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GetFEM: src/gmm/gmm_blas.h Source File
GetFEM  5.4.2
gmm_blas.h
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2 /*===========================================================================
3 
4  Copyright (C) 2002-2020 Yves Renard
5 
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7 
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30 ===========================================================================*/
31 
32 /**@file gmm_blas.h
33  @author Yves Renard <Yves.Renard@insa-lyon.fr>
34  @date October 13, 2002.
35  @brief Basic linear algebra functions.
36 */
37 
38 #ifndef GMM_BLAS_H__
39 #define GMM_BLAS_H__
40 
41 #include "gmm_scaled.h"
42 #include "gmm_transposed.h"
43 #include "gmm_conjugated.h"
44 
45 namespace gmm {
46 
47  /* ******************************************************************** */
48  /* */
49  /* Generic algorithms */
50  /* */
51  /* ******************************************************************** */
52 
53 
54  /* ******************************************************************** */
55  /* Miscellaneous */
56  /* ******************************************************************** */
57 
58  /** clear (fill with zeros) a vector or matrix. */
59  template <typename L> inline void clear(L &l)
60  { linalg_traits<L>::do_clear(l); }
61  /** @cond DOXY_SHOW_ALL_FUNCTIONS
62  skip all these redundant definitions in doxygen documentation..
63  */
64  template <typename L> inline void clear(const L &l)
65  { linalg_traits<L>::do_clear(linalg_const_cast(l)); }
66 
67  ///@endcond
68  /** count the number of non-zero entries of a vector or matrix. */ template <typename L> inline size_type nnz(const L& l)
69  { return nnz(l, typename linalg_traits<L>::linalg_type()); }
70 
71  ///@cond DOXY_SHOW_ALL_FUNCTIONS
72  template <typename L> inline size_type nnz(const L& l, abstract_vector) {
73  auto it = vect_const_begin(l), ite = vect_const_end(l);
74  size_type res(0);
75  for (; it != ite; ++it) ++res;
76  return res;
77  }
78 
79  template <typename L> inline size_type nnz(const L& l, abstract_matrix) {
80  return nnz(l, typename principal_orientation_type<typename
81  linalg_traits<L>::sub_orientation>::potype());
82  }
83 
84  template <typename L> inline size_type nnz(const L& l, row_major) {
85  size_type res(0);
86  for (size_type i = 0; i < mat_nrows(l); ++i)
87  res += nnz(mat_const_row(l, i));
88  return res;
89  }
90 
91  template <typename L> inline size_type nnz(const L& l, col_major) {
92  size_type res(0);
93  for (size_type i = 0; i < mat_ncols(l); ++i)
94  res += nnz(mat_const_col(l, i));
95  return res;
96  }
97 
98  ///@endcond
99 
100 
101  /** fill a vector or matrix with x. */
102  template <typename L> inline
103  void fill(L& l, typename gmm::linalg_traits<L>::value_type x) {
104  typedef typename gmm::linalg_traits<L>::value_type T;
105  if (x == T(0)) gmm::clear(l);
106  fill(l, x, typename linalg_traits<L>::linalg_type());
107  }
108 
109  template <typename L> inline
110  void fill(const L& l, typename gmm::linalg_traits<L>::value_type x) {
111  fill(linalg_const_cast(l), x);
112  }
113 
114  template <typename L> inline // to be optimized for dense vectors ...
115  void fill(L& l, typename gmm::linalg_traits<L>::value_type x,
116  abstract_vector) {
117  for (size_type i = 0; i < vect_size(l); ++i) l[i] = x;
118  }
119 
120  template <typename L> inline // to be optimized for dense matrices ...
121  void fill(L& l, typename gmm::linalg_traits<L>::value_type x,
122  abstract_matrix) {
123  for (size_type i = 0; i < mat_nrows(l); ++i)
124  for (size_type j = 0; j < mat_ncols(l); ++j)
125  l(i,j) = x;
126  }
127 
128  /** fill a vector or matrix with random value (uniform [-1,1]). */
129  template <typename L> inline void fill_random(L& l)
130  { fill_random(l, typename linalg_traits<L>::linalg_type()); }
131 
132  ///@cond DOXY_SHOW_ALL_FUNCTIONS
133  template <typename L> inline void fill_random(const L& l) {
134  fill_random(linalg_const_cast(l),
135  typename linalg_traits<L>::linalg_type());
136  }
137 
138  template <typename L> inline void fill_random(L& l, abstract_vector) {
139  for (size_type i = 0; i < vect_size(l); ++i)
140  l[i] = gmm::random(typename linalg_traits<L>::value_type());
141  }
142 
143  template <typename L> inline void fill_random(L& l, abstract_matrix) {
144  for (size_type i = 0; i < mat_nrows(l); ++i)
145  for (size_type j = 0; j < mat_ncols(l); ++j)
146  l(i,j) = gmm::random(typename linalg_traits<L>::value_type());
147  }
148 
149  ///@endcond
150  /** fill a vector or matrix with random value.
151  @param l a vector or matrix.
152  @param cfill probability of a non-zero value.
153  */
154  template <typename L> inline void fill_random(L& l, double cfill)
155  { fill_random(l, cfill, typename linalg_traits<L>::linalg_type()); }
156  ///@cond DOXY_SHOW_ALL_FUNCTIONS
157 
158  template <typename L> inline void fill_random(const L& l, double cfill) {
159  fill_random(linalg_const_cast(l), cfill,
160  typename linalg_traits<L>::linalg_type());
161  }
162 
163  template <typename L> inline
164  void fill_random(L& l, double cfill, abstract_vector) {
165  typedef typename linalg_traits<L>::value_type T;
166  size_type ntot = std::min(vect_size(l),
167  size_type(double(vect_size(l))*cfill) + 1);
168  for (size_type nb = 0; nb < ntot;) {
169  size_type i = gmm::irandom(vect_size(l));
170  if (l[i] == T(0)) {
171  l[i] = gmm::random(typename linalg_traits<L>::value_type());
172  ++nb;
173  }
174  }
175  }
176 
177  template <typename L> inline
178  void fill_random(L& l, double cfill, abstract_matrix) {
179  fill_random(l, cfill, typename principal_orientation_type<typename
180  linalg_traits<L>::sub_orientation>::potype());
181  }
182 
183  template <typename L> inline
184  void fill_random(L& l, double cfill, row_major) {
185  for (size_type i=0; i < mat_nrows(l); ++i) fill_random(mat_row(l,i),cfill);
186  }
187 
188  template <typename L> inline
189  void fill_random(L& l, double cfill, col_major) {
190  for (size_type j=0; j < mat_ncols(l); ++j) fill_random(mat_col(l,j),cfill);
191  }
192 
193  /* resize a vector */
194  template <typename V> inline
195  void resize(V &v, size_type n, linalg_false)
196  { linalg_traits<V>::resize(v, n); }
197 
198  template <typename V> inline
199  void resize(V &, size_type , linalg_modifiable)
200  { GMM_ASSERT1(false, "You cannot resize a reference"); }
201 
202  template <typename V> inline
203  void resize(V &, size_type , linalg_const)
204  { GMM_ASSERT1(false, "You cannot resize a reference"); }
205 
206  ///@endcond
207  /** resize a vector. */
208  template <typename V> inline
209  void resize(V &v, size_type n) {
210  resize(v, n, typename linalg_traits<V>::is_reference());
211  }
212  ///@cond DOXY_SHOW_ALL_FUNCTIONS
213 
214  /** resize a matrix **/
215  template <typename M> inline
216  void resize(M &v, size_type m, size_type n, linalg_false) {
217  linalg_traits<M>::resize(v, m, n);
218  }
219 
220  template <typename M> inline
221  void resize(M &, size_type, size_type, linalg_modifiable)
222  { GMM_ASSERT1(false, "You cannot resize a reference"); }
223 
224  template <typename M> inline
225  void resize(M &, size_type, size_type, linalg_const)
226  { GMM_ASSERT1(false, "You cannot resize a reference"); }
227 
228  ///@endcond
229  /** resize a matrix */
230  template <typename M> inline
231  void resize(M &v, size_type m, size_type n)
232  { resize(v, m, n, typename linalg_traits<M>::is_reference()); }
233  ///@cond
234 
235  template <typename M> inline
236  void reshape(M &v, size_type m, size_type n, linalg_false)
237  { linalg_traits<M>::reshape(v, m, n); }
238 
239  template <typename M> inline
240  void reshape(M &, size_type, size_type, linalg_modifiable)
241  { GMM_ASSERT1(false, "You cannot reshape a reference"); }
242 
243  template <typename M> inline
244  void reshape(M &, size_type, size_type, linalg_const)
245  { GMM_ASSERT1(false, "You cannot reshape a reference"); }
246 
247  ///@endcond
248  /** reshape a matrix */
249  template <typename M> inline
250  void reshape(M &v, size_type m, size_type n)
251  { reshape(v, m, n, typename linalg_traits<M>::is_reference()); }
252  ///@cond DOXY_SHOW_ALL_FUNCTIONS
253 
254 
255  /* ******************************************************************** */
256  /* Scalar product */
257  /* ******************************************************************** */
258 
259  ///@endcond
260  /** scalar product between two vectors */
261  template <typename V1, typename V2> inline
262  typename strongest_value_type<V1,V2>::value_type
263  vect_sp(const V1 &v1, const V2 &v2) {
264  GMM_ASSERT2(vect_size(v1) == vect_size(v2), "dimensions mismatch, "
265  << vect_size(v1) << " !=" << vect_size(v2));
266  return vect_sp(v1, v2,
267  typename linalg_traits<V1>::storage_type(),
268  typename linalg_traits<V2>::storage_type());
269  }
270 
271  /** scalar product between two vectors, using a matrix.
272  @param ps the matrix of the scalar product.
