GetFEM  5.5
gmm_blas.h
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29 ===========================================================================*/
30 
31 /**@file gmm_blas.h
32  @author Yves Renard <[email protected]>
33  @date October 13, 2002.
34  @brief Basic linear algebra functions.
35 */
36 
37 #ifndef GMM_BLAS_H__
38 #define GMM_BLAS_H__
39 
40 #include "gmm_scaled.h"
41 #include "gmm_transposed.h"
42 #include "gmm_conjugated.h"
43 
44 namespace gmm {
45 
46  /* ******************************************************************** */
47  /* */
48  /* Generic algorithms */
49  /* */
50  /* ******************************************************************** */
51 
52 
53  /* ******************************************************************** */
54  /* Miscellaneous */
55  /* ******************************************************************** */
56 
57  /** clear (fill with zeros) a vector or matrix. */
58  template <typename L> inline void clear(L &l)
59  { linalg_traits<L>::do_clear(l); }
60  /** @cond DOXY_SHOW_ALL_FUNCTIONS
61  skip all these redundant definitions in doxygen documentation..
62  */
63  template <typename L> inline void clear(const L &l)
64  { linalg_traits<L>::do_clear(linalg_const_cast(l)); }
65 
66  ///@endcond
67  /** count the number of non-zero entries of a vector or matrix. */
68  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  typename linalg_traits<V2>::const_iterator
298  it = vect_const_begin(v2), ite = vect_const_end(v2);
299  typename strongest_value_type3<V1,V2,MATSP>::value_type res(0);
300  for (; it != ite; ++it)
301  res += vect_sp(mat_const_row(ps, it.index()), v1)* (*it);
302  return res;
303  }
304 
305  template <typename MATSP, typename V1, typename V2> inline
306  typename strongest_value_type3<V1,V2,MATSP>::value_type
307  vect_sp_with_matr(const MATSP &ps, const V1 &v1, const V2 &v2,
308  abstract_skyline)
309  { return vect_sp_with_matr(ps, v1, v2, abstract_sparse()); }
310 
311  template <typename MATSP, typename V1, typename V2> inline
312  typename strongest_value_type3<V1,V2,MATSP>::value_type
313  vect_sp_with_matr(const MATSP &ps, const V1 &v1, const V2 &v2,
314  abstract_dense) {
315  GMM_ASSERT2(vect_size(v1) == mat_ncols(ps) &&
316  vect_size(v2) == mat_nrows(ps), "dimensions mismatch");
317  typename linalg_traits<V2>::const_iterator
318  it = vect_const_begin(v2), ite = vect_const_end(v2);
319  typename strongest_value_type3<V1,V2,MATSP>::value_type res(0);
320  for (size_type i = 0; it != ite; ++i, ++it)
321  res += vect_sp(mat_const_row(ps, i), v1) * (*it);
322  return res;
323  }
324 
325  template <typename MATSP, typename V1, typename V2> inline
326  typename strongest_value_type3<V1,V2,MATSP>::value_type
327  vect_sp_with_mat(const MATSP &ps, const V1 &v1,const V2 &v2,row_and_col)
328  { return vect_sp_with_mat(ps, v1, v2, row_major()); }
329 
330  template <typename MATSP, typename V1, typename V2> inline
331  typename strongest_value_type3<V1,V2,MATSP>::value_type
332  vect_sp_with_mat(const MATSP &ps, const V1 &v1, const V2 &v2,col_major){
333  return vect_sp_with_matc(ps, v1, v2,
334  typename linalg_traits<V1>::storage_type());
335  }
336 
337  template <typename MATSP, typename V1, typename V2> inline
338  typename strongest_value_type3<V1,V2,MATSP>::value_type
339  vect_sp_with_matc(const MATSP &ps, const V1 &v1, const V2 &v2,
340  abstract_sparse) {
341  GMM_ASSERT2(vect_size(v1) == mat_ncols(ps) &&
342  vect_size(v2) == mat_nrows(ps), "dimensions mismatch");
343  typename linalg_traits<V1>::const_iterator
344  it = vect_const_begin(v1), ite = vect_const_end(v1);
345  typename strongest_value_type3<V1,V2,MATSP>::value_type res(0);
346  for (; it != ite; ++it)
347  res += vect_sp(mat_const_col(ps, it.index()), v2) * (*it);
348  return res;
349  }
350 
351  template <typename MATSP, typename V1, typename V2> inline
352  typename strongest_value_type3<V1,V2,MATSP>::value_type
353  vect_sp_with_matc(const MATSP &ps, const V1 &v1, const V2 &v2,
354  abstract_skyline)
355  { return vect_sp_with_matc(ps, v1, v2, abstract_sparse()); }
356 
357  template <typename MATSP, typename V1, typename V2> inline
358  typename strongest_value_type3<V1,V2,MATSP>::value_type
359  vect_sp_with_matc(const MATSP &ps, const V1 &v1, const V2 &v2,
360  abstract_dense) {
361  GMM_ASSERT2(vect_size(v1) == mat_ncols(ps) &&
362  vect_size(v2) == mat_nrows(ps), "dimensions mismatch");
363  typename linalg_traits<V1>::const_iterator
364  it = vect_const_begin(v1), ite = vect_const_end(v1);
365  typename strongest_value_type3<V1,V2,MATSP>::value_type res(0);
366  for (size_type i = 0; it != ite; ++i, ++it)
367  res += vect_sp(mat_const_col(ps, i), v2) * (*it);
368  return res;
369  }
370 
371  template <typename MATSP, typename V1, typename V2> inline
372  typename strongest_value_type3<V1,V2,MATSP>::value_type
373  vect_sp_with_mat(const MATSP &ps, const V1 &v1,const V2 &v2,col_and_row)
374  { return vect_sp_with_mat(ps, v1, v2, col_major()); }
375 
376  template <typename MATSP, typename V1, typename V2> inline
377  typename strongest_value_type3<V1,V2,MATSP>::value_type
378  vect_sp_with_mat(const MATSP &ps, const V1 &v1, const V2 &v2,
379  abstract_null_type) {
380  typename temporary_vector<V1>::vector_type w(mat_nrows(ps));
381  GMM_WARNING2("Warning, a temporary is used in scalar product\n");
382  mult(ps, v1, w);
383  return vect_sp(w, v2);
384  }
385 
386  template <typename IT1, typename IT2> inline
387  typename strongest_numeric_type<typename std::iterator_traits<IT1>::value_type,
388  typename std::iterator_traits<IT2>::value_type>::T
389  vect_sp_dense_(IT1 it, IT1 ite, IT2 it2) {
390  typename strongest_numeric_type<typename std::iterator_traits<IT1>::value_type,
391  typename std::iterator_traits<IT2>::value_type>::T res(0);
392  for (; it != ite; ++it, ++it2) res += (*it) * (*it2);
393  return res;
394  }
395 
396  template <typename IT1, typename V> inline
397  typename strongest_numeric_type<typename std::iterator_traits<IT1>::value_type,
398  typename linalg_traits<V>::value_type>::T
399  vect_sp_sparse_(IT1 it, IT1 ite, const V &v) {
400  typename strongest_numeric_type<typename std::iterator_traits<IT1>::value_type,
401  typename linalg_traits<V>::value_type>::T res(0);
402  for (; it != ite; ++it) res += (*it) * v[it.index()];
403  return res;
404  }
405 
406  template <typename V1, typename V2> inline
407  typename strongest_value_type<V1,V2>::value_type
408  vect_sp(const V1 &v1, const V2 &v2, abstract_dense, abstract_dense) {
409  return vect_sp_dense_(vect_const_begin(v1), vect_const_end(v1),
410  vect_const_begin(v2));
411  }
412 
413  template <typename V1, typename V2> inline
414  typename strongest_value_type<V1,V2>::value_type
415  vect_sp(const V1 &v1, const V2 &v2, abstract_skyline, abstract_dense) {
416  typename linalg_traits<V1>::const_iterator it1 = vect_const_begin(v1),
417  ite = vect_const_end(v1);
418  typename linalg_traits<V2>::const_iterator it2 = vect_const_begin(v2);
419  return vect_sp_dense_(it1, ite, it2 + it1.index());
420  }
421 
422  template <typename V1, typename V2> inline
423  typename strongest_value_type<V1,V2>::value_type
424  vect_sp(const V1 &v1, const V2 &v2, abstract_dense, abstract_skyline) {
425  typename linalg_traits<V2>::const_iterator it1 = vect_const_begin(v2),
426  ite = vect_const_end(v2);
427  typename linalg_traits<V1>::const_iterator it2 = vect_const_begin(v1);
428  return vect_sp_dense_(it1, ite, it2 + it1.index());
429  }
430 
431  template <typename V1, typename V2> inline
432  typename strongest_value_type<V1,V2>::value_type
433  vect_sp(const V1 &v1, const V2 &v2, abstract_skyline, abstract_skyline) {
434  typedef typename strongest_value_type<V1,V2>::value_type T;
435  auto it1 = vect_const_begin(v1), ite1 = vect_const_end(v1);
436  auto it2 = vect_const_begin(v2), ite2 = vect_const_end(v2);
437  size_type n = std::min(ite1.index(), ite2.index());
438  size_type l = std::max(it1.index(), it2.index());
439 
440  if (l < n) {
441  size_type m = l - it1.index(), p = l - it2.index(), q = m + n - l;
442  return vect_sp_dense_(it1+m, it1+q, it2 + p);
443  }
444  return T(0);
445  }
446 
447  template <typename V1, typename V2> inline
448  typename strongest_value_type<V1,V2>::value_type
449  vect_sp(const V1 &v1, const V2 &v2,abstract_sparse,abstract_dense) {
450  return vect_sp_sparse_(vect_const_begin(v1), vect_const_end(v1), v2);
451  }
452 
453  template <typename V1, typename V2> inline
454  typename strongest_value_type<V1,V2>::value_type
455  vect_sp(const V1 &v1, const V2 &v2, abstract_sparse, abstract_skyline) {
456  return vect_sp_sparse_(vect_const_begin(v1), vect_const_end(v1), v2);
457  }
458 
459  template <typename V1, typename V2> inline
460  typename strongest_value_type<V1,V2>::value_type
461  vect_sp(const V1 &v1, const V2 &v2, abstract_skyline, abstract_sparse) {
462  return vect_sp_sparse_(vect_const_begin(v2), vect_const_end(v2), v1);
463  }
464 
465  template <typename V1, typename V2> inline
466  typename strongest_value_type<V1,V2>::value_type
467  vect_sp(const V1 &v1, const V2 &v2, abstract_dense,abstract_sparse) {
468  return vect_sp_sparse_(vect_const_begin(v2), vect_const_end(v2), v1);
469  }
470 
471 
472  template <typename V1, typename V2> inline
473  typename strongest_value_type<V1,V2>::value_type
474  vect_sp_sparse_sparse(const V1 &v1, const V2 &v2, linalg_true) {
475  typename linalg_traits<V1>::const_iterator it1 = vect_const_begin(v1),
476  ite1 = vect_const_end(v1);
477  typename linalg_traits<V2>::const_iterator it2 = vect_const_begin(v2),
478  ite2 = vect_const_end(v2);
479  typename strongest_value_type<V1,V2>::value_type res(0);
480 
481  while (it1 != ite1 && it2 != ite2) {
482  if (it1.index() == it2.index())
483  { res += (*it1) * *it2; ++it1; ++it2; }
484  else if (it1.index() < it2.index()) ++it1; else ++it2;
485  }
486  return res;
487  }
488 
489  template <typename V1, typename V2> inline
490  typename strongest_value_type<V1,V2>::value_type
491  vect_sp_sparse_sparse(const V1 &v1, const V2 &v2, linalg_false) {
492  return vect_sp_sparse_(vect_const_begin(v1), vect_const_end(v1), v2);
493  }
494 
495  template <typename V1, typename V2> inline
496  typename strongest_value_type<V1,V2>::value_type
497  vect_sp(const V1 &v1, const V2 &v2,abstract_sparse,abstract_sparse) {
498  return vect_sp_sparse_sparse(v1, v2,
499  typename linalg_and<typename linalg_traits<V1>::index_sorted,
500  typename linalg_traits<V2>::index_sorted>::bool_type());
501  }
502 
503  /* ******************************************************************** */
504  /* Hermitian product */
505  /* ******************************************************************** */
506  ///@endcond
507  /** Hermitian product. */
508  template <typename V1, typename V2>
509  inline typename strongest_value_type<V1,V2>::value_type
510  vect_hp(const V1 &v1, const V2 &v2)
511  { return vect_sp(v1, conjugated(v2)); }
512 
513  /** Hermitian product with a matrix. */
514  template <typename MATSP, typename V1, typename V2> inline
515  typename strongest_value_type3<V1,V2,MATSP>::value_type
516  vect_hp(const MATSP &ps, const V1 &v1, const V2 &v2) {
517  return vect_sp(ps, v1, gmm::conjugated(v2));
518  }
519 
520  /* ******************************************************************** */
521  /* Trace of a matrix */
522  /* ******************************************************************** */
523 
524  /** Trace of a matrix */
525  template <typename M>
526  typename linalg_traits<M>::value_type
527  mat_trace(const M &m) {
528  typedef typename linalg_traits<M>::value_type T;
529  T res(0);
530  for (size_type i = 0; i < std::min(mat_nrows(m), mat_ncols(m)); ++i)
531  res += m(i,i);
532  return res;
533  }
534 
535  /* ******************************************************************** */
