tempest/resources/3rdparty/gmm-5.0/include/gmm/gmm_blas.h

/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
 
 Copyright (C) 2002-2015 Yves Renard
 
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/**@file gmm_blas.h
   @author  Yves Renard <Yves.Renard@insa-lyon.fr>
   @date October 13, 2002.
   @brief Basic linear algebra functions.
*/

#ifndef GMM_BLAS_H__
#define GMM_BLAS_H__

// This Version of GMM was modified for StoRM.
// To detect whether the usage of TBB is possible, this include is neccessary
#include "storm-config.h"

#ifdef STORM_HAVE_INTELTBB
#	include <new> // This fixes a potential dependency ordering problem between GMM and TBB
#	include "tbb/tbb.h"
#	include <iterator>
#endif

#include "gmm_scaled.h"
#include "gmm_transposed.h"
#include "gmm_conjugated.h"

namespace gmm {

  /* ******************************************************************** */
  /*		                                         		  */
  /*		Generic algorithms                           		  */
  /*		                                         		  */
  /* ******************************************************************** */


  /* ******************************************************************** */
  /*		Miscellaneous                           		  */
  /* ******************************************************************** */

  /** clear (fill with zeros) a vector or matrix. */
  template <typename L> inline void clear(L &l)
  { linalg_traits<L>::do_clear(l); }
  /** @cond DOXY_SHOW_ALL_FUNCTIONS 
      skip all these redundant definitions in doxygen documentation..
   */
  template <typename L> inline void clear(const L &l)
  { linalg_traits<L>::do_clear(linalg_const_cast(l)); }

  ///@endcond
  /** count the number of non-zero entries of a vector or matrix. */  template <typename L> inline size_type nnz(const L& l)
  { return nnz(l, typename linalg_traits<L>::linalg_type()); }

  ///@cond DOXY_SHOW_ALL_FUNCTIONS
  template <typename L> inline size_type nnz(const L& l, abstract_vector) { 
    typename linalg_traits<L>::const_iterator it = vect_const_begin(l),
      ite = vect_const_end(l);
    size_type res(0);
    for (; it != ite; ++it) ++res;
    return res;
  }

  template <typename L> inline size_type nnz(const L& l, abstract_matrix) {
    return nnz(l,  typename principal_orientation_type<typename
	       linalg_traits<L>::sub_orientation>::potype());
  }

  template <typename L> inline size_type nnz(const L& l, row_major) {
    size_type res(0);
    for (size_type i = 0; i < mat_nrows(l); ++i)
      res += nnz(mat_const_row(l, i));
    return res;
  } 

  template <typename L> inline size_type nnz(const L& l, col_major) {
    size_type res(0);
    for (size_type i = 0; i < mat_ncols(l); ++i)
      res += nnz(mat_const_col(l, i));
    return res;
  }

  ///@endcond


  /** fill a vector or matrix with x. */
  template <typename L> inline
  void fill(L& l, typename gmm::linalg_traits<L>::value_type x) {
    typedef typename gmm::linalg_traits<L>::value_type T;
    if (x == T(0)) gmm::clear(l);
    fill(l, x, typename linalg_traits<L>::linalg_type());
  }

  template <typename L> inline
  void fill(const L& l, typename gmm::linalg_traits<L>::value_type x) {
    fill(linalg_const_cast(l), x);
  }

  template <typename L> inline // to be optimized for dense vectors ...
  void fill(L& l,  typename gmm::linalg_traits<L>::value_type x,
		   abstract_vector) {
    for (size_type i = 0; i < vect_size(l); ++i) l[i] = x;
  }

  template <typename L> inline // to be optimized for dense matrices ...
  void fill(L& l, typename gmm::linalg_traits<L>::value_type x,
		   abstract_matrix) {
    for (size_type i = 0; i < mat_nrows(l); ++i)
      for (size_type j = 0; j < mat_ncols(l); ++j)
	l(i,j) = x;
  }

  /** fill a vector or matrix with random value (uniform [-1,1]). */
  template <typename L> inline void fill_random(L& l)
  { fill_random(l, typename linalg_traits<L>::linalg_type()); }

  ///@cond DOXY_SHOW_ALL_FUNCTIONS
  template <typename L> inline void fill_random(const L& l) {
    fill_random(linalg_const_cast(l),
		typename linalg_traits<L>::linalg_type());
  }

  template <typename L> inline void fill_random(L& l, abstract_vector) {
    for (size_type i = 0; i < vect_size(l); ++i)
      l[i] = gmm::random(typename linalg_traits<L>::value_type());
  }

  template <typename L> inline void fill_random(L& l, abstract_matrix) {
    for (size_type i = 0; i < mat_nrows(l); ++i)
      for (size_type j = 0; j < mat_ncols(l); ++j)
	l(i,j) = gmm::random(typename linalg_traits<L>::value_type());
  }

  ///@endcond
  /** fill a vector or matrix with random value.
      @param l a vector or matrix.
      @param cfill probability of a non-zero value.
  */
  template <typename L> inline void fill_random(L& l, double cfill)
  { fill_random(l, cfill, typename linalg_traits<L>::linalg_type()); }
  ///@cond DOXY_SHOW_ALL_FUNCTIONS

  template <typename L> inline void fill_random(const L& l, double cfill) {
    fill_random(linalg_const_cast(l), cfill,
		typename linalg_traits<L>::linalg_type());
  }

  template <typename L> inline
  void fill_random(L& l, double cfill, abstract_vector) {
    typedef typename linalg_traits<L>::value_type T;
    size_type ntot = std::min(vect_size(l),
			      size_type(double(vect_size(l))*cfill) + 1);
    for (size_type nb = 0; nb < ntot;) {
      size_type i = gmm::irandom(vect_size(l));
      if (l[i] == T(0)) { 
	l[i] = gmm::random(typename linalg_traits<L>::value_type());
	++nb;
      }
    }
  }

  template <typename L> inline
  void fill_random(L& l, double cfill, abstract_matrix) {
    fill_random(l, cfill, typename principal_orientation_type<typename
		linalg_traits<L>::sub_orientation>::potype());
  }

  template <typename L> inline
  void fill_random(L& l, double cfill, row_major) {
    for (size_type i=0; i < mat_nrows(l); ++i) fill_random(mat_row(l,i),cfill);
  }

  template <typename L> inline
  void fill_random(L& l, double cfill, col_major) {
    for (size_type j=0; j < mat_ncols(l); ++j) fill_random(mat_col(l,j),cfill);
  }

  /* resize a vector */
  template <typename V> inline
  void resize(V &v, size_type n, linalg_false)
  { linalg_traits<V>::resize(v, n); }

  template <typename V> inline
  void resize(V &, size_type , linalg_modifiable)
  { GMM_ASSERT1(false, "You cannot resize a reference"); }

  template <typename V> inline
  void resize(V &, size_type , linalg_const)
  { GMM_ASSERT1(false, "You cannot resize a reference"); }

  ///@endcond
  /** resize a vector. */
   template <typename V> inline
  void resize(V &v, size_type n) {
    resize(v, n, typename linalg_traits<V>::is_reference());
  }
  ///@cond DOXY_SHOW_ALL_FUNCTIONS

  /** resize a matrix **/
  template <typename M> inline
  void resize(M &v, size_type m, size_type n, linalg_false) {
    linalg_traits<M>::resize(v, m, n);
  }

  template <typename M> inline
  void resize(M &, size_type, size_type, linalg_modifiable)
  { GMM_ASSERT1(false, "You cannot resize a reference"); }

  template <typename M> inline
  void resize(M &, size_type, size_type, linalg_const)
  { GMM_ASSERT1(false, "You cannot resize a reference"); }

  ///@endcond 
  /** resize a matrix */
  template <typename M> inline
  void resize(M &v, size_type m, size_type n)
  { resize(v, m, n, typename linalg_traits<M>::is_reference()); }
  ///@cond

  template <typename M> inline
  void reshape(M &v, size_type m, size_type n, linalg_false)
  { linalg_traits<M>::reshape(v, m, n); }

  template <typename M> inline
  void reshape(M &, size_type, size_type, linalg_modifiable)
  { GMM_ASSERT1(false, "You cannot reshape a reference"); }

  template <typename M> inline
  void reshape(M &, size_type, size_type, linalg_const)
  { GMM_ASSERT1(false, "You cannot reshape a reference"); }

  ///@endcond 
  /** reshape a matrix */
  template <typename M> inline
  void reshape(M &v, size_type m, size_type n)
  { reshape(v, m, n, typename linalg_traits<M>::is_reference()); }
  ///@cond DOXY_SHOW_ALL_FUNCTIONS
  

  /* ******************************************************************** */
  /*		Scalar product                             		  */
  /* ******************************************************************** */

  ///@endcond
  /** scalar product between two vectors */
  template <typename V1, typename V2> inline
  typename strongest_value_type<V1,V2>::value_type
    vect_sp(const V1 &v1, const V2 &v2) {
    GMM_ASSERT2(vect_size(v1) == vect_size(v2), "dimensions mismatch, "
                << vect_size(v1) << " !=" << vect_size(v2));
    return vect_sp(v1, v2,
		   typename linalg_traits<V1>::storage_type(), 
		   typename linalg_traits<V2>::storage_type());
  }

  /** scalar product between two vectors, using a matrix.
      @param ps the matrix of the scalar product.
      @param v1 the first vector
      @param v2 the second vector
  */
  template <typename MATSP, typename V1, typename V2> inline
  typename strongest_value_type3<V1,V2,MATSP>::value_type
    vect_sp(const MATSP &ps, const V1 &v1, const V2 &v2) {
    return vect_sp_with_mat(ps, v1, v2,
			    typename linalg_traits<MATSP>::sub_orientation());
  }
  ///@cond DOXY_SHOW_ALL_FUNCTIONS

  template <typename MATSP, typename V1, typename V2> inline
    typename strongest_value_type3<V1,V2,MATSP>::value_type
    vect_sp_with_mat(const MATSP &ps, const V1 &v1, const V2 &v2, row_major) {
    return vect_sp_with_matr(ps, v1, v2, 
			     typename linalg_traits<V2>::storage_type());
  }

  template <typename MATSP, typename V1, typename V2> inline 
    typename strongest_value_type3<V1,V2,MATSP>::value_type
    vect_sp_with_matr(const MATSP &ps, const V1 &v1, const V2 &v2,
		      abstract_sparse) {
    GMM_ASSERT2(vect_size(v1) == mat_ncols(ps) &&
                vect_size(v2) == mat_nrows(ps), "dimensions mismatch");
    size_type nr = mat_nrows(ps);
    typename linalg_traits<V2>::const_iterator
      it = vect_const_begin(v2), ite = vect_const_end(v2);
    typename strongest_value_type3<V1,V2,MATSP>::value_type res(0);
    for (; it != ite; ++it)
      res += vect_sp(mat_const_row(ps, it.index()), v1)* (*it);
    return res;
  }

  template <typename MATSP, typename V1, typename V2> inline
    typename strongest_value_type3<V1,V2,MATSP>::value_type
    vect_sp_with_matr(const MATSP &ps, const V1 &v1, const V2 &v2,
		      abstract_skyline)
  { return vect_sp_with_matr(ps, v1, v2, abstract_sparse()); }

  template <typename MATSP, typename V1, typename V2> inline
    typename strongest_value_type3<V1,V2,MATSP>::value_type
    vect_sp_with_matr(const MATSP &ps, const V1 &v1, const V2 &v2,
		      abstract_dense) {
    GMM_ASSERT2(vect_size(v1) == mat_ncols(ps) &&
                vect_size(v2) == mat_nrows(ps), "dimensions mismatch");
    typename linalg_traits<V2>::const_iterator
      it = vect_const_begin(v2), ite = vect_const_end(v2);
    typename strongest_value_type3<V1,V2,MATSP>::value_type res(0);
    for (size_type i = 0; it != ite; ++i, ++it)
      res += vect_sp(mat_const_row(ps, i), v1) * (*it);
    return res;
  }

  template <typename MATSP, typename V1, typename V2> inline
  typename strongest_value_type3<V1,V2,MATSP>::value_type
  vect_sp_with_mat(const MATSP &ps, const V1 &v1,const V2 &v2,row_and_col)
  { return vect_sp_with_mat(ps, v1, v2, row_major()); }

  template <typename MATSP, typename V1, typename V2> inline
  typename strongest_value_type3<V1,V2,MATSP>::value_type
  vect_sp_with_mat(const MATSP &ps, const V1 &v1, const V2 &v2,col_major){
    return vect_sp_with_matc(ps, v1, v2,
			     typename linalg_traits<V1>::storage_type());
  }

