norm.py

# Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
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# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
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#     http://www.apache.org/licenses/LICENSE-2.0
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#
# 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
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#     http://www.apache.org/licenses/LICENSE-2.0
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# Unless required by applicable law or agreed to in writing, software
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# TODO: define normalization api

import six

from ...fluid.dygraph import BatchNorm  # noqa: F401
from ...fluid.dygraph import SpectralNorm  # noqa: F401

from ...framework import get_default_dtype, set_default_dtype, _non_static_mode

from ..initializer import Constant
from ...framework import ParamAttr
from ...fluid.data_feeder import check_variable_and_dtype, check_type
from ...fluid import dygraph_utils

from ..functional import batch_norm, layer_norm, instance_norm

import numpy as np
import numbers
import warnings
from ...framework import no_grad
from .. import functional as F
from paddle import _C_ops, _legacy_C_ops
from .. import Layer
from paddle import in_dynamic_mode
from paddle.fluid.framework import in_dygraph_mode, _in_legacy_dygraph

__all__ = []


class _InstanceNormBase(Layer):
    """
    This class is based class for InstanceNorm1D, 2d, 3d.

    See InstaceNorm1D, InstanceNorm2D or InstanceNorm3D for more details.
    """

    def __init__(self,
                 num_features,
                 epsilon=1e-5,
                 momentum=0.9,
                 weight_attr=None,
                 bias_attr=None,
                 data_format="NCHW",
                 name=None):
        super(_InstanceNormBase, self).__init__()

        if weight_attr == False or bias_attr == False:
            assert weight_attr == bias_attr, "weight_attr and bias_attr must be set to Fasle at the same time in InstanceNorm"
        self._epsilon = epsilon
        self._weight_attr = weight_attr
        self._bias_attr = bias_attr
        self._num_features = num_features

        if weight_attr != False and bias_attr != False:
            self.scale = self.create_parameter(
                attr=self._weight_attr,
                shape=[num_features],
                default_initializer=Constant(1.0),
                is_bias=False)
            self.bias = self.create_parameter(attr=self._bias_attr,
                                              shape=[num_features],
                                              default_initializer=Constant(0.0),
                                              is_bias=True)
        else:
            self.scale = None
            self.bias = None

    def _check_input_dim(self, input):
        raise NotImplementedError("InstanceNorm Base error")

    def forward(self, input):
        self._check_input_dim(input)

        return instance_norm(input,
                             weight=self.scale,
                             bias=self.bias,
                             eps=self._epsilon)

    def extra_repr(self):
        return 'num_features={}, epsilon={}'.format(self._num_features,
                                                    self._epsilon)


class InstanceNorm1D(_InstanceNormBase):
    r"""
    Create a callable object of `InstanceNorm1D`. Applies Instance Normalization over a 3D input (a mini-batch of 1D inputs with additional channel dimension) as described in the paper Instance Normalization: The Missing Ingredient for Fast Stylization .

    DataLayout: NCL `[batch, in_channels, length]`

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

    ..  math::

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

Where `H` means height of feature map, `W` means width of feature map.

    Parameters:
        num_features(int): Indicate the number of channels of the input ``Tensor``.
        epsilon(float, optional): A value added to the denominator for
            numerical stability. Default is 1e-5.
        momentum(float, optional): The value used for the moving_mean and moving_var computation. Default: 0.9.
        weight_attr(ParamAttr|bool, optional): The parameter attribute for Parameter `scale`
            of instance_norm. If it is set to None or one attribute of ParamAttr, instance_norm
            will create ParamAttr as weight_attr, the name of scale can be set in ParamAttr.
            If the Initializer of the weight_attr is not set, the parameter is initialized
            one. If it is set to False, will not create weight_attr. Default: None.
        bias_attr(ParamAttr|bool, optional): The parameter attribute for the bias of instance_norm.
            If it is set to None or one attribute of ParamAttr, instance_norm
            will create ParamAttr as bias_attr, the name of bias can be set in ParamAttr.
            If the Initializer of the bias_attr is not set, the bias is initialized zero.
            If it is set to False, will not create bias_attr. Default: None.
        data_format(str, optional): Specify the input data format, may be "NC", "NCL". Default "NCL".
        name(str, optional): Name for the InstanceNorm, default is None. For more information, please refer to :ref:`api_guide_Name`..


    Shape:
        - x: 2-D or 3-D tensor with shape: (batch, num_features) or (batch, num_features, length).
        - output: 3-D tensor with same shape as input x.

    Returns:
        None.


    Examples:

        .. code-block:: python

          import paddle

          x = paddle.rand((2, 2, 3))
          instance_norm = paddle.nn.InstanceNorm1D(2)
          instance_norm_out = instance_norm(x)

          print(instance_norm_out)

    """

    def _check_input_dim(self, input):
        if len(input.shape) != 2 and len(input.shape) != 3:
            raise ValueError('expected 2D or 3D input (got {}D input)'.format(
                len(input.shape)))


class InstanceNorm2D(_InstanceNormBase):
    r"""
    Create a callable object of `InstanceNorm2D`. Applies Instance Normalization over a 4D input (a mini-batch of 2D inputs with additional channel dimension) as described in the paper Instance Normalization: The Missing Ingredient for Fast Stylization .

    DataLayout: NCHW `[batch, in_channels, in_height, in_width]`


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

    ..  math::

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

Where `H` means height of feature map, `W` means width of feature map.