536  /* Euclidean norm */
537  /* ******************************************************************** */
538 
539  /** squared Euclidean norm of a vector. */
540  template <typename V>
541  typename number_traits<typename linalg_traits<V>::value_type>
542  ::magnitude_type
543  vect_norm2_sqr(const V &v) {
544  typedef typename linalg_traits<V>::value_type T;
545  typedef typename number_traits<T>::magnitude_type R;
546  auto it = vect_const_begin(v), ite = vect_const_end(v);
547  R res(0);
548  for (; it != ite; ++it) res += gmm::abs_sqr(*it);
549  return res;
550  }
551 
552  /** Euclidean norm of a vector. */
553  template <typename V> inline
554  typename number_traits<typename linalg_traits<V>::value_type>
555  ::magnitude_type
556  vect_norm2(const V &v)
557  { return sqrt(vect_norm2_sqr(v)); }
558 
559 
560  /** squared Euclidean distance between two vectors */
561  template <typename V1, typename V2> inline
562  typename number_traits<typename linalg_traits<V1>::value_type>
563  ::magnitude_type
564  vect_dist2_sqr(const V1 &v1, const V2 &v2) { // not fully optimized
565  typedef typename linalg_traits<V1>::value_type T;
566  typedef typename number_traits<T>::magnitude_type R;
567  auto it1 = vect_const_begin(v1), ite1 = vect_const_end(v1);
568  auto it2 = vect_const_begin(v2), ite2 = vect_const_end(v2);
569  size_type k1(0), k2(0);
570  R res(0);
571  while (it1 != ite1 && it2 != ite2) {
572  size_type i1 = index_of_it(it1, k1,
573  typename linalg_traits<V1>::storage_type());
574  size_type i2 = index_of_it(it2, k2,
575  typename linalg_traits<V2>::storage_type());
576 
577  if (i1 == i2) {
578  res += gmm::abs_sqr(*it2 - *it1); ++it1; ++k1; ++it2; ++k2;
579  }
580  else if (i1 < i2) {
581  res += gmm::abs_sqr(*it1); ++it1; ++k1;
582  }
583  else {
584  res += gmm::abs_sqr(*it2); ++it2; ++k2;
585  }
586  }
587  while (it1 != ite1) { res += gmm::abs_sqr(*it1); ++it1; }
588  while (it2 != ite2) { res += gmm::abs_sqr(*it2); ++it2; }
589  return res;
590  }
591 
592  /** Euclidean distance between two vectors */
593  template <typename V1, typename V2> inline
594  typename number_traits<typename linalg_traits<V1>::value_type>
595  ::magnitude_type
596  vect_dist2(const V1 &v1, const V2 &v2)
597  { return sqrt(vect_dist2_sqr(v1, v2)); }
598  ///@cond DOXY_SHOW_ALL_FUNCTIONS
599  template <typename M>
600  typename number_traits<typename linalg_traits<M>::value_type>
601  ::magnitude_type
602  mat_euclidean_norm_sqr(const M &m, row_major) {
603  typename number_traits<typename linalg_traits<M>::value_type>
604  ::magnitude_type res(0);
605  for (size_type i = 0; i < mat_nrows(m); ++i)
606  res += vect_norm2_sqr(mat_const_row(m, i));
607  return res;
608  }
609 
610  template <typename M>
611  typename number_traits<typename linalg_traits<M>::value_type>
612  ::magnitude_type
613  mat_euclidean_norm_sqr(const M &m, col_major) {
614  typename number_traits<typename linalg_traits<M>::value_type>
615  ::magnitude_type res(0);
616  for (size_type i = 0; i < mat_ncols(m); ++i)
617  res += vect_norm2_sqr(mat_const_col(m, i));
618  return res;
619  }
620  ///@endcond
621  /** squared Euclidean norm of a matrix. */
622  template <typename M> inline
623  typename number_traits<typename linalg_traits<M>::value_type>
624  ::magnitude_type
625  mat_euclidean_norm_sqr(const M &m) {
626  return mat_euclidean_norm_sqr(m,
627  typename principal_orientation_type<typename
628  linalg_traits<M>::sub_orientation>::potype());
629  }
630 
631  /** Euclidean norm of a matrix. */
632  template <typename M> inline
633  typename number_traits<typename linalg_traits<M>::value_type>
634  ::magnitude_type
635  mat_euclidean_norm(const M &m)
636  { return gmm::sqrt(mat_euclidean_norm_sqr(m)); }
637 
638  /* ******************************************************************** */
639  /* vector norm1 */
640  /* ******************************************************************** */
641  /** 1-norm of a vector */
642  template <typename V>
643  typename number_traits<typename linalg_traits<V>::value_type>
644  ::magnitude_type
645  vect_norm1(const V &v) {
646  auto it = vect_const_begin(v), ite = vect_const_end(v);
647  typename number_traits<typename linalg_traits<V>::value_type>
648  ::magnitude_type res(0);
649  for (; it != ite; ++it) res += gmm::abs(*it);
650  return res;
651  }
652 
653  /** 1-distance between two vectors */
654  template <typename V1, typename V2> inline
655  typename number_traits<typename linalg_traits<V1>::value_type>
656  ::magnitude_type
657  vect_dist1(const V1 &v1, const V2 &v2) { // not fully optimized
658  typedef typename linalg_traits<V1>::value_type T;
659  typedef typename number_traits<T>::magnitude_type R;
660  auto it1 = vect_const_begin(v1), ite1 = vect_const_end(v1);
661  auto it2 = vect_const_begin(v2), ite2 = vect_const_end(v2);
662  size_type k1(0), k2(0);
663  R res(0);
664  while (it1 != ite1 && it2 != ite2) {
665  size_type i1 = index_of_it(it1, k1,
666  typename linalg_traits<V1>::storage_type());
667  size_type i2 = index_of_it(it2, k2,
668  typename linalg_traits<V2>::storage_type());
669 
670  if (i1 == i2) {
671  res += gmm::abs(*it2 - *it1); ++it1; ++k1; ++it2; ++k2;
672  }
673  else if (i1 < i2) {
674  res += gmm::abs(*it1); ++it1; ++k1;
675  }
676  else {
677  res += gmm::abs(*it2); ++it2; ++k2;
678  }
679  }
680  while (it1 != ite1) { res += gmm::abs(*it1); ++it1; }
681  while (it2 != ite2) { res += gmm::abs(*it2); ++it2; }
682  return res;
683  }
684 
685  /* ******************************************************************** */
686  /* vector Infinity norm */
687  /* ******************************************************************** */
688  /** Infinity norm of a vector. */
689  template <typename V>
690  typename number_traits<typename linalg_traits<V>::value_type>
691  ::magnitude_type
692  vect_norminf(const V &v) {
693  auto it = vect_const_begin(v), ite = vect_const_end(v);
694  typename number_traits<typename linalg_traits<V>::value_type>
695  ::magnitude_type res(0);
696  for (; it != ite; ++it) res = std::max(res, gmm::abs(*it));
697  return res;
698  }
699 
700  /** Infinity distance between two vectors */
701  template <typename V1, typename V2> inline
702  typename number_traits<typename linalg_traits<V1>::value_type>
703  ::magnitude_type
704  vect_distinf(const V1 &v1, const V2 &v2) { // not fully optimized
705  typedef typename linalg_traits<V1>::value_type T;
706  typedef typename number_traits<T>::magnitude_type R;
707  auto it1 = vect_const_begin(v1), ite1 = vect_const_end(v1);
708  auto it2 = vect_const_begin(v2), ite2 = vect_const_end(v2);
709  size_type k1(0), k2(0);
710  R res(0);
711  while (it1 != ite1 && it2 != ite2) {
712  size_type i1 = index_of_it(it1, k1,
713  typename linalg_traits<V1>::storage_type());
714  size_type i2 = index_of_it(it2, k2,
715  typename linalg_traits<V2>::storage_type());
716 
717  if (i1 == i2) {
718  res = std::max(res, gmm::abs(*it2 - *it1)); ++it1; ++k1; ++it2; ++k2;
719  }
720  else if (i1 < i2) {
721  res = std::max(res, gmm::abs(*it1)); ++it1; ++k1;
722  }
723  else {
724  res = std::max(res, gmm::abs(*it2)); ++it2; ++k2;
725  }
726  }
727  while (it1 != ite1) { res = std::max(res, gmm::abs(*it1)); ++it1; }
728  while (it2 != ite2) { res = std::max(res, gmm::abs(*it2)); ++it2; }
729  return res;
730  }
731 
732  /* ******************************************************************** */
733  /* matrix norm1 */
734  /* ******************************************************************** */
735  ///@cond DOXY_SHOW_ALL_FUNCTIONS
736  template <typename M>
737  typename number_traits<typename linalg_traits<M>::value_type>
738  ::magnitude_type
739  mat_norm1(const M &m, col_major) {
740  typename number_traits<typename linalg_traits<M>::value_type>
741  ::magnitude_type res(0);
742  for (size_type i = 0; i < mat_ncols(m); ++i)
743  res = std::max(res, vect_norm1(mat_const_col(m,i)));
744  return res;
745  }
746 
747  template <typename M>
748  typename number_traits<typename linalg_traits<M>::value_type>
749  ::magnitude_type
750  mat_norm1(const M &m, row_major) {
751  typedef typename linalg_traits<M>::value_type T;
752  typedef typename number_traits<T>::magnitude_type R;
753  typedef typename linalg_traits<M>::storage_type store_type;
754 
755  std::vector<R> aux(mat_ncols(m));
756  for (size_type i = 0; i < mat_nrows(m); ++i) {
757  typename linalg_traits<M>::const_sub_row_type row = mat_const_row(m, i);
758  auto it = vect_const_begin(row), ite = vect_const_end(row);
759  for (size_type k = 0; it != ite; ++it, ++k)
760  aux[index_of_it(it, k, store_type())] += gmm::abs(*it);
761  }
762  return vect_norminf(aux);
763  }
764 
765  template <typename M>
766  typename number_traits<typename linalg_traits<M>::value_type>
767  ::magnitude_type
768  mat_norm1(const M &m, col_and_row)
769  { return mat_norm1(m, col_major()); }
770 
771  template <typename M>
772  typename number_traits<typename linalg_traits<M>::value_type>
773  ::magnitude_type
774  mat_norm1(const M &m, row_and_col)
775  { return mat_norm1(m, col_major()); }
776  ///@endcond
777  /** 1-norm of a matrix */
778  template <typename M>
779  typename number_traits<typename linalg_traits<M>::value_type>
780  ::magnitude_type
781  mat_norm1(const M &m) {
782  return mat_norm1(m, typename linalg_traits<M>::sub_orientation());
783  }
784 
785 
786  /* ******************************************************************** */
787  /* matrix Infinity norm */
788  /* ******************************************************************** */
789  ///@cond DOXY_SHOW_ALL_FUNCTIONS
790  template <typename M>
791  typename number_traits<typename linalg_traits<M>::value_type>
792  ::magnitude_type
793  mat_norminf(const M &m, row_major) {
794  typename number_traits<typename linalg_traits<M>::value_type>
795  ::magnitude_type res(0);
796  for (size_type i = 0; i < mat_nrows(m); ++i)
797  res = std::max(res, vect_norm1(mat_const_row(m,i)));
798  return res;
799  }
800 
801  template <typename M>
802  typename number_traits<typename linalg_traits<M>::value_type>
803  ::magnitude_type
804  mat_norminf(const M &m, col_major) {
805  typedef typename linalg_traits<M>::value_type T;
806  typedef typename number_traits<T>::magnitude_type R;
807  typedef typename linalg_traits<M>::storage_type store_type;
808 
809  std::vector<R> aux(mat_nrows(m));
810  for (size_type i = 0; i < mat_ncols(m); ++i) {
811  typename linalg_traits<M>::const_sub_col_type col = mat_const_col(m, i);
812  auto it = vect_const_begin(col), ite = vect_const_end(col);
813  for (size_type k = 0; it != ite; ++it, ++k)
814  aux[index_of_it(it, k, store_type())] += gmm::abs(*it);
815  }
816  return vect_norminf(aux);
817  }
818 
819  template <typename M>
820  typename number_traits<typename linalg_traits<M>::value_type>
821  ::magnitude_type
822  mat_norminf(const M &m, col_and_row)
823  { return mat_norminf(m, row_major()); }
824 
825  template <typename M>
826  typename number_traits<typename linalg_traits<M>::value_type>
827  ::magnitude_type
828  mat_norminf(const M &m, row_and_col)
829  { return mat_norminf(m, row_major()); }
830  ///@endcond
831  /** infinity-norm of a matrix.*/
832  template <typename M>
833  typename number_traits<typename linalg_traits<M>::value_type>
834  ::magnitude_type
835  mat_norminf(const M &m) {
836  return mat_norminf(m, typename linalg_traits<M>::sub_orientation());
837  }
838 
839  /* ******************************************************************** */
840  /* Max norm for matrices */
841  /* ******************************************************************** */
842  ///@cond DOXY_SHOW_ALL_FUNCTIONS
843  template <typename M>
844  typename number_traits<typename linalg_traits<M>::value_type>
845  ::magnitude_type
846  mat_maxnorm(const M &m, row_major) {
847  typename number_traits<typename linalg_traits<M>::value_type>
