DTBT06(3)

📦 version 3.12.0, in opensuse-leap 16.0

< pink>okay bestie, welcome to dtbt06.f(3) from the Library Functions Manual 💅 this page is literally all about a tiny LAPACK test-ratio routine, and we're gonna get into every detail. no cap.

💖 NAME 💖

The page is for this exact file path, character for character:

/home/abuild/rpmbuild/BUILD/lapack-
static-3.12.0-build/lapack-3.12.0/TESTING/LIN/dtbt06.f

✨ SYNOPSIS ✨

Functions/Subroutines

       subroutine DTBT06 (rcond, rcondc, uplo, diag, n, kd, ab, ldab, work,
           rat)
           DTBT06

🦋 Function/Subroutine Documentation 🦋

Here's the full signature, exactly as it appears:

   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 🎀

DTBT06 computes a test ratio comparing RCOND (the reciprocal condition number of a triangular matrix A) and RCONDC, the estimate computed by DTBCON. 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. That's the whole assignment, and it ate. 🔥

🍓 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. It's the order of the matrix A, and N >= 0.

KD

KD is INTEGER. It's the number of superdiagonals or subdiagonals of the triangular band matrix A, and KD >= 0.

AB

AB is a DOUBLE PRECISION array, dimension (LDAB,N). It holds 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. It's the leading dimension of the array AB, and LDAB >= KD+1.

WORK

WORK is a DOUBLE PRECISION array, dimension (N).

RAT

RAT is DOUBLE PRECISION. 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.

👑 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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