loss.py

#   Copyright (c) 2020 PaddlePaddle Authors. 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 paddle

# TODO: define loss functions of neural network
import numpy as np
import paddle
import paddle.fluid as fluid
from ...fluid.framework import core, in_dygraph_mode
from ...fluid.layers.nn import _elementwise_op_in_dygraph
from ...fluid.layers import bpr_loss  #DEFINE_ALIAS
from ...fluid.layers import center_loss  #DEFINE_ALIAS
from ...fluid.layers import dice_loss  #DEFINE_ALIAS
from ...fluid.layers import iou_similarity  #DEFINE_ALIAS
from ...fluid.layers import log_loss  #DEFINE_ALIAS
from ...fluid.layers import npair_loss  #DEFINE_ALIAS
from ...fluid.layers import rank_loss  #DEFINE_ALIAS
from ...fluid.layers import reshape
from ...fluid.layers import sigmoid_cross_entropy_with_logits  #DEFINE_ALIAS
from ...fluid.layers import sigmoid_focal_loss  #DEFINE_ALIAS
from ...fluid.layers import smooth_l1  #DEFINE_ALIAS
from ...fluid.layers import softmax_with_cross_entropy  #DEFINE_ALIAS
from ...fluid.layers import square_error_cost  #DEFINE_ALIAS
from ...fluid.layers import ssd_loss  #DEFINE_ALIAS
from ...fluid.layers import teacher_student_sigmoid_loss  #DEFINE_ALIAS

from ...fluid.layers import edit_distance  #DEFINE_ALIAS
from ...fluid.layers import huber_loss  #DEFINE_ALIAS
from ...fluid.layers import sampled_softmax_with_cross_entropy  #DEFINE_ALIAS
from ...fluid.layer_helper import LayerHelper
from ...fluid.framework import in_dygraph_mode
from ...fluid.framework import _varbase_creator
from ...fluid.framework import Variable

__all__ = [
    'binary_cross_entropy',
    'bpr_loss',
    'center_loss',
    'cross_entropy',
    'dice_loss',
    'edit_distance',
    'huber_loss',
    'iou_similarity',
    'kl_div',
    'l1_loss',
    'log_loss',
    'mse_loss',
    'margin_ranking_loss',
    #       'nce',
    'nll_loss',
    'npair_loss',
    'rank_loss',
    'sampled_softmax_with_cross_entropy',
    'sigmoid_cross_entropy_with_logits',
    'sigmoid_focal_loss',
    'smooth_l1',
    'smooth_l1_loss',
    'softmax_with_cross_entropy',
    'square_error_cost',
    'ssd_loss',
    'teacher_student_sigmoid_loss'
]


def binary_cross_entropy(input, label, weight=None, reduction='mean',
                         name=None):
    """
    This op measures the binary_cross_entropy loss between input predictions ``input``
    and target labels ``label`` . The binary_cross_entropy loss can be described as:

    If :attr:`weight` is set, the loss is:

    .. math::
        Out = -1 * weight * (label * log(input) + (1 - label) * log(1 - input))

    If :attr:`weight` is None, the loss is:

    .. math::
        Out = -1 * (label * log(input) + (1 - label) * log(1 - input))

    If :attr:`reduction` set to ``'none'``, the interface will return the original loss `Out`.

    If :attr:`reduction` set to ``'mean'``, the reduced mean loss is:

    .. math::
        Out = MEAN(Out)

    If :attr:`reduction` set to ``'sum'``, the reduced sum loss is:

    .. math::
        Out = SUM(Out)

    Note that the input predictions ``input`` always be the output of sigmoid, and the target labels ``label``
    should be numbers between 0 and 1.

    Parameters:
        input (Tensor): The input predications tensor. 2-D tensor with shape: [N, *],
            N is batch_size, `*` means number of additional dimensions. The ``input``
            should always be the output of sigmod.  Available dtype is float32, float64.
        label (Tensor): The target labels tensor. 2-D tensor with the same shape as
            ``input``. The target labels which values should be numbers between 0 and 1.
            Available dtype is float32, float64.
        weight (Tensor, optional): A manual rescaling weight given to the loss of each
            batch element. If given, has to be a Tensor of size nbatch and the data type
            is float32, float64. Default is ``'None'``.
        reduction (str, optional): Indicate how to average the loss by batch_size,
            the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
            If :attr:`reduction` is ``'none'``, the unreduced loss is returned;
            If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned;
            If :attr:`reduction` is ``'sum'``, the summed loss is returned.
            Default is ``'mean'``.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.