273  @param v1 the first vector
274  @param v2 the second vector
275  */
276  template <typename MATSP, typename V1, typename V2> inline
277  typename strongest_value_type3<V1,V2,MATSP>::value_type
278  vect_sp(const MATSP &ps, const V1 &v1, const V2 &v2) {
279  return vect_sp_with_mat(ps, v1, v2,
280  typename linalg_traits<MATSP>::sub_orientation());
281  }
282  ///@cond DOXY_SHOW_ALL_FUNCTIONS
283 
284  template <typename MATSP, typename V1, typename V2> inline
285  typename strongest_value_type3<V1,V2,MATSP>::value_type
286  vect_sp_with_mat(const MATSP &ps, const V1 &v1, const V2 &v2, row_major) {
287  return vect_sp_with_matr(ps, v1, v2,
288  typename linalg_traits<V2>::storage_type());
289  }
290 
291  template <typename MATSP, typename V1, typename V2> inline
292  typename strongest_value_type3<V1,V2,MATSP>::value_type
293  vect_sp_with_matr(const MATSP &ps, const V1 &v1, const V2 &v2,
294  abstract_sparse) {
295  GMM_ASSERT2(vect_size(v1) == mat_ncols(ps) &&
296  vect_size(v2) == mat_nrows(ps), "dimensions mismatch");
297  size_type nr = mat_nrows(ps);
298  typename linalg_traits<V2>::const_iterator
299  it = vect_const_begin(v2), ite = vect_const_end(v2);
300  typename strongest_value_type3<V1,V2,MATSP>::value_type res(0);
301  for (; it != ite; ++it)
302  res += vect_sp(mat_const_row(ps, it.index()), v1)* (*it);
303  return res;
304  }
305 
306  template <typename MATSP, typename V1, typename V2> inline
307  typename strongest_value_type3<V1,V2,MATSP>::value_type
308  vect_sp_with_matr(const MATSP &ps, const V1 &v1, const V2 &v2,
309  abstract_skyline)
310  { return vect_sp_with_matr(ps, v1, v2, abstract_sparse()); }
311 
312  template <typename MATSP, typename V1, typename V2> inline
313  typename strongest_value_type3<V1,V2,MATSP>::value_type
314  vect_sp_with_matr(const MATSP &ps, const V1 &v1, const V2 &v2,
315  abstract_dense) {
316  GMM_ASSERT2(vect_size(v1) == mat_ncols(ps) &&
317  vect_size(v2) == mat_nrows(ps), "dimensions mismatch");
318  typename linalg_traits<V2>::const_iterator
319  it = vect_const_begin(v2), ite = vect_const_end(v2);
320  typename strongest_value_type3<V1,V2,MATSP>::value_type res(0);
321  for (size_type i = 0; it != ite; ++i, ++it)
322  res += vect_sp(mat_const_row(ps, i), v1) * (*it);
323  return res;
324  }
325 
326  template <typename MATSP, typename V1, typename V2> inline
327  typename strongest_value_type3<V1,V2,MATSP>::value_type
328  vect_sp_with_mat(const MATSP &ps, const V1 &v1,const V2 &v2,row_and_col)
329  { return vect_sp_with_mat(ps, v1, v2, row_major()); }
330 
331  template <typename MATSP, typename V1, typename V2> inline
332  typename strongest_value_type3<V1,V2,MATSP>::value_type
333  vect_sp_with_mat(const MATSP &ps, const V1 &v1, const V2 &v2,col_major){
334  return vect_sp_with_matc(ps, v1, v2,
335  typename linalg_traits<V1>::storage_type());
336  }
337 
338  template <typename MATSP, typename V1, typename V2> inline
339  typename strongest_value_type3<V1,V2,MATSP>::value_type
340  vect_sp_with_matc(const MATSP &ps, const V1 &v1, const V2 &v2,
341  abstract_sparse) {
342  GMM_ASSERT2(vect_size(v1) == mat_ncols(ps) &&
343  vect_size(v2) == mat_nrows(ps), "dimensions mismatch");
344  typename linalg_traits<V1>::const_iterator
345  it = vect_const_begin(v1), ite = vect_const_end(v1);
346  typename strongest_value_type3<V1,V2,MATSP>::value_type res(0);
347  for (; it != ite; ++it)
348  res += vect_sp(mat_const_col(ps, it.index()), v2) * (*it);
349  return res;
350  }
351 
352  template <typename MATSP, typename V1, typename V2> inline
353  typename strongest_value_type3<V1,V2,MATSP>::value_type
354  vect_sp_with_matc(const MATSP &ps, const V1 &v1, const V2 &v2,
355  abstract_skyline)
356  { return vect_sp_with_matc(ps, v1, v2, abstract_sparse()); }
357 
358  template <typename MATSP, typename V1, typename V2> inline
359  typename strongest_value_type3<V1,V2,MATSP>::value_type
360  vect_sp_with_matc(const MATSP &ps, const V1 &v1, const V2 &v2,
361  abstract_dense) {
362  GMM_ASSERT2(vect_size(v1) == mat_ncols(ps) &&
363  vect_size(v2) == mat_nrows(ps), "dimensions mismatch");
364  typename linalg_traits<V1>::const_iterator
365  it = vect_const_begin(v1), ite = vect_const_end(v1);
366  typename strongest_value_type3<V1,V2,MATSP>::value_type res(0);
367  for (size_type i = 0; it != ite; ++i, ++it)
368  res += vect_sp(mat_const_col(ps, i), v2) * (*it);
369  return res;
370  }
371 
372  template <typename MATSP, typename V1, typename V2> inline
373  typename strongest_value_type3<V1,V2,MATSP>::value_type
374  vect_sp_with_mat(const MATSP &ps, const V1 &v1,const V2 &v2,col_and_row)
375  { return vect_sp_with_mat(ps, v1, v2, col_major()); }
376 
377  template <typename MATSP, typename V1, typename V2> inline
378  typename strongest_value_type3<V1,V2,MATSP>::value_type
379  vect_sp_with_mat(const MATSP &ps, const V1 &v1, const V2 &v2,
380  abstract_null_type) {
381  typename temporary_vector<V1>::vector_type w(mat_nrows(ps));
382  GMM_WARNING2("Warning, a temporary is used in scalar product\n");
383  mult(ps, v1, w);
384  return vect_sp(w, v2);
385  }
386 
387  template <typename IT1, typename IT2> inline
388  typename strongest_numeric_type<typename std::iterator_traits<IT1>::value_type,
389  typename std::iterator_traits<IT2>::value_type>::T
390  vect_sp_dense_(IT1 it, IT1 ite, IT2 it2) {
391  typename strongest_numeric_type<typename std::iterator_traits<IT1>::value_type,
392  typename std::iterator_traits<IT2>::value_type>::T res(0);
393  for (; it != ite; ++it, ++it2) res += (*it) * (*it2);
394  return res;
395  }
396 
397  template <typename IT1, typename V> inline
398  typename strongest_numeric_type<typename std::iterator_traits<IT1>::value_type,
399  typename linalg_traits<V>::value_type>::T
400  vect_sp_sparse_(IT1 it, IT1 ite, const V &v) {
401  typename strongest_numeric_type<typename std::iterator_traits<IT1>::value_type,
402  typename linalg_traits<V>::value_type>::T res(0);
403  for (; it != ite; ++it) res += (*it) * v[it.index()];
404  return res;
405  }
406 
407  template <typename V1, typename V2> inline
408  typename strongest_value_type<V1,V2>::value_type
409  vect_sp(const V1 &v1, const V2 &v2, abstract_dense, abstract_dense) {
410  return vect_sp_dense_(vect_const_begin(v1), vect_const_end(v1),
411  vect_const_begin(v2));
412  }
413 
414  template <typename V1, typename V2> inline
415  typename strongest_value_type<V1,V2>::value_type
416  vect_sp(const V1 &v1, const V2 &v2, abstract_skyline, abstract_dense) {
417  typename linalg_traits<V1>::const_iterator it1 = vect_const_begin(v1),
418  ite = vect_const_end(v1);
419  typename linalg_traits<V2>::const_iterator it2 = vect_const_begin(v2);
420  return vect_sp_dense_(it1, ite, it2 + it1.index());
421  }
422 
423  template <typename V1, typename V2> inline
424  typename strongest_value_type<V1,V2>::value_type
425  vect_sp(const V1 &v1, const V2 &v2, abstract_dense, abstract_skyline) {
426  typename linalg_traits<V2>::const_iterator it1 = vect_const_begin(v2),
427  ite = vect_const_end(v2);
428  typename linalg_traits<V1>::const_iterator it2 = vect_const_begin(v1);
429  return vect_sp_dense_(it1, ite, it2 + it1.index());
430  }
431 
432  template <typename V1, typename V2> inline
433  typename strongest_value_type<V1,V2>::value_type
434  vect_sp(const V1 &v1, const V2 &v2, abstract_skyline, abstract_skyline) {
435  typedef typename strongest_value_type<V1,V2>::value_type T;
436  auto it1 = vect_const_begin(v1), ite1 = vect_const_end(v1);
437  auto it2 = vect_const_begin(v2), ite2 = vect_const_end(v2);
438  size_type n = std::min(ite1.index(), ite2.index());
439  size_type l = std::max(it1.index(), it2.index());
440 
441  if (l < n) {
442  size_type m = l - it1.index(), p = l - it2.index(), q = m + n - l;
443  return vect_sp_dense_(it1+m, it1+q, it2 + p);
444  }
445  return T(0);
446  }
447 
448  template <typename V1, typename V2> inline
449  typename strongest_value_type<V1,V2>::value_type
450  vect_sp(const V1 &v1, const V2 &v2,abstract_sparse,abstract_dense) {
451  return vect_sp_sparse_(vect_const_begin(v1), vect_const_end(v1), v2);
452  }
453 
454  template <typename V1, typename V2> inline
455  typename strongest_value_type<V1,V2>::value_type
456  vect_sp(const V1 &v1, const V2 &v2, abstract_sparse, abstract_skyline) {
457  return vect_sp_sparse_(vect_const_begin(v1), vect_const_end(v1), v2);
458  }
459 
460  template <typename V1, typename V2> inline
461  typename strongest_value_type<V1,V2>::value_type
462  vect_sp(const V1 &v1, const V2 &v2, abstract_skyline, abstract_sparse) {
463  return vect_sp_sparse_(vect_const_begin(v2), vect_const_end(v2), v1);
464  }
465 
466  template <typename V1, typename V2> inline
467  typename strongest_value_type<V1,V2>::value_type
468  vect_sp(const V1 &v1, const V2 &v2, abstract_dense,abstract_sparse) {
469  return vect_sp_sparse_(vect_const_begin(v2), vect_const_end(v2), v1);
470  }
471 
472 
473  template <typename V1, typename V2> inline
474  typename strongest_value_type<V1,V2>::value_type
475  vect_sp_sparse_sparse(const V1 &v1, const V2 &v2, linalg_true) {
476  typename linalg_traits<V1>::const_iterator it1 = vect_const_begin(v1),
477  ite1 = vect_const_end(v1);
478  typename linalg_traits<V2>::const_iterator it2 = vect_const_begin(v2),
479  ite2 = vect_const_end(v2);
480  typename strongest_value_type<V1,V2>::value_type res(0);
481 
482  while (it1 != ite1 && it2 != ite2) {
483  if (it1.index() == it2.index())
484  { res += (*it1) * *it2; ++it1; ++it2; }
485  else if (it1.index() < it2.index()) ++it1; else ++it2;
486  }
487  return res;
488  }
489 
490  template <typename V1, typename V2> inline
491  typename strongest_value_type<V1,V2>::value_type
492  vect_sp_sparse_sparse(const V1 &v1, const V2 &v2, linalg_false) {
493  return vect_sp_sparse_(vect_const_begin(v1), vect_const_end(v1), v2);
494  }
495 
496  template <typename V1, typename V2> inline
497  typename strongest_value_type<V1,V2>::value_type
498  vect_sp(const V1 &v1, const V2 &v2,abstract_sparse,abstract_sparse) {
499  return vect_sp_sparse_sparse(v1, v2,
500  typename linalg_and<typename linalg_traits<V1>::index_sorted,
501  typename linalg_traits<V2>::index_sorted>::bool_type());
502  }
503 
504  /* ******************************************************************** */
505  /* Hermitian product */
506  /* ******************************************************************** */
507  ///@endcond
508  /** Hermitian product. */
509  template <typename V1, typename V2>
510  inline typename strongest_value_type<V1,V2>::value_type
511  vect_hp(const V1 &v1, const V2 &v2)
512  { return vect_sp(v1, conjugated(v2)); }
513 
514  /** Hermitian product with a matrix. */
515  template <typename MATSP, typename V1, typename V2> inline
516  typename strongest_value_type3<V1,V2,MATSP>::value_type
517  vect_hp(const MATSP &ps, const V1 &v1, const V2 &v2) {
518  return vect_sp(ps, v1, gmm::conjugated(v2));
519  }
520 
521  /* ******************************************************************** */
522  /* Trace of a matrix */
523  /* ******************************************************************** */
524 
525  /** Trace of a matrix */
526  template <typename M>
527  typename linalg_traits<M>::value_type
528  mat_trace(const M &m) {
529  typedef typename linalg_traits<M>::value_type T;
530  T res(0);
531  for (size_type i = 0; i < std::min(mat_nrows(m), mat_ncols(m)); ++i)
532  res += m(i,i);
533  return res;
534  }
535 
536  /* ******************************************************************** */
537  /* Euclidean norm */
538  /* ******************************************************************** */
539 
540  /** squared Euclidean norm of a vector. */
541  template <typename V>
542  typename number_traits<typename linalg_traits<V>::value_type>
543  ::magnitude_type
544  vect_norm2_sqr(const V &v) {
545  typedef typename linalg_traits<V>::value_type T;
546  typedef typename number_traits<T>::magnitude_type R;
547  auto it = vect_const_begin(v), ite = vect_const_end(v);
548  R res(0);
549  for (; it != ite; ++it) res += gmm::abs_sqr(*it);
550  return res;
551  }
552 
553  /** Euclidean norm of a vector. */
554  template <typename V> inline
555  typename number_traits<typename linalg_traits<V>::value_type>
556  ::magnitude_type
557  vect_norm2(const V &v)
558  { return sqrt(vect_norm2_sqr(v)); }
559 
560 
561  /** squared Euclidean distance between two vectors */
562  template <typename V1, typename V2> inline
563  typename number_traits<typename linalg_traits<V1>::value_type>
564  ::magnitude_type
565  vect_dist2_sqr(const V1 &v1, const V2 &v2) { // not fully optimized
566  typedef typename linalg_traits<V1>::value_type T;
567  typedef typename number_traits<T>::magnitude_type R;
568  auto it1 = vect_const_begin(v1), ite1 = vect_const_end(v1);
569  auto it2 = vect_const_begin(v2), ite2 = vect_const_end(v2);
570  size_type k1(0), k2(0);
571  R res(0);
572  while (it1 != ite1 && it2 != ite2) {
573  size_type i1 = index_of_it(it1, k1,
574  typename linalg_traits<V1>::storage_type());
575  size_type i2 = index_of_it(it2, k2,
576  typename linalg_traits<V2>::storage_type());
577 
578  if (i1 == i2) {
579  res += gmm::abs_sqr(*it2 - *it1); ++it1; ++k1; ++it2; ++k2;
580  }
581  else if (i1 < i2) {
582  res += gmm::abs_sqr(*it1); ++it1; ++k1;
583  }
584  else {
585  res += gmm::abs_sqr(*it2); ++it2; ++k2;
586  }
587  }
588  while (it1 != ite1) { res += gmm::abs_sqr(*it1); ++it1; }
589  while (it2 != ite2) { res += gmm::abs_sqr(*it2); ++it2; }
590  return res;
591  }
592 
593  /** Euclidean distance between two vectors */
594  template <typename V1, typename V2> inline
595  typename number_traits<typename linalg_traits<V1>::value_type>
596  ::magnitude_type
597  vect_dist2(const V1 &v1, const V2 &v2)
598  { return sqrt(vect_dist2_sqr(v1, v2)); }
599  ///@cond DOXY_SHOW_ALL_FUNCTIONS
600  template <typename M>
601  typename number_traits<typename linalg_traits<M>::value_type>
602  ::magnitude_type
603  mat_euclidean_norm_sqr(const M &m, row_major) {
604  typename number_traits<typename linalg_traits<M>::value_type>
