dtype())
    transition_exps = helper.create_tmp_variable(dtype=helper.input_dtype())
    log_likelihood = helper.create_tmp_variable(dtype=helper.input_dtype())
    helper.append_op(
        type='linear_chain_crf',
        inputs={"Emission": [input],
                "Transition": transition,
                "Label": label},
        outputs={
            "Alpha": [alpha],
            "EmissionExps": [emission_exps],
            "TransitionExps": transition_exps,
            "LogLikelihood": log_likelihood
        })

    return log_likelihood


def crf_decoding(input, param_attr, label=None):
    helper = LayerHelper('crf_decoding', **locals())
    transition = helper.get_parameter(param_attr.name)
    viterbi_path = helper.create_tmp_variable(dtype=helper.input_dtype())
    helper.append_op(
        type='crf_decoding',
        inputs={"Emission": [input],
                "Transition": transition,
                "Label": label},
        outputs={"ViterbiPath": [viterbi_path]})

    return viterbi_path


def cos_sim(X, Y, **kwargs):
    """
    This function performs the cosine similarity between two tensors
    X and Y and returns that as the output.
    """
    helper = LayerHelper('cos_sim', **kwargs)
    out = helper.create_tmp_variable(dtype=X.dtype)
    xnorm = helper.create_tmp_variable(dtype=X.dtype)
    ynorm = helper.create_tmp_variable(dtype=X.dtype)
    helper.append_op(
        type='cos_sim',
        inputs={'X': [X],
                'Y': [Y]},
        outputs={'Out': [out],
                 'XNorm': [xnorm],
                 'YNorm': [ynorm]})
    return out


def dropout(x, dropout_prob, is_test=False, seed=0, **kwargs):
    helper = LayerHelper('dropout', **kwargs)
    out = helper.create_tmp_variable(dtype=x.dtype)
    mask = helper.create_tmp_variable(dtype=x.dtype, stop_gradient=True)
    helper.append_op(
        type='dropout',
        inputs={'X': [x]},
        outputs={'Out': [out],
                 'Mask': [mask]},
        attrs={'dropout_prob': dropout_prob,
               'is_test': is_test,
               'seed': seed})
    return out


def cross_entropy(input, label, **kwargs):
    """
    **Cross Entropy Layer**

    This layer computes the cross entropy between `input` and `label`. It supports
    both standard cross-entropy and soft-label cross-entropy loss computation.

    1) One-hot cross-entropy:
	`soft_label = False`, `Label[i, 0]` indicates the class index for sample i:

        .. math::

            Y[i] = -\log(X[i, Label[i]])

    2) Soft-label cross-entropy:
	`soft_label = True`, `Label[i, j]` indicates the soft label of class j
	for sample i:

        .. math::

            Y[i] = \sum_j{-Label[i, j] * log(X[i, j])}

       Please make sure that in this case the summation of each row of `label`
       equals one.

    3) One-hot cross-entropy with vecterized `label`:
	 As a special case of 2), when each row of 'label' has only one
	 non-zero element which is equal to 1, soft-label cross-entropy degenerates
         to a one-hot cross-entropy with one-hot label representation.

    Args:
        input (Variable|list):  a 2-D tensor with shape [N x D], where N is the
            batch size and D is the number of classes. This input is a probability
            computed by the previous operator, which is almost always the result
            of a softmax operator.
        label (Variable|list): the ground truth which is a 2-D tensor. When
              `soft_label` is set to `False`, `label` is a tensor<int64> with shape
              [N x 1]. When `soft_label` is set to `True`, `label` is a
              tensor<float/double> with shape [N x D].
        soft_label (bool, via `**kwargs`): a flag indicating whether to interpretate
              the given labels as soft labels, default `False`.

    Returns:
         A 2-D tensor with shape [N x 1], the cross entropy loss.

    Raises:
        `ValueError`: 1) the 1st dimension of `input` and `label` are not equal; 2) when \
              `soft_label == True`, and the 2nd dimension of `input` and `label` are not \
               equal; 3) when `soft_label == False`, and the 2nd dimension of `label` is not 1.

    Examples:
        .. code-block:: python

          predict = fluid.layers.fc(input=net, size=classdim, act='softmax')
          cost = fluid.layers.cross_entropy(input=predict, label=label)
    """
    helper = LayerHelper('cross_entropy', **kwargs)
    out = helper.create_tmp_variable(dtype=input.dtype)
    helper.append_op(
        type='cross_entropy',
        inputs={'X': [input],
                'Label': [label]},
        outputs={'Y': [out]},
        attrs=kwargs)
    return out


def square_error_cost(input, label, **kwargs):
    """
    **Square error cost layer**

    This layer accepts input predictions and target label and returns the squared error cost.
    For predictions, :math:`X`, and target labels, :math:`Y`, the equation is:

    .. math::

        Out = (X - Y)^2

    In the above equation:

        * :math:`X`: Input predictions, a tensor.
        * :math:`Y`: Input labels, a tensor.
        * :math:`Out`: Output value, same shape with :math:`X`.

    Args:
       input(Variable): Input tensor, has predictions.
       label(Variable): Label tensor, has target labels.

    Returns:
        Variable: The tensor variable storing the element-wise squared error difference \
                  of input and label.

