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 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 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 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 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
