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

#include <src/eigen/Eigen/src/LU/PartialPivLU.h>

Inheritance diagram for Eigen::PartialPivLU< _MatrixType >:

Collaboration diagram for Eigen::PartialPivLU< _MatrixType >:

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

typedef _MatrixType	MatrixType

typedef SolverBase< PartialPivLU >	Base

typedef PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime >	PermutationType

typedef Transpositions< RowsAtCompileTime, MaxRowsAtCompileTime >	TranspositionType

typedef MatrixType::PlainObject	PlainObject

enum

typedef internal::traits< PartialPivLU< _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

typedef Eigen::Index	Index
	The interface type of indices.

typedef internal::traits< Derived >::StorageKind	StorageKind

Public Member Functions
	PartialPivLU ()
	Default Constructor.

	PartialPivLU (Index size)
	Default Constructor with memory preallocation.

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

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

RealScalar	rcond () const

const Inverse< PartialPivLU >	inverse () const

Scalar	determinant () const

MatrixType	reconstructedMatrix () const

Index	rows () const

Index	cols () const

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

ConstTransposeReturnType	transpose () const

AdjointReturnType	adjoint () const

EIGEN_DEVICE_FUNC PartialPivLU< _MatrixType > &	derived ()

EIGEN_DEVICE_FUNC const PartialPivLU< _MatrixType > &	derived () const

EIGEN_DEVICE_FUNC Derived &	const_cast_derived () const

EIGEN_DEVICE_FUNC const Derived &	const_derived () const

EIGEN_DEVICE_FUNC Index	size () const

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

Protected Member Functions
void	compute ()

Static Protected Member Functions
static void	check_template_parameters ()

Protected Attributes
MatrixType	m_lu

PermutationType	m_p

TranspositionType	m_rowsTranspositions

RealScalar	m_l1_norm

signed char	m_det_p

bool	m_isInitialized

Detailed Description

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

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

◆ AdjointReturnType

typedef internal::conditional<NumTraits<Scalar>::IsComplex,CwiseUnaryOp<internal::scalar_conjugate_op<Scalar>,ConstTransposeReturnType>,ConstTransposeReturnType>::type Eigen::SolverBase< PartialPivLU< _MatrixType > >::AdjointReturnType

inherited

◆ Base

template<typename _MatrixType >

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

◆ CoeffReturnType

typedef Scalar Eigen::SolverBase< PartialPivLU< _MatrixType > >::CoeffReturnType

inherited

◆ ConstTransposeReturnType

typedef internal::add_const<Transpose<constDerived>>::type Eigen::SolverBase< PartialPivLU< _MatrixType > >::ConstTransposeReturnType

inherited

◆ Index

template<typename Derived >

typedef Eigen::Index Eigen::EigenBase< Derived >::Index

inherited

The interface type of indices.

To change this, #define the preprocessor symbol EIGEN_DEFAULT_DENSE_INDEX_TYPE.

See also: StorageIndex, TopicPreprocessorDirectives.

◆ MatrixType

template<typename _MatrixType >

typedef _MatrixType Eigen::PartialPivLU< _MatrixType >::MatrixType

◆ PermutationType

template<typename _MatrixType >

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

◆ PlainObject

template<typename _MatrixType >

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

◆ Scalar

typedef internal::traits<PartialPivLU< _MatrixType > >::Scalar Eigen::SolverBase< PartialPivLU< _MatrixType > >::Scalar

inherited

◆ StorageKind

template<typename Derived >

typedef internal::traits<Derived>::StorageKind Eigen::EigenBase< Derived >::StorageKind

inherited

◆ TranspositionType

template<typename _MatrixType >

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

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

inherited

         {
      RowsAtCompileTime = internal::traits<Derived>::RowsAtCompileTime,
      ColsAtCompileTime = internal::traits<Derived>::ColsAtCompileTime,
      SizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::RowsAtCompileTime,
                                                          internal::traits<Derived>::ColsAtCompileTime>::ret),
      MaxRowsAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime,
      MaxColsAtCompileTime = internal::traits<Derived>::MaxColsAtCompileTime,
      MaxSizeAtCompileTime = (internal::size_at_compile_time<internal::traits<Derived>::MaxRowsAtCompileTime,
                                                             internal::traits<Derived>::MaxColsAtCompileTime>::ret),
      IsVectorAtCompileTime = internal::traits<Derived>::MaxRowsAtCompileTime == 1
                           || internal::traits<Derived>::MaxColsAtCompileTime == 1
    };

