TESTING/LIN/ctbt06.f(3)

🌸 NAME 🌸

Okay so this page is TESTING/LIN/ctbt06.f(3) from the Library Functions Manual, and the name section is literally just TESTING/LIN/ctbt06.f — short, sweet, iconic. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

There's a subroutine called ctbt06, and here's the exact call:

subroutine ctbt06 (rcond, rcondc, uplo, diag, n, kd, ab, ldab, rwork,
           rat)

CTBT06 — yes bestie, same name again, uppercase main-character energy. ✨

🫶 Function/Subroutine Documentation 🫶

Here's the full signature with all the types, no cap:

subroutine ctbt06 (real rcond, real rcondc, character uplo, character diag,
           integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab,
           real, dimension( * ) rwork, real rat)

CTBT06 — okay it said it again, and we respect the repetition. 👑

Purpose

CTBT06 computes a test ratio comparing RCOND (the reciprocal condition number of a triangular matrix A) and RCONDC, the estimate computed by CTBCON. 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 — this one 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)) ). 💖
• RCONDC — also REAL. This is the estimate of the reciprocal condition number computed by CTBCON. 🦋
• UPLO — a CHARACTER, bestie. It specifies whether the matrix A is upper or lower triangular:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• DIAG — another CHARACTER. It specifies whether or not the matrix A is unit triangular:
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• N — an INTEGER. The order of the matrix A. N >= 0. 🎀
• KD — an INTEGER. The number of superdiagonals or subdiagonals of the triangular band matrix A. KD >= 0. 🌈
• AB — a COMPLEX array, dimension (LDAB,N). It's 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 — an INTEGER. The leading dimension of the array AB. LDAB >= KD+1. 🌟
• RWORK — a REAL array, dimension (N). 🍓
• RAT — a 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. 😭💖

Author

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

Definition at line 124 of file ctbt06.f.

Line 124 of ctbt06.f — noted, bestie. 📍

Author

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Signing off with LAPACK, Version 3.12.0, and the page TESTING/LIN/ctbt06.f(3) — periodt, mwah! 💖🎀🦋