  template <typename MATSP, typename V1, typename V2> inline
    typename strongest_value_type3<V1,V2,MATSP>::value_type
    vect_sp_with_matc(const MATSP &ps, const V1 &v1, const V2 &v2,
		      abstract_sparse) {
    GMM_ASSERT2(vect_size(v1) == mat_ncols(ps) &&
                vect_size(v2) == mat_nrows(ps), "dimensions mismatch");
    typename linalg_traits<V1>::const_iterator
      it = vect_const_begin(v1), ite = vect_const_end(v1);
    typename strongest_value_type3<V1,V2,MATSP>::value_type res(0);
    for (; it != ite; ++it)
      res += vect_sp(mat_const_col(ps, it.index()), v2) * (*it);
    return res;
  }

  template <typename MATSP, typename V1, typename V2> inline
    typename strongest_value_type3<V1,V2,MATSP>::value_type
    vect_sp_with_matc(const MATSP &ps, const V1 &v1, const V2 &v2,
		      abstract_skyline)
  { return vect_sp_with_matc(ps, v1, v2, abstract_sparse()); }

  template <typename MATSP, typename V1, typename V2> inline
    typename strongest_value_type3<V1,V2,MATSP>::value_type
    vect_sp_with_matc(const MATSP &ps, const V1 &v1, const V2 &v2,
		      abstract_dense) {
    GMM_ASSERT2(vect_size(v1) == mat_ncols(ps) &&
                vect_size(v2) == mat_nrows(ps), "dimensions mismatch");
    typename linalg_traits<V1>::const_iterator
      it = vect_const_begin(v1), ite = vect_const_end(v1);
    typename strongest_value_type3<V1,V2,MATSP>::value_type res(0);
    for (size_type i = 0; it != ite; ++i, ++it)
      res += vect_sp(mat_const_col(ps, i), v2) * (*it);
    return res;
  }

  template <typename MATSP, typename V1, typename V2> inline
  typename strongest_value_type3<V1,V2,MATSP>::value_type
  vect_sp_with_mat(const MATSP &ps, const V1 &v1,const V2 &v2,col_and_row)
  { return vect_sp_with_mat(ps, v1, v2, col_major()); }

  template <typename MATSP, typename V1, typename V2> inline
  typename strongest_value_type3<V1,V2,MATSP>::value_type
  vect_sp_with_mat(const MATSP &ps, const V1 &v1, const V2 &v2,
		   abstract_null_type) {
    typename temporary_vector<V1>::vector_type w(mat_nrows(ps));
    GMM_WARNING2("Warning, a temporary is used in scalar product\n");
    mult(ps, v1, w); 
    return vect_sp(w, v2);
  }

  template <typename IT1, typename IT2> inline
  typename strongest_numeric_type<typename std::iterator_traits<IT1>::value_type,
				  typename std::iterator_traits<IT2>::value_type>::T
  vect_sp_dense_(IT1 it, IT1 ite, IT2 it2) {
    typename strongest_numeric_type<typename std::iterator_traits<IT1>::value_type,
      typename std::iterator_traits<IT2>::value_type>::T res(0);
    for (; it != ite; ++it, ++it2) res += (*it) * (*it2);
    return res;
  }
  
  template <typename IT1, typename V> inline
    typename strongest_numeric_type<typename std::iterator_traits<IT1>::value_type,
				    typename linalg_traits<V>::value_type>::T
    vect_sp_sparse_(IT1 it, IT1 ite, const V &v) {
      typename strongest_numeric_type<typename std::iterator_traits<IT1>::value_type,
	typename linalg_traits<V>::value_type>::T res(0);
    for (; it != ite; ++it) res += (*it) * v[it.index()];
    return res;
  }

  template <typename V1, typename V2> inline
  typename strongest_value_type<V1,V2>::value_type
    vect_sp(const V1 &v1, const V2 &v2, abstract_dense, abstract_dense) {
    return vect_sp_dense_(vect_const_begin(v1), vect_const_end(v1),
			  vect_const_begin(v2));
  }

  template <typename V1, typename V2> inline
    typename strongest_value_type<V1,V2>::value_type
    vect_sp(const V1 &v1, const V2 &v2, abstract_skyline, abstract_dense) {
    typename linalg_traits<V1>::const_iterator it1 = vect_const_begin(v1),
      ite =  vect_const_end(v1);
    typename linalg_traits<V2>::const_iterator it2 = vect_const_begin(v2);
    return vect_sp_dense_(it1, ite, it2 + it1.index());
  }

  template <typename V1, typename V2> inline
    typename strongest_value_type<V1,V2>::value_type
    vect_sp(const V1 &v1, const V2 &v2, abstract_dense, abstract_skyline) {
    typename linalg_traits<V2>::const_iterator it1 = vect_const_begin(v2),
      ite =  vect_const_end(v2);
    typename linalg_traits<V1>::const_iterator it2 = vect_const_begin(v1);
    return vect_sp_dense_(it1, ite, it2 + it1.index());
  }

  template <typename V1, typename V2> inline
    typename strongest_value_type<V1,V2>::value_type
    vect_sp(const V1 &v1, const V2 &v2, abstract_skyline, abstract_skyline) {
    typedef typename strongest_value_type<V1,V2>::value_type T;
    typename linalg_traits<V1>::const_iterator it1 = vect_const_begin(v1),
      ite1 =  vect_const_end(v1);
    typename linalg_traits<V2>::const_iterator it2 = vect_const_begin(v2),
      ite2 =  vect_const_end(v2);
    size_type n = std::min(ite1.index(), ite2.index());
    size_type l = std::max(it1.index(), it2.index());

    if (l < n) {
      size_type m = l - it1.index(), p = l - it2.index(), q = m + n - l;
      return vect_sp_dense_(it1+m, it1+q, it2 + p);
    }
    return T(0);
  }

  template <typename V1, typename V2> inline
    typename strongest_value_type<V1,V2>::value_type
  vect_sp(const V1 &v1, const V2 &v2,abstract_sparse,abstract_dense) {
    return vect_sp_sparse_(vect_const_begin(v1), vect_const_end(v1), v2);
  }

  template <typename V1, typename V2> inline
    typename strongest_value_type<V1,V2>::value_type
    vect_sp(const V1 &v1, const V2 &v2, abstract_sparse, abstract_skyline) {
    return vect_sp_sparse_(vect_const_begin(v1), vect_const_end(v1), v2);
  }

  template <typename V1, typename V2> inline
    typename strongest_value_type<V1,V2>::value_type
    vect_sp(const V1 &v1, const V2 &v2, abstract_skyline, abstract_sparse) {
    return vect_sp_sparse_(vect_const_begin(v2), vect_const_end(v2), v1);
  }

  template <typename V1, typename V2> inline
    typename strongest_value_type<V1,V2>::value_type
    vect_sp(const V1 &v1, const V2 &v2, abstract_dense,abstract_sparse) {
    return vect_sp_sparse_(vect_const_begin(v2), vect_const_end(v2), v1);
  }


  template <typename V1, typename V2> inline
  typename strongest_value_type<V1,V2>::value_type
  vect_sp_sparse_sparse(const V1 &v1, const V2 &v2, linalg_true) {
    typename linalg_traits<V1>::const_iterator it1 = vect_const_begin(v1),
      ite1 = vect_const_end(v1);
    typename linalg_traits<V2>::const_iterator it2 = vect_const_begin(v2),
      ite2 = vect_const_end(v2);
    typename strongest_value_type<V1,V2>::value_type res(0);
    
    while (it1 != ite1 && it2 != ite2) {
      if (it1.index() == it2.index())
	{ res += (*it1) * *it2; ++it1; ++it2; }
      else if (it1.index() < it2.index()) ++it1; else ++it2;
    }
    return res;
  }

  template <typename V1, typename V2> inline
  typename strongest_value_type<V1,V2>::value_type
  vect_sp_sparse_sparse(const V1 &v1, const V2 &v2, linalg_false) {
    return vect_sp_sparse_(vect_const_begin(v1), vect_const_end(v1), v2);
  }

  template <typename V1, typename V2> inline
    typename strongest_value_type<V1,V2>::value_type
    vect_sp(const V1 &v1, const V2 &v2,abstract_sparse,abstract_sparse) {
    return vect_sp_sparse_sparse(v1, v2,
	    typename linalg_and<typename linalg_traits<V1>::index_sorted,
	    typename linalg_traits<V2>::index_sorted>::bool_type());
  }
  
  /* ******************************************************************** */
  /*		Hermitian product                             		  */
  /* ******************************************************************** */
  ///@endcond
  /** Hermitian product. */
  template <typename V1, typename V2>
  inline typename strongest_value_type<V1,V2>::value_type
  vect_hp(const V1 &v1, const V2 &v2)
  { return vect_sp(v1, conjugated(v2)); }

  /** Hermitian product with a matrix. */
  template <typename MATSP, typename V1, typename V2> inline
  typename strongest_value_type3<V1,V2,MATSP>::value_type
    vect_hp(const MATSP &ps, const V1 &v1, const V2 &v2) {
    return vect_sp(ps, v1, gmm::conjugated(v2));
  }

  /* ******************************************************************** */
  /*		Trace of a matrix                             		  */
  /* ******************************************************************** */
  
  /** Trace of a matrix */
   template <typename M>
   typename linalg_traits<M>::value_type
   mat_trace(const M &m) {
     typedef typename linalg_traits<M>::value_type T;
     T res(0);
     for (size_type i = 0; i < std::min(mat_nrows(m), mat_ncols(m)); ++i)
       res += m(i,i);
     return res;
  }

  /* ******************************************************************** */
  /*		Euclidean norm                             		  */
  /* ******************************************************************** */

  /** squared Euclidean norm of a vector. */
  template <typename V>
  typename number_traits<typename linalg_traits<V>::value_type>
  ::magnitude_type
  vect_norm2_sqr(const V &v) {
    typedef typename linalg_traits<V>::value_type T;
    typedef typename number_traits<T>::magnitude_type R;
    typename linalg_traits<V>::const_iterator
      it = vect_const_begin(v), ite = vect_const_end(v);
    R res(0);
    for (; it != ite; ++it) res += gmm::abs_sqr(*it);
    return res;
  }

  /** Euclidean norm of a vector. */
  template <typename V> inline
   typename number_traits<typename linalg_traits<V>::value_type>
   ::magnitude_type 
  vect_norm2(const V &v)
  { return sqrt(vect_norm2_sqr(v)); }
  

  /** squared Euclidean distance between two vectors */
  template <typename V1, typename V2> inline
   typename number_traits<typename linalg_traits<V1>::value_type>
   ::magnitude_type
  vect_dist2_sqr(const V1 &v1, const V2 &v2) { // not fully optimized 
    typedef typename linalg_traits<V1>::value_type T;
    typedef typename number_traits<T>::magnitude_type R;
    typename linalg_traits<V1>::const_iterator
      it1 = vect_const_begin(v1), ite1 = vect_const_end(v1);
    typename linalg_traits<V2>::const_iterator
      it2 = vect_const_begin(v2), ite2 = vect_const_end(v2);
    size_type k1(0), k2(0);
    R res(0);
    while (it1 != ite1 && it2 != ite2) {
      size_type i1 = index_of_it(it1, k1,
				 typename linalg_traits<V1>::storage_type());
      size_type i2 = index_of_it(it2, k2,
				 typename linalg_traits<V2>::storage_type());

      if (i1 == i2) {
	res += gmm::abs_sqr(*it2 - *it1); ++it1; ++k1; ++it2; ++k2;
      }
      else if (i1 < i2) {
	res += gmm::abs_sqr(*it1); ++it1; ++k1; 
      }
      else  {
	res += gmm::abs_sqr(*it2); ++it2; ++k2; 
      }
    }
    while (it1 != ite1) { res += gmm::abs_sqr(*it1); ++it1; }
    while (it2 != ite2) { res += gmm::abs_sqr(*it2); ++it2; }
    return res;
  }
 
  /** Euclidean distance between two vectors */
  template <typename V1, typename V2> inline
   typename number_traits<typename linalg_traits<V1>::value_type>
   ::magnitude_type
  vect_dist2(const V1 &v1, const V2 &v2)
  { return sqrt(vect_dist2_sqr(v1, v2)); }
  ///@cond DOXY_SHOW_ALL_FUNCTIONS
  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_euclidean_norm_sqr(const M &m, row_major) {
    typename number_traits<typename linalg_traits<M>::value_type>
      ::magnitude_type res(0);
    for (size_type i = 0; i < mat_nrows(m); ++i)
      res += vect_norm2_sqr(mat_const_row(m, i));
    return res;
  }

