text: # Copyright 2015 The TensorFlow 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.
  # ==============================================================================
  # pylint: disable=not-callable
  # pylint: disable=redefined-builtin
  """Layers that can merge several inputs into one.
  """
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  from tensorflow.python.keras import backend as K
  from tensorflow.python.keras.engine.base_layer import Layer
  from tensorflow.python.keras.utils import tf_utils
  from tensorflow.python.ops import array_ops
  from tensorflow.python.ops import math_ops
  from tensorflow.python.ops import nn
  from tensorflow.python.util.tf_export import keras_export
  
  
  class _Merge(Layer):
    """Generic merge layer for elementwise merge functions.
  
    Used to implement `Sum`, `Average`, etc.
    """
  
    def __init__(self, **kwargs):
      """Intializes a Merge layer.
  
      Arguments:
        **kwargs: standard layer keyword arguments.
      """
      super(_Merge, self).__init__(**kwargs)
      self.supports_masking = True
      self._supports_ragged_inputs = True
  
    def _merge_function(self, inputs):
      raise NotImplementedError
  
    def _compute_elemwise_op_output_shape(self, shape1, shape2):
      """Computes the shape of the resultant of an elementwise operation.
  
      Arguments:
          shape1: tuple or None. Shape of the first tensor
          shape2: tuple or None. Shape of the second tensor
  
      Returns:
          expected output shape when an element-wise operation is
          carried out on 2 tensors with shapes shape1 and shape2.
          tuple or None.
  
      Raises:
          ValueError: if shape1 and shape2 are not compatible for
              element-wise operations.
      """
      if None in [shape1, shape2]:
        return None
      elif len(shape1) < len(shape2):
        return self._compute_elemwise_op_output_shape(shape2, shape1)
      elif not shape2:
        return shape1
      output_shape = list(shape1[:-len(shape2)])
      for i, j in zip(shape1[-len(shape2):], shape2):
        if i is None or j is None:
          output_shape.append(None)
        elif i == 1:
          output_shape.append(j)
        elif j == 1:
          output_shape.append(i)
        else:
          if i != j:
            raise ValueError(
                'Operands could not be broadcast '
                'together with shapes ' + str(shape1) + ' ' + str(shape2))
          output_shape.append(i)
      return tuple(output_shape)
  
    @tf_utils.shape_type_conversion
    def build(self, input_shape):
      # Used purely for shape validation.
      if not isinstance(input_shape[0], tuple):
        raise ValueError('A merge layer should be called on a list of inputs.')
      if len(input_shape) < 2:
        raise ValueError('A merge layer should be called '
                         'on a list of at least 2 inputs. '
                         'Got ' + str(len(input_shape)) + ' inputs.')
      batch_sizes = {s[0] for s in input_shape if s is not None} - {None}
      if len(batch_sizes) > 1:
        raise ValueError(
            'Can not merge tensors with different '
            'batch sizes. Got tensors with shapes : ' + str(input_shape))
      if input_shape[0] is None:
        output_shape = None
      else:
        output_shape = input_shape[0][1:]
      for i in range(1, len(input_shape)):
        if input_shape[i] is None:
          shape = None
        else:
          shape = input_shape[i][1:]
        output_shape = self._compute_elemwise_op_output_shape(output_shape, shape)
      # If the inputs have different ranks, we have to reshape them
      # to make them broadcastable.
      if None not in input_shape and len(set(map(len, input_shape))) == 1:
        self._reshape_required = False
      else:
        self._reshape_required = True
  
