NAME

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

SYNOPSIS

SUBROUTINE ZGBCON( NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, RWORK, INFO )

CHARACTER NORM

INTEGER INFO, KL, KU, LDAB, N

DOUBLE PRECISION ANORM, RCOND

INTEGER IPIV( ∗ )

DOUBLE PRECISION RWORK( ∗ )

COMPLEX∗16 AB( LDAB, ∗ ), WORK( ∗ )

#include <sunperf.h>

void zgbcon(char norm, int n, int kl, int ku, doublecomplex ∗zab, int ldab, int ∗ipivot, double anorm, double ∗drcond, int ∗info) ;

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)) ).
 

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) 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 (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) COMPLEX∗16 array, dimension (2∗N)

RWORK (workspace) DOUBLE PRECISION array, dimension (N)

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

SunOS 5.0  —  Last change: 10 Dec 1998