◆ anonymous enum

template<typename _MatrixType >

anonymous enum

Enumerator
MaxRowsAtCompileTime
MaxColsAtCompileTime

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

Constructor & Destructor Documentation

◆ PartialPivLU() [1/4]

template<typename MatrixType >

Eigen::PartialPivLU< MatrixType >::PartialPivLU

Default Constructor.

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

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

◆ PartialPivLU() [2/4]

template<typename MatrixType >

Eigen::PartialPivLU< MatrixType >::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()

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

◆ PartialPivLU() [3/4]

template<typename MatrixType >

template<typename InputType >

Eigen::PartialPivLU< MatrixType >::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 >::compute(), and Eigen::EigenBase< Derived >::derived().

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◆ PartialPivLU() [4/4]

template<typename MatrixType >

template<typename InputType >

Eigen::PartialPivLU< MatrixType >::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 >::compute().

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Member Function Documentation

◆ _solve_impl()

template<typename _MatrixType >

template<typename RhsType , typename DstType >

EIGEN_DEVICE_FUNC void Eigen::PartialPivLU< _MatrixType >::_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.
      */
 
      eigen_assert(rhs.rows() == m_lu.rows());
 
      // 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_assert, Eigen::PartialPivLU< _MatrixType >::m_lu, and Eigen::PartialPivLU< _MatrixType >::permutationP().

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◆ _solve_impl_transposed()

template<typename _MatrixType >

template<bool Conjugate, typename RhsType , typename DstType >

EIGEN_DEVICE_FUNC void Eigen::PartialPivLU< _MatrixType >::_solve_impl_transposed	(	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.
      */
 
      eigen_assert(rhs.rows() == m_lu.cols());
 
      if (Conjugate) {
        // Step 1
        dst = m_lu.template triangularView<Upper>().adjoint().solve(rhs);
        // Step 2
        m_lu.template triangularView<UnitLower>().adjoint().solveInPlace(dst);
      } else {
        // Step 1
        dst = m_lu.template triangularView<Upper>().transpose().solve(rhs);
        // Step 2
        m_lu.template triangularView<UnitLower>().transpose().solveInPlace(dst);
      }
      // Step 3
      dst = permutationP().transpose() * dst;
    }

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

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◆ addTo()

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::EigenBase< Derived >::addTo ( Dest & dst ) const

inlineinherited

  {
    // This is the default implementation,
    // derived class can reimplement it in a more optimized way.
    typename Dest::PlainObject res(rows(),cols());
    evalTo(res);
    dst += res;
  }

◆ adjoint()

AdjointReturnType Eigen::SolverBase< PartialPivLU< _MatrixType > >::adjoint ( ) const

inlineinherited

Returns: an expression of the adjoint of the factored matrix

A typical usage is to solve for the adjoint problem A' x = b:

x = dec.adjoint().solve(b);

For real scalar types, this function is equivalent to transpose().

See also: transpose(), solve()

    {
      return AdjointReturnType(derived().transpose());
    }

◆ applyThisOnTheLeft()

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::EigenBase< Derived >::applyThisOnTheLeft ( Dest & dst ) const

inlineinherited

  {
    // This is the default implementation,
    // derived class can reimplement it in a more optimized way.
    dst = this->derived() * dst;
  }

References Eigen::EigenBase< Derived >::derived().

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◆ applyThisOnTheRight()

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::EigenBase< Derived >::applyThisOnTheRight ( Dest & dst ) const

inlineinherited

  {
    // This is the default implementation,
    // derived class can reimplement it in a more optimized way.
    dst = dst * this->derived();
  }

References Eigen::EigenBase< Derived >::derived().

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◆ check_template_parameters()

template<typename _MatrixType >

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

inlinestaticprotected

    {
      EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar);
    }

References EIGEN_STATIC_ASSERT_NON_INTEGER.

