SGERFS(3)

💅 SGERFS(3) — like, the LAPACK manual, but make it make sense

okay so bestie, welcome to the LAPACK girlies' corner 💖 this is from Version 3.12.0, and the whole thing lives at /home/abui...RC/sgerfs.f(3) — yes the path is truncated in the header, that's just how it is, we don't fix it, we respect it 🎀

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgerfs.f — that's the file, that's the whole name section, she's literally just a path and honestly? iconic. 👑

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine SGERFS (trans, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x,
    ldx, ferr, berr, work, iwork, info)

SGERFS — that's her, that's the girl 🌸

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🧚 Function/Subroutine Documentation 🧚

subroutine SGERFS (character trans, integer n, integer nrhs, real,
    dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af,
    integer ldaf, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b,
    integer ldb, real, dimension( ldx, * ) x, integer ldx, real, dimension(
    * ) ferr, real, dimension( * ) berr, real, dimension( * ) work, integer,
    dimension( * ) iwork, integer info)

SGERFS

💜 Purpose:

!> !> SGERFS improves the computed solution to a system of linear !> equations and provides error bounds and backward error estimates for !> the solution. !>

ngl bestie, that's the whole gig: you already got a solution, she makes it better and then hands you receipts for how wrong it might still be. main character energy fr fr ✨

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🌈 Parameters 🌈

• TRANS — bestie this is a CHARACTER*1 and it picks which version of the system you're solving. the vibes are:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose = Transpose)
• N — N is INTEGER. it's the order of the matrix A. rule: N >= 0. no negative girlies allowed 🚫
• NRHS — NRHS is INTEGER. the number of right hand sides, aka the number of columns of the matrices B and X. rule: NRHS >= 0. 🫶
• A — A is REAL array, dimension (LDA,N). the original N-by-N matrix A. the OG. the blueprint. 💖
• LDA — LDA is INTEGER. the leading dimension of the array A. rule: LDA >= max(1,N). ⭐
• AF — AF is REAL array, dimension (LDAF,N). the factors L and U from the factorization A = P*L*U as computed by SGETRF. she's the pre-chewed version, we love a shortcut 🍓
• LDAF — LDAF is INTEGER. the leading dimension of the array AF. rule: LDAF >= max(1,N). 🌸
• IPIV — IPIV is INTEGER array, dimension (N). the pivot indices from SGETRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i). the swap receipts 💅
• B — B is REAL array, dimension (LDB,NRHS). the right hand side matrix B. 🎀
• LDB — LDB is INTEGER. the leading dimension of the array B. rule: LDB >= max(1,N). 🦋
• X — X is REAL array, dimension (LDX,NRHS). on entry, the solution matrix X, as computed by SGETRS. on exit, the improved solution matrix X. she goes in mid and comes out ✨glowed up✨
• LDX — LDX is INTEGER. the leading dimension of the array X. rule: LDX >= max(1,N). 💜
• FERR — FERR is REAL 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 like… she's a lil dramatic, she rounds up, but she's trustworthy 😭
• BERR — BERR is REAL 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). the "how much would i have to fudge the inputs to make this technically correct" number 💀
• WORK — WORK is REAL array, dimension (3*N). scratch space, mind your business 🔥
• IWORK — IWORK is INTEGER array, dimension (N). also scratch space, integer flavoured 🧚
• INFO — INFO is INTEGER. the vibe check:
  • = 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 it, that's the whole internal tea ☕

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🌺 Author 🌺

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

Definition at line 183 of file sgerfs.f. 📍

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🎀 Author (again, but the auto-gen one) 🎀

Generated automatically by Doxygen for LAPACK from the source code. she wasn't hand-written, she was born this way 🤖💖

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okay bestie that's the whole page, no cap, nothing skipped 🫶

LAPACK, Version 3.12.0 — and the file is /home/abui...RC/sgerfs.f(3), mwah, bye, go refine some solutions iteratively 💅✨