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Eigen::HouseholderQR Class Reference

Householder QR decomposition of a matrix. More...

#include <ForwardDeclarations.h>

Public Types

enum  { MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }
 
typedef SolverBase< HouseholderQRBase
 
typedef internal::plain_diag_type< MatrixType >::type HCoeffsType
 
typedef HouseholderSequence< MatrixType, typename internal::remove_all< typename HCoeffsType::ConjugateReturnType >::typeHouseholderSequenceType
 
typedef Matrix< Scalar, RowsAtCompileTime, RowsAtCompileTime,(MatrixType::Flags &RowMajorBit) ? RowMajor :ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTimeMatrixQType
 
typedef _MatrixType MatrixType
 
typedef internal::plain_row_type< MatrixType >::type RowVectorType
 

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 >
HouseholderQRcompute (const EigenBase< InputType > &matrix)
 
const HCoeffsTypehCoeffs () const
 
HouseholderSequenceType householderQ () const
 
 HouseholderQR ()
 Default Constructor. 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...
 
 HouseholderQR (Index rows, Index cols)
 Default Constructor with memory preallocation. More...
 
MatrixType::RealScalar logAbsDeterminant () const
 
const MatrixTypematrixQR () const
 
Index rows () const
 

Protected Member Functions

void computeInPlace ()
 

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 >
 

Detailed Description

Householder QR decomposition of a matrix.

Template Parameters
_MatrixTypethe 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

\[ \mathbf{A} = \mathbf{Q} \, \mathbf{R} \]

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.

See also
MatrixBase::householderQr()

Definition at line 273 of file ForwardDeclarations.h.

Member Typedef Documentation

◆ Base

Definition at line 62 of file HouseholderQR.h.

◆ HCoeffsType

Definition at line 71 of file HouseholderQR.h.

◆ HouseholderSequenceType

Definition at line 73 of file HouseholderQR.h.

◆ MatrixQType

typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime, (MatrixType::Flags&RowMajorBit) ? RowMajor : ColMajor, MaxRowsAtCompileTime, MaxRowsAtCompileTime> Eigen::HouseholderQR::MatrixQType

Definition at line 70 of file HouseholderQR.h.

◆ MatrixType

typedef _MatrixType Eigen::HouseholderQR::MatrixType

Definition at line 61 of file HouseholderQR.h.

◆ RowVectorType

Definition at line 72 of file HouseholderQR.h.

Member Enumeration Documentation

◆ anonymous enum

anonymous enum
Enumerator
MaxRowsAtCompileTime 
MaxColsAtCompileTime 

Definition at line 66 of file HouseholderQR.h.

Constructor & Destructor Documentation

◆ HouseholderQR() [1/4]

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&).

Definition at line 81 of file HouseholderQR.h.

◆ HouseholderQR() [2/4]

Eigen::HouseholderQR::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 89 of file HouseholderQR.h.

◆ HouseholderQR() [3/4]

template<typename InputType >
Eigen::HouseholderQR::HouseholderQR ( const EigenBase< InputType > &  matrix)
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:

HouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols());
qr.compute(matrix);
See also
compute()

Definition at line 108 of file HouseholderQR.h.

◆ HouseholderQR() [4/4]

template<typename InputType >
Eigen::HouseholderQR::HouseholderQR ( EigenBase< InputType > &  matrix)
inlineexplicit

Constructs a QR factorization from a given matrix.

This overloaded constructor is provided for inplace decomposition when MatrixType is a Eigen::Ref.

See also
HouseholderQR(const EigenBase&)

Definition at line 126 of file HouseholderQR.h.

Member Function Documentation

◆ _solve_impl()

template<typename RhsType , typename DstType >
void Eigen::HouseholderQR::_solve_impl ( const RhsType &  rhs,
DstType &  dst 
) const

Definition at line 361 of file HouseholderQR.h.

◆ _solve_impl_transposed()

template<bool Conjugate, typename RhsType , typename DstType >
void Eigen::HouseholderQR::_solve_impl_transposed ( const RhsType &  rhs,
DstType &  dst 
) const

Definition at line 379 of file HouseholderQR.h.

◆ absDeterminant()

MatrixType::RealScalar Eigen::HouseholderQR::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 247 of file HouseholderQR.h.

◆ check_template_parameters()

static void Eigen::HouseholderQR::check_template_parameters ( )
inlinestaticprotected

Definition at line 233 of file HouseholderQR.h.

◆ cols()

Index Eigen::HouseholderQR::cols ( ) const
inline

Definition at line 215 of file HouseholderQR.h.

◆ compute()

template<typename InputType >
HouseholderQR& Eigen::HouseholderQR::compute ( const EigenBase< InputType > &  matrix)
inline

Definition at line 179 of file HouseholderQR.h.

◆ computeInPlace()

void Eigen::HouseholderQR::computeInPlace ( )
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.

See also
class HouseholderQR, HouseholderQR(const MatrixType&)

Definition at line 404 of file HouseholderQR.h.

◆ hCoeffs()

const HCoeffsType& Eigen::HouseholderQR::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 221 of file HouseholderQR.h.

◆ householderQ()

HouseholderSequenceType Eigen::HouseholderQR::householderQ ( ) 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:

MatrixXf A(MatrixXf::Random(5,3)), thinQ(MatrixXf::Identity(5,3)), Q;
A.setRandom();
HouseholderQR<MatrixXf> qr(A);
Q = qr.householderQ();
thinQ = qr.householderQ() * thinQ;
std::cout << "The complete unitary matrix Q is:\n" << Q << "\n\n";
std::cout << "The thin matrix Q is:\n" << thinQ << "\n\n";

Output:

 

Definition at line 163 of file HouseholderQR.h.

◆ logAbsDeterminant()

MatrixType::RealScalar Eigen::HouseholderQR::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 256 of file HouseholderQR.h.

◆ matrixQR()

const MatrixType& Eigen::HouseholderQR::matrixQR ( ) const
inline
Returns
a reference to the matrix where the Householder QR decomposition is stored in a LAPACK-compatible way.

Definition at line 172 of file HouseholderQR.h.

◆ rows()

Index Eigen::HouseholderQR::rows ( ) const
inline

Definition at line 214 of file HouseholderQR.h.

Friends And Related Function Documentation

◆ SolverBase< HouseholderQR >

friend class SolverBase< HouseholderQR >
friend

Definition at line 63 of file HouseholderQR.h.

Member Data Documentation

◆ m_hCoeffs

HCoeffsType Eigen::HouseholderQR::m_hCoeffs
protected

Definition at line 241 of file HouseholderQR.h.

◆ m_isInitialized

bool Eigen::HouseholderQR::m_isInitialized
protected

Definition at line 243 of file HouseholderQR.h.

◆ m_qr

MatrixType Eigen::HouseholderQR::m_qr
protected

Definition at line 240 of file HouseholderQR.h.

◆ m_temp

RowVectorType Eigen::HouseholderQR::m_temp
protected

Definition at line 242 of file HouseholderQR.h.


The documentation for this class was generated from the following files:
Q
Quaternion Q
Definition: testQuaternion.cpp:27
A
Definition: test_numpy_dtypes.cpp:298
matrix
Map< Matrix< T, Dynamic, Dynamic, ColMajor >, 0, OuterStride<> > matrix(T *data, int rows, int cols, int stride)
Definition: gtsam/3rdparty/Eigen/blas/common.h:110
Eigen::Quaternion
The quaternion class used to represent 3D orientations and rotations.
Definition: ForwardDeclarations.h:293
qr
HouseholderQR< MatrixXf > qr(A)
thinQ
thinQ
Definition: HouseholderQR_householderQ.cpp:5


gtsam
Author(s):
autogenerated on Fri Nov 1 2024 03:44:47