Eigen::SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ > Class Template Reference

#include <Eigen/src/SparseCholesky/SimplicialCholesky.h>

Detailed Description

template<typename MatrixType_, int UpLo_, typename Ordering_>
class Eigen::SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ >

A direct sparse LDLT Cholesky factorizations without square root, for symmetric non-hermitian matrices.

This class provides a LDL^T Cholesky factorizations without square root of sparse matrices that are symmetric but not hermitian. For real matrices, this is equivalent to the regular LDLT factorization. The factorization allows for solving A.X = B where X and B can be either dense or sparse.

In order to reduce the fill-in, a symmetric permutation P is applied prior to the factorization such that the factorized matrix is P A P^-1.

Template Parameters

MatrixType_	the type of the sparse matrix A, it must be a SparseMatrix<>
UpLo_	the triangular part that will be used for the computations. It can be Lower or Upper. Default is Lower.
Ordering_	The ordering method to use, either AMDOrdering<> or NaturalOrdering<>. Default is AMDOrdering<>

This class follows the sparse solver concept .

See also

class SimplicialNonHermitianLLT, SimplicialLDLT, class AMDOrdering, class NaturalOrdering

Inheritance diagram for Eigen::SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ >:

Public Member Functions
void	analyzePattern (const MatrixType &a)
SimplicialNonHermitianLDLT &	compute (const MatrixType &matrix)
Scalar	determinant () const
void	factorize (const MatrixType &a)
const MatrixL	matrixL () const
const MatrixU	matrixU () const
	SimplicialNonHermitianLDLT ()
	SimplicialNonHermitianLDLT (const MatrixType &matrix)
const VectorType	vectorD () const
Public Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ > >
ComputationInfo	info () const
	Reports whether previous computation was successful.
const PermutationMatrix< Dynamic, Dynamic, StorageIndex > &	permutationP () const
const PermutationMatrix< Dynamic, Dynamic, StorageIndex > &	permutationPinv () const
SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ > &	setShift (const DiagonalScalar &offset, const DiagonalScalar &scale=1)
	SimplicialCholeskyBase ()
Public Member Functions inherited from Eigen::SparseSolverBase< SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ > >
const Solve< SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ >, Rhs >	solve (const MatrixBase< Rhs > &b) const
const Solve< SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ >, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const
	SparseSolverBase ()

Additional Inherited Members
Protected Member Functions inherited from Eigen::SimplicialCholeskyBase< SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ > >
void	compute (const MatrixType &matrix)

Constructor & Destructor Documentation

SimplicialNonHermitianLDLT() [1/2]

template<typename MatrixType_, int UpLo_, typename Ordering_>

Eigen::SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ >::SimplicialNonHermitianLDLT ( )

inline

Default constructor

SimplicialNonHermitianLDLT() [2/2]

template<typename MatrixType_, int UpLo_, typename Ordering_>

Eigen::SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ >::SimplicialNonHermitianLDLT ( const MatrixType & matrix )

inlineexplicit

Constructs and performs the LLT factorization of matrix

Member Function Documentation

analyzePattern()

template<typename MatrixType_, int UpLo_, typename Ordering_>

void Eigen::SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ >::analyzePattern ( const MatrixType & a )

inline

Performs a symbolic decomposition on the sparcity of matrix.

This function is particularly useful when solving for several problems having the same structure.

See also

factorize()

compute()

template<typename MatrixType_, int UpLo_, typename Ordering_>

SimplicialNonHermitianLDLT & Eigen::SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ >::compute ( const MatrixType & matrix )

inline

Computes the sparse Cholesky decomposition of matrix

determinant()

template<typename MatrixType_, int UpLo_, typename Ordering_>

Scalar Eigen::SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ >::determinant ( ) const

inline

Returns

the determinant of the underlying matrix from the current factorization

factorize()

template<typename MatrixType_, int UpLo_, typename Ordering_>

void Eigen::SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ >::factorize ( const MatrixType & a )

inline

Performs a numeric decomposition of matrix

The given matrix must has the same sparcity than the matrix on which the symbolic decomposition has been performed.

See also

analyzePattern()

matrixL()

template<typename MatrixType_, int UpLo_, typename Ordering_>

const MatrixL Eigen::SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ >::matrixL ( ) const

inline

Returns

an expression of the factor L

matrixU()

template<typename MatrixType_, int UpLo_, typename Ordering_>

const MatrixU Eigen::SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ >::matrixU ( ) const

inline

Returns

an expression of the factor U (= L^*)

vectorD()

template<typename MatrixType_, int UpLo_, typename Ordering_>

const VectorType Eigen::SimplicialNonHermitianLDLT< MatrixType_, UpLo_, Ordering_ >::vectorD ( ) const

inline

Returns

a vector expression of the diagonal D

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

• /usr/local/google/home/cantonios/dev/eigen/Eigen/src/SparseCholesky/SimplicialCholesky.h