GetFEM  5.5
gmm_interface.h
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30 
31 
32 /**@file gmm_interface.h
33  @author Yves Renard <Yves.Renard@insa-lyon.fr>
34  @date October 13, 2002.
35  @brief gmm interface for STL vectors.
36 */
37 
38 #ifndef GMM_INTERFACE_H__
39 #define GMM_INTERFACE_H__
40 
41 #include "gmm_blas.h"
42 #include "gmm_sub_index.h"
43 
44 namespace gmm {
45 
46  /* ********************************************************************* */
47  /* */
48  /* What is needed for a Vector type : */
49  /* Vector v(n) defines a vector with n components. */
50  /* v[i] allows to access to the ith component of v. */
51  /* linalg_traits<Vector> should be filled with appropriate definitions */
52  /* */
53  /* for a dense vector : the minimum is two random iterators (begin and */
54  /* end) and a pointer to a valid origin. */
55  /* for a sparse vector : the minimum is two forward iterators, with */
56  /* a method it.index() which gives the index of */
57  /* a non zero element, an interface object */
58  /* should describe the method to add new non */
59  /* zero element, and a pointer to a valid */
60  /* origin. */
61  /* */
62  /* What is needed for a Matrix type : */
63  /* Matrix m(n, m) defines a matrix with n rows and m columns. */
64  /* m(i, j) allows to access to the element at row i and column j. */
65  /* linalg_traits<Matrix> should be filled with appropriate definitions */
66  /* */
67  /* What is needed for an iterator on dense vector */
68  /* to be standard random access iterator */
69  /* */
70  /* What is needed for an iterator on a sparse vector */
71  /* to be a standard bidirectional iterator */
72  /* elt should be sorted with increasing indices. */
73  /* it.index() gives the index of the non-zero element. */
74  /* */
75  /* Remark : If original iterators are not convenient, they could be */
76  /* redefined and interfaced in linalg_traits<Vector> without changing */
77  /* the original Vector type. */
78  /* */
79  /* ********************************************************************* */
80 
81  /* ********************************************************************* */
82  /* Simple references on vectors */
83  /* ********************************************************************* */
84 
85  template <typename PT> struct simple_vector_ref {
86  typedef simple_vector_ref<PT> this_type;
87  typedef typename std::iterator_traits<PT>::value_type V;
88  typedef V * CPT;
89  typedef typename std::iterator_traits<PT>::reference ref_V;
90  typedef typename linalg_traits<this_type>::iterator iterator;
91  typedef typename linalg_traits<this_type>::reference reference;
92  typedef typename linalg_traits<this_type>::porigin_type porigin_type;
93 
94  iterator begin_, end_;
95  porigin_type origin;
96  size_type size_;
97 
98  simple_vector_ref(ref_V v) : begin_(vect_begin(const_cast<V&>(v))),
99  end_(vect_end(const_cast<V&>(v))),
100  origin(linalg_origin(const_cast<V&>(v))),
101  size_(vect_size(v)) {}
102 
103  simple_vector_ref(const simple_vector_ref<CPT> &cr)
104  : begin_(cr.begin_),end_(cr.end_),origin(cr.origin),size_(cr.size_) {}
105 
106  simple_vector_ref() {}
107 
108  reference operator[](size_type i) const
109  { return linalg_traits<V>::access(origin, begin_, end_, i); }
110  };
111 
112  template <typename IT, typename ORG, typename PT> inline
113  void set_to_begin(IT &it, ORG o, simple_vector_ref<PT> *,linalg_modifiable) {
114  typedef typename linalg_traits<simple_vector_ref<PT> >::V_reference ref_t;
115  set_to_begin(it, o, PT(), ref_t());
116  }
117 
118  template <typename IT, typename ORG, typename PT> inline
119  void set_to_begin(IT &it, ORG o, const simple_vector_ref<PT> *,
120  linalg_modifiable) {
121  typedef typename linalg_traits<simple_vector_ref<PT> >::V_reference ref_t;
122  set_to_begin(it, o, PT(), ref_t());
123  }
124 
125  template <typename IT, typename ORG, typename PT> inline
126  void set_to_end(IT &it, ORG o, simple_vector_ref<PT> *, linalg_modifiable) {
127  typedef typename linalg_traits<simple_vector_ref<PT> >::V_reference ref_t;
128  set_to_end(it, o, PT(), ref_t());
129  }
130 
131  template <typename IT, typename ORG, typename PT> inline
132  void set_to_end(IT &it, ORG o, const simple_vector_ref<PT> *,
133  linalg_modifiable) {
134  typedef typename linalg_traits<simple_vector_ref<PT> >::V_reference ref_t;
135  set_to_end(it, o, PT(), ref_t());
136  }
137 
138 
139  template <typename PT> struct linalg_traits<simple_vector_ref<PT> > {
140  typedef simple_vector_ref<PT> this_type;
141  typedef this_type *pthis_type;
142  typedef typename std::iterator_traits<PT>::value_type V;
143  typedef typename linalg_traits<V>::origin_type origin_type;
144  typedef V *pV;
145  typedef typename linalg_traits<V>::is_reference V_reference;
146  typedef typename which_reference<PT>::is_reference is_reference;
147  typedef abstract_vector linalg_type;
148  typedef typename linalg_traits<V>::value_type value_type;
149  typedef typename select_ref<value_type, typename
150  linalg_traits<V>::reference, PT>::ref_type reference;
151  typedef typename select_ref<const origin_type *, origin_type *,
152  PT>::ref_type porigin_type;
153  typedef typename select_ref<typename linalg_traits<V>::const_iterator,
154  typename linalg_traits<V>::iterator, PT>::ref_type iterator;
155  typedef typename linalg_traits<V>::const_iterator const_iterator;
156  typedef typename linalg_traits<V>::storage_type storage_type;
157  typedef linalg_true index_sorted;
158  static size_type size(const this_type &v) { return v.size_; }
159  static inline iterator begin(this_type &v) {
160  iterator it = v.begin_;
161  set_to_begin(it, v.origin, pthis_type(), is_reference());
162  return it;
163  }
164  static inline const_iterator begin(const this_type &v) {
165  const_iterator it = v.begin_;
166  set_to_begin(it, v.origin, pthis_type(), is_reference());
167  return it;
168  }
169  static inline iterator end(this_type &v) {
170  iterator it = v.end_;
