TESTING/LIN/stbt06.f(3)

🌸 NAME 🌸

TESTING/LIN/stbt06.f

okay so this is the manual page for TESTING/LIN/stbt06.f, and it lives in the Library Functions Manual — we're keeping every detail, no cap. 💖

✨ SYNOPSIS ✨

🌟 Functions/Subroutines 🌟

       subroutine stbt06 (rcond, rcondc, uplo, diag, n, kd, ab, ldab, work,
           rat)
           STBT06

💅 Function/Subroutine Documentation 💅

🦋 subroutine stbt06 🦋

   subroutine stbt06 (real rcond, real rcondc, character uplo, character diag,
       integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab,
       real, dimension( * ) work, real rat)
       STBT06

🌟 Purpose 🌟

STBT06 computes a test ratio comparing RCOND (the reciprocal condition number of a triangular matrix A) and RCONDC, the estimate computed by STBCON. 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. Lowkey that's the whole plot. 🫶

🍓 Parameters 🍓

• RCOND — REAL. 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)) ). That's the formula, bestie — don't lose it. 💅
• RCONDC — REAL. The estimate of the reciprocal condition number computed by STBCON.
• UPLO — CHARACTER. Specifies whether the matrix A is upper or lower triangular. = 'U': Upper triangular. = 'L': Lower triangular.
• DIAG — CHARACTER. Specifies whether or not the matrix A is unit triangular. = 'N': Non-unit triangular. = 'U': Unit triangular.
• N — INTEGER. The order of the matrix A. N >= 0. yes, zero is allowed, slay. ✨
• KD — INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0.
• AB — REAL array, dimension (LDAB,N). The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
• LDAB — INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• WORK — REAL array, dimension (N).
• RAT — REAL. 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. iconic. 👑

👑 Author 👑

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

Definition at line 123 of file stbt06.f.

🌈 Author 🌈

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Signing off, bestie 💖: this footer situation is LAPACK Version 3.12.0, page TESTING/LIN/stbt06.f(3). No separate date is listed in the footer, so I'm not inventing one — periodt. 🎀