Note

Go to the end to download the full example code

# Computing source timecourses with an XFit-like multi-dipole model#

MEGIN’s XFit program offers a “guided ECD modeling” interface, where multiple dipoles can be fitted interactively. By manually selecting subsets of sensors and time ranges, dipoles can be fitted to specific signal components. Then, source timecourses can be computed using a multi-dipole model. The advantage of using a multi-dipole model over fitting each dipole in isolation, is that when multiple dipoles contribute to the same signal component, the model can make sure that activity assigned to one dipole is not also assigned to another. This example shows how to build a multi-dipole model for estimating source timecourses for evokeds or single epochs.

The XFit program is the recommended approach for guided ECD modeling, because
it offers a convenient graphical user interface for it. These dipoles can then
be imported into MNE-Python by using the `mne.read_dipole()`

function for
building and applying the multi-dipole model. In addition, this example will
also demonstrate how to perform guided ECD modeling using only MNE-Python
functionality, which is less convenient than using XFit, but has the benefit of
being reproducible.

```
# Author: Marijn van Vliet <w.m.vanvliet@gmail.com>
#
# License: BSD-3-Clause
```

Importing everything and setting up the data paths for the MNE-Sample dataset.

```
import mne
from mne.datasets import sample
from mne.channels import read_vectorview_selection
from mne.minimum_norm import make_inverse_operator, apply_inverse, apply_inverse_epochs
import matplotlib.pyplot as plt
import numpy as np
data_path = sample.data_path()
meg_path = data_path / "MEG" / "sample"
raw_fname = meg_path / "sample_audvis_raw.fif"
cov_fname = meg_path / "sample_audvis-shrunk-cov.fif"
bem_dir = data_path / "subjects" / "sample" / "bem"
bem_fname = bem_dir / "sample-5120-5120-5120-bem-sol.fif"
```

Read the MEG data from the audvis experiment. Make epochs and evokeds for the left and right auditory conditions.

```
raw = mne.io.read_raw_fif(raw_fname)
raw = raw.pick_types(meg=True, eog=True, stim=True)
info = raw.info
# Create epochs for auditory events
events = mne.find_events(raw)
event_id = dict(right=1, left=2)
epochs = mne.Epochs(
raw,
events,
event_id,
tmin=-0.1,
tmax=0.3,
baseline=(None, 0),
reject=dict(mag=4e-12, grad=4000e-13, eog=150e-6),
)
# Create evokeds for left and right auditory stimulation
evoked_left = epochs["left"].average()
evoked_right = epochs["right"].average()
```

```
Opening raw data file /home/circleci/mne_data/MNE-sample-data/MEG/sample/sample_audvis_raw.fif...
Read a total of 3 projection items:
PCA-v1 (1 x 102) idle
PCA-v2 (1 x 102) idle
PCA-v3 (1 x 102) idle
Range : 25800 ... 192599 = 42.956 ... 320.670 secs
Ready.
NOTE: pick_types() is a legacy function. New code should use inst.pick(...).
320 events found
Event IDs: [ 1 2 3 4 5 32]
Not setting metadata
145 matching events found
Setting baseline interval to [-0.09989760657919393, 0.0] s
Applying baseline correction (mode: mean)
Created an SSP operator (subspace dimension = 3)
3 projection items activated
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
NOTE: pick_channels() is a legacy function. New code should use inst.pick(...).
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on MAG : ['MEG 1711']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
Rejecting epoch based on EOG : ['EOG 061']
NOTE: pick_channels() is a legacy function. New code should use inst.pick(...).
```

