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
223
224
225
226
227
228
229
230
231
232
233
|
/* integration/qelg.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
struct extrapolation_table
{
size_t n;
double rlist2[52];
size_t nres;
double res3la[3];
};
static void
initialise_table (struct extrapolation_table *table);
static void
append_table (struct extrapolation_table *table, double y);
static void
initialise_table (struct extrapolation_table *table)
{
table->n = 0;
table->nres = 0;
}
#ifdef JUNK
static void
initialise_table (struct extrapolation_table *table, double y)
{
table->n = 0;
table->rlist2[0] = y;
table->nres = 0;
}
#endif
static void
append_table (struct extrapolation_table *table, double y)
{
size_t n;
n = table->n;
table->rlist2[n] = y;
table->n++;
}
/* static inline void
qelg (size_t * n, double epstab[],
double * result, double * abserr,
double res3la[], size_t * nres); */
static inline void
qelg (struct extrapolation_table *table, double *result, double *abserr);
static inline void
qelg (struct extrapolation_table *table, double *result, double *abserr)
{
double *epstab = table->rlist2;
double *res3la = table->res3la;
const size_t n = table->n - 1;
const double current = epstab[n];
double absolute = GSL_DBL_MAX;
double relative = 5 * GSL_DBL_EPSILON * fabs (current);
const size_t newelm = n / 2;
const size_t n_orig = n;
size_t n_final = n;
size_t i;
const size_t nres_orig = table->nres;
*result = current;
*abserr = GSL_DBL_MAX;
if (n < 2)
{
*result = current;
*abserr = GSL_MAX_DBL (absolute, relative);
return;
}
epstab[n + 2] = epstab[n];
epstab[n] = GSL_DBL_MAX;
for (i = 0; i < newelm; i++)
{
double res = epstab[n - 2 * i + 2];
double e0 = epstab[n - 2 * i - 2];
double e1 = epstab[n - 2 * i - 1];
double e2 = res;
double e1abs = fabs (e1);
double delta2 = e2 - e1;
double err2 = fabs (delta2);
double tol2 = GSL_MAX_DBL (fabs (e2), e1abs) * GSL_DBL_EPSILON;
double delta3 = e1 - e0;
double err3 = fabs (delta3);
double tol3 = GSL_MAX_DBL (e1abs, fabs (e0)) * GSL_DBL_EPSILON;
double e3, delta1, err1, tol1, ss;
if (err2 <= tol2 && err3 <= tol3)
{
/* If e0, e1 and e2 are equal to within machine accuracy,
convergence is assumed. */
*result = res;
absolute = err2 + err3;
relative = 5 * GSL_DBL_EPSILON * fabs (res);
*abserr = GSL_MAX_DBL (absolute, relative);
return;
}
e3 = epstab[n - 2 * i];
epstab[n - 2 * i] = e1;
delta1 = e1 - e3;
err1 = fabs (delta1);
tol1 = GSL_MAX_DBL (e1abs, fabs (e3)) * GSL_DBL_EPSILON;
/* If two elements are very close to each other, omit a part of
the table by adjusting the value of n */
if (err1 <= tol1 || err2 <= tol2 || err3 <= tol3)
{
n_final = 2 * i;
break;
}
ss = (1 / delta1 + 1 / delta2) - 1 / delta3;
/* Test to detect irregular behaviour in the table, and
eventually omit a part of the table by adjusting the value of
n. */
if (fabs (ss * e1) <= 0.0001)
{
n_final = 2 * i;
break;
}
/* Compute a new element and eventually adjust the value of
result. */
res = e1 + 1 / ss;
epstab[n - 2 * i] = res;
{
const double error = err2 + fabs (res - e2) + err3;
if (error <= *abserr)
{
*abserr = error;
*result = res;
}
}
}
/* Shift the table */
{
const size_t limexp = 50 - 1;
if (n_final == limexp)
{
n_final = 2 * (limexp / 2);
}
}
if (n_orig % 2 == 1)
{
for (i = 0; i <= newelm; i++)
{
epstab[1 + i * 2] = epstab[i * 2 + 3];
}
}
else
{
for (i = 0; i <= newelm; i++)
{
epstab[i * 2] = epstab[i * 2 + 2];
}
}
if (n_orig != n_final)
{
for (i = 0; i <= n_final; i++)
{
epstab[i] = epstab[n_orig - n_final + i];
}
}
table->n = n_final + 1;
if (nres_orig < 3)
{
res3la[nres_orig] = *result;
*abserr = GSL_DBL_MAX;
}
else
{ /* Compute error estimate */
*abserr = (fabs (*result - res3la[2]) + fabs (*result - res3la[1])
+ fabs (*result - res3la[0]));
res3la[0] = res3la[1];
res3la[1] = res3la[2];
res3la[2] = *result;
}
/* In QUADPACK the variable table->nres is incremented at the top of
qelg, so it increases on every call. This leads to the array
res3la being accessed when its elements are still undefined, so I
have moved the update to this point so that its value more
useful. */
table->nres = nres_orig + 1;
*abserr = GSL_MAX_DBL (*abserr, 5 * GSL_DBL_EPSILON * fabs (*result));
return;
}
|
