DTRRFS(3)

💅 NAME 💅

ok so bestie, welcome to dtrrfs.f(3) — that's the manual page for this file, and the file itself lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dtrrfs.f ✨ like that's the whole entire path, no cap, I'm not shortening it, we don't do that here 🫶

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🦋 SYNOPSIS 🦋

Functions/Subroutines

ok so there's exactly one icon in this file and she's serving:

subroutine DTRRFS (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx,
    ferr, berr, work, iwork, info)
    DTRRFS

that's it. that's the girl. DTRRFS 💅

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✨ Function/Subroutine Documentation ✨

subroutine DTRRFS (character uplo, character trans, character diag, integer
    n, integer nrhs, double precision, dimension( lda, * ) a, integer lda,
    double precision, dimension( ldb, * ) b, integer ldb, double precision,
    dimension( ldx, * ) x, integer ldx, double precision, dimension( * )
    ferr, double precision, dimension( * ) berr, double precision,
    dimension( * ) work, integer, dimension( * ) iwork, integer info)
    DTRRFS

🎀 Purpose 🎀

so like, !> — yes the source literally has all these !> comment markers, they're part of the vibe, we keep them, no edits 💖

!> DTRRFS provides error bounds and backward error estimates for the !> solution to a system of linear equations with a triangular !> coefficient matrix.

!>

!> The solution matrix X must be computed by DTRTRS or some other !> means before entering this routine. DTRRFS does not do iterative !> refinement because doing so cannot improve the backward error.

⚠️ okay so this is the important part bestie — X has to already exist before you call her. She's not computing the solution, she's just judging it. And she straight up does not do iterative refinement, because (her words, not mine) doing so cannot improve the backward error. periodt. 🔥

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🌸 Parameters 🌸

• UPLO — !> UPLO is CHARACTER*1 / !> = 'U': A is upper triangular; / !> = 'L': A is lower triangular. — so like, which triangle of A are we even talking about, bestie 💀
• TRANS — !> TRANS is CHARACTER*1 / !> Specifies the form of the system of equations: with the options being:
  • !> = 'N': A * X = B (No transpose)
  • !> = 'T': A**T * X = B (Transpose)
  • !> = 'C': A**H * X = B (Conjugate transpose = Transpose)

yeah 'C' and 'T' are the same thing here, it's giving "we support both spellings" energy 🫶

• DIAG — !> DIAG is CHARACTER*1
  • !> = 'N': A is non-unit triangular;
  • !> = 'U': A is unit triangular.
• N — !> N is INTEGER / !> The order of the matrix A. N >= 0. — the size, and she said N >= 0, so zero is allowed, don't come at her 🌈
• NRHS — !> NRHS is INTEGER / !> The number of right hand sides, i.e., the number of columns / !> of the matrices B and X. NRHS >= 0. — how many right-hand sides we're serving, also >= 0 ⭐
• A — !> A is DOUBLE PRECISION array, dimension (LDA,N) / !> The triangular matrix A. If UPLO = 'U', the leading N-by-N / !> upper triangular part of the array A contains the upper / !> triangular matrix, and the strictly lower triangular part of / !> A is not referenced. If UPLO = 'L', the leading N-by-N lower / !> triangular part of the array A contains the lower triangular / !> matrix, and the strictly upper triangular part of A is not / !> referenced. If DIAG = 'U', the diagonal elements of A are / !> also not referenced and are assumed to be 1.

ngl this is the beefiest one 💀 the half of A you didn't pick is not referenced (she's ignoring it, respectfully), and if DIAG = 'U' she also ignores the diagonal and just assumes it's 1. icon behaviour honestly 👑

• LDA — !> LDA is INTEGER / !> The leading dimension of the array A. LDA >= max(1,N). — leading dimension of A, and like >= max(1,N) bestie, write it down 🎀
• B — !> B is DOUBLE PRECISION array, dimension (LDB,NRHS) / !> The right hand side matrix B. — that's the right hand side, the whole point 💜
• LDB — !> LDB is INTEGER / !> The leading dimension of the array B. LDB >= max(1,N). — same deal, max(1,N) 🦋
• X — !> X is DOUBLE PRECISION array, dimension (LDX,NRHS) / !> The solution matrix X. — the solution! the main character! 👑
• LDX — !> LDX is INTEGER / !> The leading dimension of the array X. LDX >= max(1,N). — yes, also max(1,N), she's consistent ✨
• 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 like, per-column error budget 💅 and important caveat bestie: it's almost always a slight overestimate of the true error — she's not lying to you, she's just being a little dramatic 😭

• 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). — the smallest change to A or B that would make X(j) exact, fr fr 🍓
• WORK — !> WORK is DOUBLE PRECISION array, dimension (3*N) — workspace, size 3*N, don't forget the three 🌸
• IWORK — !> IWORK is INTEGER array, dimension (N) — integer workspace, size N 🧚
• INFO — !> INFO is INTEGER
  • !> = 0: successful exit
  • !> < 0: if INFO = -i, the i-th argument had an illegal value

so 0 = slay, negative = somebody's argument was illegal and she's telling you exactly which one via -i 💀🔍

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👑 Author 👑

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

Definition at line 180 of file dtrrfs.f. — line 180, screenshot it 📸

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. — yeah she's a Doxygen baby, born fully documented 🍼

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and that's the whole page bestie, you ate 💅

🎀 cute little sign-off: this is LAPACK, Version 3.12.0, dated /home/abui...RC/dtrrfs.f(3) at the bottom of the original — so yeah, version 3.12.0, and the file is dtrrfs.f(3). mwah 💖✨🦋