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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 Raw data structure
Step1:  Loading continuous data
.. sidebar
Step2:  As you can see above, 
Step3:  By default, the 
Step4:  Querying the Raw object
.. sidebar
Step5:  <div class="alert alert-info"><h4>Note</h4><p>Most of the fields of ``raw.info`` reflect metadata recorded at
    acquisition time, and should not be changed by the user. There are a few
    exceptions (such as ``raw.info['bads']`` and ``raw.info['projs']``), but
    in most cases there are dedicated MNE-Python functions or methods to
    update the 
Step6:  Modifying Raw objects
.. sidebar
Step7:  Similar to the 
Step8:  If you want the channels in a specific order (e.g., for plotting),
Step9:  Changing channel name and type
.. sidebar
Step10:  This next example replaces spaces in the channel names with underscores,
using a Python dict comprehension_
Step11:  If for some reason the channel types in your 
Step12:  Selection in the time domain
If you want to limit the time domain of a 
Step13:  
Step14:  Remember that sample times don't always align exactly with requested tmin
or tmax values (due to sampling), which is why the max values of the
cropped files don't exactly match the requested tmax (see
time-as-index for further details).
If you need to select discontinuous spans of a 
Step15:  <div class="alert alert-danger"><h4>Warning</h4><p>Be careful when concatenating 
Step16:  You can see that it contains 2 arrays. This combination of data and times
makes it easy to plot selections of raw data (although note that we're
transposing the data array so that each channel is a column instead of a row,
to match what matplotlib expects when plotting 2-dimensional y against
1-dimensional x)
Step17:  Extracting channels by name
The 
Step18:  Extracting channels by type
There are several ways to select all channels of a given type from a
Step19:  Some of the parameters of 
Step20:  If you want the array of times, 
Step21:  The 
Step22:  Summary of ways to extract data from Raw objects
The following table summarizes the various ways of extracting data from a
Step23:  It is also possible to export the data to a 
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Python Code:
import os
import numpy as np
import matplotlib.pyplot as plt
import mne
Explanation: The Raw data structure: continuous data
This tutorial covers the basics of working with raw EEG/MEG data in Python. It
introduces the :class:~mne.io.Raw data structure in detail, including how to
load, query, subselect, export, and plot data from a :class:~mne.io.Raw
object. For more info on visualization of :class:~mne.io.Raw objects, see
tut-visualize-raw. For info on creating a :class:~mne.io.Raw object
from simulated data in a :class:NumPy array &lt;numpy.ndarray&gt;, see
tut_creating_data_structures.
   :depth: 2
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)
Explanation: Loading continuous data
.. sidebar:: Datasets in MNE-Python
There are ``data_path`` functions for several example datasets in
MNE-Python (e.g., :func:`mne.datasets.kiloword.data_path`,
:func:`mne.datasets.spm_face.data_path`, etc). All of them will check the
default download location first to see if the dataset is already on your
computer, and only download it if necessary.  The default download
location is also configurable; see the documentation of any of the
``data_path`` functions for more information.
As mentioned in the introductory tutorial &lt;tut-overview&gt;,
MNE-Python data structures are based around
the :file:.fif file format from Neuromag. This tutorial uses an
example dataset &lt;sample-dataset&gt; in :file:.fif format, so here we'll
use the function :func:mne.io.read_raw_fif to load the raw data; there are
reader functions for a wide variety of other data formats
&lt;data-formats&gt; as well.
There are also several other example datasets
&lt;datasets&gt; that can be downloaded with just a few lines
of code. Functions for downloading example datasets are in the
:mod:mne.datasets submodule; here we'll use
:func:mne.datasets.sample.data_path to download the "sample-dataset"
dataset, which contains EEG, MEG, and structural MRI data from one subject
performing an audiovisual experiment. When it's done downloading,
:func:~mne.datasets.sample.data_path will return the folder location where
it put the files; you can navigate there with your file browser if you want
to examine the files yourself. Once we have the file path, we can load the
data with :func:~mne.io.read_raw_fif. This will return a
:class:~mne.io.Raw object, which we'll store in a variable called raw.
