---
name: "dla_gbrcond.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/dla_gbrcond.f"
---

# dla\_gbrcond.f(3)

## NAME

SRC/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 (character trans, integer n, integer kl, integer ku, double precision, dimension( ldab, \* ) ab, integer ldab, double precision, dimension( ldafb, \* ) afb, integer ldafb, integer, dimension( \* ) ipiv, integer cmode, double precision, dimension( \* ) c, integer info, 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.

Definition at line **167** of file **dla\_gbrcond.f**.

## Author

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