LU decomposition of a matrix with partial pivoting, and related features. More...

#include <PartialPivLU.h>

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

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

typedef MatrixType_	MatrixType

typedef SolverBase< PartialPivLU >	Base

using	PermutationIndex = PermutationIndex_

typedef PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime, PermutationIndex >	PermutationType

typedef Transpositions< RowsAtCompileTime, MaxRowsAtCompileTime, PermutationIndex >	TranspositionType

typedef MatrixType::PlainObject	PlainObject

Public Types inherited from Eigen::SolverBase< PartialPivLU< MatrixType_, PermutationIndex_ > >
enum

typedef EigenBase< PartialPivLU< MatrixType_, PermutationIndex_ > >	Base

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

typedef Scalar	CoeffReturnType

typedef Transpose< const PartialPivLU< 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
	PartialPivLU ()
	Default Constructor. More...

	PartialPivLU (Index size)
	Default Constructor with memory preallocation. More...

template<typename InputType >
	PartialPivLU (const EigenBase< InputType > &matrix)

template<typename InputType >
	PartialPivLU (EigenBase< InputType > &matrix)

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

const MatrixType &	matrixLU () const

const PermutationType &	permutationP () const

RealScalar	rcond () const

const Inverse< PartialPivLU >	inverse () const

Scalar	determinant () const

MatrixType	reconstructedMatrix () const

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

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

template<bool Conjugate, typename RhsType , typename DstType >
EIGEN_DEVICE_FUNC void	_solve_impl_transposed (const RhsType &rhs, DstType &dst) const

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

	~SolverBase ()

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

const ConstTransposeReturnType	transpose () const

const AdjointReturnType	adjoint () const

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

constexpr EIGEN_DEVICE_FUNC const PartialPivLU< 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	compute ()

Protected Member Functions inherited from Eigen::SolverBase< PartialPivLU< MatrixType_, PermutationIndex_ > >
void	_check_solve_assertion (const Rhs &b) const

Protected Attributes
MatrixType	m_lu

PermutationType	m_p

TranspositionType	m_rowsTranspositions

RealScalar	m_l1_norm

signed char	m_det_p

bool	m_isInitialized

Friends
class	SolverBase< PartialPivLU >

Detailed Description

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

LU decomposition of a matrix with partial pivoting, and related features.

Template Parameters

MatrixType_ the type of the matrix of which we are computing the LU decomposition

This class represents a LU decomposition of a square invertible matrix, with partial pivoting: the matrix A is decomposed as A = PLU where L is unit-lower-triangular, U is upper-triangular, and P is a permutation matrix.

Typically, partial pivoting LU decomposition is only considered numerically stable for square invertible matrices. Thus LAPACK's dgesv and dgesvx require the matrix to be square and invertible. The present class does the same. It will assert that the matrix is square, but it won't (actually it can't) check that the matrix is invertible: it is your task to check that you only use this decomposition on invertible matrices.

The guaranteed safe alternative, working for all matrices, is the full pivoting LU decomposition, provided by class FullPivLU.

This is not a rank-revealing LU decomposition. Many features are intentionally absent from this class, such as rank computation. If you need these features, use class FullPivLU.

This LU decomposition is suitable to invert invertible matrices. It is what MatrixBase::inverse() uses in the general case. On the other hand, it is not suitable to determine whether a given matrix is invertible.

The data of the LU decomposition can be directly accessed through the methods matrixLU(), permutationP().

This class supports the inplace decomposition mechanism.

See also: MatrixBase::partialPivLu(), MatrixBase::determinant(), MatrixBase::inverse(), MatrixBase::computeInverse(), class FullPivLU

Member Typedef Documentation

◆ Base

template<typename MatrixType_ , typename PermutationIndex_ >

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

◆ MatrixType

template<typename MatrixType_ , typename PermutationIndex_ >

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

◆ PermutationIndex

template<typename MatrixType_ , typename PermutationIndex_ >

using Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::PermutationIndex = PermutationIndex_

◆ PermutationType

template<typename MatrixType_ , typename PermutationIndex_ >

typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime, PermutationIndex> Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::PermutationType

◆ PlainObject

template<typename MatrixType_ , typename PermutationIndex_ >

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

◆ TranspositionType

template<typename MatrixType_ , typename PermutationIndex_ >

typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime, PermutationIndex> Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::TranspositionType

Member Enumeration Documentation

◆ anonymous enum

template<typename MatrixType_ , typename PermutationIndex_ >

anonymous enum

Enumerator
MaxRowsAtCompileTime
MaxColsAtCompileTime

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

Constructor & Destructor Documentation

◆ PartialPivLU() [1/4]

template<typename MatrixType , typename PermutationIndex >

Eigen::PartialPivLU< MatrixType, PermutationIndex >::PartialPivLU

Default Constructor.

