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

#include <FullPivHouseholderQR.h>

Inheritance diagram for Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >:

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

typedef MatrixType_	MatrixType

typedef SolverBase< FullPivHouseholderQR >	Base

typedef PermutationIndex_	PermutationIndex

typedef internal::FullPivHouseholderQRMatrixQReturnType< MatrixType, PermutationIndex >	MatrixQReturnType

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

typedef Matrix< PermutationIndex, 1, internal::min_size_prefer_dynamic(ColsAtCompileTime, RowsAtCompileTime), RowMajor, 1, internal::min_size_prefer_fixed(MaxColsAtCompileTime, MaxRowsAtCompileTime)>	IntDiagSizeVectorType

typedef PermutationMatrix< ColsAtCompileTime, MaxColsAtCompileTime, PermutationIndex >	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_, PermutationIndex_ > >
enum

typedef EigenBase< FullPivHouseholderQR< MatrixType_, PermutationIndex_ > >	Base

typedef internal::traits< FullPivHouseholderQR< MatrixType_, PermutationIndex_ > >::Scalar	Scalar

typedef Scalar	CoeffReturnType

typedef Transpose< const FullPivHouseholderQR< MatrixType_, PermutationIndex_ > >	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
	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::Scalar	determinant () const

MatrixType::RealScalar	absDeterminant () const

MatrixType::RealScalar	logAbsDeterminant () const

MatrixType::Scalar	signDeterminant () 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)

FullPivHouseholderQR &	setThreshold (Default_t)

RealScalar	threshold () const

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, PermutationIndex > &	compute (const EigenBase< InputType > &matrix)

Public Member Functions inherited from Eigen::SolverBase< FullPivHouseholderQR< MatrixType_, PermutationIndex_ > >
	SolverBase ()

	~SolverBase ()

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

const ConstTransposeReturnType	transpose () const

const AdjointReturnType	adjoint () const

constexpr EIGEN_DEVICE_FUNC FullPivHouseholderQR< MatrixType_, PermutationIndex_ > &	derived ()

constexpr EIGEN_DEVICE_FUNC const FullPivHouseholderQR< MatrixType_, PermutationIndex_ > &	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< FullPivHouseholderQR< MatrixType_, PermutationIndex_ > >
void	_check_solve_assertion (const Rhs &b) const

Friends
class	SolverBase< FullPivHouseholderQR >

Detailed Description

template<typename MatrixType_, typename PermutationIndex_>
class Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >

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_ , typename PermutationIndex_ >

typedef SolverBase<FullPivHouseholderQR> Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::Base

◆ ColVectorType

template<typename MatrixType_ , typename PermutationIndex_ >

typedef internal::plain_col_type<MatrixType>::type Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::ColVectorType

◆ HCoeffsType

template<typename MatrixType_ , typename PermutationIndex_ >

typedef internal::plain_diag_type<MatrixType>::type Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::HCoeffsType

◆ IntDiagSizeVectorType

template<typename MatrixType_ , typename PermutationIndex_ >

typedef Matrix<PermutationIndex, 1, internal::min_size_prefer_dynamic(ColsAtCompileTime, RowsAtCompileTime), RowMajor, 1, internal::min_size_prefer_fixed(MaxColsAtCompileTime, MaxRowsAtCompileTime)> Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::IntDiagSizeVectorType

◆ MatrixQReturnType

template<typename MatrixType_ , typename PermutationIndex_ >

typedef internal::FullPivHouseholderQRMatrixQReturnType<MatrixType, PermutationIndex> Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::MatrixQReturnType

◆ MatrixType

template<typename MatrixType_ , typename PermutationIndex_ >

typedef MatrixType_ Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::MatrixType

◆ PermutationIndex

template<typename MatrixType_ , typename PermutationIndex_ >

typedef PermutationIndex_ Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::PermutationIndex

◆ PermutationType

template<typename MatrixType_ , typename PermutationIndex_ >

typedef PermutationMatrix<ColsAtCompileTime, MaxColsAtCompileTime, PermutationIndex> Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::PermutationType

◆ PlainObject

template<typename MatrixType_ , typename PermutationIndex_ >

typedef MatrixType::PlainObject Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::PlainObject

◆ RowVectorType

template<typename MatrixType_ , typename PermutationIndex_ >

typedef internal::plain_row_type<MatrixType>::type Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::RowVectorType

Member Enumeration Documentation

◆ anonymous enum

template<typename MatrixType_ , typename PermutationIndex_ >

anonymous enum

Enumerator
MaxRowsAtCompileTime
MaxColsAtCompileTime

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

Constructor & Destructor Documentation

◆ FullPivHouseholderQR() [1/4]

template<typename MatrixType_ , typename PermutationIndex_ >

Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::FullPivHouseholderQR ( )

inline

Default Constructor.

