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dMatrix.h
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1 /*
2 
3 Copyright (C) 1994-2013 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 3 of the License, or (at your
10 option) any later version.
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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, see
19 <http://www.gnu.org/licenses/>.
20 
21 */
22 
23 #if !defined (octave_dMatrix_h)
24 #define octave_dMatrix_h 1
25 
26 #include "MArray.h"
27 #include "MDiagArray2.h"
28 #include "MatrixType.h"
29 
30 #include "mx-defs.h"
31 #include "mx-op-decl.h"
32 #include "DET.h"
33 
34 class
35 OCTAVE_API
36 Matrix : public MArray<double>
37 {
38 public:
39 
40  typedef ColumnVector column_vector_type;
41  typedef RowVector row_vector_type;
42 
43  typedef void (*solve_singularity_handler) (double rcon);
44 
45  Matrix (void) : MArray<double> () { }
46 
47  Matrix (octave_idx_type r, octave_idx_type c)
48  : MArray<double> (dim_vector (r, c)) { }
49 
50  Matrix (octave_idx_type r, octave_idx_type c, double val)
51  : MArray<double> (dim_vector (r, c), val) { }
52 
53  Matrix (const dim_vector& dv) : MArray<double> (dv.redim (2)) { }
54 
55  Matrix (const dim_vector& dv, double val)
56  : MArray<double> (dv.redim (2), val) { }
57 
58  Matrix (const Matrix& a) : MArray<double> (a) { }
59 
60  template <class U>
61  Matrix (const MArray<U>& a) : MArray<double> (a.as_matrix ()) { }
62 
63  template <class U>
64  Matrix (const Array<U>& a) : MArray<double> (a.as_matrix ()) { }
65 
66  explicit Matrix (const RowVector& rv);
67 
68  explicit Matrix (const ColumnVector& cv);
69 
70  explicit Matrix (const DiagMatrix& a);
71 
72  explicit Matrix (const PermMatrix& a);
73 
74  explicit Matrix (const boolMatrix& a);
75 
76  explicit Matrix (const charMatrix& a);
77 
78  Matrix& operator = (const Matrix& a)
79  {
80  MArray<double>::operator = (a);
81  return *this;
82  }
83 
84  bool operator == (const Matrix& a) const;
85  bool operator != (const Matrix& a) const;
86 
87  bool is_symmetric (void) const;
88 
89  // destructive insert/delete/reorder operations
90 
91  Matrix& insert (const Matrix& a, octave_idx_type r, octave_idx_type c);
92  Matrix& insert (const RowVector& a, octave_idx_type r, octave_idx_type c);
93  Matrix& insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c);
94  Matrix& insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c);
95 
96  Matrix& fill (double val);
97  Matrix& fill (double val, octave_idx_type r1, octave_idx_type c1,
98  octave_idx_type r2, octave_idx_type c2);
99 
100  Matrix append (const Matrix& a) const;
101  Matrix append (const RowVector& a) const;
102  Matrix append (const ColumnVector& a) const;
103  Matrix append (const DiagMatrix& a) const;
104 
105  Matrix stack (const Matrix& a) const;
106  Matrix stack (const RowVector& a) const;
107  Matrix stack (const ColumnVector& a) const;
108  Matrix stack (const DiagMatrix& a) const;
109 
110  friend OCTAVE_API Matrix real (const ComplexMatrix& a);
111  friend OCTAVE_API Matrix imag (const ComplexMatrix& a);
112 
113  friend class ComplexMatrix;
114 
115  Matrix transpose (void) const { return MArray<double>::transpose (); }
116 
117  // resize is the destructive equivalent for this one
118 
119  Matrix extract (octave_idx_type r1, octave_idx_type c1,
120  octave_idx_type r2, octave_idx_type c2) const;
121 
122  Matrix extract_n (octave_idx_type r1, octave_idx_type c1,
123  octave_idx_type nr, octave_idx_type nc) const;
124 
125  // extract row or column i.
