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

#include <ForwardDeclarations.h>

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

typedef SolverBase< PartialPivLU >	Base

typedef _MatrixType	MatrixType

typedef PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime >	PermutationType

typedef MatrixType::PlainObject	PlainObject

typedef Transpositions< RowsAtCompileTime, MaxRowsAtCompileTime >	TranspositionType

Public Member Functions
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

Index	cols () const

template<typename MatrixType >
void	compute ()

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

Scalar	determinant () const

const Inverse< PartialPivLU >	inverse () const

const MatrixType &	matrixLU () const

	PartialPivLU ()
	Default Constructor. More...

template<typename MatrixType >
	PartialPivLU ()

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

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

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

template<typename MatrixType >
	PartialPivLU (Index size)

const PermutationType &	permutationP () const

RealScalar	rcond () const

MatrixType	reconstructedMatrix () const

Index	rows () const

template<typename Rhs >
const Solve< PartialPivLU, Rhs >	solve (const MatrixBase< Rhs > &b) const

Protected Member Functions
void	compute ()

Static Protected Member Functions
static void	check_template_parameters ()

Protected Attributes
signed char	m_det_p

bool	m_isInitialized

RealScalar	m_l1_norm

MatrixType	m_lu

PermutationType	m_p

TranspositionType	m_rowsTranspositions

Detailed Description

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

Definition at line 250 of file ForwardDeclarations.h.

Member Typedef Documentation

◆ Base

typedef SolverBase<PartialPivLU> Eigen::PartialPivLU::Base

Definition at line 81 of file PartialPivLU.h.

◆ MatrixType

typedef _MatrixType Eigen::PartialPivLU::MatrixType

Definition at line 80 of file PartialPivLU.h.

◆ PermutationType

typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> Eigen::PartialPivLU::PermutationType

Definition at line 88 of file PartialPivLU.h.

◆ PlainObject

typedef MatrixType::PlainObject Eigen::PartialPivLU::PlainObject

Definition at line 90 of file PartialPivLU.h.

◆ TranspositionType

typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> Eigen::PartialPivLU::TranspositionType

Definition at line 89 of file PartialPivLU.h.

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

Enumerator
MaxRowsAtCompileTime
MaxColsAtCompileTime

Definition at line 84 of file PartialPivLU.h.

Constructor & Destructor Documentation

◆ PartialPivLU() [1/6]

Eigen::PartialPivLU::PartialPivLU ( )

Default Constructor.

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

◆ PartialPivLU() [2/6]

Eigen::PartialPivLU::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()

◆ PartialPivLU() [3/6]

template<typename InputType >

Eigen::PartialPivLU::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.

Definition at line 315 of file PartialPivLU.h.

◆ PartialPivLU() [4/6]

template<typename InputType >

Eigen::PartialPivLU::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.

Definition at line 328 of file PartialPivLU.h.

◆ PartialPivLU() [5/6]

template<typename MatrixType >

Eigen::PartialPivLU::PartialPivLU ( )

Definition at line 292 of file PartialPivLU.h.

◆ PartialPivLU() [6/6]

template<typename MatrixType >

Eigen::PartialPivLU::PartialPivLU ( Index size )

Definition at line 303 of file PartialPivLU.h.

Member Function Documentation

◆ _solve_impl()

template<typename RhsType , typename DstType >

EIGEN_DEVICE_FUNC void Eigen::PartialPivLU::_solve_impl	(	const RhsType &	rhs,
		DstType &	dst
	)		const

inline

Definition at line 226 of file PartialPivLU.h.

◆ _solve_impl_transposed()

template<bool Conjugate, typename RhsType , typename DstType >

EIGEN_DEVICE_FUNC void Eigen::PartialPivLU::_solve_impl_transposed	(	const RhsType &	rhs,
		DstType &	dst
	)		const

inline

Definition at line 248 of file PartialPivLU.h.

◆ check_template_parameters()

static void Eigen::PartialPivLU::check_template_parameters ( )

inlinestaticprotected

Definition at line 276 of file PartialPivLU.h.

◆ cols()

Index Eigen::PartialPivLU::cols ( ) const

inline

Definition at line 221 of file PartialPivLU.h.

