SRC/zsyrfs.f(3)

💅 SRC/zsyrfs.f(3) 💅

Manual: Library Functions Manual — okay so this is the whole entry for SRC/zsyrfs.f, and it’s literally all about the zsyrfs subroutine. Let’s go, bestie. ✨

🌸 NAME 🌸

SRC/zsyrfs.f

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines

       subroutine zsyrfs (uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x,
           ldx, ferr, berr, work, rwork, info)
           ZSYRFS

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💖 Function/Subroutine Documentation 💖

   subroutine zsyrfs (character uplo, integer n, integer nrhs, complex*16,
       dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af,
       integer ldaf, integer, dimension( * ) ipiv, complex*16, dimension( ldb,
       * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx,
       double precision, dimension( * ) ferr, double precision, dimension( * )
       berr, complex*16, dimension( * ) work, double precision, dimension( * )
       rwork, integer info)
       ZSYRFS

🎯 Purpose

Okay so ZSYRFS 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. Literally that’s the whole glow-up job. ✨

🔧 Parameters

• UPLO — UPLO is CHARACTER*1; = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. 🦋
• N — N is INTEGER. The order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• A — A is 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 — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
• AF — AF is 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 — LDAF is INTEGER. The leading dimension of the array AF. LDAF >= max(1,N).
• IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZSYTRF.
• B — B is COMPLEX*16 array, dimension (LDB,NRHS). The right hand side matrix B.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — X is COMPLEX*16 array, dimension (LDX,NRHS). On entry, the solution matrix X, as computed by ZSYTRS. On exit, the improved solution matrix X.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• FERR — FERR is 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 estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error.
• BERR — BERR is 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 — WORK is COMPLEX*16 array, dimension (2*N).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N).
• INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value.

🧚 Internal Parameters

ITMAX is the maximum number of steps of iterative refinement. 🫶

👑 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 190 of file zsyrfs.f.

👑 Author

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