    def call(self, inputs):
      if not isinstance(inputs, (list, tuple)):
        raise ValueError('A merge layer should be called on a list of inputs.')
      if self._reshape_required:
        reshaped_inputs = []
        input_ndims = list(map(K.ndim, inputs))
        if None not in input_ndims:
          # If ranks of all inputs are available,
          # we simply expand each of them at axis=1
          # until all of them have the same rank.
          max_ndim = max(input_ndims)
          for x in inputs:
            x_ndim = K.ndim(x)
            for _ in range(max_ndim - x_ndim):
              x = array_ops.expand_dims(x, axis=1)
            reshaped_inputs.append(x)
          return self._merge_function(reshaped_inputs)
        else:
          # Transpose all inputs so that batch size is the last dimension.
          # (batch_size, dim1, dim2, ... ) -> (dim1, dim2, ... , batch_size)
          transposed = False
          for x in inputs:
            x_ndim = K.ndim(x)
            if x_ndim is None:
              x_shape = array_ops.shape(x)
              batch_size = x_shape[0]
              new_shape = K.concatenate(
                  [x_shape[1:],
                   array_ops.expand_dims(batch_size, axis=-1)])
              x_transposed = array_ops.reshape(
                  x,
                  array_ops.stack(
                      [batch_size, math_ops.reduce_prod(x_shape[1:])], axis=0))
              x_transposed = array_ops.transpose(x_transposed, perm=(1, 0))
              x_transposed = array_ops.reshape(x_transposed, new_shape)
              reshaped_inputs.append(x_transposed)
              transposed = True
            elif x_ndim > 1:
              dims = list(range(1, x_ndim)) + [0]
              reshaped_inputs.append(array_ops.transpose(x, perm=dims))
              transposed = True
            else:
              # We don't transpose inputs if they are 1D vectors or scalars.
              reshaped_inputs.append(x)
          y = self._merge_function(reshaped_inputs)
          y_ndim = K.ndim(y)
          if transposed:
            # If inputs have been transposed, we have to transpose the output too.
            if y_ndim is None:
              y_shape = array_ops.shape(y)
              y_ndim = array_ops.shape(y_shape)[0]
              batch_size = y_shape[y_ndim - 1]
              new_shape = K.concatenate([
                  array_ops.expand_dims(batch_size, axis=-1), y_shape[:y_ndim - 1]
              ])
              y = array_ops.reshape(y, (-1, batch_size))
              y = array_ops.transpose(y, perm=(1, 0))
              y = array_ops.reshape(y, new_shape)
            elif y_ndim > 1:
              dims = [y_ndim - 1] + list(range(y_ndim - 1))
              y = array_ops.transpose(y, perm=dims)
          return y
      else:
        return self._merge_function(inputs)
  
    @tf_utils.shape_type_conversion
    def compute_output_shape(self, input_shape):
      if input_shape[0] is None:
        output_shape = None
      else:
        output_shape = input_shape[0][1:]
      for i in range(1, len(input_shape)):
        if input_shape[i] is None:
          shape = None
        else:
          shape = input_shape[i][1:]
        output_shape = self._compute_elemwise_op_output_shape(output_shape, shape)
      batch_sizes = {s[0] for s in input_shape if s is not None} - {None}
      if len(batch_sizes) == 1:
        output_shape = (list(batch_sizes)[0],) + output_shape
      else:
        output_shape = (None,) + output_shape
      return output_shape
  
    def compute_mask(self, inputs, mask=None):
      if mask is None:
        return None
      if not isinstance(mask, (tuple, list)):
        raise ValueError('`mask` should be a list.')
      if not isinstance(inputs, (tuple, list)):
        raise ValueError('`inputs` should be a list.')
      if len(mask) != len(inputs):
        raise ValueError('The lists `inputs` and `mask` '
                         'should have the same length.')
      if all(m is None for m in mask):
        return None
      masks = [array_ops.expand_dims(m, axis=0) for m in mask if m is not None]
      return K.all(K.concatenate(masks, axis=0), axis=0, keepdims=False)
  
  
  @keras_export('keras.layers.Add')
  class Add(_Merge):
    """Layer that adds a list of inputs.
  
    It takes as input a list of tensors,
    all of the same shape, and returns
    a single tensor (also of the same shape).
  
    Examples:
  
    >>> input_shape = (2, 3, 4)
    >>> x1 = tf.random.normal(input_shape)
    >>> x2 = tf.random.normal(input_shape)
    >>> y = tf.keras.layers.Add()([x1, x2])
    >>> print(y.shape)
    (2, 3, 4)
  
    Used in a functional model:
  
    >>> input1 = tf.keras.layers.Input(shape=(16,))
    >>> x1 = tf.keras.layers.Dense(8, activation='relu')(input1)
    >>> input2 = tf.keras.layers.Input(shape=(32,))
    >>> x2 = tf.keras.layers.Dense(8, activation='relu')(input2)
    >>> # equivalent to `added = tf.keras.layers.add([x1, x2])`
    >>> added = tf.keras.layers.Add()([x1, x2])
    >>> out = tf.keras.layers.Dense(4)(added)
    >>> model = tf.keras.models.Model(inputs=[input1, input2], outputs=out)
  
    """
  
    def _merge_function(self, inputs):
      output = inputs[0]
      for i in range(1, len(inputs)):
        output += inputs[i]
      return output
  
  
  @keras_export('keras.layers.Subtract')
  class Subtract(_Merge):
    """Layer that subtracts two inputs.
  