    Examples:
        .. code-block:: python

          y = layers.data(name='y', shape=[1], dtype='float32')
          y_predict = layers.data(name='y_predict', shape=[1], dtype='float32')
          cost = layers.square_error_cost(input=y_predict, label=y)

    """
    helper = LayerHelper('square_error_cost', **kwargs)
    minus_out = helper.create_tmp_variable(dtype=input.dtype)
    helper.append_op(
        type='elementwise_sub',
        inputs={'X': [input],
                'Y': [label]},
        outputs={'Out': [minus_out]})

    square_out = helper.create_tmp_variable(dtype=input.dtype)
    helper.append_op(
        type='square', inputs={'X': [minus_out]},
        outputs={'Out': [square_out]})
    return square_out


def accuracy(input, label, k=1, correct=None, total=None, **kwargs):
    """
    This function computes the accuracy using the input and label.
    The output is the top_k inputs and their indices.
    """
    helper = LayerHelper("accuracy", **kwargs)
    topk_out = helper.create_tmp_variable(dtype=input.dtype)
    topk_indices = helper.create_tmp_variable(dtype="int64")
    helper.append_op(
        type="top_k",
        inputs={"X": [input]},
        outputs={"Out": [topk_out],
                 "Indices": [topk_indices]},
        attrs={"k": k})
    acc_out = helper.create_tmp_variable(dtype="float32")
    if correct is None:
        correct = helper.create_tmp_variable(dtype="int64")
    if total is None:
        total = helper.create_tmp_variable(dtype="int64")
    helper.append_op(
        type="accuracy",
        inputs={
            "Out": [topk_out],
            "Indices": [topk_indices],
            "Label": [label]
        },
        outputs={
            "Accuracy": [acc_out],
            "Correct": [correct],
            "Total": [total],
        })
    return acc_out


def chunk_eval(input,
               label,
               chunk_scheme,
               num_chunk_types,
               excluded_chunk_types=None,
               **kwargs):
    """
    This function computes and outputs the precision, recall and
    F1-score of chunk detection.
    """
    helper = LayerHelper("chunk_eval", **kwargs)

    # prepare output
    precision = helper.create_tmp_variable(dtype="float32")
    recall = helper.create_tmp_variable(dtype="float32")
    f1_score = helper.create_tmp_variable(dtype="float32")
    num_infer_chunks = helper.create_tmp_variable(dtype="int64")
    num_label_chunks = helper.create_tmp_variable(dtype="int64")
    num_correct_chunks = helper.create_tmp_variable(dtype="int64")

    helper.append_op(
        type="chunk_eval",
        inputs={"Inference": [input],
                "Label": [label]},
        outputs={
            "Precision": [precision],
            "Recall": [recall],
            "F1-Score": [f1_score],
            "NumInferChunks": [num_infer_chunks],
            "NumLabelChunks": [num_label_chunks],
            "NumCorrectChunks": [num_correct_chunks]
        },
        attrs={
            "num_chunk_types": num_chunk_types,
            "chunk_scheme": chunk_scheme,
            "excluded_chunk_types": excluded_chunk_types or []
        })
    return precision, recall, f1_score, num_infer_chunks, num_label_chunks, num_correct_chunks


def sequence_conv(input,
                  num_filters,
                  filter_size=3,
                  filter_stride=1,
                  padding=None,
                  bias_attr=None,
                  param_attr=None,
                  act=None):
    """
    This function creates the op for sequence_conv, using the inputs and
    other convolutional configurations for the filters and stride as given
    in the input parameters to the function.
    """

    # FIXME(dzh) : want to unify the argument of python layer
    # function. So we ignore some unecessary attributes.
    # such as, padding_trainable, context_start.

    helper = LayerHelper('sequence_conv', **locals())
    dtype = helper.input_dtype()
    filter_shape = [filter_size * input.shape[1], num_filters]
    filter_param = helper.create_parameter(
        attr=helper.param_attr, shape=filter_shape, dtype=dtype)
    pre_bias = helper.create_tmp_variable(dtype)

    helper.append_op(
        type='sequence_conv',
        inputs={
            'X': [input],
            'Filter': [filter_param],
        },
        outputs={"Out": pre_bias},
        attrs={
            'contextStride': filter_stride,
            'contextStart': -int(filter_size / 2),
            'contextLength': filter_size
        })
    pre_act = helper.append_bias_op(pre_bias)
    return helper.append_activation(pre_act)


def conv2d(input,
           num_filters,
           filter_size,
           stride=None,
           padding=None,
           groups=None,
           param_attr=None,
           bias_attr=None,
           act=None):
    """
    **Convlution2D Layer**

    The convolution2D layer calculates the output based on the input, filter
    and strides, paddings, dilations, groups parameters. Input(Input) and Output(Output)
    are in NCHW format. Where N is batch size, C is the number of channels, H is the height
    of the feature, and W is the width of the feature.
    The details of convolution layer, please refer UFLDL's `convolution,
    <http://ufldl.stanford.edu/tutorial/supervised/FeatureExtractionUsingConvolution/>`_ .
    If bias attribution and activation type are provided, bias is added to the output of the convolution,
    and the corresponding activation function is applied to the final result.
    For each input :math:`X`, the equation is:


    .. math::

        Out = \sigma (W \\ast X + b)

    In the above equation:

        * :math:`X`: Input value, a tensor with NCHW format.
        * :math:`W`: Filter value, a tensor with MCHW format.
        * :math:`\\ast`: Convolution operation.
        * :math:`b`: Bias value, a 2-D tensor with shape [M, 1].
        * :math:`\\sigma`: Activation function.
        * :math:`Out`: Output value, the shape of :math:`Out` and :math:`X` may be different.

