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ZSYRFS(l)) ZSYRFS(l)NAMEZSYRFS - 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 solutionSYNOPSISSUBROUTINE ZSYRFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO ) CHARACTER UPLO INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS INTEGER IPIV( * ) DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * ) COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ), X( LDX, * )PURPOSEZSYRFS 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.ARGUMENTSUPLO (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) COMPLEX*16 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) 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**T or A = L*D*L**T as computed by ZSYTRF. 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 ZSYTRF. B (input) COMPLEX*16 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) COMPLEX*16 array, dimension (LDX,NRHS) On entry, the solution matrix X, as computed by ZSYTRS. 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 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 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) COMPLEX*16 array, dimension (2*N) RWORK (workspace) DOUBLE PRECISION array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO =, the i-th argument had an illegal value-iPARAMETERSITMAX is the maximum number of steps of iterative refinement.LAPACK version 3.015 June 2000 ZSYRFS(l)

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