171  set_to_end(it, v.origin, pthis_type(), is_reference());
172  return it;
173  }
174  static inline const_iterator end(const this_type &v) {
175  const_iterator it = v.end_;
176  set_to_end(it, v.origin, pthis_type(), is_reference());
177  return it;
178  }
179  static origin_type* origin(this_type &v) { return v.origin; }
180  static const origin_type* origin(const this_type &v) { return v.origin; }
181  static void clear(origin_type* o, const iterator &it, const iterator &ite)
182  { linalg_traits<V>::clear(o, it, ite); }
183  static void do_clear(this_type &v) { clear(v.origin, v.begin_, v.end_); }
184  static value_type access(const origin_type *o, const const_iterator &it,
185  const const_iterator &ite, size_type i)
186  { return linalg_traits<V>::access(o, it, ite, i); }
187  static reference access(origin_type *o, const iterator &it,
188  const iterator &ite, size_type i)
189  { return linalg_traits<V>::access(o, it, ite, i); }
190  };
191 
192  template <typename PT>
193  std::ostream &operator << (std::ostream &o, const simple_vector_ref<PT>& v)
194  { gmm::write(o,v); return o; }
195 
196  template <typename T, typename alloc>
197  simple_vector_ref<const std::vector<T,alloc> *>
198  vref(const std::vector<T, alloc> &vv)
199  { return simple_vector_ref<const std::vector<T,alloc> *>(vv); }
200 
201 
202  /* ********************************************************************* */
203  /* */
204  /* Traits for S.T.L. object */
205  /* */
206  /* ********************************************************************* */
207 
208  template <typename T, typename alloc>
209  struct linalg_traits<std::vector<T, alloc> > {
210  typedef std::vector<T, alloc> this_type;
211  typedef this_type origin_type;
212  typedef linalg_false is_reference;
213  typedef abstract_vector linalg_type;
214  typedef T value_type;
215  typedef T& reference;
216  typedef typename this_type::iterator iterator;
217  typedef typename this_type::const_iterator const_iterator;
218  typedef abstract_dense storage_type;
219  typedef linalg_true index_sorted;
220  static size_type size(const this_type &v) { return v.size(); }
221  static iterator begin(this_type &v) { return v.begin(); }
222  static const_iterator begin(const this_type &v) { return v.begin(); }
223  static iterator end(this_type &v) { return v.end(); }
224  static const_iterator end(const this_type &v) { return v.end(); }
225  static origin_type* origin(this_type &v) { return &v; }
226  static const origin_type* origin(const this_type &v) { return &v; }
227  static void clear(origin_type*, const iterator &it, const iterator &ite)
228  { std::fill(it, ite, value_type(0)); }
229  static void do_clear(this_type &v) { std::fill(v.begin(), v.end(), T(0)); }
230  static value_type access(const origin_type *, const const_iterator &it,
231  const const_iterator &, size_type i)
232  { return it[i]; }
233  static reference access(origin_type *, const iterator &it,
234  const iterator &, size_type i)
235  { return it[i]; }
236  static void resize(this_type &v, size_type n) { v.resize(n); }
237  };
238 
239 
240 
241  template <typename T>
242  inline size_type nnz(const std::vector<T>& l) { return l.size(); }
243 
244  /* ********************************************************************* */
245  /* */
246  /* Traits for ref objects */
247  /* */
248  /* ********************************************************************* */
249 
250  template <typename IT, typename V>
251  struct tab_ref_with_origin : public gmm::tab_ref<IT> {
252  typedef tab_ref_with_origin<IT, V> this_type;
253  // next line replaced by the 4 following lines in order to please aCC
254  //typedef typename linalg_traits<this_type>::porigin_type porigin_type;
255  typedef typename linalg_traits<V>::origin_type origin_type;
256  typedef typename std::iterator_traits<IT>::pointer PT;
257  typedef typename select_ref<const origin_type *, origin_type *,
258  PT>::ref_type porigin_type;
259 
260 
261  porigin_type origin;
262 
263  tab_ref_with_origin() {}
264  template <class PT> tab_ref_with_origin(const IT &b, const IT &e, PT p)
265  : gmm::tab_ref<IT>(b,e), origin(porigin_type(p)) {}
266  tab_ref_with_origin(const IT &b, const IT &e, porigin_type p)
267  : gmm::tab_ref<IT>(b,e), origin(p) {}
268 
269  tab_ref_with_origin(const V &v, const sub_interval &si)
270  : gmm::tab_ref<IT>(vect_begin(const_cast<V&>(v))+si.min,
271  vect_begin(const_cast<V&>(v))+si.max),
272  origin(linalg_origin(const_cast<V&>(v))) {}
273  tab_ref_with_origin(V &v, const sub_interval &si)
274  : gmm::tab_ref<IT>(vect_begin(const_cast<V&>(v))+si.min,
275  vect_begin(const_cast<V&>(v))+si.max),
276  origin(linalg_origin(const_cast<V&>(v))) {}
277  };
278 
279  template <typename IT, typename V>
280  struct linalg_traits<tab_ref_with_origin<IT, V> > {
281  typedef typename std::iterator_traits<IT>::pointer PT;
282  typedef typename linalg_traits<V>::origin_type origin_type;
283  typedef tab_ref_with_origin<IT, V> this_type;
284  typedef typename which_reference<PT>::is_reference is_reference;
285  typedef abstract_vector linalg_type;
286  typedef typename select_ref<const origin_type *, origin_type *,
287  PT>::ref_type porigin_type;
288  typedef typename std::iterator_traits<IT>::value_type value_type;
289  typedef typename std::iterator_traits<IT>::reference reference;
290  typedef typename this_type::iterator iterator;
291  typedef typename this_type::iterator const_iterator;
292  typedef abstract_dense storage_type;
293  typedef linalg_true index_sorted;
294  static size_type size(const this_type &v) { return v.size(); }
295  static iterator begin(this_type &v) { return v.begin(); }
296  static const_iterator begin(const this_type &v) { return v.begin(); }
297  static iterator end(this_type &v) { return v.end(); }
298  static const_iterator end(const this_type &v) { return v.end(); }
299  static origin_type* origin(this_type &v) { return v.origin; }
300  static const origin_type* origin(const this_type &v) { return v.origin; }
