activation.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.

from ...fluid.layers import sigmoid  # noqa: F401
from ...tensor.math import tanh  # noqa: F401
from ...tensor.math import tanh_  # noqa: F401

from ...fluid.dygraph.inplace_utils import inplace_apis_in_dygraph_only
from ...tensor.manipulation import chunk
from ...tensor.math import multiply

import warnings
from ...fluid.layer_helper import LayerHelper
from ...fluid.framework import in_dygraph_mode, convert_np_dtype_to_dtype_
from ...fluid import core
from ...fluid.data_feeder import check_variable_and_dtype, check_dtype
import paddle

__all__ = []


def elu(x, alpha=1.0, name=None):
    r"""
    elu activation.

    .. math::

        elu(x) = max(0, x) + min(0, \\alpha * (e^{x}-1))

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        alpha (float, optional): The 'alpha' value of the ELU formulation. Default is 1.0.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            x = paddle.to_tensor([[-1., 6.], [1., 15.6]])
            out = F.elu(x, alpha=0.2)
            # [[-0.12642411  6.        ]
            #  [ 1.          15.6      ]]
    """

    if in_dygraph_mode():
        return core.ops.elu(x, 'alpha', alpha)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], 'elu')
    helper = LayerHelper("elu", **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type='elu',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'alpha': alpha})
    return out


@inplace_apis_in_dygraph_only
def elu_(x, alpha=1.0, name=None):
    r"""
    Inplace version of ``elu`` API, the output Tensor will be inplaced with input ``x``.
    Please refer to :ref:`api_nn_cn_elu`.
    """
    return core.ops.elu_(x, 'alpha', alpha)


def gelu(x, approximate=False, name=None):
    r"""
    gelu activation.

    if approximate is True

    .. math::

        gelu(x) = 0.5 * x * (1 + tanh(\\sqrt{\\frac{2}{\\pi}} * (x + 0.044715x^{3})))

    else

    .. math::

        gelu(x) = 0.5 * x * (1 + erf(\\frac{x}{\\sqrt{2}}))

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        approximate (bool, optional): Wether to enable approximation. Default is False.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            x = paddle.to_tensor([[-1, 0.5], [1, 1.5]])
            out1 = F.gelu(x)
            # [[-0.15865529,  0.34573123],
            #  [ 0.84134471,  1.39978933]]
            out2 = F.gelu(x, True)
            # [[-0.15880799,  0.34571400],
            #  [ 0.84119201,  1.39957154]]
    """

    if in_dygraph_mode():
        return core.ops.gelu(x, 'approximate', approximate)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], 'gelu')
    helper = LayerHelper("gelu", **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type='gelu',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'approximate': approximate})
    return out


def hardshrink(x, threshold=0.5, name=None):
    r"""
    hard shrinkage activation

    .. math::

        hardshrink(x)=
            \\left\\{
            \\begin{aligned}
            &x, & & if \\ x > threshold \\\\
            &x, & & if \\ x < -threshold \\\\
            &0, & & if \\ others
            \\end{aligned}
            \\right.

    Args:
        x (Tensor): The input Tensor with data type float32, float64.
        threshold (float, optional): The value of threshold for hardthrink. Default is 0.5
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            x = paddle.to_tensor([-1, 0.3, 2.5])
            out = F.hardshrink(x) # [-1., 0., 2.5]

    """
    if in_dygraph_mode():
        return core.ops.hard_shrink(x, 'threshold', threshold)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
                             'hardshrink')
    helper = LayerHelper('hardshrink', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type='hard_shrink',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'threshold': threshold})
    return out


def hardtanh(x, min=-1.0, max=1.0, name=None):
    r"""
    hardtanh activation

    .. math::

        hardtanh(x)= \\begin{cases}
                        max, \\text{if } x > max \\\\
                        min, \\text{if } x < min \\\\
                        x,  \\text{otherwise}
                      \\end{cases}

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        min (float, optional): The minimum value of the linear region range. Default is -1.
        max (float, optional): The maximum value of the linear region range. Default is 1.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

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

            x = paddle.to_tensor(np.array([-1.5, 0.3, 2.5]))
            out = F.hardtanh(x) # [-1., 0.3, 1.]
    """

    if in_dygraph_mode():
        return core.ops.brelu(x, 't_min', min, 't_max', max)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
                             'hardtanh')

    helper = LayerHelper('hardtanh', **locals())
    out = helper.create_variable_for_type_inference(dtype=x.dtype)
    helper.append_op(
        type='brelu',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'t_min': min,
               't_max': max})
    return out


def hardsigmoid(x, slope=0.1666667, offset=0.5, name=None):
    r"""
    hardsigmoid activation.

