Tridiagonal decomposition of a selfadjoint matrix
_MatrixType | the type of the matrix of which we are computing the tridiagonal decomposition; this is expected to be an instantiation of the Matrix class template. |
This class performs a tridiagonal decomposition of a selfadjoint matrix such that:
where
is unitary and
a real symmetric tridiagonal matrix.
A tridiagonal matrix is a matrix which has nonzero elements only on the main diagonal and the first diagonal below and above it. The Hessenberg decomposition of a selfadjoint matrix is in fact a tridiagonal decomposition. This class is used in SelfAdjointEigenSolver to compute the eigenvalues and eigenvectors of a selfadjoint matrix.
Call the function compute() to compute the tridiagonal decomposition of a given matrix. Alternatively, you can use the Tridiagonalization(const MatrixType&) constructor which computes the tridiagonal Schur decomposition at construction time. Once the decomposition is computed, you can use the matrixQ() and matrixT() functions to retrieve the matrices Q and T in the decomposition.
The documentation of Tridiagonalization(const MatrixType&) contains an example of the typical use of this class.
Definition at line 75 of file Eigenvalues.
Public Types | |
enum | { Size = MatrixType::RowsAtCompileTime, SizeMinusOne = Size == Dynamic ? Dynamic : (Size > 1 ? Size - 1 : 1), Options = MatrixType::Options, MaxSize = MatrixType::MaxRowsAtCompileTime, MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : (MaxSize > 1 ? MaxSize - 1 : 1) } |
enum | { Size = MatrixType::RowsAtCompileTime, SizeMinusOne = Size == Dynamic ? Dynamic : (Size > 1 ? Size - 1 : 1), Options = MatrixType::Options, MaxSize = MatrixType::MaxRowsAtCompileTime, MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : (MaxSize > 1 ? MaxSize - 1 : 1) } |
enum | { Size = MatrixType::RowsAtCompileTime, SizeMinusOne = Size == Dynamic ? Dynamic : (Size > 1 ? Size - 1 : 1), Options = MatrixType::Options, MaxSize = MatrixType::MaxRowsAtCompileTime, MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : (MaxSize > 1 ? MaxSize - 1 : 1) } |
typedef _MatrixType | MatrixType |
Synonym for the template parameter _MatrixType . | |
typedef MatrixType::Scalar | Scalar |
typedef NumTraits< Scalar >::Real | RealScalar |
typedef MatrixType::Index | Index |
typedef Matrix< Scalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 > | CoeffVectorType |
typedef internal::plain_col_type < MatrixType, RealScalar > ::type | DiagonalType |
typedef Matrix< RealScalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 > | SubDiagonalType |
typedef internal::remove_all < typename MatrixType::RealReturnType > ::type | MatrixTypeRealView |
typedef internal::TridiagonalizationMatrixTReturnType < MatrixTypeRealView > | MatrixTReturnType |
typedef internal::conditional < NumTraits< Scalar > ::IsComplex, const typename Diagonal< const MatrixType > ::RealReturnType, const Diagonal< const MatrixType > >::type | DiagonalReturnType |
typedef internal::conditional < NumTraits< Scalar > ::IsComplex, const typename Diagonal< Block< const MatrixType, SizeMinusOne, SizeMinusOne > >::RealReturnType, const Diagonal< Block< const MatrixType, SizeMinusOne, SizeMinusOne > > >::type | SubDiagonalReturnType |
typedef HouseholderSequence < MatrixType, CoeffVectorType > ::ConjugateReturnType | HouseholderSequenceType |
Return type of matrixQ() | |
typedef _MatrixType | MatrixType |
Synonym for the template parameter _MatrixType . | |
typedef MatrixType::Scalar | Scalar |
typedef NumTraits< Scalar >::Real | RealScalar |
typedef MatrixType::Index | Index |
typedef Matrix< Scalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 > | CoeffVectorType |
typedef internal::plain_col_type < MatrixType, RealScalar > ::type | DiagonalType |