301  static void clear(origin_type*, const iterator &it, const iterator &ite)
302  { std::fill(it, ite, value_type(0)); }
303  static inline void do_clear(this_type &v)
304  { std::fill(v.begin(), v.end(), value_type(0)); }
305  static value_type access(const origin_type *, const const_iterator &it,
306  const const_iterator &, size_type i)
307  { return it[i]; }
308  static reference access(origin_type *, const iterator &it,
309  const iterator &, size_type i)
310  { return it[i]; }
311  };
312 
313  template <typename IT, typename V> std::ostream &operator <<
314  (std::ostream &o, const tab_ref_with_origin<IT, V>& m)
315  { gmm::write(o,m); return o; }
316 
317 
318  template <typename IT, typename V>
319  struct tab_ref_reg_spaced_with_origin : public gmm::tab_ref_reg_spaced<IT> {
320  typedef tab_ref_reg_spaced_with_origin<IT, V> this_type;
321  typedef typename linalg_traits<this_type>::porigin_type porigin_type;
322 
323  porigin_type origin;
324 
325  tab_ref_reg_spaced_with_origin() {}
326  tab_ref_reg_spaced_with_origin(const IT &b, size_type n, size_type s,
327  const porigin_type p)
328  : gmm::tab_ref_reg_spaced<IT>(b,n,s), origin(p) {}
329  tab_ref_reg_spaced_with_origin(const V &v, const sub_slice &si)
330  : gmm::tab_ref_reg_spaced<IT>(vect_begin(const_cast<V&>(v)) + si.min,
331  si.N, (si.max - si.min)/si.N),
332  origin(linalg_origin(const_cast<V&>(v))) {}
333  tab_ref_reg_spaced_with_origin(V &v, const sub_slice &si)
334  : gmm::tab_ref_reg_spaced<IT>(vect_begin(const_cast<V&>(v)) + si.min,
335  si.N, (si.max - si.min)/si.N),
336  origin(linalg_origin(const_cast<V&>(v))) {}
337  };
338 
339  template <typename IT, typename V>
340  struct linalg_traits<tab_ref_reg_spaced_with_origin<IT, V> > {
341  typedef typename std::iterator_traits<IT>::pointer PT;
342  typedef tab_ref_reg_spaced_with_origin<IT, V> this_type;
343  typedef typename linalg_traits<V>::origin_type origin_type;
344  typedef typename select_ref<const origin_type *, origin_type *,
345  PT>::ref_type porigin_type;
346  typedef typename which_reference<PT>::is_reference is_reference;
347  typedef abstract_vector linalg_type;
348  typedef typename std::iterator_traits<IT>::value_type value_type;
349  typedef typename std::iterator_traits<IT>::reference reference;
350  typedef typename this_type::iterator iterator;
351  typedef typename this_type::iterator const_iterator;
352  typedef abstract_dense storage_type;
353  typedef linalg_true index_sorted;
354  static size_type size(const this_type &v) { return v.size(); }
355  static iterator begin(this_type &v) { return v.begin(); }
356  static const_iterator begin(const this_type &v) { return v.begin(); }
357  static iterator end(this_type &v) { return v.end(); }
358  static const_iterator end(const this_type &v) { return v.end(); }
359  static origin_type* origin(this_type &v) { return v.origin; }
360  static const origin_type* origin(const this_type &v) { return v.origin; }
361  static void clear(origin_type*, const iterator &it, const iterator &ite)
362  { std::fill(it, ite, value_type(0)); }
363  static void do_clear(this_type &v)
364  { std::fill(v.begin(), v.end(), value_type(0)); }
365  static value_type access(const origin_type *, const const_iterator &it,
366  const const_iterator &, size_type i)
367  { return it[i]; }
368  static reference access(origin_type *, const iterator &it,
369  const iterator &, size_type i)
370  { return it[i]; }
371  };
372 
373  template <typename IT, typename V> std::ostream &operator <<
374  (std::ostream &o, const tab_ref_reg_spaced_with_origin<IT, V>& m)
375  { gmm::write(o,m); return o; }
376 
377 
378  template <typename IT, typename ITINDEX, typename V>
379  struct tab_ref_index_ref_with_origin
380  : public gmm::tab_ref_index_ref<IT, ITINDEX> {
381  typedef tab_ref_index_ref_with_origin<IT, ITINDEX, V> this_type;
382  typedef typename linalg_traits<this_type>::porigin_type porigin_type;
383 
384  porigin_type origin;
385 
386  tab_ref_index_ref_with_origin() {}
387  tab_ref_index_ref_with_origin(const IT &b, const ITINDEX &bi,
388  const ITINDEX &ei, porigin_type p)
389  : gmm::tab_ref_index_ref<IT, ITINDEX>(b, bi, ei), origin(p) {}
390 
391  tab_ref_index_ref_with_origin(const V &v, const sub_index &si)
392  : gmm::tab_ref_index_ref<IT, ITINDEX>(vect_begin(const_cast<V&>(v)),
393  si.begin(), si.end()),
394  origin(linalg_origin(const_cast<V&>(v))) {}
395  tab_ref_index_ref_with_origin(V &v, const sub_index &si)
396  : gmm::tab_ref_index_ref<IT, ITINDEX>(vect_begin(const_cast<V&>(v)),
397  si.begin(), si.end()),
398  origin(linalg_origin(const_cast<V&>(v))) {}
399  };
400 
401  template <typename IT, typename ITINDEX, typename V>
402  struct linalg_traits<tab_ref_index_ref_with_origin<IT, ITINDEX, V> > {
403  typedef typename std::iterator_traits<IT>::pointer PT;
404  typedef tab_ref_index_ref_with_origin<IT, ITINDEX, V> this_type;
405  typedef typename linalg_traits<V>::origin_type origin_type;
406  typedef typename select_ref<const origin_type *, origin_type *,
407  PT>::ref_type porigin_type;
408  typedef typename which_reference<PT>::is_reference is_reference;
409  typedef abstract_vector linalg_type;
410  typedef typename std::iterator_traits<IT>::value_type value_type;
411  typedef typename std::iterator_traits<IT>::reference reference;
412  typedef typename this_type::iterator iterator;
413  typedef typename this_type::iterator const_iterator;
414  typedef abstract_dense storage_type;
415  typedef linalg_true index_sorted;
416  static size_type size(const this_type &v) { return v.size(); }
417  static iterator begin(this_type &v) { return v.begin(); }
418  static const_iterator begin(const this_type &v) { return v.begin(); }
419  static iterator end(this_type &v) { return v.end(); }
420  static const_iterator end(const this_type &v) { return v.end(); }
421  static origin_type* origin(this_type &v) { return v.origin; }
422  static const origin_type* origin(const this_type &v) { return v.origin; }
