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Eigen::JacobiRotation< Scalar > Class Template Reference

Detailed Description

template<typename Scalar>
class Eigen::JacobiRotation< Scalar >

Rotation given by a cosine-sine pair.

This is defined in the Jacobi module.

#include <Eigen/Jacobi>

This class represents a Jacobi or Givens rotation. This is a 2D rotation in the plane J of angle $ \theta $ defined by its cosine c and sine s as follow: $ J = \left ( \begin{array}{cc} c & \overline s \\ -s & \overline c \end{array} \right ) $

You can apply the respective counter-clockwise rotation to a column vector v by applying its adjoint on the left: $ v = J^* v $ that translates to the following Eigen code:

* v.applyOnTheLeft(J.adjoint());
*
See Also
MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()

Public Member Functions

JacobiRotation adjoint () const
 
 JacobiRotation ()
 
 JacobiRotation (const Scalar &c, const Scalar &s)
 
void makeGivens (const Scalar &p, const Scalar &q, Scalar *z=0)
 
template<typename Derived >
bool makeJacobi (const MatrixBase< Derived > &, Index p, Index q)
 
bool makeJacobi (const RealScalar &x, const Scalar &y, const RealScalar &z)
 
JacobiRotation operator* (const JacobiRotation &other)
 
JacobiRotation transpose () const
 

Constructor & Destructor Documentation

template<typename Scalar>
Eigen::JacobiRotation< Scalar >::JacobiRotation ( )
inline

Default constructor without any initialization.

template<typename Scalar>
Eigen::JacobiRotation< Scalar >::JacobiRotation ( const Scalar &  c,
const Scalar &  s 
)
inline

Construct a planar rotation from a cosine-sine pair (c, s).

Member Function Documentation

template<typename Scalar>
JacobiRotation Eigen::JacobiRotation< Scalar >::adjoint ( ) const
inline

Returns the adjoint transformation

template<typename Scalar >
void Eigen::JacobiRotation< Scalar >::makeGivens ( const Scalar &  p,
const Scalar &  q,
Scalar *  z = 0 
)

Makes *this as a Givens rotation G such that applying $ G^* $ to the left of the vector $ V = \left ( \begin{array}{c} p \\ q \end{array} \right )$ yields: $ G^* V = \left ( \begin{array}{c} r \\ 0 \end{array} \right )$.

The value of z is returned if z is not null (the default is null). Also note that G is built such that the cosine is always real.

Example:

JacobiRotation<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;

Output:

Here is the vector v:
  0.68
-0.211
Here is the vector J' * v:
0.712
    0

This function implements the continuous Givens rotation generation algorithm found in Anderson (2000), Discontinuous Plane Rotations and the Symmetric Eigenvalue Problem. LAPACK Working Note 150, University of Tennessee, UT-CS-00-454, December 4, 2000.

See Also
MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
template<typename Scalar >
template<typename Derived >
bool Eigen::JacobiRotation< Scalar >::makeJacobi ( const MatrixBase< Derived > &  m,
Index  p,
Index  q 
)
inline

Makes *this as a Jacobi rotation J such that applying J on both the right and left sides of the 2x2 selfadjoint matrix $ B = \left ( \begin{array}{cc} \text{this}_{pp} & \text{this}_{pq} \\ (\text{this}_{pq})^* & \text{this}_{qq} \end{array} \right )$ yields a diagonal matrix $ A = J^* B J $

Example:

m = (m + m.adjoint()).eval();
JacobiRotation<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;

Output:

Here is the matrix m:
 1.36 0.355
0.355  1.19
Here is the matrix J' * m * J:
 1.64     0
    0 0.913
See Also
JacobiRotation::makeJacobi(RealScalar, Scalar, RealScalar), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
template<typename Scalar >
bool Eigen::JacobiRotation< Scalar >::makeJacobi ( const RealScalar &  x,
const Scalar &  y,
const RealScalar &  z 
)

Makes *this as a Jacobi rotation J such that applying J on both the right and left sides of the selfadjoint 2x2 matrix $ B = \left ( \begin{array}{cc} x & y \\ \overline y & z \end{array} \right )$ yields a diagonal matrix $ A = J^* B J $

See Also
MatrixBase::makeJacobi(const MatrixBase<Derived>&, Index, Index), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
template<typename Scalar>
JacobiRotation Eigen::JacobiRotation< Scalar >::operator* ( const JacobiRotation< Scalar > &  other)
inline

Concatenates two planar rotation

template<typename Scalar>
JacobiRotation Eigen::JacobiRotation< Scalar >::transpose ( ) const
inline

Returns the transposed transformation


The documentation for this class was generated from the following files: