def do_mvar_evaluation(X, morder, whit_max=3., whit_min=1., thr_cons=0.8):
'''
Fit MVAR model to data using scot and do some basic checks.
X: array (trials, channels, samples)
morder: the model order
Returns:
(is_white, consistency, is_stable)
'''
print('starting checks and MVAR fitting...')
# tsdata_to_var from MVGC requires sources x samples x trials
# X is of shape trials x sources x samples (which is what ScoT uses)
X_trans = X.transpose(1, 2, 0)
A, SIG, E = _tsdata_to_var(X_trans, morder)
del A, SIG
whi = False
dw, pval = dw_whiteness(X_trans, E)
if np.all(dw < whit_max) and np.all(dw > whit_min):
whi = True
cons = consistency(X_trans, E)
del dw, pval, E
from scot.var import VAR
mvar = VAR(morder)
mvar.fit(X) # scot func which requires shape trials x sources x samples
is_st = mvar.is_stable()
if cons < thr_cons or is_st is False or whi is False:
print('ERROR: Model order not ideal - check parameters !!')
return str(whi), cons, str(is_st)
def test_residuals(self):
l = 100000
var0 = VAR(2)
var0.coef = np.array([[0.2, 0.1, 0.4, -0.1], [0.3, -0.2, 0.1, 0]])
x = var0.simulate(l)
var = VAR(2)
var.fit(x)
self.assertEqual(x.shape, var.residuals.shape)
self.assertTrue(np.allclose(var.rescov, np.eye(var.rescov.shape[0]), 1e-2, 1e-2))
def test_residuals(self):
l = 100000
var0 = VAR(2)
var0.coef = np.array([[0.2, 0.1, 0.4, -0.1], [0.3, -0.2, 0.1, 0]])
x = var0.simulate(l)
var = VAR(2)
var.fit(x)
self.assertEqual(x.shape, var.residuals.shape)
self.assertTrue(
np.allclose(var.rescov, np.eye(var.rescov.shape[0]), 1e-2, 1e-2))
def test_fit(self):
var0 = VAR(2)
var0.coef = np.array([[0.2, 0.1, 0.4, -0.1], [0.3, -0.2, 0.1, 0]])
l = 100000
x = var0.simulate(l)
y = x.copy()
var = VAR(2)
var.fit(x)
# make sure the input remains unchanged
self.assertTrue(np.all(x == y))
# that limit is rather generous, but we don't want tests to fail due to random variation
self.assertTrue(np.all(np.abs(var0.coef - var.coef) < 0.02))
def test_fit(self):
var0 = VAR(2)
var0.coef = np.array([[0.2, 0.1, 0.4, -0.1], [0.3, -0.2, 0.1, 0]])
l = 100000
x = var0.simulate(l)
y = x.copy()
var = VAR(2)
var.fit(x)
# make sure the input remains unchanged
self.assertTrue(np.all(x == y))
# that limit is rather generous, but we don't want tests to fail due to random variation
self.assertTrue(np.all(np.abs(var0.coef - var.coef) < 0.02))
def compute_order(X, m_max, verbose=True):
"""
Estimate VAR order with the Bayesian Information Criterion (BIC).
Parameters
----------
X : ndarray, shape (trials, n_channels, n_samples)
m_max : int
The maximum model order to test
Reference
---------
[1] provides the equation:BIC(m) = 2*log[det(Σ)]+ 2*(p**2)*m*log(N*n*m)/(N*n*m),
Σ is the noise covariance matrix, p is the channels, N is the trials, n
is the n_samples, m is model order.
[1] Mingzhou Ding, Yonghong Chen. Granger Causality: Basic Theory and Application
to Neuroscience.Elsevier Science, 7 February 2008.
URL: https://gist.github.com/dongqunxi/b23d1679b9bffa8e458c11f93bd8d6ff
Returns
-------
o_m : int
Estimated order
bic : list
List with the BICs for the orders from 1 to m_max.
