Householder QR decomposition of a matrix.
| MatrixType | the type of the matrix of which we are computing the QR decomposition |
This class performs a QR decomposition of a matrix A into matrices Q and R such that
![\[ \mathbf{A} = \mathbf{Q} \, \mathbf{R} \]](form_264.png)
by using Householder transformations. Here, Q a unitary matrix and R an upper triangular matrix. The result is stored in a compact way compatible with LAPACK.
Note that no pivoting is performed. This is not a rank-revealing decomposition. If you want that feature, use FullPivHouseholderQR or ColPivHouseholderQR instead.
This Householder QR decomposition is faster, but less numerically stable and less feature-full than FullPivHouseholderQR or ColPivHouseholderQR.
Public Types | |
| enum | { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, Options = MatrixType::Options, MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime } |
| typedef _MatrixType | MatrixType |
| typedef MatrixType::Scalar | Scalar |
| typedef MatrixType::RealScalar | RealScalar |
| typedef MatrixType::Index | Index |
| typedef Matrix< Scalar, RowsAtCompileTime, RowsAtCompileTime,(MatrixType::Flags &RowMajorBit)?RowMajor:ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTime > | MatrixQType |
| typedef internal::plain_diag_type < MatrixType >::type | HCoeffsType |
| typedef internal::plain_row_type < MatrixType >::type | RowVectorType |
| typedef HouseholderSequence < MatrixType, HCoeffsType > ::ConjugateReturnType | HouseholderSequenceType |
Public Member Functions | |
| HouseholderQR () | |
| Default Constructor. | |
| HouseholderQR (Index rows, Index cols) | |
| Default Constructor with memory preallocation. | |
| HouseholderQR (const MatrixType &matrix) | |
| template<typename Rhs > | |
| const internal::solve_retval < HouseholderQR, Rhs > | solve (const MatrixBase< Rhs > &b) const |
| This method finds a solution x to the equation Ax=b, where A is the matrix of which *this is the QR decomposition, if any exists. | |
| HouseholderSequenceType | householderQ () const |
| const MatrixType & | matrixQR () const |
| HouseholderQR & | compute (const MatrixType &matrix) |
| MatrixType::RealScalar | absDeterminant () const |
| MatrixType::RealScalar | logAbsDeterminant () const |
| Index | rows () const |
| Index | cols () const |
| const HCoeffsType & | hCoeffs () const |
Protected Attributes | |
| MatrixType | m_qr |
| HCoeffsType | m_hCoeffs |
| RowVectorType | m_temp |
| bool | m_isInitialized |
| typedef internal::plain_diag_type<MatrixType>::type Eigen::HouseholderQR::HCoeffsType |
| typedef HouseholderSequence<MatrixType,HCoeffsType>::ConjugateReturnType Eigen::HouseholderQR::HouseholderSequenceType |
| typedef MatrixType::Index Eigen::HouseholderQR::Index |
| typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, (MatrixType::Flags&RowMajorBit) ? RowMajor : ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTime> Eigen::HouseholderQR::MatrixQType |
| typedef _MatrixType Eigen::HouseholderQR::MatrixType |
| typedef MatrixType::RealScalar Eigen::HouseholderQR::RealScalar |
| typedef MatrixType::Scalar Eigen::HouseholderQR::Scalar |
| anonymous enum |
| Eigen::HouseholderQR::HouseholderQR | ( | ) | [inline] |
Default Constructor.
The default constructor is useful in cases in which the user intends to perform decompositions via HouseholderQR::compute(const MatrixType&).
Default Constructor with memory preallocation.
Like the default constructor but with preallocation of the internal data according to the specified problem size.
| Eigen::HouseholderQR::HouseholderQR | ( | const MatrixType & | matrix | ) | [inline] |
| MatrixType::RealScalar Eigen::HouseholderQR::absDeterminant | ( | ) | const |
| HouseholderQR< MatrixType > & Eigen::HouseholderQR::compute | ( | const MatrixType & | matrix | ) |
| const HCoeffsType& Eigen::HouseholderQR::hCoeffs | ( | ) | const [inline] |
| HouseholderSequenceType Eigen::HouseholderQR::householderQ | ( | ) | const [inline] |
| MatrixType::RealScalar Eigen::HouseholderQR::logAbsDeterminant | ( | ) | const |
| const MatrixType& Eigen::HouseholderQR::matrixQR | ( | ) | const [inline] |
| const internal::solve_retval<HouseholderQR, Rhs> Eigen::HouseholderQR::solve | ( | const MatrixBase< Rhs > & | b | ) | const [inline] |
This method finds a solution x to the equation Ax=b, where A is the matrix of which *this is the QR decomposition, if any exists.
| b | the right-hand-side of the equation to solve. |
Example:
Output:
HCoeffsType Eigen::HouseholderQR::m_hCoeffs [protected] |
bool Eigen::HouseholderQR::m_isInitialized [protected] |
MatrixType Eigen::HouseholderQR::m_qr [protected] |
RowVectorType Eigen::HouseholderQR::m_temp [protected] |
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