GNU Octave 10.1.0
A high-level interpreted language, primarily intended for numerical computations, mostly compatible with Matlab
 
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dMatrix.h
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1////////////////////////////////////////////////////////////////////////
2//
3// Copyright (C) 1994-2025 The Octave Project Developers
4//
5// See the file COPYRIGHT.md in the top-level directory of this
6// distribution or <https://octave.org/copyright/>.
7//
8// This file is part of Octave.
9//
10// Octave is free software: you can redistribute it and/or modify it
11// under the terms of the GNU General Public License as published by
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13// (at your option) any later version.
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17// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18// GNU General Public License for more details.
19//
20// You should have received a copy of the GNU General Public License
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24////////////////////////////////////////////////////////////////////////
25
26#if ! defined (octave_dMatrix_h)
27#define octave_dMatrix_h 1
28
29#include "octave-config.h"
30
31#include "DET.h"
32#include "MArray.h"
33#include "MDiagArray2.h"
34#include "MatrixType.h"
35#include "dNDArray.h"
36#include "mx-defs.h"
37#include "mx-op-decl.h"
38
39class OCTAVE_API Matrix : public NDArray
40{
41public:
42
43 typedef ColumnVector column_vector_type;
44 typedef RowVector row_vector_type;
45
46 typedef ColumnVector real_column_vector_type;
47 typedef RowVector real_row_vector_type;
48
49 typedef Matrix real_matrix_type;
50 typedef ComplexMatrix complex_matrix_type;
51
52 typedef DiagMatrix real_diag_matrix_type;
53 typedef ComplexDiagMatrix complex_diag_matrix_type;
54
55 typedef double real_elt_type;
56 typedef Complex complex_elt_type;
57
58 typedef void (*solve_singularity_handler) (double rcon);
59
60 Matrix () = default;
61
62 Matrix (const Matrix& a) = default;
63
64 Matrix& operator = (const Matrix& a) = default;
65
66 ~Matrix () = default;
67
70
71 Matrix (octave_idx_type r, octave_idx_type c, double val)
72 : NDArray (dim_vector (r, c), val) { }
73
74 Matrix (const dim_vector& dv) : NDArray (dv.redim (2)) { }
75
76 Matrix (const dim_vector& dv, double val)
77 : NDArray (dv.redim (2), val) { }
78
79 template <typename U>
80 Matrix (const MArray<U>& a) : NDArray (a.as_matrix ()) { }
81
82 template <typename U>
83 Matrix (const Array<U>& a) : NDArray (a.as_matrix ()) { }
84
85 explicit OCTAVE_API Matrix (const RowVector& rv);
86
87 explicit OCTAVE_API Matrix (const ColumnVector& cv);
88
89 explicit OCTAVE_API Matrix (const DiagMatrix& a);
90
91 explicit OCTAVE_API Matrix (const MDiagArray2<double>& a);
92
93 explicit OCTAVE_API Matrix (const DiagArray2<double>& a);
94
95 explicit OCTAVE_API Matrix (const PermMatrix& a);
96
97 explicit OCTAVE_API Matrix (const boolMatrix& a);
98
99 explicit Matrix (const charMatrix& a);
100
101 OCTAVE_API bool operator == (const Matrix& a) const;
102 OCTAVE_API bool operator != (const Matrix& a) const;
103
104 OCTAVE_API bool issymmetric () const;
105
106 // destructive insert/delete/reorder operations
107
108 OCTAVE_API Matrix&
109 insert (const Matrix& a, octave_idx_type r, octave_idx_type c);
110 OCTAVE_API Matrix&
111 insert (const RowVector& a, octave_idx_type r, octave_idx_type c);
112 OCTAVE_API Matrix&
113 insert (const ColumnVector& a, octave_idx_type r, octave_idx_type c);
114 OCTAVE_API Matrix&
115 insert (const DiagMatrix& a, octave_idx_type r, octave_idx_type c);
116
117 OCTAVE_API Matrix& fill (double val);
118 OCTAVE_API Matrix&
119 fill (double val, octave_idx_type r1, octave_idx_type c1,
120 octave_idx_type r2, octave_idx_type c2);
121
122 OCTAVE_API Matrix append (const Matrix& a) const;
123 OCTAVE_API Matrix append (const RowVector& a) const;
124 OCTAVE_API Matrix append (const ColumnVector& a) const;
125 OCTAVE_API Matrix append (const DiagMatrix& a) const;
126
127 OCTAVE_API Matrix stack (const Matrix& a) const;
128 OCTAVE_API Matrix stack (const RowVector& a) const;
129 OCTAVE_API Matrix stack (const ColumnVector& a) const;
130 OCTAVE_API Matrix stack (const DiagMatrix& a) const;
131
132 friend OCTAVE_API Matrix real (const ComplexMatrix& a);
133 friend OCTAVE_API Matrix imag (const ComplexMatrix& a);
134
135 friend class ComplexMatrix;
136
137 Matrix hermitian () const { return MArray<double>::transpose (); }
138 Matrix transpose () const { return MArray<double>::transpose (); }
139
140 // resize is the destructive equivalent for this one
141
142 OCTAVE_API Matrix
143 extract (octave_idx_type r1, octave_idx_type c1,
144 octave_idx_type r2, octave_idx_type c2) const;
145
146 OCTAVE_API Matrix
147 extract_n (octave_idx_type r1, octave_idx_type c1,
148 octave_idx_type nr, octave_idx_type nc) const;
149
150 // extract row or column i.
