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_random_diagonal_spd():
"""Testing random_diagonal_spd function"""
d = my_mfd.random_diagonal_spd(15)
diag = np.diag(d)
assert_array_almost_equal(d, np.diag(diag))
assert_array_less(0.0, diag)