◆ cols()

template<typename _MatrixType >

Index Eigen::PartialPivLU< _MatrixType >::cols ( ) const

inline

221{ return m_lu.cols(); }

References Eigen::PartialPivLU< _MatrixType >::m_lu.

◆ compute() [1/2]

template<typename MatrixType >

void Eigen::PartialPivLU< MatrixType >::compute

protected

{
  check_template_parameters();
 
  // the row permutation is stored as int indices, so just to be sure:
  eigen_assert(m_lu.rows()<NumTraits<int>::highest());
 
  m_l1_norm = m_lu.cwiseAbs().colwise().sum().maxCoeff();
 
  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, and Eigen::internal::partial_lu_inplace().

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

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◆ compute() [2/2]

template<typename _MatrixType >

template<typename InputType >

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

inline

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

References Eigen::PartialPivLU< _MatrixType >::compute(), Eigen::EigenBase< Derived >::derived(), and Eigen::PartialPivLU< _MatrixType >::m_lu.

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◆ const_cast_derived()

template<typename Derived >

EIGEN_DEVICE_FUNC Derived & Eigen::EigenBase< Derived >::const_cast_derived ( ) const

inlineinherited

52 { return *static_cast<Derived*>(const_cast<EigenBase*>(this)); }

Referenced by Eigen::TriangularViewImpl< _MatrixType, _Mode, Dense >::swap().

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◆ const_derived()

template<typename Derived >

EIGEN_DEVICE_FUNC const Derived & Eigen::EigenBase< Derived >::const_derived ( ) const

inlineinherited

55 { return *static_cast<const Derived*>(this); }

◆ derived() [1/2]

EIGEN_DEVICE_FUNC PartialPivLU< _MatrixType > & Eigen::EigenBase< PartialPivLU< _MatrixType > >::derived ( )

inlineinherited

Returns: a reference to the derived object

45{ return *static_cast<Derived*>(this); }

◆ derived() [2/2]

EIGEN_DEVICE_FUNC const PartialPivLU< _MatrixType > & Eigen::EigenBase< PartialPivLU< _MatrixType > >::derived ( ) const

inlineinherited

Returns: a const reference to the derived object

48{ return *static_cast<const Derived*>(this); }

◆ determinant()

template<typename MatrixType >

PartialPivLU< MatrixType >::Scalar Eigen::PartialPivLU< MatrixType >::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.

◆ evalTo()

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::EigenBase< Derived >::evalTo ( Dest & dst ) const

inlineinherited

72 { derived().evalTo(dst); }

Referenced by Eigen::EigenBase< Derived >::subTo().

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◆ inverse()

template<typename _MatrixType >

const Inverse< PartialPivLU > Eigen::PartialPivLU< _MatrixType >::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 >::m_isInitialized.

◆ matrixLU()

template<typename _MatrixType >

const MatrixType & Eigen::PartialPivLU< _MatrixType >::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 >::m_isInitialized, and Eigen::PartialPivLU< _MatrixType >::m_lu.

◆ permutationP()

template<typename _MatrixType >

const PermutationType & Eigen::PartialPivLU< _MatrixType >::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 >::m_isInitialized, and Eigen::PartialPivLU< _MatrixType >::m_p.

Referenced by Eigen::PartialPivLU< _MatrixType >::_solve_impl(), and Eigen::PartialPivLU< _MatrixType >::_solve_impl_transposed().

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◆ rcond()

template<typename _MatrixType >

RealScalar Eigen::PartialPivLU< _MatrixType >::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 >::m_isInitialized, Eigen::PartialPivLU< _MatrixType >::m_l1_norm, and Eigen::internal::rcond_estimate_helper().

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◆ reconstructedMatrix()

template<typename MatrixType >

MatrixType Eigen::PartialPivLU< MatrixType >::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.

◆ rows()

template<typename _MatrixType >

Index Eigen::PartialPivLU< _MatrixType >::rows ( ) const

inline

220{ return m_lu.rows(); }

References Eigen::PartialPivLU< _MatrixType >::m_lu.

◆ size()

template<typename Derived >

EIGEN_DEVICE_FUNC Index Eigen::EigenBase< Derived >::size ( ) const

inlineinherited

Returns: the number of coefficients, which is rows()*cols().

See also: rows(), cols(), SizeAtCompileTime.

