layers.py

# Copyright (c) 2016 Baidu, Inc. All Rights Reserved
#
# 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.

import functools

from paddle.trainer.config_parser import *
from .activations import LinearActivation, SigmoidActivation, TanhActivation, \
    ReluActivation, IdentityActivation, SoftmaxActivation
from .evaluators import *
from .poolings import MaxPooling, AvgPooling, BasePoolingType
from .attrs import *
from .default_decorators import *

try:
    import cPickle as pickle
except ImportError:
    import pickle
import copy

__all__ = ["full_matrix_projection", "AggregateLevel", "ExpandLevel",
           "identity_projection", "dotmul_projection",
           "table_projection", "mixed_layer", "data_layer",
           "embedding_layer", "fc_layer", "grumemory",
           "pooling_layer", "lstmemory", "last_seq", "first_seq",
           "cos_sim", "hsigmoid",
           "regression_cost", 'classification_cost', "LayerOutput",
           'img_conv_layer', 'img_pool_layer', 'batch_norm_layer',
           'img_cmrnorm_layer', 'img_rnorm_layer', 'addto_layer',
           'concat_layer', 'lstm_step_layer', 'recurrent_group',
           'memory', 'StaticInput', 'expand_layer', 'scaling_layer',
           'power_layer', 'interpolation_layer', 'trans_layer',
           'sum_to_one_norm_layer',
           'get_output_layer', 'LayerType', 'context_projection',
           'beam_search', 'maxid_layer', 'GeneratedInput', 'SubsequenceInput',
           'gru_step_layer', 'recurrent_layer',
           'BaseGeneratedInput', 'conv_operator', 'conv_shift_layer',
           'tensor_layer', 'selective_fc_layer', 'sampling_id_layer',
           'slope_intercept_layer', 'trans_full_matrix_projection',
           'convex_comb_layer', 'ctc_layer', 'crf_layer', 'crf_decoding_layer',
           'cross_entropy_with_selfnorm', 'cross_entropy',
           'multi_binary_label_cross_entropy',
           'rank_cost', 'lambda_cost', 'huber_cost',
           'block_expand_layer',
           ]


class LayerType(object):
    """
    Layer type enumerations.
    """

    DATA = "data"
    MIXED_LAYER = "mixed"
    LSTMEMORY = "lstmemory"
    GRUMEMORY = "gated_recurrent"
    SEQUENCE_LAST_INSTANCE = "seqlastins"
    SEQUENCE_FIRST_INSTANCE = "seqfirstins"
    POOLING_MAX = "max"
    POOLING_AVG = 'average'
    FC_LAYER = "fc"
    COST = 'cost'
    COSINE_SIM = 'cos_vm'
    HSIGMOID = 'hsigmoid'
    CONV_LAYER = "conv"
    POOL_LAYER = "pool"
    BATCH_NORM_LAYER = 'batch_norm'
    NORM_LAYER = 'norm'
    SUM_TO_ONE_NORM_LAYER = 'sum_to_one_norm'
    ADDTO_LAYER = 'addto'

    CONCAT_LAYER = 'concat'
    CONCAT_PROJ_LAYER = 'concat2'

    LSTM_STEP_LAYER = 'lstm_step'
    GRU_STEP_LAYER = 'gru_step'
    GET_OUTPUT_LAYER = 'get_output'

    EXPAND_LAYER = 'expand'
    INTERPOLATION_LAYER = 'interpolation'
    POWER_LAYER = 'power'
    SCALING_LAYER = 'scaling'
    TRANS_LAYER = 'trans'

    MEMORY = 'memory'
    MAXID_LAYER = 'maxid'
    EOSID_LAYER = 'eos_id'
    RECURRENT_LAYER = 'recurrent'

    CONV_SHIFT_LAYER = "conv_shift"
    TENSOR_LAYER = "tensor"
    SEL_FC_LAYER = "selective_fc"
    SAMPLING_ID_LAYER = "sampling_id"
    SLOPE_INTERCEPT_LAYER = "slope_intercept"
    CONVEX_COMBINATION_LAYER = "convex_comb"
    BLOCK_EXPAND = "blockexpand"

    CTC_LAYER = "ctc"
    CRF_LAYER = "crf"
    CRF_DECODING_LAYER = "crf_decoding"

    RANK_COST = "rank-cost"
    LAMBDA_COST = "lambda_cost"
    HUBER = "huber"
    CROSS_ENTROPY = "multi-class-cross-entropy"
    CROSS_ENTROPY_WITH_SELFNORM = "multi_class_cross_entropy_with_selfnorm"
    SOFT_BIN_CLASS_CROSS_ENTROPY = "soft_binary_class_cross_entropy"
    MULTI_BIN_LABEL_CROSS_ENTROPY = "multi_binary_label_cross_entropy"

    @staticmethod
    def is_layer_type(type_name):
        """
        If type_name is a layer type.

        :param type_name: layer type name. Because layer type enumerations are
                          strings.
        :type type_name: basestring
        :return: True if is a layer_type
        :rtype: bool
        """
        for key in dir(LayerType):
            if key.isupper():
                att = getattr(LayerType, key)
                if isinstance(att, basestring) and type_name == att:
                    return True
        return False


class AggregateLevel(object):
    EACH_TIMESTEP = 'non-seq'
    EACH_SEQUENCE = 'seq'


class LayerOutput(object):
    """
    LayerOutput is output for layer function. It is used internally by several
    reasons.

    - Check layer connection make sense.

        - FC(Softmax) => Cost(MSE Error) is not good for example.

    - Tracking layer connection.

    - Pass to layer methods as input.

    :param name: Layer output name.
    :type name: basestring
    :param layer_type: Current Layer Type. One of LayerType enumeration.
    :type layer_type: basestring
    :param activation: Layer Activation.
    :type activation: BaseActivation.
    :param parents: Layer's parents.
    :type parents: list|tuple
    """

    def __init__(self, name, layer_type, parents=None, activation=None,
                 num_filters=None, img_norm_type=None, size=None, outputs=None):
        assert isinstance(name, basestring)
        assert isinstance(layer_type, basestring)
        assert LayerType.is_layer_type(layer_type)
        self.name = name
        self.layer_type = layer_type
        self.parents = [] if parents is None else parents
        self.activation = activation
        self.num_filters = num_filters
        self.img_norm_type = img_norm_type
        self.size = size
        if outputs is None:
            outputs = ['default']
        self.outputs = outputs

    def __repr__(self):
        """
        Disable __repr__ for debug reason. Will be implemented when release
        """
        assert False, "this method should not be invoked"

    def __str__(self):
        """
        Disable __str__ for debug reason. Will be implemented when release
        """
        assert False, "this method should not be invoked"


ERROR_CLIPPING = 'error_clipping_threshold'
DROPOUT = 'drop_rate'


def layer_support(*attrs):
    def decorator(method):
        @functools.wraps(method)
        def wrapper(*args, **kwargs):
            for attr in attrs:
                for each in args:
                    if isinstance(each, ExtraLayerAttribute):
                        setattr(each, '_'.join(['can', attr]), True)
                for key in kwargs:
                    val = kwargs[key]
                    if isinstance(val, ExtraLayerAttribute):
                        setattr(val, '_'.join(['can', attr]), True)
            for each in args:
                if isinstance(each, ExtraLayerAttribute):
                    each.check(method.__name__)
            for key in kwargs:
                val = kwargs[key]
                if isinstance(val, ExtraLayerAttribute):
                    val.check(method.__name__)
            return method(*args, **kwargs)

        return wrapper

    return decorator


@wrap_param_attr_default()
def full_matrix_projection(input, size=0, param_attr=None):
    """
    Full Matrix Projection. It performs full matrix multiplication.

    ..  math::
        out.row[i] += in.row[i] * weight

    There are two styles of usage.

    1. When used in mixed_layer like this, you can only set the input:

    .. code-block:: python

       with mixed_layer(size=100) as m:
           m += full_matrix_projection(input=layer)

    2. When used as an independant object like this, you must set the size:

    .. code-block:: python

       proj = full_matrix_projection(input=layer,
                                     size=100,
                                     param_attr=ParamAttr(name='_proj'))

    :param input: input layer
    :type input: LayerOutput
    :param size: The parameter size. Means the width of parameter.
    :type size: int
    :param param_attr: Parameter config, None if use default.
    :type param_attr: ParameterAttribute
    :return: A FullMatrixProjection Object.
    :rtype: FullMatrixProjection
    """
    proj = FullMatrixProjection(input_layer_name=input.name,
                                size=size,
                                **param_attr.attr)
    proj.origin = input
    proj.origin.projection = "matrix"
    return proj


@wrap_param_attr_default()
def table_projection(input, size=0, param_attr=None):
    """
    Table Projection. It selects rows from parameter where row\_id
    is in input\_ids.

    .. math::
       out.row[i] += table.row[ids[i]]

    where :math:`out` is output, :math:`table` is parameter, :math:`ids` is input\_ids,
    and :math:`i` is row\_id.

    There are two styles of usage.

    1. When used in mixed_layer like this, you can only set the input:

    .. code-block:: python

       with mixed_layer(size=100) as m:
           m += table_projection(input=layer)

    2. When used as an independant object like this, you must set the size:

    .. code-block:: python

       proj = table_projection(input=layer,
                               size=100,
                               param_attr=ParamAttr(name='_proj'))


    :param input: Input layer, which must contains id fields.
    :type input: LayerOutput
    :param size: The parameter size. Means the width of parameter.
    :type size: int
    :param param_attr: Parameter config, None if use default.
    :type param_attr: ParameterAttribute
    :return: A TableProjection Object.
    :rtype: TableProjection
    """
    proj = TableProjection(input_layer_name=input.name,
                           size=size,
                           **param_attr.attr)
    proj.origin = input
    proj.origin.projection = "table"
    return proj


def identity_projection(input, offset=None):
    """
    1. IdentityProjection if offset=None. It performs:

    .. math::
       out.row[i] += in.row[i]

    The example usage is:

    .. code-block:: python

       proj = identity_projection(input=layer)


    2. IdentityOffsetProjection if offset!=None. It likes IdentityProjection,
    but layer size may be smaller than input size.
    It select dimesions [offset, offset+layer_size) from input:

    .. math::
       out.row[i] += in.row[i + \\textrm{offset}]

    The example usage is:

    .. code-block:: python

       proj = identity_projection(input=layer,
                                  offset=10)

    Note that both of two projections should not have any parameter.

    :param input: Input Layer.
    :type input: LayerOutput.
    :param offset: Offset, None if use default.
    :type offset: int
    :return: A IdentityProjection or IdentityOffsetProjection Object
    :rtype: IdentityProjection or IdentityOffsetProjection
    """
    if offset is None:
        proj = IdentityProjection(input_layer_name=input.name)
        proj.origin = input
        proj.origin.projection = 'identity'
    else:
        proj = IdentityOffsetProjection(input_layer_name=input.name,
                                        offset=offset)
        proj.origin = input
        proj.origin.projection = 'identity_offset'
    return proj


@wrap_param_attr_default()
def dotmul_projection(input, param_attr=None, scale=1):
    """
    1. DotMulProjection if input is a layer.
    It performs element-wise multiplication with weight.

    ..  math::
        out.row[i] += in.row[i] .* weight

    where :math:`.*` means element-wise multiplication.

    The example usage is:

    .. code-block:: python

       proj = dotmul_projection(input=layer)

    2. DotMulOperator if input is a list or tuple.
    It takes two inputs, performs element-wise multiplication:

    .. math::
       out.row[i] += scale * (in1.row[i] .* in2.row[i])

    where :math:`.*` means element-wise multiplication, and
    scale is a config scalar, its default value is one.

    The example usage is:

    .. code-block:: python

       op = dotmul_projection(input=[layer1, layer2],
                              scale=2.0)

    :param input: Input layer.
    :type input: LayerOutput|list|tuple
    :param param_attr: Parameter config, None if use default.
    :type param_attr: ParameterAttribute
    :param scale: config scalar, default value is one.
    :type scale: float
    :return: A DotMulProjection or DotMulOperator Object.
    :rtype: DotMulProjection or DotMulOperator
    """
    if isinstance(input, LayerOutput):
        proj = DotMulProjection(input_layer_name=input.name,
                                size=input.size,
                                **param_attr.attr)
        proj.origin = input
        proj.origin.projection = "dot_mul"
        return proj
    else:
        assert isinstance(input, list) or isinstance(input, tuple)
        assert len(input) == 2
        assert param_attr is None
        op = DotMulOperator(input_layer_name=[x.name for x in input],
                            scale=scale)
        op.origin = input
        op.origin.operator = "dot_mul"
        return op


@wrap_bias_attr_default(['padding_attr'])
def context_projection(input, context_len, context_start=None,
                       padding_attr=False):
    """
    Context Projection.

    It just simply reorganizes input sequence, combines "context_len" sequence
    to one context from context_start. "context_start" will be set to
    -(context_len - 1) / 2 by default. If context position out of sequence
    length, padding will be filled as zero if padding_attr = False, otherwise
    it is trainable.

    For example, origin sequence is [A B C D E F G], context len is 3, then
    after context projection and not set padding_attr, sequence will
    be [ 0AB ABC BCD CDE DEF EFG FG0 ].