605  ::magnitude_type res(0);
606  for (size_type i = 0; i < mat_nrows(m); ++i)
607  res += vect_norm2_sqr(mat_const_row(m, i));
608  return res;
609  }
610 
611  template <typename M>
612  typename number_traits<typename linalg_traits<M>::value_type>
613  ::magnitude_type
614  mat_euclidean_norm_sqr(const M &m, col_major) {
615  typename number_traits<typename linalg_traits<M>::value_type>
616  ::magnitude_type res(0);
617  for (size_type i = 0; i < mat_ncols(m); ++i)
618  res += vect_norm2_sqr(mat_const_col(m, i));
619  return res;
620  }
621  ///@endcond
622  /** squared Euclidean norm of a matrix. */
623  template <typename M> inline
624  typename number_traits<typename linalg_traits<M>::value_type>
625  ::magnitude_type
626  mat_euclidean_norm_sqr(const M &m) {
627  return mat_euclidean_norm_sqr(m,
628  typename principal_orientation_type<typename
629  linalg_traits<M>::sub_orientation>::potype());
630  }
631 
632  /** Euclidean norm of a matrix. */
633  template <typename M> inline
634  typename number_traits<typename linalg_traits<M>::value_type>
635  ::magnitude_type
636  mat_euclidean_norm(const M &m)
637  { return gmm::sqrt(mat_euclidean_norm_sqr(m)); }
638 
639  /* ******************************************************************** */
640  /* vector norm1 */
641  /* ******************************************************************** */
642  /** 1-norm of a vector */
643  template <typename V>
644  typename number_traits<typename linalg_traits<V>::value_type>
645  ::magnitude_type
646  vect_norm1(const V &v) {
647  auto it = vect_const_begin(v), ite = vect_const_end(v);
648  typename number_traits<typename linalg_traits<V>::value_type>
649  ::magnitude_type res(0);
650  for (; it != ite; ++it) res += gmm::abs(*it);
651  return res;
652  }
653 
654  /** 1-distance between two vectors */
655  template <typename V1, typename V2> inline
656  typename number_traits<typename linalg_traits<V1>::value_type>
657  ::magnitude_type
658  vect_dist1(const V1 &v1, const V2 &v2) { // not fully optimized
659  typedef typename linalg_traits<V1>::value_type T;
660  typedef typename number_traits<T>::magnitude_type R;
661  auto it1 = vect_const_begin(v1), ite1 = vect_const_end(v1);
662  auto it2 = vect_const_begin(v2), ite2 = vect_const_end(v2);
663  size_type k1(0), k2(0);
664  R res(0);
665  while (it1 != ite1 && it2 != ite2) {
666  size_type i1 = index_of_it(it1, k1,
667  typename linalg_traits<V1>::storage_type());
668  size_type i2 = index_of_it(it2, k2,
669  typename linalg_traits<V2>::storage_type());
670 
671  if (i1 == i2) {
672  res += gmm::abs(*it2 - *it1); ++it1; ++k1; ++it2; ++k2;
673  }
674  else if (i1 < i2) {
675  res += gmm::abs(*it1); ++it1; ++k1;
676  }
677  else {
678  res += gmm::abs(*it2); ++it2; ++k2;
679  }
680  }
681  while (it1 != ite1) { res += gmm::abs(*it1); ++it1; }
682  while (it2 != ite2) { res += gmm::abs(*it2); ++it2; }
683  return res;
684  }
685 
686  /* ******************************************************************** */
687  /* vector Infinity norm */
688  /* ******************************************************************** */
689  /** Infinity norm of a vector. */
690  template <typename V>
691  typename number_traits<typename linalg_traits<V>::value_type>
692  ::magnitude_type
693  vect_norminf(const V &v) {
694  auto it = vect_const_begin(v), ite = vect_const_end(v);
695  typename number_traits<typename linalg_traits<V>::value_type>
696  ::magnitude_type res(0);
697  for (; it != ite; ++it) res = std::max(res, gmm::abs(*it));
698  return res;
699  }
700 
701  /** Infinity distance between two vectors */
702  template <typename V1, typename V2> inline
703  typename number_traits<typename linalg_traits<V1>::value_type>
704  ::magnitude_type
705  vect_distinf(const V1 &v1, const V2 &v2) { // not fully optimized
706  typedef typename linalg_traits<V1>::value_type T;
707  typedef typename number_traits<T>::magnitude_type R;
708  auto it1 = vect_const_begin(v1), ite1 = vect_const_end(v1);
709  auto it2 = vect_const_begin(v2), ite2 = vect_const_end(v2);
710  size_type k1(0), k2(0);
711  R res(0);
712  while (it1 != ite1 && it2 != ite2) {
713  size_type i1 = index_of_it(it1, k1,
714  typename linalg_traits<V1>::storage_type());
715  size_type i2 = index_of_it(it2, k2,
716  typename linalg_traits<V2>::storage_type());
717 
718  if (i1 == i2) {
719  res = std::max(res, gmm::abs(*it2 - *it1)); ++it1; ++k1; ++it2; ++k2;
720  }
721  else if (i1 < i2) {
722  res = std::max(res, gmm::abs(*it1)); ++it1; ++k1;
723  }
724  else {
725  res = std::max(res, gmm::abs(*it2)); ++it2; ++k2;
726  }
727  }
728  while (it1 != ite1) { res = std::max(res, gmm::abs(*it1)); ++it1; }
729  while (it2 != ite2) { res = std::max(res, gmm::abs(*it2)); ++it2; }
730  return res;
731  }
732 
733  /* ******************************************************************** */
734  /* matrix norm1 */
735  /* ******************************************************************** */
736  ///@cond DOXY_SHOW_ALL_FUNCTIONS
737  template <typename M>
738  typename number_traits<typename linalg_traits<M>::value_type>
739  ::magnitude_type
740  mat_norm1(const M &m, col_major) {
741  typename number_traits<typename linalg_traits<M>::value_type>
742  ::magnitude_type res(0);
743  for (size_type i = 0; i < mat_ncols(m); ++i)
744  res = std::max(res, vect_norm1(mat_const_col(m,i)));
745  return res;
746  }
747 
748  template <typename M>
749  typename number_traits<typename linalg_traits<M>::value_type>
750  ::magnitude_type
751  mat_norm1(const M &m, row_major) {
752  typedef typename linalg_traits<M>::value_type T;
753  typedef typename number_traits<T>::magnitude_type R;
754  typedef typename linalg_traits<M>::storage_type store_type;
755 
756  std::vector<R> aux(mat_ncols(m));
757  for (size_type i = 0; i < mat_nrows(m); ++i) {
758  typename linalg_traits<M>::const_sub_row_type row = mat_const_row(m, i);
759  auto it = vect_const_begin(row), ite = vect_const_end(row);
760  for (size_type k = 0; it != ite; ++it, ++k)
761  aux[index_of_it(it, k, store_type())] += gmm::abs(*it);
762  }
763  return vect_norminf(aux);
764  }
765 
766  template <typename M>
767  typename number_traits<typename linalg_traits<M>::value_type>
768  ::magnitude_type
769  mat_norm1(const M &m, col_and_row)
770  { return mat_norm1(m, col_major()); }
771 
772  template <typename M>
773  typename number_traits<typename linalg_traits<M>::value_type>
774  ::magnitude_type
775  mat_norm1(const M &m, row_and_col)
776  { return mat_norm1(m, col_major()); }
777  ///@endcond
778  /** 1-norm of a matrix */
779  template <typename M>
780  typename number_traits<typename linalg_traits<M>::value_type>
781  ::magnitude_type
782  mat_norm1(const M &m) {
783  return mat_norm1(m, typename linalg_traits<M>::sub_orientation());
784  }
785 
786 
787  /* ******************************************************************** */
788  /* matrix Infinity norm */
789  /* ******************************************************************** */
790  ///@cond DOXY_SHOW_ALL_FUNCTIONS
791  template <typename M>
792  typename number_traits<typename linalg_traits<M>::value_type>
793  ::magnitude_type
794  mat_norminf(const M &m, row_major) {
795  typename number_traits<typename linalg_traits<M>::value_type>
796  ::magnitude_type res(0);
797  for (size_type i = 0; i < mat_nrows(m); ++i)
798  res = std::max(res, vect_norm1(mat_const_row(m,i)));
799  return res;
800  }
801 
802  template <typename M>
803  typename number_traits<typename linalg_traits<M>::value_type>
804  ::magnitude_type
805  mat_norminf(const M &m, col_major) {
806  typedef typename linalg_traits<M>::value_type T;
807  typedef typename number_traits<T>::magnitude_type R;
808  typedef typename linalg_traits<M>::storage_type store_type;
809 
810  std::vector<R> aux(mat_nrows(m));
811  for (size_type i = 0; i < mat_ncols(m); ++i) {
812  typename linalg_traits<M>::const_sub_col_type col = mat_const_col(m, i);
813  auto it = vect_const_begin(col), ite = vect_const_end(col);
814  for (size_type k = 0; it != ite; ++it, ++k)
815  aux[index_of_it(it, k, store_type())] += gmm::abs(*it);
816  }
817  return vect_norminf(aux);
818  }
819 
820  template <typename M>
821  typename number_traits<typename linalg_traits<M>::value_type>
822  ::magnitude_type
823  mat_norminf(const M &m, col_and_row)
824  { return mat_norminf(m, row_major()); }
825 
826  template <typename M>
827  typename number_traits<typename linalg_traits<M>::value_type>
828  ::magnitude_type
829  mat_norminf(const M &m, row_and_col)
830  { return mat_norminf(m, row_major()); }
831  ///@endcond
832  /** infinity-norm of a matrix.*/
833  template <typename M>
834  typename number_traits<typename linalg_traits<M>::value_type>
835  ::magnitude_type
836  mat_norminf(const M &m) {
837  return mat_norminf(m, typename linalg_traits<M>::sub_orientation());
838  }
839 
840  /* ******************************************************************** */
841  /* Max norm for matrices */
842  /* ******************************************************************** */
843  ///@cond DOXY_SHOW_ALL_FUNCTIONS
844  template <typename M>
845  typename number_traits<typename linalg_traits<M>::value_type>
846  ::magnitude_type
847  mat_maxnorm(const M &m, row_major) {
848  typename number_traits<typename linalg_traits<M>::value_type>
849  ::magnitude_type res(0);
850  for (size_type i = 0; i < mat_nrows(m); ++i)
851  res = std::max(res, vect_norminf(mat_const_row(m,i)));
852  return res;
853  }
854 
855  template <typename M>
856  typename number_traits<typename linalg_traits<M>::value_type>
857  ::magnitude_type
858  mat_maxnorm(const M &m, col_major) {
859  typename number_traits<typename linalg_traits<M>::value_type>
860  ::magnitude_type res(0);
861  for (size_type i = 0; i < mat_ncols(m); ++i)
862  res = std::max(res, vect_norminf(mat_const_col(m,i)));
863  return res;
864  }
865  ///@endcond
866  /** max-norm of a matrix. */
867  template <typename M>
868  typename number_traits<typename linalg_traits<M>::value_type>
869  ::magnitude_type
870  mat_maxnorm(const M &m) {
871  return mat_maxnorm(m,
872  typename principal_orientation_type<typename
873  linalg_traits<M>::sub_orientation>::potype());
874  }
875 
876  /* ******************************************************************** */
877  /* Clean */
878  /* ******************************************************************** */
879  /** Clean a vector or matrix (replace near-zero entries with zeroes). */
880 
881  template <typename L> inline void clean(L &l, double threshold);
882 
883  ///@cond DOXY_SHOW_ALL_FUNCTIONS
884 
885  template <typename L, typename T>
886  void clean(L &l, double threshold, abstract_dense, T) {
887  typedef typename number_traits<T>::magnitude_type R;
888  auto it = vect_begin(l), ite = vect_end(l);
889  for (; it != ite; ++it)
890  if (gmm::abs(*it) < R(threshold)) *it = T(0);
891  }
892 
893  template <typename L, typename T>
894  void clean(L &l, double threshold, abstract_skyline, T)
895  { gmm::clean(l, threshold, abstract_dense(), T()); }
896 
897  template <typename L, typename T>
898  void clean(L &l, double threshold, abstract_sparse, T) {
899  typedef typename number_traits<T>::magnitude_type R;
900  auto it = vect_begin(l), ite = vect_end(l);
901  std::vector<size_type> ind;
902  for (; it != ite; ++it)
903  if (gmm::abs(*it) < R(threshold)) ind.push_back(it.index());
904  for (size_type i = 0; i < ind.size(); ++i) l[ind[i]] = T(0);
905  }
906 
907  template <typename L, typename T>
908  void clean(L &l, double threshold, abstract_dense, std::complex<T>) {
909  auto it = vect_begin(l), ite = vect_end(l);
910  for (; it != ite; ++it){
911  if (gmm::abs((*it).real()) < T(threshold))
912  *it = std::complex<T>(T(0), (*it).imag());
913  if (gmm::abs((*it).imag()) < T(threshold))
914  *it = std::complex<T>((*it).real(), T(0));
915  }
916  }
917 
918  template <typename L, typename T>
919  void clean(L &l, double threshold, abstract_skyline, std::complex<T>)
920  { gmm::clean(l, threshold, abstract_dense(), std::complex<T>()); }
921 
922  template <typename L, typename T>
923  void clean(L &l, double threshold, abstract_sparse, std::complex<T>) {
924  auto it = vect_begin(l), ite = vect_end(l);
925  std::vector<size_type> ind;
926  for (; it != ite; ++it) {
927  bool r = (gmm::abs((*it).real()) < T(threshold));
928  bool i = (gmm::abs((*it).imag()) < T(threshold));
929  if (r && i) ind.push_back(it.index());
930  else if (r) *it = std::complex<T>(T(0), (*it).imag());
931  else if (i) *it = std::complex<T>((*it).real(), T(0));
932  }
933  for (size_type i = 0; i < ind.size(); ++i)
934  l[ind[i]] = std::complex<T>(T(0),T(0));
935  }
936 
937  template <typename L> inline void clean(L &l, double threshold,
938  abstract_vector) {
939  gmm::clean(l, threshold, typename linalg_traits<L>::storage_type(),
940  typename linalg_traits<L>::value_type());
941  }
942 
943  template <typename L> inline void clean(const L &l, double threshold);
944 
945  template <typename L> void clean(L &l, double threshold, row_major) {
946  for (size_type i = 0; i < mat_nrows(l); ++i)
947  gmm::clean(mat_row(l, i), threshold);
948  }
949 
950  template <typename L> void clean(L &l, double threshold, col_major) {
951  for (size_type i = 0; i < mat_ncols(l); ++i)
952  gmm::clean(mat_col(l, i), threshold);
953  }
954 
955  template <typename L> inline void clean(L &l, double threshold,
956  abstract_matrix) {
957  gmm::clean(l, threshold,
958  typename principal_orientation_type<typename
959  linalg_traits<L>::sub_orientation>::potype());
960  }
961 
962  template <typename L> inline void clean(L &l, double threshold)
963  { clean(l, threshold, typename linalg_traits<L>::linalg_type()); }
964 
965  template <typename L> inline void clean(const L &l, double threshold)
966  { gmm::clean(linalg_const_cast(l), threshold); }
967 
968  /* ******************************************************************** */
969  /* Copy */
970  /* ******************************************************************** */
971  ///@endcond
972  /** Copy vectors or matrices.
