Eigen::LLT< MatrixType_, UpLo_ > Class Template Reference

Standard Cholesky decomposition (LL^T) of a matrix and associated features. More...

#include <LLT.h>

Inheritance diagram for Eigen::LLT< MatrixType_, UpLo_ >:

Public Types
enum	{ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime }
enum	{ PacketSize = internal::packet_traits<Scalar>::size , AlignmentMask = int(PacketSize) - 1 , UpLo = UpLo_ }
typedef MatrixType_	MatrixType
typedef SolverBase< LLT >	Base
typedef internal::LLT_Traits< MatrixType, UpLo >	Traits
Public Types inherited from Eigen::SolverBase< LLT< MatrixType_, UpLo_ > >
enum
typedef EigenBase< LLT< MatrixType_, UpLo_ > >	Base
typedef internal::traits< LLT< MatrixType_, UpLo_ > >::Scalar	Scalar
typedef Scalar	CoeffReturnType
typedef Transpose< const LLT< MatrixType_, UpLo_ > >	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
	LLT ()
	Default Constructor. More...
	LLT (Index size)
	Default Constructor with memory preallocation. More...
template<typename InputType >
	LLT (const EigenBase< InputType > &matrix)
template<typename InputType >
	LLT (EigenBase< InputType > &matrix)
	Constructs a LLT factorization from a given matrix. More...
Traits::MatrixU	matrixU () const
Traits::MatrixL	matrixL () const
template<typename Derived >
void	solveInPlace (const MatrixBase< Derived > &bAndX) const
template<typename InputType >
LLT &	compute (const EigenBase< InputType > &matrix)
RealScalar	rcond () const
const MatrixType &	matrixLLT () const
MatrixType	reconstructedMatrix () const
ComputationInfo	info () const
	Reports whether previous computation was successful. More...
const LLT &	adjoint () const EIGEN_NOEXCEPT
EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT
EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT
template<typename VectorType >
LLT &	rankUpdate (const VectorType &vec, const RealScalar &sigma=1)
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 >
LLT< MatrixType, UpLo_ > &	compute (const EigenBase< InputType > &a)
template<typename VectorType >
LLT< MatrixType_, UpLo_ > &	rankUpdate (const VectorType &v, const RealScalar &sigma)
Public Member Functions inherited from Eigen::SolverBase< LLT< MatrixType_, UpLo_ > >
	SolverBase ()
	~SolverBase ()
const Solve< LLT< MatrixType_, UpLo_ >, Rhs >	solve (const MatrixBase< Rhs > &b) const
const ConstTransposeReturnType	transpose () const
const AdjointReturnType	adjoint () const
constexpr EIGEN_DEVICE_FUNC LLT< MatrixType_, UpLo_ > &	derived ()
constexpr EIGEN_DEVICE_FUNC const LLT< MatrixType_, UpLo_ > &	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 Attributes
MatrixType	m_matrix
RealScalar	m_l1_norm
bool	m_isInitialized
ComputationInfo	m_info

Friends
class	SolverBase< LLT >

Additional Inherited Members
Protected Member Functions inherited from Eigen::SolverBase< LLT< MatrixType_, UpLo_ > >
void	_check_solve_assertion (const Rhs &b) const

Detailed Description

template<typename MatrixType_, int UpLo_>
class Eigen::LLT< MatrixType_, UpLo_ >

Standard Cholesky decomposition (LL^T) of a matrix and associated features.

Template Parameters

MatrixType_	the type of the matrix of which we are computing the LL^T Cholesky decomposition
UpLo_	the triangular part that will be used for the decomposition: Lower (default) or Upper. The other triangular part won't be read.

This class performs a LL^T Cholesky decomposition of a symmetric, positive definite matrix A such that A = LL^* = U^*U, where L is lower triangular.

While the Cholesky decomposition is particularly useful to solve selfadjoint problems like D^*D x = b, for that purpose, we recommend the Cholesky decomposition without square root which is more stable and even faster. Nevertheless, this standard Cholesky decomposition remains useful in many other situations like generalised eigen problems with hermitian matrices.

Remember that Cholesky decompositions are not rank-revealing. This LLT decomposition is only stable on positive definite matrices, use LDLT instead for the semidefinite case. Also, do not use a Cholesky decomposition to determine whether a system of equations has a solution.