423  static void clear(origin_type*, const iterator &it, const iterator &ite)
424  { std::fill(it, ite, value_type(0)); }
425  static void do_clear(this_type &v)
426  { std::fill(v.begin(), v.end(), value_type(0)); }
427  static value_type access(const origin_type *, const const_iterator &it,
428  const const_iterator &, size_type i)
429  { return it[i]; }
430  static reference access(origin_type *, const iterator &it,
431  const iterator &, size_type i)
432  { return it[i]; }
433  };
434 
435  template <typename IT, typename ITINDEX, typename V>
436  std::ostream &operator <<
437  (std::ostream &o, const tab_ref_index_ref_with_origin<IT, ITINDEX, V>& m)
438  { gmm::write(o,m); return o; }
439 
440 
441  template<typename ITER, typename MIT, typename PT>
442  struct dense_compressed_iterator {
443  typedef ITER value_type;
444  typedef ITER *pointer;
445  typedef ITER &reference;
446  typedef ptrdiff_t difference_type;
447  typedef std::random_access_iterator_tag iterator_category;
448  typedef size_t size_type;
449  typedef dense_compressed_iterator<ITER, MIT, PT> iterator;
450  typedef typename std::iterator_traits<PT>::value_type *MPT;
451 
452  ITER it;
453  size_type N, nrows, ncols, i;
454  PT origin;
455 
456  iterator operator ++(int) { iterator tmp = *this; i++; return tmp; }
457  iterator operator --(int) { iterator tmp = *this; i--; return tmp; }
458  iterator &operator ++() { ++i; return *this; }
459  iterator &operator --() { --i; return *this; }
460  iterator &operator +=(difference_type ii) { i += ii; return *this; }
461  iterator &operator -=(difference_type ii) { i -= ii; return *this; }
462  iterator operator +(difference_type ii) const
463  { iterator itt = *this; return (itt += ii); }
464  iterator operator -(difference_type ii) const
465  { iterator itt = *this; return (itt -= ii); }
466  difference_type operator -(const iterator &ii) const
467  { return (N ? (it - ii.it) / N : 0) + i - ii.i; }
468 
469  ITER operator *() const { return it+i*N; }
470  ITER operator [](int ii) const { return it + (i+ii) * N; }
471 
472  bool operator ==(const iterator &ii) const
473  { return (*this - ii) == difference_type(0); }
474  bool operator !=(const iterator &ii) const { return !(ii == *this); }
475  bool operator < (const iterator &ii) const
476  { return (*this - ii) < difference_type(0); }
477  bool operator > (const iterator &ii) const
478  { return (*this - ii) > difference_type(0); }
479  bool operator >=(const iterator &ii) const
480  { return (*this - ii) >= difference_type(0); }
481 
482  dense_compressed_iterator() {}
483  dense_compressed_iterator(const dense_compressed_iterator<MIT,MIT,MPT> &ii)
484  : it(ii.it), N(ii.N), nrows(ii.nrows), ncols(ii.ncols), i(ii.i),
485  origin(ii.origin) {}
486  dense_compressed_iterator(const ITER &iter, size_type n, size_type r,
487  size_type c, size_type ii, PT o)
488  : it(iter), N(n), nrows(r), ncols(c), i(ii), origin(o) { }
489 
490  };
491 
492  /* ******************************************************************** */
493  /* Read only reference on a compressed sparse vector */
494  /* ******************************************************************** */
495 
496  template <typename PT1, typename PT2, int shift = 0>
497  struct cs_vector_ref_iterator {
498  PT1 pr;
499  PT2 ir;
500 
501  typedef typename std::iterator_traits<PT1>::value_type value_type;
502  typedef PT1 pointer;
503  typedef typename std::iterator_traits<PT1>::reference reference;
504  typedef size_t size_type;
505  typedef ptrdiff_t difference_type;
506  typedef std::bidirectional_iterator_tag iterator_category;
507  typedef cs_vector_ref_iterator<PT1, PT2, shift> iterator;
508 
509  cs_vector_ref_iterator() {}
510  cs_vector_ref_iterator(PT1 p1, PT2 p2) : pr(p1), ir(p2) {}
511 
512  inline size_type index() const { return (*ir) - shift; }
513  iterator &operator ++() { ++pr; ++ir; return *this; }
514  iterator operator ++(int) { iterator tmp = *this; ++(*this); return tmp; }
515  iterator &operator --() { --pr; --ir; return *this; }
516  iterator operator --(int) { iterator tmp = *this; --(*this); return tmp; }
517 
518  reference operator *() const { return *pr; }
519  pointer operator ->() const { return pr; }
520 
521  bool operator ==(const iterator &i) const { return (i.pr==pr);}
522  bool operator !=(const iterator &i) const { return (i.pr!=pr);}
523  };
524 
525  template <typename PT1, typename PT2, int shift = 0> struct cs_vector_ref {
526  PT1 pr;
527  PT2 ir;
528  size_type n, size_;
529 
530  typedef cs_vector_ref<PT1, PT2, shift> this_type;
531  typedef typename std::iterator_traits<PT1>::value_type value_type;
532  typedef typename linalg_traits<this_type>::const_iterator const_iterator;
533 
534  cs_vector_ref(PT1 pt1, PT2 pt2, size_type nnz, size_type ns)
535  : pr(pt1), ir(pt2), n(nnz), size_(ns) {}
536  cs_vector_ref() {}
537 
538  size_type size() const { return size_; }
539 
540  const_iterator begin() const { return const_iterator(pr, ir); }
541  const_iterator end() const { return const_iterator(pr+n, ir+n); }
542 
543  value_type operator[](size_type i) const
544  { return linalg_traits<this_type>::access(pr, begin(), end(),i); }
545  };
546 
547  template <typename PT1, typename PT2, int shift>
548  struct linalg_traits<cs_vector_ref<PT1, PT2, shift> > {
549  typedef cs_vector_ref<PT1, PT2, shift> this_type;
550  typedef linalg_const is_reference;
551  typedef abstract_vector linalg_type;
552  typedef typename std::iterator_traits<PT1>::value_type value_type;
553  typedef value_type origin_type;
554  typedef typename std::iterator_traits<PT1>::value_type reference;
555  typedef cs_vector_ref_iterator<typename const_pointer<PT1>::pointer,
556  typename const_pointer<PT2>::pointer, shift> const_iterator;
557  typedef abstract_null_type iterator;
558  typedef abstract_sparse storage_type;
559  typedef linalg_true index_sorted;
560  static size_type size(const this_type &v) { return v.size(); }