973  @param l1 source vector or matrix.
974  @param l2 destination.
975  */
976  template <typename L1, typename L2> inline
977  void copy(const L1& l1, L2& l2) {
978  if ((const void *)(&l1) != (const void *)(&l2)) {
979  if (same_origin(l1,l2))
980  GMM_WARNING2("Warning : a conflict is possible in copy\n");
981 
982  copy(l1, l2, typename linalg_traits<L1>::linalg_type(),
983  typename linalg_traits<L2>::linalg_type());
984  }
985  }
986  ///@cond DOXY_SHOW_ALL_FUNCTIONS
987 
988  template <typename L1, typename L2> inline
989  void copy(const L1& l1, const L2& l2) { copy(l1, linalg_const_cast(l2)); }
990 
991  template <typename L1, typename L2> inline
992  void copy(const L1& l1, L2& l2, abstract_vector, abstract_vector) {
993  GMM_ASSERT2(vect_size(l1) == vect_size(l2), "dimensions mismatch, "
994  << vect_size(l1) << " !=" << vect_size(l2));
995  copy_vect(l1, l2, typename linalg_traits<L1>::storage_type(),
996  typename linalg_traits<L2>::storage_type());
997  }
998 
999  template <typename L1, typename L2> inline
1000  void copy(const L1& l1, L2& l2, abstract_matrix, abstract_matrix) {
1001  size_type m = mat_nrows(l1), n = mat_ncols(l1);
1002  if (!m || !n) return;
1003  GMM_ASSERT2(n==mat_ncols(l2) && m==mat_nrows(l2), "dimensions mismatch");
1004  copy_mat(l1, l2, typename linalg_traits<L1>::sub_orientation(),
1005  typename linalg_traits<L2>::sub_orientation());
1006  }
1007 
1008  template <typename V1, typename V2, typename C1, typename C2> inline
1009  void copy_vect(const V1 &v1, const V2 &v2, C1, C2)
1010  { copy_vect(v1, const_cast<V2 &>(v2), C1(), C2()); }
1011 
1012 
1013  template <typename L1, typename L2>
1014  void copy_mat_by_row(const L1& l1, L2& l2) {
1015  size_type nbr = mat_nrows(l1);
1016  for (size_type i = 0; i < nbr; ++i)
1017  copy(mat_const_row(l1, i), mat_row(l2, i));
1018  }
1019 
1020  template <typename L1, typename L2>
1021  void copy_mat_by_col(const L1 &l1, L2 &l2) {
1022  size_type nbc = mat_ncols(l1);
1023  for (size_type i = 0; i < nbc; ++i) {
1024  copy(mat_const_col(l1, i), mat_col(l2, i));
1025  }
1026  }
1027 
1028  template <typename L1, typename L2> inline
1029  void copy_mat(const L1& l1, L2& l2, row_major, row_major)
1030  { copy_mat_by_row(l1, l2); }
1031 
1032  template <typename L1, typename L2> inline
1033  void copy_mat(const L1& l1, L2& l2, row_major, row_and_col)
1034  { copy_mat_by_row(l1, l2); }
1035 
1036  template <typename L1, typename L2> inline
1037  void copy_mat(const L1& l1, L2& l2, row_and_col, row_and_col)
1038  { copy_mat_by_row(l1, l2); }
1039 
1040  template <typename L1, typename L2> inline
1041  void copy_mat(const L1& l1, L2& l2, row_and_col, row_major)
1042  { copy_mat_by_row(l1, l2); }
1043 
1044  template <typename L1, typename L2> inline
1045  void copy_mat(const L1& l1, L2& l2, col_and_row, row_major)
1046  { copy_mat_by_row(l1, l2); }
1047 
1048  template <typename L1, typename L2> inline
1049  void copy_mat(const L1& l1, L2& l2, row_major, col_and_row)
1050  { copy_mat_by_row(l1, l2); }
1051 
1052  template <typename L1, typename L2> inline
1053  void copy_mat(const L1& l1, L2& l2, col_and_row, row_and_col)
1054  { copy_mat_by_row(l1, l2); }
1055 
1056  template <typename L1, typename L2> inline
1057  void copy_mat(const L1& l1, L2& l2, row_and_col, col_and_row)
1058  { copy_mat_by_row(l1, l2); }
1059 
1060  template <typename L1, typename L2> inline
1061  void copy_mat(const L1& l1, L2& l2, col_major, col_major)
1062  { copy_mat_by_col(l1, l2); }
1063 
1064  template <typename L1, typename L2> inline
1065  void copy_mat(const L1& l1, L2& l2, col_major, col_and_row)
1066  { copy_mat_by_col(l1, l2); }
1067 
1068  template <typename L1, typename L2> inline
1069  void copy_mat(const L1& l1, L2& l2, col_major, row_and_col)
1070  { copy_mat_by_col(l1, l2); }
1071 
1072  template <typename L1, typename L2> inline
1073  void copy_mat(const L1& l1, L2& l2, row_and_col, col_major)
1074  { copy_mat_by_col(l1, l2); }
1075 
1076  template <typename L1, typename L2> inline
1077  void copy_mat(const L1& l1, L2& l2, col_and_row, col_major)
1078  { copy_mat_by_col(l1, l2); }
1079 
1080  template <typename L1, typename L2> inline
1081  void copy_mat(const L1& l1, L2& l2, col_and_row, col_and_row)
1082  { copy_mat_by_col(l1, l2); }
1083 
1084  template <typename L1, typename L2> inline
1085  void copy_mat_mixed_rc(const L1& l1, L2& l2, size_type i) {
1086  copy_mat_mixed_rc(l1, l2, i, typename linalg_traits<L1>::storage_type());
1087  }
1088 
1089  template <typename L1, typename L2>
1090  void copy_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_sparse) {
1091  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1092  for (; it != ite; ++it)
1093  l2(i, it.index()) = *it;
1094  }
1095 
1096  template <typename L1, typename L2>
1097  void copy_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_skyline) {
1098  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1099  for (; it != ite; ++it)
1100  l2(i, it.index()) = *it;
1101  }
1102 
1103  template <typename L1, typename L2>
1104  void copy_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_dense) {
1105  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1106  for (size_type j = 0; it != ite; ++it, ++j) l2(i, j) = *it;
1107  }
1108 
1109  template <typename L1, typename L2> inline
1110  void copy_mat_mixed_cr(const L1& l1, L2& l2, size_type i) {
1111  copy_mat_mixed_cr(l1, l2, i, typename linalg_traits<L1>::storage_type());
1112  }
1113 
1114  template <typename L1, typename L2>
1115  void copy_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_sparse) {
1116  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1117  for (; it != ite; ++it) l2(it.index(), i) = *it;
1118  }
1119 
1120  template <typename L1, typename L2>
1121  void copy_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_skyline) {
1122  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1123  for (; it != ite; ++it) l2(it.index(), i) = *it;
1124  }
1125 
1126  template <typename L1, typename L2>
1127  void copy_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_dense) {
1128  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1129  for (size_type j = 0; it != ite; ++it, ++j) l2(j, i) = *it;
1130  }
1131 
1132  template <typename L1, typename L2>
1133  void copy_mat(const L1& l1, L2& l2, row_major, col_major) {
1134  clear(l2);
1135  size_type nbr = mat_nrows(l1);
1136  for (size_type i = 0; i < nbr; ++i)
1137  copy_mat_mixed_rc(mat_const_row(l1, i), l2, i);
1138  }
1139 
1140  template <typename L1, typename L2>
1141  void copy_mat(const L1& l1, L2& l2, col_major, row_major) {
1142  clear(l2);
1143  size_type nbc = mat_ncols(l1);
1144  for (size_type i = 0; i < nbc; ++i)
1145  copy_mat_mixed_cr(mat_const_col(l1, i), l2, i);
1146  }
1147 
1148  template <typename L1, typename L2> inline
1149  void copy_vect(const L1 &l1, L2 &l2, abstract_dense, abstract_dense) {
1150  std::copy(vect_const_begin(l1), vect_const_end(l1), vect_begin(l2));
1151  }
1152 
1153  template <typename L1, typename L2> inline // to be optimised ?
1154  void copy_vect(const L1 &l1, L2 &l2, abstract_skyline, abstract_skyline) {
1155  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1156  while (it1 != ite1 && *it1 == typename linalg_traits<L1>::value_type(0))
1157  ++it1;
1158 
1159  if (ite1 - it1 > 0) {
1160  clear(l2);
1161  auto it2 = vect_begin(l2), ite2 = vect_end(l2);
1162  while (*(ite1-1) == typename linalg_traits<L1>::value_type(0)) ite1--;
1163 
1164  if (it2 == ite2) {
1165  l2[it1.index()] = *it1; ++it1;
1166  l2[ite1.index()-1] = *(ite1-1); --ite1;
1167  if (it1 < ite1)
1168  { it2 = vect_begin(l2); ++it2; std::copy(it1, ite1, it2); }
1169  }
1170  else {
1171  ptrdiff_t m = it1.index() - it2.index();
1172  if (m >= 0 && ite1.index() <= ite2.index())
1173  std::copy(it1, ite1, it2 + m);
1174  else {
1175  if (m < 0) l2[it1.index()] = *it1;
1176  if (ite1.index() > ite2.index()) l2[ite1.index()-1] = *(ite1-1);
1177  it2 = vect_begin(l2); ite2 = vect_end(l2);
1178  m = it1.index() - it2.index();
1179  std::copy(it1, ite1, it2 + m);
1180  }
1181  }
1182  }
1183  }
1184 
1185  template <typename L1, typename L2>
1186  void copy_vect(const L1& l1, L2& l2, abstract_sparse, abstract_dense) {
1187  clear(l2);
1188  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1189  for (; it != ite; ++it) { l2[it.index()] = *it; }
1190  }
1191 
1192  template <typename L1, typename L2>
1193  void copy_vect(const L1& l1, L2& l2, abstract_sparse, abstract_skyline) {
1194  clear(l2);
1195  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1196  for (; it != ite; ++it) l2[it.index()] = *it;
1197  }
1198 
1199  template <typename L1, typename L2>
1200  void copy_vect(const L1& l1, L2& l2, abstract_skyline, abstract_dense) {
1201  typedef typename linalg_traits<L1>::value_type T;
1202  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1203  if (it == ite)
1204  gmm::clear(l2);
1205  else {
1206  auto it2 = vect_begin(l2), ite2 = vect_end(l2);
1207 
1208  size_type i = it.index(), j;
1209  for (j = 0; j < i; ++j, ++it2) *it2 = T(0);
1210  for (; it != ite; ++it, ++it2) *it2 = *it;
1211  for (; it2 != ite2; ++it2) *it2 = T(0);
1212  }
1213  }
1214 
1215  template <typename L1, typename L2>
1216  void copy_vect(const L1& l1, L2& l2, abstract_sparse, abstract_sparse) {
1217  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1218  clear(l2);
1219  // cout << "copy " << l1 << " of size " << vect_size(l1) << " nnz = " << nnz(l1) << endl;
1220  for (; it != ite; ++it) {
1221  // cout << "*it = " << *it << endl;
1222  // cout << "it.index() = " << it.index() << endl;
1223  if (*it != (typename linalg_traits<L1>::value_type)(0))
1224  l2[it.index()] = *it;
1225  }
1226  }
1227 
1228  template <typename L1, typename L2>
1229  void copy_vect(const L1& l1, L2& l2, abstract_dense, abstract_sparse) {
1230  clear(l2);
1231  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1232  for (size_type i = 0; it != ite; ++it, ++i)
1233  if (*it != (typename linalg_traits<L1>::value_type)(0))
1234  l2[i] = *it;
1235  }
1236 
1237  template <typename L1, typename L2> // to be optimised ...
1238  void copy_vect(const L1& l1, L2& l2, abstract_dense, abstract_skyline) {
1239  clear(l2);
1240  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1241  for (size_type i = 0; it != ite; ++it, ++i)
1242  if (*it != (typename linalg_traits<L1>::value_type)(0))
1243  l2[i] = *it;
1244  }
1245 
1246 
1247  template <typename L1, typename L2>
1248  void copy_vect(const L1& l1, L2& l2, abstract_skyline, abstract_sparse) {
1249  clear(l2);
1250  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1251  for (; it != ite; ++it)
1252  if (*it != (typename linalg_traits<L1>::value_type)(0))
1253  l2[it.index()] = *it;
1254  }
1255 
1256  /* ******************************************************************** */
1257  /* Matrix and vector addition */
1258  /* algorithms are built in order to avoid some conflicts with */
1259  /* repeated arguments or with overlapping part of a same object. */
1260  /* In the latter case, conflicts are still possible. */
1261  /* ******************************************************************** */
1262  ///@endcond
1263  /** Add two vectors or matrices
1264  @param l1
1265  @param l2 contains on output, l2+l1.
