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add examples for makeJacobi and makeGivens

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This commit is contained in:
Gael Guennebaud
2009-09-03 11:17:16 +02:00
parent c893917d65
commit 16c7b1daab
6 changed files with 49 additions and 12 deletions
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39
Eigen/src/Jacobi/Jacobi.h
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@@ -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()