code: def calculate_feature_matrix(
      features,
      entityset=None,
      cutoff_time=None,
      instance_ids=None,
      dataframes=None,
      relationships=None,
      cutoff_time_in_index=False,
      training_window=None,
      approximate=None,
      save_progress=None,
      verbose=False,
      chunk_size=None,
      n_jobs=1,
      dask_kwargs=None,
      progress_callback=None,
      include_cutoff_time=True,
  ):
      """Calculates a matrix for a given set of instance ids and calculation times.
  
      Args:
          features (list[:class:`.FeatureBase`]): Feature definitions to be calculated.
  
          entityset (EntitySet): An already initialized entityset. Required if `dataframes` and `relationships`
              not provided
  
          cutoff_time (pd.DataFrame or Datetime): Specifies times at which to calculate
              the features for each instance. The resulting feature matrix will use data
              up to and including the cutoff_time. Can either be a DataFrame or a single
              value. If a DataFrame is passed the instance ids for which to calculate features
              must be in a column with the same name as the target dataframe index or a column
              named `instance_id`. The cutoff time values in the DataFrame must be in a column with
              the same name as the target dataframe time index or a column named `time`. If the
              DataFrame has more than two columns, any additional columns will be added to the
              resulting feature matrix. If a single value is passed, this value will be used for
              all instances.
  
          instance_ids (list): List of instances to calculate features on. Only
              used if cutoff_time is a single datetime.
  
          dataframes (dict[str -> tuple(DataFrame, str, str, dict[str -> str/Woodwork.LogicalType], dict[str->str/set], boolean)]):
              Dictionary of DataFrames. Entries take the format
              {dataframe name -> (dataframe, index column, time_index, logical_types, semantic_tags, make_index)}.
              Note that only the dataframe is required. If a Woodwork DataFrame is supplied, any other parameters
              will be ignored.
  
          relationships (list[(str, str, str, str)]): list of relationships
              between dataframes. List items are a tuple with the format
              (parent dataframe name, parent column, child dataframe name, child column).
  
          cutoff_time_in_index (bool): If True, return a DataFrame with a MultiIndex
              where the second index is the cutoff time (first is instance id).
              DataFrame will be sorted by (time, instance_id).
  
          training_window (Timedelta or str, optional):
              Window defining how much time before the cutoff time data
              can be used when calculating features. If ``None``, all data before cutoff time is used.
              Defaults to ``None``.
  
          approximate (Timedelta or str): Frequency to group instances with similar
              cutoff times by for features with costly calculations. For example,
              if bucket is 24 hours, all instances with cutoff times on the same
              day will use the same calculation for expensive features.
  
          verbose (bool, optional): Print progress info. The time granularity is
              per chunk.
  
          chunk_size (int or float or None): maximum number of rows of
              output feature matrix to calculate at time. If passed an integer
              greater than 0, will try to use that many rows per chunk. If passed
              a float value between 0 and 1 sets the chunk size to that
              percentage of all rows. if None, and n_jobs > 1 it will be set to 1/n_jobs
  
          n_jobs (int, optional): number of parallel processes to use when
              calculating feature matrix. Requires Dask if not equal to 1.
  
          dask_kwargs (dict, optional): Dictionary of keyword arguments to be
              passed when creating the dask client and scheduler. Even if n_jobs
              is not set, using `dask_kwargs` will enable multiprocessing.
              Main parameters:
  
              cluster (str or dask.distributed.LocalCluster):
                  cluster or address of cluster to send tasks to. If unspecified,
                  a cluster will be created.
              diagnostics port (int):
                  port number to use for web dashboard.  If left unspecified, web
                  interface will not be enabled.
  
              Valid keyword arguments for LocalCluster will also be accepted.
  
          save_progress (str, optional): path to save intermediate computational results.
  
          progress_callback (callable): function to be called with incremental progress updates.
              Has the following parameters:
  
                  update: percentage change (float between 0 and 100) in progress since last call
                  progress_percent: percentage (float between 0 and 100) of total computation completed
                  time_elapsed: total time in seconds that has elapsed since start of call
  
          include_cutoff_time (bool): Include data at cutoff times in feature calculations. Defaults to ``True``.
  