848  ::magnitude_type res(0);
849  for (size_type i = 0; i < mat_nrows(m); ++i)
850  res = std::max(res, vect_norminf(mat_const_row(m,i)));
851  return res;
852  }
853 
854  template <typename M>
855  typename number_traits<typename linalg_traits<M>::value_type>
856  ::magnitude_type
857  mat_maxnorm(const M &m, col_major) {
858  typename number_traits<typename linalg_traits<M>::value_type>
859  ::magnitude_type res(0);
860  for (size_type i = 0; i < mat_ncols(m); ++i)
861  res = std::max(res, vect_norminf(mat_const_col(m,i)));
862  return res;
863  }
864  ///@endcond
865  /** max-norm of a matrix. */
866  template <typename M>
867  typename number_traits<typename linalg_traits<M>::value_type>
868  ::magnitude_type
869  mat_maxnorm(const M &m) {
870  return mat_maxnorm
871  (m, typename principal_orientation_type
872  <typename linalg_traits<M>::sub_orientation>::potype());
873  }
874 
875  /* ******************************************************************** */
876  /* Clean */
877  /* ******************************************************************** */
878  /** Clean a vector or matrix (replace near-zero entries with zeroes). */
879 
880  template <typename L> inline void clean(L &l, double threshold);
881 
882  ///@cond DOXY_SHOW_ALL_FUNCTIONS
883 
884  template <typename L, typename T>
885  void clean(L &l, double threshold, abstract_dense, T) {
886  typedef typename number_traits<T>::magnitude_type R;
887  auto it = vect_begin(l), ite = vect_end(l);
888  for (; it != ite; ++it)
889  if (gmm::abs(*it) < R(threshold)) *it = T(0);
890  }
891 
892  template <typename L, typename T>
893  void clean(L &l, double threshold, abstract_skyline, T)
894  { gmm::clean(l, threshold, abstract_dense(), T()); }
895 
896  template <typename L, typename T>
897  void clean(L &l, double threshold, abstract_sparse, T) {
898  typedef typename number_traits<T>::magnitude_type R;
899  auto it = vect_begin(l), ite = vect_end(l);
900  std::vector<size_type> ind;
901  for (; it != ite; ++it)
902  if (gmm::abs(*it) < R(threshold)) ind.push_back(it.index());
903  for (size_type i = 0; i < ind.size(); ++i) l[ind[i]] = T(0);
904  }
905 
906  template <typename L, typename T>
907  void clean(L &l, double threshold, abstract_dense, std::complex<T>) {
908  auto it = vect_begin(l), ite = vect_end(l);
909  for (; it != ite; ++it){
910  if (gmm::abs((*it).real()) < T(threshold))
911  *it = std::complex<T>(T(0), (*it).imag());
912  if (gmm::abs((*it).imag()) < T(threshold))
913  *it = std::complex<T>((*it).real(), T(0));
914  }
915  }
916 
917  template <typename L, typename T>
918  void clean(L &l, double threshold, abstract_skyline, std::complex<T>)
919  { gmm::clean(l, threshold, abstract_dense(), std::complex<T>()); }
920 
921  template <typename L, typename T>
922  void clean(L &l, double threshold, abstract_sparse, std::complex<T>) {
923  auto it = vect_begin(l), ite = vect_end(l);
924  std::vector<size_type> ind;
925  for (; it != ite; ++it) {
926  bool r = (gmm::abs((*it).real()) < T(threshold));
927  bool i = (gmm::abs((*it).imag()) < T(threshold));
928  if (r && i) ind.push_back(it.index());
929  else if (r) *it = std::complex<T>(T(0), (*it).imag());
930  else if (i) *it = std::complex<T>((*it).real(), T(0));
931  }
932  for (size_type i = 0; i < ind.size(); ++i)
933  l[ind[i]] = std::complex<T>(T(0),T(0));
934  }
935 
936  template <typename L> inline void clean(L &l, double threshold,
937  abstract_vector) {
938  gmm::clean(l, threshold, typename linalg_traits<L>::storage_type(),
939  typename linalg_traits<L>::value_type());
940  }
941 
942  template <typename L> inline void clean(const L &l, double threshold);
943 
944  template <typename L> void clean(L &l, double threshold, row_major) {
945  for (size_type i = 0; i < mat_nrows(l); ++i)
946  gmm::clean(mat_row(l, i), threshold);
947  }
948 
949  template <typename L> void clean(L &l, double threshold, col_major) {
950  for (size_type i = 0; i < mat_ncols(l); ++i)
951  gmm::clean(mat_col(l, i), threshold);
952  }
953 
954  template <typename L> inline void clean(L &l, double threshold,
955  abstract_matrix) {
956  gmm::clean(l, threshold,
957  typename principal_orientation_type<typename
958  linalg_traits<L>::sub_orientation>::potype());
959  }
960 
961  template <typename L> inline void clean(L &l, double threshold)
962  { clean(l, threshold, typename linalg_traits<L>::linalg_type()); }
963 
964  template <typename L> inline void clean(const L &l, double threshold)
965  { gmm::clean(linalg_const_cast(l), threshold); }
966 
967  /* ******************************************************************** */
968  /* Copy */
969  /* ******************************************************************** */
970  ///@endcond
971  /** Copy vectors or matrices.
972  @param l1 source vector or matrix.
973  @param l2 destination.
974  */
975  template <typename L1, typename L2> inline
976  void copy(const L1& l1, L2& l2) {
977  if ((const void *)(&l1) != (const void *)(&l2)) {
978  if (same_origin(l1,l2))
979  GMM_WARNING2("Warning : a conflict is possible in copy\n");
980 
981  copy(l1, l2, typename linalg_traits<L1>::linalg_type(),
982  typename linalg_traits<L2>::linalg_type());
983  }
984  }
985  ///@cond DOXY_SHOW_ALL_FUNCTIONS
986 
987  template <typename L1, typename L2> inline
988  void copy(const L1& l1, const L2& l2) { copy(l1, linalg_const_cast(l2)); }
989 
990  template <typename L1, typename L2> inline
991  void copy(const L1& l1, L2& l2, abstract_vector, abstract_vector) {
992  GMM_ASSERT2(vect_size(l1) == vect_size(l2), "dimensions mismatch, "
993  << vect_size(l1) << " !=" << vect_size(l2));
994  copy_vect(l1, l2, typename linalg_traits<L1>::storage_type(),
995  typename linalg_traits<L2>::storage_type());
996  }
997 
998  template <typename L1, typename L2> inline
999  void copy(const L1& l1, L2& l2, abstract_matrix, abstract_matrix) {
1000  size_type m = mat_nrows(l1), n = mat_ncols(l1);
1001  if (!m || !n) return;
1002  GMM_ASSERT2(n==mat_ncols(l2) && m==mat_nrows(l2), "dimensions mismatch");
1003  copy_mat(l1, l2, typename linalg_traits<L1>::sub_orientation(),
1004  typename linalg_traits<L2>::sub_orientation());
1005  }
1006 
1007  template <typename V1, typename V2, typename C1, typename C2> inline
1008  void copy_vect(const V1 &v1, const V2 &v2, C1, C2)
1009  { copy_vect(v1, const_cast<V2 &>(v2), C1(), C2()); }
1010 
1011 
1012  template <typename L1, typename L2>
1013  void copy_mat_by_row(const L1& l1, L2& l2) {
1014  size_type nbr = mat_nrows(l1);
1015  for (size_type i = 0; i < nbr; ++i)
1016  copy(mat_const_row(l1, i), mat_row(l2, i));
1017  }
1018 
1019  template <typename L1, typename L2>
1020  void copy_mat_by_col(const L1 &l1, L2 &l2) {
1021  size_type nbc = mat_ncols(l1);
1022  for (size_type i = 0; i < nbc; ++i) {
1023  copy(mat_const_col(l1, i), mat_col(l2, i));
1024  }
1025  }
1026 
1027  template <typename L1, typename L2> inline
1028  void copy_mat(const L1& l1, L2& l2, row_major, row_major)
1029  { copy_mat_by_row(l1, l2); }
1030 
1031  template <typename L1, typename L2> inline
1032  void copy_mat(const L1& l1, L2& l2, row_major, row_and_col)
1033  { copy_mat_by_row(l1, l2); }
1034 
1035  template <typename L1, typename L2> inline
1036  void copy_mat(const L1& l1, L2& l2, row_and_col, row_and_col)
1037  { copy_mat_by_row(l1, l2); }
1038 
1039  template <typename L1, typename L2> inline
1040  void copy_mat(const L1& l1, L2& l2, row_and_col, row_major)
1041  { copy_mat_by_row(l1, l2); }
1042 
1043  template <typename L1, typename L2> inline
1044  void copy_mat(const L1& l1, L2& l2, col_and_row, row_major)
1045  { copy_mat_by_row(l1, l2); }
1046 
1047  template <typename L1, typename L2> inline
1048  void copy_mat(const L1& l1, L2& l2, row_major, col_and_row)
1049  { copy_mat_by_row(l1, l2); }
1050 
1051  template <typename L1, typename L2> inline
1052  void copy_mat(const L1& l1, L2& l2, col_and_row, row_and_col)
1053  { copy_mat_by_row(l1, l2); }
1054 
1055  template <typename L1, typename L2> inline
1056  void copy_mat(const L1& l1, L2& l2, row_and_col, col_and_row)
1057  { copy_mat_by_row(l1, l2); }
1058 
1059  template <typename L1, typename L2> inline
1060  void copy_mat(const L1& l1, L2& l2, col_major, col_major)
1061  { copy_mat_by_col(l1, l2); }
1062 
1063  template <typename L1, typename L2> inline
1064  void copy_mat(const L1& l1, L2& l2, col_major, col_and_row)
1065  { copy_mat_by_col(l1, l2); }
1066 
1067  template <typename L1, typename L2> inline
1068  void copy_mat(const L1& l1, L2& l2, col_major, row_and_col)
1069  { copy_mat_by_col(l1, l2); }
1070 
1071  template <typename L1, typename L2> inline
1072  void copy_mat(const L1& l1, L2& l2, row_and_col, col_major)
1073  { copy_mat_by_col(l1, l2); }
1074 
1075  template <typename L1, typename L2> inline
1076  void copy_mat(const L1& l1, L2& l2, col_and_row, col_major)
1077  { copy_mat_by_col(l1, l2); }
1078 
1079  template <typename L1, typename L2> inline
1080  void copy_mat(const L1& l1, L2& l2, col_and_row, col_and_row)
1081  { copy_mat_by_col(l1, l2); }
1082 
1083  template <typename L1, typename L2> inline
1084  void copy_mat_mixed_rc(const L1& l1, L2& l2, size_type i) {
1085  copy_mat_mixed_rc(l1, l2, i, typename linalg_traits<L1>::storage_type());
1086  }
1087 
1088  template <typename L1, typename L2>
1089  void copy_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_sparse) {
1090  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1091  for (; it != ite; ++it)
1092  l2(i, it.index()) = *it;
1093  }
1094 
1095  template <typename L1, typename L2>
1096  void copy_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_skyline) {
1097  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1098  for (; it != ite; ++it)
1099  l2(i, it.index()) = *it;
1100  }
1101 
1102  template <typename L1, typename L2>
1103  void copy_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_dense) {
1104  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1105  for (size_type j = 0; it != ite; ++it, ++j) l2(i, j) = *it;
1106  }
1107 
1108  template <typename L1, typename L2> inline
1109  void copy_mat_mixed_cr(const L1& l1, L2& l2, size_type i) {
1110  copy_mat_mixed_cr(l1, l2, i, typename linalg_traits<L1>::storage_type());
1111  }
1112 
1113  template <typename L1, typename L2>
1114  void copy_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_sparse) {
1115  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1116  for (; it != ite; ++it) l2(it.index(), i) = *it;
1117  }
1118 
1119  template <typename L1, typename L2>
1120  void copy_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_skyline) {
1121  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1122  for (; it != ite; ++it) l2(it.index(), i) = *it;
1123  }
1124 
1125  template <typename L1, typename L2>
1126  void copy_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_dense) {
1127  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1128  for (size_type j = 0; it != ite; ++it, ++j) l2(j, i) = *it;
1129  }
1130 
1131  template <typename L1, typename L2>
1132  void copy_mat(const L1& l1, L2& l2, row_major, col_major) {
1133  clear(l2);
1134  size_type nbr = mat_nrows(l1);
1135  for (size_type i = 0; i < nbr; ++i)
1136  copy_mat_mixed_rc(mat_const_row(l1, i), l2, i);
1137  }
1138 
1139  template <typename L1, typename L2>
1140  void copy_mat(const L1& l1, L2& l2, col_major, row_major) {
1141  clear(l2);
1142  size_type nbc = mat_ncols(l1);
1143  for (size_type i = 0; i < nbc; ++i)
1144  copy_mat_mixed_cr(mat_const_col(l1, i), l2, i);
1145  }
1146 
1147  template <typename L1, typename L2> inline
1148  void copy_vect(const L1 &l1, L2 &l2, abstract_dense, abstract_dense) {
1149  std::copy(vect_const_begin(l1), vect_const_end(l1), vect_begin(l2));
1150  }
1151 
1152  template <typename L1, typename L2> inline // to be optimised ?