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

271 : m_lu(), m_p(), m_rowsTranspositions(), m_l1_norm(0), m_det_p(0), m_isInitialized(false) {}

Eigen::PartialPivLU::m_isInitialized

bool m_isInitialized

Definition: PartialPivLU.h:266

Eigen::PartialPivLU::m_l1_norm

RealScalar m_l1_norm

Definition: PartialPivLU.h:264

Eigen::PartialPivLU::m_rowsTranspositions

TranspositionType m_rowsTranspositions

Definition: PartialPivLU.h:263

Eigen::PartialPivLU::m_p

PermutationType m_p

Definition: PartialPivLU.h:262

Eigen::PartialPivLU::m_det_p

signed char m_det_p

Definition: PartialPivLU.h:265

Eigen::PartialPivLU::m_lu

MatrixType m_lu

Definition: PartialPivLU.h:261

◆ PartialPivLU() [2/4]

template<typename MatrixType , typename PermutationIndex >

Eigen::PartialPivLU< MatrixType, PermutationIndex >::PartialPivLU ( Index size )

explicit

Default Constructor with memory preallocation.

Like the default constructor but with preallocation of the internal data according to the specified problem size.

See also: PartialPivLU()

275 : m_lu(size, size), m_p(size), m_rowsTranspositions(size), m_l1_norm(0), m_det_p(0), m_isInitialized(false) {}

Eigen::EigenBase::size

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT

Definition: EigenBase.h:64

◆ PartialPivLU() [3/4]

template<typename MatrixType , typename PermutationIndex >

template<typename InputType >

Eigen::PartialPivLU< MatrixType, PermutationIndex >::PartialPivLU ( const EigenBase< InputType > & matrix )

explicit

Constructor.

Parameters

matrix the matrix of which to compute the LU decomposition.

Warning: The matrix should have full rank (e.g. if it's square, it should be invertible). If you need to deal with non-full rank, use class FullPivLU instead.

     : m_lu(matrix.rows(), matrix.cols()),
       m_p(matrix.rows()),
       m_rowsTranspositions(matrix.rows()),
       m_l1_norm(0),
       m_det_p(0),
       m_isInitialized(false) {
   compute(matrix.derived());
 }

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

◆ PartialPivLU() [4/4]

template<typename MatrixType , typename PermutationIndex >

template<typename InputType >

Eigen::PartialPivLU< MatrixType, PermutationIndex >::PartialPivLU ( EigenBase< InputType > & matrix )

explicit

Constructor for inplace decomposition

Parameters

matrix the matrix of which to compute the LU decomposition.

Warning: The matrix should have full rank (e.g. if it's square, it should be invertible). If you need to deal with non-full rank, use class FullPivLU instead.

     : m_lu(matrix.derived()),
       m_p(matrix.rows()),
       m_rowsTranspositions(matrix.rows()),
       m_l1_norm(0),
       m_det_p(0),
       m_isInitialized(false) {
   compute();
 }

References Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::compute().

Member Function Documentation

◆ _solve_impl()

template<typename MatrixType_ , typename PermutationIndex_ >

template<typename RhsType , typename DstType >

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

inline

                                                                              {
     /* The decomposition PA = LU can be rewritten as A = P^{-1} L U.
      * So we proceed as follows:
      * Step 1: compute c = Pb.
      * Step 2: replace c by the solution x to Lx = c.
      * Step 3: replace c by the solution x to Ux = c.
      */
  
     // Step 1
     dst = permutationP() * rhs;
  
     // Step 2
     m_lu.template triangularView<UnitLower>().solveInPlace(dst);
  
     // Step 3
     m_lu.template triangularView<Upper>().solveInPlace(dst);
   }

References Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::m_lu, and Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::permutationP().