"""
from scot.var import VAR
from scipy import linalg
N, p, n = X.shape
bic = []
for m in range(m_max):
mvar = VAR(m + 1)
mvar.fit(X)
sigma = mvar.rescov
m_bic = np.log(linalg.det(sigma))
m_bic += (p**2) * (m + 1) * np.log(N * n) / (N * n)
bic.append(m_bic)
if verbose:
print(('model order: %d, BIC value: %.2f' % (m + 1, bic[m])))
o_m = np.argmin(bic) + 1
return o_m, bic
def test_fit_regularized(self):
l = 100000
var0 = VAR(2)
var0.coef = np.array([[0.2, 0.1, 0.4, -0.1], [0.3, -0.2, 0.1, 0]])
x = var0.simulate(l)
y = x.copy()
var = VAR(10, delta=1)
var.fit(x)
# make sure the input remains unchanged
self.assertTrue(np.all(x == y))
b0 = np.zeros((2, 20))
b0[:, 0:2] = var0.coef[:, 0:2]
b0[:, 10:12] = var0.coef[:, 2:4]
# that limit is rather generous, but we don't want tests to fail due to random variation
self.assertTrue(np.all(np.abs(b0 - var.coef) < 0.02))
def test_fit_regularized(self):
l = 100000
var0 = VAR(2)
var0.coef = np.array([[0.2, 0.1, 0.4, -0.1], [0.3, -0.2, 0.1, 0]])
x = var0.simulate(l)
y = x.copy()
var = VAR(10, delta=1)
var.fit(x)
# make sure the input remains unchanged
self.assertTrue(np.all(x == y))
b0 = np.zeros((2, 20))
b0[:, 0:2] = var0.coef[:, 0:2]
b0[:, 10:12] = var0.coef[:, 2:4]
# that limit is rather generous, but we don't want tests to fail due to random variation
self.assertTrue(np.all(np.abs(b0 - var.coef) < 0.02))
# Generate data from a VAR(1) process
model0 = VAR(1)
model0.coef = np.array([[0.3, -0.6], [0, -0.9]])
x = model0.simulate(10000).squeeze()
# Transform data with PCA
w, v = pca(x)
y = np.dot(w.T, x)
# Verify that transformed data y is decorrelated
print("Covariance of x:\n", np.cov(x.squeeze()))
print("\nCovariance of y:\n", np.cov(y.squeeze()))
model1, model2 = VAR(1), VAR(1)
# Fit model1 to the original data
model1.fit(x)
# Fit model2 to the PCA transformed data
model2.fit(y)
# The coefficients estimated on x (2) are exactly equal to the back-transformed
# coefficients estimated on y (4)
print("\n(1) True VAR coefficients:\n", model0.coef)
print("\n(2) VAR coefficients estimated on x:\n", model1.coef)
print("\n(3) VAR coefficients estimated on y:\n", model2.coef)
print("\n(4) VAR coefficients estimated on y and transformed back:\n", w.dot(model2.coef).dot(w.T))
print("\n(5) Check if (2) and (4) are equal:\n", np.isclose(model1.coef, w.dot(model2.coef).dot(w.T)))
def testFunctionality(self):
""" generate VAR signals, and apply the api to them
do this for every backend """
np.random.seed(3141592)
# original model coefficients
b01 = np.zeros((3, 6))
b02 = np.zeros((3, 6))
b01[1:3, 2:6] = [[0.4, -0.2, 0.3, 0.0],
[-0.7, 0.0, 0.9, 0.0]]
b02[0:3, 2:6] = [[0.4, 0.0, 0.0, 0.0],
[0.4, 0.0, 0.4, 0.0],
[0.0, 0.0, 0.4, 0.0]]
m0 = b01.shape[0]
cl = np.array([0, 1, 0, 1, 0, 0, 1, 1, 1, 0])
l = 200
t = len(cl)
# generate VAR sources with non-gaussian innovation process, otherwise ICA won't work
noisefunc = lambda: np.random.normal(size=(1, m0)) ** 3 / 1e3
var = VAR(2)
var.coef = b01
sources1 = var.simulate([l, sum(cl == 0)], noisefunc)
var.coef = b02
sources2 = var.simulate([l, sum(cl == 1)], noisefunc)
var.fit(sources1)
var.fit(sources2)
sources = np.zeros((t, m0, l))
sources[cl == 0, :, :] = sources1
sources[cl == 1, :, :] = sources2
# simulate volume conduction... 3 sources smeared over 7 channels
mix = [[0.5, 1.0, 0.5, 0.2, 0.0, 0.0, 0.0],
[0.0, 0.2, 0.5, 1.0, 0.5, 0.2, 0.0],
[0.0, 0.0, 0.0, 0.2, 0.5, 1.0, 0.5]]
data = datatools.dot_special(np.transpose(mix), sources)
data += np.random.randn(*data.shape) * 0.001 # add small noise
for backend_name, backend_gen in scot.backend.items():
np.random.seed(3141592) # reset random seed so we're independent of module order
