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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 The Evoked data structure
Step1:  Creating Evoked objects from Epochs
Step2:  You may have noticed that MNE informed us that "baseline correction" has been
applied. This happened automatically by during creation of the
~mne.Epochs object, but may also be initiated (or disabled!) manually
Step3:  Basic visualization of Evoked objects
We can visualize the average evoked response for left-auditory stimuli using
the 
Step4:  Like the plot() methods for 
Step5:  To select based on time in seconds, the 
Step6:  Similarities among the core data structures
Step7:  Notice that 
Step8:  If you want to load only some of the conditions present in a .fif file,
Step9:  Above, when we created an 
Step10:  This can be remedied by either passing a baseline parameter to
Step11:  Notice that 
Step12:  This approach will weight each epoch equally and create a single
Step13:  However, this may not always be the case; if for statistical reasons it is
important to average the same number of epochs from different conditions,
you can use 
Step14:  Note that the nave attribute of the resulting ~mne.Evoked object will
reflect the effective number of averages, and depends on both the nave
attributes of the contributing ~mne.Evoked objects and the weights at
which they are combined. Keeping track of effective nave is important for
inverse imaging, because nave is used to scale the noise covariance
estimate (which in turn affects the magnitude of estimated source activity).
See minimum_norm_estimates for more information (especially the
whitening_and_scaling section). Note that mne.grand_average does
not adjust nave to reflect effective number of averaged epochs; rather
it simply sets nave to the number of evokeds that were averaged
together. For this reason, it is best to use mne.combine_evoked rather than
mne.grand_average if you intend to perform inverse imaging on the resulting
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Python Code:
import os
import mne
Explanation: The Evoked data structure: evoked/averaged data
This tutorial covers the basics of creating and working with :term:evoked
data. It introduces the :class:~mne.Evoked data structure in detail,
including how to load, query, subselect, export, and plot data from an
:class:~mne.Evoked object. For info on creating an :class:~mne.Evoked
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)
events = mne.find_events(raw, stim_channel='STI 014')
# we'll skip the "face" and "buttonpress" conditions, to save memory:
event_dict = {'auditory/left': 1, 'auditory/right': 2, 'visual/left': 3,
              'visual/right': 4}
epochs = mne.Epochs(raw, events, tmin=-0.3, tmax=0.7, event_id=event_dict,
                    preload=True)
evoked = epochs['auditory/left'].average()
del raw  # reduce memory usage
Explanation: Creating Evoked objects from Epochs
:class:~mne.Evoked objects typically store an EEG or MEG signal that has
been averaged over multiple :term:epochs, which is a common technique for
estimating stimulus-evoked activity. The data in an :class:~mne.Evoked
object are stored in an :class:array &lt;numpy.ndarray&gt; of shape
(n_channels, n_times) (in contrast to an :class:~mne.Epochs object,
which stores data of shape (n_epochs, n_channels, n_times)). Thus to
create an :class:~mne.Evoked object, we'll start by epoching some raw data,
and then averaging together all the epochs from one condition:
End of explanation
print(f'Epochs baseline: {epochs.baseline}')
print(f'Evoked baseline: {evoked.baseline}')
Explanation: You may have noticed that MNE informed us that "baseline correction" has been
applied. This happened automatically by during creation of the
~mne.Epochs object, but may also be initiated (or disabled!) manually:
We will discuss this in more detail later.
The information about the baseline period of ~mne.Epochs is transferred to
derived ~mne.Evoked objects to maintain provenance as you process your
data:
End of explanation
evoked.plot()
Explanation: Basic visualization of Evoked objects
We can visualize the average evoked response for left-auditory stimuli using
the :meth:~mne.Evoked.plot method, which yields a butterfly plot of each
channel type:
End of explanation
print(evoked.data[:2, :3])  # first 2 channels, first 3 timepoints
Explanation: Like the plot() methods for :meth:Raw &lt;mne.io.Raw.plot&gt; and
:meth:Epochs &lt;mne.Epochs.plot&gt; objects,
:meth:evoked.plot() &lt;mne.Evoked.plot&gt; has many parameters for customizing
the plot output, such as color-coding channel traces by scalp location, or
plotting the :term:global field power alongside the channel traces.
See tut-visualize-evoked for more information about visualizing
:class:~mne.Evoked objects.
Subselecting Evoked data
.. sidebar:: Evokeds are not memory-mapped
:class:~mne.Evoked objects use a :attr:~mne.Evoked.data attribute
  rather than a :meth:~mne.Epochs.get_data method; this reflects the fact
  that the data in :class:~mne.Evoked objects are always loaded into
  memory, never memory-mapped_ from their location on disk (because they
  are typically much smaller than :class:~mne.io.Raw or
  :class:~mne.Epochs objects).
