68 EssentialPart& essential,
70 RealScalar& beta)
const
75 EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
76 VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1);
78 RealScalar tailSqNorm = size()==1 ? RealScalar(0) : tail.squaredNorm();
80 const RealScalar tol = (std::numeric_limits<RealScalar>::min)();
82 if(tailSqNorm <= tol && numext::abs2(numext::imag(c0))<=tol)
85 beta = numext::real(c0);
90 beta = sqrt(numext::abs2(c0) + tailSqNorm);
91 if (numext::real(c0)>=RealScalar(0))
93 essential = tail / (c0 - beta);
94 tau =
conj((beta - c0) / beta);
117 const EssentialPart& essential,
127 Map<typename internal::plain_row_type<PlainObject>::type> tmp(workspace,cols());
128 Block<Derived, EssentialPart::SizeAtCompileTime, Derived::ColsAtCompileTime> bottom(derived(), 1, 0, rows()-1, cols());
129 tmp.noalias() = essential.adjoint() * bottom;
131 this->row(0) -= tau * tmp;
132 bottom.noalias() -= tau * essential * tmp;
155 const EssentialPart& essential,
165 Map<typename internal::plain_col_type<PlainObject>::type> tmp(workspace,rows());
166 Block<Derived, Derived::RowsAtCompileTime, EssentialPart::SizeAtCompileTime> right(derived(), 0, 1, rows(), cols()-1);
167 tmp.noalias() = right * essential;
169 this->col(0) -= tau * tmp;
170 right.noalias() -= tau * tmp * essential.adjoint();