561  static iterator begin(this_type &v) { return v.begin(); }
562  static const_iterator begin(const this_type &v) { return v.begin(); }
563  static iterator end(this_type &v) { return v.end(); }
564  static const_iterator end(const this_type &v) { return v.end(); }
565  static const origin_type* origin(const this_type &v) { return v.pr; }
566  static value_type access(const origin_type *, const const_iterator &b,
567  const const_iterator &e, size_type i) {
568  if (b.ir == e.ir) return value_type(0);
569  PT2 p = std::lower_bound(b.ir, e.ir, i+shift);
570  return (*p == i+shift && p != e.ir) ? b.pr[p-b.ir] : value_type(0);
571  }
572  };
573 
574  template <typename PT1, typename PT2, int shift>
575  std::ostream &operator <<
576  (std::ostream &o, const cs_vector_ref<PT1, PT2, shift>& m)
577  { gmm::write(o,m); return o; }
578 
579  template <typename PT1, typename PT2, int shift>
580  inline size_type nnz(const cs_vector_ref<PT1, PT2, shift>& l) { return l.n; }
581 
582  /* ******************************************************************** */
583  /* Read only reference on a compressed sparse column matrix */
584  /* ******************************************************************** */
585 
586  template <typename PT1, typename PT2, typename PT3, int shift = 0>
587  struct sparse_compressed_iterator {
588  typedef typename std::iterator_traits<PT1>::value_type value_type;
589  typedef const value_type *pointer;
590  typedef const value_type &reference;
591  typedef ptrdiff_t difference_type;
592  typedef size_t size_type;
593  typedef std::random_access_iterator_tag iterator_category;
594  typedef sparse_compressed_iterator<PT1, PT2, PT3, shift> iterator;
595 
596  PT1 pr;
597  PT2 ir;
598  PT3 jc;
599  size_type n;
600  const value_type *origin;
601 
602  iterator operator ++(int) { iterator tmp = *this; jc++; return tmp; }
603  iterator operator --(int) { iterator tmp = *this; jc--; return tmp; }
604  iterator &operator ++() { jc++; return *this; }
605  iterator &operator --() { jc--; return *this; }
606  iterator &operator +=(difference_type i) { jc += i; return *this; }
607  iterator &operator -=(difference_type i) { jc -= i; return *this; }
608  iterator operator +(difference_type i) const
609  { iterator itt = *this; return (itt += i); }
610  iterator operator -(difference_type i) const
611  { iterator itt = *this; return (itt -= i); }
612  difference_type operator -(const iterator &i) const { return jc - i.jc; }
613 
614  reference operator *() const { return pr + *jc - shift; }
615  reference operator [](int ii) { return pr + *(jc+ii) - shift; }
616 
617  bool operator ==(const iterator &i) const { return (jc == i.jc); }
618  bool operator !=(const iterator &i) const { return !(i == *this); }
619  bool operator < (const iterator &i) const { return (jc < i.jc); }
620  bool operator > (const iterator &i) const { return (jc > i.jc); }
621  bool operator >=(const iterator &i) const { return (jc >= i.jc); }
622 
623  sparse_compressed_iterator() {}
624  sparse_compressed_iterator(PT1 p1, PT2 p2, PT3 p3, size_type nn,
625  const value_type *o)
626  : pr(p1), ir(p2), jc(p3), n(nn), origin(o) { }
627 
628  };
629 
630  template <typename PT1, typename PT2, typename PT3, int shift = 0>
631  struct csc_matrix_ref {
632  PT1 pr; // values.
633  PT2 ir; // row indexes.
634  PT3 jc; // column repartition on pr and ir.
635  size_type nc, nr;
636 
637  typedef typename std::iterator_traits<PT1>::value_type value_type;
638  csc_matrix_ref(PT1 pt1, PT2 pt2, PT3 pt3, size_type nrr, size_type ncc)
639  : pr(pt1), ir(pt2), jc(pt3), nc(ncc), nr(nrr) {}
640  csc_matrix_ref() {}
641 
642  size_type nrows() const { return nr; }
643  size_type ncols() const { return nc; }
644 
645  value_type operator()(size_type i, size_type j) const
646  { return mat_col(*this, j)[i]; }
647  };
648 
649  template <typename PT1, typename PT2, typename PT3, int shift>
650  struct linalg_traits<csc_matrix_ref<PT1, PT2, PT3, shift> > {
651  typedef csc_matrix_ref<PT1, PT2, PT3, shift> this_type;
652  typedef linalg_const is_reference;
653  typedef abstract_matrix linalg_type;
654  typedef typename std::iterator_traits<PT1>::value_type value_type;
655  typedef typename std::iterator_traits<PT1>::value_type reference;
656  typedef value_type origin_type;
657  typedef abstract_sparse storage_type;
658  typedef abstract_null_type sub_row_type;
659  typedef abstract_null_type const_sub_row_type;
660  typedef abstract_null_type row_iterator;
661  typedef abstract_null_type const_row_iterator;
662  typedef abstract_null_type sub_col_type;
663  typedef cs_vector_ref<typename const_pointer<PT1>::pointer,
664  typename const_pointer<PT2>::pointer, shift> const_sub_col_type;
665  typedef sparse_compressed_iterator<typename const_pointer<PT1>::pointer,
666  typename const_pointer<PT2>::pointer,
667  typename const_pointer<PT3>::pointer,
668  shift> const_col_iterator;
669  typedef abstract_null_type col_iterator;
670  typedef col_major sub_orientation;
671  typedef linalg_true index_sorted;
672  static size_type nrows(const this_type &m) { return m.nrows(); }
673  static size_type ncols(const this_type &m) { return m.ncols(); }
674  static const_col_iterator col_begin(const this_type &m)
675  { return const_col_iterator(m.pr, m.ir, m.jc, m.nr, m.pr); }
676  static const_col_iterator col_end(const this_type &m)
677  { return const_col_iterator(m.pr, m.ir, m.jc + m.nc, m.nr, m.pr); }
678  static const_sub_col_type col(const const_col_iterator &it) {
679  return const_sub_col_type(it.pr + *(it.jc) - shift,
680  it.ir + *(it.jc) - shift, *(it.jc + 1) - *(it.jc), it.n);
681  }
682  static const origin_type* origin(const this_type &m) { return m.pr; }
683  static value_type access(const const_col_iterator &itcol, size_type j)
684  { return col(itcol)[j]; }
685  };
686 
687 
688  template <typename PT1, typename PT2, typename PT3, int shift>
689  std::ostream &operator <<
690  (std::ostream &o, const csc_matrix_ref<PT1, PT2, PT3, shift>& m)
