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CSparse.h
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1 /*
2 
3 Copyright (C) 2004-2013 David Bateman
4 Copyright (C) 1998-2004 Andy Adler
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 3 of the License, or (at your
11 option) any 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, see
20 <http://www.gnu.org/licenses/>.
21 
22 */
23 
24 #if !defined (octave_CSparse_h)
25 #define octave_CSparse_h 1
26 
27 #include "dMatrix.h"
28 #include "dNDArray.h"
29 #include "CNDArray.h"
30 #include "dColVector.h"
31 #include "CColVector.h"
32 #include "oct-cmplx.h"
33 
34 #include "DET.h"
35 #include "MSparse.h"
36 #include "MSparse-defs.h"
37 #include "Sparse-op-defs.h"
38 #include "MatrixType.h"
39 
40 class PermMatrix;
41 class DiagMatrix;
42 class ComplexDiagMatrix;
43 class SparseMatrix;
44 class SparseBoolMatrix;
45 
46 class
47 OCTAVE_API
48 SparseComplexMatrix : public MSparse<Complex>
49 {
50 public:
51 
52  typedef void (*solve_singularity_handler) (double rcond);
53 
54  SparseComplexMatrix (void) : MSparse<Complex> () { }
55 
56  SparseComplexMatrix (octave_idx_type r,
57  octave_idx_type c) : MSparse<Complex> (r, c) { }
58 
59  SparseComplexMatrix (const dim_vector& dv, octave_idx_type nz = 0)
60  : MSparse<Complex> (dv, nz) { }
61 
62  explicit SparseComplexMatrix (octave_idx_type r, octave_idx_type c,
63  Complex val)
64  : MSparse<Complex> (r, c, val) { }
65 
66  SparseComplexMatrix (octave_idx_type r, octave_idx_type c, double val)
67  : MSparse<Complex> (r, c, Complex (val)) { }
68 
69  SparseComplexMatrix (const SparseComplexMatrix& a)
70  : MSparse<Complex> (a) { }
71 
72  SparseComplexMatrix (const SparseComplexMatrix& a, const dim_vector& dv)
73  : MSparse<Complex> (a, dv) { }
74 
75  SparseComplexMatrix (const MSparse<Complex>& a) : MSparse<Complex> (a) { }
76 
77  SparseComplexMatrix (const Sparse<Complex>& a) : MSparse<Complex> (a) { }
78 
79  explicit SparseComplexMatrix (const ComplexMatrix& a)
80  : MSparse<Complex> (a) { }
81 
82  explicit SparseComplexMatrix (const ComplexNDArray& a)
83  : MSparse<Complex> (a) { }
84 
85  SparseComplexMatrix (const Array<Complex>& a, const idx_vector& r,
86  const idx_vector& c, octave_idx_type nr = -1,
87  octave_idx_type nc = -1, bool sum_terms = true,
88  octave_idx_type nzm = -1)
89  : MSparse<Complex> (a, r, c, nr, nc, sum_terms, nzm) { }
90 
91  explicit SparseComplexMatrix (const SparseMatrix& a);
92 
93  explicit SparseComplexMatrix (const SparseBoolMatrix& a);
94 
95  explicit SparseComplexMatrix (const ComplexDiagMatrix& a);
96 
97  SparseComplexMatrix (octave_idx_type r, octave_idx_type c,
98  octave_idx_type num_nz)
99  : MSparse<Complex> (r, c, num_nz) { }
100 
101  SparseComplexMatrix& operator = (const SparseComplexMatrix& a)
102  {
103  MSparse<Complex>::operator = (a);
104  return *this;
105  }
106 
107  bool operator == (const SparseComplexMatrix& a) const;
108  bool operator != (const SparseComplexMatrix& a) const;
109 
110  bool is_hermitian (void) const;
111 
112  SparseComplexMatrix max (int dim = -1) const;
113  SparseComplexMatrix max (Array<octave_idx_type>& index, int dim = -1) const;
114  SparseComplexMatrix min (int dim = -1) const;
115  SparseComplexMatrix min (Array<octave_idx_type>& index, int dim = -1) const;
116 
117  SparseComplexMatrix& insert (const SparseComplexMatrix& a,
118  octave_idx_type r, octave_idx_type c);
119  SparseComplexMatrix& insert (const SparseMatrix& a,
120  octave_idx_type r, octave_idx_type c);
121  SparseComplexMatrix& insert (const SparseComplexMatrix& a,
122  const Array<octave_idx_type>& indx);
123  SparseComplexMatrix& insert (const SparseMatrix& a,
124  const Array<octave_idx_type>& indx);
125 
126  SparseComplexMatrix concat (const SparseComplexMatrix& rb,
127  const Array<octave_idx_type>& ra_idx);
128  SparseComplexMatrix concat (const SparseMatrix& rb,
129  const Array<octave_idx_type>& ra_idx);
130 
131  ComplexMatrix matrix_value (void) const;
132 
133  SparseComplexMatrix hermitian (void) const; // complex conjugate transpose
134  SparseComplexMatrix transpose (void) const
135  { return MSparse<Complex>::transpose (); }
136 
137  friend SparseComplexMatrix conj (const SparseComplexMatrix& a);
138 
139  // extract row or column i.
