Simulating and Localizing Multi-Source EEG Activity — Multiple Runs

This tutorial extends the single-run simulation/localization workflow presented in the “Simulating and Localizing Multi-Source EEG Activity with MVPURE_py tutorial”.

The simulation, forward modeling, preprocessing, MVPURE_py localization, and LCMV comparison are essentially the same as in that tutorial. We therefore assume that you already know that workflow and focus on the new part:

How to repeat the complete experiment many times and aggregate the results.

Repeating the experiment is important because the source locations are randomly sampled in every run. A single run therefore gives only one realization of the experiment, whereas multiple runs allow us to characterize the distribution and variability of localization performance.

The notebook follows the structure of the original script, but separates the workflow into:

1. one-time setup and data loading,

2. a repeated simulation/localization loop,

3. collection of results from every run,

4. aggregation and visualization of the results,

For the details of the individual simulation steps, see the previous tutorial linked above.

import os
import time
import pickle

import numpy as np
import matplotlib.pyplot as plt
import mne

from mvpure_py import simulation, utils

# ------------------------------------------------------------
# HELPER VISUALIZATION FUNCTION
# ------------------------------------------------------------
def violin_plot_from_results(
        ax,
        snr_dict: dict,
        results_key: str,
        title: str | None = None,
        xlabel: str ="Rank",
        ylabel: str | None = None,
        color: str = "indigo",
        include_lcmv: bool = False,
        lcmv_color: str = "crimson",
        show_means: bool = True,
):
    """
    Create a violin plot of the results stored in `snr_dict`.
    """
    # Collect distributions for each rank
    data = [
        results[results_key]
        for _, results in snr_dict['by_rank'].items()
    ]

    labels = [str(i) for i in range(1, len(data) + 1)]

    if include_lcmv:
        if results_key == "n_correctly_localized":
            lcmv_key = "lcmv_n_correctly_localized"
        elif results_key == "mean_error":
            lcmv_key = "lcmv_mean_error"
        else:
            raise ValueError(f"Unsupported results_key: {results_key}")

        data.append(snr_dict[lcmv_key])
        labels.append("LCMV-NAI")

    positions = np.arange(1, len(data) + 1)

    vp = ax.violinplot(
        data,
        positions=positions,
        showmeans=show_means,
        showmedians=False,
        showextrema=False,
    )

    # Color all violins
    for i, body in enumerate(vp['bodies']):
        if include_lcmv and i == len(data) - 1:
            body.set_facecolor(lcmv_color)
        else:
            body.set_facecolor(color)

        body.set_edgecolor('black')
        body.set_alpha(0.7)

    # Optionally customize mean lines
    if show_means:
        vp['cmeans'].set_color('black')
        vp['cmeans'].set_linewidth(2)

    ax.set_xticks(positions)
    ax.set_xticklabels(labels, fontdict={"fontsize": 11})
    xticklabels = ax.get_xticklabels()
    xticklabels[-1].set_rotation(45)
    xticklabels[-1].set_ha('right')

    ax.grid(True)
    ax.set_title(title, fontdict={"fontsize": 13})

    if xlabel is not None:
        ax.set_xlabel(xlabel, fontdict={"fontsize": 12})
    if ylabel is not None:
        ax.set_ylabel(ylabel, fontdict={"fontsize": 12})

1. Experiment configuration

Most parameters below are inherited directly from the original simulation script.

The important new parameter is N_RUNS: instead of generating one dataset and evaluating it once, we repeat the experiment N_RUNS times.

For a quick notebook run, use a small value such as N_RUNS = 10. Once the workflow is verified, N_RUNS can be increased to the desired number of repetitions, e.g. 100 or 1000.

The parameters defining the simulated sources, their activity, and the sensor-level noise remain fixed across runs. What changes between runs is the random realization of the simulated experiment, including the selected source locations and simulated activity.

labels_to_use = [
    "cuneus-lh",
    "cuneus-rh",
    "lateraloccipital-lh",
    "lateraloccipital-rh",
    "inferiorparietal-lh",
    "inferiorparietal-rh",
    "superiorparietal-lh",
    "superiorparietal-rh",
    "superiortemporal-lh",
    "superiortemporal-rh",
    "supramarginal-lh",
    "supramarginal-rh",
    "superiorfrontal-lh",
    "superiorfrontal-rh",
    "insula-lh",
    "insula-rh",
    "caudalanteriorcingulate-lh",
    "caudalanteriorcingulate-rh"
]

labels_to_use_poststimuli = [
    'lateraloccipital-rh',
    'superiorfrontal-rh',
    'caudalanteriorcingulate-lh',
    'caudalmiddlefrontal-lh',
    'lateraloccipital-lh'
]

SUBJECT = "sample_subject"
SUBJECTS_DIR = "subjects"

mne.set_config("SUBJECTS_DIR", SUBJECTS_DIR)

N_VERTICES_PER_BG_LABEL = 1
N_VERTICES_PER_ACTIVITY_LABEL = 1
N_EPOCHS = 100

ERP_FACTOR = 15e-9
ORDER_BG = 7
ORDER = 3
TARGET_STD_BG = 15e-9
TARGET_STD = 15e-9
COUPLING_BG = 0.5
COUPLING = 0.8
NOISE_BG = 1.0
NOISE = 1.0
GAUSSIAN_FILTER_SIGMA_BG = 3
GAUSSIAN_FILTER_SIGMA = 3
N_DOMINANT_EIGVALS = 2
NOISE_FACTOR_SENSORS = 0.3

FIND_CLOSE = False

# NEW: number of independent repetitions of the experiment.
# Use 10 for a quick test; use larger number e.g., 1000 for the full experiment.
N_RUNS = 10

SNR_DB = 1.0

2. Load the data and forward model once

These objects do not change between runs, so there is no reason to load them inside the loop.

