def test():
print('\n'+'_'*80 + '\nk_means [see ./fig/k_means.png]')
import random
n = 2
m = 20
k = 4
s = randn(n,m)+np.kron(ones(1,m),10*randn(n,1))
for i in range(k-1):
s = np.hstack((s,randn(n,m)+np.kron(ones(1,m),10*randn(n,1))))
k_means(s,k).plot()
def __init__(self,s):
"""
x ∈ R^n
"""
s = sampled_convex_set.remove_interior_points(s)
n = s.shape[0]
m = s.shape[1]
A_ub = np.bmat([[zeros(m,n),-eye(m)],[zeros(m,n),eye(m)]])
b_ub = np.bmat([[zeros(m)],[ones(m)]])
A_eq = np.bmat([[-eye(n),s],[zeros(1,n),ones(1,m)]])
b_eq = np.bmat([[zeros(n)],[ones(1)]])
self.P = poly(A_ub,b_ub,A_eq,b_eq)
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 xposxneg_2_xy(x_pos, x_neg): # TODO: validate
"""
x_pos ∈ R^{n,m_pos}
x_neg ∈ R^{n,m_neg}
to
x ∈ R^{n,m}
y ∈ {-1,1}^m
"""
n = x_pos.shape[0]
m_pos = x_pos.shape[1]
m_neg = x_neg.shape[1]
assert x_neg.shape[0] == n
x = np.bmat([[x_pos, x_neg]])
y = np.bmat([[ones(m_pos)], [-ones(m_neg)]])
return (x, y) # = self.xposxneg_2_xy(x_pos,x_neg)
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 soft_dual_alternative(self, x, y, λ=0.1):
assert λ >= 0 and λ <= 1, "λ ∈ R[0,1]"
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) ],\
[ ones(1,m) ]\
])
b_ub = np.bmat([\
[ zeros(m) ],\
[ ones(m)/float(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
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
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 test():
P1 = poly.rand(2,4,0,1).affine_transform(eye(2),2*ones(2,1))
P2 = poly.rand(2,4,0,1).affine_transform(eye(2),-2*ones(2,1))
problem = interset(P1,P2,2)
problem.solve()
print(problem)