Public Types | Public Member Functions | Protected Member Functions | Protected Attributes
SimplicialLLT< _MatrixType, _UpLo > Class Template Reference

A direct sparse LLT Cholesky factorizations. More...

#include <SimplicialCholesky.h>

+ Inheritance diagram for SimplicialLLT< _MatrixType, _UpLo >:

List of all members.

Public Types

enum  
enum  { UpLo }
typedef SimplicialCholeskyBase
< SimplicialLLT
Base
typedef SparseMatrix< Scalar,
ColMajor, Index
CholMatrixType
typedef MatrixType::Index Index
typedef Traits::MatrixL MatrixL
typedef _MatrixType MatrixType
typedef Traits::MatrixU MatrixU
typedef MatrixType::RealScalar RealScalar
typedef MatrixType::Scalar Scalar
typedef internal::traits
< SimplicialLLT
Traits
typedef Matrix< Scalar,
Dynamic, 1 > 
VectorType

Public Member Functions

void analyzePattern (const MatrixType &a)
Index cols () const
SimplicialLLTcompute (const MatrixType &matrix)
SimplicialLLT< _MatrixType,
_UpLo > & 
derived ()
const SimplicialLLT
< _MatrixType, _UpLo > & 
derived () const
Scalar determinant () const
void factorize (const MatrixType &a)
ComputationInfo info () const
 Reports whether previous computation was successful.
const MatrixL matrixL () const
const MatrixU matrixU () const
const PermutationMatrix
< Dynamic, Dynamic, Index > & 
permutationP () const
const PermutationMatrix
< Dynamic, Dynamic, Index > & 
permutationPinv () const
Index rows () const
SimplicialLLT< _MatrixType,
_UpLo > & 
setShift (const RealScalar &offset, const RealScalar &scale=1)
 SimplicialLLT ()
 SimplicialLLT (const MatrixType &matrix)
const internal::solve_retval
< SimplicialCholeskyBase, Rhs > 
solve (const MatrixBase< Rhs > &b) const
const
internal::sparse_solve_retval
< SimplicialCholeskyBase, Rhs > 
solve (const SparseMatrixBase< Rhs > &b) const

Protected Member Functions

void analyzePattern (const MatrixType &a, bool doLDLT)
void analyzePattern_preordered (const CholMatrixType &a, bool doLDLT)
void factorize_preordered (const CholMatrixType &a)
void ordering (const MatrixType &a, CholMatrixType &ap)

Protected Attributes

bool m_analysisIsOk
VectorType m_diag
bool m_factorizationIsOk
ComputationInfo m_info
bool m_isInitialized
CholMatrixType m_matrix
VectorXi m_nonZerosPerCol
PermutationMatrix< Dynamic,
Dynamic, Index
m_P
VectorXi m_parent
PermutationMatrix< Dynamic,
Dynamic, Index
m_Pinv
RealScalar m_shiftOffset
RealScalar m_shiftScale

Detailed Description

template<typename _MatrixType, int _UpLo>
class Eigen::SimplicialLLT< _MatrixType, _UpLo >

A direct sparse LLT Cholesky factorizations.

This class provides a LL^T Cholesky factorizations of sparse matrices that are selfadjoint and positive definite. 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:
_MatrixTypethe type of the sparse matrix A, it must be a SparseMatrix<>
_UpLothe triangular part that will be used for the computations. It can be Lower or Upper. Default is Lower.
See also:
class SimplicialLDLT

Member Typedef Documentation

typedef MatrixType::Index Index
typedef Traits::MatrixL MatrixL
typedef _MatrixType MatrixType
typedef Traits::MatrixU MatrixU
typedef MatrixType::RealScalar RealScalar
typedef MatrixType::Scalar Scalar
typedef internal::traits<SimplicialLLT> Traits

Member Enumeration Documentation

anonymous enum
inherited
anonymous enum
Enumerator:
UpLo 

Constructor & Destructor Documentation

SimplicialLLT ( )
inline

Default constructor

SimplicialLLT ( const MatrixType matrix)
inline

Constructs and performs the LLT factorization of matrix


Member Function Documentation

void analyzePattern ( const MatrixType a,
bool  doLDLT 
)
inlineprotectedinherited
void 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()

References SimplicialCholeskyBase< Derived >::analyzePattern().

void analyzePattern_preordered ( const CholMatrixType a,
bool  doLDLT 
)
protectedinherited
Index cols ( void  ) const
inlineinherited
SimplicialLLT& compute ( const MatrixType matrix)
inline

Computes the sparse Cholesky decomposition of matrix

Reimplemented from SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo > >.

SimplicialLLT< _MatrixType, _UpLo > & derived ( )
inlineinherited
const SimplicialLLT< _MatrixType, _UpLo > & derived ( ) const
inlineinherited
Scalar determinant ( ) const
inline
Returns:
the determinant of the underlying matrix from the current factorization

References abs2(), SparseMatrix< _Scalar, _Options, _Index >::diagonal(), and SimplicialCholeskyBase< Derived >::m_matrix.

void 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()

Reimplemented from SimplicialCholeskyBase< SimplicialLLT< _MatrixType, _UpLo > >.

void factorize_preordered ( const CholMatrixType a)
protectedinherited
ComputationInfo info ( ) const
inlineinherited

Reports whether previous computation was successful.

Returns:
Success if computation was succesful, NumericalIssue if the matrix.appears to be negative.
const MatrixL matrixL ( ) const
inline
const MatrixU matrixU ( ) const
inline
void ordering ( const MatrixType a,
CholMatrixType ap 
)
protectedinherited
const PermutationMatrix<Dynamic,Dynamic,Index>& permutationP ( ) const
inlineinherited
Returns:
the permutation P
See also:
permutationPinv()
const PermutationMatrix<Dynamic,Dynamic,Index>& permutationPinv ( ) const
inlineinherited
Returns:
the inverse P^-1 of the permutation P
See also:
permutationP()
Index rows ( void  ) const
inlineinherited
SimplicialLLT< _MatrixType, _UpLo > & setShift ( const RealScalar offset,
const RealScalar scale = 1 
)
inlineinherited

Sets the shift parameters that will be used to adjust the diagonal coefficients during the numerical factorization.

During the numerical factorization, the diagonal coefficients are transformed by the following linear model:
d_ii = offset + scale * d_ii

The default is the identity transformation with offset=0, and scale=1.

Returns:
a reference to *this.
const internal::solve_retval<SimplicialCholeskyBase, Rhs> solve ( const MatrixBase< Rhs > &  b) const
inlineinherited
Returns:
the solution x of $ A x = b $ using the current decomposition of A.
See also:
compute()
const internal::sparse_solve_retval<SimplicialCholeskyBase, Rhs> solve ( const SparseMatrixBase< Rhs > &  b) const
inlineinherited
Returns:
the solution x of $ A x = b $ using the current decomposition of A.
See also:
compute()

Member Data Documentation

bool m_analysisIsOk
protectedinherited
VectorType m_diag
protectedinherited
bool m_factorizationIsOk
protectedinherited
ComputationInfo m_info
mutableprotectedinherited
bool m_isInitialized
protectedinherited
CholMatrixType m_matrix
protectedinherited
VectorXi m_nonZerosPerCol
protectedinherited
PermutationMatrix<Dynamic,Dynamic,Index> m_P
protectedinherited
VectorXi m_parent
protectedinherited
PermutationMatrix<Dynamic,Dynamic,Index> m_Pinv
protectedinherited
RealScalar m_shiftOffset
protectedinherited
RealScalar m_shiftScale
protectedinherited

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