SRC/zherfs.f(3)

💅 SRC/zherfs.f 💅

okay so this page lives in the Library Functions Manual and it's literally the whole glow-up arc of ZHERFS — bestie, it's giving "your solution but better" and honestly? obsessed. 🫶

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✨ NAME ✨

SRC/zherfs.f

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🦋 SYNOPSIS 🦋

Functions/Subroutines

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

ZHERFS — that's her, that's the icon. 👑

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🌸 Function/Subroutine Documentation 🌸

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

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🎀 Purpose 🎀

so what does she actually do, you ask?? ZHERFS improves the computed solution to a system of linear equations when the coefficient matrix is Hermitian indefinite, and it also provides error bounds and backward error estimates for the solution. like, not only does she fix your answer, she hands you the receipts on how wrong the old one was. main character energy fr fr. ✨

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💜 Parameters 💜

UPLO

UPLO is CHARACTER*1

• = 'U': Upper triangle of A is stored;
• = 'L': Lower triangle of A is stored.

pick a side, bestie, but only one 💅

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.

lowkey the other triangle just does not exist to her. not referenced means not referenced, periodt. 🙈

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. 🦋 she came in mid, she leaves iconic.

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.

ngl she's a slight overestimate girlie, but that's on purpose and it's reliable, so we forgive her. 💖

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 😭

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🧚 Internal Parameters 🧚

ITMAX is the maximum number of steps of iterative refinement. that's her little secret sauce, iykyk. ⭐

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👑 Author 👑

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

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Definition at line 190 of file zherfs.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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and that's the whole page, bestie!! 🌸 written by Doxygen's little autogen hands, straight from the source code, for LAPACK, Version 3.12.0, and this file right here is SRC/zherfs.f(3). slay, bye 💅✨🎀