691  { gmm::write(o,m); return o; }
692 
693  /* ******************************************************************** */
694  /* Read only reference on a compressed sparse row matrix */
695  /* ******************************************************************** */
696 
697  template <typename PT1, typename PT2, typename PT3, int shift = 0>
698  struct csr_matrix_ref {
699  PT1 pr; // values.
700  PT2 ir; // column indexes.
701  PT3 jc; // row repartition on pr and ir.
702  size_type nc, nr;
703 
704  typedef typename std::iterator_traits<PT1>::value_type value_type;
705  csr_matrix_ref(PT1 pt1, PT2 pt2, PT3 pt3, size_type nrr, size_type ncc)
706  : pr(pt1), ir(pt2), jc(pt3), nc(ncc), nr(nrr) {}
707  csr_matrix_ref() {}
708 
709  size_type nrows() const { return nr; }
710  size_type ncols() const { return nc; }
711 
712  value_type operator()(size_type i, size_type j) const
713  { return mat_row(*this, i)[j]; }
714  };
715 
716  template <typename PT1, typename PT2, typename PT3, int shift>
717  struct linalg_traits<csr_matrix_ref<PT1, PT2, PT3, shift> > {
718  typedef csr_matrix_ref<PT1, PT2, PT3, shift> this_type;
719  typedef linalg_const is_reference;
720  typedef abstract_matrix linalg_type;
721  typedef typename std::iterator_traits<PT1>::value_type value_type;
722  typedef typename std::iterator_traits<PT1>::value_type reference;
723  typedef value_type origin_type;
724  typedef abstract_sparse storage_type;
725  typedef abstract_null_type sub_col_type;
726  typedef abstract_null_type const_sub_col_type;
727  typedef abstract_null_type col_iterator;
728  typedef abstract_null_type const_col_iterator;
729  typedef abstract_null_type sub_row_type;
730  typedef cs_vector_ref<typename const_pointer<PT1>::pointer,
731  typename const_pointer<PT2>::pointer, shift>
732  const_sub_row_type;
733  typedef sparse_compressed_iterator<typename const_pointer<PT1>::pointer,
734  typename const_pointer<PT2>::pointer,
735  typename const_pointer<PT3>::pointer,
736  shift> const_row_iterator;
737  typedef abstract_null_type row_iterator;
738  typedef row_major sub_orientation;
739  typedef linalg_true index_sorted;
740  static size_type nrows(const this_type &m) { return m.nrows(); }
741  static size_type ncols(const this_type &m) { return m.ncols(); }
742  static const_row_iterator row_begin(const this_type &m)
743  { return const_row_iterator(m.pr, m.ir, m.jc, m.nc, m.pr); }
744  static const_row_iterator row_end(const this_type &m)
745  { return const_row_iterator(m.pr, m.ir, m.jc + m.nr, m.nc, m.pr); }
746  static const_sub_row_type row(const const_row_iterator &it) {
747  return const_sub_row_type(it.pr + *(it.jc) - shift,
748  it.ir + *(it.jc) - shift, *(it.jc + 1) - *(it.jc), it.n);
749  }
750  static const origin_type* origin(const this_type &m) { return m.pr; }
751  static value_type access(const const_row_iterator &itrow, size_type j)
752  { return row(itrow)[j]; }
753  };
754 
755  template <typename PT1, typename PT2, typename PT3, int shift>
756  std::ostream &operator <<
757  (std::ostream &o, const csr_matrix_ref<PT1, PT2, PT3, shift>& m)
758  { gmm::write(o,m); return o; }
759 
760  /* ********************************************************************* */
761  /* */
762  /* Simple interface for C arrays */
763  /* */
764  /* ********************************************************************* */
765 
766  template <class PT> struct array1D_reference {
767 
768  typedef typename std::iterator_traits<PT>::value_type value_type;
769 
770  PT begin, end;
771 
772  const value_type &operator[](size_type i) const { return *(begin+i); }
773  value_type &operator[](size_type i) { return *(begin+i); }
774 
775  array1D_reference(PT begin_, size_type s) : begin(begin_), end(begin_+s) {}
776  };
777 
778  template <typename PT>
779  struct linalg_traits<array1D_reference<PT> > {
780  typedef array1D_reference<PT> this_type;
781  typedef this_type origin_type;
782  typedef typename which_reference<PT>::is_reference is_reference;
783  typedef abstract_vector linalg_type;
784  typedef typename std::iterator_traits<PT>::value_type value_type;
785  typedef typename std::iterator_traits<PT>::reference reference;
786  typedef PT iterator;
787  typedef PT const_iterator;
788  typedef abstract_dense storage_type;
789  typedef linalg_true index_sorted;
790  static size_type size(const this_type &v) { return v.end - v.begin; }
791  static iterator begin(this_type &v) { return v.begin; }
792  static const_iterator begin(const this_type &v) { return v.begin; }
793  static iterator end(this_type &v) { return v.end; }
794  static const_iterator end(const this_type &v) { return v.end; }
795  static origin_type* origin(this_type &v) { return &v; }
796  static const origin_type* origin(const this_type &v) { return &v; }
797  static void clear(origin_type*, const iterator &it, const iterator &ite)
798  { std::fill(it, ite, value_type(0)); }
799  static void do_clear(this_type &v)
800  { std::fill(v.begin, v.end, value_type(0)); }
801  static value_type access(const origin_type *, const const_iterator &it,
802  const const_iterator &, size_type i)
803  { return it[i]; }
804  static reference access(origin_type *, const iterator &it,
805  const iterator &, size_type i)
806  { return it[i]; }
807  static void resize(this_type &, size_type )
808  { GMM_ASSERT1(false, "Not resizable vector"); }
809  };
810 
811  template<typename PT> std::ostream &operator <<
812  (std::ostream &o, const array1D_reference<PT>& v)
813  { gmm::write(o,v); return o; }
814 
815  template <class PT> struct array2D_col_reference {
816 
817  typedef typename std::iterator_traits<PT>::value_type T;
818  typedef typename std::iterator_traits<PT>::reference reference;
819  typedef typename const_reference<reference>::reference const_reference;
820  typedef PT iterator;
821  typedef typename const_pointer<PT>::pointer const_iterator;
822 
823  PT begin_;
824  size_type nbl, nbc;
825 
826  inline const_reference operator ()(size_type l, size_type c) const {
827  GMM_ASSERT2(l < nbl && c < nbc, "out of range");