Guided dipole modeling, meaning fitting dipoles to a manually selected subset of sensors as a manually chosen time, can now be performed in MEGINs XFit on the evokeds we computed above. However, it is possible to do it completely in MNE-Python.

```
# Setup conductor model
cov = mne.read_cov(cov_fname)
bem = mne.read_bem_solution(bem_fname)
# Fit two dipoles at t=80ms. The first dipole is fitted using only the sensors
# on the left side of the helmet. The second dipole is fitted using only the
# sensors on the right side of the helmet.
picks_left = read_vectorview_selection("Left", info=info)
evoked_fit_left = evoked_left.copy().crop(0.08, 0.08)
evoked_fit_left.pick_channels(picks_left, ordered=False)
cov_fit_left = cov.copy().pick_channels(picks_left, ordered=False)
picks_right = read_vectorview_selection("Right", info=info)
evoked_fit_right = evoked_right.copy().crop(0.08, 0.08)
evoked_fit_right.pick_channels(picks_right, ordered=False)
cov_fit_right = cov.copy().pick_channels(picks_right, ordered=False)
# Any SSS projections that are active on this data need to be re-normalized
# after picking channels.
evoked_fit_left.info.normalize_proj()
evoked_fit_right.info.normalize_proj()
cov_fit_left["projs"] = evoked_fit_left.info["projs"]
cov_fit_right["projs"] = evoked_fit_right.info["projs"]
# Fit the dipoles with the subset of sensors.
dip_left, _ = mne.fit_dipole(evoked_fit_left, cov_fit_left, bem)
dip_right, _ = mne.fit_dipole(evoked_fit_right, cov_fit_right, bem)
```

```
365 x 365 full covariance (kind = 1) found.
Read a total of 4 projection items:
PCA-v1 (1 x 102) active
PCA-v2 (1 x 102) active
PCA-v3 (1 x 102) active
Average EEG reference (1 x 59) active
Loading surfaces...
Loading the solution matrix...
Three-layer model surfaces loaded.
Loaded linear collocation BEM solution from /home/circleci/mne_data/MNE-sample-data/subjects/sample/bem/sample-5120-5120-5120-bem-sol.fif
NOTE: pick_channels() is a legacy function. New code should use inst.pick(...).
NOTE: pick_channels() is a legacy function. New code should use inst.pick(...).
BEM : <ConductorModel | BEM (3 layers) solver=mne>
MRI transform : identity
Head origin : 0.4 -12.9 37.7 mm rad = 71.8 mm.
Guess grid : 20.0 mm
Guess mindist : 5.0 mm
Guess exclude : 20.0 mm
Using normal MEG coil definitions.
Noise covariance : <Covariance | size : 153 x 153, n_samples : 38720, data : [[ 2.58607874e-23 6.29495097e-24 7.04486582e-25 ... 9.78988420e-24
-8.81501987e-24 5.79536167e-25]
[ 6.29495097e-24 9.22800262e-24 1.50545865e-25 ... 2.24472969e-24
-4.41763741e-24 1.51116585e-25]
[ 7.04486582e-25 1.50545865e-25 6.49899073e-26 ... 6.11191910e-25
-5.30776654e-25 3.58725785e-26]
...
[ 9.78988420e-24 2.24472969e-24 6.11191910e-25 ... 1.82015291e-23
-4.83338121e-24 4.85132759e-25]
[-8.81501987e-24 -4.41763741e-24 -5.30776654e-25 ... -4.83338121e-24
1.76790821e-23 -3.26581206e-25]
[ 5.79536167e-25 1.51116585e-25 3.58725785e-26 ... 4.85132759e-25
-3.26581206e-25 3.61643686e-26]]>
Coordinate transformation: MRI (surface RAS) -> head
1.000000 0.000000 0.000000 0.00 mm
0.000000 1.000000 0.000000 0.00 mm
0.000000 0.000000 1.000000 0.00 mm
0.000000 0.000000 0.000000 1.00
Coordinate transformation: MEG device -> head
0.991420 -0.039936 -0.124467 -6.13 mm
0.060661 0.984012 0.167456 0.06 mm
0.115790 -0.173570 0.977991 64.74 mm
0.000000 0.000000 0.000000 1.00
0 bad channels total
Read 153 MEG channels from info
105 coil definitions read
Coordinate transformation: MEG device -> head
0.991420 -0.039936 -0.124467 -6.13 mm
0.060661 0.984012 0.167456 0.06 mm
0.115790 -0.173570 0.977991 64.74 mm
0.000000 0.000000 0.000000 1.00
MEG coil definitions created in head coordinates.
Decomposing the sensor noise covariance matrix...
Created an SSP operator (subspace dimension = 3)
Computing rank from covariance with rank=None
Using tolerance 1.1e-13 (2.2e-16 eps * 153 dim * 3.2 max singular value)
Estimated rank (mag + grad): 150
MEG: rank 150 computed from 153 data channels with 3 projectors
Setting small MEG eigenvalues to zero (without PCA)
Created the whitener using a noise covariance matrix with rank 150 (3 small eigenvalues omitted)
---- Computing the forward solution for the guesses...
Guess surface (inner skull) is in MRI (surface RAS) coordinates
Filtering (grid = 20 mm)...
Surface CM = ( 0.7 -10.0 44.3) mm
Surface fits inside a sphere with radius 91.8 mm
Surface extent:
x = -66.7 ... 68.8 mm
y = -88.0 ... 79.0 mm
z = -44.5 ... 105.8 mm
Grid extent:
x = -80.0 ... 80.0 mm
y = -100.0 ... 80.0 mm
z = -60.0 ... 120.0 mm
900 sources before omitting any.
396 sources after omitting infeasible sources not within 20.0 - 91.8 mm.
Source spaces are in MRI coordinates.
Checking that the sources are inside the surface and at least 5.0 mm away (will take a few...)
Checking surface interior status for 396 points...
Found 42/396 points inside an interior sphere of radius 43.6 mm
