rtc::EigenSystem< T, M > Class Template Reference

#include <rtcEigenSystem.h>

List of all members.

Public Member Functions
void	balance ()
void	eigenSort (Vec< T, M > &d, SMat< T, M > &v)
	EigenSystem (SMat< T, M > &a_)
void	hessenbergReduce ()
void	householderReduce (Vec< T, M > &d, Vec< T, M > &e, bool vecs=true)
void	householderSolve (Vec< T, M > &d, Vec< T, M > &e, bool vecs=true)
bool	jacobi (Vec< T, M > &eigenvalues, SMat< T, M > &eigenvectors)
bool	jacobi (Vec< T, M > &eigenvalues, SMat< T, M > &eigenvectors, int *nrot)
bool	jacobi2 (Vec< T, M > &eigenvalues, SMat< T, M > &eigenvectors) const
void	qr (Vec< T, M > &wreal, Vec< T, M > &wimag)
	~EigenSystem ()
Protected Member Functions
void	rotate (double &g, double &h, SMat< T, M > &a, const int i, const int j, const int k, const int l, const double s, const double tau) const
void	rotateT (double &g, double &h, SMat< T, M > &a, const int i, const int j, const int k, const int l, const double s, const double tau) const
Protected Attributes
SMat< T, M > &	a

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Detailed Description

template<class T, int M>
class rtc::EigenSystem< T, M >

Eigen Value/Vector System, a composition of SMat<T,M> and Vec<T,M>

All methods have been vetted against each other but not compared to external references like Matlab. Also, there has been no test of challenging matrices, only random, well-conditioned ones. Since these methods have all been taken from Numerical Recipes for C (online), they should all function well. However, I've parsed all but the QR algorithm into 0-based index referencing (I put a wrapper on QR because the internal indexing was too complicated), so there is a possibility that some mistakes were made in this transcription (unlikely, however, since they appear to work.

Definition at line 60 of file rtcEigenSystem.h.

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Constructor & Destructor Documentation

template<class T , int M>

rtc::EigenSystem< T, M >::EigenSystem

(

SMat< T, M > &

a_

)

[inline]

Ctor that accepts system matrix.

Definition at line 106 of file rtcEigenSystem.h.

template<class T , int M>

rtc::EigenSystem< T, M >::~EigenSystem

(

)

[inline]

Dtor to delete memory and indicate conclusion

Definition at line 112 of file rtcEigenSystem.h.

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Member Function Documentation

template<class T , int M>

void rtc::EigenSystem< T, M >::balance

(

)

[inline]

Balance an unbalanced non-symmetric real-valued matrix. Taken from Numerical Recipes in C.

Definition at line 543 of file rtcEigenSystem.h.

template<class T , int M>

void rtc::EigenSystem< T, M >::eigenSort	(	Vec< T, M > &	d,
		SMat< T, M > &	v
	)			[inline]

Sorts eigenvalues (and corresponding eigenvectors) into descending order by straight insertion. Taken from Numerical Recipes in C.

Returns:

d is the vector of eigenvalues (e.g., from jacobi())

v is the matrix of eigenvectors

Definition at line 518 of file rtcEigenSystem.h.

template<class T , int M>

void rtc::EigenSystem< T, M >::hessenbergReduce

(

)

[inline]

Reduce to Hessenberg form, for real non-symmetric matrices. Best to run EigenSystem<T,M>::balance() first, though not required. Taken from Numerical Recipes in C.

Definition at line 585 of file rtcEigenSystem.h.

template<class T , int M>

void rtc::EigenSystem< T, M >::householderReduce	(	Vec< T, M > &	d,
		Vec< T, M > &	e,
		bool	vecs = true
	)			[inline]

Householder reduction of real, symmetric matrices. Taken from Numerical Recipes in C.

Returns:

d is diagonal of tri-diagonal matrix output

e is the off-diagonal with e(0) = 0.

*nrot is the number of Jacobi rotations required

Definition at line 354 of file rtcEigenSystem.h.

template<class T , int M>

void rtc::EigenSystem< T, M >::householderSolve	(	Vec< T, M > &	d,
		Vec< T, M > &	e,
		bool	vecs = true
	)			[inline]

Householder Eigenvector Solve of real, symmetric matrices. Taken from Numerical Recipes in C.

Parameters:

	d	is the diagonal from householderReduce()
	e	is the off-diagonal from householderReduce()
	vecs	should be set if eigenvectors are wanted

Definition at line 444 of file rtcEigenSystem.h.

template<class T , int M>

bool rtc::EigenSystem< T, M >::jacobi	(	Vec< T, M > &	d,
		SMat< T, M > &	v
	)			[inline]

Jacobi method for real symmetric matrices. Taken from Numerical Recipes in C.

Returns:

d is the vector of eigenvalues

v is the matrix whose columns are the corresponding eigenvectors

Definition at line 123 of file rtcEigenSystem.h.

template<class T , int M>

bool rtc::EigenSystem< T, M >::jacobi	(	Vec< T, M > &	d,
		SMat< T, M > &	v,
		int *	nrot
	)			[inline]

Jacobi method for real symmetric matrices. Taken from Numerical Recipes in C.

Returns:

d is the vector of eigenvalues

v is the matrix whose columns are the corresponding eigenvectors

*nrot is the number of Jacobi rotations required

Definition at line 135 of file rtcEigenSystem.h.

template<class T , int M>

bool rtc::EigenSystem< T, M >::jacobi2	(	Vec< T, M > &	eigenvalues,
		SMat< T, M > &	eigenvectors
	)			const [inline]

Jacobi method for real symmetric matrices. Taken from Numerical Recipes in C. Press, Vetterling, Teukolsky, Flannery Numerical Recipes in C, 2nd edition Cambridge University Press, 1992 p. 467

Returns:

d is the vector of eigenvalues

v is the matrix whose columns are the corresponding eigenvectors

Definition at line 239 of file rtcEigenSystem.h.

template<class T , int M>

void rtc::EigenSystem< T, M >::qr	(	Vec< T, M > &	wreal,
		Vec< T, M > &	wimag
	)			[inline]

Perform a QR Decomposition, for real non-symmetric matrices. Precondition: works on output of hessenbergReduce(). Taken from Numerical Recipes in C.

Definition at line 620 of file rtcEigenSystem.h.

template<class T , int M>

void rtc::EigenSystem< T, M >::rotate	(	double &	g,
		double &	h,
		SMat< T, M > &	a,
		const int	i,
		const int	j,
		const int	k,
		const int	l,
		const double	s,
		const double	tau
	)			const [inline, protected]

Definition at line 208 of file rtcEigenSystem.h.

template<class T , int M>

void rtc::EigenSystem< T, M >::rotateT	(	double &	g,
		double &	h,
		SMat< T, M > &	a,
		const int	i,
		const int	j,
		const int	k,
		const int	l,
		const double	s,
		const double	tau
	)			const [inline, protected]

Definition at line 218 of file rtcEigenSystem.h.

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Member Data Documentation

template<class T, int M>

SMat<T,M>& rtc::EigenSystem< T, M >::a [protected]

Definition at line 92 of file rtcEigenSystem.h.

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

• rtcEigenSystem.h