Householder rank-revealing QR decomposition of a matrix with full pivoting. More...

#include </home/runner/work/allwpilib/allwpilib/wpimath/src/main/native/thirdparty/eigen/include/Eigen/src/QR/FullPivHouseholderQR.h>

Inheritance diagram for Eigen::FullPivHouseholderQR< _MatrixType >:

Public Types
enum	{ MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime , MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }

typedef _MatrixType	MatrixType

typedef SolverBase< FullPivHouseholderQR >	Base

typedef internal::FullPivHouseholderQRMatrixQReturnType< MatrixType >	MatrixQReturnType

typedef internal::plain_diag_type< MatrixType >::type	HCoeffsType

typedef Matrix< StorageIndex, 1, EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime, RowsAtCompileTime), RowMajor, 1, EIGEN_SIZE_MIN_PREFER_FIXED(MaxColsAtCompileTime, MaxRowsAtCompileTime)>	IntDiagSizeVectorType

typedef PermutationMatrix< ColsAtCompileTime, MaxColsAtCompileTime >	PermutationType

typedef internal::plain_row_type< MatrixType >::type	RowVectorType

typedef internal::plain_col_type< MatrixType >::type	ColVectorType

typedef MatrixType::PlainObject	PlainObject

Public Types inherited from Eigen::SolverBase< FullPivHouseholderQR< _MatrixType > >
enum

typedef EigenBase< FullPivHouseholderQR< _MatrixType > >	Base

typedef internal::traits< FullPivHouseholderQR< _MatrixType > >::Scalar	Scalar

typedef Scalar	CoeffReturnType

typedef internal::add_const< Transpose< constDerived > >::type	ConstTransposeReturnType

typedef internal::conditional< NumTraits< Scalar >::IsComplex, CwiseUnaryOp< internal::scalar_conjugate_op< Scalar >, ConstTransposeReturnType >, ConstTransposeReturnType >::type	AdjointReturnType

Public Types inherited from Eigen::EigenBase< FullPivHouseholderQR< _MatrixType > >
typedef Eigen::Index	Index
	The interface type of indices. More...

typedef internal::traits< FullPivHouseholderQR< _MatrixType > >::StorageKind	StorageKind

Public Member Functions
	FullPivHouseholderQR ()
	Default Constructor. More...

	FullPivHouseholderQR (Index rows, Index cols)
	Default Constructor with memory preallocation. More...

template<typename InputType >
	FullPivHouseholderQR (const EigenBase< InputType > &matrix)
	Constructs a QR factorization from a given matrix. More...

template<typename InputType >
	FullPivHouseholderQR (EigenBase< InputType > &matrix)
	Constructs a QR factorization from a given matrix. More...

MatrixQReturnType	matrixQ (void) const

const MatrixType &	matrixQR () const

template<typename InputType >
FullPivHouseholderQR &	compute (const EigenBase< InputType > &matrix)

const PermutationType &	colsPermutation () const

const IntDiagSizeVectorType &	rowsTranspositions () const

MatrixType::RealScalar	absDeterminant () const

MatrixType::RealScalar	logAbsDeterminant () const

Index	rank () const

Index	dimensionOfKernel () const

bool	isInjective () const

bool	isSurjective () const

bool	isInvertible () const

const Inverse< FullPivHouseholderQR >	inverse () const

Index	rows () const

Index	cols () const

const HCoeffsType &	hCoeffs () const

FullPivHouseholderQR &	setThreshold (const RealScalar &threshold)
	Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine when pivots are to be considered nonzero. More...

FullPivHouseholderQR &	setThreshold (Default_t)
	Allows to come back to the default behavior, letting Eigen use its default formula for determining the threshold. More...

RealScalar	threshold () const
	Returns the threshold that will be used by certain methods such as rank(). More...

Index	nonzeroPivots () const

RealScalar	maxPivot () 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

template<typename InputType >
FullPivHouseholderQR< MatrixType > &	compute (const EigenBase< InputType > &matrix)
	Performs the QR factorization of the given matrix matrix. More...

Public Member Functions inherited from Eigen::SolverBase< FullPivHouseholderQR< _MatrixType > >
	SolverBase ()
	Default constructor. More...

