# sla_gbrcond.f man page

sla_gbrcond.f —

## Synopsis

### Functions/Subroutines

REAL functionsla_gbrcond(TRANS, N, KL, KU, AB, LDAB, AFB, LDAFB, IPIV, CMODE, C, INFO, WORK, IWORK)SLA_GBRCONDestimates the Skeel condition number for a general banded matrix.

## Function/Subroutine Documentation

### REAL function sla_gbrcond (characterTRANS, integerN, integerKL, integerKU, real, dimension( ldab, * )AB, integerLDAB, real, dimension( ldafb, * )AFB, integerLDAFB, integer, dimension( * )IPIV, integerCMODE, real, dimension( * )C, integerINFO, real, dimension( * )WORK, integer, dimension( * )IWORK)

**SLA_GBRCOND** estimates the Skeel condition number for a general banded matrix.

**Purpose:**

```
SLA_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 REAL 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 REAL array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as
computed by SGBTRF. 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 SGBTRF; 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 REAL 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 REAL 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 168 of file sla_gbrcond.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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