    Example:

        Input:
            Input shape: $(N, C_{in}, H_{in}, W_{in})$

            Filter shape: $(C_{out}, C_{in}, H_f, W_f)$

        Output:
            Output shape: $(N, C_{out}, H_{out}, W_{out})$
        Where
    .. math::

        H_{out}&= \\frac{(H_{in} + 2 * paddings[0] - (dilations[0] * (H_f - 1) + 1))}{strides[0]} + 1 \\\\
        W_{out}&= \\frac{(W_{in} + 2 * paddings[1] - (dilations[1] * (W_f - 1) + 1))}{strides[1]} + 1

    Args:
        input(Variable): The input image with [N, C, H, W] format.
        num_filters(int): The number of filter. It is as same as the output
            image channel.
        filter_size(int|tuple|None): The filter size. If filter_size is a tuple,
            it must contain two integers, (filter_size_H, filter_size_W).
            Otherwise, the filter will be a square.
        stride(int|tuple): The stride size. If stride is a tuple, it must
            contain two integers, (stride_H, stride_W). Otherwise, the
            stride_H = stride_W = stride. Default: stride = 1.
        padding(int|tuple): The padding size. If padding is a tuple, it must
            contain two integers, (padding_H, padding_W). Otherwise, the
            padding_H = padding_W = padding. Default: padding = 0.
        groups(int): The groups number of the Conv2d Layer. According to grouped
            convolution in Alex Krizhevsky's Deep CNN paper: when group=2,
            the first half of the filters is only connected to the first half
            of the input channels, while the second half of the filters is only
            connected to the second half of the input channels. Default: groups=1
        param_attr(ParamAttr): The parameters to the Conv2d Layer. Default: None
        bias_attr(ParamAttr): Bias parameter for the Conv2d layer. Default: None
        act(str): Activation type. Default: None

    Returns:
        Variable: The tensor variable storing the convolution and \
                  non-linearity activation result.

    Raises:
        ValueError: If the shapes of input, filter_size, stride, padding and groups mismatch.

    Examples:
        .. code-block:: python

          data = fluid.layers.data(name='data', shape=[3, 32, 32], dtype='float32')
          conv2d = fluid.layers.conv2d(input=data, num_filters=2, filter_size=3, act="relu")
    """

    if stride is None:
        stride = [1, 1]
    helper = LayerHelper('conv2d', **locals())
    dtype = helper.input_dtype()

    num_channels = input.shape[1]
    if groups is None:
        num_filter_channels = num_channels
    else:
        if num_channels % groups != 0:
            raise ValueError("num_channels must be divisible by groups.")
        num_filter_channels = num_channels / groups

    if isinstance(filter_size, int):
        filter_size = [filter_size, filter_size]
    if isinstance(stride, int):
        stride = [stride, stride]
    if isinstance(padding, int):
        padding = [padding, padding]

    input_shape = input.shape
    filter_shape = [num_filters, num_filter_channels] + filter_size

    def _get_default_param_initializer():
        std = (2.0 / (filter_size[0]**2 * num_channels))**0.5
        return Normal(0.0, std, 0)

    filter_param = helper.create_parameter(
        attr=helper.param_attr,
        shape=filter_shape,
        dtype=dtype,
        default_initializer=_get_default_param_initializer())

    pre_bias = helper.create_tmp_variable(dtype)

    helper.append_op(
        type='conv2d',
        inputs={
            'Input': input,
            'Filter': filter_param,
        },
        outputs={"Output": pre_bias},
        attrs={'strides': stride,
               'paddings': padding,
               'groups': groups})

    pre_act = helper.append_bias_op(pre_bias, dim_start=1, dim_end=2)

    return helper.append_activation(pre_act)


def sequence_pool(input, pool_type, **kwargs):
    """
    This function add the operator for sequence pooling.
    It pools features of all time-steps of each instance, and is applied
    on top of the input using pool_type mentioned in the parameters.

    It supports four pool_type:

    - average: :math:`Out[i] = \\frac{\sum_i X_i}{N}`
    - sum:     :math:`Out[i] = \sum_jX_{ij}`
    - sqrt:    :math:`Out[i] = \\frac{\sum_jX_{ij}}{\sqrt{len(X_i)}}`
    - max:     :math:`Out[i] = max(X_i)`

    .. code-block:: text

       x is a 1-level LoDTensor:
         x.lod = [[0, 2, 5, 7]]
         x.data = [1, 3, 2, 4, 6, 5, 1]
         x.dims = [7, 1]

       then output is a Tensor:
         out.dim = [3, 1]
         with condition len(x.lod[-1]) - 1 == out.dims[0]

       for different pool_type:
         average: out.data = [2, 4, 3], where 2=(1+3)/2, 4=(2+4+6)/3, 3=(5+1)/2
         sum    : out.data = [4, 12, 6], where 4=1+3, 12=2+4+6, 6=5+1
         sqrt   : out.data = [2.82, 6.93, 4.24], where 2.82=(1+3)/sqrt(2),
                    6.93=(2+4+6)/sqrt(3), 4.24=(5+1)/sqrt(2)
         max    : out.data = [3, 6, 5], where 3=max(1,3), 6=max(2,4,6), 5=max(5,1)

    Args:
        input(variable): The input variable which is a LoDTensor.
        pool_type (string): The pooling type of sequence_pool.
            It supports average, sum, sqrt and max.

    Returns:
        The sequence pooling variable which is a Tensor.

    Examples:

        .. code-block:: python

             x = fluid.layers.data(name='x', shape=[7, 1],
                              dtype='float32', lod_level=1)
             avg_x = fluid.layers.sequence_pool(input=x, pool_type='average')
             sum_x = fluid.layers.sequence_pool(input=x, pool_type='sum')
             sqrt_x = fluid.layers.sequence_pool(input=x, pool_type='sqrt')
             max_x = fluid.layers.sequence_pool(input=x, pool_type='max')
    """
    helper = LayerHelper('sequence_pool', input=input, **kwargs)
    dtype = helper.input_dtype()
    pool_out = helper.create_tmp_variable(dtype)
    max_index = helper.create_tmp_variable(dtype)

    helper.append_op(
        type="sequence_pool",
        inputs={"X": input},
        outputs={"Out": pool_out,
                 "MaxIndex": max_index},
        attrs={"pooltype": pool_type.upper()})

    # when pool_type is max, variable max_index is initialized,
    # so we stop the gradient explicitly here
    if pool_type == 'max':
        max_index.stop_gradient = True

    return pool_out


def sequence_first_step(input, **kwargs):
    """
    This funciton get the first step of sequence.