◆ compute() [1/3]

void Eigen::PartialPivLU::compute ( )

protected

◆ compute() [2/3]

template<typename MatrixType >

void Eigen::PartialPivLU::compute ( )

Definition at line 515 of file PartialPivLU.h.

◆ compute() [3/3]

template<typename InputType >

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

inline

Definition at line 129 of file PartialPivLU.h.

◆ determinant()

PartialPivLU< MatrixType >::Scalar Eigen::PartialPivLU::determinant ( ) const

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()

Definition at line 539 of file PartialPivLU.h.

◆ inverse()

const Inverse<PartialPivLU> Eigen::PartialPivLU::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()

Definition at line 197 of file PartialPivLU.h.

◆ matrixLU()

const MatrixType& Eigen::PartialPivLU::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()

Definition at line 141 of file PartialPivLU.h.

◆ permutationP()

const PermutationType& Eigen::PartialPivLU::permutationP ( ) const

inline

Returns: the permutation matrix P.

Definition at line 149 of file PartialPivLU.h.

◆ rcond()

RealScalar Eigen::PartialPivLU::rcond ( ) const

inline

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

Definition at line 184 of file PartialPivLU.h.

◆ reconstructedMatrix()

MatrixType Eigen::PartialPivLU::reconstructedMatrix ( ) const

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

Definition at line 549 of file PartialPivLU.h.

◆ rows()

Index Eigen::PartialPivLU::rows ( ) const

inline

Definition at line 220 of file PartialPivLU.h.

◆ solve()

template<typename Rhs >

const Solve<PartialPivLU, Rhs> Eigen::PartialPivLU::solve ( const MatrixBase< Rhs > & b ) const

inline

This method returns the solution x to the equation Ax=b, where A is the matrix of which *this is the LU decomposition.

Parameters

b	the right-hand-side of the equation to solve. Can be a vector or a matrix, the only requirement in order for the equation to make sense is that b.rows()==A.rows(), where A is the matrix of which *this is the LU decomposition.

Returns: the solution.

Example:

Output:

Since this PartialPivLU class assumes anyway that the matrix A is invertible, the solution theoretically exists and is unique regardless of b.

See also: TriangularView::solve(), inverse(), computeInverse()

Definition at line 175 of file PartialPivLU.h.

Member Data Documentation

◆ m_det_p

signed char Eigen::PartialPivLU::m_det_p

protected

Definition at line 287 of file PartialPivLU.h.

◆ m_isInitialized

bool Eigen::PartialPivLU::m_isInitialized

protected

Definition at line 288 of file PartialPivLU.h.

◆ m_l1_norm

RealScalar Eigen::PartialPivLU::m_l1_norm

protected

Definition at line 286 of file PartialPivLU.h.

◆ m_lu

MatrixType Eigen::PartialPivLU::m_lu

protected

Definition at line 283 of file PartialPivLU.h.

◆ m_p

PermutationType Eigen::PartialPivLU::m_p

protected

Definition at line 284 of file PartialPivLU.h.

◆ m_rowsTranspositions

TranspositionType Eigen::PartialPivLU::m_rowsTranspositions

protected

Definition at line 285 of file PartialPivLU.h.

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

Public Types

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Base

◆ MatrixType

◆ PermutationType

◆ PlainObject

◆ TranspositionType

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ PartialPivLU() [1/6]

◆ PartialPivLU() [2/6]

◆ PartialPivLU() [3/6]

◆ PartialPivLU() [4/6]

◆ PartialPivLU() [5/6]

◆ PartialPivLU() [6/6]

Member Function Documentation

◆ _solve_impl()

◆ _solve_impl_transposed()

◆ check_template_parameters()

◆ cols()

◆ compute() [1/3]

◆ compute() [2/3]

◆ compute() [3/3]

◆ determinant()

◆ inverse()

◆ matrixLU()

◆ permutationP()

◆ rcond()

◆ reconstructedMatrix()

◆ rows()

◆ solve()

Member Data Documentation

◆ m_det_p

◆ m_isInitialized

◆ m_l1_norm

◆ m_lu

◆ m_p

◆ m_rowsTranspositions