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.
  # ============================================================================
  """adam"""
  import numpy as np
  
  from mindspore.common import dtype as mstype
  from mindspore.common.initializer import initializer
  from mindspore.ops import operations as P
  from mindspore.ops import composite as C
  from mindspore.ops import functional as F
  from mindspore.common.parameter import Parameter
  from mindspore.common.tensor import Tensor
  from mindspore._checkparam import Validator as validator
  from mindspore._checkparam import Rel
  from .optimizer import Optimizer
  
  _adam_opt = C.MultitypeFuncGraph("adam_opt")
  _scaler_one = Tensor(1, mstype.int32)
  _scaler_ten = Tensor(10, mstype.float32)
  
  
  @_adam_opt.register("Tensor", "Tensor", "Tensor", "Tensor", "Number", "Tensor", "Tensor", "Tensor",
                      "Tensor", "Bool", "Bool")
  def _update_run_op(beta1, beta2, eps, lr, weight_decay, param, m, v, gradient, decay_flag, optim_filter):
      """
      Update parameters.
  
      Args:
          beta1 (Tensor): The exponential decay rate for the 1st moment estimations. Should be in range (0.0, 1.0).
          beta2 (Tensor): The exponential decay rate for the 2nd moment estimations. Should be in range (0.0, 1.0).
          eps (Tensor): Term added to the denominator to improve numerical stability. Should be greater than 0.
          lr (Tensor): Learning rate.
          weight_decay (Number): Weight decay. Should be equal to or greater than 0.
          param (Tensor): Parameters.
          m (Tensor): m value of parameters.
          v (Tensor): v value of parameters.
          gradient (Tensor): Gradient of parameters.
          decay_flag (bool): Applies weight decay or not.
          optim_filter (bool): Applies parameter update or not.
  
      Returns:
          Tensor, the new value of v after updating.
      """
      if optim_filter:
          op_mul = P.Mul()
          op_square = P.Square()
          op_sqrt = P.Sqrt()
          op_cast = P.Cast()
          op_reshape = P.Reshape()
          op_shape = P.Shape()
  
          param_fp32 = op_cast(param, mstype.float32)
          m_fp32 = op_cast(m, mstype.float32)
          v_fp32 = op_cast(v, mstype.float32)
          gradient_fp32 = op_cast(gradient, mstype.float32)
  
          next_m = op_mul(beta1, m_fp32) + op_mul(op_cast(F.tuple_to_array((1.0,)), mstype.float32)
                                                  - beta1, gradient_fp32)
  
          next_v = op_mul(beta2, v_fp32) + op_mul(op_cast(F.tuple_to_array((1.0,)), mstype.float32)
                                                  - beta2, op_square(gradient_fp32))
  
          update = next_m / (eps + op_sqrt(next_v))
          if decay_flag:
              update = op_mul(weight_decay, param_fp32) + update
  
          update_with_lr = op_mul(lr, update)
          next_param = param_fp32 - op_reshape(update_with_lr, op_shape(param_fp32))
  
          next_param = F.depend(next_param, F.assign(param, op_cast(next_param, F.dtype(param))))
          next_param = F.depend(next_param, F.assign(m, op_cast(next_m, F.dtype(m))))
          next_param = F.depend(next_param, F.assign(v, op_cast(next_v, F.dtype(v))))
  
          return op_cast(next_param, F.dtype(param))
      return gradient
  
  
  @_adam_opt.register("Function", "Function", "Function", "Function", "Bool", "Bool", "Bool", "Tensor", "Tensor",
                      "Tensor", "Tensor", "Tensor", "Tensor", "RowTensor", "Tensor", "Tensor", "Tensor", "Bool", "Bool")
  def _run_opt_with_sparse(opt, sparse_opt, push, pull, use_locking, use_nesterov, target, beta1_power,
                           beta2_power, beta1, beta2, eps, lr, gradient, param, m, v, ps_parameter, cache_enable):
      """Apply sparse adam optimizer to the weight parameter when the gradient is sparse."""
      success = True
      indices = gradient.indices
      values = gradient.values
      if ps_parameter and not cache_enable:
          op_shape = P.Shape()
          shapes = (op_shape(param), op_shape(m), op_shape(v),
                    op_shape(beta1_power), op_shape(beta2_power), op_shape(lr), op_shape(beta1),
                    op_shape(beta2), op_shape(eps), op_shape(values), op_shape(indices))
          success = F.depend(success, pull(push((beta1_power, beta2_power, lr, beta1, beta2,
                                                 eps, values, indices), shapes), param))
          return success
  
