|
1
|
1 // xpow.cc -*- C++ -*- |
|
|
2 /* |
|
|
3 |
|
1009
|
4 Copyright (C) 1992, 1993, 1994, 1995 John W. Eaton |
|
1
|
5 |
|
|
6 This file is part of Octave. |
|
|
7 |
|
|
8 Octave is free software; you can redistribute it and/or modify it |
|
|
9 under the terms of the GNU General Public License as published by the |
|
|
10 Free Software Foundation; either version 2, or (at your option) any |
|
|
11 later version. |
|
|
12 |
|
|
13 Octave is distributed in the hope that it will be useful, but WITHOUT |
|
|
14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
|
|
15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
|
|
16 for more details. |
|
|
17 |
|
|
18 You should have received a copy of the GNU General Public License |
|
|
19 along with Octave; see the file COPYING. If not, write to the Free |
|
1315
|
20 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
|
1
|
21 |
|
|
22 */ |
|
|
23 |
|
240
|
24 #ifdef HAVE_CONFIG_H |
|
1192
|
25 #include <config.h> |
|
1
|
26 #endif |
|
|
27 |
|
|
28 #include <assert.h> |
|
164
|
29 #include <Complex.h> |
|
|
30 |
|
|
31 #include "xpow.h" |
|
453
|
32 #include "dMatrix.h" |
|
|
33 #include "CMatrix.h" |
|
|
34 #include "dDiagMatrix.h" |
|
|
35 #include "CDiagMatrix.h" |
|
|
36 #include "CColVector.h" |
|
|
37 #include "EIG.h" |
|
164
|
38 #include "tree-const.h" |
|
1
|
39 #include "error.h" |
|
|
40 |
|
|
41 // This function also appears in tree-const.cc. Maybe it should be a |
|
|
42 // member function of the Matrix class. |
|
|
43 |
|
|
44 static int |
|
|
45 any_element_is_negative (const Matrix& a) |
|
|
46 { |
|
|
47 int nr = a.rows (); |
|
|
48 int nc = a.columns (); |
|
|
49 for (int j = 0; j < nc; j++) |
|
|
50 for (int i = 0; i < nr; i++) |
|
|
51 if (a.elem (i, j) < 0.0) |
|
|
52 return 1; |
|
|
53 return 0; |
|
|
54 } |
|
|
55 |
|
767
|
56 // Safer pow functions. |
|
|
57 // |
|
|
58 // op2 \ op1: s m cs cm |
|
|
59 // +-- +---+---+----+----+ |
|
|
60 // scalar | | 1 | 5 | 7 | 11 | |
|
|
61 // +---+---+----+----+ |
|
|
62 // matrix | 2 | E | 8 | E | |
|
|
63 // +---+---+----+----+ |
|
|
64 // complex_scalar | 3 | 6 | 9 | 12 | |
|
|
65 // +---+---+----+----+ |
|
|
66 // complex_matrix | 4 | E | 10 | E | |
|
|
67 // +---+---+----+----+ |
|
|
68 // |
|
|
69 // E -> error, trapped in arith-ops.cc. |
|
1
|
70 |
|
767
|
71 // -*- 1 -*- |
|
1
|
72 tree_constant |
|
|
73 xpow (double a, double b) |
|
|
74 { |
|
|
75 if (a < 0.0 && (int) b != b) |
|
|
76 { |
|
|
77 Complex atmp (a); |
|
|
78 return tree_constant (pow (atmp, b)); |
|
|
79 } |
|
|
80 else |
|
|
81 return tree_constant (pow (a, b)); |
|
|
82 } |
|
|
83 |
|
767
|
84 // -*- 2 -*- |
|
1
|
85 tree_constant |
|
164
|
86 xpow (double a, const Matrix& b) |
|
1
|
87 { |
|
|
88 tree_constant retval; |
|
|
89 |
|
|
90 int nr = b.rows (); |
|
|
91 int nc = b.columns (); |
|
|
92 |
|
|
93 if (nr == 0 || nc == 0 || nr != nc) |
