[eigen] Iterators with dense matrices: (was: Areas of eigen3 variation and using eigen2/3 in generic code)

["Paul C. Leopardi" <paul.leopardi@xxxxxxxxxxxx>]

On Monday 04 January 2010 06:02:43 Benoit Jacob wrote:
> 2010/1/3 Jesse Perla <jesseperla@xxxxxxxxx>:
> >  Or any way to return a
> > random access iterator for begin() and end() that I could use with
> > std::transform, etc?  The "start" and "end" seem different than normal
> > iterators
> 
> Indeed, we do not have any iterators in Eigen for dense matrices and
> vectors. Do you have a use case for that? So far, index-based access
> has been all we have needed, as we were 100% focused on linear
> algebra.

Hi all,
Sorry to break into the discussion at this point, but I am also thinking of 
migrating from uBLAS to Eigen. My GluCat code ( http://glucat.sf.net ) 
compiles with an optional macro definition, GLUCAT_USE_DENSE_MATRICES
which is used as follows.

typedef ublas::column_major  orientation_t;
typedef ublas::compressed_matrix< Scalar_T, orientation_t > basis_matrix_t;
#ifdef _GLUCAT_USE_DENSE_MATRICES
    typedef ublas::matrix< Scalar_T, orientation_t > matrix_t;
#else
    typedef basis_matrix_t matrix_t;
#endif

Code which uses matrices does not know if the matrix is dense or sparse, and 
so uses uBLAS begin1(), end1(), begin(), end(), as follows:

 /// Square of Frobenius norm
  template< typename Matrix_T >
  typename Matrix_T::value_type
  norm_frob2(const Matrix_T& val)
  {
    typedef typename Matrix_T::value_type Scalar_T;
    typedef typename Matrix_T::size_type matrix_index_t;

    Scalar_T result = Scalar_T(0);
    for (typename Matrix_T::const_iterator1
        val_it1 = val.begin1();
        val_it1 != val.end1();
        ++val_it1)
      for (typename Matrix_T::const_iterator2
          val_it2 = val_it1.begin();
          val_it2 != val_it1.end();
          ++val_it2)
      {
        if (numeric_traits<Scalar_T>::isNaN(*val_it2))
          return numeric_traits<Scalar_T>::NaN();
        result += (*val_it2) * (*val_it2);
      } 
    return result;
  }

What is the equivalent code using Eigen? Do I need to code dense and sparse 
versions of every matrix routine so that the code can take advantage of 
iterators when using sparse matrices?
Best, Paul