828  return *(begin_ + c*nbl+l);
829  }
830  inline reference operator ()(size_type l, size_type c) {
831  GMM_ASSERT2(l < nbl && c < nbc, "out of range");
832  return *(begin_ + c*nbl+l);
833  }
834 
835  void resize(size_type, size_type);
836  void reshape(size_type m, size_type n) {
837  GMM_ASSERT2(n*m == nbl*nbc, "dimensions mismatch");
838  nbl = m; nbc = n;
839  }
840 
841  void fill(T a, T b = T(0)) {
842  std::fill(begin_, begin_+nbc*nbl, b);
843  iterator p = begin_, e = begin_+nbc*nbl;
844  while (p < e) { *p = a; p += nbl+1; }
845  }
846  inline size_type nrows() const { return nbl; }
847  inline size_type ncols() const { return nbc; }
848 
849  iterator begin() { return begin_; }
850  const_iterator begin() const { return begin_; }
851  iterator end() { return begin_+nbl*nbc; }
852  const_iterator end() const { return begin_+nbl*nbc; }
853 
854  array2D_col_reference(PT begin__, size_type nrows_, size_type ncols_)
855  : begin_(begin__), nbl(nrows_), nbc(ncols_) {}
856  };
857 
858  template <typename PT> struct linalg_traits<array2D_col_reference<PT> > {
859  typedef array2D_col_reference<PT> this_type;
860  typedef this_type origin_type;
861  typedef typename which_reference<PT>::is_reference is_reference;
862  typedef abstract_matrix linalg_type;
863  typedef typename std::iterator_traits<PT>::value_type value_type;
864  typedef typename std::iterator_traits<PT>::reference reference;
865  typedef abstract_dense storage_type;
866  typedef tab_ref_reg_spaced_with_origin<typename this_type::iterator,
867  this_type> sub_row_type;
868  typedef tab_ref_reg_spaced_with_origin<typename this_type::const_iterator,
869  this_type> const_sub_row_type;
870  typedef dense_compressed_iterator<typename this_type::iterator,
871  typename this_type::iterator,
872  this_type *> row_iterator;
873  typedef dense_compressed_iterator<typename this_type::const_iterator,
874  typename this_type::iterator,
875  const this_type *> const_row_iterator;
876  typedef tab_ref_with_origin<typename this_type::iterator,
877  this_type> sub_col_type;
878  typedef tab_ref_with_origin<typename this_type::const_iterator,
879  this_type> const_sub_col_type;
880  typedef dense_compressed_iterator<typename this_type::iterator,
881  typename this_type::iterator,
882  this_type *> col_iterator;
883  typedef dense_compressed_iterator<typename this_type::const_iterator,
884  typename this_type::iterator,
885  const this_type *> const_col_iterator;
886  typedef col_and_row sub_orientation;
887  typedef linalg_true index_sorted;
888  static size_type nrows(const this_type &m) { return m.nrows(); }
889  static size_type ncols(const this_type &m) { return m.ncols(); }
890  static const_sub_row_type row(const const_row_iterator &it)
891  { return const_sub_row_type(*it, it.nrows, it.ncols, it.origin); }
892  static const_sub_col_type col(const const_col_iterator &it)
893  { return const_sub_col_type(*it, *it + it.nrows, it.origin); }
894  static sub_row_type row(const row_iterator &it)
895  { return sub_row_type(*it, it.nrows, it.ncols, it.origin); }
896  static sub_col_type col(const col_iterator &it)
897  { return sub_col_type(*it, *it + it.nrows, it.origin); }
898  static row_iterator row_begin(this_type &m)
899  { return row_iterator(m.begin(), 1, m.nrows(), m.ncols(), 0, &m); }
900  static row_iterator row_end(this_type &m)
901  { return row_iterator(m.begin(), 1, m.nrows(), m.ncols(), m.nrows(), &m); }
902  static const_row_iterator row_begin(const this_type &m)
903  { return const_row_iterator(m.begin(), 1, m.nrows(), m.ncols(), 0, &m); }
904  static const_row_iterator row_end(const this_type &m) {
905  return const_row_iterator(m.begin(), 1, m.nrows(),
906  m.ncols(), m.nrows(), &m);
907  }
908  static col_iterator col_begin(this_type &m)
909  { return col_iterator(m.begin(), m.nrows(), m.nrows(), m.ncols(), 0, &m); }
910  static col_iterator col_end(this_type &m) {
911  return col_iterator(m.begin(), m.nrows(), m.nrows(), m.ncols(),
912  m.ncols(), &m);
913  }
914  static const_col_iterator col_begin(const this_type &m) {
915  return const_col_iterator(m.begin(), m.nrows(), m.nrows(),
916  m.ncols(), 0, &m);
917  }
918  static const_col_iterator col_end(const this_type &m) {
919  return const_col_iterator(m.begin(), m.nrows(),m.nrows(),m.ncols(),
920  m.ncols(), &m);
921  }
922  static origin_type* origin(this_type &m) { return &m; }
923  static const origin_type* origin(const this_type &m) { return &m; }
924  static void do_clear(this_type &m) { m.fill(value_type(0)); }
925  static value_type access(const const_col_iterator &itcol, size_type j)
926  { return (*itcol)[j]; }
927  static reference access(const col_iterator &itcol, size_type j)
928  { return (*itcol)[j]; }
929  static void resize(this_type &v, size_type m, size_type n)
930  { v.resize(m,n); }
931  static void reshape(this_type &v, size_type m, size_type n)
932  { v.reshape(m, n); }
933  };
934 
935  template<typename PT> std::ostream &operator <<
936  (std::ostream &o, const array2D_col_reference<PT>& m)
937  { gmm::write(o,m); return o; }
938 
939 
940 
941  template <class PT> struct array2D_row_reference {
942 
943  typedef typename std::iterator_traits<PT>::value_type T;
944  typedef typename std::iterator_traits<PT>::reference reference;
945  typedef typename const_reference<reference>::reference const_reference;
946  typedef PT iterator;
947  typedef typename const_pointer<PT>::pointer const_iterator;
948 
949  PT begin_;
950  size_type nbl, nbc;
951 
952  inline const_reference operator ()(size_type l, size_type c) const {
953  GMM_ASSERT2(l < nbl && c < nbc, "out of range");
954  return *(begin_ + l*nbc+c);
955  }
956  inline reference operator ()(size_type l, size_type c) {
957  GMM_ASSERT2(l < nbl && c < nbc, "out of range");
958  return *(begin_ + l*nbc+c);
959  }
960 
961  void resize(size_type, size_type);
962  void reshape(size_type m, size_type n) {
963  GMM_ASSERT2(n*m == nbl*nbc, "dimensions mismatch");
964  nbl = m; nbc = n;
965  }
966 
967  void fill(T a, T b = T(0)) {