    Returns:
        output (Tensor): If ``reduction`` is ``'none'``, the shape of output is
            same as ``input`` , else the shape of output is scalar.

    Examples:
        .. code-block:: python

            import paddle
            import numpy as np
            input_data = np.array([0.5, 0.6, 0.7]).astype("float32")
            label_data = np.array([1.0, 0.0, 1.0]).astype("float32")

            paddle.disable_static()
            input = paddle.to_tensor(input_data)
            label = paddle.to_tensor(label_data)
            output = paddle.nn.functional.binary_cross_entropy(input, label)
            print(output.numpy())  # [0.65537095]
            paddle.enable_static()

    """
    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "The value of 'reduction' in binary_cross_entropy should be 'sum', "
            "'mean' or 'none', but received %s, which is not allowed." %
            reduction)

    if in_dygraph_mode():
        one = _varbase_creator(dtype=input.dtype)
        core.ops.fill_constant(one, 'value',
                               float(1.0), 'force_cpu', False, 'dtype',
                               one.dtype, 'str_value', '1.0', 'shape', [1])
        one.stop_gradient = True
        label_minus = core.ops.elementwise_sub(label, one)
        input_minus = core.ops.elementwise_sub(one, input)
        input_minus_log = core.ops.log(input_minus)
        input_log = core.ops.log(input)
        loss_1 = core.ops.elementwise_mul(label_minus, input_minus_log)
        loss_2 = core.ops.elementwise_mul(label, input_log)
        out = core.ops.elementwise_sub(loss_1, loss_2)

        if weight is not None:
            out = core.ops.elementwise_mul(out, weight, 'axis', -1)

        if reduction == 'sum':
            return core.ops.reduce_sum(out, 'dim', [0], 'keep_dim', False,
                                       "reduce_all", True)
        elif reduction == 'mean':
            return core.ops.reduce_mean(out, 'dim', [0], 'keep_dim', False,
                                        "reduce_all", True)
        else:
            return out

    fluid.data_feeder.check_variable_and_dtype(
        input, 'input', ['float32', 'float64'], 'binary_cross_entropy')
    fluid.data_feeder.check_variable_and_dtype(
        label, 'label', ['float32', 'float64'], 'binary_cross_entropy')

    one = paddle.fill_constant(shape=[1], value=1.0, dtype=input.dtype)
    one.stop_gradient = True
    label_minus = paddle.elementwise_sub(label, one)
    input_minus = paddle.elementwise_sub(one, input)
    input_minus_log = paddle.log(input_minus)
    input_log = paddle.log(input)
    loss_1 = paddle.multiply(label_minus, input_minus_log)
    loss_2 = paddle.multiply(label, input_log)

    sub_name = name if weight is None and reduction is 'none' else None
    out = paddle.elementwise_sub(loss_1, loss_2, name=sub_name)

    if weight is not None:
        if isinstance(weight, paddle.framework.Variable):
            weight_name = name if reduction is 'none' else None
            out = paddle.multiply(out, weight, axis=-1, name=weight_name)
        else:
            raise ValueError(
                "The weight is not a Tensor, please convert to Tensor.")

    if reduction == 'sum':
        return paddle.sum(out, name=name)
    elif reduction == 'mean':
        return paddle.mean(out, name=name)
    else:
        return out


def smooth_l1_loss(input, label, reduction='mean', delta=1.0, name=None):
    """
    This operator calculates smooth_l1_loss. Creates a criterion that uses a squared
    term if the absolute element-wise error falls below 1 and an L1 term otherwise.
    In some cases it can prevent exploding gradients and it is more robust and less
    sensitivity to outliers. Also known as the Huber loss:

    .. math::

         loss(x,y)=\\frac{1}{n}\\sum_{i}z_i


    where z_i is given by:

    .. math::

         \\mathop{z_i}=\\left\\{\\begin{array}{rcl}
        0.5(x_i - y_i)^2 & & {if |x_i - y_i| < delta} \\\\
        delta * |x_i - y_i| - 0.5 * delta^2 & & {otherwise}
        \\end{array} \\right.

