template<typename _MatrixType, int _UpLo>
class Eigen::LDLT< _MatrixType, _UpLo >
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.
- See Also
- MatrixBase::ldlt(), class LLT
|const internal::solve_retval<LDLT, Rhs> solve
||const MatrixBase< Rhs > &
- a solution x of 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
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.
- See Also