<SYSTEM_TASK:>
Given the following text description, write Python code to implement the functionality described below step by step
<END_TASK>
<USER_TASK:>
Description:
 The Epochs data structure
Step1:  
Step2:  As we saw in the tut-events-vs-annotations tutorial, we can extract an
events array from 
Step3:  <div class="alert alert-info"><h4>Note</h4><p>We could also have loaded the events from file, using
    
Step4:  You'll see from the output that
Step5:  Notice that the Event IDs are in quotes; since we didn't provide an event
dictionary, the 
Step6:  This time let's pass preload=True and provide an event dictionary; our
provided dictionary will get stored as the event_id attribute and will
make referencing events and pooling across event types easier
Step7:  Notice that the output now mentions "1 bad epoch dropped". In the tutorial
section tut-reject-epochs-section we saw how you can specify channel
amplitude criteria for rejecting epochs, but here we haven't specified any
such criteria. In this case, it turns out that the last event was too close
the end of the (cropped) raw file to accommodate our requested tmax of
0.7 seconds, so the final epoch was dropped because it was too short. Here
are the drop_log entries for the last 4 epochs (empty lists indicate
epochs that were not dropped)
Step8:  <div class="alert alert-info"><h4>Note</h4><p>If you forget to provide the event dictionary to the 
Step9:  Notice that the individual epochs are sequentially numbered along the bottom
axis and are separated by vertical dashed lines.
Epoch plots are interactive (similar to 
Step10:  We can also pool across conditions easily, thanks to how MNE-Python handles
the / character in epoch labels (using what is sometimes called
"tag-based indexing")
Step11:  You can also pool conditions by passing multiple tags as a list. Note that
MNE-Python will not complain if you ask for tags not present in the object,
as long as it can find some match
Step12:  However, if no match is found, an error is returned
Step13:  Selecting epochs by index
Step14:  Selecting, dropping, and reordering channels
You can use the 
Step15:  Changing channel name and type
You can change the name or type of a channel using
Step16:  Selection in the time domain
To change the temporal extent of the 
Step17:  Cropping removed part of the baseline. When printing the
cropped 
Step18:  However, if you wanted to expand the time domain of an 
Step19:  Note that although time shifting respects the sampling frequency (the spacing
between samples), it does not enforce the assumption that there is a sample
occurring at exactly time=0.
Extracting data in other forms
The 
Step20:  Note that if your analysis requires repeatedly extracting single epochs from
an 
Step21:  See the tut-epochs-dataframe tutorial for many more examples of the
Step22:  The MNE-Python naming convention for epochs files is that the file basename
(the part before the .fif or .fif.gz extension) should end with
-epo or _epo, and a warning will be issued if the filename you
provide does not adhere to that convention.
As a final note, be aware that the class of the epochs object is different
when epochs are loaded from disk rather than generated from a
Step23:  In almost all cases this will not require changing anything about your code.
However, if you need to do type checking on epochs objects, you can test
against the base class that these classes are derived from
Step24:  Iterating over Epochs
Iterating over an 
Step25:  If you want to iterate over 
<ASSISTANT_TASK:>
Python Code:
import os
import mne
Explanation: The Epochs data structure: discontinuous data
This tutorial covers the basics of creating and working with :term:epoched
&lt;epochs&gt; data. It introduces the :class:~mne.Epochs data structure in
detail, including how to load, query, subselect, export, and plot data from an
:class:~mne.Epochs object. For more information about visualizing
:class:~mne.Epochs objects, see tut-visualize-epochs. For info on
creating an :class:~mne.Epochs object from (possibly simulated) data in a
:class:NumPy array &lt;numpy.ndarray&gt;, see tut-creating-data-structures.