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

       : m_qr(),
         m_hCoeffs(),
         m_rows_transpositions(),
         m_cols_transpositions(),
         m_cols_permutation(),
         m_temp(),
         m_isInitialized(false),
         m_usePrescribedThreshold(false) {}

◆ FullPivHouseholderQR() [2/4]

template<typename MatrixType_ , typename PermutationIndex_ >

Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::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()

       : m_qr(rows, cols),
         m_hCoeffs((std::min)(rows, cols)),
         m_rows_transpositions((std::min)(rows, cols)),
         m_cols_transpositions((std::min)(rows, cols)),
         m_cols_permutation(cols),
         m_temp(cols),
         m_isInitialized(false),
         m_usePrescribedThreshold(false) {}

◆ FullPivHouseholderQR() [3/4]

template<typename MatrixType_ , typename PermutationIndex_ >

template<typename InputType >

Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::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);

qr

HouseholderQR< MatrixXf > qr(A)

matrix

Eigen::Map< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic, Eigen::ColMajor >, 0, Eigen::OuterStride<> > matrix(T *data, int rows, int cols, int stride)

Definition: common.h:85

See also: compute()

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

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

◆ FullPivHouseholderQR() [4/4]

template<typename MatrixType_ , typename PermutationIndex_ >

template<typename InputType >

Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::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&)

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

References Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace().

Member Function Documentation

◆ _solve_impl()

template<typename MatrixType_ , typename PermutationIndex_ >

template<typename RhsType , typename DstType >

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

                                                                                                              {
   const Index l_rank = rank();
  
   // FIXME introduce nonzeroPivots() and use it here. and more generally,
   // make the same improvements in this dec as in FullPivLU.
   if (l_rank == 0) {
     dst.setZero();
     return;
   }
  
   typename RhsType::PlainObject c(rhs);
  
   Matrix<typename RhsType::Scalar, 1, RhsType::ColsAtCompileTime> temp(rhs.cols());
   for (Index k = 0; k < l_rank; ++k) {
     Index remainingSize = rows() - k;
     c.row(k).swap(c.row(m_rows_transpositions.coeff(k)));
     c.bottomRightCorner(remainingSize, rhs.cols())
         .applyHouseholderOnTheLeft(m_qr.col(k).tail(remainingSize - 1), m_hCoeffs.coeff(k), &temp.coeffRef(0));
   }
  
   m_qr.topLeftCorner(l_rank, l_rank).template triangularView<Upper>().solveInPlace(c.topRows(l_rank));
  
   for (Index i = 0; i < l_rank; ++i) dst.row(m_cols_permutation.indices().coeff(i)) = c.row(i);
   for (Index i = l_rank; i < cols(); ++i) dst.row(m_cols_permutation.indices().coeff(i)).setZero();
 }

References calibrate::c, Eigen::PlainObjectBase< Derived >::coeff(), Eigen::Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ >::coeffRef(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::cols(), i, Eigen::PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_ >::indices(), k, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_cols_permutation, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_hCoeffs, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_qr, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_rows_transpositions, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::rank(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::rows(), and setZero().

◆ _solve_impl_transposed()

template<typename MatrixType_ , typename PermutationIndex_ >

template<bool Conjugate, typename RhsType , typename DstType >

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

                                                                                                       {
   const Index l_rank = rank();
  
   if (l_rank == 0) {
     dst.setZero();
     return;
   }
  
   typename RhsType::PlainObject c(m_cols_permutation.transpose() * rhs);
  
   m_qr.topLeftCorner(l_rank, l_rank)
       .template triangularView<Upper>()
       .transpose()
       .template conjugateIf<Conjugate>()
       .solveInPlace(c.topRows(l_rank));
  
   dst.topRows(l_rank) = c.topRows(l_rank);
   dst.bottomRows(rows() - l_rank).setZero();
  
