[Eigen] day 9. Gauss elimination, matrix to upper triangular form

//gauss elimination that makes m to upper triangular
inline void u_m(mxd::r _m , vxd::r _v){
 
    i::t idx = 0;
 
    while(idx < _m.rows()){
 
        mxd::b A00     = _m.block(0      , 0       , idx                     , idx                    );
        mxd::b a10     = _m.block(idx    , 0       , 1                       , idx                    );
        mxd::b A20     = _m.block(idx + 1, 0       , _m .rows() - (idx + 1)  , idx                    );
 
        mxd::b a01     = _m.block(0      , idx     , idx                     , 1                      );
        mxd::b alpha11 = _m.block(idx    , idx     , 1                       , 1                      );
        mxd::b a21     = _m.block(idx + 1, idx     , _m.rows() - (idx + 1)   , 1                      );
 
        mxd::b A02     = _m.block(0      , idx + 1 , idx                     , _m.cols() - (idx + 1)  );
        mxd::b a12     = _m.block(idx    , idx + 1 , 1                       , _m.cols() - (idx + 1)  );
        mxd::b A22     = _m.block(idx + 1, idx + 1 , _m.rows() - (idx + 1)   , _m.cols() - (idx + 1)  );
 
        vxd::b b0      = _v.segment(0       ,   idx                  );
        vxd::b betha1  = _v.segment(idx     ,   1                    );
        vxd::b b2      = _v.segment(idx + 1 , _v.rows() - (idx + 1)  );
 
 
 
        a21 = a21 / alpha11.value();
        A22 = A22 - a21 * a12;
        b2  = b2 - betha1.value() * a21;
 
        idx++;
 
    }
 
}
 

    mxd::t m2(3,3);
 
    m2 <<   2, 4, -2,
            4,-2,  6,
            6,-4,  2;
 
    vxd::t v(3);
    v << -10, 20, 18;
 
    u_m(m2,v);
    co(m2);
    co(v);
 

output = 
  2   4  -2
  2 -10  10
  3 1.6  -8
output = 
-10
 40
-16