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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: computes the reciprocal pivot growth factor norm(A)/norm(U)

```NAME
LAPACK-3 - computes the reciprocal pivot growth factor norm(A)/norm(U)

SYNOPSIS
DOUBLE PRECISION FUNCTION  ZLA_GBRPVGRW(  N,  KL,  KU, NCOLS, AB, LDAB,
AFB, LDAFB )

IMPLICIT     NONE

INTEGER      N, KL, KU, NCOLS, LDAB, LDAFB

COMPLEX*16   AB( LDAB, * ), AFB( LDAFB, * )

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.

ARGUMENTS
N       (input) INTEGER
The number of linear equations, i.e., the order of the
matrix A.  N >= 0.

KL      (input) INTEGER
The number of subdiagonals within the band of A.  KL >= 0.

KU      (input) INTEGER
The number of superdiagonals within the band of A.  KU >= 0.

NCOLS   (input) INTEGER
The number of columns of the matrix A.  NCOLS >= 0.

AB      (input) 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    (input) INTEGER
The leading dimension of the array AB.  LDAB >= KL+KU+1.

AFB     (input) 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   (input) INTEGER
The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.

LAPACK routine (version 3.2.2)March 2011                       LAPACK-3(3)
```