code: def cdf_to_gaussian_forward_transform(
      input_batch: DataEntry, outputs: np.ndarray
  ) -> np.ndarray:
      """
      Forward transformation of the CDFtoGaussianTransform.
  
      Parameters
      ----------
      input_batch
          Input data to the predictor.
      outputs
          Predictor outputs.
      Returns
      -------
      outputs
          Forward transformed outputs.
      """
  
      def _empirical_cdf_inverse_transform(
          batch_target_sorted: np.ndarray,
          batch_predictions: np.ndarray,
          slopes: np.ndarray,
          intercepts: np.ndarray,
      ) -> np.ndarray:
          """
          Apply forward transformation of the empirical CDF.
  
          Parameters
          ----------
          batch_target_sorted
              Sorted targets of the input batch.
          batch_predictions
              Predictions of the underlying probability distribution
          slopes
              Slopes of the piece-wise linear function.
          intercepts
              Intercepts of the piece-wise linear function.
  
          Returns
          -------
          outputs
              Forward transformed outputs.
          """
  
          num_timesteps = batch_target_sorted.shape[1]
          indices = np.floor(batch_predictions * num_timesteps)
          # indices = indices - 1
          # for now project into [0, 1]
          indices = np.clip(indices, 0, num_timesteps - 1)
          indices = indices.astype(int)
  
          transformed = np.where(
              np.take_along_axis(slopes, indices, axis=1) != 0.0,
              (
                  batch_predictions
                  - np.take_along_axis(intercepts, indices, axis=1)
              )
              / np.take_along_axis(slopes, indices, axis=1),
              np.take_along_axis(batch_target_sorted, indices, axis=1),
          )
          return transformed
  
      # applies inverse cdf to all outputs
      samples = outputs.shape[1]
      for sample_index in range(0, samples):
          outputs[
              :, sample_index, :, :
          ] = _empirical_cdf_inverse_transform(
              tensor_to_numpy(input_batch["past_target_sorted"]),
              CDFtoGaussianTransform.standard_gaussian_cdf(
                  outputs[:, sample_index, :, :]
              ),
              tensor_to_numpy(input_batch["slopes"]),
              tensor_to_numpy(input_batch["intercepts"]),
          )
      return outputs
  
imports: from typing import Callable, Iterator, List, Optional, Tuple, Type
  import numpy
  from toolz import valmap
  from gluonts.core.component import validated, tensor_to_numpy
  from gluonts.dataset.common import DataEntry
  from gluonts.exceptions import assert_data_error
  from ._base import FlatMapTransformation, MapTransformation, SimpleTransformation
label_desc: Use image node_id 3 for calling a global function with example usage: cdf_to_gaussian_forward_transform(input_batch, outputs) and returns: outputs, transformed