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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:
 Source alignment and coordinate frames
The aim of this tutorial is to show how to visually assess that the data are
well aligned in space for computing the forward solution, and understand
the different coordinate frames involved in this process.
   
Step1:  Understanding coordinate frames
For M/EEG source imaging, there are three coordinate frames that we must
bring into alignment using two 3D transformation matrices &lt;trans_matrices&gt;_
that define how to rotate and translate points in one coordinate frame
to their equivalent locations in another.
Step2:  Coordinate frame definitions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. raw
Step3:  It is quite clear that the MRI surfaces (head, brain) are not well aligned
to the head digitization points (dots).
A good example
Here is the same plot, this time with the trans properly defined
(using a precomputed matrix).
Step4:  Defining the head↔MRI trans using the GUI
You can try creating the head↔MRI transform yourself using
Step5:  Alignment without MRI
The surface alignments above are possible if you have the surfaces available
from Freesurfer. 
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Python Code:
import os.path as op
import numpy as np
from mayavi import mlab
import mne
from mne.datasets import sample
print(__doc__)
data_path = sample.data_path()
subjects_dir = op.join(data_path, 'subjects')
raw_fname = op.join(data_path, 'MEG', 'sample', 'sample_audvis_raw.fif')
trans_fname = op.join(data_path, 'MEG', 'sample',
                      'sample_audvis_raw-trans.fif')
raw = mne.io.read_raw_fif(raw_fname)
trans = mne.read_trans(trans_fname)
src = mne.read_source_spaces(op.join(subjects_dir, 'sample', 'bem',
                                     'sample-oct-6-src.fif'))
Explanation: Source alignment and coordinate frames
The aim of this tutorial is to show how to visually assess that the data are
well aligned in space for computing the forward solution, and understand
the different coordinate frames involved in this process.
   :depth: 2
Let's start out by loading some data.
End of explanation
mne.viz.plot_alignment(raw.info, trans=trans, subject='sample',
                       subjects_dir=subjects_dir, surfaces='head-dense',
                       show_axes=True, dig=True, eeg=[], meg='sensors',
                       coord_frame='meg')
mlab.view(45, 90, distance=0.6, focalpoint=(0., 0., 0.))
print('Distance from head origin to MEG origin: %0.1f mm'
      % (1000 * np.linalg.norm(raw.info['dev_head_t']['trans'][:3, 3])))
print('Distance from head origin to MRI origin: %0.1f mm'
      % (1000 * np.linalg.norm(trans['trans'][:3, 3])))
Explanation: Understanding coordinate frames
For M/EEG source imaging, there are three coordinate frames that we must
bring into alignment using two 3D transformation matrices &lt;trans_matrices&gt;_
that define how to rotate and translate points in one coordinate frame
to their equivalent locations in another.
:func:mne.viz.plot_alignment is a very useful function for inspecting
these transformations, and the resulting alignment of EEG sensors, MEG
sensors, brain sources, and conductor models. If the subjects_dir and
subject parameters are provided, the function automatically looks for the
Freesurfer MRI surfaces to show from the subject's folder.
We can use the show_axes argument to see the various coordinate frames
given our transformation matrices. These are shown by axis arrows for each
coordinate frame:
shortest arrow is (R)ight/X
medium is forward/(A)nterior/Y
longest is up/(S)uperior/Z
i.e., a RAS coordinate system in each case. We can also set
the coord_frame argument to choose which coordinate
frame the camera should initially be aligned with.
Let's take a look:
End of explanation
mne.viz.plot_alignment(raw.info, trans=None, subject='sample', src=src,
                       subjects_dir=subjects_dir, dig=True,
                       surfaces=['head-dense', 'white'], coord_frame='meg')
Explanation: Coordinate frame definitions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
.. raw:: html
<style>
   .pink {color:DarkSalmon; font-weight:bold}
   .blue {color:DeepSkyBlue; font-weight:bold}
   .gray {color:Gray; font-weight:bold}
   .magenta {color:Magenta; font-weight:bold}
   .purple {color:Indigo; font-weight:bold}
   .green {color:LimeGreen; font-weight:bold}
   .red {color:Red; font-weight:bold}
   </style>
.. role:: pink
.. role:: blue
.. role:: gray
.. role:: magenta
.. role:: purple
.. role:: green
.. role:: red
Neuromag head coordinate frame ("head", :pink:pink axes)
     Defined by the intersection of 1) the line between the LPA
     (:red:red sphere) and RPA (:purple:purple sphere), and
     2) the line perpendicular to this LPA-RPA line one that goes through
     the Nasion (:green:green sphere).