    Parameters:
        num_features(int): Indicate the number of channels of the input ``Tensor``.
        epsilon(float, optional): A value added to the denominator for
            numerical stability. Default is 1e-5.
        momentum(float, optional): The value used for the moving_mean and moving_var computation. Default: 0.9.
        weight_attr(ParamAttr|bool, optional): The parameter attribute for Parameter `scale`
            of instance_norm. If it is set to None or one attribute of ParamAttr, instance_norm
            will create ParamAttr as weight_attr, the name of scale can be set in ParamAttr.
            If the Initializer of the weight_attr is not set, the parameter is initialized
            one. If it is set to False, will not create weight_attr. Default: None.
        bias_attr(ParamAttr|bool, optional): The parameter attribute for the bias of instance_norm.
            If it is set to None or one attribute of ParamAttr, instance_norm
            will create ParamAttr as bias_attr, the name of bias can be set in ParamAttr.
            If the Initializer of the bias_attr is not set, the bias is initialized zero.
    `       If it is set to False, will not create bias_attr. Default: None.
        data_format(str, optional): Specify the input data format, could be "NCHW". Default: NCHW.
        name(str, optional): Name for the InstanceNorm, default is None. For more information, please refer to :ref:`api_guide_Name`..

    Shape:
        - x: 4-D tensor with shape: (batch, num_features, height, weight).
        - output: 4-D tensor with same shape as input x.

    Returns:
        None.


    Examples:

        .. code-block:: python

            import paddle

            x = paddle.rand((2, 2, 2, 3))
            instance_norm = paddle.nn.InstanceNorm2D(2)
            instance_norm_out = instance_norm(x)

            print(instance_norm_out)
    """

    def _check_input_dim(self, input):
        if len(input.shape) != 4:
            raise ValueError('expected 4D input (got {}D input)'.format(
                len(input.shape)))


class InstanceNorm3D(_InstanceNormBase):
    r"""
    Create a callable object of `InstanceNorm3D`. Applies Instance Normalization over a 5D input (a mini-batch of 3D inputs with additional channel dimension) as described in the paper Instance Normalization: The Missing Ingredient for Fast Stylization .

    DataLayout: NCHW `[batch, in_channels, D, in_height, in_width]`


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

    ..  math::

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

Where `H` means height of feature map, `W` means width of feature map.

    Parameters:
        num_features(int): Indicate the number of channels of the input ``Tensor``.
        epsilon(float, optional): A value added to the denominator for
            numerical stability. Default is 1e-5.
        momentum(float, optional): The value used for the moving_mean and moving_var computation. Default: 0.9.
        weight_attr(ParamAttr|bool, optional): The parameter attribute for Parameter `scale`
            of instance_norm. If it is set to None or one attribute of ParamAttr, instance_norm
            will create ParamAttr as weight_attr, the name of scale can be set in ParamAttr.
            If the Initializer of the weight_attr is not set, the parameter is initialized
            one. If it is set to False, will not create weight_attr. Default: None.
        bias_attr(ParamAttr|bool, optional): The parameter attribute for the bias of instance_norm.
            If it is set to None or one attribute of ParamAttr, instance_norm
            will create ParamAttr as bias_attr, the name of bias can be set in ParamAttr.
            If the Initializer of the bias_attr is not set, the bias is initialized zero.
            If it is set to False, will not create bias_attr. Default: None.
        data_format(str, optional): Specify the input data format, could be "NCDHW". Default: NCDHW.
        name(str, optional): Name for the InstanceNorm, default is None. For more information, please refer to :ref:`api_guide_Name`..

    Shape:
        - x: 5-D tensor with shape: (batch, num_features, dims, height, weight).
        - output: 5-D tensor with same shape as input x.

    Returns:
        None.


    Examples:

        .. code-block:: python

            import paddle

            x = paddle.rand((2, 2, 2, 2, 3))
            instance_norm = paddle.nn.InstanceNorm3D(2)
            instance_norm_out = instance_norm(x)

            print(instance_norm_out.numpy)
    """

    def _check_input_dim(self, input):
        if len(input.shape) != 5:
            raise ValueError('expected 5D input (got {}D input)'.format(
                len(input.shape)))


class GroupNorm(Layer):
    """
    This interface is used to construct a callable object of the ``GroupNorm`` class.
    For more details, refer to code examples.
    It implements the function of the Group Normalization Layer.
    Refer to `Group Normalization <https://arxiv.org/abs/1803.08494>`_ .

    Parameters:
        num_groups(int): The number of groups that divided from channels.
        num_channels(int): The number of channels of input.
        epsilon(float, optional): The small value added to the variance to prevent
            division by zero. Default: 1e-05.
        weight_attr(ParamAttr|bool, optional): The parameter attribute for the learnable
            scale :math:`g`. If it is set to False, no scale will be added to the output units.
            If it is set to None, the bias is initialized one. Default: None.
        bias_attr(ParamAttr|bool, optional): The parameter attribute for the learnable
            bias :math:`b`. If it is set to False, no bias will be added to the output units.
            If it is set to None, the bias is initialized zero. Default: None.
        data_format(str, optional): Specify the input data format. Only NCHW is supported. Default: NCHW.
        name(str, optional): Name for the GroupNorm, default is None. For more information, please refer to :ref:`api_guide_Name`..

    Shape:
        - x: Tensor with shape: (batch, num_features, *).
        - output: The same shape as input x.

    Returns:
        None

    Examples:
        .. code-block:: python

            import paddle
            import numpy as np

            paddle.disable_static()
            np.random.seed(123)
            x_data = np.random.random(size=(2, 6, 2, 2)).astype('float32')
            x = paddle.to_tensor(x_data)
            group_norm = paddle.nn.GroupNorm(num_channels=6, num_groups=6)
            group_norm_out = group_norm(x)

            print(group_norm_out.numpy())
    """

    def __init__(self,
                 num_groups,
                 num_channels,
                 epsilon=1e-05,
                 weight_attr=None,
                 bias_attr=None,
                 data_format='NCHW',
                 name=None):
        super(GroupNorm, self).__init__()
        self._weight_attr = weight_attr
        self._bias_attr = bias_attr
        self._epsilon = epsilon
        self._num_channels = num_channels
        self._num_groups = num_groups
        if data_format != 'NCHW':
            raise ValueError("unsupported data layout:" + data_format)

        param_shape = [self._num_channels]

        if weight_attr == False:
            self.weight = self.create_parameter(
                attr=None, shape=param_shape, default_initializer=Constant(1.0))
            self.weight.stop_gradient = True
        else:
            self.weight = self.create_parameter(
                attr=self._weight_attr,
                shape=param_shape,
                default_initializer=Constant(1.0))
            self.weight.stop_gradient = self._weight_attr != None and self._weight_attr.learning_rate == 0.

