|
3146
|
1 /* |
|
|
2 |
|
|
3 Copyright (C) 1996 John W. Eaton |
|
|
4 |
|
|
5 This file is part of Octave. |
|
|
6 |
|
|
7 Octave is free software; you can redistribute it and/or modify it |
|
|
8 under the terms of the GNU General Public License as published by the |
|
|
9 Free Software Foundation; either version 2, or (at your option) any |
|
|
10 later version. |
|
|
11 |
|
|
12 Octave is distributed in the hope that it will be useful, but WITHOUT |
|
|
13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
|
|
14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
|
|
15 for more details. |
|
|
16 |
|
|
17 You should have received a copy of the GNU General Public License |
|
|
18 along with Octave; see the file COPYING. If not, write to the Free |
|
|
19 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
|
|
20 |
|
|
21 */ |
|
|
22 |
|
|
23 #ifdef HAVE_CONFIG_H |
|
|
24 #include <config.h> |
|
|
25 #endif |
|
|
26 |
|
|
27 #include "Range.h" |
|
3220
|
28 #include "CColVector.h" |
|
|
29 #include "CMatrix.h" |
|
|
30 #include "dRowVector.h" |
|
3146
|
31 #include "dMatrix.h" |
|
|
32 #include "f77-fcn.h" |
|
|
33 #include "lo-error.h" |
|
3220
|
34 #include "lo-ieee.h" |
|
|
35 #include "lo-specfun.h" |
|
3146
|
36 #include "mx-inlines.cc" |
|
|
37 |
|
|
38 extern "C" |
|
|
39 { |
|
3887
|
40 int F77_FUNC (zbesj, ZBESJ) (const double&, const double&, |
|
4062
|
41 const double&, const int&, const int&, |
|
|
42 double*, double*, int&, int&); |
|
3146
|
43 |
|
3887
|
44 int F77_FUNC (zbesy, ZBESY) (const double&, const double&, |
|
4062
|
45 const double&, const int&, const int&, |
|
|
46 double*, double*, int&, |
|
|
47 double*, double*, int&); |
|
3220
|
48 |
|
3887
|
49 int F77_FUNC (zbesi, ZBESI) (const double&, const double&, |
|
4062
|
50 const double&, const int&, const int&, |
|
|
51 double*, double*, int&, int&); |
|
3146
|
52 |
|
3887
|
53 int F77_FUNC (zbesk, ZBESK) (const double&, const double&, |
|
4062
|
54 const double&, const int&, const int&, |
|
|
55 double*, double*, int&, int&); |
|
3220
|
56 |
|
3887
|
57 int F77_FUNC (zbesh, ZBESH) (const double&, const double&, |
|
4062
|
58 const double&, const int&, const int&, |
|
|
59 const int&, double*, double*, int&, int&); |
|
3146
|
60 |
|
3887
|
61 int F77_FUNC (zairy, ZAIRY) (const double&, const double&, |
|
4062
|
62 const int&, const int&, |
|
|
63 double&, double&, int&, int&); |
|
3220
|
64 |
|
3887
|
65 int F77_FUNC (zbiry, ZBIRY) (const double&, const double&, |
|
4062
|
66 const int&, const int&, |
|
|
67 double&, double&, int&); |
|
3146
|
68 |
|
3887
|
69 int F77_FUNC (xdacosh, XDACOSH) (const double&, double&); |
|
3146
|
70 |
|
3887
|
71 int F77_FUNC (xdasinh, XDASINH) (const double&, double&); |
|
3146
|
72 |
|
3887
|
73 int F77_FUNC (xdatanh, XDATANH) (const double&, double&); |
|
3146
|
74 |
|
3887
|
75 int F77_FUNC (xderf, XDERF) (const double&, double&); |
|
3146
|
76 |
|
3887
|
77 int F77_FUNC (xderfc, XDERFC) (const double&, double&); |
|
3146
|
78 |
|
3887
|
79 int F77_FUNC (xdbetai, XDBETAI) (const double&, const double&, |
|
4062
|
80 const double&, double&); |
|
3146
|
81 |
|
3887
|
82 int F77_FUNC (xdgamma, XDGAMMA) (const double&, double&); |
|
3146
|
83 |
|
4004
|
84 int F77_FUNC (xgammainc, XGAMMAINC) (const double&, const double&, double&); |
|
3146
|
85 |
|
3887
|
86 int F77_FUNC (dlgams, DLGAMS) (const double&, double&, double&); |
|
