def mixture_stddev(mixture_weight_vector, mean_vector, stddev_vector):
  """Computes the standard deviation of a mixture distribution.

  This function works regardless of the component distribution, so long as
  each component's mean and standard deviation can be provided.

  Args:
    mixture_weight_vector: A 2D tensor with shape [batch_size, num_components]
    mean_vector: A 2D tensor of mixture component means. Has shape `[batch_size,
      num_components]`.
    stddev_vector: A 2D tensor of mixture component standard deviations. Has
      shape `[batch_size, num_components]`.

  Returns:
    A 1D tensor of shape `[batch_size]` representing the standard deviation of
    the mixture distribution with given weights and component means and standard
    deviations.
  Raises:
    ValueError: If the shapes of the input tensors are not as expected.
  """
  tensorshape_util.assert_has_rank(mixture_weight_vector.shape, 2)
  if not tensorshape_util.is_compatible_with(mean_vector.shape,
                                             mixture_weight_vector.shape):
    raise ValueError("Expecting means to have same shape as mixture weights.")
  if not tensorshape_util.is_compatible_with(stddev_vector.shape,
                                             mixture_weight_vector.shape):
    raise ValueError("Expecting stddevs to have same shape as mixture weights.")

  # Reshape the distribution parameters for batched vectorized dot products.
  pi_for_dot_prod = tf.expand_dims(mixture_weight_vector, axis=1)
  mu_for_dot_prod = tf.expand_dims(mean_vector, axis=2)
  sigma_for_dot_prod = tf.expand_dims(stddev_vector, axis=2)

  # weighted average of component means under mixture distribution.
  mean_wa = tf.matmul(pi_for_dot_prod, mu_for_dot_prod)
  mean_wa = tf.reshape(mean_wa, (-1,))
  # weighted average of component variances under mixture distribution.
  var_wa = tf.matmul(pi_for_dot_prod, tf.square(sigma_for_dot_prod))
  var_wa = tf.reshape(var_wa, (-1,))
  # weighted average of component squared means under mixture distribution.
  sq_mean_wa = tf.matmul(pi_for_dot_prod, tf.square(mu_for_dot_prod))
  sq_mean_wa = tf.reshape(sq_mean_wa, (-1,))
  mixture_variance = var_wa + sq_mean_wa - tf.square(mean_wa)
  return tf.sqrt(mixture_variance)
Computes the standard deviation of a mixture distribution.

  This function works regardless of the component distribution, so long as
  each component's mean and standard deviation can be provided.

  Args:
    mixture_weight_vector: A 2D tensor with shape [batch_size, num_components]
    mean_vector: A 2D tensor of mixture component means. Has shape `[batch_size,
      num_components]`.
    stddev_vector: A 2D tensor of mixture component standard deviations. Has
      shape `[batch_size, num_components]`.

  Returns:
    A 1D tensor of shape `[batch_size]` representing the standard deviation of
    the mixture distribution with given weights and component means and standard
    deviations.
  Raises:
    ValueError: If the shapes of the input tensors are not as expected.