JacobiRotation< Scalar > Class Template Reference

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

List of all members.

Public Member Functions
JacobiRotation	adjoint () const
	JacobiRotation ()
	JacobiRotation (const Scalar &c, const Scalar &s)
void	makeGivens (const Scalar &p, const Scalar &q, Scalar *z=0)
template<typename Derived >
bool	makeJacobi (const MatrixBase< Derived > &, typename Derived::Index p, typename Derived::Index q)
bool	makeJacobi (RealScalar x, Scalar y, RealScalar z)
JacobiRotation	operator* (const JacobiRotation &other)
JacobiRotation	transpose () const

---

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 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()

---

Constructor & Destructor Documentation

JacobiRotation

(

)

[inline]

Default constructor without any initialization.

JacobiRotation	(	const Scalar &	c,
		const Scalar &	s
	)		[inline]

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

---

Member Function Documentation

JacobiRotation adjoint

(

)

const [inline]

Returns the adjoint transformation

void makeGivens	(	const Scalar &	p,
		const Scalar &	q,
		Scalar *	z = 0
	)

Makes *this as a Givens rotation G such that applying to the left of the vector yields: .

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:

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:

Here is the vector v:
0.68
-0.211
Here is the vector J' * v:
0.712
0

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()

bool 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 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()

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 yields a diagonal matrix

See also:

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

JacobiRotation operator*

(

const JacobiRotation< Scalar > &

other

)

[inline]

Concatenates two planar rotation

JacobiRotation transpose

(

)

const [inline]

Returns the transposed transformation

---

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