def test_split_gof_meg(forward, idx, weights):
"""Test GOF splitting on MEG data."""
gain = forward['sol']['data'][:, idx]
# close to orthogonal
norms = np.linalg.norm(gain, axis=0)
triu = np.triu_indices(len(idx), 1)
prods = np.abs(np.dot(gain.T, gain) / np.outer(norms, norms))[triu]
assert_array_less(prods, 5e-3) # approximately orthogonal
# first, split across time (one dipole per time point)
M = gain * weights
gof_split = _split_gof(M, np.diag(weights), gain)
assert_allclose(gof_split.sum(0), 100., atol=1e-5) # all sum to 100
assert_allclose(gof_split, 100 * np.eye(len(weights)), atol=1) # loc
# next, summed to a single time point (all dipoles active at one time pt)
weights = np.array(weights)[:, np.newaxis]
x = gain @ weights
assert x.shape == (gain.shape[0], 1)
gof_split = _split_gof(x, weights, gain)
want = (norms * weights.T).T ** 2
want = 100 * want / want.sum()
assert_allclose(gof_split, want, atol=1e-3, rtol=1e-2)
assert_allclose(gof_split.sum(), 100, rtol=1e-5)
def test_split_gof_basic(mod):
"""Test splitting the goodness of fit."""
# first a trivial case
gain = np.array([[0., 1., 1.], [1., 1., 0.]]).T
M = np.ones((3, 1))
X = np.ones((2, 1))
M_est = gain @ X
assert_allclose(M_est, np.array([[1., 2., 1.]]).T) # a reasonable estimate
if mod == 'mult':
gain *= [1., -0.5]
X[1] *= -2
elif mod == 'augment':
gain = np.concatenate((gain, np.zeros((3, 1))), axis=1)
X = np.concatenate((X, [[1.]]))
elif mod == 'sign':
gain[1] *= -1
M[1] *= -1
M_est[1] *= -1
elif mod in ('zero', 'less'):
gain = np.array([[1, 1., 1.], [1., 1., 1.]]).T
if mod == 'zero':
X[:, 0] = [1., 0.]
else:
X[:, 0] = [1., 0.5]
M_est = gain @ X
else:
assert mod is None
res = M - M_est
gof = 100 * (1. - (res * res).sum() / (M * M).sum())
gof_split = _split_gof(M, X, gain)
assert_allclose(gof_split.sum(), gof)
want = gof_split[[0, 0]]
if mod == 'augment':
want = np.concatenate((want, [[0]]))
if mod in ('mult', 'less'):
assert_array_less(gof_split[1], gof_split[0])
elif mod == 'zero':
assert_allclose(gof_split[0], gof_split.sum(0))
assert_allclose(gof_split[1], 0., atol=1e-6)
else:
assert_allclose(gof_split, want, atol=1e-12)