[Eigen] Day 7. Quadrants slicing and redicing with diagonal matrix and LU matrix , transpose

inline mxd::t m_diagonal(mxd::t _m,vxd::t _entries){
 
    for(z::t i(0) ; i < _m.cols() ; ++i){
 
        mxd::b tl   = _m.block(i,      i     ,  1                   ,  1                            );
        mxd::b tr   = _m.block(i     , i + 1 ,  1                   ,  _m.cols() - (i + 1)          );
        mxd::b bl   = _m.block(i + 1 , i     ,  _m.rows() - (i + 1) ,  1                            );
        mxd::b br   = _m.block(i + 1 , i + 1 ,  _m.rows() - (i + 1) ,  _m.cols() - (i + 1)          );
 
        co(tl,"tl");
        co(tr,"tr");
        co(bl,"bl");
        co(br,"br");
 
        tl << _entries(i);
        tr.setZero();
        bl.setZero();
    }
 
    return _m;
 
}
 

tl = 
1
tr = 
2 3 4 5
bl = 
6
1
6
1
br = 
 7  8  9 10
 2  3  4  5
 7  8  9 10
 2  3  4  5
tl = 
7
tr = 
 8  9 10
bl = 
2
7
2
br = 
 3  4  5
 8  9 10
 3  4  5
tl = 
3
tr = 
4 5
bl = 
8
3
br = 
 9 10
 4  5
tl = 
9
tr = 
10
bl = 
4
br = 
5
tl = 
5
tr = 
 
bl = 
 
br = 
 
output = 
1 0 0 0 0
0 2 0 0 0
0 0 3 0 0
0 0 0 4 0
0 0 0 0 5

inline mxd::t m_lower(mxd::t _m){
 
    for(z::t i(0) ; i < _m.cols() ; ++i){
 
        mxd::b tl   = _m.block(i,      i     ,  1                   ,  1                            );
        mxd::b tr   = _m.block(i     , i + 1 ,  1                   ,  _m.cols() - (i + 1)          );
        mxd::b bl   = _m.block(i + 1 , i     ,  _m.rows() - (i + 1) ,  1                            );
        mxd::b br   = _m.block(i + 1 , i + 1 ,  _m.rows() - (i + 1) ,  _m.cols() - (i + 1)          );
 
        co(tl,"tl");
        co(tr,"tr");
        co(bl,"bl");
        co(br,"br");
 
        tl << 1;
        tr.setZero();
    }
    return _m;
}
 
inline mxd::t m_upper(mxd::t _m){
 
    for(z::t i(0) ; i < _m.cols() ; ++i){
 
        mxd::b tl   = _m.block(i,      i     ,  1                   ,  1                            );
        mxd::b tr   = _m.block(i     , i + 1 ,  1                   ,  _m.cols() - (i + 1)          );
        mxd::b bl   = _m.block(i + 1 , i     ,  _m.rows() - (i + 1) ,  1                            );
        mxd::b br   = _m.block(i + 1 , i + 1 ,  _m.rows() - (i + 1) ,  _m.cols() - (i + 1)          );
 
        co(tl,"tl");
        co(tr,"tr");
        co(bl,"bl");
        co(br,"br");
 
        tl << 1;
        bl.setZero();
    }
    return _m;
}
 
 

inline mxd::t m_transpose(mxd::t _m){
 
    mxd::t m_(_m.cols(), _m.rows());
    m_.setZero();
 
    for(z::t i(0) ; i < _m.cols() ; ++i){
 
        mxd::b col   = _m.block(0, i ,_m.rows(),1 );
 
        mxd::b rows  = m_.block(i, 0, 1, _m.cols());
 
        for(z::t x(0) ; x < _m.cols() ; ++x){
            rows.col(x) = col.row(x);
        }
 
        co(col, "col");
        co(rows, "rows");
 
 
 
    }
    return m_;
}