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Eigen::HouseholderQR< _MatrixType > Class Template Reference
Dense linear problems and decompositions » Reference » QR_Module

Householder QR decomposition of a matrix. More...

#include <ForwardDeclarations.h>

Public Types

enum  { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, 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 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
 
typedef MatrixType::StorageIndex StorageIndex
 

Public Member Functions

template<typename RhsType , typename DstType >
EIGEN_DEVICE_FUNC void _solve_impl (const RhsType &rhs, DstType &dst) const
 
template<typename RhsType , typename DstType >
void _solve_impl (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
 
template<typename Rhs >
const Solve< HouseholderQR, Rhs > solve (const MatrixBase< Rhs > &b) 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
 

Detailed Description

template<typename _MatrixType>
class Eigen::HouseholderQR< _MatrixType >

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 254 of file ForwardDeclarations.h.

Member Typedef Documentation

template<typename _MatrixType>
typedef internal::plain_diag_type<MatrixType>::type Eigen::HouseholderQR< _MatrixType >::HCoeffsType

Definition at line 60 of file HouseholderQR.h.

template<typename _MatrixType>
typedef HouseholderSequence<MatrixType,typename internal::remove_all<typename HCoeffsType::ConjugateReturnType>::type> Eigen::HouseholderQR< _MatrixType >::HouseholderSequenceType

Definition at line 62 of file HouseholderQR.h.

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

Definition at line 59 of file HouseholderQR.h.

template<typename _MatrixType>
typedef _MatrixType Eigen::HouseholderQR< _MatrixType >::MatrixType

Definition at line 48 of file HouseholderQR.h.

template<typename _MatrixType>
typedef MatrixType::RealScalar Eigen::HouseholderQR< _MatrixType >::RealScalar

Definition at line 56 of file HouseholderQR.h.

template<typename _MatrixType>
typedef internal::plain_row_type<MatrixType>::type Eigen::HouseholderQR< _MatrixType >::RowVectorType

Definition at line 61 of file HouseholderQR.h.

template<typename _MatrixType>
typedef MatrixType::Scalar Eigen::HouseholderQR< _MatrixType >::Scalar

Definition at line 55 of file HouseholderQR.h.

template<typename _MatrixType>
typedef MatrixType::StorageIndex Eigen::HouseholderQR< _MatrixType >::StorageIndex

Definition at line 58 of file HouseholderQR.h.

Member Enumeration Documentation

template<typename _MatrixType>
anonymous enum
Enumerator
RowsAtCompileTime 
ColsAtCompileTime 
MaxRowsAtCompileTime 
MaxColsAtCompileTime 

Definition at line 49 of file HouseholderQR.h.

Constructor & Destructor Documentation

template<typename _MatrixType>
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 70 of file HouseholderQR.h.

template<typename _MatrixType>
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 78 of file HouseholderQR.h.

template<typename _MatrixType>
template<typename InputType >
Eigen::HouseholderQR< _MatrixType >::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 97 of file HouseholderQR.h.

template<typename _MatrixType>
template<typename InputType >
Eigen::HouseholderQR< _MatrixType >::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 115 of file HouseholderQR.h.

Member Function Documentation

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

Definition at line 350 of file HouseholderQR.h.

template<typename MatrixType >
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 236 of file HouseholderQR.h.

template<typename _MatrixType>
static void Eigen::HouseholderQR< _MatrixType >::check_template_parameters ( )
inlinestaticprotected

Definition at line 222 of file HouseholderQR.h.

template<typename _MatrixType>
Index Eigen::HouseholderQR< _MatrixType >::cols ( void  ) const
inline

Definition at line 206 of file HouseholderQR.h.

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

Definition at line 170 of file HouseholderQR.h.

template<typename MatrixType >
void Eigen::HouseholderQR< MatrixType >::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 379 of file HouseholderQR.h.

template<typename _MatrixType>
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 212 of file HouseholderQR.h.

template<typename _MatrixType>
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:

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 154 of file HouseholderQR.h.













template<typename MatrixType > 

      

        

          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 245 of file HouseholderQR.h.













template<typename _MatrixType> 



  

  
      

        

          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 163 of file HouseholderQR.h.













template<typename _MatrixType> 



  

  
      

        

          Index Eigen::HouseholderQR< _MatrixType >::rows 
          (
          void 
          )
           const
        

      

  		
  
inline  
  







Definition at line 205 of file HouseholderQR.h.













template<typename _MatrixType> 



template<typename Rhs > 



  

  
      

        

          const Solve<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

  

    
bthe right-hand-side of the equation to solve.

  

  




Returns
a solution.


Example: 
typedef Matrix<float,3,3> Matrix3x3;
Matrix3x3 m = Matrix3x3::Random();
Matrix3f y = Matrix3f::Random();
cout << "Here is the matrix m:" << endl << m << endl;
cout << "Here is the matrix y:" << endl << y << endl;
Matrix3f x;
x = m.householderQr().solve(y);
assert(y.isApprox(m*x));
cout << "Here is a solution x to the equation mx=y:" << endl << x << endl;
 Output: 
 

Definition at line 140 of file HouseholderQR.h.







Member Data Documentation








template<typename _MatrixType> 



  

  
      

        

          HCoeffsType Eigen::HouseholderQR< _MatrixType >::m_hCoeffs
        

      

  		
  
protected  
  







Definition at line 230 of file HouseholderQR.h.













template<typename _MatrixType> 



  

  
      

        

          bool Eigen::HouseholderQR< _MatrixType >::m_isInitialized
        

      

  		
  
protected  
  







Definition at line 232 of file HouseholderQR.h.













template<typename _MatrixType> 



  

  
      

        

          MatrixType Eigen::HouseholderQR< _MatrixType >::m_qr
        

      

  		
  
protected  
  







Definition at line 229 of file HouseholderQR.h.













template<typename _MatrixType> 



  

  
      

        

          RowVectorType Eigen::HouseholderQR< _MatrixType >::m_temp
        

      

  		
  
protected  
  







Definition at line 231 of file HouseholderQR.h.







The documentation for this class was generated from the following files:







gtsam

Author(s): 

autogenerated on Sat May 8 2021 02:52:44