Eigen::HouseholderQR< MatrixType_ > Class Template Reference

Householder QR decomposition of a matrix. More...

#include <HouseholderQR.h>

Inheritance diagram for Eigen::HouseholderQR< MatrixType_ >:

Public Types
enum	{ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime , MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }
typedef MatrixType_	MatrixType
typedef SolverBase< HouseholderQR >	Base
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, internal::remove_all_t< typename HCoeffsType::ConjugateReturnType > >	HouseholderSequenceType
Public Types inherited from Eigen::SolverBase< HouseholderQR< MatrixType_ > >
enum
typedef EigenBase< HouseholderQR< MatrixType_ > >	Base
typedef internal::traits< HouseholderQR< MatrixType_ > >::Scalar	Scalar
typedef Scalar	CoeffReturnType
typedef Transpose< const HouseholderQR< MatrixType_ > >	ConstTransposeReturnType
typedef std::conditional_t< NumTraits< Scalar >::IsComplex, CwiseUnaryOp< internal::scalar_conjugate_op< Scalar >, const ConstTransposeReturnType >, const ConstTransposeReturnType >	AdjointReturnType
Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index	Index
	The interface type of indices. More...
typedef internal::traits< Derived >::StorageKind	StorageKind

Public Member Functions
	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...
HouseholderSequenceType	householderQ () const
const MatrixType &	matrixQR () const
template<typename InputType >
HouseholderQR &	compute (const EigenBase< InputType > &matrix)
MatrixType::Scalar	determinant () const
MatrixType::RealScalar	absDeterminant () const
MatrixType::RealScalar	logAbsDeterminant () const
MatrixType::Scalar	signDeterminant () const
Index	rows () const
Index	cols () const
const HCoeffsType &	hCoeffs () const
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
Public Member Functions inherited from Eigen::SolverBase< HouseholderQR< MatrixType_ > >
	SolverBase ()
	~SolverBase ()
const Solve< HouseholderQR< MatrixType_ >, Rhs >	solve (const MatrixBase< Rhs > &b) const
const ConstTransposeReturnType	transpose () const
const AdjointReturnType	adjoint () const
constexpr EIGEN_DEVICE_FUNC HouseholderQR< MatrixType_ > &	derived ()
constexpr EIGEN_DEVICE_FUNC const HouseholderQR< MatrixType_ > &	derived () const
Public Member Functions inherited from Eigen::EigenBase< Derived >
constexpr EIGEN_DEVICE_FUNC Derived &	derived ()
constexpr EIGEN_DEVICE_FUNC const Derived &	derived () const
EIGEN_DEVICE_FUNC Derived &	const_cast_derived () const
EIGEN_DEVICE_FUNC const Derived &	const_derived () const
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT
template<typename Dest >
EIGEN_DEVICE_FUNC void	evalTo (Dest &dst) const
template<typename Dest >
EIGEN_DEVICE_FUNC void	addTo (Dest &dst) const
template<typename Dest >
EIGEN_DEVICE_FUNC void	subTo (Dest &dst) const
template<typename Dest >
EIGEN_DEVICE_FUNC void	applyThisOnTheRight (Dest &dst) const
template<typename Dest >
EIGEN_DEVICE_FUNC void	applyThisOnTheLeft (Dest &dst) const
template<typename Device >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper< Derived, Device >	device (Device &device)
template<typename Device >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper< const Derived, Device >	device (Device &device) const

Protected Member Functions
void	computeInPlace ()
Protected Member Functions inherited from Eigen::SolverBase< HouseholderQR< MatrixType_ > >
void	_check_solve_assertion (const Rhs &b) const

Protected Attributes
MatrixType	m_qr
HCoeffsType	m_hCoeffs
RowVectorType	m_temp
bool	m_isInitialized

Friends
class	SolverBase< HouseholderQR >

Detailed Description

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

Householder QR decomposition of a matrix.