1266  */
1267  template <typename L1, typename L2> inline
1268  void add(const L1& l1, L2& l2) {
1269  add_spec(l1, l2, typename linalg_traits<L2>::linalg_type());
1270  }
1271  ///@cond
1272 
1273  template <typename L1, typename L2> inline
1274  void add(const L1& l1, const L2& l2) { add(l1, linalg_const_cast(l2)); }
1275 
1276  template <typename L1, typename L2> inline
1277  void add_spec(const L1& l1, L2& l2, abstract_vector) {
1278  GMM_ASSERT2(vect_size(l1) == vect_size(l2), "dimensions mismatch, "
1279  << vect_size(l1) << " !=" << vect_size(l2));
1280  add(l1, l2, typename linalg_traits<L1>::storage_type(),
1281  typename linalg_traits<L2>::storage_type());
1282  }
1283 
1284  template <typename L1, typename L2> inline
1285  void add_spec(const L1& l1, L2& l2, abstract_matrix) {
1286  GMM_ASSERT2(mat_nrows(l1)==mat_nrows(l2) && mat_ncols(l1)==mat_ncols(l2),
1287  "dimensions mismatch l1 is " << mat_nrows(l1) << "x"
1288  << mat_ncols(l1) << " and l2 is " << mat_nrows(l2)
1289  << "x" << mat_ncols(l2));
1290  add(l1, l2, typename linalg_traits<L1>::sub_orientation(),
1291  typename linalg_traits<L2>::sub_orientation());
1292  }
1293 
1294  template <typename L1, typename L2>
1295  void add(const L1& l1, L2& l2, row_major, row_major) {
1296  auto it1 = mat_row_begin(l1), ite = mat_row_end(l1);
1297  auto it2 = mat_row_begin(l2);
1298  for ( ; it1 != ite; ++it1, ++it2)
1299  add(linalg_traits<L1>::row(it1), linalg_traits<L2>::row(it2));
1300  }
1301 
1302  template <typename L1, typename L2>
1303  void add(const L1& l1, L2& l2, col_major, col_major) {
1304  auto it1 = mat_col_const_begin(l1), ite = mat_col_const_end(l1);
1305  typename linalg_traits<L2>::col_iterator it2 = mat_col_begin(l2);
1306  for ( ; it1 != ite; ++it1, ++it2)
1307  add(linalg_traits<L1>::col(it1), linalg_traits<L2>::col(it2));
1308  }
1309 
1310  template <typename L1, typename L2> inline
1311  void add_mat_mixed_rc(const L1& l1, L2& l2, size_type i) {
1312  add_mat_mixed_rc(l1, l2, i, typename linalg_traits<L1>::storage_type());
1313  }
1314 
1315  template <typename L1, typename L2>
1316  void add_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_sparse) {
1317  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1318  for (; it != ite; ++it) l2(i, it.index()) += *it;
1319  }
1320 
1321  template <typename L1, typename L2>
1322  void add_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_skyline) {
1323  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1324  for (; it != ite; ++it) l2(i, it.index()) += *it;
1325  }
1326 
1327  template <typename L1, typename L2>
1328  void add_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_dense) {
1329  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1330  for (size_type j = 0; it != ite; ++it, ++j) l2(i, j) += *it;
1331  }
1332 
1333  template <typename L1, typename L2> inline
1334  void add_mat_mixed_cr(const L1& l1, L2& l2, size_type i) {
1335  add_mat_mixed_cr(l1, l2, i, typename linalg_traits<L1>::storage_type());
1336  }
1337 
1338  template <typename L1, typename L2>
1339  void add_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_sparse) {
1340  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1341  for (; it != ite; ++it) l2(it.index(), i) += *it;
1342  }
1343 
1344  template <typename L1, typename L2>
1345  void add_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_skyline) {
1346  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1347  for (; it != ite; ++it) l2(it.index(), i) += *it;
1348  }
1349 
1350  template <typename L1, typename L2>
1351  void add_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_dense) {
1352  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1353  for (size_type j = 0; it != ite; ++it, ++j) l2(j, i) += *it;
1354  }
1355 
1356  template <typename L1, typename L2>
1357  void add(const L1& l1, L2& l2, row_major, col_major) {
1358  size_type nbr = mat_nrows(l1);
1359  for (size_type i = 0; i < nbr; ++i)
1360  add_mat_mixed_rc(mat_const_row(l1, i), l2, i);
1361  }
1362 
1363  template <typename L1, typename L2>
1364  void add(const L1& l1, L2& l2, col_major, row_major) {
1365  size_type nbc = mat_ncols(l1);
1366  for (size_type i = 0; i < nbc; ++i)
1367  add_mat_mixed_cr(mat_const_col(l1, i), l2, i);
1368  }
1369 
1370  template <typename L1, typename L2> inline
1371  void add(const L1& l1, L2& l2, row_and_col, row_major)
1372  { add(l1, l2, row_major(), row_major()); }
1373 
1374  template <typename L1, typename L2> inline
1375  void add(const L1& l1, L2& l2, row_and_col, row_and_col)
1376  { add(l1, l2, row_major(), row_major()); }
1377 
1378  template <typename L1, typename L2> inline
1379  void add(const L1& l1, L2& l2, row_and_col, col_and_row)
1380  { add(l1, l2, row_major(), row_major()); }
1381 
1382  template <typename L1, typename L2> inline
1383  void add(const L1& l1, L2& l2, col_and_row, row_and_col)
1384  { add(l1, l2, row_major(), row_major()); }
1385 
1386  template <typename L1, typename L2> inline
1387  void add(const L1& l1, L2& l2, row_major, row_and_col)
1388  { add(l1, l2, row_major(), row_major()); }
1389 
1390  template <typename L1, typename L2> inline
1391  void add(const L1& l1, L2& l2, col_and_row, row_major)
1392  { add(l1, l2, row_major(), row_major()); }
1393 
1394  template <typename L1, typename L2> inline
1395  void add(const L1& l1, L2& l2, row_major, col_and_row)
1396  { add(l1, l2, row_major(), row_major()); }
1397 
1398  template <typename L1, typename L2> inline
1399  void add(const L1& l1, L2& l2, row_and_col, col_major)
1400  { add(l1, l2, col_major(), col_major()); }
1401 
1402  template <typename L1, typename L2> inline
1403  void add(const L1& l1, L2& l2, col_major, row_and_col)
1404  { add(l1, l2, col_major(), col_major()); }
1405 
1406  template <typename L1, typename L2> inline
1407  void add(const L1& l1, L2& l2, col_and_row, col_major)
1408  { add(l1, l2, col_major(), col_major()); }
1409 
1410  template <typename L1, typename L2> inline
1411  void add(const L1& l1, L2& l2, col_and_row, col_and_row)
1412  { add(l1, l2, col_major(), col_major()); }
1413 
1414  template <typename L1, typename L2> inline
1415  void add(const L1& l1, L2& l2, col_major, col_and_row)
1416  { add(l1, l2, col_major(), col_major()); }
1417 
1418  ///@endcond
1419  /** Addition of two vectors/matrices
1420  @param l1
1421  @param l2
1422  @param l3 contains l1+l2 on output
1423  */
1424  template <typename L1, typename L2, typename L3> inline
1425  void add(const L1& l1, const L2& l2, L3& l3) {
1426  add_spec(l1, l2, l3, typename linalg_traits<L2>::linalg_type());
1427  }
1428  ///@cond DOXY_SHOW_ALL_FUNCTIONS
1429 
1430  template <typename L1, typename L2, typename L3> inline
1431  void add(const L1& l1, const L2& l2, const L3& l3)
1432  { add(l1, l2, linalg_const_cast(l3)); }
1433 
1434  template <typename L1, typename L2, typename L3> inline
1435  void add_spec(const L1& l1, const L2& l2, L3& l3, abstract_matrix)
1436  { copy(l2, l3); add(l1, l3); }
1437 
1438  template <typename L1, typename L2, typename L3> inline
1439  void add_spec(const L1& l1, const L2& l2, L3& l3, abstract_vector) {
1440  GMM_ASSERT2(vect_size(l1) == vect_size(l2), "dimensions mismatch, "
1441  << vect_size(l1) << " !=" << vect_size(l2));
1442  GMM_ASSERT2(vect_size(l1) == vect_size(l3), "dimensions mismatch, "
1443  << vect_size(l1) << " !=" << vect_size(l3));
1444  if ((const void *)(&l1) == (const void *)(&l3))
1445  add(l2, l3);
1446  else if ((const void *)(&l2) == (const void *)(&l3))
1447  add(l1, l3);
1448  else
1449  add(l1, l2, l3, typename linalg_traits<L1>::storage_type(),
1450  typename linalg_traits<L2>::storage_type(),
1451  typename linalg_traits<L3>::storage_type());
1452  }
1453 
1454  template <typename IT1, typename IT2, typename IT3>
1455  void add_full_(IT1 it1, IT2 it2, IT3 it3, IT3 ite) {
1456  for (; it3 != ite; ++it3, ++it2, ++it1) *it3 = *it1 + *it2;
1457  }
1458 
1459  template <typename IT1, typename IT2, typename IT3>
1460  void add_almost_full_(IT1 it1, IT1 ite1, IT2 it2, IT3 it3, IT3 ite3) {
1461  IT3 it = it3;
1462  for (; it != ite3; ++it, ++it2) *it = *it2;
1463  for (; it1 != ite1; ++it1)
1464  *(it3 + it1.index()) += *it1;
1465  }
1466 
1467  template <typename IT1, typename IT2, typename IT3>
1468  void add_to_full_(IT1 it1, IT1 ite1, IT2 it2, IT2 ite2,
1469  IT3 it3, IT3 ite3) {
1470  typedef typename std::iterator_traits<IT3>::value_type T;
1471  IT3 it = it3;
1472  for (; it != ite3; ++it) *it = T(0);
1473  for (; it1 != ite1; ++it1) *(it3 + it1.index()) = *it1;
1474  for (; it2 != ite2; ++it2) *(it3 + it2.index()) += *it2;
1475  }
1476 
1477  template <typename L1, typename L2, typename L3> inline
1478  void add(const L1& l1, const L2& l2, L3& l3,
1479  abstract_dense, abstract_dense, abstract_dense) {
1480  add_full_(vect_const_begin(l1), vect_const_begin(l2),
1481  vect_begin(l3), vect_end(l3));
1482  }
1483 
1484  // generic function for add(v1, v2, v3).
1485  // Need to be specialized to optimize particular additions.
1486  template <typename L1, typename L2, typename L3,
1487  typename ST1, typename ST2, typename ST3>
1488  inline void add(const L1& l1, const L2& l2, L3& l3, ST1, ST2, ST3)
1489  { copy(l2, l3); add(l1, l3, ST1(), ST3()); }
1490 
1491  template <typename L1, typename L2, typename L3> inline
1492  void add(const L1& l1, const L2& l2, L3& l3,
1493  abstract_sparse, abstract_dense, abstract_dense) {
1494  add_almost_full_(vect_const_begin(l1), vect_const_end(l1),
1495  vect_const_begin(l2), vect_begin(l3), vect_end(l3));
1496  }
1497 
1498  template <typename L1, typename L2, typename L3> inline
1499  void add(const L1& l1, const L2& l2, L3& l3,
1500  abstract_dense, abstract_sparse, abstract_dense)
1501  { add(l2, l1, l3, abstract_sparse(), abstract_dense(), abstract_dense()); }
1502 
1503  template <typename L1, typename L2, typename L3> inline
1504  void add(const L1& l1, const L2& l2, L3& l3,
1505  abstract_sparse, abstract_sparse, abstract_dense) {
1506  add_to_full_(vect_const_begin(l1), vect_const_end(l1),
1507  vect_const_begin(l2), vect_const_end(l2),
1508  vect_begin(l3), vect_end(l3));
1509  }
1510 
1511 
1512  template <typename L1, typename L2, typename L3>
1513  void add_spspsp(const L1& l1, const L2& l2, L3& l3, linalg_true) {
1514  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1515  auto it2 = vect_const_begin(l2), ite2 = vect_const_end(l2);
1516  clear(l3);
1517  while (it1 != ite1 && it2 != ite2) {
1518  ptrdiff_t d = it1.index() - it2.index();
1519  if (d < 0)
1520  { l3[it1.index()] += *it1; ++it1; }
1521  else if (d > 0)
1522  { l3[it2.index()] += *it2; ++it2; }
1523  else
1524  { l3[it1.index()] = *it1 + *it2; ++it1; ++it2; }
1525  }
1526  for (; it1 != ite1; ++it1) l3[it1.index()] += *it1;
1527  for (; it2 != ite2; ++it2) l3[it2.index()] += *it2;
1528  }
1529 
1530  template <typename L1, typename L2, typename L3>
1531  void add_spspsp(const L1& l1, const L2& l2, L3& l3, linalg_false)
1532  { copy(l2, l3); add(l2, l3); }
1533 
1534  template <typename L1, typename L2, typename L3>
1535  void add(const L1& l1, const L2& l2, L3& l3,
1536  abstract_sparse, abstract_sparse, abstract_sparse) {
1537  add_spspsp(l1, l2, l3, typename linalg_and<typename
1538  linalg_traits<L1>::index_sorted,
1539  typename linalg_traits<L2>::index_sorted>::bool_type());
1540  }
1541 
1542  template <typename L1, typename L2>
1543  void add(const L1& l1, L2& l2, abstract_dense, abstract_dense) {
1544  auto it1 = vect_const_begin(l1);
1545  auto it2 = vect_begin(l2), ite = vect_end(l2);
1546  for (; it2 != ite; ++it2, ++it1) *it2 += *it1;
1547  }
1548 
1549  template <typename L1, typename L2>
1550  void add(const L1& l1, L2& l2, abstract_dense, abstract_skyline) {
1551  typedef typename linalg_traits<L1>::value_type T;
1552 
1553  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1554  size_type i1 = 0, ie1 = vect_size(l1);
1555  while (it1 != ite1 && *it1 == T(0)) { ++it1; ++i1; }
1556  if (it1 != ite1) {
1557  auto it2 = vect_begin(l2), ite2 = vect_end(l2);
1558  while (ie1 && *(ite1-1) == T(0)) { ite1--; --ie1; }
1559 
1560  if (it2 == ite2 || i1 < it2.index()) {
1561  l2[i1] = *it1; ++i1; ++it1;
1562  if (it1 == ite1) return;
1563  it2 = vect_begin(l2); ite2 = vect_end(l2);
1564  }
1565  if (ie1 > ite2.index()) {
1566  --ite1; l2[ie1 - 1] = *ite1;
1567  it2 = vect_begin(l2);
1568  }
1569  it2 += i1 - it2.index();
1570  for (; it1 != ite1; ++it1, ++it2) { *it2 += *it1; }
1571  }
1572  }
1573 
1574 
1575  template <typename L1, typename L2>
1576  void add(const L1& l1, L2& l2, abstract_skyline, abstract_dense) {
1577  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1578  if (it1 != ite1) {
1579  auto it2 = vect_begin(l2);
1580  it2 += it1.index();
1581  for (; it1 != ite1; ++it2, ++it1) *it2 += *it1;
1582  }
1583  }
1584 
1585 
1586  template <typename L1, typename L2>
1587  void add(const L1& l1, L2& l2, abstract_sparse, abstract_dense) {
1588  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1589  for (; it1 != ite1; ++it1) l2[it1.index()] += *it1;
1590  }
1591 
1592  template <typename L1, typename L2>
1593  void add(const L1& l1, L2& l2, abstract_sparse, abstract_sparse) {
1594  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1595  for (; it1 != ite1; ++it1) l2[it1.index()] += *it1;
1596  }
1597 
1598  template <typename L1, typename L2>
1599  void add(const L1& l1, L2& l2, abstract_sparse, abstract_skyline) {
1600  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1601  for (; it1 != ite1; ++it1) l2[it1.index()] += *it1;
1602  }
1603 
1604 
1605  template <typename L1, typename L2>
1606  void add(const L1& l1, L2& l2, abstract_skyline, abstract_sparse) {
1607  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1608  for (; it1 != ite1; ++it1)
1609  if (*it1 != typename linalg_traits<L1>::value_type(0))
1610  l2[it1.index()] += *it1;
1611  }
1612 
1613  template <typename L1, typename L2>
1614  void add(const L1& l1, L2& l2, abstract_skyline, abstract_skyline) {
1615  typedef typename linalg_traits<L1>::value_type T1;
1616  typedef typename linalg_traits<L2>::value_type T2;
1617 
1618  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1619 
1620  while (it1 != ite1 && *it1 == T1(0)) ++it1;
1621  if (ite1 != it1) {
1622  auto it2 = vect_begin(l2), ite2 = vect_end(l2);
1623  while (*(ite1-1) == T1(0)) ite1--;
1624  if (it2 == ite2 || it1.index() < it2.index()) {
1625  l2[it1.index()] = T2(0);
1626  it2 = vect_begin(l2); ite2 = vect_end(l2);
1627  }
1628  if (ite1.index() > ite2.index()) {
1629  l2[ite1.index() - 1] = T2(0);
1630  it2 = vect_begin(l2);
1631  }
1632  it2 += it1.index() - it2.index();
1633  for (; it1 != ite1; ++it1, ++it2) *it2 += *it1;
1634  }
1635  }
1636 
1637  template <typename L1, typename L2>
1638  void add(const L1& l1, L2& l2, abstract_dense, abstract_sparse) {
1639  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1640  for (size_type i = 0; it1 != ite1; ++it1, ++i)
1641  if (*it1 != typename linalg_traits<L1>::value_type(0)) l2[i] += *it1;
1642  }
1643 
1644  /* ******************************************************************** */
1645  /* Matrix-vector mult */
1646  /* ******************************************************************** */
1647  ///@endcond
1648  /** matrix-vector or matrix-matrix product.