151
152 OCTAVE_API RowVector row (octave_idx_type i) const;
153
154 OCTAVE_API ColumnVector column (octave_idx_type i) const;
155
156 void resize (octave_idx_type nr, octave_idx_type nc, double rfv = 0)
157 {
158 MArray<double>::resize (dim_vector (nr, nc), rfv);
159 }
160
161private:
162 Matrix tinverse (MatrixType& mattype, octave_idx_type& info, double& rcon,
163 bool force, bool calc_cond) const;
164
165 Matrix finverse (MatrixType& mattype, octave_idx_type& info, double& rcon,
166 bool force, bool calc_cond) const;
167
168public:
169 OCTAVE_API Matrix inverse () const;
170 OCTAVE_API Matrix inverse (octave_idx_type& info) const;
171 OCTAVE_API Matrix
172 inverse (octave_idx_type& info, double& rcon,
173 bool force = false, bool calc_cond = true) const;
174
175 OCTAVE_API Matrix inverse (MatrixType& mattype) const;
176 OCTAVE_API Matrix inverse (MatrixType& mattype, octave_idx_type& info) const;
177 OCTAVE_API Matrix
178 inverse (MatrixType& mattype, octave_idx_type& info, double& rcon,
179 bool force = false, bool calc_cond = true) const;
180
181 OCTAVE_API Matrix pseudo_inverse (double tol = 0.0) const;
182
183 OCTAVE_API ComplexMatrix fourier () const;
184 OCTAVE_API ComplexMatrix ifourier () const;
185
186 OCTAVE_API ComplexMatrix fourier2d () const;
187 OCTAVE_API ComplexMatrix ifourier2d () const;
188
189 OCTAVE_API DET determinant () const;
190 OCTAVE_API DET determinant (octave_idx_type& info) const;
191 OCTAVE_API DET
192 determinant (octave_idx_type& info, double& rcon,
193 bool calc_cond = true) const;
194 OCTAVE_API DET
195 determinant (MatrixType& mattype, octave_idx_type& info,
196 double& rcon, bool calc_cond = true) const;
197
198 OCTAVE_API double rcond () const;
199 OCTAVE_API double rcond (MatrixType& mattype) const;
200
201private:
202 // Upper triangular matrix solvers
203 Matrix utsolve (MatrixType& mattype, const Matrix& b, octave_idx_type& info,
204 double& rcon, solve_singularity_handler sing_handler,
205 bool calc_cond = false,
206 blas_trans_type transt = blas_no_trans) const;
207
208 // Lower triangular matrix solvers
209 Matrix ltsolve (MatrixType& mattype, const Matrix& b, octave_idx_type& info,
210 double& rcon, solve_singularity_handler sing_handler,
211 bool calc_cond = false,
212 blas_trans_type transt = blas_no_trans) const;
213
214 // Full matrix solvers (lu/cholesky)
215 Matrix fsolve (MatrixType& mattype, const Matrix& b, octave_idx_type& info,
216 double& rcon, solve_singularity_handler sing_handler,
217 bool calc_cond = false) const;
218
219public:
220 // Generic interface to solver with no probing of type
221 OCTAVE_API Matrix solve (MatrixType& mattype, const Matrix& b) const;
222 OCTAVE_API Matrix
223 solve (MatrixType& mattype, const Matrix& b, octave_idx_type& info) const;
224 OCTAVE_API Matrix
225 solve (MatrixType& mattype, const Matrix& b, octave_idx_type& info,
226 double& rcon) const;
227 OCTAVE_API Matrix
228 solve (MatrixType& mattype, const Matrix& b, octave_idx_type& info,
229 double& rcon, solve_singularity_handler sing_handler,
230 bool singular_fallback = true,
231 blas_trans_type transt = blas_no_trans) const;
232
233 OCTAVE_API ComplexMatrix
234 solve (MatrixType& mattype, const ComplexMatrix& b) const;
235 OCTAVE_API ComplexMatrix
236 solve (MatrixType& mattype, const ComplexMatrix& b,
237 octave_idx_type& info) const;
