ZQRT14(3)

Hiii bestie 💖 welcome to ZQRT14(3) from the Library Functions Manual — this is the group chat for a double precision function that does a very specific lil check, and honestly it’s giving main character energy. ✨

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🎀 NAME

The NAME section is literally just this file path, no cap: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/zqrt14.f.

✨ SYNOPSIS

🦋 Functions/Subroutines

   double precision function ZQRT14 (trans, m, n, nrhs, a, lda, x, ldx,
       work, lwork)
       ZQRT14

💅 Function/Subroutine Documentation

Okay so here’s the full signature, bestie — copy it exactly, pls:

   double precision function ZQRT14 (character trans, integer m, integer n,
       integer nrhs, complex*16, dimension( lda, * ) a, integer lda,
       complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension(
       lwork ) work, integer lwork)
       ZQRT14

And yes, it’s ZQRT14 again. Iconic. 💅

🌸 Purpose

ZQRT14 checks whether X is in the row space of A or A'. It does so by scaling both X and A such that their norms are 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.

💖 Parameters

Here’s the whole cast, no skips:

• 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*16 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*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; the leading dimension of the array X.
• WORK — WORK is COMPLEX*16 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 zqrt14.f.

👑 Author

And this last Author bit says: Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole page, bestie 🫶 — it’s from LAPACK Version 3.12.0, and the source/path footer vibe is /home/abui...IN/zqrt14.f(3). Byeee 💅✨