def testModelIdentification(self):
""" generate VAR signals, mix them, and see if MVARICA can reconstruct the signals
do this for every backend """
# original model coefficients
b0 = np.zeros((3, 6))
b0[1:3, 2:6] = [[0.4, -0.2, 0.3, 0.0],
[-0.7, 0.0, 0.9, 0.0]]
m0 = b0.shape[0]
l, t = 1000, 100
# 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 = b0
sources = var.simulate([l, t], noisefunc)
# 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.backend.' + b) for b in scot.backend.__all__]
for bm in backend_modules:
api = scot.Workspace({'model_order': 2}, backend=bm.backend)
api.set_data(data)
# apply MVARICA
# - default setting of 0.99 variance should reduce to 3 channels with this data
# - automatically determine delta (enough data, so it should most likely be 0)
api.do_mvarica()
#result = varica.mvarica(data, 2, delta='auto', backend=bm.backend)
# ICA does not define the ordering and sign of components
# so wee need to test all combinations to find if one of them fits the original coefficients
permutations = np.array(
[[0, 1, 2, 3, 4, 5], [0, 1, 4, 5, 2, 3], [2, 3, 4, 5, 0, 1], [2, 3, 0, 1, 4, 5], [4, 5, 0, 1, 2, 3],
[4, 5, 2, 3, 0, 1]])
signperms = np.array(
[[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, -1, -1], [1, 1, -1, -1, 1, 1], [1, 1, -1, -1, -1, -1],
[-1, -1, 1, 1, 1, 1], [-1, -1, 1, 1, -1, -1], [-1, -1, -1, -1, 1, 1], [-1, -1, -1, -1, -1, -1]])
best, d = np.inf, None
for perm in permutations:
b = api.var_.coef[perm[::2] // 2, :]
b = b[:, perm]
for sgn in signperms:
c = b * np.repeat([sgn], 3, 0) * np.repeat([sgn[::2]], 6, 0).T
err = np.sum((c - b0) ** 2)
if err < best:
best = err
d = c
self.assertTrue(np.all(abs(d - b0) < 0.05))
def test_predict(self):
l = 100000
var = VAR(2)
var.coef = np.array([[0.2, 0.1, 0.4, -0.1], [0.3, -0.2, 0.1, 0]])
x = var.simulate(l)
z = var.predict(x)
# that limit is rather generous, but we don't want tests to fail due to random variation
self.assertTrue(np.abs(np.var(x[100:, :] - z[100:, :]) - 1) < 0.02)
def test_whiteness(self):
r = np.random.randn(100, 5, 10) # gaussian white noise
r0 = r.copy()
var = VAR(0)
var.residuals = r
p = var.test_whiteness(20)
self.assertTrue(np.all(r == r0)) # make sure we don't modify the input
self.assertTrue(p>0.05) # test should be non-significant for white noise
r[3:,1,:] = r[:-3,0,:] # create cross-correlation at lag 3
p = var.test_whiteness(20)
self.assertFalse(p>0.05) # now test should be significant
def test_simulate(self):
noisefunc = lambda: [1, 1] # use deterministic function instead of noise
num_samples = 100
b = np.array([[0.2, 0.1, 0.4, -0.1], [0.3, -0.2, 0.1, 0]])
var = VAR(2)
var.coef = b
x = var.simulate(num_samples, noisefunc)
# make sure we got expected values within reasonable accuracy
for n in range(10, num_samples):
self.assertTrue(np.all(
np.abs(x[n, :] - 1 - np.dot(b[:, 0::2], x[n - 1, :]) - np.dot(b[:, 1::2], x[n - 2, :])) < epsilon))
def testModelIdentification(self):
""" generate independent signals, mix them, and see if ICA can reconstruct the mixing matrix
do this for every backend """
# original model coefficients
b0 = np.zeros((3, 3)) # no connectivity
m0 = b0.shape[0]
l, t = 100, 100
# generate VAR sources with non-gaussian innovation process, otherwise ICA won't work
noisefunc = lambda: np.random.normal(size=(1, m0)) ** 3
var = VAR(1)
var.coef = b0
sources = var.simulate([l, t], noisefunc)
# 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.backend.' + b) for b in scot.backend.__all__]
for bm in backend_modules:
result = plainica.plainica(data, backend=bm.backend)
i = result.mixing.dot(result.unmixing)
self.assertTrue(np.allclose(i, np.eye(i.shape[0]), rtol=1e-6, atol=1e-7))
permutations = [[0, 1, 2], [0, 2, 1], [1, 0, 2], [1, 2, 0], [2, 0, 1], [2, 1, 0]]
bestdiff = np.inf
bestmix = None
absmix = np.abs(result.mixing)
absmix /= np.max(absmix)
for p in permutations:
estmix = absmix[p, :]
diff = np.sum((np.abs(estmix) - np.abs(mix)) ** 2)
if diff < bestdiff:
bestdiff = diff
bestmix = estmix
self.assertTrue(np.allclose(bestmix, mix, rtol=1e-1, atol=1e-1))
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_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 testFunctionality(self):
""" generate VAR signals, and apply the api to them
do this for every backend """
# 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 = 1000
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)
print(var.coef)
var.fit(sources2)
print(var.coef)
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.backend.' + b) for b in scot.backend.__all__]
for bm in backend_modules:
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))
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, 18))
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.assertFalse(np.any(np.isnan(api.activations_)))
self.assertFalse(np.any(np.isinf(api.activations_)))
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, 18))
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, 18))