  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_euclidean_norm_sqr(const M &m, col_major) {
    typename number_traits<typename linalg_traits<M>::value_type>
      ::magnitude_type res(0);
    for (size_type i = 0; i < mat_ncols(m); ++i)
      res += vect_norm2_sqr(mat_const_col(m, i));
    return res;
  }
  ///@endcond
  /** squared Euclidean norm of a matrix. */
  template <typename M> inline
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_euclidean_norm_sqr(const M &m) {
    return mat_euclidean_norm_sqr(m,
		     typename principal_orientation_type<typename
		     linalg_traits<M>::sub_orientation>::potype());
  }

  /** Euclidean norm of a matrix. */
  template <typename M> inline
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_euclidean_norm(const M &m)
  { return gmm::sqrt(mat_euclidean_norm_sqr(m)); }

  /* ******************************************************************** */
  /*		vector norm1                                    	  */
  /* ******************************************************************** */
  /** 1-norm of a vector */
  template <typename V>
  typename number_traits<typename linalg_traits<V>::value_type>
  ::magnitude_type
  vect_norm1(const V &v) {
    typename linalg_traits<V>::const_iterator
      it = vect_const_begin(v), ite = vect_const_end(v);
    typename number_traits<typename linalg_traits<V>::value_type>
	::magnitude_type res(0);
    for (; it != ite; ++it) res += gmm::abs(*it);
    return res;
  }

  /* ******************************************************************** */
  /*		vector Infinity norm                              	  */
  /* ******************************************************************** */
  /** Infinity norm of a vector. */
  template <typename V>
  typename number_traits<typename linalg_traits<V>::value_type>
  ::magnitude_type 
  vect_norminf(const V &v) {
    typename linalg_traits<V>::const_iterator
      it = vect_const_begin(v), ite = vect_const_end(v);
      typename number_traits<typename linalg_traits<V>::value_type>
	::magnitude_type res(0);
    for (; it != ite; ++it) res = std::max(res, gmm::abs(*it));
    return res;
  }

  /* ******************************************************************** */
  /*		matrix norm1                                    	  */
  /* ******************************************************************** */
  ///@cond DOXY_SHOW_ALL_FUNCTIONS
  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_norm1(const M &m, col_major) {
    typename number_traits<typename linalg_traits<M>::value_type>
      ::magnitude_type res(0);
    for (size_type i = 0; i < mat_ncols(m); ++i)
      res = std::max(res, vect_norm1(mat_const_col(m,i)));
    return res;
  }

  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_norm1(const M &m, row_major) {
    typedef typename linalg_traits<M>::value_type T;
    typedef typename number_traits<T>::magnitude_type R;
    typedef typename linalg_traits<M>::storage_type store_type;
    
    std::vector<R> aux(mat_ncols(m));
    for (size_type i = 0; i < mat_nrows(m); ++i) {
      typedef typename linalg_traits<M>::const_sub_row_type row_type;
      row_type row = mat_const_row(m, i);
      typename linalg_traits<row_type>::const_iterator
	it = vect_const_begin(row), ite = vect_const_end(row);
      for (size_type k = 0; it != ite; ++it, ++k)
	aux[index_of_it(it, k, store_type())] += gmm::abs(*it);
    }
    return vect_norminf(aux);
  }

  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_norm1(const M &m, col_and_row)
  { return mat_norm1(m, col_major()); }

  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_norm1(const M &m, row_and_col)
  { return mat_norm1(m, col_major()); }
  ///@endcond
  /** 1-norm of a matrix */
  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_norm1(const M &m) {
    return mat_norm1(m, typename linalg_traits<M>::sub_orientation());
  }


  /* ******************************************************************** */
  /*		matrix Infinity norm                              	  */
  /* ******************************************************************** */
  ///@cond DOXY_SHOW_ALL_FUNCTIONS
  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_norminf(const M &m, row_major) {
    typename number_traits<typename linalg_traits<M>::value_type>
      ::magnitude_type res(0);
    for (size_type i = 0; i < mat_nrows(m); ++i)
      res = std::max(res, vect_norm1(mat_const_row(m,i)));
    return res;
  }

  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_norminf(const M &m, col_major) {
    typedef typename linalg_traits<M>::value_type T;
    typedef typename number_traits<T>::magnitude_type R;
    typedef typename linalg_traits<M>::storage_type store_type;
    
    std::vector<R> aux(mat_nrows(m));
    for (size_type i = 0; i < mat_ncols(m); ++i) {
      typedef typename linalg_traits<M>::const_sub_col_type col_type;
      col_type col = mat_const_col(m, i);
      typename linalg_traits<col_type>::const_iterator
	it = vect_const_begin(col), ite = vect_const_end(col);
      for (size_type k = 0; it != ite; ++it, ++k)
	aux[index_of_it(it, k, store_type())] += gmm::abs(*it);
    }
    return vect_norminf(aux);
  }

  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_norminf(const M &m, col_and_row)
  { return mat_norminf(m, row_major()); }

  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_norminf(const M &m, row_and_col)
  { return mat_norminf(m, row_major()); }
  ///@endcond
  /** infinity-norm of a matrix.*/
  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_norminf(const M &m) {
    return mat_norminf(m, typename linalg_traits<M>::sub_orientation());
  }

  /* ******************************************************************** */
  /*		Max norm for matrices                              	  */
  /* ******************************************************************** */
  ///@cond DOXY_SHOW_ALL_FUNCTIONS
  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_maxnorm(const M &m, row_major) {
    typename number_traits<typename linalg_traits<M>::value_type>
      ::magnitude_type res(0);
    for (size_type i = 0; i < mat_nrows(m); ++i)
      res = std::max(res, vect_norminf(mat_const_row(m,i)));
    return res;
  }

  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_maxnorm(const M &m, col_major) {
    typename number_traits<typename linalg_traits<M>::value_type>
      ::magnitude_type res(0);
    for (size_type i = 0; i < mat_ncols(m); ++i)
      res = std::max(res, vect_norminf(mat_const_col(m,i)));
    return res;
  }
  ///@endcond
  /** max-norm of a matrix. */
  template <typename M>
   typename number_traits<typename linalg_traits<M>::value_type>
   ::magnitude_type
   mat_maxnorm(const M &m) {
    return mat_maxnorm(m,
		     typename principal_orientation_type<typename
		     linalg_traits<M>::sub_orientation>::potype());
  }

  /* ******************************************************************** */
  /*		Clean                                    		  */
  /* ******************************************************************** */
  /** Clean a vector or matrix (replace near-zero entries with zeroes).   */
  
  template <typename L> inline void clean(L &l, double threshold);

  ///@cond DOXY_SHOW_ALL_FUNCTIONS

  template <typename L, typename T>
  void clean(L &l, double threshold, abstract_dense, T) {
    typedef typename number_traits<T>::magnitude_type R;
    typename linalg_traits<L>::iterator it = vect_begin(l), ite = vect_end(l);
    for (; it != ite; ++it)
      if (gmm::abs(*it) < R(threshold)) *it = T(0);
  }

  template <typename L, typename T>
  void clean(L &l, double threshold, abstract_skyline, T)
  { gmm::clean(l, threshold, abstract_dense(), T()); }

  template <typename L, typename T>
  void clean(L &l, double threshold, abstract_sparse, T) {
    typedef typename number_traits<T>::magnitude_type R;
    typename linalg_traits<L>::iterator it = vect_begin(l), ite = vect_end(l);
    std::vector<size_type> ind;
    for (; it != ite; ++it)
      if (gmm::abs(*it) < R(threshold)) ind.push_back(it.index());
    for (size_type i = 0; i < ind.size(); ++i) l[ind[i]] = T(0);
  }
  
  template <typename L, typename T>
  void clean(L &l, double threshold, abstract_dense, std::complex<T>) {
    typename linalg_traits<L>::iterator it = vect_begin(l), ite = vect_end(l);
    for (; it != ite; ++it){
      if (gmm::abs((*it).real()) < T(threshold))
	*it = std::complex<T>(T(0), (*it).imag());
      if (gmm::abs((*it).imag()) < T(threshold))
	*it = std::complex<T>((*it).real(), T(0));
    }
  }

  template <typename L, typename T>
  void clean(L &l, double threshold, abstract_skyline, std::complex<T>)
  { gmm::clean(l, threshold, abstract_dense(), std::complex<T>()); }

  template <typename L, typename T>
  void clean(L &l, double threshold, abstract_sparse, std::complex<T>) {
    typename linalg_traits<L>::iterator it = vect_begin(l), ite = vect_end(l);
    std::vector<size_type> ind;
    for (; it != ite; ++it) {
      bool r = (gmm::abs((*it).real()) < T(threshold));
      bool i = (gmm::abs((*it).imag()) < T(threshold));
      if (r && i) ind.push_back(it.index());
      else if (r) *it = std::complex<T>(T(0), (*it).imag());
      else if (i) *it = std::complex<T>((*it).real(), T(0));
    }
    for (size_type i = 0; i < ind.size(); ++i)
      l[ind[i]] = std::complex<T>(T(0),T(0));
  }

  template <typename L> inline void clean(L &l, double threshold,
					  abstract_vector) {
    gmm::clean(l, threshold, typename linalg_traits<L>::storage_type(),
	       typename linalg_traits<L>::value_type());
  }

  template <typename L> inline void clean(const L &l, double threshold);

  template <typename L> void clean(L &l, double threshold, row_major) {
    for (size_type i = 0; i < mat_nrows(l); ++i)
      gmm::clean(mat_row(l, i), threshold);
  }

  template <typename L> void clean(L &l, double threshold, col_major) {
    for (size_type i = 0; i < mat_ncols(l); ++i)
      gmm::clean(mat_col(l, i), threshold);
  }

  template <typename L> inline void clean(L &l, double threshold,
					  abstract_matrix) {
    gmm::clean(l, threshold,
	       typename principal_orientation_type<typename
	       linalg_traits<L>::sub_orientation>::potype());
  }

  template <typename L> inline void clean(L &l, double threshold)
  { clean(l, threshold, typename linalg_traits<L>::linalg_type()); }
 
  template <typename L> inline void clean(const L &l, double threshold)
  { gmm::clean(linalg_const_cast(l), threshold); }

  /* ******************************************************************** */
  /*		Copy                                    		  */
  /* ******************************************************************** */
  ///@endcond
  /** Copy vectors or matrices. 
      @param l1 source vector or matrix.
      @param l2 destination.
  */
  template <typename L1, typename L2> inline
  void copy(const L1& l1, L2& l2) { 
    if ((const void *)(&l1) != (const void *)(&l2)) {
      if (same_origin(l1,l2))
	GMM_WARNING2("Warning : a conflict is possible in copy\n");
     
      copy(l1, l2, typename linalg_traits<L1>::linalg_type(),
	   typename linalg_traits<L2>::linalg_type());
    }
  }
  ///@cond DOXY_SHOW_ALL_FUNCTIONS

  template <typename L1, typename L2> inline
  void copy(const L1& l1, const L2& l2) { copy(l1, linalg_const_cast(l2)); }

  template <typename L1, typename L2> inline
  void copy(const L1& l1, L2& l2, abstract_vector, abstract_vector) {
    GMM_ASSERT2(vect_size(l1) == vect_size(l2), "dimensions mismatch, "
                << vect_size(l1) << " !=" << vect_size(l2));
    copy_vect(l1, l2, typename linalg_traits<L1>::storage_type(),
	      typename linalg_traits<L2>::storage_type());
  }

  template <typename L1, typename L2> inline
  void copy(const L1& l1, L2& l2, abstract_matrix, abstract_matrix) {
    size_type m = mat_nrows(l1), n = mat_ncols(l1);
    if (!m || !n) return;
    GMM_ASSERT2(n==mat_ncols(l2) && m==mat_nrows(l2), "dimensions mismatch");
    copy_mat(l1, l2, typename linalg_traits<L1>::sub_orientation(),
	     typename linalg_traits<L2>::sub_orientation());
  }

  template <typename V1, typename V2, typename C1, typename C2> inline 
  void copy_vect(const V1 &v1, const V2 &v2, C1, C2)
  { copy_vect(v1, const_cast<V2 &>(v2), C1(), C2()); }
  

  template <typename L1, typename L2>
  void copy_mat_by_row(const L1& l1, L2& l2) {
    size_type nbr = mat_nrows(l1);
    for (size_type i = 0; i < nbr; ++i)
      copy_vect(mat_const_row(l1, i), mat_row(l2, i),
      		typename linalg_traits<L1>::storage_type(),
		typename linalg_traits<L2>::storage_type());
  }

