-
Notifications
You must be signed in to change notification settings - Fork 59
/
toms757.html
413 lines (384 loc) · 11.8 KB
/
toms757.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
<html>
<head>
<title>
TOMS757 - Uncommon Special Functions
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TOMS757 <br> Uncommon Special Functions
</h1>
<hr>
<p>
<b>TOMS757</b>
is a FORTRAN90 library which
evaluates a number of
uncommon special functions, by Allan McLeod.
</p>
<p>
<b>TOMS757</b> is a FORTRAN90 version of ACM TOMS algorithm 757.
</p>
<p>
The special functions include:
<ul>
<li>
the Abramowitz function of several orders;
</li>
<li>
integrals of the Airy functions Ai(x) and Bi(x);
</li>
<li>
Clausen's integral;
</li>
<li>
Debye integrals of several orders;
</li>
<li>
integrals of the Bessel functions I0, J0, K0 and Y0;
</li>
<li>
Struve functions;
</li>
<li>
the synchrotron radiation integral;
</li>
<li>
the transport integral of several orders;
</li>
</ul>
</p>
<p>
The original, true, correct version of ACM TOMS Algorithm 757
is available through ACM:
<a href = "http://www.acm.org/pubs/calgo/">
http://www.acm.org/pubs/calgo</a>
or NETLIB:
<a href = "http://www.netlib.org/toms/index.html">
http://www.netlib.org/toms/index.html</a>
</p>
<p>
The version displayed here has been converted to FORTRAN90,
and other internal changes have been made to suit me.
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TOMS757</b> is available in
<a href = "../../f77_src/toms757/toms757.html">a FORTRAN77 version</a> and
<a href = "../../f_src/toms757/toms757.html">a FORTRAN90 version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/test_values/test_values.html">
TEST_VALUES</a>,
a FORTRAN90 library which
contains routines which store selected values of various
special functions.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Allan McLeod,<br>
Department of Mathematics and Statistics,<br>
Paisley University, Scotland.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Allan Mcleod,<br>
Algorithm 757, MISCFUN: A software package to compute uncommon
special functions,<br>
ACM Transactions on Mathematical Software,<br>
Volume 22, Number 3, September 1996, pages 288-301.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "toms757.f90">toms757.f90</a>, the source code;
</li>
<li>
<a href = "toms757.sh">toms757.sh</a>,
commands to compile the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "toms757_prb.f90">toms757_prb.f90</a>,
the sample test code;
</li>
<li>
<a href = "toms757_prb.sh">toms757_prb.sh</a>,
commands to compile the test code;
</li>
<li>
<a href = "toms757_prb_output.txt">toms757_prb_output.txt</a>,
output from a run of the test code;
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>ABRAM0</b> evaluates the Abramowitz function of order 0.
</li>
<li>
<b>ABRAM0_VALUES</b> returns some values of the Abramowitz0 function.
</li>
<li>
<b>ABRAM1</b> evaluates the Abramowitz function of order 1.
</li>
<li>
<b>ABRAM1_VALUES</b> returns some values of the Abramowitz1 function.
</li>
<li>
<b>ABRAM2</b> evaluates the Abramowitz function of order 2.
</li>
<li>
<b>ABRAM2_VALUES</b> returns some values of the Abramowitz2 function.
</li>
<li>
<b>AIRY_AI_INT</b> calculates the integral of the Airy function Ai.
</li>
<li>
<b>AIRY_AI_INT_VALUES</b> returns some values of the integral of the Airy function.
</li>
<li>
<b>AIRY_BI_INT</b> calculates the integral of the Airy function Bi.
</li>
<li>
<b>AIRY_BI_INT_VALUES</b> returns some values of the integral of the Airy function.
</li>
<li>
<b>AIRY_GI</b> computes the modified Airy function Gi(x).
</li>
<li>
<b>AIRY_GI_VALUES</b> returns some values of the Airy Gi function.
</li>
<li>
<b>AIRY_HI</b> computes the modified Airy function Hi(x).
</li>
<li>
<b>AIRY_HI_VALUES</b> returns some values of the Airy Hi function.
</li>
<li>
<b>ARCTAN_INT</b> calculates the inverse tangent integral.
</li>
<li>
<b>ARCTAN_INT_VALUES</b> returns some values of the inverse tangent integral.
</li>
<li>
<b>BESSEL_I0_INT</b> computes the integral of the modified Bessel function I0(X).
</li>
<li>
<b>BESSEL_I0_INT_VALUES</b> returns some values of the Bessel I0 integral.
</li>
<li>
<b>BESSEL_J0_INT</b> calculates the integral of the Bessel function J0.
</li>
<li>
<b>BESSEL_J0_INT_VALUES</b> returns some values of the Bessel J0 integral.
</li>
<li>
<b>BESSEL_K0_INT</b> calculates the integral of the modified Bessel function K0(X).
</li>
<li>
<b>BESSEL_K0_INT_VALUES</b> returns some values of the Bessel K0 integral.
</li>
<li>
<b>BESSEL_Y0_INT</b> calculates the integral of the Bessel function Y0.
