Robust Cholesky decomposition of a matrix with pivoting. More...
#include <LDLT.h>
Public Types | |
enum | { RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, Options = MatrixType::Options & ~RowMajorBit, MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime, MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, UpLo = _UpLo } |
typedef MatrixType::Index | Index |
typedef _MatrixType | MatrixType |
typedef PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime > | PermutationType |
typedef NumTraits< typename MatrixType::Scalar >::Real | RealScalar |
typedef MatrixType::Scalar | Scalar |
typedef Matrix< Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1 > | TmpMatrixType |
typedef internal::LDLT_Traits< MatrixType, UpLo > | Traits |
typedef Transpositions< RowsAtCompileTime, MaxRowsAtCompileTime > | TranspositionType |
Public Member Functions | |
Index | cols () const |
LDLT & | compute (const MatrixType &matrix) |
ComputationInfo | info () const |
Reports whether previous computation was successful. More... | |
bool | isNegative (void) const |
bool | isPositive () const |
LDLT () | |
Default Constructor. More... | |
LDLT (Index size) | |
Default Constructor with memory preallocation. More... | |
LDLT (const MatrixType &matrix) | |
Constructor with decomposition. More... | |
Traits::MatrixL | matrixL () const |
const MatrixType & | matrixLDLT () const |
Traits::MatrixU | matrixU () const |
template<typename Derived > | |
LDLT & | rankUpdate (const MatrixBase< Derived > &w, const RealScalar &alpha=1) |
template<typename Derived > | |
LDLT< MatrixType, _UpLo > & | rankUpdate (const MatrixBase< Derived > &w, const typename NumTraits< typename MatrixType::Scalar >::Real &sigma) |
MatrixType | reconstructedMatrix () const |
Index | rows () const |
void | setZero () |
template<typename Rhs > | |
const internal::solve_retval< LDLT, Rhs > | solve (const MatrixBase< Rhs > &b) const |
template<typename Derived > | |
bool | solveInPlace (MatrixBase< Derived > &bAndX) const |
const TranspositionType & | transpositionsP () const |
Diagonal< const MatrixType > | vectorD () const |
Protected Attributes | |
bool | m_isInitialized |
MatrixType | m_matrix |
int | m_sign |
TmpMatrixType | m_temporary |
TranspositionType | m_transpositions |
Robust Cholesky decomposition of a matrix with pivoting.
MatrixType | the type of the matrix of which to compute the LDL^T Cholesky decomposition |
UpLo | the triangular part that will be used for the decompositon: Lower (default) or Upper. The other triangular part won't be read. |
Perform a robust Cholesky decomposition of a positive semidefinite or negative semidefinite matrix such that , 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.
typedef MatrixType::Index Eigen::LDLT< _MatrixType, _UpLo >::Index |
typedef _MatrixType Eigen::LDLT< _MatrixType, _UpLo >::MatrixType |
typedef PermutationMatrix<RowsAtCompileTime, MaxRowsAtCompileTime> Eigen::LDLT< _MatrixType, _UpLo >::PermutationType |
typedef NumTraits<typename MatrixType::Scalar>::Real Eigen::LDLT< _MatrixType, _UpLo >::RealScalar |
typedef MatrixType::Scalar Eigen::LDLT< _MatrixType, _UpLo >::Scalar |
typedef Matrix<Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1> Eigen::LDLT< _MatrixType, _UpLo >::TmpMatrixType |
typedef internal::LDLT_Traits<MatrixType,UpLo> Eigen::LDLT< _MatrixType, _UpLo >::Traits |
typedef Transpositions<RowsAtCompileTime, MaxRowsAtCompileTime> Eigen::LDLT< _MatrixType, _UpLo >::TranspositionType |
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Default Constructor.
The default constructor is useful in cases in which the user intends to perform decompositions via LDLT::compute(const MatrixType&).
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Constructor with decomposition.
This calculates the decomposition for the input matrix.
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LDLT< MatrixType, _UpLo > & Eigen::LDLT< MatrixType, _UpLo >::compute | ( | const MatrixType & | a | ) |
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LDLT& Eigen::LDLT< _MatrixType, _UpLo >::rankUpdate | ( | const MatrixBase< Derived > & | w, |
const RealScalar & | alpha = 1 |
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LDLT<MatrixType,_UpLo>& Eigen::LDLT< _MatrixType, _UpLo >::rankUpdate | ( | const MatrixBase< Derived > & | w, |
const typename NumTraits< typename MatrixType::Scalar >::Real & | sigma | ||
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Update the LDLT decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T.
w | a vector to be incorporated into the decomposition. |
sigma | a scalar, +1 for updates and -1 for "downdates," which correspond to removing previously-added column vectors. Optional; default value is +1. |
MatrixType Eigen::LDLT< MatrixType, _UpLo >::reconstructedMatrix | ( | ) | const |
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This function also supports in-place solves using the syntax x = decompositionObject.solve(x)
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More precisely, this method solves using the decomposition by solving the systems , , , and in succession. If the matrix is singular, then will also be singular (all the other matrices are invertible). In that case, the least-square solution of is computed. This does not mean that this function computes the least-square solution of is is singular.
bool Eigen::LDLT< MatrixType, _UpLo >::solveInPlace | ( | MatrixBase< Derived > & | bAndX | ) | const |
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