|
|
94 error ("for x^A, A must be square"); |
|
|
95 else |
|
|
96 { |
|
|
97 EIG b_eig (b); |
|
|
98 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
|
|
99 ComplexMatrix Q (b_eig.eigenvectors ()); |
|
|
100 |
|
|
101 for (int i = 0; i < nr; i++) |
|
|
102 { |
|
|
103 Complex elt = lambda.elem (i); |
|
|
104 if (imag (elt) == 0.0) |
|
|
105 lambda.elem (i) = pow (a, real (elt)); |
|
|
106 else |
|
|
107 lambda.elem (i) = pow (a, elt); |
|
|
108 } |
|
|
109 ComplexDiagMatrix D (lambda); |
|
|
110 |
|
|
111 ComplexMatrix result = Q * D * Q.inverse (); |
|
|
112 retval = tree_constant (result); |
|
|
113 } |
|
|
114 |
|
|
115 return retval; |
|
|
116 } |
|
|
117 |
|
767
|
118 // -*- 3 -*- |
|
1
|
119 tree_constant |
|
164
|
120 xpow (double a, const Complex& b) |
|
1
|
121 { |
|
|
122 Complex result; |
|
|
123 Complex atmp (a); |
|
|
124 result = pow (atmp, b); |
|
|
125 return tree_constant (result); |
|
|
126 } |
|
|
127 |
|
767
|
128 // -*- 4 -*- |
|
1
|
129 tree_constant |
|
164
|
130 xpow (double a, const ComplexMatrix& b) |
|
1
|
131 { |
|
|
132 tree_constant retval; |
|
|
133 |
|
|
134 int nr = b.rows (); |
|
|
135 int nc = b.columns (); |
|
|
136 |
|
|
137 if (nr == 0 || nc == 0 || nr != nc) |
|
|
138 error ("for x^A, A must be square"); |
|
|
139 else |
|
|
140 { |
|
|
141 EIG b_eig (b); |
|
|
142 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
|
|
143 ComplexMatrix Q (b_eig.eigenvectors ()); |
|
|
144 |
|
|
145 for (int i = 0; i < nr; i++) |
|
|
146 { |
|
|
147 Complex elt = lambda.elem (i); |
|
|
148 if (imag (elt) == 0.0) |
|
|
149 lambda.elem (i) = pow (a, real (elt)); |
|
|
150 else |
|
|
151 lambda.elem (i) = pow (a, elt); |
|
|
152 } |
|
|
153 ComplexDiagMatrix D (lambda); |
|
|
154 |
|
|
155 ComplexMatrix result = Q * D * Q.inverse (); |
|
|
156 retval = tree_constant (result); |
|
|
157 } |
|
|
158 |
|
|
159 return retval; |
|
|
160 } |
|
|
161 |
|
767
|
162 // -*- 5 -*- |
|
1
|
163 tree_constant |
|
164
|
164 xpow (const Matrix& a, double b) |
|
1
|
165 { |
|
|
166 tree_constant retval; |
|
|
167 |
|
|
168 int nr = a.rows (); |
|
|
169 int nc = a.columns (); |
|
|
170 |
|
|
171 if (nr == 0 || nc == 0 || nr != nc) |
|
|
172 { |
|
|
173 error ("for A^b, A must be square"); |
|
|
174 return retval; |
|
|
175 } |
|
|
176 |
|
|
177 if ((int) b == b) |
|
|
178 { |
|
|
179 int btmp = (int) b; |
|
|
180 if (btmp == 0) |
|
|
181 { |
|
|
182 DiagMatrix result (nr, nr, 1.0); |
|
|
183 retval = tree_constant (result); |
|
|
184 } |
|
|
185 else |
|
|
186 { |
|
|
187 // Too much copying? |
|
|
188 // XXX FIXME XXX -- we shouldn\'t do this if the exponent is large... |
|
|
189 Matrix atmp; |
|
|
190 if (btmp < 0) |
|
|
191 { |
|
|
192 btmp = -btmp; |
|
|
193 atmp = a.inverse (); |
|
|
194 } |
|
|
195 else |
|
|
196 atmp = a; |
|
|
197 |
|
|
198 Matrix result (atmp); |
|
|
