code: def _sparse_rmsprop_update_numpy(
      self,
      var,
      gindexs,
      gvalues,
      mg,
      rms,
      mom,
      lr,
      decay,
      momentum,
      epsilon,
      centered,
  ):
      mg_t = copy.deepcopy(mg)
      rms_t = copy.deepcopy(rms)
      mom_t = copy.deepcopy(mom)
      var_t = copy.deepcopy(var)
      for i in range(len(gindexs)):
          gindex = gindexs[i]
          gvalue = gvalues[i]
          rms_t[gindex] = (
              rms[gindex] * decay + (1 - decay) * gvalue * gvalue
          )
          denom_t = rms_t[gindex] + epsilon
          if centered:
              mg_t[gindex] = mg_t[gindex] * decay + (1 - decay) * gvalue
              denom_t -= mg_t[gindex] * mg_t[gindex]
          mom_t[gindex] = momentum * mom[
              gindex
          ] + lr * gvalue / np.sqrt(denom_t)
          var_t[gindex] = var[gindex] - mom_t[gindex]
      return var_t, mg_t, rms_t, mom_t
  
imports: import copy
  import itertools
  import math
  import numpy
  from tensorflow.python.eager import context
  from tensorflow.python.framework import constant_op
  from tensorflow.python.framework import dtypes
  from tensorflow.python.framework import indexed_slices
  from tensorflow.python.framework import test_util
  from tensorflow.python.ops import embedding_ops
  from tensorflow.python.ops import math_ops
  from tensorflow.python.ops import resource_variable_ops
  from tensorflow.python.ops import variables
  from tensorflow.python.platform import test
  from tensorflow.python.training import rmsprop
label_desc: Use image node_id 2 for calling the RMSPropOptimizerTest obj's underlying member method code with example usage: obj._sparse_rmsprop_update_numpy(var, gindexs, gvalues, mg, rms, mom, lr, decay, momentum, epsilon, centered) and returns: var_t,  mg_t,  rms_t,  mom_t