# sla_gbrpvgrw(3) [centos man page]

```sla_gbrpvgrw.f(3)						      LAPACK							 sla_gbrpvgrw.f(3)

NAME
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 (integerN, integerKL, integerKU, integerNCOLS, real, dimension( ldab, * )AB, integerLDAB, real, dimension( ldafb, *
)AFB, integerLDAFB)
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:
September 2012

Definition at line 117 of file sla_gbrpvgrw.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						 sla_gbrpvgrw.f(3)```

## Check Out this Related Man Page

```zla_gbrpvgrw.f(3)						      LAPACK							 zla_gbrpvgrw.f(3)

NAME
zla_gbrpvgrw.f -

SYNOPSIS
Functions/Subroutines
DOUBLE PRECISION function zla_gbrpvgrw (N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)
ZLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

Function/Subroutine Documentation
DOUBLE PRECISION function zla_gbrpvgrw (integerN, integerKL, integerKU, integerNCOLS, complex*16, dimension( ldab, * )AB, integerLDAB,
complex*16, dimension( ldafb, * )AFB, integerLDAFB)
ZLA_GBRPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

Purpose:

ZLA_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 COMPLEX*16 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*16 array, dimension (LDAFB,N)
Details of the LU factorization of the band matrix A, as
computed by ZGBTRF.  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