Template 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

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

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()

Member Typedef Documentation

Base

template<typename MatrixType_ >

typedef SolverBase<HouseholderQR> Eigen::HouseholderQR< MatrixType_ >::Base

HCoeffsType

template<typename MatrixType_ >

typedef internal::plain_diag_type<MatrixType>::type Eigen::HouseholderQR< MatrixType_ >::HCoeffsType

HouseholderSequenceType

template<typename MatrixType_ >

typedef HouseholderSequence<MatrixType, internal::remove_all_t<typename HCoeffsType::ConjugateReturnType> > Eigen::HouseholderQR< MatrixType_ >::HouseholderSequenceType

MatrixQType

template<typename MatrixType_ >

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

MatrixType

template<typename MatrixType_ >

typedef MatrixType_ Eigen::HouseholderQR< MatrixType_ >::MatrixType

RowVectorType

template<typename MatrixType_ >

typedef internal::plain_row_type<MatrixType>::type Eigen::HouseholderQR< MatrixType_ >::RowVectorType

Member Enumeration Documentation

anonymous enum

template<typename MatrixType_ >

anonymous enum

Enumerator
MaxRowsAtCompileTime
MaxColsAtCompileTime

       {
    MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
    MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime
  };

Constructor & Destructor Documentation

HouseholderQR() [1/4]

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&).

: m_qr(), m_hCoeffs(), m_temp(), m_isInitialized(false) {}

HouseholderQR() [2/4]

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()

      : m_qr(rows, cols), m_hCoeffs((std::min)(rows, cols)), m_temp(cols), m_isInitialized(false) {}

HouseholderQR() [3/4]

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()

      : m_qr(matrix.rows(), matrix.cols()),
        m_hCoeffs((std::min)(matrix.rows(), matrix.cols())),
        m_temp(matrix.cols()),
        m_isInitialized(false) {
    compute(matrix.derived());
  }

References Eigen::HouseholderQR< MatrixType_ >::compute(), and matrix().

HouseholderQR() [4/4]

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&)

      : m_qr(matrix.derived()),
        m_hCoeffs((std::min)(matrix.rows(), matrix.cols())),
        m_temp(matrix.cols()),
        m_isInitialized(false) {
    computeInPlace();
  }

References Eigen::HouseholderQR< MatrixType_ >::computeInPlace().

Member Function Documentation

_solve_impl()

template<typename MatrixType_ >

template<typename RhsType , typename DstType >

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

                                                                                   {
  const Index rank = (std::min)(rows(), cols());
 
  typename RhsType::PlainObject c(rhs);
 
  c.applyOnTheLeft(householderQ().setLength(rank).adjoint());
 
  m_qr.topLeftCorner(rank, rank).template triangularView<Upper>().solveInPlace(c.topRows(rank));
 
  dst.topRows(rank) = c.topRows(rank);
  dst.bottomRows(cols() - rank).setZero();
}

References Eigen::SolverBase< HouseholderQR< MatrixType_ > >::adjoint(), calibrate::c, Eigen::HouseholderQR< MatrixType_ >::cols(), Eigen::HouseholderQR< MatrixType_ >::householderQ(), Eigen::HouseholderQR< MatrixType_ >::m_qr, min, and Eigen::HouseholderQR< MatrixType_ >::rows().

_solve_impl_transposed()

template<typename MatrixType_ >

template<bool Conjugate, typename RhsType , typename DstType >

void Eigen::HouseholderQR< MatrixType_ >::_solve_impl_transposed	(	const RhsType &	rhs,
		DstType &	dst
	)		const

                                                                                              {
  const Index rank = (std::min)(rows(), cols());
 
  typename RhsType::PlainObject c(rhs);
 
  m_qr.topLeftCorner(rank, rank)
      .template triangularView<Upper>()
      .transpose()
      .template conjugateIf<Conjugate>()
      .solveInPlace(c.topRows(rank));
 
  dst.topRows(rank) = c.topRows(rank);
  dst.bottomRows(rows() - rank).setZero();
 
  dst.applyOnTheLeft(householderQ().setLength(rank).template conjugateIf<!Conjugate>());
}