End of explanation
print(raw)
Explanation: As you can see above, :func:~mne.io.read_raw_fif automatically displays
some information about the file it's loading. For example, here it tells us
that there are three "projection items" in the file along with the recorded
data; those are :term:SSP projectors &lt;projector&gt; calculated to remove
environmental noise from the MEG signals, and are discussed in a the tutorial
tut-projectors-background.
In addition to the information displayed during loading, you can
get a glimpse of the basic details of a :class:~mne.io.Raw object by
printing it:
End of explanation
raw.crop(tmax=60).load_data()
Explanation: By default, the :samp:mne.io.read_raw_{*} family of functions will not
load the data into memory (instead the data on disk are memory-mapped_,
meaning the data are only read from disk as-needed). Some operations (such as
filtering) require that the data be copied into RAM; to do that we could have
passed the preload=True parameter to :func:~mne.io.read_raw_fif, but we
can also copy the data into RAM at any time using the
:meth:~mne.io.Raw.load_data method. However, since this particular tutorial
doesn't do any serious analysis of the data, we'll first
:meth:~mne.io.Raw.crop the :class:~mne.io.Raw object to 60 seconds so it
uses less memory and runs more smoothly on our documentation server.
End of explanation
n_time_samps = raw.n_times
time_secs = raw.times
ch_names = raw.ch_names
n_chan = len(ch_names)  # note: there is no raw.n_channels attribute
print('the (cropped) sample data object has {} time samples and {} channels.'
      ''.format(n_time_samps, n_chan))
print('The last time sample is at {} seconds.'.format(time_secs[-1]))
print('The first few channel names are {}.'.format(', '.join(ch_names[:3])))
print()  # insert a blank line in the output
# some examples of raw.info:
print('bad channels:', raw.info['bads'])  # chs marked "bad" during acquisition
print(raw.info['sfreq'], 'Hz')            # sampling frequency
print(raw.info['description'], '\n')      # miscellaneous acquisition info
print(raw.info)
Explanation: Querying the Raw object
.. sidebar:: Attributes vs. Methods
**Attributes** are usually static properties of Python objects — things
that are pre-computed and stored as part of the object's representation
in memory. Attributes are accessed with the ``.`` operator and do not
require parentheses after the attribute name (example: ``raw.ch_names``).
**Methods** are like specialized functions attached to an object.
Usually they require additional user input and/or need some computation
to yield a result. Methods always have parentheses at the end; additional
arguments (if any) go inside those parentheses (examples:
``raw.estimate_rank()``, ``raw.drop_channels(['EEG 030', 'MEG 2242'])``).
We saw above that printing the :class:~mne.io.Raw object displays some
basic information like the total number of channels, the number of time
points at which the data were sampled, total duration, and the approximate
size in memory. Much more information is available through the various
attributes and methods of the :class:~mne.io.Raw class. Some useful
attributes of :class:~mne.io.Raw objects include a list of the channel
names (:attr:~mne.io.Raw.ch_names), an array of the sample times in seconds
(:attr:~mne.io.Raw.times), and the total number of samples
(:attr:~mne.io.Raw.n_times); a list of all attributes and methods is given
in the documentation of the :class:~mne.io.Raw class.
The Raw.info attribute
There is also quite a lot of information stored in the raw.info
attribute, which stores an :class:~mne.Info object that is similar to a
:class:Python dictionary &lt;dict&gt; (in that it has fields accessed via named
keys). Like Python dictionaries, raw.info has a .keys() method that
shows all the available field names; unlike Python dictionaries, printing
raw.info will print a nicely-formatted glimpse of each field's data. See
tut-info-class for more on what is stored in :class:~mne.Info
objects, and how to interact with them.
