DTRT03(3)

🌸 DTRT03(3) — a LAPACK vibe check 🌸

okay so you're in the Library Functions Manual bestie, welcome 💅 and the star of today's episode is a little Fortran file living its best life at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dtrt03.f. Yes that's the whole path. No I'm not shortening it, it's iconic. ✨

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🎀 NAME 🎀

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dtrt03.f

like... that's her. that's the file. she tests things. 🫶

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⭐ SYNOPSIS ⭐

Functions/Subroutines

ok so there's exactly one function here and she's carrying the whole page:

subroutine DTRT03 (uplo, trans, diag, n, nrhs, a, lda, scale, cnorm,
    tscal, x, ldx, b, ldb, work, resid)

DTRT03 — that's the name, that's the whole name, no cap. 💖

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🦋 Function/Subroutine Documentation 🦋

here's the full signature in all her glory, character by character, because we do not play about types in this house:

subroutine DTRT03 (character uplo, character trans, character diag, integer
    n, integer nrhs, double precision, dimension( lda, * ) a, integer lda,
    double precision scale, double precision, dimension( * ) cnorm, double
    precision tscal, double precision, dimension( ldx, * ) x, integer ldx,
    double precision, dimension( ldb, * ) b, integer ldb, double precision,
    dimension( * ) work, double precision resid)

yeah. DTRT03. she's a whole subroutine. 🔥

✨ Purpose ✨ — the actual plot

DTRT03 computes the residual for the solution to a scaled triangular system of equations A*x = s*b or A'*x = s*b.

so picture it: A is a triangular matrix, A' is the transpose of A, s is a scalar, and x and b are N by NRHS matrices. and the test ratio is literally the maximum, over the number of right hand sides, of:

norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS )

where op(A) means either A or A', and EPS is the machine epsilon. it's giving "how wrong are you, on a scale" energy and honestly? obsessed. 😭

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💜 Parameters 💜 (all sixteen of them, we're not skipping a single one)

• UPLO — is CHARACTER*1 and tells you whether A is upper or lower triangular. = 'U': upper triangular 🌈, = 'L': lower triangular 🦋.
• TRANS — is CHARACTER*1, specifies the operation applied to A. = 'N': A *x = s*b (no transpose) ✨, = 'T': A'*x = s*b (transpose) 🔥, = 'C': A'*x = s*b (conjugate transpose = transpose, same thing here bestie, 'C' is just 'T' in a cuter outfit) 💅.
• DIAG — is CHARACTER*1, says whether or not A is unit triangular. = 'N': non-unit triangular, = 'U': unit triangular 👑.
• N — is INTEGER, the order of the matrix A. N >= 0. zero is fine, we love a boundary case 🎀.
• NRHS — is INTEGER, the number of right hand sides, i.e. the number of columns of the matrices X and B. NRHS >= 0 🫶.
• 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 (rude, but okay). 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. ✨
• LDA — is INTEGER, the leading dimension of the array A. LDA >= max(1,N) 💀 don't test her.
• SCALE — is DOUBLE PRECISION, the scaling factor s used in solving the triangular system 💖.
• CNORM — is DOUBLE PRECISION array, dimension (N), the 1-norms of the columns of A, not counting the diagonal (again: diagonal erasure, we support it) 🌸.
• TSCAL — is DOUBLE PRECISION, the scaling factor used in computing the 1-norms in CNORM. fun fact: CNORM actually contains the column norms of TSCAL*A 🧚.
• X — is DOUBLE PRECISION array, dimension (LDX,NRHS), the computed solution vectors for the system of linear equations. the main character of the whole operation honestly ⭐.
• LDX — is INTEGER, the leading dimension of the array X. LDX >= max(1,N) 🦋.
• B — is DOUBLE PRECISION array, dimension (LDB,NRHS), the right hand side vectors for the system of linear equations 💜.
• LDB — is INTEGER, the leading dimension of the array B. LDB >= max(1,N) 🌈.
• WORK — is DOUBLE PRECISION array, dimension (N). that's it. that's the description. she works. 💅
• RESID — is DOUBLE PRECISION, the maximum over the number of right hand sides of

norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).

this is the number you came for. the whole point. the final boss. 👑

⚠️ quick vibe check: LDA, LDX, and LDB all have >= max(1,N) requirements and N/NRHS both have >= 0 requirements — those are the documented constraints, so respect them or don't come crying to me 😭

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👑 Author 👑

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

four whole institutions contributed, we stan a collaborative effort 🫶🌸

Definition at line 167 of file dtrt03.f. go look, she's really there 💖

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🧚 Author (yes, another one) 🧚

Generated automatically by Doxygen for LAPACK from the source code. no human hand-wrote this page and honestly? you can tell. but we love her anyway 😭

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🌟 SEE ALSO 🌟

not listed on this page bestie — the only thing this manpage points at is its own source file, dtrt03.f. iykyk 💅

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💖 that's the whole page, no notes, no cap, ate and left no crumbs 💖

LAPACK — Version 3.12.0 — and the footer says /home/abui...IN/dtrt03.f(3), so like... that's the file, that's the version, that's the whole sign-off. mwah. 🎀✨🦋💜