    :param input: Input Sequence.
    :type input: LayerOutput
    :param context_len: context length.
    :type context_len: int
    :param context_start: context start position. Default is
                          -(context_len - 1)/2
    :type context_start: int
    :param padding_attr: Padding Parameter Attribute. If false, it means padding
                         always be zero. Otherwise Padding is learnable, and
                         parameter attribute is set by this parameter.
    :type padding_attr: bool|ParameterAttribute
    :return: Projection
    :rtype: Projection
    """
    context_start = -(
        context_len - 1) / 2 if context_start is None else context_start

    extra_dict = dict()
    trainable = isinstance(padding_attr, ParameterAttribute)
    if trainable:
        extra_dict = padding_attr.attr

    proj = ContextProjection(input_layer_name=input.name,
                             context_length=context_len,
                             context_start=context_start,
                             trainable_padding=trainable,
                             **extra_dict)
    proj.origin = input
    proj.origin.projection = 'context'
    return proj


class MixedLayerType(LayerOutput):
    """
    The internal object for trainer_helpers.
    """

    class AddToSealedMixedLayerException(Exception):
        def __init__(self):
            Exception.__init__(self)

    def __init__(self, name, size, act, bias_attr, layer_attr,
                 parents=None):
        """
        Ctor.
        :param name: layer name.
        :type name: basestring
        :param size: layer size.
        :type size: int
        :param act: activation type.
        :type act: BaseActivation
        :param bias_attr: The Bias Attribute. If no bias, then pass False or
                          something not type of ParameterAttribute. None will
                          get a default Bias.
        :type bias_attr: ParameterAttribute or None means has bias. Any other
                         type means no bias.
        :param layer_attr: Extra Layer Attribute.
        :type layer_attr: ExtraLayerAttribute or None
        """
        LayerOutput.__init__(self, name, LayerType.MIXED_LAYER, parents,
                             size=size, activation=act)
        self.bias_attr = bias_attr
        self.layer_attr = layer_attr
        self.inputs = []
        self.finalized = False

    def __add__(self, other):
        """
        + += operator
        :param other: Other projection.
        :type other: Projection
        :return: self.
        :rtype: MixedLayerType
        """
        if not self.finalized:
            assert isinstance(other, Projection)
            self.inputs.append(other)
            self.parents.append(other.origin)
            return self
        else:
            raise MixedLayerType.AddToSealedMixedLayerException()

    def __enter__(self):
        assert len(self.inputs) == 0
        return self

    def __exit__(self, *args, **kwargs):
        del args, kwargs  # unused parameter to suppress warning
        assert len(self.inputs) != 0
        MixedLayer(
            name=self.name,
            size=self.size,
            active_type=self.activation.name,
            bias=ParamAttr.to_bias(self.bias_attr),
            inputs=self.inputs,
            **ExtraLayerAttribute.to_kwargs(self.layer_attr)
        )


@wrap_name_default("mixed")
@wrap_act_default(act=LinearActivation())
@wrap_bias_attr_default(has_bias=False)
@layer_support(ERROR_CLIPPING, DROPOUT)
def mixed_layer(size, input=None, name=None, act=None, bias_attr=False,
                layer_attr=None):
    """
    Mixed Layer. A mixed layer will add all inputs together, then activate.
    Each inputs is a projection or operator.

    There are two styles of usages.

    1. When not set inputs parameter, use mixed_layer like this:

    .. code-block:: python

       with mixed_layer(size=256) as m:
           m += full_matrix_projection(input=layer1)
           m += identity_projection(input=layer2)

    2. You can also set all inputs when invoke mixed_layer as follows:

    .. code-block:: python

       m = mixed_layer(size=256,
                       input=[full_matrix_projection(input=layer1),
                              full_matrix_projection(input=layer2)])

    :param name: mixed layer name. Can be referenced by other layer.
    :type name: basestring
    :param size: layer size.
    :type size: int
    :param input: inputs layer. It is an optional parameter. If set,
                  then this function will just return layer's name.
    :param act: Activation Type.
    :type act: BaseActivation
    :param bias_attr: The Bias Attribute. If no bias, then pass False or
                      something not type of ParameterAttribute. None will get a
                      default Bias.
    :type bias_attr: ParameterAttribute or None or bool
    :param layer_attr: The extra layer config. Default is None.
    :type layer_attr: ExtraLayerAttribute
    :return: MixedLayerType object can add inputs or layer name.
    :rtype: MixedLayerType
    """

    if input is None:
        return MixedLayerType(name, size, act, bias_attr, layer_attr)
    else:
        with mixed_layer(name=name, size=size, act=act, bias_attr=bias_attr,
                         layer_attr=layer_attr) as m:
            if isinstance(input, list) or isinstance(input, tuple):
                for each in input:
                    m += each
            else:
                m += input
        return m


@layer_support()
def data_layer(name, size, layer_attr=None):
    """
    Define DataLayer For NeuralNetwork.

    The example usage is:

    ..  code-block:: python

        data = data_layer(name="input",
                          size=1000)

    :param name: Name of this data layer.
    :type name: basestring
    :param size: Size of this data layer.
    :type size: int
    :param layer_attr: Extra Layer Attribute.
    :type layer_attr: ExtraLayerAttribute.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    Layer(type=LayerType.DATA, name=name, size=size,
          **ExtraLayerAttribute.to_kwargs(layer_attr))

    return LayerOutput(name, LayerType.DATA, size=size)


@wrap_name_default("embedding")
@wrap_param_attr_default()
@layer_support(ERROR_CLIPPING)
def embedding_layer(input, size, name=None, param_attr=None, layer_attr=None):
    """
    Define a embedding Layer.

    :param name: Name of this embedding layer.
    :type name: basestring
    :param input: The input layer for this embedding. NOTE: must be Index Data.
    :type input: LayerOutput
    :param size: The embedding dimension.
    :type size: int
    :param param_attr: The embedding parameter attribute. See ParameterAttribute
                      for details.
    :type param_attr: ParameterAttribute|None
    :param layer_attr: Extra layer Config. Default is None.
    :type layer_attr: ExtraLayerAttribute|None
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    with mixed_layer(name=name, size=size, act=LinearActivation(),
                     bias_attr=False,
                     layer_attr=layer_attr) as mix:
        mix += table_projection(input=input, size=size, param_attr=param_attr)
    return mix


@wrap_name_default()
@wrap_param_attr_default()
@wrap_bias_attr_default()
@wrap_act_default()
@layer_support(ERROR_CLIPPING, DROPOUT)
def fc_layer(input, size, act=None, name=None,
             param_attr=None, bias_attr=None, layer_attr=None):
    """
    Helper for declare fully connected layer.

    The example usage is:

    .. code-block:: python

       fc = fc_layer(input=layer,
                     size=1024,
                     act=LinearActivation(),
                     bias_attr=False)

    which is equal to:

    .. code-block:: python

       with mixed_layer(size=1024) as fc:
           fc += full_matrix_projection(input=layer)

    :param name: The Layer Name.
    :type name: basestring
    :param input: The input layer. Could be a list/tuple of input layer.
    :type input: LayerOutput|list|tuple
    :param size: The layer dimension.
    :type size: int
    :param act: Activation Type. Default is tanh.
    :type act: BaseActivation
    :param param_attr: The Parameter Attribute|list.
    :type param_attr: ParameterAttribute
    :param bias_attr: The Bias Attribute. If no bias, then pass False or
                      something not type of ParameterAttribute. None will get a
                      default Bias.
    :type bias_attr: ParameterAttribute|None|Any
    :param layer_attr: Extra Layer config.
    :type layer_attr: ExtraLayerAttribute|None
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    if isinstance(input, LayerOutput):
        input = [input]
        assert not isinstance(param_attr, list)
        param_attr = [param_attr]
    else:
        if isinstance(param_attr, list) or isinstance(param_attr, tuple):
            assert len(input) == len(param_attr)
        else:
            param_attr = [copy.deepcopy(param_attr) for _ in range(len(input))]

    assert isinstance(input, list)

    def __idx_to_input__(i):
        attr = param_attr[i]
        assert isinstance(attr, ParameterAttribute)
        return Input(input[i].name, **attr.attr)

    Layer(
        inputs=map(__idx_to_input__, range(len(input))),
        name=name,
        type=LayerType.FC_LAYER,
        size=size,
        bias=ParamAttr.to_bias(bias_attr),
        active_type=act.name,
        **ExtraLayerAttribute.to_kwargs(layer_attr)
    )
    return LayerOutput(name, LayerType.FC_LAYER, input, activation=act,
                       size=size)


@wrap_name_default("seq_pooling")
@wrap_bias_attr_default(has_bias=False)
@wrap_param_default(['pooling_type'], default_factory=lambda _: MaxPooling())
@layer_support()
def pooling_layer(input, pooling_type=None, name=None, bias_attr=None,
                  agg_level=AggregateLevel.EACH_TIMESTEP,
                  layer_attr=None):
    """
    Pooling layer for sequence inputs, not used for Image.

    The example usage is:

    .. code-block:: python

       seq_pool = pooling_layer(input=layer,
                                pooling_type=AvgPooling(),
                                agg_level=AggregateLevel.EACH_SEQUENCE)

    :param agg_level: AggregateLevel.EACH_TIMESTEP or AggregateLevel.EACH_SEQUENCE
    :type agg_level: AggregateLevel
    :param name: layer name.
    :type name: basestring
    :param input: input layer name.
    :type input: LayerOutput
    :param pooling_type: Type of pooling, MaxPooling(default), AvgPooling,
                         SumPooling, SquareRootNPooling.
    :type pooling_type: BasePoolingType|None
    :param bias_attr: Bias parameter attribute. False if no bias.
    :type bias_attr: ParameterAttribute|None|False
    :param layer_attr: The Extra Attributes for layer, such as dropout.
    :type layer_attr: ExtraLayerAttribute|None
    :return: LayerOutput object.
    :rtype: LayerType
    """
    extra_dict = dict()
    if isinstance(pooling_type, AvgPooling):
        extra_dict['average_strategy'] = pooling_type.strategy
    extra_dict.update(ExtraLayerAttribute.to_kwargs(layer_attr))

    Layer(
        name=name,
        type=pooling_type.name,
        inputs=[Input(input.name)],
        bias=ParamAttr.to_bias(bias_attr),
        trans_type=agg_level,
        **extra_dict
    )

    return LayerOutput(name, pooling_type.name, parents=[input],
                       size=input.size)


@wrap_bias_attr_default()
@wrap_param_attr_default()
@wrap_act_default(param_names=['gate_act'],
                  act=SigmoidActivation())
@wrap_act_default(param_names=["act", 'state_act'], act=TanhActivation())
@wrap_name_default("lstmemory")
@layer_support(DROPOUT)
def lstmemory(input, name=None, reverse=False, act=None,
              gate_act=None,
              state_act=None, bias_attr=None, param_attr=None,
              layer_attr=None):
    """
    Long Short-term Memory Cell.

    The memory cell was implemented as follow equations.

    ..  math::

        i_t & = \\sigma(W_{xi}x_{t} + W_{hi}h_{t-1} + W_{ci}c_{t-1} + b_i)

        f_t & = \\sigma(W_{xf}x_{t} + W_{hf}h_{t-1} + W_{cf}c_{t-1} + b_f)

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

        o_t & = \\sigma(W_{xo}x_{t} + W_{ho}h_{t-1} + W_{co}c_t + b_o)

        h_t & = o_t tanh(c_t)


    NOTE: In paddle's implementation, the multiply operation
    :math:`W_{xi}x_{t}` , :math:`W_{xf}x_{t}`,
    :math:`W_{xc}x_t`, :math:`W_{xo}x_{t}` is not done by
    lstmemory layer, so it must use a mixed_layer do this full_matrix_projection
    before lstm is used.

    NOTE: This is a low level user interface. You may use network.simple_lstm
    to config a simple plain lstm layer.

    Please refer **Generating Sequences With Recurrent Neural Networks** if you
    want to know what lstm is. Link_ is here.

    .. _Link: http://arxiv.org/abs/1308.0850

    TODO(yuyang18): Check lstm can input multiple values or not?

    :param name: The lstmemory layer name.
    :type name: basestring
    :param input: input layer name.
    :type input: LayerOutput
    :param reverse: is sequence process reversed or not.
    :type reverse: bool
    :param act: activation type, TanhActivation by default. :math:`h_t`
    :type act: BaseActivation
    :param gate_act: gate activation type, SigmoidActivation by default.
    :type gate_act: BaseActivation
    :param state_act: state activation type, TanhActivation by default.
    :type state_act: BaseActivation

    :param bias_attr: Bias attribute. None means default bias. False means no
                      bias.
    :type bias_attr: ParameterAttribute|None|False
    :param param_attr: Parameter Attribute.
    :type param_attr: ParameterAttribute|None|False
    :param layer_attr: Extra Layer attribute
    :type layer_attr: ExtraLayerAttribute|None
    :return: LayerOutput object.
    :rtype: LayerOutput
    """

    assert gate_act.support_hppl
    assert state_act.support_hppl
    assert act.support_hppl

    Layer(name=name,
          type=LayerType.LSTMEMORY,
          active_type=act.name,
          active_state_type=state_act.name,
          active_gate_type=gate_act.name,
          reversed=reverse,
          bias=ParamAttr.to_bias(bias_attr),
          inputs=[Input(input.name, **param_attr.attr)],
          **ExtraLayerAttribute.to_kwargs(layer_attr))

    return LayerOutput(name, LayerType.LSTMEMORY, [input],
                       size=input.size / 4 if input.size is not None else None)

@wrap_bias_attr_default()
@wrap_param_attr_default()
@wrap_act_default(param_names=['gate_act'],
                  act=SigmoidActivation())
@wrap_act_default(param_names=["act"], act=TanhActivation())
@wrap_name_default("gru")
@layer_support(DROPOUT)
def grumemory(input, name=None, reverse=False, act=None,
              gate_act=None,
              bias_attr=None, param_attr=None,
              layer_attr=None):
    """
    Gate Recurrent Unit Layer.