    .. code-block:: text

       x is a 1-level LoDTensor:
         x.lod = [[0, 2, 5, 7]]
         x.data = [1, 3, 2, 4, 6, 5, 1]
         x.dims = [7, 1]

       then output is a Tensor:
         out.dim = [3, 1]
         with condition len(x.lod[-1]) - 1 == out.dims[0]
         out.data = [1, 2, 5], where 1=first(1,3), 2=first(2,4,6), 5=first(5,1)

    Args:
        input(variable): The input variable which is a LoDTensor.

    Returns:
        The sequence's first step variable which is a Tensor.

    Examples:

        .. code-block:: python

             x = fluid.layers.data(name='x', shape=[7, 1],
                              dtype='float32', lod_level=1)
             x_first_step = fluid.layers.sequence_first_step(input=x)
    """
    return sequence_pool(input=input, pool_type="first")


def sequence_last_step(input, **kwargs):
    """
    This funciton get the last step of sequence.

    .. code-block:: text

       x is a 1-level LoDTensor:
         x.lod = [[0, 2, 5, 7]]
         x.data = [1, 3, 2, 4, 6, 5, 1]
         x.dims = [7, 1]

       then output is a Tensor:
         out.dim = [3, 1]
         with condition len(x.lod[-1]) - 1 == out.dims[0]
         out.data = [3, 6, 1], where 3=last(1,3), 6=last(2,4,6), 1=last(5,1)

    Args:
        input(variable): The input variable which is a LoDTensor.

    Returns:
        The sequence's last step variable which is a Tensor.

    Examples:

        .. code-block:: python

             x = fluid.layers.data(name='x', shape=[7, 1],
                              dtype='float32', lod_level=1)
             x_last_step = fluid.layers.sequence_last_step(input=x)
    """
    return sequence_pool(input=input, pool_type="last")


def pool2d(input,
           pool_size,
           pool_type,
           pool_stride=None,
           pool_padding=None,
           global_pooling=False,
           name=None):
    """
    This function adds the operator for pooling in 2 dimensions, using the
    pooling configurations mentioned in input parameters.
    """
    if pool_padding is None:
        pool_padding = [0, 0]
    if pool_stride is None:
        pool_stride = [1, 1]
    if pool_type not in ["max", "avg"]:
        raise ValueError(
            "Unknown pool_type: '%s'. It can only be 'max' or 'avg'.",
            str(pool_type))
    if isinstance(pool_size, int):
        pool_size = [pool_size, pool_size]
    if isinstance(pool_stride, int):
        pool_stride = [pool_stride, pool_stride]
    if isinstance(pool_padding, int):
        pool_padding = [pool_padding, pool_padding]

    helper = LayerHelper('pool2d', **locals())
    dtype = helper.input_dtype()
    pool_out = helper.create_tmp_variable(dtype)

    helper.append_op(
        type="pool2d",
        inputs={"X": input},
        outputs={"Out": pool_out},
        attrs={
            "pooling_type": pool_type,
            "ksize": pool_size,
            "global_pooling": global_pooling,
            "strides": pool_stride,
            "paddings": pool_padding
        })

    return pool_out


def batch_norm(input,
               act=None,
               is_test=False,
               momentum=0.9,
               epsilon=1e-05,
               param_attr=None,
               bias_attr=None,
               data_layout='NCHW',
               name=None):
    """
    This function helps create an operator to implement
    the BatchNorm layer using the configurations from the input parameters.
    """
    helper = LayerHelper('batch_norm', **locals())
    dtype = helper.input_dtype()

    input_shape = input.shape
    if data_layout == 'NCHW':
        channel_num = input_shape[1]
    else:
        if data_layout == 'NHWC':
            channel_num = input_shape[-1]
        else:
            raise ValueError("unsupported data layout:" + data_layout)

    param_shape = [channel_num]

    # create parameter
    scale = helper.create_parameter(
        attr=helper.param_attr,
        shape=param_shape,
        dtype=dtype,
        default_initializer=Constant(1.0))

    bias = helper.create_parameter(
        attr=helper.bias_attr, shape=param_shape, dtype=dtype, is_bias=True)

    mean = helper.create_global_variable(
        dtype=input.dtype,
        shape=param_shape,
        persistable=True,
        stop_gradient=True)
    helper.set_variable_initializer(var=mean, initializer=Constant(0.0))

    variance = helper.create_global_variable(
        dtype=input.dtype,
        shape=param_shape,
        persistable=True,
        stop_gradient=True)
    helper.set_variable_initializer(var=variance, initializer=Constant(1.0))

    # create output
    # mean and mean_out share the same memory
    mean_out = mean
    # variance and variance out share the same memory
    variance_out = variance
    saved_mean = helper.create_tmp_variable(dtype=dtype, stop_gradient=True)
    saved_variance = helper.create_tmp_variable(dtype=dtype, stop_gradient=True)

    batch_norm_out = helper.create_tmp_variable(dtype)

    helper.append_op(
        type="batch_norm",
        inputs={
            "X": input,
            "Scale": scale,
            "Bias": bias,
            "Mean": mean,
            "Variance": variance
        },
        outputs={
            "Y": batch_norm_out,
            "MeanOut": mean_out,
            "VarianceOut": variance_out,
            "SavedMean": saved_mean,
            "SavedVariance": saved_variance
        },
        attrs={"momentum": momentum,
               "epsilon": epsilon,
               "is_test": is_test})

    return helper.append_activation(batch_norm_out)


def beam_search_decode(ids, scores, name=None):
    helper = LayerHelper('beam_search_decode', **locals())
    sentence_ids = helper.create_tmp_variable(dtype=ids.dtype)
    sentence_scores = helper.create_tmp_variable(dtype=ids.dtype)

    helper.append_op(
        type="beam_search_decode",
        inputs={"Ids": ids,
                "Scores": scores},
        outputs={
            "SentenceIds": sentence_ids,
            "SentenceScores": sentence_scores
        })

    return sentence_ids, sentence_scores


def conv2d_transpose(input,
                     num_filters,
                     output_size=None,
                     filter_size=None,
                     padding=None,
                     stride=None,
                     dilation=None,
                     param_attr=None,
                     name=None):
    """
    The transpose of conv2d layer.