api = scot.Workspace({'model_order': 2}, reducedim=3, backend=backend_gen())
api.set_data(data)
api.do_ica()
self.assertEqual(api.mixing_.shape, (3, 7))
self.assertEqual(api.unmixing_.shape, (7, 3))
api.do_mvarica()
self.assertEqual(api.get_connectivity('S').shape, (3, 3, 512))
self.assertFalse(np.any(np.isnan(api.activations_)))
self.assertFalse(np.any(np.isinf(api.activations_)))
api.set_data(data)
api.fit_var()
self.assertEqual(api.get_connectivity('S').shape, (3, 3, 512))
self.assertEqual(api.get_tf_connectivity('S', 100, 50).shape, (3, 3, 512, (l-100)//50))
tfc1 = api.get_tf_connectivity('PDC', 100, 5, baseline=None) # no baseline
tfc2 = api.get_tf_connectivity('PDC', 100, 5, baseline=[110, -10]) # invalid baseline
tfc3 = api.get_tf_connectivity('PDC', 100, 5, baseline=[0, 0]) # one-window baseline
tfc4 = tfc1 - tfc1[:, :, :, [0]]
tfc5 = api.get_tf_connectivity('PDC', 100, 5, baseline=[-np.inf, np.inf]) # full trial baseline
tfc6 = tfc1 - np.mean(tfc1, axis=3, keepdims=True)
self.assertTrue(np.allclose(tfc1, tfc2))
self.assertTrue(np.allclose(tfc3, tfc4))
self.assertTrue(np.allclose(tfc5, tfc6, rtol=1e-05, atol=1e-06))
api.set_data(data, cl)
self.assertFalse(np.any(np.isnan(api.data_)))
self.assertFalse(np.any(np.isinf(api.data_)))
api.do_cspvarica()
self.assertEqual(api.get_connectivity('S').shape, (3,3,512))
self.assertFalse(np.any(np.isnan(api.activations_)))
self.assertFalse(np.any(np.isinf(api.activations_)))
for c in np.unique(cl):
api.set_used_labels([c])
api.fit_var()
fc = api.get_connectivity('S')
self.assertEqual(fc.shape, (3, 3, 512))
tfc = api.get_tf_connectivity('S', 100, 50)
self.assertEqual(tfc.shape, (3, 3, 512, (l-100)//50))
api.set_data(data)
api.remove_sources([0, 2])
api.fit_var()
self.assertEqual(api.get_connectivity('S').shape, (1, 1, 512))
self.assertEqual(api.get_tf_connectivity('S', 100, 50).shape, (1, 1, 512, (l-100)//50))
try:
api.optimize_var()
except NotImplementedError:
pass
api.fit_var()
self.assertEqual(api.get_connectivity('S').shape, (1, 1, 512))
self.assertEqual(api.get_tf_connectivity('S', 100, 50).shape, (1, 1, 512, (l-100)//50))
def testFunctionality(self):
""" generate VAR signals, and apply the api to them
do this for every backend """
np.random.seed(3141592)
# original model coefficients
b01 = np.zeros((3, 6))
b02 = np.zeros((3, 6))
b01[1:3, 2:6] = [[0.4, -0.2, 0.3, 0.0],
[-0.7, 0.0, 0.9, 0.0]]
b02[0:3, 2:6] = [[0.4, 0.0, 0.0, 0.0],
[0.4, 0.0, 0.4, 0.0],
[0.0, 0.0, 0.4, 0.0]]
m0 = b01.shape[0]
cl = np.array([0, 1, 0, 1, 0, 0, 1, 1, 1, 0])
l = 200
t = len(cl)
# generate VAR sources with non-gaussian innovation process, otherwise ICA won't work
noisefunc = lambda: np.random.normal(size=(1, m0)) ** 3
var = VAR(2)
var.coef = b01
sources1 = var.simulate([l, sum(cl==0)], noisefunc)
var.coef = b02
sources2 = var.simulate([l, sum(cl==1)], noisefunc)
var.fit(sources1)
var.fit(sources2)
sources = np.zeros((l,m0,t))
sources[:,:,cl==0] = sources1
sources[:,:,cl==1] = sources2
# simulate volume conduction... 3 sources measured with 7 channels
mix = [[0.5, 1.0, 0.5, 0.2, 0.0, 0.0, 0.0],
[0.0, 0.2, 0.5, 1.0, 0.5, 0.2, 0.0],
[0.0, 0.0, 0.0, 0.2, 0.5, 1.0, 0.5]]
data = datatools.dot_special(sources, mix)
backend_modules = [import_module('scot.' + b) for b in scot.backends]
for bm in backend_modules:
np.random.seed(3141592) # reset random seed so we're independent of module order
api = scot.Workspace({'model_order': 2}, reducedim=3, backend=bm.backend)
api.set_data(data)
api.do_ica()
self.assertEqual(api.mixing_.shape, (3, 7))
self.assertEqual(api.unmixing_.shape, (7, 3))
api.do_mvarica()
self.assertEqual(api.get_connectivity('S').shape, (3, 3, 512))
self.assertFalse(np.any(np.isnan(api.activations_)))