140 
141  ComplexRowVector row (octave_idx_type i) const;
142 
143  ComplexColumnVector column (octave_idx_type i) const;
144 
145 private:
146  SparseComplexMatrix dinverse (MatrixType &mattyp, octave_idx_type& info,
147  double& rcond, const bool force = false,
148  const bool calccond = true) const;
149 
150  SparseComplexMatrix tinverse (MatrixType &mattyp, octave_idx_type& info,
151  double& rcond, const bool force = false,
152  const bool calccond = true) const;
153 
154 public:
155  SparseComplexMatrix inverse (void) const;
156  SparseComplexMatrix inverse (MatrixType& mattype) const;
157  SparseComplexMatrix inverse (MatrixType& mattype,
158  octave_idx_type& info) const;
159  SparseComplexMatrix inverse (MatrixType& mattype, octave_idx_type& info,
160  double& rcond, int force = 0,
161  int calc_cond = 1) const;
162 
163  ComplexDET determinant (void) const;
164  ComplexDET determinant (octave_idx_type& info) const;
165  ComplexDET determinant (octave_idx_type& info, double& rcond,
166  int calc_cond = 1) const;
167 
168 private:
169  // Diagonal matrix solvers
170  ComplexMatrix dsolve (MatrixType &typ, const Matrix& b, octave_idx_type& info,
171  double& rcond, solve_singularity_handler sing_handler,
172  bool calc_cond = false) const;
173 
174  ComplexMatrix dsolve (MatrixType &typ, const ComplexMatrix& b,
175  octave_idx_type& info, double& rcond,
176  solve_singularity_handler sing_handler,
177  bool calc_cond = false) const;
178 
179  SparseComplexMatrix dsolve (MatrixType &typ, const SparseMatrix& b,
180  octave_idx_type& info, double& rcond,
181  solve_singularity_handler sing_handler,
182  bool calc_cond = false) const;
183 
184  SparseComplexMatrix dsolve (MatrixType &typ, const SparseComplexMatrix& b,
185  octave_idx_type& info, double& rcond,
186  solve_singularity_handler sing_handler,
187  bool calc_cond = false) const;
188 
189  // Upper triangular matrix solvers
190  ComplexMatrix utsolve (MatrixType &typ, const Matrix& b,
191  octave_idx_type& info, double& rcond,
192  solve_singularity_handler sing_handler,
193  bool calc_cond = false) const;
194 
195  ComplexMatrix utsolve (MatrixType &typ, const ComplexMatrix& b,
196  octave_idx_type& info, double& rcond,
197  solve_singularity_handler sing_handler,
198  bool calc_cond = false) const;
199 
200  SparseComplexMatrix utsolve (MatrixType &typ, const SparseMatrix& b,
201  octave_idx_type& info, double& rcond,
202  solve_singularity_handler sing_handler,
203  bool calc_cond = false) const;
204 
205  SparseComplexMatrix utsolve (MatrixType &typ, const SparseComplexMatrix& b,
206  octave_idx_type& info, double& rcond,
207  solve_singularity_handler sing_handler,
208  bool calc_cond = false) const;
209 
210  // Lower triangular matrix solvers
211  ComplexMatrix ltsolve (MatrixType &typ, const Matrix& b,
212  octave_idx_type& info, double& rcond,
213  solve_singularity_handler sing_handler,
214  bool calc_cond = false) const;
215 
216  ComplexMatrix ltsolve (MatrixType &typ, const ComplexMatrix& b,
217  octave_idx_type& info, double& rcond,
218  solve_singularity_handler sing_handler,
219  bool calc_cond = false) const;
220 
221  SparseComplexMatrix ltsolve (MatrixType &typ, const SparseMatrix& b,
222  octave_idx_type& info, double& rcond,
223  solve_singularity_handler sing_handler,
224  bool calc_cond = false) const;
225 
226  SparseComplexMatrix ltsolve (MatrixType &typ, const SparseComplexMatrix& b,
227  octave_idx_type& info, double& rcond,
228  solve_singularity_handler sing_handler,
229  bool calc_cond = false) const;
230 
231  // Tridiagonal matrix solvers
232  ComplexMatrix trisolve (MatrixType &typ, const Matrix& b,