	~SolverBase ()

const Solve< FullPivHouseholderQR< _MatrixType >, Rhs >	solve (const MatrixBase< Rhs > &b) const

ConstTransposeReturnType	transpose () const

AdjointReturnType	adjoint () const

EIGEN_DEVICE_FUNC FullPivHouseholderQR< _MatrixType > &	derived ()

EIGEN_DEVICE_FUNC const FullPivHouseholderQR< _MatrixType > &	derived () const

Public Member Functions inherited from Eigen::EigenBase< FullPivHouseholderQR< _MatrixType > >
EIGEN_DEVICE_FUNC FullPivHouseholderQR< _MatrixType > &	derived ()

EIGEN_DEVICE_FUNC const FullPivHouseholderQR< _MatrixType > &	derived () const

EIGEN_DEVICE_FUNC FullPivHouseholderQR< _MatrixType > &	const_cast_derived () const

EIGEN_DEVICE_FUNC const FullPivHouseholderQR< _MatrixType > &	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

EIGEN_DEVICE_FUNC void	evalTo (Dest &dst) const

EIGEN_DEVICE_FUNC void	addTo (Dest &dst) const

EIGEN_DEVICE_FUNC void	subTo (Dest &dst) const

EIGEN_DEVICE_FUNC void	applyThisOnTheRight (Dest &dst) const

EIGEN_DEVICE_FUNC void	applyThisOnTheLeft (Dest &dst) const

Protected Member Functions
void	computeInPlace ()

Protected Member Functions inherited from Eigen::SolverBase< FullPivHouseholderQR< _MatrixType > >
void	_check_solve_assertion (const Rhs &b) const

Static Protected Member Functions
static void	check_template_parameters ()

Protected Attributes
MatrixType	m_qr

HCoeffsType	m_hCoeffs

IntDiagSizeVectorType	m_rows_transpositions

IntDiagSizeVectorType	m_cols_transpositions

PermutationType	m_cols_permutation

RowVectorType	m_temp

bool	m_isInitialized

bool	m_usePrescribedThreshold

RealScalar	m_prescribedThreshold

RealScalar	m_maxpivot

Index	m_nonzero_pivots

RealScalar	m_precision

Index	m_det_pq

Friends
class	SolverBase< FullPivHouseholderQR >

Detailed Description

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

Householder rank-revealing QR decomposition of a matrix with full pivoting.

Template Parameters

_MatrixType the type of the matrix of which we are computing the QR decomposition

This class performs a rank-revealing QR decomposition of a matrix A into matrices P, P', Q and R such that

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

by using Householder transformations. Here, P and P' are permutation matrices, Q a unitary matrix and R an upper triangular matrix.

This decomposition performs a very prudent full pivoting in order to be rank-revealing and achieve optimal numerical stability. The trade-off is that it is slower than HouseholderQR and ColPivHouseholderQR.

This class supports the inplace decomposition mechanism.

See also: MatrixBase::fullPivHouseholderQr()

Member Typedef Documentation

◆ Base

template<typename _MatrixType >

typedef SolverBase<FullPivHouseholderQR> Eigen::FullPivHouseholderQR< _MatrixType >::Base

◆ ColVectorType

template<typename _MatrixType >

typedef internal::plain_col_type<MatrixType>::type Eigen::FullPivHouseholderQR< _MatrixType >::ColVectorType

◆ HCoeffsType

template<typename _MatrixType >

typedef internal::plain_diag_type<MatrixType>::type Eigen::FullPivHouseholderQR< _MatrixType >::HCoeffsType

◆ IntDiagSizeVectorType

template<typename _MatrixType >

typedef Matrix<StorageIndex, 1, EIGEN_SIZE_MIN_PREFER_DYNAMIC(ColsAtCompileTime,RowsAtCompileTime), RowMajor, 1, EIGEN_SIZE_MIN_PREFER_FIXED(MaxColsAtCompileTime,MaxRowsAtCompileTime)> Eigen::FullPivHouseholderQR< _MatrixType >::IntDiagSizeVectorType

◆ MatrixQReturnType

template<typename _MatrixType >

typedef internal::FullPivHouseholderQRMatrixQReturnType<MatrixType> Eigen::FullPivHouseholderQR< _MatrixType >::MatrixQReturnType

◆ MatrixType

template<typename _MatrixType >

typedef _MatrixType Eigen::FullPivHouseholderQR< _MatrixType >::MatrixType

◆ PermutationType

template<typename _MatrixType >

typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime> Eigen::FullPivHouseholderQR< _MatrixType >::PermutationType

◆ PlainObject

template<typename _MatrixType >

typedef MatrixType::PlainObject Eigen::FullPivHouseholderQR< _MatrixType >::PlainObject

◆ RowVectorType

template<typename _MatrixType >

typedef internal::plain_row_type<MatrixType>::type Eigen::FullPivHouseholderQR< _MatrixType >::RowVectorType

Member Enumeration Documentation

◆ anonymous enum

template<typename _MatrixType >

anonymous enum

Enumerator
MaxRowsAtCompileTime
MaxColsAtCompileTime

Constructor & Destructor Documentation

◆ FullPivHouseholderQR() [1/4]

template<typename _MatrixType >

Eigen::FullPivHouseholderQR< _MatrixType >::FullPivHouseholderQR ( )

inline

Default Constructor.

