Reduces a square matrix to Hessenberg form by an orthogonal similarity transformation
_MatrixType | the type of the matrix of which we are computing the Hessenberg decomposition |
This class performs an Hessenberg decomposition of a matrix . In the real case, the Hessenberg decomposition consists of an orthogonal matrix
and a Hessenberg matrix
such that
. An orthogonal matrix is a matrix whose inverse equals its transpose (
). A Hessenberg matrix has zeros below the subdiagonal, so it is almost upper triangular. The Hessenberg decomposition of a complex matrix is
with
unitary (that is,
).
Call the function compute() to compute the Hessenberg decomposition of a given matrix. Alternatively, you can use the HessenbergDecomposition(const MatrixType&) constructor which computes the Hessenberg decomposition at construction time. Once the decomposition is computed, you can use the matrixH() and matrixQ() functions to construct the matrices H and Q in the decomposition.
The documentation for matrixH() contains an example of the typical use of this class.
Definition at line 71 of file Eigenvalues.
Public Types | |
enum | { Size = MatrixType::RowsAtCompileTime, SizeMinusOne = Size == Dynamic ? Dynamic : Size - 1, Options = MatrixType::Options, MaxSize = MatrixType::MaxRowsAtCompileTime, MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : MaxSize - 1 } |
enum | { Size = MatrixType::RowsAtCompileTime, SizeMinusOne = Size == Dynamic ? Dynamic : Size - 1, Options = MatrixType::Options, MaxSize = MatrixType::MaxRowsAtCompileTime, MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : MaxSize - 1 } |
enum | { Size = MatrixType::RowsAtCompileTime, SizeMinusOne = Size == Dynamic ? Dynamic : Size - 1, Options = MatrixType::Options, MaxSize = MatrixType::MaxRowsAtCompileTime, MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : MaxSize - 1 } |
enum | { Size = MatrixType::RowsAtCompileTime, SizeMinusOne = Size == Dynamic ? Dynamic : Size - 1, Options = MatrixType::Options, MaxSize = MatrixType::MaxRowsAtCompileTime, MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : MaxSize - 1 } |
enum | { Size = MatrixType::RowsAtCompileTime, SizeMinusOne = Size == Dynamic ? Dynamic : Size - 1, Options = MatrixType::Options, MaxSize = MatrixType::MaxRowsAtCompileTime, MaxSizeMinusOne = MaxSize == Dynamic ? Dynamic : MaxSize - 1 } |
typedef _MatrixType | MatrixType |
Synonym for the template parameter _MatrixType . | |
typedef MatrixType::Scalar | Scalar |
Scalar type for matrices of type MatrixType. | |
typedef MatrixType::Index | Index |
typedef Matrix< Scalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 > | CoeffVectorType |
Type for vector of Householder coefficients. | |
typedef HouseholderSequence < MatrixType, CoeffVectorType > ::ConjugateReturnType | HouseholderSequenceType |
Return type of matrixQ() | |
typedef internal::HessenbergDecompositionMatrixHReturnType < MatrixType > | MatrixHReturnType |
typedef _MatrixType | MatrixType |
Synonym for the template parameter _MatrixType . | |
typedef MatrixType::Scalar | Scalar |
Scalar type for matrices of type MatrixType. | |
typedef MatrixType::Index | Index |
typedef Matrix< Scalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 > | CoeffVectorType |
Type for vector of Householder coefficients. | |
typedef HouseholderSequence < MatrixType, CoeffVectorType > ::ConjugateReturnType | HouseholderSequenceType |
Return type of matrixQ() | |
typedef internal::HessenbergDecompositionMatrixHReturnType < MatrixType > | MatrixHReturnType |
typedef _MatrixType | MatrixType |
Synonym for the template parameter _MatrixType . | |
typedef MatrixType::Scalar | Scalar |
Scalar type for matrices of type MatrixType. | |
typedef MatrixType::Index | Index |
typedef Matrix< Scalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 > | CoeffVectorType |
Type for vector of Householder coefficients. | |
typedef HouseholderSequence < MatrixType, CoeffVectorType > ::ConjugateReturnType | HouseholderSequenceType |
Return type of matrixQ() | |
typedef internal::HessenbergDecompositionMatrixHReturnType < MatrixType > | MatrixHReturnType |
