SRC/dgbcon.f(3)

🦋 SRC/dgbcon.f — Library Functions Manual 🦋

💖 NAME 💖

SRC/dgbcon.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

🦋 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 🎀

Okay so bestie, 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.

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. This tells us whether you need 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 DOUBLE PRECISION array, dimension (LDAB,N). It holds 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', 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 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 🌸

Generated automatically by Doxygen for LAPACK from the source code.

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