      if not target:
          success = F.depend(success, sparse_opt(param, m, v, beta1_power, beta2_power, lr, beta1, beta2,
                                                 eps, values, indices))
      else:
          op_mul = P.Mul()
          op_square = P.Square()
          op_sqrt = P.Sqrt()
          scatter_add = P.ScatterAdd(use_locking)
  
          success = F.depend(success, F.assign(m, op_mul(beta1, m)))
          success = F.depend(success, F.assign(v, op_mul(beta2, v)))
  
          grad_indices = gradient.indices
          grad_value = gradient.values
  
          next_m = scatter_add(m,
                               grad_indices,
                               op_mul(F.tuple_to_array((1.0,)) - beta1, grad_value))
  
          next_v = scatter_add(v,
                               grad_indices,
                               op_mul(F.tuple_to_array((1.0,)) - beta2, op_square(grad_value)))
  
          if use_nesterov:
              m_temp = next_m * _scaler_ten
              F.assign(m, op_mul(beta1, next_m))
              div_value = scatter_add(m,
                                      op_mul(grad_indices, _scaler_one),
                                      op_mul(F.tuple_to_array((1.0,)) - beta1, grad_value))
              param_update = div_value / (op_sqrt(next_v) + eps)
              F.assign(m, m_temp / _scaler_ten)
          else:
              param_update = next_m / (op_sqrt(next_v) + eps)
  
          lr_t = lr * op_sqrt(1 - beta2_power) / (1 - beta1_power)
          next_param = param - lr_t * param_update
  
          success = F.depend(success, F.assign(param, next_param))
          success = F.depend(success, F.assign(m, next_m))
          success = F.depend(success, F.assign(v, next_v))
  
      return success
  
  
  @_adam_opt.register("Function", "Function", "Function", "Function", "Bool", "Bool", "Bool", "Tensor", "Tensor",
                      "Tensor", "Tensor", "Tensor", "Tensor", "Tensor", "Tensor", "Tensor", "Tensor", "Bool", "Bool")
  def _run_opt_with_one_number(opt, sparse_opt, push, pull, use_locking, use_nesterov, target,
                               beta1_power, beta2_power, beta1, beta2, eps, lr, gradient, param,
                               moment1, moment2, ps_parameter, cache_enable):
      """Apply adam optimizer to the weight parameter using Tensor."""
      success = True
      if ps_parameter and not cache_enable:
          op_shape = P.Shape()
          success = F.depend(success, pull(push((beta1_power, beta2_power, lr, beta1, beta2, eps, gradient),
                                                (op_shape(param), op_shape(moment1), op_shape(moment2))), param))
      else:
          success = F.depend(success, opt(param, moment1, moment2, beta1_power, beta2_power, lr, beta1, beta2,
                                          eps, gradient))
      return success
  
  
  @_adam_opt.register("Function", "Tensor", "Tensor", "Tensor", "Tensor", "Tensor", "Tensor", "Tensor", "Tensor",
                      "Tensor", "Tensor")
  def _run_off_load_opt(opt, beta1_power, beta2_power, beta1, beta2, eps, lr, gradient, param, moment1, moment2):
      """Apply AdamOffload optimizer to the weight parameter using Tensor."""
      success = True
      delat_param = opt(moment1, moment2, beta1_power, beta2_power, lr, beta1, beta2, eps, gradient)
      success = F.depend(success, F.assign_add(param, delat_param))
      return success
  
  
  def _check_param_value(beta1, beta2, eps, prim_name):
      """Check the type of inputs."""
      validator.check_value_type("beta1", beta1, [float], prim_name)
      validator.check_value_type("beta2", beta2, [float], prim_name)
      validator.check_value_type("eps", eps, [float], prim_name)
      validator.check_float_range(beta1, 0.0, 1.0, Rel.INC_NEITHER, "beta1", prim_name)
      validator.check_float_range(beta2, 0.0, 1.0, Rel.INC_NEITHER, "beta2", prim_name)
      validator.check_positive_float(eps, "eps", prim_name)
  
  
  class Adam(Optimizer):
      r"""
      Updates gradients by the Adaptive Moment Estimation (Adam) algorithm.
  