    It takes as input a list of tensors of size 2,
    both of the same shape, and returns a single tensor, (inputs[0] - inputs[1]),
    also of the same shape.
  
    Examples:
  
    ```python
        import keras
  
        input1 = keras.layers.Input(shape=(16,))
        x1 = keras.layers.Dense(8, activation='relu')(input1)
        input2 = keras.layers.Input(shape=(32,))
        x2 = keras.layers.Dense(8, activation='relu')(input2)
        # Equivalent to subtracted = keras.layers.subtract([x1, x2])
        subtracted = keras.layers.Subtract()([x1, x2])
  
        out = keras.layers.Dense(4)(subtracted)
        model = keras.models.Model(inputs=[input1, input2], outputs=out)
    ```
    """
  
    @tf_utils.shape_type_conversion
    def build(self, input_shape):
      super(Subtract, self).build(input_shape)
      if len(input_shape) != 2:
        raise ValueError('A `Subtract` layer should be called '
                         'on exactly 2 inputs')
  
    def _merge_function(self, inputs):
      if len(inputs) != 2:
        raise ValueError('A `Subtract` layer should be called '
                         'on exactly 2 inputs')
      return inputs[0] - inputs[1]
  
  
  @keras_export('keras.layers.Multiply')
  class Multiply(_Merge):
    """Layer that multiplies (element-wise) a list of inputs.
  
    It takes as input a list of tensors, all of the same shape, and returns
    a single tensor (also of the same shape).
  
    >>> tf.keras.layers.Multiply()([np.arange(5).reshape(5, 1),
    ...                             np.arange(5, 10).reshape(5, 1)])
    <tf.Tensor: shape=(5, 1), dtype=int64, numpy=
    array([[ 0],
         [ 6],
         [14],
         [24],
         [36]])>
  
    >>> x1 = tf.keras.layers.Dense(8)(np.arange(10).reshape(5, 2))
    >>> x2 = tf.keras.layers.Dense(8)(np.arange(10, 20).reshape(5, 2))
    >>> multiplied = tf.keras.layers.Multiply()([x1, x2])
    >>> multiplied.shape
    TensorShape([5, 8])
    """
  
    def _merge_function(self, inputs):
      output = inputs[0]
      for i in range(1, len(inputs)):
        output *= inputs[i]
      return output
  
  
  @keras_export('keras.layers.Average')
  class Average(_Merge):
    """Layer that averages a list of inputs element-wise.
  
    It takes as input a list of tensors, all of the same shape, and returns
    a single tensor (also of the same shape).
  
    Example:
  
    >>> x1 = np.ones((2, 2))
    >>> x2 = np.zeros((2, 2))
    >>> y = tf.keras.layers.Average()([x1, x2])
    >>> y.numpy().tolist()
    [[0.5, 0.5], [0.5, 0.5]]
  
    Usage in a functional model:
  
    >>> input1 = tf.keras.layers.Input(shape=(16,))
    >>> x1 = tf.keras.layers.Dense(8, activation='relu')(input1)
    >>> input2 = tf.keras.layers.Input(shape=(32,))
    >>> x2 = tf.keras.layers.Dense(8, activation='relu')(input2)
    >>> avg = tf.keras.layers.Average()([x1, x2])
    >>> out = tf.keras.layers.Dense(4)(avg)
    >>> model = tf.keras.models.Model(inputs=[input1, input2], outputs=out)
  
    Raises:
      ValueError: If there is a shape mismatch between the inputs and the shapes
        cannot be broadcasted to match.
    """
  
    def _merge_function(self, inputs):
      output = inputs[0]
      for i in range(1, len(inputs)):
        output += inputs[i]
      return output / len(inputs)
  
  
  @keras_export('keras.layers.Maximum')
  class Maximum(_Merge):
    """Layer that computes the maximum (element-wise) a list of inputs.
  
    It takes as input a list of tensors, all of the same shape, and returns
    a single tensor (also of the same shape).
  