126 
127  RowVector row (octave_idx_type i) const;
128 
129  ColumnVector column (octave_idx_type i) const;
130 
131  void resize (octave_idx_type nr, octave_idx_type nc, double rfv = 0)
132  {
133  MArray<double>::resize (dim_vector (nr, nc), rfv);
134  }
135 
136 private:
137  Matrix tinverse (MatrixType &mattype, octave_idx_type& info, double& rcon,
138  int force, int calc_cond) const;
139 
140  Matrix finverse (MatrixType &mattype, octave_idx_type& info, double& rcon,
141  int force, int calc_cond) const;
142 
143 public:
144  Matrix inverse (void) const;
145  Matrix inverse (octave_idx_type& info) const;
146  Matrix inverse (octave_idx_type& info, double& rcon, int force = 0,
147  int calc_cond = 1) const;
148 
149  Matrix inverse (MatrixType &mattype) const;
150  Matrix inverse (MatrixType &mattype, octave_idx_type& info) const;
151  Matrix inverse (MatrixType &mattype, octave_idx_type& info, double& rcon,
152  int force = 0, int calc_cond = 1) const;
153 
154  Matrix pseudo_inverse (double tol = 0.0) const;
155 
156  ComplexMatrix fourier (void) const;
157  ComplexMatrix ifourier (void) const;
158 
159  ComplexMatrix fourier2d (void) const;
160  ComplexMatrix ifourier2d (void) const;
161 
162  DET determinant (void) const;
163  DET determinant (octave_idx_type& info) const;
164  DET determinant (octave_idx_type& info, double& rcon,
165  int calc_cond = 1) const;
166  DET determinant (MatrixType &mattype, octave_idx_type& info,
167  double& rcon, int calc_cond = 1) const;
168 
169  double rcond (void) const;
170  double rcond (MatrixType &mattype) const;
171 
172 private:
173  // Upper triangular matrix solvers
174  Matrix utsolve (MatrixType &typ, const Matrix& b, octave_idx_type& info,
175  double& rcon, solve_singularity_handler sing_handler,
176  bool calc_cond = false,
177  blas_trans_type transt = blas_no_trans) const;
178 
179  // Lower triangular matrix solvers
180  Matrix ltsolve (MatrixType &typ, const Matrix& b, octave_idx_type& info,
181  double& rcon, solve_singularity_handler sing_handler,
182  bool calc_cond = false,
183  blas_trans_type transt = blas_no_trans) const;
184 
185  // Full matrix solvers (lu/cholesky)
186  Matrix fsolve (MatrixType &typ, const Matrix& b, octave_idx_type& info,
187  double& rcon, solve_singularity_handler sing_handler,
188  bool calc_cond = false) const;
189 
190 public:
191  // Generic interface to solver with no probing of type
192  Matrix solve (MatrixType &typ, const Matrix& b) const;
193  Matrix solve (MatrixType &typ, const Matrix& b, octave_idx_type& info) const;
194  Matrix solve (MatrixType &typ, const Matrix& b, octave_idx_type& info,
195  double& rcon) const;
196  Matrix solve (MatrixType &typ, const Matrix& b, octave_idx_type& info,
197  double& rcon, solve_singularity_handler sing_handler,
198  bool singular_fallback = true,
199  blas_trans_type transt = blas_no_trans) const;
200 
201  ComplexMatrix solve (MatrixType &typ, const ComplexMatrix& b) const;
202  ComplexMatrix solve (MatrixType &typ, const ComplexMatrix& b,
203  octave_idx_type& info) const;
204  ComplexMatrix solve (MatrixType &typ, const ComplexMatrix& b,
205  octave_idx_type& info, double& rcon) const;
206  ComplexMatrix solve (MatrixType &typ, const ComplexMatrix& b,
207  octave_idx_type& info, double& rcon,
208  solve_singularity_handler sing_handler,
209  bool singular_fallback = true,
210  blas_trans_type transt = blas_no_trans) const;
211 
212  ColumnVector solve (MatrixType &typ, const ColumnVector& b) const;
213  ColumnVector solve (MatrixType &typ, const ColumnVector& b,
214  octave_idx_type& info) const;
215  ColumnVector solve (MatrixType &typ, const ColumnVector& b,
216  octave_idx_type& info, double& rcon) const;
217  ColumnVector solve (MatrixType &typ, const ColumnVector& b,