      The Adam algorithm is proposed in `Adam: A Method for Stochastic Optimization <https://arxiv.org/abs/1412.6980>`_.
  
      The updating formulas are as follows,
  
      .. math::
          \begin{array}{ll} \\
              m = \beta_1 * m + (1 - \beta_1) * g \\
              v = \beta_2 * v + (1 - \beta_2) * g * g \\
              l = \alpha * \frac{\sqrt{1-\beta_2^t}}{1-\beta_1^t} \\
              w = w - l * \frac{m}{\sqrt{v} + \epsilon}
          \end{array}
  
      :math:`m` represents the 1st moment vector `moment1`, :math:`v` represents the 2nd moment vector `moment2`,
      :math:`g` represents `gradients`, :math:`l` represents scaling factor `lr`, :math:`\beta_1, \beta_2` represent
      `beta1` and `beta2`, :math:`t` represents updating step while :math:`beta_1^t` and :math:`beta_2^t` represent
      `beta1_power` and `beta2_power`, :math:`\alpha` represents `learning_rate`, :math:`w` represents `params`,
      :math:`\epsilon` represents `eps`.
  
      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 is supported.
  
          The sparse strategy is applied while the SparseGatherV2 operator is used for forward network.
          The sparse feature is under continuous development. If the sparse strategy wants to be executed on the host,
          set the target to the CPU.
  
      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" is in the keys, the value of the corresponding learning rate will be used.
                If not, the `learning_rate` in the API will be used.
  
              - weight_decay: Optional. If "weight_decay" is in the keys, the value of the corresponding weight decay
                will be used. If not, the `weight_decay` in the API will be used.
  
              - order_params: Optional. If "order_params" is in the keys, the value must be the order of parameters and
                the order will be followed in the optimizer. There are no other keys in the `dict` and the parameters
                which in the 'order_params' must be in one of group parameters.
  
              - grad_centralization: Optional. If "grad_centralization" is in the keys, the set value will be used.
                If not, the `grad_centralization` in the base class will be used. This parameter only works on the
                convolution layer.
  
          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 the 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: 1e-3.
          beta1 (float): The exponential decay rate for the 1st moment estimations. Should be in range (0.0, 1.0).
                         Default: 0.9.
          beta2 (float): The exponential decay rate for the 2nd moment estimations. Should be in range (0.0, 1.0).
                         Default: 0.999.
          eps (float): Term added to the denominator to improve numerical stability. Should be greater than 0. Default:
                       1e-8.
          use_locking (bool): Whether to enable a lock to protect variable tensors from being updated.
              If true, updates of the var, m, and v tensors will be protected by a lock.
              If false, the result is unpredictable. Default: False.
          use_nesterov (bool): Whether to use Nesterov Accelerated Gradient (NAG) algorithm to update the gradients.
              If true, update the gradients using NAG.
              If false, update the gradients without using NAG. Default: False.
          weight_decay (float): Weight decay (L2 penalty). It must be equal to or greater than 0. Default: 0.0.
          loss_scale (float): A floating point value for the loss scale. Should be greater than 0. Default: 1.0.
  
      Inputs:
          - **gradients** (tuple[Tensor]) - The gradients of `params`, the shape is the same as `params`.
  
      Outputs:
          Tensor[bool], the value is True.
  
      Supported Platforms:
          ``Ascend`` ``GPU``
  
      Examples:
          >>> net = Net()
          >>> #1) All parameters use the same learning rate and weight decay
          >>> optim = nn.Adam(params=net.trainable_params())
          >>>
          >>> #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, 'grad_centralization':True},
          ...                 {'params': no_conv_params, 'lr': 0.01},
          ...                 {'order_params': net.trainable_params()}]
          >>> optim = nn.Adam(group_params, learning_rate=0.1, weight_decay=0.0)
          >>> # The conv_params's parameters will use default learning rate of 0.1 and weight decay of 0.01 and grad
          >>> # centralization of True.
          >>> # The no_conv_params's parameters will use learning rate of 0.01 and default weight decay of 0.0 and grad
          >>> # centralization of False.
          >>> # 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=1e-3, beta1=0.9, beta2=0.999, eps=1e-8, use_locking=False,
                   use_nesterov=False, weight_decay=0.0, loss_scale=1.0):
          super(Adam, self).__init__(learning_rate, params, weight_decay, loss_scale)
          _check_param_value(beta1, beta2, eps, self.cls_name)
          validator.check_value_type("use_locking", use_locking, [bool], self.cls_name)
          validator.check_value_type("use_nesterov", use_nesterov, [bool], self.cls_name)
  
