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.
  # ==============================================================================
  
  """Momentum for TensorFlow."""
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  from tensorflow.python.framework import ops
  from tensorflow.python.ops import math_ops
  from tensorflow.python.training import optimizer
  from tensorflow.python.training import training_ops
  from tensorflow.python.util.tf_export import tf_export
  
  
  @tf_export("train.MomentumOptimizer")
  class MomentumOptimizer(optimizer.Optimizer):
    """Optimizer that implements the Momentum algorithm.
  
    Computes (if `use_nesterov = False`):
  
    ```
    accumulation = momentum * accumulation + gradient
    variable -= learning_rate * accumulation
    ```
  
    Note that in the dense version of this algorithm, `accumulation` is updated
    and applied regardless of a gradient's value, whereas the sparse version (when
    the gradient is an `IndexedSlices`, typically because of `tf.gather` or an
    embedding) only updates variable slices and corresponding `accumulation` terms
    when that part of the variable was used in the forward pass.
    """
  
    def __init__(self, learning_rate, momentum,
                 use_locking=False, name="Momentum", use_nesterov=False):
      """Construct a new Momentum optimizer.
  
      Args:
        learning_rate: A `Tensor` or a floating point value.  The learning rate.
        momentum: A `Tensor` or a floating point value.  The momentum.
        use_locking: If `True` use locks for update operations.
        name: Optional name prefix for the operations created when applying
          gradients.  Defaults to "Momentum".
        use_nesterov: If `True` use Nesterov Momentum.
          See [Sutskever et al., 2013](
          http://jmlr.org/proceedings/papers/v28/sutskever13.pdf).
          This implementation always computes gradients at the value of the
          variable(s) passed to the optimizer. Using Nesterov Momentum makes the
          variable(s) track the values called `theta_t + mu*v_t` in the paper.
  
      @compatibility(eager)
      When eager execution is enabled, `learning_rate` and `momentum` can each be
      a callable that takes no arguments and returns the actual value to use. This
      can be useful for changing these values across different invocations of
      optimizer functions.
      @end_compatibility
      """
      super(MomentumOptimizer, self).__init__(use_locking, name)
      self._learning_rate = learning_rate
      self._momentum = momentum
      self._use_nesterov = use_nesterov
  
    def _create_slots(self, var_list):
      for v in var_list:
        self._zeros_slot(v, "momentum", self._name)
  
    def _prepare(self):
      learning_rate = self._learning_rate
      if callable(learning_rate):
        learning_rate = learning_rate()
      self._learning_rate_tensor = ops.convert_to_tensor(learning_rate,
                                                         name="learning_rate")
      momentum = self._momentum
      if callable(momentum):
        momentum = momentum()
      self._momentum_tensor = ops.convert_to_tensor(momentum, name="momentum")
  
    def _apply_dense(self, grad, var):
      mom = self.get_slot(var, "momentum")
      return training_ops.apply_momentum(
          var, mom,
          math_ops.cast(self._learning_rate_tensor, var.dtype.base_dtype),
          grad,
          math_ops.cast(self._momentum_tensor, var.dtype.base_dtype),
          use_locking=self._use_locking,
          use_nesterov=self._use_nesterov).op
  
    def _resource_apply_dense(self, grad, var):
      mom = self.get_slot(var, "momentum")
      return training_ops.resource_apply_momentum(
          var.handle, mom.handle,
          math_ops.cast(self._learning_rate_tensor, grad.dtype.base_dtype),
          grad,
          math_ops.cast(self._momentum_tensor, grad.dtype.base_dtype),
          use_locking=self._use_locking,
          use_nesterov=self._use_nesterov)
  
    def _apply_sparse(self, grad, var):
      mom = self.get_slot(var, "momentum")
      return training_ops.sparse_apply_momentum(
          var, mom,
          math_ops.cast(self._learning_rate_tensor, var.dtype.base_dtype),
          grad.values, grad.indices,
          math_ops.cast(self._momentum_tensor, var.dtype.base_dtype),
          use_locking=self._use_locking,
          use_nesterov=self._use_nesterov).op
  
    def _resource_apply_sparse(self, grad, var, indices):
      mom = self.get_slot(var, "momentum")
      return training_ops.resource_sparse_apply_momentum(
          var.handle, mom.handle,
          math_ops.cast(self._learning_rate_tensor, grad.dtype),
          grad, indices,
          math_ops.cast(self._momentum_tensor, grad.dtype),
          use_locking=self._use_locking,
          use_nesterov=self._use_nesterov)
  