Eigen::internal Namespace Reference

Classes
struct	traits< TridiagonalizationMatrixTReturnType< MatrixType > >
struct	tridiagonalization_inplace_selector
struct	tridiagonalization_inplace_selector< MatrixType, 3, false >
struct	tridiagonalization_inplace_selector< MatrixType, 1, IsComplex >
struct	TridiagonalizationMatrixTReturnType
struct	traits< HessenbergDecompositionMatrixHReturnType< MatrixType > >
struct	HessenbergDecompositionMatrixHReturnType
	More...
struct	complex_schur_reduce_to_hessenberg
struct	complex_schur_reduce_to_hessenberg< MatrixType, false >
struct	eigenvalues_selector
struct	eigenvalues_selector< Derived, false >
struct	traits< solve_retval_base< DecompositionType, Rhs > >
class	solve_retval_base
struct	llt_inplace< Lower >
struct	llt_inplace< Upper >
struct	LLT_Traits< MatrixType, Lower >
struct	LLT_Traits< MatrixType, Upper >
struct	solve_retval< LLT< _MatrixType, UpLo >, Rhs >
struct	ldlt_inplace< Lower >
struct	ldlt_inplace< Upper >
struct	LDLT_Traits< MatrixType, Lower >
struct	LDLT_Traits< MatrixType, Upper >
struct	solve_retval< LDLT< _MatrixType, _UpLo >, Rhs >
struct	solve_retval< HouseholderQR< _MatrixType >, Rhs >
struct	solve_retval< FullPivHouseholderQR< _MatrixType >, Rhs >
struct	solve_retval< ColPivHouseholderQR< _MatrixType >, Rhs >
Functions
template<typename MatrixType , typename CoeffVectorType >
void	tridiagonalization_inplace (MatrixType &matA, CoeffVectorType &hCoeffs)
template<typename MatrixType , typename DiagonalType , typename SubDiagonalType >
void	tridiagonalization_inplace (MatrixType &mat, DiagonalType &diag, SubDiagonalType &subdiag, bool extractQ)
	Performs a full tridiagonalization in place.
template<int StorageOrder, typename RealScalar , typename Scalar , typename Index >
static void	tridiagonal_qr_step (RealScalar *diag, RealScalar *subdiag, Index start, Index end, Scalar *matrixQ, Index n)
template<typename RealScalar >
std::complex< RealScalar >	sqrt (const std::complex< RealScalar > &z)
	Computes the principal value of the square root of the complex z.
template<typename MatrixQR , typename HCoeffs >
void	householder_qr_inplace_unblocked (MatrixQR &mat, HCoeffs &hCoeffs, typename MatrixQR::Scalar *tempData=0)
template<typename MatrixQR , typename HCoeffs >
void	householder_qr_inplace_blocked (MatrixQR &mat, HCoeffs &hCoeffs, typename MatrixQR::Index maxBlockSize=32, typename MatrixQR::Scalar *tempData=0)

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Function Documentation

template<typename MatrixQR , typename HCoeffs >

void Eigen::internal::householder_qr_inplace_blocked	(	MatrixQR &	mat,
		HCoeffs &	hCoeffs,
		typename MatrixQR::Index	maxBlockSize = 32,
		typename MatrixQR::Scalar *	tempData = 0
	)

Definition at line 243 of file QR.

template<typename MatrixQR , typename HCoeffs >

void Eigen::internal::householder_qr_inplace_unblocked	(	MatrixQR &	mat,
		HCoeffs &	hCoeffs,
		typename MatrixQR::Scalar *	tempData = 0
	)

Definition at line 207 of file QR.

template<typename RealScalar >

std::complex< RealScalar > Eigen::internal::sqrt

(

const std::complex< RealScalar > &

z )

Computes the principal value of the square root of the complex z.

Definition at line 234 of file Eigenvalues.

template<int StorageOrder, typename RealScalar , typename Scalar , typename Index >

static void Eigen::internal::tridiagonal_qr_step	(	RealScalar *	diag,
		RealScalar *	subdiag,
		Index	start,
		Index	end,
		Scalar *	matrixQ,
		Index	n
	)		[static]

Definition at line 434 of file Eigenvalues.

template<typename MatrixType , typename CoeffVectorType >

void Eigen::internal::tridiagonalization_inplace	(	MatrixType &	matA,
		CoeffVectorType &	hCoeffs
	)

Definition at line 360 of file Eigenvalues.

template<typename MatrixType , typename DiagonalType , typename SubDiagonalType >

void Eigen::internal::tridiagonalization_inplace	(	MatrixType &	mat,
		DiagonalType &	diag,
		SubDiagonalType &	subdiag,
		bool	extractQ
	)

Performs a full tridiagonalization in place.

Parameters:

[in,out]	mat	On input, the selfadjoint matrix whose tridiagonal decomposition is to be computed. Only the lower triangular part referenced. The rest is left unchanged. On output, the orthogonal matrix Q in the decomposition if extractQ is true.
[out]	diag	The diagonal of the tridiagonal matrix T in the decomposition.
[out]	subdiag	The subdiagonal of the tridiagonal matrix T in the decomposition.
[in]	extractQ	If true, the orthogonal matrix Q in the decomposition is computed and stored in mat.

Computes the tridiagonal decomposition of the selfadjoint matrix mat in place such that where is unitary and a real symmetric tridiagonal matrix.

The tridiagonal matrix T is passed to the output parameters diag and subdiag. If extractQ is true, then the orthogonal matrix Q is passed to mat. Otherwise the lower part of the matrix mat is destroyed.

The vectors diag and subdiag are not resized. The function assumes that they are already of the correct size. The length of the vector diag should equal the number of rows in mat, and the length of the vector subdiag should be one left.

This implementation contains an optimized path for 3-by-3 matrices which is especially useful for plane fitting.

Note:

Currently, it requires two temporary vectors to hold the intermediate Householder coefficients, and to reconstruct the matrix Q from the Householder reflectors.

Example (this uses the same matrix as the example in Tridiagonalization::Tridiagonalization(const MatrixType&)):

Output:

See also:

class Tridiagonalization

Definition at line 440 of file Eigenvalues.