    The memory cell was implemented as follow equations.

    1. update gate :math:`z`: defines how much of the previous memory to
    keep around or the unit updates its activations. The update gate
    is computed by:

    ..  math::

        z_t = \\sigma(W_{z}x_{t} + U_{z}h_{t-1} + b_z)

    2. reset gate :math:`r`: determines how to combine the new input with the
    previous memory. The reset gate is computed similarly to the update gate:

    ..  math::

        r_t = \\sigma(W_{r}x_{t} + U_{r}h_{t-1} + b_r)

    3. The candidate activation :math:`\\tilde{h_t}` is computed similarly to that
    of the traditional recurrent unit:

    ..  math::

        {\\tilde{h_t}} = tanh(W x_{t} + U (r_{t} \odot h_{t-1}) + b)

    4. The hidden activation :math:`h_t` of the GRU at time t is a linear interpolation
    between the previous activation :math:`h_{t-1}` and the candidate activation
    :math:`\\tilde{h_t}`:

    ..  math::

        h_t = (1 - z_t) h_{t-1} + z_t {\\tilde{h_t}}

    NOTE: In paddle's implementation, the multiply operation
    :math:`W_{r}x_{t}`, :math:`W_{z}x_{t}` and :math:`W x_t` are not computed in
    gate_recurrent layer. So it must use a mixed_layer with full_matrix_projection
    or fc_layer to compute them before GRU.

    The details can refer to `Empirical Evaluation of Gated Recurrent
    Neural Networks on Sequence Modeling. <https://arxiv.org/abs/1412.3555>`_

    The simple usage is:

    .. code-block:: python

       gru = grumemory(input)

    :param name: The gru layer name.
    :type name: None|basestring
    :param input: input layer.
    :type input: LayerOutput.
    :param reverse: Wether sequence process is reversed or not.
    :type reverse: bool
    :param act: activation type, TanhActivation by default. This activation
                affects the :math:`{\\tilde{h_t}}`.
    :type act: BaseActivation
    :param gate_act: gate activation type, SigmoidActivation by default.
                     This activation affects the :math:`z_t` and :math:`r_t`. It is the
                     :math:`\\sigma` in the above formula.
    :type gate_act: BaseActivation
    :param bias_attr: Bias attribute. None means default bias. False means no
                      bias.
    :type bias_attr: ParameterAttribute|None|False
    :param param_attr: Parameter Attribute.
    :type param_attr: ParameterAttribute|None|False
    :param layer_attr: Extra Layer attribute
    :type layer_attr: ExtraLayerAttribute|None
    :return: LayerOutput object.
    :rtype: LayerOutput
    """

    assert act.support_hppl
    assert gate_act.support_hppl

    Layer(name=name,
          type=LayerType.GRUMEMORY,
          active_type=act.name,
          active_gate_type=gate_act.name,
          reversed=reverse,
          bias=ParamAttr.to_bias(bias_attr),
          inputs=[Input(input.name, **param_attr.attr)],
          **ExtraLayerAttribute.to_kwargs(layer_attr)
          )

    return LayerOutput(name, LayerType.GRUMEMORY, [input],
                       size=input.size / 3 if input.size is not None else None)

@wrap_name_default()
@layer_support()
def last_seq(input, name=None, agg_level=AggregateLevel.EACH_TIMESTEP,
             layer_attr=None):
    """
    Get Last Timestamp Activation of a sequence.

    :param agg_level: Aggregated level
    :param name: Layer name.
    :type name: basestring
    :param input: Input layer name.
    :type input: LayerOutput
    :param layer_attr: extra layer attributes.
    :type layer_attr: ExtraLayerAttribute.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    Layer(
        name=name,
        type=LayerType.SEQUENCE_LAST_INSTANCE,
        inputs=[input.name],
        trans_type=agg_level,
        **ExtraLayerAttribute.to_kwargs(layer_attr)
    )
    return LayerOutput(name, LayerType.SEQUENCE_LAST_INSTANCE, parents=[input],
                       size=input.size)


@wrap_name_default()
@layer_support()
def first_seq(input, name=None, agg_level=AggregateLevel.EACH_TIMESTEP,
              layer_attr=None):
    """
    Get First Timestamp Activation of a sequence.

    :param agg_level: aggregation level
    :param name: Layer name.
    :type name: basestring
    :param input: Input layer name.
    :type input: LayerOutput
    :param layer_attr: extra layer attributes.
    :type layer_attr: ExtraLayerAttribute.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    Layer(
        name=name,
        type=LayerType.SEQUENCE_FIRST_INSTANCE,
        inputs=[input.name],
        trans_type=agg_level,
        **ExtraLayerAttribute.to_kwargs(layer_attr)
    )
    return LayerOutput(name, LayerType.SEQUENCE_FIRST_INSTANCE,
                       parents=[input], size=input.size)


class ExpandLevel(object):
    FROM_TIMESTEP = AggregateLevel.EACH_TIMESTEP
    FROM_SEQUENCE = AggregateLevel.EACH_SEQUENCE

@wrap_name_default()
@layer_support()
def expand_layer(input, expand_as,
                 name=None,
                 bias_attr=False,
                 expand_level=ExpandLevel.FROM_TIMESTEP,
                 layer_attr=None):
    """
    A layer for "Expand Dense data or (sequence data where the length of each
    sequence is one) to sequence data."

    The example usage is:

    .. code-block:: python

       expand = expand_layer(input=layer1,
                             expand_as=layer2,
                             expand_level=ExpandLevel.FROM_TIMESTEP)

    :param input: Input layer
    :type input: LayerOutput
    :param expand_as: Expand as this layer's sequence info.
    :type expand_as: LayerOutput
    :param name: Layer name.
    :type name: basestring
    :param bias_attr: Bias attribute. None means default bias. False means no
                      bias.
    :type bias_attr: ParameterAttribute|None|False
    :param expand_level: whether input layer is timestep(default) or sequence.
    :type expand_level: ExpandLevel
    :param layer_attr: extra layer attributes.
    :type layer_attr: ExtraLayerAttribute.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """

    Layer(
        inputs=[input.name, expand_as.name],
        name=name,
        bias=ParamAttr.to_bias(bias_attr=bias_attr),
        type=LayerType.EXPAND_LAYER,
        trans_type=expand_level,
        **ExtraAttr.to_kwargs(layer_attr)
    )
    return LayerOutput(name=name,
                       size=input.size,
                       layer_type=LayerType.EXPAND_LAYER,
                       parents=[input, expand_as])



@wrap_name_default()
@layer_support()
def interpolation_layer(input, weight, name=None, layer_attr=None):
    """
    This layer is for linear interpolation with two inputs,
    which is used in NEURAL TURING MACHINE.

    .. math::
       y.row[i] = w[i] * x_1.row[i] + (1 - w[i]) * x_2.row[i]

    where :math:`x_1` and :math:`x_2` are two (batchSize x dataDim) inputs,
    :math:`w` is (batchSize x 1) weight vector, and :math:`y` is
    (batchSize x dataDim) output.

    The example usage is:

    .. code-block:: python

       interpolation = interpolation_layer(input=[layer1, layer2], weight=layer3)

    :param input: Input layer.
    :type input: list|tuple
    :param weight: Weight layer.
    :type weight: LayerOutput
    :param name: Layer name.
    :type name: basestring
    :param layer_attr: extra layer attributes.
    :type layer_attr: ExtraLayerAttribute.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    assert isinstance(input, list) or isinstance(input, tuple)
    assert len(input) == 2
    assert input[0].size == input[1].size
    assert weight.size == 1
    Layer(
        name=name,
        type=LayerType.INTERPOLATION_LAYER,
        inputs=[weight.name, input[0].name, input[1].name],
        **ExtraAttr.to_kwargs(layer_attr)
    )
    return LayerOutput(name, LayerType.INTERPOLATION_LAYER,
                       parents=[weight, input[0], input[1]],
                       size=input[0].size)


@wrap_name_default()
@layer_support()
def power_layer(input, weight, name=None, layer_attr=None):
    """
    This layer applies a power function to a vector element-wise,
    which is used in NEURAL TURING MACHINE.

    .. math::
       y = x^w

    where :math:`x` is a input vector, :math:`w` is scalar weight,
    and :math:`y` is a output vector.

    The example usage is:

    .. code-block:: python

       power = power_layer(input=layer1, weight=layer2)

    :param input: Input layer.
    :type input: LayerOutput
    :param weight: Weight layer.
    :type weight: LayerOutput
    :param name: Layer name.
    :type name: basestring
    :param layer_attr: extra layer attributes.
    :type layer_attr: ExtraLayerAttribute.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    assert weight.size == 1
    Layer(
        name=name,
        type=LayerType.POWER_LAYER,
        inputs=[input.name, weight.name],
        **ExtraAttr.to_kwargs(layer_attr)
    )
    return LayerOutput(name, LayerType.POWER_LAYER,
                       parents=[input, weight], size=input.size)


@wrap_name_default()
@layer_support()
def scaling_layer(input, weight, name=None, layer_attr=None):
    """
    A layer for each row of a matrix, multiplying with a element of a vector.

    .. math::
       y.row[i] = w[i] * x.row[i]

    where :math:`x` is (batchSize x dataDim) input, :math:`w` is
    (batchSize x 1) weight vector, and :math:`y` is (batchSize x dataDim) output.

    The example usage is:

    .. code-block:: python

       scale = scaling_layer(input=layer1, weight=layer2)

    :param input: Input layer.
    :type input: LayerOutput
    :param weight: Weight layer.
    :type weight: LayerOutput
    :param name: Layer name.
    :type name: basestring
    :param layer_attr: extra layer attributes.
    :type layer_attr: ExtraLayerAttribute.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    assert weight.size == 1
    Layer(
        name=name,
        type=LayerType.SCALING_LAYER,
        inputs=[weight.name, input.name],
        **ExtraAttr.to_kwargs(layer_attr)
    )
    return LayerOutput(name, LayerType.SCALING_LAYER, parents=[weight, input],
                       size=input.size)


@wrap_name_default()
@layer_support()
def trans_layer(input, name=None, layer_attr=None):
    """
    A layer for transposition.

    .. math::
       y = x^\mathrm{T}

    where :math:`x` is (M x N) input, and :math:`y` is (N x M) output.

    The example usage is:

    .. code-block:: python

       trans = trans_layer(input=layer)

    :param input: Input layer.
    :type input: LayerOutput
    :param name: Layer name.
    :type name: basestring
    :param layer_attr: extra layer attributes.
    :type layer_attr: ExtraLayerAttribute.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    Layer(
        name=name,
        type=LayerType.TRANS_LAYER,
        inputs=[input.name],
        **ExtraAttr.to_kwargs(layer_attr)
    )
    return LayerOutput(name, LayerType.TRANS_LAYER, parents=[input],
                       size=input.size)


@wrap_name_default()
@layer_support()
def cos_sim(a, b, scale=5, size=1, name=None, layer_attr=None):
    """
    Cosine Similarity Layer. The cosine similarity equation is here.

    ..  math::
        similarity = cos(\\theta) = {\\mathbf{a} \\cdot \\mathbf{b}
        \\over \\|\\mathbf{b}\\| \\|\\mathbf{b}\\|}

    And the input dimension is :math:`a \in R^M`, :math:`b \in R^{MN}`. The
    similarity will be calculated N times by step M. The output dimension is
    :math:`R^N`. The scale will be multiplied to similarity.

    :param name: layer name
    :type name: basestring
    :param a: input layer a
    :type a: LayerOutput
    :param b: input layer b
    :type b: LayerOutput
    :param scale: scale for cosine value. default is 5.
    :type scale: float
    :param size: layer size. NOTE size_a * size should equal size_b.
    :type size: int
    :param layer_attr: Extra Layer Attribute.
    :type layer_attr: ExtraLayerAttribute
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    Layer(
        name=name,
        type=LayerType.COSINE_SIM,
        size=size,
        cos_scale=scale,
        inputs=[a.name, b.name],
        **ExtraLayerAttribute.to_kwargs(layer_attr)
    )
    return LayerOutput(name, LayerType.COSINE_SIM, parents=[a, b])

@wrap_name_default()
@wrap_bias_attr_default(has_bias=True)
@layer_support()
def hsigmoid(input, label, num_classes, name=None, bias_attr=None, layer_attr=None):
    """
    Organize the classes into a binary tree. At each node, a sigmoid function
    is used to calculate the probability of belonging to the right branch.
    This idea is from "F. Morin, Y. Bengio (AISTATS 05):
    Hierarchical Probabilistic Neural Network Language Model."