      Returns:
          pd.DataFrame: The feature matrix.
      """
      assert (
          isinstance(features, list)
          and features != []
          and all(
              [isinstance(feature, FeatureBase) for feature in features]
          )
      ), "features must be a non-empty list of features"
  
      # handle loading entityset
      from featuretools.entityset.entityset import EntitySet
  
      if not isinstance(entityset, EntitySet):
          if dataframes is not None:
              entityset = EntitySet(
                  "entityset", dataframes, relationships
              )
          else:
              raise TypeError(
                  "No dataframes or valid EntitySet provided"
              )
  
      if entityset.dataframe_type == Library.DASK:
          if approximate:
              msg = "Using approximate is not supported with Dask dataframes"
              raise ValueError(msg)
          if training_window:
              msg = "Using training_window is not supported with Dask dataframes"
              raise ValueError(msg)
  
      target_dataframe = entityset[features[0].dataframe_name]
  
      cutoff_time = _validate_cutoff_time(cutoff_time, target_dataframe)
      entityset._check_time_indexes()
  
      if isinstance(cutoff_time, pd.DataFrame):
          if instance_ids:
              msg = "Passing 'instance_ids' is valid only if 'cutoff_time' is a single value or None - ignoring"
              warnings.warn(msg)
          pass_columns = [
              col
              for col in cutoff_time.columns
              if col not in ["instance_id", "time"]
          ]
          # make sure dtype of instance_id in cutoff time
          # is same as column it references
          target_dataframe = features[0].dataframe
          ltype = target_dataframe.ww.logical_types[
              target_dataframe.ww.index
          ]
          cutoff_time.ww.init(logical_types={"instance_id": ltype})
      else:
          pass_columns = []
          if cutoff_time is None:
              if entityset.time_type == "numeric":
                  cutoff_time = np.inf
              else:
                  cutoff_time = datetime.now()
  
          if instance_ids is None:
              index_col = target_dataframe.ww.index
              df = entityset._handle_time(
                  dataframe_name=target_dataframe.ww.name,
                  df=target_dataframe,
                  time_last=cutoff_time,
                  training_window=training_window,
                  include_cutoff_time=include_cutoff_time,
              )
              instance_ids = df[index_col]
  
          if is_instance(instance_ids, dd, "Series"):
              instance_ids = instance_ids.compute()
          elif is_instance(instance_ids, ps, "Series"):
              instance_ids = instance_ids.to_pandas()
  
          # convert list or range object into series
          if not isinstance(instance_ids, pd.Series):
              instance_ids = pd.Series(instance_ids)
  
          cutoff_time = (cutoff_time, instance_ids)
  
      _check_cutoff_time_type(cutoff_time, entityset.time_type)
  
      # Approximate provides no benefit with a single cutoff time, so ignore it
      if isinstance(cutoff_time, tuple) and approximate is not None:
          msg = (
              "Using approximate with a single cutoff_time value or no cutoff_time "
              "provides no computational efficiency benefit"
          )
          warnings.warn(msg)
          cutoff_time = pd.DataFrame(
              {
                  "instance_id": cutoff_time[1],
                  "time": [cutoff_time[0]] * len(cutoff_time[1]),
              },
          )
          target_dataframe = features[0].dataframe
          ltype = target_dataframe.ww.logical_types[
              target_dataframe.ww.index
          ]
          cutoff_time.ww.init(logical_types={"instance_id": ltype})
  
      feature_set = FeatureSet(features)
  
      # Get features to approximate
      if approximate is not None:
          approximate_feature_trie = gather_approximate_features(
              feature_set
          )
          # Make a new FeatureSet that ignores approximated features
          feature_set = FeatureSet(
              features,
              approximate_feature_trie=approximate_feature_trie,
          )
  
      # Check if there are any non-approximated aggregation features
      no_unapproximated_aggs = True
      for feature in features:
          if isinstance(feature, AggregationFeature):
              # do not need to check if feature is in to_approximate since
              # only base features of direct features can be in to_approximate
              no_unapproximated_aggs = False
              break
  
          if approximate is not None:
              all_approx_features = {
                  f
                  for _, feats in feature_set.approximate_feature_trie
                  for f in feats
              }
          else:
              all_approx_features = set()
          deps = feature.get_dependencies(
              deep=True, ignored=all_approx_features
          )
          for dependency in deps:
              if isinstance(dependency, AggregationFeature):
                  no_unapproximated_aggs = False
                  break
  
      cutoff_df_time_col = "time"
      target_time = "_original_time"
  
      if approximate is not None:
          # If there are approximated aggs, bin times
          binned_cutoff_time = bin_cutoff_times(
              cutoff_time, approximate
          )
  
