Tridiagonalization< _MatrixType > Class Template Reference

Trigiagonal decomposition of a selfadjoint matrix. More...

Public Types
enum	{   Size,   SizeMinusOne,   PacketSize }
typedef Matrix< Scalar, SizeMinusOne, 1 >	CoeffVectorType
typedef NestByValue < DiagonalCoeffs< MatrixType > >::RealReturnType	DiagonalReturnType
typedef Matrix< RealScalar, Size, 1 >	DiagonalType
typedef _MatrixType	MatrixType
typedef ei_packet_traits < Scalar >::type	Packet
typedef NumTraits< Scalar >::Real	RealScalar
typedef MatrixType::Scalar	Scalar
typedef NestByValue < DiagonalCoeffs< NestByValue < Block< MatrixType, SizeMinusOne, SizeMinusOne > > > >::RealReturnType	SubDiagonalReturnType
typedef Matrix< RealScalar, SizeMinusOne, 1 >	SubDiagonalType

Public Member Functions
void	compute (const MatrixType &matrix)
const DiagonalReturnType	diagonal (void) const
CoeffVectorType	householderCoefficients (void) const
MatrixType	matrixQ (void) const
MatrixType	matrixT (void) const
const MatrixType &	packedMatrix (void) const
const SubDiagonalReturnType	subDiagonal (void) const
	Tridiagonalization (int size=Size==Dynamic?2:Size)
	Tridiagonalization (const MatrixType &matrix)

Static Public Member Functions
static void	decomposeInPlace (MatrixType &mat, DiagonalType &diag, SubDiagonalType &subdiag, bool extractQ=true)

Protected Attributes
CoeffVectorType	m_hCoeffs
MatrixType	m_matrix

Detailed Description

template<typename _MatrixType>
class Eigen::Tridiagonalization< _MatrixType >

Trigiagonal decomposition of a selfadjoint matrix.

Warning

This is not considered to be part of the stable public API yet. Changes may happen in future releases. See Experimental parts of Eigen

Parameters

MatrixType

the type of the matrix of which we are performing the tridiagonalization

This class performs a tridiagonal decomposition of a selfadjoint matrix such that: where is unitary and a real symmetric tridiagonal matrix.

See Also

MatrixBase::tridiagonalize()

Constructor & Destructor Documentation

Tridiagonalization ( int  size = Size==Dynamic ? 2 : Size )

inline

This constructor initializes a Tridiagonalization object for further use with Tridiagonalization::compute()

Member Function Documentation

void compute ( const MatrixType &  matrix )

inline

Computes or re-compute the tridiagonalization for the matrix matrix.

This method allows to re-use the allocated data.

void decomposeInPlace ( MatrixType &  mat, DiagonalType &  diag, SubDiagonalType &  subdiag, bool  extractQ = true  )

static

Performs a full decomposition in place

const Tridiagonalization< MatrixType >::DiagonalReturnType diagonal

(

void

)

const

Returns

an expression of the diagonal vector

CoeffVectorType householderCoefficients ( void  ) const

inline

Returns

the householder coefficients allowing to reconstruct the matrix Q from the packed data.

See Also

packedMatrix()

Tridiagonalization< MatrixType >::MatrixType matrixQ

(

void

)

const

reconstructs and returns the matrix Q

Tridiagonalization< MatrixType >::MatrixType matrixT

(

void

)

const

constructs and returns the tridiagonal matrix T. Note that the matrix T is equivalent to the diagonal and sub-diagonal of the packed matrix. Therefore, it might be often sufficient to directly use the packed matrix, or the vector expressions returned by diagonal() and subDiagonal() instead of creating a new matrix.

const MatrixType& packedMatrix ( void  ) const

inline

Returns

the internal result of the decomposition.

The returned matrix contains the following information:

• the strict upper part is equal to the input matrix A
• the diagonal and lower sub-diagonal represent the tridiagonal symmetric matrix (real).
• the rest of the lower part contains the Householder vectors that, combined with Householder coefficients returned by householderCoefficients(), allows to reconstruct the matrix Q as follow: Q = H_{N-1} ... H_1 H_0 where the matrices H are the Householder transformations: H_i = (I - h_i * v_i * v_i') where h_i == householderCoefficients()[i] and v_i is a Householder vector: v_i = [ 0, ..., 0, 1, M(i+2,i), ..., M(N-1,i) ]

See LAPACK for further details on this packed storage.

const Tridiagonalization< MatrixType >::SubDiagonalReturnType subDiagonal

(

void

)

const

Returns

an expression of the sub-diagonal vector

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

• QR