        if bias_attr == False:
            self.bias = self.create_parameter(attr=None,
                                              shape=param_shape,
                                              default_initializer=Constant(0.0),
                                              is_bias=True)
            self.bias.stop_gradient = True
        else:
            self.bias = self.create_parameter(attr=self._bias_attr,
                                              shape=param_shape,
                                              is_bias=True)
            self.bias.stop_gradient = self._bias_attr != None and self._bias_attr.learning_rate == 0.

    def forward(self, input):
        mean_out = self._helper.create_variable_for_type_inference(
            dtype=input.dtype, stop_gradient=True)
        variance_out = self._helper.create_variable_for_type_inference(
            dtype=input.dtype, stop_gradient=True)

        if in_dygraph_mode():
            pre_act = _C_ops.group_norm(input, self.weight, self.bias,
                                        self._epsilon, self._num_groups, "NCHW")

            return dygraph_utils._append_activation_in_dygraph(pre_act,
                                                               act=None)

        elif _in_legacy_dygraph():
            pre_act, _, _ = _legacy_C_ops.group_norm(
                input,
                self.weight,
                self.bias,
                mean_out,
                variance_out,
                'epsilon',
                self._epsilon,
                'groups',
                self._num_groups,
            )
            return dygraph_utils._append_activation_in_dygraph(pre_act,
                                                               act=None)

        inputs = {'X': input}
        if self.bias is not None:
            inputs['Bias'] = self.bias
        if self.weight is not None:
            inputs['Scale'] = self.weight

        # create output
        group_norm_out = self._helper.create_variable_for_type_inference(
            dtype=input.dtype)

        self._helper.append_op(type="group_norm",
                               inputs=inputs,
                               outputs={
                                   "Y": group_norm_out,
                                   "Mean": mean_out,
                                   "Variance": variance_out,
                               },
                               attrs={
                                   "epsilon": self._epsilon,
                                   "groups": self._num_groups
                               })

        return self._helper.append_activation(group_norm_out, None)

    def extra_repr(self):
        return 'num_groups={}, num_channels={}, epsilon={}'.format(
            self._num_groups, self._num_channels, self._epsilon)


class LayerNorm(Layer):
    r"""
    Construct a callable object of the ``LayerNorm`` class.
    For more details, refer to code examples.
    It implements the function of the Layer Normalization Layer and can be applied to mini-batch input data.
    Refer to `Layer Normalization <https://arxiv.org/pdf/1607.06450v1.pdf>`_

    The formula is as follows:

    ..  math::

        \mu & = \frac{1}{H}\sum_{i=1}^{H} x_i

        \sigma & = \sqrt{\frac{1}{H}\sum_{i=1}^{H}{(x_i - \mu)^2} + \epsilon}

        y & = f(\frac{g}{\sigma}(x - \mu) + b)

    - :math:`x`: the vector representation of the summed inputs to the neurons in that layer.
    - :math:`H`: the number of hidden units in a layers
    - :math:`\epsilon`: the small value added to the variance to prevent division by zero.
    - :math:`g`: the trainable scale parameter.
    - :math:`b`: the trainable bias parameter.

    Parameters:
        normalized_shape(int|list|tuple): Input shape from an expected input of
            size :math:`[*, normalized_shape[0], normalized_shape[1], ..., normalized_shape[-1]]`.
            If it is a single integer, this module will normalize over the last dimension
            which is expected to be of that specific size.
        epsilon(float, optional): The small value added to the variance to prevent
            division by zero. Default: 1e-05.
        weight_attr(ParamAttr|bool, optional): The parameter attribute for the learnable
            gain :math:`g`. If False, weight is None. If is None, a default :code:`ParamAttr` would be added as scale. The
            :attr:`param_attr` is initialized as 1 if it is added. Default: None.
        bias_attr(ParamAttr|bool, optional): The parameter attribute for the learnable
            bias :math:`b`. If is False, bias is None. If is None, a default :code:`ParamAttr` would be added as bias. The
            :attr:`bias_attr` is initialized as 0 if it is added. Default: None.
        name(str, optional): Name for the LayerNorm, default is None. For more information, please refer to :ref:`api_guide_Name`..

    Shape:
        - x: 2-D, 3-D, 4-D or 5-D tensor.
        - output: same shape as input x.

    Returns:
        None

    Examples:

        .. code-block:: python

          import paddle

          x = paddle.rand((2, 2, 2, 3))
          layer_norm = paddle.nn.LayerNorm(x.shape[1:])
          layer_norm_out = layer_norm(x)

          print(layer_norm_out)
    """

    def __init__(self,
                 normalized_shape,
                 epsilon=1e-05,
                 weight_attr=None,
                 bias_attr=None,
                 name=None):
        super(LayerNorm, self).__init__()
        if isinstance(normalized_shape, numbers.Integral):
            normalized_shape = [normalized_shape]

        self._normalized_shape = list(normalized_shape)
        self._epsilon = epsilon
        self._weight_attr = weight_attr
        self._bias_attr = bias_attr
        param_shape = [np.prod(self._normalized_shape)]

        if weight_attr is False:
            self.weight = None
        else:
            self.weight = self.create_parameter(
                attr=self._weight_attr,
                shape=param_shape,
                default_initializer=Constant(1.0))

        if bias_attr is False:
            self.bias = None
        else:
            self.bias = self.create_parameter(attr=self._bias_attr,
                                              shape=param_shape,
                                              is_bias=True)