238 OCTAVE_API ComplexMatrix
239 solve (MatrixType& mattype, const ComplexMatrix& b,
240 octave_idx_type& info, double& rcon) const;
241 OCTAVE_API ComplexMatrix
242 solve (MatrixType& mattype, const ComplexMatrix& b,
243 octave_idx_type& info, double& rcon,
244 solve_singularity_handler sing_handler,
245 bool singular_fallback = true,
246 blas_trans_type transt = blas_no_trans) const;
247
248 OCTAVE_API ColumnVector
249 solve (MatrixType& mattype, const ColumnVector& b) const;
250 OCTAVE_API ColumnVector
251 solve (MatrixType& mattype, const ColumnVector& b,
252 octave_idx_type& info) const;
253 OCTAVE_API ColumnVector
254 solve (MatrixType& mattype, const ColumnVector& b,
255 octave_idx_type& info, double& rcon) const;
256 OCTAVE_API ColumnVector
257 solve (MatrixType& mattype, const ColumnVector& b, octave_idx_type& info,
258 double& rcon, solve_singularity_handler sing_handler,
259 blas_trans_type transt = blas_no_trans) const;
260
261 OCTAVE_API ComplexColumnVector
262 solve (MatrixType& mattype, const ComplexColumnVector& b) const;
263 OCTAVE_API ComplexColumnVector
264 solve (MatrixType& mattype, const ComplexColumnVector& b,
265 octave_idx_type& info) const;
266 OCTAVE_API ComplexColumnVector
267 solve (MatrixType& mattype, const ComplexColumnVector& b,
268 octave_idx_type& info, double& rcon) const;
269 OCTAVE_API ComplexColumnVector
270 solve (MatrixType& mattype, const ComplexColumnVector& b,
271 octave_idx_type& info, double& rcon,
272 solve_singularity_handler sing_handler,
273 blas_trans_type transt = blas_no_trans) const;
274
275 // Generic interface to solver with probing of type
276 OCTAVE_API Matrix solve (const Matrix& b) const;
277 OCTAVE_API Matrix solve (const Matrix& b, octave_idx_type& info) const;
278 OCTAVE_API Matrix
279 solve (const Matrix& b, octave_idx_type& info, double& rcon) const;
280 OCTAVE_API Matrix
281 solve (const Matrix& b, octave_idx_type& info, double& rcon,
282 solve_singularity_handler sing_handler,
283 blas_trans_type transt = blas_no_trans) const;
284
285 OCTAVE_API ComplexMatrix solve (const ComplexMatrix& b) const;
286 OCTAVE_API ComplexMatrix
287 solve (const ComplexMatrix& b, octave_idx_type& info) const;
288 OCTAVE_API ComplexMatrix
289 solve (const ComplexMatrix& b, octave_idx_type& info,
290 double& rcon) const;
291 OCTAVE_API ComplexMatrix
292 solve (const ComplexMatrix& b, octave_idx_type& info, double& rcon,
293 solve_singularity_handler sing_handler,
294 blas_trans_type transt = blas_no_trans) const;
295
296 OCTAVE_API ColumnVector solve (const ColumnVector& b) const;
297 OCTAVE_API ColumnVector
298 solve (const ColumnVector& b, octave_idx_type& info) const;
299 OCTAVE_API ColumnVector
300 solve (const ColumnVector& b, octave_idx_type& info, double& rcon) const;
301 OCTAVE_API ColumnVector
302 solve (const ColumnVector& b, octave_idx_type& info, double& rcon,
303 solve_singularity_handler sing_handler,
304 blas_trans_type transt = blas_no_trans) const;
305
306 OCTAVE_API ComplexColumnVector solve (const ComplexColumnVector& b) const;
307 OCTAVE_API ComplexColumnVector
308 solve (const ComplexColumnVector& b, octave_idx_type& info) const;
309 OCTAVE_API ComplexColumnVector
310 solve (const ComplexColumnVector& b, octave_idx_type& info,
311 double& rcon) const;
312 OCTAVE_API ComplexColumnVector