    Parameters:
        input (Tensor): Input tensor, the data type is float32 or float64. Shape is
            (N, C), where C is number of classes, and if shape is more than 2D, this
            is (N, C, D1, D2,..., Dk), k >= 1.
        label (Tensor): Label tensor, the data type is float32 or float64. The shape of label
            is the same as the shape of input.
        reduction (str, optional): Indicate how to average the loss by batch_size,
            the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
            If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned;
            If :attr:`reduction` is ``'sum'``, the reduced sum loss is returned.
            If :attr:`reduction` is ``'none'``, the unreduced loss is returned.
            Default is ``'mean'``.
        delta (float, optional): Specifies the hyperparameter delta to be used.
            The value determines how large the errors need to be to use L1. Errors
            smaller than delta are minimized with L2. Parameter is ignored for
            negative/zero values. Default = 1.0
        name (str, optional): Name for the operation (optional, default is
            None). For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        The tensor variable storing the smooth_l1_loss of input and label.

    Return type: Tensor.

    Examples:
        .. code-block:: python

            import paddle
            import numpy as np

            paddle.disable_static()
            input_data = np.random.rand(3,3).astype("float32")
            label_data = np.random.rand(3,3).astype("float32")
            input = paddle.to_tensor(input_data)
            label = paddle.to_tensor(label_data)
            output = paddle.nn.functioanl.smooth_l1_loss(input, label)
            print(output.numpy())
    """
    fluid.data_feeder.check_variable_and_dtype(
        input, 'input', ['float32', 'float64'], 'smooth_l1_loss')
    fluid.data_feeder.check_variable_and_dtype(
        label, 'label', ['float32', 'float64'], 'smooth_l1_loss')

    out = huber_loss(input=input, label=label, delta=delta)

    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "The value of 'reduction' in smooth_l1_loss should be 'sum', 'mean' or"
            " 'none', but received %s, which is not allowed." % reduction)
    if reduction == 'none':
        return out
    elif reduction == 'mean':
        return fluid.layers.reduce_mean(out)
    elif reduction == 'sum':
        return fluid.layers.reduce_sum(out)


def margin_ranking_loss(input,
                        other,
                        label,
                        margin=0.0,
                        reduction='mean',
                        name=None):
    """

    This op the calcluate the the margin rank loss between the input, other and label, use the math function as follows.

    .. math::
        margin\_rank\_loss = max(0, -label * (input - other) + margin)

    If :attr:`reduction` set to ``'mean'``, the reduced mean loss is:

    .. math::
        Out = MEAN(margin\_rank\_loss)

    If :attr:`reduction` set to ``'sum'``, the reduced sum loss is:

    .. math::
        Out = SUM(margin\_rank\_loss)

    If :attr:`reduction` set to ``'none'``, just return the origin ``margin_rank_loss``.

    Parameters:
        input(Tensor): the first input tensor, it's data type should be float32, float64.
        other(Tensor): the second input tensor, it's data type should be float32, float64.
        label(Tensor): the label value corresponding to input, it's data type should be float32, float64.
        margin (float, optional): The margin value to add, default value is 0;
        reduction (str, optional): Indicate the reduction to apply to the loss, the candicates are ``'none'``, ``'mean'``, ``'sum'``.If :attr:`reduction` is ``'none'``, the unreduced loss is returned; If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned. If :attr:`reduction` is ``'sum'``, the reduced sum loss is returned. Default is ``'mean'``.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.

    Returns: Tensor, if :attr:`reduction` is ``'mean'`` or ``'sum'``, the out shape is :math:`[1]`, otherwise the shape is the same as `input` .The same dtype as input tensor.

    Examples:

        .. code-block:: python

            import numpy as np
            import paddle

            paddle.disable_static()

            input = paddle.to_variable(np.array([[1, 2], [3, 4]]).astype('float32'))
            other = paddle.to_variable(np.array([[2, 1], [2, 4]]).astype('float32'))
            label = paddle.to_variable(np.array([[1, -1], [-1, -1]]).astype('float32'))
            loss = paddle.nn.functional.margin_ranking_loss(input, other, label)
            print(loss.numpy()) # [0.75]
    """
    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "The value of 'reduction' in MarginRankingLoss should be 'sum', 'mean' or 'none', but "
            "received %s, which is not allowed." % reduction)
    if fluid.framework.in_dygraph_mode():
        out = core.ops.elementwise_sub(other, input)
        out = core.ops.elementwise_mul(out, label)
        if margin != 0.0:
            margin = fluid.dygraph.base.to_variable([margin], dtype=out.dtype)
            out = core.ops.elementwise_add(out, margin)
        out = core.ops.relu(out)
        if reduction == 'sum':
            return core.ops.reduce_sum(out, 'reduce_all', True)
        elif reduction == 'mean':
            return core.ops.mean(out)
        return out