typedef _MatrixType | MatrixType |
Synonym for the template parameter _MatrixType . | |
typedef MatrixType::Scalar | Scalar |
Scalar type for matrices of type MatrixType. | |
typedef MatrixType::Index | Index |
typedef Matrix< Scalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 > | CoeffVectorType |
Type for vector of Householder coefficients. | |
typedef HouseholderSequence < MatrixType, CoeffVectorType > ::ConjugateReturnType | HouseholderSequenceType |
Return type of matrixQ() | |
typedef internal::HessenbergDecompositionMatrixHReturnType < MatrixType > | MatrixHReturnType |
typedef _MatrixType | MatrixType |
Synonym for the template parameter _MatrixType . | |
typedef MatrixType::Scalar | Scalar |
Scalar type for matrices of type MatrixType. | |
typedef MatrixType::Index | Index |
typedef Matrix< Scalar, SizeMinusOne, 1, Options &~RowMajor, MaxSizeMinusOne, 1 > | CoeffVectorType |
Type for vector of Householder coefficients. | |
typedef HouseholderSequence < MatrixType, CoeffVectorType > ::ConjugateReturnType | HouseholderSequenceType |
Return type of matrixQ() | |
typedef internal::HessenbergDecompositionMatrixHReturnType < MatrixType > | MatrixHReturnType |
Public Member Functions | |
HessenbergDecomposition (Index size=Size==Dynamic?2:Size) | |
Default constructor; the decomposition will be computed later. | |
HessenbergDecomposition (const MatrixType &matrix) | |
Constructor; computes Hessenberg decomposition of given matrix. | |
HessenbergDecomposition & | compute (const MatrixType &matrix) |
Computes Hessenberg decomposition of given matrix. | |
const CoeffVectorType & | householderCoefficients () const |
Returns the Householder coefficients. | |
const MatrixType & | packedMatrix () const |
Returns the internal representation of the decomposition. | |
HouseholderSequenceType | matrixQ () const |
Reconstructs the orthogonal matrix Q in the decomposition. | |
MatrixHReturnType | matrixH () const |
Constructs the Hessenberg matrix H in the decomposition. | |
HessenbergDecomposition (Index size=Size==Dynamic?2:Size) | |
Default constructor; the decomposition will be computed later. | |
HessenbergDecomposition (const MatrixType &matrix) | |
Constructor; computes Hessenberg decomposition of given matrix. | |
HessenbergDecomposition & | compute (const MatrixType &matrix) |
Computes Hessenberg decomposition of given matrix. | |
const CoeffVectorType & | householderCoefficients () const |
Returns the Householder coefficients. | |
const MatrixType & | packedMatrix () const |
Returns the internal representation of the decomposition. | |
HouseholderSequenceType | matrixQ () const |
Reconstructs the orthogonal matrix Q in the decomposition. | |
MatrixHReturnType | matrixH () const |
Constructs the Hessenberg matrix H in the decomposition. | |
HessenbergDecomposition (Index size=Size==Dynamic?2:Size) | |
Default constructor; the decomposition will be computed later. | |
HessenbergDecomposition (const MatrixType &matrix) | |
Constructor; computes Hessenberg decomposition of given matrix. | |
HessenbergDecomposition & | compute (const MatrixType &matrix) |
Computes Hessenberg decomposition of given matrix. | |
const CoeffVectorType & | householderCoefficients () const |
Returns the Householder coefficients. | |
const MatrixType & | packedMatrix () const |
Returns the internal representation of the decomposition. | |
HouseholderSequenceType | matrixQ () const |
Reconstructs the orthogonal matrix Q in the decomposition. | |
MatrixHReturnType | matrixH () const |
Constructs the Hessenberg matrix H in the decomposition. | |
HessenbergDecomposition (Index size=Size==Dynamic?2:Size) | |
Default constructor; the decomposition will be computed later. | |
HessenbergDecomposition (const MatrixType &matrix) | |
Constructor; computes Hessenberg decomposition of given matrix. | |
HessenbergDecomposition & | compute (const MatrixType &matrix) |
Computes Hessenberg decomposition of given matrix. | |
const CoeffVectorType & | householderCoefficients () const |
Returns the Householder coefficients. | |