1153  void copy_vect(const L1 &l1, L2 &l2, abstract_skyline, abstract_skyline) {
1154  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1155  while (it1 != ite1 && *it1 == typename linalg_traits<L1>::value_type(0))
1156  ++it1;
1157 
1158  if (ite1 - it1 > 0) {
1159  clear(l2);
1160  auto it2 = vect_begin(l2), ite2 = vect_end(l2);
1161  while (*(ite1-1) == typename linalg_traits<L1>::value_type(0))
1162  ite1--;
1163 
1164  if (it2 == ite2) {
1165  l2[it1.index()] = *it1;
1166  ++it1;
1167  l2[ite1.index()-1] = *(ite1-1);
1168  --ite1;
1169  if (it1 < ite1) {
1170  it2 = vect_begin(l2);
1171  ++it2;
1172  std::copy(it1, ite1, it2);
1173  }
1174  } else {
1175  ptrdiff_t m = it1.index() - it2.index();
1176  if (m >= 0 && ite1.index() <= ite2.index())
1177  std::copy(it1, ite1, it2 + m);
1178  else {
1179  if (m < 0)
1180  l2[it1.index()] = *it1;
1181  if (ite1.index() > ite2.index())
1182  l2[ite1.index()-1] = *(ite1-1);
1183  it2 = vect_begin(l2);
1184  ite2 = vect_end(l2);
1185  m = it1.index() - it2.index();
1186  std::copy(it1, ite1, it2 + m);
1187  }
1188  }
1189  }
1190  }
1191 
1192  template <typename L1, typename L2>
1193  void copy_vect(const L1& l1, L2& l2, abstract_sparse, abstract_dense) {
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_sparse, abstract_skyline) {
1201  clear(l2);
1202  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1203  for (; it != ite; ++it) l2[it.index()] = *it;
1204  }
1205 
1206  template <typename L1, typename L2>
1207  void copy_vect(const L1& l1, L2& l2, abstract_skyline, abstract_dense) {
1208  typedef typename linalg_traits<L1>::value_type T;
1209  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1210  if (it == ite)
1211  gmm::clear(l2);
1212  else {
1213  auto it2 = vect_begin(l2), ite2 = vect_end(l2);
1214 
1215  size_type i = it.index(), j;
1216  for (j = 0; j < i; ++j, ++it2) *it2 = T(0);
1217  for (; it != ite; ++it, ++it2) *it2 = *it;
1218  for (; it2 != ite2; ++it2) *it2 = T(0);
1219  }
1220  }
1221 
1222  template <typename L1, typename L2>
1223  void copy_vect(const L1& l1, L2& l2, abstract_sparse, abstract_sparse) {
1224  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1225  clear(l2);
1226  // cout << "copy " << l1 << " of size " << vect_size(l1) << " nnz = " << nnz(l1) << endl;
1227  for (; it != ite; ++it) {
1228  // cout << "*it = " << *it << endl;
1229  // cout << "it.index() = " << it.index() << endl;
1230  if (*it != (typename linalg_traits<L1>::value_type)(0))
1231  l2[it.index()] = *it;
1232  }
1233  }
1234 
1235  template <typename L1, typename L2>
1236  void copy_vect(const L1& l1, L2& l2, abstract_dense, abstract_sparse) {
1237  clear(l2);
1238  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1239  for (size_type i = 0; it != ite; ++it, ++i)
1240  if (*it != (typename linalg_traits<L1>::value_type)(0))
1241  l2[i] = *it;
1242  }
1243 
1244  template <typename L1, typename L2> // to be optimised ...
1245  void copy_vect(const L1& l1, L2& l2, abstract_dense, abstract_skyline) {
1246  clear(l2);
1247  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1248  for (size_type i = 0; it != ite; ++it, ++i)
1249  if (*it != (typename linalg_traits<L1>::value_type)(0))
1250  l2[i] = *it;
1251  }
1252 
1253 
1254  template <typename L1, typename L2>
1255  void copy_vect(const L1& l1, L2& l2, abstract_skyline, abstract_sparse) {
1256  clear(l2);
1257  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1258  for (; it != ite; ++it)
1259  if (*it != (typename linalg_traits<L1>::value_type)(0))
1260  l2[it.index()] = *it;
1261  }
1262 
1263  /* ******************************************************************** */
1264  /* Matrix and vector addition */
1265  /* algorithms are built in order to avoid some conflicts with */
1266  /* repeated arguments or with overlapping part of a same object. */
1267  /* In the latter case, conflicts are still possible. */
1268  /* ******************************************************************** */
1269  ///@endcond
1270  /** Add two vectors or matrices
1271  @param l1
1272  @param l2 contains on output, l2+l1.
1273  */
1274  template <typename L1, typename L2> inline
1275  void add(const L1& l1, L2& l2) {
1276  add_spec(l1, l2, typename linalg_traits<L2>::linalg_type());
1277  }
1278  ///@cond
1279 
1280  template <typename L1, typename L2> inline
1281  void add(const L1& l1, const L2& l2) { add(l1, linalg_const_cast(l2)); }
1282 
1283  template <typename L1, typename L2> inline
1284  void add_spec(const L1& l1, L2& l2, abstract_vector) {
1285  GMM_ASSERT2(vect_size(l1) == vect_size(l2), "dimensions mismatch, "
1286  << vect_size(l1) << " !=" << vect_size(l2));
1287  add(l1, l2, typename linalg_traits<L1>::storage_type(),
1288  typename linalg_traits<L2>::storage_type());
1289  }
1290 
1291  template <typename L1, typename L2> inline
1292  void add_spec(const L1& l1, L2& l2, abstract_matrix) {
1293  GMM_ASSERT2(mat_nrows(l1)==mat_nrows(l2) && mat_ncols(l1)==mat_ncols(l2),
1294  "dimensions mismatch l1 is " << mat_nrows(l1) << "x"
1295  << mat_ncols(l1) << " and l2 is " << mat_nrows(l2)
1296  << "x" << mat_ncols(l2));
1297  add(l1, l2, typename linalg_traits<L1>::sub_orientation(),
1298  typename linalg_traits<L2>::sub_orientation());
1299  }
1300 
1301  template <typename L1, typename L2>
1302  void add(const L1& l1, L2& l2, row_major, row_major) {
1303  auto it1 = mat_row_begin(l1), ite = mat_row_end(l1);
1304  auto it2 = mat_row_begin(l2);
1305  for ( ; it1 != ite; ++it1, ++it2)
1306  add(linalg_traits<L1>::row(it1), linalg_traits<L2>::row(it2));
1307  }
1308 
1309  template <typename L1, typename L2>
1310  void add(const L1& l1, L2& l2, col_major, col_major) {
1311  auto it1 = mat_col_const_begin(l1), ite = mat_col_const_end(l1);
1312  typename linalg_traits<L2>::col_iterator it2 = mat_col_begin(l2);
1313  for ( ; it1 != ite; ++it1, ++it2)
1314  add(linalg_traits<L1>::col(it1), linalg_traits<L2>::col(it2));
1315  }
1316 
1317  template <typename L1, typename L2> inline
1318  void add_mat_mixed_rc(const L1& l1, L2& l2, size_type i) {
1319  add_mat_mixed_rc(l1, l2, i, typename linalg_traits<L1>::storage_type());
1320  }
1321 
1322  template <typename L1, typename L2>
1323  void add_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_sparse) {
1324  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1325  for (; it != ite; ++it) l2(i, it.index()) += *it;
1326  }
1327 
1328  template <typename L1, typename L2>
1329  void add_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_skyline) {
1330  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1331  for (; it != ite; ++it) l2(i, it.index()) += *it;
1332  }
1333 
1334  template <typename L1, typename L2>
1335  void add_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_dense) {
1336  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1337  for (size_type j = 0; it != ite; ++it, ++j) l2(i, j) += *it;
1338  }
1339 
1340  template <typename L1, typename L2> inline
1341  void add_mat_mixed_cr(const L1& l1, L2& l2, size_type i) {
1342  add_mat_mixed_cr(l1, l2, i, typename linalg_traits<L1>::storage_type());
1343  }
1344 
1345  template <typename L1, typename L2>
1346  void add_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_sparse) {
1347  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1348  for (; it != ite; ++it) l2(it.index(), i) += *it;
1349  }
1350 
1351  template <typename L1, typename L2>
1352  void add_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_skyline) {
1353  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1354  for (; it != ite; ++it) l2(it.index(), i) += *it;
1355  }
1356 
1357  template <typename L1, typename L2>
1358  void add_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_dense) {
1359  auto it = vect_const_begin(l1), ite = vect_const_end(l1);
1360  for (size_type j = 0; it != ite; ++it, ++j) l2(j, i) += *it;
1361  }
1362 
1363  template <typename L1, typename L2>
1364  void add(const L1& l1, L2& l2, row_major, col_major) {
1365  size_type nbr = mat_nrows(l1);
1366  for (size_type i = 0; i < nbr; ++i)
1367  add_mat_mixed_rc(mat_const_row(l1, i), l2, i);
1368  }
1369 
1370  template <typename L1, typename L2>
1371  void add(const L1& l1, L2& l2, col_major, row_major) {
1372  size_type nbc = mat_ncols(l1);
1373  for (size_type i = 0; i < nbc; ++i)
1374  add_mat_mixed_cr(mat_const_col(l1, i), l2, i);
1375  }
1376 
1377  template <typename L1, typename L2> inline
1378  void add(const L1& l1, L2& l2, row_and_col, row_major)
1379  { add(l1, l2, row_major(), row_major()); }
1380 
1381  template <typename L1, typename L2> inline
1382  void add(const L1& l1, L2& l2, row_and_col, row_and_col)
1383  { add(l1, l2, row_major(), row_major()); }
1384 
1385  template <typename L1, typename L2> inline
1386  void add(const L1& l1, L2& l2, row_and_col, col_and_row)
1387  { add(l1, l2, row_major(), row_major()); }
1388 
1389  template <typename L1, typename L2> inline
1390  void add(const L1& l1, L2& l2, col_and_row, row_and_col)
1391  { add(l1, l2, row_major(), row_major()); }
1392 
1393  template <typename L1, typename L2> inline
1394  void add(const L1& l1, L2& l2, row_major, row_and_col)
1395  { add(l1, l2, row_major(), row_major()); }
1396 
1397  template <typename L1, typename L2> inline
1398  void add(const L1& l1, L2& l2, col_and_row, row_major)
1399  { add(l1, l2, row_major(), row_major()); }
1400 
1401  template <typename L1, typename L2> inline
1402  void add(const L1& l1, L2& l2, row_major, col_and_row)
1403  { add(l1, l2, row_major(), row_major()); }
1404 
1405  template <typename L1, typename L2> inline
1406  void add(const L1& l1, L2& l2, row_and_col, col_major)
1407  { add(l1, l2, col_major(), col_major()); }
1408 