    helper = LayerHelper("margin_ranking_loss", **locals())
    fluid.data_feeder.check_variable_and_dtype(
        input, 'input', ['float32', 'float64'], 'margin_rank_loss')
    fluid.data_feeder.check_variable_and_dtype(
        other, 'other', ['float32', 'float64'], 'margin_rank_loss')
    fluid.data_feeder.check_variable_and_dtype(
        label, 'label', ['float32', 'float64'], 'margin_rank_loss')

    out = paddle.elementwise_sub(other, input)
    out = paddle.multiply(out, label)

    if margin != 0.0:
        margin_var = out.block.create_var(dtype=out.dtype)
        paddle.fill_constant([1], out.dtype, margin, out=margin_var)
        out = paddle.add(out, margin_var)

    result_out = helper.create_variable_for_type_inference(input.dtype)

    if reduction == 'none':
        helper.append_op(
            type="relu", inputs={"X": out}, outputs={"Out": result_out})
        return result_out
    elif reduction == 'sum':
        out = paddle.nn.functional.relu(out)
        attrs = {"dim": [0], "keep_dim": False, "reduce_all": True}
        helper.append_op(
            type="reduce_sum",
            inputs={"X": out},
            outputs={"Out": result_out},
            attrs=attrs)
        return result_out
    elif reduction == 'mean':
        out = paddle.nn.functional.relu(out)
        helper.append_op(
            type="mean",
            inputs={"X": out},
            outputs={"Out": result_out},
            attrs={})
        return result_out


def l1_loss(input, label, reduction='mean', name=None):
    """
    This operator computes the L1 Loss of Tensor ``input`` and ``label`` as follows.

    If `reduction` set to ``'none'``, the loss is:

    .. math::
        Out = \lvert input - label\rvert

    If `reduction` set to ``'mean'``, the loss is:

    .. math::
        Out = MEAN(\lvert input - label\rvert)

    If `reduction` set to ``'sum'``, the loss is:

    .. math::
        Out = SUM(\lvert input - label\rvert)


    Parameters:
        input (Tensor): The input tensor. The shapes is [N, *], where N is batch size and `*` means any number of additional dimensions. It's data type should be float32, float64, int32, int64.
        label (Tensor): label. The shapes is [N, *], same shape as ``input`` . It's data type should be float32, float64, int32, int64.
        reduction (str, optional): Indicate the reduction to apply to the loss,
            the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
            If `reduction` is ``'none'``, the unreduced loss is returned;
            If `reduction` is ``'mean'``, the reduced mean loss is returned.
            If `reduction` is ``'sum'``, the reduced sum loss is returned.
            Default is ``'mean'``.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.
    Returns:
        Tensor, the L1 Loss of Tensor ``input`` and ``label``.
            If `reduction` is ``'none'``, the shape of output loss is [N, *], the same as ``input`` .
            If `reduction` is ``'mean'`` or ``'sum'``, the shape of output loss is [1].
    Examples:
        .. code-block:: python
            import paddle
            import numpy as np

            paddle.disable_static()
            input_data = np.array([[1.5, 0.8], [0.2, 1.3]]).astype("float32")
            label_data = np.array([[1.7, 1], [0.4, 0.5]]).astype("float32")
            input = paddle.to_variable(input_data)
            label = paddle.to_variable(label_data)

            l1_loss = paddle.nn.functional.l1_loss(input, label)
            print(l1_loss.numpy())
            # [0.35]

            l1_loss = paddle.nn.functional.l1_loss(input, label, reduction='none')
            print(l1_loss.numpy())
            # [[0.20000005 0.19999999]
            # [0.2        0.79999995]]

            l1_loss = paddle.nn.functional.l1_loss(input, label, reduction='sum')
            print(l1_loss.numpy())
            # [1.4]
    """
    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "The value of 'reduction' in L1Loss should be 'sum', 'mean' or 'none', but "
            "received %s, which is not allowed." % reduction)

    if in_dygraph_mode():
        unreduced = _elementwise_op_in_dygraph(
            input, label, axis=-1, act='abs', op_name='elementwise_sub')
        if reduction == 'mean':
            return core.ops.mean(unreduced)
        elif reduction == 'sum':
            return core.ops.reduce_sum(unreduced, 'dim', [0], 'keep_dim', False,
                                       'reduce_all', True)
        else:
            return unreduced

