add examples for makeJacobi and makeGivens

Eigen/Jacobi

@@ -8,11 +8,15 @@
 namespace Eigen {
 
 /** \defgroup Jacobi_Module Jacobi module
-  * This module provides Jacobi rotations.
+  * This module provides Jacobi and Givens rotations.
   *
   * \code
   * #include <Eigen/Jacobi>
   * \endcode
+  *
+  * In addition to listed classes, it defines the two following MatrixBase methods to apply a Jacobi or Givens rotation:
+  *  - MatrixBase::applyOnTheLeft()
+  *  - MatrixBase::applyOnTheRight().
   */
 
 #include "src/Jacobi/Jacobi.h"

Eigen/src/Jacobi/Jacobi.h

@@ -26,16 +26,23 @@
 #ifndef EIGEN_JACOBI_H
 #define EIGEN_JACOBI_H
 
-/** \ingroup Jacobi
+/** \ingroup Jacobi_Module
+  * \jacobi_module
   * \class PlanarRotation
   * \brief Represents a rotation in the plane from a cosine-sine pair.
   *
   * This class represents a Jacobi or Givens rotation.
-  * This is a 2D clock-wise rotation in the plane \c J of angle \f$ \theta \f$ defined by
+  * This is a 2D rotation in the plane \c J of angle \f$ \theta \f$ defined by
   * its cosine \c c and sine \c s as follow:
   * \f$ J = \left ( \begin{array}{cc} c & \overline s \\ -s  & \overline c \end{array} \right ) \f$
   *
-  * \sa MatrixBase::makeJacobi(), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+  * You can apply the respective counter-clockwise rotation to a column vector \c v by
+  * applying its adjoint on the left: \f$ v = J^* v \f$ that translates to the following Eigen code:
+  * \code
+  * v.applyOnTheLeft(J.adjoint());
+  * \endcode
+  *
+  * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
   */
 template<typename Scalar> class PlanarRotation
 {
@@ -79,11 +86,10 @@ template<typename Scalar> class PlanarRotation
     Scalar m_c, m_s;
 };
 
-/** Makes \c *this as a Jacobi rotation \a J such that applying \a J on both the right and left sides of the 2x2 matrix
-  * \f$ B = \left ( \begin{array}{cc} x & y \\ * & z \end{array} \right )\f$ yields
-  * a diagonal matrix \f$ A = J^* B J \f$
+/** Makes \c *this as a Jacobi rotation \a J such that applying \a J on both the right and left sides of the selfadjoint 2x2 matrix
+  * \f$ B = \left ( \begin{array}{cc} x & y \\ * & z \end{array} \right )\f$ yields a diagonal matrix \f$ A = J^* B J \f$
   *
-  * \sa MatrixBase::makeJacobi(), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
+  * \sa MatrixBase::makeJacobi(const MatrixBase<Derived>&, int, int), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
   */
 template<typename Scalar>
 bool PlanarRotation<Scalar>::makeJacobi(RealScalar x, Scalar y, RealScalar z)
@@ -116,10 +122,13 @@ bool PlanarRotation<Scalar>::makeJacobi(RealScalar x, Scalar y, RealScalar z)
   }
 }
 
-/** Makes \c *this as a Jacobi rotation \c J such that applying \a J on both the right and left sides of the 2x2 matrix
+/** Makes \c *this as a Jacobi rotation \c J such that applying \a J on both the right and left sides of the 2x2 selfadjoint matrix
   * \f$ B = \left ( \begin{array}{cc} \text{this}_{pp} & \text{this}_{pq} \\ * & \text{this}_{qq} \end{array} \right )\f$ yields
   * a diagonal matrix \f$ A = J^* B J \f$
   *
+  * Example: \include Jacobi_makeJacobi.cpp
+  * Output: \verbinclude Jacobi_makeJacobi.out
+  *
   * \sa PlanarRotation::makeJacobi(RealScalar, Scalar, RealScalar), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
   */
 template<typename Scalar>
@@ -136,6 +145,9 @@ inline bool PlanarRotation<Scalar>::makeJacobi(const MatrixBase<Derived>& m, int
   * The value of \a z is returned if \a z is not null (the default is null).
   * Also note that G is built such that the cosine is always real.
   *
+  * Example: \include Jacobi_makeGivens.cpp
+  * Output: \verbinclude Jacobi_makeGivens.out
+  *
   * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
   */
 template<typename Scalar>
@@ -171,9 +183,11 @@ void PlanarRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar
 }
 
 // specialization for reals
+// TODO compute z
 template<typename Scalar>
 void PlanarRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* z, ei_meta_false)
 {
+  ei_assert(z==0 && "not implemented yet");
   // from Golub's "Matrix Computations", algorithm 5.1.3
   if(q==0)
   {
@@ -197,7 +211,8 @@ void PlanarRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar
 *   Implementation of MatrixBase methods
 ****************************************************************************************/
 
-/** Applies the clock wise 2D rotation \a j to the set of 2D vectors of cordinates \a x and \a y:
+/** \jacobi_module
+  * Applies the clock wise 2D rotation \a j to the set of 2D vectors of cordinates \a x and \a y:
   * \f$ \left ( \begin{array}{cc} x \\ y \end{array} \right )  =  J \left ( \begin{array}{cc} x \\ y \end{array} \right ) \f$
   *
   * \sa MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
@@ -205,7 +220,8 @@ void PlanarRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar
 template<typename VectorX, typename VectorY, typename OtherScalar>
 void ei_apply_rotation_in_the_plane(VectorX& _x, VectorY& _y, const PlanarRotation<OtherScalar>& j);
 
-/** Applies the rotation in the plane \a j to the rows \a p and \a q of \c *this, i.e., it computes B = J * B,
+/** \jacobi_module
+  * Applies the rotation in the plane \a j to the rows \a p and \a q of \c *this, i.e., it computes B = J * B,
   * with \f$ B = \left ( \begin{array}{cc} \text{*this.row}(p) \\ \text{*this.row}(q) \end{array} \right ) \f$.
   *
   * \sa class PlanarRotation, MatrixBase::applyOnTheRight(), ei_apply_rotation_in_the_plane()
@@ -219,7 +235,8 @@ inline void MatrixBase<Derived>::applyOnTheLeft(int p, int q, const PlanarRotati
   ei_apply_rotation_in_the_plane(x, y, j);
 }
 
-/** Applies the rotation in the plane \a j to the columns \a p and \a q of \c *this, i.e., it computes B = B * J
+/** \ingroup Jacobi_Module
+  * Applies the rotation in the plane \a j to the columns \a p and \a q of \c *this, i.e., it computes B = B * J
   * with \f$ B = \left ( \begin{array}{cc} \text{*this.col}(p) & \text{*this.col}(q) \end{array} \right ) \f$.
   *
   * \sa class PlanarRotation, MatrixBase::applyOnTheLeft(), ei_apply_rotation_in_the_plane()

doc/Doxyfile.in

@@ -208,6 +208,7 @@ ALIASES                = "only_for_vectors=This is only for vectors (either row-
                          "lu_module=This is defined in the %LU module. \code #include <Eigen/LU> \endcode" \
                          "cholesky_module=This is defined in the %Cholesky module. \code #include <Eigen/Cholesky> \endcode" \
                          "qr_module=This is defined in the %QR module. \code #include <Eigen/QR> \endcode" \
+                         "jacobi_module=This is defined in the %Jacobi module. \code #include <Eigen/Jacobi> \endcode" \
                          "svd_module=This is defined in the %SVD module. \code #include <Eigen/SVD> \endcode" \
                          "geometry_module=This is defined in the %Geometry module. \code #include <Eigen/Geometry> \endcode" \
                          "leastsquares_module=This is defined in the %LeastSquares module. \code #include <Eigen/LeastSquares> \endcode" \

doc/snippets/Jacobi_makeGivens.cpp

@@ -0,0 +1,6 @@
+Vector2f v = Vector2f::Random();
+PlanarRotation<float> G;
+G.makeGivens(v.x(), v.y());
+cout << "Here is the vector v:" << endl << v << endl;
+v.applyOnTheLeft(0, 1, G.adjoint());
+cout << "Here is the vector J' * v:" << endl << v << endl;

doc/snippets/Jacobi_makeJacobi.cpp

@@ -0,0 +1,8 @@
+Matrix2f m = Matrix2f::Random();
+m = (m + m.adjoint()).eval();
+PlanarRotation<float> J;
+J.makeJacobi(m, 0, 1);
+cout << "Here is the matrix m:" << endl << m << endl;
+m.applyOnTheLeft(0, 1, J.adjoint());
+m.applyOnTheRight(0, 1, J);
+cout << "Here is the matrix J' * m * J:" << endl << m << endl;

doc/snippets/compile_snippet.cpp.in

@@ -4,6 +4,7 @@
 #include <Eigen/QR>
 #include <Eigen/Cholesky>
 #include <Eigen/Geometry>
+#include <Eigen/Jacobi>
 
 using namespace Eigen;
 using namespace std;