def fuz_asym_lin_reg_QP_krauthann20(list_of_coordinates, h, k1, k2):
n = len(list_of_coordinates[0]) - 1
new_list = [(1, *c) for c in list_of_coordinates]
k2 = k2 / 4
# caching sum to access later
sum_matrix = []
for x in range(n + 2):
row = []
for y in range(n + 2):
row.append(sum([i[x] * i[y] for i in new_list]))
sum_matrix.append(row)
Q_matrix = []
for j in range(n + 1):
row = []
# line l
for i in range(n + 1):
row.append(k2 * sum_matrix[j][i]) # l
row.append(0.) # u
row.append(0.) # a
Q_matrix.append(row)
row = []
# line u
for i in range(n + 1):
row.append(0.) # l
row.append(k2 * sum_matrix[j][i]) # u
row.append(0.) # a
Q_matrix.append(row)
row = []
# line a
for i in range((n + 1)):
row.append(0.) # l
row.append(0.) # u
row.append(k1 * sum_matrix[j][i]) # a
Q_matrix.append(row)
Q = np.array(Q_matrix) * 2 # times 2 for algorithm in quadprog
p_vector = []
for j in range(n + 1):
p_vector.append(0.) # l
p_vector.append(0.) # u
p_vector.append(-2 * sum_matrix[n + 1][j] * k1) # a
p = np.array(p_vector)
# Gh
G_buffer = []
h_buffer = []
for el in new_list:
# lower then upper
row = []
for j in range(n + 1):
row.append(-(1 - h) * el[j])
row.append(0.)
row.append(el[j])
G_buffer.append(row)
h_buffer.append(el[n + 1])
# higher then lower
row = []
for j in range(n + 1):
row.append(0.)
row.append(-(1 - h) * el[j])
row.append(-el[j])
G_buffer.append(row)
h_buffer.append(-el[n + 1])
# u_j, l_j >= 0
for j in range(n + 1):
row_u = [] # l
row_l = [] # u
for i in range(n + 1):
if i == j:
row_l.append(-1.)
row_l.append(0.)
row_l.append(0.)
row_u.append(0)
row_u.append(-1.)
row_u.append(0)
else:
row_l.append(0.)
row_l.append(0.)
row_l.append(0.)
row_u.append(0.)
row_u.append(0.)
row_u.append(0.)
G_buffer.append(row_l)
h_buffer.append(0.)
G_buffer.append(row_u)
h_buffer.append(0.)
G = np.array(G_buffer)
h = np.array(h_buffer)
res = cvxopt_solve_qp(Q, p, G, h)
return AsymLinearSolution(l=res[::3], u=res[1::3], a=res[2::3])
def fuz_asym_lin_reg_QP_expert_adv(list_of_coordinates,
h=0,
k1=1,
k2=1,
k3=1,
t=2):
n = len(list_of_coordinates[0]) - 1
p = len(list_of_coordinates)
new_list = [(1, *c) for c in list_of_coordinates]
# get factors from linear regression
lin_reg = lin_reg_QP(list_of_coordinates)
estimates = []
sigma = 0
for x in new_list:
estimate = 0
for j in range(n + 1):
estimate += x[j] * lin_reg[j]
estimates.append(estimate)
sigma += (x[n + 1] - estimate)**2
sigma /= (p - n - 1)
sigma = sigma**0.5
R, S = set(), set()
for j in range(len(new_list)):
if estimates[j] - (sigma * t) <= new_list[j][
n + 1] <= estimates[j] + (sigma * t):
R.add(new_list[j])
else:
S.add(new_list[j])
sum_matrix = []
# caching sum to access later
for x in range(n + 2):
row = []
for y in range(n + 2):
row.append(
float(sum([i[x] * i[y] for num, i in enumerate(new_list)])))
sum_matrix.append(row)
Q_matrix = []
for j in range(n + 1):
row = []
# line l
for i in range(n + 1):
row.append(k2 * sum_matrix[j][i]) # l
row.append(0.) # u
row.append(0.) # a
row.append(0.) # e_l
row.append(0.) # e_u
Q_matrix.append(row)
row = []
# line u
for i in range(n + 1):
row.append(0.) # l
row.append(k2 * sum_matrix[j][i]) # u
row.append(0.) # a
row.append(0.) # e_l
row.append(0.) # e_u
Q_matrix.append(row)
row = []
# line a
for i in range((n + 1)):
row.append(0.) # l
row.append(0.) # u
row.append(k1 * sum_matrix[j][i]) # a
row.append(0.) # e_l
row.append(0.) # e_u
Q_matrix.append(row)
row_l = [0 for _ in range((n + 1) * 3)]
row_l.append(k3)
row_l.append(0)
Q_matrix.append(row_l) # row for e_l
row_u = [0 for _ in range((n + 1) * 3 + 1)]
row_u.append(k3)
Q_matrix.append(row_u) # row for e_u
Q = np.array(Q_matrix) * 2 # times 2 for algorithm in quadprog
p_vector = []
for j in range(n + 1):
p_vector.append(0.) # l
p_vector.append(0.) # u
p_vector.append(-2 * sum_matrix[n + 1][j] * k1) # a
p_vector.append(0.) # e_l
p_vector.append(0.) # e_u
p = np.array(p_vector)
# Gh
G_buffer = []
h_buffer = []
for num, el in enumerate(new_list):
if el in R:
# lower then upper
row = []
for j in range(n + 1):
row.append(-(1 - h) * el[j]) # l
row.append(0.) # u
row.append(el[j]) # a
row.append(0.) # e_l
row.append(0.) # e_u
G_buffer.append(row)
h_buffer.append(el[n + 1])
# higher then lower
row = []
for j in range(n + 1):
row.append(0.) # l
row.append(-(1 - h) * el[j]) # u
row.append(-el[j]) # a
row.append(0.) # e_l
row.append(0.) # e_u
G_buffer.append(row)
h_buffer.append(-el[n + 1])
if el in S:
# lower then upper + e
row = []
for j in range(n + 1):
row.append(-(1 - h) * el[j]) # l
row.append(0.) # u
row.append(el[j])
row.append(-1.) # e_l
row.append(0.) # e_u
G_buffer.append(row)
h_buffer.append(el[n + 1])
# higher then lower + e
row = []
for j in range(n + 1):
row.append(0.) # l
row.append(-(1 - h) * el[j]) # u
row.append(-el[j])
row.append(0.) # e_l
row.append(-1.) # e_u
G_buffer.append(row)
h_buffer.append(-el[n + 1])
# u_j, l_j >= 0
for j in range(n + 1):
row_u = [] # l
row_l = [] # u
for i in range(n + 1):
if i == j:
row_l.append(-1.)
row_l.append(0.)
row_l.append(0.)
row_u.append(0)
row_u.append(-1.)
row_u.append(0)
else:
row_l.append(0.)
row_l.append(0.)
row_l.append(0.)
row_u.append(0.)
row_u.append(0.)
row_u.append(0.)
row_u.append(0.) # e_l
row_u.append(0.) # e_u
row_l.append(0.) # e_l
row_l.append(0.) # e_u
G_buffer.append(row_l)
h_buffer.append(0.)
G_buffer.append(row_u)
h_buffer.append(0.)
G = np.array(G_buffer)
h = np.array(h_buffer)
res = cvxopt_solve_qp(Q, p, G, h)
return AsymLinearExpertSolution(l=res[:-2:3],
u=res[1:-1:3],
a=res[2::3],
e_l=res[-2],
e_u=res[-1])
def fuz_sym_lin_reg_QP(list_of_coordinates, h=0, k1=1, k2=1):
n = len(list_of_coordinates[0]) - 1
new_list = [(1, *c) for c in list_of_coordinates]
# caching sum to access later
sum_matrix = []
for x in range(n + 2):
row = []
for y in range(n + 2):
row.append(sum([i[x] * i[y] for i in new_list]))
sum_matrix.append(row)
Q_matrix = []
for j in range(n + 1):
row = []
# line c
for i in range(n + 1):
row.append(k2 * sum_matrix[j][i])
row.append(0.) # a
Q_matrix.append(row)
row = []
# line a
for i in range((n + 1)):
row.append(0.) # c
row.append(k1 * sum_matrix[j][i])
Q_matrix.append(row)
Q = np.array(Q_matrix) * 2
p_vector = []
for j in range(n + 1):
p_vector.append(0.) # c
p_vector.append(-2 * sum_matrix[n + 1][j] * k1)
p = np.array(p_vector)
# Gh
G_buffer = []
h_buffer = []
for el in new_list:
# lower then upper
row = []
for j in range(n + 1):
row.append(-(1 - h) * el[j])
row.append(el[j])
G_buffer.append(row)
h_buffer.append(el[n + 1])
# higher then lower
row = []
for j in range(n + 1):
row.append(-(1 - h) * el[j])
row.append(-el[j])
G_buffer.append(row)
h_buffer.append(-el[n + 1])
# c_j >= 0
for j in range(n + 1):
row = []
for i in range(n + 1):
if i == j:
row.append(-1.)
row.append(0.)
else:
row.append(0.)
row.append(0.)
G_buffer.append(row)
h_buffer.append(0.)
G = np.array(G_buffer)
h = np.array(h_buffer)
res = cvxopt_solve_qp(Q, p, G, h)
return SymLinearSolution(c=res[::2], a=res[1::2])