Public Member Functions
SimplicialLDLT< _MatrixType, _UpLo > Class Template Reference

A direct sparse LDLT Cholesky factorizations without square root. More...

#include <SimplicialCholesky.h>

+ Inheritance diagram for SimplicialLDLT< _MatrixType, _UpLo >:

List of all members.

Public Member Functions

void analyzePattern (const MatrixType &a)
SimplicialLDLTcompute (const MatrixType &matrix)
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
SimplicialLDLT< _MatrixType,
_UpLo > & 
setShift (const RealScalar &offset, const RealScalar &scale=1)
 SimplicialLDLT ()
 SimplicialLDLT (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
const VectorType vectorD () const

Detailed Description

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

A direct sparse LDLT Cholesky factorizations without square root.

This class provides a LDL^T Cholesky factorizations without square root 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 SimplicialLLT

Constructor & Destructor Documentation

SimplicialLDLT ( ) [inline]

Default constructor

SimplicialLDLT ( const MatrixType &  matrix) [inline]

Constructs and performs the LLT factorization of matrix


Member Function Documentation

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()
SimplicialLDLT& compute ( const MatrixType &  matrix) [inline]

Computes the sparse Cholesky decomposition of matrix

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

Scalar determinant ( ) const [inline]
Returns:
the determinant of the underlying matrix from the current factorization
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< SimplicialLDLT< _MatrixType, _UpLo > >.

ComputationInfo info ( ) const [inline, inherited]

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]
Returns:
an expression of the factor L
const MatrixU matrixU ( ) const [inline]
Returns:
an expression of the factor U (= L^*)
const PermutationMatrix<Dynamic,Dynamic,Index>& permutationP ( ) const [inline, inherited]
Returns:
the permutation P
See also:
permutationPinv()
const PermutationMatrix<Dynamic,Dynamic,Index>& permutationPinv ( ) const [inline, inherited]
Returns:
the inverse P^-1 of the permutation P
See also:
permutationP()
SimplicialLDLT< _MatrixType, _UpLo > & setShift ( const RealScalar &  offset,
const RealScalar &  scale = 1 
) [inline, inherited]

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 [inline, inherited]
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 [inline, inherited]
Returns:
the solution x of $ A x = b $ using the current decomposition of A.
See also:
compute()

References EigenBase< Derived >::derived(), and SparseMatrixBase< Derived >::rows().

const VectorType vectorD ( ) const [inline]
Returns:
a vector expression of the diagonal D

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