ZQRT16(3)

💅 ZQRT16(3) — like, the residual-checking queen of LAPACK

okay so bestie, welcome to section 3 of the manual, and the file we're stanning today is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zqrt16.f ✨ (the header on this page shows it all cozy as /home/abui...IN/zqrt16.f(3), but like, you get it 🎀)

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✨ SYNOPSIS ✨

Functions/Subroutines 🦋

subroutine ZQRT16 (trans, m, n, nrhs, a, lda, x, ldx, b, ldb, rwork, resid)

like, that's it. that's the whole vibe. ZQRT16 💅

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🌸 Function/Subroutine Documentation 🌸

subroutine ZQRT16 (character trans, integer m, integer n, integer nrhs,
    complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
    ldx, * ) x, integer ldx, complex*16, dimension( ldb, * ) b, integer ldb,
    double precision, dimension( * ) rwork, double precision resid)

ZQRT16 — say it with me 👑 no cap, this subroutine is the whole main character.

🎯 Purpose 🎯

!> !> ZQRT16 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. so yeah — it's literally checking how good your solution actually is 🔥 (and yes the !> marks are part of the source, we love a literal transcript bestie 💖)

🧚 Parameters (the whole cast, nobody gets cut) 🧚

• TRANS — is CHARACTER*1, and it tells us which flavor of system we're solving, like a little menu of vibes:
  • = 'N': A *x = b
  • = 'T': A^T*x = b, where A^T is the transpose of A
  • = 'C': A^H*x = b, where A^H is the conjugate transpose of A
• M — is INTEGER, and it's the number of rows of the matrix A. constraint: M >= 0 🫶
• N — is INTEGER, the number of columns of the matrix A. constraint: N >= 0 ⭐
• NRHS — is INTEGER, the number of columns of B, the matrix of right hand sides. constraint: NRHS >= 0 💜
• A — is COMPLEX*16 array, dimension (LDA,N). it's the original M x N matrix A. iconic, honestly 🌈
• LDA — is INTEGER, the leading dimension of the array A. constraint: LDA >= max(1,M) ✨
• X — is COMPLEX*16 array, dimension (LDX,NRHS). these are the computed solution vectors for the system of linear equations, i.e. the girlies we're grading 💅
• LDX — is INTEGER, the leading dimension of the array X. and watch out, it's conditional: if TRANS = 'N', LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M) 🙈
• B — is COMPLEX*16 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 — not me warning you that it gets rewritten 😭 that's a real side effect bestie, don't say I didn't tell you.
• LDB — is INTEGER, the leading dimension of the array B. also conditional: IF TRANS = 'N', LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N) 🦋
• RWORK — is DOUBLE PRECISION array, dimension (M) 🌸
• RESID — is DOUBLE PRECISION, and it's the maximum over the number of right hand sides of

norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).

like, the final grade. the report card. periodt 🔥

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👑 Author 👑

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

Definition at line 131 of file zqrt16.f. 🎀 (yes it lives at line 131, note it and move on bestie)

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⭐ Author (yes, again, it's a whole thing) ⭐

Generated automatically by Doxygen for LAPACK from the source code. — so nobody hand-wrote this beauty, the robots did it 🫶

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k so that's the page, and before you go: this whole thing is LAPACK Version 3.12.0, and the footer sings it as /home/abui...IN/zqrt16.f(3) — ty for coming to my ted talk, mwah 💖🎀🦋