typedef Matrix< RealScalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 > | SubDiagonalType |
typedef internal::remove_all < typename MatrixType::RealReturnType > ::type | MatrixTypeRealView |
typedef internal::TridiagonalizationMatrixTReturnType < MatrixTypeRealView > | MatrixTReturnType |
typedef internal::conditional < NumTraits< Scalar > ::IsComplex, const typename Diagonal< const MatrixType > ::RealReturnType, const Diagonal< const MatrixType > >::type | DiagonalReturnType |
typedef internal::conditional < NumTraits< Scalar > ::IsComplex, const typename Diagonal< Block< const MatrixType, SizeMinusOne, SizeMinusOne > >::RealReturnType, const Diagonal< Block< const MatrixType, SizeMinusOne, SizeMinusOne > > >::type | SubDiagonalReturnType |
typedef HouseholderSequence < MatrixType, CoeffVectorType > ::ConjugateReturnType | HouseholderSequenceType |
Return type of matrixQ() | |
typedef _MatrixType | MatrixType |
Synonym for the template parameter _MatrixType . | |
typedef MatrixType::Scalar | Scalar |
typedef NumTraits< Scalar >::Real | RealScalar |
typedef MatrixType::Index | Index |
typedef Matrix< Scalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 > | CoeffVectorType |
typedef internal::plain_col_type < MatrixType, RealScalar > ::type | DiagonalType |
typedef Matrix< RealScalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 > | SubDiagonalType |
typedef internal::remove_all < typename MatrixType::RealReturnType > ::type | MatrixTypeRealView |
typedef internal::TridiagonalizationMatrixTReturnType < MatrixTypeRealView > | MatrixTReturnType |
typedef internal::conditional < NumTraits< Scalar > ::IsComplex, const typename Diagonal< const MatrixType > ::RealReturnType, const Diagonal< const MatrixType > >::type | DiagonalReturnType |
typedef internal::conditional < NumTraits< Scalar > ::IsComplex, const typename Diagonal< Block< const MatrixType, SizeMinusOne, SizeMinusOne > >::RealReturnType, const Diagonal< Block< const MatrixType, SizeMinusOne, SizeMinusOne > > >::type | SubDiagonalReturnType |
typedef HouseholderSequence < MatrixType, CoeffVectorType > ::ConjugateReturnType | HouseholderSequenceType |
Return type of matrixQ() | |
Public Member Functions | |
Tridiagonalization (Index size=Size==Dynamic?2:Size) | |
Default constructor. | |
Tridiagonalization (const MatrixType &matrix) | |
Constructor; computes tridiagonal decomposition of given matrix. | |
Tridiagonalization & | compute (const MatrixType &matrix) |
Computes tridiagonal decomposition of given matrix. | |
CoeffVectorType | householderCoefficients () const |
Returns the Householder coefficients. | |
const MatrixType & | packedMatrix () const |
Returns the internal representation of the decomposition. | |
HouseholderSequenceType | matrixQ () const |
Returns the unitary matrix Q in the decomposition. | |
MatrixTReturnType | matrixT () const |
Returns an expression of the tridiagonal matrix T in the decomposition. | |
DiagonalReturnType | diagonal () const |
Returns the diagonal of the tridiagonal matrix T in the decomposition. | |
SubDiagonalReturnType | subDiagonal () const |
Returns the subdiagonal of the tridiagonal matrix T in the decomposition. | |
Tridiagonalization (Index size=Size==Dynamic?2:Size) | |
Default constructor. | |
Tridiagonalization (const MatrixType &matrix) | |
Constructor; computes tridiagonal decomposition of given matrix. | |
Tridiagonalization & | compute (const MatrixType &matrix) |
Computes tridiagonal decomposition of given matrix. | |
CoeffVectorType | householderCoefficients () const |
Returns the Householder coefficients. | |
const MatrixType & | packedMatrix () const |
Returns the internal representation of the decomposition. | |
HouseholderSequenceType | matrixQ () const |
Returns the unitary matrix Q in the decomposition. | |
MatrixTReturnType | matrixT () const |
Returns an expression of the tridiagonal matrix T in the decomposition. | |
DiagonalReturnType | diagonal () const |
Returns the diagonal of the tridiagonal matrix T in the decomposition. | |
SubDiagonalReturnType | subDiagonal () const |
Returns the subdiagonal of the tridiagonal matrix T in the decomposition. | |
Tridiagonalization (Index size=Size==Dynamic?2:Size) | |
Default constructor. | |
Tridiagonalization (const MatrixType &matrix) | |
Constructor; computes tridiagonal decomposition of given matrix. | |
Tridiagonalization & | compute (const MatrixType &matrix) |
Computes tridiagonal decomposition of given matrix. | |
CoeffVectorType | householderCoefficients () const |
Returns the Householder coefficients. | |
const MatrixType & | packedMatrix () const |
Returns the internal representation of the decomposition. | |
HouseholderSequenceType | matrixQ () const |
Returns the unitary matrix Q in the decomposition. | |
MatrixTReturnType | matrixT () const |
Returns an expression of the tridiagonal matrix T in the decomposition. | |
DiagonalReturnType | diagonal () const |
Returns the diagonal of the tridiagonal matrix T in the decomposition. | |
SubDiagonalReturnType | subDiagonal () const |
Returns the subdiagonal of the tridiagonal matrix T in the decomposition. | |
Protected Attributes | |
MatrixType | m_matrix |
CoeffVectorType | m_hCoeffs |
bool | m_isInitialized |
typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> Eigen::Tridiagonalization< _MatrixType >::CoeffVectorType |
Definition at line 94 of file Eigenvalues.
typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> Eigen::Tridiagonalization< _MatrixType >::CoeffVectorType |
Definition at line 94 of file Eigenvalues.
typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> Eigen::Tridiagonalization< _MatrixType >::CoeffVectorType |
Definition at line 94 of file Eigenvalues.
typedef internal::conditional<NumTraits<Scalar>::IsComplex, const typename Diagonal<const MatrixType>::RealReturnType, const Diagonal<const MatrixType> >::type Eigen::Tridiagonalization< _MatrixType >::DiagonalReturnType |
Definition at line 103 of file Eigenvalues.
typedef internal::conditional<NumTraits<Scalar>::IsComplex, const typename Diagonal<const MatrixType>::RealReturnType, const Diagonal<const MatrixType> >::type Eigen::Tridiagonalization< _MatrixType >::DiagonalReturnType |
Definition at line 103 of file Eigenvalues.
typedef internal::conditional<NumTraits<Scalar>::IsComplex, const typename Diagonal<const MatrixType>::RealReturnType, const Diagonal<const MatrixType> >::type Eigen::Tridiagonalization< _MatrixType >::DiagonalReturnType |
Definition at line 103 of file Eigenvalues.
typedef internal::plain_col_type<MatrixType, RealScalar>::type Eigen::Tridiagonalization< _MatrixType >::DiagonalType |
Definition at line 95 of file Eigenvalues.
typedef internal::plain_col_type<MatrixType, RealScalar>::type Eigen::Tridiagonalization< _MatrixType >::DiagonalType |
Definition at line 95 of file Eigenvalues.
typedef internal::plain_col_type<MatrixType, RealScalar>::type Eigen::Tridiagonalization< _MatrixType >::DiagonalType |
Definition at line 95 of file Eigenvalues.
typedef HouseholderSequence<MatrixType,CoeffVectorType>::ConjugateReturnType Eigen::Tridiagonalization< _MatrixType >::HouseholderSequenceType |
Return type of matrixQ()
Definition at line 113 of file Eigenvalues.
typedef HouseholderSequence<MatrixType,CoeffVectorType>::ConjugateReturnType Eigen::Tridiagonalization< _MatrixType >::HouseholderSequenceType |
Return type of matrixQ()
Definition at line 113 of file Eigenvalues.
typedef HouseholderSequence<MatrixType,CoeffVectorType>::ConjugateReturnType Eigen::Tridiagonalization< _MatrixType >::HouseholderSequenceType |
Return type of matrixQ()
Definition at line 113 of file Eigenvalues.