1649  @param l1 a matrix.
1650  @param l2 a vector or matrix.
1651  @param l3 the product l1*l2.
1652  */
1653  template <typename L1, typename L2, typename L3> inline
1654  void mult(const L1& l1, const L2& l2, L3& l3) {
1655  mult_dispatch(l1, l2, l3, typename linalg_traits<L2>::linalg_type());
1656  }
1657  ///@cond DOXY_SHOW_ALL_FUNCTIONS
1658 
1659  template <typename L1, typename L2, typename L3> inline
1660  void mult(const L1& l1, const L2& l2, const L3& l3)
1661  { mult(l1, l2, linalg_const_cast(l3)); }
1662 
1663  template <typename L1, typename L2, typename L3> inline
1664  void mult_dispatch(const L1& l1, const L2& l2, L3& l3, abstract_vector) {
1665  size_type m = mat_nrows(l1), n = mat_ncols(l1);
1666  if (!m || !n) { gmm::clear(l3); return; }
1667  GMM_ASSERT2(n==vect_size(l2) && m==vect_size(l3), "dimensions mismatch");
1668  if (!same_origin(l2, l3))
1669  mult_spec(l1, l2, l3, typename principal_orientation_type<typename
1670  linalg_traits<L1>::sub_orientation>::potype());
1671  else {
1672  GMM_WARNING2("Warning, A temporary is used for mult\n");
1673  typename temporary_vector<L3>::vector_type temp(vect_size(l3));
1674  mult_spec(l1, l2, temp, typename principal_orientation_type<typename
1675  linalg_traits<L1>::sub_orientation>::potype());
1676  copy(temp, l3);
1677  }
1678  }
1679 
1680  template <typename L1, typename L2, typename L3>
1681  void mult_by_row(const L1& l1, const L2& l2, L3& l3, abstract_sparse) {
1682  typedef typename linalg_traits<L3>::value_type T;
1683  clear(l3);
1684  size_type nr = mat_nrows(l1);
1685  for (size_type i = 0; i < nr; ++i) {
1686  T aux = vect_sp(mat_const_row(l1, i), l2);
1687  if (aux != T(0)) l3[i] = aux;
1688  }
1689  }
1690 
1691  template <typename L1, typename L2, typename L3>
1692  void mult_by_row(const L1& l1, const L2& l2, L3& l3, abstract_skyline) {
1693  typedef typename linalg_traits<L3>::value_type T;
1694  clear(l3);
1695  size_type nr = mat_nrows(l1);
1696  for (size_type i = 0; i < nr; ++i) {
1697  T aux = vect_sp(mat_const_row(l1, i), l2);
1698  if (aux != T(0)) l3[i] = aux;
1699  }
1700  }
1701 
1702  template <typename L1, typename L2, typename L3>
1703  void mult_by_row(const L1& l1, const L2& l2, L3& l3, abstract_dense) {
1704  typename linalg_traits<L3>::iterator it=vect_begin(l3), ite=vect_end(l3);
1705  auto itr = mat_row_const_begin(l1);
1706  for (; it != ite; ++it, ++itr)
1707  *it = vect_sp(linalg_traits<L1>::row(itr), l2,
1708  typename linalg_traits<L1>::storage_type(),
1709  typename linalg_traits<L2>::storage_type());
1710  }
1711 
1712  template <typename L1, typename L2, typename L3>
1713  void mult_by_col(const L1& l1, const L2& l2, L3& l3, abstract_dense) {
1714  clear(l3);
1715  size_type nc = mat_ncols(l1);
1716  for (size_type i = 0; i < nc; ++i)
1717  add(scaled(mat_const_col(l1, i), l2[i]), l3);
1718  }
1719 
1720  template <typename L1, typename L2, typename L3>
1721  void mult_by_col(const L1& l1, const L2& l2, L3& l3, abstract_sparse) {
1722  typedef typename linalg_traits<L2>::value_type T;
1723  clear(l3);
1724  auto it = vect_const_begin(l2), ite = vect_const_end(l2);
1725  for (; it != ite; ++it)
1726  if (*it != T(0)) add(scaled(mat_const_col(l1, it.index()), *it), l3);
1727  }
1728 
1729  template <typename L1, typename L2, typename L3>
1730  void mult_by_col(const L1& l1, const L2& l2, L3& l3, abstract_skyline) {
1731  typedef typename linalg_traits<L2>::value_type T;
1732  clear(l3);
1733  auto it = vect_const_begin(l2), ite = vect_const_end(l2);
1734  for (; it != ite; ++it)
1735  if (*it != T(0)) add(scaled(mat_const_col(l1, it.index()), *it), l3);
1736  }
1737 
1738  template <typename L1, typename L2, typename L3> inline
1739  void mult_spec(const L1& l1, const L2& l2, L3& l3, row_major)
1740  { mult_by_row(l1, l2, l3, typename linalg_traits<L3>::storage_type()); }
1741 
1742  template <typename L1, typename L2, typename L3> inline
1743  void mult_spec(const L1& l1, const L2& l2, L3& l3, col_major)
1744  { mult_by_col(l1, l2, l3, typename linalg_traits<L2>::storage_type()); }
1745 
1746  template <typename L1, typename L2, typename L3> inline
1747  void mult_spec(const L1& l1, const L2& l2, L3& l3, abstract_null_type)
1748  { mult_ind(l1, l2, l3, typename linalg_traits<L1>::storage_type()); }
1749 
1750  template <typename L1, typename L2, typename L3>
1751  void mult_ind(const L1& l1, const L2& l2, L3& l3, abstract_indirect) {
1752  GMM_ASSERT1(false, "gmm::mult(m, ., .) undefined for this kind of matrix");
1753  }
1754 
1755  template <typename L1, typename L2, typename L3, typename L4> inline
1756  void mult(const L1& l1, const L2& l2, const L3& l3, L4& l4) {
1757  size_type m = mat_nrows(l1), n = mat_ncols(l1);
1758  copy(l3, l4);
1759  if (!m || !n) { gmm::copy(l3, l4); return; }
1760  GMM_ASSERT2(n==vect_size(l2) && m==vect_size(l4), "dimensions mismatch");
1761  if (!same_origin(l2, l4)) {
1762  mult_add_spec(l1, l2, l4, typename principal_orientation_type<typename
1763  linalg_traits<L1>::sub_orientation>::potype());
1764  }
1765  else {
1766  GMM_WARNING2("Warning, A temporary is used for mult\n");
1767  typename temporary_vector<L2>::vector_type temp(vect_size(l2));
1768  copy(l2, temp);
1769  mult_add_spec(l1,temp, l4, typename principal_orientation_type<typename
1770  linalg_traits<L1>::sub_orientation>::potype());
1771  }
1772  }
1773 
1774  template <typename L1, typename L2, typename L3, typename L4> inline
1775  void mult(const L1& l1, const L2& l2, const L3& l3, const L4& l4)
1776  { mult(l1, l2, l3, linalg_const_cast(l4)); }
1777 
1778  ///@endcond
1779  /** Multiply-accumulate. l3 += l1*l2; */
1780  template <typename L1, typename L2, typename L3> inline
1781  void mult_add(const L1& l1, const L2& l2, L3& l3) {
1782  size_type m = mat_nrows(l1), n = mat_ncols(l1);
1783  if (!m || !n) return;
1784  GMM_ASSERT2(n==vect_size(l2) && m==vect_size(l3), "dimensions mismatch");
1785  if (!same_origin(l2, l3)) {
1786  mult_add_spec(l1, l2, l3, typename principal_orientation_type<typename
1787  linalg_traits<L1>::sub_orientation>::potype());
1788  }
1789  else {
1790  GMM_WARNING2("Warning, A temporary is used for mult\n");
1791  typename temporary_vector<L3>::vector_type temp(vect_size(l2));
1792  copy(l2, temp);
1793  mult_add_spec(l1,temp, l3, typename principal_orientation_type<typename
1794  linalg_traits<L1>::sub_orientation>::potype());
1795  }
1796  }
1797  ///@cond DOXY_SHOW_ALL_FUNCTIONS
1798 
1799  template <typename L1, typename L2, typename L3> inline
1800  void mult_add(const L1& l1, const L2& l2, const L3& l3)
1801  { mult_add(l1, l2, linalg_const_cast(l3)); }
1802 
1803  template <typename L1, typename L2, typename L3>
1804  void mult_add_by_row(const L1& l1, const L2& l2, L3& l3, abstract_sparse) {
1805  typedef typename linalg_traits<L3>::value_type T;
1806  size_type nr = mat_nrows(l1);
1807  for (size_type i = 0; i < nr; ++i) {
1808  T aux = vect_sp(mat_const_row(l1, i), l2);
1809  if (aux != T(0)) l3[i] += aux;
1810  }
1811  }
1812 
1813  template <typename L1, typename L2, typename L3>
1814  void mult_add_by_row(const L1& l1, const L2& l2, L3& l3, abstract_skyline) {
1815  typedef typename linalg_traits<L3>::value_type T;
1816  size_type nr = mat_nrows(l1);
1817  for (size_type i = 0; i < nr; ++i) {
1818  T aux = vect_sp(mat_const_row(l1, i), l2);
1819  if (aux != T(0)) l3[i] += aux;
1820  }
1821  }
1822 
1823  template <typename L1, typename L2, typename L3>
1824  void mult_add_by_row(const L1& l1, const L2& l2, L3& l3, abstract_dense) {
1825  auto it=vect_begin(l3), ite=vect_end(l3);
1826  auto itr = mat_row_const_begin(l1);
1827  for (; it != ite; ++it, ++itr)
1828  *it += vect_sp(linalg_traits<L1>::row(itr), l2);
1829  }
1830 
1831  template <typename L1, typename L2, typename L3>
1832  void mult_add_by_col(const L1& l1, const L2& l2, L3& l3, abstract_dense) {
1833  size_type nc = mat_ncols(l1);
1834  for (size_type i = 0; i < nc; ++i)
1835  add(scaled(mat_const_col(l1, i), l2[i]), l3);
1836  }
1837 
1838  template <typename L1, typename L2, typename L3>
1839  void mult_add_by_col(const L1& l1, const L2& l2, L3& l3, abstract_sparse) {
1840  auto it = vect_const_begin(l2), ite = vect_const_end(l2);
1841  for (; it != ite; ++it)
1842  if (*it != typename linalg_traits<L2>::value_type(0))
1843  add(scaled(mat_const_col(l1, it.index()), *it), l3);
1844  }
1845 
1846  template <typename L1, typename L2, typename L3>
1847  void mult_add_by_col(const L1& l1, const L2& l2, L3& l3, abstract_skyline) {
1848  auto it = vect_const_begin(l2), ite = vect_const_end(l2);
1849  for (; it != ite; ++it)
1850  if (*it != typename linalg_traits<L2>::value_type(0))
1851  add(scaled(mat_const_col(l1, it.index()), *it), l3);
1852  }
1853 
1854  template <typename L1, typename L2, typename L3> inline
1855  void mult_add_spec(const L1& l1, const L2& l2, L3& l3, row_major)
1856  { mult_add_by_row(l1, l2, l3, typename linalg_traits<L3>::storage_type()); }
1857 
1858  template <typename L1, typename L2, typename L3> inline
1859  void mult_add_spec(const L1& l1, const L2& l2, L3& l3, col_major)
1860  { mult_add_by_col(l1, l2, l3, typename linalg_traits<L2>::storage_type()); }
1861 
1862  template <typename L1, typename L2, typename L3> inline
1863  void mult_add_spec(const L1& l1, const L2& l2, L3& l3, abstract_null_type)
1864  { mult_ind(l1, l2, l3, typename linalg_traits<L1>::storage_type()); }
1865 
1866  template <typename L1, typename L2, typename L3>
1867  void transposed_mult(const L1& l1, const L2& l2, const L3& l3)
1868  { mult(gmm::transposed(l1), l2, l3); }
1869 
1870 
1871  /* ******************************************************************** */
1872  /* Matrix-matrix mult */
1873  /* ******************************************************************** */
1874 
1875 
1876  struct g_mult {}; // generic mult, less optimized
1877  struct c_mult {}; // col x col -> col mult
1878  struct r_mult {}; // row x row -> row mult
1879  struct rcmult {}; // row x col -> col mult
1880  struct crmult {}; // col x row -> row mult
1881 
1882 
1883  template<typename SO1, typename SO2, typename SO3> struct mult_t;
1884  #define DEFMU__ template<> struct mult_t
1885  DEFMU__<row_major , row_major , row_major > { typedef r_mult t; };
1886  DEFMU__<row_major , row_major , col_major > { typedef g_mult t; };
1887  DEFMU__<row_major , row_major , col_and_row> { typedef r_mult t; };
1888  DEFMU__<row_major , row_major , row_and_col> { typedef r_mult t; };
1889  DEFMU__<row_major , col_major , row_major > { typedef rcmult t; };
1890  DEFMU__<row_major , col_major , col_major > { typedef rcmult t; };
1891  DEFMU__<row_major , col_major , col_and_row> { typedef rcmult t; };
1892  DEFMU__<row_major , col_major , row_and_col> { typedef rcmult t; };
1893  DEFMU__<row_major , col_and_row, row_major > { typedef r_mult t; };
1894  DEFMU__<row_major , col_and_row, col_major > { typedef rcmult t; };
1895  DEFMU__<row_major , col_and_row, col_and_row> { typedef rcmult t; };
1896  DEFMU__<row_major , col_and_row, row_and_col> { typedef rcmult t; };
1897  DEFMU__<row_major , row_and_col, row_major > { typedef r_mult t; };
1898  DEFMU__<row_major , row_and_col, col_major > { typedef rcmult t; };
1899  DEFMU__<row_major , row_and_col, col_and_row> { typedef r_mult t; };
1900  DEFMU__<row_major , row_and_col, row_and_col> { typedef r_mult t; };
1901  DEFMU__<col_major , row_major , row_major > { typedef crmult t; };
1902  DEFMU__<col_major , row_major , col_major > { typedef g_mult t; };
1903  DEFMU__<col_major , row_major , col_and_row> { typedef crmult t; };
1904  DEFMU__<col_major , row_major , row_and_col> { typedef crmult t; };
1905  DEFMU__<col_major , col_major , row_major > { typedef g_mult t; };