313 solve (const ComplexColumnVector& b, octave_idx_type& info, double& rcon,
314 solve_singularity_handler sing_handler,
315 blas_trans_type transt = blas_no_trans) const;
316
317 // Singular solvers
318 OCTAVE_API Matrix lssolve (const Matrix& b) const;
319 OCTAVE_API Matrix lssolve (const Matrix& b, octave_idx_type& info) const;
320 OCTAVE_API Matrix
321 lssolve (const Matrix& b, octave_idx_type& info,
322 octave_idx_type& rank) const;
323 OCTAVE_API Matrix
324 lssolve (const Matrix& b, octave_idx_type& info, octave_idx_type& rank,
325 double& rcon) const;
326
327 OCTAVE_API ComplexMatrix lssolve (const ComplexMatrix& b) const;
328 OCTAVE_API ComplexMatrix
329 lssolve (const ComplexMatrix& b, octave_idx_type& info) const;
330 OCTAVE_API ComplexMatrix
331 lssolve (const ComplexMatrix& b, octave_idx_type& info,
332 octave_idx_type& rank) const;
333 OCTAVE_API ComplexMatrix
334 lssolve (const ComplexMatrix& b, octave_idx_type& info,
335 octave_idx_type& rank, double& rcon) const;
336
337 OCTAVE_API ColumnVector lssolve (const ColumnVector& b) const;
338 OCTAVE_API ColumnVector
339 lssolve (const ColumnVector& b, octave_idx_type& info) const;
340 OCTAVE_API ColumnVector
341 lssolve (const ColumnVector& b, octave_idx_type& info,
342 octave_idx_type& rank) const;
343 OCTAVE_API ColumnVector
344 lssolve (const ColumnVector& b, octave_idx_type& info,
345 octave_idx_type& rank, double& rcon) const;
346
347 OCTAVE_API ComplexColumnVector lssolve (const ComplexColumnVector& b) const;
348 OCTAVE_API ComplexColumnVector
349 lssolve (const ComplexColumnVector& b, octave_idx_type& info) const;
350 OCTAVE_API ComplexColumnVector
351 lssolve (const ComplexColumnVector& b, octave_idx_type& info,
352 octave_idx_type& rank) const;
353 OCTAVE_API ComplexColumnVector
354 lssolve (const ComplexColumnVector& b, octave_idx_type& info,
355 octave_idx_type& rank, double& rcon) const;
356
357 OCTAVE_API Matrix& operator += (const DiagMatrix& a);
358 OCTAVE_API Matrix& operator -= (const DiagMatrix& a);
359
360 // unary operations
361
362 // other operations
363
364 OCTAVE_API boolMatrix all (int dim = -1) const;
365 OCTAVE_API boolMatrix any (int dim = -1) const;
366
367 OCTAVE_API Matrix cumprod (int dim = -1) const;
368 OCTAVE_API Matrix cumsum (int dim = -1) const;
369 OCTAVE_API Matrix prod (int dim = -1) const;
370 OCTAVE_API Matrix sum (int dim = -1) const;
371 OCTAVE_API Matrix sumsq (int dim = -1) const;
372 OCTAVE_API Matrix abs () const;
373
374 OCTAVE_API Matrix diag (octave_idx_type k = 0) const;
375
376 OCTAVE_API DiagMatrix diag (octave_idx_type m, octave_idx_type n) const;
377
378 OCTAVE_API ColumnVector row_min () const;
379 OCTAVE_API ColumnVector row_max () const;
380
381 OCTAVE_API ColumnVector row_min (Array<octave_idx_type>& index) const;
382 OCTAVE_API ColumnVector row_max (Array<octave_idx_type>& index) const;
383
384 OCTAVE_API RowVector column_min () const;
385 OCTAVE_API RowVector column_max () const;
386
387 OCTAVE_API RowVector column_min (Array<octave_idx_type>& index) const;
388 OCTAVE_API RowVector column_max (Array<octave_idx_type>& index) const;
389
390 // i/o
391
392 friend OCTAVE_API std::ostream&
393 operator << (std::ostream& os, const Matrix& a);
394 friend OCTAVE_API std::istream&
395 operator >> (std::istream& is, Matrix& a);
396};
397
398// Publish externally used friend functions.