   Matrix<Scalar, 1, DstType::ColsAtCompileTime> temp(dst.cols());
   const Index size = (std::min)(rows(), cols());
   for (Index k = size - 1; k >= 0; --k) {
     Index remainingSize = rows() - k;
  
     dst.bottomRightCorner(remainingSize, dst.cols())
         .applyHouseholderOnTheLeft(m_qr.col(k).tail(remainingSize - 1).template conjugateIf<!Conjugate>(),
                                    m_hCoeffs.template conjugateIf<Conjugate>().coeff(k), &temp.coeffRef(0));
  
     dst.row(k).swap(dst.row(m_rows_transpositions.coeff(k)));
   }
 }

References calibrate::c, Eigen::PlainObjectBase< Derived >::coeff(), Eigen::Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ >::coeffRef(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::cols(), k, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_cols_permutation, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_hCoeffs, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_qr, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_rows_transpositions, min, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::rank(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::rows(), Eigen::EigenBase< Derived >::size(), and Eigen::PermutationBase< Derived >::transpose().

◆ absDeterminant()

template<typename MatrixType , typename PermutationIndex >

MatrixType::RealScalar Eigen::FullPivHouseholderQR< MatrixType, PermutationIndex >::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: determinant(), logAbsDeterminant(), MatrixBase::determinant()

                                                                                                        {
   using std::abs;
   eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
   eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
   return isInjective() ? abs(m_qr.diagonal().prod()) : RealScalar(0);
 }

References abs(), eigen_assert, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::isInjective(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized, and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_qr.

◆ cols()

template<typename MatrixType_ , typename PermutationIndex_ >

Index Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::cols ( ) const

inline

337 { return m_qr.cols(); }

References Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_qr.

Referenced by gdb.printers._MatrixEntryIterator::__next__(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::_solve_impl(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::_solve_impl_transposed(), gdb.printers.EigenMatrixPrinter::children(), gdb.printers.EigenSparseMatrixPrinter::children(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::dimensionOfKernel(), Eigen::internal::FullPivHouseholderQRMatrixQReturnType< MatrixType, PermutationIndex >::evalTo(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::isInjective(), gdb.printers.EigenMatrixPrinter::to_string(), and gdb.printers.EigenSparseMatrixPrinter::to_string().

◆ colsPermutation()

template<typename MatrixType_ , typename PermutationIndex_ >

const PermutationType& Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::colsPermutation ( ) const

inline

Returns: a const reference to the column permutation matrix

                                                  {
     eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
     return m_cols_permutation;
   }

References eigen_assert, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_cols_permutation, and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized.

◆ compute() [1/2]

template<typename MatrixType_ , typename PermutationIndex_ >

template<typename InputType >

FullPivHouseholderQR& Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::compute ( const EigenBase< InputType > & matrix )

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

◆ compute() [2/2]

template<typename MatrixType_ , typename PermutationIndex_ >

template<typename InputType >

FullPivHouseholderQR<MatrixType, PermutationIndex>& Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::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&)

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

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

◆ computeInPlace()

template<typename MatrixType , typename PermutationIndex >

void Eigen::FullPivHouseholderQR< MatrixType, PermutationIndex >::computeInPlace

protected

                                                                         {
   eigen_assert(m_qr.cols() <= NumTraits<PermutationIndex>::highest());
   using std::abs;
   Index rows = m_qr.rows();
   Index cols = m_qr.cols();
   Index size = (std::min)(rows, cols);
  
   m_hCoeffs.resize(size);
  
   m_temp.resize(cols);
  
   m_precision = NumTraits<Scalar>::epsilon() * RealScalar(size);
  
   m_rows_transpositions.resize(size);
   m_cols_transpositions.resize(size);
   Index number_of_transpositions = 0;
  
   RealScalar biggest(0);
  
   m_nonzero_pivots = size;  // the generic case is that in which all pivots are nonzero (invertible case)
   m_maxpivot = RealScalar(0);
  
   for (Index k = 0; k < size; ++k) {
     Index row_of_biggest_in_corner, col_of_biggest_in_corner;
     typedef internal::scalar_score_coeff_op<Scalar> Scoring;
     typedef typename Scoring::result_type Score;
  
     Score score = m_qr.bottomRightCorner(rows - k, cols - k)
                       .unaryExpr(Scoring())
                       .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);
     row_of_biggest_in_corner += k;
     col_of_biggest_in_corner += k;
     RealScalar biggest_in_corner =
         internal::abs_knowing_score<Scalar>()(m_qr(row_of_biggest_in_corner, col_of_biggest_in_corner), score);
     if (k == 0) biggest = biggest_in_corner;
  
     // if the corner is negligible, then we have less than full rank, and we can finish early
     if (internal::isMuchSmallerThan(biggest_in_corner, biggest, m_precision)) {
       m_nonzero_pivots = k;
       for (Index i = k; i < size; i++) {
         m_rows_transpositions.coeffRef(i) = internal::convert_index<PermutationIndex>(i);
         m_cols_transpositions.coeffRef(i) = internal::convert_index<PermutationIndex>(i);
         m_hCoeffs.coeffRef(i) = Scalar(0);
       }
       break;
     }
  
     m_rows_transpositions.coeffRef(k) = internal::convert_index<PermutationIndex>(row_of_biggest_in_corner);
     m_cols_transpositions.coeffRef(k) = internal::convert_index<PermutationIndex>(col_of_biggest_in_corner);
     if (k != row_of_biggest_in_corner) {
       m_qr.row(k).tail(cols - k).swap(m_qr.row(row_of_biggest_in_corner).tail(cols - k));
       ++number_of_transpositions;
     }
     if (k != col_of_biggest_in_corner) {
       m_qr.col(k).swap(m_qr.col(col_of_biggest_in_corner));
       ++number_of_transpositions;
     }
  
     RealScalar beta;
     m_qr.col(k).tail(rows - k).makeHouseholderInPlace(m_hCoeffs.coeffRef(k), beta);
     m_qr.coeffRef(k, k) = beta;
  
     // remember the maximum absolute value of diagonal coefficients
     if (abs(beta) > m_maxpivot) m_maxpivot = abs(beta);
  
     m_qr.bottomRightCorner(rows - k, cols - k - 1)
         .applyHouseholderOnTheLeft(m_qr.col(k).tail(rows - k - 1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k + 1));
   }
  
   m_cols_permutation.setIdentity(cols);
   for (Index k = 0; k < size; ++k) m_cols_permutation.applyTranspositionOnTheRight(k, m_cols_transpositions.coeff(k));
  
   m_det_p = (number_of_transpositions % 2) ? -1 : 1;
   m_isInitialized = true;
 }

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

◆ determinant()

template<typename MatrixType , typename PermutationIndex >

MatrixType::Scalar Eigen::FullPivHouseholderQR< MatrixType, PermutationIndex >::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.

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 isInjective() ? (detQ * Scalar(m_det_p)) * m_qr.diagonal().prod() : Scalar(0);
 }

References eigen_assert, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::isInjective(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_det_p, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_hCoeffs, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_qr, and Eigen::run().

◆ dimensionOfKernel()

template<typename MatrixType_ , typename PermutationIndex_ >

Index Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::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&).

                                          {
     eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
     return cols() - rank();
   }

References Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::cols(), eigen_assert, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized, and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::rank().

◆ hCoeffs()

template<typename MatrixType_ , typename PermutationIndex_ >

const HCoeffsType& Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::hCoeffs ( ) const

inline

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

For advanced uses only.

343 { return m_hCoeffs; }

References Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_hCoeffs.

◆ inverse()

template<typename MatrixType_ , typename PermutationIndex_ >

const Inverse<FullPivHouseholderQR> Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::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.

                                                              {
     eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
     return Inverse<FullPivHouseholderQR>(*this);
   }

References eigen_assert, and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized.

◆ isInjective()

template<typename MatrixType_ , typename PermutationIndex_ >

bool Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::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&).

                                   {
     eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
     return rank() == cols();
   }

References Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::cols(), eigen_assert, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized, and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::rank().

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::absDeterminant(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::determinant(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::isInvertible(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::logAbsDeterminant(), and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::signDeterminant().

◆ isInvertible()

template<typename MatrixType_ , typename PermutationIndex_ >

bool Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::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&).

                                    {
     eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
     return isInjective() && isSurjective();
   }

References eigen_assert, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::isInjective(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::isSurjective(), and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized.

◆ isSurjective()

template<typename MatrixType_ , typename PermutationIndex_ >

bool Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::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&).

                                    {
     eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
     return rank() == rows();
   }

References eigen_assert, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::rank(), and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::rows().

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::isInvertible().

◆ logAbsDeterminant()

template<typename MatrixType , typename PermutationIndex >

MatrixType::RealScalar Eigen::FullPivHouseholderQR< MatrixType, PermutationIndex >::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: determinant(), absDeterminant(), MatrixBase::determinant()

                                                                                                           {
   eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
   eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
   return isInjective() ? m_qr.diagonal().cwiseAbs().array().log().sum() : -NumTraits<RealScalar>::infinity();
 }

References eigen_assert, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::isInjective(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized, and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_qr.

