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OSVR-Core
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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 | MatrixType |
| typedef MatrixType::Scalar | Scalar |
| typedef NumTraits< typename MatrixType::Scalar >::Real | RealScalar |
| typedef MatrixType::Index | Index |
| typedef Matrix< Scalar, RowsAtCompileTime, 1, Options, MaxRowsAtCompileTime, 1 > | TmpMatrixType |
| typedef Transpositions< RowsAtCompileTime, MaxRowsAtCompileTime > | TranspositionType |
| typedef PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime > | PermutationType |
| typedef internal::LDLT_Traits< MatrixType, UpLo > | Traits |
Public Member Functions | |
| LDLT () | |
| Default Constructor. More... | |
| LDLT (Index size) | |
| Default Constructor with memory preallocation. More... | |
| LDLT (const MatrixType &matrix) | |
| Constructor with decomposition. More... | |
| void | setZero () |
| Clear any existing decomposition. More... | |
| Traits::MatrixU | matrixU () const |
| Traits::MatrixL | matrixL () const |
| const TranspositionType & | transpositionsP () const |
| Diagonal< const MatrixType > | vectorD () const |
| bool | isPositive () const |
| bool | isNegative (void) const |
| template<typename Rhs > | |
| const internal::solve_retval< LDLT, Rhs > | solve (const MatrixBase< Rhs > &b) const |
| template<typename Derived > | |
| bool | solveInPlace (MatrixBase< Derived > &bAndX) const |
| LDLT & | compute (const MatrixType &matrix) |
| Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of matrix. | |
| template<typename Derived > | |
| LDLT & | rankUpdate (const MatrixBase< Derived > &w, const RealScalar &alpha=1) |
| const MatrixType & | matrixLDLT () const |
| MatrixType | reconstructedMatrix () const |
| Index | rows () const |
| Index | cols () const |
| ComputationInfo | info () const |
| Reports whether previous computation was successful. More... | |
| template<typename Derived > | |
| LDLT< MatrixType, _UpLo > & | rankUpdate (const MatrixBase< Derived > &w, const typename LDLT< MatrixType, _UpLo >::RealScalar &sigma) |
| Update the LDLT decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T. More... | |
Static Protected Member Functions | |
| static void | check_template_parameters () |
Protected Attributes | |
| MatrixType | m_matrix |
| TranspositionType | m_transpositions |
| TmpMatrixType | m_temporary |
| internal::SignMatrix | m_sign |
| bool | m_isInitialized |
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 \( A \) 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.
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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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Default Constructor with memory preallocation.
Like the default constructor but with preallocation of the internal data according to the specified problem size.
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Constructor with decomposition.
This calculates the decomposition for the input matrix.
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Reports whether previous computation was successful.
Success if computation was succesful, NumericalIssue if the matrix.appears to be negative.
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TODO: document the storage layout
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| LDLT<MatrixType,_UpLo>& Eigen::LDLT< _MatrixType, _UpLo >::rankUpdate | ( | const MatrixBase< Derived > & | w, |
| const typename LDLT< MatrixType, _UpLo >::RealScalar & | 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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Clear any existing decomposition.
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This function also supports in-place solves using the syntax x = decompositionObject.solve(x) .
More precisely, this method solves \( A x = b \) using the decomposition \( A = P^T L D L^* P \) by solving the systems \( P^T y_1 = b \), \( L y_2 = y_1 \), \( D y_3 = y_2 \), \( L^* y_4 = y_3 \) and \( P x = y_4 \) in succession. If the matrix \( A \) is singular, then \( D \) will also be singular (all the other matrices are invertible). In that case, the least-square solution of \( D y_3 = y_2 \) is computed. This does not mean that this function computes the least-square solution of \( A x = b \) is \( A \) is singular.
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1.8.12