References calibrate::c, Eigen::HouseholderQR< MatrixType_ >::cols(), Eigen::HouseholderQR< MatrixType_ >::householderQ(), Eigen::HouseholderQR< MatrixType_ >::m_qr, min, and Eigen::HouseholderQR< MatrixType_ >::rows().

absDeterminant()

template<typename MatrixType >

MatrixType::RealScalar Eigen::HouseholderQR< MatrixType >::absDeterminant

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. Also, do not rely on the determinant being exactly zero for testing singularity or rank-deficiency.

See also

determinant(), logAbsDeterminant(), MatrixBase::determinant()

                                                                              {
  using std::abs;
  eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
  eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
  return abs(m_qr.diagonal().prod());
}

References abs(), eigen_assert, Eigen::HouseholderQR< MatrixType_ >::m_isInitialized, and Eigen::HouseholderQR< MatrixType_ >::m_qr.

cols()

template<typename MatrixType_ >

Index Eigen::HouseholderQR< MatrixType_ >::cols ( ) const

inline

{ return m_qr.cols(); }

References Eigen::HouseholderQR< MatrixType_ >::m_qr.

Referenced by gdb.printers._MatrixEntryIterator::__next__(), Eigen::HouseholderQR< MatrixType_ >::_solve_impl(), Eigen::HouseholderQR< MatrixType_ >::_solve_impl_transposed(), gdb.printers.EigenMatrixPrinter::children(), gdb.printers.EigenSparseMatrixPrinter::children(), Eigen::HouseholderQR< MatrixType_ >::computeInPlace(), Eigen::internal::householder_qr_inplace_unblocked(), Eigen::internal::householder_qr_inplace_blocked< MatrixQR, HCoeffs, MatrixQRScalar, InnerStrideIsOne >::run(), gdb.printers.EigenMatrixPrinter::to_string(), and gdb.printers.EigenSparseMatrixPrinter::to_string().

compute()

template<typename MatrixType_ >

template<typename InputType >

HouseholderQR& Eigen::HouseholderQR< MatrixType_ >::compute ( const EigenBase< InputType > &  matrix )

inline

                                                             {
    m_qr = matrix.derived();
    computeInPlace();
    return *this;
  }

References Eigen::HouseholderQR< MatrixType_ >::computeInPlace(), Eigen::HouseholderQR< MatrixType_ >::m_qr, and matrix().

Referenced by ctms_decompositions(), and Eigen::HouseholderQR< MatrixType_ >::HouseholderQR().

computeInPlace()

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&)

                                               {
  Index rows = m_qr.rows();
  Index cols = m_qr.cols();
  Index size = (std::min)(rows, cols);
 
  m_hCoeffs.resize(size);
 
  m_temp.resize(cols);
 
  internal::householder_qr_inplace_blocked<MatrixType, HCoeffsType>::run(m_qr, m_hCoeffs, 48, m_temp.data());
 
  m_isInitialized = true;
}

References Eigen::HouseholderQR< MatrixType_ >::cols(), Eigen::HouseholderQR< MatrixType_ >::m_hCoeffs, Eigen::HouseholderQR< MatrixType_ >::m_isInitialized, Eigen::HouseholderQR< MatrixType_ >::m_qr, Eigen::HouseholderQR< MatrixType_ >::m_temp, min, Eigen::HouseholderQR< MatrixType_ >::rows(), Eigen::internal::householder_qr_inplace_blocked< MatrixQR, HCoeffs, MatrixQRScalar, InnerStrideIsOne >::run(), and Eigen::EigenBase< Derived >::size().

Referenced by Eigen::HouseholderQR< MatrixType_ >::compute(), and Eigen::HouseholderQR< MatrixType_ >::HouseholderQR().

determinant()

template<typename MatrixType >

MatrixType::Scalar Eigen::HouseholderQR< MatrixType >::determinant

Returns

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. Also, do not rely on the determinant being exactly zero for testing singularity or rank-deficiency.

