# sla_gbrpvgrw.f man page

sla_gbrpvgrw.f —

## Synopsis

### Functions/Subroutines

real function sla_gbrpvgrw (N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)
SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

## Function/Subroutine Documentation

### real function sla_gbrpvgrw (integer N, integer KL, integer KU, integer NCOLS, real, dimension( ldab, * ) AB, integer LDAB, real, dimension( ldafb, * ) AFB, integer LDAFB)

SLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

Purpose:

``` SLA_GBRPVGRW computes the reciprocal pivot growth factor
norm(A)/norm(U). The "max absolute element" 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 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.```
Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

Definition at line 119 of file sla_gbrpvgrw.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sla_gbrpvgrw(3) is an alias of sla_gbrpvgrw.f(3).

Sat Jun 24 2017 Version 3.7.1 LAPACK