text: # Copyright 2020 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.
  # ==============================================================================
  """RMSprop optimizer implementation."""
  # pylint: disable=g-classes-have-attributes
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  import numpy as np
  
  from tensorflow.python.framework import ops
  from tensorflow.python.keras import backend_config
  from tensorflow.python.keras.optimizer_v2 import optimizer_v2
  from tensorflow.python.ops import array_ops
  from tensorflow.python.ops import control_flow_ops
  from tensorflow.python.ops import math_ops
  from tensorflow.python.ops import state_ops
  from tensorflow.python.training import gen_training_ops
  from tensorflow.python.util.tf_export import keras_export
  
  
  @keras_export("keras.optimizers.RMSprop")
  class RMSprop(optimizer_v2.OptimizerV2):
    r"""Optimizer that implements the RMSprop algorithm.
  
    The gist of RMSprop is to:
  
    - Maintain a moving (discounted) average of the square of gradients
    - Divide the gradient by the root of this average
  
    This implementation of RMSprop uses plain momentum, not Nesterov momentum.
  
    The centered version additionally maintains a moving average of the
    gradients, and uses that average to estimate the variance.
  
    Args:
      learning_rate: A `Tensor`, floating point value, or a schedule that is a
        `tf.keras.optimizers.schedules.LearningRateSchedule`, or a callable
        that takes no arguments and returns the actual value to use. The
        learning rate. Defeaults to 0.001.
      rho: Discounting factor for the history/coming gradient. Defaults to 0.9.
      momentum: A scalar or a scalar `Tensor`. Defaults to 0.0.
      epsilon: A small constant for numerical stability. This epsilon is
        "epsilon hat" in the Kingma and Ba paper (in the formula just before
        Section 2.1), not the epsilon in Algorithm 1 of the paper. Defaults to
        1e-7.
      centered: Boolean. If `True`, gradients are normalized by the estimated
        variance of the gradient; if False, by the uncentered second moment.
        Setting this to `True` may help with training, but is slightly more
        expensive in terms of computation and memory. Defaults to `False`.
      name: Optional name prefix for the operations created when applying
        gradients. Defaults to `"RMSprop"`.
      **kwargs: Keyword arguments. Allowed to be one of
        `"clipnorm"` or `"clipvalue"`.
        `"clipnorm"` (float) clips gradients by norm; `"clipvalue"` (float) clips
        gradients by value.
  
    Note that in the dense implementation of this algorithm, variables and their
    corresponding accumulators (momentum, gradient moving average, square
    gradient moving average) will be updated even if the gradient is zero
    (i.e. accumulators will decay, momentum will be applied). The sparse
    implementation (used when the gradient is an `IndexedSlices` object,
    typically because of `tf.gather` or an embedding lookup in the forward pass)
    will not update variable slices or their accumulators unless those slices
    were used in the forward pass (nor is there an "eventual" correction to
    account for these omitted updates). This leads to more efficient updates for
    large embedding lookup tables (where most of the slices are not accessed in
    a particular graph execution), but differs from the published algorithm.
  
    Usage:
  
    >>> opt = tf.keras.optimizers.RMSprop(learning_rate=0.1)
    >>> var1 = tf.Variable(10.0)
    >>> loss = lambda: (var1 ** 2) / 2.0    # d(loss) / d(var1) = var1
    >>> step_count = opt.minimize(loss, [var1]).numpy()
    >>> var1.numpy()
    9.683772
  
    Reference:
      - [Hinton, 2012](
        http://www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf)
    """
  
    _HAS_AGGREGATE_GRAD = True
  
    def __init__(self,
                 learning_rate=0.001,
                 rho=0.9,
                 momentum=0.0,
                 epsilon=1e-7,
                 centered=False,
                 name="RMSprop",
                 **kwargs):
      """Construct a new RMSprop optimizer.
  