968  std::fill(begin_, begin_+nbc*nbl, b);
969  iterator p = begin_, e = begin_+nbc*nbl;
970  while (p < e) { *p = a; p += nbc+1; }
971  }
972  inline size_type nrows() const { return nbl; }
973  inline size_type ncols() const { return nbc; }
974 
975  iterator begin() { return begin_; }
976  const_iterator begin() const { return begin_; }
977  iterator end() { return begin_+nbl*nbc; }
978  const_iterator end() const { return begin_+nbl*nbc; }
979 
980  array2D_row_reference(PT begin__, size_type nrows_, size_type ncols_)
981  : begin_(begin__), nbl(nrows_), nbc(ncols_) {}
982  };
983 
984  template <typename PT> struct linalg_traits<array2D_row_reference<PT> > {
985  typedef array2D_row_reference<PT> this_type;
986  typedef this_type origin_type;
987  typedef typename which_reference<PT>::is_reference is_reference;
988  typedef abstract_matrix linalg_type;
989  typedef typename std::iterator_traits<PT>::value_type value_type;
990  typedef typename std::iterator_traits<PT>::reference reference;
991  typedef abstract_dense storage_type;
992  typedef tab_ref_reg_spaced_with_origin<typename this_type::iterator,
993  this_type> sub_col_type;
994  typedef tab_ref_reg_spaced_with_origin<typename this_type::const_iterator,
995  this_type> const_sub_col_type;
996  typedef dense_compressed_iterator<typename this_type::iterator,
997  typename this_type::iterator,
998  this_type *> col_iterator;
999  typedef dense_compressed_iterator<typename this_type::const_iterator,
1000  typename this_type::iterator,
1001  const this_type *> const_col_iterator;
1002  typedef tab_ref_with_origin<typename this_type::iterator,
1003  this_type> sub_row_type;
1004  typedef tab_ref_with_origin<typename this_type::const_iterator,
1005  this_type> const_sub_row_type;
1006  typedef dense_compressed_iterator<typename this_type::iterator,
1007  typename this_type::iterator,
1008  this_type *> row_iterator;
1009  typedef dense_compressed_iterator<typename this_type::const_iterator,
1010  typename this_type::iterator,
1011  const this_type *> const_row_iterator;
1012  typedef col_and_row sub_orientation;
1013  typedef linalg_true index_sorted;
1014  static size_type ncols(const this_type &m) { return m.ncols(); }
1015  static size_type nrows(const this_type &m) { return m.nrows(); }
1016  static const_sub_col_type col(const const_col_iterator &it)
1017  { return const_sub_col_type(*it, it.ncols, it.nrows, it.origin); }
1018  static const_sub_row_type row(const const_row_iterator &it)
1019  { return const_sub_row_type(*it, *it + it.ncols, it.origin); }
1020  static sub_col_type col(const col_iterator &it)
1021  { return sub_col_type(*it, *it, it.ncols, it.nrows, it.origin); }
1022  static sub_row_type row(const row_iterator &it)
1023  { return sub_row_type(*it, *it + it.ncols, it.origin); }
1024  static col_iterator col_begin(this_type &m)
1025  { return col_iterator(m.begin(), 1, m.ncols(), m.nrows(), 0, &m); }
1026  static col_iterator col_end(this_type &m)
1027  { return col_iterator(m.begin(), 1, m.ncols(), m.nrows(), m.ncols(), &m); }
1028  static const_col_iterator col_begin(const this_type &m)
1029  { return const_col_iterator(m.begin(), 1, m.ncols(), m.nrows(), 0, &m); }
1030  static const_col_iterator col_end(const this_type &m) {
1031  return const_col_iterator(m.begin(), 1, m.ncols(),
1032  m.nrows(), m.ncols(), &m);
1033  }
1034  static row_iterator row_begin(this_type &m)
1035  { return row_iterator(m.begin(), m.ncols(), m.ncols(), m.nrows(), 0, &m); }
1036  static row_iterator row_end(this_type &m) {
1037  return row_iterator(m.begin(), m.ncols(), m.ncols(), m.nrows(),
1038  m.nrows(), &m);
1039  }
1040  static const_row_iterator row_begin(const this_type &m) {
1041  return const_row_iterator(m.begin(), m.ncols(), m.ncols(), m.nrows(),
1042  0, &m);
1043  }
1044  static const_row_iterator row_end(const this_type &m) {
1045  return const_row_iterator(m.begin(), m.ncols(), m.ncols(), m.nrows(),
1046  m.nrows(), &m);
1047  }
1048  static origin_type* origin(this_type &m) { return &m; }
1049  static const origin_type* origin(const this_type &m) { return &m; }
1050  static void do_clear(this_type &m) { m.fill(value_type(0)); }
1051  static value_type access(const const_row_iterator &itrow, size_type j)
1052  { return (*itrow)[j]; }
1053  static reference access(const row_iterator &itrow, size_type j)
1054  { return (*itrow)[j]; }
1055  static void resize(this_type &v, size_type m, size_type n)
1056  { v.resize(m,n); }
1057  static void reshape(this_type &v, size_type m, size_type n)
1058  { v.reshape(m, n); }
1059  };
1060 
1061  template<typename PT> std::ostream &operator <<
1062  (std::ostream &o, const array2D_row_reference<PT>& m)
1063  { gmm::write(o,m); return o; }
1064 
1065 
1066 
1067 
1068 
1069 
1070 }
1071 
1072 
1073 #endif // GMM_INTERFACE_H__
gmm::tab_ref_index_ref
indexed array reference (given a container X, and a set of indexes I, this class provides a pseudo-co...
Definition: gmm_ref.h:303
gmm::tab_ref_reg_spaced
provide a "strided" view a of container
Definition: gmm_ref.h:425
gmm_blas.h
Basic linear algebra functions.
gmm::nnz
size_type nnz(const L &l)
count the number of non-zero entries of a vector or matrix.
Definition: gmm_blas.h:68
gmm::reshape
void reshape(M &v, size_type m, size_type n)
*‍/
Definition: gmm_blas.h:250
gmm::fill
void fill(L &l, typename gmm::linalg_traits< L >::value_type x)
*‍/
Definition: gmm_blas.h:103
gmm::clear
void clear(L &l)
clear (fill with zeros) a vector or matrix.
Definition: gmm_blas.h:58
gmm::resize
void resize(V &v, size_type n)
*‍/
Definition: gmm_blas.h:209
gmm_sub_index.h
sub-indices.
bgeot::operator-
rational_fraction< T > operator-(const polynomial< T > &P, const rational_fraction< T > &Q)
Subtract Q from P.
Definition: bgeot_poly.h:755
bgeot::operator+
rational_fraction< T > operator+(const polynomial< T > &P, const rational_fraction< T > &Q)
Add Q to P.
Definition: bgeot_poly.h:748
bgeot::size_type
size_t size_type
used as the common size type in the library
Definition: bgeot_poly.h:48