code: def smooth_loss_and_suggest(lr_finder_results, window=10):
      """
      Smooth loss using a Hamming filter.
  
      Parameters
      ----------
          loss : np.array
              Loss values
  
      Returns
      -------
          loss_smoothed : np.array
              Smoothed loss values
          lr: np.array
              Learning rate values
          suggested_lr: float
              Suggested learning rate based on gradient
      """
      lr = lr_finder_results["lr"]
      loss = lr_finder_results["loss"]
      # Derive window size from num lr searches, ensure window is divisible by 2
      half_window = math.ceil(round(len(loss) * 0.1) / 2)
      # Pad sequence and initialialize hamming filter
      loss = np.pad(np.array(loss), pad_width=half_window, mode="edge")
      window = np.hamming(half_window * 2)
      # Convolve the over the loss distribution
      try:
          loss = np.convolve(
              window / window.sum(),
              loss,
              mode="valid",
          )[1:]
      except ValueError:
          log.warning(
              f"The number of loss values ({len(loss)}) is too small to apply smoothing with a the window size of "
              f"{window}."
          )
      # Suggest the lr with steepest negative gradient
      try:
          # Find the steepest gradient and the minimum loss after that
          suggestion = lr[np.argmin(np.gradient(loss))]
      except ValueError:
          log.error(
              f"The number of loss values ({len(loss)}) is too small to estimate a learning rate. Increase the number of "
              "samples or manually set the learning rate."
          )
          raise
      return (loss, lr, suggestion)
  
imports: from __future__ import annotations
  import logging
  import math
  import os
  import sys
  from collections import OrderedDict
  from typing import TYPE_CHECKING, Iterable, Optional, Union
  import numpy
  import pandas
  import pytorch_lightning
  import torch
  from neuralprophet import utils_torch
  from neuralprophet.hdays_utils import get_country_holidays
  from neuralprophet.logger import ProgressBar
label_desc: Use image node_id 23 for calling a global function with example usage: smooth_loss_and_suggest(lr_finder_results, window) and returns: loss,  lr,  suggestion