const MatrixType & | packedMatrix () const |
Returns the internal representation of the decomposition. | |
HouseholderSequenceType | matrixQ () const |
Reconstructs the orthogonal matrix Q in the decomposition. | |
MatrixHReturnType | matrixH () const |
Constructs the Hessenberg matrix H in the decomposition. | |
HessenbergDecomposition (Index size=Size==Dynamic?2:Size) | |
Default constructor; the decomposition will be computed later. | |
HessenbergDecomposition (const MatrixType &matrix) | |
Constructor; computes Hessenberg decomposition of given matrix. | |
HessenbergDecomposition & | compute (const MatrixType &matrix) |
Computes Hessenberg decomposition of given matrix. | |
const CoeffVectorType & | householderCoefficients () const |
Returns the Householder coefficients. | |
const MatrixType & | packedMatrix () const |
Returns the internal representation of the decomposition. | |
HouseholderSequenceType | matrixQ () const |
Reconstructs the orthogonal matrix Q in the decomposition. | |
MatrixHReturnType | matrixH () const |
Constructs the Hessenberg matrix H in the decomposition. | |
Protected Attributes | |
MatrixType | m_matrix |
CoeffVectorType | m_hCoeffs |
VectorType | m_temp |
bool | m_isInitialized |
Private Types | |
typedef Matrix< Scalar, 1, Size, Options|RowMajor, 1, MaxSize > | VectorType |
typedef NumTraits< Scalar >::Real | RealScalar |
typedef Matrix< Scalar, 1, Size, Options|RowMajor, 1, MaxSize > | VectorType |
typedef NumTraits< Scalar >::Real | RealScalar |
typedef Matrix< Scalar, 1, Size, Options|RowMajor, 1, MaxSize > | VectorType |
typedef NumTraits< Scalar >::Real | RealScalar |
typedef Matrix< Scalar, 1, Size, Options|RowMajor, 1, MaxSize > | VectorType |
typedef NumTraits< Scalar >::Real | RealScalar |
typedef Matrix< Scalar, 1, Size, Options|RowMajor, 1, MaxSize > | VectorType |
typedef NumTraits< Scalar >::Real | RealScalar |
Static Private Member Functions | |
static void | _compute (MatrixType &matA, CoeffVectorType &hCoeffs, VectorType &temp) |
static void | _compute (MatrixType &matA, CoeffVectorType &hCoeffs, VectorType &temp) |
static void | _compute (MatrixType &matA, CoeffVectorType &hCoeffs, VectorType &temp) |
static void | _compute (MatrixType &matA, CoeffVectorType &hCoeffs, VectorType &temp) |
static void | _compute (MatrixType &matA, CoeffVectorType &hCoeffs, VectorType &temp) |
typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> Eigen::HessenbergDecomposition< _MatrixType >::CoeffVectorType |
Type for vector of Householder coefficients.
This is column vector with entries of type Scalar. The length of the vector is one less than the size of MatrixType, if it is a fixed-side type.
Definition at line 96 of file Eigenvalues.
typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> Eigen::HessenbergDecomposition< _MatrixType >::CoeffVectorType |
Type for vector of Householder coefficients.
This is column vector with entries of type Scalar. The length of the vector is one less than the size of MatrixType, if it is a fixed-side type.
Definition at line 96 of file Eigenvalues.
typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> Eigen::HessenbergDecomposition< _MatrixType >::CoeffVectorType |
Type for vector of Householder coefficients.
This is column vector with entries of type Scalar. The length of the vector is one less than the size of MatrixType, if it is a fixed-side type.
Definition at line 96 of file Eigenvalues.
typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> Eigen::HessenbergDecomposition< _MatrixType >::CoeffVectorType |
Type for vector of Householder coefficients.
This is column vector with entries of type Scalar. The length of the vector is one less than the size of MatrixType, if it is a fixed-side type.
Definition at line 96 of file Eigenvalues.
typedef Matrix<Scalar, SizeMinusOne, 1, Options & ~RowMajor, MaxSizeMinusOne, 1> Eigen::HessenbergDecomposition< _MatrixType >::CoeffVectorType |
Type for vector of Householder coefficients.
This is column vector with entries of type Scalar. The length of the vector is one less than the size of MatrixType, if it is a fixed-side type.
