# zla_gbrpvgrw.f man page

zla_gbrpvgrw.f —

## Synopsis

### Functions/Subroutines

DOUBLE PRECISION functionzla_gbrpvgrw(N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB)ZLA_GBRPVGRWcomputes 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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 117 of file zla_gbrpvgrw.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zla_gbrpvgrw(3) is an alias of zla_gbrpvgrw.f(3).