1409  template <typename L1, typename L2> inline
1410  void add(const L1& l1, L2& l2, col_major, row_and_col)
1411  { add(l1, l2, col_major(), col_major()); }
1412 
1413  template <typename L1, typename L2> inline
1414  void add(const L1& l1, L2& l2, col_and_row, col_major)
1415  { add(l1, l2, col_major(), col_major()); }
1416 
1417  template <typename L1, typename L2> inline
1418  void add(const L1& l1, L2& l2, col_and_row, col_and_row)
1419  { add(l1, l2, col_major(), col_major()); }
1420 
1421  template <typename L1, typename L2> inline
1422  void add(const L1& l1, L2& l2, col_major, col_and_row)
1423  { add(l1, l2, col_major(), col_major()); }
1424 
1425  ///@endcond
1426  /** Addition of two vectors/matrices
1427  @param l1
1428  @param l2
1429  @param l3 contains l1+l2 on output
1430  */
1431  template <typename L1, typename L2, typename L3> inline
1432  void add(const L1& l1, const L2& l2, L3& l3) {
1433  add_spec(l1, l2, l3, typename linalg_traits<L2>::linalg_type());
1434  }
1435  ///@cond DOXY_SHOW_ALL_FUNCTIONS
1436 
1437  template <typename L1, typename L2, typename L3> inline
1438  void add(const L1& l1, const L2& l2, const L3& l3)
1439  { add(l1, l2, linalg_const_cast(l3)); }
1440 
1441  template <typename L1, typename L2, typename L3> inline
1442  void add_spec(const L1& l1, const L2& l2, L3& l3, abstract_matrix)
1443  { copy(l2, l3); add(l1, l3); }
1444 
1445  template <typename L1, typename L2, typename L3> inline
1446  void add_spec(const L1& l1, const L2& l2, L3& l3, abstract_vector) {
1447  GMM_ASSERT2(vect_size(l1) == vect_size(l2), "dimensions mismatch, "
1448  << vect_size(l1) << " !=" << vect_size(l2));
1449  GMM_ASSERT2(vect_size(l1) == vect_size(l3), "dimensions mismatch, "
1450  << vect_size(l1) << " !=" << vect_size(l3));
1451  if ((const void *)(&l1) == (const void *)(&l3))
1452  add(l2, l3);
1453  else if ((const void *)(&l2) == (const void *)(&l3))
1454  add(l1, l3);
1455  else
1456  add(l1, l2, l3, typename linalg_traits<L1>::storage_type(),
1457  typename linalg_traits<L2>::storage_type(),
1458  typename linalg_traits<L3>::storage_type());
1459  }
1460 
1461  template <typename IT1, typename IT2, typename IT3>
1462  void add_full_(IT1 it1, IT2 it2, IT3 it3, IT3 ite) {
1463  for (; it3 != ite; ++it3, ++it2, ++it1) *it3 = *it1 + *it2;
1464  }
1465 
1466  template <typename IT1, typename IT2, typename IT3>
1467  void add_almost_full_(IT1 it1, IT1 ite1, IT2 it2, IT3 it3, IT3 ite3) {
1468  IT3 it = it3;
1469  for (; it != ite3; ++it, ++it2) *it = *it2;
1470  for (; it1 != ite1; ++it1)
1471  *(it3 + it1.index()) += *it1;
1472  }
1473 
1474  template <typename IT1, typename IT2, typename IT3>
1475  void add_to_full_(IT1 it1, IT1 ite1, IT2 it2, IT2 ite2,
1476  IT3 it3, IT3 ite3) {
1477  typedef typename std::iterator_traits<IT3>::value_type T;
1478  IT3 it = it3;
1479  for (; it != ite3; ++it) *it = T(0);
1480  for (; it1 != ite1; ++it1) *(it3 + it1.index()) = *it1;
1481  for (; it2 != ite2; ++it2) *(it3 + it2.index()) += *it2;
1482  }
1483 
1484  template <typename L1, typename L2, typename L3> inline
1485  void add(const L1& l1, const L2& l2, L3& l3,
1486  abstract_dense, abstract_dense, abstract_dense) {
1487  add_full_(vect_const_begin(l1), vect_const_begin(l2),
1488  vect_begin(l3), vect_end(l3));
1489  }
1490 
1491  // generic function for add(v1, v2, v3).
1492  // Need to be specialized to optimize particular additions.
1493  template <typename L1, typename L2, typename L3,
1494  typename ST1, typename ST2, typename ST3>
1495  inline void add(const L1& l1, const L2& l2, L3& l3, ST1, ST2, ST3)
1496  { copy(l2, l3); add(l1, l3, ST1(), ST3()); }
1497 
1498  template <typename L1, typename L2, typename L3> inline
1499  void add(const L1& l1, const L2& l2, L3& l3,
1500  abstract_sparse, abstract_dense, abstract_dense) {
1501  add_almost_full_(vect_const_begin(l1), vect_const_end(l1),
1502  vect_const_begin(l2), vect_begin(l3), vect_end(l3));
1503  }
1504 
1505  template <typename L1, typename L2, typename L3> inline
1506  void add(const L1& l1, const L2& l2, L3& l3,
1507  abstract_dense, abstract_sparse, abstract_dense)
1508  { add(l2, l1, l3, abstract_sparse(), abstract_dense(), abstract_dense()); }
1509 
1510  template <typename L1, typename L2, typename L3> inline
1511  void add(const L1& l1, const L2& l2, L3& l3,
1512  abstract_sparse, abstract_sparse, abstract_dense) {
1513  add_to_full_(vect_const_begin(l1), vect_const_end(l1),
1514  vect_const_begin(l2), vect_const_end(l2),
1515  vect_begin(l3), vect_end(l3));
1516  }
1517 
1518 
1519  template <typename L1, typename L2, typename L3>
1520  void add_spspsp(const L1& l1, const L2& l2, L3& l3, linalg_true) {
1521  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1522  auto it2 = vect_const_begin(l2), ite2 = vect_const_end(l2);
1523  clear(l3);
1524  while (it1 != ite1 && it2 != ite2) {
1525  ptrdiff_t d = it1.index() - it2.index();
1526  if (d < 0)
1527  { l3[it1.index()] += *it1; ++it1; }
1528  else if (d > 0)
1529  { l3[it2.index()] += *it2; ++it2; }
1530  else
1531  { l3[it1.index()] = *it1 + *it2; ++it1; ++it2; }
1532  }
1533  for (; it1 != ite1; ++it1) l3[it1.index()] += *it1;
1534  for (; it2 != ite2; ++it2) l3[it2.index()] += *it2;
1535  }
1536 
1537  template <typename L1, typename L2, typename L3>
1538  void add_spspsp(const L1& l1, const L2& l2, L3& l3, linalg_false)
1539  { copy(l1, l3); add(l2, l3); }
1540 
1541  template <typename L1, typename L2, typename L3>
1542  void add(const L1& l1, const L2& l2, L3& l3,
1543  abstract_sparse, abstract_sparse, abstract_sparse) {
1544  add_spspsp(l1, l2, l3,
1545  typename linalg_and<typename linalg_traits<L1>::index_sorted,
1546  typename linalg_traits<L2>::index_sorted>
1547  ::bool_type());
1548  }
1549 
1550  template <typename L1, typename L2>
1551  void add(const L1& l1, L2& l2, abstract_dense, abstract_dense) {
1552  auto it1 = vect_const_begin(l1);
1553  auto it2 = vect_begin(l2), ite = vect_end(l2);
1554  for (; it2 != ite; ++it2, ++it1) *it2 += *it1;
1555  }
1556 
1557  template <typename L1, typename L2>
1558  void add(const L1& l1, L2& l2, abstract_dense, abstract_skyline) {
1559  typedef typename linalg_traits<L1>::value_type T;
1560 
1561  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1562  size_type i1 = 0, ie1 = vect_size(l1);
1563  while (it1 != ite1 && *it1 == T(0)) { ++it1; ++i1; }
1564  if (it1 != ite1) {
1565  auto it2 = vect_begin(l2), ite2 = vect_end(l2);
1566  while (ie1 && *(ite1-1) == T(0)) { ite1--; --ie1; }
1567 
1568  if (it2 == ite2 || i1 < it2.index()) {
1569  l2[i1] = *it1; ++i1; ++it1;
1570  if (it1 == ite1) return;
1571  it2 = vect_begin(l2);
1572  ite2 = vect_end(l2);
1573  }
1574  if (ie1 > ite2.index()) {
1575  --ite1; l2[ie1 - 1] = *ite1;
1576  it2 = vect_begin(l2);
1577  }
1578  it2 += i1 - it2.index();
1579  for (; it1 != ite1; ++it1, ++it2) { *it2 += *it1; }
1580  }
1581  }
1582 
1583 
1584  template <typename L1, typename L2>
1585  void add(const L1& l1, L2& l2, abstract_skyline, abstract_dense) {
1586  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1587  if (it1 != ite1) {
1588  auto it2 = vect_begin(l2);
1589  it2 += it1.index();
1590  for (; it1 != ite1; ++it2, ++it1) *it2 += *it1;
1591  }
1592  }
1593 
1594 
1595  template <typename L1, typename L2>
1596  void add(const L1& l1, L2& l2, abstract_sparse, abstract_dense) {
1597  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1598  for (; it1 != ite1; ++it1) l2[it1.index()] += *it1;
1599  }
1600 
1601  template <typename L1, typename L2>
1602  void add(const L1& l1, L2& l2, abstract_sparse, abstract_sparse) {
1603  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1604  for (; it1 != ite1; ++it1) l2[it1.index()] += *it1;
1605  }
1606 
1607  template <typename L1, typename L2>
1608  void add(const L1& l1, L2& l2, abstract_sparse, abstract_skyline) {
1609  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1610  for (; it1 != ite1; ++it1) l2[it1.index()] += *it1;
1611  }
1612 
1613 
1614  template <typename L1, typename L2>
1615  void add(const L1& l1, L2& l2, abstract_skyline, abstract_sparse) {
1616  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1617  for (; it1 != ite1; ++it1)
1618  if (*it1 != typename linalg_traits<L1>::value_type(0))
1619  l2[it1.index()] += *it1;
1620  }
1621 
1622  template <typename L1, typename L2>
1623  void add(const L1& l1, L2& l2, abstract_skyline, abstract_skyline) {
1624  typedef typename linalg_traits<L1>::value_type T1;
1625  typedef typename linalg_traits<L2>::value_type T2;
1626 
1627  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1628 
1629  while (it1 != ite1 && *it1 == T1(0)) ++it1;
1630  if (ite1 != it1) {
1631  auto it2 = vect_begin(l2), ite2 = vect_end(l2);
1632  while (*(ite1-1) == T1(0)) ite1--;
1633  if (it2 == ite2 || it1.index() < it2.index()) {
1634  l2[it1.index()] = T2(0);
1635  it2 = vect_begin(l2); ite2 = vect_end(l2);
1636  }
1637  if (ite1.index() > ite2.index()) {
1638  l2[ite1.index() - 1] = T2(0);
1639  it2 = vect_begin(l2);
1640  }
1641  it2 += it1.index() - it2.index();
1642  for (; it1 != ite1; ++it1, ++it2) *it2 += *it1;
1643  }
1644  }
1645 
1646  template <typename L1, typename L2>
1647  void add(const L1& l1, L2& l2, abstract_dense, abstract_sparse) {
1648  auto it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
1649  for (size_type i = 0; it1 != ite1; ++it1, ++i)
1650  if (*it1 != typename linalg_traits<L1>::value_type(0)) l2[i] += *it1;
1651  }
1652 
1653  /* ******************************************************************** */
1654  /* Matrix-vector mult */
1655  /* ******************************************************************** */
1656  ///@endcond
1657  /** matrix-vector or matrix-matrix product.
