def __init__(self,a,b,c,d,P):
n = P.n
m = P.A_ub.shape[0]
r = P.A_eq.shape[0]
A_ub = np.bmat([[P.A_ub,-P.b_ub],[zeros(1,n),-ones(1)]])
b_ub = zeros(m+1)
A_eq = np.bmat([[P.A_eq,-P.b_eq],[c.T,-d]])
b_eq = np.bmat([[zeros(r)],[ones(1)]])
P = poly(A_ub,b_ub,A_eq,b_eq)
Q = None
c = np.bmat([[a],[b]])
self.QP = QP(None,c,P)
self.n = n
def bias(self, x_pos, x_neg):
m_pos = x_pos.shape[1]
m_neg = x_neg.shape[1]
Q = None
c = np.bmat([\
[ zeros(1) ],\
[ ones(m_pos) ],\
[ ones(m_neg) ]\
])
A_ub = np.bmat([\
[ ones(m_pos), -eye(m_pos), zeros(m_pos,m_neg) ],\
[ -ones(m_neg), zeros(m_neg,m_pos), -eye(m_neg) ],\
[ zeros(m_pos), -eye(m_pos), zeros(m_pos,m_neg) ],\
[ zeros(m_neg), zeros(m_neg,m_pos), -eye(m_neg) ]\
])
b_ub = np.bmat([\
[ -ones(m_pos) ],\
[ -ones(m_neg) ],\
[ zeros(m_pos) ],\
[ zeros(m_neg) ]\
])
for i in range(m_pos):
b_ub[i, 0] += self.a(x_pos[:, i])
for i in range(m_neg):
b_ub[i + m_pos, 0] -= self.a(x_neg[:, i])
P = poly(A_ub, b_ub)
sol = QP(Q, c, P).solve()
b = sol[0, 0]
return b
def dual(self, x, y):
m = y.shape[0]
c_dual = -ones(m)
Q_dual = eye(m)
for i in range(m):
for j in range(m):
Q_dual[i, j] = y[i, 0] * y[j, 0] * self.K(x[:, i], x[:, j])
A_ub = -eye(m)
b_ub = zeros(m)
A_eq = y.T
b_eq = zeros(1)
P_dual = poly(A_ub, b_ub, A_eq, b_eq)
z = QP(Q_dual, c_dual, P_dual).solve()
return z
class linear_fractional(object):
"""
min J = (a.T*x-b)/(c.T*x-d)
x ∈ R^n
s.t. x ∈ POLYHEDRON
"""
def __init__(self,a,b,c,d,P):
n = P.n
m = P.A_ub.shape[0]
r = P.A_eq.shape[0]
A_ub = np.bmat([[P.A_ub,-P.b_ub],[zeros(1,n),-ones(1)]])
b_ub = zeros(m+1)
A_eq = np.bmat([[P.A_eq,-P.b_eq],[c.T,-d]])
b_eq = np.bmat([[zeros(r)],[ones(1)]])
P = poly(A_ub,b_ub,A_eq,b_eq)
Q = None
c = np.bmat([[a],[b]])
self.QP = QP(None,c,P)
self.n = n
def __repr__(self):
s = '\n'+'_'*80 + '\n'+self.__class__.__name__+'\n' + self.__doc__
if self.sol is not None:
s += '\n x\t= ' + str(self.sol)
return s
def solve(self):
x = self.QP.solve()
print('*'*80)
print(x)
print('*'*80)
if x is not None:
if x[-1,0] != 0:
self.sol = x[0:self.n,0]/x[-1,0]
else:
self.sol = None
else:
self.sol = None
return self.sol
@staticmethod
def test():
n = 2
a = randn(n)
b = randn(1)
c = randn(n)
d = randn(1)
P = poly.rand(n,1,1)
problem = linear_fractional(a,b,c,d,P)
problem.solve()
print(problem)
def soft_dual(self, x, y, λ=0.1):
assert λ >= 0, "λ >= 0"
m = y.shape[0]
c_dual = None
Q_dual = eye(m)
for i in range(m):
for j in range(m):
Q_dual[i, j] = y[i, 0] * y[j, 0] * self.K(x[:, i], x[:, j])
A_ub = np.bmat([\
[ -eye(m) ],\
[ eye(m) ]\
])
b_ub = np.bmat([\
[ zeros(m) ],\
[ λ*ones(1) ]\
])
A_eq = y.T
b_eq = zeros(1)
P_dual = poly(A_ub, b_ub, A_eq, b_eq)
z = QP(Q_dual, c_dual, P_dual).solve()
return z
''' Created on Dec 8, 2015 @author: sandur2 ''' from constraint import Constraint from QP import QP c1 = Constraint(4, [1.,0.,0.,0.], [3.]) c2 = Constraint(4, [-1.,0.,0.,0.], [0.]) c3 = Constraint(4, [0.,1.,0.,0.], [3.]) c4 = Constraint(4, [0.,-1.,0.,0.], [0.]) c5 = Constraint(4, [0.,0.,1.,0.], [7.]) c6 = Constraint(4, [0.,0.,-1.,0.], [-4.]) c7 = Constraint(4, [0.,0.,0.,1.], [7.]) c8 = Constraint(4, [0.,0.,0.,-1.], [-4.]) qp = QP(4) qp.add_constraint(c1) qp.add_constraint(c2) qp.add_constraint(c3) qp.add_constraint(c4) qp.add_constraint(c5) qp.add_constraint(c6) qp.add_constraint(c7) qp.add_constraint(c8) sol = qp.solve() print(sol['x'])
def __init__(self, x_pos, x_neg, p='inf', λ=1):
"""
x_pos ∈ R^{n,m_pos}
x_neg ∈ R^{n,m_neg}
"""
n = x_pos.shape[0]
m_pos = x_pos.shape[1]
m_neg = x_neg.shape[1]
assert x_neg.shape[0] is n
if p is 1:
Q = None
c = np.bmat([[zeros(n + 1)], [λ * ones(m_pos + m_neg)], [ones(n)]])
A_ub = np.bmat([\
[ -x_pos.T, ones(m_pos), -eye(m_pos), zeros(m_pos,m_neg), zeros(m_pos,n) ],\
[ x_neg.T, -ones(m_neg), zeros(m_neg,m_pos), -eye(m_neg), zeros(m_neg,n) ],\
[ -eye(n), zeros(n), zeros(n,m_pos), zeros(n,m_neg), -eye(n) ],\
[ eye(n), zeros(n), zeros(n,m_pos), zeros(n,m_neg), -eye(n) ],\
[ zeros(m_pos,n), zeros(m_pos), -eye(m_pos), zeros(m_pos,m_neg), zeros(m_pos,n) ],\
[ zeros(m_neg,n), zeros(m_neg), zeros(m_neg,m_pos), -eye(m_neg), zeros(m_neg,n) ]])
b_ub = np.bmat([\
[ -ones(m_pos) ],\
[ -ones(m_neg) ],\
[ zeros(n) ],\
[ zeros(n) ],\
[ zeros(m_pos) ],\
[ zeros(m_neg) ]])
P = poly(A_ub, b_ub)
sol = QP(Q, c, P).solve()
self.a = sol[0:n, 0]
self.b = sol[n, 0]
if p is 2:
Q = zeros(n + 1 + m_pos + m_neg, n + 1 + m_pos + m_neg)
Q[0:n, 0:n] = 2 * eye(n)
c = zeros(n + 1 + m_pos + m_neg, 1)
c[(n + 1 + 1 - 1):(n + 1 + m_pos +
m_neg)] = λ * ones(m_pos + m_neg, 1)
A_ub = np.bmat([\
[ -x_pos.T, ones(m_pos), -eye(m_pos), zeros(m_pos,m_neg) ],\
[ x_neg.T, -ones(m_neg), zeros(m_neg,m_pos), -eye(m_neg) ],\
[ zeros(m_pos,n), zeros(m_pos), -eye(m_pos), zeros(m_pos,m_neg) ],\
[ zeros(m_neg,n), zeros(m_neg), zeros(m_neg,m_pos), -eye(m_neg) ]])
b_ub = np.bmat([\
[ -ones(m_pos) ],\
[ -ones(m_neg) ],\
[ zeros(m_pos) ],\
[ zeros(m_neg) ]\
])
P = poly(A_ub, b_ub)
sol = QP(Q, c, P).solve()
self.a = sol[0:n, 0]
self.b = sol[n, 0]
if p is 'inf':
Q = None
c = np.bmat([[zeros(n + 1)], [λ * ones(m_pos + m_neg)], [ones(1)]])
A_ub = np.bmat([\
[ -x_pos.T, ones(m_pos), -eye(m_pos), zeros(m_pos,m_neg), zeros(m_pos) ],\
[ x_neg.T, -ones(m_neg), zeros(m_neg,m_pos), -eye(m_neg), zeros(m_neg) ],\
[ -eye(n), zeros(n), zeros(n,m_pos), zeros(n,m_neg), -ones(n) ],\
[ eye(n), zeros(n), zeros(n,m_pos), zeros(n,m_neg), -ones(n) ],\
[ zeros(m_pos,n), zeros(m_pos), -eye(m_pos), zeros(m_pos,m_neg), zeros(m_pos) ],\
[ zeros(m_neg,n), zeros(m_neg), zeros(m_neg,m_pos), -eye(m_neg), zeros(m_neg) ]])
b_ub = np.bmat([\
[ -ones(m_pos) ],\
[ -ones(m_neg) ],\
[ zeros(n) ],\
[ zeros(n) ],\
[ zeros(m_pos) ],\
[ zeros(m_neg) ]])
P = poly(A_ub, b_ub)
sol = QP(Q, c, P).solve()
self.a = sol[0:n, 0]
self.b = sol[n, 0]
def get_feasible(self):
Q = eye(self.n)
c = None
return QP(Q, c, self).solve()