A = L1*U*L2
- L1andL2are unit lower bidiagonal withkandn-k- 1 subdiagonal elements, respectively, wherek=n/2, and
- Uis an upper bidiagonal matrix with nonzeroes in only the main diagonal and first superdiagonal.
- The order of the matrixA;n≥0.
- Arrays containing elements ofA.The arraydlof dimension(contains the subdiagonal elements ofn- 1)A.The arraydof dimensionncontains the diagonal elements ofA.The arrayduof dimension(contains the superdiagonal elements ofn- 1)A.
- Overwritten by the(multipliers that define the matrixn-1)Lfrom theLUfactorization ofA.
- Overwritten by thendiagonal element reciprocals of the upper triangular matrixUfrom the factorization ofA.
- Overwritten by the(elements of the superdiagonal ofn-1)U.
- If, the execution is successful.info= 0If, theinfo=-ii-th parameter had an illegal value.Ifis 0. The factorization has been completed, butinfo=i,uiiUis exactly singular. Division by zero will occur if you use the factorUfor solving a system of linear equations.
- The current implementation of BABE has a potential accuracy issue on very small or large data close to the underflow or overflow threshold respectively. Scale the matrix before applying the solver in the case of such input data.
- Applying the?dttrfbfactorization to non-diagonally dominant systems may lead to an accuracy loss, or false singularity detected due to no pivoting.