Eigen::JacobiRotation Class Reference

Detailed Description

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 defined by its cosine c and sine s as follow:

You can apply the respective counter-clockwise rotation to a column vector v by applying its adjoint on the left: 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)
template<typename Derived >
bool	makeJacobi (const MatrixBase< Derived > &, Index p, Index q)
template<typename Scalar >
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]

Eigen::JacobiRotation::JacobiRotation ( )

inline

Default constructor without any initialization.

JacobiRotation() [2/2]

Eigen::JacobiRotation::JacobiRotation ( const Scalar &  c, const Scalar &  s  )

inline

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

Member Function Documentation

adjoint()

JacobiRotation Eigen::JacobiRotation::adjoint ( ) const

inline

Returns the adjoint transformation

makeJacobi() [1/2]

template<typename Derived >

bool Eigen::JacobiRotation::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 yields a diagonal matrix

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:

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()

makeJacobi() [2/2]

template<typename Scalar >

bool Eigen::JacobiRotation::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 yields a diagonal matrix

See also

MatrixBase::makeJacobi(const MatrixBase<Derived>&, Index, Index), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()

operator*()

JacobiRotation Eigen::JacobiRotation::operator* ( const JacobiRotation &  other )

inline

Concatenates two planar rotation

transpose()

JacobiRotation Eigen::JacobiRotation::transpose ( ) const

inline

Returns the transposed transformation

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

• ForwardDeclarations.h
• Jacobi.h