Definition at line 96 of file Eigenvalues.
typedef HouseholderSequence<MatrixType,CoeffVectorType>::ConjugateReturnType Eigen::HessenbergDecomposition< _MatrixType >::HouseholderSequenceType |
Return type of matrixQ()
Definition at line 99 of file Eigenvalues.
typedef HouseholderSequence<MatrixType,CoeffVectorType>::ConjugateReturnType Eigen::HessenbergDecomposition< _MatrixType >::HouseholderSequenceType |
Return type of matrixQ()
Definition at line 99 of file Eigenvalues.
typedef HouseholderSequence<MatrixType,CoeffVectorType>::ConjugateReturnType Eigen::HessenbergDecomposition< _MatrixType >::HouseholderSequenceType |
Return type of matrixQ()
Definition at line 99 of file Eigenvalues.
typedef HouseholderSequence<MatrixType,CoeffVectorType>::ConjugateReturnType Eigen::HessenbergDecomposition< _MatrixType >::HouseholderSequenceType |
Return type of matrixQ()
Definition at line 99 of file Eigenvalues.
typedef HouseholderSequence<MatrixType,CoeffVectorType>::ConjugateReturnType Eigen::HessenbergDecomposition< _MatrixType >::HouseholderSequenceType |
Return type of matrixQ()
Definition at line 99 of file Eigenvalues.
typedef MatrixType::Index Eigen::HessenbergDecomposition< _MatrixType >::Index |
Definition at line 88 of file Eigenvalues.
typedef MatrixType::Index Eigen::HessenbergDecomposition< _MatrixType >::Index |
Definition at line 88 of file Eigenvalues.
typedef MatrixType::Index Eigen::HessenbergDecomposition< _MatrixType >::Index |
Definition at line 88 of file Eigenvalues.
typedef MatrixType::Index Eigen::HessenbergDecomposition< _MatrixType >::Index |
Definition at line 88 of file Eigenvalues.
typedef MatrixType::Index Eigen::HessenbergDecomposition< _MatrixType >::Index |
Definition at line 88 of file Eigenvalues.
typedef internal::HessenbergDecompositionMatrixHReturnType<MatrixType> Eigen::HessenbergDecomposition< _MatrixType >::MatrixHReturnType |
Definition at line 101 of file Eigenvalues.
typedef internal::HessenbergDecompositionMatrixHReturnType<MatrixType> Eigen::HessenbergDecomposition< _MatrixType >::MatrixHReturnType |
Definition at line 101 of file Eigenvalues.
typedef internal::HessenbergDecompositionMatrixHReturnType<MatrixType> Eigen::HessenbergDecomposition< _MatrixType >::MatrixHReturnType |
Definition at line 101 of file Eigenvalues.
typedef internal::HessenbergDecompositionMatrixHReturnType<MatrixType> Eigen::HessenbergDecomposition< _MatrixType >::MatrixHReturnType |
Definition at line 101 of file Eigenvalues.
typedef internal::HessenbergDecompositionMatrixHReturnType<MatrixType> Eigen::HessenbergDecomposition< _MatrixType >::MatrixHReturnType |
Definition at line 101 of file Eigenvalues.
typedef _MatrixType Eigen::HessenbergDecomposition< _MatrixType >::MatrixType |
Synonym for the template parameter _MatrixType
.
Definition at line 76 of file Eigenvalues.
typedef _MatrixType Eigen::HessenbergDecomposition< _MatrixType >::MatrixType |
Synonym for the template parameter _MatrixType
.
Definition at line 76 of file Eigenvalues.
typedef _MatrixType Eigen::HessenbergDecomposition< _MatrixType >::MatrixType |
Synonym for the template parameter _MatrixType
.
Definition at line 76 of file Eigenvalues.
typedef _MatrixType Eigen::HessenbergDecomposition< _MatrixType >::MatrixType |
Synonym for the template parameter _MatrixType
.
Definition at line 76 of file Eigenvalues.
typedef _MatrixType Eigen::HessenbergDecomposition< _MatrixType >::MatrixType |
Synonym for the template parameter _MatrixType
.
Definition at line 76 of file Eigenvalues.
typedef NumTraits<Scalar>::Real Eigen::HessenbergDecomposition< _MatrixType >::RealScalar [private] |
Definition at line 283 of file Eigenvalues.
typedef NumTraits<Scalar>::Real Eigen::HessenbergDecomposition< _MatrixType >::RealScalar [private] |
Definition at line 283 of file Eigenvalues.
typedef NumTraits<Scalar>::Real Eigen::HessenbergDecomposition< _MatrixType >::RealScalar [private] |
Definition at line 283 of file Eigenvalues.
typedef NumTraits<Scalar>::Real Eigen::HessenbergDecomposition< _MatrixType >::RealScalar [private] |
Definition at line 283 of file Eigenvalues.
typedef NumTraits<Scalar>::Real Eigen::HessenbergDecomposition< _MatrixType >::RealScalar [private] |
Definition at line 283 of file Eigenvalues.
typedef MatrixType::Scalar Eigen::HessenbergDecomposition< _MatrixType >::Scalar |
Scalar type for matrices of type MatrixType.