  template <typename L1, typename L2>
  void copy_mat_by_col(const L1 &l1, L2 &l2) {
    size_type nbc = mat_ncols(l1);
    for (size_type i = 0; i < nbc; ++i) {
      copy_vect(mat_const_col(l1, i), mat_col(l2, i),
      		typename linalg_traits<L1>::storage_type(),
		typename linalg_traits<L2>::storage_type());
    }
  }

  template <typename L1, typename L2> inline
  void copy_mat(const L1& l1, L2& l2, row_major, row_major)
  { copy_mat_by_row(l1, l2); }

  template <typename L1, typename L2> inline
  void copy_mat(const L1& l1, L2& l2, row_major, row_and_col)
  { copy_mat_by_row(l1, l2); }

  template <typename L1, typename L2> inline
  void copy_mat(const L1& l1, L2& l2, row_and_col, row_and_col)
  { copy_mat_by_row(l1, l2); }

  template <typename L1, typename L2> inline
  void copy_mat(const L1& l1, L2& l2, row_and_col, row_major)
  { copy_mat_by_row(l1, l2); }

  template <typename L1, typename L2> inline
  void copy_mat(const L1& l1, L2& l2, col_and_row, row_major)
  { copy_mat_by_row(l1, l2); }

  template <typename L1, typename L2> inline
  void copy_mat(const L1& l1, L2& l2, row_major, col_and_row)
  { copy_mat_by_row(l1, l2); }

  template <typename L1, typename L2> inline
  void copy_mat(const L1& l1, L2& l2, col_and_row, row_and_col)
  { copy_mat_by_row(l1, l2); }

  template <typename L1, typename L2> inline
  void copy_mat(const L1& l1, L2& l2, row_and_col, col_and_row)
  { copy_mat_by_row(l1, l2); }

  template <typename L1, typename L2> inline
  void copy_mat(const L1& l1, L2& l2, col_major, col_major)
  { copy_mat_by_col(l1, l2); }

  template <typename L1, typename L2> inline
  void copy_mat(const L1& l1, L2& l2, col_major, col_and_row)
  { copy_mat_by_col(l1, l2); }

  template <typename L1, typename L2> inline
  void copy_mat(const L1& l1, L2& l2, col_major, row_and_col)
  { copy_mat_by_col(l1, l2); }

  template <typename L1, typename L2> inline
  void copy_mat(const L1& l1, L2& l2, row_and_col, col_major)
  { copy_mat_by_col(l1, l2); }

  template <typename L1, typename L2> inline
  void copy_mat(const L1& l1, L2& l2, col_and_row, col_major)
  { copy_mat_by_col(l1, l2); }

  template <typename L1, typename L2> inline
  void copy_mat(const L1& l1, L2& l2, col_and_row, col_and_row)
  { copy_mat_by_col(l1, l2); }
  
  template <typename L1, typename L2> inline
  void copy_mat_mixed_rc(const L1& l1, L2& l2, size_type i) {
    copy_mat_mixed_rc(l1, l2, i, typename linalg_traits<L1>::storage_type());
  }

  template <typename L1, typename L2>
  void copy_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_sparse) {
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (; it != ite; ++it)
      l2(i, it.index()) = *it;
  }

  template <typename L1, typename L2>
  void copy_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_skyline) {
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (; it != ite; ++it)
      l2(i, it.index()) = *it;
  }

  template <typename L1, typename L2>
  void copy_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_dense) {
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (size_type j = 0; it != ite; ++it, ++j) l2(i, j) = *it;
  }

  template <typename L1, typename L2> inline
  void copy_mat_mixed_cr(const L1& l1, L2& l2, size_type i) {
    copy_mat_mixed_cr(l1, l2, i, typename linalg_traits<L1>::storage_type());
  }

  template <typename L1, typename L2>
  void copy_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_sparse) {
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (; it != ite; ++it) l2(it.index(), i) = *it;
  }

  template <typename L1, typename L2>
  void copy_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_skyline) {
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (; it != ite; ++it) l2(it.index(), i) = *it;
  }

  template <typename L1, typename L2>
  void copy_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_dense) {
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (size_type j = 0; it != ite; ++it, ++j) l2(j, i) = *it;
  }

  template <typename L1, typename L2>
  void copy_mat(const L1& l1, L2& l2, row_major, col_major) {
    clear(l2);
    size_type nbr = mat_nrows(l1);
    for (size_type i = 0; i < nbr; ++i)
      copy_mat_mixed_rc(mat_const_row(l1, i), l2, i);
  }
  
  template <typename L1, typename L2>
  void copy_mat(const L1& l1, L2& l2, col_major, row_major) {
    clear(l2);
    size_type nbc = mat_ncols(l1);
    for (size_type i = 0; i < nbc; ++i)
      copy_mat_mixed_cr(mat_const_col(l1, i), l2, i);
  }
  
  template <typename L1, typename L2> inline
  void copy_vect(const L1 &l1, L2 &l2, abstract_dense, abstract_dense) {
    std::copy(vect_const_begin(l1), vect_const_end(l1), vect_begin(l2));
  }

  template <typename L1, typename L2> inline // to be optimised ?
  void copy_vect(const L1 &l1, L2 &l2, abstract_skyline, abstract_skyline) {
    typename linalg_traits<L1>::const_iterator it1 = vect_const_begin(l1),
      ite1 = vect_const_end(l1);
    while (it1 != ite1 && *it1 == typename linalg_traits<L1>::value_type(0))
      ++it1;

    if (ite1 - it1 > 0) {
      clear(l2);
      typename linalg_traits<L2>::iterator it2 = vect_begin(l2), 
	ite2 = vect_end(l2);
      while (*(ite1-1) == typename linalg_traits<L1>::value_type(0)) ite1--;

      if (it2 == ite2) {
	l2[it1.index()] = *it1; ++it1;
	l2[ite1.index()-1] = *(ite1-1); --ite1;
	if (it1 < ite1)
	  { it2 = vect_begin(l2); ++it2; std::copy(it1, ite1, it2); }
      }
      else {
	ptrdiff_t m = it1.index() - it2.index();
	if (m >= 0 && ite1.index() <= ite2.index())
	  std::copy(it1, ite1, it2 + m);
	else {
	  if (m < 0) l2[it1.index()] = *it1;
	  if (ite1.index() > ite2.index()) l2[ite1.index()-1] = *(ite1-1);
	  it2 = vect_begin(l2); ite2 = vect_end(l2);
	  m = it1.index() - it2.index();
	  std::copy(it1, ite1, it2 + m);
	}
      }
    }
  }
  
  template <typename L1, typename L2>
  void copy_vect(const L1& l1, L2& l2, abstract_sparse, abstract_dense) {
    clear(l2);
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (; it != ite; ++it) { l2[it.index()] = *it; }
  }

  template <typename L1, typename L2>
  void copy_vect(const L1& l1, L2& l2, abstract_sparse, abstract_skyline) {
    clear(l2);
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (; it != ite; ++it) l2[it.index()] = *it;
  }

  template <typename L1, typename L2>
  void copy_vect(const L1& l1, L2& l2, abstract_skyline, abstract_dense) {
    typedef typename linalg_traits<L1>::value_type T;
    typedef typename linalg_traits<L1>::const_iterator l1_const_iterator;
    typedef typename linalg_traits<L2>::iterator l2_iterator;
    l1_const_iterator it = vect_const_begin(l1), ite = vect_const_end(l1);
    if (it == ite)
      gmm::clear(l2);
    else {
      l2_iterator it2 = vect_begin(l2), ite2 = vect_end(l2);
      
      size_type i = it.index(), j;
      for (j = 0; j < i; ++j, ++it2) *it2 = T(0);
      for (; it != ite; ++it, ++it2) *it2 = *it;
      for (; it2 != ite2; ++it2) *it2 = T(0);
    }
  }
    
  template <typename L1, typename L2>
  void copy_vect(const L1& l1, L2& l2, abstract_sparse, abstract_sparse) {
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    clear(l2);
    for (; it != ite; ++it)
      if (*it != (typename linalg_traits<L1>::value_type)(0))
	l2[it.index()] = *it;
  }
  
  template <typename L1, typename L2>
  void copy_vect(const L1& l1, L2& l2, abstract_dense, abstract_sparse) {
    clear(l2);
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (size_type i = 0; it != ite; ++it, ++i)
      if (*it != (typename linalg_traits<L1>::value_type)(0))
	l2[i] = *it;
  }

  template <typename L1, typename L2> // to be optimised ...
  void copy_vect(const L1& l1, L2& l2, abstract_dense, abstract_skyline) {
    clear(l2);
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (size_type i = 0; it != ite; ++it, ++i)
      if (*it != (typename linalg_traits<L1>::value_type)(0))
	l2[i] = *it;
  }

  
  template <typename L1, typename L2>
  void copy_vect(const L1& l1, L2& l2, abstract_skyline, abstract_sparse) {
    clear(l2);
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (; it != ite; ++it)
      if (*it != (typename linalg_traits<L1>::value_type)(0))
	l2[it.index()] = *it;
  }

  /* ******************************************************************** */
  /*   Matrix and vector addition                                         */
  /*   algorithms are built in order to avoid some conflicts with         */
  /*   repeated arguments or with overlapping part of a same object.      */
  /*   In the latter case, conflicts are still possible.                  */
  /* ******************************************************************** */
  ///@endcond
  /** Add two vectors or matrices
      @param l1
      @param l2 contains on output, l2+l1.
  */
  template <typename L1, typename L2> inline
    void add(const L1& l1, L2& l2) {
      add_spec(l1, l2, typename linalg_traits<L2>::linalg_type());
  }
  ///@cond

  template <typename L1, typename L2> inline
  void add(const L1& l1, const L2& l2) { add(l1, linalg_const_cast(l2)); }

  template <typename L1, typename L2> inline
    void add_spec(const L1& l1, L2& l2, abstract_vector) {
    GMM_ASSERT2(vect_size(l1) == vect_size(l2), "dimensions mismatch, "
                << vect_size(l1) << " !=" << vect_size(l2));
    add(l1, l2, typename linalg_traits<L1>::storage_type(),
	typename linalg_traits<L2>::storage_type());
  }

  template <typename L1, typename L2> inline
    void add_spec(const L1& l1, L2& l2, abstract_matrix) {
    GMM_ASSERT2(mat_nrows(l1)==mat_nrows(l2) && mat_ncols(l1)==mat_ncols(l2),
                "dimensions mismatch");
    add(l1, l2, typename linalg_traits<L1>::sub_orientation(),
	typename linalg_traits<L2>::sub_orientation());
  }

  template <typename L1, typename L2>
  void add(const L1& l1, L2& l2, row_major, row_major) {
    typename linalg_traits<L1>::const_row_iterator it1 = mat_row_begin(l1),
      ite = mat_row_end(l1);
    typename linalg_traits<L2>::row_iterator it2 = mat_row_begin(l2);
    for ( ; it1 != ite; ++it1, ++it2)
      add(linalg_traits<L1>::row(it1), linalg_traits<L2>::row(it2));
  }

  template <typename L1, typename L2>
  void add(const L1& l1, L2& l2, col_major, col_major) {
    typename linalg_traits<L1>::const_col_iterator
      it1 = mat_col_const_begin(l1),
      ite = mat_col_const_end(l1);
    typename linalg_traits<L2>::col_iterator it2 = mat_col_begin(l2);
    for ( ; it1 != ite; ++it1, ++it2)
      add(linalg_traits<L1>::col(it1),  linalg_traits<L2>::col(it2));
  }
  
    template <typename L1, typename L2> inline
  void add_mat_mixed_rc(const L1& l1, L2& l2, size_type i) {
    add_mat_mixed_rc(l1, l2, i, typename linalg_traits<L1>::storage_type());
  }

  template <typename L1, typename L2>
  void add_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_sparse) {
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (; it != ite; ++it) l2(i, it.index()) += *it;
  }

  template <typename L1, typename L2>
  void add_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_skyline) {
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (; it != ite; ++it) l2(i, it.index()) += *it;
  }

  template <typename L1, typename L2>
  void add_mat_mixed_rc(const L1& l1, L2& l2, size_type i, abstract_dense) {
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (size_type j = 0; it != ite; ++it, ++j) l2(i, j) += *it;
  }

  template <typename L1, typename L2> inline
  void add_mat_mixed_cr(const L1& l1, L2& l2, size_type i) {
    add_mat_mixed_cr(l1, l2, i, typename linalg_traits<L1>::storage_type());
  }

  template <typename L1, typename L2>
  void add_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_sparse) {
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (; it != ite; ++it) l2(it.index(), i) += *it;
  }

  template <typename L1, typename L2>
  void add_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_skyline) {
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (; it != ite; ++it) l2(it.index(), i) += *it;
  }

  template <typename L1, typename L2>
  void add_mat_mixed_cr(const L1& l1, L2& l2, size_type i, abstract_dense) {
    typename linalg_traits<L1>::const_iterator
      it  = vect_const_begin(l1), ite = vect_const_end(l1);
    for (size_type j = 0; it != ite; ++it, ++j) l2(j, i) += *it;
  }

  template <typename L1, typename L2>
  void add(const L1& l1, L2& l2, row_major, col_major) {
    size_type nbr = mat_nrows(l1);
    for (size_type i = 0; i < nbr; ++i)
      add_mat_mixed_rc(mat_const_row(l1, i), l2, i);
  }
  
  template <typename L1, typename L2>
  void add(const L1& l1, L2& l2, col_major, row_major) {
    size_type nbc = mat_ncols(l1);
    for (size_type i = 0; i < nbc; ++i)
      add_mat_mixed_cr(mat_const_col(l1, i), l2, i);
  }

  template <typename L1, typename L2> inline
  void add(const L1& l1, L2& l2, row_and_col, row_major)
  { add(l1, l2, row_major(), row_major()); }

  template <typename L1, typename L2> inline
  void add(const L1& l1, L2& l2, row_and_col, row_and_col)
  { add(l1, l2, row_major(), row_major()); }

  template <typename L1, typename L2> inline
  void add(const L1& l1, L2& l2, row_and_col, col_and_row)
  { add(l1, l2, row_major(), row_major()); }

  template <typename L1, typename L2> inline
  void add(const L1& l1, L2& l2, col_and_row, row_and_col)
  { add(l1, l2, row_major(), row_major()); }

  template <typename L1, typename L2> inline
  void add(const L1& l1, L2& l2, row_major, row_and_col)
  { add(l1, l2, row_major(), row_major()); }

  template <typename L1, typename L2> inline
  void add(const L1& l1, L2& l2, col_and_row, row_major)
  { add(l1, l2, row_major(), row_major()); }

  template <typename L1, typename L2> inline
  void add(const L1& l1, L2& l2, row_major, col_and_row)
  { add(l1, l2, row_major(), row_major()); }

  template <typename L1, typename L2> inline
  void add(const L1& l1, L2& l2, row_and_col, col_major)
  { add(l1, l2, col_major(), col_major()); }

  template <typename L1, typename L2> inline
  void add(const L1& l1, L2& l2, col_major, row_and_col)
  { add(l1, l2, col_major(), col_major()); }

  template <typename L1, typename L2> inline
  void add(const L1& l1, L2& l2, col_and_row, col_major)
  { add(l1, l2, col_major(), col_major()); }

  template <typename L1, typename L2> inline
  void add(const L1& l1, L2& l2, col_and_row, col_and_row)
  { add(l1, l2, col_major(), col_major()); }

  template <typename L1, typename L2> inline
  void add(const L1& l1, L2& l2, col_major, col_and_row)
  { add(l1, l2, col_major(), col_major()); }

  ///@endcond
  /** Addition of two vectors/matrices
      @param l1
      @param l2
      @param l3 contains l1+l2 on output
  */
  template <typename L1, typename L2, typename L3> inline
  void add(const L1& l1, const L2& l2, L3& l3) {
    add_spec(l1, l2, l3, typename linalg_traits<L2>::linalg_type());
  }
  ///@cond DOXY_SHOW_ALL_FUNCTIONS

  template <typename L1, typename L2, typename L3> inline
  void add(const L1& l1, const L2& l2, const L3& l3)
  { add(l1, l2, linalg_const_cast(l3)); }

  template <typename L1, typename L2, typename L3> inline
    void add_spec(const L1& l1, const L2& l2, L3& l3, abstract_matrix)
  { copy(l2, l3); add(l1, l3); }

  template <typename L1, typename L2, typename L3> inline
    void add_spec(const L1& l1, const L2& l2, L3& l3, abstract_vector) {
    GMM_ASSERT2(vect_size(l1) == vect_size(l2) &&
                vect_size(l1) == vect_size(l3), "dimensions mismatch");
    if ((const void *)(&l1) == (const void *)(&l3))
      add(l2, l3);
    else if ((const void *)(&l2) == (const void *)(&l3))
      add(l1, l3);
    else
      add(l1, l2, l3, typename linalg_traits<L1>::storage_type(),
	  typename linalg_traits<L2>::storage_type(),
	  typename linalg_traits<L3>::storage_type());
  }

  template <typename IT1, typename IT2, typename IT3>
    void add_full_(IT1 it1, IT2 it2, IT3 it3, IT3 ite) {
    for (; it3 != ite; ++it3, ++it2, ++it1) *it3 = *it1 + *it2;
  }

  template <typename IT1, typename IT2, typename IT3>
    void add_almost_full_(IT1 it1, IT1 ite1, IT2 it2, IT3 it3, IT3 ite3) {
    IT3 it = it3;
    for (; it != ite3; ++it, ++it2) *it = *it2;
    for (; it1 != ite1; ++it1)
      *(it3 + it1.index()) += *it1;
  }

  template <typename IT1, typename IT2, typename IT3>
  void add_to_full_(IT1 it1, IT1 ite1, IT2 it2, IT2 ite2,
		    IT3 it3, IT3 ite3) {
    typedef typename std::iterator_traits<IT3>::value_type T;
    IT3 it = it3;
    for (; it != ite3; ++it) *it = T(0);
    for (; it1 != ite1; ++it1) *(it3 + it1.index()) = *it1;
    for (; it2 != ite2; ++it2) *(it3 + it2.index()) += *it2;    
  }
  
  template <typename L1, typename L2, typename L3> inline
  void add(const L1& l1, const L2& l2, L3& l3,
	   abstract_dense, abstract_dense, abstract_dense) {
    add_full_(vect_const_begin(l1), vect_const_begin(l2),
	      vect_begin(l3), vect_end(l3));
  }
  
  // generic function for add(v1, v2, v3).
  // Need to be specialized to optimize particular additions.
  template <typename L1, typename L2, typename L3,
	    typename ST1, typename ST2, typename ST3>
  inline void add(const L1& l1, const L2& l2, L3& l3, ST1, ST2, ST3)
  { copy(l2, l3); add(l1, l3, ST1(), ST3()); }

  template <typename L1, typename L2, typename L3> inline
  void add(const L1& l1, const L2& l2, L3& l3,
	   abstract_sparse, abstract_dense, abstract_dense) {
    add_almost_full_(vect_const_begin(l1), vect_const_end(l1),
		     vect_const_begin(l2), vect_begin(l3), vect_end(l3));
  }
  
  template <typename L1, typename L2, typename L3> inline
  void add(const L1& l1, const L2& l2, L3& l3,
	   abstract_dense, abstract_sparse, abstract_dense)
  { add(l2, l1, l3, abstract_sparse(), abstract_dense(), abstract_dense()); }
  
  template <typename L1, typename L2, typename L3> inline
  void add(const L1& l1, const L2& l2, L3& l3,
	   abstract_sparse, abstract_sparse, abstract_dense) {
    add_to_full_(vect_const_begin(l1), vect_const_end(l1),
		 vect_const_begin(l2), vect_const_end(l2),
		 vect_begin(l3), vect_end(l3));
  }


  template <typename L1, typename L2, typename L3>
  void add_spspsp(const L1& l1, const L2& l2, L3& l3, linalg_true) {
    typename linalg_traits<L1>::const_iterator
      it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
    typename linalg_traits<L2>::const_iterator
      it2 = vect_const_begin(l2), ite2 = vect_const_end(l2);
    clear(l3);
    while (it1 != ite1 && it2 != ite2) {
      ptrdiff_t d = it1.index() - it2.index();
      if (d < 0)
	{ l3[it1.index()] += *it1; ++it1; }
      else if (d > 0)
	{ l3[it2.index()] += *it2; ++it2; }
      else
	{ l3[it1.index()] = *it1 + *it2; ++it1; ++it2; }
    }
    for (; it1 != ite1; ++it1) l3[it1.index()] += *it1;
    for (; it2 != ite2; ++it2) l3[it2.index()] += *it2;   
  }

  template <typename L1, typename L2, typename L3>
  void add_spspsp(const L1& l1, const L2& l2, L3& l3, linalg_false)
  { copy(l2, l3); add(l2, l3); }
  
  template <typename L1, typename L2, typename L3>
  void add(const L1& l1, const L2& l2, L3& l3,
	   abstract_sparse, abstract_sparse, abstract_sparse) {
    add_spspsp(l1, l2, l3, typename linalg_and<typename
	       linalg_traits<L1>::index_sorted,
	       typename linalg_traits<L2>::index_sorted>::bool_type());
  }

  template <typename L1, typename L2>
  void add(const L1& l1, L2& l2, abstract_dense, abstract_dense) {
    typename linalg_traits<L1>::const_iterator it1 = vect_const_begin(l1); 
    typename linalg_traits<L2>::iterator
             it2 = vect_begin(l2), ite = vect_end(l2);
    for (; it2 != ite; ++it2, ++it1) *it2 += *it1;
  }

  template <typename L1, typename L2>
  void add(const L1& l1, L2& l2, abstract_dense, abstract_skyline) {
    typedef typename linalg_traits<L1>::const_iterator const_l1_iterator;
    typedef typename linalg_traits<L2>::iterator l2_iterator;
    typedef typename linalg_traits<L1>::value_type T;

    const_l1_iterator it1 = vect_const_begin(l1), ite1 = vect_const_end(l1); 
    size_type i1 = 0, ie1 = vect_size(l1);
    while (it1 != ite1 && *it1 == T(0)) { ++it1; ++i1; }
    if (it1 != ite1) {
      l2_iterator it2 = vect_begin(l2), ite2 = vect_end(l2);
      while (ie1 && *(ite1-1) == T(0)) { ite1--; --ie1; }

      if (it2 == ite2 || i1 < it2.index()) {
	l2[i1] = *it1; ++i1; ++it1;
	if (it1 == ite1) return;
	it2 = vect_begin(l2); ite2 = vect_end(l2);
      }
      if (ie1 > ite2.index()) {
	--ite1; l2[ie1 - 1] = *ite1;
	it2 = vect_begin(l2);
      }
      it2 += i1 - it2.index();
      for (; it1 != ite1; ++it1, ++it2) { *it2 += *it1; }
    }
  }


  template <typename L1, typename L2>
  void add(const L1& l1, L2& l2, abstract_skyline, abstract_dense) {
    typename linalg_traits<L1>::const_iterator it1 = vect_const_begin(l1),
      ite1 = vect_const_end(l1);
    if (it1 != ite1) {
      typename linalg_traits<L2>::iterator it2 = vect_begin(l2);
      it2 += it1.index();
      for (; it1 != ite1; ++it2, ++it1) *it2 += *it1;
    }
  }

  
  template <typename L1, typename L2>
  void add(const L1& l1, L2& l2, abstract_sparse, abstract_dense) {
    typename linalg_traits<L1>::const_iterator
      it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
    for (; it1 != ite1; ++it1) l2[it1.index()] += *it1;
  }
  
  template <typename L1, typename L2>
  void add(const L1& l1, L2& l2, abstract_sparse, abstract_sparse) {
    typename linalg_traits<L1>::const_iterator
      it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
    for (; it1 != ite1; ++it1) l2[it1.index()] += *it1;
  }

  template <typename L1, typename L2>
  void add(const L1& l1, L2& l2, abstract_sparse, abstract_skyline) {
    typename linalg_traits<L1>::const_iterator
      it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
    for (; it1 != ite1; ++it1) l2[it1.index()] += *it1;
  }


  template <typename L1, typename L2>
  void add(const L1& l1, L2& l2, abstract_skyline, abstract_sparse) {
    typename linalg_traits<L1>::const_iterator
      it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
    for (; it1 != ite1; ++it1)
      if (*it1 != typename linalg_traits<L1>::value_type(0))
	l2[it1.index()] += *it1;
  }

  template <typename L1, typename L2>
  void add(const L1& l1, L2& l2, abstract_skyline, abstract_skyline) {
    typedef typename linalg_traits<L1>::const_iterator const_l1_iterator;
    typedef typename linalg_traits<L2>::iterator l2_iterator;
    typedef typename linalg_traits<L1>::value_type T1;
    typedef typename linalg_traits<L2>::value_type T2;

    const_l1_iterator it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
    
    while (it1 != ite1 && *it1 == T1(0)) ++it1;
    if (ite1 != it1) {
      l2_iterator it2 = vect_begin(l2), ite2 = vect_end(l2);
      while (*(ite1-1) == T1(0)) ite1--;
      if (it2 == ite2 || it1.index() < it2.index()) {
	l2[it1.index()] = T2(0);
	it2 = vect_begin(l2); ite2 = vect_end(l2);
      }
      if (ite1.index() > ite2.index()) {
	l2[ite1.index() - 1] = T2(0);
	it2 = vect_begin(l2); 
      }
      it2 += it1.index() - it2.index();
      for (; it1 != ite1; ++it1, ++it2) *it2 += *it1;
    }
  }
  
  template <typename L1, typename L2>
  void add(const L1& l1, L2& l2, abstract_dense, abstract_sparse) {
    typename linalg_traits<L1>::const_iterator
      it1 = vect_const_begin(l1), ite1 = vect_const_end(l1);
    for (size_type i = 0; it1 != ite1; ++it1, ++i)
      if (*it1 != typename linalg_traits<L1>::value_type(0)) l2[i] += *it1;
  } 