3146
|
87 } |
|
|
88 |
|
|
89 #if !defined (HAVE_ACOSH) |
|
|
90 double |
|
|
91 acosh (double x) |
|
|
92 { |
|
|
93 double retval; |
|
|
94 F77_XFCN (dacosh, DACOSH, (x, retval)); |
|
|
95 return retval; |
|
|
96 } |
|
|
97 #endif |
|
|
98 |
|
|
99 #if !defined (HAVE_ASINH) |
|
|
100 double |
|
|
101 asinh (double x) |
|
|
102 { |
|
|
103 double retval; |
|
|
104 F77_XFCN (dasinh, DASINH, (x, retval)); |
|
|
105 return retval; |
|
|
106 } |
|
|
107 #endif |
|
|
108 |
|
|
109 #if !defined (HAVE_ATANH) |
|
|
110 double |
|
|
111 atanh (double x) |
|
|
112 { |
|
|
113 double retval; |
|
|
114 F77_XFCN (datanh, DATANH, (x, retval)); |
|
|
115 return retval; |
|
|
116 } |
|
|
117 #endif |
|
|
118 |
|
|
119 #if !defined (HAVE_ERF) |
|
|
120 double |
|
|
121 erf (double x) |
|
|
122 { |
|
|
123 double retval; |
|
|
124 F77_XFCN (derf, DERF, (x, retval)); |
|
|
125 return retval; |
|
|
126 } |
|
|
127 #endif |
|
|
128 |
|
|
129 #if !defined (HAVE_ERFC) |
|
|
130 double |
|
|
131 erfc (double x) |
|
|
132 { |
|
|
133 double retval; |
|
|
134 F77_XFCN (derfc, DERFC, (x, retval)); |
|
|
135 return retval; |
|
|
136 } |
|
|
137 #endif |
|
|
138 |
|
|
139 double |
|
3156
|
140 xgamma (double x) |
|
3146
|
141 { |
|
3156
|
142 double result; |
|
|
143 F77_XFCN (xdgamma, XDGAMMA, (x, result)); |
|
|
144 return result; |
|
3146
|
145 } |
|
|
146 |
|
|
147 double |
|
3156
|
148 xlgamma (double x) |
|
3146
|
149 { |
|
3156
|
150 double result; |
|
3146
|
151 double sgngam; |
|
3156
|
152 F77_XFCN (dlgams, DLGAMS, (x, result, sgngam)); |
|
|
153 return result; |
|
3146
|
154 } |
|
|
155 |
|
3220
|
156 static inline Complex |
|
|
157 zbesj (const Complex& z, double alpha, int kode, int& ierr); |
|
|
158 |
|
|
159 static inline Complex |
|
|
160 zbesy (const Complex& z, double alpha, int kode, int& ierr); |
|
|
161 |
|
|
162 static inline Complex |
|
|
163 zbesi (const Complex& z, double alpha, int kode, int& ierr); |
|
|
164 |
|
|
165 static inline Complex |
|
|
166 zbesk (const Complex& z, double alpha, int kode, int& ierr); |
|
|
167 |
|
|
168 static inline Complex |
|
|
169 zbesh1 (const Complex& z, double alpha, int kode, int& ierr); |
|
|
170 |
|
|
171 static inline Complex |
|
|
172 zbesh2 (const Complex& z, double alpha, int kode, int& ierr); |
|
|
173 |
|
|
174 static inline Complex |
|
|
175 bessel_return_value (const Complex& val, int ierr) |
|
3146
|
176 { |
|
3220
|
177 static const Complex inf_val = Complex (octave_Inf, octave_Inf); |
|
|
178 static const Complex nan_val = Complex (octave_NaN, octave_NaN); |
|
|
179 |
|
|
180 Complex retval; |
|
|
181 |
|
|
182 switch (ierr) |
|
|
183 { |
|
|
184 case 0: |
|
|
185 case 3: |
|
|
186 retval = val; |
|
|
187 break; |
|
|
188 |
|
|
189 case 2: |
|
|
190 retval = inf_val; |
|
|
191 break; |
|
|
192 |
|
|
193 default: |
|
|
194 retval = nan_val; |
|
|
195 break; |
|
|
196 } |
|
|
197 |
|
3146
|
198 return retval; |
|
|
199 } |
|
|
200 |
|
3220
|
201 static inline Complex |
|
|
202 zbesj (const Complex& z, double alpha, int kode, int& ierr) |
|
3146
|
203 { |
|
3220
|
204 Complex retval; |
|
|
205 |
|
|
206 if (alpha >= 0.0) |
|
|
207 { |
|
|
208 double yr = 0.0; |
|
|
209 double yi = 0.0; |
|
|
210 |
|
|
211 int nz; |
|
|
212 |
|
|
213 double zr = z.real (); |
|
|
214 double zi = z.imag (); |
|
|
215 |
|
3887
|
216 F77_FUNC (zbesj, ZBESJ) (zr, zi, alpha, kode, 1, &yr, &yi, nz, ierr); |
|
3220
|
217 |