    The example usage is:

    ..  code-block:: python

        cost = hsigmoid(input=[layer1, layer2],
                        label=data_layer,
                        num_classes=3)

    :param input: Input layers. It could be a LayerOutput or list/tuple of
                 LayerOutput.
    :type input: LayerOutput|list|tuple
    :param label: Label layer.
    :type label: LayerOutput
    :param num_classes: number of classes.
    :type num_classes: int
    :param name: layer name
    :type name: basestring
    :param bias_attr: Bias attribute. None means default bias.
                      False means no bias.
    :type bias_attr: ParameterAttribute|False
    :param layer_attr: Extra Layer Attribute.
    :type layer_attr: ExtraLayerAttribute
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    if isinstance(input, LayerOutput):
        input = [input]
    assert isinstance(input, list) or isinstance(input, tuple)
    assert isinstance(label, LayerOutput)
    assert label.layer_type == LayerType.DATA

    ipts_for_layer = []
    parents = []
    for each_input in input:
        assert isinstance(each_input, LayerOutput)
        ipts_for_layer.append(each_input.name)
        parents.append(each_input)
    ipts_for_layer.append(label.name)
    parents.append(label)

    Layer(
        name=name,
        type=LayerType.HSIGMOID,
        num_classes=num_classes,
        bias=ParamAttr.to_bias(bias_attr),
        inputs=ipts_for_layer,
        **ExtraLayerAttribute.to_kwargs(layer_attr)
    )
    return LayerOutput(name, LayerType.HSIGMOID, parents=parents)

@wrap_name_default("conv")
@wrap_param_attr_default()
@wrap_bias_attr_default()
@wrap_act_default(act=ReluActivation())
@layer_support(DROPOUT)
def img_conv_layer(input, filter_size, num_filters,
                   name=None, num_channels=None,
                   act=None, groups=1, stride=1, padding=0, bias_attr=None,
                   param_attr=None, shared_biases=True, layer_attr=None,
                   filter_size_y=None, stride_y=None, padding_y=None):
    """
    Convolution layer for image. Paddle only support square input currently and
    thus input image's width equals height.

    The details of convolution layer, please refer UFLDL's `convolution
    <http://ufldl.stanford.edu/tutorial/supervised/
    FeatureExtractionUsingConvolution/>`_ .

    The num_channel means input image's channel number. It may be 1 or 3 when
    input is raw pixels of image(mono or RGB), or it may be the previous layer's
    num_filters * num_group.

    There are several group of filter in paddle
    implementation. Each group will process some channel of inputs. For example,
    if input num_channel = 256, group = 4, num_filter=32, the paddle will create
    32*4 = 128 filters to process inputs. The channels will be split into 4
    pieces. First 256/4 = 64 channels will process by first 32 filters. The rest
    channels will be processed by rest group of filters.

    :param name: Layer name.
    :type name: basestring
    :param input: Layer Input.
    :type input: LayerOutput
    :param filter_size: The x dimension of a filter kernel.
    :type filter_size: int
    :param filter_size_y: The y dimension of a filter kernel. Since paddle now
                        support rectangular filters, the filter's shape
                        will be (filter_size, filter_size_y).
    :type filter_size_y: int
    :param num_filters: Each filter group's number of filter
    :param act: Activation type. Default is tanh
    :type act: BaseActivation
    :param groups: Group size of filters.
    :type groups: int
    :param stride: The x dimension of the stride.
    :type stride: int
    :param stride_y: The y dimension of the stride.
    :type stride_y: int
    :param padding: The x dimension of the padding.
    :type padding: int
    :param padding_y: The y dimension of the padding.
    :type padding_y: int
    :param bias_attr: Convolution bias attribute. None means default bias.
                      False means no bias.
    :type bias_attr: ParameterAttribute|False
    :param num_channels: number of input channels. If None will be set
                        automatically from previous output.
    :type num_channels: int
    :param param_attr: Convolution param attribute. None means default attribute
    :type param_attr: ParameterAttribute
    :param shared_biases: Is biases will be shared between filters or not.
    :type shared_biases: bool
    :param layer_attr: Layer Extra Attribute.
    :type layer_attr: ExtraLayerAttribute
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    if num_channels is None:
        assert input.num_filters is not None
        num_channels = input.num_filters
    if filter_size_y is None:
        filter_size_y = filter_size
    if stride_y is None:
        stride_y = stride
    if padding_y is None:
        padding_y = padding
    if param_attr.attr.get('initial_smart') == True: # special initial for conv layers.
        init_w = (2.0 / (filter_size ** 2 * num_channels)) ** 0.5
        param_attr = ParameterAttribute(initial_mean=0.0, initial_std=init_w)
    Layer(
        name=name,
        inputs=Input(input.name, conv=Conv(
            filter_size=filter_size, padding=padding, stride=stride,
            channels=num_channels, groups=groups,
            filter_size_y=filter_size_y, padding_y=padding_y, stride_y=stride_y),
            **param_attr.attr),
        active_type=act.name,
        num_filters=num_filters,
        bias=ParamAttr.to_bias(bias_attr),
        shared_biases=shared_biases,
        type=LayerType.CONV_LAYER,
        **ExtraLayerAttribute.to_kwargs(layer_attr)
    )
    return LayerOutput(name, LayerType.CONV_LAYER, parents=[input],
                       activation=act, num_filters=num_filters)


@wrap_name_default("pool")
@layer_support()
def img_pool_layer(input, pool_size, name=None,
                   num_channels=None, pool_type=None,
                   stride=1, start=None, padding=0, layer_attr=None):
    """
    Image pooling Layer.

    The details of pooling layer, please refer ufldl's pooling_ .

    .. _pooling: http://ufldl.stanford.edu/tutorial/supervised/Pooling/

    :param padding: pooling padding
    :type padding: int
    :param name: name of pooling layer
    :type name: basestring.
    :param input: layer's input
    :type input: LayerOutput
    :param pool_size: pooling size
    :type pool_size: int
    :param num_channels: number of input channel.
    :type num_channels: int
    :param pool_type: pooling type. MaxPooling or AveragePooling. Default is
                      MaxPooling.
    :type pool_type: BasePoolingType
    :param stride: stride of pooling.
    :type stride: int
    :param start: start position of pooling operation.
    :type start: int
    :param layer_attr: Extra Layer attribute.
    :type layer_attr: ExtraLayerAttribute
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    if num_channels is None:
        assert input.num_filters is not None
        num_channels = input.num_filters

    if pool_type is None:
        pool_type = MaxPooling()
    elif isinstance(pool_type, AvgPooling):
        pool_type.name = 'avg'

    Layer(
        name=name,
        type=LayerType.POOL_LAYER,
        inputs=[Input(input.name,
                      pool=Pool(
                          pool_type=pool_type.name + '-projection',
                          channels=num_channels,
                          size_x=pool_size,
                          start=start,
                          stride=stride,
                          padding=padding
                      ))],
        **ExtraLayerAttribute.to_kwargs(layer_attr)
    )
    return LayerOutput(name, LayerType.POOL_LAYER, parents=[input],
                       num_filters=num_channels)


def __img_norm_layer__(name, input, size, norm_type, scale, power,
                       num_channels, blocked, layer_attr):
    if num_channels is None:
        assert input.num_filters is not None
        num_channels = input.num_filters

    Layer(
        name=name, type=LayerType.NORM_LAYER, inputs=Input(
            input.name, norm=Norm(norm_type=norm_type,
                                  channels=num_channels, size=size,
                                  scale=scale,
                                  pow=power, blocked=blocked)
        ),
        **ExtraLayerAttribute.to_kwargs(layer_attr)
    )
    return LayerOutput(name, layer_type=LayerType.NORM_LAYER, parents=[input],
                       num_filters=num_channels, img_norm_type=norm_type)


@wrap_name_default("crmnorm")
@layer_support()
def img_cmrnorm_layer(input, size, scale=0.0128, power=0.75,
                      name=None, num_channels=None,
                      blocked=0, layer_attr=None):
    """
    Convolution cross-map-response-normalize layer.
    The details please refer to
    `Alex's paper <http://www.cs.toronto.edu/~fritz/absps/imagenet.pdf>`_.

    :param name: layer name.
    :type name: None|basestring
    :param input: layer's input.
    :type input: LayerOutput
    :param size: cross map response size.
    :type size: int
    :param scale: The hyper-parameter.
    :type scale: float
    :param power: The hyper-parameter.
    :type power: float
    :param num_channels: input layer's filers number or channels. If
                         num_channels is None, it will be set automatically.
    :param blocked: namely normalize in number of blocked feature maps.
    :param layer_attr: Extra Layer Attribute.
    :type layer_attr: ExtraLayerAttribute
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    return __img_norm_layer__(name, input, size, "cmrnorm-projection", scale,
                              power, num_channels, blocked, layer_attr)


@wrap_name_default("rnorm")
@layer_support()
def img_rnorm_layer(input, size, scale, power, name=None, num_channels=None,
                    layer_attr=None):
    """
    Normalize the input in local region, namely response normalization
    across feature maps.

    :param name: The name of this layer.
    :rtype name: None|basestring
    :param input: The input of this layer.
    :param size:
    :param scale:
    :param power:
    :param num_channels:
    :param layer_attr:
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    return __img_norm_layer__(name, input, size, 'rnorm', scale, power,
                              num_channels, 0, layer_attr)


@wrap_bias_attr_default()
@wrap_param_attr_default(default_factory=lambda _: ParamAttr(initial_mean=1.0,
                                                             initial_std=0.))
@wrap_act_default(act=ReluActivation())
@wrap_name_default("batch_norm")
@layer_support(DROPOUT)
def batch_norm_layer(input, act=None, name=None, num_channels=None,
                     bias_attr=None, param_attr=None, layer_attr=None,
                     batch_norm_type=None,
                     moving_average_fraction=0.9,
                     use_global_stats=None):
    """
    Batch Normalization Layer. The notation of this layer as follow.

    :math:`x` is the input features over a mini-batch.

    ..  math::

        \\mu_{\\beta} &\\gets \\frac{1}{m} \\sum_{i=1}^{m} x_i \\qquad &//\\
        \ mini-batch\ mean \\\\
        \\sigma_{\\beta}^{2} &\\gets \\frac{1}{m} \\sum_{i=1}^{m}(x_i - \\
        \\mu_{\\beta})^2 \\qquad &//\ mini-batch\ variance \\\\
        \\hat{x_i} &\\gets \\frac{x_i - \\mu_\\beta} {\\sqrt{\\
        \\sigma_{\\beta}^{2} + \\epsilon}} \\qquad &//\ normalize \\\\
        y_i &\\gets \\gamma \\hat{x_i} + \\beta \\qquad &//\ scale\ and\ shift

    The details of batch normalization please refer to this
    `paper <http://arxiv.org/abs/1502.03167>`_.

    :param name: layer name.
    :type name: basestring
    :param input: batch normalization input. Better be linear activation.
                Because there is an activation inside batch_normalization.
    :type input: LayerOutput
    :param batch_norm_type: We have batch_norm and cudnn_batch_norm. batch_norm
                            supports both CPU and GPU. cudnn_batch_norm requires
                            cuDNN version greater or equal to v4 (>=v4). But
                            cudnn_batch_norm is faster and needs less memory
                            than batch_norm. By default (None), we will
                            automaticly select cudnn_batch_norm for GPU and
                            batch_norm for CPU. Otherwise, select batch norm
                            type based on the specified type. If you use cudnn_batch_norm,
                            we suggested you use latest version, such as v5.1.
    :type type: None|string, None or "batch_norm" or "cudnn_batch_norm"
    :param act: Activation Type. Better be relu. Because batch
                     normalization will normalize input near zero.
    :type act: BaseActivation
    :param num_channels: num of image channels or previous layer's number of
                         filters. None will automatically get from layer's
                         input.
    :type num_channels: int
    :param bias_attr: :math:`\\beta`, better be zero when initialize. So the
                      initial_std=0, initial_mean=1 is best practice.
    :type bias_attr: ParameterAttribute
    :param param_attr: :math:`\\gamma`, better be one when initialize. So the
                       initial_std=0, initial_mean=1 is best practice.
    :type param_attr: ParameterAttribute
    :param layer_attr: Extra Layer Attribute.
    :type layer_attr: ExtraLayerAttribute
    :param use_global_stats: whether use moving mean/variance statistics
                             during testing peroid. If None or True,
                             it will use moving mean/variance statistics during
                             testing. If False, it will use the mean
                             and variance of current batch of test data for
                             testing.
    :type use_global_stats: bool|None.
    :param moving_average_fraction: Factor used in the moving average
                                   computation, referred to as facotr,
                                   :math:`runningMean = newMean*(1-factor)
                                   + runningMean*factor`
    :type moving_average_fraction: float.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    if not isinstance(act, ReluActivation):
        logger.log(logging.WARN,
                   "%s is not recommend for batch normalization's activation, "
                   "maybe the relu is better" % act.name)

    if not isinstance(input.activation, LinearActivation):
        logger.log(logging.WARN,
                   "The activation should be inside batch normalization, the "
                   "previous layer's activation may be Linear")

    if num_channels is None:
        if input.num_filters is not None:
            num_channels = input.num_filters
        else:
            num_channels = input.size
    assert (batch_norm_type is None) or (batch_norm_type == "batch_norm") or \
           (batch_norm_type == "cudnn_batch_norm")
    Layer(
        name=name,
        inputs=Input(input.name,
                     image=Image(channels=num_channels),
                     **param_attr.attr),
        active_type=act.name,
        type=LayerType.BATCH_NORM_LAYER,
        batch_norm_type=batch_norm_type,
        bias=ParamAttr.to_bias(bias_attr),
        moving_average_fraction=moving_average_fraction,
        use_global_stats=use_global_stats,
        **ExtraLayerAttribute.to_kwargs(layer_attr)
    )

    return LayerOutput(name=name, layer_type=LayerType.BATCH_NORM_LAYER,
                       parents=[input], activation=act,
                       num_filters=num_channels)


@wrap_name_default()
@layer_support()
def sum_to_one_norm_layer(input, name=None, layer_attr=None):
    """
    A layer for sum-to-one normalization,
    which is used in NEURAL TURING MACHINE.

