
DSYRFS(l) ) DSYRFS(l)
NAME
DSYRFS  improve the computed solution to a system of linear equations when the coeffi
cient matrix is symmetric indefinite, and provides error bounds and backward error esti
mates for the solution
SYNOPSIS
SUBROUTINE DSYRFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR,
WORK, IWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
INTEGER IPIV( * ), IWORK( * )
DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ), FERR( *
), WORK( * ), X( LDX, * )
PURPOSE
DSYRFS improves the computed solution to a system of linear equations when the coefficient
matrix is symmetric indefinite, 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) DOUBLE PRECISION array, dimension (LDA,N)
The symmetric matrix A. If UPLO = 'U', the leading NbyN 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 NbyN 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) DOUBLE PRECISION 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**T or A = L*D*L**T as computed by DSYTRF.
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 DSYTRF.
B (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by DSYTRS. 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 bound for each solution vector X(j) (the jth 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 esti
mate is as reliable as the estimate for RCOND, and is almost always a slight over
estimate of the true error.
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 solu
tion).
WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refinement.
LAPACK version 3.0 15 June 2000 DSYRFS(l) 
