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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 localization with single dipole fit
This shows how to fit a dipole using mne-python.
For a comparison of fits between MNE-C and mne-python, see
Step1:  Let's localize the N100m (using MEG only)
Step2:  Calculate and visualise magnetic field predicted by dipole with maximum GOF
and compare to the measured data, highlighting the ipsilateral (right) source
Step3:  Estimate the time course of a single dipole with fixed position and
orientation (the one that maximized GOF)over the entire interval
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Python Code:
from os import path as op
import numpy as np
import matplotlib.pyplot as plt
import mne
from mne.forward import make_forward_dipole
from mne.evoked import combine_evoked
from mne.simulation import simulate_evoked
data_path = mne.datasets.sample.data_path()
subjects_dir = op.join(data_path, 'subjects')
fname_ave = op.join(data_path, 'MEG', 'sample', 'sample_audvis-ave.fif')
fname_cov = op.join(data_path, 'MEG', 'sample', 'sample_audvis-cov.fif')
fname_bem = op.join(subjects_dir, 'sample', 'bem', 'sample-5120-bem-sol.fif')
fname_trans = op.join(data_path, 'MEG', 'sample',
                      'sample_audvis_raw-trans.fif')
fname_surf_lh = op.join(subjects_dir, 'sample', 'surf', 'lh.white')
Explanation: Source localization with single dipole fit
This shows how to fit a dipole using mne-python.
For a comparison of fits between MNE-C and mne-python, see:
https://gist.github.com/Eric89GXL/ca55f791200fe1dc3dd2
Note that for 3D graphics you may need to choose a specific IPython
backend, such as:
%matplotlib qt or %matplotlib wx
End of explanation
evoked = mne.read_evokeds(fname_ave, condition='Right Auditory',
                          baseline=(None, 0))
evoked.pick_types(meg=True, eeg=False)
evoked_full = evoked.copy()
evoked.crop(0.07, 0.08)
# Fit a dipole
dip = mne.fit_dipole(evoked, fname_cov, fname_bem, fname_trans)[0]
# Plot the result in 3D brain with the MRI image.
dip.plot_locations(fname_trans, 'sample', subjects_dir, mode='orthoview')
Explanation: Let's localize the N100m (using MEG only)
End of explanation
fwd, stc = make_forward_dipole(dip, fname_bem, evoked.info, fname_trans)
pred_evoked = simulate_evoked(fwd, stc, evoked.info, cov=None, nave=np.inf)
# find time point with highest GOF to plot
best_idx = np.argmax(dip.gof)
best_time = dip.times[best_idx]
print('Highest GOF %0.1f%% at t=%0.1f ms with confidence volume %0.1f cm^3'
      % (dip.gof[best_idx], best_time * 1000,
         dip.conf['vol'][best_idx] * 100 ** 3))
# rememeber to create a subplot for the colorbar
fig, axes = plt.subplots(nrows=1, ncols=4, figsize=[10., 3.4])
vmin, vmax = -400, 400  # make sure each plot has same colour range
# first plot the topography at the time of the best fitting (single) dipole
plot_params = dict(times=best_time, ch_type='mag', outlines='skirt',
                   colorbar=False)
evoked.plot_topomap(time_format='Measured field', axes=axes[0], **plot_params)
# compare this to the predicted field
pred_evoked.plot_topomap(time_format='Predicted field', axes=axes[1],
                         **plot_params)
# Subtract predicted from measured data (apply equal weights)
diff = combine_evoked([evoked, -pred_evoked], weights='equal')
plot_params['colorbar'] = True
diff.plot_topomap(time_format='Difference', axes=axes[2], **plot_params)
plt.suptitle('Comparison of measured and predicted fields '
             'at {:.0f} ms'.format(best_time * 1000.), fontsize=16)
Explanation: Calculate and visualise magnetic field predicted by dipole with maximum GOF
and compare to the measured data, highlighting the ipsilateral (right) source
End of explanation
dip_fixed = mne.fit_dipole(evoked_full, fname_cov, fname_bem, fname_trans,
                           pos=dip.pos[best_idx], ori=dip.ori[best_idx])[0]
dip_fixed.plot()
Explanation: Estimate the time course of a single dipole with fixed position and
orientation (the one that maximized GOF)over the entire interval
End of explanation
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