    fluid.data_feeder.check_variable_and_dtype(
        input, 'input', ['float32', 'float64', 'int32', 'int64'], 'l1_loss')
    fluid.data_feeder.check_variable_and_dtype(
        label, 'label', ['float32', 'float64', 'int32', 'int64'], 'l1_loss')

    if reduction == 'sum':
        unreduced = paddle.elementwise_sub(input, label, act='abs')
        return paddle.sum(unreduced, name=name)
    elif reduction == 'mean':
        unreduced = paddle.elementwise_sub(input, label, act='abs')
        return paddle.mean(unreduced, name=name)
    else:
        return paddle.elementwise_sub(input, label, act='abs', name=name)


def nll_loss(input,
             label,
             weight=None,
             ignore_index=-100,
             reduction='mean',
             name=None):
    """
    This api returns negative log likelihood.
    See more detail in :ref:`api_nn_loss_NLLLoss` .

    Parameters:
         input (Tensor): Input tensor, the shape is :math:`[N, C]`, `C` is the number of classes.
             But in K-dimension situation, the shape is :math:`[N, C, d_1, d_2, ..., d_K]`.
             The data type is float32, float64.
         label (Tensor): Label tensor, the shape is :math:`[N,]` or :math:`[N, d_1, d_2, ..., d_K]`.
             The data type is int64.
         weight (Tensor, optional): Weight tensor, a manual rescaling weight given
             to each class. If given, it has to be a 1D Tensor whose size is `[C, ]`. Otherwise,
             it treated as if having all ones. the data type is
             float32, float64, Default is ``'None'``.
         ignore_index (int64, optional): Specifies a target value that is ignored
             and does not contribute to the input gradient.
         reduction (str, optional): Indicate how to average the loss,
             the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
             If `reduction` is ``'mean'``, the reduced mean loss is returned;
             if `reduction` is ``'sum'``, the reduced sum loss is returned;
             if `reduction` is ``'none'``, no reduction will be apllied.
             Default is ``'mean'``.
         name (str, optional): Name for the operation (optional, default is None).
             For more information, please refer to :ref:`api_guide_Name`.

    Returns:
         `Tensor`, the value of negative log likelihood loss.

    Examples:
        .. code-block:: python
                import paddle
                import numpy as np
                from paddle.nn.functional import nll_loss
                log_softmax = paddle.nn.LogSoftmax(axis=1)

                input_np = np.array([[0.88103855, 0.9908683 , 0.6226845 ],
                                     [0.53331435, 0.07999352, 0.8549948 ],
                                     [0.25879037, 0.39530203, 0.698465  ],
                                     [0.73427284, 0.63575995, 0.18827209],
                                     [0.05689114, 0.0862954 , 0.6325046 ]]).astype(np.float32)
                label_np = np.array([0, 2, 1, 1, 0]).astype(np.int64)

                place = paddle.CPUPlace()
                paddle.disable_static(place)
                input = paddle.to_variable(input_np)
                log_out = log_softmax(input)
                label = paddle.to_variable(label_np)
                result = nll_loss(log_out, label)
                print(result.numpy()) # [1.0720209]
    """
    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "The value of 'reduction' in nll_loss should be 'sum', 'mean' or "
            "'none', but received %s, which is not allowed." % reduction)

    input_shape = list(input.shape)
    input_dims = len(input_shape)
    if input_dims < 2:
        raise ValueError('Expected 2 or more dimensions (got {})'.format(
            input_dims))
    n = input_shape[0]
    c = input_shape[1]
    if in_dygraph_mode():
        if input_dims != 2 and input_dims != 4:
            input, _ = core.ops.reshape2(input, 'shape', [n, c, 1, -1])
            label, _ = core.ops.reshape2(label, 'shape', [n, 1, -1])
            out_shape = [n] + input_shape[2:]
        out, total_weight = core.ops.nll_loss(input, label, weight,
                                              'ignore_index', ignore_index,
                                              'reduction', reduction)
        if input_dims != 2 and input_dims != 4 and reduction == 'none':
            out, _ = core.ops.reshape2(out, 'shape', out_shape)
        return out

    helper = LayerHelper('nll_loss', **locals())

    if input_dims != 2 and input_dims != 4:
        input = reshape(input, shape=[n, c, 1, -1])
        label = reshape(label, shape=[n, 1, -1])
        out_shape = [n] + input_shape[2:]