199 for (int i = 1; i < btmp; i++) |
|
|
200 result = result * atmp; |
|
|
201 |
|
|
202 retval = tree_constant (result); |
|
|
203 } |
|
|
204 } |
|
|
205 else |
|
|
206 { |
|
|
207 EIG a_eig (a); |
|
|
208 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
|
|
209 ComplexMatrix Q (a_eig.eigenvectors ()); |
|
|
210 |
|
|
211 for (int i = 0; i < nr; i++) |
|
|
212 lambda.elem (i) = pow (lambda.elem (i), b); |
|
|
213 |
|
|
214 ComplexDiagMatrix D (lambda); |
|
|
215 |
|
|
216 ComplexMatrix result = Q * D * Q.inverse (); |
|
|
217 retval = tree_constant (result); |
|
|
218 } |
|
|
219 |
|
|
220 return retval; |
|
|
221 } |
|
|
222 |
|
767
|
223 // -*- 6 -*- |
|
1
|
224 tree_constant |
|
164
|
225 xpow (const Matrix& a, const Complex& b) |
|
1
|
226 { |
|
|
227 int nr = a.rows (); |
|
|
228 int nc = a.columns (); |
|
|
229 |
|
|
230 if (nr == 0 || nc == 0 || nr != nc) |
|
|
231 { |
|
|
232 error ("for A^b, A must be square"); |
|
|
233 return tree_constant (); |
|
|
234 } |
|
|
235 |
|
|
236 EIG a_eig (a); |
|
|
237 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
|
|
238 ComplexMatrix Q (a_eig.eigenvectors ()); |
|
|
239 |
|
|
240 for (int i = 0; i < nr; i++) |
|
|
241 lambda.elem (i) = pow (lambda.elem (i), b); |
|
|
242 |
|
|
243 ComplexDiagMatrix D (lambda); |
|
|
244 |
|
|
245 ComplexMatrix result = Q * D * Q.inverse (); |
|
|
246 |
|
|
247 return tree_constant (result); |
|
|
248 } |
|
|
249 |
|
767
|
250 // -*- 7 -*- |
|
1
|
251 tree_constant |
|
164
|
252 xpow (const Complex& a, double b) |
|
1
|
253 { |
|
|
254 Complex result; |
|
|
255 result = pow (a, b); |
|
|
256 return tree_constant (result); |
|
|
257 } |
|
|
258 |
|
767
|
259 // -*- 8 -*- |
|
1
|
260 tree_constant |
|
164
|
261 xpow (const Complex& a, const Matrix& b) |
|
1
|
262 { |
|
|
263 tree_constant retval; |
|
|
264 |
|
|
265 int nr = b.rows (); |
|
|
266 int nc = b.columns (); |
|
|
267 |
|
|
268 if (nr == 0 || nc == 0 || nr != nc) |
|
|
269 { |
|
|
270 error ("for x^A, A must be square"); |
|
|
271 } |
|
|
272 else |
|
|
273 { |
|
|
274 EIG b_eig (b); |
|
|
275 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
|
|
276 ComplexMatrix Q (b_eig.eigenvectors ()); |
|
|
277 |
|
|
278 for (int i = 0; i < nr; i++) |
|
|
279 { |
|
|
280 Complex elt = lambda.elem (i); |
|
|
281 if (imag (elt) == 0.0) |
|
|
282 lambda.elem (i) = pow (a, real (elt)); |
|
|
283 else |
|
|
284 lambda.elem (i) = pow (a, elt); |
|
|
285 } |
|
|
286 ComplexDiagMatrix D (lambda); |
|
|
287 |
|
|
288 ComplexMatrix result = Q * D * Q.inverse (); |
|
|
289 retval = tree_constant (result); |
|
|
290 } |
|
|
291 |
|
|
292 return retval; |
|
|
293 } |
|
|
294 |
|
767
|
295 // -*- 9 -*- |
|
1
|
296 tree_constant |
|
164
|
297 xpow (const Complex& a, const Complex& b) |
|
1
|
298 { |
|
|
299 Complex result; |
|
|
300 result = pow (a, b); |
|
|
301 return tree_constant (result); |
|