    .. math::
       out[i] = \\frac {in[i]} {\sum_{k=1}^N in[k]}

    where :math:`in` is a (batchSize x dataDim) input vector,
    and :math:`out` is a (batchSize x dataDim) output vector.

    The example usage is:

    .. code-block:: python

       sum_to_one_norm = sum_to_one_norm_layer(input=layer)

    :param input: Input layer.
    :type input: LayerOutput
    :param name: Layer name.
    :type name: basestring
    :param layer_attr: extra layer attributes.
    :type layer_attr: ExtraLayerAttribute.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    Layer(
        name=name,
        type=LayerType.SUM_TO_ONE_NORM_LAYER,
        inputs=[input.name],
        **ExtraAttr.to_kwargs(layer_attr)
    )
    return LayerOutput(name, LayerType.SUM_TO_ONE_NORM_LAYER, parents=[input],
                       size=input.size)


@wrap_name_default("addto")
@wrap_act_default(act=LinearActivation())
@wrap_bias_attr_default(has_bias=False)
@layer_support(DROPOUT)
def addto_layer(input, act=None, name=None, bias_attr=None,
                layer_attr=None):
    """
    AddtoLayer.

    ..  math::

        y = f(\\sum_{i} x_i + b)

    where :math:`y` is output, :math:`x` is input, :math:`b` is bias,
    and :math:`f` is activation function.

    The example usage is:

    ..  code-block:: python

        addto = addto_layer(input=[layer1, layer2],
                            act=ReluActivation(),
                            bias_attr=False)

    This layer just simply add all input layers together, then activate the sum
    inputs. Each input of this layer should be the same size, which is also the
    output size of this layer.

    There is no weight matrix for each input, because it just a simple add operation.
    If you want to a complicated operation before add, please use mixed_layer.

    It is a very good way to set dropout outside the layers. Since not all
    paddle layer support dropout, you can add an add_to layer, set dropout here.
    Please refer to dropout_layer for details.

    :param name: Layer name.
    :type name: basestring
    :param input: Input layers. It could be a LayerOutput or list/tuple of
                 LayerOutput.
    :type input: LayerOutput|list|tuple
    :param act: Activation Type, default is tanh.
    :type act: BaseActivation
    :param bias_attr: Bias attribute. If False, means no bias. None is default
                      bias.
    :type bias_attr: ParameterAttribute|bool
    :param layer_attr: Extra Layer attribute.
    :type layer_attr: ExtraLayerAttribute
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    num_filters = None
    if isinstance(input, LayerOutput):
        input = [input]

    assert isinstance(input, list) or isinstance(input, tuple)
    ipts_for_layer = []
    for each_input in input:
        assert isinstance(each_input, LayerOutput)
        ipts_for_layer.append(Input(each_input.name))
        if each_input.num_filters is not None:
            num_filters = each_input.num_filters

    Layer(
        name=name, type=LayerType.ADDTO_LAYER, inputs=ipts_for_layer,
        bias=ParamAttr.to_bias(bias_attr),
        active_type=act.name,
        **ExtraLayerAttribute.to_kwargs(layer_attr)
    )
    assert isinstance(input, list) or isinstance(input, tuple)
    return LayerOutput(name, LayerType.ADDTO_LAYER, parents=input,
                       activation=act, num_filters=num_filters)


@wrap_act_default(act=IdentityActivation())
@wrap_name_default("concat")
@layer_support()
def concat_layer(input, act=None, name=None, layer_attr=None):
    """
    Concat all input vector into one huge vector.
    Inputs can be list of LayerOutput or list of projection.

    :param name: Layer name.
    :type name: basestring
    :param input: input layers or projections
    :type input: list|tuple
    :param act: Activation type.
    :type act: BaseActivation
    :param layer_attr: Extra Layer Attribute.
    :type layer_attr: ExtraLayerAttribute
    :return: LayerOutput object.
    :rtype: LayerOutput
    """

    if isinstance(input, LayerOutput):
        input = [input]
    elif isinstance(input, Projection):
        input = [input]
    else:
        assert isinstance(input, list) or isinstance(input, tuple)

    def __is_type__(o, tp):
        if not isinstance(o, list) and not isinstance(o, tuple):
            if o == tp:
                return True
            elif len(o.__bases__) == 0:
                return False
            else:
                for bs in o.__bases__:
                    if __is_type__(bs, tp):
                        return True
                return False
        else:
            tmp = map(lambda _x: __is_type__(_x, tp), o)
            a = tmp[0]
            for b in tmp[1:]:
                assert a == b
            return a

    def __reduce_concat_type__(a, b):
        assert __is_type__([a, b], Projection) or __is_type__([a, b],
                                                              LayerOutput)
        return a

    is_concat_layer = __is_type__(reduce(__reduce_concat_type__,
                                         map(type, input)), LayerOutput)

    layer_type = (LayerType.CONCAT_LAYER if is_concat_layer
                  else LayerType.CONCAT_PROJ_LAYER)

    Layer(
        name=name, type=layer_type,
        inputs=[x.name for x in input] if is_concat_layer else input,
        active_type=act.name,
        **ExtraLayerAttribute.to_kwargs(layer_attr)
    )

    sz = 0
    for each_input in input:
        if each_input.size is not None:
            sz += each_input.size
        else:
            sz = None
            break

    return LayerOutput(name, layer_type=layer_type,
                       parents=input if is_concat_layer else [
                           x.origin for x in input],
                       activation=act, size=sz)


def memory(name, size, is_seq=False, boot_layer=None,
           boot_bias=None, boot_bias_active_type=None,
           boot_with_const_id=None):
    """
    The memory layers is a layer cross each time step. Reference this output
    as previous time step layer :code:`name` 's output.

    The default memory is zero in first time step, previous time step's
    output in the rest time steps.

    If boot_bias, the first time step value is this bias and
    with activation.

    If boot_with_const_id, then the first time stop is a IndexSlot, the
    Arguments.ids()[0] is this :code:`cost_id`.

    If boot_layer is not null, the memory is just the boot_layer's output.
    Set :code:`is_seq` is true boot layer is sequence.


    The same name layer in recurrent group will set memory on each time
    step.

    :param name: memory's name.
    :type name: basestring
    :param size: size of memory.
    :type size: int
    :param is_seq: is sequence for boot_layer
    :type is_seq: bool
    :param boot_layer: boot layer of memory.
    :type boot_layer: LayerOutput|None
    :param boot_bias: boot layer's bias
    :type boot_bias: ParameterAttribute|None
    :param boot_bias_active_type: boot layer's active type.
    :type boot_bias_active_type: BaseActivation
    :param boot_with_const_id: boot layer's id.
    :type boot_with_const_id: int
    :return: LayerOutput object which is a memory.
    :rtype: LayerOutput
    """
    if boot_bias_active_type is None:
        boot_bias_active_type = LinearActivation()

    assert boot_bias is None or isinstance(boot_bias, ParameterAttribute)
    if isinstance(boot_bias, ParameterAttribute):
        boot_bias = ParamAttr.to_bias(boot_bias)

    assert boot_layer is None or isinstance(boot_layer, LayerOutput)

    agent_name = Memory(name, size,
                        is_seq,
                        boot_layer.name if boot_layer is not None else None,
                        boot_bias,
                        boot_bias_active_type.name,
                        boot_with_const_id)

    lout = LayerOutput(name=agent_name, size=size,
                       layer_type=LayerType.MEMORY,
                       parents=[boot_layer] if boot_layer is not None
                       else None)
    return lout


@wrap_bias_attr_default()
@wrap_act_default(param_names=['gate_act',
                               'state_act'],
                  act=SigmoidActivation())
@wrap_act_default(act=TanhActivation())
@wrap_name_default('lstm_step')
@layer_support()
def lstm_step_layer(input, state, size, act=None,
                    name=None, gate_act=None, state_act=None,
                    bias_attr=None, layer_attr=None):
    """
    LSTM Step Layer. It used in recurrent_group. The lstm equations are shown
    as follow.

    ..  math::

        i_t & = \\sigma(W_{xi}x_{t} + W_{hi}h_{t-1} + W_{ci}c_{t-1} + b_i)

        f_t & = \\sigma(W_{xf}x_{t} + W_{hf}h_{t-1} + W_{cf}c_{t-1} + b_f)

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

        o_t & = \\sigma(W_{xo}x_{t} + W_{ho}h_{t-1} + W_{co}c_t + b_o)

        h_t & = o_t tanh(c_t)


    The input of lstm step is :math:`Wx_t + Wh_{t-1}`, and user should use
    :code:`mixed_layer` and :code:`full_matrix_projection` to calculate these
    input vector.

    The state of lstm step is :math:`c_{t-1}`. And lstm step layer will do

    ..  math::

        i_t = \\sigma(input + W_{ci}c_{t-1} + b_i)

        ...


    This layer contains two outputs. Default output is :math:`h_t`. The other
    output is :math:`o_t`, which name is 'state' and can use
    :code:`get_output_layer` to extract this output.

    :param name: Layer's name.
    :type name: basestring
    :param size: Layer's size. NOTE: lstm layer's size, should be equal as
                 :code:`input.size/4`, and should be equal as
                 :code:`state.size`.
    :type size: int
    :param input: input layer. :math:`Wx_t + Wh_{t-1}`
    :type input: LayerOutput
    :param state: State Layer. :math:`c_{t-1}`
    :type state: LayerOutput
    :param act: Activation type. Default is tanh
    :type act: BaseActivation
    :param gate_act: Gate Activation Type. Default is sigmoid, and should
                          be sigmoid only.
    :type gate_act: BaseActivation
    :param state_act: State Activation Type. Default is sigmoid, and should
                           be sigmoid only.
    :type state_act: BaseActivation
    :param bias_attr: Bias Attribute.
    :type bias_attr: ParameterAttribute
    :param layer_attr: layer's extra attribute.
    :type layer_attr: ExtraLayerAttribute
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    Layer(
        name=name,
        type=LayerType.LSTM_STEP_LAYER,
        active_type=act.name,
        active_gate_type=gate_act.name,
        active_state_type=state_act.name,
        bias=ParamAttr.to_bias(bias_attr),
        size=size, inputs=[input.name, state.name],
        **ExtraLayerAttribute.to_kwargs(layer_attr)
    )

    return LayerOutput(name=name, layer_type=LayerType.LSTM_STEP_LAYER,
                       parents=[input, state], activation=act,
                       size=size, outputs=['default', 'state'])


@wrap_bias_attr_default()
@wrap_act_default(param_names=['gate_act'],
                  act=SigmoidActivation())
@wrap_act_default(act=TanhActivation())
@wrap_name_default('gru_step')
@layer_support()
def gru_step_layer(input, output_mem, size=None, act=None,
                   name=None, gate_act=None,
                   bias_attr=None, layer_attr=None):
    """

    :param input:
    :type input: LayerOutput
    :param output_mem:
    :param size:
    :param act:
    :param name:
    :param gate_act:
    :param bias_attr:
    :param layer_attr:
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    assert input.size % 3 == 0
    if size is None:
        size = input.size / 3
    Layer(
        name=name,
        type=LayerType.GRU_STEP_LAYER,
        inputs=[
            input.name,
            output_mem.name
        ],
        bias=ParamAttr.to_bias(bias_attr),
        size=size,
        active_type=act.name,
        active_gate_type=gate_act.name,
        **ExtraAttr.to_kwargs(layer_attr)
    )
    return LayerOutput(
        name=name, layer_type=LayerType.GRU_STEP_LAYER,
        parents=[input, output_mem],
        size=size, activation=act)


@wrap_name_default()
@layer_support()
def get_output_layer(input, arg_name, name=None, layer_attr=None):
    """
    Get layer's output by name. In paddle, a layer might return multiple value,
    but return one layer output. If user want to reference another output beside
    default output, use get_output_layer first to get another output from input.

