CQRT14(3)

🎀 NAME 🎀

okay bestie, this is the cqrt14.f(3) page from the Library Functions Manual — header path and all: /home/abui...IN/cqrt14.f(3).

The NAME line is literally one long path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/cqrt14.f

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

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💜 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 — yes, that’s the name again, main character energy 💅.

🌸 Purpose 🌸

CQRT14 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.

the precision of it all? obsessed. ✨

🎀 Parameters 🎀

TRANS

• 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 — M is INTEGER; the number of rows of the matrix A.

N

• N — N is INTEGER; the number of columns of the matrix A.

NRHS

• NRHS — NRHS is INTEGER; the number of right hand sides, i.e., the number of columns of X.

A

• A — A is COMPLEX array, dimension (LDA,N); the M-by-N matrix A.

LDA

• LDA — LDA is INTEGER; the leading dimension of the array A.

X

• 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 — LDX is INTEGER; the leading dimension of the array X.

WORK

• WORK — WORK is COMPLEX array dimension (LWORK)

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.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie 💖 big shoutout to LAPACK, Version 3.12.0, and /home/abui...IN/cqrt14.f(3) in the footer — the date didn’t show up in the footer text, so no invented date, periodt. 🫶