    >>> tf.keras.layers.Maximum()([np.arange(5).reshape(5, 1),
    ...                            np.arange(5, 10).reshape(5, 1)])
    <tf.Tensor: shape=(5, 1), dtype=int64, numpy=
    array([[5],
         [6],
         [7],
         [8],
         [9]])>
  
    >>> x1 = tf.keras.layers.Dense(8)(np.arange(10).reshape(5, 2))
    >>> x2 = tf.keras.layers.Dense(8)(np.arange(10, 20).reshape(5, 2))
    >>> maxed = tf.keras.layers.Maximum()([x1, x2])
    >>> maxed.shape
    TensorShape([5, 8])
    """
  
    def _merge_function(self, inputs):
      output = inputs[0]
      for i in range(1, len(inputs)):
        output = math_ops.maximum(output, inputs[i])
      return output
  
  
  @keras_export('keras.layers.Minimum')
  class Minimum(_Merge):
    """Layer that computes the minimum (element-wise) a list of inputs.
  
    It takes as input a list of tensors, all of the same shape, and returns
    a single tensor (also of the same shape).
  
    >>> tf.keras.layers.Minimum()([np.arange(5).reshape(5, 1),
    ...                            np.arange(5, 10).reshape(5, 1)])
    <tf.Tensor: shape=(5, 1), dtype=int64, numpy=
    array([[0],
         [1],
         [2],
         [3],
         [4]])>
  
    >>> x1 = tf.keras.layers.Dense(8)(np.arange(10).reshape(5, 2))
    >>> x2 = tf.keras.layers.Dense(8)(np.arange(10, 20).reshape(5, 2))
    >>> minned = tf.keras.layers.Minimum()([x1, x2])
    >>> minned.shape
    TensorShape([5, 8])
    """
  
    def _merge_function(self, inputs):
      output = inputs[0]
      for i in range(1, len(inputs)):
        output = math_ops.minimum(output, inputs[i])
      return output
  
  
  @keras_export('keras.layers.Concatenate')
  class Concatenate(_Merge):
    """Layer that concatenates a list of inputs.
  
    It takes as input a list of tensors, all of the same shape except
    for the concatenation axis, and returns a single tensor that is the
    concatenation of all inputs.
  
    >>> x = np.arange(20).reshape(2, 2, 5)
    >>> print(x)
    [[[ 0  1  2  3  4]
      [ 5  6  7  8  9]]
     [[10 11 12 13 14]
      [15 16 17 18 19]]]
    >>> y = np.arange(20, 30).reshape(2, 1, 5)
    >>> print(y)
    [[[20 21 22 23 24]]
     [[25 26 27 28 29]]]
    >>> tf.keras.layers.Concatenate(axis=1)([x, y])
    <tf.Tensor: shape=(2, 3, 5), dtype=int64, numpy=
    array([[[ 0,  1,  2,  3,  4],
            [ 5,  6,  7,  8,  9],
            [20, 21, 22, 23, 24]],
           [[10, 11, 12, 13, 14],
            [15, 16, 17, 18, 19],
            [25, 26, 27, 28, 29]]])>
  
    >>> x1 = tf.keras.layers.Dense(8)(np.arange(10).reshape(5, 2))
    >>> x2 = tf.keras.layers.Dense(8)(np.arange(10, 20).reshape(5, 2))
    >>> concatted = tf.keras.layers.Concatenate()([x1, x2])
    >>> concatted.shape
    TensorShape([5, 16])
  
    """
  
    def __init__(self, axis=-1, **kwargs):
      """Instantiates a Concatenate layer.
  
      >>> x = np.arange(20).reshape(2, 2, 5)
      >>> print(x)
      [[[ 0  1  2  3  4]
        [ 5  6  7  8  9]]
       [[10 11 12 13 14]
        [15 16 17 18 19]]]
      >>> y = np.arange(20, 30).reshape(2, 1, 5)
      >>> print(y)
      [[[20 21 22 23 24]]
       [[25 26 27 28 29]]]
      >>> tf.keras.layers.Concatenate(axis=1)([x, y])
      <tf.Tensor: shape=(2, 3, 5), dtype=int64, numpy=
      array([[[ 0,  1,  2,  3,  4],
              [ 5,  6,  7,  8,  9],
              [20, 21, 22, 23, 24]],
             [[10, 11, 12, 13, 14],
              [15, 16, 17, 18, 19],
              [25, 26, 27, 28, 29]]])>
  
