[eigen] Recursion and block matrices

[Norman Goldstein <normvcr@xxxxxxxxx>]

I haven't been able to figure out how to write a routine that calls 
itself recursively
with successively smaller sub-blocks of the original matrix.  Here is a 
simple example,
which, adds the identity matrix  to the main diagonal of the input 
matrix (the point is
to illustrate the recursion/blocks issue :-) ).

//////////////////////////////// CODE 
//////////////////////////////////////////////////////////////////////////////
#include <Eigen/Core>
using namespace Eigen;

#include <iostream>
using namespace std;

template< class Derived >
void incr( const DenseBase< Derived >& mat )
{
  DenseBase< Derived >& matV =
    const_cast< DenseBase< Derived >& >( mat );

  ++matV(0,0);       // <--------- Line 13

  if( ( 1 == mat.rows() ) ||
      ( 1 == mat.cols() ) )
  {
    return;
  }
  else
  {
    incr( mat.bottomRightCorner( mat.rows() - 1,
                                                     mat.cols() - 1 ) );
  }
}// incr


int main( int argc, char* argv[] )
{
  MatrixXd mat( 2, 3 );
  mat << 1, 2, 3, 4, 5, 6;
  cout << "Before: " << mat << endl;

  incr( mat );

  cout << "After: " << mat << endl;
  return 0;
}// main
//////////////////////////////// END CODE 
/////////////////////////////////////////////////////////////

The current error is,

    Line 13:3: error: lvalue required as increment operand

which makes sense, since not all expressions are l-values.
I've tried replacing "DenseBase" with various combinations of Map and Block,
but no success.

Any suggestions?

On a related issue,  Block< Block > is, conceptually, simply a Block (at 
least at run-time).
Any comments on how this "meta complexity" is addressed, in general?

Thank you.