233  octave_idx_type& info, double& rcond,
234  solve_singularity_handler sing_handler,
235  bool calc_cond = false) const;
236 
237  ComplexMatrix trisolve (MatrixType &typ, const ComplexMatrix& b,
238  octave_idx_type& info, double& rcond,
239  solve_singularity_handler sing_handler,
240  bool calc_cond = false) const;
241 
242  SparseComplexMatrix trisolve (MatrixType &typ, const SparseMatrix& b,
243  octave_idx_type& info, double& rcond,
244  solve_singularity_handler sing_handler,
245  bool calc_cond = false) const;
246 
247  SparseComplexMatrix trisolve (MatrixType &typ, const SparseComplexMatrix& b,
248  octave_idx_type& info, double& rcond,
249  solve_singularity_handler sing_handler,
250  bool calc_cond = false) const;
251 
252  // Banded matrix solvers (umfpack/cholesky)
253  ComplexMatrix bsolve (MatrixType &typ, const Matrix& b,
254  octave_idx_type& info, double& rcond,
255  solve_singularity_handler sing_handler,
256  bool calc_cond = false) const;
257 
258  ComplexMatrix bsolve (MatrixType &typ, const ComplexMatrix& b,
259  octave_idx_type& info, double& rcond,
260  solve_singularity_handler sing_handler,
261  bool calc_cond = false) const;
262 
263  SparseComplexMatrix bsolve (MatrixType &typ, const SparseMatrix& b,
264  octave_idx_type& info, double& rcond,
265  solve_singularity_handler sing_handler,
266  bool calc_cond = false) const;
267 
268  SparseComplexMatrix bsolve (MatrixType &typ, const SparseComplexMatrix& b,
269  octave_idx_type& info, double& rcond,
270  solve_singularity_handler sing_handler,
271  bool calc_cond = false) const;
272 
273  // Full matrix solvers (umfpack/cholesky)
274  void * factorize (octave_idx_type& err, double &rcond, Matrix &Control,
275  Matrix &Info, solve_singularity_handler sing_handler,
276  bool calc_cond) const;
277 
278  ComplexMatrix fsolve (MatrixType &typ, const Matrix& b,
279  octave_idx_type& info, double& rcond,
280  solve_singularity_handler sing_handler,
281  bool calc_cond = false) const;
282 
283  ComplexMatrix fsolve (MatrixType &typ, const ComplexMatrix& b,
284  octave_idx_type& info, double& rcond,
285  solve_singularity_handler sing_handler,
286  bool calc_cond = false) const;
287 
288  SparseComplexMatrix fsolve (MatrixType &typ, const SparseMatrix& b,
289  octave_idx_type& info, double& rcond,
290  solve_singularity_handler sing_handler,
291  bool calc_cond = false) const;
292 
293  SparseComplexMatrix fsolve (MatrixType &typ, const SparseComplexMatrix& b,
294  octave_idx_type& info, double& rcond,
295  solve_singularity_handler sing_handler,
296  bool calc_cond = false) const;
297 
298 public:
299  // Generic interface to solver with no probing of type
300  ComplexMatrix solve (MatrixType &typ, const Matrix& b) const;
301  ComplexMatrix solve (MatrixType &typ, const Matrix& b,
302  octave_idx_type& info) const;
303  ComplexMatrix solve (MatrixType &typ, const Matrix& b, octave_idx_type& info,
304  double& rcond) const;
305  ComplexMatrix solve (MatrixType &typ, const Matrix& b, octave_idx_type& info,
306  double& rcond, solve_singularity_handler sing_handler,
307  bool singular_fallback = true) const;
308 
309  ComplexMatrix solve (MatrixType &typ, const ComplexMatrix& b) const;
310  ComplexMatrix solve (MatrixType &typ, const ComplexMatrix& b,
311  octave_idx_type& info) const;
312  ComplexMatrix solve (MatrixType &typ, const ComplexMatrix& b,
313  octave_idx_type& info, double& rcond) const;
314  ComplexMatrix solve (MatrixType &typ, const ComplexMatrix& b,
315  octave_idx_type& info, double& rcond,
316  solve_singularity_handler sing_handler,