    :param name: Layer's name.
    :type name: basestring
    :param input: get output layer's input. And this layer should contains
                   multiple outputs.
    :type input: LayerOutput
    :param arg_name: Output name from input.
    :type arg_name: basestring
    :param layer_attr: Layer's extra attribute.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    # GetOutputLayer
    assert arg_name in input.outputs, 'Get Output From an not existed input.' \
                                      ' The get output name is %s, which not' \
                                      ' in %s' % (
                                          arg_name, ",".join(input.outputs))
    Layer(name=name, type=LayerType.GET_OUTPUT_LAYER,
          inputs=[Input(input.name, input_layer_argument=arg_name)],
          size=input.size,
          **ExtraLayerAttribute.to_kwargs(layer_attr))

    return LayerOutput(name=name, layer_type=LayerType.GET_OUTPUT_LAYER,
                       parents=[input], size=input.size)


@wrap_name_default()
@wrap_act_default()
@wrap_bias_attr_default()
@wrap_param_attr_default()
@layer_support()
def recurrent_layer(input, act=None, bias_attr=None,
                    param_attr=None, name=None, layer_attr=None):
    """
    TODO(yuyang18): Add docs

    :param input:
    :param size:
    :param act:
    :param bias_attr:
    :param param_attr:
    :param name:
    :param layer_attr:
    :return: LayerOutput object.
    """
    Layer(name=name,
          type=LayerType.RECURRENT_LAYER,
          inputs=Input(input.name, **param_attr.attr),
          active_type=act.name,
          size=input.size,
          bias=ParamAttr.to_bias(bias_attr),
          **ExtraAttr.to_kwargs(layer_attr))
    return LayerOutput(name=name, layer_type=LayerType.RECURRENT_LAYER,
                       parents=[input], size=input.size, activation=act)


class StaticInput(object):
    """
    StaticInput is only used in recurrent_group which defines a read-only memory
    that can be a sequence or non-sequence.
    """
    def __init__(self, input, is_seq=False, size=None):
        assert isinstance(input, LayerOutput)
        self.input = input
        self.is_seq = is_seq
        assert input.size is not None or size is not None
        if size is not None:
            input.size = size


class SubsequenceInput(object):
    """
    Input sequence has sub-sequence, used in recurrent_group.

    The example usage is:

    .. code-block:: python

       input = SubsequenceInput(layer)
    """
    def __init__(self, input):
        assert isinstance(input, LayerOutput)
        assert input.size is not None
        self.input = input


@wrap_name_default("recurrent_group")
def recurrent_group(step, input, reverse=False, name=None):
    """
    Recurrent Group. It supports time steps and sequence steps mechanisms.

    The basic usage (time steps) is:

    .. code-block:: python

       def step(input):
           output = fc_layer(input=layer,
                             size=1024,
                             act=LinearActivation(),
                             bias_attr=False)
           return output

       group = recurrent_group(input=layer,
                               step=step)

    You can see following configs for further usages:

    - time steps: lstmemory_group, paddle/gserver/tests/sequence_layer_group.conf, \
                  demo/seqToseq/seqToseq_net.py
    - sequence steps: paddle/gserver/tests/sequence_nest_layer_group.conf

    :param step: recurrent one time step function.The input of this function is
                 input of the group. The return of this function will be
                 recurrent group's return value.

                 The recurrent group scatter a sequence into time steps. And
                 for each time step, will invoke step function, and return
                 a time step result. Then gather each time step of output into
                 layer group's output.

    :type step: callable

    :param name: recurrent_group's name.
    :type name: basestring

    :param input: Input links array.

                  LayerOutput will be scattered into time steps.
                  SubsequenceInput will be scattered into sequence steps.
                  StaticInput will be imported to each time step, and doesn't change
                  through time. It's a mechanism to access layer outside step function.

    :type input: LayerOutput|StaticInput|SubsequenceInput|list|tuple

    :param reverse: If reverse is set true, the recurrent unit will process the
                    input sequence in a reverse order.
    :type reverse: bool
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    model_type('recurrent_nn')

    def is_single_input(x):
        return isinstance(x, LayerOutput) or isinstance(x, StaticInput) \
               or isinstance(x, SubsequenceInput)

    if is_single_input(input):
        input = [input]
    assert isinstance(input, list) or isinstance(input, tuple)

    def is_in_links(x):
        return isinstance(x, LayerOutput) or isinstance(x, SubsequenceInput)

    in_links = filter(is_in_links, input)

    contains_sub_seq = [False]

    def map_in_links(x):
        if isinstance(x, SubsequenceInput):
            contains_sub_seq[0] = True
            return Link(name=x.input.name, has_subseq=True)
        else:
            return x.name

    RecurrentLayerGroupWithoutOutLinksBegin(
        name=name, in_links=map(map_in_links, in_links),
        seq_reversed=reverse)
    in_args = []
    for each_input in input:
        assert is_single_input(each_input)
        if isinstance(each_input, LayerOutput):
            in_args.append(each_input)
        elif isinstance(each_input, SubsequenceInput):
            in_args.append(each_input.input)
        else:
            mem_name = "__%s_memory__" % each_input.input.name
            mem = memory(name=mem_name,
                         is_seq=each_input.is_seq,
                         size=each_input.input.size,
                         boot_layer=each_input.input)
            with mixed_layer(name=mem_name, size=each_input.input.size,
                             act=IdentityActivation()) as mix:
                mix += identity_projection(mem)
            in_args.append(mem)

    layer_outs = step(*in_args)

    if isinstance(layer_outs, LayerOutput):
        layer_outs = [layer_outs]

    for ot in layer_outs:
        assert isinstance(ot, LayerOutput)
        if contains_sub_seq[0]:
            RecurrentLayerGroupSetOutLink(Link(ot.name, has_subseq=True))
        else:
            RecurrentLayerGroupSetOutLink(ot.name)

    RecurrentLayerGroupEnd(name=name)

    if len(layer_outs) == 1:
        return layer_outs[0]
    else:
        return layer_outs

class BaseGeneratedInput(object):
    def __init__(self):
        self.bos_id = None
        self.eos_id = None

    def before_real_step(self):
        raise NotImplementedError()

    def after_real_step(self, *args):
        raise NotImplementedError()


class GeneratedInput(BaseGeneratedInput):
    def after_real_step(self, input):
        return maxid_layer(input=input, name='__beam_search_predict__')

    def before_real_step(self):
        predict_id = memory(name='__beam_search_predict__',
                            size=self.size,
                            boot_with_const_id=self.bos_id)

        trg_emb = embedding_layer(input=predict_id,
                                  size=self.embedding_size,
                                  param_attr=ParamAttr(
                                      name=self.embedding_name))
        return trg_emb

    def __init__(self, size, embedding_name, embedding_size):
        self.size = size
        self.embedding_name = embedding_name
        self.embedding_size = embedding_size


@wrap_name_default()
def maxid_layer(input, name=None, layer_attr=None):
    """
    A layer for finding the id which has the maximal value for each sample.
    The result is stored in output.ids.

    The example usage is:

    .. code-block:: python

       maxid = maxid_layer(input=layer)

    :param input: Input layer name.
    :type input: LayerOutput
    :param name: Layer name.
    :type name: basestring
    :param layer_attr: extra layer attributes.
    :type layer_attr: ExtraLayerAttribute.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """

    assert isinstance(input, LayerOutput)
    Layer(name=name,
          type='maxid',
          inputs=[input.name],
          **ExtraLayerAttribute.to_kwargs(layer_attr))
    return LayerOutput(name=name,
                       layer_type=LayerType.MAXID_LAYER,
                       parents=[input])


@wrap_name_default()
def eos_layer(input, eos_id, name=None, layer_attr=None):
    """
    A layer for checking EOS for each sample:
    - output_id = (input_id == conf.eos_id)

    The result is stored in output\_.ids.
    It is used by recurrent layer group.

    The example usage is:

    .. code-block:: python

       eos = eos_layer(input=layer, eos_id=id)

    :param name: Layer name.
    :type name: basestring
    :param input: Input layer name.
    :type input: LayerOutput
    :param eos_id: end id of sequence
    :type eos_id: int
    :param layer_attr: extra layer attributes.
    :type layer_attr: ExtraLayerAttribute.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    Layer(name=name,
          type=LayerType.EOSID_LAYER,
          eos_id=eos_id,
          inputs=[input.name],
          **ExtraLayerAttribute.to_kwargs(layer_attr))
    return LayerOutput(name=name, layer_type=LayerType.EOSID_LAYER,
                       parents=[input])


@wrap_name_default()
def beam_search(step, input, bos_id, eos_id, beam_size,
                result_file, dict_file="", id_input=None,
                max_length=500, name=None,
                num_results_per_sample=None):
    """
    Beam search is a heuristic search algorithm used in sequence generation.
    It explores a graph by expanding the most promising nodes in a limited set
    to maintain tractability.

    The example usage is:

    .. code-block:: python

        def rnn_step(input):
            last_time_step_output = memory(name='rnn', size=512)
            with mixed_layer(size=512) as simple_rnn:
                simple_rnn += full_matrix_projection(input)
                simple_rnn += last_time_step_output
            return simple_rnn

        beam_gen = beam_search(name="decoder",
                               step=rnn_step,
                               input=[StaticInput("encoder_last")],
                               bos_id=0,
                               eos_id=1,
                               beam_size=5,
                               result_file="./generated_sequences.txt")

    Please see the following demo for more details:

    - machine translation : demo/seqToseq/translation/gen.conf \
                            demo/seqToseq/seqToseq_net.py

    :param name: Name of the recurrent unit that generates sequences.
    :type name: base string
    :param step: A callable function that defines the calculation in a time
                 step, and it is appled to sequences with arbitrary length by
                 sharing a same set of weights.

                 You can refer to the first parameter of recurrent_group, or
                 demo/seqToseq/seqToseq_net.py for more details.
    :type step: callable
    :param input: Input data for the recurrent unit
    :type input: StaticInput|GeneratedInput
    :param bos_id: Index of the start symbol in the dictionary. The start symbol
                   is a special token for NLP task, which indicates the
                   beginning of a sequence. In the generation task, the start
                   symbol is ensential, since it is used to initialize the RNN
                   internal state.
    :type bos_id: int
    :param eos_id: Index of the end symbol in the dictionary. The end symbol is
                   a special token for NLP task, which indicates the end of a
                   sequence. The generation process will stop once the end
                   symbol is generated, or a pre-defined max iteration number
                   is exceeded.
    :type eos_id: int
    :param beam_size: Beam search for sequence generation is an iterative search
                      algorithm. To maintain tractability, every iteration only
                      only stores a predetermined number, called the beam_size,
                      of the most promising next words. The greater the beam
                      size, the fewer candidate words are pruned.
    :type beam_size: int
    :param result_file: Path of the file to store the generated results.
    :type result_file: basestring
    :param dict_file: Path of dictionary. This is an optional parameter.
                      Every line is a word in the dictionary with
                      (line number - 1) as the word index.
                      If this parameter is set to None, or to an empty string,
                      only word index are printed in the generated results.
    :type dict_file: basestring
    :param num_results_per_sample: Number of the generated results per input
                                  sequence. This number must always be less than
                                  beam size.
    :type num_results_per_sample: int
    :param id_input: Index of the input sequence, and the specified index will
                     be prited in the gereated results. This an optional
                     parameter.
    :type id_input: LayerOutput
    :return: The seq_text_printer that prints the generated sequence to a file.
    :rtype: evaluator
    """

    if num_results_per_sample is None:
        num_results_per_sample = beam_size
    if num_results_per_sample > beam_size:
        logger.warning("num_results_per_sample should be less than beam_size")

    if isinstance(input, StaticInput) or isinstance(input,
                                                    BaseGeneratedInput):
        input = [input]

    generated_input_index = -1

    real_input = []
    for i, each_input in enumerate(input):
        # print type(each_input)
        assert isinstance(each_input, StaticInput) or isinstance(each_input,
                                                          BaseGeneratedInput)
        if isinstance(each_input, BaseGeneratedInput):
            assert generated_input_index == -1
            generated_input_index = i
        else:
            real_input.append(each_input)

    assert generated_input_index != -1

    gipt = input[generated_input_index]
    assert isinstance(gipt, BaseGeneratedInput)

    gipt.bos_id = bos_id
    gipt.eos_id = eos_id

    def __real_step__(*args):
        eos_name = "__%s_eos_layer__" % name
        RecurrentLayerGroupSetGenerator(Generator(
            eos_layer_name=eos_name,
            max_num_frames=max_length,
            beam_size=beam_size,
            num_results_per_sample=num_results_per_sample))

        args = list(args)
        args.insert(generated_input_index, gipt.before_real_step())

        predict = gipt.after_real_step(step(*args))

        eos_layer(input=predict, eos_id=eos_id, name=eos_name)

        return predict

    tmp = recurrent_group(step=__real_step__, input=real_input, reverse=False,
                          name=name)

    if id_input is None:
        inputs = [tmp.name]
    else:
        assert isinstance(id_input, LayerOutput)
        inputs = [id_input.name, tmp.name]
        tmp.parents.append(id_input)

    Evaluator(name='target_printer',
              type='seq_text_printer',
              dict_file=dict_file,
              result_file=result_file,
              inputs=inputs
              )
    return tmp


@wrap_name_default()
def regression_cost(input, label, cost='square_error', name=None):
    """
    Regression Layer.

    TODO(yuyang18): Complete this method.

