SRC/zgbcon.f(3)

🌸 NAME 🌸

SRC/zgbcon.f — library functions manual, bestie ✨. This page is all about the ZGBCON subroutine, and it's lowkey iconic.

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

• ZGBCON — the main character of this page 💅

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

🧚 Function/Subroutine Documentation 🧚

🎀 subroutine zgbcon 🎀

       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

🎀 Purpose 🎀

Okay so 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)) ).

💖 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.
• 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 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 — 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 COMPLEX*16 array, dimension (2*N).
• RWORK — RWORK is DOUBLE PRECISION 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 145 of file zgbcon.f. 🧭

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie 💖 — LAPACK Version 3.12.0, source page SRC/zgbcon.f(3). Periodt 🎀✨