    This layer is also known as deconvolution layer.

    Args:
        input(Variable): The input image with [N, C, H, W] format.
        num_filters(int): The number of filter. It is as same as the output
            image channel.
        output_size(int|tuple|None): The output image size. If output size is a
            tuple, it must contain two integers, (image_H, image_W). This
            parameter only works when filter_size is None.
        filter_size(int|tuple|None): The filter size. If filter_size is a tuple,
            it must contain two integers, (filter_size_H, filter_size_W).
            Otherwise, the filter will be a square.  None if use output size to
            calculate filter_size
        padding(int|tuple): The padding size. If padding is a tuple, it must
            contain two integers, (padding_H, padding_W). Otherwise, the
            padding_H = padding_W = padding.
        stride(int|tuple): The stride size. If stride is a tuple, it must
            contain two integers, (stride_H, stride_W). Otherwise, the
            stride_H = stride_W = stride.
        dilation(int|tuple): The dilation size. If dilation is a tuple, it must
            contain two integers, (dilation_H, dilation_W). Otherwise, the
            dilation_H = dilation_W = dilation.
        param_attr: Parameter Attribute.
        name(str|None): A name for this layer(optional). If set None, the layer
                       will be named automatically.

    Returns:
        Variable: Output image.
    """
    helper = LayerHelper("conv2d_transpose", **locals())
    if not isinstance(input, Variable):
        raise TypeError("Input of conv2d_transpose must be Variable")
    input_channel = input.shape[1]

    op_attr = dict()

    if isinstance(padding, int):
        op_attr['paddings'] = [padding, padding]
    elif padding is not None:
        op_attr['paddings'] = padding

    if isinstance(stride, int):
        op_attr['strides'] = [stride, stride]
    elif stride is not None:
        op_attr['strides'] = stride

    if isinstance(dilation, int):
        op_attr['dilations'] = [dilation, dilation]
    elif dilation is not None:
        op_attr['dilations'] = dilation

    if filter_size is None:
        if output_size is None:
            raise ValueError("output_size must be set when filter_size is None")
        if isinstance(output_size, int):
            output_size = [output_size, output_size]

        padding = op_attr.get('paddings', [0, 0])
        stride = op_attr.get('strides', [1, 1])
        dilation = op_attr.get('dilations', [1, 1])

        h_in = input.shape[2]
        w_in = input.shape[3]

        filter_size_h = (output_size[0] - (h_in - 1) * stride[0] + 2 *
                         padding[0] - 1) / dilation[0] + 1
        filter_size_w = (output_size[1] - (w_in - 1) * stride[1] + 2 *
                         padding[1] - 1) / dilation[1] + 1
        filter_size = [filter_size_h, filter_size_w]

    elif isinstance(filter_size, int):
        filter_size = [filter_size, filter_size]

    filter_shape = [input_channel, num_filters] + filter_size
    img_filter = helper.create_parameter(
        dtype=input.dtype, shape=filter_shape, attr=helper.param_attr)

    out = helper.create_tmp_variable(dtype=input.dtype)
    helper.append_op(
        type='conv2d_transpose',
        inputs={'Input': [input],
                'Filter': [img_filter]},
        outputs={'Output': out},
        attrs=op_attr)

    return out


def sequence_expand(x, y, name=None):
    """Sequence Expand Layer. This layer will expand the input variable **x**
    according to LoD information of **y**. And the following examples will
    explain how sequence_expand works:

    .. code-block:: text

        * Case 1
            x is a LoDTensor:
                x.lod = [[0,       2, 3],
                         [0, 1,    3, 4]]
                x.data = [a, b, c, d]
                x.dims = [4, 1]

            y is a LoDTensor:
                y.lod = [[0,    2,    4],
                         [0, 3, 6, 7, 8]]

            with condition len(y.lod[-1]) - 1 == x.dims[0]

            then output is a 2-level LoDTensor:
                out.lod = [[0,                2,    4],
                           [0,       3,       6, 7, 8]]
                out.data = [a, a, a, b, b, b, c, d]
                out.dims = [8, 1]

        * Case 2
            x is a Tensor:
                x.data = [a, b, c]
                x.dims = [3, 1]

            y is a LoDTensor:
                y.lod = [[0, 2, 3, 6]]

            with condition len(y.lod[-1]) - 1 == x.dims[0]

            then output is a 1-level LoDTensor:
                out.lod = [[0,    2, 3,      6]]
                out.data = [a, a, b, c, c, c]
                out.dims = [6, 1]

    Args:
        x (Variable): The input variable which is a Tensor or LoDTensor.
        y (Variable): The input variable which is a LoDTensor.
        name(str|None): A name for this layer(optional). If set None, the layer
                       will be named automatically.

    Returns:
        Variable: The expanded variable which is a LoDTensor.