    :param name: layer name.
    :param input: Network prediction.
    :param label: Data label.
    :param cost: Cost method.
    :return: LayerOutput object.
    """
    Layer(inputs=[Input(input.name), Input(label.name)], type=cost, name=name)
    return LayerOutput(
        name, LayerType.COST, parents=[input, label]
    )


@wrap_name_default("cost")
def classification_cost(input, label, name=None,
                        cost="multi-class-cross-entropy",
                        evaluator=classification_error_evaluator):
    """
    classification cost Layer.

    :param name: layer name.
    :type name: basestring
    :param input: input layer name. network output.
    :type input: LayerOutput
    :param label: label layer name. data_layer often.
    :type label: LayerOutput
    :param cost: cost method.
    :type cost: basestring
    :param evaluator: Evaluator method.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    assert input.layer_type != LayerType.DATA
    assert isinstance(input.activation, SoftmaxActivation)
    assert label.layer_type == LayerType.DATA
    Layer(name=name, type=cost, inputs=[Input(input.name), Input(label.name)])

    def __add_evaluator__(e):
        assert callable(e)
        assert hasattr(e, 'is_evaluator')
        assert isinstance(e.is_evaluator, bool)
        assert e.is_evaluator
        assert hasattr(e, "for_classification")
        assert isinstance(e.for_classification, bool)
        assert e.for_classification

        e(name=e.__name__, input=input, label=label)

    if not isinstance(evaluator, list) and not isinstance(evaluator, tuple):
        evaluator = [evaluator]

    for each_evaluator in evaluator:
        __add_evaluator__(each_evaluator)

    return LayerOutput(name, LayerType.COST, parents=[input, label])

def conv_operator(input, filter_size, num_filters,
                  num_channel=None, stride=1, padding=0,
                  filter_size_y=None, stride_y=None, padding_y=None):
    """
    Different from img_conv_layer, conv_op is an Operator, which can be used
    in mixed_layer. And conv_op takes two inputs to perform convolution.
    The first input is the image and the second is filter kernel. It only
    support GPU mode.

    The example usage is:

    .. code-block:: python

       op = conv_operator(input=[layer1, layer2],
                          filter_size=3.0,
                          num_filters=64,
                          num_channels=64)

    :param input: Input layer.
    :type input: LayerOutput|list|tuple
    :param filter_size: The x dimension of a filter kernel.
    :type filter_size: int
    :param filter_size_y: The y dimension of a filter kernel. Since paddle now
                        support rectangular filters, the filter's shape
                        will be (filter_size, filter_size_y).
    :type filter_size_y: int
    :param num_filter: channel of output data.
    :type num_filter: int
    :param num_channel: channel of input data.
    :type num_channel: int
    :param stride: The x dimension of the stride.
    :type stride: int
    :param stride_y: The y dimension of the stride.
    :type stride_y: int
    :param padding: The x dimension of padding.
    :type padding: int
    :param padding_y: The y dimension of padding.
    :type padding_y: int
    :return: A ConvOperator Object.
    :rtype: ConvOperator
    """
    assert isinstance(input, list) or isinstance(input, tuple)
    if filter_size_y is None:
        filter_size_y = filter_size
    if stride_y is None:
        stride_y = stride
    if padding_y is None:
        padding_y = padding
    op = ConvOperator(input_layer_name=[x.name for x in input],
                      num_filters = num_filter,
                      conv_conf=Conv(filter_size=filter_size,
                                     padding=padding,
                                     stride=stride,
                                     channels=num_channel,
                                     filter_size_y=filter_size_y,
                                     padding_y=padding_y,
                                     stride_y=stride_y))
    op.origin = input
    op.origin.operator = "conv_op"
    return op


@wrap_name_default()
def conv_shift_layer(input, name=None):
    """
    This layer performs cyclic convolution for two input. For example:
      - a[in]: contains M elements.
      - b[in]: contains N elements (N should be odd).
      - c[out]: contains M elements.

    .. math::

        c[i] = \sum_{j=-(N-1)/2}^{(N-1)/2}a_{i+j} * b_{j}

    In this formular:
     - a's index is computed modulo M.
     - b's index is computed modulo N.

    The example usage is:

    .. code-block:: python

       conv_shift = conv_shif_layer(input=[layer1, layer2])

    :param name: layer name
    :type name: basestring
    :param input: Input layer.
    :type input: LayerOutput|list|tuple.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    assert isinstance(input, list) or isinstance(input, tuple)
    Layer(
        name=name,
        type=LayerType.CONV_SHIFT_LAYER,
        inputs=[x.name for x in input],
    )

    return LayerOutput(name, LayerType.CONV_SHIFT_LAYER, parents=input)


@wrap_name_default()
@wrap_param_attr_default()
@wrap_bias_attr_default()
@layer_support(ERROR_CLIPPING, DROPOUT)
def tensor_layer(input, size, act=None, name=None,
                 param_attr=None, bias_attr=None, layer_attr=None):
    """
    This layer performs tensor operation for two input.
    For example, each sample:

    .. math::
       y_{i} = x_{1} * W_{i} * {x_{2}^\mathrm{T}}, i=0,1,...,K-1

    In this formular:
      - :math:`x_{1}`: the first input contains M elements.
      - :math:`x_{2}`: the second input contains N elements.
      - :math:`y_{i}`: the i-th element of y.
      - :math:`W_{i}`: the i-th learned weight, shape if [M, N]
      - :math:`{x_{2}}^\mathrm{T}`: the transpose of :math:`x_{2}`.

    The simple usage is:

    .. code-block:: python

       tensor = tensor_layer(input=[layer1, layer2])

    :param name: layer name
    :type name: basestring
    :param input: Input layer.
    :type input: LayerOutput|list|tuple.
    :param size: the layer dimension.
    :type size: int.
    :param act: Activation Type. Default is tanh.
    :type act: BaseActivation
    :param param_attr: The Parameter Attribute.
    :type param_attr: ParameterAttribute|list
    :param bias_attr: The Bias Attribute. If no bias, then pass False or
                      something not type of ParameterAttribute. None will get a
                      default Bias.
    :type bias_attr: ParameterAttribute|None|Any
    :param layer_attr: Extra Layer config.
    :type layer_attr: ExtraLayerAttribute|None
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    assert isinstance(input, list) or isinstance(input, tuple)
    assert len(input) == 2
    Layer(
        name=name,
        size=size,
        type=LayerType.TENSOR_LAYER,
        active_type=act.name,
        bias=ParamAttr.to_bias(bias_attr),
        inputs=[Input(input[0].name, **param_attr),
                Input(input[1].name)],
        **ExtraLayerAttribute.to_kwargs(layer_attr)
    )
    return LayerOutput(name, LayerType.TENSOR_LAYER, parents=input,
                       activation=act, size=size)


@wrap_param_attr_default()
def trans_full_matrix_projection(input, size=0, param_attr=None):
    """
    Different from full_matrix_projection, this projection performs matrix
    multiplication, using transpose of weight.

    ..  math::
        out.row[i] += in.row[i] * w^\mathrm{T}

    :math:`w^\mathrm{T}` means transpose of weight.
    The simply usage is:

    .. code-block:: python

       proj = trans_full_matrix_projection(input=layer,
                                           size=100,
                                           param_attr=ParamAttr(
                                                name='_proj',
                                                initial_mean=0.0,
                                                initial_std=0.01))

    :param input: input layer
    :type input: LayerOutput
    :param size: The parameter size. Means the width of parameter.
    :type size: int
    :param param_attr: Parameter config, None if use default.
    :type param_attr: ParameterAttribute
    :return: A TransposedFullMatrixProjection Object.
    :rtype: TransposedFullMatrixProjection
    """
    proj = TransposedFullMatrixProjection(input_layer_name=input.name,
                                          size=size,
                                          **param_attr.attr)
    proj.origin = input
    proj.origin.projection = "trans_matrix"
    return proj


@wrap_name_default()
@wrap_param_attr_default()
@wrap_bias_attr_default()
@wrap_act_default()
def selective_fc_layer(input, size, act=None, name=None,
                       pass_generation=False,
                       has_selected_colums=True,
                       mul_ratio=0.02,
                       param_attr=None, bias_attr=None, layer_attr=None):
    """
    Selectived fully connected layer. Different from fc_layer, the output
    of this layer maybe sparse. It requires an additional input to indicate
    several selected columns for output. If the selected columns is not
    specified, selective_fc_layer acts exactly like fc_layer.

    The simple usage is:

    .. code-block:: python

       sel_fc = selective_fc_layer(input=input, 128, act=TanhActivation())

    :param name: The Layer Name.
    :type name: basestring
    :param input: The input layer.
    :type input: LayerOutput|list|tuple
    :param size: The layer dimension.
    :type size: int
    :param act: Activation Type. Default is tanh.
    :type act: BaseActivation
    :param param_attr: The Parameter Attribute.
    :type param_attr: ParameterAttribute
    :param bias_attr: The Bias Attribute. If no bias, then pass False or
                      something not type of ParameterAttribute. None will get a
                      default Bias.
    :type bias_attr: ParameterAttribute|None|Any
    :param layer_attr: Extra Layer config.
    :type layer_attr: ExtraLayerAttribute|None
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    if isinstance(input, LayerOutput):
        input = [input]
        assert not isinstance(param_attr, list)
        param_attr = [param_attr]
    else:
        if isinstance(param_attr, list) or isinstance(param_attr, tuple):
            assert len(input) == len(param_attr)
        else:
            param_attr = [copy.deepcopy(param_attr) for _ in range(len(input))]

    assert isinstance(input, list)

    def __idx_to_input__(i):
        attr = param_attr[i]
        assert isinstance(attr, ParameterAttribute)
        return Input(input[i].name, **attr.attr)

    Layer(
        inputs=map(__idx_to_input__, range(len(input))),
        name=name,
        type=LayerType.SEL_FC_LAYER,
        size=size,
        active_type=act.name,
        selective_fc_pass_generation=pass_generation,
        has_selected_colums=has_selected_colums,
        selective_fc_full_mul_ratio=mul_ratio,
        **ExtraLayerAttribute.to_kwargs(layer_attr)
    )
    return LayerOutput(name, LayerType.SEL_FC_LAYER, input, activation=act,
                       size=size)


@wrap_name_default()
def sampling_id_layer(input, name=None):
    """
    A layer for sampling id from multinomial distribution from the input layer.
    Sampling one id for one sample.

    The simple usage is:

    .. code-block:: python

       samping_id = sampling_id_layer(input=input)

    :param input: The input layer.
    :type input: LayerOutput
    :param name: The Layer Name.
    :type name: basestring
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    Layer(
        name=name,
        type=LayerType.SAMPLING_ID_LAYER,
        inputs=[Input(input.name)],
    )
    return LayerOutput(name, LayerType.SAMPLING_ID_LAYER, input)


@wrap_name_default()
def slope_intercept_layer(input, name=None, slope=1.0, intercept=0.0):
    """
    This layer for applying a slope and an intercept to the input
    element-wise. There is no activation and weight.

    ..  math::
        y = slope * x + intercept

    The simple usage is:

    .. code-block:: python

       scale = slope_intercept_layer(input=input, slope=-1.0, intercept=1.0)

    :param input: The input layer.
    :type input: LayerOutput
    :param name: The Layer Name.
    :type name: basestring
    :param slope: the scale factor.
    :type slope: float.
    :param intercept: the offset.
    :type intercept: float.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    Layer(
        name=name,
        type=LayerType.SLOPE_INTERCEPT_LAYER,
        slope=slope,
        intercept=intercept,
        inputs=[Input(input.name)],
    )
    return LayerOutput(name, LayerType.SLOPE_INTERCEPT_LAYER, input)


@wrap_name_default()
def convex_comb_layer(input, size, name=None):
    """
    A layer for convex weighted average of vectors takes two inputs.
      - Input: a vector containing the convex weights (batchSize x weightdim),
               and a matrix in a vector form (batchSize x (weightdim * datadim)).
      - Output: a vector (batchSize * datadim).

    .. math::

       y[i][j] = \sum_{j}(x_{1}(i, j) * x_{2}(i,j + i * dataDim)),

                   i = 0,1,...,(batchSize-1); j = 0, 1,...,(dataDim-1)

    In this formular:
      - :math:`x_{1}`: the first input.
      - :math:`x_{2}`: the second input.
      - :math:`y`: the output.

    The simple usage is:

    .. code-block:: python

       convex_comb = convex_comb_layer(input=inputs,
                                       size=elem_dim)

    :param input: The input layers.
    :type input: LayerOutput
    :param size: the dimension of this layer.
    :type size: int
    :param name: The Layer Name.
    :type name: basestring
    :return: LayerOutput object.
    :rtype: LayerOutput
    """

    assert isinstance(input, list) or isinstance(input, tuple)
    assert len(input) == 2
    Layer(
        name=name,
        type=LayerType.CONVEX_COMBINATION_LAYER,
        size=size,
        inputs=[Input(input[0].name), Input(input[1].name)],
    )
    return LayerOutput(name, LayerType.CONVEX_COMBINATION_LAYER, input, size=size)

@wrap_name_default()
def block_expand_layer(input,
                       channel=0,
                       block_x=0,
                       block_y=0,
                       stride_x=0,
                       stride_y=0,
                       padding_x=0,
                       padding_y=0,
                       name=None):
    """
    Expand feature map to minibatch matrix.
       - matrix width is: block_y * block_x * channel
       - matirx height is: outputH * outputW

    .. math::

       outputH = 1 + (2 * padding_y + imgSizeH - block_y + stride_y - 1) / stride_y

       outputW = 1 + (2 * padding_x + imgSizeW - block_x + stride_x - 1) / stride_x

    The expand method is the same with ExpandConvLayer, but saved the transposed
    value. After expanding, output.sequenceStartPositions will store timeline.
    The number of time steps are outputH * outputW and the dimension of each
    time step is block_y * block_x * channel. This layer can be used after
    convolution neural network, and before recurrent neural network.

