DGBCON(3)

📦 version 3.12.0, in opensuse-leap 16.0

NAME 🌸

okay so literally the entire plot of this page is one (1) file, and that file is bestie:

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

SYNOPSIS ✨

Functions/Subroutines 🎀


   subroutine DGBCON (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work,
       iwork, info)

That's DGBCON — the icon, the moment, the whole vibe 💅

Function/Subroutine Documentation 💅


   subroutine DGBCON (character norm, integer n, integer kl, integer ku, double
       precision, dimension( ldab, * ) ab, integer ldab, integer, dimension( *
       ) ipiv, double precision anorm, double precision rcond, double
       precision, dimension( * ) work, integer, dimension( * ) iwork, integer
       info)

DGBCON 👑

Purpose 🔥

So what does DGBCON actually DO? Bestie, okay: DGBCON estimates the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by DGBTRF. Lowkey iconic honestly.

An estimate is obtained for norm(inv(A)), and 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.

N

N is INTEGER — the order of the matrix A. N >= 0. no negatives pls 🙈

KL

KL is INTEGER — the number of subdiagonals within the band of A. KL >= 0.

KU

KU is INTEGER — the number of superdiagonals within the band of A. KU >= 0.

AB

AB is DOUBLE PRECISION array, dimension (LDAB,N) — details of the LU factorization of the band matrix A, as computed by DGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1.

LDAB

LDAB is INTEGER — the leading dimension of the array AB. LDAB >= 2*KL+KU+1.

IPIV

IPIV is INTEGER array, dimension (N) — the pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i).

ANORM

ANORM is DOUBLE PRECISION — if NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original matrix A.

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 144 of file dgbcon.f.

Author 🫶

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