We use the same sample-subject epoched data and forward solution as in the previous tutorial. The epochs provide the sampling frequency, timing, channel information, and other MNE metadata; the forward solution provides the lead field and source-space geometry.

print("Loading data...")

epoched = mne.read_epochs(
    os.path.join(
        SUBJECTS_DIR,
        SUBJECT,
        "_eeg",
        "_pre",
        f"{SUBJECT}_oddball-epo.fif",
    )
)

forward_path = os.path.join(
    SUBJECTS_DIR,
    SUBJECT,
    "forward",
    f"{SUBJECT}_ico4-fwd.fif",
)

fwd_vector = mne.read_forward_solution(forward_path)

fwd = mne.convert_forward_solution(
    fwd_vector,
    surf_ori=True,
    force_fixed=True,
    use_cps=True,
)

leadfield = fwd["sol"]["data"]
src = fwd["src"]

sfreq = epoched.info["sfreq"]
tmin, tmax = epoched.tmin, 0.25
times = np.arange(tmin, tmax, 1 / sfreq)
n_times = len(times)

post_mask = (times >= 0.05) & (times <= 0.2)

print(f"Sampling frequency: {sfreq:.2f} Hz")
print(f"Number of time points: {n_times}")
print(f"Number of sources in forward model: {leadfield.shape[1]}")

Loading data...
Reading /Volumes/UMK/oddball/subjects/sample_subject/_eeg/_pre/sample_subject_oddball-epo.fif ...
    Found the data of interest:
        t =    -199.22 ...     800.78 ms
        0 CTF compensation matrices available
Not setting metadata
621 matching events found
No baseline correction applied
0 projection items activated
Reading forward solution from /Volumes/UMK/oddball/subjects/sample_subject/forward/sample_subject_ico4-fwd.fif...
    Reading a source space...
    [done]
    Reading a source space...
    [done]
    2 source spaces read
    Desired named matrix (kind = 3523 (FIFF_MNE_FORWARD_SOLUTION_GRAD)) not available
    Read EEG forward solution (5124 sources, 128 channels, free orientations)
    Source spaces transformed to the forward solution coordinate frame
    No patch info available. The standard source space normals will be employed in the rotation to the local surface coordinates....
    Changing to fixed-orientation forward solution with surface-based source orientations...
    [done]
Sampling frequency: 256.00 Hz
Number of time points: 115
Number of sources in forward model: 5124

3. What changes between runs?

The key stochastic step is the selection of source vertices.

For every run we call simulation.get_random_vertices(...) again. This means that the background and post-stimulus sources are re-sampled, subject to the same anatomical constraints.

Everything downstream is then recomputed for that realization:

random vertices → source simulation → sensor simulation → preprocessing → covariance → localization → evaluation

This is the main conceptual difference from the previous tutorial.

4. Store results from all runs

Instead of keeping only the result of the current run, we append the relevant metrics to FULL_RESULTS.

Results are stored separately for each tested rank. For every rank we keep:

• number of correctly localized sources,

• mean localization error.

We also store, for each run:

• the rank(s) with the smallest mean error,

• the rank(s) with the largest number of correctly localized sources,

• the corresponding LCMV metrics.

Keeping the per-run values is preferable to storing only an average: it lets us inspect variability, compare methods, and perform additional analyses later without repeating the simulations.

FULL_RESULTS = {
    "by_rank": {},
    "best_rank_mse": [],
    "best_rank_n_locs": [],
    "lcmv_n_correctly_localized": [],
    "lcmv_mean_error": [],
}

5. Run the complete experiment repeatedly

The code below is close to the original single-run implementation.

The main structural change is that the whole simulation-localization block is inside:

for n in range(N_RUNS):
    ...

The source locations are sampled on every iteration, so each iteration is an independent realization of the same experimental condition.

start = time.time()

for n in range(N_RUNS):
    print(f"==== RUN {n + 1}/{N_RUNS} ====")

    # ------------------------------------------------------------
    # 1. Random source locations
    # ------------------------------------------------------------
    labels_info = simulation.get_random_vertices(
        n_vertices_per_label_bg=N_VERTICES_PER_BG_LABEL,
        n_vertices_per_poststimuli_label=N_VERTICES_PER_ACTIVITY_LABEL,
        noise_labels=labels_to_use,
        poststimuli_labels=labels_to_use_poststimuli,
        subject=SUBJECT,
        subjects_dir=SUBJECTS_DIR,
        src=src,
        find_close=FIND_CLOSE
    )

    noise_vertices, poststimuli_vertices = simulation.split_vertices(
        labels_info,
        labels_to_use_poststimuli,
    )

    leadfield_subset_indices_noise, lh_vert_to_lf_noise, rh_vert_to_lf_noise = (
        utils.translation.transform_vertices_to_leadfield_indices(
            vertices=noise_vertices,
            src=src,
            hemi="both",
            include_mapping=True,
        )
    )

    leadfield_subset_poststimuli_indices, lh_vert_to_lf_stimuli, rh_vert_to_lf_stimuli = (
        utils.translation.transform_vertices_to_leadfield_indices(
            vertices=poststimuli_vertices,
            src=src,
            hemi="both",
            include_mapping=True,
        )
    )

    leadfield_subset_indices = np.unique(
        np.concatenate(
            (
                leadfield_subset_indices_noise,
                leadfield_subset_poststimuli_indices,
            )
        )
    )

    leadfield_to_label_mapping = simulation.assign_label_to_leadfield_index(
        labels_info=labels_info,
        lh_vert_to_lf=lh_vert_to_lf_noise | lh_vert_to_lf_stimuli,
        rh_vert_to_lf=rh_vert_to_lf_noise | rh_vert_to_lf_stimuli,
    )

    # ------------------------------------------------------------
    # 2. Simulate source activity
    # ------------------------------------------------------------
    X_epochs = simulation.simulate_source_epochs(
        n_epochs=N_EPOCHS,
        lf_subset_indices=leadfield_subset_indices,
        n_times=n_times,
        bg_lf_subset_indices=leadfield_subset_indices_noise,
        poststimuli_mask=post_mask,
        poststimuli_lf_subset_indices=leadfield_subset_poststimuli_indices,
        lf_to_label=leadfield_to_label_mapping,
        sfreq=sfreq,
        erp_factor=ERP_FACTOR,
        snr_db=SNR_DB,
        order_bg=ORDER_BG,
        order=ORDER,
        target_std_bg=TARGET_STD_BG,
        target_std=TARGET_STD,
        coupling_bg=COUPLING_BG,
        coupling=COUPLING,
        noise_bg=NOISE_BG,
        noise=NOISE,
        gaussian_filter_sigma=GAUSSIAN_FILTER_SIGMA,
        gaussian_filter_sigma_bg=GAUSSIAN_FILTER_SIGMA_BG,
        n_dominant_eigvals=N_DOMINANT_EIGVALS,
        seed=n,
    )

    # ------------------------------------------------------------
    # 3. Project source activity to sensors
    # ------------------------------------------------------------
    sim_epochs = simulation.simulate_sensor_epochs(
        X_epochs=X_epochs,
        leadfield=leadfield,
        lf_subset_indices=leadfield_subset_indices,
        src=src,
        tmin=tmin,
        sfreq=sfreq,
        noise_factor=NOISE_FACTOR_SENSORS,
        info=epoched.info,
    )

