code: def decompose(x, type_, m, filter_=None):
      """
      Decompose the time series into trend, seasonal, and random components.
  
      Parameters
      ----------
      x : np.array, shape=(n_samples,)
          The time series of which the trend, seasonal, and noise/random
          components will be extracted.
  
      type_: str
          The type of decomposition that will be performed - 'multiplicative' or
          'additive'. We would use 'multiplicative' generally when we see an
          increasing trend. We use 'additive' when the trend is relatively
          stable over time.
  
      m: int
          The frequency in terms of number of observations. This behaves
          similarly to R's frequency for a time series (ts).
  
      filter_: np.array, optional (default=None)
          A filter by which the convolution will be performed.
  
      Returns
      -------
      decomposed_tuple : namedtuple
          A named tuple with ``x``, ``trend``, ``seasonal``, and ``random``
          components where ``x`` is the input signal, ``trend`` is the overall
          trend, ``seasonal`` is the seasonal component, and `random` is the
          noisy component. The input signal ``x`` can be mostly reconstructed by
          the other three components with a number of points missing equal to
          ``m``.
  
      Notes
      -----
      This function is generally used in conjunction with
      :func:`pmdarima.utils.visualization.decomposed_plot`,
      which plots the decomposed components. Also there is an example script in
      the ``examples`` folder of the repo and the ``Examples`` section of the
      docs as well.
  
       References
      ----------
      .. [1] Example of decompose using both multiplicative and additive types:
             https://anomaly.io/seasonal-trend-decomposition-in-r/index.html
  
      .. [2] R documentation for decompose:
             https://www.rdocumentation.org/packages/stats/versions/3.6.1/topics/decompose
      """  # noqa: E501
  
      multiplicative = "multiplicative"
      additive = "additive"
      is_m_odd = m % 2 == 1
  
      # Helper function to stay consistent and concise based on 'type_'
      def _decomposer_helper(a, b):
          if type_ == multiplicative:
              return a / b
          else:
              return a - b
  
      # Since R's ts class has a frequency as input I think this it acceptable
      # to ask the user for the frequency.
      try:
          assert isinstance(m, int) and m > 1
      except (ValueError, AssertionError):
          raise ValueError("'f' should be a positive integer")
  
      if filter_ is None:
          filter_ = np.ones((m,)) / m
  
      # We only accept the values in multiplicative or additive
      if type_ not in (multiplicative, additive):
          err_msg = "'type_' can only take values '{}' or '{}'"
          raise ValueError(err_msg.format(multiplicative, additive))
  
      # There needs to be at least 2 periods. This is due to the behavior of
      # convolutions and how they behave with respect to losing endpoints
      if (x.shape[0] / m) < 2:
          raise ValueError("time series has no or less than 2 periods")
  
      # Take half of m for the convolution / sma process.
      half_m = m // 2
      trend = np.convolve(x, filter_, mode="valid")
  
      if not is_m_odd:
          trend = trend[:-1]  # we remove the final index if m is even.
  
      # Remove the effect of the trend on the original signal and pad for reshape
      sma_xs = range(half_m, len(trend) + half_m)
      detrend = _decomposer_helper(x[sma_xs], trend)
      num_seasons = math.ceil((1.0 * trend.shape[0]) / m)
      pad_length = (num_seasons * m) - trend.shape[0]
      if pad_length > 0:
          buffer = pad_length * [np.nan]
          detrend = np.array(detrend.tolist() + buffer)
  
      # Determine the seasonal effect of the signal
      m_arr = np.reshape(detrend, (num_seasons, m))
      seasonal = np.nanmean(m_arr, axis=0).tolist()
      seasonal = np.array(seasonal[half_m:] + seasonal[:half_m])
      temp = seasonal
      for i in range(m_arr.shape[0]):
          seasonal = np.concatenate((seasonal, temp))
      if pad_length > 0:
          seasonal = seasonal[:-pad_length]
      if is_m_odd:
          seasonal = seasonal[:-1]
  
      # We buffer the trend and seasonal components so that they are the same
      # length as the other outputs. This counters the effects of losing data
      # by the convolution/sma
      buffer = [np.nan] * half_m
      trend = list(buffer + trend.tolist() + buffer)
  
      # Remove the trend and seasonal effects from the original signal to get
      # the random/noisy effects within the original signal.
      random = _decomposer_helper(
          _decomposer_helper(x, trend), seasonal
      )
  
      # Create a namedtuple so the output mirrors the output of the R function.
      decomposed = namedtuple("decomposed", "x trend seasonal random")
      decomposed_tuple = decomposed(x, trend, seasonal, random)
  
      return decomposed_tuple
  
imports: from collections import namedtuple
  import math
  from sklearn.linear_model import LinearRegression
  from sklearn.pipeline import make_pipeline
  from sklearn.preprocessing import StandardScaler
  from scipy.linalg import svd
  from statsmodels import api
  from statsmodels.tools import add_constant
  from abc import ABCMeta, abstractmethod
  from numpy.linalg import solve
  import numpy
  from .arima import _aicc
  from ..compat.numpy import DTYPE
  from .stationarity import _BaseStationarityTest
  from ..utils.array import c, diff, check_endog
  from ._arima import C_canova_hansen_sd_test
label_desc: Use image node_id 1 for calling a global function with example usage: decompose(x, type_, m, filter_) and returns: decomposed_tuple, unknown, unknown