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JacobiRotation< Scalar > Class Template Reference


Detailed Description

template<typename Scalar>
class 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()

Definition at line 47 of file Jacobi.h.

#include <src/Jacobi/Jacobi.h>

List of all members.

Public Types

typedef NumTraits< Scalar >::Real RealScalar

Public Member Functions

 JacobiRotation ()
 Default constructor without any initialization.
 JacobiRotation (const Scalar &c, const Scalar &s)
 Construct a planar rotation from a cosine-sine pair (c, s).
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 $.
bool makeJacobi (RealScalar x, Scalar y, 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 $.
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 )$.

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

Member Typedef Documentation

template<typename Scalar>
typedef NumTraits<Scalar>::Real JacobiRotation< Scalar >::RealScalar

Definition at line 50 of file Jacobi.h.


Constructor & Destructor Documentation

template<typename Scalar>
JacobiRotation< Scalar >::JacobiRotation ( ) [inline]

Default constructor without any initialization.

Definition at line 53 of file Jacobi.h.

Referenced by JacobiRotation< Scalar >::adjoint(), JacobiRotation< Scalar >::operator*(), and JacobiRotation< Scalar >::transpose().

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

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

Definition at line 56 of file Jacobi.h.


Member Function Documentation

template<typename Scalar>
JacobiRotation JacobiRotation< Scalar >::adjoint ( ) const [inline]
template<typename Scalar>
Scalar JacobiRotation< Scalar >::c ( ) const [inline]

Definition at line 59 of file Jacobi.h.

References JacobiRotation< Scalar >::m_c.

template<typename Scalar>
Scalar& JacobiRotation< Scalar >::c ( ) [inline]
template<typename Scalar >
void 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()

Definition at line 158 of file Jacobi.h.

Referenced by ComplexSchur< MatrixType >::reduceToTriangularForm(), RealSchur< MatrixType >::splitOffTwoRows(), and internal::tridiagonal_qr_step().

template<typename Scalar >
void JacobiRotation< Scalar >::makeGivens ( const Scalar &  p,
const Scalar &  q,
Scalar *  z,
internal::true_type   
) [protected]

Definition at line 166 of file Jacobi.h.

References abs(), abs2(), real(), and internal::sqrt().

template<typename Scalar >
void JacobiRotation< Scalar >::makeGivens ( const Scalar &  p,
const Scalar &  q,
Scalar *  z,
internal::false_type   
) [protected]

Definition at line 221 of file Jacobi.h.

References abs(), abs2(), internal::sqrt(), and t().

template<typename Scalar >
bool JacobiRotation< Scalar >::makeJacobi ( RealScalar  x,
Scalar  y,
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()

Definition at line 95 of file Jacobi.h.

References abs(), abs2(), internal::sqrt(), and t().

template<typename Scalar >
template<typename Derived >
bool 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()

Definition at line 136 of file Jacobi.h.

References real().

Referenced by internal::real_2x2_jacobi_svd().

template<typename Scalar>
JacobiRotation JacobiRotation< Scalar >::operator* ( const JacobiRotation< Scalar > &  other) [inline]

Concatenates two planar rotation.

Definition at line 64 of file Jacobi.h.

References JacobiRotation< Scalar >::JacobiRotation(), JacobiRotation< Scalar >::m_c, and JacobiRotation< Scalar >::m_s.

template<typename Scalar>
Scalar& JacobiRotation< Scalar >::s ( ) [inline]
template<typename Scalar>
Scalar JacobiRotation< Scalar >::s ( ) const [inline]

Definition at line 61 of file Jacobi.h.

References JacobiRotation< Scalar >::m_s.

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

Member Data Documentation

template<typename Scalar>
Scalar JacobiRotation< Scalar >::m_c [protected]
template<typename Scalar>
Scalar JacobiRotation< Scalar >::m_s [protected]



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