    # ------------------------------------------------------------
    # 4. Preprocessing
    # ------------------------------------------------------------
    sim_epochs = sim_epochs.filter(
        l_freq=1,
        h_freq=45,
        method="iir",
    )

    noise_cov = mne.compute_covariance(
        sim_epochs,
        tmin=-0.2,
        tmax=0,
        method="empirical",
    )

    data_cov = mne.compute_covariance(
        sim_epochs,
        tmin=0.05,
        tmax=0.2,
        method="empirical",
    )

    sim_epochs.set_eeg_reference("average", projection=True)
    sim_epochs.apply_proj()
    sim_evoked = sim_epochs.average()
    sim_evoked = sim_evoked.copy().crop(
        tmin=0.05,
        tmax=0.2
    )

    # ------------------------------------------------------------
    # 5. MVPURE localization for every rank
    # ------------------------------------------------------------
    locs_results_summary = simulation.evaluate_localization_for_each_rank(
        subject=SUBJECT,
        subjects_dir=SUBJECTS_DIR,
        n_sources=len(labels_to_use_poststimuli) * N_VERTICES_PER_ACTIVITY_LABEL,
        R=data_cov.data,
        N=noise_cov.data,
        forward=fwd,
        true_vertices=poststimuli_vertices,
        localizer_to_use="mai_mvp",
        plot_sum_error_by_rank=False,
        plot_correct_sources_by_rank=False,
        plot_mean_error_by_rank=False,
        show_progress=False,
    )

    mse = []
    n_corr_locs = []

    for rank, items in locs_results_summary.items():
        if rank not in FULL_RESULTS["by_rank"]:
            FULL_RESULTS["by_rank"][rank] = {
                "n_correctly_localized": [],
                "mean_error": [],
            }

        mse.append(items["error_info"]["mean_error"])
        n_corr_locs.append(items["n_correctly_localized"])

        FULL_RESULTS["by_rank"][rank]["n_correctly_localized"].append(
            items["n_correctly_localized"]
        )
        FULL_RESULTS["by_rank"][rank]["mean_error"].append(
            items["error_info"]["mean_error"]
        )

    FULL_RESULTS["best_rank_mse"].append(
        [i + 1 for i, x in enumerate(mse) if x == min(mse)]
    )

    FULL_RESULTS["best_rank_n_locs"].append(
        [i + 1 for i, x in enumerate(n_corr_locs) if x == max(n_corr_locs)]
    )

    # ------------------------------------------------------------
    # 6. LCMV comparison
    # ------------------------------------------------------------
    (
        lcmv_top_vertices,
        lcmv_n_correctly_localized,
        lcmv_error_info,
    ) = simulation.compare_with_strongest_sources_lcmv(
        signal=sim_evoked,
        n_sources=len(labels_to_use_poststimuli) * N_VERTICES_PER_ACTIVITY_LABEL,
        true_vertices=poststimuli_vertices,
        forward=fwd,
        R=data_cov,
        N=noise_cov,
        reg=0.05,
        pick_ori=None,
    )

    FULL_RESULTS["lcmv_n_correctly_localized"].append(
        lcmv_n_correctly_localized
    )
    FULL_RESULTS["lcmv_mean_error"].append(
        lcmv_error_info["mean_error"]
    )

elapsed = time.time() - start
print(f"Elapsed time: {elapsed:.2f} s ({elapsed / 60:.2f} min)")

==== RUN 1/10 ====
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Setting up band-pass filter from 1 - 45 Hz

IIR filter parameters
---------------------
Butterworth bandpass zero-phase (two-pass forward and reverse) non-causal filter:
- Filter order 16 (effective, after forward-backward)
- Cutoffs at 1.00, 45.00 Hz: -6.02, -6.02 dB
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 5200
[done]
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 3900
[done]
EEG channel type selected for re-referencing
Adding average EEG reference projection.
1 projection items deactivated
Average reference projection was added, but has not been applied yet. Use the apply_proj method to apply it.
Created an SSP operator (subspace dimension = 1)
1 projection items activated
SSP projectors applied...
Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1912, 2570, 201, 2151, 4619]
  Selected indices (sorted, matches H_res columns): [201, 1912, 2151, 2570, 4619]
  Index max values (sorted to match H_res/sorted_sources): [2.14955894 1.26719123 2.33060145 1.99242278 2.42994718]
  Rank parameter (r): 1

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1912, 2570, 201, 2151, 257]
  Selected indices (sorted, matches H_res columns): [201, 257, 1912, 2151, 2570]
  Index max values (sorted to match H_res/sorted_sources): [2.82344823 3.12011346 1.26719123 3.0052794  2.56713989]
  Rank parameter (r): 2

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1912, 2570, 411, 4750, 201]
  Selected indices (sorted, matches H_res columns): [201, 411, 1912, 2570, 4750]
  Index max values (sorted to match H_res/sorted_sources): [3.80738377 3.25994592 1.26719123 2.56713989 3.58457047]
  Rank parameter (r): 3

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1912, 2570, 411, 2115, 4750]
  Selected indices (sorted, matches H_res columns): [411, 1912, 2115, 2570, 4750]
  Index max values (sorted to match H_res/sorted_sources): [3.25994592 1.26719123 3.90041559 2.56713989 4.24021027]
  Rank parameter (r): 4

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1912, 2570, 411, 2115, 3732]
  Selected indices (sorted, matches H_res columns): [411, 1912, 2115, 2570, 3732]
  Index max values (sorted to match H_res/sorted_sources): [3.25994592 1.26719123 3.90041559 2.56713989 4.53309263]
  Rank parameter (r): 5

Computing rank from covariance with rank=None
    Using tolerance 5.2e-13 (2.2e-16 eps * 128 dim * 18  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Computing rank from covariance with rank=None
    Using tolerance 2.8e-13 (2.2e-16 eps * 128 dim * 10  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Making LCMV beamformer with rank {'eeg': 127}
Computing inverse operator with 128 channels.
    128 out of 128 channels remain after picking
Selected 128 channels
Whitening the forward solution.
    Created an SSP operator (subspace dimension = 1)
Computing rank from covariance with rank={'eeg': 127}
    Setting small EEG eigenvalues to zero (without PCA)
Creating the source covariance matrix
Adjusting source covariance matrix.
Computing beamformer filters for 5124 sources
Filter computation complete
==== RUN 2/10 ====
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   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Setting up band-pass filter from 1 - 45 Hz