    fluid.data_feeder.check_variable_and_dtype(
        input, 'input', ['float32', 'float64'], 'nll_loss')
    fluid.data_feeder.check_variable_and_dtype(label, 'label', ['int64'],
                                               'nll_loss')
    inputs = {'X': input, 'Label': label}
    attrs = {'reduction': reduction, 'ignore_index': ignore_index}
    if weight is not None:
        if isinstance(weight, Variable):
            inputs['Weight'] = weight

    out = helper.create_variable_for_type_inference(dtype=input.dtype)
    total_weight = helper.create_variable_for_type_inference(dtype=input.dtype)
    outputs = {'Out': out, 'Total_weight': total_weight}

    helper.append_op(
        type='nll_loss', inputs=inputs, outputs=outputs, attrs=attrs)
    if input_dims != 2 and input_dims != 4 and reduction == 'none':
        out = reshape(out, shape=out_shape)

    return out


def kl_div(input, label, reduction='mean', name=None):
    """
    This operator calculates the Kullback-Leibler divergence loss
    between Input(X) and Input(Target). Notes that Input(X) is the
    log-probability and Input(Target) is the probability.

    KL divergence loss is calculated as follows:

    $$l(x, y) = y * (\log(y) - x)$$

    While :math:`x` is input and :math:`y` is label.

    While :attr:`reduction` is :attr:`none`, output loss is in
    the same shape as input, loss in each point is calculated
    seperately and no reduction is applied.

    While :attr:`reduction` is :attr:`mean`, output loss is in
    shape of [1] and loss value is the mean value of all losses.

    While :attr:`reduction` is :attr:`sum`, output loss is in
    shape of [1] and loss value is the sum value of all losses.

    While :attr:`reduction` is :attr:`batchmean`, output loss is
    in shape of [1] and loss value is the sum value of all losses
    divided by batch size.

    Args:
        input (Tensor): The input tensor. The shapes is [N, *], where N is batch size and `*` means
             any number of additional dimensions. It's data type should be float32, float64.
        label (Tensor): label. The shapes is [N, *], same shape as ``input`` . It's data type should be float32, float64.
        reduction (Tensor): Indicate how to average the loss,
             the candicates are ``'none'`` | ``'batchmean'`` | ``'mean'`` | ``'sum'``.
             If `reduction` is ``'mean'``, the reduced mean loss is returned;
             If `reduction` is ``'batchmean'``, the sum loss divided by batch size is returned;
             if `reduction` is ``'sum'``, the reduced sum loss is returned;
             if `reduction` is ``'none'``, no reduction will be apllied.
             Default is ``'mean'``.
        name(str, optional): Name for the operation (optional, default is None). For more information,
            please refer to :ref:`api_guide_Name`.

    Returns:
        Tensor: The KL divergence loss. The data type is same as input tensor

    Examples:
        .. code-block:: python

            import paddle
            import numpy as np
            import paddle.nn.functional as F

            paddle.enable_imperative()

            shape = (5, 20)
            input = np.random.uniform(-10, 10, shape).astype('float32')
            target = np.random.uniform(-10, 10, shape).astype('float32')

            # 'batchmean' reduction, loss shape will be [N]
            pred_loss = F.kl_div(paddle.to_variable(input),
                                 paddle.to_variable(target), reduction='batchmean')
            # shape=[5]

            # 'mean' reduction, loss shape will be [1]
            pred_loss = F.kl_div(paddle.to_variable(input),
                                 paddle.to_variable(target), reduction='mean')
            # shape=[1]

            # 'sum' reduction, loss shape will be [1]
            pred_loss = F.kl_div(paddle.to_variable(input),
                                 paddle.to_variable(target), reduction='sum')
            # shape=[1]

            # 'none' reduction, loss shape is same with input shape
            pred_loss = F.kl_div(paddle.to_variable(input),
                                 paddle.to_variable(target), reduction='none')
            # shape=[5, 20]

    """
    if paddle.in_dynamic_mode():
        out = core.ops.kldiv_loss(input, label, 'reduction', reduction)
        return out

    helper = LayerHelper('kl_div', **locals())

    fluid.data_feeder.check_variable_and_dtype(input, 'input',
                                               ['float32', 'float64'], 'kl_div')
    fluid.data_feeder.check_variable_and_dtype(label, 'label',
                                               ['float32', 'float64'], 'kl_div')
    fluid.data_feeder.check_type(reduction, 'reduction', str, 'kl_div')

    loss = helper.create_variable_for_type_inference(dtype=input.dtype)
    helper.append_op(
        type='kldiv_loss',
        inputs={'X': input,
                'Target': label},
        outputs={'Loss': loss},
        attrs={'reduction': reduction})
    return loss


def mse_loss(input, label, reduction='mean', name=None):
    """
    This op accepts input predications and label and returns the mean square error.

