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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
NAG Ltd.
Date:
September 2012
Definition at line 117 of file zla_gbrpvgrw.f.

# Author

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