Document HouseholderSequence.

Incomplete: I did not explain the difference between OnTheLeft and OnTheRight,
and there is only one example.

1 files changed, 31 insertions, 0 deletions

diff --git a/doc/snippets/HouseholderSequence_HouseholderSequence.cpp b/doc/snippets/HouseholderSequence_HouseholderSequence.cpp
new file mode 100644
index 000000000..2632b83b9
--- /dev/null
+++ b/doc/snippets/HouseholderSequence_HouseholderSequence.cpp
@@ -0,0 +1,31 @@
+Matrix3d v = Matrix3d::Random();
+cout << "The matrix v is:" << endl;
+cout << v << endl;
+
+Vector3d v0(1, v(1,0), v(2,0));
+cout << "The first Householder vector is: v_0 = " << v0.transpose() << endl;
+Vector3d v1(0, 1, v(2,1));
+cout << "The second Householder vector is: v_1 = " << v1.transpose()  << endl;
+Vector3d v2(0, 0, 1);
+cout << "The third Householder vector is: v_2 = " << v2.transpose() << endl;
+
+Vector3d h = Vector3d::Random();
+cout << "The Householder coefficients are: h = " << h.transpose() << endl;
+
+Matrix3d H0 = Matrix3d::Identity() - h(0) * v0 * v0.adjoint();
+cout << "The first Householder reflection is represented by H_0 = " << endl;
+cout << H0 << endl;
+Matrix3d H1 = Matrix3d::Identity() - h(1) * v1 * v1.adjoint();
+cout << "The second Householder reflection is represented by H_1 = " << endl;
+cout << H1 << endl;
+Matrix3d H2 = Matrix3d::Identity() - h(2) * v2 * v2.adjoint();
+cout << "The third Householder reflection is represented by H_2 = " << endl;
+cout << H2 << endl;
+cout << "Their product is H_0 H_1 H_2 = " << endl;
+cout << H0 * H1 * H2 << endl;
+
+HouseholderSequence<Matrix3d, Vector3d> hhSeq(v, h);
+Matrix3d hhSeqAsMatrix(hhSeq);
+cout << "If we construct a HouseholderSequence from v and h" << endl;
+cout << "and convert it to a matrix, we get:" << endl;
+cout << hhSeqAsMatrix << endl;