self.assertFalse(np.any(np.isinf(api.activations_)))
api.set_data(data)
api.fit_var()
self.assertEqual(api.get_connectivity('S').shape, (3, 3, 512))
self.assertEqual(api.get_tf_connectivity('S', 100, 50).shape, (3, 3, 512, (l-100)//50))
api.set_data(data, cl)
self.assertFalse(np.any(np.isnan(api.data_)))
self.assertFalse(np.any(np.isinf(api.data_)))
api.do_cspvarica()
self.assertEqual(api.get_connectivity('S').shape, (3,3,512))
self.assertFalse(np.any(np.isnan(api.activations_)))
self.assertFalse(np.any(np.isinf(api.activations_)))
for c in np.unique(cl):
api.set_used_labels([c])
api.fit_var()
fc = api.get_connectivity('S')
self.assertEqual(fc.shape, (3, 3, 512))
tfc = api.get_tf_connectivity('S', 100, 50)
self.assertEqual(tfc.shape, (3, 3, 512, (l-100)//50))
api.set_data(data)
api.remove_sources([0, 2])
api.fit_var()
self.assertEqual(api.get_connectivity('S').shape, (1, 1, 512))
self.assertEqual(api.get_tf_connectivity('S', 100, 50).shape, (1, 1, 512, (l-100)//50))
try:
api.optimize_var()
except NotImplementedError:
pass
api.fit_var()
self.assertEqual(api.get_connectivity('S').shape, (1, 1, 512))
self.assertEqual(api.get_tf_connectivity('S', 100, 50).shape, (1, 1, 512, (l-100)//50))
# Prevent execution of the main script in worker threads
if __name__ == "__main__":
midata = fetch("mi")[0]
raweeg = midata["eeg"]
triggers = midata["triggers"]
classes = midata["labels"]
fs = midata["fs"]
locs = midata["locations"]
# Prepare data
#
# Here we cut out segments from 3s to 4s after each trigger. This is right
# in the middle of the motor imagery period.
data = cut_segments(raweeg, triggers, 3 * fs, 4 * fs)
# only use every 10th trial to make the example run faster
data = data[::10]
var = VAR(model_order=5)
var.fit(data)
for n_jobs in [-1, None, 1, 2, 3, 4, 5, 6, 7, 8]:
# Set random seed for repeatable results
np.random.seed(42)
var.n_jobs = n_jobs
start = time.perf_counter()
p = var.test_whiteness(10, repeats=1000)
time1 = time.perf_counter()
print('n_jobs: {:>4s}, whiteness test: {:.2f}s, p = {}'.format(str(n_jobs), time1 - start, p))
from scot.var import VAR
# Generate data from a VAR(1) process
model0 = VAR(1)
model0.coef = np.array([[0.3, -0.6], [0, -0.9]])
x = model0.simulate(10000).squeeze()
# Transform data with PCA
w, v = pca(x)
y = x.dot(w)
print('Covariance of x:\n', np.cov(x.squeeze().T))
print('\nCovariance of y:\n', np.cov(y.squeeze().T))
model1, model2 = VAR(1), VAR(1)
# Fit model1 to the original data
model1.fit(x)
# Fit model2 to the PCA transformed data
model2.fit(y)
# The coefficients estimated on x (2) are exactly equal to the back-transformed
# coefficients estimated on y (4)
print('\n(1) True VAR coefficients:\n', model0.coef)
print('\n(2) VAR coefficients estimated on x:\n', model1.coef)
print('\n(3) VAR coefficients estimated on y:\n', model2.coef)
print('\n(4) VAR coefficients estimated on y and transformed back:\n',
w.dot(model2.coef).dot(w.T))
def compute_order_extended(X,
m_max,
m_min=1,
m_step=1,
n_jobs=None,
verbose=True):
"""
Estimate VAR order with the Bayesian Information Criterion (BIC).
Parameters:
-----------
X : ndarray, shape (trials, n_channels, n_samples)
m_max : int
The maximum model order to test,
m_min : int
The minimum model order to test.
m_step : int
The step size for checking the model order interval
given by m_min and m_max.
n_jobs : None | int, optional
Number of jobs to run in parallel for various tasks (e.g. whiteness
testing). If set to None, joblib is not used at all. Note that the main
script must be guarded with `if __name__ == '__main__':` when using
parallelization.
verbose : bool
Plot results for other information criteria as well.
