code: def generate_df_with_arbitrary_trends_and_shifts(
      start_date="2015-01-01",
      length=365,
      freq="D",
      seed=10,
      trend_slopes=None,
      trend_intervals=None,
      level_shifts=None,
      level_shift_magnitudes=None,
  ):
      """Generates a Pandas DataFrame that represents time series data with arbitrary trends and level shifts.
      Example Usage: Calling `generate_df_with_arbitrary_trends_and_shifts(trend_slopes=[-1., 1.], trend_intervals=[.3, 1.],
      level_shifts=[(.3, .6)], level_shift_magnitudes=[100.])` produces a time series with a slope of -1 for the first 30%
      of the interval. The next 70% ((1. - .3)*100 = 70) of the interval has a slope of 1. The time series across the interval
      .3 to .6, of the entire length, will have a positive level shift of magnitude 100.
  
      Parameters
      ----------
      start_date : `str`
          The start date of the time series data in "YYYY-MM-DD" format. Defaults to '2015-01-01'.
      length : `int`
          The number of data points in the time series. Defaults to 365.
      freq : `str`
          Frequency of the timestamps (based on pandas date_range frequencies). Defaults to "D" for daily.
      seed : `int`
          The seed for the random number generator. Defaults to 10.
      trend_slopes : `Optional[List[float]]`
          A list of slopes representing trends in the time series. Each slope applies to a corresponding
          interval from 'trend_intervals'. Defaults to None and  the series produced has a slope of 1.
      trend_intervals : `Optional[List[float]]`
          A list of values between 0 and 1 that represent the intervals of the corresponding trends in
          'trend_slopes'. The start of a new interval indicates the end of the previous one. The final
          interval must end at 1. Defaults to None.
      level_shifts : `Optional[List[Tuple[float, float]]]`
          A list of tuples where each tuple contains two float values between 0 and 1. Each tuple
          represents the start and end of a level shift in the time series. Defaults to None.
      level_shift_magnitudes : `Optional[List[float]]`
          A list of magnitudes for each level shift. Each magnitude corresponds to a tuple from
          'level_shifts'. Defaults to None.
  
      Returns
      -------
          df : `pandas.DataFrame`
              A DataFrame representing the generated time series with columns:
                  `"timestamp"` : time column.
                  `"y"` : value column.
  
      Raises
      ------
      ValueError: If the first trend interval does not have a positive value.
      ValueError: If the last trend interval does not end at 1.
      ValueError: If the trend intervals are not strictly monotonically increasing.
      ValueError: If each level shift does not have a start and end specified for its duration.
      ValueError: If the start and end points of a level shift are not valid fractions of the time series duration.
      ValueError: If the number of trend slopes is not equal to the number of trend intervals.
      ValueError: If the number of level shifts is not equal to the number of level shift magnitudes.
      """
      if len(trend_slopes) != len(trend_intervals):
          raise ValueError(
              "Each trend needs an interval specified for its duration."
          )
  
      def _verify_intervals(intervals):
          if intervals[0] <= 0:
              raise ValueError(
                  "The beginning trend must have a positive value"
              )
          if float(intervals[-1]) != 1.0:
              raise ValueError("The final interval must end at 1.")
          for i in range(len(intervals) - 1):
              if intervals[i + 1] <= intervals[i]:
                  raise ValueError(
                      "The intervals must be strictly monotonically increasing."
                  )
  
      def _verify_level_shifts(level_shift_starts, level_shift_ends):
          if len(level_shift_starts) != len(level_shift_ends):
              raise ValueError(
                  "Each level shift needs a start and end specified for its duration."
              )
          for ls_start, ls_end in zip(
              level_shift_starts, level_shift_ends
          ):
              if ls_end <= ls_start or ls_start < 0 or ls_end > 1:
                  raise ValueError(
                      "Level shift start and end points should be valid fractions of the time series duration, with end > start."
                  )
  
      np.random.seed(seed)
      if trend_slopes and trend_intervals:
          _verify_intervals(trend_intervals)
  
      if level_shifts and level_shift_magnitudes:
          level_shift_starts, level_shift_ends = zip(*level_shifts)
          _verify_level_shifts(level_shift_starts, level_shift_ends)
          if len(level_shifts) != len(level_shift_magnitudes):
              raise ValueError(
                  "Each level shift needs a magnitude specified."
              )
      ts = pd.date_range(start_date, freq=freq, periods=length)
      trend_slopes = trend_slopes or [1.0]
      trend_intervals = trend_intervals or [1.0]
      level_shifts = level_shifts or []
      level_shift_magnitudes = level_shift_magnitudes or []
      hop_size = length / len(trend_slopes)
      trend_intervals_indices = (
          [0]
          + [
              int(hop_size * (i + 1))
              for i in range(len(trend_slopes) - 1)
          ]
          + [length]
      )
      base_value_with_trend_changes = np.array([])
      for i in range(len(trend_intervals_indices) - 1):
          cur_trend_magnitude = trend_slopes[i]
          begin, end = (
              trend_intervals_indices[i],
              trend_intervals_indices[i + 1] - 1,
          )
          interval_length = end - begin + 1
          prev_endpoint = (
              base_value_with_trend_changes[-1]
              if len(base_value_with_trend_changes) > 0
              else 0.0
          )
          base_value_with_trend_changes = np.concatenate(
              (
                  base_value_with_trend_changes,
                  cur_trend_magnitude
                  * np.arange(interval_length, dtype=np.float64)
                  + prev_endpoint,
              )
          )
      for (ls_start, ls_end), ls_magnitude in zip(
          level_shifts, level_shift_magnitudes
      ):
          ls_start_index = int(ls_start * length)
          ls_end_index = int(ls_end * length)
          base_value_with_trend_changes[
              ls_start_index:ls_end_index
          ] += ls_magnitude
      df = pd.DataFrame(
          {"timestamp": ts, "y": base_value_with_trend_changes}
      )
      return df
  
imports: import datetime
  import warnings
  import numpy
  import pandas
  from greykite.common.constants import ADJUSTMENT_DELTA_COL
  from greykite.common.constants import ANOMALY_COL
  from greykite.common.constants import END_TIME_COL
  from greykite.common.constants import EVENT_DF_LABEL_COL
  from greykite.common.constants import METRIC_COL
  from greykite.common.constants import START_TIME_COL
  from greykite.common.constants import TIME_COL
  from greykite.common.constants import VALUE_COL
  from greykite.common.constants import TimeFeaturesEnum
  from greykite.common.features.timeseries_features import add_daily_events
  from greykite.common.features.timeseries_features import build_time_features_df
  from greykite.common.features.timeseries_features import fourier_series_multi_fcn
  from greykite.common.features.timeseries_features import get_default_origin_for_time_vars
  from greykite.common.features.timeseries_features import get_fourier_col_name
  from greykite.common.features.timeseries_features import get_holidays
  from greykite.common.python_utils import assert_equal
label_desc: Use image node_id 11 for calling a global function with example usage: generate_df_with_arbitrary_trends_and_shifts(start_date, length, freq, seed, trend_slopes, trend_intervals, level_shifts, level_shift_magnitudes) and returns: df