Paddle/python/paddle/v2/fluid/layers/nn.py

"""
All layers just related to the neural network.
"""

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

__all__ = [
    'fc', 'embedding', 'dynamic_lstm', 'gru_unit', 'linear_chain_crf',
    'crf_decoding', 'cos_sim', 'cross_entropy', 'square_error_cost', 'accuracy',
    'chunk_eval', 'sequence_conv', 'conv2d', 'sequence_pool', 'pool2d',
    'batch_norm', 'beam_search_decode', 'conv2d_transpose', 'sequence_expand',
    'lstm_unit', 'reduce_sum'
]


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

    This layer accepts multiple inputs and applies a linear transformation to each input.
    If activation type is provided, the corresponding activation function is applied to the
    output of the linear transformation. For each input :math:`X`, the equation is:

    .. math::

        Out = Act(WX + b)

    In the above equation:

        * :math:`X`: Input value, a tensor with rank at least 2.
        * :math:`W`: Weight, a 2-D tensor with shape [M, N].
        * :math:`b`: Bias, a 2-D tensor with shape [M, 1].
        * :math:`Act`: Activation function.
        * :math:`Out`: Output value, same shape with :math:`X`.

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

    Args:
       input(Variable|list): Input tensors. Each tensor has a rank of atleast 2
       size(int): Output size
       num_flatten_dims(int): Number of columns in input
       param_attr(ParamAttr|list): The parameters/weights to the FC Layer
       bias_attr(ParamAttr|list): Bias parameter for the FC layer
       act(str): Activation type
       name(str): Name/alias of the function

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

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

    Examples:
        .. code-block:: python

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

    dtype = helper.input_dtype()

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

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


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

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

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

    Args:
       input(Variable): Input to the function
       size(int): Output size
       is_sparse(bool): Boolean flag that specifying whether the input is sparse
       param_attr(ParamAttr): Parameters for this layer
       dtype(np.dtype|core.DataType|str): The type of data : float32, float_16, int etc

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

    Examples:
        .. code-block:: python

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

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


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

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

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


def gru_unit(input,
             hidden,
             size,
             weight=None,
             bias=None,
             activation='tanh',
             gate_activation='sigmoid'):
    """
    GRUUnit Operator implements partial calculations of the GRU unit as following:

    $$
    update \ gate: u_t = actGate(xu_t + W_u * h_{t-1} + b_u) \\
    reset \ gate: r_t = actGate(xr_t + W_r * h_{t-1} + b_r)  \\
    output \ candidate: {h}_t = actNode(xc_t + W_c * dot(r_t, h_{t-1}) + b_c) \\
    output: h_t = dot((1 - u_t), h_{t-1}) + dot(u_t, {h}_t)
    $$

    which is same as one time step of GRU Operator.

    @note To implement the complete GRU unit, fully-connected operator must be
    used before to feed xu, xr and xc as the Input of GRUUnit operator.

    TODO(ChunweiYan) add more document here
    """
    activation_dict = dict(
        identity=0,
        sigmoid=1,
        tanh=2,
        relu=3, )
    activation = activation_dict[activation]
    gate_activation = activation_dict[gate_activation]

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

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

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

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

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

    return updated_hidden, reset_hidden_pre, gate


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

    return log_likelihood


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

    return viterbi_path


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


def cross_entropy(input, label, **kwargs):
    """
    This function computes cross_entropy using the input and label.
    """
    helper = LayerHelper('cross_entropy', **kwargs)
    out = helper.create_tmp_variable(dtype=input.dtype)
    helper.append_op(
        type='cross_entropy',
        inputs={'X': [input],
                'Label': [label]},
        outputs={'Y': [out]},
        attrs=kwargs)
    return out


def square_error_cost(input, label, **kwargs):
    """
    This functions returns the squared error cost using the input and label.
    The output is appending the op to do the above.
    """
    helper = LayerHelper('square_error_cost', **kwargs)
    minus_out = helper.create_tmp_variable(dtype=input.dtype)
    helper.append_op(
        type='elementwise_sub',
        inputs={'X': [input],
                'Y': [label]},
        outputs={'Out': [minus_out]})