Example:

MatrixXd A(3, 3);
A << 4, -1, 2, -1, 6, 0, 2, 0, 5;
cout << "The matrix A is" << endl << A << endl;
 
LLT<MatrixXd> lltOfA(A);        // compute the Cholesky decomposition of A
MatrixXd L = lltOfA.matrixL();  // retrieve factor L  in the decomposition
// The previous two lines can also be written as "L = A.llt().matrixL()"
 
cout << "The Cholesky factor L is" << endl << L << endl;
cout << "To check this, let us compute L * L.transpose()" << endl;
cout << L * L.transpose() << endl;
cout << "This should equal the matrix A" << endl;

Output:

Performance: for best performance, it is recommended to use a column-major storage format with the Lower triangular part (the default), or, equivalently, a row-major storage format with the Upper triangular part. Otherwise, you might get a 20% slowdown for the full factorization step, and rank-updates can be up to 3 times slower.

This class supports the inplace decomposition mechanism.

Note that during the decomposition, only the lower (or upper, as defined by UpLo_) triangular part of A is considered. Therefore, the strict lower part does not have to store correct values.

See also

MatrixBase::llt(), SelfAdjointView::llt(), class LDLT

Member Typedef Documentation

Base

template<typename MatrixType_ , int UpLo_>

typedef SolverBase<LLT> Eigen::LLT< MatrixType_, UpLo_ >::Base

MatrixType

template<typename MatrixType_ , int UpLo_>

typedef MatrixType_ Eigen::LLT< MatrixType_, UpLo_ >::MatrixType

Traits

template<typename MatrixType_ , int UpLo_>

typedef internal::LLT_Traits<MatrixType, UpLo> Eigen::LLT< MatrixType_, UpLo_ >::Traits

Member Enumeration Documentation

anonymous enum

template<typename MatrixType_ , int UpLo_>

anonymous enum

Enumerator
MaxColsAtCompileTime

{ MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime };

anonymous enum

template<typename MatrixType_ , int UpLo_>

anonymous enum

Enumerator
PacketSize
AlignmentMask
UpLo

{ PacketSize = internal::packet_traits<Scalar>::size, AlignmentMask = int(PacketSize) - 1, UpLo = UpLo_ };

Constructor & Destructor Documentation

LLT() [1/4]

template<typename MatrixType_ , int UpLo_>

Eigen::LLT< MatrixType_, UpLo_ >::LLT ( )

inline

Default Constructor.

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

: m_matrix(), m_isInitialized(false) {}

LLT() [2/4]

template<typename MatrixType_ , int UpLo_>

Eigen::LLT< MatrixType_, UpLo_ >::LLT ( Index  size )

inlineexplicit

Default Constructor with memory preallocation.

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

See also

LLT()

: m_matrix(size, size), m_isInitialized(false) {}

LLT() [3/4]

template<typename MatrixType_ , int UpLo_>

template<typename InputType >

Eigen::LLT< MatrixType_, UpLo_ >::LLT ( const EigenBase< InputType > &  matrix )

inlineexplicit

                                                   : m_matrix(matrix.rows(), matrix.cols()), m_isInitialized(false) {
    compute(matrix.derived());
  }

References Eigen::LLT< MatrixType_, UpLo_ >::compute(), and matrix().

LLT() [4/4]

template<typename MatrixType_ , int UpLo_>

template<typename InputType >

Eigen::LLT< MatrixType_, UpLo_ >::LLT ( EigenBase< InputType > &  matrix )

inlineexplicit

Constructs a LLT factorization from a given matrix.

This overloaded constructor is provided for inplace decomposition when MatrixType is a Eigen::Ref.

See also

LLT(const EigenBase&)

                                             : m_matrix(matrix.derived()), m_isInitialized(false) {
    compute(matrix.derived());
  }

References Eigen::LLT< MatrixType_, UpLo_ >::compute(), and matrix().

Member Function Documentation

_solve_impl()

template<typename MatrixType_ , int UpLo_>

template<typename RhsType , typename DstType >

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

                                                                                {
  _solve_impl_transposed<true>(rhs, dst);
}

_solve_impl_transposed()

template<typename MatrixType_ , int UpLo_>

template<bool Conjugate, typename RhsType , typename DstType >

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

                                                                                           {
  dst = rhs;
 
  matrixL().template conjugateIf<!Conjugate>().solveInPlace(dst);
  matrixU().template conjugateIf<!Conjugate>().solveInPlace(dst);
}

References Eigen::LLT< MatrixType_, UpLo_ >::matrixL(), and Eigen::LLT< MatrixType_, UpLo_ >::matrixU().

adjoint()

template<typename MatrixType_ , int UpLo_>

const LLT& Eigen::LLT< MatrixType_, UpLo_ >::adjoint ( ) const

inline

Returns

the adjoint of *this, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.

