# dla_gbrcond.f (3) - Linux Man Pages

dla_gbrcond.f -

## SYNOPSIS

### Functions/Subroutines

DOUBLE PRECISION function dla_gbrcond (TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, CMODE, C, INFO, WORK, IWORK)
DLA_GBRCOND estimates the Skeel condition number for a general banded matrix.

## Function/Subroutine Documentation

### DOUBLE PRECISION function dla_gbrcond (characterTRANS, integerN, integerKL, integerKU, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( ldafb, * )AFB, integerLDAFB, integer, dimension( * )IPIV, integerCMODE, double precision, dimension( * )C, integerINFO, double precision, dimension( * )WORK, integer, dimension( * )IWORK)

DLA_GBRCOND estimates the Skeel condition number for a general banded matrix.

Purpose:

```    DLA_GBRCOND Estimates the Skeel condition number of  op(A) * op2(C)
where op2 is determined by CMODE as follows
CMODE =  1    op2(C) = C
CMODE =  0    op2(C) = I
CMODE = -1    op2(C) = inv(C)
The Skeel condition number  cond(A) = norminf( |inv(A)||A| )
is computed by computing scaling factors R such that
diag(R)*A*op2(C) is row equilibrated and computing the standard
infinity-norm condition number.
```

Parameters:

TRANS

```          TRANS is CHARACTER*1
Specifies the form of the system of equations:
= 'N':  A * X = B     (No transpose)
= 'T':  A**T * X = B  (Transpose)
= 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
```

N

```          N is INTEGER
The number of linear equations, i.e., 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)
On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
The j-th column of A is stored in the j-th column of the
array AB as follows:
AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
```

LDAB

```          LDAB is INTEGER
The leading dimension of the array AB.  LDAB >= KL+KU+1.
```

AFB

```          AFB is DOUBLE PRECISION array, dimension (LDAFB,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.
```

LDAFB

```          LDAFB is INTEGER
The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
```

IPIV

```          IPIV is INTEGER array, dimension (N)
The pivot indices from the factorization A = P*L*U
as computed by DGBTRF; row i of the matrix was interchanged
with row IPIV(i).
```

CMODE

```          CMODE is INTEGER
Determines op2(C) in the formula op(A) * op2(C) as follows:
CMODE =  1    op2(C) = C
CMODE =  0    op2(C) = I
CMODE = -1    op2(C) = inv(C)
```

C

```          C is DOUBLE PRECISION array, dimension (N)
The vector C in the formula op(A) * op2(C).
```

INFO

```          INFO is INTEGER
= 0:  Successful exit.
i > 0:  The ith argument is invalid.
```

WORK

```          WORK is DOUBLE PRECISION array, dimension (5*N).
Workspace.
```

IWORK

```          IWORK is INTEGER array, dimension (N).
Workspace.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 169 of file dla_gbrcond.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.