    A 3-part piecewise linear approximation of sigmoid(https://arxiv.org/abs/1603.00391),
    which is much faster than sigmoid.

    .. math::

        hardsigmoid(x)=
            \\left\\{
            \\begin{aligned}
            &0, & & \\text{if } x \\leq -3 \\\\
            &1, & & \\text{if } x \\geq 3 \\\\
            &slope * x + offset, & & \\text{otherwise}
            \\end{aligned}
            \\right.

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        slope (float, optional): The slope of hardsigmoid function. Default is 0.1666667.
        offset (float, optional): The offset of hardsigmoid function. Default is 0.5.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            x = paddle.to_tensor([-4., 5., 1.])
            out = F.hardsigmoid(x) # [0., 1., 0.666667]
    """

    if in_dygraph_mode():
        return core.ops.hard_sigmoid(x, 'slope', slope, 'offset', offset)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
                             'hardsigmoid')

    helper = LayerHelper('hardsigmoid', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type='hard_sigmoid',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'slope': slope,
               'offset': offset})
    return out


def hardswish(x, name=None):
    r"""
    hardswish activation

    hardswish is proposed in MobileNetV3, and performs better in computational stability
    and efficiency compared to swish function. For more details please refer
    to: https://arxiv.org/pdf/1905.02244.pdf

    .. math::

        hardswish(x)=
            \\left\\{
            \\begin{aligned}
            &0, & & \\text{if } x \\leq -3 \\\\
            &x, & & \\text{if } x \\geq 3 \\\\
            &\\frac{x(x+3)}{6}, & & \\text{otherwise}
            \\end{aligned}
            \\right.

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            x = paddle.to_tensor([-4., 5., 1.])
            out = F.hardswish(x) # [0., 5., 0.666667]
    """

    if in_dygraph_mode():
        return core.ops.hard_swish(x)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
                             'hardswish')

    helper = LayerHelper('hardswish', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(type='hard_swish', inputs={'X': x}, outputs={'Out': out})
    return out


def leaky_relu(x, negative_slope=0.01, name=None):
    r"""
    leaky_relu activation

    .. math::
        leaky\\_relu(x)=
            \\left\\{
            \\begin{aligned}
            &x, & & if \\ x >= 0 \\\\
            &negative\_slope * x, & & otherwise \\\\
            \\end{aligned}
            \\right. \\\\

    Args:
        x (Tensor): The input Tensor with data type float32, float64.
        negative_slope (float, optional): Slope of the activation function at
            :math:`x < 0` . Default is 0.01.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            x = paddle.to_tensor([-2., 0., 1.])
            out = F.leaky_relu(x) # [-0.02, 0., 1.]

    """
    if in_dygraph_mode():
        return core.ops.leaky_relu(x, 'alpha', negative_slope)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
                             'leaky_relu')
    helper = LayerHelper('leaky_relu', **locals())
    out = helper.create_variable_for_type_inference(dtype=x.dtype)
    helper.append_op(
        type='leaky_relu',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'alpha': negative_slope})
    return out


def prelu(x, weight, name=None):
    """
    prelu activation.