1658  @param l1 a matrix.
1659  @param l2 a vector or matrix.
1660  @param l3 the product l1*l2.
1661  */
1662  template <typename L1, typename L2, typename L3> inline
1663  void mult(const L1& l1, const L2& l2, L3& l3) {
1664  mult_dispatch(l1, l2, l3, typename linalg_traits<L2>::linalg_type());
1665  }
1666  ///@cond DOXY_SHOW_ALL_FUNCTIONS
1667 
1668  template <typename L1, typename L2, typename L3> inline
1669  void mult(const L1& l1, const L2& l2, const L3& l3)
1670  { mult(l1, l2, linalg_const_cast(l3)); }
1671 
1672  template <typename L1, typename L2, typename L3> inline
1673  void mult_dispatch(const L1& l1, const L2& l2, L3& l3, abstract_vector) {
1674  size_type m = mat_nrows(l1), n = mat_ncols(l1);
1675  if (!m || !n) { gmm::clear(l3); return; }
1676  GMM_ASSERT2(n==vect_size(l2) && m==vect_size(l3), "dimensions mismatch");
1677  if (!same_origin(l2, l3))
1678  mult_spec(l1, l2, l3, typename principal_orientation_type<typename
1679  linalg_traits<L1>::sub_orientation>::potype());
1680  else {
1681  GMM_WARNING2("Warning, A temporary is used for mult\n");
1682  typename temporary_vector<L3>::vector_type temp(vect_size(l3));
1683  mult_spec(l1, l2, temp, typename principal_orientation_type<typename
1684  linalg_traits<L1>::sub_orientation>::potype());
1685  copy(temp, l3);
1686  }
1687  }
1688 
1689  template <typename L1, typename L2, typename L3>
1690  void mult_by_row(const L1& l1, const L2& l2, L3& l3, abstract_sparse) {
1691  typedef typename linalg_traits<L3>::value_type T;
1692  clear(l3);
1693  size_type nr = mat_nrows(l1);
1694  for (size_type i = 0; i < nr; ++i) {
1695  T aux = vect_sp(mat_const_row(l1, i), l2);
1696  if (aux != T(0)) l3[i] = aux;
1697  }
1698  }
1699 
1700  template <typename L1, typename L2, typename L3>
1701  void mult_by_row(const L1& l1, const L2& l2, L3& l3, abstract_skyline) {
1702  typedef typename linalg_traits<L3>::value_type T;
1703  clear(l3);
1704  size_type nr = mat_nrows(l1);
1705  for (size_type i = 0; i < nr; ++i) {
1706  T aux = vect_sp(mat_const_row(l1, i), l2);
1707  if (aux != T(0)) l3[i] = aux;
1708  }
1709  }
1710 
1711  template <typename L1, typename L2, typename L3>
1712  void mult_by_row(const L1& l1, const L2& l2, L3& l3, abstract_dense) {
1713  typename linalg_traits<L3>::iterator it=vect_begin(l3), ite=vect_end(l3);
1714  auto itr = mat_row_const_begin(l1);
1715  for (; it != ite; ++it, ++itr)
1716  *it = vect_sp(linalg_traits<L1>::row(itr), l2,
1717  typename linalg_traits<L1>::storage_type(),
1718  typename linalg_traits<L2>::storage_type());
1719  }
1720 
1721  template <typename L1, typename L2, typename L3>
1722  void mult_by_col(const L1& l1, const L2& l2, L3& l3, abstract_dense) {
1723  clear(l3);
1724  size_type nc = mat_ncols(l1);
1725  for (size_type i = 0; i < nc; ++i)
1726  add(scaled(mat_const_col(l1, i), l2[i]), 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_sparse) {
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>
1739  void mult_by_col(const L1& l1, const L2& l2, L3& l3, abstract_skyline) {
1740  typedef typename linalg_traits<L2>::value_type T;
1741  clear(l3);
1742  auto it = vect_const_begin(l2), ite = vect_const_end(l2);
1743  for (; it != ite; ++it)
1744  if (*it != T(0)) add(scaled(mat_const_col(l1, it.index()), *it), l3);
1745  }
1746 
1747  template <typename L1, typename L2, typename L3> inline
1748  void mult_spec(const L1& l1, const L2& l2, L3& l3, row_major)
1749  { mult_by_row(l1, l2, l3, typename linalg_traits<L3>::storage_type()); }
1750 
1751  template <typename L1, typename L2, typename L3> inline
1752  void mult_spec(const L1& l1, const L2& l2, L3& l3, col_major)
1753  { mult_by_col(l1, l2, l3, typename linalg_traits<L2>::storage_type()); }
1754 
1755  template <typename L1, typename L2, typename L3> inline
1756  void mult_spec(const L1& l1, const L2& l2, L3& l3, abstract_null_type)
1757  { mult_ind(l1, l2, l3, typename linalg_traits<L1>::storage_type()); }
1758 
1759  template <typename L1, typename L2, typename L3>
1760  void mult_ind(const L1& l1, const L2& l2, L3& l3, abstract_indirect) {
1761  GMM_ASSERT1(false, "gmm::mult(m, ., .) undefined for this kind of matrix");
1762  }
1763 
1764  template <typename L1, typename L2, typename L3, typename L4> inline
1765  void mult(const L1& l1, const L2& l2, const L3& l3, L4& l4) {
1766  size_type m = mat_nrows(l1), n = mat_ncols(l1);
1767  copy(l3, l4);
1768  if (!m || !n) { gmm::copy(l3, l4); return; }
1769  GMM_ASSERT2(n==vect_size(l2) && m==vect_size(l4), "dimensions mismatch");
1770  if (!same_origin(l2, l4)) {
1771  mult_add_spec(l1, l2, l4, typename principal_orientation_type<typename
1772  linalg_traits<L1>::sub_orientation>::potype());
1773  }
1774  else {
1775  GMM_WARNING2("Warning, A temporary is used for mult\n");
1776  typename temporary_vector<L2>::vector_type temp(vect_size(l2));
1777  copy(l2, temp);
1778  mult_add_spec(l1,temp, l4, typename principal_orientation_type<typename
1779  linalg_traits<L1>::sub_orientation>::potype());
1780  }
1781  }
1782 
1783  template <typename L1, typename L2, typename L3, typename L4> inline
1784  void mult(const L1& l1, const L2& l2, const L3& l3, const L4& l4)
1785  { mult(l1, l2, l3, linalg_const_cast(l4)); }
1786 
1787  ///@endcond
1788  /** Multiply-accumulate. l3 += l1*l2; */
1789  template <typename L1, typename L2, typename L3> inline
1790  void mult_add(const L1& l1, const L2& l2, L3& l3) {
1791  size_type m = mat_nrows(l1), n = mat_ncols(l1);
1792  if (!m || !n) return;
1793  GMM_ASSERT2(n==vect_size(l2) && m==vect_size(l3), "dimensions mismatch");
1794  if (!same_origin(l2, l3)) {
1795  mult_add_spec(l1, l2, l3, typename principal_orientation_type<typename
1796  linalg_traits<L1>::sub_orientation>::potype());
1797  }
1798  else {
1799  GMM_WARNING2("Warning, A temporary is used for mult\n");
1800  typename temporary_vector<L3>::vector_type temp(vect_size(l2));
1801  copy(l2, temp);
1802  mult_add_spec(l1,temp, l3, typename principal_orientation_type<typename
1803  linalg_traits<L1>::sub_orientation>::potype());
1804  }
1805  }
1806  ///@cond DOXY_SHOW_ALL_FUNCTIONS
1807 
1808  template <typename L1, typename L2, typename L3> inline
1809  void mult_add(const L1& l1, const L2& l2, const L3& l3)
1810  { mult_add(l1, l2, linalg_const_cast(l3)); }
1811 
1812  template <typename L1, typename L2, typename L3>
1813  void mult_add_by_row(const L1& l1, const L2& l2, L3& l3, abstract_sparse) {
1814  typedef typename linalg_traits<L3>::value_type T;
1815  size_type nr = mat_nrows(l1);
1816  for (size_type i = 0; i < nr; ++i) {
1817  T aux = vect_sp(mat_const_row(l1, i), l2);
1818  if (aux != T(0)) l3[i] += aux;
1819  }
1820  }
1821 
1822  template <typename L1, typename L2, typename L3>
1823  void mult_add_by_row(const L1& l1, const L2& l2, L3& l3, abstract_skyline) {
1824  typedef typename linalg_traits<L3>::value_type T;
1825  size_type nr = mat_nrows(l1);
1826  for (size_type i = 0; i < nr; ++i) {
1827  T aux = vect_sp(mat_const_row(l1, i), l2);
1828  if (aux != T(0)) l3[i] += aux;
1829  }
1830  }
1831 
1832  template <typename L1, typename L2, typename L3>
1833  void mult_add_by_row(const L1& l1, const L2& l2, L3& l3, abstract_dense) {
1834  auto it=vect_begin(l3), ite=vect_end(l3);
1835  auto itr = mat_row_const_begin(l1);
1836  for (; it != ite; ++it, ++itr)
1837  *it += vect_sp(linalg_traits<L1>::row(itr), l2);
1838  }
1839 
1840  template <typename L1, typename L2, typename L3>
1841  void mult_add_by_col(const L1& l1, const L2& l2, L3& l3, abstract_dense) {
1842  size_type nc = mat_ncols(l1);
1843  for (size_type i = 0; i < nc; ++i)
1844  add(scaled(mat_const_col(l1, i), l2[i]), l3);
1845  }
1846 
1847  template <typename L1, typename L2, typename L3>
1848  void mult_add_by_col(const L1& l1, const L2& l2, L3& l3, abstract_sparse) {
1849  auto it = vect_const_begin(l2), ite = vect_const_end(l2);
1850  for (; it != ite; ++it)
1851  if (*it != typename linalg_traits<L2>::value_type(0))
1852  add(scaled(mat_const_col(l1, it.index()), *it), l3);
1853  }
1854 
1855  template <typename L1, typename L2, typename L3>
1856  void mult_add_by_col(const L1& l1, const L2& l2, L3& l3, abstract_skyline) {
1857  auto it = vect_const_begin(l2), ite = vect_const_end(l2);
1858  for (; it != ite; ++it)
1859  if (*it != typename linalg_traits<L2>::value_type(0))
1860  add(scaled(mat_const_col(l1, it.index()), *it), l3);
1861  }
1862 
1863  template <typename L1, typename L2, typename L3> inline
1864  void mult_add_spec(const L1& l1, const L2& l2, L3& l3, row_major)
1865  { mult_add_by_row(l1, l2, l3, typename linalg_traits<L3>::storage_type()); }
1866 
1867  template <typename L1, typename L2, typename L3> inline
1868  void mult_add_spec(const L1& l1, const L2& l2, L3& l3, col_major)
1869  { mult_add_by_col(l1, l2, l3, typename linalg_traits<L2>::storage_type()); }
1870 
1871  template <typename L1, typename L2, typename L3> inline
1872  void mult_add_spec(const L1& l1, const L2& l2, L3& l3, abstract_null_type)
1873  { mult_ind(l1, l2, l3, typename linalg_traits<L1>::storage_type()); }
1874 
1875  template <typename L1, typename L2, typename L3>
1876  void transposed_mult(const L1& l1, const L2& l2, const L3& l3)
1877  { mult(gmm::transposed(l1), l2, l3); }
1878 
1879 
1880  /* ******************************************************************** */
1881  /* Matrix-matrix mult */
1882  /* ******************************************************************** */
1883 
1884 
1885  struct g_mult {}; // generic mult, less optimized
1886  struct c_mult {}; // col x col -> col mult
1887  struct r_mult {}; // row x row -> row mult
1888  struct rcmult {}; // row x col -> col mult
1889  struct crmult {}; // col x row -> row mult
1890 
1891 
1892  template<typename SO1, typename SO2, typename SO3> struct mult_t;
1893  #define DEFMU__ template<> struct mult_t
1894  DEFMU__<row_major , row_major , row_major > { typedef r_mult t; };
1895  DEFMU__<row_major , row_major , col_major > { typedef g_mult t; };
1896  DEFMU__<row_major , row_major , col_and_row> { typedef r_mult t; };
1897  DEFMU__<row_major , row_major , row_and_col> { typedef r_mult t; };
