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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Permutation t-test on source data with spatio-temporal clustering
This example tests if the evoked response is significantly different between
two conditions across subjects. Here just for demonstration purposes
we simulate data from multiple subjects using one subject's data.
The multiple comparisons problem is addressed with a cluster-level
permutation test across space and time.
Step1:  Set parameters
Step2:  Read epochs for all channels, removing a bad one
Step3:  Transform to source space
Step4:  Transform to common cortical space
Normally you would read in estimates across several subjects and morph
them to the same cortical space (e.g. fsaverage). For example purposes,
we will simulate this by just having each "subject" have the same
response (just noisy in source space) here.
<div class="alert alert-info"><h4>Note</h4><p>Note that for 7 subjects with a two-sided statistical test, the minimum
    significance under a permutation test is only p = 1/(2 ** 6) = 0.015,
    which is large.</p></div>
Step5:  It's a good idea to spatially smooth the data, and for visualization
purposes, let's morph these to fsaverage, which is a grade 5 source space
with vertices 0
Step6:  Finally, we want to compare the overall activity levels in each condition,
the diff is taken along the last axis (condition). The negative sign makes
it so condition1 > condition2 shows up as "red blobs" (instead of blue).
Step7:  Compute statistic
To use an algorithm optimized for spatio-temporal clustering, we
just pass the spatial connectivity matrix (instead of spatio-temporal)
Step8:  Visualize the clusters
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Python Code:
# Authors: Alexandre Gramfort <alexandre.gramfort@inria.fr>
#          Eric Larson <larson.eric.d@gmail.com>
# License: BSD (3-clause)
import os.path as op
import numpy as np
from numpy.random import randn
from scipy import stats as stats
import mne
from mne.epochs import equalize_epoch_counts
from mne.stats import (spatio_temporal_cluster_1samp_test,
                       summarize_clusters_stc)
from mne.minimum_norm import apply_inverse, read_inverse_operator
from mne.datasets import sample
print(__doc__)
Explanation: Permutation t-test on source data with spatio-temporal clustering
This example tests if the evoked response is significantly different between
two conditions across subjects. Here just for demonstration purposes
we simulate data from multiple subjects using one subject's data.
The multiple comparisons problem is addressed with a cluster-level
permutation test across space and time.
End of explanation
data_path = sample.data_path()
raw_fname = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw.fif'
event_fname = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw-eve.fif'
subjects_dir = data_path + '/subjects'
src_fname = subjects_dir + '/fsaverage/bem/fsaverage-ico-5-src.fif'
tmin = -0.2
tmax = 0.3  # Use a lower tmax to reduce multiple comparisons
#   Setup for reading the raw data
raw = mne.io.read_raw_fif(raw_fname)
events = mne.read_events(event_fname)
Explanation: Set parameters
End of explanation
raw.info['bads'] += ['MEG 2443']
picks = mne.pick_types(raw.info, meg=True, eog=True, exclude='bads')
event_id = 1  # L auditory
reject = dict(grad=1000e-13, mag=4000e-15, eog=150e-6)
epochs1 = mne.Epochs(raw, events, event_id, tmin, tmax, picks=picks,
                     baseline=(None, 0), reject=reject, preload=True)
event_id = 3  # L visual
epochs2 = mne.Epochs(raw, events, event_id, tmin, tmax, picks=picks,
                     baseline=(None, 0), reject=reject, preload=True)
#    Equalize trial counts to eliminate bias (which would otherwise be
#    introduced by the abs() performed below)
equalize_epoch_counts([epochs1, epochs2])
Explanation: Read epochs for all channels, removing a bad one
End of explanation
fname_inv = data_path + '/MEG/sample/sample_audvis-meg-oct-6-meg-inv.fif'
snr = 3.0
lambda2 = 1.0 / snr ** 2
method = "dSPM"  # use dSPM method (could also be MNE, sLORETA, or eLORETA)
inverse_operator = read_inverse_operator(fname_inv)
sample_vertices = [s['vertno'] for s in inverse_operator['src']]
#    Let's average and compute inverse, resampling to speed things up
evoked1 = epochs1.average()
evoked1.resample(50, npad='auto')
condition1 = apply_inverse(evoked1, inverse_operator, lambda2, method)
evoked2 = epochs2.average()
evoked2.resample(50, npad='auto')
condition2 = apply_inverse(evoked2, inverse_operator, lambda2, method)
#    Let's only deal with t > 0, cropping to reduce multiple comparisons
condition1.crop(0, None)
condition2.crop(0, None)
tmin = condition1.tmin
tstep = condition1.tstep * 1000  # convert to milliseconds
Explanation: Transform to source space
End of explanation
n_vertices_sample, n_times = condition1.data.shape
n_subjects = 7
print('Simulating data for %d subjects.' % n_subjects)
#    Let's make sure our results replicate, so set the seed.
np.random.seed(0)
X = randn(n_vertices_sample, n_times, n_subjects, 2) * 10
X[:, :, :, 0] += condition1.data[:, :, np.newaxis]
X[:, :, :, 1] += condition2.data[:, :, np.newaxis]
Explanation: Transform to common cortical space
Normally you would read in estimates across several subjects and morph
them to the same cortical space (e.g. fsaverage). For example purposes,
we will simulate this by just having each "subject" have the same
response (just noisy in source space) here.
<div class="alert alert-info"><h4>Note</h4><p>Note that for 7 subjects with a two-sided statistical test, the minimum
    significance under a permutation test is only p = 1/(2 ** 6) = 0.015,
    which is large.</p></div>
End of explanation
# Read the source space we are morphing to
src = mne.read_source_spaces(src_fname)
fsave_vertices = [s['vertno'] for s in src]
morph_mat = mne.compute_source_morph(
    src=inverse_operator['src'], subject_to='fsaverage',
    spacing=fsave_vertices, subjects_dir=subjects_dir).morph_mat
n_vertices_fsave = morph_mat.shape[0]
#    We have to change the shape for the dot() to work properly
X = X.reshape(n_vertices_sample, n_times * n_subjects * 2)
print('Morphing data.')
X = morph_mat.dot(X)  # morph_mat is a sparse matrix
X = X.reshape(n_vertices_fsave, n_times, n_subjects, 2)
Explanation: It's a good idea to spatially smooth the data, and for visualization
purposes, let's morph these to fsaverage, which is a grade 5 source space
with vertices 0:10242 for each hemisphere. Usually you'd have to morph
each subject's data separately (and you might want to use morph_data
instead), but here since all estimates are on 'sample' we can use one
morph matrix for all the heavy lifting.
End of explanation
X = np.abs(X)  # only magnitude
X = X[:, :, :, 0] - X[:, :, :, 1]  # make paired contrast
Explanation: Finally, we want to compare the overall activity levels in each condition,
the diff is taken along the last axis (condition). The negative sign makes
it so condition1 > condition2 shows up as "red blobs" (instead of blue).
End of explanation
print('Computing connectivity.')
connectivity = mne.spatial_src_connectivity(src)
#    Note that X needs to be a multi-dimensional array of shape
#    samples (subjects) x time x space, so we permute dimensions
X = np.transpose(X, [2, 1, 0])
#    Now let's actually do the clustering. This can take a long time...
#    Here we set the threshold quite high to reduce computation.
p_threshold = 0.001
t_threshold = -stats.distributions.t.ppf(p_threshold / 2., n_subjects - 1)
print('Clustering.')
T_obs, clusters, cluster_p_values, H0 = clu = \
    spatio_temporal_cluster_1samp_test(X, connectivity=connectivity, n_jobs=1,
                                       threshold=t_threshold, buffer_size=None,
                                       verbose=True)
#    Now select the clusters that are sig. at p < 0.05 (note that this value
#    is multiple-comparisons corrected).
good_cluster_inds = np.where(cluster_p_values < 0.05)[0]
Explanation: Compute statistic
To use an algorithm optimized for spatio-temporal clustering, we
just pass the spatial connectivity matrix (instead of spatio-temporal)
End of explanation
print('Visualizing clusters.')
#    Now let's build a convenient representation of each cluster, where each
#    cluster becomes a "time point" in the SourceEstimate
stc_all_cluster_vis = summarize_clusters_stc(clu, tstep=tstep,
                                             vertices=fsave_vertices,
                                             subject='fsaverage')
#    Let's actually plot the first "time point" in the SourceEstimate, which
#    shows all the clusters, weighted by duration
subjects_dir = op.join(data_path, 'subjects')
# blue blobs are for condition A < condition B, red for A > B
brain = stc_all_cluster_vis.plot(
    hemi='both', views='lateral', subjects_dir=subjects_dir,
    time_label='temporal extent (ms)', size=(800, 800),
    smoothing_steps=5, clim=dict(kind='value', pos_lims=[0, 1, 40]))
# brain.save_image('clusters.png')
Explanation: Visualize the clusters
End of explanation
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