    .. math::

        prelu(x) = max(0, x) + weight * min(0, x)

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        weight (Tensor): The learnable parameter with data type same as ``x``.
            The weight shape is [1] or [in], where `in` is the input channel of ``x``.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

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

            data = np.array([[[[-2.0,  3.0, -4.0,  5.0],
                               [ 3.0, -4.0,  5.0, -6.0],
                               [-7.0, -8.0,  8.0,  9.0]],
                              [[ 1.0, -2.0, -3.0,  4.0],
                               [-5.0,  6.0,  7.0, -8.0],
                               [ 6.0,  7.0,  8.0,  9.0]]]], 'float32')
            x = paddle.to_tensor(data)
            w = paddle.to_tensor(np.array([0.25]).astype('float32'))
            out = F.prelu(x, w)
            # [[[[-0.5 ,  3.  , -1.  ,  5.  ],
            #    [ 3.  , -1.  ,  5.  , -1.5 ],
            #    [-1.75, -2.  ,  8.  ,  9.  ]],
            #   [[ 1.  , -0.5 , -0.75,  4.  ],
            #    [-1.25,  6.  ,  7.  , -2.  ],
            #    [ 6.  ,  7.  ,  8.  ,  9.  ]]]]
    """
    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], 'prelu')
    check_variable_and_dtype(weight, 'weight',
                             ['float16', 'float32', 'float64'], 'prelu')

    helper = LayerHelper('prelu', **locals())
    assert len(weight.shape
               ) == 1, "The dim count of weight shape should be 1 in prelu()."

    # NOTE(): The input of this API should be ``N,C,...`` format,
    # which means x.shape[0] is batch_size and x.shape[0] is channel.
    mode = 'all'
    if weight.shape[0] > 1:
        assert len(
            x.shape
        ) > 1, "The dim count of x should be equal or larger than 2 in prelu() when weight shape is not [1]."
        assert weight.shape[0] == x.shape[
            1], "The weight size should be equal to x input channel in prelu() when weight shape is not [1]."
        mode = 'channel'

    if in_dygraph_mode():
        return core.ops.prelu(x, weight, 'mode', mode)

    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type="prelu",
        inputs={"X": x,
                "Alpha": weight},
        outputs={"Out": out},
        attrs={"mode": mode})
    return out


def relu(x, name=None):
    """
    relu activation.

    .. math::

        out = max(x, 0)

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

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

            x = paddle.to_tensor(np.array([-2, 0, 1]).astype('float32'))
            out = F.relu(x) # [0., 0., 1.]
    """

    if in_dygraph_mode():
        return core.ops.relu(x)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], 'relu')
    helper = LayerHelper('relu', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(type='relu', inputs={'X': x}, outputs={'Out': out})
    return out


@inplace_apis_in_dygraph_only
def relu_(x, name=None):
    """
    Inplace version of ``relu`` API, the output Tensor will be inplaced with input ``x``.
    Please refer to :ref:`api_nn_cn_relu`.
    """
    return core.ops.relu_(x)


def log_sigmoid(x, name=None):
    r"""
    log_sigmoid activation.

    .. math::

        log\\_sigmoid(x) = log \\frac{1}{1 + e^{-x}}

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            x = paddle.to_tensor([1.0, 2.0, 3.0, 4.0])
            out = F.log_sigmoid(x) # [-0.313262 -0.126928 -0.0485874 -0.0181499]
    """

    if in_dygraph_mode():
        return core.ops.logsigmoid(x)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
                             'log_sigmoid')
    helper = LayerHelper("log_sigmoid", **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(type='logsigmoid', inputs={'X': x}, outputs={'Out': out})
    return out


def maxout(x, groups, axis=1, name=None):
    r"""
    maxout activation.

    Assumed the input shape is (N, Ci, H, W).
    The output shape is (N, Co, H, W).
    Then Co = Ci/groups and the operator formula is as follows:

    .. math::

        &out_{si+j} = \\max_{k} x_{gsi + sk + j} \\\\
        &g = groups \\\\
        &s = \\frac{input.size}{num\\_channels} \\\\
        &0 \\le i < \\frac{num\\_channels}{groups} \\\\
        &0 \\le j < s \\\\
        &0 \\le k < groups

    Parameters:
        x (Tensor): The input is 4-D Tensor with shape [N, C, H, W] or [N, H, W, C], the data type
            of input is float32 or float64.
        groups (int, optional): The groups number of maxout. `groups` specifies the
            index of channel dimension where maxout will be performed. This must be
            a factor of number of features. Default is 1.
        axis (int, optional): The axis along which to perform maxout calculations.
            It should be 1 when data format is NCHW, be -1 or 3 when data format
            is NHWC. If ``axis`` < 0, it works the same way as :math:`axis + D` ,
            where D is the dimensions of ``x`` . ``axis`` only supports 1, 3 or -1.
            Default is 1.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type as ``x`` .

