# zgbcon.f man page

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 (character NORM, integer N, integer KL, integer KU, complex*16, dimension( ldab, * ) AB, integer LDAB, integer, dimension( * ) IPIV, double precision ANORM, double precision RCOND, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer INFO)

**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

Univ. of Colorado Denver

NAG Ltd.

**Date:**December 2016

Definition at line 149 of file zgbcon.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zgbcon(3) is an alias of zgbcon.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK