-
Notifications
You must be signed in to change notification settings - Fork 0
/
quanc8.cpp
228 lines (199 loc) · 5.73 KB
/
quanc8.cpp
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
#include <math.h>
/*
fun : The name of the user defined function f(x).
a : The lower limit of integration.
b : The upper limit of integration.
abserr : The absolute error tolerance. Should be positive.
relerr : The relative error tolerance. Should be positive.
result : An approximation to the integral I.
errest : An estimate of the absolute error in I.
nofun : The number of function evaluations used in the
calculation of result.
posn : If flag < 0, then posn is the point reached when
the limit on nfe was approached.
flag : Error indicator.
= 0, normal return.
= 1, invalid user input, relerr < 0, abserr < 0
< 0, If flag = -n then n subintervals did not
converge. A small number (say 10) of
unconverged subintervals may be acceptable.
Check posn for further information.
*/
int quanc8(double(*fun)(double x), double a, double b,
double abserr, double relerr,
double *resultR, double *errestR,
int *nofunR,
double *posnR, int *flag)
{ /* begin function quanc8 */
/* this code has been translated from fortran, hence use
elements 1 .. n */
double w0, w1, w2, w3, w4, area, x0, f0, stone, step, cor11;
double qprev, qnow, qdiff, qleft, esterr, tolerr;
static double qright[32], f[17], x[17], fsave[9][31];
static double xsave[9][31];
double posn, result, errest;
double temp, temp1;
int nofun;
int levmin, levmax, levout, nomax, nofin, lev, nim, i, j, ii;
/* check user input */
if (abserr < 0.0 || relerr < 0.0)
{
*flag = 1;
*resultR = 0.0;
*errestR = 0.0;
*posnR = 0.0;
*nofunR = 0;
return (0);
}
/* *** stage 1 *** general initialization
set constants. */
levmin = 1;
levmax = 30;
levout = 6;
nomax = 5000;
{
ii = 1;
for (i = 0; i <= levout; i++) ii *= 2;
} /* ---> ii = 2 ** (levout+1) */
nofin = nomax - 8 * (levmax - levout + ii);
/* note that there will be trouble when nofun reaches nofin */
temp = 14175.0;
w0 = 3956.0 / temp;
w1 = 23552.0 / temp;
w2 = -3712.0 / temp;
w3 = 41984.0 / temp;
w4 = -18160.0 / temp;
/* initialize running sums to zero. */
*flag = 0;
posn = 0.0;
result = 0.0;
cor11 = 0.0;
errest = 0.0;
area = 0.0;
nofun = 0;
if (a == b) goto ExitQuanc8;
/* *** stage 2 *** initialization for first interval */
lev = 0;
nim = 1;
x0 = a;
x[16] = b;
qprev = 0.0;
/* set up evenly spaced panels */
f0 = (*fun) (x0);
stone = (b - a) / 16.0;
x[8] = 0.5 * (x0 + x[16]);
x[4] = 0.5 * (x0 + x[8]);
x[12] = 0.5 * (x[8] + x[16]);
x[2] = 0.5 * (x0 + x[4]);
x[6] = 0.5 * (x[4] + x[8]);
x[10] = 0.5 * (x[8] + x[12]);
x[14] = 0.5 * (x[12] + x[16]);
for (j = 2; j <= 16; j = j + 2) f[j] = (*fun) (x[j]);
nofun = 9;
/* *** stage 3 *** central calculation
requires qprev,x0,x2,x4,...,x16,f0,f2,f4,...,f16.
calculates x1,x3,...x15, f1,f3,...f15,qleft,qright,qnow,qdiff,area.
*/
Stage3:
x[1] = 0.5 * (x0 + x[2]);
f[1] = (*fun) (x[1]);
for (j = 3; j <= 15; j = j + 2)
{
x[j] = 0.5 * (x[j - 1] + x[j + 1]);
f[j] = (*fun) (x[j]);
}
nofun += 8;
step = (x[16] - x0) / 16.0;
qleft = (w0 * (f0 + f[8]) + w1 * (f[1] + f[7]) + w2 * (f[2] + f[6])
+ w3 * (f[3] + f[5]) + w4 * f[4]) * step;
qright[lev + 1] = (w0 * (f[8] + f[16]) + w1 * (f[9] + f[15]) + w2 * (f[10] + f[14])
+ w3 * (f[11] + f[13]) + w4 * f[12]) * step;
qnow = qleft + qright[lev + 1];
qdiff = qnow - qprev;
area += qdiff;
/* *** stage 4 *** interval convergence test */
esterr = fabs(qdiff) / 1023.0;
{
tolerr = abserr;
temp = relerr * fabs(area);
if (temp > tolerr) tolerr = temp;
} /* ---> tolerr = max(abserr, relerr * abs(area)) */
tolerr *= (step / stone);
if (lev < levmin) goto Stage5; /* keep subdividing */
if (lev >= levmax) goto Stage6B; /* too many nested levels */
if (nofun > nofin) goto Stage6; /* close to limit on fn calls */
if (esterr <= tolerr) goto Stage7; /* this interval has converged */
/* *** stage 5 *** no convergence
locate next interval. */
Stage5:
nim *= 2;
++lev;
/* store right hand elements for future use. */
for (i = 1; i <= 8; i++)
{
fsave[i][lev] = f[i + 8];
xsave[i][lev] = x[i + 8];
}
/* assemble left hand elements for immediate use. */
qprev = qleft;
for (i = 1; i <= 8; i++)
{
j = (-i);
f[2 * j + 18] = f[j + 9];
x[2 * j + 18] = x[j + 9];
}
goto Stage3;
/* *** stage 6 *** trouble section
number of function values is about to exceed limit. */
Stage6:
nofin *= 2;
levmax = levout;
posn = x0; /* this is our trouble spot */
goto Stage7;
/* current level is levmax. */
Stage6B:
--(*flag); /* another interval has not converged */
/* *** stage 7 *** interval converged
add contributions into running sums. */
Stage7:
result += qnow;
errest += esterr;
cor11 += qdiff / 1023.0;
/* locate next interval. */
while (nim != (2 * (nim / 2)))
{
nim /= 2;
--lev;
}
++nim;
if (lev <= 0) goto Stage8;
/* assemble elements required for the next interval. */
qprev = qright[lev];
x0 = x[16];
f0 = f[16];
for (i = 1; i <= 8; i++)
{
f[2 * i] = fsave[i][lev];
x[2 * i] = xsave[i][lev];
}
goto Stage3;
/* *** stage 8 *** finalize and return */
Stage8:
result += cor11;
/* make sure errest not less than roundoff level. */
if (errest == 0.0) goto ExitQuanc8;
temp1 = fabs(result);
temp = temp1 + errest;
while (temp == temp1)
{
errest *= 2.0;
temp = temp1 + errest;
}
ExitQuanc8:
/* --- return variables --- */
*resultR = result;
*errestR = errest;
*posnR = posn;
*nofunR = nofun;
return (0);
} /* end of quanc8() */