typedef MatrixType::Index Eigen::Tridiagonalization< _MatrixType >::Index |
Definition at line 84 of file Eigenvalues.
typedef MatrixType::Index Eigen::Tridiagonalization< _MatrixType >::Index |
Definition at line 84 of file Eigenvalues.
typedef MatrixType::Index Eigen::Tridiagonalization< _MatrixType >::Index |
Definition at line 84 of file Eigenvalues.
typedef internal::TridiagonalizationMatrixTReturnType<MatrixTypeRealView> Eigen::Tridiagonalization< _MatrixType >::MatrixTReturnType |
Definition at line 98 of file Eigenvalues.
typedef internal::TridiagonalizationMatrixTReturnType<MatrixTypeRealView> Eigen::Tridiagonalization< _MatrixType >::MatrixTReturnType |
Definition at line 98 of file Eigenvalues.
typedef internal::TridiagonalizationMatrixTReturnType<MatrixTypeRealView> Eigen::Tridiagonalization< _MatrixType >::MatrixTReturnType |
Definition at line 98 of file Eigenvalues.
typedef _MatrixType Eigen::Tridiagonalization< _MatrixType >::MatrixType |
Synonym for the template parameter _MatrixType
.
Definition at line 80 of file Eigenvalues.
typedef _MatrixType Eigen::Tridiagonalization< _MatrixType >::MatrixType |
Synonym for the template parameter _MatrixType
.
Definition at line 80 of file Eigenvalues.
typedef _MatrixType Eigen::Tridiagonalization< _MatrixType >::MatrixType |
Synonym for the template parameter _MatrixType
.
Definition at line 80 of file Eigenvalues.
typedef internal::remove_all<typename MatrixType::RealReturnType>::type Eigen::Tridiagonalization< _MatrixType >::MatrixTypeRealView |
Definition at line 97 of file Eigenvalues.
typedef internal::remove_all<typename MatrixType::RealReturnType>::type Eigen::Tridiagonalization< _MatrixType >::MatrixTypeRealView |
Definition at line 97 of file Eigenvalues.
typedef internal::remove_all<typename MatrixType::RealReturnType>::type Eigen::Tridiagonalization< _MatrixType >::MatrixTypeRealView |
Definition at line 97 of file Eigenvalues.
typedef NumTraits<Scalar>::Real Eigen::Tridiagonalization< _MatrixType >::RealScalar |
Definition at line 83 of file Eigenvalues.
typedef NumTraits<Scalar>::Real Eigen::Tridiagonalization< _MatrixType >::RealScalar |
Definition at line 83 of file Eigenvalues.
typedef NumTraits<Scalar>::Real Eigen::Tridiagonalization< _MatrixType >::RealScalar |
Definition at line 83 of file Eigenvalues.
typedef MatrixType::Scalar Eigen::Tridiagonalization< _MatrixType >::Scalar |
Definition at line 82 of file Eigenvalues.
typedef MatrixType::Scalar Eigen::Tridiagonalization< _MatrixType >::Scalar |
Definition at line 82 of file Eigenvalues.
typedef MatrixType::Scalar Eigen::Tridiagonalization< _MatrixType >::Scalar |
Definition at line 82 of file Eigenvalues.
typedef internal::conditional<NumTraits<Scalar>::IsComplex, const typename Diagonal< Block<const MatrixType,SizeMinusOne,SizeMinusOne> >::RealReturnType, const Diagonal< Block<const MatrixType,SizeMinusOne,SizeMinusOne> > >::type Eigen::Tridiagonalization< _MatrixType >::SubDiagonalReturnType |
Definition at line 110 of file Eigenvalues.
typedef internal::conditional<NumTraits<Scalar>::IsComplex, const typename Diagonal< Block<const MatrixType,SizeMinusOne,SizeMinusOne> >::RealReturnType, const Diagonal< Block<const MatrixType,SizeMinusOne,SizeMinusOne> > >::type Eigen::Tridiagonalization< _MatrixType >::SubDiagonalReturnType |
Definition at line 110 of file Eigenvalues.