    If :attr:`reduction` is set to ``'none'``, loss is calculated as:

    .. math::
        Out = (input - label)^2

    If :attr:`reduction` is set to ``'mean'``, loss is calculated as:

    .. math::
        Out = \operatorname{mean}((input - label)^2)

    If :attr:`reduction` is set to ``'sum'``, loss is calculated as:

    .. math::
        Out = \operatorname{sum}((input - label)^2)

    Parameters:
        input (Tensor): Input tensor, the data type should be float32 or float64.
        label (Tensor): Label tensor, the data type should be float32 or float64.
        reduction (string, optional): The reduction method for the output,
            could be 'none' | 'mean' | 'sum'.
            If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned.
            If :attr:`reduction` is ``'sum'``, the reduced sum loss is returned.
            If :attr:`reduction` is ``'none'``, the unreduced loss is returned.
            Default is ``'mean'``.
        name (str, optional): Name for the operation (optional, default is None). For more information, please refer to :ref:`api_guide_Name`.


    Returns:
        Tensor: The tensor tensor storing the mean square error difference of input and label.

    Return type: Tensor.

    Examples:

        .. code-block:: python
            import numpy as np
            import paddle


            # static graph mode
            paddle.enable_static()
            mse_loss = paddle.nn.loss.MSELoss()
            input = paddle.data(name="input", shape=[1])
            label = paddle.data(name="label", shape=[1])
            place = paddle.CPUPlace()
            input_data = np.array([1.5]).astype("float32")
            label_data = np.array([1.7]).astype("float32")

            output = mse_loss(input,label)
            exe = paddle.static.Executor(place)
            exe.run(paddle.static.default_startup_program())
            output_data = exe.run(
                paddle.static.default_main_program(),
                feed={"input":input_data, "label":label_data},
                fetch_list=[output],
                return_numpy=True)
            print(output_data)
            # [array([0.04000002], dtype=float32)]

            # dynamic graph mode
            paddle.disable_static()
            input = paddle.to_variable(input_data)
            label = paddle.to_variable(label_data)
            output = mse_loss(input, label)
            print(output.numpy())
            # [0.04000002]

    """

    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "'reduction' in 'mse_loss' should be 'sum', 'mean' or 'none', "
            "but received {}.".format(reduction))

    if not paddle.fluid.framework.in_dygraph_mode():
        paddle.fluid.data_feeder.check_variable_and_dtype(
            input, 'input', ['float32', 'float64'], 'mse_loss')
        paddle.fluid.data_feeder.check_variable_and_dtype(
            label, 'label', ['float32', 'float64'], 'mse_loss')

    if reduction == 'none':
        return paddle.fluid.layers.square(
            paddle.fluid.layers.elementwise_sub(input, label), name=name)
    elif reduction == 'mean':
        return paddle.mean(
            paddle.fluid.layers.square(
                paddle.fluid.layers.elementwise_sub(input, label)),
            name=name)
    else:
        return paddle.sum(paddle.fluid.layers.square(
            paddle.fluid.layers.elementwise_sub(input, label)),
                          name=name)


def cross_entropy(input,
                  label,
                  weight=None,
                  ignore_index=-100,
                  reduction='mean'):
    """
    This operator implements the cross entropy loss function. This OP combines ``LogSoftmax``,
    and ``NLLLoss`` together.

    It is useful when training a classification problem with ``C`` classes.
    If provided, the optional argument ``weight`` should be a 1D Variable assigning
    weight to each of the classes.

    For predictions label, and target label, the loss is calculated as follows.

