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31 lines
1.3 KiB
31 lines
1.3 KiB
Matrix3d v = Matrix3d::Random();
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cout << "The matrix v is:" << endl;
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cout << v << endl;
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Vector3d v0(1, v(1,0), v(2,0));
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cout << "The first Householder vector is: v_0 = " << v0.transpose() << endl;
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Vector3d v1(0, 1, v(2,1));
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cout << "The second Householder vector is: v_1 = " << v1.transpose() << endl;
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Vector3d v2(0, 0, 1);
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cout << "The third Householder vector is: v_2 = " << v2.transpose() << endl;
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Vector3d h = Vector3d::Random();
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cout << "The Householder coefficients are: h = " << h.transpose() << endl;
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Matrix3d H0 = Matrix3d::Identity() - h(0) * v0 * v0.adjoint();
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cout << "The first Householder reflection is represented by H_0 = " << endl;
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cout << H0 << endl;
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Matrix3d H1 = Matrix3d::Identity() - h(1) * v1 * v1.adjoint();
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cout << "The second Householder reflection is represented by H_1 = " << endl;
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cout << H1 << endl;
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Matrix3d H2 = Matrix3d::Identity() - h(2) * v2 * v2.adjoint();
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cout << "The third Householder reflection is represented by H_2 = " << endl;
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cout << H2 << endl;
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cout << "Their product is H_0 H_1 H_2 = " << endl;
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cout << H0 * H1 * H2 << endl;
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HouseholderSequence<Matrix3d, Vector3d> hhSeq(v, h);
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Matrix3d hhSeqAsMatrix(hhSeq);
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cout << "If we construct a HouseholderSequence from v and h" << endl;
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cout << "and convert it to a matrix, we get:" << endl;
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cout << hhSeqAsMatrix << endl;
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