The default constructor is useful in cases in which the user intends to perform decompositions via FullPivHouseholderQR::compute(const MatrixType&).

◆ FullPivHouseholderQR() [2/4]

template<typename _MatrixType >

Eigen::FullPivHouseholderQR< _MatrixType >::FullPivHouseholderQR	(	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: FullPivHouseholderQR()

◆ FullPivHouseholderQR() [3/4]

template<typename _MatrixType >

template<typename InputType >

Eigen::FullPivHouseholderQR< _MatrixType >::FullPivHouseholderQR ( 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:

FullPivHouseholderQR<MatrixType> qr(matrix.rows(), matrix.cols());

qr.compute(matrix);

Eigen::FullPivHouseholderQR< MatrixType >

See also: compute()

◆ FullPivHouseholderQR() [4/4]

template<typename _MatrixType >

template<typename InputType >

Eigen::FullPivHouseholderQR< _MatrixType >::FullPivHouseholderQR ( 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: FullPivHouseholderQR(const EigenBase&)

Member Function Documentation

◆ _solve_impl()

template<typename _MatrixType >

template<typename RhsType , typename DstType >

void Eigen::FullPivHouseholderQR< _MatrixType >::_solve_impl	(	const RhsType &	rhs,
		DstType &	dst
	)		const

◆ _solve_impl_transposed()

template<typename _MatrixType >

template<bool Conjugate, typename RhsType , typename DstType >

void Eigen::FullPivHouseholderQR< _MatrixType >::_solve_impl_transposed	(	const RhsType &	rhs,
		DstType &	dst
	)		const

◆ absDeterminant()

template<typename MatrixType >

MatrixType::RealScalar Eigen::FullPivHouseholderQR< 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.

See also: logAbsDeterminant(), MatrixBase::determinant()

◆ check_template_parameters()

template<typename _MatrixType >

static void Eigen::FullPivHouseholderQR< _MatrixType >::check_template_parameters ( )

inlinestaticprotected

◆ cols()

template<typename _MatrixType >

Index Eigen::FullPivHouseholderQR< _MatrixType >::cols ( void ) const

inline

◆ colsPermutation()

template<typename _MatrixType >

const PermutationType & Eigen::FullPivHouseholderQR< _MatrixType >::colsPermutation ( ) const

inline

Returns: a const reference to the column permutation matrix

◆ compute() [1/2]

template<typename _MatrixType >

template<typename InputType >

FullPivHouseholderQR & Eigen::FullPivHouseholderQR< _MatrixType >::compute ( const EigenBase< InputType > & matrix )

◆ compute() [2/2]

template<typename _MatrixType >

template<typename InputType >

FullPivHouseholderQR< MatrixType > & Eigen::FullPivHouseholderQR< _MatrixType >::compute ( const EigenBase< InputType > & 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 FullPivHouseholderQR, FullPivHouseholderQR(const MatrixType&)

◆ computeInPlace()

template<typename MatrixType >

void Eigen::FullPivHouseholderQR< MatrixType >::computeInPlace

protected

◆ dimensionOfKernel()

template<typename _MatrixType >

Index Eigen::FullPivHouseholderQR< _MatrixType >::dimensionOfKernel ( ) const

inline

Returns: the dimension of the kernel of the matrix of which *this is the QR decomposition.

Note: This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).

◆ hCoeffs()

template<typename _MatrixType >

const HCoeffsType & Eigen::FullPivHouseholderQR< _MatrixType >::hCoeffs ( ) const

inline

Returns: a const reference to the vector of Householder coefficients used to represent the factor Q.

For advanced uses only.

◆ inverse()

template<typename _MatrixType >

const Inverse< FullPivHouseholderQR > Eigen::FullPivHouseholderQR< _MatrixType >::inverse ( ) const

inline

Returns: the inverse of the matrix of which *this is the QR decomposition.