          self.beta1 = Tensor(beta1, mstype.float32)
          self.beta2 = Tensor(beta2, mstype.float32)
          self.beta1_power = Parameter(initializer(1, [1], mstype.float32), name="beta1_power")
          self.beta2_power = Parameter(initializer(1, [1], mstype.float32), name="beta2_power")
          self.eps = Tensor(eps, mstype.float32)
          self.use_nesterov = use_nesterov
          self.use_locking = use_locking
          self.moment1 = self.parameters.clone(prefix="moment1", init='zeros')
          self.moment2 = self.parameters.clone(prefix="moment2", init='zeros')
  
          self._is_device = True
          self.hyper_map = C.HyperMap()
          self.opt = P.Adam(use_locking, use_nesterov)
          self.sparse_opt = P.FusedSparseAdam(use_locking, use_nesterov)
          self.sparse_opt.add_prim_attr("primitive_target", "CPU")
          self._ps_pull = P.Pull()
          self._ps_push = P.Push("Adam", [0, 1, 2])
          self._ps_push.add_prim_attr("use_nesterov", use_nesterov)
  
      def construct(self, gradients):
          params = self.parameters
          moment1 = self.moment1
          moment2 = self.moment2
          gradients = self.decay_weight(gradients)
          gradients = self.scale_grad(gradients)
          gradients = self._grad_sparse_indices_deduplicate(gradients)
          gradients = self.gradients_centralization(gradients)
          lr = self.get_lr()
  
          beta1_power = self.beta1_power * self.beta1
          self.beta1_power = beta1_power
          beta2_power = self.beta2_power * self.beta2
          self.beta2_power = beta2_power
          if self.is_group_lr:
              success = self.map_(F.partial(_adam_opt, self.opt, self.sparse_opt, self._ps_push, self._ps_pull,
                                            self.use_locking, self.use_nesterov, self._is_device,
                                            beta1_power, beta2_power, self.beta1, self.beta2, self.eps),
                                  lr, gradients, params, moment1, moment2, self.ps_parameters, self.cache_enable)
          else:
              success = self.map_(F.partial(_adam_opt, self.opt, self.sparse_opt, self._ps_push, self._ps_pull,
                                            self.use_locking, self.use_nesterov, self._is_device,
                                            beta1_power, beta2_power, self.beta1, self.beta2, self.eps, lr),
                                  gradients, params, moment1, moment2, self.ps_parameters, self.cache_enable)
          return success
  
      @Optimizer.target.setter
      def target(self, value):
          """If the input value is set to "CPU", the parameters will be updated on the host using the Fused
             optimizer operation."""
          if not isinstance(value, str):
              raise TypeError("The value must be str type, but got value type is {}".format(type(value)))
  
          if value not in ('CPU', 'Ascend', 'GPU'):
              raise ValueError("The value must be 'CPU', 'Ascend' or 'GPU', but got value {}".format(value))
  
          if self._target == "CPU" and value in('Ascend', 'GPU'):
              raise ValueError("In the CPU environment, target cannot be set to 'GPU' and 'Ascend'.")
  
          if self._target == "Ascend" and value == 'GPU':
              raise ValueError("In the Ascend environment, target cannot be set to 'GPU'.")
  
          self._is_device = (value != 'CPU')
          self._target = value
  
  
  class AdamWeightDecay(Optimizer):
      """
      Implements the Adam algorithm to fix the weight decay.
  
      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.
  
      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" is in the keys, the value of the corresponding learning rate will be used.
                If not, the `learning_rate` in the API will be used.
  
              - weight_decay: Optional. If "weight_decay" is in the keys, the value of the corresponding weight decay
                will be used. If not, the `weight_decay` in the API will be used.
  
              - order_params: Optional. If "order_params" is in the keys, the value must be the order of parameters and
                the order will be followed in the optimizer. There are no other keys in the `dict` and the parameters
                which in the '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 the 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: 1e-3.
          beta1 (float): The exponential decay rate for the 1st moment estimations. Default: 0.9.
              Should be in range (0.0, 1.0).
          beta2 (float): The exponential decay rate for the 2nd moment estimations. Default: 0.999.
              Should be in range (0.0, 1.0).
          eps (float): Term added to the denominator to improve numerical stability. Default: 1e-6.
              Should be greater than 0.
          weight_decay (float): Weight decay (L2 penalty). It must 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:
          tuple[bool], all elements are True.
  
      Supported Platforms:
          ``Ascend`` ``GPU``
  
      Examples:
          >>> net = Net()
          >>> #1) All parameters use the same learning rate and weight decay
          >>> optim = nn.AdamWeightDecay(params=net.trainable_params())
          >>>
          >>> #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.AdamWeightDecay(group_params, learning_rate=0.1, weight_decay=0.0)
          >>> # The conv_params's parameters will use default learning rate of 0.1 and weight decay of 0.01.
          >>> # The no_conv_params's parameters will use learning rate of 0.01 and default weight decay of 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=1e-3, beta1=0.9, beta2=0.999, eps=1e-6, weight_decay=0.0):
          super(AdamWeightDecay, self).__init__(learning_rate, params, weight_decay)
          _check_param_value(beta1, beta2, eps, self.cls_name)
          self.beta1 = Tensor(np.array([beta1]).astype(np.float32))
          self.beta2 = Tensor(np.array([beta2]).astype(np.float32))
          self.eps = Tensor(np.array([eps]).astype(np.float32))
          self.moments1 = self.parameters.clone(prefix="adam_m", init='zeros')
          self.moments2 = self.parameters.clone(prefix="adam_v", init='zeros')
          self.hyper_map = C.HyperMap()
  
      def construct(self, gradients):
          lr = self.get_lr()
          if self.is_group:
              if self.is_group_lr:
                  optim_result = self.hyper_map(F.partial(_adam_opt, self.beta1, self.beta2, self.eps),
                                                lr, self.weight_decay, self.parameters, self.moments1, self.moments2,
                                                gradients, self.decay_flags, self.optim_filter)
              else:
                  optim_result = self.hyper_map(F.partial(_adam_opt, self.beta1, self.beta2, self.eps, lr),
                                                self.weight_decay, self.parameters, self.moments1, self.moments2,
                                                gradients, self.decay_flags, self.optim_filter)
          else:
              optim_result = self.hyper_map(F.partial(_adam_opt, self.beta1, self.beta2, self.eps, lr, self.weight_decay),
                                            self.parameters, self.moments1, self.moments2,
                                            gradients, self.decay_flags, self.optim_filter)
          if self.use_parallel:
              self.broadcast_params(optim_result)
          return optim_result
  
  
  class AdamOffload(Optimizer):
      r"""
      This optimizer will offload Adam optimizer to host CPU and keep parameters being updated on the device,
      to minimize the memory cost. Although that would bring about an increase of performance overhead,
      the optimizer could be used to run a larger model.
  
      The Adam algorithm is proposed in `Adam: A Method for Stochastic Optimization <https://arxiv.org/abs/1412.6980>`_.
  
      The updating formulas are as follows,
  
      .. math::
          \begin{array}{ll} \\
              m = \beta_1 * m + (1 - \beta_1) * g \\
              v = \beta_2 * v + (1 - \beta_2) * g * g \\
              l = \alpha * \frac{\sqrt{1-\beta_2^t}}{1-\beta_1^t} \\
              w = w - l * \frac{m}{\sqrt{v} + \epsilon}
          \end{array}
  
      :math:`m` represents the 1st moment vector `moment1`, :math:`v` represents the 2nd moment vector `moment2`,
      :math:`g` represents `gradients`, :math:`l` represents scaling factor `lr`, :math:`\beta_1, \beta_2` represent
      `beta1` and `beta2`, :math:`t` represents updating step while :math:`beta_1^t` and :math:`beta_2^t` represent
      `beta1_power` and `beta2_power`, :math:`\alpha` represents `learning_rate`, :math:`w` represents `params`,
      :math:`\epsilon` represents `eps`.
  
      Note:
          This optimizer only supports `GRAPH_MODE` currently.
  
          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 is supported.
  
      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" is in the keys, the value of the corresponding learning rate will be used.
                If not, the `learning_rate` in the API will be used.
  