Definition at line 87 of file Eigenvalues.
typedef MatrixType::Scalar Eigen::HessenbergDecomposition< _MatrixType >::Scalar |
Scalar type for matrices of type MatrixType.
Definition at line 87 of file Eigenvalues.
typedef MatrixType::Scalar Eigen::HessenbergDecomposition< _MatrixType >::Scalar |
Scalar type for matrices of type MatrixType.
Definition at line 87 of file Eigenvalues.
typedef MatrixType::Scalar Eigen::HessenbergDecomposition< _MatrixType >::Scalar |
Scalar type for matrices of type MatrixType.
Definition at line 87 of file Eigenvalues.
typedef MatrixType::Scalar Eigen::HessenbergDecomposition< _MatrixType >::Scalar |
Scalar type for matrices of type MatrixType.
Definition at line 87 of file Eigenvalues.
typedef Matrix<Scalar, 1, Size, Options | RowMajor, 1, MaxSize> Eigen::HessenbergDecomposition< _MatrixType >::VectorType [private] |
Definition at line 282 of file Eigenvalues.
typedef Matrix<Scalar, 1, Size, Options | RowMajor, 1, MaxSize> Eigen::HessenbergDecomposition< _MatrixType >::VectorType [private] |
Definition at line 282 of file Eigenvalues.
typedef Matrix<Scalar, 1, Size, Options | RowMajor, 1, MaxSize> Eigen::HessenbergDecomposition< _MatrixType >::VectorType [private] |
Definition at line 282 of file Eigenvalues.
typedef Matrix<Scalar, 1, Size, Options | RowMajor, 1, MaxSize> Eigen::HessenbergDecomposition< _MatrixType >::VectorType [private] |
Definition at line 282 of file Eigenvalues.
typedef Matrix<Scalar, 1, Size, Options | RowMajor, 1, MaxSize> Eigen::HessenbergDecomposition< _MatrixType >::VectorType [private] |
Definition at line 282 of file Eigenvalues.
anonymous enum |
Definition at line 78 of file Eigenvalues.
anonymous enum |
Definition at line 78 of file Eigenvalues.
anonymous enum |
Definition at line 78 of file Eigenvalues.
anonymous enum |
Definition at line 78 of file Eigenvalues.
anonymous enum |
Definition at line 78 of file Eigenvalues.
Eigen::HessenbergDecomposition< _MatrixType >::HessenbergDecomposition | ( | Index | size = Size==Dynamic ? 2 : Size | ) | [inline] |
Default constructor; the decomposition will be computed later.
[in] | size | The size of the matrix whose Hessenberg 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 114 of file Eigenvalues.
Eigen::HessenbergDecomposition< _MatrixType >::HessenbergDecomposition | ( | const MatrixType & | matrix | ) | [inline] |
Constructor; computes Hessenberg decomposition of given matrix.
[in] | matrix | Square matrix whose Hessenberg decomposition is to be computed. |
This constructor calls compute() to compute the Hessenberg decomposition.
Definition at line 132 of file Eigenvalues.
Eigen::HessenbergDecomposition< _MatrixType >::HessenbergDecomposition | ( | Index | size = Size==Dynamic ? 2 : Size | ) | [inline] |
Default constructor; the decomposition will be computed later.
[in] | size | The size of the matrix whose Hessenberg 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 114 of file Eigenvalues.
Eigen::HessenbergDecomposition< _MatrixType >::HessenbergDecomposition | ( | const MatrixType & | matrix | ) | [inline] |
Constructor; computes Hessenberg decomposition of given matrix.
[in] | matrix | Square matrix whose Hessenberg decomposition is to be computed. |
This constructor calls compute() to compute the Hessenberg decomposition.
Definition at line 132 of file Eigenvalues.
Eigen::HessenbergDecomposition< _MatrixType >::HessenbergDecomposition | ( | Index | size = Size==Dynamic ? 2 : Size | ) | [inline] |
Default constructor; the decomposition will be computed later.
