TESTING/LIN/dqrt14.f(3)

💅 TESTING/LIN/dqrt14.f 💅

okay so this page is from the Library Functions Manual, and it's all about TESTING/LIN/dqrt14.f — yes bestie, the file and the function dqrt14 are the main characters here. no cap. 💖

✨ NAME ✨

TESTING/LIN/dqrt14.f — that's the name, and it's literally the Fortran file that documents dqrt14.

🎀 SYNOPSIS 🎀

Functions/Subroutines

double precision function dqrt14 (trans, m, n, nrhs, a, lda, x, ldx,
           work, lwork)

DQRT14

🦋 Function/Subroutine Documentation 🦋

double precision function dqrt14 (character trans, integer m, integer n,
       integer nrhs, double precision, dimension( lda, * ) a, integer lda,
       double precision, dimension( ldx, * ) x, integer ldx, double precision,
       dimension( lwork ) work, integer lwork)

DQRT14

🌸 Purpose 🌸

okay so DQRT14 checks whether X is in the row space of A or A'. It does this by scaling both X and A so their norms are in the range [sqrt(eps), 1/sqrt(eps)]. then it computes a QR factorization of [A,X] when TRANS = 'T', or an LQ factorization of [A',X]' when TRANS = 'N'. finally it returns the norm of the trailing triangle, scaled by MAX(M,N,NRHS)*eps. that's the whole check, periodt. 💅

🎛️ Parameters 🎛️

• TRANS — CHARACTER*1, the switch that says which direction we're checking:
  • = 'N': No transpose, check for X in the row space of A.
  • = 'T': Transpose, check for X in the row space of A'.
• M — INTEGER, the number of rows of the matrix A.
• N — INTEGER, the number of columns of the matrix A.
• NRHS — INTEGER, the number of right hand sides, i.e., the number of columns of X.
• A — DOUBLE PRECISION array, dimension (LDA,N), the M-by-N matrix A.
• LDA — INTEGER, the leading dimension of the array A.
• X — DOUBLE PRECISION array, dimension (LDX,NRHS). If TRANS = 'N', the N-by-NRHS matrix X. IF TRANS = 'T', the M-by-NRHS matrix X.
• LDX — INTEGER, the leading dimension of the array X.
• WORK — DOUBLE PRECISION array dimension (LWORK).
• LWORK — INTEGER, length of workspace array required. If TRANS = 'N', LWORK >= (M+NRHS)*(N+2); if TRANS = 'T', 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 dqrt14.f.

💻 Author 💻

Generated automatically by Doxygen for LAPACK from the source code.

---

okay bestie, that's the whole page. the footer vibe is LAPACK Version 3.12.0 and the page tag is TESTING/LIN/dqrt14.f(3). no date listed on this footer, just the version and the file tag — and that's a wrap. 💖✨