    Examples:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            x = paddle.rand([1, 2, 3, 4])
            # [[[[0.5002636  0.22272532 0.17402348 0.2874594 ]
            #    [0.95313174 0.6228939  0.7129065  0.7087491 ]
            #    [0.02879342 0.88725346 0.61093384 0.38833922]]
            #   [[0.5231306  0.03807496 0.91661984 0.15602879]
            #    [0.666127   0.616567   0.30741522 0.24044901]
            #    [0.7142536  0.7351477  0.31588817 0.23782359]]]]
            out = F.maxout(x, groups=2)
            # [[[[0.5231306  0.22272532 0.91661984 0.2874594 ]
            #    [0.95313174 0.6228939  0.7129065  0.7087491 ]
            #    [0.7142536  0.88725346 0.61093384 0.38833922]]]]
    """

    if in_dygraph_mode():
        return core.ops.maxout(x, 'groups', groups, 'axis', axis)

    check_variable_and_dtype(x, 'x', ['float32', 'float64'], 'maxout')
    if axis not in [1, -1, 3]:
        raise ValueError(
            "Attr(axis) should be 1 when data format is NCHW, -1 or 3 when data format is NHWC. Received "
            "Attr(axis): %s." % str(axis))
    if axis == -1:
        axis = 3

    helper = LayerHelper('maxout', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type='maxout',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'groups': groups,
               'axis': axis})
    return out


def relu6(x, name=None):
    """
    relu6 activation

    .. math::

        relu6(x) = min(max(0,x), 6)

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

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

            x = paddle.to_tensor(np.array([-1, 0.3, 6.5]))
            out = F.relu6(x) # [0, 0.3, 6]
    """
    threshold = 6.0
    if in_dygraph_mode():
        return core.ops.relu6(x, 'threshold', threshold)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], 'relu6')
    helper = LayerHelper('relu6', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type='relu6',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'threshold': threshold})
    return out


def selu(x,
         scale=1.0507009873554804934193349852946,
         alpha=1.6732632423543772848170429916717,
         name=None):
    r"""
    selu activation

    .. math::

        selu(x)= scale *
                 \\begin{cases}
                   x, \\text{if } x > 0 \\\\
                   alpha * e^{x} - alpha, \\text{if } x <= 0
                 \\end{cases}

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        scale (float, optional): The value of scale(must be greater than 1.0) for selu. Default is 1.0507009873554804934193349852946
        alpha (float, optional): The value of alpha(must be no less than zero) for selu. Default is 1.6732632423543772848170429916717
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

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

            x = paddle.to_tensor(np.array([[0.0, 1.0],[2.0, 3.0]]))
            out = F.selu(x) # [[0, 1.050701],[2.101402, 3.152103]]
    """
    if scale <= 1.0:
        raise ValueError(
            "The scale must be greater than 1.0. Received: {}.".format(scale))

    if alpha < 0:
        raise ValueError(
            "The alpha must be no less than zero. Received: {}.".format(alpha))

    if in_dygraph_mode():
        return core.ops.selu(x, 'scale', scale, 'alpha', alpha)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], 'selu')
    helper = LayerHelper('selu', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type='selu',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'scale': scale,
               'alpha': alpha})
    return out


def silu(x, name=None):
    """
    silu activation.
    .. math:
        silu(x) = \frac{x}{1 + e^{-x}}
    
    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.
    
    Returns:
        A Tensor with the same data type and shape as ``x`` .
    
