code: def gaussian_timeseries(
      mean: Union[float, np.ndarray] = 0.0,
      std: Union[float, np.ndarray] = 1.0,
      start: Optional[Union[pd.Timestamp, int]] = pd.Timestamp(
          "2000-01-01"
      ),
      end: Optional[Union[pd.Timestamp, int]] = None,
      length: Optional[int] = None,
      freq: Union[str, int] = None,
      column_name: Optional[str] = "gaussian",
      dtype: np.dtype = np.float64,
  ) -> TimeSeries:
      """
      Creates a gaussian univariate TimeSeries by sampling all the series values independently,
      from a gaussian distribution with mean `mean` and standard deviation `std`.
  
      Parameters
      ----------
      mean
          The mean of the gaussian distribution that is sampled at each step.
          If a float value is given, the same mean is used at every step.
          If a numpy.ndarray of floats with the same length as `length` is
          given, a different mean is used at each time step.
      std
          The standard deviation of the gaussian distribution that is sampled at each step.
          If a float value is given, the same standard deviation is used at every step.
          If an array of dimension `(length, length)` is given, it will
          be used as covariance matrix for a multivariate gaussian distribution.
      start
          The start of the returned TimeSeries' index. If a pandas Timestamp is passed, the TimeSeries will have a pandas
          DatetimeIndex. If an integer is passed, the TimeSeries will have a pandas RangeIndex index. Works only with
          either `length` or `end`.
      end
          Optionally, the end of the returned index. Works only with either `start` or `length`. If `start` is
          set, `end` must be of same type as `start`. Else, it can be either a pandas Timestamp or an integer.
      length
          Optionally, the length of the returned index. Works only with either `start` or `end`.
      freq
          The time difference between two adjacent entries in the returned index. In case `start` is a timestamp,
          a DateOffset alias is expected; see
          `docs <https://pandas.pydata.org/pandas-docs/stable/user_guide/TimeSeries.html#dateoffset-objects>`_.
          By default, "D" (daily) is used.
          If `start` is an integer, `freq` will be interpreted as the step size in the underlying RangeIndex.
          The freq is optional for generating an integer index (if not specified, 1 is used).
      column_name
          Optionally, the name of the value column for the returned TimeSeries
      dtype
          The desired NumPy dtype (np.float32 or np.float64) for the resulting series
  
      Returns
      -------
      TimeSeries
          A white noise TimeSeries created as indicated above.
      """
  
      if type(mean) == np.ndarray:
          raise_if_not(
              mean.shape == (length,),
              "If a vector of means is provided, "
              "it requires the same length as the TimeSeries.",
              logger,
          )
      if type(std) == np.ndarray:
          raise_if_not(
              std.shape == (length, length),
              "If a matrix of standard deviations is provided, "
              "its shape has to match the length of the TimeSeries.",
              logger,
          )
  
      index = generate_index(
          start=start, end=end, freq=freq, length=length
      )
      values = np.random.normal(mean, std, size=len(index)).astype(
          dtype
      )
  
      return TimeSeries.from_times_and_values(
          index, values, freq=freq, columns=pd.Index([column_name])
      )
  
file_path: darts/darts/utils/timeseries_generation.py
imports: import math
  from typing import List, Optional, Sequence, Tuple, Union
  import holidays
  import numpy
  import pandas
  from darts import TimeSeries
  from darts.logging import get_logger, raise_if, raise_if_not, raise_log
label_desc: Use image node_id 5 for calling a global function with example usage: gaussian_timeseries(mean, std, start, end, length, freq, column_name, dtype) and returns: TimeSeries