STRT01(3)

🎀 STRT01(3) 🎀

okay bestie, welcome to the LAPACK corner of the Library Functions Manual — yes, that's the manual we're in, and yes it's as dramatic as it sounds 💅

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/strt01.f

like... that's the whole name. it's a path. it's giving "my parents named me after the street I was born on" 😭 but that's literally it, no cap 🫶

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine STRT01 (uplo, diag, n, a, lda, ainv, ldainv, rcond, work, resid) — the whole squad, assembled. also just... STRT01. that's the vibe 🦋

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💖 Function/Subroutine Documentation 💖

subroutine STRT01 (character uplo, character diag, integer n, real,
    dimension( lda, * ) a, integer lda, real, dimension( ldainv, * ) ainv,
    integer ldainv, real rcond, real, dimension( * ) work, real resid)

STRT01 👑 (yes the exact same name again, she said "I'm the main character" and honestly? correct.)

🔥 Purpose 🔥

!> !> STRT01 computes the residual for a triangular matrix A times its !> inverse: !> RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ), !> where EPS is the machine epsilon. !>

so bestie, it's a vibe check on your triangular matrix inverse 🔍 — it measures how far off A*AINV is from the identity, scaled by N, norm(A), norm(AINV) and EPS (the machine epsilon). tiny resid = slay. big resid = 💀

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🌈 Parameters 🌈

• UPLO — UPLO is CHARACTER*1. tells us which triangle of A is the real one: = 'U': Upper triangular or = 'L': Lower triangular. pick a side, icon 💅
• DIAG — DIAG is CHARACTER*1. is A unit triangular or not: = 'N': Non-unit triangular, = 'U': Unit triangular. no in-between, it's giving binary 🎀
• N — N is INTEGER. The order of the matrix A. N >= 0. zero is allowed, queen of boundaries ⭐
• A — A is REAL array, dimension (LDA,N). The triangular matrix A. and here's the lore: 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. and if DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. so half your array is basically decorative, we love a low-effort icon 🙈
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). respect the constraint or perish 😤
• AINV — AINV is REAL array, dimension (LDAINV,N). On entry, the (triangular) inverse of the matrix A, in the same storage format as A. On exit, the contents of AINV are destroyed. 🫠 bestie she does NOT survive — she gets wrecked on the way out, that's not a bug that's canon. plan accordingly 💀
• LDAINV — LDAINV is INTEGER. The leading dimension of the array AINV. LDAINV >= max(1,N). same rules, different array, stay in your lane ✨
• RCOND — RCOND is REAL. The reciprocal condition number of A, computed as 1/(norm(A) * norm(AINV)). it's the "how trustworthy is this inverse" number, essentially 🧚
• WORK — WORK is REAL array, dimension (N). scratch space. does its job. leaves. king behavior 🫶
• RESID — RESID is REAL. norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS ). that's the output, the final grade, the report card, the vibe check result 💅

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👑 Author 👑

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

four whole institutions took credit for this one subroutine and honestly? teamwork makes the dream work 🫶

Definition at line 122 of file strt01.f. go look, it's right there, line one-two-two, screenshot it 🔥

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code.

not me being auto-generated 😭 no human wrote this prose, the machine did it, and the machine ate fr fr 🤖✨

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and that's the page, bestie!! little sign-off for the fine print: this is LAPACK, Version 3.12.0, and the header/footer date tag on the original was /home/abui...IN/strt01.f(3) — she abbreviates her own address, iconic 💜🌈

go forth and compute residuals 💖🎀🦋