typedef internal::conditional<NumTraits<Scalar>::IsComplex, const typename Diagonal< Block<const MatrixType,SizeMinusOne,SizeMinusOne> >::RealReturnType, const Diagonal< Block<const MatrixType,SizeMinusOne,SizeMinusOne> > >::type Eigen::Tridiagonalization< _MatrixType >::SubDiagonalReturnType |
Definition at line 110 of file Eigenvalues.
typedef Matrix<RealScalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> Eigen::Tridiagonalization< _MatrixType >::SubDiagonalType |
Definition at line 96 of file Eigenvalues.
typedef Matrix<RealScalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> Eigen::Tridiagonalization< _MatrixType >::SubDiagonalType |
Definition at line 96 of file Eigenvalues.
typedef Matrix<RealScalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> Eigen::Tridiagonalization< _MatrixType >::SubDiagonalType |
Definition at line 96 of file Eigenvalues.
anonymous enum |
Definition at line 86 of file Eigenvalues.
anonymous enum |
Definition at line 86 of file Eigenvalues.
anonymous enum |
Definition at line 86 of file Eigenvalues.
Eigen::Tridiagonalization< _MatrixType >::Tridiagonalization | ( | Index | size = Size==Dynamic ? 2 : Size | ) | [inline] |
Default constructor.
[in] | size | Positive integer, size of the matrix whose tridiagonal decomposition will be computed. |
The default constructor is useful in cases in which the user intends to perform decompositions via compute(). The size
parameter is only used as a hint. It is not an error to give a wrong size
, but it may impair performance.
Definition at line 127 of file Eigenvalues.
Eigen::Tridiagonalization< _MatrixType >::Tridiagonalization | ( | const MatrixType & | matrix | ) | [inline] |
Constructor; computes tridiagonal decomposition of given matrix.
[in] | matrix | Selfadjoint matrix whose tridiagonal decomposition is to be computed. |
This constructor calls compute() to compute the tridiagonal decomposition.
Example:
Output:
Definition at line 143 of file Eigenvalues.
Eigen::Tridiagonalization< _MatrixType >::Tridiagonalization | ( | Index | size = Size==Dynamic ? 2 : Size | ) | [inline] |
Default constructor.
[in] | size | Positive integer, size of the matrix whose tridiagonal decomposition will be computed. |
The default constructor is useful in cases in which the user intends to perform decompositions via compute(). The size
parameter is only used as a hint. It is not an error to give a wrong size
, but it may impair performance.
Definition at line 127 of file Eigenvalues.
Eigen::Tridiagonalization< _MatrixType >::Tridiagonalization | ( | const MatrixType & | matrix | ) | [inline] |
Constructor; computes tridiagonal decomposition of given matrix.
[in] | matrix | Selfadjoint matrix whose tridiagonal decomposition is to be computed. |
This constructor calls compute() to compute the tridiagonal decomposition.
Example:
Output:
Definition at line 143 of file Eigenvalues.
Eigen::Tridiagonalization< _MatrixType >::Tridiagonalization | ( | Index | size = Size==Dynamic ? 2 : Size | ) | [inline] |
Default constructor.
[in] | size | Positive integer, size of the matrix whose tridiagonal decomposition will be computed. |
The default constructor is useful in cases in which the user intends to perform decompositions via compute(). The size
parameter is only used as a hint. It is not an error to give a wrong size
, but it may impair performance.
Definition at line 127 of file Eigenvalues.
Eigen::Tridiagonalization< _MatrixType >::Tridiagonalization | ( | const MatrixType & | matrix | ) | [inline] |
Constructor; computes tridiagonal decomposition of given matrix.
[in] | matrix | Selfadjoint matrix whose tridiagonal decomposition is to be computed. |
This constructor calls compute() to compute the tridiagonal decomposition.
Example:
Output:
Definition at line 143 of file Eigenvalues.
