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# zherfs

```
NAME
ZHERFS - improve the computed solution to a system of linear
equations when the coefficient matrix is Hermitian indefin-
ite, and provides error bounds and backward error estimates
for the solution

SYNOPSIS
SUBROUTINE ZHERFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B,
LDB, X, LDX, FERR, BERR, WORK, RWORK,
INFO )

CHARACTER      UPLO

INTEGER        INFO, LDA, LDAF, LDB, LDX, N, NRHS

INTEGER        IPIV( * )

DOUBLE         PRECISION BERR( * ), FERR( * ), RWORK( *
)

COMPLEX*16     A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
WORK( * ), X( LDX, * )

PURPOSE
ZHERFS improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian indefin-
ite, and provides error bounds and backward error estimates
for the solution.

ARGUMENTS
UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

N       (input) INTEGER
The order of the matrix A.  N >= 0.

NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of
columns of the matrices B and X.  NRHS >= 0.

A       (input) COMPLEX*16 array, dimension (LDA,N)
The Hermitian matrix A.  If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper
triangular part of the matrix A, and the strictly
lower triangular part of A is not referenced.  If
UPLO = 'L', the leading N-by-N lower triangular part
of A contains the lower triangular part of the
matrix A, and the strictly upper triangular part of
A is not referenced.

LDA     (input) INTEGER
The leading dimension of the array A.  LDA >=
max(1,N).

AF      (input) COMPLEX*16 array, dimension (LDAF,N)
The factored form of the matrix A.  AF contains the
block diagonal matrix D and the multipliers used to
obtain the factor U or L from the factorization A =
U*D*U**H or A = L*D*L**H as computed by ZHETRF.

LDAF    (input) INTEGER
The leading dimension of the array AF.  LDAF >=
max(1,N).

IPIV    (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure
of D as determined by ZHETRF.

B       (input) COMPLEX*16 array, dimension (LDB,NRHS)
The right hand side matrix B.

LDB     (input) INTEGER
The leading dimension of the array B.  LDB >=
max(1,N).

X       (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by
ZHETRS.  On exit, the improved solution matrix X.

LDX     (input) INTEGER
The leading dimension of the array X.  LDX >=
max(1,N).

FERR    (output) DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bounds for each solution
vector X(j) (the j-th column of the solution matrix
X).  If XTRUE is the true solution, FERR(j) bounds
the magnitude of the largest entry in (X(j) - XTRUE)
divided by the magnitude of the largest entry in
X(j).  The quality of the error bound depends on the
quality of the estimate of norm(inv(A)) computed in
the code; if the estimate of norm(inv(A)) is accu-
rate, the error bound is guaranteed.

BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
The componentwise relative backward error of each
solution vector X(j) (i.e., the smallest relative
change in any entry of A or B that makes X(j) an
exact solution).

WORK    (workspace) COMPLEX*16 array, dimension (2*N)

RWORK   (workspace) DOUBLE PRECISION array, dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value

PARAMETERS
ITMAX is the maximum number of steps of iterative refine-
ment.
```