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

Robust Cholesky decomposition of a matrix with pivoting. More...

List of all members.

Public Member Functions

LDLTcompute (const MatrixType &matrix)
bool isNegative (void) const
bool isPositive (void) const
 LDLT ()
 Default Constructor.
 LDLT (Index size)
 Default Constructor with memory preallocation.
Traits::MatrixL matrixL () const
const MatrixType & matrixLDLT () const
Traits::MatrixU matrixU () const
MatrixType reconstructedMatrix () const
template<typename Rhs >
const internal::solve_retval
< LDLT, Rhs > 
solve (const MatrixBase< Rhs > &b) const
const TranspositionTypetranspositionsP () const
Diagonal< const MatrixType > vectorD (void) const

Detailed Description

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

Robust Cholesky decomposition of a matrix with pivoting.

Parameters:
MatrixTypethe type of the matrix of which to compute the LDL^T Cholesky decomposition

Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite matrix $ A $ such that $ A = P^TLDL^*P $, where P is a permutation matrix, L is lower triangular with a unit diagonal and D is a diagonal matrix.

The decomposition uses pivoting to ensure stability, so that L will have zeros in the bottom right rank(A) - n submatrix. Avoiding the square root on D also stabilizes the computation.

Remember that Cholesky decompositions are not rank-revealing. Also, do not use a Cholesky decomposition to determine whether a system of equations has a solution.

See also:
MatrixBase::ldlt(), class LLT

Constructor & Destructor Documentation

LDLT ( ) [inline]

Default Constructor.

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

LDLT ( Index  size) [inline]

Default Constructor with memory preallocation.

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

See also:
LDLT()

Member Function Documentation

LDLT< MatrixType, _UpLo > & compute ( const MatrixType &  a)

Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of matrix

bool isNegative ( void  ) const [inline]
Returns:
true if the matrix is negative (semidefinite)
bool isPositive ( void  ) const [inline]
Returns:
true if the matrix is positive (semidefinite)
Traits::MatrixL matrixL ( void  ) const [inline]
Returns:
a view of the lower triangular matrix L
const MatrixType& matrixLDLT ( ) const [inline]
Returns:
the internal LDLT decomposition matrix

TODO: document the storage layout

Traits::MatrixU matrixU ( ) const [inline]
Returns:
a view of the upper triangular matrix U
MatrixType reconstructedMatrix ( ) const
Returns:
the matrix represented by the decomposition, i.e., it returns the product: P^T L D L^* P. This function is provided for debug purpose.
const internal::solve_retval<LDLT, Rhs> solve ( const MatrixBase< Rhs > &  b) const [inline]
Returns:
a solution x of $ A x = b $ using the current decomposition of A.

This method just tries to find as good a solution as possible. If you want to check whether a solution exists or if it is accurate, just call this function to get a result and then compute the error of this result, or use MatrixBase::isApprox() directly, for instance like this:

 bool a_solution_exists = (A*result).isApprox(b, precision); 

This method avoids dividing by zero, so that the non-existence of a solution doesn't by itself mean that you'll get inf or nan values.

See also:
solveInPlace(), MatrixBase::ldlt()
const TranspositionType& transpositionsP ( ) const [inline]
Returns:
the permutation matrix P as a transposition sequence.
Diagonal<const MatrixType> vectorD ( void  ) const [inline]
Returns:
the coefficients of the diagonal matrix D

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