NAME

DGBCON - estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,

SYNOPSIS

SUBROUTINE DGBCON(
NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, IWORK, INFO )

CHARACTER NORM

INTEGER INFO, KL, KU, LDAB, N

DOUBLE PRECISION ANORM, RCOND

INTEGER IPIV( ∗ ), IWORK( ∗ )

DOUBLE PRECISION AB( LDAB, ∗ ), WORK( ∗ )

PURPOSE

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)) ).
 

ARGUMENTS

NORM    (input) 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       (input) INTEGER
The order of the matrix A.  N >= 0.

KL      (input) INTEGER
The number of subdiagonals within the band of A.  KL >= 0.

KU      (input) INTEGER
The number of superdiagonals within the band of A.  KU >= 0.

AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)
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    (input) INTEGER
The leading dimension of the array AB.  LDAB >= 2∗KL+KU+1.

IPIV    (input) INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i).

ANORM   (input) 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   (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) ∗ norm(inv(A))).

WORK    (workspace) DOUBLE PRECISION array, dimension (3∗N)

IWORK   (workspace) INTEGER array, dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

  —  LAPACK version 2.0  —  08 October 1994