As usual we'll start by importing the modules we need:
End of explanation
sample_data_folder = mne.datasets.sample.data_path()
sample_data_raw_file = os.path.join(sample_data_folder, 'MEG', 'sample',
                                    'sample_audvis_raw.fif')
raw = mne.io.read_raw_fif(sample_data_raw_file, verbose=False).crop(tmax=60)
Explanation: :class:~mne.Epochs objects are a data structure for representing and
analyzing equal-duration chunks of the EEG/MEG signal. :class:~mne.Epochs
are most often used to represent data that is time-locked to repeated
experimental events (such as stimulus onsets or subject button presses), but
can also be used for storing sequential or overlapping frames of a continuous
signal (e.g., for analysis of resting-state activity; see
fixed-length-events). Inside an :class:~mne.Epochs object, the data
are stored in an :class:array &lt;numpy.ndarray&gt; of shape (n_epochs,
n_channels, n_times).
:class:~mne.Epochs objects have many similarities with :class:~mne.io.Raw
objects, including:
They can be loaded from and saved to disk in .fif format, and their
  data can be exported to a :class:NumPy array &lt;numpy.ndarray&gt; through the
  :meth:~mne.Epochs.get_data method or to a :class:Pandas DataFrame
  &lt;pandas.DataFrame&gt; through the :meth:~mne.Epochs.to_data_frame method.
Both :class:~mne.Epochs and :class:~mne.io.Raw objects support channel
  selection by index or name, including :meth:~mne.Epochs.pick,
  :meth:~mne.Epochs.pick_channels and :meth:~mne.Epochs.pick_types
  methods.
:term:SSP projector &lt;projector&gt; manipulation is possible through
  :meth:~mne.Epochs.add_proj, :meth:~mne.Epochs.del_proj, and
  :meth:~mne.Epochs.plot_projs_topomap methods.
Both :class:~mne.Epochs and :class:~mne.io.Raw objects have
  :meth:~mne.Epochs.copy, :meth:~mne.Epochs.crop,
  :meth:~mne.Epochs.time_as_index, :meth:~mne.Epochs.filter, and
  :meth:~mne.Epochs.resample methods.
Both :class:~mne.Epochs and :class:~mne.io.Raw objects have
  :attr:~mne.Epochs.times, :attr:~mne.Epochs.ch_names,
  :attr:~mne.Epochs.proj, and :class:info &lt;mne.Info&gt; attributes.
Both :class:~mne.Epochs and :class:~mne.io.Raw objects have built-in
  plotting methods :meth:~mne.Epochs.plot, :meth:~mne.Epochs.plot_psd,
  and :meth:~mne.Epochs.plot_psd_topomap.
Creating Epoched data from a Raw object
The example dataset we've been using thus far doesn't include pre-epoched
data, so in this section we'll load the continuous data and create epochs
based on the events recorded in the :class:~mne.io.Raw object's STIM
channels. As we often do in these tutorials, we'll :meth:~mne.io.Raw.crop
the :class:~mne.io.Raw data to save memory:
End of explanation
events = mne.find_events(raw, stim_channel='STI 014')
Explanation: As we saw in the tut-events-vs-annotations tutorial, we can extract an
events array from :class:~mne.io.Raw objects using :func:mne.find_events:
End of explanation
epochs = mne.Epochs(raw, events, tmin=-0.3, tmax=0.7)
Explanation: <div class="alert alert-info"><h4>Note</h4><p>We could also have loaded the events from file, using
    :func:`mne.read_events`::
        sample_data_events_file = os.path.join(sample_data_folder,
                                               'MEG', 'sample',
                                               'sample_audvis_raw-eve.fif')
        events_from_file = mne.read_events(sample_data_events_file)
    See `tut-section-events-io` for more details.</p></div>
The :class:~mne.io.Raw object and the events array are the bare minimum
needed to create an :class:~mne.Epochs object, which we create with the
:class:mne.Epochs class constructor. However, you will almost surely want
to change some of the other default parameters. Here we'll change tmin
and tmax (the time relative to each event at which to start and end each
epoch). Note also that the :class:~mne.Epochs constructor accepts
parameters reject and flat for rejecting individual epochs based on
signal amplitude. See the tut-reject-epochs-section section for
examples.