|
|
218 if (zi == 0.0 && zr > 0.0) |
|
|
219 yi = 0.0; |
|
|
220 |
|
|
221 retval = bessel_return_value (Complex (yr, yi), ierr); |
|
|
222 } |
|
|
223 else |
|
|
224 { |
|
|
225 alpha = -alpha; |
|
|
226 |
|
|
227 Complex tmp = cos (M_PI * alpha) * zbesj (z, alpha, kode, ierr); |
|
|
228 |
|
|
229 if (ierr == 0 || ierr == 3) |
|
|
230 { |
|
|
231 tmp -= sin (M_PI * alpha) * zbesy (z, alpha, kode, ierr); |
|
|
232 |
|
|
233 retval = bessel_return_value (tmp, ierr); |
|
|
234 } |
|
|
235 else |
|
|
236 retval = Complex (octave_NaN, octave_NaN); |
|
|
237 } |
|
|
238 |
|
3146
|
239 return retval; |
|
|
240 } |
|
|
241 |
|
3220
|
242 static inline Complex |
|
|
243 zbesy (const Complex& z, double alpha, int kode, int& ierr) |
|
3146
|
244 { |
|
3220
|
245 Complex retval; |
|
3146
|
246 |
|
|
247 if (alpha >= 0.0) |
|
|
248 { |
|
3220
|
249 double yr = 0.0; |
|
|
250 double yi = 0.0; |
|
|
251 |
|
|
252 int nz; |
|
|
253 |
|
|
254 double wr, wi; |
|
3146
|
255 |
|
3220
|
256 double zr = z.real (); |
|
|
257 double zi = z.imag (); |
|
|
258 |
|
|
259 ierr = 0; |
|
|
260 |
|
|
261 if (zr == 0.0 && zi == 0.0) |
|
3146
|
262 { |
|
3220
|
263 yr = -octave_Inf; |
|
|
264 yi = 0.0; |
|
|
265 } |
|
|
266 else |
|
|
267 { |
|
3887
|
268 F77_FUNC (zbesy, ZBESY) (zr, zi, alpha, kode, 1, &yr, &yi, nz, |
|
3220
|
269 &wr, &wi, ierr); |
|
|
270 |
|
|
271 if (zi == 0.0 && zr > 0.0) |
|
|
272 yi = 0.0; |
|
3146
|
273 } |
|
|
274 |
|
3220
|
275 return bessel_return_value (Complex (yr, yi), ierr); |
|
|
276 } |
|
|
277 else |
|
|
278 { |
|
|
279 alpha = -alpha; |
|
3146
|
280 |
|
3220
|
281 Complex tmp = cos (M_PI * alpha) * zbesy (z, alpha, kode, ierr); |
|
3146
|
282 |
|
3220
|
283 if (ierr == 0 || ierr == 3) |
|
3146
|
284 { |
|
3220
|
285 tmp += sin (M_PI * alpha) * zbesj (z, alpha, kode, ierr); |
|
|
286 |
|
|
287 retval = bessel_return_value (tmp, ierr); |
|
|
288 } |
|
|
289 else |
|
|
290 retval = Complex (octave_NaN, octave_NaN); |
|
|
291 } |
|
|
292 |
|
|
293 return retval; |
|
|
294 } |
|
|
295 |
|
|
296 static inline Complex |
|
|
297 zbesi (const Complex& z, double alpha, int kode, int& ierr) |
|
|
298 { |
|
|
299 Complex retval; |
|
3146
|
300 |
|
3220
|
301 if (alpha >= 0.0) |
|
|
302 { |
|
|
303 double yr = 0.0; |
|
|
304 double yi = 0.0; |
|
|
305 |
|
|
306 int nz; |
|
3146
|
307 |
|
3220
|
308 double zr = z.real (); |
|
|
309 double zi = z.imag (); |
|
|
310 |
|
3887
|
311 F77_FUNC (zbesi, ZBESI) (zr, zi, alpha, kode, 1, &yr, &yi, nz, ierr); |
|
3146
|
312 |
|
3220
|
313 if (zi == 0.0 && zr > 0.0) |
|
|
314 yi = 0.0; |
|
|
315 |
|
|
316 retval = bessel_return_value (Complex (yr, yi), ierr); |
|
3146
|
317 } |
|
|
318 else |
|
3220
|
319 { |
|
|
320 alpha = -alpha; |
|
|
321 |
|
|
322 Complex tmp = zbesi (z, alpha, kode, ierr); |
|
|
323 |
|
|
324 if (ierr == 0 || ierr == 3) |
|
|
325 { |
|
|
326 tmp += (2.0 / M_PI) * sin (M_PI * alpha) |
|
|
327 * zbesk (z, alpha, kode, ierr); |
|
|
328 |
|
|
329 retval = bessel_return_value (tmp, ierr); |
|
|
330 } |
|
|
331 else |
|
|
332 retval = Complex (octave_NaN, octave_NaN); |
|
|
333 } |
|
|
334 |
|
|
335 return retval; |
|
|
336 } |
|
|
337 |
|
|
338 static inline Complex |
|
|
339 zbesk (const Complex& z, double alpha, int kode, int& ierr) |
|
|
340 { |
|
|
341 Complex retval; |
|
|
342 |
|
|
343 if (alpha >= 0.0) |
|
|
344 { |
|
|
345 double yr = 0.0; |
|
|
346 double yi = 0.0; |
|
|
347 |
|
|
