ZTRT06(3)

🌸 ZTRT06(3) — the vibe check for triangular condition numbers 💅

okay so bestie, this is a man page from the LAPACK library, and honestly? it's a whole little icon. it lives at /home/abui...IN/ztrt06.f(3) and it's a Fortran file: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ztrt06.f.

it's a library functions manual entry, and we're gonna get into it. periodt. ✨

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✨ SYNOPSIS ✨

Functions/Subroutines 🧚

subroutine ZTRT06 (rcond, rcondc, uplo, diag, n, a, lda, rwork, rat)

that's it, that's the function. it's called ZTRT06. iconic name, no notes. 👑

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💖 Function/Subroutine Documentation 💖

subroutine ZTRT06 (double precision rcond, double precision rcondc,
    character uplo, character diag, integer n, complex*16, dimension( lda, * )
    a, integer lda, double precision, dimension( * ) rwork, double
    precision rat)

so this is the full signature with all the types spelled out, because Fortran is not subtle and honestly we love that for it. 🫶

🎀 Purpose

ZTRT06 computes a test ratio comparing RCOND (the reciprocal condition number of a triangular matrix A) and RCONDC, the estimate computed by ZTRCON. 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.

okay so basically: ZTRT06 computes a test ratio that compares RCOND (the reciprocal condition number of a triangular matrix A, computed the direct way) against RCONDC (the estimate that ZTRCON spat out). and when one of them is zero and the other one isn't? it peeks at A itself to figure out whether that underflow is actually justified. detective behavior, lowkey. 🕵️‍♀️

🌈 Parameters

• RCOND — DOUBLE PRECISION. this is the estimate of the reciprocal condition number you get by forming the explicit inverse of matrix A and computing RCOND = 1/( norm(A) * norm(inv(A)) ). doing it the long way, respect. 💪
• RCONDC — DOUBLE PRECISION. the estimate of the reciprocal condition number computed by ZTRCON. that's the other one, the fancy one. ✨
• UPLO — CHARACTER. tells you whether matrix A is upper or lower triangular:
  • = 'U': upper triangular
  • = 'L': lower triangular
• DIAG — CHARACTER. tells you whether A is unit triangular or not:
  • = 'N': non-unit triangular
  • = 'U': unit triangular
• N — INTEGER. the order of matrix A. constraint: N >= 0. no negative girlies allowed. 🙅‍♀️
• A — COMPLEX*16 array, dimension (LDA,N). the triangular matrix A itself, main character energy:
  • if UPLO = 'U', the leading n by n upper triangular part of 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 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.
• LDA — INTEGER. the leading dimension of the array A. constraint: LDA >= max(1,N). don't skimp on it. 💅
• RWORK — DOUBLE PRECISION array, dimension (N). it's workspace. that's literally all it says, bestie. it's giving "just trust me". 🙈
• RAT — DOUBLE PRECISION. the test ratio, the star of the show:
  • if both RCOND and RCONDC are nonzero: RAT = MAX( RCOND, RCONDC )/MIN( RCOND, RCONDC ) - 1.
  • if RAT = 0, the two estimates are exactly the same. twin behavior. 👯‍♀️

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👑 Author

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

four whole institutions collaborated on this and honestly? teamwork makes the dream work. 🫶

Definition at line 120 of file ztrt06.f.

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🌸 Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code. so yes, a robot wrote this man page and it ate. 🤖💅

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and that's the whole thing, bestie — we got every flag, every constraint, every "not referenced", every last decimal. no details left behind. 😭🔥

LAPACK — Version 3.12.0 🌈 and the original header/footer lived at /home/abui...IN/ztrt06.f(3), dated by that very version. mwah, bye! 💖🎀🦋