Rotation given by a cosine-sine pair. More...

#include <ForwardDeclarations.h>

Public Types
typedef NumTraits< Scalar >::Real	RealScalar

Public Member Functions
JacobiRotation	adjoint () const

Scalar &	c ()

Scalar	c () 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)

template<typename Scalar >
bool	makeJacobi (const RealScalar &x, const Scalar &y, const RealScalar &z)

JacobiRotation	operator* (const JacobiRotation &other)

Scalar &	s ()

Scalar	s () const

JacobiRotation	transpose () const

Protected Member Functions
void	makeGivens (const Scalar &p, const Scalar &q, Scalar *r, internal::false_type)

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

Protected Attributes
Scalar	m_c

Scalar	m_s

Detailed Description

Rotation given by a cosine-sine pair.

\jacobi_module

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 263 of file ForwardDeclarations.h.

Member Typedef Documentation

◆ RealScalar

typedef NumTraits<Scalar>::Real Eigen::JacobiRotation::RealScalar

Definition at line 37 of file Jacobi.h.

Constructor & Destructor Documentation

◆ JacobiRotation() [1/2]

Eigen::JacobiRotation::JacobiRotation ( )

inline

Default constructor without any initialization.

Definition at line 40 of file Jacobi.h.

◆ JacobiRotation() [2/2]

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

inline

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

Definition at line 43 of file Jacobi.h.

Member Function Documentation

◆ adjoint()

JacobiRotation Eigen::JacobiRotation::adjoint ( ) const

inline

Returns the adjoint transformation

Definition at line 62 of file Jacobi.h.

◆ c() [1/2]

Scalar& Eigen::JacobiRotation::c ( )

inline

Definition at line 45 of file Jacobi.h.

◆ c() [2/2]

Scalar Eigen::JacobiRotation::c ( ) const

inline

Definition at line 46 of file Jacobi.h.

◆ makeGivens() [1/3]

void Eigen::JacobiRotation::makeGivens	(	const Scalar &	p,
		const Scalar &	q,
		Scalar *	r,
		internal::false_type
	)

protected

Definition at line 215 of file Jacobi.h.

◆ makeGivens() [2/3]

void Eigen::JacobiRotation::makeGivens	(	const Scalar &	p,
		const Scalar &	q,
		Scalar *	r,
		internal::true_type
	)

protected

Definition at line 156 of file Jacobi.h.

◆ makeGivens() [3/3]

void Eigen::JacobiRotation::makeGivens	(	const Scalar &	p,
		const Scalar &	q,
		Scalar *	r = `0`
	)

◆ makeJacobi() [1/3]

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 $B = \left ( \begin{array}{cc} \text{this}_{pp} & \text{this}_{pq} \\ (\text{this}_{pq})^* & \text{this}_{qq} \end{array} \right )$ yields a diagonal matrix $ A = J^* B J $

Example:

Output:

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

Definition at line 126 of file Jacobi.h.

◆ makeJacobi() [2/3]

bool Eigen::JacobiRotation::makeJacobi	(	const RealScalar &	x,
		const Scalar &	y,
		const RealScalar &	z
	)

◆ makeJacobi() [3/3]

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 $B = \left ( \begin{array}{cc} x & y \\ \overline y & z \end{array} \right )$ yields a diagonal matrix $ A = J^* B J $

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

Definition at line 83 of file Jacobi.h.

◆ operator*()

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

inline

Concatenates two planar rotation

Definition at line 51 of file Jacobi.h.

◆ s() [1/2]

Scalar& Eigen::JacobiRotation::s ( )

inline

Definition at line 47 of file Jacobi.h.

◆ s() [2/2]

Scalar Eigen::JacobiRotation::s ( ) const

inline

Definition at line 48 of file Jacobi.h.

◆ transpose()

JacobiRotation Eigen::JacobiRotation::transpose ( ) const

inline

Returns the transposed transformation

Definition at line 59 of file Jacobi.h.

Member Data Documentation

◆ m_c

Scalar Eigen::JacobiRotation::m_c

protected

Definition at line 74 of file Jacobi.h.

◆ m_s

Scalar Eigen::JacobiRotation::m_s

protected

Definition at line 74 of file Jacobi.h.

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

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ RealScalar

Constructor & Destructor Documentation

◆ JacobiRotation() [1/2]

◆ JacobiRotation() [2/2]

Member Function Documentation

◆ adjoint()

◆ c() [1/2]

◆ c() [2/2]

◆ makeGivens() [1/3]

◆ makeGivens() [2/3]

◆ makeGivens() [3/3]

◆ makeJacobi() [1/3]

◆ makeJacobi() [2/3]

◆ makeJacobi() [3/3]

◆ operator*()

◆ s() [1/2]

◆ s() [2/2]

◆ transpose()

Member Data Documentation

◆ m_c

◆ m_s