  /* ******************************************************************** */
  /*		Matrix-vector mult                                    	  */
  /* ******************************************************************** */
  ///@endcond
  /** matrix-vector or matrix-matrix product.
      @param l1 a matrix.
      @param l2 a vector or matrix.
      @param l3 the product l1*l2.
  */
  template <typename L1, typename L2, typename L3> inline
  void mult(const L1& l1, const L2& l2, L3& l3) {
    mult_dispatch(l1, l2, l3, typename linalg_traits<L2>::linalg_type());
  }
  ///@cond DOXY_SHOW_ALL_FUNCTIONS

  template <typename L1, typename L2, typename L3> inline
  void mult(const L1& l1, const L2& l2, const L3& l3)
  { mult(l1, l2, linalg_const_cast(l3)); }

  template <typename L1, typename L2, typename L3> inline
  void mult_dispatch(const L1& l1, const L2& l2, L3& l3, abstract_vector) {
    size_type m = mat_nrows(l1), n = mat_ncols(l1);
    if (!m || !n) { gmm::clear(l3); return; }
    GMM_ASSERT2(n==vect_size(l2) && m==vect_size(l3), "dimensions mismatch");
    if (!same_origin(l2, l3))
      mult_spec(l1, l2, l3, typename principal_orientation_type<typename
		linalg_traits<L1>::sub_orientation>::potype());
    else {
      GMM_WARNING2("Warning, A temporary is used for mult\n");
      typename temporary_vector<L3>::vector_type temp(vect_size(l3));
      mult_spec(l1, l2, temp, typename principal_orientation_type<typename
		linalg_traits<L1>::sub_orientation>::potype());
      copy(temp, l3);
    }
  }

  template <typename L1, typename L2, typename L3>
  void mult_by_row(const L1& l1, const L2& l2, L3& l3, abstract_sparse) {
    typedef typename  linalg_traits<L3>::value_type T;
    clear(l3);
    size_type nr = mat_nrows(l1);
    for (size_type i = 0; i < nr; ++i) {
      T aux = vect_sp(mat_const_row(l1, i), l2);
      if (aux != T(0)) l3[i] = aux;
    }
  }

  template <typename L1, typename L2, typename L3>
  void mult_by_row(const L1& l1, const L2& l2, L3& l3, abstract_skyline) {
    typedef typename  linalg_traits<L3>::value_type T;
    clear(l3); 
    size_type nr = mat_nrows(l1);
    for (size_type i = 0; i < nr; ++i) {
      T aux = vect_sp(mat_const_row(l1, i), l2);
      if (aux != T(0)) l3[i] = aux;
    }
  }
    
#ifdef STORM_HAVE_INTELTBB
    /* Official Intel Hint on blocked_range vs. linear iterators: http://software.intel.com/en-us/forums/topic/289505
     
     */
    template <typename IT1, typename IT2>
    class forward_range_mult {
        IT1 my_begin;
        IT1 my_end;
        IT2 my_begin_row;
        size_t my_size;
    public:
        IT1 begin() const {return my_begin;}
        IT2 begin_row() const {return my_begin_row;}
        IT1 end() const {return my_end;}
        bool empty() const {return my_begin==my_end;}
        bool is_divisible() const {return my_size>1;}
        forward_range_mult( IT1 first, IT1 last, IT2 row_first, size_t size ) : my_begin(first), my_end(last), my_begin_row(row_first), my_size(size) {
            assert( size==size_t(std::distance( first,last )));
        }
        forward_range_mult( IT1 first, IT1 last, IT2 row_first) : my_begin(first), my_end(last), my_begin_row(row_first) {
            my_size = std::distance( first,last );
        }
        forward_range_mult( forward_range_mult& r, tbb::split ) {
            size_t h = r.my_size/2;
            my_end = r.my_end;
            my_begin = r.my_begin;
            my_begin_row = r.my_begin_row;
            std::advance( my_begin, h ); // Might be scaling issue
            std::advance( my_begin_row, h );
            my_size = r.my_size-h;
            r.my_end = my_begin;
            r.my_size = h;
        }
    };
    
    
    template <typename L1, typename L2, typename L3>
    class tbbHelper_mult_by_row {
        L2 const* my_l2;
        
        // Typedefs for Iterator Types
        typedef typename linalg_traits<L3>::iterator frm_IT1;
        typedef typename linalg_traits<L1>::const_row_iterator frm_IT2;
        
    public:
        void operator()( const forward_range_mult<frm_IT1, frm_IT2>& r ) const {
            L2 const& l2 = *my_l2;
            
            frm_IT1 it = r.begin();
            frm_IT1 ite = r.end();
            frm_IT2 itr = r.begin_row();
            
            for (; it != ite; ++it, ++itr) {
                *it = vect_sp(linalg_traits<L1>::row(itr), l2,
                              typename linalg_traits<L1>::storage_type(),
                              typename linalg_traits<L2>::storage_type());
            }
        }
        
        tbbHelper_mult_by_row(L2 const* l2) :
        my_l2(l2)
        {}
    };
#endif

  template <typename L1, typename L2, typename L3>
  void mult_by_row(const L1& l1, const L2& l2, L3& l3, abstract_dense) {
    typename linalg_traits<L3>::iterator it=vect_begin(l3), ite=vect_end(l3);
    typename linalg_traits<L1>::const_row_iterator
      itr = mat_row_const_begin(l1); 
#ifdef STORM_HAVE_INTELTBB
      tbb::parallel_for(forward_range_mult<typename linalg_traits<L3>::iterator, typename linalg_traits<L1>::const_row_iterator>(it, ite, itr), tbbHelper_mult_by_row<L1, L2, L3>(&l2));
#else
      for (; it != ite; ++it, ++itr)
          *it = vect_sp(linalg_traits<L1>::row(itr), l2,
                typename linalg_traits<L1>::storage_type(),
                typename linalg_traits<L2>::storage_type());
#endif
  }

  template <typename L1, typename L2, typename L3>
  void mult_by_col(const L1& l1, const L2& l2, L3& l3, abstract_dense) {
    clear(l3);
    size_type nc = mat_ncols(l1);
    for (size_type i = 0; i < nc; ++i)
      add(scaled(mat_const_col(l1, i), l2[i]), l3);
  }

  template <typename L1, typename L2, typename L3>
  void mult_by_col(const L1& l1, const L2& l2, L3& l3, abstract_sparse) {
    typedef typename linalg_traits<L2>::value_type T;
    clear(l3);
    typename linalg_traits<L2>::const_iterator it = vect_const_begin(l2),
      ite = vect_const_end(l2);
    for (; it != ite; ++it)
      if (*it != T(0)) add(scaled(mat_const_col(l1, it.index()), *it), l3);
  }

  template <typename L1, typename L2, typename L3>
  void mult_by_col(const L1& l1, const L2& l2, L3& l3, abstract_skyline) {
    typedef typename linalg_traits<L2>::value_type T;
    clear(l3); 
    typename linalg_traits<L2>::const_iterator it = vect_const_begin(l2),
      ite = vect_const_end(l2);
    for (; it != ite; ++it)
      if (*it != T(0)) add(scaled(mat_const_col(l1, it.index()), *it), l3);
  }

  template <typename L1, typename L2, typename L3> inline
  void mult_spec(const L1& l1, const L2& l2, L3& l3, row_major)
  { mult_by_row(l1, l2, l3, typename linalg_traits<L3>::storage_type()); }

  template <typename L1, typename L2, typename L3> inline
  void mult_spec(const L1& l1, const L2& l2, L3& l3, col_major)
  { mult_by_col(l1, l2, l3, typename linalg_traits<L2>::storage_type()); }

  template <typename L1, typename L2, typename L3> inline
  void mult_spec(const L1& l1, const L2& l2, L3& l3, abstract_null_type)
  { mult_ind(l1, l2, l3, typename linalg_traits<L1>::storage_type()); }

  template <typename L1, typename L2, typename L3>
  void mult_ind(const L1& l1, const L2& l2, L3& l3, abstract_indirect) {
    GMM_ASSERT1(false, "gmm::mult(m, ., .) undefined for this kind of matrix");
  }

  template <typename L1, typename L2, typename L3, typename L4> inline
  void mult(const L1& l1, const L2& l2, const L3& l3, L4& l4) {
    size_type m = mat_nrows(l1), n = mat_ncols(l1);
    copy(l3, l4);
    if (!m || !n) { gmm::copy(l3, l4); return; }
    GMM_ASSERT2(n==vect_size(l2) && m==vect_size(l4), "dimensions mismatch");
    if (!same_origin(l2, l4)) {
      mult_add_spec(l1, l2, l4, typename principal_orientation_type<typename
		    linalg_traits<L1>::sub_orientation>::potype());
    }
    else {
      GMM_WARNING2("Warning, A temporary is used for mult\n");
      typename temporary_vector<L2>::vector_type temp(vect_size(l2));
      copy(l2, temp);
      mult_add_spec(l1,temp, l4, typename principal_orientation_type<typename
		linalg_traits<L1>::sub_orientation>::potype());
    }
  }

  template <typename L1, typename L2, typename L3, typename L4> inline
  void mult(const L1& l1, const L2& l2, const L3& l3, const L4& l4)
  { mult(l1, l2, l3, linalg_const_cast(l4)); } 

  ///@endcond
  /** Multiply-accumulate. l3 += l1*l2; */
  template <typename L1, typename L2, typename L3> inline
  void mult_add(const L1& l1, const L2& l2, L3& l3) {
    size_type m = mat_nrows(l1), n = mat_ncols(l1);
    if (!m || !n) return;
    GMM_ASSERT2(n==vect_size(l2) && m==vect_size(l3), "dimensions mismatch");
    if (!same_origin(l2, l3)) {
      mult_add_spec(l1, l2, l3, typename principal_orientation_type<typename
		    linalg_traits<L1>::sub_orientation>::potype());
    }
    else {
      GMM_WARNING2("Warning, A temporary is used for mult\n");
      typename temporary_vector<L3>::vector_type temp(vect_size(l2));
      copy(l2, temp);
      mult_add_spec(l1,temp, l3, typename principal_orientation_type<typename
		linalg_traits<L1>::sub_orientation>::potype());
    }
  }
    
