TESTING/LIN/cqrt17.f(3)

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💅 TESTING/LIN/cqrt17.f(3) 💅

okay so bestie, welcome to the Library Functions Manual page for TESTING/LIN/cqrt17.f — manual name folded in right at the top like a little name tag. This is the CQRT17 situation and she's here to compute a ratio. icon behavior, no cap. 🎀

🌸 NAME 🌸

TESTING/LIN/cqrt17.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

       real function cqrt17 (trans, iresid, m, n, nrhs, a, lda, x, ldx, b, ldb,
           c, work, lwork)
           CQRT17

🦋 Function/Subroutine Documentation 🦋

   real function cqrt17 (character trans, integer iresid, integer m, integer n,
       integer nrhs, complex, dimension( lda, * ) a, integer lda, complex,
       dimension( ldx, * ) x, integer ldx, complex, dimension( ldb, * ) b,
       integer ldb, complex, dimension( ldb, * ) c, complex, dimension( lwork )
       work, integer lwork)
       CQRT17

🎀 Purpose 🎀

okay so CQRT17 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 🍓

  • TRANS — CHARACTER*1. Specifies whether or not the transpose of A is used.
    • = 'N': No transpose, op(A) = A.
    • = 'C': Conjugate transpose, op(A) = A**H.
  • IRESID — INTEGER. IRESID = 1 indicates zero-residual problem. IRESID = 2 indicates non-zero residual.
  • M — INTEGER. The number of rows of the matrix A.
    • If TRANS = 'N', the number of rows of the matrix B.
    • If TRANS = 'C', the number of rows of the matrix X.
  • N — INTEGER. The number of columns of the matrix A.
    • If TRANS = 'N', the number of rows of the matrix X.
    • If TRANS = 'C', the number of rows of the matrix B.
  • NRHS — INTEGER. The number of columns of the matrices X and B.
  • A — COMPLEX array, dimension (LDA,N). The m-by-n matrix A.
  • LDA — INTEGER. The leading dimension of the array A. LDA >= M.
  • X — COMPLEX array, dimension (LDX,NRHS).
    • If TRANS = 'N', the n-by-nrhs matrix X.
    • If TRANS = 'C', the m-by-nrhs matrix X.
  • LDX — INTEGER. The leading dimension of the array X.
    • If TRANS = 'N', LDX >= N.
    • If TRANS = 'C', LDX >= M.
  • B — COMPLEX array, dimension (LDB,NRHS).
    • If TRANS = 'N', the m-by-nrhs matrix B.
    • If TRANS = 'C', the n-by-nrhs matrix B.
  • LDB — INTEGER. The leading dimension of the array B.
    • If TRANS = 'N', LDB >= M.
    • If TRANS = 'C', LDB >= N.
  • C — COMPLEX array, dimension (LDB,NRHS).
  • WORK — COMPLEX array, dimension (LWORK).
  • LWORK — INTEGER. The length of the 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 cqrt17.f.

🌈 Author 🌈

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