ZHERFS(3)

Okay bestie, this is ZHERFS(3) — yes, the whole manual page, and no we are not skipping the “boring” parts. 💅 The source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zherfs.f — that’s the exact path, character for character (the original just wrapped it).

🌸 NAME 🌸

The official NAME line points at the file /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zherfs.f. So yeah: the thing this page documents lives in that file. 💖

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

Here’s the short version, bestie:

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

💖 Function/Subroutine Documentation 💖

Full signature drip, exactly like the source:

   subroutine ZHERFS (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)
       ZHERFS

And the name is ZHERFS again, because obviously. 👑

🎯 Purpose

ZHERFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and it provides error bounds and backward error estimates for the solution. It’s giving careful, precise, and honestly very helpful. ✨

🧚 Parameters

Every single one, no skips:

• 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 Hermitian 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**H or A = L*D*L**H as computed by ZHETRF.
• 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 ZHETRF.
• 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 ZHETRS. 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. That’s the whole note, bestie. 🫶

🌟 Author 🌟

Shoutout to the author squad:

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

📍 Definition at line 190 of file zherfs.f. 📍

Exactly: Definition at line 190 of file zherfs.f. This is where the source says it’s defined. 🎀

🖋️ Author 🖋️

Generated automatically by Doxygen for LAPACK from the source code. So it’s not a person in this bit, it’s the doc generator doing its thing. 💻✨

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💖 Cute sign-off, bestie: LAPACK Version 3.12.0, and the footer path is /home/abui...RC/zherfs.f(3). There’s no date in this footer — just those two facts — so we’re not inventing one. 🫶🎀