    Examples:
        .. code-block:: python

            x = fluid.layers.data(name='x', shape=[10], dtype='float32')
            y = fluid.layers.data(name='y', shape=[10, 20],
                             dtype='float32', lod_level=1)
            out = layers.sequence_expand(x=x, y=y)
    """
    helper = LayerHelper('sequence_expand', input=x, **locals())
    dtype = helper.input_dtype()
    tmp = helper.create_tmp_variable(dtype)
    helper.append_op(
        type='sequence_expand', inputs={'X': x,
                                        'Y': y}, outputs={'Out': tmp})
    return tmp


def lstm_unit(x_t,
              hidden_t_prev,
              cell_t_prev,
              forget_bias=0.0,
              param_attr=None,
              bias_attr=None,
              name=None):
    """Lstm unit layer. The equation of a lstm step is:

        .. math::

            i_t & = \sigma(W_{x_i}x_{t} + W_{h_i}h_{t-1} + b_i)

            f_t & = \sigma(W_{x_f}x_{t} + W_{h_f}h_{t-1} + b_f)

            c_t & = f_tc_{t-1} + i_t tanh (W_{x_c}x_t + W_{h_c}h_{t-1} + b_c)

            o_t & = \sigma(W_{x_o}x_{t} + W_{h_o}h_{t-1} + b_o)

            h_t & = o_t tanh(c_t)

    The inputs of lstm unit include :math:`x_t`, :math:`h_{t-1}` and
    :math:`c_{t-1}`. The 2nd dimensions of :math:`h_{t-1}` and :math:`c_{t-1}`
    should be same. The implementation separates the linear transformation and
    non-linear transformation apart. Here, we take :math:`i_t` as an example.
    The linear transformation is applied by calling a `fc` layer and the
    equation is:

        .. math::

            L_{i_t} = W_{x_i}x_{t} + W_{h_i}h_{t-1} + b_i

    The non-linear transformation is applied by calling `lstm_unit_op` and the
    equation is:

        .. math::

            i_t = \sigma(L_{i_t})

    This layer has two outputs including :math:`h_t` and :math:`o_t`.

    Args:
        x_t (Variable): The input value of current step, a 2-D tensor with shape
            M x N, M for batch size and N for input size.
        hidden_t_prev (Variable): The hidden value of lstm unit, a 2-D tensor
            with shape M x S, M for batch size and S for size of lstm unit.
        cell_t_prev (Variable): The cell value of lstm unit, a 2-D tensor with
            shape M x S, M for batch size and S for size of lstm unit.
        forget_bias (float): The forget bias of lstm unit.
        param_attr (ParamAttr): The attributes of parameter weights, used to set
            initializer, name etc.
        bias_attr (ParamAttr): The attributes of bias weights, if not False,
            bias weights will be created and be set to default value.
        name(str|None): A name for this layer(optional). If set None, the layer
                       will be named automatically.

    Returns:
        tuple: The hidden value and cell value of lstm unit.

    Raises:
        ValueError: The ranks of **x_t**, **hidden_t_prev** and **cell_t_prev**\
                not be 2 or the 1st dimensions of **x_t**, **hidden_t_prev** \
                and **cell_t_prev** not be the same or the 2nd dimensions of \
                **hidden_t_prev** and **cell_t_prev** not be the same.

    Examples:

        .. code-block:: python

             x_t = fluid.layers.fc(input=x_t_data, size=10)
             prev_hidden = fluid.layers.fc(input=prev_hidden_data, size=30)
             prev_cell = fluid.layers.fc(input=prev_cell_data, size=30)
             hidden_value, cell_value = fluid.layers.lstm_unit(x_t=x_t,
                                                    hidden_t_prev=prev_hidden,
                                                    cell_t_prev=prev_cell)
    """
    helper = LayerHelper('lstm_unit', **locals())

    if len(x_t.shape) != 2:
        raise ValueError("Rank of x_t must be 2.")

    if len(hidden_t_prev.shape) != 2:
        raise ValueError("Rank of hidden_t_prev must be 2.")

    if len(cell_t_prev.shape) != 2:
        raise ValueError("Rank of cell_t_prev must be 2.")

    if x_t.shape[0] != hidden_t_prev.shape[0] or x_t.shape[
            0] != cell_t_prev.shape[0]:
        raise ValueError("The 1st dimensions of x_t, hidden_t_prev and "
                         "cell_t_prev must be the same.")

    if hidden_t_prev.shape[1] != cell_t_prev.shape[1]:
        raise ValueError("The 2nd dimensions of hidden_t_prev and "
                         "cell_t_prev must be the same.")

    if bias_attr is None:
        bias_attr = ParamAttr()

    size = cell_t_prev.shape[1]
    concat_out = concat(input=[x_t, hidden_t_prev], axis=1)
    fc_out = fc(input=concat_out,
                size=4 * size,
                param_attr=param_attr,
                bias_attr=bias_attr)
    dtype = x_t.dtype
    c = helper.create_tmp_variable(dtype)
    h = helper.create_tmp_variable(dtype)

    helper.append_op(
        type='lstm_unit',
        inputs={"X": fc_out,
                "C_prev": cell_t_prev},
        outputs={"C": c,
                 "H": h},
        attrs={"forget_bias": forget_bias})

    return h, c


def reduce_sum(input, dim=None, keep_dim=False, name=None):
    """
    Computes the sum of tensor elements over the given dimension.

    Args:
        input (Variable): The input variable which is a Tensor or LoDTensor.
        dim (int|None): The dimension along which the sum is performed. If
            :attr:`None`, sum all elements of :attr:`input` and return a
            Tensor variable with a single element, otherwise must be in the
            range :math:`[-rank(input), rank(input))`. If :math:`dim < 0`,
            the dimension to reduce is :math:`rank + dim`.
        keep_dim (bool): Whether to reserve the reduced dimension in the
            output Tensor. The result tensor will have one fewer dimension
            than the :attr:`input` unless :attr:`keep_dim` is true.
        name(str|None): A name for this layer(optional). If set None, the layer
                       will be named automatically.

    Returns:
        Variable: The reduced Tensor variable.