      Args:
        learning_rate: A `Tensor`, floating point value, or a schedule that is a
          `tf.keras.optimizers.schedules.LearningRateSchedule`, or a callable
          that takes no arguments and returns the actual value to use. The
          learning rate. Defeaults to 0.001.
        rho: Discounting factor for the history/coming gradient. Defaults to 0.9.
        momentum: A scalar or a scalar `Tensor`. Defaults to 0.0.
        epsilon: A small constant for numerical stability. This epsilon is
          "epsilon hat" in the Kingma and Ba paper (in the formula just before
          Section 2.1), not the epsilon in Algorithm 1 of the paper. Defaults to
          1e-7.
        centered: Boolean. If `True`, gradients are normalized by the estimated
          variance of the gradient; if False, by the uncentered second moment.
          Setting this to `True` may help with training, but is slightly more
          expensive in terms of computation and memory. Defaults to `False`.
        name: Optional name prefix for the operations created when applying
          gradients. Defaults to "RMSprop".
        **kwargs: keyword arguments. Allowed to be {`clipnorm`, `clipvalue`, `lr`,
          `decay`}. `clipnorm` is clip gradients by norm; `clipvalue` is clip
          gradients by value, `decay` is included for backward compatibility to
          allow time inverse decay of learning rate. `lr` is included for backward
          compatibility, recommended to use `learning_rate` instead.
  
      @compatibility(eager)
      When eager execution is enabled, `learning_rate`, `decay`, `momentum`, and
      `epsilon` 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(RMSprop, self).__init__(name, **kwargs)
      self._set_hyper("learning_rate", kwargs.get("lr", learning_rate))
      self._set_hyper("decay", self._initial_decay)
      self._set_hyper("rho", rho)
  
      self._momentum = False
      if isinstance(momentum, ops.Tensor) or callable(momentum) or momentum > 0:
        self._momentum = True
      if isinstance(momentum, (int, float)) and (momentum < 0 or momentum > 1):
        raise ValueError("`momentum` must be between [0, 1].")
      self._set_hyper("momentum", momentum)
  
      self.epsilon = epsilon or backend_config.epsilon()
      self.centered = centered
  
    def _create_slots(self, var_list):
      for var in var_list:
        self.add_slot(var, "rms")
      if self._momentum:
        for var in var_list:
          self.add_slot(var, "momentum")
      if self.centered:
        for var in var_list:
          self.add_slot(var, "mg")
  
    def _prepare_local(self, var_device, var_dtype, apply_state):
      super(RMSprop, self)._prepare_local(var_device, var_dtype, apply_state)
  
      rho = array_ops.identity(self._get_hyper("rho", var_dtype))
      apply_state[(var_device, var_dtype)].update(
          dict(
              neg_lr_t=-apply_state[(var_device, var_dtype)]["lr_t"],
              epsilon=ops.convert_to_tensor_v2_with_dispatch(
                  self.epsilon, var_dtype),
              rho=rho,
              momentum=array_ops.identity(self._get_hyper("momentum", var_dtype)),
              one_minus_rho=1. - rho))
  
    def _resource_apply_dense(self, grad, var, apply_state=None):
      var_device, var_dtype = var.device, var.dtype.base_dtype
      coefficients = ((apply_state or {}).get((var_device, var_dtype))
                      or self._fallback_apply_state(var_device, var_dtype))
  
      rms = self.get_slot(var, "rms")
      if self._momentum:
        mom = self.get_slot(var, "momentum")
        if self.centered:
          mg = self.get_slot(var, "mg")
          return gen_training_ops.ResourceApplyCenteredRMSProp(
              var=var.handle,
              mg=mg.handle,
              ms=rms.handle,
              mom=mom.handle,
              lr=coefficients["lr_t"],
              rho=coefficients["rho"],
              momentum=coefficients["momentum"],
              epsilon=coefficients["epsilon"],
              grad=grad,
              use_locking=self._use_locking)
        else:
          return gen_training_ops.ResourceApplyRMSProp(
              var=var.handle,
              ms=rms.handle,
              mom=mom.handle,
              lr=coefficients["lr_t"],
              rho=coefficients["rho"],
              momentum=coefficients["momentum"],
              epsilon=coefficients["epsilon"],
              grad=grad,
              use_locking=self._use_locking)
      else:
        rms_t = (coefficients["rho"] * rms +
                 coefficients["one_minus_rho"] * math_ops.square(grad))
        rms_t = state_ops.assign(rms, rms_t, use_locking=self._use_locking)
        denom_t = rms_t
        if self.centered:
          mg = self.get_slot(var, "mg")
          mg_t = coefficients["rho"] * mg + coefficients["one_minus_rho"] * grad
          mg_t = state_ops.assign(mg, mg_t, use_locking=self._use_locking)
          denom_t = rms_t - math_ops.square(mg_t)
        var_t = var - coefficients["lr_t"] * grad / (
            math_ops.sqrt(denom_t) + coefficients["epsilon"])
        return state_ops.assign(var, var_t, use_locking=self._use_locking).op
  