Tridiagonalization& Eigen::Tridiagonalization< _MatrixType >::compute | ( | const MatrixType & | matrix | ) | [inline] |
Computes tridiagonal decomposition of given matrix.
[in] | matrix | Selfadjoint matrix whose tridiagonal decomposition is to be computed. |
*this
The tridiagonal decomposition is computed by bringing the columns of the matrix successively in the required form using Householder reflections. The cost is flops, where
denotes the size of the given matrix.
This method reuses of the allocated data in the Tridiagonalization object, if the size of the matrix does not change.
Example:
Output:
Definition at line 169 of file Eigenvalues.
Tridiagonalization& Eigen::Tridiagonalization< _MatrixType >::compute | ( | const MatrixType & | matrix | ) | [inline] |
Computes tridiagonal decomposition of given matrix.
[in] | matrix | Selfadjoint matrix whose tridiagonal decomposition is to be computed. |
*this
The tridiagonal decomposition is computed by bringing the columns of the matrix successively in the required form using Householder reflections. The cost is flops, where
denotes the size of the given matrix.
This method reuses of the allocated data in the Tridiagonalization object, if the size of the matrix does not change.
Example:
Output:
Definition at line 169 of file Eigenvalues.
Tridiagonalization& Eigen::Tridiagonalization< _MatrixType >::compute | ( | const MatrixType & | matrix | ) | [inline] |
Computes tridiagonal decomposition of given matrix.
[in] | matrix | Selfadjoint matrix whose tridiagonal decomposition is to be computed. |
*this
The tridiagonal decomposition is computed by bringing the columns of the matrix successively in the required form using Householder reflections. The cost is flops, where
denotes the size of the given matrix.
This method reuses of the allocated data in the Tridiagonalization object, if the size of the matrix does not change.
Example:
Output:
Definition at line 169 of file Eigenvalues.
DiagonalReturnType Eigen::Tridiagonalization< _MatrixType >::diagonal | ( | ) | const |
Returns the diagonal of the tridiagonal matrix T in the decomposition.
Example:
Output:
DiagonalReturnType Eigen::Tridiagonalization< _MatrixType >::diagonal | ( | ) | const |
Returns the diagonal of the tridiagonal matrix T in the decomposition.
Example:
Output:
Tridiagonalization< MatrixType >::DiagonalReturnType Tridiagonalization< MatrixType >::diagonal | ( | ) | const |
Returns the diagonal of the tridiagonal matrix T in the decomposition.
Example:
Output:
Definition at line 319 of file Eigenvalues.
CoeffVectorType Eigen::Tridiagonalization< _MatrixType >::householderCoefficients | ( | ) | const [inline] |
Returns the Householder coefficients.
The Householder coefficients allow the reconstruction of the matrix in the tridiagonal decomposition from the packed data.
Example:
Output:
Definition at line 194 of file Eigenvalues.
CoeffVectorType Eigen::Tridiagonalization< _MatrixType >::householderCoefficients | ( | ) | const [inline] |
Returns the Householder coefficients.
The Householder coefficients allow the reconstruction of the matrix in the tridiagonal decomposition from the packed data.
Example:
Output:
Definition at line 194 of file Eigenvalues.
CoeffVectorType Eigen::Tridiagonalization< _MatrixType >::householderCoefficients | ( | ) | const [inline] |
Returns the Householder coefficients.
The Householder coefficients allow the reconstruction of the matrix in the tridiagonal decomposition from the packed data.
Example:
Output:
Definition at line 194 of file Eigenvalues.
HouseholderSequenceType Eigen::Tridiagonalization< _MatrixType >::matrixQ | ( | void | ) | const [inline] |
Returns the unitary matrix Q in the decomposition.
This function returns a light-weight object of template class HouseholderSequence. You can either apply it directly to a matrix or you can convert it to a matrix of type MatrixType.
Definition at line 252 of file Eigenvalues.
HouseholderSequenceType Eigen::Tridiagonalization< _MatrixType >::matrixQ | ( | void | ) | const [inline] |
Returns the unitary matrix Q in the decomposition.