    Examples:
        .. code-block:: python
        import paddle
        import paddle.nn.functional as F
        
        x = paddle.to_tensor([1.0, 2.0, 3.0, 4.0])
        out = F.silu(x) # [ 0.731059, 1.761594, 2.857722, 3.928055 ]
    """

    if in_dygraph_mode():
        return core.ops.silu(x)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], 'silu')
    helper = LayerHelper("silu", **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(type='silu', inputs={'X': x}, outputs={'Out': out})
    return out


def softmax(x, axis=-1, dtype=None, name=None):
    r"""
    This operator implements the softmax layer. The calculation process is as follows:

    1. The dimension :attr:`axis` of ``x`` will be permuted to the last.

    2. Then ``x`` will be logically flattened to a 2-D matrix. The matrix's second
    dimension(row length) is the same as the dimension :attr:`axis` of ``x``,
    and the first dimension(column length) is the product of all other dimensions
    of ``x``. For each row of the matrix, the softmax operator squashes the
    K-dimensional(K is the width of the matrix, which is also the size of ``x``'s
    dimension :attr:`axis`) vector of arbitrary real values to a K-dimensional
    vector of real values in the range [0, 1] that add up to 1.

    3. After the softmax operation is completed, the inverse operations of steps 1 and 2
    are performed to restore the two-dimensional matrix to the same dimension as the ``x`` .

    It computes the exponential of the given dimension and the sum of exponential
    values of all the other dimensions in the K-dimensional vector input.
    Then the ratio of the exponential of the given dimension and the sum of
    exponential values of all the other dimensions is the output of the softmax
    operator.

    For each row :math:`i` and each column :math:`j` in the matrix, we have:

    .. math::

        softmax[i, j] = \\frac{\\exp(x[i, j])}{\\sum_j(exp(x[i, j])}

    Example:

    .. code-block:: text

        Case 1:
          Input:
            x.shape = [2, 3, 4]
            x.data = [[[2.0, 3.0, 4.0, 5.0],
                       [3.0, 4.0, 5.0, 6.0],
                       [7.0, 8.0, 8.0, 9.0]],
                      [[1.0, 2.0, 3.0, 4.0],
                       [5.0, 6.0, 7.0, 8.0],
                       [6.0, 7.0, 8.0, 9.0]]]

          Attrs:
            axis = -1

          Output:
            out.shape = [2, 3, 4]
            out.data = [[[0.0320586 , 0.08714432, 0.23688282, 0.64391426],
                         [0.0320586 , 0.08714432, 0.23688282, 0.64391426],
                         [0.07232949, 0.19661193, 0.19661193, 0.53444665]],
                        [[0.0320586 , 0.08714432, 0.23688282, 0.64391426],
                         [0.0320586 , 0.08714432, 0.23688282, 0.64391426],
                         [0.0320586 , 0.08714432, 0.23688282, 0.64391426]]]

        Case 2:
          Input:
            x.shape = [2, 3, 4]
            x.data = [[[2.0, 3.0, 4.0, 5.0],
                       [3.0, 4.0, 5.0, 6.0],
                       [7.0, 8.0, 8.0, 9.0]],
                      [[1.0, 2.0, 3.0, 4.0],
                       [5.0, 6.0, 7.0, 8.0],
                       [6.0, 7.0, 8.0, 9.0]]]
          Attrs:
            axis = 1

          Output:
            out.shape = [2, 3, 4]
            out.data = [[[0.00657326, 0.00657326, 0.01714783, 0.01714783],
                         [0.01786798, 0.01786798, 0.04661262, 0.04661262],
                         [0.97555875, 0.97555875, 0.93623955, 0.93623955]],
                        [[0.00490169, 0.00490169, 0.00490169, 0.00490169],
                         [0.26762315, 0.26762315, 0.26762315, 0.26762315],
                         [0.72747516, 0.72747516, 0.72747516, 0.72747516]]]

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        axis (int, optional): The axis along which to perform log_softmax
            calculations. It should be in range [-D, D), where D is the
            dimensions of ``x`` . If ``axis`` < 0, it works the same way as
            :math:`axis + D` . Default is -1.
        dtype (str, optional): The data type of the output tensor, can be float32, float64.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same shape and data type (use ``dtype`` if it is
        specified) as x.