          # Think about collisions: what if original time is a feature
          binned_cutoff_time.ww[target_time] = cutoff_time[
              cutoff_df_time_col
          ]
  
          cutoff_time_to_pass = binned_cutoff_time
  
      else:
          cutoff_time_to_pass = cutoff_time
  
      if isinstance(cutoff_time, pd.DataFrame):
          cutoff_time_len = cutoff_time.shape[0]
      else:
          cutoff_time_len = len(cutoff_time[1])
  
      chunk_size = _handle_chunk_size(chunk_size, cutoff_time_len)
      tqdm_options = {
          "total": (cutoff_time_len / FEATURE_CALCULATION_PERCENTAGE),
          "bar_format": PBAR_FORMAT,
          "disable": True,
      }
  
      if verbose:
          tqdm_options.update({"disable": False})
      elif progress_callback is not None:
          # allows us to utilize progress_bar updates without printing to anywhere
          tqdm_options.update(
              {"file": open(os.devnull, "w"), "disable": False}
          )
  
      with make_tqdm_iterator(**tqdm_options) as progress_bar:
          if n_jobs != 1 or dask_kwargs is not None:
              feature_matrix = parallel_calculate_chunks(
                  cutoff_time=cutoff_time_to_pass,
                  chunk_size=chunk_size,
                  feature_set=feature_set,
                  approximate=approximate,
                  training_window=training_window,
                  save_progress=save_progress,
                  entityset=entityset,
                  n_jobs=n_jobs,
                  no_unapproximated_aggs=no_unapproximated_aggs,
                  cutoff_df_time_col=cutoff_df_time_col,
                  target_time=target_time,
                  pass_columns=pass_columns,
                  progress_bar=progress_bar,
                  dask_kwargs=dask_kwargs or {},
                  progress_callback=progress_callback,
                  include_cutoff_time=include_cutoff_time,
              )
          else:
              feature_matrix = calculate_chunk(
                  cutoff_time=cutoff_time_to_pass,
                  chunk_size=chunk_size,
                  feature_set=feature_set,
                  approximate=approximate,
                  training_window=training_window,
                  save_progress=save_progress,
                  entityset=entityset,
                  no_unapproximated_aggs=no_unapproximated_aggs,
                  cutoff_df_time_col=cutoff_df_time_col,
                  target_time=target_time,
                  pass_columns=pass_columns,
                  progress_bar=progress_bar,
                  progress_callback=progress_callback,
                  include_cutoff_time=include_cutoff_time,
              )
  
          # ensure rows are sorted by input order
          if isinstance(feature_matrix, pd.DataFrame):
              if isinstance(cutoff_time, pd.DataFrame):
                  feature_matrix = feature_matrix.ww.reindex(
                      pd.MultiIndex.from_frame(
                          cutoff_time[["instance_id", "time"]],
                          names=feature_matrix.index.names,
                      ),
                  )
              else:
                  # Maintain index dtype
                  index_dtype = feature_matrix.index.get_level_values(
                      0
                  ).dtype
                  feature_matrix = feature_matrix.ww.reindex(
                      cutoff_time[1].astype(index_dtype),
                      level=0,
                  )
              if not cutoff_time_in_index:
                  feature_matrix.ww.reset_index(
                      level="time", drop=True, inplace=True
                  )
  
          if save_progress and os.path.exists(
              os.path.join(save_progress, "temp")
          ):
              shutil.rmtree(os.path.join(save_progress, "temp"))
  
          # force to 100% since we saved last 5 percent
          previous_progress = progress_bar.n
          progress_bar.update(progress_bar.total - progress_bar.n)
  
          if progress_callback is not None:
              (
                  update,
                  progress_percent,
                  time_elapsed,
              ) = update_progress_callback_parameters(
                  progress_bar, previous_progress
              )
              progress_callback(update, progress_percent, time_elapsed)
  
          progress_bar.refresh()
  
      return feature_matrix
  
imports: import logging
  import math
  import os
  import shutil
  import time
  import warnings
  from datetime import datetime
  import cloudpickle
  import numpy
  import pandas
  from woodwork.logical_types import Age, AgeNullable, Boolean, BooleanNullable, Integer, IntegerNullable
  from featuretools.computational_backends.feature_set import FeatureSet
  from featuretools.computational_backends.feature_set_calculator import FeatureSetCalculator
  from featuretools.computational_backends.utils import _check_cutoff_time_type, _validate_cutoff_time, bin_cutoff_times, create_client_and_cluster, gather_approximate_features, gen_empty_approx_features_df, get_ww_types_from_features, save_csv_decorator
  from featuretools.entityset.relationship import RelationshipPath
  from featuretools.feature_base import AggregationFeature, FeatureBase
  from featuretools.utils import Trie
  from featuretools.utils.gen_utils import Library, import_or_none, import_or_raise, is_instance, make_tqdm_iterator
label_desc: Use image node_id 1 for calling a global function with example usage: calculate_feature_matrix(features, entityset, cutoff_time, instance_ids, dataframes, relationships, cutoff_time_in_index, training_window, approximate, save_progress, verbose, chunk_size, n_jobs, dask_kwargs, progress_callback, include_cutoff_time) and returns: feature_matrix