This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:

x = decomposition.adjoint().solve(b) 

{ return *this; }

cols()

template<typename MatrixType_ , int UpLo_>

EIGEN_CONSTEXPR Index Eigen::LLT< MatrixType_, UpLo_ >::cols ( ) const

inline

{ return m_matrix.cols(); }

References Eigen::LLT< MatrixType_, UpLo_ >::m_matrix.

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_ , int UpLo_>

template<typename InputType >

LLT<MatrixType, UpLo_>& Eigen::LLT< MatrixType_, UpLo_ >::compute

(

const EigenBase< InputType > &

a

)

Computes / recomputes the Cholesky decomposition A = LL^* = U^*U of matrix

Returns

a reference to *this

Example:

#include <iostream>
#include <Eigen/Dense>
 
int main() {
  Eigen::Matrix2f A, b;
  Eigen::LLT<Eigen::Matrix2f> llt;
  A << 2, -1, -1, 3;
  b << 1, 2, 3, 1;
  std::cout << "Here is the matrix A:\n" << A << std::endl;
  std::cout << "Here is the right hand side b:\n" << b << std::endl;
  std::cout << "Computing LLT decomposition..." << std::endl;
  llt.compute(A);
  std::cout << "The solution is:\n" << llt.solve(b) << std::endl;
  A(1, 1)++;
  std::cout << "The matrix A is now:\n" << A << std::endl;
  std::cout << "Computing LLT decomposition..." << std::endl;
  llt.compute(A);
  std::cout << "The solution is now:\n" << llt.solve(b) << std::endl;
}

Output:

                                                                                     {
  eigen_assert(a.rows() == a.cols());
  const Index size = a.rows();
  m_matrix.resize(size, size);
  if (!internal::is_same_dense(m_matrix, a.derived())) m_matrix = a.derived();
 
  // Compute matrix L1 norm = max abs column sum.
  m_l1_norm = RealScalar(0);
  // TODO move this code to SelfAdjointView
  for (Index col = 0; col < size; ++col) {
    RealScalar abs_col_sum;
    if (UpLo_ == Lower)
      abs_col_sum =
          m_matrix.col(col).tail(size - col).template lpNorm<1>() + m_matrix.row(col).head(col).template lpNorm<1>();
    else
      abs_col_sum =
          m_matrix.col(col).head(col).template lpNorm<1>() + m_matrix.row(col).tail(size - col).template lpNorm<1>();
    if (abs_col_sum > m_l1_norm) m_l1_norm = abs_col_sum;
  }
 
  m_isInitialized = true;
  bool ok = Traits::inplace_decomposition(m_matrix);
  m_info = ok ? Success : NumericalIssue;
 
  return *this;
}

References a, col(), eigen_assert, Eigen::internal::is_same_dense(), Eigen::Lower, Eigen::LLT< MatrixType_, UpLo_ >::m_info, Eigen::LLT< MatrixType_, UpLo_ >::m_isInitialized, Eigen::LLT< MatrixType_, UpLo_ >::m_l1_norm, Eigen::LLT< MatrixType_, UpLo_ >::m_matrix, Eigen::NumericalIssue, Eigen::EigenBase< Derived >::size(), and Eigen::Success.

compute() [2/2]

template<typename MatrixType_ , int UpLo_>

template<typename InputType >

LLT& Eigen::LLT< MatrixType_, UpLo_ >::compute

(

const EigenBase< InputType > &

matrix

)

Referenced by cholesky(), ctms_decompositions(), and Eigen::LLT< MatrixType_, UpLo_ >::LLT().

info()

template<typename MatrixType_ , int UpLo_>

ComputationInfo Eigen::LLT< MatrixType_, UpLo_ >::info ( ) const

inline

Reports whether previous computation was successful.

Returns

Success if computation was successful, NumericalIssue if the matrix.appears not to be positive definite.

                               {
    eigen_assert(m_isInitialized && "LLT is not initialized.");
    return m_info;
  }

References eigen_assert, Eigen::LLT< MatrixType_, UpLo_ >::m_info, and Eigen::LLT< MatrixType_, UpLo_ >::m_isInitialized.

Referenced by cholesky().

matrixL()

template<typename MatrixType_ , int UpLo_>

Traits::MatrixL Eigen::LLT< MatrixType_, UpLo_ >::matrixL ( ) const

inline

Returns

a view of the lower triangular matrix L

                                                {
    eigen_assert(m_isInitialized && "LLT is not initialized.");
    return Traits::getL(m_matrix);
  }

References eigen_assert, Eigen::LLT< MatrixType_, UpLo_ >::m_isInitialized, and Eigen::LLT< MatrixType_, UpLo_ >::m_matrix.

Referenced by __attribute__(), Eigen::LLT< MatrixType_, UpLo_ >::_solve_impl_transposed(), cholesky(), Eigen::GeneralizedSelfAdjointEigenSolver< MatrixType_ >::compute(), main(), Eigen::LLT< MatrixType_, UpLo_ >::reconstructedMatrix(), and Eigen::LLT< MatrixType_, UpLo_ >::solveInPlace().

matrixLLT()

template<typename MatrixType_ , int UpLo_>

const MatrixType& Eigen::LLT< MatrixType_, UpLo_ >::matrixLLT ( ) const

inline

Returns

the LLT decomposition matrix

TODO: document the storage layout

                                             {
    eigen_assert(m_isInitialized && "LLT is not initialized.");
    return m_matrix;
  }

References eigen_assert, Eigen::LLT< MatrixType_, UpLo_ >::m_isInitialized, and Eigen::LLT< MatrixType_, UpLo_ >::m_matrix.

matrixU()

template<typename MatrixType_ , int UpLo_>

Traits::MatrixU Eigen::LLT< MatrixType_, UpLo_ >::matrixU ( ) const

inline

Returns

a view of the upper triangular matrix U

                                                {
    eigen_assert(m_isInitialized && "LLT is not initialized.");
    return Traits::getU(m_matrix);
  }

References eigen_assert, Eigen::LLT< MatrixType_, UpLo_ >::m_isInitialized, and Eigen::LLT< MatrixType_, UpLo_ >::m_matrix.

Referenced by Eigen::LLT< MatrixType_, UpLo_ >::_solve_impl_transposed(), cholesky(), Eigen::GeneralizedSelfAdjointEigenSolver< MatrixType_ >::compute(), and Eigen::LLT< MatrixType_, UpLo_ >::solveInPlace().

rankUpdate() [1/2]

template<typename MatrixType_ , int UpLo_>

template<typename VectorType >

LLT<MatrixType_, UpLo_>& Eigen::LLT< MatrixType_, UpLo_ >::rankUpdate	(	const VectorType &	v,
		const RealScalar &	sigma
	)

Performs a rank one update (or dowdate) of the current decomposition. If A = LL^* before the rank one update, then after it we have LL^* = A + sigma * v v^* where v must be a vector of same dimension.

                                                                                                         {
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(VectorType);
  eigen_assert(v.size() == m_matrix.cols());
  eigen_assert(m_isInitialized);
  if (internal::llt_inplace<typename MatrixType::Scalar, UpLo>::rankUpdate(m_matrix, v, sigma) >= 0)
    m_info = NumericalIssue;
  else
    m_info = Success;
 
  return *this;
}

References eigen_assert, EIGEN_STATIC_ASSERT_VECTOR_ONLY, Eigen::LLT< MatrixType_, UpLo_ >::m_info, Eigen::LLT< MatrixType_, UpLo_ >::m_isInitialized, Eigen::LLT< MatrixType_, UpLo_ >::m_matrix, Eigen::NumericalIssue, calibrate::sigma, Eigen::Success, and v.

rankUpdate() [2/2]

template<typename MatrixType_ , int UpLo_>

template<typename VectorType >

LLT& Eigen::LLT< MatrixType_, UpLo_ >::rankUpdate	(	const VectorType &	vec,
		const RealScalar &	sigma = 1
	)

rcond()

template<typename MatrixType_ , int UpLo_>

RealScalar Eigen::LLT< MatrixType_, UpLo_ >::rcond ( ) const

inline

Returns

an estimate of the reciprocal condition number of the matrix of which *this is the Cholesky decomposition.

                           {
    eigen_assert(m_isInitialized && "LLT is not initialized.");
    eigen_assert(m_info == Success && "LLT failed because matrix appears to be negative");
    return internal::rcond_estimate_helper(m_l1_norm, *this);
  }

References eigen_assert, Eigen::LLT< MatrixType_, UpLo_ >::m_info, Eigen::LLT< MatrixType_, UpLo_ >::m_isInitialized, Eigen::LLT< MatrixType_, UpLo_ >::m_l1_norm, Eigen::internal::rcond_estimate_helper(), and Eigen::Success.

Referenced by cholesky().

reconstructedMatrix()

template<typename MatrixType , int UpLo_>

MatrixType Eigen::LLT< MatrixType, UpLo_ >::reconstructedMatrix

Returns

the matrix represented by the decomposition, i.e., it returns the product: L L^*. This function is provided for debug purpose.