1906  DEFMU__<col_major , col_major , col_major > { typedef c_mult t; };
1907  DEFMU__<col_major , col_major , col_and_row> { typedef c_mult t; };
1908  DEFMU__<col_major , col_major , row_and_col> { typedef c_mult t; };
1909  DEFMU__<col_major , col_and_row, row_major > { typedef crmult t; };
1910  DEFMU__<col_major , col_and_row, col_major > { typedef c_mult t; };
1911  DEFMU__<col_major , col_and_row, col_and_row> { typedef c_mult t; };
1912  DEFMU__<col_major , col_and_row, row_and_col> { typedef c_mult t; };
1913  DEFMU__<col_major , row_and_col, row_major > { typedef crmult t; };
1914  DEFMU__<col_major , row_and_col, col_major > { typedef c_mult t; };
1915  DEFMU__<col_major , row_and_col, col_and_row> { typedef c_mult t; };
1916  DEFMU__<col_major , row_and_col, row_and_col> { typedef c_mult t; };
1917  DEFMU__<col_and_row, row_major , row_major > { typedef r_mult t; };
1918  DEFMU__<col_and_row, row_major , col_major > { typedef c_mult t; };
1919  DEFMU__<col_and_row, row_major , col_and_row> { typedef r_mult t; };
1920  DEFMU__<col_and_row, row_major , row_and_col> { typedef r_mult t; };
1921  DEFMU__<col_and_row, col_major , row_major > { typedef rcmult t; };
1922  DEFMU__<col_and_row, col_major , col_major > { typedef c_mult t; };
1923  DEFMU__<col_and_row, col_major , col_and_row> { typedef c_mult t; };
1924  DEFMU__<col_and_row, col_major , row_and_col> { typedef c_mult t; };
1925  DEFMU__<col_and_row, col_and_row, row_major > { typedef r_mult t; };
1926  DEFMU__<col_and_row, col_and_row, col_major > { typedef c_mult t; };
1927  DEFMU__<col_and_row, col_and_row, col_and_row> { typedef c_mult t; };
1928  DEFMU__<col_and_row, col_and_row, row_and_col> { typedef c_mult t; };
1929  DEFMU__<col_and_row, row_and_col, row_major > { typedef r_mult t; };
1930  DEFMU__<col_and_row, row_and_col, col_major > { typedef c_mult t; };
1931  DEFMU__<col_and_row, row_and_col, col_and_row> { typedef c_mult t; };
1932  DEFMU__<col_and_row, row_and_col, row_and_col> { typedef r_mult t; };
1933  DEFMU__<row_and_col, row_major , row_major > { typedef r_mult t; };
1934  DEFMU__<row_and_col, row_major , col_major > { typedef c_mult t; };
1935  DEFMU__<row_and_col, row_major , col_and_row> { typedef r_mult t; };
1936  DEFMU__<row_and_col, row_major , row_and_col> { typedef r_mult t; };
1937  DEFMU__<row_and_col, col_major , row_major > { typedef rcmult t; };
1938  DEFMU__<row_and_col, col_major , col_major > { typedef c_mult t; };
1939  DEFMU__<row_and_col, col_major , col_and_row> { typedef c_mult t; };
1940  DEFMU__<row_and_col, col_major , row_and_col> { typedef c_mult t; };
1941  DEFMU__<row_and_col, col_and_row, row_major > { typedef rcmult t; };
1942  DEFMU__<row_and_col, col_and_row, col_major > { typedef rcmult t; };
1943  DEFMU__<row_and_col, col_and_row, col_and_row> { typedef rcmult t; };
1944  DEFMU__<row_and_col, col_and_row, row_and_col> { typedef rcmult t; };
1945  DEFMU__<row_and_col, row_and_col, row_major > { typedef r_mult t; };
1946  DEFMU__<row_and_col, row_and_col, col_major > { typedef c_mult t; };
1947  DEFMU__<row_and_col, row_and_col, col_and_row> { typedef r_mult t; };
1948  DEFMU__<row_and_col, row_and_col, row_and_col> { typedef r_mult t; };
1949 
1950  template <typename L1, typename L2, typename L3>
1951  void mult_dispatch(const L1& l1, const L2& l2, L3& l3, abstract_matrix) {
1952  typedef typename temporary_matrix<L3>::matrix_type temp_mat_type;
1953  size_type n = mat_ncols(l1);
1954  if (n == 0) { gmm::clear(l3); return; }
1955  GMM_ASSERT2(n == mat_nrows(l2) && mat_nrows(l1) == mat_nrows(l3) &&
1956  mat_ncols(l2) == mat_ncols(l3), "dimensions mismatch");
1957 
1958  if (same_origin(l2, l3) || same_origin(l1, l3)) {
1959  GMM_WARNING2("A temporary is used for mult");
1960  temp_mat_type temp(mat_nrows(l3), mat_ncols(l3));
1961  mult_spec(l1, l2, temp, typename mult_t<
1962  typename linalg_traits<L1>::sub_orientation,
1963  typename linalg_traits<L2>::sub_orientation,
1964  typename linalg_traits<temp_mat_type>::sub_orientation>::t());
1965  copy(temp, l3);
1966  }
1967  else
1968  mult_spec(l1, l2, l3, typename mult_t<
1969  typename linalg_traits<L1>::sub_orientation,
1970  typename linalg_traits<L2>::sub_orientation,
1971  typename linalg_traits<L3>::sub_orientation>::t());
1972  }
1973 
1974  // Completely generic but inefficient
1975 
1976  template <typename L1, typename L2, typename L3>
1977  void mult_spec(const L1& l1, const L2& l2, L3& l3, g_mult) {
1978  typedef typename linalg_traits<L3>::value_type T;
1979  GMM_WARNING2("Inefficient generic matrix-matrix mult is used");
1980  for (size_type i = 0; i < mat_nrows(l3) ; ++i)
1981  for (size_type j = 0; j < mat_ncols(l3) ; ++j) {
1982  T a(0);
1983  for (size_type k = 0; k < mat_nrows(l2) ; ++k) a += l1(i, k)*l2(k, j);
1984  l3(i, j) = a;
1985  }
1986  }
1987 
1988  // row x col matrix-matrix mult
1989 
1990  template <typename L1, typename L2, typename L3>
1991  void mult_row_col_with_temp(const L1& l1, const L2& l2, L3& l3, col_major) {
1992  typedef typename temporary_col_matrix<L1>::matrix_type temp_col_mat;
1993  temp_col_mat temp(mat_nrows(l1), mat_ncols(l1));
1994  copy(l1, temp);
1995  mult(temp, l2, l3);
1996  }
1997 
1998  template <typename L1, typename L2, typename L3>
1999  void mult_row_col_with_temp(const L1& l1, const L2& l2, L3& l3, row_major) {
2000  typedef typename temporary_row_matrix<L2>::matrix_type temp_row_mat;
2001  temp_row_mat temp(mat_nrows(l2), mat_ncols(l2));
2002  copy(l2, temp);
2003  mult(l1, temp, l3);
2004  }
2005 
2006  template <typename L1, typename L2, typename L3>
2007  void mult_spec(const L1& l1, const L2& l2, L3& l3, rcmult) {
2008  if (is_sparse(l1) && is_sparse(l2)) {
2009  GMM_WARNING3("Inefficient row matrix - col matrix mult for "
2010  "sparse matrices, using temporary");
2011  mult_row_col_with_temp(l1, l2, l3,
2012  typename principal_orientation_type<typename
2013  linalg_traits<L3>::sub_orientation>::potype());
2014  }
2015  else {
2016  auto it2b = linalg_traits<L2>::col_begin(l2), it2 = it2b,
2017  ite = linalg_traits<L2>::col_end(l2);
2018  size_type i,j, k = mat_nrows(l1);
2019 
2020  for (i = 0; i < k; ++i) {
2021  typename linalg_traits<L1>::const_sub_row_type r1=mat_const_row(l1, i);
2022  for (it2 = it2b, j = 0; it2 != ite; ++it2, ++j)
2023  l3(i,j) = vect_sp(r1, linalg_traits<L2>::col(it2));
2024  }
2025  }
2026  }
2027 
2028  // row - row matrix-matrix mult
2029 
2030  template <typename L1, typename L2, typename L3> inline
2031  void mult_spec(const L1& l1, const L2& l2, L3& l3, r_mult) {
2032  mult_spec(l1, l2, l3,r_mult(),typename linalg_traits<L1>::storage_type());
2033  }
2034 
2035  template <typename L1, typename L2, typename L3>
2036  void mult_spec(const L1& l1, const L2& l2, L3& l3, r_mult, abstract_dense) {
2037  // optimizable
2038  clear(l3);
2039  size_type nn = mat_nrows(l3), mm = mat_nrows(l2);
2040  for (size_type i = 0; i < nn; ++i) {
2041  for (size_type j = 0; j < mm; ++j) {
2042  add(scaled(mat_const_row(l2, j), l1(i, j)), mat_row(l3, i));
2043  }
2044  }
2045  }
2046 
2047  template <typename L1, typename L2, typename L3>
2048  void mult_spec(const L1& l1, const L2& l2, L3& l3, r_mult, abstract_sparse) {
2049  // optimizable
2050  clear(l3);
2051  size_type nn = mat_nrows(l3);
2052  for (size_type i = 0; i < nn; ++i) {
2053  typename linalg_traits<L1>::const_sub_row_type rl1=mat_const_row(l1, i);
2054  auto it = vect_const_begin(rl1), ite = vect_const_end(rl1);
2055  for (; it != ite; ++it)
2056  add(scaled(mat_const_row(l2, it.index()), *it), mat_row(l3, i));
2057  }
2058  }
2059 
2060  template <typename L1, typename L2, typename L3>
2061  void mult_spec(const L1& l1, const L2& l2, L3& l3, r_mult, abstract_skyline)
2062  { mult_spec(l1, l2, l3, r_mult(), abstract_sparse()); }
2063 
2064  // col - col matrix-matrix mult
2065 
2066  template <typename L1, typename L2, typename L3> inline
2067  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult) {
2068  mult_spec(l1, l2,l3,c_mult(),typename linalg_traits<L2>::storage_type(),
2069  typename linalg_traits<L2>::sub_orientation());
2070  }
2071 
2072 
2073  template <typename L1, typename L2, typename L3, typename ORIEN>
2074  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult,
2075  abstract_dense, ORIEN) {
2076  typedef typename linalg_traits<L2>::value_type T;
2077  size_type nn = mat_ncols(l3), mm = mat_ncols(l1);
2078 
2079  for (size_type i = 0; i < nn; ++i) {
2080  clear(mat_col(l3, i));
2081  for (size_type j = 0; j < mm; ++j) {
2082  T b = l2(j, i);
2083  if (b != T(0)) add(scaled(mat_const_col(l1, j), b), mat_col(l3, i));
2084  }
2085  }
2086  }
2087 
2088  template <typename L1, typename L2, typename L3, typename ORIEN>
2089  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult,
2090  abstract_sparse, ORIEN) {
2091  // optimizable
2092  clear(l3);
2093  size_type nn = mat_ncols(l3);
2094  for (size_type i = 0; i < nn; ++i) {
2095  typename linalg_traits<L2>::const_sub_col_type rc2 = mat_const_col(l2, i);
2096  auto it = vect_const_begin(rc2), ite = vect_const_end(rc2);
2097  for (; it != ite; ++it)
2098  add(scaled(mat_const_col(l1, it.index()), *it), mat_col(l3, i));
2099  }
2100  }
2101 
2102  template <typename L1, typename L2, typename L3>
2103  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult,
2104  abstract_sparse, row_major) {
2105  typedef typename linalg_traits<L2>::value_type T;
2106  GMM_WARNING3("Inefficient matrix-matrix mult for sparse matrices");
2107  clear(l3);
2108  size_type mm = mat_nrows(l2), nn = mat_ncols(l3);
2109  for (size_type i = 0; i < nn; ++i)
2110  for (size_type j = 0; j < mm; ++j) {
2111  T a = l2(i,j);
2112  if (a != T(0)) add(scaled(mat_const_col(l1, j), a), mat_col(l3, i));
2113  }
2114  }
2115 
2116  template <typename L1, typename L2, typename L3, typename ORIEN> inline
2117  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult,
2118  abstract_skyline, ORIEN)
2119  { mult_spec(l1, l2, l3, c_mult(), abstract_sparse(), ORIEN()); }
2120 
2121 
2122  // col - row matrix-matrix mult
2123 
2124  template <typename L1, typename L2, typename L3> inline
2125  void mult_spec(const L1& l1, const L2& l2, L3& l3, crmult)
2126  { mult_spec(l1,l2,l3,crmult(), typename linalg_traits<L1>::storage_type()); }
2127 
2128 
2129  template <typename L1, typename L2, typename L3>
2130  void mult_spec(const L1& l1, const L2& l2, L3& l3, crmult, abstract_dense) {
2131  // optimizable
2132  clear(l3);
2133  size_type nn = mat_ncols(l1), mm = mat_nrows(l1);
2134  for (size_type i = 0; i < nn; ++i) {
2135  for (size_type j = 0; j < mm; ++j)
2136  add(scaled(mat_const_row(l2, i), l1(j, i)), mat_row(l3, j));
2137  }
2138  }
2139 
2140  template <typename L1, typename L2, typename L3>
2141  void mult_spec(const L1& l1, const L2& l2, L3& l3, crmult, abstract_sparse) {
2142  // optimizable
2143  clear(l3);
2144  size_type nn = mat_ncols(l1);
2145  for (size_type i = 0; i < nn; ++i) {
2146  typename linalg_traits<L1>::const_sub_col_type rc1 = mat_const_col(l1, i);
2147  auto it = vect_const_begin(rc1), ite = vect_const_end(rc1);
2148  for (; it != ite; ++it)
2149  add(scaled(mat_const_row(l2, i), *it), mat_row(l3, it.index()));
2150  }
2151  }
2152 
2153  template <typename L1, typename L2, typename L3> inline
2154  void mult_spec(const L1& l1, const L2& l2, L3& l3, crmult, abstract_skyline)
2155  { mult_spec(l1, l2, l3, crmult(), abstract_sparse()); }
2156 
2157 
2158  /* ******************************************************************** */
2159  /* Symmetry test. */
2160  /* ******************************************************************** */
2161 
2162  ///@endcond
2163  /** test if A is symmetric.
