Eigen  3.4.90 (git rev 9589cc4e7fd8e4538bedef80dd36c7738977a8be)
 
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Eigen::JacobiRotation< Scalar > Class Template Reference
Dense matrix and array manipulation » Reference » Jacobi module

#include <Eigen/src/Jacobi/Jacobi.h>

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 *r=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

◆ 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

◆ adjoint()

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

Returns the adjoint transformation

◆ makeGivens()

template<typename Scalar>
void Eigen::JacobiRotation< Scalar >::makeGivens ( const Scalar & p,
const Scalar & q,
Scalar * r = 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 r is returned if r is not null (the default is null). Also note that G is built such that the cosine is always real.

Example:

Vector2f v = Vector2f::Random();
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;
Eigen::JacobiRotation::JacobiRotation
JacobiRotation()
Definition Jacobi.h:43
Eigen::JacobiRotation::adjoint
JacobiRotation adjoint() const
Definition Jacobi.h:67
Eigen::JacobiRotation::makeGivens
void makeGivens(const Scalar &p, const Scalar &q, Scalar *r=0)
Definition Jacobi.h:152
Eigen::Vector2f
Matrix< float, 2, 1 > Vector2f
2×1 vector of type float.
Definition Matrix.h:478

Output: 

Here is the vector v:
-0.824
 0.924
Here is the vector J' * v:
     1.24
-5.96e-08

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,
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:

Matrix2f m = Matrix2f::Random();
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;
Eigen::JacobiRotation::makeJacobi
bool makeJacobi(const MatrixBase< Derived > &, Index p, Index q)
Definition Jacobi.h:131
Eigen::Matrix2f
Matrix< float, 2, 2 > Matrix2f
2×2 matrix of type float.
Definition Matrix.h:478

Output: 

Here is the matrix m:
 -1.65  0.871
 0.871 -0.397
Here is the matrix J' * m * J:
 -2.09      0
     0 0.0494
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()

◆ operator*()

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

Concatenates two planar rotation

◆ transpose()

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: