# dgbcon.f (3) - Linux Manuals

dgbcon.f -

## SYNOPSIS

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine dgbcon (characterNORM, integerN, integerKL, integerKU, double precision, dimension( ldab, * )AB, integerLDAB, integer, dimension( * )IPIV, double precisionANORM, double precisionRCOND, double precision, dimension( * )WORK, integer, dimension( * )IWORK, integerINFO)

DGBCON

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)) ).
```

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 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

```          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 DOUBLE PRECISION array, dimension (3*N)
```

IWORK

```          IWORK is INTEGER 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