text: # Copyright 2020 Huawei Technologies Co., Ltd
  #
  # 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"""
  from mindspore.ops import functional as F, composite as C, operations as P
  from mindspore._checkparam import Validator as validator
  from mindspore._checkparam import Rel
  from .optimizer import Optimizer
  
  _rmsprop_opt = C.MultitypeFuncGraph("rmsprop_opt")
  _centered_rmsprop_opt = C.MultitypeFuncGraph("rmsprop_opt")
  
  
  @_rmsprop_opt.register("Function", "Number", "Number", "Number", "Tensor", "Tensor", "Tensor", "Tensor", "Tensor")
  def _rmsprop_opt_(opt, decay, epsilon, momentum, learning_rate, weight, ms, mom, grad):
      """Apply rmsprop optimizer to the weight parameter using dynamic learning rate."""
      success = True
      success = F.depend(success, opt(weight, ms, mom, learning_rate, grad, decay, momentum, epsilon))
      return success
  
  
  @_centered_rmsprop_opt.register("Function", "Number", "Number", "Number", "Tensor", "Tensor", "Tensor", "Tensor",
                                  "Tensor", "Tensor")
  def _centered_rmsprop_opt_(opt, decay, epsilon, momentum, learning_rate, weight, mg, ms, mom, grad):
      """Apply centered rmsprop optimizer to the weight parameter using dynamic learning rate."""
      success = True
      success = F.depend(success, opt(weight, mg, ms, mom, grad, learning_rate, decay, momentum, epsilon))
      return success
  
  
  class RMSProp(Optimizer):
      """
      Implements Root Mean Squared Propagation (RMSProp) algorithm.
  
      Note:
          When separating parameter groups, the weight decay in each group will be applied on the parameters if the
          weight decay is positive. When not separating parameter groups, the `weight_decay` in the API will be applied
          on the parameters without 'beta' or 'gamma' in their names if `weight_decay` is positive.
  
          To improve parameter groups performance, the customized order of parameters can be supported.
  
          Update `params` according to the RMSProp algorithm.
  
          The equation is as follows:
  
          ..  math::
              s_{t} = \\rho s_{t-1} + (1 - \\rho)(\\nabla Q_{i}(w))^2
  
          ..  math::
              m_{t} = \\beta m_{t-1} + \\frac{\\eta} {\\sqrt{s_{t} + \\epsilon}} \\nabla Q_{i}(w)
  
          ..  math::
              w = w - m_{t}
  
          The first equation calculates moving average of the squared gradient for
          each weight. Then dividing the gradient by :math:`\\sqrt{ms_{t} + \\epsilon}`.
  
          if centered is True:
  
          ..  math::
              g_{t} = \\rho g_{t-1} + (1 - \\rho)\\nabla Q_{i}(w)
  
          ..  math::
              s_{t} = \\rho s_{t-1} + (1 - \\rho)(\\nabla Q_{i}(w))^2
  
          ..  math::
              m_{t} = \\beta m_{t-1} + \\frac{\\eta} {\\sqrt{s_{t} - g_{t}^2 + \\epsilon}} \\nabla Q_{i}(w)
  
          ..  math::
              w = w - m_{t}
  
          where :math:`w` represents `params`, which will be updated.
          :math:`g_{t}` is mean gradients, :math:`g_{t-1}` is the last moment of :math:`g_{t}`.
          :math:`s_{t}` is the mean square gradients, :math:`s_{t-1}` is the last moment of :math:`s_{t}`,
          :math:`m_{t}` is moment, the delta of `w`, :math:`m_{t-1}` is the last moment of :math:`m_{t}`.
          :math:`\\rho` represents `decay`. :math:`\\beta` is the momentum term, represents `momentum`.
          :math:`\\epsilon` is a smoothing term to avoid division by zero, represents `epsilon`.
          :math:`\\eta` is learning rate, represents `learning_rate`. :math:`\\nabla Q_{i}(w)` is gradientse,
          represents `gradients`.
  
      Args:
          params (Union[list[Parameter], list[dict]]): When the `params` is a list of `Parameter` which will be updated,
              the element in `params` must be class `Parameter`. When the `params` is a list of `dict`, the "params",
              "lr", "weight_decay" and "order_params" are the keys can be parsed.
  
              - params: Required. The value must be a list of `Parameter`.
  
              - lr: Optional. If "lr" in the keys, the value of corresponding learning rate will be used.
                If not, the `learning_rate` in the API will be used.
  
              - weight_decay: Optional. If "weight_decay" in the keys, the value of corresponding weight decay
                will be used. If not, the `weight_decay` in the API will be used.
  
              - order_params: Optional. If "order_params" in the keys, the value must be the order of parameters and
                the order will be followed in optimizer. There are no other keys in the `dict` and the parameters which
                in the value of 'order_params' must be in one of group parameters.
  
          learning_rate (Union[float, Tensor, Iterable, LearningRateSchedule]): A value or a graph for the learning rate.
              When the learning_rate is an Iterable or a Tensor in a 1D dimension, use dynamic learning rate, then
              the i-th step will take the i-th value as the learning rate. When the learning_rate is LearningRateSchedule,
              use dynamic learning rate, the i-th learning rate will be calculated during the process of training
              according to the formula of LearningRateSchedule. When the learning_rate is a float or a Tensor in a zero
              dimension, use fixed learning rate. Other cases are not supported. The float learning rate must be
              equal to or greater than 0. If the type of `learning_rate` is int, it will be converted to float.
              Default: 0.1.
          decay (float): Decay rate. Should be equal to or greater than 0. Default: 0.9.
          momentum (float): Hyperparameter of type float, means momentum for the moving average. Should be equal to or
                            greater than 0. Default: 0.0.
          epsilon (float): Term added to the denominator to improve numerical stability. Should be greater than
                           0. Default: 1e-10.
          use_locking (bool):  Whether to enable a lock to protect the variable and accumlation tensors from being
                               updated. Default: False.
          centered (bool): If true, gradients are normalized by the estimated variance of the gradient. Default: False.
          loss_scale (float): A floating point value for the loss scale. Should be greater than 0. Default: 1.0.
          weight_decay (float): Weight decay (L2 penalty). Should be equal to or greater than 0. Default: 0.0.
  
      Inputs:
          - **gradients** (tuple[Tensor]) - The gradients of `params`, the shape is the same as `params`.
  
      Outputs:
          Tensor[bool], the value is True.
  
      Examples:
          >>> net = Net()
          >>> #1) All parameters use the same learning rate and weight decay
          >>> optim = nn.RMSProp(params=net.trainable_params(), learning_rate=lr)
          >>>
          >>> #2) Use parameter groups and set different values
          >>> conv_params = list(filter(lambda x: 'conv' in x.name, net.trainable_params()))
          >>> no_conv_params = list(filter(lambda x: 'conv' not in x.name, net.trainable_params()))
          >>> group_params = [{'params': conv_params, 'weight_decay': 0.01},
          >>>                 {'params': no_conv_params, 'lr': 0.01},
          >>>                 {'order_params': net.trainable_params()}]
          >>> optim = nn.RMSProp(group_params, learning_rate=0.1, weight_decay=0.0)
          >>> # The conv_params's parameters will use a learning rate of default value 0.1 and a weight decay of 0.01.
          >>> # The no_conv_params's parameters will use a learning rate of 0.01 and a weight decay of default value 0.0.
          >>> # The final parameters order in which the optimizer will be followed is the value of 'order_params'.
          >>>
          >>> loss = nn.SoftmaxCrossEntropyWithLogits()
          >>> model = Model(net, loss_fn=loss, optimizer=optim)
      """
      def __init__(self, params, learning_rate=0.1, decay=0.9, momentum=0.0, epsilon=1e-10,
                   use_locking=False, centered=False, loss_scale=1.0, weight_decay=0.0):
          super(RMSProp, self).__init__(learning_rate, params, weight_decay, loss_scale)
          validator.check_value_type("decay", decay, [float], self.cls_name)
          validator.check_number_range("decay", decay, 0.0, float("inf"), Rel.INC_LEFT, self.cls_name)
          validator.check_value_type("momentum", momentum, [float], self.cls_name)
          validator.check_number_range("momentum", momentum, 0.0, float("inf"), Rel.INC_LEFT, self.cls_name)
          validator.check_value_type("epsilon", epsilon, [float], self.cls_name)
          validator.check_number_range("epsilon", epsilon, 0.0, float("inf"), Rel.INC_NEITHER, self.cls_name)
          validator.check_value_type("use_locking", use_locking, [bool], self.cls_name)
          validator.check_value_type("centered", centered, [bool], self.cls_name)
  
          self.centered = centered
          if centered:
              self.opt = P.ApplyCenteredRMSProp(use_locking)
              self.mg = self.parameters.clone(prefix="mean_grad", init='zeros')
          else:
              self.opt = P.ApplyRMSProp(use_locking)
  
          self.momentum = momentum
          self.ms = self.parameters.clone(prefix="mean_square", init='ones')
          self.moment = self.parameters.clone(prefix="moment", init='zeros')
          self.hyper_map = C.HyperMap()
          self.epsilon = epsilon
          self.decay = decay
  
      def construct(self, gradients):
          params = self.parameters
          gradients = self.decay_weight(gradients)
          gradients = self.scale_grad(gradients)
          lr = self.get_lr()
          if self.centered:
              if self.is_group_lr:
                  success = self.hyper_map(F.partial(_centered_rmsprop_opt, self.opt, self.decay, self.epsilon,
                                                     self.momentum), lr, params, self.mg, self.ms, self.moment, gradients)
              else:
                  success = self.hyper_map(F.partial(_centered_rmsprop_opt, self.opt, self.decay, self.epsilon,
                                                     self.momentum, lr), params, self.mg, self.ms, self.moment, gradients)
  
          else:
              if self.is_group_lr:
                  success = self.hyper_map(F.partial(_rmsprop_opt, self.opt, self.decay, self.epsilon,
                                                     self.momentum), lr, params, self.ms, self.moment, gradients)
              else:
                  success = self.hyper_map(F.partial(_rmsprop_opt, self.opt, self.decay, self.epsilon,
                                                     self.momentum, lr), params, self.ms, self.moment, gradients)
          return success
  