SQRT17(3)

💅 SQRT17(3) 💅

Okay bestie, this page is from the LAPACK Library Functions Manual, and the header shorthand path is /home/abui...IN/sqrt17.f(3). The title is SQRT17(3), and she is here to compute a residual ratio with main-character energy. ✨

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/sqrt17.f

Yes, that whole snack is the name line. No cap. 💖

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✨ SYNOPSIS ✨

Functions/Subroutines

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

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🦋 Function/Subroutine Documentation 🦋

   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

SQRT17 is literally the function name, and she is serving. 🫶

🎀 Purpose 🎀

SQRT17 computes the ratio:

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

where:

R = B - op(A)*X

op(A) is A or A**T, depending on TRANS. EPS is the machine epsilon, and:

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

The norm used is the 1-norm. Iconic. 🌈

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💖 Parameters 💖

• TRANS — TRANS is CHARACTER*1. Specifies whether or not the transpose of A is used.
  • = 'N': No transpose, op(A) = A.
  • = 'T': Transpose, op(A) = A**T.
• IRESID — IRESID is INTEGER.
  • IRESID = 1 indicates zero-residual problem.
  • IRESID = 2 indicates non-zero residual.
• M — M is INTEGER. The number of rows of the matrix A.
  • If TRANS = 'N', the number of rows of the matrix B.
  • If TRANS = 'T', the number of rows of the matrix X.
• N — N is INTEGER. The number of columns of the matrix A.
  • If TRANS = 'N', the number of rows of the matrix X.
  • If TRANS = 'T', the number of rows of the matrix B.
• NRHS — NRHS is INTEGER. The number of columns of the matrices X and B.
• A — A is REAL array, dimension (LDA,N). The m-by-n matrix A.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= M.
• X — X is REAL array, dimension (LDX,NRHS).
  • If TRANS = 'N', the n-by-nrhs matrix X.
  • If TRANS = 'T', the m-by-nrhs matrix X.
• LDX — LDX is INTEGER. The leading dimension of the array X.
  • If TRANS = 'N', LDX >= N.
  • If TRANS = 'T', LDX >= M.
• B — B is REAL array, dimension (LDB,NRHS).
  • If TRANS = 'N', the m-by-nrhs matrix B.
  • If TRANS = 'T', the n-by-nrhs matrix B.
• LDB — LDB is INTEGER. The leading dimension of the array B.
  • If TRANS = 'N', LDB >= M.
  • If TRANS = 'T', LDB >= N.
• C — C is REAL array, dimension (LDB,NRHS).
• WORK — WORK is REAL array, dimension (LWORK).
• LWORK — LWORK is INTEGER. The length of the array WORK. LWORK >= NRHS*(M+N).

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👑 Author 👑

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

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📍 Definition at line 151 of file sqrt17.f. 📍

That’s the exact spot: line 151 of sqrt17.f. Slay. 💅

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🪄 Author 🪄

Generated automatically by Doxygen for LAPACK from the source code.

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Sign-off time, bestie: LAPACK, Version 3.12.0 — source /home/abui...IN/sqrt17.f(3) — the footer didn’t print a date, but the vibe is timeless 💖🎀✨