ZQRT17(3)

Hey bestie 💖 welcome to ZQRT17(3), from the Library Functions Manual — manual name folded in near the top like a little bow 🎀.

🌸 NAME 🌸

This iconic little file lives at:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zqrt17.f

✨ SYNOPSIS ✨

Functions/Subroutines

double precision function ZQRT17 (trans, iresid, m, n, nrhs, a, lda, x,
    ldx, b, ldb, c, work, lwork)

ZQRT17

🌟 Function/Subroutine Documentation 🌟

double precision function ZQRT17 (character trans, integer iresid, 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, complex*16, dimension( ldb, * ) c,
    complex*16, dimension( lwork ) work, integer lwork)

ZQRT17

🎯 Purpose 🎯

Okay so ZQRT17 computes the ratio

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

where R = B - op(A)*X, op(A) is A or A**H, 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. Periodt. ✨

🧸 Parameters 🧸

Bestie, here’s every single parameter, no skips, no cap:

• TRANS — TRANS is CHARACTER*1. Tells us whether the transpose of A is used or not.
  • = 'N': No transpose, op(A) = A.
  • = 'C': Conjugate transpose, op(A) = A**H.
• IRESID — IRESID is INTEGER. IRESID = 1 means zero-residual problem. IRESID = 2 means non-zero residual.
• M — M is INTEGER. Number of rows of matrix A. If TRANS = 'N', it’s the number of rows of matrix B. If TRANS = 'C', it’s the number of rows of matrix X.
• N — N is INTEGER. Number of columns of matrix A. If TRANS = 'N', it’s the number of rows of matrix X. If TRANS = 'C', it’s the number of rows of matrix B.
• NRHS — NRHS is INTEGER. Number of columns of matrices X and B.
• A — A is COMPLEX*16 array, dimension (LDA,N). It’s the m-by-n matrix A.
• LDA — LDA is INTEGER. Leading dimension of array A; LDA >= M.
• X — X is COMPLEX*16 array, dimension (LDX,NRHS). If TRANS = 'N', it’s the n-by-nrhs matrix X. If TRANS = 'C', it’s the m-by-nrhs matrix X.
• LDX — LDX is INTEGER. Leading dimension of array X. If TRANS = 'N', LDX >= N. If TRANS = 'C', LDX >= M.
• B — B is COMPLEX*16 array, dimension (LDB,NRHS). If TRANS = 'N', it’s the m-by-nrhs matrix B. If TRANS = 'C', it’s the n-by-nrhs matrix B.
• LDB — LDB is INTEGER. Leading dimension of array B. If TRANS = 'N', LDB >= M. If TRANS = 'C', LDB >= N.
• C — C is COMPLEX*16 array, dimension (LDB,NRHS).
• WORK — WORK is COMPLEX*16 array, dimension (LWORK).
• LWORK — LWORK is INTEGER. Length of array WORK; LWORK >= NRHS*(M+N).

👑 Author 👑

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

Definition at line 151 of file zqrt17.f.

🦋 Author 🦋

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