ZGBCON(3)

🎀 zgbcon.f(3) 🎀

Library Functions Manual, bestie — this is the page for the Fortran source file at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zgbcon.f. No cap, it's giving linear algebra royalty. 👑

🌸 NAME 🌸

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

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine ZGBCON (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work,
    rwork, info)
    ZGBCON

💖 Function/Subroutine Documentation 💖

subroutine ZGBCON (character norm, integer n, integer kl, integer ku,
    complex*16, dimension( ldab, * ) ab, integer ldab, integer, dimension( *
    ) ipiv, double precision anorm, double precision rcond, complex*16,
    dimension( * ) work, double precision, dimension( * ) rwork, integer
    info)

ZGBCON — iconic subroutine name, main character energy, no notes. 🫶

🦋 Purpose 🦋

ZGBCON estimates the reciprocal of the condition number of a complex general band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by ZGBTRF.

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)) ).

Condition-number vibe check complete, fr fr. ✨

🍓 Parameters 🍓

• NORM — CHARACTER*1. Specifies whether the 1-norm condition number or the infinity-norm condition number is required:
  • = '1' or 'O': 1-norm;
  • = 'I': Infinity-norm.
• N — INTEGER. The order of the matrix A. N >= 0.
• KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0.
• KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0.
• AB — COMPLEX*16 array, dimension (LDAB,N). Details of the LU factorization of the band matrix A, as computed by ZGBTRF. 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 — INTEGER. The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
• IPIV — INTEGER array, dimension (N). The pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i).
• ANORM — 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 — DOUBLE PRECISION. The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
• WORK — COMPLEX*16 array, dimension (2*N).
• RWORK — DOUBLE PRECISION array, dimension (N).
• INFO — 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 145 of file zgbcon.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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💖 Okay bestie, that's the whole page. Footer source/version: LAPACK Version 3.12.0; footer path: /home/abui...RC/zgbcon.f(3). No separate date is given in the original footer, so I'm not inventing one. That page ate, periodt — iykyk. 🫶