IIR filter parameters
---------------------
Butterworth bandpass zero-phase (two-pass forward and reverse) non-causal filter:
- Filter order 16 (effective, after forward-backward)
- Cutoffs at 1.00, 45.00 Hz: -6.02, -6.02 dB
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 5200
[done]
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 3900
[done]
EEG channel type selected for re-referencing
Adding average EEG reference projection.
1 projection items deactivated
Average reference projection was added, but has not been applied yet. Use the apply_proj method to apply it.
Created an SSP operator (subspace dimension = 1)
1 projection items activated
SSP projectors applied...
Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [2040, 458, 4755, 686, 475]
  Selected indices (sorted, matches H_res columns): [458, 475, 686, 2040, 4755]
  Index max values (sorted to match H_res/sorted_sources): [4.88690889 5.63391534 5.49563375 4.45534792 5.36035964]
  Rank parameter (r): 1

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [2040, 458, 4755, 1842, 2188]
  Selected indices (sorted, matches H_res columns): [458, 1842, 2040, 2188, 4755]
  Index max values (sorted to match H_res/sorted_sources): [5.42951899 6.33762811 4.45534792 6.56662027 6.07303972]
  Rank parameter (r): 2

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [2040, 458, 4755, 1841, 4481]
  Selected indices (sorted, matches H_res columns): [458, 1841, 2040, 4481, 4755]
  Index max values (sorted to match H_res/sorted_sources): [5.42951899 6.95050071 4.45534792 7.24534668 6.44088187]
  Rank parameter (r): 3

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [2040, 458, 4755, 2188, 1841]
  Selected indices (sorted, matches H_res columns): [458, 1841, 2040, 2188, 4755]
  Index max values (sorted to match H_res/sorted_sources): [5.42951899 7.85531936 4.45534792 7.30786679 6.44088187]
  Rank parameter (r): 4

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [2040, 458, 4755, 2188, 1841]
  Selected indices (sorted, matches H_res columns): [458, 1841, 2040, 2188, 4755]
  Index max values (sorted to match H_res/sorted_sources): [5.42951899 8.15340665 4.45534792 7.30786679 6.44088187]
  Rank parameter (r): 5

Computing rank from covariance with rank=None
    Using tolerance 4.6e-13 (2.2e-16 eps * 128 dim * 16  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Computing rank from covariance with rank=None
    Using tolerance 2.7e-13 (2.2e-16 eps * 128 dim * 9.5  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Making LCMV beamformer with rank {'eeg': 127}
Computing inverse operator with 128 channels.
    128 out of 128 channels remain after picking
Selected 128 channels
Whitening the forward solution.
    Created an SSP operator (subspace dimension = 1)
Computing rank from covariance with rank={'eeg': 127}
    Setting small EEG eigenvalues to zero (without PCA)
Creating the source covariance matrix
Adjusting source covariance matrix.
Computing beamformer filters for 5124 sources
Filter computation complete
==== RUN 3/10 ====
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Setting up band-pass filter from 1 - 45 Hz

IIR filter parameters
---------------------
Butterworth bandpass zero-phase (two-pass forward and reverse) non-causal filter:
- Filter order 16 (effective, after forward-backward)
- Cutoffs at 1.00, 45.00 Hz: -6.02, -6.02 dB
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 5200
[done]
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 3900
[done]
EEG channel type selected for re-referencing
Adding average EEG reference projection.
1 projection items deactivated
Average reference projection was added, but has not been applied yet. Use the apply_proj method to apply it.
Created an SSP operator (subspace dimension = 1)
1 projection items activated
SSP projectors applied...
Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1692, 2042, 329, 2156, 2571]
  Selected indices (sorted, matches H_res columns): [329, 1692, 2042, 2156, 2571]
  Index max values (sorted to match H_res/sorted_sources): [2.25687342 1.86929064 2.13301082 2.33803454 2.42796607]
  Rank parameter (r): 1

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1692, 2571, 2042, 329, 2034]
  Selected indices (sorted, matches H_res columns): [329, 1692, 2034, 2042, 2571]
  Index max values (sorted to match H_res/sorted_sources): [3.16108116 1.86929064 3.28930475 3.0332807  2.76657492]
  Rank parameter (r): 2

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1692, 2571, 2042, 4935, 2249]
  Selected indices (sorted, matches H_res columns): [1692, 2042, 2249, 2571, 4935]
  Index max values (sorted to match H_res/sorted_sources): [1.86929064 3.55866679 4.20297367 2.76657492 3.94641548]
  Rank parameter (r): 3

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1692, 2571, 2042, 366, 3393]
  Selected indices (sorted, matches H_res columns): [366, 1692, 2042, 2571, 3393]
  Index max values (sorted to match H_res/sorted_sources): [4.30237386 1.86929064 3.55866679 2.76657492 4.72627125]
  Rank parameter (r): 4

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1692, 2571, 2042, 366, 3393]
  Selected indices (sorted, matches H_res columns): [366, 1692, 2042, 2571, 3393]
  Index max values (sorted to match H_res/sorted_sources): [4.30237386 1.86929064 3.55866679 2.76657492 5.0053849 ]
  Rank parameter (r): 5

Computing rank from covariance with rank=None
    Using tolerance 5.8e-13 (2.2e-16 eps * 128 dim * 21  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Computing rank from covariance with rank=None
    Using tolerance 2.8e-13 (2.2e-16 eps * 128 dim * 9.7  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Making LCMV beamformer with rank {'eeg': 127}
Computing inverse operator with 128 channels.
    128 out of 128 channels remain after picking
Selected 128 channels
Whitening the forward solution.
    Created an SSP operator (subspace dimension = 1)
Computing rank from covariance with rank={'eeg': 127}
    Setting small EEG eigenvalues to zero (without PCA)
Creating the source covariance matrix
Adjusting source covariance matrix.
Computing beamformer filters for 5124 sources
Filter computation complete
==== RUN 4/10 ====
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Setting up band-pass filter from 1 - 45 Hz

IIR filter parameters
---------------------
Butterworth bandpass zero-phase (two-pass forward and reverse) non-causal filter:
- Filter order 16 (effective, after forward-backward)
- Cutoffs at 1.00, 45.00 Hz: -6.02, -6.02 dB
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 5200
[done]
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 3900
[done]
EEG channel type selected for re-referencing
Adding average EEG reference projection.
1 projection items deactivated
Average reference projection was added, but has not been applied yet. Use the apply_proj method to apply it.
Created an SSP operator (subspace dimension = 1)
1 projection items activated
SSP projectors applied...
Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [135, 1934, 4881, 4517, 2673]
  Selected indices (sorted, matches H_res columns): [135, 1934, 2673, 4517, 4881]
  Index max values (sorted to match H_res/sorted_sources): [0.909107   1.47102952 1.82601673 1.77309039 1.6521332 ]
  Rank parameter (r): 1

