[Eigen] 복습 3일차, Linear combination algorithm

chaptor 3-1 practice

    //chaptor 3-1 practice
    v3d::t u;
    v3d::t v;
    v3d::t w;
 
    u << -2,  0,  4 ;
    v <<  3, -1,  6 ;
    w <<  2, -5, -5 ;
 
    //define 3v - 2u
    co( 3 * v - 2 * u, "a)"                );
    //define ||u + v + w||
    co( (u + v + w).norm() , "b"           );
    //define vector -3u to w(v+5) 
    co( d_poToPo(-3 * u, v + 5 * w ), "c"  );
    //define proj vector u on w
    co( v_proj(u,w), "d"                   );
 

implementing linear combination algorithm

//linear combination with a recursive method
inline vxd::t v_comb(mxd::t _v, vxd::t coefficient, int _dimention, int acc = 0){
 
    if(acc == _dimention){ return VectorXd(_v.cols()).setZero(); }
    return  v_comb(_v, coefficient, _dimention, ++acc) + (_v.col(acc) * coefficient[acc]);
 
}
 
//linear combination with a for-statement
inline vxd::t v_comb(mxd::t _v, vxd::t coefficients){
 
    vxd::t v_(_v.cols());  v_.setZero();
 
    for(z::t i(0) ; i < _v.cols() ; ++i){  v_ = v_ + _v.col(i) * coefficients[i];  }
 
    return  v_;
}
 
//inner product( dot product)
inline double d_dot(vxd::t _v1, vxd::t _v2 , int _dim){
 
    if(_dim == -1) return 0;
 
    return _v1[_dim] * _v2[_dim] + d_dot(_v1, _v2 , --_dim);
}

    vxd::t v(3);
    mxd::t m(3,3);
 
    m <<    1,2,3,
            1,2,3,
            1,2,3;
 
    v << 10, 20, 30;
 
    co(v_comb(m, v, 3));
    co(v_comb(m,v));
 
output = 
140
140
140
output = 
140
140
140

implementing dot product algorithm

 
 
//inner product( dot product)
inline double d_dot(vxd::t _v1, vxd::t _v2 , int _dim , int acc = 0){
 
    if( acc == _dim ) return 0;
 
    return _v1[acc] * _v2[acc] + d_dot(_v1, _v2 , _dim, ++acc);
}
 
    v  << 1,1,0;
    v2 << 3,1,1;
 
    co( d_dot(v,v2,v.rows() ));
 
output = 
4