def riemannian(covmats,
tol=10e-9,
max_iter=50,
init=None,
sample_weight=None):
if init is None:
output = CovMat(covmats.mean(0), False)
else:
output = init
k = 0
nu = 1.0
tau = numpy.finfo(numpy.double).max
crit = numpy.finfo(numpy.double).max
while crit > tol and k < max_iter and nu > tol:
k += 1
tmp = CovMats([(output.invsqrtm * covmat * output.invsqrtm).logm
for covmat in covmats], False)
average = CovMat(tmp.average(0, sample_weight), False)
crit = average.norm(ord='fro')
h = nu * crit
output = output.sqrtm * (nu * average).expm * output.sqrtm
if h < tau:
nu *= 0.95
tau = h
else:
nu *= 0.5
# if k == max_iter:
# print("Max iter reach")
return output
def wasserstein(covmats,
tol=10e-4,
max_iter=1,
init=None,
sample_weight=None):
if init is None:
output = CovMat(covmats.mean(0))
else:
output = init
k = 0
crit = numpy.finfo(numpy.double).max
while (crit > tol) and (k < max_iter):
k += 1
tmp = CovMats([(output.sqrtm * covmat * output.sqrtm).sqrtm
for covmat in covmats], False)
average = CovMat(tmp.average(0, sample_weight), False)
new_output = average.sqrtm
crit = (new_output - output.sqrtm).norm(ord='fro')
output = new_output
# if k == max_iter:
# print("Max iter reach")
return output * output
def log_determinant(covmats,
tol=10e-5,
max_iter=50,
init=None,
sample_weight=None):
if init is None:
output = CovMat(covmats.mean(0), False)
else:
output = init
k = 0
crit = numpy.finfo(numpy.double).max
while crit > tol and k < max_iter:
k += 1
tmp = CovMats([(0.5 * (covmat + output)).inverse
for covmat in covmats], False)
new_output = CovMat(tmp.average(0, sample_weight), False).inverse
crit = (new_output - output).norm(ord='fro')
output = new_output
# if k == max_iter:
# print("Max iter reach")
return output
def riemannian(covmats, tol=10e-9, max_iter=50, init=None, sample_weight=None):
if init is None:
output = CovMat(covmats.mean(0), False)
else:
output = init
k = 0
nu = 1.0
tau = numpy.finfo(numpy.double).max
crit = numpy.finfo(numpy.double).max
while crit > tol and k < max_iter and nu > tol:
k += 1
tmp = CovMats([(output.invsqrtm * covmat * output.invsqrtm).logm for covmat in covmats], False)
average = CovMat(tmp.average(0, sample_weight), False)
crit = average.norm(ord='fro')
h = nu * crit
output = output.sqrtm * (nu * average).expm * output.sqrtm
if h < tau:
nu *= 0.95
tau = h
else:
nu *= 0.5
# if k == max_iter:
# print("Max iter reach")
return output
def compute(matrice_order, loop_number):
covmats = CovMats.random(1, matrice_order)
for i in range(0, loop_number):
mean = Mean.log_euclidean(covmats)
covmats.add_all(
[Geodesic.log_euclidean(covmat, mean) for covmat in covmats])
def test_mean_riemann():
covmats = CovMats.random(10, 10)
old_dist = mean_riemann(covmats.numpy_array)
covmats.reset_covmats_fields()
new_dist = Mean.euclidean(covmats)
return _get_state(old_dist, new_dist, "mean riemann")
def test_mean_log_euclidean():
covmats = CovMats.random(10, 10)
old_dist = mean_logeuclid(covmats.numpy_array)
covmats.reset_covmats_fields()
new_dist = Mean.log_euclidean(covmats)
return _get_state(old_dist, new_dist, "mean log euclidian")
def test_mean_log_determinant():
covmats = CovMats.random(10, 10)
old_dist = mean_logdet(covmats.numpy_array)
covmats.reset_covmats_fields()
new_dist = Mean.log_determinant(covmats)
return _get_state(old_dist, new_dist, "mean log determinant")
def test_mean_log_determinant():
covmats = CovMats.random(10, 10)
old_dist = mean_logdet(covmats.numpy_array)
covmats.reset_covmats_fields()
new_dist = Mean.log_determinant(covmats)
return _get_state(old_dist, new_dist, "mean log determinant")
def test_mean_wasserstein():
covmats = CovMats.random(10, 10)
old_dist = mean_wasserstein(covmats.numpy_array)
covmats.reset_covmats_fields()
new_dist = Mean.wasserstein(covmats)
return _get_state(old_dist, new_dist, "mean wasserstein")
def test_mean_wasserstein():
covmats = CovMats.random(10, 10)
old_dist = mean_wasserstein(covmats.numpy_array)
covmats.reset_covmats_fields()
new_dist = Mean.wasserstein(covmats)
return _get_state(old_dist, new_dist, "mean wasserstein")
def test_tangent():
covmat = CovMat.random(10)
covmats = CovMats.random(10, 10)
old = tangent_space(covmats.numpy_array, covmat.numpy_array)
covmats.reset_covmats_fields()
new = TangentSpace.tangent(covmats, covmat)
return _get_state(old, new, "tangent space")
def test_untangent():
covmat = CovMat.random(10)
covmats = CovMats.random(10, 10)
tangent = TangentSpace.tangent(covmats, covmat)
old = untangent_space(tangent, covmat.numpy_array)
covmats.reset_covmats_fields()
new = TangentSpace.untangent(tangent, covmat)