Found 0/396 points outside an exterior sphere of radius 91.8 mm
Found 186/354 points outside using surface Qhull
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Found 9/168 points outside using solid angles
Total 201/396 points inside the surface
Interior check completed in 112.8 ms
195 source space points omitted because they are outside the inner skull surface.
45 source space points omitted because of the 5.0-mm distance limit.
156 sources remaining after excluding the sources outside the surface and less than 5.0 mm inside.
Go through all guess source locations...
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[done 156 sources]
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---- Fitted : 79.9 ms, distance to inner skull : 4.9828 mm
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Projections have already been applied. Setting proj attribute to True.
1 time points fitted
BEM : <ConductorModel | BEM (3 layers) solver=mne>
MRI transform : identity
Head origin : 0.4 -12.9 37.7 mm rad = 71.8 mm.
Guess grid : 20.0 mm
Guess mindist : 5.0 mm
Guess exclude : 20.0 mm
Using normal MEG coil definitions.
Noise covariance : <Covariance | size : 152 x 152, n_samples : 38720, data : [[ 1.69262885e-23 -4.19272571e-25 3.91546253e-26 ... -4.01298483e-24
-4.64516797e-26 -1.19806525e-25]
[-4.19272571e-25 1.33734643e-23 -4.87121666e-26 ... 5.27849772e-25
2.17670368e-24 4.61094719e-26]
[ 3.91546253e-26 -4.87121666e-26 1.47048282e-26 ... -3.57358697e-26
-1.03235995e-25 -1.14274862e-26]
...
[-4.01298483e-24 5.27849772e-25 -3.57358697e-26 ... 3.19294391e-23
-1.09342253e-24 -2.00283865e-26]
[-4.64516797e-26 2.17670368e-24 -1.03235995e-25 ... -1.09342253e-24
2.12915739e-23 1.54166863e-25]
[-1.19806525e-25 4.61094719e-26 -1.14274862e-26 ... -2.00283865e-26
1.54166863e-25 3.75855684e-26]]>
Coordinate transformation: MRI (surface RAS) -> head
1.000000 0.000000 0.000000 0.00 mm
0.000000 1.000000 0.000000 0.00 mm
0.000000 0.000000 1.000000 0.00 mm
0.000000 0.000000 0.000000 1.00
Coordinate transformation: MEG device -> head
0.991420 -0.039936 -0.124467 -6.13 mm
0.060661 0.984012 0.167456 0.06 mm
0.115790 -0.173570 0.977991 64.74 mm
0.000000 0.000000 0.000000 1.00
0 bad channels total
Read 152 MEG channels from info
105 coil definitions read
Coordinate transformation: MEG device -> head
0.991420 -0.039936 -0.124467 -6.13 mm
0.060661 0.984012 0.167456 0.06 mm
0.115790 -0.173570 0.977991 64.74 mm
0.000000 0.000000 0.000000 1.00
MEG coil definitions created in head coordinates.
Decomposing the sensor noise covariance matrix...
Created an SSP operator (subspace dimension = 3)
Computing rank from covariance with rank=None
Using tolerance 1.3e-13 (2.2e-16 eps * 152 dim * 3.8 max singular value)
Estimated rank (mag + grad): 149
MEG: rank 149 computed from 152 data channels with 3 projectors
Setting small MEG eigenvalues to zero (without PCA)
Created the whitener using a noise covariance matrix with rank 149 (3 small eigenvalues omitted)
---- Computing the forward solution for the guesses...
Guess surface (inner skull) is in MRI (surface RAS) coordinates
Filtering (grid = 20 mm)...
Surface CM = ( 0.7 -10.0 44.3) mm
Surface fits inside a sphere with radius 91.8 mm
Surface extent:
x = -66.7 ... 68.8 mm
y = -88.0 ... 79.0 mm
z = -44.5 ... 105.8 mm
Grid extent:
x = -80.0 ... 80.0 mm
y = -100.0 ... 80.0 mm
z = -60.0 ... 120.0 mm
900 sources before omitting any.
396 sources after omitting infeasible sources not within 20.0 - 91.8 mm.
Source spaces are in MRI coordinates.
Checking that the sources are inside the surface and at least 5.0 mm away (will take a few...)
Checking surface interior status for 396 points...
Found 42/396 points inside an interior sphere of radius 43.6 mm
Found 0/396 points outside an exterior sphere of radius 91.8 mm
Found 186/354 points outside using surface Qhull
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
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Found 9/168 points outside using solid angles
Total 201/396 points inside the surface
Interior check completed in 109.7 ms
195 source space points omitted because they are outside the inner skull surface.
45 source space points omitted because of the 5.0-mm distance limit.
156 sources remaining after excluding the sources outside the surface and less than 5.0 mm inside.
Go through all guess source locations...
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[done 156 sources]
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[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
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---- Fitted : 79.9 ms, distance to inner skull : 4.9340 mm
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 1.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 1.0s finished
Projections have already been applied. Setting proj attribute to True.
1 time points fitted
```