  /** Multiply-accumulate. l4 = l1*l2 + l3; */
  template <typename L1, typename L2, typename L3, typename L4> inline
  void mult_add(const L1& l1, const L2& l2, const L3& l3, L4& l4) {
      size_type m = mat_nrows(l1), n = mat_ncols(l1);
      if (!m || !n) return;
      GMM_ASSERT2(n==vect_size(l2) && m==vect_size(l3) && vect_size(l3) == vect_size(l4), "dimensions mismatch");
      if (!same_origin(l2, l3)) {
          mult_add_spec(l1, l2, l3, l4, typename principal_orientation_type<typename
                        linalg_traits<L1>::sub_orientation>::potype());
      }
      else {
          GMM_WARNING2("Warning, A temporary is used for mult\n");
          typename temporary_vector<L3>::vector_type temp(vect_size(l2));
          copy(l2, temp);
          mult_add_spec(l1, temp, l3, l4, typename principal_orientation_type<typename
                        linalg_traits<L1>::sub_orientation>::potype());
      }
  }
  ///@cond DOXY_SHOW_ALL_FUNCTIONS

  template <typename L1, typename L2, typename L3> inline
  void mult_add(const L1& l1, const L2& l2, const L3& l3)
  { mult_add(l1, l2, linalg_const_cast(l3)); } 

  template <typename L1, typename L2, typename L3>
  void mult_add_by_row(const L1& l1, const L2& l2, L3& l3, abstract_sparse) {
    typedef typename linalg_traits<L3>::value_type T;
    size_type nr = mat_nrows(l1);
    for (size_type i = 0; i < nr; ++i) {
      T aux = vect_sp(mat_const_row(l1, i), l2);
      if (aux != T(0)) l3[i] += aux;
    }
  }

  template <typename L1, typename L2, typename L3>
  void mult_add_by_row(const L1& l1, const L2& l2, L3& l3, abstract_skyline) {
    typedef typename linalg_traits<L3>::value_type T;
    size_type nr = mat_nrows(l1);
    for (size_type i = 0; i < nr; ++i) {
      T aux = vect_sp(mat_const_row(l1, i), l2);
      if (aux != T(0)) l3[i] += aux;
    }
  }

  template <typename L1, typename L2, typename L3>
  void mult_add_by_row(const L1& l1, const L2& l2, L3& l3, abstract_dense) {
    typename linalg_traits<L3>::iterator it=vect_begin(l3), ite=vect_end(l3);
    typename linalg_traits<L1>::const_row_iterator
      itr = mat_row_const_begin(l1);
    for (; it != ite; ++it, ++itr)
      *it += vect_sp(linalg_traits<L1>::row(itr), l2);
  }

  template <typename L1, typename L2, typename L3, typename L4>
  void mult_add_by_row(const L1& l1, const L2& l2, const L3& l3, L4& l4, abstract_dense) {
      typename linalg_traits<L3>::const_iterator add_it=vect_begin(l3), add_ite=vect_end(l3);
      typename linalg_traits<L4>::iterator target_it=vect_begin(l4), target_ite=vect_end(l4);
      typename linalg_traits<L1>::const_row_iterator
      itr = mat_row_const_begin(l1);
      for (; add_it != add_ite; ++add_it, ++target_it, ++itr)
          *target_it = vect_sp(linalg_traits<L1>::row(itr), l2) + *add_it;
  }

  template <typename L1, typename L2, typename L3>
  void mult_add_by_col(const L1& l1, const L2& l2, L3& l3, abstract_dense) {
    size_type nc = mat_ncols(l1);
    for (size_type i = 0; i < nc; ++i)
      add(scaled(mat_const_col(l1, i), l2[i]), l3);
  }

  template <typename L1, typename L2, typename L3>
  void mult_add_by_col(const L1& l1, const L2& l2, L3& l3, abstract_sparse) {
    typename linalg_traits<L2>::const_iterator it = vect_const_begin(l2),
      ite = vect_const_end(l2);
    for (; it != ite; ++it)
      if (*it != typename linalg_traits<L2>::value_type(0))
	add(scaled(mat_const_col(l1, it.index()), *it), l3);
  }

  template <typename L1, typename L2, typename L3>
  void mult_add_by_col(const L1& l1, const L2& l2, L3& l3, abstract_skyline) {
    typename linalg_traits<L2>::const_iterator it = vect_const_begin(l2),
      ite = vect_const_end(l2);
    for (; it != ite; ++it)
      if (*it != typename linalg_traits<L2>::value_type(0))
	add(scaled(mat_const_col(l1, it.index()), *it), l3);
  }

  template <typename L1, typename L2, typename L3> inline
  void mult_add_spec(const L1& l1, const L2& l2, L3& l3, row_major)
  { mult_add_by_row(l1, l2, l3, typename linalg_traits<L3>::storage_type()); }

  template <typename L1, typename L2, typename L3, typename L4> inline
  void mult_add_spec(const L1& l1, const L2& l2, const L3& l3, L4& l4, row_major)
  { mult_add_by_row(l1, l2, l3, l4, typename linalg_traits<L3>::storage_type()); }
    
  template <typename L1, typename L2, typename L3> inline
  void mult_add_spec(const L1& l1, const L2& l2, L3& l3, col_major)
  { mult_add_by_col(l1, l2, l3, typename linalg_traits<L2>::storage_type()); }

  template <typename L1, typename L2, typename L3> inline
  void mult_add_spec(const L1& l1, const L2& l2, L3& l3, abstract_null_type)
  { mult_ind(l1, l2, l3, typename linalg_traits<L1>::storage_type()); }

  template <typename L1, typename L2, typename L3>
  void transposed_mult(const L1& l1, const L2& l2, const L3& l3)
  { mult(gmm::transposed(l1), l2, l3); }


  /* ******************************************************************** */
  /*		Matrix-matrix mult                                    	  */
  /* ******************************************************************** */
  

  struct g_mult {};  // generic mult, less optimized
  struct c_mult {};  // col x col -> col mult
  struct r_mult {};  // row x row -> row mult
  struct rcmult {};  // row x col -> col mult
  struct crmult {};  // col x row -> row mult


  template<typename SO1, typename SO2, typename SO3> struct mult_t;
  #define DEFMU__ template<> struct mult_t
  DEFMU__<row_major  , row_major  , row_major  > { typedef r_mult t; };
  DEFMU__<row_major  , row_major  , col_major  > { typedef g_mult t; };
  DEFMU__<row_major  , row_major  , col_and_row> { typedef r_mult t; };
  DEFMU__<row_major  , row_major  , row_and_col> { typedef r_mult t; };
  DEFMU__<row_major  , col_major  , row_major  > { typedef rcmult t; };
  DEFMU__<row_major  , col_major  , col_major  > { typedef rcmult t; };
  DEFMU__<row_major  , col_major  , col_and_row> { typedef rcmult t; };
  DEFMU__<row_major  , col_major  , row_and_col> { typedef rcmult t; };
  DEFMU__<row_major  , col_and_row, row_major  > { typedef r_mult t; };
  DEFMU__<row_major  , col_and_row, col_major  > { typedef rcmult t; };
  DEFMU__<row_major  , col_and_row, col_and_row> { typedef rcmult t; };
  DEFMU__<row_major  , col_and_row, row_and_col> { typedef rcmult t; };
  DEFMU__<row_major  , row_and_col, row_major  > { typedef r_mult t; };
  DEFMU__<row_major  , row_and_col, col_major  > { typedef rcmult t; };
  DEFMU__<row_major  , row_and_col, col_and_row> { typedef r_mult t; };
  DEFMU__<row_major  , row_and_col, row_and_col> { typedef r_mult t; };
  DEFMU__<col_major  , row_major  , row_major  > { typedef crmult t; };
  DEFMU__<col_major  , row_major  , col_major  > { typedef g_mult t; };
  DEFMU__<col_major  , row_major  , col_and_row> { typedef crmult t; };
  DEFMU__<col_major  , row_major  , row_and_col> { typedef crmult t; };
  DEFMU__<col_major  , col_major  , row_major  > { typedef g_mult t; };
  DEFMU__<col_major  , col_major  , col_major  > { typedef c_mult t; };
  DEFMU__<col_major  , col_major  , col_and_row> { typedef c_mult t; };
  DEFMU__<col_major  , col_major  , row_and_col> { typedef c_mult t; };
  DEFMU__<col_major  , col_and_row, row_major  > { typedef crmult t; };
  DEFMU__<col_major  , col_and_row, col_major  > { typedef c_mult t; };
  DEFMU__<col_major  , col_and_row, col_and_row> { typedef c_mult t; };
  DEFMU__<col_major  , col_and_row, row_and_col> { typedef c_mult t; };
  DEFMU__<col_major  , row_and_col, row_major  > { typedef crmult t; };
  DEFMU__<col_major  , row_and_col, col_major  > { typedef c_mult t; };
  DEFMU__<col_major  , row_and_col, col_and_row> { typedef c_mult t; };
  DEFMU__<col_major  , row_and_col, row_and_col> { typedef c_mult t; };
  DEFMU__<col_and_row, row_major  , row_major  > { typedef r_mult t; };
  DEFMU__<col_and_row, row_major  , col_major  > { typedef c_mult t; };
  DEFMU__<col_and_row, row_major  , col_and_row> { typedef r_mult t; };
  DEFMU__<col_and_row, row_major  , row_and_col> { typedef r_mult t; };
  DEFMU__<col_and_row, col_major  , row_major  > { typedef rcmult t; };
  DEFMU__<col_and_row, col_major  , col_major  > { typedef c_mult t; };
  DEFMU__<col_and_row, col_major  , col_and_row> { typedef c_mult t; };
  DEFMU__<col_and_row, col_major  , row_and_col> { typedef c_mult t; };
  DEFMU__<col_and_row, col_and_row, row_major  > { typedef r_mult t; };
  DEFMU__<col_and_row, col_and_row, col_major  > { typedef c_mult t; };
  DEFMU__<col_and_row, col_and_row, col_and_row> { typedef c_mult t; };
  DEFMU__<col_and_row, col_and_row, row_and_col> { typedef c_mult t; };
  DEFMU__<col_and_row, row_and_col, row_major  > { typedef r_mult t; };
  DEFMU__<col_and_row, row_and_col, col_major  > { typedef c_mult t; };
  DEFMU__<col_and_row, row_and_col, col_and_row> { typedef c_mult t; };
  DEFMU__<col_and_row, row_and_col, row_and_col> { typedef r_mult t; };
  DEFMU__<row_and_col, row_major  , row_major  > { typedef r_mult t; };
  DEFMU__<row_and_col, row_major  , col_major  > { typedef c_mult t; };
  DEFMU__<row_and_col, row_major  , col_and_row> { typedef r_mult t; };
  DEFMU__<row_and_col, row_major  , row_and_col> { typedef r_mult t; };
  DEFMU__<row_and_col, col_major  , row_major  > { typedef rcmult t; };
  DEFMU__<row_and_col, col_major  , col_major  > { typedef c_mult t; };
  DEFMU__<row_and_col, col_major  , col_and_row> { typedef c_mult t; };
  DEFMU__<row_and_col, col_major  , row_and_col> { typedef c_mult t; };
  DEFMU__<row_and_col, col_and_row, row_major  > { typedef rcmult t; };
  DEFMU__<row_and_col, col_and_row, col_major  > { typedef rcmult t; };
  DEFMU__<row_and_col, col_and_row, col_and_row> { typedef rcmult t; };
  DEFMU__<row_and_col, col_and_row, row_and_col> { typedef rcmult t; };
  DEFMU__<row_and_col, row_and_col, row_major  > { typedef r_mult t; };
  DEFMU__<row_and_col, row_and_col, col_major  > { typedef c_mult t; };
  DEFMU__<row_and_col, row_and_col, col_and_row> { typedef r_mult t; };
  DEFMU__<row_and_col, row_and_col, row_and_col> { typedef r_mult t; };

  template <typename L1, typename L2, typename L3>
  void mult_dispatch(const L1& l1, const L2& l2, L3& l3, abstract_matrix) {
    typedef typename temporary_matrix<L3>::matrix_type temp_mat_type;
    size_type n = mat_ncols(l1);
    if (n == 0) { gmm::clear(l3); return; }
    GMM_ASSERT2(n == mat_nrows(l2) && mat_nrows(l1) == mat_nrows(l3) &&
                mat_ncols(l2) == mat_ncols(l3),	"dimensions mismatch");

    if (same_origin(l2, l3) || same_origin(l1, l3)) {
      GMM_WARNING2("A temporary is used for mult");
      temp_mat_type temp(mat_nrows(l3), mat_ncols(l3));
      mult_spec(l1, l2, temp, typename mult_t<
		typename linalg_traits<L1>::sub_orientation,
		typename linalg_traits<L2>::sub_orientation,
		typename linalg_traits<temp_mat_type>::sub_orientation>::t());
      copy(temp, l3);
    }
    else
      mult_spec(l1, l2, l3, typename mult_t<
		typename linalg_traits<L1>::sub_orientation,
		typename linalg_traits<L2>::sub_orientation,
		typename linalg_traits<L3>::sub_orientation>::t());
  }

  // Completely generic but inefficient

  template <typename L1, typename L2, typename L3>
  void mult_spec(const L1& l1, const L2& l2, L3& l3, g_mult) {
    typedef typename linalg_traits<L3>::value_type T;
    GMM_WARNING2("Inefficient generic matrix-matrix mult is used");
    for (size_type i = 0; i < mat_nrows(l3) ; ++i)
      for (size_type j = 0; j < mat_ncols(l3) ; ++j) {
	T a(0);
	for (size_type k = 0; k < mat_nrows(l2) ; ++k) a += l1(i, k)*l2(k, j);
	l3(i, j) = a;
      }
  }