return _get_state(old, new, "untangent")
def test_untangent():
covmat = CovMat.random(10)
covmats = CovMats.random(10, 10)
tangent = TangentSpace.tangent(covmats, covmat)
old = untangent_space(tangent, covmat.numpy_array)
covmats.reset_covmats_fields()
new = TangentSpace.untangent(tangent, covmat)
return _get_state(old, new, "untangent")
def log_determinant(covmats, tol=10e-5, max_iter=50, init=None, sample_weight=None):
if init is None:
output = CovMat(covmats.mean(0), False)
else:
output = init
k = 0
crit = numpy.finfo(numpy.double).max
while crit > tol and k < max_iter:
k += 1
tmp = CovMats([(0.5 * (covmat + output)).inverse for covmat in covmats], False)
new_output = CovMat(tmp.average(0, sample_weight), False).inverse
crit = (new_output - output).norm(ord='fro')
output = new_output
# if k == max_iter:
# print("Max iter reach")
return output
def wasserstein(covmats, tol=10e-4, max_iter=1, init=None, sample_weight=None):
if init is None:
output = CovMat(covmats.mean(0))
else:
output = init
k = 0
crit = numpy.finfo(numpy.double).max
while (crit > tol) and (k < max_iter):
k += 1
tmp = CovMats([(output.sqrtm * covmat * output.sqrtm).sqrtm for covmat in covmats], False)
average = CovMat(tmp.average(0, sample_weight), False)
new_output = average.sqrtm
crit = (new_output - output.sqrtm).norm(ord='fro')
output = new_output
# if k == max_iter:
# print("Max iter reach")
return output * output
def untangent(tangent, covmat_ref):
nt, nd = tangent.shape
ne = int((numpy.sqrt(1 + 8 * nd) - 1) / 2)
idx = numpy.triu_indices_from(covmat_ref.numpy_array)
covmats = CovMats(numpy.empty((nt, ne, ne)))
covmats[:, idx[0], idx[1]] = tangent
for i, covmat in enumerate(covmats):
covmats[i] = numpy.diag(numpy.diag(covmats[i])) + numpy.triu(
covmats[i], 1) / numpy.sqrt(2) + numpy.triu(
covmats[i], 1).T / numpy.sqrt(2)
covmats[i] = (covmat_ref.sqrtm * covmat.expm *
covmat_ref.sqrtm).numpy_array
return covmats
def compute(matrice_order, loop_number):
covmats = CovMats.random(1, matrice_order)
for i in range(0, loop_number):
mean = Mean.log_euclidean(covmats)
covmats.add_all([Geodesic.log_euclidean(covmat, mean) for covmat in covmats])
sys.path.append(
os.path.abspath(os.path.join(os.path.dirname(__file__), "..", "..")))
from Utils.CovMat import CovMat
from Utils.CovMats import CovMats
size = [10, 25, 50, 75, 100, 250, 500, 750, 1000]
# WARMUP
print("Warm up...")
for i in range(0, 10):
warm_up_covmat = CovMat.random(1000)
warm_up_covmat.expm
for i in range(0, len(size)):
covmats = CovMats.random(10, size[i])
t = timeit.Timer(
"mean_wasserstein(covmats.numpy_array)",
setup=
"from __main__ import covmats; from oldPyRiemann.mean import mean_wasserstein; import Utils.OpenBLAS"
)
old_time = t.timeit(number=size[len(size) - i - 1]) / size[len(size) - i -
1]
t = timeit.Timer(
"covmats.reset_fields(); Mean.wasserstein(covmats)",
setup="from Utils.Mean import Mean; from __main__ import covmats")
new_time = t.timeit(number=size[len(size) - i - 1]) / size[len(size) - i -
1]
import timeit
sys.path.append(os.path.abspath(os.path.join(os.path.dirname(__file__), "..", "..")))
from Utils.CovMat import CovMat
from Utils.CovMats import CovMats
size = [10, 25, 50, 75, 100, 250, 500, 750, 1000]
# WARMUP
print("Warm up...")
for i in range(0, 10):
warm_up_covmat = CovMat.random(1000)
warm_up_covmat.expm
for i in range(0, len(size)):
covmats = CovMats.random(10, size[i])
covmat = CovMat.random(size[i])
t = timeit.Timer("tangent_space(covmats.numpy_array, covmat.numpy_array)",
setup="from __main__ import covmats, covmat; from oldPyRiemann.tangentspace import tangent_space; import Utils.OpenBLAS")
old_time = t.timeit(number=size[len(size) - i - 1]) / size[len(size) - i - 1]
t = timeit.Timer("covmats.reset_fields(); covmat.reset_fields(); TangentSpace.tangent(covmats, covmat)",
setup="from Utils.TangentSpace import TangentSpace; from __main__ import covmats, covmat")
new_time = t.timeit(number=size[len(size) - i - 1]) / size[len(size) - i - 1]
print("matrix size : " + "10x" + str(size[i]) + "x" + str(size[i]) + "\t\told time : " + str(
old_time) + " sec\t\t" + "new time : " + str(new_time) + " sec\t\t" + "speed up : " + str(
old_time / new_time))
def log_euclidean(covmats, sample_weight=None):
logm_covmats = CovMats([covmat.logm for covmat in covmats], False)
return CovMat(logm_covmats.average(0, sample_weight), False).expm
def log_euclidean(covmats, sample_weight=None):
logm_covmats = CovMats([covmat.logm for covmat in covmats], False)
return CovMat(logm_covmats.average(0, sample_weight), False).expm