◆ matrixQ()

template<typename MatrixType , typename PermutationIndex >

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

inline

Returns: Expression object representing the matrix Q

                                                                   {
   eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
   return MatrixQReturnType(m_qr, m_hCoeffs, m_rows_transpositions);
 }

References eigen_assert, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_hCoeffs, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_qr, and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_rows_transpositions.

◆ matrixQR()

template<typename MatrixType_ , typename PermutationIndex_ >

const MatrixType& Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::matrixQR ( ) const

inline

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

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

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

◆ maxPivot()

template<typename MatrixType_ , typename PermutationIndex_ >

RealScalar Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::maxPivot ( ) const

inline

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

408 { return m_maxpivot; }

References Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_maxpivot.

◆ nonzeroPivots()

template<typename MatrixType_ , typename PermutationIndex_ >

Index Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::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()

                                      {
     eigen_assert(m_isInitialized && "LU is not initialized.");
     return m_nonzero_pivots;
   }

References eigen_assert, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized, and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_nonzero_pivots.

◆ rank()

template<typename MatrixType_ , typename PermutationIndex_ >

Index Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::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&).

                             {
     using std::abs;
     eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
     RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
     Index result = 0;
     for (Index i = 0; i < m_nonzero_pivots; ++i) result += (abs(m_qr.coeff(i, i)) > premultiplied_threshold);
     return result;
   }

References abs(), eigen_assert, i, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_maxpivot, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_nonzero_pivots, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_qr, and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::threshold().

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::_solve_impl(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::_solve_impl_transposed(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::dimensionOfKernel(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::isInjective(), and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::isSurjective().

◆ rows()

template<typename MatrixType_ , typename PermutationIndex_ >

Index Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::rows ( ) const

inline

336 { return m_qr.rows(); }

References Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_qr.

Referenced by gdb.printers._MatrixEntryIterator::__next__(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::_solve_impl(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::_solve_impl_transposed(), gdb.printers.EigenMatrixPrinter::children(), gdb.printers.EigenSparseMatrixPrinter::children(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace(), Eigen::internal::FullPivHouseholderQRMatrixQReturnType< MatrixType, PermutationIndex >::evalTo(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::isSurjective(), gdb.printers.EigenMatrixPrinter::to_string(), and gdb.printers.EigenSparseMatrixPrinter::to_string().

◆ rowsTranspositions()

template<typename MatrixType_ , typename PermutationIndex_ >

const IntDiagSizeVectorType& Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::rowsTranspositions ( ) const

inline

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

                                                           {
     eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
     return m_rows_transpositions;
   }

References eigen_assert, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized, and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_rows_transpositions.

◆ setThreshold() [1/2]

template<typename MatrixType_ , typename PermutationIndex_ >

FullPivHouseholderQR& Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::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)

                                                                   {
     m_usePrescribedThreshold = true;
     m_prescribedThreshold = threshold;
     return *this;
   }

References Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_prescribedThreshold, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_usePrescribedThreshold, and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::threshold().

◆ setThreshold() [2/2]

template<typename MatrixType_ , typename PermutationIndex_ >

FullPivHouseholderQR& Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::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:361

See the documentation of setThreshold(const RealScalar&).

                                                 {
     m_usePrescribedThreshold = false;
     return *this;
   }

References Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_usePrescribedThreshold.

◆ signDeterminant()

template<typename MatrixType , typename PermutationIndex >

MatrixType::Scalar Eigen::FullPivHouseholderQR< MatrixType, PermutationIndex >::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.

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

                                                                                                     {
   eigen_assert(m_isInitialized && "FullPivHouseholderQR 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 isInjective() ? (detQ * Scalar(m_det_p)) * m_qr.diagonal().array().sign().prod() : Scalar(0);
 }

References eigen_assert, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::isInjective(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_det_p, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_hCoeffs, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_qr, and Eigen::run().

◆ threshold()

template<typename MatrixType_ , typename PermutationIndex_ >

RealScalar Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::threshold ( ) const

inline

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

See the documentation of setThreshold(const RealScalar&).

                                {
     eigen_assert(m_isInitialized || m_usePrescribedThreshold);
     return m_usePrescribedThreshold ? m_prescribedThreshold
                                     // this formula comes from experimenting (see "LU precision tuning" thread on the
                                     // list) and turns out to be identical to Higham's formula used already in LDLt.
                                     : NumTraits<Scalar>::epsilon() * RealScalar(m_qr.diagonalSize());
   }

References eigen_assert, oomph::SarahBL::epsilon, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_prescribedThreshold, Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_qr, and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_usePrescribedThreshold.