[in] | size | The size of the matrix whose Hessenberg 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 114 of file Eigenvalues.
Eigen::HessenbergDecomposition< _MatrixType >::HessenbergDecomposition | ( | const MatrixType & | matrix | ) | [inline] |
Constructor; computes Hessenberg decomposition of given matrix.
[in] | matrix | Square matrix whose Hessenberg decomposition is to be computed. |
This constructor calls compute() to compute the Hessenberg decomposition.
Definition at line 132 of file Eigenvalues.
Eigen::HessenbergDecomposition< _MatrixType >::HessenbergDecomposition | ( | Index | size = Size==Dynamic ? 2 : Size | ) | [inline] |
Default constructor; the decomposition will be computed later.
[in] | size | The size of the matrix whose Hessenberg 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 114 of file Eigenvalues.
Eigen::HessenbergDecomposition< _MatrixType >::HessenbergDecomposition | ( | const MatrixType & | matrix | ) | [inline] |
Constructor; computes Hessenberg decomposition of given matrix.
[in] | matrix | Square matrix whose Hessenberg decomposition is to be computed. |
This constructor calls compute() to compute the Hessenberg decomposition.
Definition at line 132 of file Eigenvalues.
Eigen::HessenbergDecomposition< _MatrixType >::HessenbergDecomposition | ( | Index | size = Size==Dynamic ? 2 : Size | ) | [inline] |
Default constructor; the decomposition will be computed later.
[in] | size | The size of the matrix whose Hessenberg 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 114 of file Eigenvalues.
Eigen::HessenbergDecomposition< _MatrixType >::HessenbergDecomposition | ( | const MatrixType & | matrix | ) | [inline] |
Constructor; computes Hessenberg decomposition of given matrix.
[in] | matrix | Square matrix whose Hessenberg decomposition is to be computed. |
This constructor calls compute() to compute the Hessenberg decomposition.
Definition at line 132 of file Eigenvalues.
void HessenbergDecomposition< MatrixType >::_compute | ( | MatrixType & | matA, |
CoeffVectorType & | hCoeffs, | ||
VectorType & | temp | ||
) | [static, private] |
Definition at line 306 of file Eigenvalues.
static void Eigen::HessenbergDecomposition< _MatrixType >::_compute | ( | MatrixType & | matA, |
CoeffVectorType & | hCoeffs, | ||
VectorType & | temp | ||
) | [static, private] |
static void Eigen::HessenbergDecomposition< _MatrixType >::_compute | ( | MatrixType & | matA, |
CoeffVectorType & | hCoeffs, | ||
VectorType & | temp | ||
) | [static, private] |
static void Eigen::HessenbergDecomposition< _MatrixType >::_compute | ( | MatrixType & | matA, |
CoeffVectorType & | hCoeffs, | ||
VectorType & | temp | ||
) | [static, private] |
static void Eigen::HessenbergDecomposition< _MatrixType >::_compute | ( | MatrixType & | matA, |
CoeffVectorType & | hCoeffs, | ||
VectorType & | temp | ||
) | [static, private] |
HessenbergDecomposition& Eigen::HessenbergDecomposition< _MatrixType >::compute | ( | const MatrixType & | matrix | ) | [inline] |
Computes Hessenberg decomposition of given matrix.
[in] | matrix | Square matrix whose Hessenberg decomposition is to be computed. |
*this
The Hessenberg decomposition is computed by bringing the columns of the matrix successively in the required form using Householder reflections (see, e.g., Algorithm 7.4.2 in Golub & Van Loan, Matrix Computations). The cost is flops, where
denotes the size of the given matrix.
This method reuses of the allocated data in the HessenbergDecomposition object.
Example:
Output:
Definition at line 164 of file Eigenvalues.
HessenbergDecomposition& Eigen::HessenbergDecomposition< _MatrixType >::compute | ( | const MatrixType & | matrix | ) | [inline] |
Computes Hessenberg decomposition of given matrix.
[in] | matrix | Square matrix whose Hessenberg decomposition is to be computed. |
*this
The Hessenberg decomposition is computed by bringing the columns of the matrix successively in the required form using Householder reflections (see, e.g., Algorithm 7.4.2 in Golub & Van Loan, Matrix Computations). The cost is flops, where
denotes the size of the given matrix.
