TESTING/LIN/sqrt14.f(3)

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💖 TESTING/LIN/sqrt14.f 💖

okay bestie, this page is serving Library Functions Manual energy, and it's all about the SQRT14 routine. it's giving “let me check if X is in the row space” detective vibes 🕵️‍♀️✨

✨ NAME ✨

TESTING/LIN/sqrt14.f

🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines 🧚

  • real function sqrt14 (trans, m, n, nrhs, a, lda, x, ldx, work, lwork) — the SQRT14 function, front and center.

🦋 Function/Subroutine Documentation 🦋

here's the full signature, character-for-character, no edits, no cap:

real function sqrt14 (character trans, integer m, integer n, integer nrhs,
       real, dimension( lda, * ) a, integer lda, real, dimension( ldx, * ) x,
       integer ldx, real, dimension( lwork ) work, integer lwork)

SQRT14 💅

🎀 Purpose 🎀

okay so SQRT14 is checking 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 computing a QR factorization of [A,X] when TRANS = 'T', or an LQ factorization of [A',X]' when TRANS = 'N', and returning the norm of the trailing triangle, scaled by MAX(M,N,NRHS)*eps. slay 💖

✨ Parameters ✨

  • TRANS — TRANS is CHARACTER*1. = 'N': no transpose, check for X in the row space of A; = 'T': transpose, check for X in the 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 REAL array, dimension (LDA,N). the M-by-N matrix A.
  • LDA — LDA is INTEGER. the leading dimension of the array A.
  • X — X is REAL array, dimension (LDX,NRHS). if TRANS = 'N', the N-by-NRHS matrix X; if TRANS = 'T', the M-by-NRHS matrix X.
  • LDX — LDX is INTEGER. the leading dimension of the array X.
  • WORK — WORK is REAL array dimension (LWORK).
  • LWORK — LWORK is 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 📍

Definition at line 114 of file sqrt14.f.

🌈 Author (Doxygen edition) 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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