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::rank(), and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::setThreshold().

Friends And Related Function Documentation

◆ SolverBase< FullPivHouseholderQR >

template<typename MatrixType_ , typename PermutationIndex_ >

friend class SolverBase< FullPivHouseholderQR >

friend

Member Data Documentation

◆ m_cols_permutation

template<typename MatrixType_ , typename PermutationIndex_ >

PermutationType Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_cols_permutation

protected

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::_solve_impl(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::_solve_impl_transposed(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::colsPermutation(), and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace().

◆ m_cols_transpositions

template<typename MatrixType_ , typename PermutationIndex_ >

IntDiagSizeVectorType Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_cols_transpositions

protected

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace().

◆ m_det_p

template<typename MatrixType_ , typename PermutationIndex_ >

Index Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_det_p

protected

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::determinant(), and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::signDeterminant().

◆ m_hCoeffs

template<typename MatrixType_ , typename PermutationIndex_ >

HCoeffsType Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_hCoeffs

protected

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::_solve_impl(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::_solve_impl_transposed(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::determinant(), Eigen::internal::FullPivHouseholderQRMatrixQReturnType< MatrixType, PermutationIndex >::evalTo(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::hCoeffs(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::matrixQ(), and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::signDeterminant().

◆ m_isInitialized

template<typename MatrixType_ , typename PermutationIndex_ >

bool Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_isInitialized

protected

◆ m_maxpivot

template<typename MatrixType_ , typename PermutationIndex_ >

RealScalar Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_maxpivot

protected

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::maxPivot(), and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::rank().

◆ m_nonzero_pivots

template<typename MatrixType_ , typename PermutationIndex_ >

Index Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_nonzero_pivots

protected

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::nonzeroPivots(), and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::rank().

◆ m_precision

template<typename MatrixType_ , typename PermutationIndex_ >

RealScalar Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_precision

protected

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace().

◆ m_prescribedThreshold

template<typename MatrixType_ , typename PermutationIndex_ >

RealScalar Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_prescribedThreshold

protected

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::setThreshold(), and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::threshold().

◆ m_qr

template<typename MatrixType_ , typename PermutationIndex_ >

MatrixType Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_qr

protected

◆ m_rows_transpositions

template<typename MatrixType_ , typename PermutationIndex_ >

IntDiagSizeVectorType Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_rows_transpositions

protected

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::_solve_impl(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::_solve_impl_transposed(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::matrixQ(), and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::rowsTranspositions().

◆ m_temp

template<typename MatrixType_ , typename PermutationIndex_ >

RowVectorType Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_temp

protected

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace().

◆ m_usePrescribedThreshold

template<typename MatrixType_ , typename PermutationIndex_ >

bool Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::m_usePrescribedThreshold

protected

Referenced by Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::setThreshold(), and Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::threshold().

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

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_p

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

template<typename MatrixType_, typename PermutationIndex_> class Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >

Member Typedef Documentation

◆ Base

◆ ColVectorType

◆ HCoeffsType

◆ IntDiagSizeVectorType

◆ MatrixQReturnType

◆ MatrixType

◆ PermutationIndex

◆ 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()

◆ cols()

◆ colsPermutation()

◆ compute() [1/2]

◆ compute() [2/2]

◆ computeInPlace()

◆ determinant()

◆ dimensionOfKernel()

◆ hCoeffs()

◆ inverse()

◆ isInjective()

◆ isInvertible()

◆ isSurjective()

◆ logAbsDeterminant()

◆ matrixQ()

◆ matrixQR()

◆ maxPivot()

◆ nonzeroPivots()

◆ rank()

◆ rows()

◆ rowsTranspositions()

◆ setThreshold() [1/2]

◆ setThreshold() [2/2]

◆ signDeterminant()

◆ threshold()

Friends And Related Function Documentation

◆ SolverBase< FullPivHouseholderQR >

Member Data Documentation

◆ m_cols_permutation

◆ m_cols_transpositions

◆ m_det_p

◆ m_hCoeffs

◆ m_isInitialized

◆ m_maxpivot

◆ m_nonzero_pivots

◆ m_precision

◆ m_prescribedThreshold

◆ m_qr

◆ m_rows_transpositions

◆ m_temp

◆ m_usePrescribedThreshold

template<typename MatrixType_, typename PermutationIndex_>
class Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >