def intersection(*cons):
if not all(isinstance(c, constraint) for c in cons):
t = type([c for c in cons if not isinstance(c, constraint)][0])
raise TypeError("Not a constraint : "+ repr(t))
cons = [c for c in cons if not isinstance(c, noConstraint)]
if all(isinstance(c, quadratic.quad_constraints) for c in cons):
q = np.vstack([c.quad_part for c in cons])
l = np.vstack([c.lin_part for c in cons])
o = np.hstack([c.offset for c in cons])
intersection = quadratic.quad_constraints(q, l, o)
return intersection
intersection = cons_op()
intersection._cons_list = list(cons)
intersection._op = 'I'
return intersection
def intersection(*cons):
if not all(isinstance(c, constraint) for c in cons):
t = type([c for c in cons if not isinstance(c, constraint)][0])
raise TypeError("Not a constraint : " + repr(t))
cons = [c for c in cons if not isinstance(c, noConstraint)]
if all(isinstance(c, quadratic.quad_constraints) for c in cons):
q = np.vstack([c.quad_part for c in cons])
l = np.vstack([c.lin_part for c in cons])
o = np.hstack([c.offset for c in cons])
intersection = quadratic.quad_constraints(q, l, o)
return intersection
intersection = cons_op()
intersection._cons_list = list(cons)
intersection._op = 'I'
return intersection
def distr_norm(self, X_s, y, sigma = 1.):
"""
Return the value of the norm of X_s.T*y and an instance of truncated :
the distribution of X_s.T*y
This is implementing the forward stepwise paper in the general case
Parameters
----------
X_s : np.float(p, k):
X_s is a full ranked matrix
y : np.float(p):
y is the data, and satisfies the constraints
sigma: float
sigma is the variance of the normal distribution under wich
y is chosen
Returns
-------
distr : truncated_chi
distr is an object used to study the distribution of
np.linalg.norm(np.dot(X_s.T, y)), when y is a gaussian vector,
chosen under the constraints and on the slice given by nu
"""
p, _ = y.shape
# P_s = projection(X_s)
k = min(X_s.shape)
z = np.dot(X_s.T, y)
z_norm = np.linalg.norm(z)
eta = z / z_norm
nu = np.dot(np.linalg.pinv(X_s).T, eta)
# print "nu : ", nu
# Computation of the intervals
q = np.zeros((1, p, p))
lin = (-nu).reshape((1, p))
off = np.array([float( \
- np.dot(nu.T, y) \
+ np.linalg.norm(nu)**2 * z_norm) \
])
cons_eta = quadratic.quad_constraints(q, lin, off)
cons_inter = cons_op.intersection(self, cons_eta)
I = cons_inter.bounds(nu, y)
I = I + float(z_norm)
# Computation of theta
Sig_s = np.dot(X_s.T, X_s)
Sig_s_inv = np.linalg.inv(Sig_s)
theta_s = float(sigma / np.sqrt(np.dot(eta.T, np.dot(Sig_s_inv, eta))))
distr = truncated_chi(I._U, k, theta_s)
return distr
def distr_norm(self, X_s, y, sigma=1.):
"""
Return the value of the norm of X_s.T*y and an instance of truncated :
the distribution of X_s.T*y
This is implementing the forward stepwise paper in the general case
Parameters
----------
X_s : np.float(p, k):
X_s is a full ranked matrix
y : np.float(p):
y is the data, and satisfies the constraints
sigma: float
sigma is the variance of the normal distribution under wich
y is chosen
Returns
-------
distr : truncated_chi
distr is an object used to study the distribution of
np.linalg.norm(np.dot(X_s.T, y)), when y is a gaussian vector,
chosen under the constraints and on the slice given by nu
"""
p, _ = y.shape
# P_s = projection(X_s)
k = min(X_s.shape)
z = np.dot(X_s.T, y)
z_norm = np.linalg.norm(z)
eta = z / z_norm
nu = np.dot(np.linalg.pinv(X_s).T, eta)
# print "nu : ", nu
# Computation of the intervals
q = np.zeros((1, p, p))
lin = (-nu).reshape((1, p))
off = np.array([float( \
- np.dot(nu.T, y) \
+ np.linalg.norm(nu)**2 * z_norm) \
])
cons_eta = quadratic.quad_constraints(q, lin, off)
cons_inter = cons_op.intersection(self, cons_eta)
I = cons_inter.bounds(nu, y)
I = I + float(z_norm)
# Computation of theta
Sig_s = np.dot(X_s.T, X_s)
Sig_s_inv = np.linalg.inv(Sig_s)
theta_s = float(sigma / np.sqrt(np.dot(eta.T, np.dot(Sig_s_inv, eta))))
distr = truncated_chi(I._U, k, theta_s)
return distr