|
302 } |
|
|
303 |
|
767
|
304 // -*- 10 -*- |
|
1
|
305 tree_constant |
|
164
|
306 xpow (const Complex& a, const ComplexMatrix& b) |
|
1
|
307 { |
|
|
308 tree_constant retval; |
|
|
309 |
|
|
310 int nr = b.rows (); |
|
|
311 int nc = b.columns (); |
|
|
312 |
|
|
313 if (nr == 0 || nc == 0 || nr != nc) |
|
|
314 error ("for x^A, A must be square"); |
|
|
315 else |
|
|
316 { |
|
|
317 EIG b_eig (b); |
|
|
318 ComplexColumnVector lambda (b_eig.eigenvalues ()); |
|
|
319 ComplexMatrix Q (b_eig.eigenvectors ()); |
|
|
320 |
|
|
321 for (int i = 0; i < nr; i++) |
|
|
322 { |
|
|
323 Complex elt = lambda.elem (i); |
|
|
324 if (imag (elt) == 0.0) |
|
|
325 lambda.elem (i) = pow (a, real (elt)); |
|
|
326 else |
|
|
327 lambda.elem (i) = pow (a, elt); |
|
|
328 } |
|
|
329 ComplexDiagMatrix D (lambda); |
|
|
330 |
|
|
331 ComplexMatrix result = Q * D * Q.inverse (); |
|
|
332 retval = tree_constant (result); |
|
|
333 } |
|
|
334 |
|
|
335 return retval; |
|
|
336 } |
|
|
337 |
|
767
|
338 // -*- 11 -*- |
|
1
|
339 tree_constant |
|
164
|
340 xpow (const ComplexMatrix& a, double b) |
|
1
|
341 { |
|
|
342 tree_constant retval; |
|
|
343 |
|
|
344 int nr = a.rows (); |
|
|
345 int nc = a.columns (); |
|
|
346 |
|
|
347 if (nr == 0 || nc == 0 || nr != nc) |
|
|
348 { |
|
|
349 error ("for A^b, A must be square"); |
|
|
350 return retval; |
|
|
351 } |
|
|
352 |
|
|
353 if ((int) b == b) |
|
|
354 { |
|
|
355 int btmp = (int) b; |
|
|
356 if (btmp == 0) |
|
|
357 { |
|
|
358 DiagMatrix result (nr, nr, 1.0); |
|
|
359 retval = tree_constant (result); |
|
|
360 } |
|
|
361 else |
|
|
362 { |
|
|
363 // Too much copying? |
|
|
364 // XXX FIXME XXX -- we shouldn\'t do this if the exponent is large... |
|
|
365 ComplexMatrix atmp; |
|
|
366 if (btmp < 0) |
|
|
367 { |
|
|
368 btmp = -btmp; |
|
|
369 atmp = a.inverse (); |
|
|
370 } |
|
|
371 else |
|
|
372 atmp = a; |
|
|
373 |
|
|
374 ComplexMatrix result (atmp); |
|
|
375 for (int i = 1; i < btmp; i++) |
|
|
376 result = result * atmp; |
|
|
377 |
|
|
378 retval = tree_constant (result); |
|
|
379 } |
|
|
380 } |
|
|
381 else |
|
|
382 { |
|
|
383 EIG a_eig (a); |
|
|
384 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
|
|
385 ComplexMatrix Q (a_eig.eigenvectors ()); |
|
|
386 |
|
|
387 for (int i = 0; i < nr; i++) |
|
|
388 lambda.elem (i) = pow (lambda.elem (i), b); |
|
|
389 |
|
|
390 ComplexDiagMatrix D (lambda); |
|
|
391 |
|
|
392 ComplexMatrix result = Q * D * Q.inverse (); |
|
|
393 retval = tree_constant (result); |
|
|
394 } |
|
|
395 |
|
|
396 return retval; |
|
|
397 } |
|
|
398 |
|
767
|
399 // -*- 12 -*- |
|
1
|
400 tree_constant |
|
164
|
401 xpow (const ComplexMatrix& a, const Complex& b) |
|
1
|
402 { |
|
|
403 int nr = a.rows (); |
|
|
404 int nc = a.columns (); |
|
|
405 |
|
|
406 if (nr == 0 || nc == 0 || nr != nc) |
|
|
407 { |
|
|