              - weight_decay: Optional. If "weight_decay" is in the keys, the value of the corresponding weight decay
                will be used. If not, the `weight_decay` in the API will be used.
  
              - order_params: Optional. If "order_params" is in the keys, the value must be the order of parameters and
                the order will be followed in the optimizer. There are no other keys in the `dict` and the parameters
                which in the '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 the 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: 1e-3.
          beta1 (float): The exponential decay rate for the 1st moment estimations. Should be in range (0.0, 1.0).
                         Default: 0.9.
          beta2 (float): The exponential decay rate for the 2nd moment estimations. Should be in range (0.0, 1.0).
                         Default: 0.999.
          eps (float): Term added to the denominator to improve numerical stability. Should be greater than 0. Default:
                       1e-8.
          use_locking (bool): Whether to enable a lock to protect variable tensors from being updated.
              If true, updates of the var, m, and v tensors will be protected by a lock.
              If false, the result is unpredictable. Default: False.
          use_nesterov (bool): Whether to use Nesterov Accelerated Gradient (NAG) algorithm to update the gradients.
              If true, update the gradients using NAG.
              If false, update the gradients without using NAG. Default: False.
          weight_decay (float): Weight decay (L2 penalty). It must be equal to or greater than 0. Default: 0.0.
          loss_scale (float): A floating point value for the loss scale. Should be greater than 0. Default: 1.0.
  
      Inputs:
          - **gradients** (tuple[Tensor]) - The gradients of `params`, the shape is the same as `params`.
  
      Outputs:
          Tensor[bool], the value is True.
  
      Supported Platforms:
          ``Ascend`` ``GPU`` ``CPU``
  
      Examples:
          >>> net = Net()
          >>> #1) All parameters use the same learning rate and weight decay
          >>> optim = nn.AdamOffload(params=net.trainable_params())
          >>>
          >>> #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.AdamOffload(group_params, learning_rate=0.1, weight_decay=0.0)
          >>> # The conv_params's parameters will use default learning rate of 0.1 and weight decay of 0.01.
          >>> # The no_conv_params's parameters will use learning rate of 0.01 and default weight decay of 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=1e-3, beta1=0.9, beta2=0.999, eps=1e-8, use_locking=False,
                   use_nesterov=False, weight_decay=0.0, loss_scale=1.0):
          super(AdamOffload, self).__init__(learning_rate, params, weight_decay, loss_scale)
          _check_param_value(beta1, beta2, eps, self.cls_name)
          validator.check_value_type("use_locking", use_locking, [bool], self.cls_name)
          validator.check_value_type("use_nesterov", use_nesterov, [bool], self.cls_name)
  
          self.beta1 = Tensor(beta1, mstype.float32)
          self.beta2 = Tensor(beta2, mstype.float32)
          self.beta1_power = Parameter(initializer(1, [1], mstype.float32), name="beta1_power")
          self.beta2_power = Parameter(initializer(1, [1], mstype.float32), name="beta2_power")
          self.eps = Tensor(eps, mstype.float32)
          self.use_nesterov = use_nesterov
          self.use_locking = use_locking
          self.moment1 = self.parameters.clone(prefix="moment1", init='zeros')
          self.moment2 = self.parameters.clone(prefix="moment2", init='zeros')
  
          self.hyper_map = C.HyperMap()
          self.opt = P.AdamNoUpdateParam(use_locking, use_nesterov)
          self.opt.add_prim_attr("primitive_target", "CPU")
  
      def construct(self, gradients):
          params = self.parameters
          moment1 = self.moment1
          moment2 = self.moment2
          gradients = self.decay_weight(gradients)
          gradients = self.scale_grad(gradients)
          lr = self.get_lr()
  
          beta1_power = self.beta1_power * self.beta1
          self.beta1_power = beta1_power
          beta2_power = self.beta2_power * self.beta2
          self.beta2_power = beta2_power
          if self.is_group_lr:
              success = self.map_(F.partial(_adam_opt, self.opt,
                                            beta1_power, beta2_power, self.beta1, self.beta2, self.eps),
                                  lr, gradients, params, moment1, moment2)
          else:
              success = self.map_(F.partial(_adam_opt, self.opt,
                                            beta1_power, beta2_power, self.beta1, self.beta2, self.eps, lr),
                                  gradients, params, moment1, moment2)
          return success
  