    Examples:
        .. code-block:: python

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

            x = np.array([[[2.0, 3.0, 4.0, 5.0],
                        [3.0, 4.0, 5.0, 6.0],
                        [7.0, 8.0, 8.0, 9.0]],
                        [[1.0, 2.0, 3.0, 4.0],
                        [5.0, 6.0, 7.0, 8.0],
                        [6.0, 7.0, 8.0, 9.0]]], 'float32')
            x = paddle.to_tensor(x)
            out1 = F.softmax(x)
            out2 = F.softmax(x, dtype='float64')
            # out1's data type is float32; out2's data type is float64
            # out1 and out2's value is as follows:
            # [[[0.0320586 , 0.08714432, 0.23688282, 0.64391426],
            #   [0.0320586 , 0.08714432, 0.23688282, 0.64391426],
            #   [0.07232949, 0.19661193, 0.19661193, 0.53444665]],
            # [[0.0320586 , 0.08714432, 0.23688282, 0.64391426],
            #   [0.0320586 , 0.08714432, 0.23688282, 0.64391426],
            #   [0.0320586 , 0.08714432, 0.23688282, 0.64391426]]]
    """

    if (dtype is not None) and (not isinstance(dtype, core.VarDesc.VarType)):
        dtype = convert_np_dtype_to_dtype_(dtype)
    use_cudnn = True

    if in_dygraph_mode():
        outs_cast = x if dtype is None \
            else core.ops.cast(x, 'in_dtype', x.dtype, 'out_dtype', dtype)
        return core.ops.softmax(outs_cast, 'axis', axis, 'use_cudnn', use_cudnn)

    if dtype is None:
        check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
                                 'softmax')
    else:
        check_dtype(dtype, 'dtype', ['float32', 'float64'], 'softmax',
                    'If dtype is not None, it only support float32 or float64.')

    helper = LayerHelper("softmax", **locals())
    outs_cast = x
    if dtype is not None:
        outs_cast = helper.create_variable_for_type_inference(dtype)
        helper.append_op(
            type='cast',
            inputs={'X': x},
            outputs={'Out': outs_cast},
            attrs={'in_dtype': x.dtype,
                   'out_dtype': dtype})

    outs_softmax = helper.create_variable_for_type_inference(outs_cast.dtype)
    helper.append_op(
        type='softmax',
        inputs={'X': outs_cast},
        outputs={'Out': outs_softmax},
        attrs={'axis': axis,
               'use_cudnn': use_cudnn})

    return outs_softmax


@inplace_apis_in_dygraph_only
def softmax_(x, axis=-1, dtype=None, name=None):
    r"""
    Inplace version of ``softmax`` API, the output Tensor will be inplaced with input ``x``.
    Please refer to :ref:`api_nn_cn_softmax`.
    """
    if (dtype is not None) and (not isinstance(dtype, core.VarDesc.VarType)):
        dtype = convert_np_dtype_to_dtype_(dtype)
    use_cudnn = True
    return core.ops.softmax_(x, 'axis', axis, 'use_cudnn', use_cudnn)


def softplus(x, beta=1, threshold=20, name=None):
    r"""
    softplus activation

    .. math::

        softplus(x) = \\frac{1}{beta} * \\log(1 + e^{beta * x}) \\\\
        \\text{For numerical stability, the implementation reverts to the linear function when: beta * x > threshold.}

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        beta (float, optional): The value of beta for softplus. Default is 1
        threshold (float, optional): The value of threshold for softplus. Default is 20
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

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

            x = paddle.to_tensor(np.array([-0.4, -0.2, 0.1, 0.3]))
            out = F.softplus(x) # [0.513015, 0.598139, 0.744397, 0.854355]
    """
    if in_dygraph_mode():
        return core.ops.softplus(x, 'beta', beta, 'threshold', threshold)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
                             'softplus')
    helper = LayerHelper('softplus', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type='softplus',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'beta': beta,
               'threshold': threshold})
    return out


def softshrink(x, threshold=0.5, name=None):
    r"""
    softshrink activation

    .. math::

        softshrink(x)= \\begin{cases}
                        x - threshold, \\text{if } x > threshold \\\\
                        x + threshold, \\text{if } x < -threshold \\\\
                        0,  \\text{otherwise}
                      \\end{cases}

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        threshold (float, optional): The value of threshold(must be no less than zero) for softplus. Default is 0.5
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

