SYNOPSIS
- SUBROUTINE SSYRFS(
- 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( * )
- REAL A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
PURPOSE
SSYRFS 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) REAL array, dimension (LDA,N)
- The symmetric 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) REAL 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 SSYTRF.
- 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 SSYTRF.
- B (input) REAL 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) REAL array, dimension (LDX,NRHS)
- On entry, the solution matrix X, as computed by SSYTRS. On exit, the improved solution matrix X.
- LDX (input) INTEGER
- The leading dimension of the array X. LDX >= max(1,N).
- FERR (output) REAL 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.
- BERR (output) REAL 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) REAL 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 illegal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refinement.