348 int nz; |
|
|
349 |
|
|
350 double zr = z.real (); |
|
|
351 double zi = z.imag (); |
|
|
352 |
|
|
353 ierr = 0; |
|
|
354 |
|
|
355 if (zr == 0.0 && zi == 0.0) |
|
|
356 { |
|
|
357 yr = octave_Inf; |
|
|
358 yi = 0.0; |
|
|
359 } |
|
|
360 else |
|
|
361 { |
|
3887
|
362 F77_FUNC (zbesk, ZBESK) (zr, zi, alpha, kode, 1, &yr, &yi, nz, ierr); |
|
3220
|
363 |
|
|
364 if (zi == 0.0 && zr > 0.0) |
|
|
365 yi = 0.0; |
|
|
366 } |
|
|
367 |
|
|
368 retval = bessel_return_value (Complex (yr, yi), ierr); |
|
|
369 } |
|
|
370 else |
|
|
371 { |
|
|
372 Complex tmp = zbesk (z, -alpha, kode, ierr); |
|
|
373 |
|
|
374 retval = bessel_return_value (tmp, ierr); |
|
|
375 } |
|
3146
|
376 |
|
|
377 return retval; |
|
|
378 } |
|
|
379 |
|
3220
|
380 static inline Complex |
|
|
381 zbesh1 (const Complex& z, double alpha, int kode, int& ierr) |
|
3146
|
382 { |
|
3220
|
383 Complex retval; |
|
3146
|
384 |
|
3220
|
385 if (alpha >= 0.0) |
|
3146
|
386 { |
|
3220
|
387 double yr = 0.0; |
|
|
388 double yi = 0.0; |
|
|
389 |
|
|
390 int nz; |
|
|
391 |
|
|
392 double zr = z.real (); |
|
|
393 double zi = z.imag (); |
|
3146
|
394 |
|
3887
|
395 F77_FUNC (zbesh, ZBESH) (zr, zi, alpha, kode, 1, 1, &yr, &yi, nz, ierr); |
|
3146
|
396 |
|
3220
|
397 retval = bessel_return_value (Complex (yr, yi), ierr); |
|
|
398 } |
|
|
399 else |
|
|
400 { |
|
|
401 alpha = -alpha; |
|
|
402 |
|
|
403 static const Complex eye = Complex (0.0, 1.0); |
|
3146
|
404 |
|
3220
|
405 Complex tmp = exp (M_PI * alpha * eye) * zbesh1 (z, alpha, kode, ierr); |
|
3146
|
406 |
|
3220
|
407 retval = bessel_return_value (tmp, ierr); |
|
|
408 } |
|
3146
|
409 |
|
3220
|
410 return retval; |
|
|
411 } |
|
3146
|
412 |
|
3220
|
413 static inline Complex |
|
|
414 zbesh2 (const Complex& z, double alpha, int kode, int& ierr) |
|
|
415 { |
|
|
416 Complex retval; |
|
3146
|
417 |
|
3220
|
418 if (alpha >= 0.0) |
|
|
419 { |
|
|
420 double yr = 0.0; |
|
|
421 double yi = 0.0; |
|
|
422 |
|
|
423 int nz; |
|
3146
|
424 |
|
3220
|
425 double zr = z.real (); |
|
|
426 double zi = z.imag (); |
|
3146
|
427 |
|
3887
|
428 F77_FUNC (zbesh, ZBESH) (zr, zi, alpha, kode, 2, 1, &yr, &yi, nz, ierr); |
|
3220
|
429 |
|
|
430 retval = bessel_return_value (Complex (yr, yi), ierr); |
|
3146
|
431 } |
|
|
432 else |
|
3220
|
433 { |
|
|
434 alpha = -alpha; |
|
|
435 |
|
|
436 static const Complex eye = Complex (0.0, 1.0); |
|
|
437 |
|
|
438 Complex tmp = exp (-M_PI * alpha * eye) * zbesh2 (z, alpha, kode, ierr); |
|
|
439 |
|
|
440 retval = bessel_return_value (tmp, ierr); |
|
|
441 } |
|
|
442 |
|
|
443 return retval; |
|
|
444 } |
|
|
445 |
|
|
446 typedef Complex (*fptr) (const Complex&, double, int, int&); |
|
|
447 |
|
|
448 static inline Complex |
|
|
449 do_bessel (fptr f, const char *, double alpha, const Complex& x, |
|
|
450 bool scaled, int& ierr) |
|
|
451 { |
|
|
452 Complex retval; |
|
|
453 |
|
|
454 retval = f (x, alpha, (scaled ? 2 : 1), ierr); |
|
|
455 |
|
|
456 return retval; |
|
|
457 } |
|
|
458 |
|
|
459 static inline ComplexMatrix |
|
|
460 do_bessel (fptr f, const char *, double alpha, const ComplexMatrix& x, |
|
|
461 bool scaled, Array2<int>& ierr) |
|
|
462 { |
|
|
463 int nr = x.rows (); |
|
|
464 int nc = x.cols (); |
|
|
465 |
|
|
466 ComplexMatrix retval (nr, nc); |
|
|
467 |
|
|
468 ierr.resize (nr, nc); |
|
|
469 |
|
|
470 for (int j = 0; j < nc; j++) |
|
|
