1 Matrix3d v = Matrix3d::Random(); 2 cout << "The matrix v is:" << endl; 3 cout << v << endl; 4 5 Vector3d v0(1, v(1,0), v(2,0)); 6 cout << "The first Householder vector is: v_0 = " << v0.transpose() << endl; 7 Vector3d v1(0, 1, v(2,1)); 8 cout << "The second Householder vector is: v_1 = " << v1.transpose() << endl; 9 Vector3d v2(0, 0, 1); 10 cout << "The third Householder vector is: v_2 = " << v2.transpose() << endl; 11 12 Vector3d h = Vector3d::Random(); 13 cout << "The Householder coefficients are: h = " << h.transpose() << endl; 14 15 Matrix3d H0 = Matrix3d::Identity() - h(0) * v0 * v0.adjoint(); 16 cout << "The first Householder reflection is represented by H_0 = " << endl; 17 cout << H0 << endl; 18 Matrix3d H1 = Matrix3d::Identity() - h(1) * v1 * v1.adjoint(); 19 cout << "The second Householder reflection is represented by H_1 = " << endl; 20 cout << H1 << endl; 21 Matrix3d H2 = Matrix3d::Identity() - h(2) * v2 * v2.adjoint(); 22 cout << "The third Householder reflection is represented by H_2 = " << endl; 23 cout << H2 << endl; 24 cout << "Their product is H_0 H_1 H_2 = " << endl; 25 cout << H0 * H1 * H2 << endl; 26 27 HouseholderSequence<Matrix3d, Vector3d> hhSeq(v, h); 28 Matrix3d hhSeqAsMatrix(hhSeq); 29 cout << "If we construct a HouseholderSequence from v and h" << endl; 30 cout << "and convert it to a matrix, we get:" << endl; 31 cout << hhSeqAsMatrix << endl; 32