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Eigen
3.3.4
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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.
This class supports the inplace decomposition mechanism.
Public Types | |
typedef Eigen::Index | Index |
Public Member Functions | |
const LDLT & | adjoint () const |
template<typename InputType > | |
LDLT< MatrixType, _UpLo > & | compute (const EigenBase< InputType > &a) |
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... | |
template<typename InputType > | |
LDLT (const EigenBase< InputType > &matrix) | |
Constructor with decomposition. More... | |
template<typename InputType > | |
LDLT (EigenBase< InputType > &matrix) | |
Constructs a LDLT factorization from a given matrix. More... | |
Traits::MatrixL | matrixL () const |
const MatrixType & | matrixLDLT () const |
Traits::MatrixU | matrixU () const |
template<typename Derived > | |
LDLT< MatrixType, _UpLo > & | rankUpdate (const MatrixBase< Derived > &w, const typename LDLT< MatrixType, _UpLo >::RealScalar &sigma) |
RealScalar | rcond () const |
MatrixType | reconstructedMatrix () const |
void | setZero () |
template<typename Rhs > | |
const Solve< LDLT, Rhs > | solve (const MatrixBase< Rhs > &b) const |
const TranspositionType & | transpositionsP () const |
Diagonal< const MatrixType > | vectorD () const |
typedef Eigen::Index Eigen::LDLT< _MatrixType, _UpLo >::Index |
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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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Constructs a LDLT factorization from a given matrix.
This overloaded constructor is provided for inplace decomposition when MatrixType
is a Eigen::Ref.
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*this
, that is, a const reference to the decomposition itself as the underlying matrix is self-adjoint.This method is provided for compatibility with other matrix decompositions, thus enabling generic code such as:
LDLT<MatrixType,_UpLo>& Eigen::LDLT< _MatrixType, _UpLo >::compute | ( | const EigenBase< InputType > & | a | ) |
Compute / recompute the LDLT decomposition A = L D L^* = U^* D U of 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. |
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*this
is the LDLT decomposition. 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)
.
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:
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.
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.
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