◆ _solve_impl_transposed()

template<typename MatrixType_ , typename PermutationIndex_ >

template<bool Conjugate, typename RhsType , typename DstType >

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

inline

                                                                                         {
     /* The decomposition PA = LU can be rewritten as A^T = U^T L^T P.
      * So we proceed as follows:
      * Step 1: compute c as the solution to L^T c = b
      * Step 2: replace c by the solution x to U^T x = c.
      * Step 3: update  c = P^-1 c.
      */
  
     eigen_assert(rhs.rows() == m_lu.cols());
  
     // Step 1
     dst = m_lu.template triangularView<Upper>().transpose().template conjugateIf<Conjugate>().solve(rhs);
     // Step 2
     m_lu.template triangularView<UnitLower>().transpose().template conjugateIf<Conjugate>().solveInPlace(dst);
     // Step 3
     dst = permutationP().transpose() * dst;
   }

References eigen_assert, Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::m_lu, Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::permutationP(), and Eigen::PermutationBase< Derived >::transpose().

◆ cols()

template<typename MatrixType_ , typename PermutationIndex_ >

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

inline

214 { return m_lu.cols(); }

References Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::m_lu.

Referenced by gdb.printers._MatrixEntryIterator::__next__(), gdb.printers.EigenMatrixPrinter::children(), gdb.printers.EigenSparseMatrixPrinter::children(), gdb.printers.EigenMatrixPrinter::to_string(), and gdb.printers.EigenSparseMatrixPrinter::to_string().

◆ compute() [1/2]

template<typename MatrixType , typename PermutationIndex >

void Eigen::PartialPivLU< MatrixType, PermutationIndex >::compute

protected

                                                          {
   eigen_assert(m_lu.rows() < NumTraits<PermutationIndex>::highest());
  
   if (m_lu.cols() > 0)
     m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff();
   else
     m_l1_norm = RealScalar(0);
  
   eigen_assert(m_lu.rows() == m_lu.cols() && "PartialPivLU is only for square (and moreover invertible) matrices");
   const Index size = m_lu.rows();
  
   m_rowsTranspositions.resize(size);
  
   typename TranspositionType::StorageIndex nb_transpositions;
   internal::partial_lu_inplace(m_lu, m_rowsTranspositions, nb_transpositions);
   m_det_p = (nb_transpositions % 2) ? -1 : 1;
  
   m_p = m_rowsTranspositions;
  
   m_isInitialized = true;
 }

References eigen_assert, Eigen::internal::partial_lu_inplace(), and size.

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

◆ compute() [2/2]

template<typename MatrixType_ , typename PermutationIndex_ >

template<typename InputType >

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

inline

                                                             {
     m_lu = matrix.derived();
     compute();
     return *this;
   }

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

Referenced by ctms_decompositions().

◆ determinant()

template<typename MatrixType , typename PermutationIndex >

PartialPivLU< MatrixType, PermutationIndex >::Scalar Eigen::PartialPivLU< MatrixType, PermutationIndex >::determinant

Returns: the determinant of the matrix of which *this is the LU decomposition. It has only linear complexity (that is, O(n) where n is the dimension of the square matrix) as the LU decomposition has already been computed.

Note: For fixed-size matrices of size up to 4, MatrixBase::determinant() offers optimized paths.

Warning: a determinant can be very big or small, so for matrices of large enough dimension, there is a risk of overflow/underflow.

See also: MatrixBase::determinant()

           {
   eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
   return Scalar(m_det_p) * m_lu.diagonal().prod();
 }

References eigen_assert.

Referenced by lu_verify_assert().

◆ inverse()

template<typename MatrixType_ , typename PermutationIndex_ >

const Inverse<PartialPivLU> Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::inverse ( ) const

inline

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

Warning: The matrix being decomposed here is assumed to be invertible. If you need to check for invertibility, use class FullPivLU instead.

See also: MatrixBase::inverse(), LU::inverse()

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

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

Referenced by lu_partial_piv(), and lu_verify_assert().

◆ matrixLU()

template<typename MatrixType_ , typename PermutationIndex_ >

const MatrixType& Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::matrixLU ( ) const

inline

Returns: the LU decomposition matrix: the upper-triangular part is U, the unit-lower-triangular part is L (at least for square matrices; in the non-square case, special care is needed, see the documentation of class FullPivLU).

See also: matrixL(), matrixU()

                                             {
     eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
     return m_lu;
   }

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

Referenced by lu_verify_assert().