End of explanation
print(raw.time_as_index(20))
print(raw.time_as_index([20, 30, 40]), '\n')
print(np.diff(raw.time_as_index([1, 2, 3])))
Explanation: <div class="alert alert-info"><h4>Note</h4><p>Most of the fields of ``raw.info`` reflect metadata recorded at
    acquisition time, and should not be changed by the user. There are a few
    exceptions (such as ``raw.info['bads']`` and ``raw.info['projs']``), but
    in most cases there are dedicated MNE-Python functions or methods to
    update the :class:`~mne.Info` object safely (such as
    :meth:`~mne.io.Raw.add_proj` to update ``raw.info['projs']``).</p></div>
Time, sample number, and sample index
.. sidebar:: Sample numbering in VectorView data
For data from VectorView systems, it is important to distinguish *sample
number* from *sample index*. See :term:`first_samp` for more information.
One method of :class:~mne.io.Raw objects that is frequently useful is
:meth:~mne.io.Raw.time_as_index, which converts a time (in seconds) into
the integer index of the sample occurring closest to that time. The method
can also take a list or array of times, and will return an array of indices.
It is important to remember that there may not be a data sample at exactly
the time requested, so the number of samples between time = 1 second and
time = 2 seconds may be different than the number of samples between
time = 2 and time = 3:
End of explanation
eeg_and_eog = raw.copy().pick_types(meg=False, eeg=True, eog=True)
print(len(raw.ch_names), '→', len(eeg_and_eog.ch_names))
Explanation: Modifying Raw objects
.. sidebar:: len(raw)
Although the :class:`~mne.io.Raw` object underlyingly stores data samples
in a :class:`NumPy array &lt;numpy.ndarray&gt;` of shape (n_channels,
n_timepoints), the :class:`~mne.io.Raw` object behaves differently from
:class:`NumPy arrays &lt;numpy.ndarray&gt;` with respect to the :func:`len`
function. ``len(raw)`` will return the number of timepoints (length along
data axis 1), not the number of channels (length along data axis 0).
Hence in this section you'll see ``len(raw.ch_names)`` to get the number
of channels.
:class:~mne.io.Raw objects have a number of methods that modify the
:class:~mne.io.Raw instance in-place and return a reference to the modified
instance. This can be useful for method chaining_
(e.g., raw.crop(...).filter(...).pick_channels(...).plot())
but it also poses a problem during interactive analysis: if you modify your
:class:~mne.io.Raw object for an exploratory plot or analysis (say, by
dropping some channels), you will then need to re-load the data (and repeat
any earlier processing steps) to undo the channel-dropping and try something
else. For that reason, the examples in this section frequently use the
:meth:~mne.io.Raw.copy method before the other methods being demonstrated,
so that the original :class:~mne.io.Raw object is still available in the
variable raw for use in later examples.
Selecting, dropping, and reordering channels
Altering the channels of a :class:~mne.io.Raw object can be done in several
ways. As a first example, we'll use the :meth:~mne.io.Raw.pick_types method
to restrict the :class:~mne.io.Raw object to just the EEG and EOG channels:
End of explanation
raw_temp = raw.copy()
print('Number of channels in raw_temp:')
print(len(raw_temp.ch_names), end=' → drop two → ')
raw_temp.drop_channels(['EEG 037', 'EEG 059'])
print(len(raw_temp.ch_names), end=' → pick three → ')
raw_temp.pick_channels(['MEG 1811', 'EEG 017', 'EOG 061'])
print(len(raw_temp.ch_names))
Explanation: Similar to the :meth:~mne.io.Raw.pick_types method, there is also the
:meth:~mne.io.Raw.pick_channels method to pick channels by name, and a
corresponding :meth:~mne.io.Raw.drop_channels method to remove channels by
name:
End of explanation
channel_names = ['EOG 061', 'EEG 003', 'EEG 002', 'EEG 001']
eog_and_frontal_eeg = raw.copy().reorder_channels(channel_names)
print(eog_and_frontal_eeg.ch_names)
Explanation: If you want the channels in a specific order (e.g., for plotting),
:meth:~mne.io.Raw.reorder_channels works just like
:meth:~mne.io.Raw.pick_channels but also reorders the channels; for
example, here we pick the EOG and frontal EEG channels, putting the EOG
first and the EEG in reverse order:
End of explanation
raw.rename_channels({'EOG 061': 'blink detector'})
Explanation: Changing channel name and type
.. sidebar:: Long channel names
Due to limitations in the :file:`.fif` file format (which MNE-Python uses
to save :class:`~mne.io.Raw` objects), channel names are limited to a
maximum of 15 characters.
You may have noticed that the EEG channel names in the sample data are
numbered rather than labelled according to a standard nomenclature such as
the 10-20 &lt;ten_twenty_&gt; or 10-05 &lt;ten_oh_five_&gt; systems, or perhaps it
bothers you that the channel names contain spaces. It is possible to rename
channels using the :meth:~mne.io.Raw.rename_channels method, which takes a
Python dictionary to map old names to new names. You need not rename all
channels at once; provide only the dictionary entries for the channels you
want to rename. Here's a frivolous example:
End of explanation
print(raw.ch_names[-3:])
channel_renaming_dict = {name: name.replace(' ', '_') for name in raw.ch_names}
raw.rename_channels(channel_renaming_dict)
print(raw.ch_names[-3:])
Explanation: This next example replaces spaces in the channel names with underscores,
using a Python dict comprehension_:
End of explanation
raw.set_channel_types({'EEG_001': 'eog'})
print(raw.copy().pick_types(meg=False, eog=True).ch_names)
Explanation: If for some reason the channel types in your :class:~mne.io.Raw object are
inaccurate, you can change the type of any channel with the
:meth:~mne.io.Raw.set_channel_types method. The method takes a
:class:dictionary &lt;dict&gt; mapping channel names to types; allowed types are
ecg, eeg, emg, eog, exci, ias, misc, resp, seeg, stim, syst, ecog, hbo,
hbr. A common use case for changing channel type is when using frontal EEG
electrodes as makeshift EOG channels:
End of explanation
raw_selection = raw.copy().crop(tmin=10, tmax=12.5)
print(raw_selection)
Explanation: Selection in the time domain
If you want to limit the time domain of a :class:~mne.io.Raw object, you
can use the :meth:~mne.io.Raw.crop method, which modifies the
:class:~mne.io.Raw object in place (we've seen this already at the start of
this tutorial, when we cropped the :class:~mne.io.Raw object to 60 seconds
to reduce memory demands). :meth:~mne.io.Raw.crop takes parameters tmin
and tmax, both in seconds (here we'll again use :meth:~mne.io.Raw.copy
first to avoid changing the original :class:~mne.io.Raw object):
End of explanation
print(raw_selection.times.min(), raw_selection.times.max())
raw_selection.crop(tmin=1)
print(raw_selection.times.min(), raw_selection.times.max())
Explanation: :meth:~mne.io.Raw.crop also modifies the :attr:~mne.io.Raw.first_samp and
:attr:~mne.io.Raw.times attributes, so that the first sample of the cropped
object now corresponds to time = 0. Accordingly, if you wanted to re-crop
raw_selection from 11 to 12.5 seconds (instead of 10 to 12.5 as above)
then the subsequent call to :meth:~mne.io.Raw.crop should get tmin=1
(not tmin=11), and leave tmax unspecified to keep everything from
tmin up to the end of the object:
End of explanation
raw_selection1 = raw.copy().crop(tmin=30, tmax=30.1)     # 0.1 seconds
raw_selection2 = raw.copy().crop(tmin=40, tmax=41.1)     # 1.1 seconds
raw_selection3 = raw.copy().crop(tmin=50, tmax=51.3)     # 1.3 seconds
raw_selection1.append([raw_selection2, raw_selection3])  # 2.5 seconds total
print(raw_selection1.times.min(), raw_selection1.times.max())
Explanation: Remember that sample times don't always align exactly with requested tmin
or tmax values (due to sampling), which is why the max values of the
cropped files don't exactly match the requested tmax (see
time-as-index for further details).