399
400extern OCTAVE_API Matrix real (const ComplexMatrix& a);
401extern OCTAVE_API Matrix imag (const ComplexMatrix& a);
402
403// column vector by row vector -> matrix operations
404
405extern OCTAVE_API Matrix operator * (const ColumnVector& a,
406 const RowVector& b);
407
408// Other functions.
409
410extern OCTAVE_API Matrix Givens (double, double);
411
412extern OCTAVE_API Matrix Sylvester (const Matrix&, const Matrix&,
413 const Matrix&);
414
415extern OCTAVE_API Matrix xgemm (const Matrix& a, const Matrix& b,
416 blas_trans_type transa = blas_no_trans,
417 blas_trans_type transb = blas_no_trans);
418
419extern OCTAVE_API Matrix operator * (const Matrix& a, const Matrix& b);
420
421extern OCTAVE_API Matrix min (double d, const Matrix& m);
422extern OCTAVE_API Matrix min (const Matrix& m, double d);
423extern OCTAVE_API Matrix min (const Matrix& a, const Matrix& b);
424
425extern OCTAVE_API Matrix max (double d, const Matrix& m);
426extern OCTAVE_API Matrix max (const Matrix& m, double d);
427extern OCTAVE_API Matrix max (const Matrix& a, const Matrix& b);
428
429extern OCTAVE_API Matrix linspace (const ColumnVector& x1,
430 const ColumnVector& x2,
431 octave_idx_type n);
432
433MS_CMP_OP_DECLS (Matrix, double, OCTAVE_API)
434MS_BOOL_OP_DECLS (Matrix, double, OCTAVE_API)
435
436SM_CMP_OP_DECLS (double, Matrix, OCTAVE_API)
437SM_BOOL_OP_DECLS (double, Matrix, OCTAVE_API)
438
439MM_CMP_OP_DECLS (Matrix, Matrix, OCTAVE_API)
440MM_BOOL_OP_DECLS (Matrix, Matrix, OCTAVE_API)
441
442MARRAY_FORWARD_DEFS (MArray, Matrix, double)
443
444template <typename T>
445void read_int (std::istream& is, bool swap_bytes, T& val);
446
447#endif
operator<<
template std::ostream & operator<<(std::ostream &, const Array< bool > &)
operator+=
ComplexColumnVector operator+=(ComplexColumnVector &x, const Complex &y)
Definition CColVector.h:156
operator-=
ComplexColumnVector operator-=(ComplexColumnVector &x, const Complex &y)
Definition CColVector.h:156
MARRAY_FORWARD_DEFS
#define MARRAY_FORWARD_DEFS(B, R, T)
Definition MArray.h:128
operator>>
std::istream & operator>>(std::istream &is, SparseBoolMatrix &a)
Definition boolSparse.cc:279
Array
N Dimensional Array with copy-on-write semantics.
Definition Array.h:130
Array< T >::resize
void resize(const dim_vector &dv, const T &rfv)
Definition Array-base.cc:1031
MArray
Template for N-dimensional array classes with like-type math operators.
Definition MArray.h:61
MArray::transpose
MArray< T > transpose() const
Definition MArray.h:97
MDiagArray2
Template for two dimensional diagonal array with math operators.
