# zgbcon(3) [centos man page]

```zgbcon.f(3)							      LAPACK							       zgbcon.f(3)

NAME
zgbcon.f -

SYNOPSIS
Functions/Subroutines
subroutine zgbcon (NORM, N, KL, KU, AB, LDAB, IPIV, ANORM, RCOND, WORK, RWORK, INFO)
ZGBCON

Function/Subroutine Documentation
subroutine zgbcon (characterNORM, integerN, integerKL, integerKU, complex*16, dimension( ldab, * )AB, integerLDAB, integer, dimension( * )IPIV,
double precisionANORM, double precisionRCOND, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)
ZGBCON

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)) ).

Parameters:
NORM

NORM is 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

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

NAG Ltd.

Date:
November 2011

Definition at line 147 of file zgbcon.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       zgbcon.f(3)```

## Check Out this Related Man Page

```ZGBCON(l)								 )								 ZGBCON(l)

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( * )

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

LAPACK version 3.0						   15 June 2000 							 ZGBCON(l)```
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