This function returns a light-weight object of template class HouseholderSequence. You can either apply it directly to a matrix or you can convert it to a matrix of type MatrixType.
Definition at line 252 of file Eigenvalues.
HouseholderSequenceType Eigen::Tridiagonalization< _MatrixType >::matrixQ | ( | void | ) | const [inline] |
Returns the unitary matrix Q in the decomposition.
This function returns a light-weight object of template class HouseholderSequence. You can either apply it directly to a matrix or you can convert it to a matrix of type MatrixType.
Definition at line 252 of file Eigenvalues.
MatrixTReturnType Eigen::Tridiagonalization< _MatrixType >::matrixT | ( | ) | const [inline] |
Returns an expression of the tridiagonal matrix T in the decomposition.
Currently, this function can be used to extract the matrix T from internal data and copy it to a dense matrix object. In most cases, it may be sufficient to directly use the packed matrix or the vector expressions returned by diagonal() and subDiagonal() instead of creating a new dense copy matrix with this function.
Definition at line 277 of file Eigenvalues.
MatrixTReturnType Eigen::Tridiagonalization< _MatrixType >::matrixT | ( | ) | const [inline] |
Returns an expression of the tridiagonal matrix T in the decomposition.
Currently, this function can be used to extract the matrix T from internal data and copy it to a dense matrix object. In most cases, it may be sufficient to directly use the packed matrix or the vector expressions returned by diagonal() and subDiagonal() instead of creating a new dense copy matrix with this function.
Definition at line 277 of file Eigenvalues.
MatrixTReturnType Eigen::Tridiagonalization< _MatrixType >::matrixT | ( | ) | const [inline] |
Returns an expression of the tridiagonal matrix T in the decomposition.
Currently, this function can be used to extract the matrix T from internal data and copy it to a dense matrix object. In most cases, it may be sufficient to directly use the packed matrix or the vector expressions returned by diagonal() and subDiagonal() instead of creating a new dense copy matrix with this function.
Definition at line 277 of file Eigenvalues.
const MatrixType& Eigen::Tridiagonalization< _MatrixType >::packedMatrix | ( | ) | const [inline] |
Returns the internal representation of the decomposition.
The returned matrix contains the following information:
See LAPACK for further details on this packed storage.
Example:
Output:
Definition at line 231 of file Eigenvalues.
const MatrixType& Eigen::Tridiagonalization< _MatrixType >::packedMatrix | ( | ) | const [inline] |
Returns the internal representation of the decomposition.
The returned matrix contains the following information:
See LAPACK for further details on this packed storage.
Example:
Output:
Definition at line 231 of file Eigenvalues.
const MatrixType& Eigen::Tridiagonalization< _MatrixType >::packedMatrix | ( | ) | const [inline] |
Returns the internal representation of the decomposition.
The returned matrix contains the following information:
See LAPACK for further details on this packed storage.
Example:
Output:
Definition at line 231 of file Eigenvalues.
SubDiagonalReturnType Eigen::Tridiagonalization< _MatrixType >::subDiagonal | ( | ) | const |
Returns the subdiagonal of the tridiagonal matrix T in the decomposition.
Tridiagonalization< MatrixType >::SubDiagonalReturnType Tridiagonalization< MatrixType >::subDiagonal | ( | ) | const |
Returns the subdiagonal of the tridiagonal matrix T in the decomposition.
Definition at line 327 of file Eigenvalues.
SubDiagonalReturnType Eigen::Tridiagonalization< _MatrixType >::subDiagonal | ( | ) | const |
Returns the subdiagonal of the tridiagonal matrix T in the decomposition.
CoeffVectorType Tridiagonalization< _MatrixType >::m_hCoeffs [protected] |
Definition at line 313 of file Eigenvalues.
bool Tridiagonalization< _MatrixType >::m_isInitialized [protected] |
Definition at line 314 of file Eigenvalues.
MatrixType Tridiagonalization< _MatrixType >::m_matrix [protected] |
Definition at line 312 of file Eigenvalues.
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