See also

absDeterminant(), logAbsDeterminant(), MatrixBase::determinant()

                                                                       {
  eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
  eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
  Scalar detQ;
  internal::householder_determinant<HCoeffsType, Scalar, NumTraits<Scalar>::IsComplex>::run(m_hCoeffs, detQ);
  return m_qr.diagonal().prod() * detQ;
}

References eigen_assert, Eigen::HouseholderQR< MatrixType_ >::m_hCoeffs, Eigen::HouseholderQR< MatrixType_ >::m_isInitialized, Eigen::HouseholderQR< MatrixType_ >::m_qr, and Eigen::run().

hCoeffs()

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.

{ return m_hCoeffs; }

References Eigen::HouseholderQR< MatrixType_ >::m_hCoeffs.

Referenced by Eigen::internal::householder_qr_inplace_unblocked(), Eigen::internal::householder_qr_inplace_update(), Eigen::internal::householder_determinant< HCoeffs, Scalar, IsComplex >::run(), Eigen::internal::householder_determinant< HCoeffs, Scalar, false >::run(), and Eigen::internal::householder_qr_inplace_blocked< MatrixQR, HCoeffs, MatrixQRScalar, InnerStrideIsOne >::run().

householderQ()

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:

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

References eigen_assert, Eigen::HouseholderQR< MatrixType_ >::m_hCoeffs, Eigen::HouseholderQR< MatrixType_ >::m_isInitialized, and Eigen::HouseholderQR< MatrixType_ >::m_qr.

Referenced by Eigen::HouseholderQR< MatrixType_ >::_solve_impl(), Eigen::HouseholderQR< MatrixType_ >::_solve_impl_transposed(), Eigen::createRandomPIMatrixOfRank(), Eigen::RealQZ< MatrixType_ >::hessenbergTriangular(), qr(), randomMatrixWithRealEivals(), randomMatrixWithImagEivals< MatrixType, 0 >::run(), randomMatrixWithImagEivals< MatrixType, 1 >::run(), Eigen::HybridNonLinearSolver< FunctorType, Scalar >::solveNumericalDiffOneStep(), and Eigen::HybridNonLinearSolver< FunctorType, Scalar >::solveOneStep().

logAbsDeterminant()

template<typename MatrixType >

MatrixType::RealScalar Eigen::HouseholderQR< MatrixType >::logAbsDeterminant

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.

Warning

Do not rely on the determinant being exactly zero for testing singularity or rank-deficiency.

See also

determinant(), absDeterminant(), MatrixBase::determinant()

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

References eigen_assert, Eigen::HouseholderQR< MatrixType_ >::m_isInitialized, and Eigen::HouseholderQR< MatrixType_ >::m_qr.

matrixQR()

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.

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

References eigen_assert, Eigen::HouseholderQR< MatrixType_ >::m_isInitialized, and Eigen::HouseholderQR< MatrixType_ >::m_qr.

Referenced by Eigen::RealQZ< MatrixType_ >::hessenbergTriangular(), qr(), Eigen::HybridNonLinearSolver< FunctorType, Scalar >::solveNumericalDiffOneStep(), and Eigen::HybridNonLinearSolver< FunctorType, Scalar >::solveOneStep().

rows()

template<typename MatrixType_ >

Index Eigen::HouseholderQR< MatrixType_ >::rows ( ) const

inline

{ return m_qr.rows(); }

References Eigen::HouseholderQR< MatrixType_ >::m_qr.

