code: def _benchmark_dtw():
      size1 = 2**10
      size2 = 2**10
      freq1 = 1 / size1
      freq2 = 1 / size2
      input1 = np.cos(np.arange(size1) * 2 * np.pi * freq1)
      input2 = np.sin(
          np.arange(size2) * 2 * np.pi * freq2
      ) + 0.1 * np.random.random(size=size2)
  
      global series1, series2
  
      series1 = _series_from_values(input1)
      series2 = _series_from_values(input2)
  
      import cProfile
  
      cProfile.run("_dtw_exact()", sort="tottime")
      cProfile.run("_dtw_multigrid()", sort="tottime")
  
imports: import matplotlib.pyplot
  import numpy
  import pandas
  import pytest
  from darts.dataprocessing import dtw
  from darts.metrics import dtw_metric, mae, mape
  from darts.timeseries import TimeSeries
  from darts.utils import timeseries_generation
label_desc: Use image node_id 4 for calling a global function with example usage: _benchmark_dtw() without return types