471 for (int i = 0; i < nr; i++) |
|
|
472 retval(i,j) = f (x(i,j), alpha, (scaled ? 2 : 1), ierr(i,j)); |
|
|
473 |
|
|
474 return retval; |
|
|
475 } |
|
|
476 |
|
|
477 static inline ComplexMatrix |
|
|
478 do_bessel (fptr f, const char *, const Matrix& alpha, const Complex& x, |
|
|
479 bool scaled, Array2<int>& ierr) |
|
|
480 { |
|
|
481 int nr = alpha.rows (); |
|
|
482 int nc = alpha.cols (); |
|
|
483 |
|
|
484 ComplexMatrix retval (nr, nc); |
|
|
485 |
|
|
486 ierr.resize (nr, nc); |
|
|
487 |
|
|
488 for (int j = 0; j < nc; j++) |
|
|
489 for (int i = 0; i < nr; i++) |
|
|
490 retval(i,j) = f (x, alpha(i,j), (scaled ? 2 : 1), ierr(i,j)); |
|
3146
|
491 |
|
|
492 return retval; |
|
|
493 } |
|
|
494 |
|
3220
|
495 static inline ComplexMatrix |
|
|
496 do_bessel (fptr f, const char *fn, const Matrix& alpha, |
|
|
497 const ComplexMatrix& x, bool scaled, Array2<int>& ierr) |
|
3146
|
498 { |
|
3220
|
499 ComplexMatrix retval; |
|
|
500 |
|
|
501 int x_nr = x.rows (); |
|
|
502 int x_nc = x.cols (); |
|
|
503 |
|
|
504 int alpha_nr = alpha.rows (); |
|
|
505 int alpha_nc = alpha.cols (); |
|
|
506 |
|
|
507 if (x_nr == alpha_nr && x_nc == alpha_nc) |
|
|
508 { |
|
|
509 int nr = x_nr; |
|
|
510 int nc = x_nc; |
|
|
511 |
|
|
512 retval.resize (nr, nc); |
|
|
513 |
|
|
514 ierr.resize (nr, nc); |
|
|
515 |
|
|
516 for (int j = 0; j < nc; j++) |
|
|
517 for (int i = 0; i < nr; i++) |
|
|
518 retval(i,j) = f (x(i,j), alpha(i,j), (scaled ? 2 : 1), ierr(i,j)); |
|
|
519 } |
|
|
520 else |
|
|
521 (*current_liboctave_error_handler) |
|
|
522 ("%s: the sizes of alpha and x must conform", fn); |
|
|
523 |
|
|
524 return retval; |
|
3146
|
525 } |
|
|
526 |
|
3220
|
527 static inline ComplexMatrix |
|
|
528 do_bessel (fptr f, const char *, const RowVector& alpha, |
|
|
529 const ComplexColumnVector& x, bool scaled, Array2<int>& ierr) |
|
3146
|
530 { |
|
3220
|
531 int nr = x.length (); |
|
|
532 int nc = alpha.length (); |
|
|
533 |
|
|
534 ComplexMatrix retval (nr, nc); |
|
3146
|
535 |
|
3220
|
536 ierr.resize (nr, nc); |
|
|
537 |
|
|
538 for (int j = 0; j < nc; j++) |
|
|
539 for (int i = 0; i < nr; i++) |
|
|
540 retval(i,j) = f (x(i), alpha(j), (scaled ? 2 : 1), ierr(i,j)); |
|
|
541 |
|
|
542 return retval; |
|
3146
|
543 } |
|
|
544 |
|
3220
|
545 #define SS_BESSEL(name, fcn) \ |
|
|
546 Complex \ |
|
|
547 name (double alpha, const Complex& x, bool scaled, int& ierr) \ |
|
|
548 { \ |
|
|
549 return do_bessel (fcn, #name, alpha, x, scaled, ierr); \ |
|
|
550 } |
|
|
551 |
|
|
552 #define SM_BESSEL(name, fcn) \ |
|
|
553 ComplexMatrix \ |
|
|
554 name (double alpha, const ComplexMatrix& x, bool scaled, \ |
|
|
555 Array2<int>& ierr) \ |
|
|
556 { \ |
|
|
557 return do_bessel (fcn, #name, alpha, x, scaled, ierr); \ |
|
|
558 } |
|
|
559 |
|
|
560 #define MS_BESSEL(name, fcn) \ |
|
|
561 ComplexMatrix \ |
|
|
562 name (const Matrix& alpha, const Complex& x, bool scaled, \ |
|
|
563 Array2<int>& ierr) \ |
|
|
564 { \ |
|
|
565 return do_bessel (fcn, #name, alpha, x, scaled, ierr); \ |
|
|
566 } |
|
|
567 |
|
|
568 #define MM_BESSEL(name, fcn) \ |
|
|
569 ComplexMatrix \ |
|
|
570 name (const Matrix& alpha, const ComplexMatrix& x, bool scaled, \ |
|
|
571 Array2<int>& ierr) \ |
|
|
572 { \ |
|
|
573 return do_bessel (fcn, #name, alpha, x, scaled, ierr); \ |
|
|
574 } |
|
|
575 |
|
|
576 #define RC_BESSEL(name, fcn) \ |
|
|
577 ComplexMatrix \ |
|
|