Now that we have the location and orientations of the dipoles, compute the
full timecourses using MNE, assigning activity to both dipoles at the same
time while preventing leakage between the two. We use a very low `lambda`

value to ensure both dipoles are fully used.

```
fwd, _ = mne.make_forward_dipole([dip_left, dip_right], bem, info)
# Apply MNE inverse
inv = make_inverse_operator(info, fwd, cov, fixed=True, depth=0)
stc_left = apply_inverse(evoked_left, inv, method="MNE", lambda2=1e-6)
stc_right = apply_inverse(evoked_right, inv, method="MNE", lambda2=1e-6)
# Plot the timecourses of the resulting source estimate
fig, axes = plt.subplots(nrows=2, sharex=True, sharey=True)
axes[0].plot(stc_left.times, stc_left.data.T)
axes[0].set_title("Left auditory stimulation")
axes[0].legend(["Dipole 1", "Dipole 2"])
axes[1].plot(stc_right.times, stc_right.data.T)
axes[1].set_title("Right auditory stimulation")
axes[1].set_xlabel("Time (s)")
fig.supylabel("Dipole amplitude")
```

```
Positions (in meters) and orientations
2 sources
Source space : <SourceSpaces: [<discrete, n_used=2>] head coords, ~3 kB>
MRI -> head transform : identity
Measurement data : instance of Info
Conductor model : instance of ConductorModel
Accurate field computations
Do computations in head coordinates
Free source orientations
Read 1 source spaces a total of 2 active source locations
Coordinate transformation: MRI (surface RAS) -> head
1.000000 0.000000 0.000000 0.00 mm
0.000000 1.000000 0.000000 0.00 mm
0.000000 0.000000 1.000000 0.00 mm
0.000000 0.000000 0.000000 1.00
Read 305 MEG channels from info
105 coil definitions read
Coordinate transformation: MEG device -> head
0.991420 -0.039936 -0.124467 -6.13 mm
0.060661 0.984012 0.167456 0.06 mm
0.115790 -0.173570 0.977991 64.74 mm
0.000000 0.000000 0.000000 1.00
MEG coil definitions created in head coordinates.
Source spaces are now in head coordinates.
Employing the head->MRI coordinate transform with the BEM model.
BEM model instance of ConductorModel is now set up
Source spaces are in head coordinates.
Checking that the sources are inside the surface (will take a few...)
Checking surface interior status for 2 points...
Found 0/2 points inside an interior sphere of radius 43.6 mm
Found 0/2 points outside an exterior sphere of radius 91.8 mm
Found 0/2 points outside using surface Qhull
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.0s finished
Found 0/2 points outside using solid angles
Total 2/2 points inside the surface
Interior check completed in 44.5 ms
Checking surface interior status for 305 points...
Found 0/305 points inside an interior sphere of radius 79.1 mm
Found 0/305 points outside an exterior sphere of radius 161.3 mm
Found 305/305 points outside using surface Qhull
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.0s finished
Found 0/ 0 points outside using solid angles
Total 0/305 points inside the surface
Interior check completed in 20.7 ms
Composing the field computation matrix...
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 1.3s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 1.3s finished
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
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[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 1.2s finished
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
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[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 1.2s finished
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
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[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 1.2s finished
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
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[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 1.2s finished
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
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[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 1.3s finished
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
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[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 1.3s finished
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
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[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 1.3s finished
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
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[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 1.3s finished
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.1s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.1s finished
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.1s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.1s finished
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.1s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.1s finished
Computing MEG at 2 source locations (free orientations)...
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.0s finished
Finished.
Changing to fixed-orientation forward solution with surface-based source orientations...
[done]
info["bads"] and noise_cov["bads"] do not match, excluding bad channels from both
Computing inverse operator with 305 channels.
305 out of 305 channels remain after picking
Selected 305 channels
Whitening the forward solution.
Created an SSP operator (subspace dimension = 3)
Computing rank from covariance with rank=None
Using tolerance 3.5e-13 (2.2e-16 eps * 305 dim * 5.2 max singular value)
Estimated rank (mag + grad): 302
MEG: rank 302 computed from 305 data channels with 3 projectors
Setting small MEG eigenvalues to zero (without PCA)
Creating the source covariance matrix
Adjusting source covariance matrix.
Computing SVD of whitened and weighted lead field matrix.
largest singular value = 13.7006
scaling factor to adjust the trace = 1.97034e+16 (nchan = 305 nzero = 3)
Preparing the inverse operator for use...
Scaled noise and source covariance from nave = 1 to nave = 65
Created the regularized inverter
Created an SSP operator (subspace dimension = 3)
Created the whitener using a noise covariance matrix with rank 302 (3 small eigenvalues omitted)
Applying inverse operator to "left"...
Picked 305 channels from the data
Computing inverse...
Eigenleads need to be weighted ...
Computing residual...
Explained 14.0% variance
[done]
Preparing the inverse operator for use...
Scaled noise and source covariance from nave = 1 to nave = 66
Created the regularized inverter
Created an SSP operator (subspace dimension = 3)
Created the whitener using a noise covariance matrix with rank 302 (3 small eigenvalues omitted)
Applying inverse operator to "right"...
Picked 305 channels from the data
Computing inverse...
Eigenleads need to be weighted ...
Computing residual...
Explained 14.8% variance
[done]
```