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [135, 1753, 1782, 4881, 3204]
  Selected indices (sorted, matches H_res columns): [135, 1753, 1782, 3204, 4881]
  Index max values (sorted to match H_res/sorted_sources): [0.909107   1.61792608 2.14292346 2.70735563 2.4421112 ]
  Rank parameter (r): 2

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [135, 1753, 3204, 1782, 13]
  Selected indices (sorted, matches H_res columns): [13, 135, 1753, 1782, 3204]
  Index max values (sorted to match H_res/sorted_sources): [3.19219834 0.909107   1.61792608 2.85226181 2.30823867]
  Rank parameter (r): 3

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [135, 1753, 3204, 2594, 1934]
  Selected indices (sorted, matches H_res columns): [135, 1753, 1934, 2594, 3204]
  Index max values (sorted to match H_res/sorted_sources): [0.909107   1.61792608 3.56958663 2.99944356 2.30823867]
  Rank parameter (r): 4

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [135, 1753, 3204, 2594, 4064]
  Selected indices (sorted, matches H_res columns): [135, 1753, 2594, 3204, 4064]
  Index max values (sorted to match H_res/sorted_sources): [0.909107   1.61792608 2.99944356 2.30823867 3.6835762 ]
  Rank parameter (r): 5

Computing rank from covariance with rank=None
    Using tolerance 7.2e-13 (2.2e-16 eps * 128 dim * 25  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Computing rank from covariance with rank=None
    Using tolerance 3.2e-13 (2.2e-16 eps * 128 dim * 11  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Making LCMV beamformer with rank {'eeg': 127}
Computing inverse operator with 128 channels.
    128 out of 128 channels remain after picking
Selected 128 channels
Whitening the forward solution.
    Created an SSP operator (subspace dimension = 1)
Computing rank from covariance with rank={'eeg': 127}
    Setting small EEG eigenvalues to zero (without PCA)
Creating the source covariance matrix
Adjusting source covariance matrix.
Computing beamformer filters for 5124 sources
Filter computation complete
==== RUN 5/10 ====
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Setting up band-pass filter from 1 - 45 Hz

IIR filter parameters
---------------------
Butterworth bandpass zero-phase (two-pass forward and reverse) non-causal filter:
- Filter order 16 (effective, after forward-backward)
- Cutoffs at 1.00, 45.00 Hz: -6.02, -6.02 dB
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 5200
[done]
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 3900
[done]
EEG channel type selected for re-referencing
Adding average EEG reference projection.
1 projection items deactivated
Average reference projection was added, but has not been applied yet. Use the apply_proj method to apply it.
Created an SSP operator (subspace dimension = 1)
1 projection items activated
SSP projectors applied...
Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1915, 1394, 2576, 2527, 1988]
  Selected indices (sorted, matches H_res columns): [1394, 1915, 1988, 2527, 2576]
  Index max values (sorted to match H_res/sorted_sources): [6.53704875 6.39350737 6.85525371 6.76798288 6.66104236]
  Rank parameter (r): 1

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1915, 264, 2249, 1394, 2576]
  Selected indices (sorted, matches H_res columns): [264, 1394, 1915, 2249, 2576]
  Index max values (sorted to match H_res/sorted_sources): [7.29688426 7.72305224 6.39350737 7.52649619 7.90272294]
  Rank parameter (r): 2

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1915, 264, 5036, 2249, 1394]
  Selected indices (sorted, matches H_res columns): [264, 1394, 1915, 2249, 5036]
  Index max values (sorted to match H_res/sorted_sources): [7.29688426 8.48515572 6.39350737 8.28144421 8.02513545]
  Rank parameter (r): 3

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1915, 264, 5036, 2576, 1232]
  Selected indices (sorted, matches H_res columns): [264, 1232, 1915, 2576, 5036]
  Index max values (sorted to match H_res/sorted_sources): [7.29688426 8.98623803 6.39350737 8.71877444 8.02513545]
  Rank parameter (r): 4

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1915, 264, 5036, 2576, 1232]
  Selected indices (sorted, matches H_res columns): [264, 1232, 1915, 2576, 5036]
  Index max values (sorted to match H_res/sorted_sources): [7.29688426 9.37019935 6.39350737 8.71877444 8.02513545]
  Rank parameter (r): 5

Computing rank from covariance with rank=None
    Using tolerance 5.2e-13 (2.2e-16 eps * 128 dim * 18  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Computing rank from covariance with rank=None
    Using tolerance 3e-13 (2.2e-16 eps * 128 dim * 10  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Making LCMV beamformer with rank {'eeg': 127}
Computing inverse operator with 128 channels.
    128 out of 128 channels remain after picking
Selected 128 channels
Whitening the forward solution.
    Created an SSP operator (subspace dimension = 1)
Computing rank from covariance with rank={'eeg': 127}
    Setting small EEG eigenvalues to zero (without PCA)
Creating the source covariance matrix
Adjusting source covariance matrix.
Computing beamformer filters for 5124 sources
Filter computation complete
==== RUN 6/10 ====
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Setting up band-pass filter from 1 - 45 Hz

IIR filter parameters
---------------------
Butterworth bandpass zero-phase (two-pass forward and reverse) non-causal filter:
- Filter order 16 (effective, after forward-backward)
- Cutoffs at 1.00, 45.00 Hz: -6.02, -6.02 dB
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 5200
[done]
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 3900
[done]
EEG channel type selected for re-referencing
Adding average EEG reference projection.
1 projection items deactivated
Average reference projection was added, but has not been applied yet. Use the apply_proj method to apply it.
Created an SSP operator (subspace dimension = 1)
1 projection items activated
SSP projectors applied...
Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [626, 1835, 4650, 1301, 2794]
  Selected indices (sorted, matches H_res columns): [626, 1301, 1835, 2794, 4650]
  Index max values (sorted to match H_res/sorted_sources): [0.7184174  1.21067705 0.94343773 1.30457736 1.1334448 ]
  Rank parameter (r): 1

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [626, 2785, 2023, 87, 4650]
  Selected indices (sorted, matches H_res columns): [87, 626, 2023, 2785, 4650]
  Index max values (sorted to match H_res/sorted_sources): [2.1685766  0.7184174  1.82374037 1.419883   2.54250654]
  Rank parameter (r): 2

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [626, 2785, 87, 2023, 4650]
  Selected indices (sorted, matches H_res columns): [87, 626, 2023, 2785, 4650]
  Index max values (sorted to match H_res/sorted_sources): [2.17264814 0.7184174  2.65257846 1.419883   3.18287527]
  Rank parameter (r): 3

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [626, 2785, 87, 4650, 2023]
  Selected indices (sorted, matches H_res columns): [87, 626, 2023, 2785, 4650]
  Index max values (sorted to match H_res/sorted_sources): [2.17264814 0.7184174  3.56073811 1.419883   2.96702093]
  Rank parameter (r): 4

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [626, 2785, 87, 4650, 1835]
  Selected indices (sorted, matches H_res columns): [87, 626, 1835, 2785, 4650]
  Index max values (sorted to match H_res/sorted_sources): [2.17264814 0.7184174  3.82509333 1.419883   2.96702093]
  Rank parameter (r): 5

Computing rank from covariance with rank=None
    Using tolerance 5.2e-13 (2.2e-16 eps * 128 dim * 18  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Computing rank from covariance with rank=None
    Using tolerance 2.7e-13 (2.2e-16 eps * 128 dim * 9.6  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Making LCMV beamformer with rank {'eeg': 127}
Computing inverse operator with 128 channels.
    128 out of 128 channels remain after picking
Selected 128 channels
Whitening the forward solution.
    Created an SSP operator (subspace dimension = 1)
Computing rank from covariance with rank={'eeg': 127}
    Setting small EEG eigenvalues to zero (without PCA)
Creating the source covariance matrix
Adjusting source covariance matrix.
Computing beamformer filters for 5124 sources
Filter computation complete
==== RUN 7/10 ====
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Setting up band-pass filter from 1 - 45 Hz

IIR filter parameters
---------------------
Butterworth bandpass zero-phase (two-pass forward and reverse) non-causal filter:
- Filter order 16 (effective, after forward-backward)
- Cutoffs at 1.00, 45.00 Hz: -6.02, -6.02 dB
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 5200
[done]
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 3900
[done]
EEG channel type selected for re-referencing
Adding average EEG reference projection.
1 projection items deactivated
Average reference projection was added, but has not been applied yet. Use the apply_proj method to apply it.
Created an SSP operator (subspace dimension = 1)
1 projection items activated
SSP projectors applied...
Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1845, 4731, 382, 4171, 3838]
  Selected indices (sorted, matches H_res columns): [382, 1845, 3838, 4171, 4731]
  Index max values (sorted to match H_res/sorted_sources): [2.25415959 2.02949245 2.42829872 2.34660335 2.17671669]
  Rank parameter (r): 1

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1845, 2696, 130, 1653, 4783]
  Selected indices (sorted, matches H_res columns): [130, 1653, 1845, 2696, 4783]
  Index max values (sorted to match H_res/sorted_sources): [3.33687788 3.51049106 2.02949245 2.92338882 3.66723627]
  Rank parameter (r): 2

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1845, 2696, 130, 4783, 1653]
  Selected indices (sorted, matches H_res columns): [130, 1653, 1845, 2696, 4783]
  Index max values (sorted to match H_res/sorted_sources): [3.63558088 4.29092904 2.02949245 2.92338882 4.09003581]
  Rank parameter (r): 3

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1845, 2696, 130, 4783, 4565]
  Selected indices (sorted, matches H_res columns): [130, 1845, 2696, 4565, 4783]
  Index max values (sorted to match H_res/sorted_sources): [3.63558088 2.02949245 2.92338882 4.78297148 4.3541731 ]
  Rank parameter (r): 4

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1845, 2696, 130, 4783, 1199]
  Selected indices (sorted, matches H_res columns): [130, 1199, 1845, 2696, 4783]
  Index max values (sorted to match H_res/sorted_sources): [3.63558088 5.03568608 2.02949245 2.92338882 4.3541731 ]
  Rank parameter (r): 5

Computing rank from covariance with rank=None
    Using tolerance 4.8e-13 (2.2e-16 eps * 128 dim * 17  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Computing rank from covariance with rank=None
    Using tolerance 2.7e-13 (2.2e-16 eps * 128 dim * 9.6  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Making LCMV beamformer with rank {'eeg': 127}
Computing inverse operator with 128 channels.
    128 out of 128 channels remain after picking
Selected 128 channels
Whitening the forward solution.
    Created an SSP operator (subspace dimension = 1)
Computing rank from covariance with rank={'eeg': 127}
    Setting small EEG eigenvalues to zero (without PCA)
Creating the source covariance matrix
Adjusting source covariance matrix.
Computing beamformer filters for 5124 sources
Filter computation complete
==== RUN 8/10 ====
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
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Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
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Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
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Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
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Reading labels from parcellation...
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
   read 0 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/lh.aparc.annot
   read 1 labels from /Volumes/UMK/oddball/subjects/sample_subject/label/rh.aparc.annot
Reading labels from parcellation...
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Setting up band-pass filter from 1 - 45 Hz

IIR filter parameters
---------------------
Butterworth bandpass zero-phase (two-pass forward and reverse) non-causal filter:
- Filter order 16 (effective, after forward-backward)
- Cutoffs at 1.00, 45.00 Hz: -6.02, -6.02 dB
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 5200
[done]
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 3900
[done]
EEG channel type selected for re-referencing
Adding average EEG reference projection.
1 projection items deactivated
Average reference projection was added, but has not been applied yet. Use the apply_proj method to apply it.
Created an SSP operator (subspace dimension = 1)
1 projection items activated
SSP projectors applied...
Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1779, 4340, 1844, 2654, 2295]
  Selected indices (sorted, matches H_res columns): [1779, 1844, 2295, 2654, 4340]
  Index max values (sorted to match H_res/sorted_sources): [1.88404056 2.25246957 2.44341905 2.37458599 2.04820683]
  Rank parameter (r): 1

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1779, 2654, 191, 4340, 1844]
  Selected indices (sorted, matches H_res columns): [191, 1779, 1844, 2654, 4340]
  Index max values (sorted to match H_res/sorted_sources): [3.05770379 1.88404056 3.43509889 2.81023299 3.23900946]
  Rank parameter (r): 2

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1779, 2654, 191, 1984, 4340]
  Selected indices (sorted, matches H_res columns): [191, 1779, 1984, 2654, 4340]
  Index max values (sorted to match H_res/sorted_sources): [3.51938726 1.88404056 3.89562546 2.81023299 4.10860867]
  Rank parameter (r): 3

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1779, 2654, 191, 177, 1984]
  Selected indices (sorted, matches H_res columns): [177, 191, 1779, 1984, 2654]
  Index max values (sorted to match H_res/sorted_sources): [4.19025248 3.51938726 1.88404056 4.58746941 2.81023299]
  Rank parameter (r): 4

