forked from johannesgerer/jburkardt-f
-
Notifications
You must be signed in to change notification settings - Fork 1
/
intlib.html
433 lines (395 loc) · 12.1 KB
/
intlib.html
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
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
<html>
<head>
<title>
INTLIB - 1-dimensional quadrature
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
INTLIB <br> 1-dimensional quadrature
</h1>
<hr>
<p>
<b>INTLIB</b>
is a FORTRAN90 library which
estimates integrals over 1D regions.
</p>
<p>
The integrand may be available as a function F(X), or as data
at equally spaced or unequally spaced points.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/cubpack/cubpack.html">
CUBPACK</a>,
a FORTRAN90 library which
estimates the integral of a function over a collection of N-dimensional
hyperrectangles and simplices.
</p>
<p>
<a href = "../../f_src/nintlib/nintlib.html">
NINTLIB</a>,
a FORTRAN90 library which
estimates integrals over multidimensional regions.
</p>
<p>
<a href = "../../f_src/product_rule/product_rule.html">
PRODUCT_RULE</a>,
a FORTRAN90 program which
constructs a product quadrature rule from 1D factor rules.
</p>
<p>
<a href = "../../datasets/quadrature_rules/quadrature_rules.html">
QUADRATURE_RULES</a>,
a dataset directory which
contains files that define quadrature rules over various 1D intervals
or multidimensional hypercubes.
</p>
<p>
<a href = "../../f_src/quadpack/quadpack.html">
QUADPACK</a>,
a FORTRAN90 library which
numerically estimates integrals.
</p>
<p>
<a href = "../../f_src/quadrule/quadrule.html">
QUADRULE</a>,
a FORTRAN90 library which
defines quadrature rules for 1D domains.
</p>
<p>
<a href = "../../f77_src/simpack/simpack.html">
SIMPACK</a>,
a FORTRAN77 library which
approximates the integral of a function over a multidimensional simplex.
</p>
<p>
<a href = "../../f_src/stroud/stroud.html">
STROUD</a>,
a FORTRAN90 library which
defines quadrature rules for a variety of multidimensional reqions.
</p>
<p>
<a href = "../../f_src/tanh_quad/tanh_quad.html">
TANH_QUAD</a>,
a FORTRAN90 library which
sets up the tanh quadrature rule;
</p>
<p>
<a href = "../../f_src/test_int/test_int.html">
TEST_INT</a>,
a FORTRAN90 library which
defines test integrands for 1D quadrature rules.
</p>
<p>
<a href = "../../f_src/test_int_2d/test_int_2d.html">
TEST_INT_2D</a>,
a FORTRAN90 library which
defines test integrands for 2D quadrature rules.
</p>
<p>
<a href = "../../f77_src/toms351/toms351.html">
TOMS351</a>,
a FORTRAN77 library which
estimates an integral using Romberg integration.
</p>
<p>
<a href = "../../f77_src/toms379/toms379.html">
TOMS379</a>,
a FORTRAN77 library which
estimates an integral.
</p>
<p>
<a href = "../../f77_src/toms418/toms418.html">
TOMS418</a>,
a FORTRAN77 library which
estimates the integral of a function with a sine or cosine factor.
</p>
<p>
<a href = "../../f77_src/toms424/toms424.html">
TOMS424</a>,
a FORTRAN77 library which
estimates the integral of a function using Clenshaw-Curtis quadrature.
</p>
<p>
<a href = "../../f77_src/toms468/toms468.html">
TOMS468</a>,
a FORTRAN77 library which
applies "automatic" integration to a function.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Milton Abramowitz, Irene Stegun,<br>
Handbook of Mathematical Functions,<br>
National Bureau of Standards, 1964,<br>
ISBN: 0-486-61272-4,<br>
LC: QA47.A34.
</li>
<li>
Roland Bulirsch, Josef Stoer,<br>
Fehlerabschaetzungen und Extrapolation mit rationaled Funktionen
bei Verfahren vom Richardson-Typus,<br>
(Error estimates and extrapolation with rational functions
in processes of Richardson type),<br>
Numerische Mathematik,<br>
Volume 6, Number 1, December 1964, pages 413-427.
</li>
<li>
Stephen Chase, Lloyd Fosdick,<br>
An Algorithm for Filon Quadrature,<br>
Communications of the Association for Computing Machinery,<br>
Volume 12, Number 8, August 1969, pages 453-457.
</li>
<li>
Stephen Chase, Lloyd Fosdick,<br>
Algorithm 353:
Filon Quadrature,<br>
Communications of the Association for Computing Machinery,<br>
Volume 12, Number 8, August 1969, pages 457-458.
</li>
<li>
William Cody,<br>
An Overview of Software Development for Special Functions,
in Numerical Analysis Dundee, 1975, <br>
edited by GA Watson,<br>
Lecture Notes in Mathematics, 506, <br>
Springer, 1976.
</li>
<li>
Philip Davis, Philip Rabinowitz,<br>
Methods of Numerical Integration,<br>
Second Edition,<br>
Dover, 2007,<br>
ISBN: 0486453391,<br>
LC: QA299.3.D28.
</li>
<li>
Carl deBoor, John Rice,<br>
CADRE: An algorithm for numerical quadrature,<br>
in Mathematical Software,<br>
edited by John Rice,<br>
Academic Press, 1971,<br>
ISBN: 012587250X,<br>
LC: QA1.M766.
</li>
<li>
Augustin Dubrulle,<br>
A short note on the implicit QL algorithm for symmetric
tridiagonal matrices,<br>
Numerische Mathematik,<br>
Volume 15, Number 5, September 1970, page 450.