Returns:
--------
o_m : int
Estimated order using BIC2.
morders : np.array of shape ((m_max - m_min) / m_step, )
The model orders corresponding to the entries in the following results
arrays.
ics : np.array of shape (n_ics, (m_max - m_min) / m_step)
The information criteria for the different model orders.
[AIC1, BIC1, AIC2, BIC2, lnFPE, HQIC]]
stability : np.array of shape ((m_max - m_min) / m_step), )
Indicates if MVAR model describes stable process (covariance
stationary).
p_white_scot : np.array of shape ((m_max - m_min) / m_step), )
p-value that the residuals are white based on the Li-McLeod Portmanteau test
implemented in SCoT. Reject hypothesis of white residuals if p is smaller
than the critical p-value.
p_white_dw : np.array of shape ((m_max - m_min) / m_step), n_rois)
Uncorrected p-values that the residuals are white based on the Durbin-Watson
test as implemented by Barnett and Seth (2012). Reject hypothesis of white
residuals if all p's are smaller than the critical p-value.
dw : np.array of shape ((m_max - m_min) / m_step), n_rois)
The Durbin-Watson statistics.
consistency : np.array of shape ((m_max - m_min) / m_step), )
Results of the MVAR consistency estimation.
References:
-----------
[1] provides the equation:BIC(m) = 2*log[det(Σ)]+ 2*(p**2)*m*log(N*n*m)/(N*n*m),
Σ is the noise covariance matrix, p is the channels, N is the trials, n
is the n_samples, m is model order.
[1] Mingzhou Ding, Yonghong Chen (2008). "Granger Causality: Basic Theory and Application
to Neuroscience." Elsevier Science
[2] Nicoletta Nicolaou and Julius Georgiou (2013). “Autoregressive Model Order Estimation
Criteria for Monitoring Awareness during Anaesthesia.” IFIP Advances in Information and
Communication Technology 412
[3] Helmut Lütkepohl (2005). "New Introduction to Multiple Time Series Analysis."
1st ed. Berlin: Springer-Verlag Berlin Heidelberg.
URL: https://gist.github.com/dongqunxi/b23d1679b9bffa8e458c11f93bd8d6ff
"""
from scot.var import VAR
from scipy import linalg
N, p, n = X.shape
aic1 = []
bic1 = []
aic2 = []
bic2 = []
lnfpe = []
hqic = []
morders = []
stability = []
p_white_scot = []
p_white_dw = []
dw = []
consistency = []
# TODO: should this be n_total = N * n * p ???
# total number of data points: n_trials * n_samples
# Esther Florin (2010): N_total is number of time points contained in each time series
n_total = N * n
# check model order min/max/step input
if m_min >= m_max:
m_min = m_max - 1
if m_min < 1:
m_min = 1
if m_step < 1:
m_step = 1
if m_step >= m_max:
m_step = m_max
for m in range(m_min, m_max + 1, m_step):
morders.append(m)
mvar = VAR(m, n_jobs=n_jobs)
mvar.fit(X)
stable = mvar.is_stable()
stability.append(stable)
p_white_scot_ = mvar.test_whiteness(h=m,
repeats=100,
get_q=False,
random_state=None)
white_scot_ = p_white_scot_ >= 0.05
p_white_scot.append(p_white_scot_)
white_dw_, cons, dw_, pval = check_whiteness_and_consistency(
X.transpose(1, 2, 0),
mvar.residuals.transpose(1, 2, 0),
alpha=0.05)
dw.append(dw_)
p_white_dw.append(pval)
consistency.append(cons)
sigma = mvar.rescov
########################################################################
# from [1]
########################################################################
m_aic = 2 * np.log(linalg.det(sigma)) + 2 * (p**2) * m / n_total
m_bic = 2 * np.log(
linalg.det(sigma)) + 2 * (p**2) * m / n_total * np.log(n_total)
aic1.append(m_aic)
bic1.append(m_bic)
########################################################################
# from [2]
########################################################################
m_aic2 = np.log(linalg.det(sigma)) + 2 * (p**2) * m / n_total
m_bic2 = np.log(
linalg.det(sigma)) + (p**2) * m / n_total * np.log(n_total)
aic2.append(m_aic2)
bic2.append(m_bic2)
########################################################################
# from [3]
########################################################################
# Akaike's final prediction error
m_ln_fpe3 = np.log(linalg.det(sigma)) + p * np.log(
(n_total + m * p + 1) / (n_total - m * p - 1))
# Hannan-Quinn criterion
m_hqc3 = np.log(linalg.det(sigma)) + 2 * (p**2) * m / n_total * np.log(
np.log(n_total))
lnfpe.append(m_ln_fpe3)
hqic.append(m_hqc3)
if verbose:
results = 'Model order: ' + str(m).zfill(2)
results += ' AIC1: %.2f' % m_aic
results += ' BIC1: %.2f' % m_bic
results += ' AIC2: %.2f' % m_aic2
results += ' BIC2: %.2f' % m_bic2
results += ' lnFPE3: %.2f' % m_ln_fpe3
results += ' HQC3: %.2f' % m_hqc3
results += ' stable: %s' % str(stable)
results += ' white1: %s' % str(white_scot_)
results += ' white2: %s' % str(white_dw_)
results += ' DWmin: %.2f' % dw_.min()
results += ' DWmax: %.2f' % dw_.max()
results += ' consistency: %.4f' % cons
print(results)
morders = np.array(morders)
o_m = morders[np.argmin(bic2)]
if verbose:
print('>>> Optimal model order according to BIC2 = %d' % o_m)
ics = [aic1, bic1, aic2, bic2, lnfpe, hqic]
ics = np.asarray(ics)
stability = np.array(stability)
p_white_scot = np.array(p_white_scot)
p_white_dw = np.array(p_white_dw)
dw = np.array(dw)
consistency = np.array(consistency)
return o_m, morders, ics, stability, p_white_scot, p_white_dw, dw, consistency
def check_model_order(X, p, whit_min=1.5, whit_max=2.5, check_stability=True):
"""
Check whiteness, consistency, and stability for all model
orders k <= p.
Computationally intensive but for high model orders probably
faster than do_mvar_evaluation().
Parameters:
-----------
X : narray, shape (n_epochs, n_sources, n_times)
The data to estimate the model order for.
p : int
The maximum model order.
whit_min : float
Lower boundary for the Durbin-Watson test.
whit_max : float
Upper boundary for the Durbin-Watson test.
check_stability : bool
Check the stability condition. Time intensive since
it fits a second MVAR model from scot.var.VAR
Returns:
--------
A: array, coefficients of the specified model
SIG:array, recovariance of this model
E: array, noise covariance of this model
"""
assert p >= 1, "The model order must be greater or equal to 1."
from scot.var import VAR
X_orig = X.copy()
X = X.transpose(1, 2, 0)
n, m, N = X.shape
p1 = p + 1
q1n = p1 * n
I = np.eye(n)
XX = np.zeros((n, p1, m + p, N))
for k in range(p1):
XX[:, k, k:k + m, :] = X
AF = np.zeros((n, q1n))
AB = np.zeros((n, q1n))
k = 1
kn = k * n
M = N * (m - k)
kf = list(range(0, kn))
kb = list(range(q1n - kn, q1n))
XF = np.reshape(XX[:, 0:k, k:m, :], (kn, M), order='F')
XB = np.reshape(XX[:, 0:k, k - 1:m - 1, :], (kn, M), order='F')
CXF = np.linalg.cholesky(XF.dot(XF.T)).T
CXB = np.linalg.cholesky(XB.dot(XB.T)).T
AF[:, kf] = np.linalg.solve(CXF.T, I)
AB[:, kb] = np.linalg.solve(CXB.T, I)
del p1, XF, XB, CXF, CXB
while k <= p:
tempF = np.reshape(XX[:, 0:k, k:m, :], (kn, M), order='F')
af = AF[:, kf]
EF = af.dot(tempF)
del af, tempF
tempB = np.reshape(XX[:, 0:k, k - 1:m - 1, :], (kn, M), order='F')
ab = AB[:, kb]
EB = ab.dot(tempB)
del ab, tempB
CEF = np.linalg.cholesky(EF.dot(EF.T)).T
CEB = np.linalg.cholesky(EB.dot(EB.T)).T
R = np.dot(np.linalg.solve(CEF.T, EF.dot(EB.T)), np.linalg.inv(CEB))
del EB, CEF, CEB
RF = np.linalg.cholesky(I - R.dot(R.T)).T