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


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


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

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

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


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

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

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

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


def conv2d(input,
           num_filters,
           filter_size,
           stride=None,
           padding=None,
           groups=None,
           param_attr=None,
           bias_attr=None,
           act=None,
           name=None):
    """
    This function creates the op for a 2-dimensional Convolution.
    This is performed using the parameters of filters(size, dimensionality etc)
    , stride and other configurations for a Convolution operation.
    This funciton can also append an activation on top of the
    conv-2d output, if mentioned in the input parameters.
    """

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

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

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

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

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

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

    pre_bias = helper.create_tmp_variable(dtype)

    helper.append_op(
        type='conv2d_cudnn',
        inputs={
            'Input': input,
            'Filter': filter_param,
        },
        outputs={"Output": pre_bias},
        attrs={'strides': stride,
               'paddings': padding,
               'groups': groups})

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

    return helper.append_activation(pre_act)


def sequence_pool(input, pool_type, **kwargs):
    """
    This function add the operator for sequence pooling.
    This is applied on top of the input using pool_type mentioned
    in the parameters.
    """
    helper = LayerHelper('sequence_pool', input=input, **kwargs)
    dtype = helper.input_dtype()
    pool_out = helper.create_tmp_variable(dtype)
    max_index = helper.create_tmp_variable(dtype)

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

    return pool_out


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

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

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

    return pool_out


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

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

    param_shape = [channel_num]

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

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

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

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

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

    batch_norm_out = helper.create_tmp_variable(dtype)

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

    return helper.append_activation(batch_norm_out)


def beam_search_decode(ids, scores):
    helper = LayerHelper('beam_search_decode', **locals())
    sentence_ids = helper.create_tmp_variable(dtype=ids.dtype)
    sentence_scores = helper.create_tmp_variable(dtype=ids.dtype)

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

    return sentence_ids, sentence_scores


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

    This layer is also known as deconvolution layer.

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

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

    op_attr = dict()

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

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

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

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

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

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

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

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

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

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

    return out


def sequence_expand(x, y):
    """Sequence Expand Layer. This layer will expand the input variable **x**
    according to LoD information of **y**. And the following examples will
    explain how sequence_expand works:

    .. code-block:: text

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

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

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

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

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

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

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

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

    Args:
        x (Variable): The input variable which is a Tensor or LoDTensor.
        y (Variable): The input variable which is a LoDTensor.

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

    Examples:
        .. code-block:: python

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


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

        .. math::

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

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

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

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

            h_t & = o_t tanh(c_t)

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

        .. math::

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

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

        .. math::

            i_t = \sigma(L_{i_t})

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

    Args:
        x_t (Variable): The input value of current step.
        hidden_t_prev (Variable): The hidden value of lstm unit.
        cell_t_prev (Variable): The cell value of lstm unit.
        forget_bias (float): The forget bias of lstm unit.
        param_attr (ParamAttr): The attributes of parameter weights, used to set
            initializer, name etc.
        bias_attr (ParamAttr): The attributes of bias weights, if not False,
            bias weights will be created and be set to default value.

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

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

    Examples:

        .. code-block:: python

             x_t = fluid.layers.fc(input=x_t_data, size=10)
             prev_hidden = fluid.layers.fc(input=prev_hidden_data, size=20)
             prev_cell = fluid.layers.fc(input=prev_cell_data, size=30)
             hidden_value, cell_value = fluid.layers.lstm_unit(x_t=x_t,
                                                    hidden_t_prev=prev_hidden,
                                                    cell_t_prev=prev_cell)
    """
    helper = LayerHelper('lstm_unit', **locals())

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

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

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

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

    if bias_attr is None:
        bias_attr = ParamAttr()

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

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

    return h, c


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

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

    Returns:
        Variable: The reduced Tensor variable.
    
    Examples:
        .. code-block:: python

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