408 error ("for A^b, A must be square"); |
|
|
409 return tree_constant (); |
|
|
410 } |
|
|
411 |
|
|
412 EIG a_eig (a); |
|
|
413 ComplexColumnVector lambda (a_eig.eigenvalues ()); |
|
|
414 ComplexMatrix Q (a_eig.eigenvectors ()); |
|
|
415 |
|
|
416 for (int i = 0; i < nr; i++) |
|
|
417 lambda.elem (i) = pow (lambda.elem (i), b); |
|
|
418 |
|
|
419 ComplexDiagMatrix D (lambda); |
|
|
420 |
|
|
421 ComplexMatrix result = Q * D * Q.inverse (); |
|
|
422 |
|
|
423 return tree_constant (result); |
|
|
424 } |
|
|
425 |
|
767
|
426 // Safer pow functions that work elementwise for matrices. |
|
|
427 // |
|
|
428 // op2 \ op1: s m cs cm |
|
|
429 // +-- +---+---+----+----+ |
|
|
430 // scalar | | * | 3 | * | 9 | |
|
|
431 // +---+---+----+----+ |
|
|
432 // matrix | 1 | 4 | 7 | 10 | |
|
|
433 // +---+---+----+----+ |
|
|
434 // complex_scalar | * | 5 | * | 11 | |
|
|
435 // +---+---+----+----+ |
|
|
436 // complex_matrix | 2 | 6 | 8 | 12 | |
|
|
437 // +---+---+----+----+ |
|
|
438 // |
|
|
439 // * -> not needed. |
|
1
|
440 |
|
767
|
441 // -*- 1 -*- |
|
1
|
442 tree_constant |
|
164
|
443 elem_xpow (double a, const Matrix& b) |
|
1
|
444 { |
|
|
445 tree_constant retval; |
|
|
446 |
|
|
447 int nr = b.rows (); |
|
|
448 int nc = b.columns (); |
|
|
449 |
|
|
450 // For now, assume the worst. |
|
|
451 if (a < 0.0) |
|
|
452 { |
|
|
453 Complex atmp (a); |
|
|
454 ComplexMatrix result (nr, nc); |
|
|
455 for (int j = 0; j < nc; j++) |
|
|
456 for (int i = 0; i < nr; i++) |
|
|
457 result.elem (i, j) = pow (atmp, b.elem (i, j)); |
|
|
458 |
|
|
459 retval = tree_constant (result); |
|
|
460 } |
|
|
461 else |
|
|
462 { |
|
|
463 Matrix result (nr, nc); |
|
|
464 for (int j = 0; j < nc; j++) |
|
|
465 for (int i = 0; i < nr; i++) |
|
|
466 result.elem (i, j) = pow (a, b.elem (i, j)); |
|
|
467 |
|
|
468 retval = tree_constant (result); |
|
|
469 } |
|
|
470 |
|
|
471 return retval; |
|
|
472 } |
|
|
473 |
|
767
|
474 // -*- 2 -*- |
|
1
|
475 tree_constant |
|
164
|
476 elem_xpow (double a, const ComplexMatrix& b) |
|
1
|
477 { |
|
|
478 int nr = b.rows (); |
|
|
479 int nc = b.columns (); |
|
|
480 |
|
|
481 ComplexMatrix result (nr, nc); |
|
|
482 for (int j = 0; j < nc; j++) |
|
|
483 for (int i = 0; i < nr; i++) |
|
|
484 result.elem (i, j) = pow (a, b.elem (i, j)); |
|
|
485 |
|
|
486 return tree_constant (result); |
|
|
487 } |
|
|
488 |
|
767
|
489 // -*- 3 -*- |
|
1
|
490 tree_constant |
|
164
|
491 elem_xpow (const Matrix& a, double b) |
|
1
|
492 { |
|
|
493 tree_constant retval; |
|
|
494 |
|
|
495 int nr = a.rows (); |
|
|
496 int nc = a.columns (); |
|
|
497 |
|
|
498 if ((int) b != b && any_element_is_negative (a)) |
|
|
499 { |
|
|
500 ComplexMatrix result (nr, nc); |
|
|
501 for (int j = 0; j < nc; j++) |
|
|
502 for (int i = 0; i < nr; i++) |
|
|
503 { |
|
|
504 Complex atmp (a.elem (i, j)); |
|
|