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

            x = paddle.to_tensor(np.array([-0.9, -0.2, 0.1, 0.8]))
            out = F.softshrink(x) # [-0.4, 0, 0, 0.3]
    """
    if threshold < 0:
        raise ValueError(
            "The threshold must be no less than zero. Received: {}.".format(
                threshold))

    if in_dygraph_mode():
        return core.ops.softshrink(x, 'lambda', threshold)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
                             'softshrink')
    helper = LayerHelper('softshrink', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type='softshrink',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'lambda': threshold})
    return out


def softsign(x, name=None):
    r"""
    softsign activation

    .. math::

        softsign(x) = \\frac{x}{1 + |x|}

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

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

            x = paddle.to_tensor(np.array([-0.4, -0.2, 0.1, 0.3]))
            out = F.softsign(x) # [-0.285714, -0.166667, 0.0909091, 0.230769]
    """
    if in_dygraph_mode():
        return core.ops.softsign(x)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
                             'softsign')
    helper = LayerHelper('softsign', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(type='softsign', inputs={'X': x}, outputs={'Out': out})
    return out


def swish(x, name=None):
    r"""
    swish activation.

    .. math::

        swish(x) = \\frac{x}{1 + e^{-x}}

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

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

            x = paddle.to_tensor(np.array([-2., 0., 1.]))
            out = F.swish(x) # [-0.238406, 0., 0.731059]
    """

    if in_dygraph_mode():
        return core.ops.swish(x, 'beta', 1.0)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'], 'swish')
    helper = LayerHelper('swish', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type='swish',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'beta': 1.0})
    return out


def tanhshrink(x, name=None):
    """
    tanhshrink activation

    .. math::

        tanhshrink(x) = x - tanh(x)

    Args:
        x (Tensor): The input Tensor with data type float32, float64.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

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

            x = paddle.to_tensor(np.array([-0.4, -0.2, 0.1, 0.3]))
            out = F.tanhshrink(x) # [-0.020051, -0.00262468, 0.000332005, 0.00868739]
    """
    if in_dygraph_mode():
        return core.ops.tanh_shrink(x)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
                             'tanhshrink')
    helper = LayerHelper('tanh_shrink', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(type='tanh_shrink', inputs={'X': x}, outputs={'Out': out})
    return out


def thresholded_relu(x, threshold=1.0, name=None):
    r"""
    thresholded relu activation.

    .. math::

        thresholded\\_relu(x) = \\begin{cases}
                                 x, \\text{if } x > threshold \\\\
                                 0, \\text{otherwise}
                                \\end{cases}

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        threshold (float, optional): The value of threshold for thresholded_relu. Default is 1.0
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same data type and shape as ``x`` .

    Examples:
        .. code-block:: python

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

            x = paddle.to_tensor(np.array([2., 0., 1.]))
            out = F.thresholded_relu(x) # [2., 0., 0.]
    """

    if in_dygraph_mode():
        return core.ops.thresholded_relu(x, 'threshold', threshold)

    check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
                             'thresholded_relu')
    helper = LayerHelper('thresholded_relu', **locals())
    out = helper.create_variable_for_type_inference(x.dtype)
    helper.append_op(
        type='thresholded_relu',
        inputs={'X': x},
        outputs={'Out': out},
        attrs={'threshold': threshold})
    return out


def log_softmax(x, axis=-1, dtype=None, name=None):
    r"""
    This operator implements the log_softmax layer. The calculation process is
    as follows:

    .. math::

        \\begin{aligned} 
        log\\_softmax[i, j] &= log(softmax(x)) \\\\
        &= log(\\frac{\\exp(X[i, j])}{\\sum_j(\\exp(X[i, j])})
        \\end{aligned}

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        axis (int, optional): The axis along which to perform log_softmax
            calculations. It should be in range [-D, D), where D is the
            dimensions of ``x`` . If ``axis`` < 0, it works the same way as
            :math:`axis + D` . Default is -1.
        dtype (str|np.dtype|core.VarDesc.VarType, optional): The desired data
            type of the output tensor. If dtype is specified, ``x`` is casted
            to ``dtype`` before the operation is performed. This is useful for
            preventing data type overflows. Supported dtype: float32, float64.
            If ``dtype`` is None, the output Tensor has the same dtype as x.
            Default is None.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.

    Returns:
        A Tensor with the same shape and data type (use ``dtype`` if it is
        specified) as x.