    Examples:
        .. code-block:: python

            # x is a Tensor variable with following elements:
            #    [[0.2, 0.3, 0.5, 0.9]
            #     [0.1, 0.2, 0.6, 0.7]]
            # Each example is followed by the correspending output tensor.
            fluid.layers.reduce_sum(x)  # [3.5]
            fluid.layers.reduce_sum(x, dim=0)  # [0.3, 0.5, 1.1, 1.6]
            fluid.layers.reduce_sum(x, dim=-1)  # [1.9, 1.6]
            fluid.layers.reduce_sum(x, dim=1, keep_dim=True)  # [[1.9], [1.6]]
    """
    helper = LayerHelper('reduce_sum', **locals())
    out = helper.create_tmp_variable(dtype=helper.input_dtype())
    helper.append_op(
        type='reduce_sum',
        inputs={'X': input},
        outputs={'Out': out},
        attrs={
            'dim': dim if dim != None else 0,
            'keep_dim': keep_dim,
            'reduce_all': True if dim == None else False
        })
    return out


def reduce_mean(input, dim=None, keep_dim=False, name=None):
    """
    Computes the mean of tensor elements over the given dimension.

    Args:
        input (Variable): The input variable which is a Tensor or LoDTensor.
        dim (int|None): The dimension along which the mean is computed. If
            :attr:`None`, compute the mean over all elements of :attr:`input`
            and return a Tensor variable with a single element, otherwise
            must be in the range :math:`[-rank(input), rank(input))`. If
            :math:`dim < 0`, the dimension to reduce is :math:`rank + dim`.
        keep_dim (bool): Whether to reserve the reduced dimension in the
            output Tensor. The result tensor will have one fewer dimension
            than the :attr:`input` unless :attr:`keep_dim` is true.
        name(str|None): A name for this layer(optional). If set None, the layer
                       will be named automatically.

    Returns:
        Variable: The reduced Tensor variable.

    Examples:
        .. code-block:: python

            # x is a Tensor variable with following elements:
            #    [[0.2, 0.3, 0.5, 0.9]
            #     [0.1, 0.2, 0.6, 0.7]]
            # Each example is followed by the correspending output tensor.
            fluid.layers.reduce_mean(x)  # [0.4375]
            fluid.layers.reduce_mean(x, dim=0)  # [0.15, 0.25, 0.55, 0.8]
            fluid.layers.reduce_mean(x, dim=-1)  # [0.475, 0.4]
            fluid.layers.reduce_mean(x, dim=1, keep_dim=True)  # [[0.475], [0.4]]
    """
    helper = LayerHelper('reduce_mean', **locals())
    out = helper.create_tmp_variable(dtype=helper.input_dtype())
    helper.append_op(
        type='reduce_mean',
        inputs={'X': input},
        outputs={'Out': out},
        attrs={
            'dim': dim if dim != None else 0,
            'keep_dim': keep_dim,
            'reduce_all': True if dim == None else False
        })
    return out


def reduce_max(input, dim=None, keep_dim=False, name=None):
    """
    Computes the maximum of tensor elements over the given dimension.

    Args:
        input (Variable): The input variable which is a Tensor or LoDTensor.
        dim (int|None): The dimension along which the maximum is computed.
            If :attr:`None`, compute the maximum over all elements of
            :attr:`input` and return a Tensor variable with a single element,
            otherwise must be in the range :math:`[-rank(input), rank(input))`.
            If :math:`dim < 0`, the dimension to reduce is :math:`rank + dim`.
        keep_dim (bool): Whether to reserve the reduced dimension in the
            output Tensor. The result tensor will have one fewer dimension
            than the :attr:`input` unless :attr:`keep_dim` is true.
        name(str|None): A name for this layer(optional). If set None, the layer
                       will be named automatically.

    Returns:
        Variable: The reduced Tensor variable.

    Examples:
        .. code-block:: python

            # x is a Tensor variable with following elements:
            #    [[0.2, 0.3, 0.5, 0.9]
            #     [0.1, 0.2, 0.6, 0.7]]
            # Each example is followed by the correspending output tensor.
            fluid.layers.reduce_max(x)  # [0.9]
            fluid.layers.reduce_max(x, dim=0)  # [0.2, 0.3, 0.6, 0.9]
            fluid.layers.reduce_max(x, dim=-1)  # [0.9, 0.7]
            fluid.layers.reduce_max(x, dim=1, keep_dim=True)  # [[0.9], [0.7]]
    """
    helper = LayerHelper('reduce_max', **locals())
    out = helper.create_tmp_variable(dtype=helper.input_dtype())
    helper.append_op(
        type='reduce_max',
        inputs={'X': input},
        outputs={'Out': out},
        attrs={
            'dim': dim if dim != None else 0,
            'keep_dim': keep_dim,
            'reduce_all': True if dim == None else False
        })
    return out


def reduce_min(input, dim=None, keep_dim=False, name=None):
    """
    Computes the minimum of tensor elements over the given dimension.

    Args:
        input (Variable): The input variable which is a Tensor or LoDTensor.
        dim (int|None): The dimension along which the minimum is computed.
            If :attr:`None`, compute the minimum over all elements of
            :attr:`input` and return a Tensor variable with a single element,
            otherwise must be in the range :math:`[-rank(input), rank(input))`.
            If :math:`dim < 0`, the dimension to reduce is :math:`rank + dim`.
        keep_dim (bool): Whether to reserve the reduced dimension in the
            output Tensor. The result tensor will have one fewer dimension
            than the :attr:`input` unless :attr:`keep_dim` is true.
        name(str|None): A name for this layer(optional). If set None, the layer
                       will be named automatically.

    Returns:
        Variable: The reduced Tensor variable.