RB = np.linalg.cholesky(I - (R.T).dot(R)).T
k = k + 1
kn = k * n
M = N * (m - k)
kf = np.arange(kn)
kb = list(range(q1n - kn, q1n))
AFPREV = AF[:, kf]
ABPREV = AB[:, kb]
AF[:, kf] = np.linalg.solve(RF.T, AFPREV - R.dot(ABPREV))
AB[:, kb] = np.linalg.solve(RB.T, ABPREV - R.T.dot(AFPREV))
del RF, RB, ABPREV
# check MVAR model properties
E = np.linalg.solve(AFPREV[:, :n], EF)
E = np.reshape(E, (n, m - k + 1, N), order='F')
if k > 1:
whi, cons, _, _ = check_whiteness_and_consistency(
X, E, whit_min, whit_max)
if check_stability:
mvar = VAR((k - 1))
mvar.fit(
X_orig
) # scot func which requires shape trials x sources x samples
is_st = mvar.is_stable()
output = 'morder %d:' % (k - 1)
output += ' white: %s' % str(whi)
output += '; consistency: %.4f' % cons
if check_stability:
output += '; stable: %s' % str(is_st)
print(output)
def testFunctionality(self):
""" generate VAR signals, and apply the api to them
do this for every backend """
np.random.seed(3141592)
# original model coefficients
b01 = np.zeros((3, 6))
b02 = np.zeros((3, 6))
b01[1:3, 2:6] = [[0.4, -0.2, 0.3, 0.0], [-0.7, 0.0, 0.9, 0.0]]
b02[0:3, 2:6] = [[0.4, 0.0, 0.0, 0.0], [0.4, 0.0, 0.4, 0.0],
[0.0, 0.0, 0.4, 0.0]]
m0 = b01.shape[0]
cl = np.array([0, 1, 0, 1, 0, 0, 1, 1, 1, 0])
l = 200
t = len(cl)
# generate VAR sources with non-gaussian innovation process, otherwise ICA won't work
noisefunc = lambda: np.random.normal(size=(1, m0))**3
var = VAR(2)
var.coef = b01
sources1 = var.simulate([l, sum(cl == 0)], noisefunc)
var.coef = b02
sources2 = var.simulate([l, sum(cl == 1)], noisefunc)
var.fit(sources1)
var.fit(sources2)
sources = np.zeros((l, m0, t))
sources[:, :, cl == 0] = sources1
sources[:, :, cl == 1] = sources2
# simulate volume conduction... 3 sources measured with 7 channels
mix = [[0.5, 1.0, 0.5, 0.2, 0.0, 0.0, 0.0],
[0.0, 0.2, 0.5, 1.0, 0.5, 0.2, 0.0],
[0.0, 0.0, 0.0, 0.2, 0.5, 1.0, 0.5]]
data = datatools.dot_special(sources, mix)
backend_modules = [import_module('scot.' + b) for b in scot.backends]
for bm in backend_modules:
np.random.seed(
3141592
) # reset random seed so we're independent of module order
api = scot.Workspace({'model_order': 2},
reducedim=3,
backend=bm.backend)
api.set_data(data)
api.do_ica()
self.assertEqual(api.mixing_.shape, (3, 7))
self.assertEqual(api.unmixing_.shape, (7, 3))
api.do_mvarica()
self.assertEqual(api.get_connectivity('S').shape, (3, 3, 512))
self.assertFalse(np.any(np.isnan(api.activations_)))
self.assertFalse(np.any(np.isinf(api.activations_)))
api.set_data(data)
api.fit_var()
self.assertEqual(api.get_connectivity('S').shape, (3, 3, 512))
self.assertEqual(
api.get_tf_connectivity('S', 100, 50).shape,
(3, 3, 512, (l - 100) // 50))
api.set_data(data, cl)
self.assertFalse(np.any(np.isnan(api.data_)))
self.assertFalse(np.any(np.isinf(api.data_)))
api.do_cspvarica()
self.assertEqual(api.get_connectivity('S').shape, (3, 3, 512))
self.assertFalse(np.any(np.isnan(api.activations_)))
self.assertFalse(np.any(np.isinf(api.activations_)))
for c in np.unique(cl):
api.set_used_labels([c])
api.fit_var()
fc = api.get_connectivity('S')
self.assertEqual(fc.shape, (3, 3, 512))
tfc = api.get_tf_connectivity('S', 100, 50)
self.assertEqual(tfc.shape, (3, 3, 512, (l - 100) // 50))
api.set_data(data)
api.remove_sources([0, 2])
api.fit_var()
self.assertEqual(api.get_connectivity('S').shape, (1, 1, 512))
self.assertEqual(
api.get_tf_connectivity('S', 100, 50).shape,
(1, 1, 512, (l - 100) // 50))
try:
api.optimize_var()
except NotImplementedError:
pass
api.fit_var()
self.assertEqual(api.get_connectivity('S').shape, (1, 1, 512))
