DQRT14(3)

✨ DQRT14 ✨

okay so this is from the Library Functions Manual, and it's a LAPACK tester bestie — it's the vibe-checker that makes sure your computed solution actually lives where it's supposed to. no cap. 🦋

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dqrt14.f

(yes that's literally the whole name, bestie, it's a Fortran file living its best life deep in the LAPACK TESTING/LIN directory 💅)

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🎀 SYNOPSIS 🎀

Functions/Subroutines

double precision function DQRT14 (trans, m, n, nrhs, a, lda, x, ldx,
    work, lwork)
    DQRT14

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👑 Function/Subroutine Documentation 👑

double precision function DQRT14 (character trans, integer m, integer n,
    integer nrhs, double precision, dimension( lda, * ) a, integer lda,
    double precision, dimension( ldx, * ) x, integer ldx, double precision,
    dimension( lwork ) work, integer lwork)

DQRT14 — she's a double precision function and she's the main character, periodt. 🌟

💖 Purpose 💖

okay so here's the tea ☕ — DQRT14 checks whether X is in the row space of A or A'. the way she does it is iconic: she scales both X and A so their norms land in the range [sqrt(eps), 1/sqrt(eps)], then she computes a QR factorization of [A,X] (if TRANS = 'T') or an LQ factorization of [A',X]' (if TRANS = 'N'), and finally she returns the norm of the trailing triangle, scaled by MAX(M,N,NRHS)*eps. slay. 💅✨

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🌈 Parameters 🌈

• TRANS — TRANS is CHARACTER*1
  • = 'N': no transpose, bestie — check for X in the row space of A
  • = 'T': transpose, so check for X in the row space of A'
• M — M is INTEGER, the number of rows of the matrix A. that's it. that's the row count. 🍓
• N — N is INTEGER, the number of columns of the matrix A. iconic column count behavior.
• NRHS — NRHS is INTEGER, the number of right hand sides, i.e., the number of columns of X. she's got multiple right hand sides and she's thriving 🫶
• A — A is DOUBLE PRECISION array, dimension (LDA,N), the M-by-N matrix A. the star of the show ngl 💜
• LDA — LDA is INTEGER, the leading dimension of the array A. keep up bestie ✨
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS)
  • if TRANS = 'N', it's the N-by-NRHS matrix X
  • if TRANS = 'T', it's the M-by-NRHS matrix X
  • (note: the source says IF TRANS = 'T' in caps — she's shouting, we love that for her 😭)
• LDX — LDX is INTEGER, the leading dimension of the array X. yes queen, declare your dimensions 📐
• WORK — WORK is DOUBLE PRECISION array dimension (LWORK) — the workspace, the behind-the-scenes girlies doing all the actual labor 🔥
• LWORK — LWORK is INTEGER, length of workspace array required
  • if TRANS = 'N', LWORK >= (M+NRHS)*(N+2)
  • if TRANS = 'T', LWORK >= (N+NRHS)*(M+2)

🚨 do not skip this one bestie: LWORK has minimums, so if you skimp on workspace she will not be okay. (M+NRHS)*(N+2) for 'N', (N+NRHS)*(M+2) for 'T'. write it down. 🎀

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🧚 Author 🧚

these legends wrote her:

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

⭐ Definition ⭐

Definition at line 114 of file dqrt14.f. — go look, she's right there 💫

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🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code. — so yeah, a robot birthed this documentation and honestly? she ate. 🙈

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and that's the whole page, bestie 💖 this was LAPACK Version 3.12.0, documented for /home/abui...IN/dqrt14.f(3) — go forth, check your row spaces, and hydrate. 🫶🌸💅