505 result.elem (i, j) = pow (atmp, b); |
|
|
506 } |
|
|
507 |
|
|
508 retval = tree_constant (result); |
|
|
509 } |
|
|
510 else |
|
|
511 { |
|
|
512 Matrix result (nr, nc); |
|
|
513 for (int j = 0; j < nc; j++) |
|
|
514 for (int i = 0; i < nr; i++) |
|
|
515 result.elem (i, j) = pow (a.elem (i, j), b); |
|
|
516 |
|
|
517 retval = tree_constant (result); |
|
|
518 } |
|
|
519 |
|
|
520 return retval; |
|
|
521 } |
|
|
522 |
|
767
|
523 // -*- 4 -*- |
|
1
|
524 tree_constant |
|
164
|
525 elem_xpow (const Matrix& a, const Matrix& b) |
|
1
|
526 { |
|
|
527 int nr = a.rows (); |
|
|
528 int nc = a.columns (); |
|
|
529 |
|
|
530 assert (nr == b.rows () && nc == b.columns ()); |
|
|
531 |
|
|
532 int convert_to_complex = 0; |
|
|
533 for (int j = 0; j < nc; j++) |
|
1321
|
534 for (int i = 0; i < nr; i++) |
|
1
|
535 { |
|
|
536 double atmp = a.elem (i, j); |
|
|
537 double btmp = b.elem (i, j); |
|
|
538 if (atmp < 0.0 && (int) btmp != btmp) |
|
|
539 { |
|
|
540 convert_to_complex = 1; |
|
|
541 goto done; |
|
|
542 } |
|
|
543 } |
|
|
544 |
|
|
545 done: |
|
|
546 |
|
|
547 if (convert_to_complex) |
|
|
548 { |
|
|
549 ComplexMatrix complex_result (nr, nc); |
|
|
550 |
|
1321
|
551 for (int j = 0; j < nc; j++) |
|
|
552 for (int i = 0; i < nr; i++) |
|
1
|
553 { |
|
|
554 Complex atmp (a.elem (i, j)); |
|
|
555 Complex btmp (b.elem (i, j)); |
|
|
556 complex_result.elem (i, j) = pow (atmp, btmp); |
|
|
557 } |
|
|
558 return tree_constant (complex_result); |
|
|
559 } |
|
|
560 else |
|
|
561 { |
|
|
562 Matrix result (nr, nc); |
|
|
563 |
|
1321
|
564 for (int j = 0; j < nc; j++) |
|
|
565 for (int i = 0; i < nr; i++) |
|
1
|
566 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
|
|
567 |
|
|
568 return tree_constant (result); |
|
|
569 } |
|
|
570 } |
|
|
571 |
|
767
|
572 // -*- 5 -*- |
|
1
|
573 tree_constant |
|
164
|
574 elem_xpow (const Matrix& a, const Complex& b) |
|
1
|
575 { |
|
|
576 int nr = a.rows (); |
|
|
577 int nc = a.columns (); |
|
|
578 |
|
|
579 ComplexMatrix result (nr, nc); |
|
|
580 for (int j = 0; j < nc; j++) |
|
|
581 for (int i = 0; i < nr; i++) |
|
|
582 result.elem (i, j) = pow (a.elem (i, j), b); |
|
|
583 |
|
|
584 return tree_constant (result); |
|
|
585 } |
|
|
586 |
|
767
|
587 // -*- 6 -*- |
|
1
|
588 tree_constant |
|
164
|
589 elem_xpow (const Matrix& a, const ComplexMatrix& b) |
|
1
|
590 { |
|
|
591 int nr = a.rows (); |
|
|
592 int nc = a.columns (); |
|
|
593 |
|
|
594 assert (nr == b.rows () && nc == b.columns ()); |
|
|
595 |
|
|
596 ComplexMatrix result (nr, nc); |
|
|
597 for (int j = 0; j < nc; j++) |
|
|
598 for (int i = 0; i < nr; i++) |
|
|
599 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
|
|
600 |
|
|
601 return tree_constant (result); |
|
|
602 } |
|
|
603 |
|
767
|
604 // -*- 7 -*- |
|
1
|
605 tree_constant |
|
164
|
606 elem_xpow (const Complex& a, const Matrix& b) |
|
1
|
607 { |
|
|
608 int nr = b.rows (); |
|
|
609 int nc = b.columns (); |
|
|
610 |
|
|
611 ComplexMatrix result (nr, nc); |
|
|
612 for (int j = 0; j < nc; j++) |
|
|
613 for (int i = 0; i < nr; i++) |
|
|
614 result.elem (i, j) = pow (a, b.elem (i, j)); |
|
|
615 |
|
|
616 return tree_constant (result); |
|
|
617 } |
|
|
618 |
|
767
|
619 // -*- 8 -*- |
|
1
|
620 tree_constant |
|
164
|
621 elem_xpow (const Complex& a, const ComplexMatrix& b) |
|
1
|
622 { |
|
|
623 int nr = b.rows (); |
|
|
624 int nc = b.columns (); |
|
|
625 |
|
|
626 ComplexMatrix result (nr, nc); |
|
|
627 for (int j = 0; j < nc; j++) |
|
|
628 for (int i = 0; i < nr; i++) |
|
|
629 result.elem (i, j) = pow (a, b.elem (i, j)); |
|
|
630 |
|
|
631 return tree_constant (result); |
|
|
632 } |
|
|
633 |
|
767
|
634 // -*- 9 -*- |
|
1
|
635 tree_constant |
|
164
|
636 elem_xpow (const ComplexMatrix& a, double b) |
|
1
|
637 { |
|
|
638 int nr = a.rows (); |
|
|
639 int nc = a.columns (); |
|
|
640 |
|
|
641 ComplexMatrix result (nr, nc); |
|
|
642 for (int j = 0; j < nc; j++) |
|
|
643 for (int i = 0; i < nr; i++) |
|
|
644 result.elem (i, j) = pow (a.elem (i, j), b); |
|
|
645 |
|
|
646 return tree_constant (result); |
|
|
647 } |
|
|
648 |
|
767
|
649 // -*- 10 -*- |
|
1
|
650 tree_constant |
|
164
|
651 elem_xpow (const ComplexMatrix& a, const Matrix& b) |
|
1
|
652 { |
|
|
653 int nr = a.rows (); |
|
|
654 int nc = a.columns (); |
|
|
655 |
|
|
656 assert (nr == b.rows () && nc == b.columns ()); |
|
|
657 |
|
|
658 ComplexMatrix result (nr, nc); |
|
|
659 for (int j = 0; j < nc; j++) |
|
|
660 for (int i = 0; i < nr; i++) |
|
|
661 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
|
|
662 |
|
|
663 return tree_constant (result); |
|
|
664 } |
|
|
665 |
|
767
|
666 // -*- 11 -*- |
|
1
|
667 tree_constant |
|
164
|
668 elem_xpow (const ComplexMatrix& a, const Complex& b) |
|
1
|
669 { |
|
|
670 int nr = a.rows (); |
|
|
671 int nc = a.columns (); |
|
|
672 |
|
|
673 ComplexMatrix result (nr, nc); |
|
|
674 for (int j = 0; j < nc; j++) |
|
|
675 for (int i = 0; i < nr; i++) |
|
|
676 result.elem (i, j) = pow (a.elem (i, j), b); |
|
|
677 |
|
|
678 return tree_constant (result); |
|
|
679 } |
|
|
680 |
|
767
|
681 // -*- 12 -*- |
|
1
|
682 tree_constant |
|
164
|
683 elem_xpow (const ComplexMatrix& a, const ComplexMatrix& b) |
|
1
|
684 { |
|
|
685 int nr = a.rows (); |
|
|
686 int nc = a.columns (); |
|
|
687 |
|
|
688 ComplexMatrix result (nr, nc); |
|
|
689 |
|
|
690 for (int j = 0; j < nc; j++) |
|
|
691 for (int i = 0; i < nr; i++) |
|
|
692 result.elem (i, j) = pow (a.elem (i, j), b.elem (i, j)); |
|
|
693 |
|
|
694 return tree_constant (result); |
|
|
695 } |
|
|
696 |
|
|
697 /* |
|
|
698 ;;; Local Variables: *** |
|
|
699 ;;; mode: C++ *** |
|
|
700 ;;; page-delimiter: "^/\\*" *** |
|
|
701 ;;; End: *** |
|
|
702 */ |
