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Eigen::JacobiRotation< Scalar > Class Template Reference
Dense matrix and array manipulation » Reference » Jacobi_Module

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#include <Jacobi.h>

Public Types

typedef NumTraits< Scalar >::Real RealScalar
 

Public Member Functions

 JacobiRotation ()
 Default constructor without any initialization. More...
 
 JacobiRotation (const Scalar &c, const Scalar &s)
 Construct a planar rotation from a cosine-sine pair (c, s). More...
 
Scalar & c ()
 
Scalar c () const
 
Scalar & s ()
 
Scalar s () const
 
JacobiRotation operator* (const JacobiRotation &other)
 Concatenates two planar rotation.
 
JacobiRotation transpose () const
 Returns the transposed transformation.
 
JacobiRotation adjoint () const
 Returns the adjoint transformation.
 
template<typename Derived >
bool makeJacobi (const MatrixBase< Derived > &, typename Derived::Index p, typename Derived::Index q)
 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 \( A = J^* B J \). More...
 
bool 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 \( A = J^* B J \). More...
 
void 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: \( G^* V = \left ( \begin{array}{c} r \\ 0 \end{array} \right )\). More...
 

Protected Member Functions

void makeGivens (const Scalar &p, const Scalar &q, Scalar *z, internal::true_type)
 
void makeGivens (const Scalar &p, const Scalar &q, Scalar *z, internal::false_type)
 

Protected Attributes

Scalar m_c
 
Scalar m_s
 

Detailed Description

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

Rotation given by a cosine-sine pair.

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()

Constructor & Destructor Documentation

§ JacobiRotation() [1/2]

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

Default constructor without any initialization.

§ JacobiRotation() [2/2]

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

§ makeGivens()

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:

Output: 

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() 








§ makeJacobi() [1/2]








template<typename Scalar > 



template<typename Derived > 



  

  
      

        

          bool Eigen::JacobiRotation< Scalar >::makeJacobi 
          (
          const MatrixBase< Derived > & 
          m, 
        

        

          
          
          typename Derived::Index 
          p, 
        

        

          
          
          typename Derived::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: 
 Output: 
See also
JacobiRotation::makeJacobi(RealScalar, Scalar, RealScalar), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight() 








§ makeJacobi() [2/2]








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() 







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





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