TESTING/LIN/sqrt17.f(3)

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version 3.12.1 · 2 versions
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🌸 TESTING/LIN/sqrt17.f(3) 🌸

okay bestie, so this one's a page from Library Functions Manual — yes, we're in the mood, we're reading a Fortran manpage 💅 and honestly? she kinda ate. Let's get into it.

✨ NAME ✨

TESTING/LIN/sqrt17.f — like, that's literally her. that's the whole name. no notes. 🎀

🦋 SYNOPSIS 🦋

Functions/Subroutines

  • real function sqrt17 (trans, iresid, m, n, nrhs, a, lda, x, ldx, b, ldb, c, work, lwork) — SQRT17 👑

💖 Function/Subroutine Documentation 💖

🌟 the signature (copy it exactly, i'm not kidding) 🌟

   real function sqrt17 (character trans, integer iresid, integer m, integer n,
       integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension(
       ldx, * ) x, integer ldx, real, dimension( ldb, * ) b, integer ldb, real,
       dimension( ldb, * ) c, real, dimension( lwork ) work, integer lwork)

SQRT17 — that's her name, that's her whole vibe. 🫶

🧮 Purpose 🧮

okay so listen, this function is out here computing a ratio, and it's giving very much "math girlboss":

   norm(R**T * op(A)) / ( norm(A) * alpha * max(M,N,NRHS) * EPS ),

where the residual R = B - op(A)*X, and op(A) is either A or A**T depending on TRANS. EPS is the machine epsilon (slay 💅), and then:

   alpha = norm(B) if IRESID = 1 (zero-residual problem)
   alpha = norm(R) if IRESID = 2 (otherwise).

and the norm in question? the 1-norm. iconic. periodt. 🔥

🎀 Parameters 🎀

  • TRANS — she's a CHARACTER*1 and she decides whether the transpose of A gets used or not:
    • = 'N': no transpose, so op(A) = A. easy. 💜
    • = 'T': transpose, so op(A) = A**T. spicy. 🌶️
  • IRESID — an INTEGER, and honestly she's just here to label your situation:
    • IRESID = 1 means zero-residual problem 🍓
    • IRESID = 2 means non-zero residual 😭
  • M — INTEGER, the number of rows of the matrix A. but also, plot twist:
    • if TRANS = 'N', it's the number of rows of the matrix B
    • if TRANS = 'T', it's the number of rows of the matrix X
  • N — INTEGER, the number of columns of the matrix A. and again, the plot thickens:
    • if TRANS = 'N', it's the number of rows of the matrix X
    • if TRANS = 'T', it's the number of rows of the matrix B
  • NRHS — INTEGER, the number of columns of the matrices X and B. that's it. that's her job. 🌈
  • A — REAL array, dimension (LDA,N) — the m-by-n matrix A. main character energy, honestly. 👑
  • LDA — INTEGER, the leading dimension of the array A. constraint: LDA >= M. don't test her. ⭐
  • X — REAL 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
  • LDX — INTEGER, the leading dimension of the array X:
    • if TRANS = 'N', then LDX >= N
    • if TRANS = 'T', then LDX >= M
  • B — REAL array, dimension (LDB,NRHS):
    • if TRANS = 'N', it's the m-by-nrhs matrix B
    • if TRANS = 'T', it's the n-by-nrhs matrix B
  • LDB — INTEGER, the leading dimension of the array B:
    • if TRANS = 'N', then LDB >= M
    • if TRANS = 'T', then LDB >= N
  • C — REAL array, dimension (LDB,NRHS). no further commentary from the source, she's mysterious like that. 🙈
  • WORK — REAL array, dimension (LWORK). the workspace. the grind. 💀
  • LWORK — INTEGER, the length of the array WORK. constraint: LWORK >= NRHS*(M+N). respect it. 🔥
ngl bestie, those dimension constraints are not a suggestion. if you get LDA, LDX, LDB or LWORK wrong you're gonna have a bad time. 😭

👑 Author 👑

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

Definition at line 151 of file sqrt17.f. (yes, line one-fifty-one, we checked 💅)

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. she's auto-generated but she's still that girl. ✨

okay and finally, the cute sign-off you asked for 🫶 — this whole thing is from LAPACK, Version 3.12.0, and the page is TESTING/LIN/sqrt17.f(3). go forth and compute your ratios, bestie. 💜🎀🦋

📦 where this page comes from