1898  DEFMU__<row_major , col_major , row_major > { typedef rcmult t; };
1899  DEFMU__<row_major , col_major , col_major > { typedef rcmult t; };
1900  DEFMU__<row_major , col_major , col_and_row> { typedef rcmult t; };
1901  DEFMU__<row_major , col_major , row_and_col> { typedef rcmult t; };
1902  DEFMU__<row_major , col_and_row, row_major > { typedef r_mult t; };
1903  DEFMU__<row_major , col_and_row, col_major > { typedef rcmult t; };
1904  DEFMU__<row_major , col_and_row, col_and_row> { typedef rcmult t; };
1905  DEFMU__<row_major , col_and_row, row_and_col> { typedef rcmult t; };
1906  DEFMU__<row_major , row_and_col, row_major > { typedef r_mult t; };
1907  DEFMU__<row_major , row_and_col, col_major > { typedef rcmult t; };
1908  DEFMU__<row_major , row_and_col, col_and_row> { typedef r_mult t; };
1909  DEFMU__<row_major , row_and_col, row_and_col> { typedef r_mult t; };
1910  DEFMU__<col_major , row_major , row_major > { typedef crmult t; };
1911  DEFMU__<col_major , row_major , col_major > { typedef g_mult t; };
1912  DEFMU__<col_major , row_major , col_and_row> { typedef crmult t; };
1913  DEFMU__<col_major , row_major , row_and_col> { typedef crmult t; };
1914  DEFMU__<col_major , col_major , row_major > { typedef g_mult t; };
1915  DEFMU__<col_major , col_major , col_major > { typedef c_mult t; };
1916  DEFMU__<col_major , col_major , col_and_row> { typedef c_mult t; };
1917  DEFMU__<col_major , col_major , row_and_col> { typedef c_mult t; };
1918  DEFMU__<col_major , col_and_row, row_major > { typedef crmult t; };
1919  DEFMU__<col_major , col_and_row, col_major > { typedef c_mult t; };
1920  DEFMU__<col_major , col_and_row, col_and_row> { typedef c_mult t; };
1921  DEFMU__<col_major , col_and_row, row_and_col> { typedef c_mult t; };
1922  DEFMU__<col_major , row_and_col, row_major > { typedef crmult t; };
1923  DEFMU__<col_major , row_and_col, col_major > { typedef c_mult t; };
1924  DEFMU__<col_major , row_and_col, col_and_row> { typedef c_mult t; };
1925  DEFMU__<col_major , row_and_col, row_and_col> { typedef c_mult t; };
1926  DEFMU__<col_and_row, row_major , row_major > { typedef r_mult t; };
1927  DEFMU__<col_and_row, row_major , col_major > { typedef c_mult t; };
1928  DEFMU__<col_and_row, row_major , col_and_row> { typedef r_mult t; };
1929  DEFMU__<col_and_row, row_major , row_and_col> { typedef r_mult t; };
1930  DEFMU__<col_and_row, col_major , row_major > { typedef rcmult t; };
1931  DEFMU__<col_and_row, col_major , col_major > { typedef c_mult t; };
1932  DEFMU__<col_and_row, col_major , col_and_row> { typedef c_mult t; };
1933  DEFMU__<col_and_row, col_major , row_and_col> { typedef c_mult t; };
1934  DEFMU__<col_and_row, col_and_row, row_major > { typedef r_mult t; };
1935  DEFMU__<col_and_row, col_and_row, col_major > { typedef c_mult t; };
1936  DEFMU__<col_and_row, col_and_row, col_and_row> { typedef c_mult t; };
1937  DEFMU__<col_and_row, col_and_row, row_and_col> { typedef c_mult t; };
1938  DEFMU__<col_and_row, row_and_col, row_major > { typedef r_mult t; };
1939  DEFMU__<col_and_row, row_and_col, col_major > { typedef c_mult t; };
1940  DEFMU__<col_and_row, row_and_col, col_and_row> { typedef c_mult t; };
1941  DEFMU__<col_and_row, row_and_col, row_and_col> { typedef r_mult t; };
1942  DEFMU__<row_and_col, row_major , row_major > { typedef r_mult t; };
1943  DEFMU__<row_and_col, row_major , col_major > { typedef c_mult t; };
1944  DEFMU__<row_and_col, row_major , col_and_row> { typedef r_mult t; };
1945  DEFMU__<row_and_col, row_major , row_and_col> { typedef r_mult t; };
1946  DEFMU__<row_and_col, col_major , row_major > { typedef rcmult t; };
1947  DEFMU__<row_and_col, col_major , col_major > { typedef c_mult t; };
1948  DEFMU__<row_and_col, col_major , col_and_row> { typedef c_mult t; };
1949  DEFMU__<row_and_col, col_major , row_and_col> { typedef c_mult t; };
1950  DEFMU__<row_and_col, col_and_row, row_major > { typedef rcmult t; };
1951  DEFMU__<row_and_col, col_and_row, col_major > { typedef rcmult t; };
1952  DEFMU__<row_and_col, col_and_row, col_and_row> { typedef rcmult t; };
1953  DEFMU__<row_and_col, col_and_row, row_and_col> { typedef rcmult t; };
1954  DEFMU__<row_and_col, row_and_col, row_major > { typedef r_mult t; };
1955  DEFMU__<row_and_col, row_and_col, col_major > { typedef c_mult t; };
1956  DEFMU__<row_and_col, row_and_col, col_and_row> { typedef r_mult t; };
1957  DEFMU__<row_and_col, row_and_col, row_and_col> { typedef r_mult t; };
1958 
1959  template <typename L1, typename L2, typename L3>
1960  void mult_dispatch(const L1& l1, const L2& l2, L3& l3, abstract_matrix) {
1961  typedef typename temporary_matrix<L3>::matrix_type temp_mat_type;
1962  size_type n = mat_ncols(l1);
1963  if (n == 0) { gmm::clear(l3); return; }
1964  GMM_ASSERT2(n == mat_nrows(l2) && mat_nrows(l1) == mat_nrows(l3) &&
1965  mat_ncols(l2) == mat_ncols(l3), "dimensions mismatch");
1966 
1967  if (same_origin(l2, l3) || same_origin(l1, l3)) {
1968  GMM_WARNING2("A temporary is used for mult");
1969  temp_mat_type temp(mat_nrows(l3), mat_ncols(l3));
1970  mult_spec(l1, l2, temp, typename mult_t<
1971  typename linalg_traits<L1>::sub_orientation,
1972  typename linalg_traits<L2>::sub_orientation,
1973  typename linalg_traits<temp_mat_type>::sub_orientation>::t());
1974  copy(temp, l3);
1975  }
1976  else
1977  mult_spec(l1, l2, l3, typename mult_t<
1978  typename linalg_traits<L1>::sub_orientation,
1979  typename linalg_traits<L2>::sub_orientation,
1980  typename linalg_traits<L3>::sub_orientation>::t());
1981  }
1982 
1983  // Completely generic but inefficient
1984 
1985  template <typename L1, typename L2, typename L3>
1986  void mult_spec(const L1& l1, const L2& l2, L3& l3, g_mult) {
1987  typedef typename linalg_traits<L3>::value_type T;
1988  GMM_WARNING2("Inefficient generic matrix-matrix mult is used");
1989  for (size_type i = 0; i < mat_nrows(l3) ; ++i)
1990  for (size_type j = 0; j < mat_ncols(l3) ; ++j) {
1991  T a(0);
1992  for (size_type k = 0; k < mat_nrows(l2) ; ++k)
1993  a += l1(i, k)*l2(k, j);
1994  l3(i, j) = a;
1995  }
1996  }
1997 
1998  // row x col matrix-matrix mult
1999 
2000  template <typename L1, typename L2, typename L3>
2001  void mult_row_col_with_temp(const L1& l1, const L2& l2, L3& l3, col_major) {
2002  typedef typename temporary_col_matrix<L1>::matrix_type temp_col_mat;
2003  temp_col_mat temp(mat_nrows(l1), mat_ncols(l1));
2004  copy(l1, temp);
2005  mult(temp, l2, l3);
2006  }
2007 
2008  template <typename L1, typename L2, typename L3>
2009  void mult_row_col_with_temp(const L1& l1, const L2& l2, L3& l3, row_major) {
2010  typedef typename temporary_row_matrix<L2>::matrix_type temp_row_mat;
2011  temp_row_mat temp(mat_nrows(l2), mat_ncols(l2));
2012  copy(l2, temp);
2013  mult(l1, temp, l3);
2014  }
2015 
2016  template <typename L1, typename L2, typename L3>
2017  void mult_spec(const L1& l1, const L2& l2, L3& l3, rcmult) {
2018  if (is_sparse(l1) && is_sparse(l2)) {
2019  GMM_WARNING3("Inefficient row matrix - col matrix mult for "
2020  "sparse matrices, using temporary");
2021  mult_row_col_with_temp
2022  (l1, l2, l3, typename principal_orientation_type
2023  <typename linalg_traits<L3>::sub_orientation>::potype());
2024  }
2025  else {
2026  auto it2b = linalg_traits<L2>::col_begin(l2), it2 = it2b,
2027  ite = linalg_traits<L2>::col_end(l2);
2028  size_type i,j, k = mat_nrows(l1);
2029 
2030  for (i = 0; i < k; ++i) {
2031  typename linalg_traits<L1>::const_sub_row_type r1=mat_const_row(l1, i);
2032  for (it2 = it2b, j = 0; it2 != ite; ++it2, ++j)
2033  l3(i,j) = vect_sp(r1, linalg_traits<L2>::col(it2));
2034  }
2035  }
2036  }
2037 
2038  // row - row matrix-matrix mult
2039 
2040  template <typename L1, typename L2, typename L3> inline
2041  void mult_spec(const L1& l1, const L2& l2, L3& l3, r_mult) {
2042  mult_spec(l1, l2, l3,r_mult(),typename linalg_traits<L1>::storage_type());
2043  }
2044 
2045  template <typename L1, typename L2, typename L3>
2046  void mult_spec(const L1& l1, const L2& l2, L3& l3, r_mult, abstract_dense) {
2047  // optimizable
2048  clear(l3);
2049  size_type nn = mat_nrows(l3), mm = mat_nrows(l2);
2050  for (size_type i = 0; i < nn; ++i) {
2051  for (size_type j = 0; j < mm; ++j) {
2052  add(scaled(mat_const_row(l2, j), l1(i, j)), mat_row(l3, i));
2053  }
2054  }
2055  }
2056 
2057  template <typename L1, typename L2, typename L3>
2058  void mult_spec(const L1& l1, const L2& l2, L3& l3, r_mult, abstract_sparse) {
2059  // optimizable
2060  clear(l3);
2061  size_type nn = mat_nrows(l3);
2062  for (size_type i = 0; i < nn; ++i) {
2063  typename linalg_traits<L1>::const_sub_row_type rl1=mat_const_row(l1, i);
2064  auto it = vect_const_begin(rl1), ite = vect_const_end(rl1);
2065  for (; it != ite; ++it)
2066  add(scaled(mat_const_row(l2, it.index()), *it), mat_row(l3, i));
2067  }
2068  }
2069 
2070  template <typename L1, typename L2, typename L3>
2071  void mult_spec(const L1& l1, const L2& l2, L3& l3, r_mult, abstract_skyline)
2072  { mult_spec(l1, l2, l3, r_mult(), abstract_sparse()); }
2073 
2074  // col - col matrix-matrix mult
2075 
2076  template <typename L1, typename L2, typename L3> inline
2077  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult) {
2078  mult_spec(l1, l2, l3, c_mult(), typename linalg_traits<L2>::storage_type(),
2079  typename linalg_traits<L2>::sub_orientation());
2080  }
2081 
2082 
2083  template <typename L1, typename L2, typename L3, typename ORIEN>
2084  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult,
2085  abstract_dense, ORIEN) {
2086  typedef typename linalg_traits<L2>::value_type T;
2087  size_type nn = mat_ncols(l3), mm = mat_ncols(l1);
2088 
2089  for (size_type i = 0; i < nn; ++i) {
2090  clear(mat_col(l3, i));
2091  for (size_type j = 0; j < mm; ++j) {
2092  T b = l2(j, i);
2093  if (b != T(0)) add(scaled(mat_const_col(l1, j), b), mat_col(l3, i));
2094  }
2095  }
2096  }
2097 
2098  template <typename L1, typename L2, typename L3, typename ORIEN>
2099  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult,
2100  abstract_sparse, ORIEN) {
2101  // optimizable