317  bool singular_fallback = true) const;
318 
319  SparseComplexMatrix solve (MatrixType &typ, const SparseMatrix& b) const;
320  SparseComplexMatrix solve (MatrixType &typ, const SparseMatrix& b,
321  octave_idx_type& info) const;
322  SparseComplexMatrix solve (MatrixType &typ, const SparseMatrix& b,
323  octave_idx_type& info, double& rcond) const;
324  SparseComplexMatrix solve (MatrixType &typ, const SparseMatrix& b,
325  octave_idx_type& info, double& rcond,
326  solve_singularity_handler sing_handler,
327  bool singular_fallback = true) const;
328 
329  SparseComplexMatrix solve (MatrixType &typ,
330  const SparseComplexMatrix& b) const;
331  SparseComplexMatrix solve (MatrixType &typ, const SparseComplexMatrix& b,
332  octave_idx_type& info) const;
333  SparseComplexMatrix solve (MatrixType &typ, const SparseComplexMatrix& b,
334  octave_idx_type& info, double& rcond) const;
335  SparseComplexMatrix solve (MatrixType &typ, const SparseComplexMatrix& b,
336  octave_idx_type& info, double& rcond,
337  solve_singularity_handler sing_handler,
338  bool singular_fallback = true) const;
339 
340  ComplexColumnVector solve (MatrixType &typ, const ColumnVector& b) const;
341  ComplexColumnVector solve (MatrixType &typ, const ColumnVector& b,
342  octave_idx_type& info) const;
343  ComplexColumnVector solve (MatrixType &typ, const ColumnVector& b,
344  octave_idx_type& info, double& rcond) const;
345  ComplexColumnVector solve (MatrixType &typ, const ColumnVector& b,
346  octave_idx_type& info, double& rcond,
347  solve_singularity_handler sing_handler) const;
348 
349  ComplexColumnVector solve (MatrixType &typ,
350  const ComplexColumnVector& b) const;
351  ComplexColumnVector solve (MatrixType &typ, const ComplexColumnVector& b,
352  octave_idx_type& info) const;
353  ComplexColumnVector solve (MatrixType &typ, const ComplexColumnVector& b,
354  octave_idx_type& info, double& rcond) const;
355  ComplexColumnVector solve (MatrixType &typ, const ComplexColumnVector& b,
356  octave_idx_type& info, double& rcond,
357  solve_singularity_handler sing_handler) const;
358 
359  // Generic interface to solver with probing of type
360  ComplexMatrix solve (const Matrix& b) const;
361  ComplexMatrix solve (const Matrix& b, octave_idx_type& info) const;
362  ComplexMatrix solve (const Matrix& b, octave_idx_type& info,
363  double& rcond) const;
364  ComplexMatrix solve (const Matrix& b, octave_idx_type& info, double& rcond,
365  solve_singularity_handler sing_handler) const;
366 
367  ComplexMatrix solve (const ComplexMatrix& b) const;
368  ComplexMatrix solve (const ComplexMatrix& b, octave_idx_type& info) const;
369  ComplexMatrix solve (const ComplexMatrix& b, octave_idx_type& info,
370  double& rcond) const;
371  ComplexMatrix solve (const ComplexMatrix& b, octave_idx_type& info,
372  double& rcond,
373  solve_singularity_handler sing_handler) const;
374 
375  SparseComplexMatrix solve (const SparseMatrix& b) const;
376  SparseComplexMatrix solve (const SparseMatrix& b,
377  octave_idx_type& info) const;
378  SparseComplexMatrix solve (const SparseMatrix& b, octave_idx_type& info,
379  double& rcond) const;
380  SparseComplexMatrix solve (const SparseMatrix& b, octave_idx_type& info,
381  double& rcond,
382  solve_singularity_handler sing_handler) const;
383 
384  SparseComplexMatrix solve (const SparseComplexMatrix& b) const;
385  SparseComplexMatrix solve (const SparseComplexMatrix& b,
386  octave_idx_type& info) const;
387  SparseComplexMatrix solve (const SparseComplexMatrix& b,
388  octave_idx_type& info, double& rcond) const;
389  SparseComplexMatrix solve (const SparseComplexMatrix& b,
