SRC/cgbcon.f(3)

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🌸 NAME 🌸

SRC/cgbcon.f

📚 SYNOPSIS 📚

🧚 Functions/Subroutines

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

🫶 FUNCTION/SUBROUTINE DOCUMENTATION 🫶

   subroutine cgbcon (character norm, integer n, integer kl, integer ku,
       complex, dimension( ldab, * ) ab, integer ldab, integer, dimension( * )
       ipiv, real anorm, real rcond, complex, dimension( * ) work, real,
       dimension( * ) rwork, integer info)
       CGBCON

🎯 Purpose 🎯

okay so CGBCON 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 CGBTRF. No cap 🧮

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

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 array, dimension (LDAB,N) — the details of the LU factorization of the band matrix A, as computed by CGBTRF. 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', it’s the 1-norm of the original matrix A. If NORM = 'I', it’s 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 COMPLEX array, dimension (2*N).

RWORK

• RWORK is REAL 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 cgbcon.f.

🪄 AUTHOR 🪄

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okay that’s the whole thing, bestie. This page is from LAPACK Version 3.12.0 and the source is SRC/cgbcon.f(3). go off, condition-number icon 💅💖