We can also fit the timecourses to single epochs. Here, we do it for each experimental condition separately.

```
stcs_left = apply_inverse_epochs(epochs["left"], inv, lambda2=1e-6, method="MNE")
stcs_right = apply_inverse_epochs(epochs["right"], inv, lambda2=1e-6, method="MNE")
```

```
Preparing the inverse operator for use...
Scaled noise and source covariance from nave = 1 to nave = 1
Created the regularized inverter
Created an SSP operator (subspace dimension = 3)
Created the whitener using a noise covariance matrix with rank 302 (3 small eigenvalues omitted)
Picked 305 channels from the data
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[done]
Preparing the inverse operator for use...
Scaled noise and source covariance from nave = 1 to nave = 1
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Created an SSP operator (subspace dimension = 3)
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Picked 305 channels from the data
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[done]
```

To summarize and visualize the single-epoch dipole amplitudes, we will create a detailed plot of the mean amplitude of the dipoles during different experimental conditions.

```
# Summarize the single epoch timecourses by computing the mean amplitude from
# 60-90ms.
amplitudes_left = []
amplitudes_right = []
for stc in stcs_left:
amplitudes_left.append(stc.crop(0.06, 0.09).mean().data)
for stc in stcs_right:
amplitudes_right.append(stc.crop(0.06, 0.09).mean().data)
amplitudes = np.vstack([amplitudes_left, amplitudes_right])
# Visualize the epoch-by-epoch dipole ampltudes in a detailed figure.
n = len(amplitudes)
n_left = len(amplitudes_left)
mean_left = np.mean(amplitudes_left, axis=0)
mean_right = np.mean(amplitudes_right, axis=0)
fig, ax = plt.subplots(figsize=(8, 4))
ax.scatter(np.arange(n), amplitudes[:, 0], label="Dipole 1")
ax.scatter(np.arange(n), amplitudes[:, 1], label="Dipole 2")
transition_point = n_left - 0.5
ax.plot([0, transition_point], [mean_left[0], mean_left[0]], color="C0")
ax.plot([0, transition_point], [mean_left[1], mean_left[1]], color="C1")
ax.plot([transition_point, n], [mean_right[0], mean_right[0]], color="C0")
ax.plot([transition_point, n], [mean_right[1], mean_right[1]], color="C1")
ax.axvline(transition_point, color="black")
ax.set_xlabel("Epochs")
ax.set_ylabel("Dipole amplitude")
ax.legend()
fig.suptitle("Single epoch dipole amplitudes")
fig.text(0.30, 0.9, "Left auditory stimulation", ha="center")
fig.text(0.70, 0.9, "Right auditory stimulation", ha="center")
```

**Total running time of the script:** ( 0 minutes 26.916 seconds)

**Estimated memory usage:** 610 MB