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
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
|
/* dbetai.f -- translated by f2c (version 20041007).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
/** This routine has been editted to be thread safe **/
#define V3P_NETLIB_SRC
#include "v3p_netlib.h"
/* Table of constant values */
static integer c__3 = 3;
static integer c__1 = 1;
static integer c__2 = 2;
/* DECK DBETAI */
doublereal dbetai_(doublereal *x, doublereal *pin, doublereal *qin)
{
/* Initialized data */
// static logical first = TRUE_;
/* System generated locals */
integer i__1;
doublereal ret_val, d__1;
/* Builtin functions */
double log(doublereal), d_int(doublereal *), exp(doublereal);
/* Local variables */
doublereal c__;
integer i__, n;
doublereal p, q, y, p1;
integer ib;
doublereal xb, xi, ps;
/* static */ doublereal eps, sml;
doublereal term;
extern doublereal d1mach_(integer *), dlbeta_(doublereal *, doublereal *);
/* static */ doublereal alneps, alnsml;
doublereal finsum;
extern /* Subroutine */ int xermsg_(char *, char *, char *, integer *,
integer *, ftnlen, ftnlen, ftnlen);
/* ***BEGIN PROLOGUE DBETAI */
/* ***PURPOSE Calculate the incomplete Beta function. */
/* ***LIBRARY SLATEC (FNLIB) */
/* ***CATEGORY C7F */
/* ***TYPE DOUBLE PRECISION (BETAI-S, DBETAI-D) */
/* ***KEYWORDS FNLIB, INCOMPLETE BETA FUNCTION, SPECIAL FUNCTIONS */
/* ***AUTHOR Fullerton, W., (LANL) */
/* ***DESCRIPTION */
/* DBETAI calculates the DOUBLE PRECISION incomplete beta function. */
/* The incomplete beta function ratio is the probability that a */
/* random variable from a beta distribution having parameters PIN and */
/* QIN will be less than or equal to X. */
/* -- Input Arguments -- All arguments are DOUBLE PRECISION. */
/* X upper limit of integration. X must be in (0,1) inclusive. */
/* PIN first beta distribution parameter. PIN must be .GT. 0.0. */
/* QIN second beta distribution parameter. QIN must be .GT. 0.0. */
/* ***REFERENCES Nancy E. Bosten and E. L. Battiste, Remark on Algorithm */
/* 179, Communications of the ACM 17, 3 (March 1974), */
/* pp. 156. */
/* ***ROUTINES CALLED D1MACH, DLBETA, XERMSG */
/* ***REVISION HISTORY (YYMMDD) */
/* 770701 DATE WRITTEN */
/* 890531 Changed all specific intrinsics to generic. (WRB) */
/* 890911 Removed unnecessary intrinsics. (WRB) */
/* 890911 REVISION DATE from Version 3.2 */
/* 891214 Prologue converted to Version 4.0 format. (BAB) */
/* 900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ) */
/* 920528 DESCRIPTION and REFERENCES sections revised. (WRB) */
/* ***END PROLOGUE DBETAI */
/* ***FIRST EXECUTABLE STATEMENT DBETAI */
// d1mach has been made thread safe, so there is no need for the
// statics in determining these values
// if (first) {
// eps = d1mach_(&c__3);
// alneps = log(eps);
// sml = d1mach_(&c__1);
// alnsml = log(sml);
// }
// first = FALSE_;
eps = d1mach_(&c__3);
alneps = log(eps);
sml = d1mach_(&c__1);
alnsml = log(sml);
if (*x < 0. || *x > 1.) {
xermsg_("SLATEC", "DBETAI", "X IS NOT IN THE RANGE (0,1)", &c__1, &
c__2, (ftnlen)6, (ftnlen)6, (ftnlen)27);
}
if (*pin <= 0. || *qin <= 0.) {
xermsg_("SLATEC", "DBETAI", "P AND/OR Q IS LE ZERO", &c__2, &c__2, (
ftnlen)6, (ftnlen)6, (ftnlen)21);
}
y = *x;
p = *pin;
q = *qin;
if (q <= p && *x < .8) {
goto L20;
}
if (*x < .2) {
goto L20;
}
y = 1. - y;
p = *qin;
q = *pin;
L20:
if ((p + q) * y / (p + 1.) < eps) {
goto L80;
}
/* EVALUATE THE INFINITE SUM FIRST. TERM WILL EQUAL */
/* Y**P/BETA(PS,P) * (1.-PS)-SUB-I * Y**I / FAC(I) . */
ps = q - d_int(&q);
if (ps == 0.) {
ps = 1.;
}
xb = p * log(y) - dlbeta_(&ps, &p) - log(p);
ret_val = 0.;
if (xb < alnsml) {
goto L40;
}
ret_val = exp(xb);
term = ret_val * p;
if (ps == 1.) {
goto L40;
}
/* Computing MAX */
d__1 = alneps / log(y);
n = (integer) max(d__1,4.);
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
xi = (doublereal) i__;
term = term * (xi - ps) * y / xi;
ret_val += term / (p + xi);
/* L30: */
}
/* NOW EVALUATE THE FINITE SUM, MAYBE. */
L40:
if (q <= 1.) {
goto L70;
}
xb = p * log(y) + q * log(1. - y) - dlbeta_(&p, &q) - log(q);
/* Computing MAX */
d__1 = xb / alnsml;
ib = (integer) max(d__1,0.);
term = exp(xb - ib * alnsml);
c__ = 1. / (1. - y);
p1 = q * c__ / (p + q - 1.);
finsum = 0.;
n = (integer) q;
if (q == (doublereal) n) {
--n;
}
i__1 = n;
for (i__ = 1; i__ <= i__1; ++i__) {
if (p1 <= 1. && term / eps <= finsum) {
goto L60;
}
xi = (doublereal) i__;
term = (q - xi + 1.) * c__ * term / (p + q - xi);
if (term > 1.) {
--ib;
}
if (term > 1.) {
term *= sml;
}
if (ib == 0) {
finsum += term;
}
/* L50: */
}
L60:
ret_val += finsum;
L70:
if (y != *x || p != *pin) {
ret_val = 1. - ret_val;
}
/* Computing MAX */
d__1 = min(ret_val,1.);
ret_val = max(d__1,0.);
return ret_val;
L80:
ret_val = 0.;
xb = p * log((max(y,sml))) - log(p) - dlbeta_(&p, &q);
if (xb > alnsml && y != 0.) {
ret_val = exp(xb);
}
if (y != *x || p != *pin) {
ret_val = 1. - ret_val;
}
return ret_val;
} /* dbetai_ */
|