Referenced by gdb.printers._MatrixEntryIterator::__next__(), Eigen::HouseholderQR< MatrixType_ >::_solve_impl(), Eigen::HouseholderQR< MatrixType_ >::_solve_impl_transposed(), gdb.printers.EigenMatrixPrinter::children(), gdb.printers.EigenSparseMatrixPrinter::children(), Eigen::HouseholderQR< MatrixType_ >::computeInPlace(), Eigen::internal::householder_qr_inplace_unblocked(), Eigen::internal::householder_qr_inplace_update(), Eigen::internal::householder_qr_inplace_blocked< MatrixQR, HCoeffs, MatrixQRScalar, InnerStrideIsOne >::run(), gdb.printers.EigenMatrixPrinter::to_string(), and gdb.printers.EigenSparseMatrixPrinter::to_string().

signDeterminant()

template<typename MatrixType >

MatrixType::Scalar Eigen::HouseholderQR< MatrixType >::signDeterminant

Returns

the sign 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.

Warning

Do not rely on the determinant being exactly zero for testing singularity or rank-deficiency.

See also

determinant(), absDeterminant(), MatrixBase::determinant()

                                                                           {
  eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
  eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
  Scalar detQ;
  internal::householder_determinant<HCoeffsType, Scalar, NumTraits<Scalar>::IsComplex>::run(m_hCoeffs, detQ);
  return detQ * m_qr.diagonal().array().sign().prod();
}

References eigen_assert, Eigen::HouseholderQR< MatrixType_ >::m_hCoeffs, Eigen::HouseholderQR< MatrixType_ >::m_isInitialized, Eigen::HouseholderQR< MatrixType_ >::m_qr, and Eigen::run().

Friends And Related Function Documentation

SolverBase< HouseholderQR >

template<typename MatrixType_ >

friend class SolverBase< HouseholderQR >

friend

Member Data Documentation

m_hCoeffs

template<typename MatrixType_ >

HCoeffsType Eigen::HouseholderQR< MatrixType_ >::m_hCoeffs

protected

Referenced by Eigen::HouseholderQR< MatrixType_ >::computeInPlace(), Eigen::HouseholderQR< MatrixType_ >::determinant(), Eigen::HouseholderQR< MatrixType_ >::hCoeffs(), Eigen::HouseholderQR< MatrixType_ >::householderQ(), and Eigen::HouseholderQR< MatrixType_ >::signDeterminant().

m_isInitialized

template<typename MatrixType_ >

bool Eigen::HouseholderQR< MatrixType_ >::m_isInitialized

protected

Referenced by Eigen::HouseholderQR< MatrixType_ >::absDeterminant(), Eigen::HouseholderQR< MatrixType_ >::computeInPlace(), Eigen::HouseholderQR< MatrixType_ >::determinant(), Eigen::HouseholderQR< MatrixType_ >::householderQ(), Eigen::HouseholderQR< MatrixType_ >::logAbsDeterminant(), Eigen::HouseholderQR< MatrixType_ >::matrixQR(), and Eigen::HouseholderQR< MatrixType_ >::signDeterminant().

m_qr

template<typename MatrixType_ >

MatrixType Eigen::HouseholderQR< MatrixType_ >::m_qr

protected

Referenced by Eigen::HouseholderQR< MatrixType_ >::_solve_impl(), Eigen::HouseholderQR< MatrixType_ >::_solve_impl_transposed(), Eigen::HouseholderQR< MatrixType_ >::absDeterminant(), Eigen::HouseholderQR< MatrixType_ >::cols(), Eigen::HouseholderQR< MatrixType_ >::compute(), Eigen::HouseholderQR< MatrixType_ >::computeInPlace(), Eigen::HouseholderQR< MatrixType_ >::determinant(), Eigen::HouseholderQR< MatrixType_ >::householderQ(), Eigen::HouseholderQR< MatrixType_ >::logAbsDeterminant(), Eigen::HouseholderQR< MatrixType_ >::matrixQR(), Eigen::HouseholderQR< MatrixType_ >::rows(), and Eigen::HouseholderQR< MatrixType_ >::signDeterminant().

m_temp

template<typename MatrixType_ >

RowVectorType Eigen::HouseholderQR< MatrixType_ >::m_temp

protected

Referenced by Eigen::HouseholderQR< MatrixType_ >::computeInPlace().

---

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

• ForwardDeclarations.h
• HouseholderQR.h