ground/gcs/src/libs/eigen/doc/snippets/HouseholderSequence_HouseholderSequence.cpp

   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;