    .. math::

        loss_j =  -\\text{input[class]} +
        \\log\\left(\\sum_{i=0}^{K}\\exp(\\text{input}_i)\\right), j = 1,..., K

    If weight is not ``None``:

    .. math::

        loss_j =  \\text{weight[class]}(-\\text{input[class]} +
        \\log\\left(\\sum_{i=0}^{K}\\exp(\\text{input}_i)\\right)), j = 1,..., K

    Parameters:
        input (Tensor): Input tensor, the data type is float32, float64. Shape is
	    (N, C), where C is number of classes, and if shape is more than 2D, this
	    is (N, C, D1, D2,..., Dk), k >= 1. 
        label (Tensor): Label tensor, the data type is int64. Shape is (N), where each 
	    value is 0 <= label[i] <= C-1, and if shape is more than 2D, this is
	    (N, D1, D2,..., Dk), k >= 1.
        weight (Tensor, optional): Weight tensor, a manual rescaling weight given
            to each class and the shape is (C). It has the same dimensions as class
	    number and the data type is float32, float64. Default is ``'None'``.
        reduction (str, optional): Indicate how to average the loss by batch_size,
            the candicates are ``'none'`` | ``'mean'`` | ``'sum'``.
            If :attr:`reduction` is ``'mean'``, the reduced mean loss is returned;
            If :attr:`size_average` is ``'sum'``, the reduced sum loss is returned.
            If :attr:`reduction` is ``'none'``, the unreduced loss is returned.
            Default is ``'mean'``.
        ignore_index (int64, optional): Specifies a target value that is ignored
            and does not contribute to the input gradient. Default is ``-100``.

    Returns:
        The tensor variable storing the cross_entropy_loss of input and label.

    Return type: Tensor.

    Examples:
        .. code-block:: python

            import paddle
            paddle.disable_static()
            input_data = np.random.random([5, 100]).astype("float64")
            label_data = np.random.randint(0, 100, size=(5)).astype(np.int64)
            weight_data = np.random.random([100]).astype("float64")
            input =  paddle.to_tensor(input_data)
            label =  paddle.to_tensor(label_data)
            weight = paddle.to_tensor(weight_data)
            loss = paddle.nn.functional.cross_entropy(input=input, label=label, weight=weight)
            print(loss.numpy())
 
    """
    if not in_dygraph_mode():
        fluid.data_feeder.check_variable_and_dtype(
            input, 'input', ['float32', 'float64'], 'cross_entropy_loss')
        fluid.data_feeder.check_variable_and_dtype(label, 'label', ['int64'],
                                                   'cross_entropy_loss')

    if reduction not in ['sum', 'mean', 'none']:
        raise ValueError(
            "The value of 'reduction' in cross_entropy_loss should be 'sum', 'mean' or"
            " 'none', but received %s, which is not allowed." % reduction)

    #step 1. log_softmax
    log_softmax_out = paddle.nn.functional.log_softmax(input)
    if weight is not None and not isinstance(weight, Variable):
        raise ValueError(
            "The weight' is not a Variable, please convert to Variable.")

    #step 2. nll_loss 
    input = log_softmax_out
    helper = LayerHelper('nll_loss', **locals())
    dtype = helper.input_dtype(input)

    if not in_dygraph_mode():
        fluid.data_feeder.check_variable_and_dtype(
            input, 'input', ['float32', 'float64'], 'nll_loss')
        fluid.data_feeder.check_variable_and_dtype(label, 'label', ['int64'],
                                                   'nll_loss')

    x_shape = list(input.shape)
    n = x_shape[0]
    c = x_shape[1]
    x_dims = len(x_shape)
    if x_dims < 2:
        raise ValueError('Expected 2 or more dimensions (got {})'.format(
            x_dims))
    if x_dims != 2 and x_dims != 4:
        input = reshape(input, shape=[n, c, 1, -1])
        label = reshape(label, shape=[n, 1, -1])
        out_shape = [n] + x_shape[2:]

    if not in_dygraph_mode():
        fluid.data_feeder.check_variable_and_dtype(
            input, 'input', ['float32', 'float64'], 'nll_loss')
        fluid.data_feeder.check_variable_and_dtype(label, 'label', ['int64'],
                                                   'nll_loss')
    inputs = {'X': input, 'Label': label}
    attrs = {'reduction': reduction, 'ignore_index': ignore_index}
    if weight is not None:
        if isinstance(weight, Variable):
            inputs['Weight'] = weight

    out = helper.create_variable_for_type_inference(dtype=input.dtype)
    total_weight = helper.create_variable_for_type_inference(dtype=input.dtype)
    outputs = {'Out': out, 'Total_weight': total_weight}

    helper.append_op(
        type='nll_loss', inputs=inputs, outputs=outputs, attrs=attrs)
    if x_dims != 2 and x_dims != 4 and reduction == 'none':
        out = reshape(out, shape=out_shape)

    return out