Householder QR decomposition of a matrix. More...
#include <ForwardDeclarations.h>
Public Member Functions | |
template<typename RhsType , typename DstType > | |
void | _solve_impl (const RhsType &rhs, DstType &dst) const |
template<bool Conjugate, typename RhsType , typename DstType > | |
void | _solve_impl_transposed (const RhsType &rhs, DstType &dst) const |
MatrixType::RealScalar | absDeterminant () const |
Index | cols () const |
template<typename InputType > | |
HouseholderQR & | compute (const EigenBase< InputType > &matrix) |
const HCoeffsType & | hCoeffs () const |
HouseholderSequenceType | householderQ () const |
HouseholderQR () | |
Default Constructor. More... | |
HouseholderQR (Index rows, Index cols) | |
Default Constructor with memory preallocation. More... | |
template<typename InputType > | |
HouseholderQR (const EigenBase< InputType > &matrix) | |
Constructs a QR factorization from a given matrix. More... | |
template<typename InputType > | |
HouseholderQR (EigenBase< InputType > &matrix) | |
Constructs a QR factorization from a given matrix. More... | |
MatrixType::RealScalar | logAbsDeterminant () const |
const MatrixType & | matrixQR () const |
Index | rows () const |
Public Member Functions inherited from Eigen::SolverBase< HouseholderQR< _MatrixType > > | |
AdjointReturnType | adjoint () const |
const Solve< HouseholderQR< _MatrixType >, Rhs > | solve (const MatrixBase< Rhs > &b) const |
SolverBase () | |
ConstTransposeReturnType | transpose () const |
~SolverBase () | |
Public Member Functions inherited from Eigen::EigenBase< Derived > | |
template<typename Dest > | |
EIGEN_DEVICE_FUNC void | addTo (Dest &dst) const |
template<typename Dest > | |
EIGEN_DEVICE_FUNC void | applyThisOnTheLeft (Dest &dst) const |
template<typename Dest > | |
EIGEN_DEVICE_FUNC void | applyThisOnTheRight (Dest &dst) const |
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index | cols () const EIGEN_NOEXCEPT |
EIGEN_DEVICE_FUNC Derived & | const_cast_derived () const |
EIGEN_DEVICE_FUNC const Derived & | const_derived () const |
EIGEN_DEVICE_FUNC Derived & | derived () |
EIGEN_DEVICE_FUNC const Derived & | derived () const |
template<typename Dest > | |
EIGEN_DEVICE_FUNC void | evalTo (Dest &dst) const |
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index | rows () const EIGEN_NOEXCEPT |
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index | size () const EIGEN_NOEXCEPT |
template<typename Dest > | |
EIGEN_DEVICE_FUNC void | subTo (Dest &dst) const |
Protected Member Functions | |
void | computeInPlace () |
Protected Member Functions inherited from Eigen::SolverBase< HouseholderQR< _MatrixType > > | |
void | _check_solve_assertion (const 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 |
Friends | |
class | SolverBase< HouseholderQR > |
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
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.
This class supports the inplace decomposition mechanism.
Definition at line 273 of file ForwardDeclarations.h.
typedef SolverBase<HouseholderQR> Eigen::HouseholderQR< _MatrixType >::Base |
Definition at line 62 of file HouseholderQR.h.
typedef internal::plain_diag_type<MatrixType>::type Eigen::HouseholderQR< _MatrixType >::HCoeffsType |
Definition at line 71 of file HouseholderQR.h.
typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> Eigen::HouseholderQR< _MatrixType >::HouseholderSequenceType |
Definition at line 73 of file HouseholderQR.h.
typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, (MatrixType::Flags&RowMajorBit) ? RowMajor : ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTime> Eigen::HouseholderQR< _MatrixType >::MatrixQType |
Definition at line 70 of file HouseholderQR.h.
typedef _MatrixType Eigen::HouseholderQR< _MatrixType >::MatrixType |
Definition at line 61 of file HouseholderQR.h.
typedef internal::plain_row_type<MatrixType>::type Eigen::HouseholderQR< _MatrixType >::RowVectorType |
Definition at line 72 of file HouseholderQR.h.
anonymous enum |
Enumerator | |
---|---|
MaxRowsAtCompileTime | |
MaxColsAtCompileTime |
Definition at line 66 of file HouseholderQR.h.
|
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 81 of file HouseholderQR.h.
|
inline |
Default Constructor with memory preallocation.
Like the default constructor but with preallocation of the internal data according to the specified problem size.
Definition at line 89 of file HouseholderQR.h.
|
inlineexplicit |
Constructs a QR factorization from a given matrix.
This constructor computes the QR factorization of the matrix matrix by calling the method compute(). It is a short cut for:
Definition at line 108 of file HouseholderQR.h.
|
inlineexplicit |
Constructs a QR factorization from a given matrix.
This overloaded constructor is provided for inplace decomposition when MatrixType
is a Eigen::Ref.
Definition at line 126 of file HouseholderQR.h.
void Eigen::HouseholderQR< _MatrixType >::_solve_impl | ( | const RhsType & | rhs, |
DstType & | dst | ||
) | const |
Definition at line 361 of file HouseholderQR.h.
void Eigen::HouseholderQR< _MatrixType >::_solve_impl_transposed | ( | const RhsType & | rhs, |
DstType & | dst | ||
) | const |
Definition at line 379 of file HouseholderQR.h.
MatrixType::RealScalar Eigen::HouseholderQR< MatrixType >::absDeterminant | ( | ) | const |
Definition at line 247 of file HouseholderQR.h.
|
inlinestaticprotected |
Definition at line 233 of file HouseholderQR.h.
|
inline |
Definition at line 215 of file HouseholderQR.h.
|
inline |
Definition at line 179 of file HouseholderQR.h.
|
protected |
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.
Definition at line 404 of file HouseholderQR.h.
|
inline |
Q
.For advanced uses only.
Definition at line 221 of file HouseholderQR.h.
|
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 163 of file HouseholderQR.h.
MatrixType::RealScalar Eigen::HouseholderQR< MatrixType >::logAbsDeterminant | ( | ) | const |
Definition at line 256 of file HouseholderQR.h.
|
inline |
Definition at line 172 of file HouseholderQR.h.
|
inline |
Definition at line 214 of file HouseholderQR.h.
|
friend |
Definition at line 63 of file HouseholderQR.h.
|
protected |
Definition at line 241 of file HouseholderQR.h.
|
protected |
Definition at line 243 of file HouseholderQR.h.
|
protected |
Definition at line 240 of file HouseholderQR.h.
|
protected |
Definition at line 242 of file HouseholderQR.h.