ZSYRFS(3)

ZSYRFS(3) 💅✨

okay bestie, welcome to the Library Functions Manual page for ZSYRFS — and yes, the NAME line is a whole path moment: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zsyrfs.f. That's the source-file icon behavior, no cap.

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

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

🫶 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 it provides error bounds and backward error estimates for the solution. that's the whole glow-up, periodt. 💖

💖 Parameters 💖

• UPLO — UPLO is CHARACTER*1; = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored. pick your triangle, bestie. 🎀
• 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. 😭 so real.
• 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. literally the step budget, bestie. 👑

👑 Author 👑

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

📍 Definition at line 📍

Definition at line 190 of file zsyrfs.f.

👑 Author (auto-generated moment) 👑

Generated automatically by Doxygen for LAPACK from the source code.

---

and that's the sign-off, bestie: source/version is LAPACK Version 3.12.0, and the page path is /home/abui...RC/zsyrfs.f(3) 💖✨