STRT06(3)

💅 STRT06(3) — like, the LAPACK testing one, from the Library Functions Manual 🎀

okay so bestie. this page is literally just one tiny Fortran subroutine that does vibe checks on condition-number estimates, and honestly? it ate. let's get into it ✨

---

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/strt06.f

yep that's the whole name, it's giving "my professor named the file after the entire filesystem" 😭 no cap, that's the path, that's the file, that's the girl.

---

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine STRT06 (rcond, rcondc, uplo, diag, n, a, lda, work, rat)

STRT06 — that's her. main character energy tbh 👑

---

👑 Function/Subroutine Documentation 👑

subroutine STRT06 (real rcond, real rcondc, character uplo, character diag,
    integer n, real, dimension( lda, * ) a, integer lda, real, dimension( *
    ) work, real rat)

STRT06 — again, iconic, we love a repeat appearance 💖

✨ Purpose ✨

!>
!> STRT06 computes a test ratio comparing RCOND (the reciprocal
!> condition number of a triangular matrix A) and RCONDC, the estimate
!> computed by STRCON.  Information about the triangular matrix A is
!> used if one estimate is zero and the other is non-zero to decide if
!> underflow in the estimate is justified.
!>

so real talk: STRT06 computes a test ratio that compares RCOND — the reciprocal condition number of a triangular matrix A — against RCONDC, which is the estimate that STRCON computed. and here's the cute part 🫶: if one of those estimates is zero and the other one isn't, it peeks at the info about the triangular matrix A to decide whether that underflow in the estimate is actually justified. detective work, honestly 🔍

🌈 Parameters 🌈

• RCOND — RCOND is REAL. it's the estimate of the reciprocal condition number you get by forming the explicit inverse of the matrix A and computing RCOND = 1/( norm(A) * norm(inv(A)) ). yes, the whole explicit-inverse situation. she did the math 💅
• RCONDC — RCONDC is REAL. the estimate of the reciprocal condition number computed by STRCON. that's it, that's the girl 🌸
• UPLO — UPLO is CHARACTER. tells us whether the matrix A is upper or lower triangular. options are:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• DIAG — DIAG is CHARACTER. says whether or not the matrix A is unit triangular:
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• N — N is INTEGER. the order of the matrix A. and N >= 0, no funny business 🙈
• A — A is REAL array, dimension (LDA,N). it's the triangular matrix A itself. and here's the tea:
  • if UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced.
  • if UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced.
  • if DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1. assumed!! we don't even look at them, we just trust 🫡
• LDA — LDA is INTEGER. the leading dimension of the array A. and LDA >= max(1,N). respect the bound fr fr
• WORK — WORK is REAL array, dimension (N). just a lil workspace, nothing dramatic 💀
• RAT — RAT is REAL. THE test ratio, the whole point of the function, the moment 👑. if both RCOND and RCONDC are nonzero:

RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.

and if RAT = 0, that means the two estimates are exactly the same. twin flames. identical. zero difference. slay 🎀

💜 Author 💜

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

and the definition is at line 119 of file strt06.f — go look, she's right there 🧚

---

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. so nobody hand-wrote this one, the machine did it and honestly the machine understood the assignment 💅✨

---

okay that's the whole page bestie, you're officially caught up 🫶 and yes, we're closing out with the official sign-off: this whole thing is LAPACK, Version 3.12.0, and the footer girlie herself is /home/abui...IN/strt06.f(3) — an abbreviated little icon, we stan a mysterious path 🌈💖 see you in the next manpage, mwah 😘