    Examples:
        .. code-block:: python

            # x is a Tensor variable with following elements:
            #    [[0.2, 0.3, 0.5, 0.9]
            #     [0.1, 0.2, 0.6, 0.7]]
            # Each example is followed by the correspending output tensor.
            fluid.layers.reduce_min(x)  # [0.1]
            fluid.layers.reduce_min(x, dim=0)  # [0.1, 0.2, 0.5, 0.7]
            fluid.layers.reduce_min(x, dim=-1)  # [0.2, 0.1]
            fluid.layers.reduce_min(x, dim=1, keep_dim=True)  # [[0.2], [0.1]]
    """
    helper = LayerHelper('reduce_min', **locals())
    out = helper.create_tmp_variable(dtype=helper.input_dtype())
    helper.append_op(
        type='reduce_min',
        inputs={'X': input},
        outputs={'Out': out},
        attrs={
            'dim': dim if dim != None else 0,
            'keep_dim': keep_dim,
            'reduce_all': True if dim == None else False
        })
    return out


def split(input, num_or_sections, dim=-1, name=None):
    """
    Split the input tensor into multiple sub-tensors.

    Args:
        input (Variable): The input variable which is a Tensor or LoDTensor.
        num_or_sections (int|list): If :attr:`num_or_sections` is an integer,
            then the integer indicates the number of equal sized sub-tensors
            that the tensor will be divided into. If :attr:`num_or_sections`
            is a list of integers, the length of list indicates the number of
            sub-tensors and the integers indicate the sizes of sub-tensors'
            :attr:`dim` dimension orderly.
        dim (int): The dimension along which to split. If :math:`dim < 0`, the
            dimension to split along is :math:`rank(input) + dim`.
        name(str|None): A name for this layer(optional). If set None, the layer
                       will be named automatically.

    Returns:
        List: The list of segmented tensor variables.

    Examples:
        .. code-block:: python

            # x is a Tensor variable with shape [3, 9, 5]:
            x0, x1, x2 = fluid.layers.split(x, num_or_sections=3, dim=1)
            x0.shape  # [3, 3, 5]
            x1.shape  # [3, 3, 5]
            x2.shape  # [3, 3, 5]
            x0, x1, x2 = fluid.layers.split(x, num_or_sections=[2, 3, 4], dim=1)
            x0.shape  # [3, 2, 5]
            x1.shape  # [3, 3, 5]
            x2.shape  # [3, 4, 5]
    """
    helper = LayerHelper('split', **locals())
    input_shape = input.shape
    dim = (len(input_shape) + dim) if dim < 0 else dim
    if isinstance(num_or_sections, int):
        assert num_or_sections > 1, 'num_or_sections must be more than 1.'
        num = num_or_sections
    else:
        assert len(num_or_sections) < input_shape[
            dim], 'len(num_or_sections) must not be more than input.shape[dim].'
        num = len(num_or_sections)
    outs = [
        helper.create_tmp_variable(dtype=helper.input_dtype())
        for i in range(num)
    ]
    helper.append_op(
        type='split',
        inputs={'X': input},
        outputs={'Out': outs},
        attrs={
            'num': num_or_sections if isinstance(num_or_sections, int) else 0,
            'sections': num_or_sections
            if isinstance(num_or_sections, list) else [],
            'axis': dim
        })
    return outs


def l2_normalize(x, axis, epsilon=1e-12, name=None):
    """
    **L2 normalize Layer**

    The l2 normalize layer normalizes `x` along dimension `axis` using an L2
    norm. For a 1-D tensor (`dim` is fixed to 0), this layer computes

    output = x / sqrt(max(sum(x**2), epsilon))

    For `x` with more dimensions, this layer independently normalizes each 1-D
    slice along dimension `axis`.

    Args:
       x(Variable|list): The input tensor to l2_normalize layer.
       axis(int): Dimension along which to normalize the input.
       epsilon(float): A lower bound value for `x`'s l2 norm. sqrt(epsilon) will
                       be used as the divisor if the l2 norm of `x` is less than
                       sqrt(epsilon).
       name(str|None): A name for this layer(optional). If set None, the layer
                       will be named automatically.


    Returns:
        Variable: The output tensor variable.

    Examples:
        .. code-block:: python

          data = fluid.layers.data(name="data",
                                   shape=(3, 17, 13),
                                   dtype="float32")
          fc = fluid.layers.l2_normalize(x=data, axis=1)
    """

    if len(x.shape) == 1: axis = 0

    helper = LayerHelper("l2_normalize", **locals())

    square = helper.create_tmp_variable(dtype=x.dtype)
    helper.append_op(type="square", inputs={"X": x}, outputs={"Out": square})

    reduced_sum = helper.create_tmp_variable(dtype=x.dtype)
    helper.append_op(
        type="reduce_sum",
        inputs={"X": square},
        outputs={"Out": reduced_sum},
        attrs={
            "dim": 1 if axis is None else axis,
            "keep_dim": True,
            "reduce_all": False
        })

    # TODO(caoying) A lower bound value epsilon for the norm is needed to
    # imporve the numeric stability of reciprocal. This requires a maximum_op.
    rsquare = helper.create_tmp_variable(dtype=x.dtype)
    helper.append_op(
        type="reciprocal", inputs={"X": reduced_sum}, outputs={"Out": rsquare})

    # TODO(caoying) the current elementwise_mul operator does not support a
    # general broadcast rule which broadcasts input(Y) to have the same
    # dimension with Input(X) starting from a specified dimension. So this
    # exanpsion is requred. Once a general broadcast relu is spported, this
    # expanding canbe removed.
    rsquare_expanded = helper.create_tmp_variable(dtype=x.dtype)
    expand_times = [1] * len(x.shape)
    expand_times[axis] = int(x.shape[axis])
    helper.append_op(
        type="expand",
        inputs={"X": rsquare},
        outputs={"Out": rsquare_expanded},
        attrs={"expand_times": expand_times})

    out = helper.create_tmp_variable(dtype=x.dtype)
    helper.append_op(
        type="elementwise_mul",
        inputs={"X": x,
                "Y": rsquare_expanded},
        outputs={"Out": out})
    return out