Householder QR decomposition of a matrix. More...
#include <HouseholderQR.h>
Public Types | |
| enum | { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, Options = MatrixType::Options, MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime } |
| typedef internal::plain_diag_type < MatrixType >::type | HCoeffsType |
| typedef HouseholderSequence < MatrixType, typename internal::remove_all< typename HCoeffsType::ConjugateReturnType > ::type > | HouseholderSequenceType |
| typedef MatrixType::Index | Index |
| typedef Matrix< Scalar, RowsAtCompileTime, RowsAtCompileTime,(MatrixType::Flags &RowMajorBit)?RowMajor:ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTime > | MatrixQType |
| typedef _MatrixType | MatrixType |
| typedef MatrixType::RealScalar | RealScalar |
| typedef internal::plain_row_type < MatrixType >::type | RowVectorType |
| typedef MatrixType::Scalar | Scalar |
Public Member Functions | |
| MatrixType::RealScalar | absDeterminant () const |
| Index | cols () const |
| HouseholderQR & | compute (const MatrixType &matrix) |
| const HCoeffsType & | hCoeffs () const |
| HouseholderSequenceType | householderQ () const |
| HouseholderQR () | |
| Default Constructor. | |
| HouseholderQR (Index rows, Index cols) | |
| Default Constructor with memory preallocation. | |
| HouseholderQR (const MatrixType &matrix) | |
| Constructs a QR factorization from a given matrix. | |
| MatrixType::RealScalar | logAbsDeterminant () const |
| const MatrixType & | matrixQR () const |
| Index | rows () const |
| template<typename Rhs > | |
| const internal::solve_retval < HouseholderQR, Rhs > | solve (const MatrixBase< Rhs > &b) const |
Static Protected Member Functions | |
| static void | check_template_parameters () |
Protected Attributes | |
| HCoeffsType | m_hCoeffs |
| bool | m_isInitialized |
| MatrixType | m_qr |
| RowVectorType | m_temp |
Detailed Description
template<typename _MatrixType>
class Eigen::HouseholderQR< _MatrixType >
Householder QR decomposition of a matrix.
- Parameters:
-
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_181.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.
- See also:
- MatrixBase::householderQr()
Definition at line 42 of file HouseholderQR.h.
Member Typedef Documentation
| typedef internal::plain_diag_type<MatrixType>::type Eigen::HouseholderQR< _MatrixType >::HCoeffsType |
Definition at line 58 of file HouseholderQR.h.
| typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> Eigen::HouseholderQR< _MatrixType >::HouseholderSequenceType |
Definition at line 60 of file HouseholderQR.h.
| typedef MatrixType::Index Eigen::HouseholderQR< _MatrixType >::Index |
Definition at line 56 of file HouseholderQR.h.
| typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, (MatrixType::Flags&RowMajorBit) ? RowMajor : ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTime> Eigen::HouseholderQR< _MatrixType >::MatrixQType |
Definition at line 57 of file HouseholderQR.h.
| typedef _MatrixType Eigen::HouseholderQR< _MatrixType >::MatrixType |
Definition at line 46 of file HouseholderQR.h.
| typedef MatrixType::RealScalar Eigen::HouseholderQR< _MatrixType >::RealScalar |
Definition at line 55 of file HouseholderQR.h.
| typedef internal::plain_row_type<MatrixType>::type Eigen::HouseholderQR< _MatrixType >::RowVectorType |
Definition at line 59 of file HouseholderQR.h.
| typedef MatrixType::Scalar Eigen::HouseholderQR< _MatrixType >::Scalar |
Definition at line 54 of file HouseholderQR.h.
Member Enumeration Documentation
| anonymous enum |
Definition at line 47 of file HouseholderQR.h.
Constructor & Destructor Documentation
| Eigen::HouseholderQR< _MatrixType >::HouseholderQR | ( | ) | [inline] |
Default Constructor.
The default constructor is useful in cases in which the user intends to perform decompositions via HouseholderQR::compute(const MatrixType&).
Definition at line 68 of file HouseholderQR.h.
| Eigen::HouseholderQR< _MatrixType >::HouseholderQR | ( | Index | rows, |
| Index | cols | ||
| ) | [inline] |
Default Constructor with memory preallocation.
Like the default constructor but with preallocation of the internal data according to the specified problem size.
