# zgbcon.f man page

zgbcon.f —

## Synopsis

### Functions/Subroutines

subroutinezgbcon(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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

Definition at line 147 of file zgbcon.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zgbcon(3) is an alias of zgbcon.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK