DTBCON(3)

🎀 DTBCON(3) — Library Functions Manual 🎀

okay bestie, this is DTBCON(3), and the manual name up top is literally Library Functions Manual ✨. It’s the page for dtbcon.f, and yes the NAME section is a whole file path, not a cute short name — it’s giving absolute-path realness 💅.

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dtbcon.f

That’s the name, no cap 🫶.

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine DTBCON (norm, uplo, diag, n, kd, ab, ldab, rcond, work,
    iwork, info)
    DTBCON

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📚 Function/Subroutine Documentation 📚

Here’s the full signature, bestie:

subroutine DTBCON (character norm, character uplo, character diag, integer
    n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab,
    double precision rcond, double precision, dimension( * ) work, integer,
    dimension( * ) iwork, integer info)
    DTBCON

Purpose

DTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm. Obsessed 💖.

The norm of A is computed, and an estimate is obtained for norm(inv(A)). Then the reciprocal of the condition number is computed as:

RCOND = 1 / ( norm(A) * norm(inv(A)) ).

Parameters

• NORM — NORM is CHARACTER*1. It specifies whether the 1-norm condition number or the infinity-norm condition number is required:
  • = '1' or 'O': 1-norm;
  • = 'I': Infinity-norm.
• UPLO — UPLO is CHARACTER*1:
  • = 'U': A is upper triangular;
  • = 'L': A is lower triangular.
• DIAG — DIAG is CHARACTER*1:
  • = 'N': A is non-unit triangular;
  • = 'U': A is 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 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).

If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.

• LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KD+1.
• RCOND — RCOND is DOUBLE PRECISION. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
• WORK — WORK is DOUBLE PRECISION array, dimension (3*N).
• IWORK — IWORK is INTEGER array, dimension (N).
• INFO — INFO is INTEGER:
  • = 0: successful exit;
  • < 0: if INFO = -i, the i-th argument had an illegal value.

Author

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

Definition at line 141 of file dtbcon.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

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💖 final footer sign-off, bestie: this page is from LAPACK Version 3.12.0, and the footer path is /home/abui...RC/dtbcon.f(3) 🦋. Date-wise there’s no date line in this copy, so I’m not inventing one — periodt ✨.