◆ permutationP()

template<typename MatrixType_ , typename PermutationIndex_ >

const PermutationType& Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::permutationP ( ) const

inline

Returns: the permutation matrix P.

                                                      {
     eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
     return m_p;
   }

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

Referenced by Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::_solve_impl(), Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::_solve_impl_transposed(), and lu_verify_assert().

◆ rcond()

template<typename MatrixType_ , typename PermutationIndex_ >

RealScalar Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::rcond ( ) const

inline

Returns: an estimate of the reciprocal condition number of the matrix of which *this is the LU decomposition.

                                   {
     eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
     return internal::rcond_estimate_helper(m_l1_norm, *this);
   }

References eigen_assert, Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::m_isInitialized, Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::m_l1_norm, and Eigen::internal::rcond_estimate_helper().

Referenced by lu_partial_piv().

◆ reconstructedMatrix()

template<typename MatrixType , typename PermutationIndex >

MatrixType Eigen::PartialPivLU< MatrixType, PermutationIndex >::reconstructedMatrix

Returns: the matrix represented by the decomposition, i.e., it returns the product: P^{-1} L U. This function is provided for debug purpose.

                                                                                  {
   eigen_assert(m_isInitialized && "LU is not initialized.");
   // LU
   MatrixType res = m_lu.template triangularView<UnitLower>().toDenseMatrix() * m_lu.template triangularView<Upper>();
  
   // P^{-1}(LU)
   res = m_p.inverse() * res;
  
   return res;
 }

References eigen_assert, and res.

Referenced by lu_partial_piv().

◆ rows()

template<typename MatrixType_ , typename PermutationIndex_ >

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

inline

213 { return m_lu.rows(); }

References Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::m_lu.

Referenced by gdb.printers._MatrixEntryIterator::__next__(), gdb.printers.EigenMatrixPrinter::children(), gdb.printers.EigenSparseMatrixPrinter::children(), gdb.printers.EigenMatrixPrinter::to_string(), and gdb.printers.EigenSparseMatrixPrinter::to_string().

Friends And Related Function Documentation

◆ SolverBase< PartialPivLU >

template<typename MatrixType_ , typename PermutationIndex_ >

friend class SolverBase< PartialPivLU >

friend

Member Data Documentation

◆ m_det_p

template<typename MatrixType_ , typename PermutationIndex_ >

signed char Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::m_det_p

protected

◆ m_isInitialized

template<typename MatrixType_ , typename PermutationIndex_ >

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

protected

Referenced by Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::inverse(), Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::matrixLU(), Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::permutationP(), and Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::rcond().

◆ m_l1_norm

template<typename MatrixType_ , typename PermutationIndex_ >

RealScalar Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::m_l1_norm

protected

Referenced by Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::rcond().

◆ m_lu

template<typename MatrixType_ , typename PermutationIndex_ >

MatrixType Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::m_lu

protected

Referenced by Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::_solve_impl(), Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::_solve_impl_transposed(), Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::cols(), Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::compute(), Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::matrixLU(), and Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::rows().

◆ m_p

template<typename MatrixType_ , typename PermutationIndex_ >

PermutationType Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::m_p

protected

Referenced by Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::permutationP().

◆ m_rowsTranspositions

template<typename MatrixType_ , typename PermutationIndex_ >

TranspositionType Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::m_rowsTranspositions

protected

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

Public Types

Public Member Functions

Protected Member Functions

Protected Attributes

Friends

Detailed Description

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

Member Typedef Documentation

◆ Base

◆ MatrixType

◆ PermutationIndex

◆ PermutationType

◆ PlainObject

◆ TranspositionType

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ PartialPivLU() [1/4]

◆ PartialPivLU() [2/4]

◆ PartialPivLU() [3/4]

◆ PartialPivLU() [4/4]

Member Function Documentation

◆ _solve_impl()

◆ _solve_impl_transposed()

◆ cols()

◆ compute() [1/2]

◆ compute() [2/2]

◆ determinant()

◆ inverse()

◆ matrixLU()

◆ permutationP()

◆ rcond()

◆ reconstructedMatrix()

◆ rows()

Friends And Related Function Documentation

◆ SolverBase< PartialPivLU >

Member Data Documentation

◆ m_det_p

◆ m_isInitialized

◆ m_l1_norm

◆ m_lu

◆ m_p

◆ m_rowsTranspositions

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