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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:
 .. _tut_stats_cluster_source_1samp
Step1:  Set parameters
Step2:  Read epochs for all channels, removing a bad one
Step3:  Transform to source space
Step4:  Transform to common cortical space
Step5:  Compute statistic
Step6:  Visualize the clusters
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Python Code:
# Authors: Alexandre Gramfort <alexandre.gramfort@telecom-paristech.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 import (io, spatial_tris_connectivity, compute_morph_matrix,
                 grade_to_tris)
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: .. _tut_stats_cluster_source_1samp:
Permutation t-test on source data with spatio-temporal clustering
Tests if the evoked response is significantly different between
conditions across subjects (simulated here 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'
tmin = -0.2
tmax = 0.3  # Use a lower tmax to reduce multiple comparisons
#   Setup for reading the raw data
raw = io.Raw(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 or sLORETA)
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)
condition1 = apply_inverse(evoked1, inverse_operator, lambda2, method)
evoked2 = epochs2.average()
evoked2.resample(50)
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
Explanation: Transform to source space
End of explanation
#    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. 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.
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]
#    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.
fsave_vertices = [np.arange(10242), np.arange(10242)]
morph_mat = compute_morph_matrix('sample', 'fsaverage', sample_vertices,
                                 fsave_vertices, 20, subjects_dir)
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)
#    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).
X = np.abs(X)  # only magnitude
X = X[:, :, :, 0] - X[:, :, :, 1]  # make paired contrast
Explanation: Transform to common cortical space
End of explanation
#    To use an algorithm optimized for spatio-temporal clustering, we
#    just pass the spatial connectivity matrix (instead of spatio-temporal)
print('Computing connectivity.')
connectivity = spatial_tris_connectivity(grade_to_tris(5))
#    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=2,
                                       threshold=t_threshold)
#    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
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', subjects_dir=subjects_dir,
                                 time_label='Duration significant (ms)')
brain.set_data_time_index(0)
brain.show_view('lateral')
brain.save_image('clusters.png')
Explanation: Visualize the clusters
End of explanation
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