def barycenter_alpha(means, kerns, T, xi):
""" The barycenter function used for optimization"""
def sig(x): return 1 / (1 + np.exp(-1 * x))
n = kerns[0].shape[0]
for i in range(len(kerns)):
kerns[i] = np.reshape(kerns[i], (n, n))
# Calculate the barycenter mean
# mm = lambda dist: np.mean(dist, x)
# mbar = sum([sig(xi)*means[i] for i in range(len(means))]) # just two dists for now
# mbar = sig(xi)*means[0] + (1-sig(xi))*means[1]
mbar = 0
# Calculate the barycenter covariance matrix`
# Kbar = np.matmul(np.random.rand(means[1].shape[0], means[1].shape[0]), np.random.rand(means[1].shape[0], means[1].shape[0]))
# Kbar = sum([xi[i] * kerns[i] for i in range(len(kerns))]) # Initialize Kbar to be the euclidean average
Kbar = sig(xi) * kerns[0] + (1-sig(xi)) * kerns[1] # Initialize Kbar to be the euclidean average
# print("KBAR:", Kbar)
update = lambda kern, Kbar2, x_i: x_i * ss.sqrtm(np.matmul(np.matmul(Kbar2, kern), Kbar2))
for t in range(1, T):
Kbar2 = ss.sqrtm(Kbar)
Kbarnew = update(kerns[0], Kbar2, sig(xi)) + update(kerns[1], Kbar2, (1-sig(xi)))
# print("t, NAN IN SQRT, diff: ", t, np.isnan(Kbar2).any(), np.mean(np.abs(Kbarnew - Kbar)))
Kbar = Kbarnew
return mbar, Kbar
def sample(var_param, n_samples, seed=None):
my_rs = rs if seed is None else npr.RandomState(seed)
s = np.sqrt(my_rs.chisquare(df, n_samples) / df)
param_dict = ms_pattern.fold(var_param)
z = my_rs.randn(n_samples, dim)
sqrtSigma = sqrtm(param_dict['Sigma'])
return param_dict['mu'] + np.dot(z, sqrtSigma)/s[:,np.newaxis]
def fun(A):
return to_scalar(spla.sqrtm(A))
def fun(A):
return to_scalar(spla.sqrtm(A))
