TESTING/LIN/stpt06.f(3)

✨ NAME ✨

Okay bestie, this page is literally TESTING/LIN/stpt06.f — and the header title is TESTING/LIN/stpt06.f(3). The manual name is folded in near the top like a little name tag: Library Functions Manual. That's the whole NAME section, no cap. 🎀

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💖 SYNOPSIS 💖

🧚 Functions/Subroutines 🧚

• subroutine stpt06 (rcond, rcondc, uplo, diag, n, ap, work, rat) — STPT06 (yes, that's the label, periodt)

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🦋 Function/Subroutine Documentation 🦋

🌈 subroutine stpt06 🌈

The full signature is giving exact-type-energy:

   subroutine stpt06 (real rcond, real rcondc, character uplo, character diag,
       integer n, real, dimension( * ) ap, real, dimension( * ) work, real rat)

This one is called STPT06, and the source doc-comment lines are prefixed with !> because Doxygen is Doxygen. Anyway, here's the tea: 🍵

🎀 Purpose 🎀

STPT06 computes a test ratio comparing RCOND (the reciprocal condition number of a triangular matrix A) and RCONDC, the estimate computed by STPCON. 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. 👑

🌸 Parameters 🌸

💖 RCOND

RCOND is REAL. It's the estimate of the reciprocal condition number obtained by forming the explicit inverse of the matrix A and computing:

RCOND = 1/( norm(A) * norm(inv(A)) ).

Explicit inverse energy. Iconic but expensive, iykyk. 💅

💜 RCONDC

RCONDC is REAL. It's the estimate of the reciprocal condition number computed by STPCON. That's the other estimate in this little comparison era. ✨

🦋 UPLO

UPLO is CHARACTER. It specifies whether the matrix A is upper or lower triangular:

• = 'U': Upper triangular
• = 'L': Lower triangular

Pick a side, bestie — upper or lower. 🎀

🎀 DIAG

DIAG is CHARACTER. It specifies whether or not the matrix A is unit triangular:

• = 'N': Non-unit triangular
• = 'U': Unit triangular

Unit or non-unit, that's the whole vibe check. 🌱

⭐ N

N is INTEGER. It's the order of the matrix A, and N >= 0. Zero is allowed, bestie, but negative is not the move. 🙈

🍓 AP

AP is a REAL array, dimension (N*(N+1)/2). It holds the upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:

if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
if UPLO = 'L',
   AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.

Packed columnwise, no gaps, no drama — okay maybe a little drama. 🫶

🌈 WORK

WORK is a REAL array, dimension (N). It's workspace. It's doing its little job. 🧚

🔥 RAT

RAT is REAL. It's the test ratio. 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. Exactly. The. Same. Periodt. 💀

👑 Author

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

Definition at line 110 of file stpt06.f. Line 110, bestie — noted and remembered. 📌

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code. Doxygen really said “I'll generate the docs, you go live your life.” ✨

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Sign-off time, bestie: the footer source/version is LAPACK Version 3.12.0, and the page is TESTING/LIN/stpt06.f(3). There's no extra printed date hanging out in this footer, so that's the whole closing-line tea. 💅🎀