End of explanation
print(epochs)
Explanation: You'll see from the output that:
all 320 events were used to create epochs
baseline correction was automatically applied (by default, baseline is
  defined as the time span from tmin to 0, but can be customized with
  the baseline parameter)
no additional metadata was provided (see tut-epochs-metadata for
  details)
the projection operators present in the :class:~mne.io.Raw file were
  copied over to the :class:~mne.Epochs object
If we print the :class:~mne.Epochs object, we'll also see a note that the
epochs are not copied into memory by default, and a count of the number of
epochs created for each integer Event ID.
End of explanation
print(epochs.event_id)
Explanation: Notice that the Event IDs are in quotes; since we didn't provide an event
dictionary, the :class:mne.Epochs constructor created one automatically and
used the string representation of the integer Event IDs as the dictionary
keys. This is more clear when viewing the event_id attribute:
End of explanation
event_dict = {'auditory/left': 1, 'auditory/right': 2, 'visual/left': 3,
              'visual/right': 4, 'face': 5, 'buttonpress': 32}
epochs = mne.Epochs(raw, events, tmin=-0.3, tmax=0.7, event_id=event_dict,
                    preload=True)
print(epochs.event_id)
del raw  # we're done with raw, free up some memory
Explanation: This time let's pass preload=True and provide an event dictionary; our
provided dictionary will get stored as the event_id attribute and will
make referencing events and pooling across event types easier:
End of explanation
print(epochs.drop_log[-4:])
Explanation: Notice that the output now mentions "1 bad epoch dropped". In the tutorial
section tut-reject-epochs-section we saw how you can specify channel
amplitude criteria for rejecting epochs, but here we haven't specified any
such criteria. In this case, it turns out that the last event was too close
the end of the (cropped) raw file to accommodate our requested tmax of
0.7 seconds, so the final epoch was dropped because it was too short. Here
are the drop_log entries for the last 4 epochs (empty lists indicate
epochs that were not dropped):
End of explanation
epochs.plot(n_epochs=10)
Explanation: <div class="alert alert-info"><h4>Note</h4><p>If you forget to provide the event dictionary to the :class:`~mne.Epochs`
    constructor, you can add it later by assigning to the ``event_id``
    attribute::
        epochs.event_id = event_dict</p></div>
Basic visualization of Epochs objects
The :class:~mne.Epochs object can be visualized (and browsed interactively)
using its :meth:~mne.Epochs.plot method:
End of explanation
print(epochs['face'])
Explanation: Notice that the individual epochs are sequentially numbered along the bottom
axis and are separated by vertical dashed lines.
Epoch plots are interactive (similar to :meth:raw.plot()
&lt;mne.io.Raw.plot&gt;) and have many of the same interactive controls as
:class:~mne.io.Raw plots. Horizontal and vertical scrollbars allow browsing
through epochs or channels (respectively), and pressing :kbd:? when the
plot is focused will show a help screen with all the available controls. See
tut-visualize-epochs for more details (as well as other ways of
visualizing epoched data).
Subselecting epochs
Now that we have our :class:~mne.Epochs object with our descriptive event
labels added, we can subselect epochs easily using square brackets. For
example, we can load all the "catch trials" where the stimulus was a face:
End of explanation
# pool across left + right
print(epochs['auditory'])
assert len(epochs['auditory']) == (len(epochs['auditory/left']) +
                                   len(epochs['auditory/right']))
# pool across auditory + visual
print(epochs['left'])
assert len(epochs['left']) == (len(epochs['auditory/left']) +
                               len(epochs['visual/left']))
Explanation: We can also pool across conditions easily, thanks to how MNE-Python handles
the / character in epoch labels (using what is sometimes called
"tag-based indexing"):
End of explanation
print(epochs[['right', 'bottom']])
Explanation: You can also pool conditions by passing multiple tags as a list. Note that
MNE-Python will not complain if you ask for tags not present in the object,
as long as it can find some match: the below example is parsed as
(inclusive) 'right' or 'bottom', and you can see from the output
that it selects only auditory/right and visual/right.
End of explanation
try:
    print(epochs[['top', 'bottom']])
except KeyError:
    print('Tag-based selection with no matches raises a KeyError!')
