33 |
|
|
34 |
#include "rat_eval.h" |
#include "rat_eval.h" |
35 |
|
|
36 |
|
static double |
37 |
|
small (double q) |
38 |
|
{ |
39 |
|
const double a[8] = { 3.387132872796366608, 133.14166789178437745, |
40 |
|
1971.5909503065514427, 13731.693765509461125, |
41 |
|
45921.953931549871457, 67265.770927008700853, |
42 |
|
33430.575583588128105, 2509.0809287301226727 |
43 |
|
}; |
44 |
|
|
45 |
|
const double b[8] = { 1.0, 42.313330701600911252, |
46 |
|
687.1870074920579083, 5394.1960214247511077, |
47 |
|
21213.794301586595867, 39307.89580009271061, |
48 |
|
28729.085735721942674, 5226.495278852854561 |
49 |
|
}; |
50 |
|
|
51 |
|
double r = 0.180625 - q * q; |
52 |
|
|
53 |
|
double x = q * rat_eval (a, 8, b, 8, r); |
54 |
|
|
55 |
|
return x; |
56 |
|
} |
57 |
|
|
58 |
|
static double |
59 |
|
intermediate (double r) |
60 |
|
{ |
61 |
|
const double a[] = { 1.42343711074968357734, 4.6303378461565452959, |
62 |
|
5.7694972214606914055, 3.64784832476320460504, |
63 |
|
1.27045825245236838258, 0.24178072517745061177, |
64 |
|
0.0227238449892691845833, 7.7454501427834140764e-4 |
65 |
|
}; |
66 |
|
|
67 |
|
const double b[] = { 1.0, 2.05319162663775882187, |
68 |
|
1.6763848301838038494, 0.68976733498510000455, |
69 |
|
0.14810397642748007459, 0.0151986665636164571966, |
70 |
|
5.475938084995344946e-4, 1.05075007164441684324e-9 |
71 |
|
}; |
72 |
|
|
73 |
|
double x = rat_eval (a, 8, b, 8, (r - 1.6)); |
74 |
|
|
75 |
|
return x; |
76 |
|
} |
77 |
|
|
78 |
|
static double |
79 |
|
tail (double r) |
80 |
|
{ |
81 |
|
const double a[] = { 6.6579046435011037772, 5.4637849111641143699, |
82 |
|
1.7848265399172913358, 0.29656057182850489123, |
83 |
|
0.026532189526576123093, 0.0012426609473880784386, |
84 |
|
2.71155556874348757815e-5, 2.01033439929228813265e-7 |
85 |
|
}; |
86 |
|
|
87 |
|
const double b[] = { 1.0, 0.59983220655588793769, |
88 |
|
0.13692988092273580531, 0.0148753612908506148525, |
89 |
|
7.868691311456132591e-4, 1.8463183175100546818e-5, |
90 |
|
1.4215117583164458887e-7, 2.04426310338993978564e-15 |
91 |
|
}; |
92 |
|
|
93 |
|
double x = rat_eval (a, 8, b, 8, (r - 5.0)); |
94 |
|
|
95 |
|
return x; |
96 |
|
} |
97 |
|
|
98 |
double |
double |
99 |
gsl_cdf_ugaussian_P_inv (double p) |
gsl_cdf_ugaussian_Pinv (double p) |
100 |
{ |
{ |
101 |
double r, x; |
double r, x, pp; |
102 |
|
|
103 |
double q = p - 0.5; |
double dp = p - 0.5; |
104 |
|
|
105 |
if (fabs (q) <= 0.425) |
if (p == 1.0) |
106 |
{ |
{ |
107 |
const double a[8] = { 3.387132872796366608, 133.14166789178437745, |
return GSL_POSINF; |
|
1971.5909503065514427, 13731.693765509461125, |
|
|
45921.953931549871457, 67265.770927008700853, |
|
|
33430.575583588128105, 2509.0809287301226727 |
|
|
}; |
|
|
|
|
|
const double b[8] = { 1.0, 42.313330701600911252, |
|
|
687.1870074920579083, 5394.1960214247511077, |
|
|
21213.794301586595867, 39307.89580009271061, |
|
|
28729.085735721942674, 5226.495278852854561 |
|
|
}; |
|
|
|
|
|
r = 0.180625 - q * q; |
|
|
|
|
|
x = q * rat_eval (a, 8, b, 8, r); |
|
|
|
|
|
return x; |
|
108 |
} |
} |
109 |
|
else if (p == 0.0) |
|
if (q < 0.0) |
|
110 |
{ |
{ |
111 |
r = p; |
return GSL_NEGINF; |
112 |
} |
} |
113 |
else |
|
114 |
|
if (fabs(dp) <= 0.425) |
115 |
{ |
{ |
116 |
r = 1.0 - p; |
x = small (dp); |
117 |
|
|
118 |
|
return x; |
119 |
} |
} |
120 |
|
|
121 |
r = sqrt (-log (r)); |
pp = (p < 0.5) ? p : 1.0 - p; |
122 |
|
|
123 |
|
r = sqrt (-log (pp)); |
124 |
|
|
125 |
if (r <= 5.0) |
if (r <= 5.0) |
126 |
{ |
{ |
127 |
const double a[] = { 1.42343711074968357734, 4.6303378461565452959, |
x = intermediate (r); |
|
5.7694972214606914055, 3.64784832476320460504, |
|
|
1.27045825245236838258, 0.24178072517745061177, |
|
|
0.0227238449892691845833, 7.7454501427834140764e-4 |
|
|
}; |
|
|
|
|
|
const double b[] = { 1.0, 2.05319162663775882187, |
|
|
1.6763848301838038494, 0.68976733498510000455, |
|
|
0.14810397642748007459, 0.0151986665636164571966, |
|
|
5.475938084995344946e-4, 1.05075007164441684324e-9 |
|
|
}; |
|
|
|
|
|
x = rat_eval (a, 8, b, 8, (r - 1.6)); |
|
128 |
} |
} |
129 |
else |
else |
130 |
{ |
{ |
131 |
const double a[] = { 6.6579046435011037772, 5.4637849111641143699, |
x = tail (r); |
|
1.7848265399172913358, 0.29656057182850489123, |
|
|
0.026532189526576123093, 0.0012426609473880784386, |
|
|
2.71155556874348757815e-5, 2.01033439929228813265e-7 |
|
|
}; |
|
|
|
|
|
const double b[] = { 1.0, 0.59983220655588793769, |
|
|
0.13692988092273580531, 0.0148753612908506148525, |
|
|
7.868691311456132591e-4, 1.8463183175100546818e-5, |
|
|
1.4215117583164458887e-7, 2.04426310338993978564e-15 |
|
|
}; |
|
|
|
|
|
x = rat_eval (a, 8, b, 8, (r - 5.0)); |
|
132 |
} |
} |
133 |
|
|
134 |
if (q < 0.0) |
if (p < 0.5) |
135 |
{ |
{ |
136 |
return -x; |
return -x; |
137 |
} |
} |
143 |
} |
} |
144 |
|
|
145 |
double |
double |
146 |
gsl_cdf_ugaussian_Q_inv (double p) |
gsl_cdf_ugaussian_Qinv (double p) |
147 |
{ |
{ |
148 |
return gsl_cdf_ugaussian_P_inv (1.0 - p); |
double r, x, pp; |
149 |
|
|
150 |
|
double dp = p - 0.5; |
151 |
|
|
152 |
|
if (p == 1.0) |
153 |
|
{ |
154 |
|
return GSL_NEGINF; |
155 |
|
} |
156 |
|
else if (p == 0.0) |
157 |
|
{ |
158 |
|
return GSL_POSINF; |
159 |
|
} |
160 |
|
|
161 |
|
if (fabs(dp) <= 0.425) |
162 |
|
{ |
163 |
|
x = small (dp); |
164 |
|
|
165 |
|
return -x; |
166 |
|
} |
167 |
|
|
168 |
|
pp = (p < 0.5) ? p : 1.0 - p; |
169 |
|
|
170 |
|
r = sqrt (-log (pp)); |
171 |
|
|
172 |
|
if (r <= 5.0) |
173 |
|
{ |
174 |
|
x = intermediate (r); |
175 |
|
} |
176 |
|
else |
177 |
|
{ |
178 |
|
x = tail (r); |
179 |
|
} |
180 |
|
|
181 |
|
if (p < 0.5) |
182 |
|
{ |
183 |
|
return x; |
184 |
|
} |
185 |
|
else |
186 |
|
{ |
187 |
|
return -x; |
188 |
|
} |
189 |
} |
} |