    def forward(self, input):
        return layer_norm(input,
                          normalized_shape=self._normalized_shape,
                          weight=self.weight,
                          bias=self.bias,
                          epsilon=self._epsilon)

    def extra_repr(self):
        return 'normalized_shape={}, epsilon={}'.format(self._normalized_shape,
                                                        self._epsilon)


class _BatchNormBase(Layer):
    """
    BatchNorm base .
    """

    def __init__(self,
                 num_features,
                 momentum=0.9,
                 epsilon=1e-05,
                 weight_attr=None,
                 bias_attr=None,
                 data_format='NCHW',
                 use_global_stats=None,
                 name=None):
        super(_BatchNormBase, self).__init__()
        self._num_features = num_features
        self._weight_attr = weight_attr
        self._bias_attr = bias_attr
        self._use_global_stats = use_global_stats

        if get_default_dtype() == 'float16':
            self._dtype = 'float32'
        else:
            self._dtype = get_default_dtype()

        param_shape = [num_features]

        # create parameter
        if weight_attr == False:
            self.weight = self.create_parameter(
                attr=None,
                shape=param_shape,
                dtype=self._dtype,
                default_initializer=Constant(1.0))
            self.weight.stop_gradient = True
        else:
            self.weight = self.create_parameter(
                attr=self._weight_attr,
                shape=param_shape,
                dtype=self._dtype,
                default_initializer=Constant(1.0))
            self.weight.stop_gradient = self._weight_attr != None and self._weight_attr.learning_rate == 0.

        if bias_attr == False:
            self.bias = self.create_parameter(attr=None,
                                              shape=param_shape,
                                              dtype=self._dtype,
                                              default_initializer=Constant(0.0),
                                              is_bias=True)
            self.bias.stop_gradient = True
        else:
            self.bias = self.create_parameter(attr=self._bias_attr,
                                              shape=param_shape,
                                              dtype=self._dtype,
                                              is_bias=True)
            self.bias.stop_gradient = self._bias_attr != None and self._bias_attr.learning_rate == 0.

        moving_mean_name = None
        moving_variance_name = None

        if name is not None:
            moving_mean_name = name + "_mean"
            moving_variance_name = name + "_variance"

        self._mean = self.create_parameter(dtype=self._dtype,
                                           attr=ParamAttr(
                                               name=moving_mean_name,
                                               initializer=Constant(0.0),
                                               trainable=False,
                                               do_model_average=True),
                                           shape=param_shape)
        self._mean.stop_gradient = True

        self._variance = self.create_parameter(dtype=self._dtype,
                                               attr=ParamAttr(
                                                   name=moving_variance_name,
                                                   initializer=Constant(1.0),
                                                   trainable=False,
                                                   do_model_average=True),
                                               shape=param_shape)
        self._variance.stop_gradient = True

        self._data_format = data_format
        self._in_place = False
        self._momentum = momentum
        self._epsilon = epsilon
        self._fuse_with_relu = False
        self._name = name

    def _check_input_dim(self, input):
        raise NotImplementedError("BatchNorm Base error")

    def _check_data_format(self, input):
        raise NotImplementedError("BatchNorm Base data format error")

    def forward(self, input):

        self._check_data_format(self._data_format)

        self._check_input_dim(input)

        if self.training:
            warnings.warn(
                "When training, we now always track global mean and variance.")

        return batch_norm(input,
                          self._mean,
                          self._variance,
                          weight=self.weight,
                          bias=self.bias,
                          training=self.training,
                          momentum=self._momentum,
                          epsilon=self._epsilon,
                          data_format=self._data_format,
                          use_global_stats=self._use_global_stats)

    def extra_repr(self):
        main_str = 'num_features={}, momentum={}, epsilon={}'.format(
            self._num_features, self._momentum, self._epsilon)
        if self._data_format != 'NCHW':
            main_str += ', data_format={}'.format(self._data_format)
        if self._name is not None:
            main_str += ', name={}'.format(self._name)
        return main_str


class BatchNorm1D(_BatchNormBase):
    r"""
    Applies Batch Normalization over a 2D or 3D input (a mini-batch of 1D inputswith additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .

    When use_global_stats = False, the :math:`\mu_{\beta}`
    and :math:`\sigma_{\beta}^{2}` are the statistics of one mini-batch.
    Calculated as follows:

    ..  math::

        \mu_{\beta} &\gets \frac{1}{m} \sum_{i=1}^{m} x_i \qquad &//\
        \ mini-batch\ mean \\
        \sigma_{\beta}^{2} &\gets \frac{1}{m} \sum_{i=1}^{m}(x_i - \
        \mu_{\beta})^2 \qquad &//\ mini-batch\ variance \\

    When use_global_stats = True, the :math:`\mu_{\beta}`
    and :math:`\sigma_{\beta}^{2}` are not the statistics of one mini-batch.
    They are global or running statistics (moving_mean and moving_variance). It usually got from the
    pre-trained model. Calculated as follows:

    .. math::
        moving\_mean = moving\_mean * momentum + \mu_{\beta} * (1. - momentum) \quad &// global \ mean \\
        moving\_variance = moving\_variance * momentum + \sigma_{\beta}^{2} * (1. - momentum) \quad &// global \ variance \\

    The normalization function formula is as follows:

    ..  math::

        \hat{x_i} &\gets \frac{x_i - \mu_\beta} {\sqrt{\sigma_{\beta}^{2} + \epsilon}} \qquad &//\ normalize \\
        y_i &\gets \gamma \hat{x_i} + \beta \qquad &//\ scale\ and\ shift

    - :math:`\epsilon` : add a smaller value to the variance to prevent division by zero
    - :math:`\gamma` : trainable proportional parameter
    - :math:`\beta` : trainable deviation parameter

