DQRT16(3)

💅 dqrt16.f(3) — Library Functions Manual (yes bestie, we're in the LAPACK section)

okay so real quick: this whole page lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dqrt16.f and honestly? iconic address. very "i have a long name and i'm proud of it" energy. ✨

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🌸 NAME

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dqrt16.f

like. that's the name. the whole path. she said "i'm not shortening it for anyone." periodt 🎀

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🦋 SYNOPSIS

Functions/Subroutines

subroutine DQRT16 (trans, m, n, nrhs, a, lda, x, ldx, b, ldb, rwork,
    resid)
    DQRT16

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💖 Function/Subroutine Documentation

subroutine DQRT16 (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( ldb, *
    ) b, integer ldb, double precision, dimension( * ) rwork, double
    precision resid)

DQRT16 — she's the one doing the vibes check on your linear solver, and no cap she takes it seriously. 👑

✨ Purpose ✨

okay so picture this, bestie:

DQRT16 computes the residual for a solution of a system of linear equations A*x = b or A'*x = b: RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ), where EPS is the machine epsilon.

that's it. that's the whole job. she checks how wrong you were, mathematically. lowkey the most honest function in the whole library 😭

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🎀 Parameters 🎀

strap in, there's a lot of them, but they all slay in their own way 💅

• TRANS — TRANS is CHARACTER*1. specifies the form of the system of equations:
  • = 'N': A *x = b
  • = 'T': A'*x = b, where A' is the transpose of A
  • = 'C': A'*x = b, where A' is the transpose of A

(yes, 'T' and 'C' do the exact same thing here. twins. matching outfits. it's giving coordinated.)

• M — M is INTEGER. the number of rows of the matrix A. M >= 0. zero is allowed, she's not gonna gatekeep 🫶
• N — N is INTEGER. the number of columns of the matrix A. N >= 0. same deal, no gatekeeping.
• NRHS — NRHS is INTEGER. the number of columns of B, the matrix of right hand sides. NRHS >= 0.
• A — A is DOUBLE PRECISION array, dimension (LDA,N). the original M x N matrix A. the main character, honestly.
• LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,M). respect the leading dimension or she WILL notice. 🙈
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS). the computed solution vectors for the system of linear equations. the answer you think you got.
• LDX — LDX is INTEGER. the leading dimension of the array X. If TRANS = 'N', LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M). read that twice, it flips depending on TRANS, iykyk 🦋
• B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.

⚠️ heads up bestie: your B does NOT come back the way you left it. she replaces it with the difference. not me gaslighting you, that's literally the docs 💀

• LDB — LDB is INTEGER. the leading dimension of the array B. IF TRANS = 'N', LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N). (the original literally shouts "IF" in caps, so we're shouting too 🔥)
• RWORK — RWORK is DOUBLE PRECISION array, dimension (M). that's it. that's the whole description. she's a working array with M slots, no further notes, mysterious queen 🌈
• RESID — RESID is DOUBLE PRECISION. the maximum over the number of right hand sides of norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ). the final verdict. the report card. the moment of truth ⭐

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👑 Author

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

four whole institutions collaborated on this and honestly? teamwork makes the dream work 💜

Definition at line 131 of file dqrt16.f. (yes, line 131, we counted, she's not hiding 🌸)

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🧚 Author (again, but the meta one)

Generated automatically by Doxygen for LAPACK from the source code. so technically a robot wrote this page, but the robot ate and left no crumbs 🤖✨

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— 💖 that's the page bestie, all of it, nothing skipped — 💖

sign-off: this is LAPACK, Version 3.12.0, and the page you just read is /home/abui...IN/dqrt16.f(3). go forth and check your residuals 🍓💅