    Examples:
        .. code-block:: python

            import paddle
            import paddle.nn.functional as F

            x = [[[-2.0, 3.0, -4.0, 5.0],
                  [3.0, -4.0, 5.0, -6.0],
                  [-7.0, -8.0, 8.0, 9.0]],
                 [[1.0, -2.0, -3.0, 4.0],
                  [-5.0, 6.0, 7.0, -8.0],
                  [6.0, 7.0, 8.0, 9.0]]]
            x = paddle.to_tensor(x)
            out1 = F.log_softmax(x)
            out2 = F.log_softmax(x, dtype='float64')
            # out1's data type is float32; out2's data type is float64
            # out1 and out2's value is as follows:
            # [[[ -7.1278396   -2.1278396   -9.127839    -0.12783948]
            #   [ -2.1270514   -9.127051    -0.12705144 -11.127051  ]
            #   [-16.313261   -17.313261    -1.3132617   -0.31326184]]
            #  [[ -3.0518122   -6.051812    -7.051812    -0.051812  ]
            #   [-12.313267    -1.3132664   -0.3132665  -15.313267  ]
            #   [ -3.4401896   -2.4401896   -1.4401896   -0.44018966]]]
    """

    if (dtype is not None) and (not isinstance(dtype, core.VarDesc.VarType)):
        dtype = convert_np_dtype_to_dtype_(dtype)

    if in_dygraph_mode():
        if dtype is not None:
            x = core.ops.cast(x, 'in_dtype', x.dtype, 'out_dtype', dtype)
        return core.ops.log_softmax(x, 'axis', axis)

    if dtype is None:
        check_variable_and_dtype(x, 'x', ['float16', 'float32', 'float64'],
                                 'log_softmax')
    else:
        check_dtype(dtype, 'dtype', ['float32', 'float64'], 'log_softmax',
                    'If dtype is not None, it only support float32 or float64.')

    helper = LayerHelper("log_softmax", **locals())
    out_cast = x
    if dtype is not None:
        out_cast = helper.create_variable_for_type_inference(dtype)
        helper.append_op(
            type='cast',
            inputs={'X': x},
            outputs={'Out': out_cast},
            attrs={'in_dtype': x.dtype,
                   'out_dtype': dtype})

    out = helper.create_variable_for_type_inference(out_cast.dtype)
    helper.append_op(
        type='log_softmax',
        inputs={'X': out_cast},
        outputs={'Out': out},
        attrs={'axis': axis})

    return out


def glu(x, axis=-1, name=None):
    r"""
    The gated linear unit. The input is evenly splited into 2 parts along a 
    given axis. The first part is used as the content, and the second part is
    passed through a sigmoid function then used as the gate. The output is a
    elementwise multiplication of the content and the gate.

    .. math::

        \mathrm{GLU}(a, b) = a \otimes \sigma(b)

    Parameters:
        x (Tensor): The input Tensor with data type float32, float64.
        axis (int, optional): The axis along which split the input tensor. It 
            should be in range [-D, D), where D is the dimensions of ``x`` . 
            If ``axis`` < 0, it works the same way as :math:`axis + D` . 
            Default is -1.
        name (str, optional): Name for the operation (optional, default is None).
            For more information, please refer to :ref:`api_guide_Name`.
    
    Returns:
        A Tensor with the same data type as x. The size of the given aixs is 
        halved.
    
    Examples:
        .. code-block:: python
        
            import paddle
            from paddle.nn import functional as F
            
            x = paddle.to_tensor(
                [[-0.22014759, -1.76358426,  0.80566144,  0.04241343],
                 [-1.94900405, -1.89956081,  0.17134808, -1.11280477]]
            )
            print(F.glu(x).numpy())
            # array([[-0.15216254, -0.9004892 ],
            #        [-1.0577879 , -0.46985325]], dtype=float32)
        
    """
    check_variable_and_dtype(x, 'input', ['float16', 'float32', 'float64'],
                             "glu")
    a, b = chunk(x, 2, axis=axis, name=name)
    gate = sigmoid(b, name=name)
    out = paddle.multiply(a, gate, name=name)
    return out