TESTING/LIN/dtbt06.f(3)

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NAME

Bestie, welcome to TESTING/LIN/dtbt06.f — aka the TESTING/LIN/dtbt06.f(3) page in the Library Functions Manual. It’s giving very specific LAPACK testing energy, and honestly? Iconic. 💅

SYNOPSIS

Functions/Subroutines

subroutine dtbt06 (rcond, rcondc, uplo, diag, n, kd, ab, ldab, work,
    rat)

DTBT06 — that’s the main character right there. ✨

Function/Subroutine Documentation

subroutine dtbt06 (double precision rcond, double precision rcondc, character uplo, character diag, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) work, double precision rat)

DTBT06

Purpose

Okay so DTBT06 computes a test ratio comparing RCOND — the reciprocal condition number of a triangular matrix A — and RCONDC, the estimate computed by DTBCON. No cap, that’s the whole vibe.

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 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)) ).
  • RCONDC — RCONDC is DOUBLE PRECISION. It’s the estimate of the reciprocal condition number computed by DTBCON. 💖
  • UPLO — UPLO is CHARACTER. It specifies whether the matrix A is upper or lower triangular:
    • 'U': Upper triangular
    • 'L': Lower triangular
  • DIAG — DIAG is CHARACTER. It specifies 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 a DOUBLE PRECISION 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 — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1. 🎀
  • WORK — WORK is a 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. Periodt. 💅

Author

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

Definition at line 123 of file dtbt06.f.

Author

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