self.assertEqual(
api.get_tf_connectivity('S', 100, 50).shape,
(1, 1, 512, (l - 100) // 50))
def testFunctionality(self):
""" generate VAR signals, and apply the api to them
do this for every backend """
np.random.seed(3141592)
# original model coefficients
b01 = np.zeros((3, 6))
b02 = np.zeros((3, 6))
b01[1:3, 2:6] = [[0.4, -0.2, 0.3, 0.0], [-0.7, 0.0, 0.9, 0.0]]
b02[0:3, 2:6] = [[0.4, 0.0, 0.0, 0.0], [0.4, 0.0, 0.4, 0.0], [0.0, 0.0, 0.4, 0.0]]
m0 = b01.shape[0]
cl = np.array([0, 1, 0, 1, 0, 0, 1, 1, 1, 0])
l = 200
t = len(cl)
# generate VAR sources with non-gaussian innovation process, otherwise ICA won't work
noisefunc = lambda: np.random.normal(size=(1, m0)) ** 3 / 1e3
var = VAR(2)
var.coef = b01
sources1 = var.simulate([l, sum(cl == 0)], noisefunc)
var.coef = b02
sources2 = var.simulate([l, sum(cl == 1)], noisefunc)
var.fit(sources1)
var.fit(sources2)
sources = np.zeros((t, m0, l))
sources[cl == 0, :, :] = sources1
sources[cl == 1, :, :] = sources2
# simulate volume conduction... 3 sources smeared over 7 channels
mix = [
[0.5, 1.0, 0.5, 0.2, 0.0, 0.0, 0.0],
[0.0, 0.2, 0.5, 1.0, 0.5, 0.2, 0.0],
[0.0, 0.0, 0.0, 0.2, 0.5, 1.0, 0.5],
]
data = datatools.dot_special(np.transpose(mix), sources)
data += np.random.randn(*data.shape) * 0.001 # add small noise
for backend_name, backend_gen in scot.backend.items():
np.random.seed(3141592) # reset random seed so we're independent of module order
api = scot.Workspace({"model_order": 2}, reducedim=3, backend=backend_gen())
api.set_data(data)
api.do_ica()
self.assertEqual(api.mixing_.shape, (3, 7))
self.assertEqual(api.unmixing_.shape, (7, 3))
api.do_mvarica()
self.assertEqual(api.get_connectivity("S").shape, (3, 3, 512))
self.assertFalse(np.any(np.isnan(api.activations_)))
self.assertFalse(np.any(np.isinf(api.activations_)))
api.set_data(data)
api.fit_var()
self.assertEqual(api.get_connectivity("S").shape, (3, 3, 512))
self.assertEqual(api.get_tf_connectivity("S", 100, 50).shape, (3, 3, 512, (l - 100) // 50))
tfc1 = api.get_tf_connectivity("PDC", 100, 5, baseline=None) # no baseline
tfc2 = api.get_tf_connectivity("PDC", 100, 5, baseline=[110, -10]) # invalid baseline
tfc3 = api.get_tf_connectivity("PDC", 100, 5, baseline=[0, 0]) # one-window baseline
tfc4 = tfc1 - tfc1[:, :, :, [0]]
tfc5 = api.get_tf_connectivity("PDC", 100, 5, baseline=[-np.inf, np.inf]) # full trial baseline
tfc6 = tfc1 - np.mean(tfc1, axis=3, keepdims=True)
self.assertTrue(np.allclose(tfc1, tfc2))
self.assertTrue(np.allclose(tfc3, tfc4))
self.assertTrue(np.allclose(tfc5, tfc6, rtol=1e-05, atol=1e-06))
api.set_data(data, cl)
self.assertFalse(np.any(np.isnan(api.data_)))
self.assertFalse(np.any(np.isinf(api.data_)))
api.do_cspvarica()
self.assertEqual(api.get_connectivity("S").shape, (3, 3, 512))
self.assertFalse(np.any(np.isnan(api.activations_)))
self.assertFalse(np.any(np.isinf(api.activations_)))
for c in np.unique(cl):
api.set_used_labels([c])
api.fit_var()
fc = api.get_connectivity("S")
self.assertEqual(fc.shape, (3, 3, 512))
tfc = api.get_tf_connectivity("S", 100, 50)
self.assertEqual(tfc.shape, (3, 3, 512, (l - 100) // 50))
api.set_data(data)
api.remove_sources([0, 2])
api.fit_var()
self.assertEqual(api.get_connectivity("S").shape, (1, 1, 512))
self.assertEqual(api.get_tf_connectivity("S", 100, 50).shape, (1, 1, 512, (l - 100) // 50))
try:
api.optimize_var()
except NotImplementedError:
pass
api.fit_var()
self.assertEqual(api.get_connectivity("S").shape, (1, 1, 512))
self.assertEqual(api.get_tf_connectivity("S", 100, 50).shape, (1, 1, 512, (l - 100) // 50))