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [1779, 2654, 191, 177, 4558]
  Selected indices (sorted, matches H_res columns): [177, 191, 1779, 2654, 4558]
  Index max values (sorted to match H_res/sorted_sources): [4.19025248 3.51938726 1.88404056 2.81023299 4.83688375]
  Rank parameter (r): 5

Computing rank from covariance with rank=None
    Using tolerance 6.3e-13 (2.2e-16 eps * 128 dim * 22  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Computing rank from covariance with rank=None
    Using tolerance 3.3e-13 (2.2e-16 eps * 128 dim * 12  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Making LCMV beamformer with rank {'eeg': 127}
Computing inverse operator with 128 channels.
    128 out of 128 channels remain after picking
Selected 128 channels
Whitening the forward solution.
    Created an SSP operator (subspace dimension = 1)
Computing rank from covariance with rank={'eeg': 127}
    Setting small EEG eigenvalues to zero (without PCA)
Creating the source covariance matrix
Adjusting source covariance matrix.
Computing beamformer filters for 5124 sources
Filter computation complete
==== RUN 9/10 ====
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Setting up band-pass filter from 1 - 45 Hz

IIR filter parameters
---------------------
Butterworth bandpass zero-phase (two-pass forward and reverse) non-causal filter:
- Filter order 16 (effective, after forward-backward)
- Cutoffs at 1.00, 45.00 Hz: -6.02, -6.02 dB
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 5200
[done]
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 3900
[done]
EEG channel type selected for re-referencing
Adding average EEG reference projection.
1 projection items deactivated
Average reference projection was added, but has not been applied yet. Use the apply_proj method to apply it.
Created an SSP operator (subspace dimension = 1)
1 projection items activated
SSP projectors applied...
Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [4573, 135, 2023, 595, 4842]
  Selected indices (sorted, matches H_res columns): [135, 595, 2023, 4573, 4842]
  Index max values (sorted to match H_res/sorted_sources): [1.03676593 1.40722614 1.30151873 0.78022538 1.48135688]
  Rank parameter (r): 1

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [4573, 2252, 135, 2023, 4459]
  Selected indices (sorted, matches H_res columns): [135, 2023, 2252, 4459, 4573]
  Index max values (sorted to match H_res/sorted_sources): [1.72851143 2.00791647 1.46361478 2.26167128 0.78022538]
  Rank parameter (r): 2

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [4573, 2252, 123, 2747, 135]
  Selected indices (sorted, matches H_res columns): [123, 135, 2252, 2747, 4573]
  Index max values (sorted to match H_res/sorted_sources): [2.14647119 2.65061676 1.46361478 2.41120364 0.78022538]
  Rank parameter (r): 3

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [4573, 2252, 123, 128, 4459]
  Selected indices (sorted, matches H_res columns): [123, 128, 2252, 4459, 4573]
  Index max values (sorted to match H_res/sorted_sources): [2.14647119 2.82155445 1.46361478 3.18357226 0.78022538]
  Rank parameter (r): 4

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [4573, 2252, 123, 128, 4161]
  Selected indices (sorted, matches H_res columns): [123, 128, 2252, 4161, 4573]
  Index max values (sorted to match H_res/sorted_sources): [2.14647119 2.82155445 1.46361478 3.52345131 0.78022538]
  Rank parameter (r): 5

Computing rank from covariance with rank=None
    Using tolerance 5.2e-13 (2.2e-16 eps * 128 dim * 18  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Computing rank from covariance with rank=None
    Using tolerance 2.9e-13 (2.2e-16 eps * 128 dim * 10  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Making LCMV beamformer with rank {'eeg': 127}
Computing inverse operator with 128 channels.
    128 out of 128 channels remain after picking
Selected 128 channels
Whitening the forward solution.
    Created an SSP operator (subspace dimension = 1)
Computing rank from covariance with rank={'eeg': 127}
    Setting small EEG eigenvalues to zero (without PCA)
Creating the source covariance matrix
Adjusting source covariance matrix.
Computing beamformer filters for 5124 sources
Filter computation complete
==== RUN 10/10 ====
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Setting up band-pass filter from 1 - 45 Hz

IIR filter parameters
---------------------
Butterworth bandpass zero-phase (two-pass forward and reverse) non-causal filter:
- Filter order 16 (effective, after forward-backward)
- Cutoffs at 1.00, 45.00 Hz: -6.02, -6.02 dB
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 5200
[done]
Reducing data rank from 128 -> 128
Estimating covariance using EMPIRICAL
Done.
Number of samples used : 3900
[done]
EEG channel type selected for re-referencing
Adding average EEG reference projection.
1 projection items deactivated
Average reference projection was added, but has not been applied yet. Use the apply_proj method to apply it.
Created an SSP operator (subspace dimension = 1)
1 projection items activated
SSP projectors applied...
Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [2076, 1950, 4404, 2713, 1736]
  Selected indices (sorted, matches H_res columns): [1736, 1950, 2076, 2713, 4404]
  Index max values (sorted to match H_res/sorted_sources): [2.11895827 1.78761154 1.61261815 2.06086976 1.95405909]
  Rank parameter (r): 1

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [2076, 2713, 1298, 4404, 1950]
  Selected indices (sorted, matches H_res columns): [1298, 1950, 2076, 2713, 4404]
  Index max values (sorted to match H_res/sorted_sources): [2.72942433 2.97047189 1.61261815 2.51976415 2.85145481]
  Rank parameter (r): 2

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [2076, 2713, 559, 1298, 341]
  Selected indices (sorted, matches H_res columns): [341, 559, 1298, 2076, 2713]
  Index max values (sorted to match H_res/sorted_sources): [3.65303966 3.27822901 3.49552122 1.61261815 2.51976415]
  Rank parameter (r): 3

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [2076, 2713, 559, 2042, 1298]
  Selected indices (sorted, matches H_res columns): [559, 1298, 2042, 2076, 2713]
  Index max values (sorted to match H_res/sorted_sources): [3.27822901 4.28012424 3.97788557 1.61261815 2.51976415]
  Rank parameter (r): 4

Calculating activity index for localizer: mai_mvp

[Activity Index Result]
  Selected indices (greedy discovery order): [2076, 2713, 559, 2042, 1539]
  Selected indices (sorted, matches H_res columns): [559, 1539, 2042, 2076, 2713]
  Index max values (sorted to match H_res/sorted_sources): [3.27822901 4.64803562 3.97788557 1.61261815 2.51976415]
  Rank parameter (r): 5

Computing rank from covariance with rank=None
    Using tolerance 5.1e-13 (2.2e-16 eps * 128 dim * 18  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Computing rank from covariance with rank=None
    Using tolerance 3.2e-13 (2.2e-16 eps * 128 dim * 11  max singular value)
    Estimated rank (eeg): 127
    EEG: rank 127 computed from 128 data channels with 1 projector
Making LCMV beamformer with rank {'eeg': 127}
Computing inverse operator with 128 channels.
    128 out of 128 channels remain after picking
Selected 128 channels
Whitening the forward solution.
    Created an SSP operator (subspace dimension = 1)
Computing rank from covariance with rank={'eeg': 127}
    Setting small EEG eigenvalues to zero (without PCA)
Creating the source covariance matrix
Adjusting source covariance matrix.
Computing beamformer filters for 5124 sources
Filter computation complete
Elapsed time: 143.08 s (2.38 min)

6. Inspect the raw multi-run result structure

FULL_RESULTS["by_rank"][rank] contains set of results per run.

