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template<typename T>
void syrfs(char *uplo, integer *n, integer *nrhs, T *a, integer *lda, T *af, integer *ldaf, integer *ipiv, T *b, integer *ldb, T *x, integer *ldx, T *ferr, T *berr, T *work, integer *iwork, integer *info)# SYRFS improves the computed solution to a system of linear equations.
Purpose:
SYRFS 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.
- Parameters:
UPLO – [in]
UPLO is CHARACTER*1
= ‘U’: Upper triangle of A is stored;
= ‘L’: Lower triangle of A is stored.N – [in]
N is INTEGER
The order of the matrix A. N >= 0.
NRHS – [in]
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
A – [in]
A is 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 – [in]
LDA is INTEGER
The leading dimension of the array A. LDA >= fla_max(1,N).
AF – [in]
AF is 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 – [in]
LDAF is INTEGER
The leading dimension of the array AF. LDAF >= fla_max(1,N).
IPIV – [in]
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D as determined by SSYTRF.
B – [in]
B is REAL array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB – [in]
LDB is INTEGER
The leading dimension of the array B. LDB >= fla_max(1,N).
X – [inout]
X is REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SSYTRS. On exit, the improved solution matrix X.
LDX – [in]
LDX is INTEGER
The leading dimension of the array X. LDX >= fla_max(1,N).
FERR – [out]
FERR is 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 – [out]
BERR is 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 – [out] WORK is REAL array, dimension (3*N)
IWORK – [out] IWORK is INTEGER array, dimension (N)
INFO – [out]
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value