578 name (const RowVector& alpha, const ComplexColumnVector& x, bool scaled, \ |
|
|
579 Array2<int>& ierr) \ |
|
|
580 { \ |
|
|
581 return do_bessel (fcn, #name, alpha, x, scaled, ierr); \ |
|
|
582 } |
|
|
583 |
|
|
584 #define ALL_BESSEL(name, fcn) \ |
|
|
585 SS_BESSEL (name, fcn) \ |
|
|
586 SM_BESSEL (name, fcn) \ |
|
|
587 MS_BESSEL (name, fcn) \ |
|
|
588 MM_BESSEL (name, fcn) \ |
|
|
589 RC_BESSEL (name, fcn) |
|
|
590 |
|
|
591 ALL_BESSEL (besselj, zbesj) |
|
|
592 ALL_BESSEL (bessely, zbesy) |
|
|
593 ALL_BESSEL (besseli, zbesi) |
|
|
594 ALL_BESSEL (besselk, zbesk) |
|
|
595 ALL_BESSEL (besselh1, zbesh1) |
|
|
596 ALL_BESSEL (besselh2, zbesh2) |
|
|
597 |
|
|
598 Complex |
|
|
599 airy (const Complex& z, bool deriv, bool scaled, int& ierr) |
|
3146
|
600 { |
|
3220
|
601 double ar = 0.0; |
|
|
602 double ai = 0.0; |
|
|
603 |
|
|
604 int nz; |
|
|
605 |
|
|
606 double zr = z.real (); |
|
|
607 double zi = z.imag (); |
|
3146
|
608 |
|
3220
|
609 int id = deriv ? 1 : 0; |
|
|
610 |
|
|
611 int kode = scaled ? 2 : 1; |
|
|
612 |
|
3887
|
613 F77_FUNC (zairy, ZAIRY) (zr, zi, id, kode, ar, ai, nz, ierr); |
|
3220
|
614 |
|
3225
|
615 if (zi == 0.0 && (! scaled || zr > 0.0)) |
|
|
616 ai = 0.0; |
|
|
617 |
|
3220
|
618 return bessel_return_value (Complex (ar, ai), ierr); |
|
3146
|
619 } |
|
|
620 |
|
3220
|
621 Complex |
|
|
622 biry (const Complex& z, bool deriv, bool scaled, int& ierr) |
|
3146
|
623 { |
|
3220
|
624 double ar = 0.0; |
|
|
625 double ai = 0.0; |
|
|
626 |
|
|
627 double zr = z.real (); |
|
|
628 double zi = z.imag (); |
|
|
629 |
|
|
630 int id = deriv ? 1 : 0; |
|
|
631 |
|
|
632 int kode = scaled ? 2 : 1; |
|
|
633 |
|
3887
|
634 F77_FUNC (zbiry, ZBIRY) (zr, zi, id, kode, ar, ai, ierr); |
|
3220
|
635 |
|
3225
|
636 if (zi == 0.0 && (! scaled || zr > 0.0)) |
|
|
637 ai = 0.0; |
|
|
638 |
|
3220
|
639 return bessel_return_value (Complex (ar, ai), ierr); |
|
3146
|
640 } |
|
|
641 |
|
3220
|
642 ComplexMatrix |
|
|
643 airy (const ComplexMatrix& z, bool deriv, bool scaled, Array2<int>& ierr) |
|
3146
|
644 { |
|
3220
|
645 int nr = z.rows (); |
|
|
646 int nc = z.cols (); |
|
|
647 |
|
|
648 ComplexMatrix retval (nr, nc); |
|
|
649 |
|
|
650 ierr.resize (nr, nc); |
|
|
651 |
|
|
652 for (int j = 0; j < nc; j++) |
|
|
653 for (int i = 0; i < nr; i++) |
|
|
654 retval(i,j) = airy (z(i,j), deriv, scaled, ierr(i,j)); |
|
|
655 |
|
|
656 return retval; |
|
3146
|
657 } |
|
|
658 |
|
3220
|
659 ComplexMatrix |
|
|
660 biry (const ComplexMatrix& z, bool deriv, bool scaled, Array2<int>& ierr) |
|
3146
|
661 { |
|
3220
|
662 int nr = z.rows (); |
|
|
663 int nc = z.cols (); |
|
|
664 |
|
|
665 ComplexMatrix retval (nr, nc); |
|
|
666 |
|
|
667 ierr.resize (nr, nc); |
|
|
668 |
|
|
669 for (int j = 0; j < nc; j++) |
|
|
670 for (int i = 0; i < nr; i++) |
|
|
671 retval(i,j) = biry (z(i,j), deriv, scaled, ierr(i,j)); |
|
|
672 |
|
|
673 return retval; |
|
3146
|
674 } |
|
|
675 |
|
|
676 static void |
|
|
677 gripe_betainc_nonconformant (int r1, int c1, int r2, int c2, int r3, |
|
|
678 int c3) |
|
|
679 { |
|
|
680 (*current_liboctave_error_handler) |
|
|
681 ("betainc: nonconformant arguments (x is %dx%d, a is %dx%d, b is %dx%d)", |
|
|
682 r1, c1, r2, c2, r3, c3); |
|
|
683 } |
|
|
684 |
|
|
685 double |
|
|
686 betainc (double x, double a, double b) |
|
|
687 { |
|
|
688 double retval; |
|
|
689 F77_XFCN (xdbetai, XDBETAI, (x, a, b, retval)); |
