dsyrfs(3)

NAME

DSYRFS - improve the computed solution to a system of lin

ear equations when the coefficient matrix is symmetric indefi

nite, and provides error bounds and backward error estimates 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 lin

ear equations when the coefficient matrix is symmetric indefi

nite, 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 lead

ing N-by-N upper triangular part of A contains the upper triangu

lar 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 ref

erenced.

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 struc

ture 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 solu

tion 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.

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).

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 i-th argument had an ille

gal value

PARAMETERS

ITMAX is the maximum number of steps of iterative refine

ment.

LAPACK version 3.0 15 June 2000

DSYRFS(3)