f01mef computes the positive definite perturbed matrix
$A+E$ from the factors provided by a previous call to
f01mdf. For a symmetric, possibly indefinite matrix
$A$,
f01mdf finds the Cheng–Higham modified Cholesky factorization
when
${\mathbf{uplo}}=\text{'L'}$. Here
$L$ is a unit lower triangular matrix,
$P$ is a permutation matrix,
$D$ is a symmetric block diagonal matrix (with blocks of order
$1$ or
$2$). The matrix
$E$ is not explicitly formed.
Cheng S H and Higham N J (1998) A modified Cholesky algorithm based on a symmetric indefinite factorization SIAM J. Matrix Anal. Appl. 19(4) 1097–1110
If on entry
${\mathbf{ifail}}=0$ or
$\mathrm{-1}$, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
See
Section 7 in
f01mdf for an indication of the accuracy of the computed factors
$L$,
$U$, and
$D$.
Background information to multithreading can be found in the
Multithreading documentation.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.