Rotation given by a cosine-sine pair. More...
#include <Jacobi.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 *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) |
Scalar & | s () |
Scalar | s () const |
JacobiRotation | transpose () const |
Protected Member Functions | |
void | makeGivens (const Scalar &p, const Scalar &q, Scalar *z, internal::true_type) |
void | makeGivens (const Scalar &p, const Scalar &q, Scalar *z, internal::false_type) |
Protected Attributes | |
Scalar | m_c |
Scalar | m_s |
Rotation given by a cosine-sine pair.
This is defined in the Jacobi module.
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:
typedef NumTraits<Scalar>::Real RealScalar |
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Default constructor without any initialization.
Referenced by JacobiRotation< Scalar >::adjoint(), JacobiRotation< Scalar >::operator*(), and JacobiRotation< Scalar >::transpose().
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Construct a planar rotation from a cosine-sine pair (c, s
).
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Returns the adjoint transformation
References conj(), JacobiRotation< Scalar >::JacobiRotation(), JacobiRotation< Scalar >::m_c, and JacobiRotation< Scalar >::m_s.
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References JacobiRotation< Scalar >::m_c.
Referenced by Eigen::internal::apply_rotation_in_the_plane().
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References JacobiRotation< Scalar >::m_c.
void makeGivens | ( | const Scalar & | p, |
const Scalar & | q, | ||
Scalar * | z = 0 |
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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:
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.
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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:
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
References real().
Referenced by Eigen::internal::real_2x2_jacobi_svd().
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
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Concatenates two planar rotation
References conj(), JacobiRotation< Scalar >::JacobiRotation(), JacobiRotation< Scalar >::m_c, and JacobiRotation< Scalar >::m_s.
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References JacobiRotation< Scalar >::m_s.
Referenced by Eigen::internal::apply_rotation_in_the_plane().
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References JacobiRotation< Scalar >::m_s.
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Returns the transposed transformation
References conj(), JacobiRotation< Scalar >::JacobiRotation(), JacobiRotation< Scalar >::m_c, and JacobiRotation< Scalar >::m_s.
Referenced by MatrixBase< Derived >::applyOnTheRight(), JacobiSVD< _MatrixType, QRPreconditioner >::compute(), and Eigen::internal::real_2x2_jacobi_svd().
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