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 *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;

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, 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;

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()

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

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

• Jacobi.h