     The axes are oriented as X origin→RPA, Y origin→Nasion,
     Z origin→upward (orthogonal to X and Y).
.. note:: This gets defined during the head digitization stage during
           acquisition, often by use of a Polhemus or other digitizer.
MEG device coordinate frame ("meg", :blue:blue axes)
     This is defined by the MEG manufacturers. From the Elekta user manual:
 The origin of the device coordinate system is located at the center
 of the posterior spherical section of the helmet with axis going
 from left to right and axis pointing front. The axis is, again
 normal to the plane with positive direction up.
.. note:: The device is coregistered with the head coordinate frame
           during acquisition via emission of sinusoidal currents in
           head position indicator (HPI) coils
           (:magenta:magenta spheres) at the beginning of the
           recording. This is stored in raw.info['dev_head_t'].
MRI coordinate frame ("mri", :gray:gray axes)
     Defined by Freesurfer, the MRI (surface RAS) origin is at the
     center of a 256×256×256 1mm anisotropic volume (may not be in the center
     of the head).
.. note:: This is aligned to the head coordinate frame that we
           typically refer to in MNE as trans.
A bad example
Let's try using trans=None, which (incorrectly!) equates the MRI
and head coordinate frames.
End of explanation
mne.viz.plot_alignment(raw.info, trans=trans, subject='sample',
                       src=src, subjects_dir=subjects_dir, dig=True,
                       surfaces=['head-dense', 'white'], coord_frame='meg')
Explanation: It is quite clear that the MRI surfaces (head, brain) are not well aligned
to the head digitization points (dots).
A good example
Here is the same plot, this time with the trans properly defined
(using a precomputed matrix).
End of explanation
# mne.gui.coregistration(subject='sample', subjects_dir=subjects_dir)
Explanation: Defining the head↔MRI trans using the GUI
You can try creating the head↔MRI transform yourself using
:func:mne.gui.coregistration.
First you must load the digitization data from the raw file
  (Head Shape Source). The MRI data is already loaded if you provide the
  subject and subjects_dir. Toggle Always Show Head Points to see
  the digitization points.
To set the landmarks, toggle Edit radio button in MRI Fiducials.
Set the landmarks by clicking the radio button (LPA, Nasion, RPA) and then
  clicking the corresponding point in the image.
After doing this for all the landmarks, toggle Lock radio button. You
  can omit outlier points, so that they don't interfere with the finetuning.
.. note:: You can save the fiducials to a file and pass
            mri_fiducials=True to plot them in
            :func:mne.viz.plot_alignment. The fiducials are saved to the
            subject's bem folder by default.
* Click Fit Head Shape. This will align the digitization points to the
  head surface. Sometimes the fitting algorithm doesn't find the correct
  alignment immediately. You can try first fitting using LPA/RPA or fiducials
  and then align according to the digitization. You can also finetune
  manually with the controls on the right side of the panel.
* Click Save As... (lower right corner of the panel), set the filename
  and read it with :func:mne.read_trans.
For more information, see step by step instructions
in these slides
&lt;http://www.slideshare.net/mne-python/mnepython-coregistration&gt;_.
Uncomment the following line to align the data yourself.
End of explanation
sphere = mne.make_sphere_model(info=raw.info, r0='auto', head_radius='auto')
src = mne.setup_volume_source_space(sphere=sphere, pos=10.)
mne.viz.plot_alignment(
    raw.info, eeg='projected', bem=sphere, src=src, dig=True,
    surfaces=['brain', 'outer_skin'], coord_frame='meg', show_axes=True)
Explanation: Alignment without MRI
The surface alignments above are possible if you have the surfaces available
from Freesurfer. :func:mne.viz.plot_alignment automatically searches for
the correct surfaces from the provided subjects_dir. Another option is
to use a spherical conductor model. It is passed through bem parameter.
End of explanation
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