390  octave_idx_type& info, double& rcond,
391  solve_singularity_handler sing_handler) const;
392 
393  ComplexColumnVector solve (const ColumnVector& b) const;
394  ComplexColumnVector solve (const ColumnVector& b,
395  octave_idx_type& info) const;
396  ComplexColumnVector solve (const ColumnVector& b, octave_idx_type& info,
397  double& rcond) const;
398  ComplexColumnVector solve (const ColumnVector& b, octave_idx_type& info,
399  double& rcond,
400  solve_singularity_handler sing_handler) const;
401 
402  ComplexColumnVector solve (const ComplexColumnVector& b) const;
403  ComplexColumnVector solve (const ComplexColumnVector& b,
404  octave_idx_type& info) const;
405  ComplexColumnVector solve (const ComplexColumnVector& b,
406  octave_idx_type& info, double& rcond) const;
407  ComplexColumnVector solve (const ComplexColumnVector& b,
408  octave_idx_type& info, double& rcond,
409  solve_singularity_handler sing_handler) const;
410 
411  SparseComplexMatrix squeeze (void) const;
412 
413  SparseComplexMatrix reshape (const dim_vector& new_dims) const;
414 
415  SparseComplexMatrix permute (const Array<octave_idx_type>& vec,
416  bool inv = false) const;
417 
418  SparseComplexMatrix ipermute (const Array<octave_idx_type>& vec) const;
419 
420  bool any_element_is_nan (void) const;
421  bool any_element_is_inf_or_nan (void) const;
422  bool all_elements_are_real (void) const;
423  bool all_integers (double& max_val, double& min_val) const;
424  bool too_large_for_float (void) const;
425 
426  SparseBoolMatrix operator ! (void) const;
427 
428  SparseBoolMatrix all (int dim = -1) const;
429  SparseBoolMatrix any (int dim = -1) const;
430 
431  SparseComplexMatrix cumprod (int dim = -1) const;
432  SparseComplexMatrix cumsum (int dim = -1) const;
433  SparseComplexMatrix prod (int dim = -1) const;
434  SparseComplexMatrix sum (int dim = -1) const;
435  SparseComplexMatrix sumsq (int dim = -1) const;
436  SparseMatrix abs (void) const;
437 
438  SparseComplexMatrix diag (octave_idx_type k = 0) const;
439 
440  // i/o
441  friend OCTAVE_API std::ostream& operator << (std::ostream& os,
442  const SparseComplexMatrix& a);
443  friend OCTAVE_API std::istream& operator >> (std::istream& is,
444  SparseComplexMatrix& a);
445 };
446 
447 extern OCTAVE_API SparseComplexMatrix operator * (const SparseMatrix&,
448  const SparseComplexMatrix&);
449 extern OCTAVE_API SparseComplexMatrix operator * (const SparseComplexMatrix&,
450  const SparseMatrix&);
451 extern OCTAVE_API SparseComplexMatrix operator * (const SparseComplexMatrix&,
452  const SparseComplexMatrix&);
453 
454 extern OCTAVE_API ComplexMatrix operator * (const Matrix&,
455  const SparseComplexMatrix&);
456 extern OCTAVE_API ComplexMatrix operator * (const ComplexMatrix&,
457  const SparseMatrix&);
458 extern OCTAVE_API ComplexMatrix operator * (const ComplexMatrix&,
459  const SparseComplexMatrix&);
460 extern OCTAVE_API ComplexMatrix mul_trans (const ComplexMatrix&,
461  const SparseComplexMatrix&);
462 extern OCTAVE_API ComplexMatrix mul_herm (const ComplexMatrix&,
463  const SparseComplexMatrix&);
464 
465 extern OCTAVE_API ComplexMatrix operator * (const SparseMatrix&,
466  const ComplexMatrix&);
467 extern OCTAVE_API ComplexMatrix operator * (const SparseComplexMatrix&,
468  const Matrix&);
469 extern OCTAVE_API ComplexMatrix operator * (const SparseComplexMatrix&,
470  const ComplexMatrix&);
471 extern OCTAVE_API ComplexMatrix trans_mul (const SparseComplexMatrix&,
472  const ComplexMatrix&);
473 extern OCTAVE_API ComplexMatrix herm_mul (const SparseComplexMatrix&,
474  const ComplexMatrix&);