Definition MDiagArray2.h:54
Matrix::Matrix
Matrix(const Array< U > &a)
Definition dMatrix.h:83
Matrix::Matrix
Matrix()=default
Matrix::real_diag_matrix_type
DiagMatrix real_diag_matrix_type
Definition dMatrix.h:52
Matrix::row_vector_type
RowVector row_vector_type
Definition dMatrix.h:44
Matrix::complex_diag_matrix_type
ComplexDiagMatrix complex_diag_matrix_type
Definition dMatrix.h:53
Matrix::real_matrix_type
Matrix real_matrix_type
Definition dMatrix.h:49
Matrix::complex_matrix_type
ComplexMatrix complex_matrix_type
Definition dMatrix.h:50
Matrix::real_row_vector_type
RowVector real_row_vector_type
Definition dMatrix.h:47
Matrix::transpose
Matrix transpose() const
Definition dMatrix.h:138
Matrix::hermitian
Matrix hermitian() const
Definition dMatrix.h:137
Matrix::complex_elt_type
Complex complex_elt_type
Definition dMatrix.h:56
Matrix::Matrix
Matrix(octave_idx_type r, octave_idx_type c)
Definition dMatrix.h:68
Matrix::Matrix
Matrix(const Matrix &a)=default
Matrix::Matrix
Matrix(octave_idx_type r, octave_idx_type c, double val)
Definition dMatrix.h:71
Matrix::Matrix
Matrix(const dim_vector &dv)
Definition dMatrix.h:74
Matrix::real_column_vector_type
ColumnVector real_column_vector_type
Definition dMatrix.h:46
Matrix::real_elt_type
double real_elt_type
Definition dMatrix.h:55
Matrix::column_vector_type
ColumnVector column_vector_type
Definition dMatrix.h:43
Matrix::resize
void resize(octave_idx_type nr, octave_idx_type nc, double rfv=0)
Definition dMatrix.h:156
Matrix::~Matrix
~Matrix()=default
Matrix::Matrix
Matrix(const MArray< U > &a)
Definition dMatrix.h:80
Matrix::Matrix
Matrix(const dim_vector &dv, double val)
Definition dMatrix.h:76
NDArray::operator=
NDArray & operator=(const NDArray &a)
Definition dNDArray.h:64
base_det
Definition DET.h:38
dim_vector
Vector representing the dimensions (size) of an Array.
Definition dim-vector.h:90
octave_idx_type
real
ColumnVector real(const ComplexColumnVector &a)
Definition dColVector.cc:137
imag
ColumnVector imag(const ComplexColumnVector &a)
Definition dColVector.cc:143
imag
Matrix imag(const ComplexMatrix &a)
Definition dMatrix.cc:392
operator*
Matrix operator*(const ColumnVector &a, const RowVector &b)
Definition dMatrix.cc:2330
read_int
void read_int(std::istream &is, bool swap_bytes, T &val)
Givens
Matrix Givens(double, double)
Definition dMatrix.cc:2687
max
Matrix max(double d, const Matrix &m)
Definition dMatrix.cc:2948
xgemm
Matrix xgemm(const Matrix &a, const Matrix &b, blas_trans_type transa=blas_no_trans, blas_trans_type transb=blas_no_trans)
Definition dMatrix.cc:2786
linspace
Matrix linspace(const ColumnVector &x1, const ColumnVector &x2, octave_idx_type n)
Definition dMatrix.cc:3012
Sylvester
Matrix Sylvester(const Matrix &, const Matrix &, const Matrix &)
Definition dMatrix.cc:2704
min
Matrix min(double d, const Matrix &m)
Definition dMatrix.cc:2884
real
Matrix real(const ComplexMatrix &a)
Definition dMatrix.cc:386
operator!=
bool operator!=(const dim_vector &a, const dim_vector &b)
Definition dim-vector.h:532
operator==
bool operator==(const dim_vector &a, const dim_vector &b)
Definition dim-vector.h:516
d
F77_RET_T const F77_DBLE const F77_DBLE F77_DBLE * d
Definition lo-slatec-proto.h:39
OCTAVE_API
#define OCTAVE_API
Definition main.in.cc:55
blas_trans_type
blas_trans_type
Definition mx-defs.h:80
blas_no_trans
@ blas_no_trans
Definition mx-defs.h:81
SM_BOOL_OP_DECLS
#define SM_BOOL_OP_DECLS(S, M, API)
Definition mx-op-decl.h:122
MS_CMP_OP_DECLS
#define MS_CMP_OP_DECLS(M, S, API)
Definition mx-op-decl.h:89
SM_CMP_OP_DECLS
#define SM_CMP_OP_DECLS(S, M, API)
Definition mx-op-decl.h:114
MS_BOOL_OP_DECLS
#define MS_BOOL_OP_DECLS(M, S, API)
Definition mx-op-decl.h:97
MM_CMP_OP_DECLS
#define MM_CMP_OP_DECLS(M1, M2, API)
Definition mx-op-decl.h:139
MM_BOOL_OP_DECLS
#define MM_BOOL_OP_DECLS(M1, M2, API)
Definition mx-op-decl.h:147
Complex
std::complex< double > Complex
Definition oct-cmplx.h:33
abs
template int8_t abs(int8_t)