                                                             {
  eigen_assert(m_isInitialized && "LLT is not initialized.");
  return matrixL() * matrixL().adjoint().toDenseMatrix();
}

References eigen_assert, Eigen::LLT< MatrixType_, UpLo_ >::m_isInitialized, and Eigen::LLT< MatrixType_, UpLo_ >::matrixL().

Referenced by cholesky(), and cholesky_cplx().

rows()

template<typename MatrixType_ , int UpLo_>

EIGEN_CONSTEXPR Index Eigen::LLT< MatrixType_, UpLo_ >::rows ( ) const

inline

{ return m_matrix.rows(); }

References Eigen::LLT< MatrixType_, UpLo_ >::m_matrix.

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().

solveInPlace()

template<typename MatrixType , int UpLo_>

template<typename Derived >

void Eigen::LLT< MatrixType, UpLo_ >::solveInPlace

(

const MatrixBase< Derived > &

bAndX

)

const

use x = llt_object.solve(x);

This is the in-place version of solve().

Parameters

bAndX

represents both the right-hand side matrix b and result x.

This version avoids a copy when the right hand side matrix b is not needed anymore.

Warning

The parameter is only marked 'const' to make the C++ compiler accept a temporary expression here. This function will const_cast it, so constness isn't honored here.

See also

LLT::solve(), MatrixBase::llt()

                                                                                {
  eigen_assert(m_isInitialized && "LLT is not initialized.");
  eigen_assert(m_matrix.rows() == bAndX.rows());
  matrixL().solveInPlace(bAndX);
  matrixU().solveInPlace(bAndX);
}

References eigen_assert, Eigen::LLT< MatrixType_, UpLo_ >::m_isInitialized, Eigen::LLT< MatrixType_, UpLo_ >::m_matrix, Eigen::LLT< MatrixType_, UpLo_ >::matrixL(), and Eigen::LLT< MatrixType_, UpLo_ >::matrixU().

Friends And Related Function Documentation

SolverBase< LLT >

template<typename MatrixType_ , int UpLo_>

friend class SolverBase< LLT >

friend

Member Data Documentation

m_info

template<typename MatrixType_ , int UpLo_>

ComputationInfo Eigen::LLT< MatrixType_, UpLo_ >::m_info

protected

Referenced by Eigen::LLT< MatrixType_, UpLo_ >::compute(), Eigen::LLT< MatrixType_, UpLo_ >::info(), Eigen::LLT< MatrixType_, UpLo_ >::rankUpdate(), and Eigen::LLT< MatrixType_, UpLo_ >::rcond().

m_isInitialized

template<typename MatrixType_ , int UpLo_>

bool Eigen::LLT< MatrixType_, UpLo_ >::m_isInitialized

protected

Referenced by Eigen::LLT< MatrixType_, UpLo_ >::compute(), Eigen::LLT< MatrixType_, UpLo_ >::info(), Eigen::LLT< MatrixType_, UpLo_ >::matrixL(), Eigen::LLT< MatrixType_, UpLo_ >::matrixLLT(), Eigen::LLT< MatrixType_, UpLo_ >::matrixU(), Eigen::LLT< MatrixType_, UpLo_ >::rankUpdate(), Eigen::LLT< MatrixType_, UpLo_ >::rcond(), Eigen::LLT< MatrixType_, UpLo_ >::reconstructedMatrix(), and Eigen::LLT< MatrixType_, UpLo_ >::solveInPlace().

m_l1_norm

template<typename MatrixType_ , int UpLo_>

RealScalar Eigen::LLT< MatrixType_, UpLo_ >::m_l1_norm

protected

Referenced by Eigen::LLT< MatrixType_, UpLo_ >::compute(), and Eigen::LLT< MatrixType_, UpLo_ >::rcond().

m_matrix

template<typename MatrixType_ , int UpLo_>

MatrixType Eigen::LLT< MatrixType_, UpLo_ >::m_matrix

protected

Used to compute and store L The strict upper part is not used and even not initialized.

Referenced by Eigen::LLT< MatrixType_, UpLo_ >::cols(), Eigen::LLT< MatrixType_, UpLo_ >::compute(), Eigen::SelfAdjointView< MatrixType_, UpLo >::llt(), Eigen::LLT< MatrixType_, UpLo_ >::matrixL(), Eigen::LLT< MatrixType_, UpLo_ >::matrixLLT(), Eigen::LLT< MatrixType_, UpLo_ >::matrixU(), Eigen::LLT< MatrixType_, UpLo_ >::rankUpdate(), Eigen::LLT< MatrixType_, UpLo_ >::rows(), and Eigen::LLT< MatrixType_, UpLo_ >::solveInPlace().

---

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

• LLT.h