    Parameters:
        num_features(int): Indicate the number of channels of the input ``Tensor``.
        epsilon(float, optional): The small value added to the variance to prevent division by zero. Default: 1e-5.
        momentum(float, optional): The value used for the moving_mean and moving_var computation. Default: 0.9.
        weight_attr(ParamAttr|bool, optional): The parameter attribute for Parameter `scale`
            of batch_norm. If it is set to None or one attribute of ParamAttr, batch_norm
            will create ParamAttr as weight_attr. If it is set to Fasle, the weight is not learnable.
            If the Initializer of the weight_attr is not set, the parameter is initialized with ones. Default: None.
        bias_attr(ParamAttr|bool, optional): The parameter attribute for the bias of batch_norm.
            If it is set to None or one attribute of ParamAttr, batch_norm
            will create ParamAttr as bias_attr. If it is set to Fasle, the weight is not learnable.
            If the Initializer of the bias_attr is not set, the bias is initialized zero. Default: None.
        data_format(str, optional): Specify the input data format, may be "NC", "NCL" or "NLC". Default "NCL".
        use_global_stats(bool|None, optional): Whether to use global mean and variance. If set to False, use the statistics of one mini-batch, if set to True, use the global statistics, if set to None, use global statistics in the test phase and use the statistics of one mini-batch in the training phase. Default: None.
        name(str, optional): Name for the BatchNorm, default is None. For more information, please refer to :ref:`api_guide_Name`..

    Shape:
        - x: 2-D or 3-D tensor with shape: (batch, num_features) or (batch, num_features, length) when data_format is "NC" or "NCL",
            (batch, length, num_features) when data_format is "NLC".
        - output: 3-D tensor with same shape as input x.

    Returns:
        None.


    Examples:
        .. code-block:: python

          import paddle

          x = paddle.rand((2, 1, 3))
          batch_norm = paddle.nn.BatchNorm1D(1)
          batch_norm_out = batch_norm(x)

          print(batch_norm_out)
    """

    def __init__(self,
                 num_features,
                 momentum=0.9,
                 epsilon=1e-05,
                 weight_attr=None,
                 bias_attr=None,
                 data_format='NCL',
                 use_global_stats=None,
                 name=None):
        super(BatchNorm1D,
              self).__init__(num_features, momentum, epsilon, weight_attr,
                             bias_attr, data_format, use_global_stats, name)

    def _check_data_format(self, input):
        if input == 'NCHW' or input == 'NC' or input == 'NCL':
            self._data_format = 'NCHW'
        elif input == "NHWC" or input == 'NLC':
            self._data_format = "NHWC"
        else:
            raise ValueError(
                'expected NC , NCL, NLC or None for data_format input')

    def _check_input_dim(self, input):
        if len(input.shape) != 2 and len(input.shape) != 3:
            raise ValueError('expected 2D or 3D input (got {}D input)'.format(
                len(input.shape)))


class BatchNorm2D(_BatchNormBase):
    r"""
    Applies Batch Normalization over a 4D input (a mini-batch of 2D inputswith additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .

    When use_global_stats = False, the :math:`\mu_{\beta}`
    and :math:`\sigma_{\beta}^{2}` are the statistics of one mini-batch.
    Calculated as follows:

    ..  math::

        \mu_{\beta} &\gets \frac{1}{m} \sum_{i=1}^{m} x_i \qquad &//
        \ mini-batch\ mean \\
        \sigma_{\beta}^{2} &\gets \frac{1}{m} \sum_{i=1}^{m}(x_i -
        \mu_{\beta})^2 \qquad &//\ mini-batch\ variance \\

    When use_global_stats = True, the :math:`\mu_{\beta}`
    and :math:`\sigma_{\beta}^{2}` are not the statistics of one mini-batch.
    They are global or running statistics (moving_mean and moving_variance). It usually got from the
    pre-trained model. Calculated as follows:

    .. math::
        moving\_mean = moving\_mean * momentum + \mu_{\beta} * (1. - momentum) \quad &// global \ mean \\
        moving\_variance = moving\_variance * momentum + \sigma_{\beta}^{2} * (1. - momentum) \quad &// global \ variance \\

    The normalization function formula is as follows:

    ..  math::

        \hat{x_i} &\gets \frac{x_i - \mu_\beta} {\sqrt{\sigma_{\beta}^{2} + \epsilon}} \qquad &//\ normalize \\
        y_i &\gets \gamma \hat{x_i} + \beta \qquad &//\ scale\ and\ shift

    - :math:`\epsilon` : add a smaller value to the variance to prevent division by zero
    - :math:`\gamma` : trainable proportional parameter
    - :math:`\beta` : trainable deviation parameter

    Parameters:
        num_features(int): Indicate the number of channels of the input ``Tensor``.
        epsilon(float, optional): The small value added to the variance to prevent division by zero. Default: 1e-5.
        momentum(float, optional): The value used for the moving_mean and moving_var computation. Default: 0.9.
        weight_attr(ParamAttr|bool, optional): The parameter attribute for Parameter `scale`
            of batch_norm. If it is set to None or one attribute of ParamAttr, batch_norm
            will create ParamAttr as weight_attr. If it is set to Fasle, the weight is not learnable.
            If the Initializer of the weight_attr is not set, the parameter is initialized with ones. Default: None.
        bias_attr(ParamAttr|bool, optional): The parameter attribute for the bias of batch_norm.
            If it is set to None or one attribute of ParamAttr, batch_norm
            will create ParamAttr as bias_attr. If it is set to Fasle, the weight is not learnable.
            If the Initializer of the bias_attr is not set, the bias is initialized zero. Default: None.
        data_format(str, optional): Specify the input data format, the data format can be "NCHW" or "NHWC". Default: NCHW.
        use_global_stats(bool|None, optional): Whether to use global mean and variance. If set to False, use the statistics of one mini-batch, if set to True, use the global statistics, if set to None, use global statistics in the test phase and use the statistics of one mini-batch in the training phase. Default: None.
        name(str, optional): Name for the BatchNorm, default is None. For more information, please refer to :ref:`api_guide_Name`..

    Shape:
        - x: 4-D tensor with shape: (batch, num_features, height, weight) when data_format is "NCHW",
            or (batch, height, weight, num_features) when data_format is "NHWC".
        - output: 4-D tensor with same shape as input x.

    Returns:
        None

    Examples:
        .. code-block:: python

          import paddle

          x = paddle.rand((2, 1, 2, 3))
          batch_norm = paddle.nn.BatchNorm2D(1)
          batch_norm_out = batch_norm(x)

          print(batch_norm_out)
    """

    def _check_data_format(self, input):
        if input == 'NCHW':
            self._data_format = input
        elif input == "NHWC":
            self._data_format = input
        else:
            raise ValueError('expected NCHW or NHWC for data_format input')

    def _check_input_dim(self, input):
        if len(input.shape) != 4:
            raise ValueError('expected 4D input (got {}D input)'.format(
                len(input.shape)))


class BatchNorm3D(_BatchNormBase):
    r"""
    Applies Batch Normalization over a 5D input (a mini-batch of 3D inputswith additional channel dimension) as described in the paper Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift .

    When use_global_stats = False, the :math:`\mu_{\beta}`
    and :math:`\sigma_{\beta}^{2}` are the statistics of one mini-batch.
    Calculated as follows:

    ..  math::

        \mu_{\beta} &\gets \frac{1}{m} \sum_{i=1}^{m} x_i \qquad &//\
        \ mini-batch\ mean \\
        \sigma_{\beta}^{2} &\gets \frac{1}{m} \sum_{i=1}^{m}(x_i - \
        \mu_{\beta})^2 \qquad &//\ mini-batch\ variance \\

    When use_global_stats = True, the :math:`\\mu_{\\beta}`
    and :math:`\\sigma_{\\beta}^{2}` are not the statistics of one mini-batch.
    They are global or running statistics (moving_mean and moving_variance). It usually got from the
    pre-trained model. Calculated as follows:

    .. math::
        moving\_mean = moving\_mean * momentum + \mu_{\beta} * (1. - momentum) \quad &// global \ mean \\
        moving\_variance = moving\_variance * momentum + \sigma_{\beta}^{2} * (1. - momentum) \quad &// global \ variance \\

    The normalization function formula is as follows:

    ..  math::

        \hat{x_i} &\gets \frac{x_i - \mu_\beta} {\sqrt{\sigma_{\beta}^{2} + \epsilon}} \qquad &//\ normalize \\
        y_i &\gets \gamma \hat{x_i} + \beta \qquad &//\ scale\ and\ shift

    - :math:`\epsilon` : add a smaller value to the variance to prevent division by zero
    - :math:`\gamma` : trainable proportional parameter
    - :math:`\beta` : trainable deviation parameter

    Parameters:
        num_features(int): Indicate the number of channels of the input ``Tensor``.
        epsilon(float, optional): The small value added to the variance to prevent division by zero. Default: 1e-5.
        momentum(float, optional): The value used for the moving_mean and moving_var computation. Default: 0.9.
        weight_attr(ParamAttr|bool, optional): The parameter attribute for Parameter `scale`
            of batch_norm. If it is set to None or one attribute of ParamAttr, batch_norm
            will create ParamAttr as weight_attr. If it is set to Fasle, the weight is not learnable.
            If the Initializer of the weight_attr is not set, the parameter is initialized with ones. Default: None.
        bias_attr(ParamAttr|bool, optional): The parameter attribute for the bias of batch_norm.
            If it is set to None or one attribute of ParamAttr, batch_norm
            will create ParamAttr as bias_attr. If it is set to Fasle, the weight is not learnable.
            If the Initializer of the bias_attr is not set, the bias is initialized zero. Default: None.
        data_format(str, optional): Specify the input data format, the data format can be "NCDHW" or "NDHWC. Default: NCDHW.
        use_global_stats(bool|None, optional): Whether to use global mean and variance. If set to False, use the statistics of one mini-batch, if set to True, use the global statistics, if set to None, use global statistics in the test phase and use the statistics of one mini-batch in the training phase. Default: None.
        name(str, optional): Name for the BatchNorm, default is None. For more information, please refer to :ref:`api_guide_Name`..

    Shape:
        - x: 5-D tensor with shape: (batch, num_features, dims, height, weight) when data_format is "NCDHW",
            or (batch, dims, height, weight, num_features) when data_format is "NDHWC".
        - output: 5-D tensor with same shape as input x.

    Returns:
        None

    Examples:
        .. code-block:: python

          import paddle

          x = paddle.rand((2, 1, 2, 2, 3))
          batch_norm = paddle.nn.BatchNorm3D(1)
          batch_norm_out = batch_norm(x)

          print(batch_norm_out)
    """

    def __init__(self,
                 num_features,
                 momentum=0.9,
                 epsilon=1e-05,
                 weight_attr=None,
                 bias_attr=None,
                 data_format='NCDHW',
                 use_global_stats=None,
                 name=None):
        super(BatchNorm3D,
              self).__init__(num_features, momentum, epsilon, weight_attr,
                             bias_attr, data_format, use_global_stats, name)

    def _check_data_format(self, input):
        if input == 'NCHW' or input == 'NCDHW':
            self._data_format = 'NCHW'
        elif input == "NHWC" or input == "NDHWC":
            self._data_format = 'NHWC'
        else:
            raise ValueError(
                'expected NCDHW, NDHWC or None for data_format input')

    def _check_input_dim(self, input):
        if len(input.shape) != 5:
            raise ValueError('expected 5D input (got {}D input)'.format(
                len(input.shape)))


class SyncBatchNorm(_BatchNormBase):
    r"""
    This interface is used to construct a callable object of the ``SyncBatchNorm`` class.
    It implements the function of the Cross-GPU Synchronized Batch Normalization Layer, and can
    be used as a normalizer function for other operations, such as conv2d and fully connected
    operations.
    The data is normalized by the mean and variance of the channel based on whole mini-batch
    , which including data in all gpus.
    Refer to `Batch Normalization: Accelerating Deep Network Training by Reducing
    Internal Covariate Shift <https://arxiv.org/pdf/1502.03167.pdf>`_
    for more details.

    When model in training mode, the :math:`\\mu_{\\beta}`
    and :math:`\\sigma_{\\beta}^{2}` are the statistics of whole mini-batch data in all gpus.
    Calculated as follows:

    ..  math::

        \mu_{\beta} &\gets \frac{1}{m} \sum_{i=1}^{m} x_i \qquad &//\
        \ mini-batch\ mean \\
        \sigma_{\beta}^{2} &\gets \frac{1}{m} \sum_{i=1}^{m}(x_i - \
        \mu_{\beta})^2 \qquad &//\ mini-batch\ variance \\

    - :math:`x` : whole mini-batch data in all gpus
    - :math:`m` : the size of the whole mini-batch data

    When model in evaluation mode, the :math:`\\mu_{\\beta}`
    and :math:`\sigma_{\beta}^{2}` are global statistics (moving_mean and moving_variance,
    which usually got from the pre-trained model). Global statistics calculated as follows:

    .. math::
        moving\_mean = moving\_mean * momentum + \mu_{\beta} * (1. - momentum) \quad &// global \ mean \\
        moving\_variance = moving\_variance * momentum + \sigma_{\beta}^{2} * (1. - momentum) \quad &// global \ variance \\

    The formula of normalization is as follows:

    ..  math::

        \hat{x_i} &\gets \frac{x_i - \mu_\beta} {\sqrt{\
        \sigma_{\beta}^{2} + \epsilon}} \qquad &//\ normalize \\
        y_i &\gets \gamma \hat{x_i} + \beta \qquad &//\ scale\ and\ shift

    - :math:`\epsilon` : add a smaller value to the variance to prevent division by zero
    - :math:`\gamma` : trainable scale parameter vector
    - :math:`\beta` : trainable shift parameter vector

    Note:
        If you want to use container to pack your model and has ``SyncBatchNorm`` in the
        evaluation phase, please use ``nn.LayerList`` or ``nn.Sequential`` instead of
        ``list`` to pack the model.

    Parameters:
        num_features(int): Indicate the number of channels of the input ``Tensor``.
        epsilon(float, optional): The small value added to the variance to prevent division by zero. Default: 1e-5.
        momentum(float, optional): The value used for the moving_mean and moving_var computation. Default: 0.9.
        weight_attr(ParamAttr|bool, optional): The parameter attribute for Parameter `scale`
             of this layer. If it is set to None or one attribute of ParamAttr, this layerr
             will create ParamAttr as param_attr. If the Initializer of the param_attr
             is not set, the parameter is initialized with ones. If it is set to False,
             this layer will not have trainable scale parameter. Default: None.
        bias_attr(ParamAttr|bool, optional): The parameter attribute for the bias of this layer.
             If it is set to None or one attribute of ParamAttr, this layer
             will create ParamAttr as bias_attr. If the Initializer of the bias_attr
             is not set, the bias is initialized zero. If it is set to False, this layer will not
             have trainable bias parameter. Default: None.

    Shapes:
        input: Tensor that the dimension from 2 to 5.
        output: Tensor with the same shape as input.

    Examples:
        .. code-block:: python

          import paddle
          import paddle.nn as nn
          import numpy as np

          x = np.array([[[[0.3, 0.4], [0.3, 0.07]], [[0.83, 0.37], [0.18, 0.93]]]]).astype('float32')
          x = paddle.to_tensor(x)

          if paddle.is_compiled_with_cuda():
              sync_batch_norm = nn.SyncBatchNorm(2)
              hidden1 = sync_batch_norm(x)
              print(hidden1)
              # [[[[0.26824948, 1.0936325],[0.26824948, -1.6301316]],[[ 0.8095662, -0.665287],[-1.2744656, 1.1301866 ]]]]
    """

    def __init__(self,
                 num_features,
                 momentum=0.9,
                 epsilon=1e-05,
                 weight_attr=None,
                 bias_attr=None,
                 data_format='NCHW',
                 name=None):
        super(SyncBatchNorm,
              self).__init__(num_features, momentum, epsilon, weight_attr,
                             bias_attr, data_format, None, name)

    def _check_data_format(self):
        if self._data_format in ['NCHW', 'NCDHW', 'NC', 'NCL']:
            self._data_format = 'NCHW'
        elif self._data_format in ["NHWC", "NDHWC", 'NLC']:
            self._data_format = 'NHWC'
        else:
            raise ValueError(
                'expected \'NCDHW\', \'NDHWC\', \'NCL\', \'NLC\', \'NC\', \'NCHW\', \'NHWC\' for data_format'
            )

    def forward(self, x):
        self._check_data_format()
        # create output
        # mean and mean_out share the same memory
        mean_out = self._mean
        # variance and variance out share the same memory
        variance_out = self._variance

        ### train mode: use mini-batch stats, eval mode: use global stats
        ### use_global_stats only support False in sync_batch_norm
        if in_dygraph_mode():
            sync_batch_norm_out, _, _, _, _, _ = _C_ops.sync_batch_norm_(
                x, self.weight, self.bias, self._mean, self._variance,
                self._momentum, self._epsilon, self._data_format,
                not self.training, False, False, False)
            return sync_batch_norm_out

        elif in_dynamic_mode():
            attrs = ("momentum", self._momentum, "epsilon", self._epsilon,
                     "is_test", not self.training, "data_layout",
                     self._data_format, "use_mkldnn", False, "fuse_with_relu",
                     False, "use_global_stats", False, 'trainable_statistics',
                     False)
            sync_batch_norm_out, _, _, _, _, _ = _legacy_C_ops.sync_batch_norm(
                x, self.weight, self.bias, self._mean, self._variance, mean_out,
                variance_out, *attrs)
            return sync_batch_norm_out

        check_variable_and_dtype(x, 'input', ['float16', 'float32', 'float64'],
                                 'SyncBatchNorm')

        attrs = {
            "momentum": self._momentum,
            "epsilon": self._epsilon,
            "is_test": not self.training,
            "data_layout": self._data_format,
            "use_mkldnn": False,
            "fuse_with_relu": False,
            "use_global_stats": False,
            "trainable_statistics": False,
        }

        inputs = {
            "X": [x],
            "Scale": [self.weight],
            "Bias": [self.bias],
            "Mean": [self._mean],
            "Variance": [self._variance]
        }

        saved_mean = self._helper.create_variable_for_type_inference(
            dtype=self._dtype, stop_gradient=True)
        saved_variance = self._helper.create_variable_for_type_inference(
            dtype=self._dtype, stop_gradient=True)
        sync_batch_norm_out = self._helper.create_variable_for_type_inference(
            self._dtype)

        outputs = {
            "Y": [sync_batch_norm_out],
            "MeanOut": [mean_out],
            "VarianceOut": [variance_out],
            "SavedMean": [saved_mean],
            "SavedVariance": [saved_variance]
        }

        self._helper.append_op(type="sync_batch_norm",
                               inputs=inputs,
                               outputs=outputs,
                               attrs=attrs)
        return sync_batch_norm_out

    @classmethod
    def convert_sync_batchnorm(cls, layer):
        """
        Helper function to convert :class: `paddle.nn.BatchNorm*d` layers in the model to :class: `paddle.nn.SyncBatchNorm` layers.

        Parameters:
            layer(paddle.nn.Layer): model containing one or more `BatchNorm*d` layers.

        Returns:
            The original model with converted SyncBatchNorm layers. If BatchNorm*d layer in the model, use SyncBatchNorm layer instead.

        Examples:

            .. code-block:: python
                import paddle
                import paddle.nn as nn

                model = nn.Sequential(nn.Conv2D(3, 5, 3), nn.BatchNorm2D(5))
                sync_model = nn.SyncBatchNorm.convert_sync_batchnorm(model)

        """
        layer_output = layer
        if isinstance(layer, _BatchNormBase):
            if layer._weight_attr != None and not isinstance(
                    layer._weight_attr,
                    bool) and layer._weight_attr.name != None:
                layer._weight_attr.name = layer._weight_attr.name + '_sync'
            if layer._bias_attr != None and not isinstance(
                    layer._bias_attr, bool) and layer._bias_attr.name != None:
                layer._bias_attr.name = layer._bias_attr.name + '_sync'

            layer_output = SyncBatchNorm(layer._num_features, layer._momentum,
                                         layer._epsilon, layer._weight_attr,
                                         layer._bias_attr, layer._data_format,
                                         layer._name)

            if layer._weight_attr != False and layer._bias_attr != False:
                with no_grad():
                    layer_output.weight = layer.weight
                    layer_output.bias = layer.bias
            layer_output._mean = layer._mean
            layer_output._variance = layer._variance

        for name, sublayer in layer.named_children():
            layer_output.add_sublayer(name,
                                      cls.convert_sync_batchnorm(sublayer))
        del layer
        return layer_output


class LocalResponseNorm(Layer):
    """
        Local Response Normalization performs a type of "lateral inhibition" by normalizing over local input regions.
        For more information, please refer to `ImageNet Classification with Deep Convolutional Neural Networks <https://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf>`_

        See more details in :ref:`api_paddle_nn_functional_local_response_norm` .

        Parameters:
            size (int): The number of channels to sum over.
            alpha (float, optional): The scaling parameter, positive. Default:1e-4
            beta (float, optional): The exponent, positive. Default:0.75
            k (float, optional): An offset, positive. Default: 1.0
            data_format (str, optional): Specify the data format of the input, and the data format of the output
                will be consistent with that of the input. An optional string from:
                If input is 3-D Tensor, the string could be `"NCL"` or `"NLC"` . When it is `"NCL"`,
                the data is stored in the order of: `[batch_size, input_channels, feature_length]`.
                If input is 4-D Tensor, the string could be  `"NCHW"`, `"NHWC"`. When it is `"NCHW"`,
                the data is stored in the order of: `[batch_size, input_channels, input_height, input_width]`.
                If input is 5-D Tensor, the string could be  `"NCDHW"`, `"NDHWC"` . When it is `"NCDHW"`,
                the data is stored in the order of: `[batch_size, input_channels, input_depth, input_height, input_width]`.
            name (str, optional): Name for the operation (optional, default is None). For more information,
                please refer to :ref:`api_guide_Name`.

        Shape:
            - input: 3-D/4-D/5-D tensor.
            - output: 3-D/4-D/5-D tensor, the same shape as input.

        Examples:

        .. code-block:: python

            import paddle

            x = paddle.rand(shape=(3, 3, 112, 112), dtype="float32")
            m = paddle.nn.LocalResponseNorm(size=5)
            y = m(x)
            print(y.shape)  # [3, 3, 112, 112]
        """

    def __init__(self,
                 size,
                 alpha=0.0001,
                 beta=0.75,
                 k=1.0,
                 data_format="NCHW",
                 name=None):
        super(LocalResponseNorm, self).__init__()
        self.size = size
        self.alpha = alpha
        self.beta = beta
        self.k = k
        self.data_format = data_format
        self.name = name

    def forward(self, input):
        out = F.local_response_norm(input, self.size, self.alpha, self.beta,
                                    self.k, self.data_format, self.name)
        return out

    def extra_repr(self):
        main_str = 'size={}, alpha={}, beta={}, k={}'.format(
            self.size, self.alpha, self.beta, self.k)
        if self.data_format != 'NCHW':
            main_str += ', data_format={}'.format(self.data_format)
        if self.name is not None:
            main_str += ', name={}'.format(self.name)
        return main_str