218  octave_idx_type& info, double& rcon,
219  solve_singularity_handler sing_handler,
220  blas_trans_type transt = blas_no_trans) const;
221 
222  ComplexColumnVector solve (MatrixType &typ,
223  const ComplexColumnVector& b) const;
224  ComplexColumnVector solve (MatrixType &typ, const ComplexColumnVector& b,
225  octave_idx_type& info) const;
226  ComplexColumnVector solve (MatrixType &typ, const ComplexColumnVector& b,
227  octave_idx_type& info, double& rcon) const;
228  ComplexColumnVector solve (MatrixType &typ, const ComplexColumnVector& b,
229  octave_idx_type& info, double& rcon,
230  solve_singularity_handler sing_handler,
231  blas_trans_type transt = blas_no_trans) const;
232 
233  // Generic interface to solver with probing of type
234  Matrix solve (const Matrix& b) const;
235  Matrix solve (const Matrix& b, octave_idx_type& info) const;
236  Matrix solve (const Matrix& b, octave_idx_type& info, double& rcon) const;
237  Matrix solve (const Matrix& b, octave_idx_type& info, double& rcon,
238  solve_singularity_handler sing_handler,
239  blas_trans_type transt = blas_no_trans) const;
240 
241  ComplexMatrix solve (const ComplexMatrix& b) const;
242  ComplexMatrix solve (const ComplexMatrix& b, octave_idx_type& info) const;
243  ComplexMatrix solve (const ComplexMatrix& b, octave_idx_type& info,
244  double& rcon) const;
245  ComplexMatrix solve (const ComplexMatrix& b, octave_idx_type& info,
246  double& rcon,
247  solve_singularity_handler sing_handler,
248  blas_trans_type transt = blas_no_trans) const;
249 
250  ColumnVector solve (const ColumnVector& b) const;
251  ColumnVector solve (const ColumnVector& b, octave_idx_type& info) const;
252  ColumnVector solve (const ColumnVector& b, octave_idx_type& info,
253  double& rcon) const;
254  ColumnVector solve (const ColumnVector& b, octave_idx_type& info,
255  double& rcon,
256  solve_singularity_handler sing_handler,
257  blas_trans_type transt = blas_no_trans) const;
258 
259  ComplexColumnVector solve (const ComplexColumnVector& b) const;
260  ComplexColumnVector solve (const ComplexColumnVector& b,
261  octave_idx_type& info) const;
262  ComplexColumnVector solve (const ComplexColumnVector& b,
263  octave_idx_type& info, double& rcon) const;
264  ComplexColumnVector solve (const ComplexColumnVector& b,
265  octave_idx_type& info, double& rcon,
266  solve_singularity_handler sing_handler,
267  blas_trans_type transt = blas_no_trans) const;
268 
269  // Singular solvers
270  Matrix lssolve (const Matrix& b) const;
271  Matrix lssolve (const Matrix& b, octave_idx_type& info) const;
272  Matrix lssolve (const Matrix& b, octave_idx_type& info,
273  octave_idx_type& rank) const;
274  Matrix lssolve (const Matrix& b, octave_idx_type& info,
275  octave_idx_type& rank, double& rcon) const;
276 
277  ComplexMatrix lssolve (const ComplexMatrix& b) const;
278  ComplexMatrix lssolve (const ComplexMatrix& b, octave_idx_type& info) const;
279  ComplexMatrix lssolve (const ComplexMatrix& b, octave_idx_type& info,
280  octave_idx_type& rank) const;
281  ComplexMatrix lssolve (const ComplexMatrix& b, octave_idx_type& info,
282  octave_idx_type& rank, double &rcon) const;
283 
284  ColumnVector lssolve (const ColumnVector& b) const;
285  ColumnVector lssolve (const ColumnVector& b, octave_idx_type& info) const;
286  ColumnVector lssolve (const ColumnVector& b, octave_idx_type& info,
287  octave_idx_type& rank) const;
288  ColumnVector lssolve (const ColumnVector& b, octave_idx_type& info,
289  octave_idx_type& rank, double& rcon) const;
290 
291  ComplexColumnVector lssolve (const ComplexColumnVector& b) const;
292  ComplexColumnVector lssolve (const ComplexColumnVector& b,
293  octave_idx_type& info) const;
