code: def parallel_variance_calculation(
      n_a: types.Int,
      avg_a: types.Float,
      m2_a: types.Float,
      n_b: types.Int,
      avg_b: types.Float,
      m2_b: types.Float,
      m2_b_c: types.Float,
  ) -> Tuple[types.Int, types.Float, types.Float, types.Float]:
      """Calculate the sufficient statistics (average & second moment) of two sets.
  
      For better precision if sets are of different sizes, `a` should be the smaller
      and `b` the bigger.
  
      For more details, see the parallel algorithm of Chan et al. at:
      https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Parallel_algorithm
  
      For stability we use `kahan_summation` to accumulate second moments.
  
      Takes in the sufficient statistics for sets `A` and `B` and calculates the
      variance and sufficient statistics for the union of `A` and `B`.
  
      If e.g. `B` is a single observation `x_b`, use `n_b=1`, `avg_b = x_b`, and
      `m2_b = 0`.
  
      To get `avg_a` and `m2_a` from a tensor `x` of shape `[n_a, ...]`, use:
  
      ```
      n_a = tf.shape(x)[0]
      avg_a = tf.math.reduce_mean(x, axis=[0])
      m2_a = tf.math.reduce_sum(tf.math.squared_difference(t, avg_a), axis=[0])
  
      ```
  
      Args:
        n_a: Number of elements in `A`.
        avg_a: The sample average of `A`.
        m2_a: The sample second moment of `A`.
        n_b: Number of elements in `B`.
        avg_b: The sample average of `B`.
        m2_b: The sample second moment of `B`.
        m2_b_c: Carry for accumulation of the sample second moment of `B`.
  
      Returns:
        A tuple `(n_ab, avg_ab, m2_ab, m2_ab_c)` such that `var_ab`,
        the variance of `A|B`, may be calculated via `var_ab = m2_ab / n_ab`,
        and the sample variance  as`sample_var_ab = m2_ab / (n_ab - 1)`.
      """
      n_ab = n_a + n_b
      delta = avg_b - avg_a
      s_delta = delta * n_b / n_ab
      avg_ab = avg_a + s_delta
      m2_ab, m2_ab_c = kahan_summation(
          m2_b, m2_b_c, m2_a + (delta * n_a * s_delta)
      )
      return n_ab, avg_ab, m2_ab, m2_ab_c
  
imports: from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  import abc
  from typing import Tuple
  import six
  import tensorflow
  from tf_agents.specs import tensor_spec
  from tf_agents.typing import types
  from tf_agents.utils import common
  from tf_agents.utils import nest_utils
label_desc: Use image node_id 1 for calling a global function with example usage: parallel_variance_calculation(n_a, avg_a, m2_a, n_b, avg_b, m2_b, m2_b_c) and returns: n_ab,  avg_ab,  m2_ab,  m2_ab_c