- See also:
- HouseholderQR()
Definition at line 76 of file HouseholderQR.h.
| Eigen::HouseholderQR< _MatrixType >::HouseholderQR | ( | const MatrixType & | matrix | ) | [inline] |
Member Function Documentation
| MatrixType::RealScalar Eigen::HouseholderQR< MatrixType >::absDeterminant | ( | ) | const |
- Returns:
- the absolute value of the determinant of the matrix of which *this is the QR decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the QR decomposition has already been computed.
- Note:
- This is only for square matrices.
- Warning:
- a determinant can be very big or small, so for matrices of large enough dimension, there is a risk of overflow/underflow. One way to work around that is to use logAbsDeterminant() instead.
- See also:
- logAbsDeterminant(), MatrixBase::determinant()
Definition at line 205 of file HouseholderQR.h.
| static void Eigen::HouseholderQR< _MatrixType >::check_template_parameters | ( | ) | [inline, static, protected] |
Definition at line 193 of file HouseholderQR.h.
| Index Eigen::HouseholderQR< _MatrixType >::cols | ( | void | ) | const [inline] |
Definition at line 183 of file HouseholderQR.h.
| HouseholderQR< MatrixType > & Eigen::HouseholderQR< MatrixType >::compute | ( | const MatrixType & | matrix | ) |
Performs the QR factorization of the given matrix matrix. The result of the factorization is stored into *this, and a reference to *this is returned.
- See also:
- class HouseholderQR, HouseholderQR(const MatrixType&)
Definition at line 356 of file HouseholderQR.h.
| const HCoeffsType& Eigen::HouseholderQR< _MatrixType >::hCoeffs | ( | ) | const [inline] |
- Returns:
- a const reference to the vector of Householder coefficients used to represent the factor
Q.
For advanced uses only.
Definition at line 189 of file HouseholderQR.h.
| HouseholderSequenceType Eigen::HouseholderQR< _MatrixType >::householderQ | ( | void | ) | const [inline] |
This method returns an expression of the unitary matrix Q as a sequence of Householder transformations.
The returned expression can directly be used to perform matrix products. It can also be assigned to a dense Matrix object. Here is an example showing how to recover the full or thin matrix Q, as well as how to perform matrix products using operator*:
Example:
Output:
Definition at line 136 of file HouseholderQR.h.
| MatrixType::RealScalar Eigen::HouseholderQR< MatrixType >::logAbsDeterminant | ( | ) | const |
- Returns:
- the natural log of the absolute value of the determinant of the matrix of which *this is the QR decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the QR decomposition has already been computed.
- Note:
- This is only for square matrices.
- This method is useful to work around the risk of overflow/underflow that's inherent to determinant computation.
- See also:
- absDeterminant(), MatrixBase::determinant()
Definition at line 214 of file HouseholderQR.h.
| const MatrixType& Eigen::HouseholderQR< _MatrixType >::matrixQR | ( | ) | const [inline] |
- Returns:
- a reference to the matrix where the Householder QR decomposition is stored in a LAPACK-compatible way.
Definition at line 145 of file HouseholderQR.h.
| Index Eigen::HouseholderQR< _MatrixType >::rows | ( | void | ) | const [inline] |
Definition at line 182 of file HouseholderQR.h.
| const internal::solve_retval<HouseholderQR, Rhs> Eigen::HouseholderQR< _MatrixType >::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.
- Parameters:
-
b the right-hand-side of the equation to solve.
- Returns:
- a solution.
- Note:
- The case where b is a matrix is not yet implemented. Also, this code is space inefficient.
Example:
Output:
Definition at line 122 of file HouseholderQR.h.
Member Data Documentation
HCoeffsType Eigen::HouseholderQR< _MatrixType >::m_hCoeffs [protected] |
Definition at line 199 of file HouseholderQR.h.
bool Eigen::HouseholderQR< _MatrixType >::m_isInitialized [protected] |
Definition at line 201 of file HouseholderQR.h.
MatrixType Eigen::HouseholderQR< _MatrixType >::m_qr [protected] |
Definition at line 198 of file HouseholderQR.h.
RowVectorType Eigen::HouseholderQR< _MatrixType >::m_temp [protected] |
Definition at line 200 of file HouseholderQR.h.
The documentation for this class was generated from the following file: