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Eigen::HouseholderQR< _MatrixType > Class Template Reference

Householder QR decomposition of a matrix. More...

#include <HouseholderQR.h>

+ Collaboration diagram for Eigen::HouseholderQR< _MatrixType >:

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, typename internal::remove_all< typename HCoeffsType::ConjugateReturnType >::type > HouseholderSequenceType
 

Public Member Functions

 HouseholderQR ()
 Default Constructor. More...
 
 HouseholderQR (Index rows, Index cols)
 Default Constructor with memory preallocation. More...
 
 HouseholderQR (const MatrixType &matrix)
 Constructs a QR factorization from a given matrix. More...
 
template<typename Rhs >
const internal::solve_retval< HouseholderQR, Rhs > solve (const MatrixBase< Rhs > &b) const
 
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
 

Detailed Description

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

Householder QR decomposition of a matrix.

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.

See also
MatrixBase::householderQr()

Definition at line 221 of file ForwardDeclarations.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 68 of file HouseholderQR.h.

68 : m_qr(), m_hCoeffs(), m_temp(), m_isInitialized(false) {}
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 76 of file HouseholderQR.h.

77  : m_qr(rows, cols),
78  m_hCoeffs((std::min)(rows,cols)),
79  m_temp(cols),
80  m_isInitialized(false) {}
template<typename _MatrixType>
Eigen::HouseholderQR< _MatrixType >::HouseholderQR ( const MatrixType &  matrix)
inline

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 94 of file HouseholderQR.h.

95  : m_qr(matrix.rows(), matrix.cols()),
96  m_hCoeffs((std::min)(matrix.rows(),matrix.cols())),
97  m_temp(matrix.cols()),
98  m_isInitialized(false)
99  {
100  compute(matrix);
101  }
matrix
Definition: math3d.h:219
Eigen::HouseholderQR::compute
HouseholderQR & compute(const MatrixType &matrix)
Definition: HouseholderQR.h:344

Member Function Documentation

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 199 of file HouseholderQR.h.

200 {
201  using std::abs;
202  eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
203  eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
204  return abs(m_qr.diagonal().prod());
205 }
template<typename MatrixType >
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 344 of file HouseholderQR.h.

345 {
346  Index rows = matrix.rows();
347  Index cols = matrix.cols();
348  Index size = (std::min)(rows,cols);
349 
350  m_qr = matrix;
351  m_hCoeffs.resize(size);
352 
353  m_temp.resize(cols);
354 
355  internal::householder_qr_inplace_blocked(m_qr, m_hCoeffs, 48, m_temp.data());
356 
357  m_isInitialized = true;
358  return *this;
359 }
matrix
Definition: math3d.h:219
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 189 of file HouseholderQR.h.

189 { return m_hCoeffs; }
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:

Output: 

 

Definition at line 136 of file HouseholderQR.h.


  137     {
  138       eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
  139       return HouseholderSequenceType(m_qr, m_hCoeffs.conjugate());
  140     }












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 208 of file HouseholderQR.h.


  209 {
  210   eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
  211   eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
  212   return m_qr.diagonal().cwiseAbs().array().log().sum();
  213 }












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 145 of file HouseholderQR.h.


  146     {
  147         eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
  148         return m_qr;
  149     }












template<typename _MatrixType> 



template<typename Rhs > 



  

  
      

        

          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

  

    
bthe 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.


  123     {
  124       eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
  125       return internal::solve_retval<HouseholderQR, Rhs>(*this, b.derived());
  126     }






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





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