294  ComplexColumnVector lssolve (const ComplexColumnVector& b,
295  octave_idx_type& info,
296  octave_idx_type& rank) const;
297  ComplexColumnVector lssolve (const ComplexColumnVector& b,
298  octave_idx_type& info,
299  octave_idx_type& rank, double& rcon) const;
300 
301  Matrix& operator += (const DiagMatrix& a);
302  Matrix& operator -= (const DiagMatrix& a);
303 
304  // unary operations
305 
306  boolMatrix operator ! (void) const;
307 
308  // other operations
309 
310  bool any_element_is_negative (bool = false) const;
311  bool any_element_is_positive (bool = false) const;
312  bool any_element_is_nan (void) const;
313  bool any_element_is_inf_or_nan (void) const;
314  bool any_element_not_one_or_zero (void) const;
315  bool all_elements_are_int_or_inf_or_nan (void) const;
316  bool all_integers (double& max_val, double& min_val) const;
317  bool too_large_for_float (void) const;
318 
319  boolMatrix all (int dim = -1) const;
320  boolMatrix any (int dim = -1) const;
321 
322  Matrix cumprod (int dim = -1) const;
323  Matrix cumsum (int dim = -1) const;
324  Matrix prod (int dim = -1) const;
325  Matrix sum (int dim = -1) const;
326  Matrix sumsq (int dim = -1) const;
327  Matrix abs (void) const;
328 
329  Matrix diag (octave_idx_type k = 0) const;
330 
331  DiagMatrix diag (octave_idx_type m, octave_idx_type n) const;
332 
333  ColumnVector row_min (void) const;
334  ColumnVector row_max (void) const;
335 
336  ColumnVector row_min (Array<octave_idx_type>& index) const;
337  ColumnVector row_max (Array<octave_idx_type>& index) const;
338 
339  RowVector column_min (void) const;
340  RowVector column_max (void) const;
341 
342  RowVector column_min (Array<octave_idx_type>& index) const;
343  RowVector column_max (Array<octave_idx_type>& index) const;
344 
345  // i/o
346 
347  friend OCTAVE_API std::ostream& operator << (std::ostream& os,
348  const Matrix& a);
349  friend OCTAVE_API std::istream& operator >> (std::istream& is, Matrix& a);
350 };
351 
352 // Publish externally used friend functions.
353 
354 extern OCTAVE_API Matrix real (const ComplexMatrix& a);
355 extern OCTAVE_API Matrix imag (const ComplexMatrix& a);
356 
357 // column vector by row vector -> matrix operations
358 
359 extern OCTAVE_API Matrix operator * (const ColumnVector& a,
360  const RowVector& b);
361 
362 // Other functions.
363 
364 extern OCTAVE_API Matrix Givens (double, double);
365 
366 extern OCTAVE_API Matrix Sylvester (const Matrix&, const Matrix&,
367  const Matrix&);
368 
369 extern OCTAVE_API Matrix xgemm (const Matrix& a, const Matrix& b,
370  blas_trans_type transa = blas_no_trans,
371  blas_trans_type transb = blas_no_trans);
372 
373 extern OCTAVE_API Matrix operator * (const Matrix& a, const Matrix& b);
374 
375 extern OCTAVE_API Matrix min (double d, const Matrix& m);
376 extern OCTAVE_API Matrix min (const Matrix& m, double d);
377 extern OCTAVE_API Matrix min (const Matrix& a, const Matrix& b);
378 
379 extern OCTAVE_API Matrix max (double d, const Matrix& m);
380 extern OCTAVE_API Matrix max (const Matrix& m, double d);
381 extern OCTAVE_API Matrix max (const Matrix& a, const Matrix& b);
382 
383 extern OCTAVE_API Matrix linspace (const ColumnVector& x1,
384  const ColumnVector& x2,
385  octave_idx_type n);
386 
387 MS_CMP_OP_DECLS (Matrix, double, OCTAVE_API)
388 MS_BOOL_OP_DECLS (Matrix, double, OCTAVE_API)
389 
390 SM_CMP_OP_DECLS (double, Matrix, OCTAVE_API)
391 SM_BOOL_OP_DECLS (double, Matrix, OCTAVE_API)
392 
393 MM_CMP_OP_DECLS (Matrix, Matrix, OCTAVE_API)
394 MM_BOOL_OP_DECLS (Matrix, Matrix, OCTAVE_API)
395 
396 MARRAY_FORWARD_DEFS (MArray, Matrix, double)
397 
398 template <class T>
399 void read_int (std::istream& is, bool swap_bytes, T& val);
400 
401 #endif
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