Note: If this matrix is not invertible, the returned matrix has undefined coefficients. Use isInvertible() to first determine whether this matrix is invertible.

◆ isInjective()

template<typename _MatrixType >

bool Eigen::FullPivHouseholderQR< _MatrixType >::isInjective ( ) const

inline

Returns: true if the matrix of which *this is the QR decomposition represents an injective linear map, i.e. has trivial kernel; false otherwise.

Note: This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).

◆ isInvertible()

template<typename _MatrixType >

bool Eigen::FullPivHouseholderQR< _MatrixType >::isInvertible ( ) const

inline

Returns: true if the matrix of which *this is the QR decomposition is invertible.

Note: This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).

◆ isSurjective()

template<typename _MatrixType >

bool Eigen::FullPivHouseholderQR< _MatrixType >::isSurjective ( ) const

inline

Returns: true if the matrix of which *this is the QR decomposition represents a surjective linear map; false otherwise.

Note: This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).

◆ logAbsDeterminant()

template<typename MatrixType >

MatrixType::RealScalar Eigen::FullPivHouseholderQR< 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.

See also: absDeterminant(), MatrixBase::determinant()

◆ matrixQ()

template<typename MatrixType >

FullPivHouseholderQR< MatrixType >::MatrixQReturnType Eigen::FullPivHouseholderQR< MatrixType >::matrixQ ( void ) const

inline

Returns: Expression object representing the matrix Q

◆ matrixQR()

template<typename _MatrixType >

const MatrixType & Eigen::FullPivHouseholderQR< _MatrixType >::matrixQR ( ) const

inline

Returns: a reference to the matrix where the Householder QR decomposition is stored

◆ maxPivot()

template<typename _MatrixType >

RealScalar Eigen::FullPivHouseholderQR< _MatrixType >::maxPivot ( ) const

inline

Returns: the absolute value of the biggest pivot, i.e. the biggest diagonal coefficient of U.

◆ nonzeroPivots()

template<typename _MatrixType >

Index Eigen::FullPivHouseholderQR< _MatrixType >::nonzeroPivots ( ) const

inline

Returns: the number of nonzero pivots in the QR decomposition. Here nonzero is meant in the exact sense, not in a fuzzy sense. So that notion isn't really intrinsically interesting, but it is still useful when implementing algorithms.

See also: rank()

◆ rank()

template<typename _MatrixType >

Index Eigen::FullPivHouseholderQR< _MatrixType >::rank ( ) const

inline

Returns: the rank of the matrix of which *this is the QR decomposition.

Note: This method has to determine which pivots should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).

◆ rows()

template<typename _MatrixType >

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

inline

◆ rowsTranspositions()

template<typename _MatrixType >

const IntDiagSizeVectorType & Eigen::FullPivHouseholderQR< _MatrixType >::rowsTranspositions ( ) const

inline

Returns: a const reference to the vector of indices representing the rows transpositions

◆ setThreshold() [1/2]

template<typename _MatrixType >

FullPivHouseholderQR & Eigen::FullPivHouseholderQR< _MatrixType >::setThreshold ( const RealScalar & threshold )

inline

Allows to prescribe a threshold to be used by certain methods, such as rank(), who need to determine when pivots are to be considered nonzero.

This is not used for the QR decomposition itself.

When it needs to get the threshold value, Eigen calls threshold(). By default, this uses a formula to automatically determine a reasonable threshold. Once you have called the present method setThreshold(const RealScalar&), your value is used instead.

Parameters

threshold The new value to use as the threshold.

A pivot will be considered nonzero if its absolute value is strictly greater than \( \vert pivot \vert \leqslant threshold \times \vert maxpivot \vert \) where maxpivot is the biggest pivot.

If you want to come back to the default behavior, call setThreshold(Default_t)

◆ setThreshold() [2/2]

template<typename _MatrixType >

FullPivHouseholderQR & Eigen::FullPivHouseholderQR< _MatrixType >::setThreshold ( Default_t )

inline

Allows to come back to the default behavior, letting Eigen use its default formula for determining the threshold.

You should pass the special object Eigen::Default as parameter here.

qr.setThreshold(Eigen::Default);

Eigen::Default

@ Default

Definition: Constants.h:362

See the documentation of setThreshold(const RealScalar&).

◆ threshold()

template<typename _MatrixType >

RealScalar Eigen::FullPivHouseholderQR< _MatrixType >::threshold ( ) const

inline

Returns the threshold that will be used by certain methods such as rank().