  // row x col matrix-matrix mult

  template <typename L1, typename L2, typename L3>
  void mult_row_col_with_temp(const L1& l1, const L2& l2, L3& l3, col_major) {
    typedef typename temporary_col_matrix<L1>::matrix_type temp_col_mat;
    temp_col_mat temp(mat_nrows(l1), mat_ncols(l1));
    copy(l1, temp);
    mult(temp, l2, l3);
  }

  template <typename L1, typename L2, typename L3>
  void mult_row_col_with_temp(const L1& l1, const L2& l2, L3& l3, row_major) {
    typedef typename temporary_row_matrix<L2>::matrix_type temp_row_mat;
    temp_row_mat temp(mat_nrows(l2), mat_ncols(l2));
    copy(l2, temp);
    mult(l1, temp, l3);
  }

  template <typename L1, typename L2, typename L3>
  void mult_spec(const L1& l1, const L2& l2, L3& l3, rcmult) {
    if (is_sparse(l1) && is_sparse(l2)) {
      GMM_WARNING3("Inefficient row matrix - col matrix mult for "
		  "sparse matrices, using temporary");
      mult_row_col_with_temp(l1, l2, l3, 
			     typename principal_orientation_type<typename
			     linalg_traits<L3>::sub_orientation>::potype());
    }
    else {
      typename linalg_traits<L2>::const_col_iterator
	it2b = linalg_traits<L2>::col_begin(l2), it2,
	ite = linalg_traits<L2>::col_end(l2);
      size_type i,j, k = mat_nrows(l1);
      
      for (i = 0; i < k; ++i) {
	typename linalg_traits<L1>::const_sub_row_type r1=mat_const_row(l1, i);
	for (it2 = it2b, j = 0; it2 != ite; ++it2, ++j)
	  l3(i,j) = vect_sp(r1, linalg_traits<L2>::col(it2));
      }
    }
  }

  // row - row matrix-matrix mult

  template <typename L1, typename L2, typename L3> inline
  void mult_spec(const L1& l1, const L2& l2, L3& l3, r_mult) {
    mult_spec(l1, l2, l3,r_mult(),typename linalg_traits<L1>::storage_type());
  }

  template <typename L1, typename L2, typename L3>
  void mult_spec(const L1& l1, const L2& l2, L3& l3, r_mult, abstract_dense) {
    // optimizable
    clear(l3);
    size_type nn = mat_nrows(l3), mm = mat_nrows(l2);
    for (size_type i = 0; i < nn; ++i) {
      for (size_type j = 0; j < mm; ++j) {
	add(scaled(mat_const_row(l2, j), l1(i, j)), mat_row(l3, i));
      }
    }
  }

  template <typename L1, typename L2, typename L3>
  void mult_spec(const L1& l1, const L2& l2, L3& l3, r_mult, abstract_sparse) {
    // optimizable
    clear(l3);
    size_type nn = mat_nrows(l3);
    for (size_type i = 0; i < nn; ++i) {
      typename linalg_traits<L1>::const_sub_row_type rl1=mat_const_row(l1, i);
      typename linalg_traits<typename linalg_traits<L1>::const_sub_row_type>::
	const_iterator it = vect_const_begin(rl1), ite = vect_const_end(rl1);
      for (; it != ite; ++it)
	add(scaled(mat_const_row(l2, it.index()), *it), mat_row(l3, i));
    }
  }

  template <typename L1, typename L2, typename L3>
  void mult_spec(const L1& l1, const L2& l2, L3& l3, r_mult, abstract_skyline)
  { mult_spec(l1, l2, l3, r_mult(), abstract_sparse()); }

  // col - col matrix-matrix mult

  template <typename L1, typename L2, typename L3> inline
  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult) {
    mult_spec(l1, l2,l3,c_mult(),typename linalg_traits<L2>::storage_type(),
	      typename linalg_traits<L2>::sub_orientation());
  }


  template <typename L1, typename L2, typename L3, typename ORIEN>
  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult,
		 abstract_dense, ORIEN) {
    typedef typename linalg_traits<L2>::value_type T;
    size_type nn = mat_ncols(l3), mm = mat_ncols(l1);

    for (size_type i = 0; i < nn; ++i) {
      clear(mat_col(l3, i));
      for (size_type j = 0; j < mm; ++j) {
	T b = l2(j, i);
	if (b != T(0)) add(scaled(mat_const_col(l1, j), b), mat_col(l3, i));
      }
    }
  }

  template <typename L1, typename L2, typename L3, typename ORIEN>
  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult,
		 abstract_sparse, ORIEN) {
    // optimizable
    clear(l3);
    size_type nn = mat_ncols(l3);
    for (size_type i = 0; i < nn; ++i) {
      typename linalg_traits<L2>::const_sub_col_type rc2=mat_const_col(l2, i);
      typename linalg_traits<typename linalg_traits<L2>::const_sub_col_type>::
	const_iterator it = vect_const_begin(rc2), ite = vect_const_end(rc2);
      for (; it != ite; ++it)
	add(scaled(mat_const_col(l1, it.index()), *it), mat_col(l3, i));
    }
  }

  template <typename L1, typename L2, typename L3>
  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult,
		 abstract_sparse, row_major) {
     typedef typename linalg_traits<L2>::value_type T;
     GMM_WARNING3("Inefficient matrix-matrix mult for sparse matrices");
     clear(l3);
     size_type mm = mat_nrows(l2), nn = mat_ncols(l3);
     for (size_type i = 0; i < nn; ++i)
       for (size_type j = 0; j < mm; ++j) {
	 T a = l2(i,j);
	 if (a != T(0)) add(scaled(mat_const_col(l1, j), a), mat_col(l3, i));
       }
   }

  template <typename L1, typename L2, typename L3, typename ORIEN> inline
  void mult_spec(const L1& l1, const L2& l2, L3& l3, c_mult,
		 abstract_skyline, ORIEN)
  { mult_spec(l1, l2, l3, c_mult(), abstract_sparse(), ORIEN()); }

  
  // col - row matrix-matrix mult

  template <typename L1, typename L2, typename L3> inline
  void mult_spec(const L1& l1, const L2& l2, L3& l3, crmult)
  { mult_spec(l1,l2,l3,crmult(), typename linalg_traits<L1>::storage_type()); }


  template <typename L1, typename L2, typename L3>
  void mult_spec(const L1& l1, const L2& l2, L3& l3, crmult, abstract_dense) {
    // optimizable
    clear(l3);
    size_type nn = mat_ncols(l1), mm = mat_nrows(l1);
    for (size_type i = 0; i < nn; ++i) {
      for (size_type j = 0; j < mm; ++j)
      add(scaled(mat_const_row(l2, i), l1(j, i)), mat_row(l3, j));
    }
  }

  template <typename L1, typename L2, typename L3>
  void mult_spec(const L1& l1, const L2& l2, L3& l3, crmult, abstract_sparse) {
    // optimizable
    clear(l3);
    size_type nn = mat_ncols(l1);
    for (size_type i = 0; i < nn; ++i) {
      typename linalg_traits<L1>::const_sub_col_type rc1=mat_const_col(l1, i);
      typename linalg_traits<typename linalg_traits<L1>::const_sub_col_type>::
	const_iterator it = vect_const_begin(rc1), ite = vect_const_end(rc1);
      for (; it != ite; ++it)
	add(scaled(mat_const_row(l2, i), *it), mat_row(l3, it.index()));
    }
  }

  template <typename L1, typename L2, typename L3> inline
  void mult_spec(const L1& l1, const L2& l2, L3& l3, crmult, abstract_skyline)
  { mult_spec(l1, l2, l3, crmult(), abstract_sparse()); }
  

  /* ******************************************************************** */
  /*		Symmetry test.                                     	  */
  /* ******************************************************************** */

  ///@endcond
  /** test if A is symmetric.
      @param A a matrix.
      @param tol a threshold.
  */
  template <typename MAT> inline
  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol
		    = magnitude_of_linalg(MAT)(-1)) {
    typedef magnitude_of_linalg(MAT) R;
    if (tol < R(0)) tol = default_tol(R()) * mat_maxnorm(A);
    if (mat_nrows(A) != mat_ncols(A)) return false;
    return is_symmetric(A, tol, typename linalg_traits<MAT>::storage_type());
  }
  ///@cond DOXY_SHOW_ALL_FUNCTIONS

  template <typename MAT> 
  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol, 
		    abstract_dense) {
    size_type m = mat_nrows(A);
    for (size_type i = 1; i < m; ++i)
      for (size_type j = 0; j < i; ++j)
	if (gmm::abs(A(i, j)-A(j, i)) > tol) return false;
    return true;
  }

  template <typename MAT> 
  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol, 
		    abstract_sparse) {
    return is_symmetric(A, tol, typename principal_orientation_type<typename
			linalg_traits<MAT>::sub_orientation>::potype());
  }

  template <typename MAT> 
  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol, 
		    row_major) {
    for (size_type i = 0; i < mat_nrows(A); ++i) {
      typedef typename linalg_traits<MAT>::const_sub_row_type row_type;
      row_type row = mat_const_row(A, i);
      typename linalg_traits<row_type>::const_iterator
	it = vect_const_begin(row), ite = vect_const_end(row);
      for (; it != ite; ++it)
	if (gmm::abs(*it - A(it.index(), i)) > tol) return false;
    }
    return true;
  }

  template <typename MAT> 
  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol, 
		    col_major) {
    for (size_type i = 0; i < mat_ncols(A); ++i) {
      typedef typename linalg_traits<MAT>::const_sub_col_type col_type;
      col_type col = mat_const_col(A, i);
      typename linalg_traits<col_type>::const_iterator
	it = vect_const_begin(col), ite = vect_const_end(col);
      for (; it != ite; ++it)
	if (gmm::abs(*it - A(i, it.index())) > tol) return false;
    }
    return true;
  }

  template <typename MAT> 
  bool is_symmetric(const MAT &A, magnitude_of_linalg(MAT) tol, 
		    abstract_skyline)
  { return is_symmetric(A, tol, abstract_sparse()); }

  ///@endcond
  /** test if A is Hermitian.
      @param A a matrix.
      @param tol a threshold.
  */
  template <typename MAT> inline
  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol
		    = magnitude_of_linalg(MAT)(-1)) {
    typedef magnitude_of_linalg(MAT) R;
    if (tol < R(0)) tol = default_tol(R()) * mat_maxnorm(A);
    if (mat_nrows(A) != mat_ncols(A)) return false;
    return is_hermitian(A, tol, typename linalg_traits<MAT>::storage_type());
  }
  ///@cond DOXY_SHOW_ALL_FUNCTIONS

  template <typename MAT> 
  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol,
		    abstract_dense) {
    size_type m = mat_nrows(A);
    for (size_type i = 1; i < m; ++i)
      for (size_type j = 0; j < i; ++j)
	if (gmm::abs(A(i, j)-gmm::conj(A(j, i))) > tol) return false;
    return true;
  }

  template <typename MAT> 
  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol, 
		    abstract_sparse) {
    return is_hermitian(A, tol, typename principal_orientation_type<typename
			linalg_traits<MAT>::sub_orientation>::potype());
  }

  template <typename MAT> 
  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol, 
		    row_major) {
    for (size_type i = 0; i < mat_nrows(A); ++i) {
      typedef typename linalg_traits<MAT>::const_sub_row_type row_type;
      row_type row = mat_const_row(A, i);
      typename linalg_traits<row_type>::const_iterator
	it = vect_const_begin(row), ite = vect_const_end(row);
      for (; it != ite; ++it)
	if (gmm::abs(gmm::conj(*it) - A(it.index(), i)) > tol) return false;
    }
    return true;
  }

  template <typename MAT> 
  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol, 
		    col_major) {
    for (size_type i = 0; i < mat_ncols(A); ++i) {
      typedef typename linalg_traits<MAT>::const_sub_col_type col_type;
      col_type col = mat_const_col(A, i);
      typename linalg_traits<col_type>::const_iterator
	it = vect_const_begin(col), ite = vect_const_end(col);
      for (; it != ite; ++it)
	if (gmm::abs(gmm::conj(*it) - A(i, it.index())) > tol) return false;
    }
    return true;
  }

  template <typename MAT> 
  bool is_hermitian(const MAT &A, magnitude_of_linalg(MAT) tol, 
		    abstract_skyline)
  { return is_hermitian(A, tol, abstract_sparse()); }
  ///@endcond
}


#endif //  GMM_BLAS_H__