|
|
690 return retval; |
|
|
691 } |
|
|
692 |
|
|
693 Matrix |
|
|
694 betainc (double x, double a, const Matrix& b) |
|
|
695 { |
|
|
696 int nr = b.rows (); |
|
|
697 int nc = b.cols (); |
|
|
698 |
|
|
699 Matrix retval (nr, nc); |
|
|
700 |
|
|
701 for (int j = 0; j < nc; j++) |
|
|
702 for (int i = 0; i < nr; i++) |
|
|
703 retval(i,j) = betainc (x, a, b(i,j)); |
|
|
704 |
|
|
705 return retval; |
|
|
706 } |
|
|
707 |
|
|
708 Matrix |
|
|
709 betainc (double x, const Matrix& a, double b) |
|
|
710 { |
|
|
711 int nr = a.rows (); |
|
|
712 int nc = a.cols (); |
|
|
713 |
|
|
714 Matrix retval (nr, nc); |
|
|
715 |
|
|
716 for (int j = 0; j < nc; j++) |
|
|
717 for (int i = 0; i < nr; i++) |
|
|
718 retval(i,j) = betainc (x, a(i,j), b); |
|
|
719 |
|
|
720 return retval; |
|
|
721 } |
|
|
722 |
|
|
723 Matrix |
|
|
724 betainc (double x, const Matrix& a, const Matrix& b) |
|
|
725 { |
|
|
726 Matrix retval; |
|
|
727 |
|
|
728 int a_nr = a.rows (); |
|
|
729 int a_nc = a.cols (); |
|
|
730 |
|
|
731 int b_nr = b.rows (); |
|
|
732 int b_nc = b.cols (); |
|
|
733 |
|
|
734 if (a_nr == b_nr && a_nc == b_nc) |
|
|
735 { |
|
|
736 retval.resize (a_nr, a_nc); |
|
|
737 |
|
|
738 for (int j = 0; j < a_nc; j++) |
|
|
739 for (int i = 0; i < a_nr; i++) |
|
|
740 retval(i,j) = betainc (x, a(i,j), b(i,j)); |
|
|
741 } |
|
|
742 else |
|
|
743 gripe_betainc_nonconformant (1, 1, a_nr, a_nc, b_nr, b_nc); |
|
|
744 |
|
|
745 return retval; |
|
|
746 } |
|
|
747 |
|
|
748 Matrix |
|
|
749 betainc (const Matrix& x, double a, double b) |
|
|
750 { |
|
|
751 int nr = x.rows (); |
|
|
752 int nc = x.cols (); |
|
|
753 |
|
|
754 Matrix retval (nr, nc); |
|
|
755 |
|
|
756 for (int j = 0; j < nc; j++) |
|
|
757 for (int i = 0; i < nr; i++) |
|
|
758 retval(i,j) = betainc (x(i,j), a, b); |
|
|
759 |
|
|
760 return retval; |
|
|
761 } |
|
|
762 |
|
|
763 Matrix |
|
|
764 betainc (const Matrix& x, double a, const Matrix& b) |
|
|
765 { |
|
|
766 Matrix retval; |
|
|
767 |
|
|
768 int nr = x.rows (); |
|
|
769 int nc = x.cols (); |
|
|
770 |
|
|
771 int b_nr = b.rows (); |
|
|
772 int b_nc = b.cols (); |
|
|
773 |
|
|
774 if (nr == b_nr && nc == b_nc) |
|
|
775 { |
|
|
776 retval.resize (nr, nc); |
|
|
777 |
|
|
778 for (int j = 0; j < nc; j++) |
|
|
779 for (int i = 0; i < nr; i++) |
|
|
780 retval(i,j) = betainc (x(i,j), a, b(i,j)); |
|
|
781 } |
|
|
782 else |
|
|
783 gripe_betainc_nonconformant (nr, nc, 1, 1, b_nr, b_nc); |
|
|
784 |
|
|
785 return retval; |
|
|
786 } |
|
|
787 |
|
|
788 Matrix |
|
|
789 betainc (const Matrix& x, const Matrix& a, double b) |
|
|
790 { |
|
|
791 Matrix retval; |
|
|
792 |
|
|
793 int nr = x.rows (); |
|
|
794 int nc = x.cols (); |
|
|
795 |
|
|
796 int a_nr = a.rows (); |
|
|
797 int a_nc = a.cols (); |
|
|
798 |
|
|
799 if (nr == a_nr && nc == a_nc) |
|
|
800 { |
|
|
801 retval.resize (nr, nc); |
|
|
802 |
|
|
803 for (int j = 0; j < nc; j++) |
|
|
804 for (int i = 0; i < nr; i++) |
|
|
805 retval(i,j) = betainc (x(i,j), a(i,j), b); |
|
|
806 } |
|
|
807 else |
|
|
808 gripe_betainc_nonconformant (nr, nc, a_nr, a_nc, 1, 1); |
|
|
809 |
|
|
810 return retval; |
|
|
811 } |
|
|
812 |
|
|
813 Matrix |
|
|
814 betainc (const Matrix& x, const Matrix& a, const Matrix& b) |
|
|
815 { |
|
|
816 Matrix retval; |
|
|
817 |
|
|
818 int nr = x.rows (); |
|
|
819 int nc = x.cols (); |
|
|
820 |
|
|