</li>
<li>
Philip Gill, GF Miller,<br>
An algorithm for the integration of unequally spaced data,<br>
The Computer Journal, <br>
Number 15, Number 1, 1972, pages 80-83.
</li>
<li>
Gene Golub,<br>
Some Modified Matrix Eigenvalue Problems,<br>
SIAM Review,<br>
Volume 15, Number 2, Part 1, April 1973, pages 318-334.
</li>
<li>
Gene Golub, John Welsch,<br>
Calculation of Gaussian Quadrature Rules,<br>
Mathematics of Computation,<br>
Volume 23, Number 106, April 1969, pages 221-230.
</li>
<li>
John Hart, Ward Cheney, Charles Lawson, Hans Maehly,
Charles Mesztenyi, John Rice, Henry Thatcher,
Christoph Witzgall,<br>
Computer Approximations,<br>
Wiley, 1968.
</li>
<li>
Tore Havie,<br>
On a Modification of the Clenshaw Curtis Quadrature Rule,<br>
BIT,<br>
Volume 9, Number 4, December 1969, pages 338-350.
</li>
<li>
Paul Hennion,<br>
Algorithm 77:
Interpolation, Differentiation and Integration,<br>
Communications of the ACM,<br>
Volume 5, 1962, page 96.
</li>
<li>
Robert Kubik,<br>
Algorithm 257:
Havie Integrator,<br>
Communications of the ACM,<br>
Volume 8, Number 6, June 1965, page 381.
</li>
<li>
James Lyness,<br>
Algorithm 379:
SQUANK (Simpson Quadrature Used Adaptively
- Noise Killed),<br>
Communications of the ACM,<br>
Volume 13, Number 4, April 1970, pages 260-263.
</li>
<li>
Roger Martin, James Wilkinson,<br>
The Implicit QL Algorithm,<br>
Numerische Mathematik,<br>
Volume 12, Number 5, December 1968, pages 377-383.
</li>
<li>
William McKeeman, Lawrence Tesler,<br>
Algorithm 182:
Nonrecursive adaptive integration,<br>
Communications of the ACM,<br>
Volume 6, 1963, page 315.
</li>
<li>
Arthur Stroud, Don Secrest,<br>
Gaussian Quadrature Formulas,<br>
Prentice Hall, 1966,<br>
LC: QA299.4G3S7.
</li>
<li>
James Wilkinson, Christian Reinsch,<br>
Handbook for Automatic Computation,<br>
Volume II, Linear Algebra, Part 2,<br>
Springer, 1971,<br>
ISBN: 0387054146.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "intlib.f90">intlib.f90</a>, the source code.
</li>
<li>
<a href = "intlib.sh">intlib.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "intlib_prb.f90">intlib_prb.f90</a>, a sample problem.
</li>
<li>
<a href = "intlib_prb.sh">intlib_prb.sh</a>,
commands to compile, link and run the sample problem.
</li>
<li>
<a href = "intlib_prb_output.txt">intlib_prb_output.txt</a>, the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>AVINT</b> estimates the integral of unevenly spaced data.
</li>
<li>
<b>CADRE</b> estimates the integral of F(X) from A to B.
</li>
<li>
<b>CHINSP</b> estimates an integral using a modified Clenshaw-Curtis scheme.
</li>
<li>
<b>CLASS</b> sets recurrence coeeficients for various orthogonal polynomials.
</li>
<li>
<b>CSPINT</b> estimates the integral of a tabulated function.
</li>
<li>
<b>CUBINT</b> approximates an integral using cubic interpolation of data.
</li>
<li>
<b>FILON_COS</b> uses Filon's method on integrals with a cosine factor.
</li>
<li>
<b>FILON_SIN</b> uses Filon's method on integrals with a sine factor.
</li>
<li>
<b>GAMMA</b> calculates the Gamma function for a real argument X.
</li>
<li>
<b>GAUS8</b> estimates the integral of a function.
</li>
<li>
<b>GAUSQ2</b> finds the eigenvalues of a symmetric tridiagonal matrix.
</li>
<li>
<b>GAUSSQ</b> computes a Gauss quadrature rule.
</li>
<li>
<b>HIORDQ</b> approximates the integral of a function using equally spaced data.
</li>
<li>
<b>IRATEX</b> estimates the integral of a function.
</li>
<li>
<b>MONTE_CARLO</b> estimates the integral of a function by Monte Carlo.
</li>
<li>
<b>PLINT</b> approximates the integral of unequally spaced data.
</li>
<li>
<b>QNC79</b> approximates the integral of F(X) using Newton-Cotes quadrature.
</li>
<li>
<b>QUAD</b> approximates the integral of F(X) by Romberg integration.
</li>
<li>
<b>R8VEC_EVEN</b> returns N values, evenly spaced between ALO and AHI.
</li>
<li>
<b>RMINSP</b> approximates the integral of a function using Romberg integration.
</li>
<li>
<b>SIMP</b> approximates the integral of a function by an adaptive Simpson's rule.
</li>
<li>
<b>SIMPNE</b> approximates the integral of unevenly spaced data.
</li>
<li>
<b>SIMPSN</b> approximates the integral of evenly spaced data.
</li>
<li>
<b>SOLVE</b> solves a special linear system.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>WEDINT</b> uses Weddle's rule to integrate data at equally spaced points.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 02 December 2005.
</i>
<!-- John Burkardt -->
</body>
</html>