def test_transform(): # TODO : class test for class CovEmbedding
"""Testing fit_transform method for class CovEmbedding"""
n_subjects = random.randint(3, 50)
shape = random.randint(1, 10)
n_samples = 300
covs = []
signals = []
for k in xrange(n_subjects):
signal = np.random.randn(n_samples, shape)
signals.append(signal)
signal -= signal.mean(axis=0)
covs.append((signal.T).dot(signal) / n_samples)
for kind in ["correlation", "precision", "partial correlation", "tangent"]:
estimators = {'kind': kind, 'cov_estimator': None}
cov_embedding = my_con.CovEmbedding(**estimators)
covs_transformed = cov_embedding.fit_transform(signals)
# Generic
assert_is_instance(covs_transformed, np.ndarray)
assert_equal(len(covs_transformed), len(covs))
for k, vec in enumerate(covs_transformed):
assert_equal(vec.size, shape * (shape + 1) / 2)
cov_new = my_con.vec_to_sym(vec)
assert_true(my_mfd.is_spd(covs[k]))
if estimators["kind"] == "tangent":
assert_array_almost_equal(cov_new, cov_new.T)
fre_sqrt = my_mfd.sqrtm(cov_embedding.mean_cov_)
assert_true(my_mfd.is_spd(fre_sqrt))
assert_true(my_mfd.is_spd(cov_embedding.whitening_))
assert_array_almost_equal(
cov_embedding.whitening_.dot(fre_sqrt), np.eye(shape))
assert_array_almost_equal(
fre_sqrt.dot(my_mfd.expm(cov_new)).dot(fre_sqrt), covs[k])
if estimators["kind"] == "precision":
assert_true(my_mfd.is_spd(cov_new))
assert_array_almost_equal(cov_new.dot(covs[k]), np.eye(shape))
if estimators["kind"] == "correlation":
assert_true(my_mfd.is_spd(cov_new))
d = np.sqrt(np.diag(np.diag(covs[k])))
assert_array_almost_equal(d.dot(cov_new).dot(d), covs[k])
if estimators["kind"] == "partial correlation":
assert_true(my_mfd.is_spd(cov_new))
prec = linalg.inv(covs[k])
d = np.sqrt(np.diag(np.diag(prec)))
assert_array_almost_equal(
d.dot(cov_new).dot(d), -prec + 2 * np.diag(np.diag(prec)))
def test_frechet_mean(): # TODO: test suite and split in several tests
"""Testing frechet_mean function"""
n = random.randint(3, 50)
shape = random.randint(1, 50)
spds = []
for k in xrange(n):
eig_min = random.uniform(1e-7, 1.)
eig_max = random.uniform(1., 1e7)
spds.append(my_mfd.random_spd(shape, eig_min, eig_max))
fre = my_mfd.frechet_mean(spds)
# Generic
assert_tuple_equal(fre.shape, spds[0].shape)
assert_array_almost_equal(fre, fre.T)
assert_array_less(0., linalg.eigvals(fre))
# Check error for non spd enteries
mat1 = np.ones((shape, shape))
with assert_raises_regexp(ValueError, "at least one matrix is not real " +\
"spd"):
my_mfd.frechet_mean([mat1])
# Check warning if gradient norm in the last step is less than tolerance
for (tol, max_iter) in [(1e-10, 1), (1e-3, 50)]:
with warnings.catch_warnings(record=True) as w:
fre = my_mfd.frechet_mean(spds, max_iter=max_iter, tol=tol)
grad_norm = my_mfd.grad_frechet_mean(spds, max_iter=max_iter,
tol=tol)
if grad_norm[-1] > tol:
assert_equal(len(w), 2)
assert_equal(len(grad_norm), max_iter)
# Gradient norm is decreasing
assert_array_less(np.diff(grad_norm), 0.)
decimal = 5
tol = 10 ** (-2 * decimal)
fre = my_mfd.frechet_mean(spds, tol=tol)
# Adaptative version requires less iterations than non adaptaive
grad_norm = my_mfd.grad_frechet_mean(spds, tol=tol)
grad_norm_fast = my_mfd.grad_frechet_mean(spds, tol=tol, adaptative=True)
assert(len(grad_norm_fast) == len(grad_norm))
# Invariance under reordering
spds.reverse()
spds.insert(0, spds[2])
spds.pop(3)
fre_new = my_mfd.frechet_mean(spds, tol=tol)
assert_array_almost_equal(fre_new, fre)
# Invariance under congruant transformation
c = my_mfd.random_non_singular(shape)
spds_cong = [c.dot(spd).dot(c.T) for spd in spds]
fre_new = my_mfd.frechet_mean(spds_cong, tol=tol)
assert_array_almost_equal(fre_new, c.dot(fre).dot(c.T))
# Invariance under inversion
spds_inv = [linalg.inv(spd) for spd in spds]
fre_new = my_mfd.frechet_mean(spds_inv, tol=tol)
assert_array_almost_equal(fre_new, linalg.inv(fre), decimal=decimal)
# Approximate Frechet mean is close to the exact one
decimal = 7
tol = 0.5 * 10 ** (-decimal)
# Diagonal matrices: exact Frechet mean is geometric mean
diags = []
for k in xrange(n):
diags.append(my_mfd.random_diagonal_spd(shape, 1e-5, 1e5))
exact_fre = np.prod(my_mfd.my_stack(diags), axis=0) ** \
(1 / float(len(diags)))
app_fre = my_mfd.frechet_mean(diags, max_iter=10, tol=tol)
assert_array_almost_equal(app_fre, exact_fre, decimal)
# 2 matrices
spd1 = my_mfd.random_spd(shape)
spd2 = my_mfd.random_spd(shape)
spd2_sqrt = my_mfd.sqrtm(spd2)
spd2_inv_sqrt = my_mfd.inv_sqrtm(spd2)
exact_fre = spd2_sqrt.dot(
my_mfd.sqrtm(spd2_inv_sqrt.dot(spd1).dot(spd2_inv_sqrt))).dot(spd2_sqrt)
app_fre = my_mfd.frechet_mean([spd1, spd2], tol=tol)
assert_array_almost_equal(app_fre, exact_fre, decimal)
# Single geodesic matrices : TODO
S = np.random.rand(shape, shape)
S = S + S.T
times = np.empty(n, dtype=float)
spds = []
for k in xrange(n):
t_k = random.uniform(-2., -1.)
times[k] = t_k
spds.append(c.dot(my_mfd.expm(t_k * S)).dot(c.T))
def test_sqrtm():
"""Testing sqrtm function"""
m = my_mfd.random_spd(12)
m_sqrt = my_mfd.sqrtm(m)
assert_array_almost_equal(m_sqrt.T, m_sqrt)
assert_array_almost_equal(m_sqrt.dot(m_sqrt), m)
