Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3  -  computes  an LU factorization of a complex m-by-n band matrix A using partial
pivoting with row interchanges

```

#### SYNOPSIS

```       SUBROUTINE CGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )

INTEGER        INFO, KL, KU, LDAB, M, N

INTEGER        IPIV( * )

COMPLEX        AB( LDAB, * )

```

#### PURPOSE

```       CGBTF2 computes an LU factorization of a  complex  m-by-n  band  matrix  A  using  partial
pivoting with row interchanges.
This is the unblocked version of the algorithm, calling Level 2 BLAS.

```

#### ARGUMENTS

```        M       (input) INTEGER
The number of rows of the matrix A.  M >= 0.

N       (input) INTEGER
The number of columns 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.

AB      (input/output) COMPLEX array, dimension (LDAB,N)
On entry, the matrix A in band storage, in rows KL+1 to
2*KL+KU+1; rows 1 to KL of the array need not be set.
The j-th column of A is stored in the j-th column of the
array AB as follows:
AB(kl+ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)
On exit, details of the factorization: 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.
See below for further details.

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

IPIV    (output) INTEGER array, dimension (min(M,N))
The pivot indices; for 1 <= i <= min(M,N), row i of the
matrix was interchanged with row IPIV(i).

INFO    (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = +i, U(i,i) is exactly zero. The factorization
has been completed, but the factor U is exactly
singular, and division by zero will occur if it is used
to solve a system of equations.

```

#### FURTHERDETAILS

```        The band storage scheme is illustrated by the following example, when
M = N = 6, KL = 2, KU = 1:
On entry:                       On exit:
*    *    *    +    +    +       *    *    *   u14  u25  u36
*    *    +    +    +    +       *    *   u13  u24  u35  u46
*   a12  a23  a34  a45  a56      *   u12  u23  u34  u45  u56
a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55  u66
a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65   *
a31  a42  a53  a64   *    *      m31  m42  m53  m64   *    *
Array elements marked * are not used by the routine; elements marked
+ need not be set on entry, but are required by the routine to store
elements of U, because of fill-in resulting from the row
interchanges.

LAPACK routine (version 3.2)               April 2011                            CGBTF2(3lapack)
```