    The simple usage is:

    .. code-block:: python

       block_expand = block_expand_layer(input,
                                         channel=128,
                                         stride_x=1,
                                         stride_y=1,
                                         block_x=1,
                                         block_x=3)

    :param input: The input layer.
    :type input: LayerOutput
    :param channel: The channel number of input layer.
    :type channel: int
    :param block_x: The width of sub block.
    :type block_x: int
    :param block_y: The width of sub block.
    :type block_y: int
    :param stride_x: The stride size in horizontal direction.
    :type stride_x: int
    :param stride_y: The stride size in vertical direction.
    :type stride_y: int
    :param padding_x: The padding size in horizontal direction.
    :type padding_x: int
    :param padding_y: The padding size in vertical direction.
    :type padding_y: int
    :param name: The name of this layer, which can not specify.
    :type name: None|basestring.
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    Layer(name=name,
          input=Input(input.name,
                      block_expand=BlockExpand(channel=channel,
                                               block_x=block_x,
                                               block_y=block_y,
                                               stride_x=stride_x,
                                               stride_y=stride_y,
                                               padding_x=padding_x,
                                               padding_y=padding_y)
                       ),
          type=LayerType.BLOCK_EXPAND,
         )

    return LayerOutput(name, LayerType.BLOCK_EXPAND,
                       parents=[input], size=size)

@wrap_name_default()
def ctc_layer(input, label, size, name=None, norm_by_times=False):
    """
    Connectionist Temporal Classification (CTC) is designed for temporal
    classication task. That is, for sequence labeling problems where the
    alignment between the inputs and the target labels is unknown.

    The simple usage:

    .. code-block:: python

      ctc = ctc_layer(input=input,
                      label=label,
                      size=9055,
                      norm_by_times=True)

    :param input: The input layers.
    :type input: LayerOutput
    :param label: The data layer of label with variable length.
    :type label: LayerOutput
    :param size: category numbers.
    :type size: int
    :param name: The name of this layer, which can not specify.
    :type name: string|None
    :param norm_by_times: Whether to normalization by times. False by default.
    :type norm_by_times: bool
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    assert isinstance(input, LayerOutput)
    assert isinstance(label, LayerOutput)
    Layer(
        name = name,
        type = LayerType.CTC_LAYER,
        size = size,
        norm_by_times = norm_by_times,
        inputs = [input.name, label.name]
    )
    return LayerOutput(name, LayerType.CTC_LAYER, [input, label], size=size)

@wrap_name_default()
def crf_layer(input, label, size, weight=None, param_attr=None, name=None):
    """
    A layer for calculating the cost of sequential conditional random
    field model.

    The simple usage:

    .. code-block:: python

      crf = crf_layer(input=input,
                      label=label,
                      size=label_dim)

    :param input: The first input layer is the feature.
    :type input: LayerOutput
    :param label: The second input layer is label.
    :type input: LayerOutput
    :param size: The category number.
    :type size: int
    :param weight: The third layer is "weight" of each sample, which is an
                  optional argument.
    :type weight: LayerOutput
    :param param_attr: Parameter attribute. None means default attribute
    :type param_attr: ParameterAttribute
    :param name: The name of this layers. It is not necessary.
    :type name: None|basestring
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    assert isinstance(input, LayerOutput)
    assert isinstance(label, LayerOutput)
    assert weight is None or isinstance(weight, LayerOutput)

    ipts = [Input(input.name, **param_attr),
            Input(label.name)]
    if weight is not None:
        ipts.append(Input(weight.name))

    Layer(
        name = name,
        type = LayerType.CRF_LAYER,
        size = size,
        inputs = ipts,
    )
    parents = [input, label]
    if weight is not None:
        parents.append(weight)
    return LayerOutput(name, LayerType.CRF_LAYER, parents, size=size)

@wrap_name_default()
def crf_decoding_layer(input, size, label=None, param_attr=None, name=None):
    """
    A layer for calculating the decoding sequence of sequential conditional
    random field model. The decoding sequence is stored in output.ids.
    If a second input is provided, it is treated as the ground-truth label, and
    this layer will also calculate error. output.value[i] is 1 for incorrect
    decoding or 0 for correct decoding.

    :param input: The first input layer.
    :type input: LayerOutput
    :param size: size of this layer.
    :type size: int
    :param label: None or ground-truth label.
    :type label: LayerOutput or None
    :param param_attr: Parameter attribute. None means default attribute
    :type param_attr: ParameterAttribute
    :param name: The name of this layers. It is not necessary.
    :type name: None|basestring
    :return: LayerOutput object.
    :rtype: LayerOutput
    """

    assert isinstance(input, LayerOutput)
    assert label is None or isinstance(label, LayerOutput)

    ipts = [Input(input.name, **param_attr)]
    if label is not None:
        ipts.append(Input(label.name))

    Layer(
        name = name,
        type = LayerType.CRF_DECODING_LAYER,
        size = size,
        inputs = ipts,
    )
    parents = [input]
    if label is not None:
        parents.append(label)
    return LayerOutput(name, LayerType.CRF_DECODING_LAYER, parents, size=size)

"""
following are cost Layers.
"""
@wrap_name_default()
def rank_cost(left, right, lable, weight=None, name=None, coeff=1.0):
    """
    A cost Layer for learning to rank using gradient descent. Details can refer
    to `papers <http://research.microsoft.com/en-us/um/people/cburges/papers/ICML_ranking.pdf>`_.
    This layer contains at least three inputs. The weight is an optional
    argument, which affects the cost.

    .. math::

       C_{i,j} & = -\\tilde{P_{ij}} * o_{i,j} + log(1 + e^{o_{i,j}})

       o_{i,j} & =  o_i - o_j

       \\tilde{P_{i,j}} & = \\{0, 0.5, 1\\} \ or \ \\{0, 1\\}

    In this formula:
      - :math:`C_{i,j}` is the cross entropy cost.
      - :math:`\\tilde{P_{i,j}}` is the label. 1 means positive order
        and 0 means reverse order.
      - :math:`o_i` and :math:`o_j`: the left output and right output.
        Their dimension is one.

    The simple usage:

    .. code-block:: python

      cost = rank_cost(left=out_left,
                       right=out_right,
                       label=label)

    :param left: The first input, the size of this layer is 1.
    :type left: LayerOutput
    :param right: The right input, the size of this layer is 1.
    :type right: LayerOutput
    :param label: Label is 1 or 0, means positive order and reverse order.
    :type label: LayerOutput
    :param weight: The weight affects the cost, namely the scale of cost.
                   It is an optional argument.
    :type weight: LayerOutput
    :param name: The name of this layers. It is not necessary.
    :type name: None|basestring
    :param coeff: The coefficient affects the gradient in the backward.
    :type coeff: float
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    assert left.size == 1
    assert right.size == 1
    assert label.size == 1

    ipts = [left.name, right.name, label.name]
    parents = [left, right, label]
    if weight is not None:
        ipts.append(weight.name)
        parents.append(weight)

    Layer(name=name,
          type=LayerType.RANK_COST,
          inputs=ipts,
          coeff=coeff,
         )

    return LayerOutput(name, LayerType.RANK_COST, parents=parents)

@wrap_name_default()
def lambda_cost(input, score, NDCG_num=5, max_sort_size=-1, coeff=1.0):
    """
    lambdaCost for lambdaRank LTR approach.

    The simple usage:

    .. code-block:: python

      cost = lambda_cost(input=input,
                         score=score,
                         NDCG_num=8,
                         max_sort_size=-1)

    :param input: The 1st input. Samples of the same query should be loaded
                  as sequence. User should provided socres for each sample.
                  The score should be the 2nd input of this layer.
    :type input: LayerOutput
    :param score: The 2nd input. Score of each sample.
    :type input: LayerOutput
    :param NDCG_num: The size of NDCG (Normalized Discounted Cumulative Gain),
                     e.g., 5 for NDCG@5. It must be less than for equal to the
                     minimum size of lists.
    :type NDCG_num: int
    :param max_sort_size: The size of partial sorting in calculating gradient.
                          If max_sort_size = -1, then for each list, the
                          algorithm will sort the entire list to get gradient.
                          In other cases, max_sort_size must be greater than or
                          equal to NDCG_num. And if max_sort_size is greater than
                          the size of a list, the algorithm will sort the entire
                          list of get gradient.
    :type max_sort_size: int
    :param name: The name of this layers. It is not necessary.
    :type name: None|basestring
    :param coeff: The coefficient affects the gradient in the backward.
    :type coeff: float
    :return: LayerOutput object.
    :rtype: LayerOutput
    """
    Layer(name=name,
          type=LayerType.LAMBDA_COST,
          inputs=[input.name, score.name],
          NDCG_num=NDCG_num,
          max_sort_size=max_sort_size,
          coeff=coeff,
         )

    return LayerOutput(name, LayerType.LAMBDA_COST, parents=[input, score])

@wrap_name_default()
def cross_entropy(input, label, name=None, coeff=1.0):
    """
    A loss layer for multi class entropy.

    .. code-block:: python

       cost = cross_entropy(input, label)

    :param input: The first input layer.
    :type input: LayerOutput.
    :param label: The input label.
    :type input: LayerOutput.
    :param type: The type of cost.
    :type type: basestring.
    :param name: The name of this layers. It is not necessary.
    :type name: None|basestring.
    :param coeff: The coefficient affects the gradient in the backward.
    :type coeff: float.
    :return: LayerOutput object.
    :rtype: LayerOutput.
    """

    Layer(name=name,
          type=LayerType.CROSS_ENTROPY,
          inputs=[input.name, label.name],
          coeff=coeff,
         )
    return LayerOutput(name, LayerType.CROSS_ENTROPY, parents=[input, label])

@wrap_name_default()
def cross_entropy_with_selfnorm(input, label, name=None, coeff=1.0,
                                softmax_selfnorm_alpha=0.1):
    """
    A loss layer for multi class entropy with selfnorm.

    .. code-block:: python

       cost = cross_entropy_with_selfnorm(input, label)

    :param input: The first input layer.
    :type input: LayerOutput.
    :param label: The input label.
    :type input: LayerOutput.
    :param type: The type of cost.
    :type type: basestring.
    :param name: The name of this layers. It is not necessary.
    :type name: None|basestring.
    :param coeff: The coefficient affects the gradient in the backward.
    :type coeff: float.
    :param softmax_selfnorm_alpha: The scale factor affects the cost.
    :type softmax_selfnorm_alpha: float.
    :return: LayerOutput object.
    :rtype: LayerOutput.
    """
    Layer(name=name,
          type=LayerType.CROSS_ENTROPY_WITH_SELFNORM,
          inputs=[input.name, label.name],
          coeff=coeff,
          softmax_selfnorm_alpha=softmax_selfnorm_alpha,
         )

    return LayerOutput(name,
                       LayerType.CROSS_ENTROPY_WITH_SELFNORM,
                       parents=[input, label])

@wrap_name_default()
def huber_cost(input, label, name=None, coeff=1.0):
    """
    A loss layer for huber loss.

    .. code-block:: python

       cost = huber_cost(input, label)

    :param input: The first input layer.
    :type input: LayerOutput.
    :param label: The input label.
    :type input: LayerOutput.
    :param type: The type of cost.
    :type type: basestring.
    :param name: The name of this layers. It is not necessary.
    :type name: None|basestring.
    :param coeff: The coefficient affects the gradient in the backward.
    :type coeff: float.
    :return: LayerOutput object.
    :rtype: LayerOutput.
    """

    Layer(name=name,
          type=LayerType.HUBER,
          inputs=[input.name, label.name],
          coeff=coeff,
         )
    return LayerOutput(name, LayerType.HUBER, parents=[input, label])

@wrap_name_default()
def multi_binary_label_cross_entropy(input, label, name=None, coeff=1.0):
    """
    A loss layer for multi binary label cross entropy.

    .. code-block:: python

       cost = multi_binary_label_cross_entropy(input, label)

    :param input: The first input layer.
    :type input: LayerOutput
    :param label: The input label.
    :type input: LayerOutput
    :param type: The type of cost.
    :type type: basestring
    :param name: The name of this layers. It is not necessary.
    :type name: None|basestring
    :param coeff: The coefficient affects the gradient in the backward.
    :type coeff: float
    :return: LayerOutput object.
    :rtype: LayerOutput
    """

    if not isinstance(input.act, SigmoidActivation):
        logger.log(logging.WARN,
                   "%s is not recommend for batch normalization's activation, "
                   "maybe the relu is better" % act.name)

    Layer(name=name,
          type=LayerType.MULTI_BIN_LABEL_CROSS_ENTROPY,
          inputs=[input.name, label.name],
          coeff=coeff,
         )
    return LayerOutput(name, LayerType.MULTI_BIN_LABEL_CROSS_ENTROPY,
                       parents=[input, label])