SRC/sgbcon.f(3)

✨ NAME ✨

okay so this page is SRC/sgbcon.f, straight out of the Library Functions Manual — and it’s all about the SGBCON subroutine, bestie. 💅

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🌸 SYNOPSIS 🌸

🧚 Functions/Subroutines

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

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🛠️ Function/Subroutine Documentation 🛠️

🎀 SGBCON 🎀

subroutine sgbcon (character norm, integer n, integer kl, integer ku, real,
    dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv,
    real anorm, real rcond, real, dimension( * ) work, integer, dimension( *
    ) iwork, integer info)
    SGBCON

🌟 Purpose

so here’s the vibe: SGBCON 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 SGBTRF.

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 says whether you want the 1-norm condition number or the infinity-norm condition number:
  • = '1' or 'O': 1-norm;
  • = 'I': Infinity-norm.
• N — N is INTEGER. The order of the matrix A. N >= 0.
• 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 REAL array, dimension (LDAB,N). It holds details of the LU factorization of the band matrix A, as computed by SGBTRF. 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 REAL. If NORM = '1' or 'O', this is the 1-norm of the original matrix A. If NORM = 'I', this is the infinity-norm of the original matrix A.
• RCOND — RCOND is REAL. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
• WORK — WORK is REAL 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 sgbcon.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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and that’s the whole page, bestie 💖 The footer says LAPACK, Version 3.12.0, and SRC/sgbcon.f(3) — and no separate date is listed. Bye! 🎀