Go to the documentation of this file.00001 Matrix3d v = Matrix3d::Random();
00002 cout << "The matrix v is:" << endl;
00003 cout << v << endl;
00004
00005 Vector3d v0(1, v(1,0), v(2,0));
00006 cout << "The first Householder vector is: v_0 = " << v0.transpose() << endl;
00007 Vector3d v1(0, 1, v(2,1));
00008 cout << "The second Householder vector is: v_1 = " << v1.transpose() << endl;
00009 Vector3d v2(0, 0, 1);
00010 cout << "The third Householder vector is: v_2 = " << v2.transpose() << endl;
00011
00012 Vector3d h = Vector3d::Random();
00013 cout << "The Householder coefficients are: h = " << h.transpose() << endl;
00014
00015 Matrix3d H0 = Matrix3d::Identity() - h(0) * v0 * v0.adjoint();
00016 cout << "The first Householder reflection is represented by H_0 = " << endl;
00017 cout << H0 << endl;
00018 Matrix3d H1 = Matrix3d::Identity() - h(1) * v1 * v1.adjoint();
00019 cout << "The second Householder reflection is represented by H_1 = " << endl;
00020 cout << H1 << endl;
00021 Matrix3d H2 = Matrix3d::Identity() - h(2) * v2 * v2.adjoint();
00022 cout << "The third Householder reflection is represented by H_2 = " << endl;
00023 cout << H2 << endl;
00024 cout << "Their product is H_0 H_1 H_2 = " << endl;
00025 cout << H0 * H1 * H2 << endl;
00026
00027 HouseholderSequence<Matrix3d, Vector3d> hhSeq(v, h);
00028 Matrix3d hhSeqAsMatrix(hhSeq);
00029 cout << "If we construct a HouseholderSequence from v and h" << endl;
00030 cout << "and convert it to a matrix, we get:" << endl;
00031 cout << hhSeqAsMatrix << endl;