2164  @param A a matrix.
2165  @param tol a threshold.
2166  */
2167  template <typename MAT> inline
2168  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol
2169  = magnitude_of_linalg(MAT)(-1)) {
2170  typedef magnitude_of_linalg(MAT) R;
2171  if (tol < R(0)) tol = default_tol(R()) * mat_maxnorm(A);
2172  if (mat_nrows(A) != mat_ncols(A)) return false;
2173  return is_symmetric(A, tol, typename linalg_traits<MAT>::storage_type());
2174  }
2175  ///@cond DOXY_SHOW_ALL_FUNCTIONS
2176 
2177  template <typename MAT>
2178  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol,
2179  abstract_dense) {
2180  size_type m = mat_nrows(A);
2181  for (size_type i = 1; i < m; ++i)
2182  for (size_type j = 0; j < i; ++j)
2183  if (gmm::abs(A(i, j)-A(j, i)) > tol) return false;
2184  return true;
2185  }
2186 
2187  template <typename MAT>
2188  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol,
2189  abstract_sparse) {
2190  return is_symmetric(A, tol, typename principal_orientation_type<typename
2191  linalg_traits<MAT>::sub_orientation>::potype());
2192  }
2193 
2194  template <typename MAT>
2195  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol,
2196  row_major) {
2197  for (size_type i = 0; i < mat_nrows(A); ++i) {
2198  typename linalg_traits<MAT>::const_sub_row_type row = mat_const_row(A, i);
2199  auto it = vect_const_begin(row), ite = vect_const_end(row);
2200  for (; it != ite; ++it)
2201  if (gmm::abs(*it - A(it.index(), i)) > tol) return false;
2202  }
2203  return true;
2204  }
2205 
2206  template <typename MAT>
2207  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol,
2208  col_major) {
2209  for (size_type i = 0; i < mat_ncols(A); ++i) {
2210  typename linalg_traits<MAT>::const_sub_col_type col = mat_const_col(A, i);
2211  auto it = vect_const_begin(col), ite = vect_const_end(col);
2212  for (; it != ite; ++it)
2213  if (gmm::abs(*it - A(i, it.index())) > tol) return false;
2214  }
2215  return true;
2216  }
2217 
2218  template <typename MAT>
2219  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol,
2220  abstract_skyline)
2221  { return is_symmetric(A, tol, abstract_sparse()); }
2222 
2223  ///@endcond
2224  /** test if A is Hermitian.
2225  @param A a matrix.
2226  @param tol a threshold.
2227  */
2228  template <typename MAT> inline
2229  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol
2230  = magnitude_of_linalg(MAT)(-1)) {
2231  typedef magnitude_of_linalg(MAT) R;
2232  if (tol < R(0)) tol = default_tol(R()) * mat_maxnorm(A);
2233  if (mat_nrows(A) != mat_ncols(A)) return false;
2234  return is_hermitian(A, tol, typename linalg_traits<MAT>::storage_type());
2235  }
2236  ///@cond DOXY_SHOW_ALL_FUNCTIONS
2237 
2238  template <typename MAT>
2239  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol,
2240  abstract_dense) {
2241  size_type m = mat_nrows(A);
2242  for (size_type i = 1; i < m; ++i)
2243  for (size_type j = 0; j < i; ++j)
2244  if (gmm::abs(A(i, j)-gmm::conj(A(j, i))) > tol) return false;
2245  return true;
2246  }
2247 
2248  template <typename MAT>
2249  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol,
2250  abstract_sparse) {
2251  return is_hermitian(A, tol, typename principal_orientation_type<typename
2252  linalg_traits<MAT>::sub_orientation>::potype());
2253  }
2254 
2255  template <typename MAT>
2256  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol,
2257  row_major) {
2258  for (size_type i = 0; i < mat_nrows(A); ++i) {
2259  typename linalg_traits<MAT>::const_sub_row_type row = mat_const_row(A, i);
2260  auto it = vect_const_begin(row), ite = vect_const_end(row);
2261  for (; it != ite; ++it)
2262  if (gmm::abs(gmm::conj(*it) - A(it.index(), i)) > tol) return false;
2263  }
2264  return true;
2265  }
2266 
2267  template <typename MAT>
2268  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol,
2269  col_major) {
2270  for (size_type i = 0; i < mat_ncols(A); ++i) {
2271  typename linalg_traits<MAT>::const_sub_col_type col = mat_const_col(A, i);
2272  auto it = vect_const_begin(col), ite = vect_const_end(col);
2273  for (; it != ite; ++it)
2274  if (gmm::abs(gmm::conj(*it) - A(i, it.index())) > tol) return false;
2275  }
2276  return true;
2277  }
2278 
2279  template <typename MAT>
2280  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol,
2281  abstract_skyline)
2282  { return is_hermitian(A, tol, abstract_sparse()); }
2283  ///@endcond
2284 }
2285 
2286 
2287 #endif // GMM_BLAS_H__
gmm::vect_dist1
number_traits< typename linalg_traits< V1 >::value_type >::magnitude_type vect_dist1(const V1 &v1, const V2 &v2)
1-distance between two vectors
Definition: gmm_blas.h:658
gmm::is_hermitian
bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol=magnitude_of_linalg(MAT)(-1))
*‍/
Definition: gmm_blas.h:2229
gmm::fill
void fill(L &l, typename gmm::linalg_traits< L >::value_type x)
*‍/
Definition: gmm_blas.h:103
bgeot::size_type
size_t size_type
used as the common size type in the library
Definition: bgeot_poly.h:49
gmm::clear
void clear(L &l)
clear (fill with zeros) a vector or matrix.
Definition: gmm_blas.h:59
gmm::vect_hp
strongest_value_type< V1, V2 >::value_type vect_hp(const V1 &v1, const V2 &v2)
*‍/
Definition: gmm_blas.h:511
gmm::mat_euclidean_norm
number_traits< typename linalg_traits< M >::value_type >::magnitude_type mat_euclidean_norm(const M &m)
Euclidean norm of a matrix.
Definition: gmm_blas.h:636
gmm::mat_norm1
number_traits< typename linalg_traits< M >::value_type >::magnitude_type mat_norm1(const M &m)
*‍/
Definition: gmm_blas.h:782
gmm::vect_sp
strongest_value_type< V1, V2 >::value_type vect_sp(const V1 &v1, const V2 &v2)
*‍/
Definition: gmm_blas.h:263
gmm::clean
void clean(L &l, double threshold)
Clean a vector or matrix (replace near-zero entries with zeroes).
gmm::is_symmetric
bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol=magnitude_of_linalg(MAT)(-1))
*‍/
Definition: gmm_blas.h:2168
gmm::vect_dist2
number_traits< typename linalg_traits< V1 >::value_type >::magnitude_type vect_dist2(const V1 &v1, const V2 &v2)
Euclidean distance between two vectors.
Definition: gmm_blas.h:597
gmm::mat_euclidean_norm_sqr
number_traits< typename linalg_traits< M >::value_type >::magnitude_type mat_euclidean_norm_sqr(const M &m)
*‍/
Definition: gmm_blas.h:626
gmm::mat_maxnorm
number_traits< typename linalg_traits< M >::value_type >::magnitude_type mat_maxnorm(const M &m)
*‍/
Definition: gmm_blas.h:870
gmm::fill_random
void fill_random(L &l)
fill a vector or matrix with random value (uniform [-1,1]).
Definition: gmm_blas.h:129
gmm_scaled.h
get a scaled view of a vector/matrix.
gmm::vect_norm2_sqr
number_traits< typename linalg_traits< V >::value_type >::magnitude_type vect_norm2_sqr(const V &v)
squared Euclidean norm of a vector.
Definition: gmm_blas.h:544
gmm::vect_distinf
number_traits< typename linalg_traits< V1 >::value_type >::magnitude_type vect_distinf(const V1 &v1, const V2 &v2)
Infinity distance between two vectors.
Definition: gmm_blas.h:705
gmm::resize
void resize(V &v, size_type n)
*‍/
Definition: gmm_blas.h:209
gmm_conjugated.h
handle conjugation of complex matrices/vectors.
gmm::vect_norm2
number_traits< typename linalg_traits< V >::value_type >::magnitude_type vect_norm2(const V &v)
Euclidean norm of a vector.
Definition: gmm_blas.h:557
gmm::reshape
void reshape(M &v, size_type m, size_type n)
*‍/
Definition: gmm_blas.h:250
gmm::conjugated
conjugated_return< L >::return_type conjugated(const L &v)
return a conjugated view of the input matrix or vector.
Definition: gmm_conjugated.h:294
gmm_transposed.h
Generic transposed matrices.
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::vect_dist2_sqr
number_traits< typename linalg_traits< V1 >::value_type >::magnitude_type vect_dist2_sqr(const V1 &v1, const V2 &v2)
squared Euclidean distance between two vectors
Definition: gmm_blas.h:565
gmm::vect_norm1
number_traits< typename linalg_traits< V >::value_type >::magnitude_type vect_norm1(const V &v)
1-norm of a vector
Definition: gmm_blas.h:646
gmm::mat_trace
linalg_traits< M >::value_type mat_trace(const M &m)
Trace of a matrix.
Definition: gmm_blas.h:528
gmm::copy
void copy(const L1 &l1, L2 &l2)
*‍/
Definition: gmm_blas.h:977
gmm::vect_norminf
number_traits< typename linalg_traits< V >::value_type >::magnitude_type vect_norminf(const V &v)
Infinity norm of a vector.
Definition: gmm_blas.h:693
gmm::mat_norminf
number_traits< typename linalg_traits< M >::value_type >::magnitude_type mat_norminf(const M &m)
*‍/
Definition: gmm_blas.h:836
gmm::mult_add
void mult_add(const L1 &l1, const L2 &l2, L3 &l3)
*‍/
Definition: gmm_blas.h:1781
gmm::add
void add(const L1 &l1, L2 &l2)
*‍/
Definition: gmm_blas.h:1268