See the documentation of setThreshold(const RealScalar&).

Friends And Related Function Documentation

◆ SolverBase< FullPivHouseholderQR >

template<typename _MatrixType >

friend class SolverBase< FullPivHouseholderQR >

friend

Member Data Documentation

◆ m_cols_permutation

template<typename _MatrixType >

PermutationType Eigen::FullPivHouseholderQR< _MatrixType >::m_cols_permutation

protected

◆ m_cols_transpositions

template<typename _MatrixType >

IntDiagSizeVectorType Eigen::FullPivHouseholderQR< _MatrixType >::m_cols_transpositions

protected

◆ m_det_pq

template<typename _MatrixType >

Index Eigen::FullPivHouseholderQR< _MatrixType >::m_det_pq

protected

◆ m_hCoeffs

template<typename _MatrixType >

HCoeffsType Eigen::FullPivHouseholderQR< _MatrixType >::m_hCoeffs

protected

◆ m_isInitialized

template<typename _MatrixType >

bool Eigen::FullPivHouseholderQR< _MatrixType >::m_isInitialized

protected

◆ m_maxpivot

template<typename _MatrixType >

RealScalar Eigen::FullPivHouseholderQR< _MatrixType >::m_maxpivot

protected

◆ m_nonzero_pivots

template<typename _MatrixType >

Index Eigen::FullPivHouseholderQR< _MatrixType >::m_nonzero_pivots

protected

◆ m_precision

template<typename _MatrixType >

RealScalar Eigen::FullPivHouseholderQR< _MatrixType >::m_precision

protected

◆ m_prescribedThreshold

template<typename _MatrixType >

RealScalar Eigen::FullPivHouseholderQR< _MatrixType >::m_prescribedThreshold

protected

◆ m_qr

template<typename _MatrixType >

MatrixType Eigen::FullPivHouseholderQR< _MatrixType >::m_qr

protected

◆ m_rows_transpositions

template<typename _MatrixType >

IntDiagSizeVectorType Eigen::FullPivHouseholderQR< _MatrixType >::m_rows_transpositions

protected

◆ m_temp

template<typename _MatrixType >

RowVectorType Eigen::FullPivHouseholderQR< _MatrixType >::m_temp

protected

◆ m_usePrescribedThreshold

template<typename _MatrixType >

bool Eigen::FullPivHouseholderQR< _MatrixType >::m_usePrescribedThreshold

protected

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

/home/runner/work/allwpilib/allwpilib/wpimath/src/main/native/thirdparty/eigen/include/Eigen/src/Core/util/ForwardDeclarations.h
/home/runner/work/allwpilib/allwpilib/wpimath/src/main/native/thirdparty/eigen/include/Eigen/src/QR/FullPivHouseholderQR.h

Public Types

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ Base

◆ ColVectorType

◆ HCoeffsType

◆ IntDiagSizeVectorType

◆ MatrixQReturnType

◆ MatrixType

◆ PermutationType

◆ PlainObject

◆ RowVectorType

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ FullPivHouseholderQR() [1/4]

◆ FullPivHouseholderQR() [2/4]

◆ FullPivHouseholderQR() [3/4]

◆ FullPivHouseholderQR() [4/4]

Member Function Documentation

◆ _solve_impl()

◆ _solve_impl_transposed()

◆ absDeterminant()

◆ check_template_parameters()

◆ cols()

◆ colsPermutation()

◆ compute() [1/2]

◆ compute() [2/2]

◆ computeInPlace()

◆ dimensionOfKernel()

◆ hCoeffs()

◆ inverse()

◆ isInjective()

◆ isInvertible()

◆ isSurjective()

◆ logAbsDeterminant()

◆ matrixQ()

◆ matrixQR()

◆ maxPivot()

◆ nonzeroPivots()

◆ rank()

◆ rows()

◆ rowsTranspositions()

◆ setThreshold() [1/2]

◆ setThreshold() [2/2]

◆ threshold()

Friends And Related Function Documentation

◆ SolverBase< FullPivHouseholderQR >

Member Data Documentation

◆ m_cols_permutation

◆ m_cols_transpositions

◆ m_det_pq

◆ m_hCoeffs

◆ m_isInitialized

◆ m_maxpivot

◆ m_nonzero_pivots

◆ m_precision

◆ m_prescribedThreshold

◆ m_qr

◆ m_rows_transpositions

◆ m_temp

◆ m_usePrescribedThreshold