821 int a_nr = a.rows (); |
|
|
822 int a_nc = a.cols (); |
|
|
823 |
|
|
824 int b_nr = b.rows (); |
|
|
825 int b_nc = b.cols (); |
|
|
826 |
|
|
827 if (nr == a_nr && nr == b_nr && nc == a_nc && nc == b_nc) |
|
|
828 { |
|
|
829 retval.resize (nr, nc); |
|
|
830 |
|
|
831 for (int j = 0; j < nc; j++) |
|
|
832 for (int i = 0; i < nr; i++) |
|
|
833 retval(i,j) = betainc (x(i,j), a(i,j), b(i,j)); |
|
|
834 } |
|
|
835 else |
|
|
836 gripe_betainc_nonconformant (nr, nc, a_nr, a_nc, b_nr, b_nc); |
|
|
837 |
|
|
838 return retval; |
|
|
839 } |
|
|
840 |
|
3164
|
841 // XXX FIXME XXX -- there is still room for improvement here... |
|
|
842 |
|
3146
|
843 double |
|
4004
|
844 gammainc (double x, double a, bool& err) |
|
3146
|
845 { |
|
|
846 double retval; |
|
3164
|
847 |
|
4004
|
848 err = false; |
|
3164
|
849 |
|
4004
|
850 if (a < 0.0 || x < 0.0) |
|
|
851 { |
|
|
852 (*current_liboctave_error_handler) |
|
|
853 ("gammainc: A and X must be non-negative"); |
|
|
854 |
|
|
855 err = true; |
|
|
856 } |
|
|
857 else |
|
|
858 F77_XFCN (xgammainc, XGAMMAINC, (a, x, retval)); |
|
3164
|
859 |
|
3146
|
860 return retval; |
|
|
861 } |
|
|
862 |
|
|
863 Matrix |
|
|
864 gammainc (double x, const Matrix& a) |
|
|
865 { |
|
|
866 int nr = a.rows (); |
|
|
867 int nc = a.cols (); |
|
|
868 |
|
4004
|
869 Matrix result (nr, nc); |
|
|
870 Matrix retval; |
|
|
871 |
|
|
872 bool err; |
|
3146
|
873 |
|
|
874 for (int j = 0; j < nc; j++) |
|
|
875 for (int i = 0; i < nr; i++) |
|
4004
|
876 { |
|
|
877 result(i,j) = gammainc (x, a(i,j), err); |
|
|
878 |
|
|
879 if (err) |
|
|
880 goto done; |
|
|
881 } |
|
|
882 |
|
|
883 retval = result; |
|
|
884 |
|
|
885 done: |
|
3146
|
886 |
|
|
887 return retval; |
|
|
888 } |
|
|
889 |
|
|
890 Matrix |
|
|
891 gammainc (const Matrix& x, double a) |
|
|
892 { |
|
|
893 int nr = x.rows (); |
|
|
894 int nc = x.cols (); |
|
|
895 |
|
4004
|
896 Matrix result (nr, nc); |
|
|
897 Matrix retval; |
|
|
898 |
|
|
899 bool err; |
|
3146
|
900 |
|
|
901 for (int j = 0; j < nc; j++) |
|
|
902 for (int i = 0; i < nr; i++) |
|
4004
|
903 { |
|
|
904 result(i,j) = gammainc (x(i,j), a, err); |
|
|
905 |
|
|
906 if (err) |
|
|
907 goto done; |
|
|
908 } |
|
|
909 |
|
|
910 retval = result; |
|
|
911 |
|
|
912 done: |
|
3146
|
913 |
|
|
914 return retval; |
|
|
915 } |
|
|
916 |
|
|
917 Matrix |
|
|
918 gammainc (const Matrix& x, const Matrix& a) |
|
|
919 { |
|
4004
|
920 Matrix result; |
|
3146
|
921 Matrix retval; |
|
|
922 |
|
|
923 int nr = x.rows (); |
|
|
924 int nc = x.cols (); |
|
|
925 |
|
|
926 int a_nr = a.rows (); |
|
|
927 int a_nc = a.cols (); |
|
|
928 |
|
|
929 if (nr == a_nr && nc == a_nc) |
|
|
930 { |
|
4004
|
931 result.resize (nr, nc); |
|
|
932 |
|
|
933 bool err; |
|
3146
|
934 |
|
|
935 for (int j = 0; j < nc; j++) |
|
|
936 for (int i = 0; i < nr; i++) |
|
4004
|
937 { |
|
|
938 result(i,j) = gammainc (x(i,j), a(i,j), err); |
|
|
939 |
|
|
940 if (err) |
|
|
941 goto done; |
|
|
942 } |
|
|
943 |
|
|
944 retval = result; |
|
3146
|
945 } |
|
|
946 else |
|
|
947 (*current_liboctave_error_handler) |
|
|
948 ("gammainc: nonconformant arguments (arg 1 is %dx%d, arg 2 is %dx%d)", |
|
|
949 nr, nc, a_nr, a_nc); |
|
|
950 |
|
4004
|
951 done: |
|
|
952 |
|
3146
|
953 return retval; |
|
|
954 } |
|
|
955 |
|
|
956 /* |
|
|
957 ;;; Local Variables: *** |
|
|
958 ;;; mode: C++ *** |
|
|
959 ;;; End: *** |
|
|
960 */ |