66{ return rows() * cols(); }

References Eigen::EigenBase< Derived >::cols(), and Eigen::EigenBase< Derived >::rows().

Referenced by Eigen::PlainObjectBase< Derived >::_resize_to_match(), Eigen::DiagonalMatrix< _Scalar, SizeAtCompileTime, MaxSizeAtCompileTime >::resize(), Eigen::DiagonalMatrix< _Scalar, SizeAtCompileTime, MaxSizeAtCompileTime >::setIdentity(), and Eigen::DiagonalMatrix< _Scalar, SizeAtCompileTime, MaxSizeAtCompileTime >::setZero().

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◆ solve()

template<typename _MatrixType >

template<typename Rhs >

const Solve< PartialPivLU, Rhs > Eigen::PartialPivLU< _MatrixType >::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()

    {
      eigen_assert(m_isInitialized && "PartialPivLU is not initialized.");
      return Solve<PartialPivLU, Rhs>(*this, b.derived());
    }

References eigen_assert, and Eigen::PartialPivLU< _MatrixType >::m_isInitialized.

◆ subTo()

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::EigenBase< Derived >::subTo ( Dest & dst ) const

inlineinherited

  {
    // This is the default implementation,
    // derived class can reimplement it in a more optimized way.
    typename Dest::PlainObject res(rows(),cols());
    evalTo(res);
    dst -= res;
  }

References Eigen::EigenBase< Derived >::cols(), Eigen::EigenBase< Derived >::evalTo(), and Eigen::EigenBase< Derived >::rows().

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◆ transpose()

ConstTransposeReturnType Eigen::SolverBase< PartialPivLU< _MatrixType > >::transpose ( ) const

inlineinherited

Returns: an expression of the transposed of the factored matrix.

A typical usage is to solve for the transposed problem A^T x = b:

x = dec.transpose().solve(b);

See also: adjoint(), solve()

    {
      return ConstTransposeReturnType(derived());
    }

Member Data Documentation

◆ m_det_p

template<typename _MatrixType >

signed char Eigen::PartialPivLU< _MatrixType >::m_det_p

protected

◆ m_isInitialized

template<typename _MatrixType >

bool Eigen::PartialPivLU< _MatrixType >::m_isInitialized

protected

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

◆ m_l1_norm

template<typename _MatrixType >

RealScalar Eigen::PartialPivLU< _MatrixType >::m_l1_norm

protected

Referenced by Eigen::PartialPivLU< _MatrixType >::rcond().

◆ m_lu

template<typename _MatrixType >

MatrixType Eigen::PartialPivLU< _MatrixType >::m_lu

protected

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

◆ m_p

template<typename _MatrixType >

PermutationType Eigen::PartialPivLU< _MatrixType >::m_p

protected

Referenced by Eigen::PartialPivLU< _MatrixType >::permutationP().

◆ m_rowsTranspositions

template<typename _MatrixType >

TranspositionType Eigen::PartialPivLU< _MatrixType >::m_rowsTranspositions

protected

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

src/eigen/Eigen/src/Core/util/ForwardDeclarations.h
src/eigen/Eigen/src/LU/PartialPivLU.h

Public Types

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ AdjointReturnType

◆ Base

◆ CoeffReturnType

◆ ConstTransposeReturnType

◆ Index

◆ MatrixType

◆ PermutationType

◆ PlainObject

◆ Scalar

◆ StorageKind

◆ TranspositionType

Member Enumeration Documentation

◆ anonymous enum

◆ 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()

◆ addTo()

◆ adjoint()

◆ applyThisOnTheLeft()

◆ applyThisOnTheRight()

◆ check_template_parameters()

◆ cols()

◆ compute() [1/2]

◆ compute() [2/2]

◆ const_cast_derived()

◆ const_derived()

◆ derived() [1/2]

◆ derived() [2/2]

◆ determinant()

◆ evalTo()

◆ inverse()

◆ matrixLU()

◆ permutationP()

◆ rcond()

◆ reconstructedMatrix()

◆ rows()

◆ size()

◆ solve()

◆ subTo()

◆ transpose()

Member Data Documentation

◆ m_det_p

◆ m_isInitialized

◆ m_l1_norm

◆ m_lu

◆ m_p

◆ m_rowsTranspositions