      Arguments:
        axis: Axis along which to concatenate.
        **kwargs: standard layer keyword arguments.
      """
      super(Concatenate, self).__init__(**kwargs)
      self.axis = axis
      self.supports_masking = True
      self._reshape_required = False
  
    @tf_utils.shape_type_conversion
    def build(self, input_shape):
      # Used purely for shape validation.
      if not isinstance(input_shape[0], tuple) or len(input_shape) < 2:
        raise ValueError('A `Concatenate` layer should be called '
                         'on a list of at least 2 inputs')
      if all(shape is None for shape in input_shape):
        return
      reduced_inputs_shapes = [list(shape) for shape in input_shape]
      shape_set = set()
      for i in range(len(reduced_inputs_shapes)):
        del reduced_inputs_shapes[i][self.axis]
        shape_set.add(tuple(reduced_inputs_shapes[i]))
  
      if len(shape_set) != 1:
        err_msg = ('A `Concatenate` layer requires inputs with matching shapes '
                   'except for the concat axis. Got inputs shapes: %s' %
                   input_shape)
        # Make sure all the shapes have same ranks.
        ranks = set(len(shape) for shape in shape_set)
        if len(ranks) != 1:
          raise ValueError(err_msg)
        # Get the only rank for the set.
        (rank,) = ranks
        for axis in range(rank):
          # Skip the Nones in the shape since they are dynamic, also the axis for
          # concat has been removed above.
          unique_dims = set(
              shape[axis] for shape in shape_set if shape[axis] is not None)
          if len(unique_dims) > 1:
            raise ValueError(err_msg)
  
    def _merge_function(self, inputs):
      return K.concatenate(inputs, axis=self.axis)
  
    @tf_utils.shape_type_conversion
    def compute_output_shape(self, input_shape):
      if not isinstance(input_shape, (tuple, list)):
        raise ValueError('A `Concatenate` layer should be called '
                         'on a list of inputs.')
      input_shapes = input_shape
      output_shape = list(input_shapes[0])
      for shape in input_shapes[1:]:
        if output_shape[self.axis] is None or shape[self.axis] is None:
          output_shape[self.axis] = None
          break
        output_shape[self.axis] += shape[self.axis]
      return tuple(output_shape)
  
    def compute_mask(self, inputs, mask=None):
      if mask is None:
        return None
      if not isinstance(mask, (tuple, list)):
        raise ValueError('`mask` should be a list.')
      if not isinstance(inputs, (tuple, list)):
        raise ValueError('`inputs` should be a list.')
      if len(mask) != len(inputs):
        raise ValueError('The lists `inputs` and `mask` '
                         'should have the same length.')
      if all(m is None for m in mask):
        return None
      # Make a list of masks while making sure
      # the dimensionality of each mask
      # is the same as the corresponding input.
      masks = []
      for input_i, mask_i in zip(inputs, mask):
        if mask_i is None:
          # Input is unmasked. Append all 1s to masks,
          masks.append(array_ops.ones_like(input_i, dtype='bool'))
        elif K.ndim(mask_i) < K.ndim(input_i):
          # Mask is smaller than the input, expand it
          masks.append(array_ops.expand_dims(mask_i, axis=-1))
        else:
          masks.append(mask_i)
      concatenated = K.concatenate(masks, axis=self.axis)
      return K.all(concatenated, axis=-1, keepdims=False)
  
    def get_config(self):
      config = {
          'axis': self.axis,
      }
      base_config = super(Concatenate, self).get_config()
      return dict(list(base_config.items()) + list(config.items()))
  
  
  @keras_export('keras.layers.Dot')
  class Dot(_Merge):
    """Layer that computes a dot product between samples in two tensors.
  
    E.g. if applied to a list of two tensors `a` and `b` of shape
    `(batch_size, n)`, the output will be a tensor of shape `(batch_size, 1)`
    where each entry `i` will be the dot product between
    `a[i]` and `b[i]`.
  
    >>> x = np.arange(10).reshape(1, 5, 2)
    >>> print(x)
    [[[0 1]
      [2 3]
      [4 5]
      [6 7]
      [8 9]]]
    >>> y = np.arange(10, 20).reshape(1, 2, 5)
    >>> print(y)
    [[[10 11 12 13 14]
      [15 16 17 18 19]]]
    >>> tf.keras.layers.Dot(axes=(1, 2))([x, y])
    <tf.Tensor: shape=(1, 2, 2), dtype=int64, numpy=
    array([[[260, 360],
            [320, 445]]])>
  
    >>> x1 = tf.keras.layers.Dense(8)(np.arange(10).reshape(5, 2))
    >>> x2 = tf.keras.layers.Dense(8)(np.arange(10, 20).reshape(5, 2))
    >>> dotted = tf.keras.layers.Dot(axes=1)([x1, x2])
    >>> dotted.shape
    TensorShape([5, 1])
  
  
    """
  
    def __init__(self, axes, normalize=False, **kwargs):
      """Initializes a layer that computes the element-wise dot product.
  
        >>> x = np.arange(10).reshape(1, 5, 2)
        >>> print(x)
        [[[0 1]
          [2 3]
          [4 5]
          [6 7]
          [8 9]]]
        >>> y = np.arange(10, 20).reshape(1, 2, 5)
        >>> print(y)
        [[[10 11 12 13 14]
          [15 16 17 18 19]]]
        >>> tf.keras.layers.Dot(axes=(1, 2))([x, y])
        <tf.Tensor: shape=(1, 2, 2), dtype=int64, numpy=
        array([[[260, 360],
                [320, 445]]])>
  
      Arguments:
        axes: Integer or tuple of integers,
          axis or axes along which to take the dot product. If a tuple, should
          be two integers corresponding to the desired axis from the first input
          and the desired axis from the second input, respectively. Note that the
          size of the two selected axes must match.
        normalize: Whether to L2-normalize samples along the
          dot product axis before taking the dot product.
          If set to True, then the output of the dot product
          is the cosine proximity between the two samples.
        **kwargs: Standard layer keyword arguments.
      """
      super(Dot, self).__init__(**kwargs)
      if not isinstance(axes, int):
        if not isinstance(axes, (list, tuple)):
          raise TypeError('Invalid type for `axes` - '
                          'should be a list or an int.')
        if len(axes) != 2:
          raise ValueError('Invalid format for `axes` - '
                           'should contain two elements.')
        if not isinstance(axes[0], int) or not isinstance(axes[1], int):
          raise ValueError('Invalid format for `axes` - '
                           'list elements should be "int".')
      self.axes = axes
      self.normalize = normalize
      self.supports_masking = True
      self._reshape_required = False
      self._supports_ragged_inputs = False
  
    @tf_utils.shape_type_conversion
    def build(self, input_shape):
      # Used purely for shape validation.
      if not isinstance(input_shape[0], tuple) or len(input_shape) != 2:
        raise ValueError('A `Dot` layer should be called '
                         'on a list of 2 inputs.')
      shape1 = input_shape[0]
      shape2 = input_shape[1]
      if shape1 is None or shape2 is None:
        return
      if isinstance(self.axes, int):
        if self.axes < 0:
          axes = [self.axes % len(shape1), self.axes % len(shape2)]
        else:
          axes = [self.axes] * 2
      else:
        axes = self.axes
      if shape1[axes[0]] != shape2[axes[1]]:
        raise ValueError('Dimension incompatibility '
                         '%s != %s. ' % (shape1[axes[0]], shape2[axes[1]]) +
                         'Layer shapes: %s, %s. ' % (shape1, shape2) +
                         'Chosen axes: %s, %s' % (axes[0], axes[1]))
  
    def _merge_function(self, inputs):
      if len(inputs) != 2:
        raise ValueError('A `Dot` layer should be called on exactly 2 inputs')
      x1 = inputs[0]
      x2 = inputs[1]
      if isinstance(self.axes, int):
        if self.axes < 0:
          axes = [self.axes % K.ndim(x1), self.axes % K.ndim(x2)]
        else:
          axes = [self.axes] * 2
      else:
        axes = []
        for i in range(len(self.axes)):
          if self.axes[i] < 0:
            axes.append(self.axes[i] % K.ndim(inputs[i]))
          else:
            axes.append(self.axes[i])
      if self.normalize:
        x1 = nn.l2_normalize(x1, axis=axes[0])
        x2 = nn.l2_normalize(x2, axis=axes[1])
      output = K.batch_dot(x1, x2, axes)
      return output
  
    @tf_utils.shape_type_conversion
    def compute_output_shape(self, input_shape):
      if not isinstance(input_shape, (tuple, list)) or len(input_shape) != 2:
        raise ValueError('A `Dot` layer should be called '
                         'on a list of 2 inputs.')
      shape1 = list(input_shape[0])
      shape2 = list(input_shape[1])
      if isinstance(self.axes, int):
        if self.axes < 0:
          axes = [self.axes % len(shape1), self.axes % len(shape2)]
        else:
          axes = [self.axes] * 2
      else:
        axes = self.axes
      shape1.pop(axes[0])
      shape2.pop(axes[1])
      shape2.pop(0)
      output_shape = shape1 + shape2
      if len(output_shape) == 1:
        output_shape += [1]
      return tuple(output_shape)
  
    def compute_mask(self, inputs, mask=None):
      return None
  
    def get_config(self):
      config = {
          'axes': self.axes,
          'normalize': self.normalize,
      }
      base_config = super(Dot, self).get_config()
      return dict(list(base_config.items()) + list(config.items()))
  
  
  @keras_export('keras.layers.add')
  def add(inputs, **kwargs):
    """Functional interface to the `tf.keras.layers.Add` layer.
  
    Arguments:
        inputs: A list of input tensors (at least 2) with the same shape.
        **kwargs: Standard layer keyword arguments.
  
    Returns:
        A tensor as the sum of the inputs. It has the same shape as the inputs.
  
    Examples:
  
    >>> input_shape = (2, 3, 4)
    >>> x1 = tf.random.normal(input_shape)
    >>> x2 = tf.random.normal(input_shape)
    >>> y = tf.keras.layers.add([x1, x2])
    >>> print(y.shape)
    (2, 3, 4)
  
    Used in a functiona model:
  
    >>> input1 = tf.keras.layers.Input(shape=(16,))
    >>> x1 = tf.keras.layers.Dense(8, activation='relu')(input1)
    >>> input2 = tf.keras.layers.Input(shape=(32,))
    >>> x2 = tf.keras.layers.Dense(8, activation='relu')(input2)
    >>> added = tf.keras.layers.add([x1, x2])
    >>> out = tf.keras.layers.Dense(4)(added)
    >>> model = tf.keras.models.Model(inputs=[input1, input2], outputs=out)
  
    """
    return Add(**kwargs)(inputs)
  
  
  @keras_export('keras.layers.subtract')
  def subtract(inputs, **kwargs):
    """Functional interface to the `Subtract` layer.
  
    Arguments:
        inputs: A list of input tensors (exactly 2).
        **kwargs: Standard layer keyword arguments.
  
    Returns:
        A tensor, the difference of the inputs.
  
    Examples:
  
    ```python
        import keras
  
        input1 = keras.layers.Input(shape=(16,))
        x1 = keras.layers.Dense(8, activation='relu')(input1)
        input2 = keras.layers.Input(shape=(32,))
        x2 = keras.layers.Dense(8, activation='relu')(input2)
        subtracted = keras.layers.subtract([x1, x2])
  
        out = keras.layers.Dense(4)(subtracted)
        model = keras.models.Model(inputs=[input1, input2], outputs=out)
    ```
    """
    return Subtract(**kwargs)(inputs)
  
  
  @keras_export('keras.layers.multiply')
  def multiply(inputs, **kwargs):
    """Functional interface to the `Multiply` layer.
  
    Arguments:
        inputs: A list of input tensors (at least 2).
        **kwargs: Standard layer keyword arguments.
  
    Returns:
        A tensor, the element-wise product of the inputs.
    """
    return Multiply(**kwargs)(inputs)
  
  
  @keras_export('keras.layers.average')
  def average(inputs, **kwargs):
    """Functional interface to the `tf.keras.layers.Average` layer.
  
    Example:
  
    >>> x1 = np.ones((2, 2))
    >>> x2 = np.zeros((2, 2))
    >>> y = tf.keras.layers.Average()([x1, x2])
    >>> y.numpy().tolist()
    [[0.5, 0.5], [0.5, 0.5]]
  
    Usage in a functional model:
  
    >>> input1 = tf.keras.layers.Input(shape=(16,))
    >>> x1 = tf.keras.layers.Dense(8, activation='relu')(input1)
    >>> input2 = tf.keras.layers.Input(shape=(32,))
    >>> x2 = tf.keras.layers.Dense(8, activation='relu')(input2)
    >>> avg = tf.keras.layers.Average()([x1, x2])
    >>> out = tf.keras.layers.Dense(4)(avg)
    >>> model = tf.keras.models.Model(inputs=[input1, input2], outputs=out)
  
    Arguments:
        inputs: A list of input tensors (at least 2).
        **kwargs: Standard layer keyword arguments.
  
