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JacobiRotation< Scalar > Class Template Reference
[Jacobi module]
#include <Jacobi.h>
Public Member Functions | |
JacobiRotation () | |
Default constructor without any initialization. | |
JacobiRotation (const Scalar &c, const Scalar &s) | |
Construct a planar rotation from a cosine-sine pair (c, s ). | |
JacobiRotation | operator* (const JacobiRotation &other) |
Concatenates two planar rotation. | |
JacobiRotation | transpose () const |
Returns the transposed transformation. | |
JacobiRotation | adjoint () const |
Returns the adjoint transformation. | |
template<typename Derived > | |
bool | makeJacobi (const MatrixBase< Derived > &, typename Derived::Index p, typename Derived::Index q) |
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 . | |
bool | 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 . | |
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: . |
Detailed Description
template<typename Scalar>
class Eigen::JacobiRotation< Scalar >
Rotation given by a cosine-sine pair.
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());
Definition at line 34 of file src/Jacobi/Jacobi.h.
Constructor & Destructor Documentation
JacobiRotation | ( | ) |
Default constructor without any initialization.
Definition at line 40 of file src/Jacobi/Jacobi.h.
JacobiRotation | ( | const Scalar & | c, |
const Scalar & | s | ||
) |
Construct a planar rotation from a cosine-sine pair (c, s
).
Definition at line 43 of file src/Jacobi/Jacobi.h.
Member Function Documentation
JacobiRotation adjoint | ( | ) | const |
Returns the adjoint transformation.
Definition at line 62 of file src/Jacobi/Jacobi.h.
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:
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.
Definition at line 148 of file src/Jacobi/Jacobi.h.
bool 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()
Definition at line 83 of file src/Jacobi/Jacobi.h.
bool makeJacobi | ( | const MatrixBase< Derived > & | m, |
typename Derived::Index | p, | ||
typename Derived::Index | q | ||
) |
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:
- See also:
- JacobiRotation::makeJacobi(RealScalar, Scalar, RealScalar), MatrixBase::applyOnTheLeft(), MatrixBase::applyOnTheRight()
Definition at line 126 of file src/Jacobi/Jacobi.h.
JacobiRotation operator* | ( | const JacobiRotation< Scalar > & | other ) |
Concatenates two planar rotation.
Definition at line 51 of file src/Jacobi/Jacobi.h.
JacobiRotation transpose | ( | ) | const |
Returns the transposed transformation.
Definition at line 59 of file src/Jacobi/Jacobi.h.
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