475 
476 extern OCTAVE_API SparseComplexMatrix operator * (const DiagMatrix&,
477  const SparseComplexMatrix&);
478 extern OCTAVE_API SparseComplexMatrix operator * (const SparseComplexMatrix&,
479  const DiagMatrix&);
480 
481 extern OCTAVE_API SparseComplexMatrix operator * (const ComplexDiagMatrix&,
482  const SparseMatrix&);
483 extern OCTAVE_API SparseComplexMatrix operator * (const SparseMatrix&,
484  const ComplexDiagMatrix&);
485 
486 extern OCTAVE_API SparseComplexMatrix operator * (const ComplexDiagMatrix&,
487  const SparseComplexMatrix&);
488 extern OCTAVE_API SparseComplexMatrix operator * (const SparseComplexMatrix&,
489  const ComplexDiagMatrix&);
490 
491 extern OCTAVE_API SparseComplexMatrix operator + (const ComplexDiagMatrix&,
492  const SparseMatrix&);
493 extern OCTAVE_API SparseComplexMatrix operator + (const DiagMatrix&,
494  const SparseComplexMatrix&);
495 extern OCTAVE_API SparseComplexMatrix operator + (const ComplexDiagMatrix&,
496  const SparseComplexMatrix&);
497 extern OCTAVE_API SparseComplexMatrix operator + (const SparseMatrix&,
498  const ComplexDiagMatrix&);
499 extern OCTAVE_API SparseComplexMatrix operator + (const SparseComplexMatrix&,
500  const DiagMatrix&);
501 extern OCTAVE_API SparseComplexMatrix operator + (const SparseComplexMatrix&,
502  const ComplexDiagMatrix&);
503 
504 extern OCTAVE_API SparseComplexMatrix operator - (const ComplexDiagMatrix&,
505  const SparseMatrix&);
506 extern OCTAVE_API SparseComplexMatrix operator - (const DiagMatrix&,
507  const SparseComplexMatrix&);
508 extern OCTAVE_API SparseComplexMatrix operator - (const ComplexDiagMatrix&,
509  const SparseComplexMatrix&);
510 extern OCTAVE_API SparseComplexMatrix operator - (const SparseMatrix&,
511  const ComplexDiagMatrix&);
512 extern OCTAVE_API SparseComplexMatrix operator - (const SparseComplexMatrix&,
513  const DiagMatrix&);
514 extern OCTAVE_API SparseComplexMatrix operator - (const SparseComplexMatrix&,
515  const ComplexDiagMatrix&);
516 
517 extern OCTAVE_API SparseComplexMatrix operator * (const PermMatrix&,
518  const SparseComplexMatrix&);
519 extern OCTAVE_API SparseComplexMatrix operator * (const SparseComplexMatrix&,
520  const PermMatrix&);
521 
522 extern OCTAVE_API SparseComplexMatrix min (const Complex& c,
523  const SparseComplexMatrix& m);
524 extern OCTAVE_API SparseComplexMatrix min (const SparseComplexMatrix& m,
525  const Complex& c);
526 extern OCTAVE_API SparseComplexMatrix min (const SparseComplexMatrix& a,
527  const SparseComplexMatrix& b);
528 
529 extern OCTAVE_API SparseComplexMatrix max (const Complex& c,
530  const SparseComplexMatrix& m);
531 extern OCTAVE_API SparseComplexMatrix max (const SparseComplexMatrix& m,
532  const Complex& c);
533 extern OCTAVE_API SparseComplexMatrix max (const SparseComplexMatrix& a,
534  const SparseComplexMatrix& b);
535 
536 SPARSE_SMS_CMP_OP_DECLS (SparseComplexMatrix, Complex, OCTAVE_API)
537 SPARSE_SMS_BOOL_OP_DECLS (SparseComplexMatrix, Complex, OCTAVE_API)
538 
539 SPARSE_SSM_CMP_OP_DECLS (Complex, SparseComplexMatrix, OCTAVE_API)
540 SPARSE_SSM_BOOL_OP_DECLS (Complex, SparseComplexMatrix, OCTAVE_API)
541 
542 SPARSE_SMSM_CMP_OP_DECLS (SparseComplexMatrix, SparseComplexMatrix, OCTAVE_API)
543 SPARSE_SMSM_BOOL_OP_DECLS (SparseComplexMatrix, SparseComplexMatrix, OCTAVE_API)
544 
545 SPARSE_FORWARD_DEFS (MSparse, SparseComplexMatrix, ComplexMatrix, Complex)
546 
547 #ifdef USE_64_BIT_IDX_T
548 #define UMFPACK_ZNAME(name) umfpack_zl_ ## name
549 #else
550 #define UMFPACK_ZNAME(name) umfpack_zi_ ## name
551 #endif
552 
553 #endif
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