def step(self, x, last_b):
# initialize
m = len(x)
mu = np.matrix(last_b).T
sigma = self.sigma
theta = self.theta
eps = self.eps
x = np.matrix(x).T # matrices are easier to manipulate
# 4. Calculate the following variables
M = mu.T * x
V = x.T * sigma * x
x_upper = sum(diag(sigma) * x) / trace(sigma)
# 5. Update the portfolio distribution
mu, sigma = self.update(x, x_upper, mu, sigma, M, V, theta, eps)
# 6. Normalize mu and sigma
mu = tools.simplex_proj(mu)
sigma = sigma / (m**2 * trace(sigma))
"""
sigma(sigma < 1e-4*eye(m)) = 1e-4;
"""
self.sigma = sigma
return mu
def update(self, b, x, eps):
""" Update portfolio weights to satisfy constraint b * x >= eps
and minimize distance to previous weights. """
x_mean = np.mean(x)
lam = max(0., (eps - np.dot(b, x)) / np.linalg.norm(x - x_mean)**2)
# limit lambda to avoid numerical problems
lam = min(100000, lam)
# update portfolio
b = b + lam * (x - x_mean)
# project it onto simplex
return tools.simplex_proj(b)
def update(self, b, x, eps):
""" Update portfolio weights to satisfy constraint b * x >= eps
and minimize distance to previous weights. """
x_mean = np.mean(x)
lam = max(0., (eps - np.dot(b, x)) / np.linalg.norm(x - x_mean)**2)
# limit lambda to avoid numerical problems
lam = min(100000, lam)
# update portfolio
b = b + lam * (x - x_mean)
# project it onto simplex
return tools.simplex_proj(b)
def update(self, b, x, eps, C):
""" Update portfolio weights to satisfy constraint b * x <= eps
and minimize distance to previous weights. """
x_mean = np.mean(x)
le = max(0., np.dot(b, x) - eps)
if self.variant == 0:
lam = le / np.linalg.norm(x - x_mean)**2
elif self.variant == 1:
lam = min(C, le / np.linalg.norm(x - x_mean)**2)
elif self.variant == 2:
lam = le / (np.linalg.norm(x - x_mean)**2 + 0.5 / C)
# limit lambda to avoid numerical problems
lam = min(100000, lam)
# update portfolio
b = b - lam * (x - x_mean)
# project it onto simplex
return tools.simplex_proj(b)
def update(self, b, x, eps, C):
""" Update portfolio weights to satisfy constraint b * x <= eps
and minimize distance to previous weights. """
x_mean = np.mean(x)
le = max(0., np.dot(b, x) - eps)
if self.variant == 0:
lam = le / np.linalg.norm(x - x_mean)**2
elif self.variant == 1:
lam = min(C, le / np.linalg.norm(x - x_mean)**2)
elif self.variant == 2:
lam = le / (np.linalg.norm(x - x_mean)**2 + 0.5 / C)
# limit lambda to avoid numerical problems
lam = min(100000, lam)
# update portfolio
b = b - lam * (x - x_mean)
# project it onto simplex
return tools.simplex_proj(b)