Explanation: However, if no match is found, an error is returned:
End of explanation
print(epochs[:10])    # epochs 0-9
print(epochs[1:8:2])  # epochs 1, 3, 5, 7
print(epochs['buttonpress'][:4])            # first 4 "buttonpress" epochs
print(epochs['buttonpress'][[0, 1, 2, 3]])  # same as previous line
Explanation: Selecting epochs by index
:class:~mne.Epochs objects can also be indexed with integers, :term:slices
&lt;slice&gt;, or lists of integers. This method of selection ignores event
labels, so if you want the first 10 epochs of a particular type, you can
select the type first, then use integers or slices:
End of explanation
epochs_eeg = epochs.copy().pick_types(meg=False, eeg=True)
print(epochs_eeg.ch_names)
new_order = ['EEG 002', 'STI 014', 'EOG 061', 'MEG 2521']
epochs_subset = epochs.copy().reorder_channels(new_order)
print(epochs_subset.ch_names)
del epochs_eeg, epochs_subset
Explanation: Selecting, dropping, and reordering channels
You can use the :meth:~mne.Epochs.pick, :meth:~mne.Epochs.pick_channels,
:meth:~mne.Epochs.pick_types, and :meth:~mne.Epochs.drop_channels methods
to modify which channels are included in an :class:~mne.Epochs object. You
can also use :meth:~mne.Epochs.reorder_channels for this purpose; any
channel names not provided to :meth:~mne.Epochs.reorder_channels will be
dropped. Note that these channel selection methods modify the object
in-place (unlike the square-bracket indexing to select epochs seen above)
so in interactive/exploratory sessions you may want to create a
:meth:~mne.Epochs.copy first.
End of explanation
epochs.rename_channels({'EOG 061': 'BlinkChannel'})
epochs.set_channel_types({'EEG 060': 'ecg'})
print(list(zip(epochs.ch_names, epochs.get_channel_types()))[-4:])
# let's set them back to the correct values before moving on
epochs.rename_channels({'BlinkChannel': 'EOG 061'})
epochs.set_channel_types({'EEG 060': 'eeg'})
Explanation: Changing channel name and type
You can change the name or type of a channel using
:meth:~mne.Epochs.rename_channels or :meth:~mne.Epochs.set_channel_types.
Both methods take :class:dictionaries &lt;dict&gt; where the keys are existing
channel names, and the values are the new name (or type) for that channel.
Existing channels that are not in the dictionary will be unchanged.
End of explanation
shorter_epochs = epochs.copy().crop(tmin=-0.1, tmax=0.1, include_tmax=True)
for name, obj in dict(Original=epochs, Cropped=shorter_epochs).items():
    print('{} epochs has {} time samples'
          .format(name, obj.get_data().shape[-1]))
Explanation: Selection in the time domain
To change the temporal extent of the :class:~mne.Epochs, you can use the
:meth:~mne.Epochs.crop method:
End of explanation
print(shorter_epochs)
Explanation: Cropping removed part of the baseline. When printing the
cropped :class:~mne.Epochs, MNE-Python will inform you about the time
period that was originally used to perform baseline correction by displaying
the string "baseline period cropped after baseline correction":
End of explanation
# shift times so that first sample of each epoch is at time zero
later_epochs = epochs.copy().shift_time(tshift=0., relative=False)
print(later_epochs.times[:3])
# shift times by a relative amount
later_epochs.shift_time(tshift=-7, relative=True)
print(later_epochs.times[:3])
del shorter_epochs, later_epochs
Explanation: However, if you wanted to expand the time domain of an :class:~mne.Epochs
object, you would need to go back to the :class:~mne.io.Raw data and
recreate the :class:~mne.Epochs with different values for tmin and/or
tmax.
It is also possible to change the "zero point" that defines the time values
in an :class:~mne.Epochs object, with the :meth:~mne.Epochs.shift_time
method. :meth:~mne.Epochs.shift_time allows shifting times relative to the
current values, or specifying a fixed time to set as the new time value of
the first sample (deriving the new time values of subsequent samples based on
the :class:~mne.Epochs object's sampling frequency).
End of explanation
eog_data = epochs.get_data(picks='EOG 061')
meg_data = epochs.get_data(picks=['mag', 'grad'])
channel_4_6_8 = epochs.get_data(picks=slice(4, 9, 2))
for name, arr in dict(EOG=eog_data, MEG=meg_data, Slice=channel_4_6_8).items():
    print('{} contains {} channels'.format(name, arr.shape[1]))
Explanation: Note that although time shifting respects the sampling frequency (the spacing
between samples), it does not enforce the assumption that there is a sample
occurring at exactly time=0.
Extracting data in other forms
The :meth:~mne.Epochs.get_data method returns the epoched data as a
:class:NumPy array &lt;numpy.ndarray&gt;, of shape (n_epochs, n_channels,
n_times); an optional picks parameter selects a subset of channels by
index, name, or type:
End of explanation
df = epochs.to_data_frame(index=['condition', 'epoch', 'time'])
df.sort_index(inplace=True)
print(df.loc[('auditory/left', slice(0, 10), slice(100, 107)),
             'EEG 056':'EEG 058'])
del df
Explanation: Note that if your analysis requires repeatedly extracting single epochs from
an :class:~mne.Epochs object, epochs.get_data(item=2) will be much
faster than epochs[2].get_data(), because it avoids the step of
subsetting the :class:~mne.Epochs object first.
You can also export :class:~mne.Epochs data to :class:Pandas DataFrames
&lt;pandas.DataFrame&gt;. Here, the :class:~pandas.DataFrame index will be
constructed by converting the time of each sample into milliseconds and
rounding it to the nearest integer, and combining it with the event types and
epoch numbers to form a hierarchical :class:~pandas.MultiIndex. Each
channel will appear in a separate column. Then you can use any of Pandas'
tools for grouping and aggregating data; for example, here we select any
epochs numbered 10 or less from the auditory/left condition, and extract
times between 100 and 107 ms on channels EEG 056 through EEG 058
(note that slice indexing within Pandas' :obj:~pandas.DataFrame.loc is
inclusive of the endpoint):
End of explanation
epochs.save('saved-audiovisual-epo.fif', overwrite=True)
epochs_from_file = mne.read_epochs('saved-audiovisual-epo.fif', preload=False)
Explanation: See the tut-epochs-dataframe tutorial for many more examples of the
:meth:~mne.Epochs.to_data_frame method.
Loading and saving Epochs objects to disk
:class:~mne.Epochs objects can be loaded and saved in the .fif format
just like :class:~mne.io.Raw objects, using the :func:mne.read_epochs
function and the :meth:~mne.Epochs.save method. Functions are also
available for loading data that was epoched outside of MNE-Python, such as
:func:mne.read_epochs_eeglab and :func:mne.read_epochs_kit.
End of explanation
print(type(epochs))
print(type(epochs_from_file))
Explanation: The MNE-Python naming convention for epochs files is that the file basename
(the part before the .fif or .fif.gz extension) should end with
-epo or _epo, and a warning will be issued if the filename you
provide does not adhere to that convention.
As a final note, be aware that the class of the epochs object is different
when epochs are loaded from disk rather than generated from a
:class:~mne.io.Raw object:
End of explanation
print(all([isinstance(epochs, mne.BaseEpochs),
           isinstance(epochs_from_file, mne.BaseEpochs)]))
Explanation: In almost all cases this will not require changing anything about your code.
However, if you need to do type checking on epochs objects, you can test
against the base class that these classes are derived from:
End of explanation
for epoch in epochs[:3]:
    print(type(epoch))
Explanation: Iterating over Epochs
Iterating over an :class:~mne.Epochs object will yield :class:arrays
&lt;numpy.ndarray&gt; rather than single-trial :class:~mne.Epochs objects:
End of explanation
for index in range(3):
    print(type(epochs[index]))
Explanation: If you want to iterate over :class:~mne.Epochs objects, you can use an
integer index as the iterator:
End of explanation
<END_TASK>