Unlike :class:~mne.io.Raw and :class:~mne.Epochs objects,
:class:~mne.Evoked objects do not support selection by square-bracket
indexing. Instead, data can be subselected by indexing the
:attr:~mne.Evoked.data attribute:
End of explanation
evoked_eeg = evoked.copy().pick_types(meg=False, eeg=True)
print(evoked_eeg.ch_names)
new_order = ['EEG 002', 'MEG 2521', 'EEG 003']
evoked_subset = evoked.copy().reorder_channels(new_order)
print(evoked_subset.ch_names)
Explanation: To select based on time in seconds, the :meth:~mne.Evoked.time_as_index
method can be useful, although beware that depending on the sampling
frequency, the number of samples in a span of given duration may not always
be the same (see the time-as-index section of the
tutorial about Raw data &lt;tut-raw-class&gt; for details).
Selecting, dropping, and reordering channels
By default, when creating :class:~mne.Evoked data from an
:class:~mne.Epochs object, only the "data" channels will be retained:
eog, ecg, stim, and misc channel types will be dropped. You
can control which channel types are retained via the picks parameter of
:meth:epochs.average() &lt;mne.Epochs.average&gt;, by passing 'all' to
retain all channels, or by passing a list of integers, channel names, or
channel types. See the documentation of :meth:~mne.Epochs.average for
details.
If you've already created the :class:~mne.Evoked object, you can use the
:meth:~mne.Evoked.pick, :meth:~mne.Evoked.pick_channels,
:meth:~mne.Evoked.pick_types, and :meth:~mne.Evoked.drop_channels methods
to modify which channels are included in an :class:~mne.Evoked object.
You can also use :meth:~mne.Evoked.reorder_channels for this purpose; any
channel names not provided to :meth:~mne.Evoked.reorder_channels will be
dropped. Note that channel selection methods modify the object in-place, so
in interactive/exploratory sessions you may want to create a
:meth:~mne.Evoked.copy first.
End of explanation
sample_data_evk_file = os.path.join(sample_data_folder, 'MEG', 'sample',
                                    'sample_audvis-ave.fif')
evokeds_list = mne.read_evokeds(sample_data_evk_file, verbose=False)
print(evokeds_list)
print(type(evokeds_list))
Explanation: Similarities among the core data structures
:class:~mne.Evoked objects have many similarities with :class:~mne.io.Raw
and :class:~mne.Epochs 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; (but through
  the :attr:~mne.Evoked.data attribute, not through a get_data()
  method). :class:Pandas DataFrame &lt;pandas.DataFrame&gt; export is also
  available through the :meth:~mne.Evoked.to_data_frame method.
You can change the name or type of a channel using
  :meth:evoked.rename_channels() &lt;mne.Evoked.rename_channels&gt; or
  :meth:evoked.set_channel_types() &lt;mne.Evoked.set_channel_types&gt;.
  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.
:term:SSP projector &lt;projector&gt; manipulation is possible through
  :meth:~mne.Evoked.add_proj, :meth:~mne.Evoked.del_proj, and
  :meth:~mne.Evoked.plot_projs_topomap methods, and the
  :attr:~mne.Evoked.proj attribute. See tut-artifact-ssp for more
  information on SSP.
Like :class:~mne.io.Raw and :class:~mne.Epochs objects,
  :class:~mne.Evoked objects have :meth:~mne.Evoked.copy,
  :meth:~mne.Evoked.crop, :meth:~mne.Evoked.time_as_index,
  :meth:~mne.Evoked.filter, and :meth:~mne.Evoked.resample methods.
Like :class:~mne.io.Raw and :class:~mne.Epochs objects,
  :class:~mne.Evoked objects have evoked.times,
  :attr:evoked.ch_names &lt;mne.Evoked.ch_names&gt;, and :class:info &lt;mne.Info&gt;
  attributes.
Loading and saving Evoked data
Single :class:~mne.Evoked objects can be saved to disk with the
:meth:evoked.save() &lt;mne.Evoked.save&gt; method. One difference between
:class:~mne.Evoked objects and the other data structures is that multiple
:class:~mne.Evoked objects can be saved into a single .fif file, using
:func:mne.write_evokeds. The example data &lt;sample-dataset&gt;
includes just such a .fif file: the data have already been epoched and
averaged, and the file contains separate :class:~mne.Evoked objects for
each experimental condition:
End of explanation
for evok in evokeds_list:
    print(evok.comment)
Explanation: Notice that :func:mne.read_evokeds returned a :class:list of
:class:~mne.Evoked objects, and each one has an evoked.comment
attribute describing the experimental condition that was averaged to
generate the estimate:
End of explanation
right_vis = mne.read_evokeds(sample_data_evk_file, condition='Right visual')
print(right_vis)
print(type(right_vis))
Explanation: If you want to load only some of the conditions present in a .fif file,
:func:~mne.read_evokeds has a condition parameter, which takes either a
string (matched against the comment attribute of the evoked objects on disk),
or an integer selecting the :class:~mne.Evoked object based on the order
it's stored in the file. Passing lists of integers or strings is also
possible. If only one object is selected, the :class:~mne.Evoked object
will be returned directly (rather than a length-one list containing it):
End of explanation
evokeds_list[0].plot(picks='eeg')
Explanation: Above, when we created an :class:~mne.Evoked object by averaging epochs,
baseline correction was applied by default when we extracted epochs from the
~mne.io.Raw object (the default baseline period is (None, 0),
which assured zero mean for times before the stimulus event). In contrast, if
we plot the first :class:~mne.Evoked object in the list that was loaded
from disk, we'll see that the data have not been baseline-corrected:
