Default Constructor.

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

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()

Constructor with decomposition.

This calculates the decomposition for the input matrix.

See also

LDLT(Index size)

Constructs a LDLT factorization from a given matrix.

This overloaded constructor is provided for inplace decomposition when MatrixType is a Eigen::Ref.

See also

LDLT(const EigenBase&)

Returns

the adjoint of *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:

x = decomposition.adjoint().solve(b) 

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

Reports whether previous computation was successful.

Returns

Success if computation was successful, NumericalIssue if the factorization failed because of a zero pivot.

Returns

true if the matrix is negative (semidefinite)

Returns

true if the matrix is positive (semidefinite)

Returns

a view of the lower triangular matrix L

Returns

the internal LDLT decomposition matrix

TODO: document the storage layout

Returns

a view of the upper triangular matrix U

Update the LDLT decomposition: given A = L D L^T, efficiently compute the decomposition of A + sigma w w^T.

Parameters

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.

See also

setZero()

Returns

an estimate of the reciprocal condition number of the matrix of which *this is the LDLT decomposition.

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.

Clear any existing decomposition

See also

rankUpdate(w,sigma)

Returns

a solution x of \( A x = b \) using the current decomposition of A.

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:

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.

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 \( A x = b \) if \( A \) is singular.

See also

MatrixBase::ldlt(), SelfAdjointView::ldlt()

Returns

the permutation matrix P as a transposition sequence.

Returns

the coefficients of the diagonal matrix D