This is the important difference from a single-run analysis: instead of one localization error for a rank, we now have a distribution of errors across independent realizations.

print("Ranks evaluated:", sorted(FULL_RESULTS["by_rank"].keys()))

for rank in sorted(FULL_RESULTS["by_rank"]):
    n_runs = len(FULL_RESULTS["by_rank"][rank]["mean_error"])
    print(f"Rank {rank}: {n_runs} runs")

print(f"Number of LCMV runs: {len(FULL_RESULTS['lcmv_mean_error'])}")

Ranks evaluated: ['rank_1', 'rank_2', 'rank_3', 'rank_4', 'rank_5']
Rank rank_1: 10 runs
Rank rank_2: 10 runs
Rank rank_3: 10 runs
Rank rank_4: 10 runs
Rank rank_5: 10 runs
Number of LCMV runs: 10

7. Aggregate performance across runs

For each rank we can now calculate summary statistics such as:

• mean localization error,

• median localization error,

• standard deviation,

• mean number of correctly localized sources.

The mean summarizes overall performance, while the standard deviation shows how sensitive the method is to the particular random source configuration.

rank_summary = {}

for rank, result in sorted(FULL_RESULTS["by_rank"].items()):
    errors = np.asarray(result["mean_error"], dtype=float)
    n_correct = np.asarray(result["n_correctly_localized"], dtype=float)

    rank_summary[rank] = {
        "mean_error": np.mean(errors),
        "median_error": np.median(errors),
        "std_error": np.std(errors),
        "mean_n_correct": np.mean(n_correct),
        "std_n_correct": np.std(n_correct),
    }

for rank, summary in rank_summary.items():
    print(
        f"Rank {rank}: "
        f"mean error = {summary['mean_error']:.3f}, "
        f"median = {summary['median_error']:.3f}, "
        f"SD = {summary['std_error']:.3f}, "
        f"mean correctly localized = {summary['mean_n_correct']:.2f}"
    )

Rank rank_1: mean error = 24.696, median = 24.230, SD = 7.313, mean correctly localized = 2.50
Rank rank_2: mean error = 19.229, median = 19.832, SD = 9.093, mean correctly localized = 3.30
Rank rank_3: mean error = 21.782, median = 23.054, SD = 8.687, mean correctly localized = 3.00
Rank rank_4: mean error = 20.682, median = 18.413, SD = 6.652, mean correctly localized = 3.00
Rank rank_5: mean error = 20.354, median = 17.631, SD = 10.935, mean correctly localized = 3.20

8. Localization error as a function of rank

Each violin represents the distribution obtained from the repeated simulations. This makes it possible to see not only the typical localization error for a given rank, but also the variability across different source configurations.

The LCMV-NAI result is shown alongside the MVPURE ranks for comparison.

Lower localization error indicates better performance.

fig, axs = plt.subplots(1, 1, figsize=(8, 4), sharey=True, sharex=True)
violin_plot_from_results(axs,
                         FULL_RESULTS,
                         results_key="mean_error",
                         ylabel="Average distance error [mm]",
                         xlabel="Rank", title=None, include_lcmv=True)
plt.show()

We can perform the same analysis for the number of correctly localized sources.

The violin plot shows the distribution of this measure across runs for each MVPURE rank and for LCMV-NAI.

Here, larger values indicate better localization performance.

fig, axs = plt.subplots(1, 1, figsize=(6, 4), sharey=True, sharex=True)
violin_plot_from_results(axs,
                         FULL_RESULTS,
                         results_key="n_correctly_localized",
                         ylabel="Number of correctly localized sources",
                         xlabel="Rank", title=None, include_lcmv=True)
plt.show()

9. Save the results

After all runs have finished, FULL_RESULTS contains the complete set of results from the experiment.

We can save this dictionary as a Python pickle (.pkl) file. This allows us to perform the analysis later without running the computationally expensive simulations again.

For example:

OUTPUT_PATH = "synthetic_results.pkl"

with open(OUTPUT_PATH, "wb") as f:
    pickle.dump(FULL_RESULTS, f)

print(f"Results saved to: {OUTPUT_PATH}")

11. Repeating the experiment for multiple SNR values

The same framework can also be used to evaluate localization performance at multiple signal-to-noise ratios.

Instead of running the experiment for a single SNR value, we can define a list of values, for example:

SNRS = [3, 5, 7, 10]

The experiment can then be wrapped in an additional loop over SNRS:

for SNR_DB in SNRS:
    for n in range(N_RUNS):
        ...

In this setup, N_RUNS independent simulations are performed for each SNR value.

The results can be stored separately for each SNR, for example in a dictionary:

ALL_RESULTS = {}

for SNR_DB in SNRS:
    # initialize results for this SNR
    ...
    ALL_RESULTS[SNR_DB] = FULL_RESULTS

This makes it possible to compare how MVPURE localization performance changes as the SNR decreases or increases.

For a multi-SNR experiment, it is useful to save the results for each SNR separately, or save the complete ALL_RESULTS dictionary in a single .pkl file.

Summary

The simulation and localization pipeline is intentionally almost unchanged from the previous tutorial. The new element is the experimental repetition layer:

                 ┌─ run 1 ─┐
                 ├─ run 2 ─┤
same parameters ─┼─ run 3 ─┼─→ aggregate results → distributions / summaries
                 ├─  ...  ─┤
                 └─ run N ─┘

Each run independently samples source locations and generates new simulated data. The resulting per-run metrics are retained, which allows us to quantify both average performance and variability.

For the full experiment, increase N_RUNS from the tutorial value to 100 or 1000. The resulting FULL_RESULTS object can then be analyzed without rerunning the simulation.