End of explanation
# Original baseline (none set).
print(f'Baseline after loading: {evokeds_list[0].baseline}')
# Apply a custom baseline correction.
evokeds_list[0].apply_baseline((None, 0))
print(f'Baseline after calling apply_baseline(): {evokeds_list[0].baseline}')
# Visualize the evoked response.
evokeds_list[0].plot(picks='eeg')
Explanation: This can be remedied by either passing a baseline parameter to
:func:mne.read_evokeds, or by applying baseline correction after loading,
as shown here:
End of explanation
left_right_aud = epochs['auditory'].average()
print(left_right_aud)
Explanation: Notice that :meth:~mne.Evoked.apply_baseline operated in-place. Similarly,
:class:~mne.Evoked objects may have been saved to disk with or without
:term:projectors &lt;projector&gt; applied; you can pass proj=True to the
:func:~mne.read_evokeds function, or use the :meth:~mne.Evoked.apply_proj
method after loading.
Combining Evoked objects
One way to pool data across multiple conditions when estimating evoked
responses is to do so prior to averaging (recall that MNE-Python can select
based on partial matching of /-separated epoch labels; see
tut-section-subselect-epochs for more info):
End of explanation
left_aud = epochs['auditory/left'].average()
right_aud = epochs['auditory/right'].average()
print([evok.nave for evok in (left_aud, right_aud)])
Explanation: This approach will weight each epoch equally and create a single
:class:~mne.Evoked object. Notice that the printed representation includes
(average, N=145), indicating that the :class:~mne.Evoked object was
created by averaging across 145 epochs. In this case, the event types were
fairly close in number:
End of explanation
left_right_aud = mne.combine_evoked([left_aud, right_aud], weights='nave')
assert left_right_aud.nave == left_aud.nave + right_aud.nave
Explanation: However, this may not always be the case; if for statistical reasons it is
important to average the same number of epochs from different conditions,
you can use :meth:~mne.Epochs.equalize_event_counts prior to averaging.
Another approach to pooling across conditions is to create separate
:class:~mne.Evoked objects for each condition, and combine them afterward.
This can be accomplished by the function :func:mne.combine_evoked, which
computes a weighted sum of the :class:~mne.Evoked objects given to it. The
weights can be manually specified as a list or array of float values, or can
be specified using the keyword 'equal' (weight each ~mne.Evoked object
by $\frac{1}{N}$, where $N$ is the number of ~mne.Evoked
objects given) or the keyword 'nave' (weight each ~mne.Evoked object
proportional to the number of epochs averaged together to create it):
End of explanation
for ix, trial in enumerate(epochs[:3].iter_evoked()):
    channel, latency, value = trial.get_peak(ch_type='eeg',
                                             return_amplitude=True)
    latency = int(round(latency * 1e3))  # convert to milliseconds
    value = int(round(value * 1e6))      # convert to µV
    print('Trial {}: peak of {} µV at {} ms in channel {}'
          .format(ix, value, latency, channel))
Explanation: Note that the nave attribute of the resulting ~mne.Evoked object will
reflect the effective number of averages, and depends on both the nave
attributes of the contributing ~mne.Evoked objects and the weights at
which they are combined. Keeping track of effective nave is important for
inverse imaging, because nave is used to scale the noise covariance
estimate (which in turn affects the magnitude of estimated source activity).
See minimum_norm_estimates for more information (especially the
whitening_and_scaling section). Note that mne.grand_average does
not adjust nave to reflect effective number of averaged epochs; rather
it simply sets nave to the number of evokeds that were averaged
together. For this reason, it is best to use mne.combine_evoked rather than
mne.grand_average if you intend to perform inverse imaging on the resulting
:class:~mne.Evoked object.
Other uses of Evoked objects
Although the most common use of :class:~mne.Evoked objects is to store
averages of epoched data, there are a couple other uses worth noting here.
First, the method :meth:epochs.standard_error() &lt;mne.Epochs.standard_error&gt;
will create an :class:~mne.Evoked object (just like
:meth:epochs.average() &lt;mne.Epochs.average&gt; does), but the data in the
:class:~mne.Evoked object will be the standard error across epochs instead
of the average. To indicate this difference, :class:~mne.Evoked objects
have a :attr:~mne.Evoked.kind attribute that takes values 'average' or
'standard error' as appropriate.
Another use of :class:~mne.Evoked objects is to represent a single trial
or epoch of data, usually when looping through epochs. This can be easily
accomplished with the :meth:epochs.iter_evoked() &lt;mne.Epochs.iter_evoked&gt;
method, and can be useful for applications where you want to do something
that is only possible for :class:~mne.Evoked objects. For example, here
we use the :meth:~mne.Evoked.get_peak method (which isn't available for
:class:~mne.Epochs objects) to get the peak response in each trial:
End of explanation
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