.TH ZHERFS 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) "
.SH NAME
ZHERFS - the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and provides error bounds and backward error estimates for the solution
.SH SYNOPSIS
.TP 19
SUBROUTINE ZHERFS(
UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB,
X, LDX, FERR, BERR, WORK, RWORK, INFO )
.TP 19
.ti +4
CHARACTER
UPLO
.TP 19
.ti +4
INTEGER
INFO, LDA, LDAF, LDB, LDX, N, NRHS
.TP 19
.ti +4
INTEGER
IPIV( * )
.TP 19
.ti +4
DOUBLE
PRECISION BERR( * ), FERR( * ), RWORK( * )
.TP 19
.ti +4
COMPLEX*16
A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
WORK( * ), X( LDX, * )
.SH PURPOSE
ZHERFS improves the computed solution to a system of linear
equations when the coefficient matrix is Hermitian indefinite, and
provides error bounds and backward error estimates for the solution.
.SH ARGUMENTS
.TP 8
UPLO (input) CHARACTER*1
= \(aqU\(aq: Upper triangle of A is stored;
.br
= \(aqL\(aq: Lower triangle of A is stored.
.TP 8
N (input) INTEGER
The order of the matrix A. N >= 0.
.TP 8
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
.TP 8
A (input) COMPLEX*16 array, dimension (LDA,N)
The Hermitian matrix A. If UPLO = \(aqU\(aq, 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 = \(aqL\(aq, 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.
.TP 8
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
.TP 8
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.
.TP 8
LDAF (input) INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
.TP 8
IPIV (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZHETRF.
.TP 8
B (input) COMPLEX*16 array, dimension (LDB,NRHS)
The right hand side matrix B.
.TP 8
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
.TP 8
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.
.TP 8
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
.TP 8
FERR (output) DOUBLE PRECISION array, dimension (NRHS)
The estimated forward error bound for each solution vector
X(j) (the j-th column of the solution matrix X).
If XTRUE is the true solution corresponding to X(j), FERR(j)
is an estimated upper bound for the magnitude of the largest
element in (X(j) - XTRUE) divided by the magnitude of the
largest element in X(j). The estimate is as reliable as
the estimate for RCOND, and is almost always a slight
overestimate of the true error.
.TP 8
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 element of A or B that makes X(j) an exact solution).
.TP 8
WORK (workspace) COMPLEX*16 array, dimension (2*N)
.TP 8
RWORK (workspace) DOUBLE PRECISION array, dimension (N)
.TP 8
INFO (output) INTEGER
= 0: successful exit
.br
< 0: if INFO = -i, the i-th argument had an illegal value
.SH PARAMETERS
ITMAX is the maximum number of steps of iterative refinement.