If you need to select discontinuous spans of a :class:~mne.io.Raw object —
or combine two or more separate :class:~mne.io.Raw objects — you can use
the :meth:~mne.io.Raw.append method:
End of explanation
sampling_freq = raw.info['sfreq']
start_stop_seconds = np.array([11, 13])
start_sample, stop_sample = (start_stop_seconds * sampling_freq).astype(int)
channel_index = 0
raw_selection = raw[channel_index, start_sample:stop_sample]
print(raw_selection)
Explanation: <div class="alert alert-danger"><h4>Warning</h4><p>Be careful when concatenating :class:`~mne.io.Raw` objects from different
    recordings, especially when saving: :meth:`~mne.io.Raw.append` only
    preserves the ``info`` attribute of the initial :class:`~mne.io.Raw`
    object (the one outside the :meth:`~mne.io.Raw.append` method call).</p></div>
Extracting data from Raw objects
So far we've been looking at ways to modify a :class:~mne.io.Raw object.
This section shows how to extract the data from a :class:~mne.io.Raw object
into a :class:NumPy array &lt;numpy.ndarray&gt;, for analysis or plotting using
functions outside of MNE-Python. To select portions of the data,
:class:~mne.io.Raw objects can be indexed using square brackets. However,
indexing :class:~mne.io.Raw works differently than indexing a :class:NumPy
array &lt;numpy.ndarray&gt; in two ways:
Along with the requested sample value(s) MNE-Python also returns an array
   of times (in seconds) corresponding to the requested samples. The data
   array and the times array are returned together as elements of a tuple.
The data array will always be 2-dimensional even if you request only a
   single time sample or a single channel.
Extracting data by index
To illustrate the above two points, let's select a couple seconds of data
from the first channel:
End of explanation
x = raw_selection[1]
y = raw_selection[0].T
plt.plot(x, y)
Explanation: You can see that it contains 2 arrays. This combination of data and times
makes it easy to plot selections of raw data (although note that we're
transposing the data array so that each channel is a column instead of a row,
to match what matplotlib expects when plotting 2-dimensional y against
1-dimensional x):
End of explanation
channel_names = ['MEG_0712', 'MEG_1022']
two_meg_chans = raw[channel_names, start_sample:stop_sample]
y_offset = np.array([5e-11, 0])  # just enough to separate the channel traces
x = two_meg_chans[1]
y = two_meg_chans[0].T + y_offset
lines = plt.plot(x, y)
plt.legend(lines, channel_names)
Explanation: Extracting channels by name
The :class:~mne.io.Raw object can also be indexed with the names of
channels instead of their index numbers. You can pass a single string to get
just one channel, or a list of strings to select multiple channels. As with
integer indexing, this will return a tuple of (data_array, times_array)
that can be easily plotted. Since we're plotting 2 channels this time, we'll
add a vertical offset to one channel so it's not plotted right on top
of the other one:
End of explanation
eeg_channel_indices = mne.pick_types(raw.info, meg=False, eeg=True)
eeg_data, times = raw[eeg_channel_indices]
print(eeg_data.shape)
Explanation: Extracting channels by type
There are several ways to select all channels of a given type from a
:class:~mne.io.Raw object. The safest method is to use
:func:mne.pick_types to obtain the integer indices of the channels you
want, then use those indices with the square-bracket indexing method shown
above. The :func:~mne.pick_types function uses the :class:~mne.Info
attribute of the :class:~mne.io.Raw object to determine channel types, and
takes boolean or string parameters to indicate which type(s) to retain. The
meg parameter defaults to True, and all others default to False,
so to get just the EEG channels, we pass eeg=True and meg=False:
End of explanation
data = raw.get_data()
print(data.shape)
Explanation: Some of the parameters of :func:mne.pick_types accept string arguments as
well as booleans. For example, the meg parameter can take values
'mag', 'grad', 'planar1', or 'planar2' to select only
magnetometers, all gradiometers, or a specific type of gradiometer. See the
docstring of :meth:mne.pick_types for full details.