</li>
<li>
<b>BESSEL_Y0_INT_VALUES</b> returns some values of the Bessel Y0 integral.
</li>
<li>
<b>CHEVAL</b> evaluates a Chebyshev series.
</li>
<li>
<b>CLAUSEN</b> calculates Clausen's integral.
</li>
<li>
<b>CLAUSEN_VALUES</b> returns some values of the Clausen's integral.
</li>
<li>
<b>DEBYE1</b> calculates the Debye function of order 1.
</li>
<li>
<b>DEBYE1_VALUES</b> returns some values of Debye's function of order 1.
</li>
<li>
<b>DEBYE2</b> calculates the Debye function of order 2.
</li>
<li>
<b>DEBYE2_VALUES</b> returns some values of Debye's function of order 2.
</li>
<li>
<b>DEBYE3</b> calculates the Debye function of order 3.
</li>
<li>
<b>DEBYE3_VALUES</b> returns some values of Debye's function of order 3.
</li>
<li>
<b>DEBYE4</b> calculates the Debye function of order 4.
</li>
<li>
<b>DEBYE4_VALUES</b> returns some values of Debye's function of order 4.
</li>
<li>
<b>EXP3_INT</b> calculates the integral of exp(-t^3).
</li>
<li>
<b>EXP3_INT_VALUES</b> returns some values of the EXP3 integral function.
</li>
<li>
<b>GOODWIN</b> calculates the integral of exp(-t^2/(t+x)).
</li>
<li>
<b>GOODWIN_VALUES</b> returns some values of the Goodwin and Staton function.
</li>
<li>
<b>I0ML0</b> calculates the difference between the Bessel I0 and Struve L0 functions.
</li>
<li>
<b>I0ML0_VALUES</b> returns some values of the I0ML0 function.
</li>
<li>
<b>I1ML1</b> calculates the difference between the Bessel I1 and Struve L1 functions.
</li>
<li>
<b>I1ML1_VALUES</b> returns some values of the I1ML1 function.
</li>
<li>
<b>LOBACHEVSKY</b> calculates the Lobachevsky function.
</li>
<li>
<b>LOBACHEVSKY_VALUES</b> returns some values of the Lobachevsky function.
</li>
<li>
<b>STROMGEN</b> calculates Stromgen's integral.
</li>
<li>
<b>STROMGEN_VALUES</b> returns some values of the Stromgen function.
</li>
<li>
<b>STRUVE_H0</b> calculates the Struve function of order 0.
</li>
<li>
<b>STRUVE_H0_VALUES</b> returns some values of the Struve H0 function.
</li>
<li>
<b>STRUVE_H1</b> calculates the Struve function of order 1.
</li>
<li>
<b>STRUVE_H1_VALUES</b> returns some values of the Struve H1 function.
</li>
<li>
<b>STRUVE_L0</b> calculates the modified Struve function of order 0.
</li>
<li>
<b>STRUVE_L0_VALUES</b> returns some values of the Struve L0 function.
</li>
<li>
<b>STRUVE_L1</b> calculates the modified Struve function of order 1.
</li>
<li>
<b>STRUVE_L1_VALUES</b> returns some values of the Struve L1 function.
</li>
<li>
<b>SYNCH1</b> calculates the synchrotron radiation function.
</li>
<li>
<b>SYNCH1_VALUES</b> returns some values of the synchrotron radiation function.
</li>
<li>
<b>SYNCH2</b> calculates the synchrotron radiation function.
</li>
<li>
<b>SYNCH2_VALUES</b> returns some values of the synchrotron radiation function.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>TIMESTRING</b> writes the current YMDHMS date into a string.
</li>
<li>
<b>TRAN02</b> calculates the transport integral of order 2.
</li>
<li>
<b>TRAN02_VALUES</b> returns some values of the order 2 transportation function.
</li>
<li>
<b>TRAN03</b> calculates the transport integral of order 3.
</li>
<li>
<b>TRAN03_VALUES</b> returns some values of the order 3 transportation function.
</li>
<li>
<b>TRAN04</b> calculates the transport integral of order 4.
</li>
<li>
<b>TRAN04_VALUES</b> returns some values of the order 4 transportation function.
</li>
<li>
<b>TRAN05</b> calculates the transport integral of order 5.
</li>
<li>
<b>TRAN05_VALUES</b> returns some values of the order 5 transportation function.
</li>
<li>
<b>TRAN06</b> calculates the transport integral of order 6.
</li>
<li>
<b>TRAN06_VALUES</b> returns some values of the order 6 transportation function.
</li>
<li>
<b>TRAN07</b> calculates the transport integral of order 7.
</li>
<li>
<b>TRAN07_VALUES</b> returns some values of the order 7 transportation function.
</li>
<li>
<b>TRAN08</b> calculates the transport integral of order 8.
</li>
<li>
<b>TRAN08_VALUES</b> returns some values of the order 8 transportation function.
</li>
<li>
<b>TRAN09</b> calculates the transport integral of order 9.
</li>
<li>
<b>TRAN09_VALUES</b> returns some values of the order 9 transportation function.
</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 03 January 2006.
</i>
<!-- John Burkardt -->
</body>
</html>