    Returns:
        A tensor, the average of the inputs.
  
    Raises:
      ValueError: If there is a shape mismatch between the inputs and the shapes
        cannot be broadcasted to match.
    """
    return Average(**kwargs)(inputs)
  
  
  @keras_export('keras.layers.maximum')
  def maximum(inputs, **kwargs):
    """Functional interface to compute maximum (element-wise) list of `inputs`.
  
    This is equivalent to the `tf.keras.layers.Maximum` layer.
  
    For example:
  
    ```python
    input1 = tf.keras.layers.Input(shape=(16,))
    x1 = tf.keras.layers.Dense(8, activation='relu')(input1) #shape=(None, 8)
    input2 = tf.keras.layers.Input(shape=(32,))
    x2 = tf.keras.layers.Dense(8, activation='relu')(input2) #shape=(None, 8)
    max_inp=tf.keras.layers.maximum([x1,x2]) #shape=(None, 8)
    out = tf.keras.layers.Dense(4)(max_inp)
    model = tf.keras.models.Model(inputs=[input1, input2], outputs=out)
    ```
  
    Arguments:
        inputs: A list of input tensors (at least 2) of same shape.
        **kwargs: Standard layer keyword arguments.
  
    Returns:
        A tensor (of same shape as input tensor) with the element-wise
        maximum of the inputs.
  
    Raises:
        ValueError: If input tensors are of different shape.
    """
    return Maximum(**kwargs)(inputs)
  
  
  @keras_export('keras.layers.minimum')
  def minimum(inputs, **kwargs):
    """Functional interface to the `Minimum` layer.
  
    Arguments:
        inputs: A list of input tensors (at least 2).
        **kwargs: Standard layer keyword arguments.
  
    Returns:
        A tensor, the element-wise minimum of the inputs.
    """
    return Minimum(**kwargs)(inputs)
  
  
  @keras_export('keras.layers.concatenate')
  def concatenate(inputs, axis=-1, **kwargs):
    """Functional interface to the `Concatenate` layer.
  
    >>> x = np.arange(20).reshape(2, 2, 5)
    >>> print(x)
    [[[ 0  1  2  3  4]
      [ 5  6  7  8  9]]
     [[10 11 12 13 14]
      [15 16 17 18 19]]]
    >>> y = np.arange(20, 30).reshape(2, 1, 5)
    >>> print(y)
    [[[20 21 22 23 24]]
     [[25 26 27 28 29]]]
    >>> tf.keras.layers.concatenate([x, y],
    ...                             axis=1)
    <tf.Tensor: shape=(2, 3, 5), dtype=int64, numpy=
    array([[[ 0,  1,  2,  3,  4],
          [ 5,  6,  7,  8,  9],
          [20, 21, 22, 23, 24]],
         [[10, 11, 12, 13, 14],
          [15, 16, 17, 18, 19],
          [25, 26, 27, 28, 29]]])>
  
    Arguments:
        inputs: A list of input tensors (at least 2).
        axis: Concatenation axis.
        **kwargs: Standard layer keyword arguments.
  
    Returns:
        A tensor, the concatenation of the inputs alongside axis `axis`.
    """
    return Concatenate(axis=axis, **kwargs)(inputs)
  
  
  @keras_export('keras.layers.dot')
  def dot(inputs, axes, normalize=False, **kwargs):
    """Functional interface to the `Dot` layer.
  
    Arguments:
        inputs: A list of input tensors (at least 2).
        axes: Integer or tuple of integers,
            axis or axes along which to take the dot product.
        normalize: Whether to L2-normalize samples along the
            dot product axis before taking the dot product.
            If set to True, then the output of the dot product
            is the cosine proximity between the two samples.
        **kwargs: Standard layer keyword arguments.
  
    Returns:
        A tensor, the dot product of the samples from the inputs.
    """
    return Dot(axes=axes, normalize=normalize, **kwargs)(inputs)
  