TESTING/LIN/cqrt14.f(3)

💖 NAME 💖

TESTING/LIN/cqrt14.f — that's the file, bestie, straight out of the Library Functions Manual ✨ (and the page header is TESTING/LIN/cqrt14.f(3), if you're keeping track 🎀).

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• real function cqrt14 (trans, m, n, nrhs, a, lda, x, ldx, work, lwork) — CQRT14

🌸 Function/Subroutine Documentation 🌸

   real function cqrt14 (character trans, integer m, integer n, integer nrhs,
       complex, dimension( lda, * ) a, integer lda, complex, dimension( ldx, *
       ) x, integer ldx, complex, dimension( lwork ) work, integer lwork)

CQRT14

💫 Purpose 💫

okay so CQRT14 checks whether X is in the row space of A or A'. It does that by scaling both X and A so their norms land in the range [sqrt(eps), 1/sqrt(eps)], then computing a QR factorization of [A,X] (if TRANS = 'C') or an LQ factorization of [A',X]' (if TRANS = 'N'), and returning the norm of the trailing triangle, scaled by MAX(M,N,NRHS)*eps. That's the whole tea ☕✨

💅 Parameters 💅

• TRANS — TRANS is CHARACTER*1
  • = 'N': No transpose, check for X in the row space of A.
  • = 'C': Conjugate transpose, check for X in row space of A'.
• M — M is INTEGER; the number of rows of the matrix A.
• N — N is INTEGER; the number of columns of the matrix A.
• NRHS — NRHS is INTEGER; the number of right hand sides, i.e., the number of columns of X.
• A — A is COMPLEX array, dimension (LDA,N); the M-by-N matrix A.
• LDA — LDA is INTEGER; the leading dimension of the array A.
• X — X is COMPLEX array, dimension (LDX,NRHS); if TRANS = 'N', the N-by-NRHS matrix X; IF TRANS = 'C', the M-by-NRHS matrix X.
• LDX — LDX is INTEGER; the leading dimension of the array X.
• WORK — WORK is COMPLEX array dimension (LWORK)
• LWORK — LWORK is INTEGER; length of workspace array required. If TRANS = 'N', LWORK >= (M+NRHS)*(N+2); if TRANS = 'C', LWORK >= (N+NRHS)*(M+2).

👑 Author 👑

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

Definition at line 114 of file cqrt14.f. 📍

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code. 💻✨

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okay bestie, that's the whole page 🫶 — the footer vibe is LAPACK Version 3.12.0 + TESTING/LIN/cqrt14.f(3), and there's no date listed in it, so that's the full sign-off situation 💅💖 no cap.