The Raw.get_data() method
If you only want the data (not the corresponding array of times),
:class:~mne.io.Raw objects have a :meth:~mne.io.Raw.get_data method. Used
with no parameters specified, it will extract all data from all channels, in
a (n_channels, n_timepoints) :class:NumPy array &lt;numpy.ndarray&gt;:
End of explanation
data, times = raw.get_data(return_times=True)
print(data.shape)
print(times.shape)
Explanation: If you want the array of times, :meth:~mne.io.Raw.get_data has an optional
return_times parameter:
End of explanation
first_channel_data = raw.get_data(picks=0)
eeg_and_eog_data = raw.get_data(picks=['eeg', 'eog'])
two_meg_chans_data = raw.get_data(picks=['MEG_0712', 'MEG_1022'],
                                  start=1000, stop=2000)
print(first_channel_data.shape)
print(eeg_and_eog_data.shape)
print(two_meg_chans_data.shape)
Explanation: The :meth:~mne.io.Raw.get_data method can also be used to extract specific
channel(s) and sample ranges, via its picks, start, and stop
parameters. The picks parameter accepts integer channel indices, channel
names, or channel types, and preserves the requested channel order given as
its picks parameter.
End of explanation
data = raw.get_data()
np.save(file='my_data.npy', arr=data)
Explanation: Summary of ways to extract data from Raw objects
The following table summarizes the various ways of extracting data from a
:class:~mne.io.Raw object.
.. cssclass:: table-bordered
.. rst-class:: midvalign
+-------------------------------------+-------------------------+
| Python code                         | Result                  |
|                                     |                         |
|                                     |                         |
+=====================================+=========================+
| raw.get_data()                  | :class:NumPy array     |
|                                     | &lt;numpy.ndarray&gt;        |
|                                     | (n_chans × n_samps)     |
+-------------------------------------+-------------------------+
| raw[:]                          | :class:tuple of (data |
+-------------------------------------+ (n_chans × n_samps),    |
| raw.get_data(return_times=True) | times (1 × n_samps))    |
+-------------------------------------+-------------------------+
| raw[0, 1000:2000]               |                         |
+-------------------------------------+                         |
| raw['MEG 0113', 1000:2000]      |                         |
+-------------------------------------+                         |
| raw.get_data(picks=0,             | :class:`tuple` of       |
| start=1000, stop=2000,              | (data (1 × 1000),       |
| return_times=True)                | times (1 × 1000))       |
+-------------------------------------+                         |
| raw.get_data(picks='MEG 0113',    |                         |
| start=1000, stop=2000,              |                         |
| return_times=True)                |                         |
+-------------------------------------+-------------------------+
| raw[7:9, 1000:2000]             |                         |
+-------------------------------------+                         |
| raw[[2, 5], 1000:2000]          | :class:tuple of       |
+-------------------------------------+ (data (2 × 1000),       |
| raw[['EEG 030', 'EOG 061'],       | times (1 × 1000))       |
| 1000:2000]                        |                         |
+-------------------------------------+-------------------------+
Exporting and saving Raw objects
:class:~mne.io.Raw objects have a built-in :meth:~mne.io.Raw.save method,
which can be used to write a partially processed :class:~mne.io.Raw object
to disk as a :file:.fif file, such that it can be re-loaded later with its
various attributes intact (but see precision for an important
note about numerical precision when saving).
There are a few other ways to export just the sensor data from a
:class:~mne.io.Raw object. One is to use indexing or the
:meth:~mne.io.Raw.get_data method to extract the data, and use
:func:numpy.save to save the data array:
End of explanation
sampling_freq = raw.info['sfreq']
start_end_secs = np.array([10, 13])
start_sample, stop_sample = (start_end_secs * sampling_freq).astype(int)
df = raw.to_data_frame(picks=['eeg'], start=start_sample, stop=stop_sample)
# then save using df.to_csv(...), df.to_hdf(...), etc
print(df.head())
Explanation: It is also possible to export the data to a :class:Pandas DataFrame
&lt;pandas.DataFrame&gt; object, and use the saving methods that :mod:Pandas
&lt;pandas&gt; affords. The :class:~mne.io.Raw object's
:meth:~mne.io.Raw.to_data_frame method is similar to
:meth:~mne.io.Raw.get_data in that it has a picks parameter for
restricting which channels are exported, and start and stop
parameters for restricting the time domain. Note that, by default, times will
be converted to milliseconds, rounded to the nearest millisecond, and used as
the DataFrame index; see the scaling_time parameter in the documentation
of :meth:~mne.io.Raw.to_data_frame for more details.
End of explanation
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