TESTING/LIN/ztbt06.f(3)

okay bestie, welcome to the Library Functions Manual page for TESTING/LIN/ztbt06.f(3) — the file is TESTING/LIN/ztbt06.f, and yes it’s giving “testing helper subroutine” energy. 💅✨

✨ NAME ✨

TESTING/LIN/ztbt06.f — that’s the file, no cap. 🎀

🌈 SYNOPSIS 🌈

Functions/Subroutines

• subroutine ztbt06 (rcond, rcondc, uplo, diag, n, kd, ab, ldab, rwork, rat) — this is the subroutine, and its name is ZTBT06. 💖

💖 Function/Subroutine Documentation 💖

subroutine ztbt06

subroutine ztbt06 (double precision rcond, double precision rcondc,
    character uplo, character diag, integer n, integer kd, complex*16,
    dimension( ldab, * ) ab, integer ldab, double precision, dimension( * )
    rwork, double precision rat)

and yep, the name on the tin is ZTBT06. 🫶

Purpose

okay so the whole point, bestie: ZTBT06 computes a test ratio comparing RCOND — the reciprocal condition number of a triangular matrix A — and RCONDC, the estimate computed by ZTBCON. Information about the triangular matrix A is used if one estimate is zero and the other is non-zero, just to decide if underflow in the estimate is justified. periodt. 💫

Parameters

• RCOND — RCOND is DOUBLE PRECISION. 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)) ). math girlie behavior. 🧮
• RCONDC — RCONDC is DOUBLE PRECISION. This is the estimate of the reciprocal condition number computed by ZTBCON. 💫
• UPLO — UPLO is CHARACTER. Tells you whether the matrix A is upper or lower triangular: = 'U': Upper triangular; = 'L': Lower triangular. pick your fave. 🦋
• 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. N >= 0. 💅
• KD — KD is INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0. 🌸
• AB — AB is COMPLEX*16 array, dimension (LDAB,N). This is 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 — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1. 🔥
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N). 🫶
• RAT — RAT is DOUBLE PRECISION. 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 124 of file ztbt06.f.

🫶 Author 🫶

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and that’s the tea ☕: LAPACK Version 3.12.0, page TESTING/LIN/ztbt06.f(3). mwah 💋✨