F07NRF (ZSYTRF) computes the Bunch–Kaufman factorization of a complex symmetric matrix.
Golub G H and Van Loan C F (1996)
Matrix Computations (3rd Edition) Johns Hopkins University Press, Baltimore
If
UPLO='U', the computed factors
U and
D are the exact factors of a perturbed matrix
A+E, where
cn is a modest linear function of
n, and
ε is the
machine precision.
The elements of
D overwrite the corresponding elements of
A; if
D has
2 by
2 blocks, only the upper or lower triangle is stored, as specified by
UPLO.
The unit diagonal elements of
U or
L and the
2 by
2 unit diagonal blocks are not stored. The remaining elements of
U or
L are stored in the corresponding columns of the array
A, but additional row interchanges must be applied to recover
U or
L explicitly (this is seldom necessary). If
IPIVi=i, for
i=1,2,…,n, then
U or
L is stored explicitly (except for its unit diagonal elements which are equal to
1).
A call to F07NRF (ZSYTRF) may be followed by calls to the routines:
The real analogue of this routine is
F07MDF (DSYTRF).
This example computes the Bunch–Kaufman factorization of the matrix
A, where