    def _resource_apply_sparse(self, grad, var, indices, apply_state=None):
      var_device, var_dtype = var.device, var.dtype.base_dtype
      coefficients = ((apply_state or {}).get((var_device, var_dtype))
                      or self._fallback_apply_state(var_device, var_dtype))
  
      rms = self.get_slot(var, "rms")
      if self._momentum:
        mom = self.get_slot(var, "momentum")
        if self.centered:
          mg = self.get_slot(var, "mg")
          return gen_training_ops.ResourceSparseApplyCenteredRMSProp(
              var=var.handle,
              mg=mg.handle,
              ms=rms.handle,
              mom=mom.handle,
              lr=coefficients["lr_t"],
              rho=coefficients["rho"],
              momentum=coefficients["momentum"],
              epsilon=coefficients["epsilon"],
              grad=grad,
              indices=indices,
              use_locking=self._use_locking)
        else:
          return gen_training_ops.ResourceSparseApplyRMSProp(
              var=var.handle,
              ms=rms.handle,
              mom=mom.handle,
              lr=coefficients["lr_t"],
              rho=coefficients["rho"],
              momentum=coefficients["momentum"],
              epsilon=coefficients["epsilon"],
              grad=grad,
              indices=indices,
              use_locking=self._use_locking)
      else:
        rms_scaled_g_values = (grad * grad) * coefficients["one_minus_rho"]
        rms_t = state_ops.assign(rms, rms * coefficients["rho"],
                                 use_locking=self._use_locking)
        with ops.control_dependencies([rms_t]):
          rms_t = self._resource_scatter_add(rms, indices, rms_scaled_g_values)
          rms_slice = array_ops.gather(rms_t, indices)
        denom_slice = rms_slice
        if self.centered:
          mg = self.get_slot(var, "mg")
          mg_scaled_g_values = grad * coefficients["one_minus_rho"]
          mg_t = state_ops.assign(mg, mg * coefficients["rho"],
                                  use_locking=self._use_locking)
          with ops.control_dependencies([mg_t]):
            mg_t = self._resource_scatter_add(mg, indices, mg_scaled_g_values)
            mg_slice = array_ops.gather(mg_t, indices)
            denom_slice = rms_slice - math_ops.square(mg_slice)
        var_update = self._resource_scatter_add(
            var, indices, coefficients["neg_lr_t"] * grad / (
                math_ops.sqrt(denom_slice) + coefficients["epsilon"]))
        if self.centered:
          return control_flow_ops.group(*[var_update, rms_t, mg_t])
        return control_flow_ops.group(*[var_update, rms_t])
  
    def set_weights(self, weights):
      params = self.weights
      # Override set_weights for backward compatibility of Keras V1 optimizer
      # since it does not include iteration at head of the weight list. Set
      # iteration to 0.
      if len(params) == len(weights) + 1:
        weights = [np.array(0)] + weights
      super(RMSprop, self).set_weights(weights)
  
    def get_config(self):
      config = super(RMSprop, self).get_config()
      config.update({
          "learning_rate": self._serialize_hyperparameter("learning_rate"),
          "decay": self._serialize_hyperparameter("decay"),
          "rho": self._serialize_hyperparameter("rho"),
          "momentum": self._serialize_hyperparameter("momentum"),
          "epsilon": self.epsilon,
          "centered": self.centered,
      })
      return config
  
  
  RMSProp = RMSprop
  