TESTING/LIN/zqrt14.f(3)

💅 TESTING/LIN/zqrt14.f(3) 💅

okay bestie, welcome to the Library Functions Manual page for TESTING/LIN/zqrt14.f — it’s giving “let’s check if X is in the row space of A or A'” energy, and every single deet is staying. No cap. 💖

🌸 NAME 🌸

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 🎀

   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

✨ Purpose: ✨

Bestie, ZQRT14 checks whether X is in the row space of A or A'. The way it does this is iconic: it scales both X and A so their norms are in the range [sqrt(eps), 1/sqrt(eps)], then computes a QR factorization of [A,X] (if TRANS = 'C') or an LQ factorization of [A',X]' (if TRANS = 'N'), and returns the norm of the trailing triangle, scaled by MAX(M,N,NRHS)*eps. That’s the whole flex. 💅

🌟 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*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', 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*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 🌈

Generated automatically by Doxygen for LAPACK from the source code.

🫶 That’s the whole page, bestie. This iconic little artifact is LAPACK, Version 3.12.0, TESTING/LIN/zqrt14.f(3). Periodt. 💖✨