This method reuses of the allocated data in the HessenbergDecomposition object.
Example:
Output:
Definition at line 164 of file Eigenvalues.
HessenbergDecomposition& Eigen::HessenbergDecomposition< _MatrixType >::compute | ( | const MatrixType & | matrix | ) | [inline] |
Computes Hessenberg decomposition of given matrix.
[in] | matrix | Square matrix whose Hessenberg decomposition is to be computed. |
*this
The Hessenberg decomposition is computed by bringing the columns of the matrix successively in the required form using Householder reflections (see, e.g., Algorithm 7.4.2 in Golub & Van Loan, Matrix Computations). The cost is flops, where
denotes the size of the given matrix.
This method reuses of the allocated data in the HessenbergDecomposition object.
Example:
Output:
Definition at line 164 of file Eigenvalues.
HessenbergDecomposition& Eigen::HessenbergDecomposition< _MatrixType >::compute | ( | const MatrixType & | matrix | ) | [inline] |
Computes Hessenberg decomposition of given matrix.
[in] | matrix | Square matrix whose Hessenberg decomposition is to be computed. |
*this
The Hessenberg decomposition is computed by bringing the columns of the matrix successively in the required form using Householder reflections (see, e.g., Algorithm 7.4.2 in Golub & Van Loan, Matrix Computations). The cost is flops, where
denotes the size of the given matrix.
This method reuses of the allocated data in the HessenbergDecomposition object.
Example:
Output:
Definition at line 164 of file Eigenvalues.
HessenbergDecomposition& Eigen::HessenbergDecomposition< _MatrixType >::compute | ( | const MatrixType & | matrix | ) | [inline] |
Computes Hessenberg decomposition of given matrix.
[in] | matrix | Square matrix whose Hessenberg decomposition is to be computed. |
*this
The Hessenberg decomposition is computed by bringing the columns of the matrix successively in the required form using Householder reflections (see, e.g., Algorithm 7.4.2 in Golub & Van Loan, Matrix Computations). The cost is flops, where
denotes the size of the given matrix.
This method reuses of the allocated data in the HessenbergDecomposition object.
Example:
Output:
Definition at line 164 of file Eigenvalues.
const CoeffVectorType& Eigen::HessenbergDecomposition< _MatrixType >::householderCoefficients | ( | ) | const [inline] |
Returns the Householder coefficients.
The Householder coefficients allow the reconstruction of the matrix in the Hessenberg decomposition from the packed data.
Definition at line 191 of file Eigenvalues.
const CoeffVectorType& Eigen::HessenbergDecomposition< _MatrixType >::householderCoefficients | ( | ) | const [inline] |
Returns the Householder coefficients.
The Householder coefficients allow the reconstruction of the matrix in the Hessenberg decomposition from the packed data.
Definition at line 191 of file Eigenvalues.
const CoeffVectorType& Eigen::HessenbergDecomposition< _MatrixType >::householderCoefficients | ( | ) | const [inline] |
Returns the Householder coefficients.
The Householder coefficients allow the reconstruction of the matrix in the Hessenberg decomposition from the packed data.
Definition at line 191 of file Eigenvalues.
const CoeffVectorType& Eigen::HessenbergDecomposition< _MatrixType >::householderCoefficients | ( | ) | const [inline] |
Returns the Householder coefficients.
The Householder coefficients allow the reconstruction of the matrix in the Hessenberg decomposition from the packed data.
Definition at line 191 of file Eigenvalues.
const CoeffVectorType& Eigen::HessenbergDecomposition< _MatrixType >::householderCoefficients | ( | ) | const [inline] |
Returns the Householder coefficients.
The Householder coefficients allow the reconstruction of the matrix in the Hessenberg decomposition from the packed data.
Definition at line 191 of file Eigenvalues.
MatrixHReturnType Eigen::HessenbergDecomposition< _MatrixType >::matrixH | ( | ) | const [inline] |
Constructs the Hessenberg matrix H in the decomposition.
The object returned by this function constructs the Hessenberg matrix H when it is assigned to a matrix or otherwise evaluated. The matrix H is constructed from the packed matrix as returned by packedMatrix(): The upper part (including the subdiagonal) of the packed matrix contains the matrix H. It may sometimes be better to directly use the packed matrix instead of constructing the matrix H.
Example:
Output:
Definition at line 274 of file Eigenvalues.