2102  clear(l3);
2103  size_type nn = mat_ncols(l3);
2104  for (size_type i = 0; i < nn; ++i) {
2105  typename linalg_traits<L2>::const_sub_col_type rc2 = mat_const_col(l2, i);
2106  auto it = vect_const_begin(rc2), ite = vect_const_end(rc2);
2107  for (; it != ite; ++it)
2108  add(scaled(mat_const_col(l1, it.index()), *it), mat_col(l3, i));
2109  }
2110  }
2111 
2112  template <typename L1, typename L2, typename L3>
2113  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult,
2114  abstract_sparse, row_major) {
2115  typedef typename linalg_traits<L2>::value_type T;
2116  GMM_WARNING3("Inefficient matrix-matrix mult for sparse matrices");
2117  clear(l3);
2118  size_type mm = mat_nrows(l2), nn = mat_ncols(l3);
2119  for (size_type i = 0; i < nn; ++i)
2120  for (size_type j = 0; j < mm; ++j) {
2121  T a = l2(i,j);
2122  if (a != T(0)) add(scaled(mat_const_col(l1, j), a), mat_col(l3, i));
2123  }
2124  }
2125 
2126  template <typename L1, typename L2, typename L3, typename ORIEN> inline
2127  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult,
2128  abstract_skyline, ORIEN)
2129  { mult_spec(l1, l2, l3, c_mult(), abstract_sparse(), ORIEN()); }
2130 
2131 
2132  // col - row matrix-matrix mult
2133 
2134  template <typename L1, typename L2, typename L3> inline
2135  void mult_spec(const L1& l1, const L2& l2, L3& l3, crmult)
2136  { mult_spec(l1,l2,l3,crmult(), typename linalg_traits<L1>::storage_type()); }
2137 
2138 
2139  template <typename L1, typename L2, typename L3>
2140  void mult_spec(const L1& l1, const L2& l2, L3& l3, crmult, abstract_dense) {
2141  // optimizable
2142  clear(l3);
2143  size_type nn = mat_ncols(l1), mm = mat_nrows(l1);
2144  for (size_type i = 0; i < nn; ++i) {
2145  for (size_type j = 0; j < mm; ++j)
2146  add(scaled(mat_const_row(l2, i), l1(j, i)), mat_row(l3, j));
2147  }
2148  }
2149 
2150  template <typename L1, typename L2, typename L3>
2151  void mult_spec(const L1& l1, const L2& l2, L3& l3, crmult, abstract_sparse) {
2152  // optimizable
2153  clear(l3);
2154  size_type nn = mat_ncols(l1);
2155  for (size_type i = 0; i < nn; ++i) {
2156  typename linalg_traits<L1>::const_sub_col_type rc1 = mat_const_col(l1, i);
2157  auto it = vect_const_begin(rc1), ite = vect_const_end(rc1);
2158  for (; it != ite; ++it)
2159  add(scaled(mat_const_row(l2, i), *it), mat_row(l3, it.index()));
2160  }
2161  }
2162 
2163  template <typename L1, typename L2, typename L3> inline
2164  void mult_spec(const L1& l1, const L2& l2, L3& l3, crmult, abstract_skyline)
2165  { mult_spec(l1, l2, l3, crmult(), abstract_sparse()); }
2166 
2167 
2168  /* ******************************************************************** */
2169  /* Symmetry test. */
2170  /* ******************************************************************** */
2171 
2172  ///@endcond
2173  /** test if A is symmetric.
2174  @param A a matrix.
2175  @param tol a threshold.
2176  */
2177  template <typename MAT> inline
2178  bool is_symmetric(const MAT &A,
2179  magnitude_of_linalg(MAT) tol = magnitude_of_linalg(MAT)(-1))
2180  {
2181  typedef magnitude_of_linalg(MAT) R;
2182  if (tol < R(0)) tol = default_tol(R()) * mat_maxnorm(A);
2183  if (mat_nrows(A) != mat_ncols(A)) return false;
2184  return is_symmetric(A, tol, typename linalg_traits<MAT>::storage_type());
2185  }
2186  ///@cond DOXY_SHOW_ALL_FUNCTIONS
2187 
2188  template <typename MAT>
2189  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol,
2190  abstract_dense) {
2191  size_type m = mat_nrows(A);
2192  for (size_type i = 1; i < m; ++i)
2193  for (size_type j = 0; j < i; ++j)
2194  if (gmm::abs(A(i, j)-A(j, i)) > tol) return false;
2195  return true;
2196  }
2197 
2198  template <typename MAT>
2199  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol,
2200  abstract_sparse) {
2201  return is_symmetric(A, tol, typename principal_orientation_type<typename
2202  linalg_traits<MAT>::sub_orientation>::potype());
2203  }
2204 
2205  template <typename MAT>
2206  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol,
2207  row_major) {
2208  for (size_type i = 0; i < mat_nrows(A); ++i) {
2209  typename linalg_traits<MAT>::const_sub_row_type row = mat_const_row(A, i);
2210  auto it = vect_const_begin(row), ite = vect_const_end(row);
2211  for (; it != ite; ++it)
2212  if (gmm::abs(*it - A(it.index(), i)) > tol) return false;
2213  }
2214  return true;
2215  }
2216 
2217  template <typename MAT>
2218  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol,
2219  col_major) {
2220  for (size_type i = 0; i < mat_ncols(A); ++i) {
2221  typename linalg_traits<MAT>::const_sub_col_type col = mat_const_col(A, i);
2222  auto it = vect_const_begin(col), ite = vect_const_end(col);
2223  for (; it != ite; ++it)
2224  if (gmm::abs(*it - A(i, it.index())) > tol) return false;
2225  }
2226  return true;
2227  }
2228 
2229  template <typename MAT>
2230  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol,
2231  abstract_skyline)
2232  { return is_symmetric(A, tol, abstract_sparse()); }
2233 
2234  ///@endcond
2235  /** test if A is Hermitian.
2236  @param A a matrix.
2237  @param tol a threshold.
2238  */
2239  template <typename MAT> inline
2240  bool is_hermitian(const MAT &A,
2241  magnitude_of_linalg(MAT) tol = magnitude_of_linalg(MAT)(-1))
2242  {
2243  typedef magnitude_of_linalg(MAT) R;
2244  if (tol < R(0)) tol = default_tol(R()) * mat_maxnorm(A);
2245  if (mat_nrows(A) != mat_ncols(A)) return false;
2246  return is_hermitian(A, tol, typename linalg_traits<MAT>::storage_type());
2247  }
2248  ///@cond DOXY_SHOW_ALL_FUNCTIONS
2249 
2250  template <typename MAT>
2251  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol,
2252  abstract_dense) {
2253  size_type m = mat_nrows(A);
2254  for (size_type i = 1; i < m; ++i)
2255  for (size_type j = 0; j < i; ++j)
2256  if (gmm::abs(A(i, j)-gmm::conj(A(j, i))) > tol) return false;
2257  return true;
2258  }
2259 
2260  template <typename MAT>
2261  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol,
2262  abstract_sparse) {
2263  return is_hermitian(A, tol, typename principal_orientation_type<typename
2264  linalg_traits<MAT>::sub_orientation>::potype());
2265  }
2266 
2267  template <typename MAT>
2268  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol,
2269  row_major) {
2270  for (size_type i = 0; i < mat_nrows(A); ++i) {
2271  typename linalg_traits<MAT>::const_sub_row_type row = mat_const_row(A, i);
2272  auto it = vect_const_begin(row), ite = vect_const_end(row);
2273  for (; it != ite; ++it)
2274  if (gmm::abs(gmm::conj(*it) - A(it.index(), i)) > 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  col_major) {
2282  for (size_type i = 0; i < mat_ncols(A); ++i) {
2283  typename linalg_traits<MAT>::const_sub_col_type col = mat_const_col(A, i);
2284  auto it = vect_const_begin(col), ite = vect_const_end(col);
2285  for (; it != ite; ++it)
2286  if (gmm::abs(gmm::conj(*it) - A(i, it.index())) > tol) return false;
2287  }
2288  return true;
2289  }
2290 
2291  template <typename MAT>
2292  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol,
2293  abstract_skyline)
2294  { return is_hermitian(A, tol, abstract_sparse()); }
2295  ///@endcond
2296 }
2297 
2298 
2299 #endif // GMM_BLAS_H__
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::mult_add
void mult_add(const L1 &l1, const L2 &l2, L3 &l3)
*‍/
Definition: gmm_blas.h:1790
gmm::reshape
void reshape(M &v, size_type m, size_type n)
*‍/
Definition: gmm_blas.h:250
gmm::copy
void copy(const L1 &l1, L2 &l2)
*‍/
Definition: gmm_blas.h:976
gmm::mat_norm1
number_traits< typename linalg_traits< M >::value_type >::magnitude_type mat_norm1(const M &m)
*‍/
Definition: gmm_blas.h:781
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:556
gmm::fill
void fill(L &l, typename gmm::linalg_traits< L >::value_type x)
*‍/
Definition: gmm_blas.h:103
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::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:657
gmm::mat_maxnorm
number_traits< typename linalg_traits< M >::value_type >::magnitude_type mat_maxnorm(const M &m)
*‍/
Definition: gmm_blas.h:869
gmm::vect_hp
strongest_value_type< V1, V2 >::value_type vect_hp(const V1 &v1, const V2 &v2)
*‍/
Definition: gmm_blas.h:510
gmm::mat_trace
linalg_traits< M >::value_type mat_trace(const M &m)
Trace of a matrix.
Definition: gmm_blas.h:527
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:635
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:704
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:564
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:543
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:692
gmm::clear
void clear(L &l)
clear (fill with zeros) a vector or matrix.
Definition: gmm_blas.h:58
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:596
gmm::resize
void resize(V &v, size_type n)
*‍/
Definition: gmm_blas.h:209
gmm::clean
void clean(L &l, double threshold)
Clean a vector or matrix (replace near-zero entries with zeroes).
gmm::mult
void mult(const L1 &l1, const L2 &l2, L3 &l3)
*‍/
Definition: gmm_blas.h:1663
gmm::is_hermitian
bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol=magnitude_of_linalg(MAT)(-1))
*‍/
Definition: gmm_blas.h:2240
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:645
gmm::vect_sp
strongest_value_type< V1, V2 >::value_type vect_sp(const V1 &v1, const V2 &v2)
*‍/
Definition: gmm_blas.h:263
gmm::add
void add(const L1 &l1, L2 &l2)
*‍/
Definition: gmm_blas.h:1275
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:625
gmm::mat_norminf
number_traits< typename linalg_traits< M >::value_type >::magnitude_type mat_norminf(const M &m)
*‍/
Definition: gmm_blas.h:835
gmm::is_symmetric
bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol=magnitude_of_linalg(MAT)(-1))
*‍/
Definition: gmm_blas.h:2178
gmm_conjugated.h
handle conjugation of complex matrices/vectors.
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:301
gmm_scaled.h
get a scaled view of a vector/matrix.
gmm_transposed.h
Generic transposed matrices.
bgeot::size_type
size_t size_type
used as the common size type in the library
Definition: bgeot_poly.h:48