---
name: "cla_gbrpvgrw"
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/cla_gbrpvgrw.f"
---

# cla\_gbrpvgrw(3)

Part of [cla\_gbrpvgrw.f(3)](/cla_gbrpvgrw.f/3.md).

## NAME

SRC/cla\_gbrpvgrw.f

## SYNOPSIS

### Functions/Subroutines

real function **cla\_gbrpvgrw** (n, kl, ku, ncols, ab, ldab, afb, ldafb)\
 **CLA\_GBRPVGRW** computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

## Function/Subroutine Documentation

### real function cla\_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, complex, dimension( ldab, \* ) ab, integer ldab, complex, dimension( ldafb, \* ) afb, integer ldafb)

**CLA\_GBRPVGRW** computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

**Purpose:**

```
!>
!> CLA_GBRPVGRW computes the reciprocal pivot growth factor
!> norm(A)/norm(U). The  norm is used. If this is
!> much less than 1, the stability of the LU factorization of the
!> (equilibrated) matrix A could be poor. This also means that the
!> solution X, estimated condition numbers, and error bounds could be
!> unreliable.
!>
```

**Parameters**

*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.
!>
```

*NCOLS*

```
!>          NCOLS is INTEGER
!>     The number of columns of the matrix A.  NCOLS >= 0.
!>
```

*AB*

```
!>          AB is COMPLEX 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 COMPLEX array, dimension (LDAFB,N)
!>     Details of the LU factorization of the band matrix A, as
!>     computed by CGBTRF.  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.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **115** of file **cla\_gbrpvgrw.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.