MatrixHReturnType Eigen::HessenbergDecomposition< _MatrixType >::matrixH | ( | ) | const [inline] |
Constructs the Hessenberg matrix H in the decomposition.
The object returned by this function constructs the Hessenberg matrix H when it is assigned to a matrix or otherwise evaluated. The matrix H is constructed from the packed matrix as returned by packedMatrix(): The upper part (including the subdiagonal) of the packed matrix contains the matrix H. It may sometimes be better to directly use the packed matrix instead of constructing the matrix H.
Example:
Output:
Definition at line 274 of file Eigenvalues.
MatrixHReturnType Eigen::HessenbergDecomposition< _MatrixType >::matrixH | ( | ) | const [inline] |
Constructs the Hessenberg matrix H in the decomposition.
The object returned by this function constructs the Hessenberg matrix H when it is assigned to a matrix or otherwise evaluated. The matrix H is constructed from the packed matrix as returned by packedMatrix(): The upper part (including the subdiagonal) of the packed matrix contains the matrix H. It may sometimes be better to directly use the packed matrix instead of constructing the matrix H.
Example:
Output:
Definition at line 274 of file Eigenvalues.
MatrixHReturnType Eigen::HessenbergDecomposition< _MatrixType >::matrixH | ( | ) | const [inline] |
Constructs the Hessenberg matrix H in the decomposition.
The object returned by this function constructs the Hessenberg matrix H when it is assigned to a matrix or otherwise evaluated. The matrix H is constructed from the packed matrix as returned by packedMatrix(): The upper part (including the subdiagonal) of the packed matrix contains the matrix H. It may sometimes be better to directly use the packed matrix instead of constructing the matrix H.
Example:
Output:
Definition at line 274 of file Eigenvalues.
MatrixHReturnType Eigen::HessenbergDecomposition< _MatrixType >::matrixH | ( | ) | const [inline] |
Constructs the Hessenberg matrix H in the decomposition.
The object returned by this function constructs the Hessenberg matrix H when it is assigned to a matrix or otherwise evaluated. The matrix H is constructed from the packed matrix as returned by packedMatrix(): The upper part (including the subdiagonal) of the packed matrix contains the matrix H. It may sometimes be better to directly use the packed matrix instead of constructing the matrix H.
Example:
Output:
Definition at line 274 of file Eigenvalues.
HouseholderSequenceType Eigen::HessenbergDecomposition< _MatrixType >::matrixQ | ( | void | ) | const [inline] |
Reconstructs the orthogonal 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 246 of file Eigenvalues.
HouseholderSequenceType Eigen::HessenbergDecomposition< _MatrixType >::matrixQ | ( | void | ) | const [inline] |
Reconstructs the orthogonal 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 246 of file Eigenvalues.
HouseholderSequenceType Eigen::HessenbergDecomposition< _MatrixType >::matrixQ | ( | void | ) | const [inline] |
Reconstructs the orthogonal 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 246 of file Eigenvalues.
HouseholderSequenceType Eigen::HessenbergDecomposition< _MatrixType >::matrixQ | ( | void | ) | const [inline] |
Reconstructs the orthogonal 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 246 of file Eigenvalues.
HouseholderSequenceType Eigen::HessenbergDecomposition< _MatrixType >::matrixQ | ( | void | ) | const [inline] |
Reconstructs the orthogonal 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 246 of file Eigenvalues.
const MatrixType& Eigen::HessenbergDecomposition< _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 226 of file Eigenvalues.
const MatrixType& Eigen::HessenbergDecomposition< _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 226 of file Eigenvalues.
const MatrixType& Eigen::HessenbergDecomposition< _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 226 of file Eigenvalues.
const MatrixType& Eigen::HessenbergDecomposition< _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 226 of file Eigenvalues.
const MatrixType& Eigen::HessenbergDecomposition< _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 226 of file Eigenvalues.
CoeffVectorType HessenbergDecomposition< _MatrixType >::m_hCoeffs [protected] |
Definition at line 288 of file Eigenvalues.
bool HessenbergDecomposition< _MatrixType >::m_isInitialized [protected] |
Definition at line 290 of file Eigenvalues.
MatrixType HessenbergDecomposition< _MatrixType >::m_matrix [protected] |
Definition at line 287 of file Eigenvalues.
VectorType HessenbergDecomposition< _MatrixType >::m_temp [protected] |
Definition at line 289 of file Eigenvalues.
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