-
Notifications
You must be signed in to change notification settings - Fork 0
/
util.py
163 lines (110 loc) · 3.91 KB
/
util.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
import numpy as np
from mpmath import mp
mp.dps = 500
def construct_s(bh):
s = []
for bhj in bh:
if bhj != 0:
s.append(np.sign(bhj))
s = np.array(s)
s = s.reshape((len(s), 1))
return s
def construct_A_XA_Ac_XAc_bhA(X, bh, n, p):
A = []
Ac = []
bhA = []
for j in range(p):
bhj = bh[j]
if bhj != 0:
A.append(j)
bhA.append(bhj)
else:
Ac.append(j)
XA = X[:, A]
XAc = X[:, Ac]
bhA = np.array(bhA).reshape((len(A), 1))
return A, XA, Ac, XAc, bhA
def check_KKT(XA, XAc, y, bhA, lamda, n):
print("\nCheck Active")
e1 = y - np.dot(XA, bhA)
e2 = np.dot(XA.T, e1)
print(e2/ (lamda * n))
if XAc is not None:
print("\nCheck In Active")
e1 = y - np.dot(XA, bhA)
e2 = np.dot(XAc.T, e1)
print(e2/ (lamda * n))
def construct_test_statistic(j, XA, y, A):
ej = []
for each_j in A:
if j == each_j:
ej.append(1)
else:
ej.append(0)
ej = np.array(ej).reshape((len(A), 1))
inv = np.linalg.pinv(np.dot(XA.T, XA))
XAinv = np.dot(XA, inv)
etaj = np.dot(XAinv, ej)
etajTy = np.dot(etaj.T, y)[0][0]
return etaj, etajTy
def compute_yz(y, etaj, zk, n):
sq_norm = (np.linalg.norm(etaj))**2
e1 = np.identity(n) - (np.dot(etaj, etaj.T))/sq_norm
a = np.dot(e1, y)
b = etaj/sq_norm
yz = a + b*zk
return yz, b
def pivot(A, bh, list_active_set, list_zk, list_bhz, etaj, etajTy, cov, tn_mu, type):
tn_sigma = np.sqrt(np.dot(np.dot(etaj.T, cov), etaj))[0][0]
z_interval = []
for i in range(len(list_active_set)):
if type == 'As':
if np.array_equal(np.sign(bh), np.sign(list_bhz[i])):
z_interval.append([list_zk[i], list_zk[i + 1] - 1e-10])
if type == 'A':
if np.array_equal(A, list_active_set[i]):
z_interval.append([list_zk[i], list_zk[i + 1] - 1e-10])
new_z_interval = []
for each_interval in z_interval:
if len(new_z_interval) == 0:
new_z_interval.append(each_interval)
else:
sub = each_interval[0] - new_z_interval[-1][1]
if abs(sub) < 0.01:
new_z_interval[-1][1] = each_interval[1]
else:
new_z_interval.append(each_interval)
z_interval = new_z_interval
numerator = 0
denominator = 0
for each_interval in z_interval:
al = each_interval[0]
ar = each_interval[1]
denominator = denominator + mp.ncdf((ar - tn_mu)/tn_sigma) - mp.ncdf((al - tn_mu)/tn_sigma)
if etajTy >= ar:
numerator = numerator + mp.ncdf((ar - tn_mu)/tn_sigma) - mp.ncdf((al - tn_mu)/tn_sigma)
elif (etajTy >= al) and (etajTy < ar):
numerator = numerator + mp.ncdf((etajTy - tn_mu)/tn_sigma) - mp.ncdf((al - tn_mu)/tn_sigma)
if denominator != 0:
return float(numerator/denominator)
else:
return None
def pivot_with_specified_interval(z_interval, etaj, etajTy, cov, tn_mu):
tn_sigma = np.sqrt(np.dot(np.dot(etaj.T, cov), etaj))[0][0]
numerator = 0
denominator = 0
for each_interval in z_interval:
al = each_interval[0]
ar = each_interval[1]
denominator = denominator + mp.ncdf((ar - tn_mu)/tn_sigma) - mp.ncdf((al - tn_mu)/tn_sigma)
if etajTy >= ar:
numerator = numerator + mp.ncdf((ar - tn_mu)/tn_sigma) - mp.ncdf((al - tn_mu)/tn_sigma)
elif (etajTy >= al) and (etajTy < ar):
numerator = numerator + mp.ncdf((etajTy - tn_mu)/tn_sigma) - mp.ncdf((al - tn_mu)/tn_sigma)
if denominator != 0:
return float(numerator/denominator)
else:
return None
def p_value(A, bh, list_active_set, list_zk, list_bhz, etaj, etajTy, cov):
value = pivot(A, bh, list_active_set, list_zk, list_bhz, etaj, etajTy, cov, 0, 'A')
return 2 * min(1 - value, value)